LMFDB - Embedded newform 189.2.w.a.88.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			88.14
Character	$\chi$	$=$	189.88
Dual form			189.2.w.a.58.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.421169 + 0.353403i) q^{2} +(0.959445 + 1.44204i) q^{3} +(-0.294807 - 1.67193i) q^{4} +(0.790369 - 0.663198i) q^{5} +(-0.105531 + 0.946411i) q^{6} +(1.85892 + 1.88266i) q^{7} +(1.01650 - 1.76063i) q^{8} +(-1.15893 + 2.76711i) q^{9} +O(q^{10})$	\(q+(0.421169 + 0.353403i) q^{2} +(0.959445 + 1.44204i) q^{3} +(-0.294807 - 1.67193i) q^{4} +(0.790369 - 0.663198i) q^{5} +(-0.105531 + 0.946411i) q^{6} +(1.85892 + 1.88266i) q^{7} +(1.01650 - 1.76063i) q^{8} +(-1.15893 + 2.76711i) q^{9} +0.567255 q^{10} +(-1.81572 - 1.52357i) q^{11} +(2.12813 - 2.02925i) q^{12} +(1.20787 + 0.439628i) q^{13} +(0.117582 + 1.44987i) q^{14} +(1.71467 + 0.503438i) q^{15} +(-2.14035 + 0.779023i) q^{16} -1.63145 q^{17} +(-1.46601 + 0.755850i) q^{18} +1.59850 q^{19} +(-1.34183 - 1.12593i) q^{20} +(-0.931333 + 4.48694i) q^{21} +(-0.226291 - 1.28336i) q^{22} +(-3.76089 - 1.36885i) q^{23} +(3.51416 - 0.223398i) q^{24} +(-0.683390 + 3.87570i) q^{25} +(0.353351 + 0.612021i) q^{26} +(-5.10220 + 0.983669i) q^{27} +(2.59966 - 3.66301i) q^{28} +(-5.04129 + 1.83488i) q^{29} +(0.544250 + 0.818001i) q^{30} +(-1.00269 - 5.68657i) q^{31} +(-4.99754 - 1.81896i) q^{32} +(0.454958 - 4.08012i) q^{33} +(-0.687116 - 0.576559i) q^{34} +(2.71781 + 0.255165i) q^{35} +(4.96807 + 1.12189i) q^{36} +(5.33779 - 9.24533i) q^{37} +(0.673238 + 0.564913i) q^{38} +(0.524924 + 2.16359i) q^{39} +(-0.364236 - 2.06569i) q^{40} +(0.546038 + 0.198741i) q^{41} +(-1.97794 + 1.56062i) q^{42} +(0.125561 - 0.712095i) q^{43} +(-2.01202 + 3.48492i) q^{44} +(0.919158 + 2.95564i) q^{45} +(-1.10021 - 1.90563i) q^{46} +(2.16222 - 12.2626i) q^{47} +(-3.17693 - 2.33903i) q^{48} +(-0.0888318 + 6.99944i) q^{49} +(-1.65750 + 1.39081i) q^{50} +(-1.56529 - 2.35261i) q^{51} +(0.378940 - 2.14908i) q^{52} +(-5.06183 + 8.76735i) q^{53} +(-2.49652 - 1.38884i) q^{54} -2.44552 q^{55} +(5.20425 - 1.35914i) q^{56} +(1.53367 + 2.30509i) q^{57} +(-2.77169 - 1.00881i) q^{58} +(-7.04133 - 2.56284i) q^{59} +(0.336217 - 3.01523i) q^{60} +(-0.978166 + 5.54746i) q^{61} +(1.58734 - 2.74936i) q^{62} +(-7.36389 + 2.96196i) q^{63} +(0.815727 + 1.41288i) q^{64} +(1.24622 - 0.453588i) q^{65} +(1.63354 - 1.55763i) q^{66} +(-2.92434 + 2.45382i) q^{67} +(0.480962 + 2.72767i) q^{68} +(-1.63444 - 6.73668i) q^{69} +(1.05448 + 1.06795i) q^{70} +(5.93296 + 10.2762i) q^{71} +(3.69379 + 4.85320i) q^{72} +(4.83477 + 8.37407i) q^{73} +(5.51543 - 2.00745i) q^{74} +(-6.24456 + 2.73305i) q^{75} +(-0.471248 - 2.67258i) q^{76} +(-0.506912 - 6.25059i) q^{77} +(-0.543536 + 1.09674i) q^{78} +(7.12739 + 5.98059i) q^{79} +(-1.17502 + 2.03519i) q^{80} +(-6.31376 - 6.41377i) q^{81} +(0.159738 + 0.276675i) q^{82} +(0.769357 - 0.280023i) q^{83} +(7.77642 + 0.234345i) q^{84} +(-1.28945 + 1.08198i) q^{85} +(0.304539 - 0.255538i) q^{86} +(-7.48280 - 5.50925i) q^{87} +(-4.52812 + 1.64810i) q^{88} +16.6454 q^{89} +(-0.657409 + 1.56965i) q^{90} +(1.41766 + 3.09124i) q^{91} +(-1.17989 + 6.69150i) q^{92} +(7.23820 - 6.90187i) q^{93} +(5.24428 - 4.40047i) q^{94} +(1.26340 - 1.06012i) q^{95} +(-2.17187 - 8.95182i) q^{96} +(1.46022 - 8.28134i) q^{97} +(-2.51103 + 2.91655i) q^{98} +(6.32018 - 3.25858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.421169	+	0.353403i	0.297811	+	0.249893i	0.779433	−	0.626486i	$-0.215507\pi$
$2$	0.421169	+	0.353403i	0.297811	+	0.249893i	−0.481621	+	0.876379i	$0.659952\pi$
$3$	0.959445	+	1.44204i	0.553936	+	0.832559i
$3$	0.959445	+	1.44204i	0.553936	+	0.832559i
$4$	−0.294807	−	1.67193i	−0.147403	−	0.835966i
$5$	0.790369	−	0.663198i	0.353464	−	0.296591i	−0.448715	−	0.893675i	$-0.648118\pi$
$5$	0.790369	−	0.663198i	0.353464	−	0.296591i	0.802179	+	0.597083i	$0.203674\pi$
$6$	−0.105531	+	0.946411i	−0.0430827	+	0.386371i
$7$	1.85892	+	1.88266i	0.702606	+	0.711579i
$7$	1.85892	+	1.88266i	0.702606	+	0.711579i
$8$	1.01650	−	1.76063i	0.359386	−	0.622476i
$9$	−1.15893	+	2.76711i	−0.386310	+	0.922369i
$10$	0.567255			0.179382
$11$	−1.81572	−	1.52357i	−0.547461	−	0.459374i	0.326619	−	0.945156i	$-0.394090\pi$
$11$	−1.81572	−	1.52357i	−0.547461	−	0.459374i	−0.874080	+	0.485782i	$0.838535\pi$
$12$	2.12813	−	2.02925i	0.614339	−	0.585793i
$13$	1.20787	+	0.439628i	0.335002	+	0.121931i	0.504044	−	0.863678i	$-0.331845\pi$
$13$	1.20787	+	0.439628i	0.335002	+	0.121931i	−0.169042	+	0.985609i	$0.554067\pi$
$14$	0.117582	+	1.44987i	0.0314250	+	0.387493i
$15$	1.71467	+	0.503438i	0.442726	+	0.129987i
$16$	−2.14035	+	0.779023i	−0.535087	+	0.194756i
$17$	−1.63145			−0.395685			−0.197842	−	0.980234i	$-0.563393\pi$
$17$	−1.63145			−0.395685			−0.197842	+	0.980234i	$0.563393\pi$
$18$	−1.46601	+	0.755850i	−0.345541	+	0.178156i
$19$	1.59850			0.366721			0.183360	−	0.983046i	$-0.441303\pi$
$19$	1.59850			0.366721			0.183360	+	0.983046i	$0.441303\pi$
$20$	−1.34183	−	1.12593i	−0.300042	−	0.251765i
$21$	−0.931333	+	4.48694i	−0.203233	+	0.979130i
$22$	−0.226291	−	1.28336i	−0.0482455	−	0.273614i
$23$	−3.76089	−	1.36885i	−0.784200	−	0.285426i	−0.0812772	−	0.996692i	$-0.525900\pi$
$23$	−3.76089	−	1.36885i	−0.784200	−	0.285426i	−0.702923	+	0.711266i	$0.748122\pi$
$24$	3.51416	−	0.223398i	0.717325	−	0.0456010i
$25$	−0.683390	+	3.87570i	−0.136678	+	0.775139i
$26$	0.353351	+	0.612021i	0.0692978	+	0.120027i
$27$	−5.10220	+	0.983669i	−0.981918	+	0.189307i
$28$	2.59966	−	3.66301i	0.491289	−	0.692243i
$29$	−5.04129	+	1.83488i	−0.936144	+	0.340729i	−0.764642	−	0.644455i	$-0.777084\pi$
$29$	−5.04129	+	1.83488i	−0.936144	+	0.340729i	−0.171502	+	0.985184i	$0.554862\pi$
$30$	0.544250	+	0.818001i	0.0993660	+	0.149346i
$31$	−1.00269	−	5.68657i	−0.180089	−	1.02134i	−0.932104	−	0.362191i	$-0.882029\pi$
$31$	−1.00269	−	5.68657i	−0.180089	−	1.02134i	0.752015	−	0.659146i	$-0.229082\pi$
$32$	−4.99754	−	1.81896i	−0.883449	−	0.321549i
$33$	0.454958	−	4.08012i	0.0791981	−	0.710257i
$34$	−0.687116	−	0.576559i	−0.117839	−	0.0988790i
$35$	2.71781	+	0.255165i	0.459394	+	0.0431307i
$36$	4.96807	+	1.12189i	0.828012	+	0.186982i
$37$	5.33779	−	9.24533i	0.877528	−	1.51992i	0.0234819	−	0.999724i	$-0.492525\pi$
$37$	5.33779	−	9.24533i	0.877528	−	1.51992i	0.854046	−	0.520198i	$-0.174142\pi$
$38$	0.673238	+	0.564913i	0.109214	+	0.0916411i
$39$	0.524924	+	2.16359i	0.0840551	+	0.346451i
$40$	−0.364236	−	2.06569i	−0.0575908	−	0.326613i
$41$	0.546038	+	0.198741i	0.0852767	+	0.0310382i	0.384306	−	0.923206i	$-0.374441\pi$
$41$	0.546038	+	0.198741i	0.0852767	+	0.0310382i	−0.299030	+	0.954244i	$0.596663\pi$
$42$	−1.97794	+	1.56062i	−0.305203	+	0.240809i
$43$	0.125561	−	0.712095i	0.0191479	−	0.108593i	−0.973736	−	0.227681i	$-0.926886\pi$
$43$	0.125561	−	0.712095i	0.0191479	−	0.108593i	0.992884	+	0.119087i	$0.0379969\pi$
$44$	−2.01202	+	3.48492i	−0.303323	+	0.525372i
$45$	0.919158	+	2.95564i	0.137020	+	0.440600i
$46$	−1.10021	−	1.90563i	−0.162218	−	0.280969i
$47$	2.16222	−	12.2626i	0.315392	−	1.78868i	−0.254620	−	0.967041i	$-0.581950\pi$
$47$	2.16222	−	12.2626i	0.315392	−	1.78868i	0.570012	−	0.821636i	$-0.306939\pi$
$48$	−3.17693	−	2.33903i	−0.458550	−	0.337610i
$49$	−0.0888318	+	6.99944i	−0.0126903	+	0.999919i
$50$	−1.65750	+	1.39081i	−0.234406	+	0.196690i
$51$	−1.56529	−	2.35261i	−0.219184	−	0.329431i
$52$	0.378940	−	2.14908i	0.0525496	−	0.298023i
$53$	−5.06183	+	8.76735i	−0.695296	+	1.20429i	0.274785	+	0.961506i	$0.411393\pi$
$53$	−5.06183	+	8.76735i	−0.695296	+	1.20429i	−0.970081	+	0.242782i	$0.921940\pi$
$54$	−2.49652	−	1.38884i	−0.339733	−	0.188997i
$55$	−2.44552			−0.329754
$56$	5.20425	−	1.35914i	0.695448	−	0.181623i
$57$	1.53367	+	2.30509i	0.203140	+	0.305317i
$58$	−2.77169	−	1.00881i	−0.363940	−	0.132463i
$59$	−7.04133	−	2.56284i	−0.916703	−	0.333653i	−0.159777	−	0.987153i	$-0.551078\pi$
$59$	−7.04133	−	2.56284i	−0.916703	−	0.333653i	−0.756926	+	0.653500i	$0.773300\pi$
$60$	0.336217	−	3.01523i	0.0434054	−	0.389264i
$61$	−0.978166	+	5.54746i	−0.125241	+	0.710279i	0.855923	+	0.517104i	$0.172990\pi$
$61$	−0.978166	+	5.54746i	−0.125241	+	0.710279i	−0.981164	+	0.193176i	$0.938121\pi$
$62$	1.58734	−	2.74936i	0.201593	−	0.349169i
$63$	−7.36389	+	2.96196i	−0.927762	+	0.373171i
$64$	0.815727	+	1.41288i	0.101966	+	0.176610i
$65$	1.24622	−	0.453588i	0.154575	−	0.0562606i
$66$	1.63354	−	1.55763i	0.201075	−	0.191732i
$67$	−2.92434	+	2.45382i	−0.357266	+	0.299781i	−0.803700	−	0.595035i	$-0.797138\pi$
$67$	−2.92434	+	2.45382i	−0.357266	+	0.299781i	0.446434	+	0.894816i	$0.352694\pi$
$68$	0.480962	+	2.72767i	0.0583252	+	0.330779i
$69$	−1.63444	−	6.73668i	−0.196763	−	0.811001i
$70$	1.05448	+	1.06795i	0.126035	+	0.127644i
$71$	5.93296	+	10.2762i	0.704112	+	1.21956i	0.967011	+	0.254735i	$0.0819882\pi$
$71$	5.93296	+	10.2762i	0.704112	+	1.21956i	−0.262899	+	0.964823i	$0.584678\pi$
$72$	3.69379	+	4.85320i	0.435318	+	0.571956i
$73$	4.83477	+	8.37407i	0.565867	+	0.980111i	0.996968	+	0.0778071i	$0.0247918\pi$
$73$	4.83477	+	8.37407i	0.565867	+	0.980111i	−0.431101	+	0.902304i	$0.641875\pi$
$74$	5.51543	−	2.00745i	0.641156	−	0.233362i
$75$	−6.24456	+	2.73305i	−0.721060	+	0.315585i
$76$	−0.471248	−	2.67258i	−0.0540558	−	0.306566i
$77$	−0.506912	−	6.25059i	−0.0577680	−	0.712321i
$78$	−0.543536	+	1.09674i	−0.0615433	+	0.124182i
$79$	7.12739	+	5.98059i	0.801894	+	0.672869i	0.948658	−	0.316303i	$-0.102442\pi$
$79$	7.12739	+	5.98059i	0.801894	+	0.672869i	−0.146765	+	0.989171i	$0.546886\pi$
$80$	−1.17502	+	2.03519i	−0.131371	+	0.227541i
$81$	−6.31376	−	6.41377i	−0.701529	−	0.712641i
$82$	0.159738	+	0.276675i	0.0176401	+	0.0305536i
$83$	0.769357	−	0.280023i	0.0844479	−	0.0307365i	−0.299451	−	0.954112i	$-0.596803\pi$
$83$	0.769357	−	0.280023i	0.0844479	−	0.0307365i	0.383899	+	0.923375i	$0.374581\pi$
$84$	7.77642	+	0.234345i	0.848477	+	0.0255692i
$85$	−1.28945	+	1.08198i	−0.139860	+	0.117357i
$86$	0.304539	−	0.255538i	0.0328392	−	0.0275554i
$87$	−7.48280	−	5.50925i	−0.802241	−	0.590654i
$88$	−4.52812	+	1.64810i	−0.482699	+	0.175688i
$89$	16.6454			1.76441			0.882205	−	0.470866i	$-0.156058\pi$
$89$	16.6454			1.76441			0.882205	+	0.470866i	$0.156058\pi$
$90$	−0.657409	+	1.56965i	−0.0692970	+	0.165456i
$91$	1.41766	+	3.09124i	0.148611	+	0.324050i
$92$	−1.17989	+	6.69150i	−0.123012	+	0.697637i
$93$	7.23820	−	6.90187i	0.750566	−	0.715690i
$94$	5.24428	−	4.40047i	0.540906	−	0.453874i
$95$	1.26340	−	1.06012i	0.129622	−	0.108766i
$96$	−2.17187	−	8.95182i	−0.221665	−	0.913641i
$97$	1.46022	−	8.28134i	0.148263	−	0.840843i	−0.816425	−	0.577451i	$-0.804048\pi$
$97$	1.46022	−	8.28134i	0.148263	−	0.840843i	0.964689	−	0.263392i	$-0.0848414\pi$
$98$	−2.51103	+	2.91655i	−0.253653	+	0.294616i
$99$	6.32018	−	3.25858i	0.635202	−	0.327500i
$100$	6.68136			0.668136
$101$	12.7486	−	4.64010i	1.26853	−	0.461708i	0.381908	−	0.924200i	$-0.375267\pi$
$101$	12.7486	−	4.64010i	1.26853	−	0.461708i	0.886623	+	0.462493i	$0.153045\pi$
$102$	0.172168	−	1.54402i	0.0170472	−	0.152881i
$103$	−4.61409	+	3.87168i	−0.454640	+	0.381488i	−0.841154	−	0.540795i	$-0.818123\pi$
$103$	−4.61409	+	3.87168i	−0.454640	+	0.381488i	0.386515	+	0.922283i	$0.373679\pi$
$104$	2.00182	−	1.67972i	0.196294	−	0.164710i
$105$	2.23963	+	4.16400i	0.218566	+	0.406364i
$106$	−5.23029	+	1.90367i	−0.508010	+	0.184901i
$107$	−4.07199	−	7.05289i	−0.393654	−	0.681828i	0.599275	−	0.800544i	$-0.295456\pi$
$107$	−4.07199	−	7.05289i	−0.393654	−	0.681828i	−0.992928	+	0.118715i	$0.962122\pi$
$108$	3.14879	+	8.24053i	0.302992	+	0.792945i
$109$	−6.58042	+	11.3976i	−0.630290	+	1.09169i	0.357202	+	0.934027i	$0.383731\pi$
$109$	−6.58042	+	11.3976i	−0.630290	+	1.09169i	−0.987492	+	0.157668i	$0.949603\pi$
$110$	−1.02998	−	0.864253i	−0.0982044	−	0.0824033i
$111$	18.4534	−	1.17310i	1.75152	−	0.111346i
$112$	−5.44537	−	2.58141i	−0.514540	−	0.243920i
$113$	2.11820	+	12.0129i	0.199263	+	1.13008i	0.906216	+	0.422816i	$0.138958\pi$
$113$	2.11820	+	12.0129i	0.199263	+	1.13008i	−0.706952	+	0.707261i	$0.749931\pi$
$114$	−0.168690	+	1.51284i	−0.0157993	+	0.141690i
$115$	−3.88031	+	1.41232i	−0.361841	+	0.131699i
$116$	4.55400	+	7.88776i	0.422828	+	0.732360i
$117$	−2.61633	+	2.83280i	−0.241880	+	0.261893i
$118$	−2.05988	−	3.56781i	−0.189627	−	0.328444i
$119$	−3.03274	−	3.07147i	−0.278010	−	0.281561i
$120$	2.62933	−	2.50715i	0.240024	−	0.228871i
$121$	−0.934555	−	5.30012i	−0.0849595	−	0.481829i
$122$	−2.37246	+	1.99073i	−0.214792	+	0.180232i
$123$	0.237301	+	0.978087i	0.0213967	+	0.0881911i
$124$	−9.21194	+	3.35287i	−0.827257	+	0.301097i
$125$	4.60961	+	7.98408i	0.412296	+	0.714118i
$126$	−4.14820	−	1.35493i	−0.369551	−	0.120707i
$127$	2.30914	−	3.99955i	0.204903	−	0.354903i	−0.745199	−	0.666843i	$-0.767645\pi$
$127$	2.30914	−	3.99955i	0.204903	−	0.354903i	0.950102	+	0.311940i	$0.100979\pi$
$128$	−2.00277	+	11.3583i	−0.177022	+	1.00394i
$129$	1.14733	−	0.502151i	0.101017	−	0.0442120i
$130$	0.685169	+	0.249381i	0.0600933	+	0.0218722i
$131$	−2.37256	−	0.863542i	−0.207292	−	0.0754480i	0.236288	−	0.971683i	$-0.424069\pi$
$131$	−2.37256	−	0.863542i	−0.207292	−	0.0754480i	−0.443579	+	0.896235i	$0.646291\pi$
$132$	−6.95580	+	0.442187i	−0.605425	+	0.0384874i
$133$	2.97148	+	3.00943i	0.257660	+	0.260951i
$134$	−2.09883			−0.181311
$135$	−3.38025	+	4.16123i	−0.290926	+	0.358142i
$136$	−1.65837	+	2.87238i	−0.142204	+	0.246304i
$137$	0.872687	−	4.94925i	0.0745587	−	0.422843i	−0.924566	−	0.381021i	$-0.875573\pi$
$137$	0.872687	−	4.94925i	0.0745587	−	0.422843i	0.999125	−	0.0418223i	$-0.0133163\pi$
$138$	1.69239	−	3.41489i	0.144065	−	0.290695i
$139$	2.79995	−	2.34944i	0.237489	−	0.199277i	−0.516274	−	0.856424i	$-0.672681\pi$
$139$	2.79995	−	2.34944i	0.237489	−	0.199277i	0.753763	+	0.657147i	$0.228237\pi$
$140$	−0.374610	−	4.61922i	−0.0316604	−	0.390395i
$141$	19.7576	−	8.64725i	1.66389	−	0.728230i
$142$	−1.13285	+	6.42473i	−0.0950669	+	0.539151i
$143$	−1.52335	−	2.63852i	−0.127389	−	0.220644i
$144$	0.324875	−	6.82541i	0.0270729	−	0.568784i
$145$	−2.76759	+	4.79361i	−0.229836	+	0.398088i
$146$	−0.923163	+	5.23552i	−0.0764015	+	0.433295i
$147$	−10.1787	+	6.58748i	−0.839522	+	0.543326i
$148$	−17.0312	−	6.19884i	−1.39995	−	0.509541i
$149$	−1.93765	−	10.9889i	−0.158738	−	0.900250i	−0.955288	−	0.295677i	$-0.904455\pi$
$149$	−1.93765	−	10.9889i	−0.158738	−	0.900250i	0.796550	−	0.604573i	$-0.206656\pi$
$150$	−3.59588	−	1.05577i	−0.293602	−	0.0862034i
$151$	−0.698546	−	0.586150i	−0.0568469	−	0.0477002i	0.613922	−	0.789367i	$-0.289591\pi$
$151$	−0.698546	−	0.586150i	−0.0568469	−	0.0477002i	−0.670768	+	0.741667i	$0.734036\pi$
$152$	1.62487	−	2.81436i	0.131794	−	0.228275i
$153$	1.89074	−	4.51440i	0.152857	−	0.364967i
$154$	1.99548	−	2.81170i	0.160800	−	0.226573i
$155$	−4.56382	−	3.82950i	−0.366575	−	0.307593i
$156$	3.46262	−	1.51548i	0.277231	−	0.121335i
$157$	10.6846	+	3.88889i	0.852728	+	0.310367i	0.731152	−	0.682215i	$-0.238983\pi$
$157$	10.6846	+	3.88889i	0.852728	+	0.310367i	0.121576	+	0.992582i	$0.461205\pi$
$158$	0.888278	+	5.03767i	0.0706676	+	0.400776i
$159$	−17.4994	+	1.11245i	−1.38779	+	0.0882231i
$160$	−5.15623	+	1.87671i	−0.407636	+	0.148367i
$161$	−4.41411	−	9.62508i	−0.347881	−	0.758562i
$162$	−0.392517	−	4.93258i	−0.0308390	−	0.387540i
$163$	−7.66798	−	13.2813i	−0.600602	−	1.04027i	−0.992730	−	0.120363i	$-0.961594\pi$
$163$	−7.66798	−	13.2813i	−0.600602	−	1.04027i	0.392128	−	0.919911i	$-0.371739\pi$
$164$	0.171307	−	0.971527i	0.0133768	−	0.0758636i
$165$	−2.34634	−	3.52653i	−0.182662	−	0.274540i
$166$	0.422990	+	0.153956i	0.0328304	+	0.0119493i
$167$	3.99112	+	22.6347i	0.308842	+	1.75153i	0.604846	+	0.796343i	$0.293235\pi$
$167$	3.99112	+	22.6347i	0.308842	+	1.75153i	−0.296004	+	0.955187i	$0.595654\pi$
$168$	6.95313	+	6.20070i	0.536445	+	0.478394i
$169$	−8.69291	−	7.29421i	−0.668685	−	0.561093i
$170$	−0.925448			−0.0709786
$171$	−1.85255	+	4.42321i	−0.141668	+	0.338252i
$172$	−1.22759			−0.0936028
$173$	19.8640	−	7.22991i	1.51023	−	0.549680i	0.551546	−	0.834144i	$-0.314038\pi$
$173$	19.8640	−	7.22991i	1.51023	−	0.549680i	0.958687	+	0.284464i	$0.0918158\pi$
$174$	−1.20454	−	4.96477i	−0.0913159	−	0.376378i
$175$	−8.56699	+	5.91802i	−0.647604	+	0.447360i
$176$	5.07317	+	1.84648i	0.382405	+	0.139184i
$177$	−3.06007	−	12.6127i	−0.230009	−	0.948032i
$178$	7.01053	+	5.88253i	0.525461	+	0.440914i
$179$	8.26313			0.617615			0.308808	−	0.951125i	$-0.400070\pi$
$179$	8.26313			0.617615			0.308808	+	0.951125i	$0.400070\pi$
$180$	4.67065	−	2.40811i	0.348129	−	0.179490i
$181$	−5.42374	+	9.39419i	−0.403143	+	0.698265i	−0.994103	−	0.108436i	$-0.965416\pi$
$181$	−5.42374	+	9.39419i	−0.403143	+	0.698265i	0.590960	+	0.806701i	$0.298749\pi$
$182$	−0.495379	+	1.80294i	−0.0367199	+	0.133643i
$183$	−8.93812	+	3.91193i	−0.660725	+	0.289178i
$184$	−6.23298	+	5.23009i	−0.459501	+	0.385567i
$185$	−1.91266	−	10.8472i	−0.140622	−	0.797505i
$186$	5.48764	−	0.348854i	0.402373	−	0.0255792i
$187$	2.96226	+	2.48563i	0.216622	+	0.181767i
$188$	−21.1396			−1.54176
$189$	−11.3365	−	7.77715i	−0.824608	−	0.565704i
$190$	0.906756			0.0657830
$191$	−0.124298	−	0.104299i	−0.00899392	−	0.00754679i	0.638280	−	0.769805i	$-0.279646\pi$
$191$	−0.124298	−	0.104299i	−0.00899392	−	0.00754679i	−0.647273	+	0.762258i	$0.724091\pi$
$192$	−1.25478	+	2.53189i	−0.0905558	+	0.182723i
$193$	−0.315907	−	1.79160i	−0.0227395	−	0.128962i	0.971325	−	0.237757i	$-0.0764121\pi$
$193$	−0.315907	−	1.79160i	−0.0227395	−	0.128962i	−0.994064	+	0.108795i	$0.965301\pi$
$194$	3.54165	−	2.97180i	0.254276	−	0.213363i
$195$	1.84977	+	1.36190i	0.132465	+	0.0975279i
$196$	11.7288	−	1.91496i	0.837769	−	0.136783i
$197$	13.6009	−	23.5575i	0.969027	−	1.67840i	0.270645	−	0.962679i	$-0.412763\pi$
$197$	13.6009	−	23.5575i	0.969027	−	1.67840i	0.698382	−	0.715725i	$-0.253904\pi$
$198$	3.81345	+	0.861155i	0.271010	+	0.0611996i
$199$	6.51737			0.462004			0.231002	−	0.972953i	$-0.425800\pi$
$199$	6.51737			0.462004			0.231002	+	0.972953i	$0.425800\pi$
$200$	6.12899	+	5.14283i	0.433385	+	0.363653i
$201$	−6.34424	−	1.86271i	−0.447488	−	0.131385i
$202$	7.00913	+	2.55112i	0.493161	+	0.179496i
$203$	−12.8258	−	6.08015i	−0.900196	−	0.426743i
$204$	−3.47194	+	3.31062i	−0.243085	+	0.231790i
$205$	0.563376	−	0.205052i	0.0393479	−	0.0143215i
$206$	−3.31157			−0.230728
$207$	8.14637	−	8.82038i	0.566212	−	0.613059i
$208$	−2.92774			−0.203002
$209$	−2.90243	−	2.43543i	−0.200765	−	0.168462i
$210$	−0.528303	+	2.54524i	−0.0364564	+	0.175638i
$211$	−3.64060	−	20.6469i	−0.250629	−	1.42139i	−0.807047	−	0.590487i	$-0.798936\pi$
$211$	−3.64060	−	20.6469i	−0.250629	−	1.42139i	0.556418	−	0.830902i	$-0.312175\pi$
$212$	16.1507	+	5.87836i	1.10923	+	0.403727i
$213$	−9.12627	+	18.4150i	−0.625322	+	1.26177i
$214$	0.777515	−	4.40951i	0.0531498	−	0.301428i
$215$	−0.373020	−	0.646090i	−0.0254398	−	0.0440629i
$216$	−3.45450	+	9.98296i	−0.235049	+	0.679254i
$217$	8.84195	−	12.4586i	0.600231	−	0.845745i
$218$	−6.79942	+	2.47479i	−0.460515	+	0.167614i
$219$	−7.43700	+	15.0064i	−0.502546	+	1.01404i
$220$	0.720955	+	4.08874i	0.0486068	+	0.275663i
$221$	−1.97058	−	0.717231i	−0.132555	−	0.0482462i
$222$	8.18658	+	6.02741i	0.549447	+	0.404533i
$223$	−4.56143	−	3.82749i	−0.305456	−	0.256308i	0.477155	−	0.878819i	$-0.341668\pi$
$223$	−4.56143	−	3.82749i	−0.305456	−	0.256308i	−0.782611	+	0.622511i	$0.786113\pi$
$224$	−5.86555	−	12.7900i	−0.391909	−	0.854566i
$225$	−9.93246	−	6.38267i	−0.662164	−	0.425512i
$226$	−3.35327	+	5.80803i	−0.223056	+	0.386344i
$227$	−13.0711	−	10.9679i	−0.867557	−	0.727967i	0.0960249	−	0.995379i	$-0.469387\pi$
$227$	−13.0711	−	10.9679i	−0.867557	−	0.727967i	−0.963582	+	0.267412i	$0.913832\pi$
$228$	3.40182	−	3.24375i	0.225291	−	0.214822i
$229$	4.16002	+	23.5926i	0.274902	+	1.55904i	0.739274	+	0.673405i	$0.235169\pi$
$229$	4.16002	+	23.5926i	0.274902	+	1.55904i	−0.464373	+	0.885640i	$0.653720\pi$
$230$	−2.13338	−	0.776488i	−0.140671	−	0.0512001i
$231$	8.52721	−	6.72808i	0.561049	−	0.442675i
$232$	−1.89393	+	10.7410i	−0.124342	+	0.705180i
$233$	−11.7904	+	20.4216i	−0.772415	+	1.33786i	0.163820	+	0.986490i	$0.447618\pi$
$233$	−11.7904	+	20.4216i	−0.772415	+	1.33786i	−0.936236	+	0.351373i	$0.885715\pi$
$234$	−2.10304	+	0.268469i	−0.137480	+	0.0175504i
$235$	−6.42356	−	11.1259i	−0.419027	−	0.725775i
$236$	−2.20905	+	12.5282i	−0.143797	+	0.815514i
$237$	−1.78588	+	16.0160i	−0.116005	+	1.04035i
$238$	−0.191829	−	2.36538i	−0.0124344	−	0.153325i
$239$	−16.5755	+	13.9085i	−1.07218	+	0.899668i	−0.995248	−	0.0973687i	$-0.968957\pi$
$239$	−16.5755	+	13.9085i	−1.07218	+	0.899668i	−0.0769337	+	0.997036i	$0.524513\pi$
$240$	−4.06218	+	0.258237i	−0.262213	+	0.0166691i
$241$	4.29114	−	24.3363i	0.276417	−	1.56764i	−0.458009	−	0.888948i	$-0.651437\pi$
$241$	4.29114	−	24.3363i	0.276417	−	1.56764i	0.734425	−	0.678689i	$-0.237452\pi$
$242$	1.47947	−	2.56252i	0.0951041	−	0.164725i
$243$	3.19117	−	15.2583i	0.204714	−	0.978822i
$244$	9.56334			0.612230
$245$	4.57180	+	5.59105i	0.292082	+	0.357199i
$246$	−0.245715	+	0.495802i	−0.0156662	+	0.0316112i
$247$	1.93077	+	0.702744i	0.122852	+	0.0447146i
$248$	−11.0312	−	4.01501i	−0.700479	−	0.254954i
$249$	1.14196	+	0.840773i	0.0723687	+	0.0532818i
$250$	−0.880170	+	4.99169i	−0.0556668	+	0.315702i
$251$	3.46762	−	6.00609i	0.218874	−	0.379101i	−0.735590	−	0.677427i	$-0.763095\pi$
$251$	3.46762	−	6.00609i	0.218874	−	0.379101i	0.954464	+	0.298326i	$0.0964283\pi$
$252$	7.12311	+	11.4387i	0.448714	+	0.720571i
$253$	4.74319	+	8.21544i	0.298202	+	0.516500i
$254$	2.38599	−	0.868430i	0.149710	−	0.0544901i
$255$	−2.79740	−	0.821333i	−0.175180	−	0.0514339i
$256$	−2.35802	+	1.97862i	−0.147377	+	0.123664i
$257$	3.84616	+	21.8127i	0.239917	+	1.36064i	0.832007	+	0.554765i	$0.187192\pi$
$257$	3.84616	+	21.8127i	0.239917	+	1.36064i	−0.592090	+	0.805872i	$0.701697\pi$
$258$	0.660683	+	0.193981i	0.0411323	+	0.0120767i
$259$	27.3284	−	7.13707i	1.69810	−	0.443476i
$260$	−1.12576	−	1.94988i	−0.0698168	−	0.120926i
$261$	0.765197	−	16.0763i	0.0473645	−	0.995097i
$262$	−0.694071	−	1.20217i	−0.0428798	−	0.0742701i
$263$	−18.9932	+	6.91296i	−1.17117	+	0.426271i	−0.853076	−	0.521787i	$-0.825265\pi$
$263$	−18.9932	+	6.91296i	−1.17117	+	0.426271i	−0.318095	+	0.948059i	$0.603043\pi$
$264$	−6.72110	−	4.94844i	−0.413655	−	0.304556i
$265$	1.81378	+	10.2864i	0.111419	+	0.631891i
$266$	0.187954	+	2.31761i	0.0115242	+	0.142102i
$267$	15.9704	+	24.0033i	0.977370	+	1.46898i
$268$	4.96473	+	4.16590i	0.303269	+	0.254473i
$269$	−0.0584552	+	0.101247i	−0.00356408	+	0.00617316i	−0.867802	−	0.496910i	$-0.834468\pi$
$269$	−0.0584552	+	0.101247i	−0.00356408	+	0.00617316i	0.864238	+	0.503083i	$0.167801\pi$
$270$	−2.89425	+	0.557991i	−0.176138	+	0.0339582i
$271$	9.14252	+	15.8353i	0.555368	+	0.961926i	0.997875	+	0.0651609i	$0.0207561\pi$
$271$	9.14252	+	15.8353i	0.555368	+	0.961926i	−0.442506	+	0.896765i	$0.645911\pi$
$272$	3.49187	−	1.27094i	0.211726	−	0.0770619i
$273$	−3.09751	+	5.01019i	−0.187470	+	0.303230i
$274$	2.11663	−	1.77606i	0.127870	−	0.107296i
$275$	7.14574	−	5.99599i	0.430905	−	0.361572i
$276$	−10.7814	+	4.71868i	−0.648965	+	0.284031i
$277$	20.5432	−	7.47710i	1.23432	−	0.449256i	0.359245	−	0.933243i	$-0.383034\pi$
$277$	20.5432	−	7.47710i	1.23432	−	0.449256i	0.875075	+	0.483988i	$0.160812\pi$
$278$	2.00955			0.120525
$279$	16.8974	+	3.81577i	1.01162	+	0.228444i
$280$	3.21190	−	4.52568i	0.191948	−	0.270461i
$281$	0.866344	−	4.91328i	0.0516817	−	0.293102i	−0.948002	−	0.318266i	$-0.896900\pi$
$281$	0.866344	−	4.91328i	0.0516817	−	0.293102i	0.999683	+	0.0251639i	$0.00801075\pi$
$282$	11.3772	+	3.34042i	0.677504	+	0.198919i
$283$	14.2275	−	11.9383i	0.845738	−	0.709659i	−0.113108	−	0.993583i	$-0.536081\pi$
$283$	14.2275	−	11.9383i	0.845738	−	0.709659i	0.958847	+	0.283924i	$0.0916363\pi$
$284$	15.4320	−	12.9490i	0.915720	−	0.768381i
$285$	2.74090	+	0.804744i	0.162357	+	0.0476689i
$286$	0.290872	−	1.64962i	0.0171996	−	0.0975438i
$287$	0.640877	+	1.39745i	0.0378298	+	0.0824888i
$288$	10.8250	−	11.7207i	0.637872	−	0.690648i
$289$	−14.3384			−0.843434
$290$	−2.85970	+	1.04084i	−0.167927	+	0.0611205i
$291$	13.3430	−	5.83980i	0.782180	−	0.342335i
$292$	12.5755	−	10.5521i	0.735928	−	0.617517i
$293$	11.0741	−	9.29225i	0.646954	−	0.542859i	−0.259191	−	0.965826i	$-0.583456\pi$
$293$	11.0741	−	9.29225i	0.646954	−	0.542859i	0.906145	+	0.422967i	$0.139011\pi$
$294$	−6.61497	−	0.822726i	−0.385793	−	0.0479824i
$295$	−7.26492	+	2.64421i	−0.422980	+	0.153952i
$296$	−10.8517	−	18.7957i	−0.630743	−	1.09248i
$297$	10.7629	+	5.98749i	0.624524	+	0.347429i
$298$	3.06745	−	5.31297i	0.177692	−	0.307772i
$299$	−3.94087	−	3.30679i	−0.227907	−	0.191236i
$300$	6.41040	+	9.63476i	0.370105	+	0.556263i
$301$	1.57404	−	1.08734i	0.0907263	−	0.0626731i
$302$	−0.0870590	−	0.493736i	−0.00500968	−	0.0284113i
$303$	18.9228	+	13.9320i	1.08708	+	0.800371i
$304$	−3.42134	+	1.24527i	−0.196227	+	0.0714210i
$305$	2.90595	+	5.03326i	0.166394	+	0.288203i
$306$	2.39172	−	1.23313i	0.136726	−	0.0704935i
$307$	−4.05722	−	7.02731i	−0.231558	−	0.401070i	0.726709	−	0.686945i	$-0.241049\pi$
$307$	−4.05722	−	7.02731i	−0.231558	−	0.401070i	−0.958267	+	0.285876i	$0.907716\pi$
$308$	−10.3011	+	2.69024i	−0.586960	+	0.153290i
$309$	−10.0101	−	2.93901i	−0.569452	−	0.167195i
$310$	−0.568784	−	3.22573i	−0.0323047	−	0.183209i
$311$	−9.04768	+	7.59190i	−0.513047	+	0.430497i	−0.862200	−	0.506568i	$-0.830914\pi$
$311$	−9.04768	+	7.59190i	−0.513047	+	0.430497i	0.349153	+	0.937066i	$0.386469\pi$
$312$	4.34285	+	1.27509i	0.245866	+	0.0721876i
$313$	−13.3212	+	4.84851i	−0.752957	+	0.274054i	−0.689850	−	0.723953i	$-0.742323\pi$
$313$	−13.3212	+	4.84851i	−0.752957	+	0.274054i	−0.0631076	+	0.998007i	$0.520101\pi$
$314$	3.12569	+	5.41386i	0.176393	+	0.305522i
$315$	−3.85582	+	7.22476i	−0.217251	+	0.407069i
$316$	7.89793	−	13.6796i	0.444293	−	0.769539i
$317$	−4.57485	+	25.9453i	−0.256949	+	1.45723i	0.534070	+	0.845440i	$0.320662\pi$
$317$	−4.57485	+	25.9453i	−0.256949	+	1.45723i	−0.791020	+	0.611791i	$0.790449\pi$
$318$	−7.76333	−	5.71579i	−0.435346	−	0.320526i
$319$	11.9492	+	4.34914i	0.669024	+	0.243505i
$320$	1.58174	+	0.575708i	0.0884222	+	0.0321831i
$321$	6.26366	−	12.6388i	0.349604	−	0.705429i
$322$	1.54244	−	5.61374i	0.0859569	−	0.312842i
$323$	−2.60787			−0.145106
$324$	−8.86204	+	12.4470i	−0.492336	+	0.691500i
$325$	−2.52931	+	4.38089i	−0.140301	+	0.243008i
$326$	1.46414	−	8.30356i	0.0810913	−	0.459892i
$327$	−22.7493	+	1.44620i	−1.25804	+	0.0799748i
$328$	0.904956	−	0.759348i	0.0499678	−	0.0419280i
$329$	27.1056	−	18.7244i	1.49438	−	1.03231i
$330$	0.258077	−	2.31447i	0.0142067	−	0.127407i
$331$	4.74520	−	26.9114i	0.260820	−	1.47918i	−0.519860	−	0.854251i	$-0.674016\pi$
$331$	4.74520	−	26.9114i	0.260820	−	1.47918i	0.780680	−	0.624931i	$-0.214873\pi$
$332$	−0.694990	−	1.20376i	−0.0381426	−	0.0660648i
$333$	19.3967	+	25.4849i	1.06293	+	1.39657i
$334$	−6.31825	+	10.9435i	−0.345719	+	0.598803i
$335$	−0.683944	+	3.87884i	−0.0373679	+	0.211924i
$336$	−1.50205	−	10.3291i	−0.0819437	−	0.563501i
$337$	−2.84774	−	1.03649i	−0.155126	−	0.0564613i	0.263290	−	0.964717i	$-0.415192\pi$
$337$	−2.84774	−	1.03649i	−0.155126	−	0.0564613i	−0.418416	+	0.908255i	$0.637415\pi$
$338$	−1.08339	−	6.14419i	−0.0589285	−	0.334200i
$339$	−15.2907	+	14.5802i	−0.830477	+	0.791889i
$340$	2.18913	+	1.83689i	0.118722	+	0.0996196i
$341$	−6.84327	+	11.8529i	−0.370584	+	0.641870i
$342$	−2.34341	+	1.20822i	−0.126717	+	0.0653333i
$343$	−13.3427	+	12.8442i	−0.720438	+	0.693519i
$344$	−1.12610	−	0.944910i	−0.0607152	−	0.0509461i
$345$	−5.75956	−	4.24051i	−0.310084	−	0.228301i
$346$	10.9212	+	3.97498i	0.587126	+	0.213696i
$347$	1.57643	+	8.94036i	0.0846270	+	0.479944i	0.997436	+	0.0715579i	$0.0227971\pi$
$347$	1.57643	+	8.94036i	0.0846270	+	0.479944i	−0.912809	+	0.408386i	$0.866092\pi$
$348$	−7.00511	+	14.1349i	−0.375513	+	0.757710i
$349$	5.92825	−	2.15771i	0.317332	−	0.115499i	−0.178443	−	0.983950i	$-0.557106\pi$
$349$	5.92825	−	2.15771i	0.317332	−	0.115499i	0.495775	+	0.868451i	$0.334884\pi$
$350$	−5.69959	−	0.535113i	−0.304656	−	0.0286030i
$351$	−6.59523	−	1.05493i	−0.352027	−	0.0563078i
$352$	6.30283	+	10.9168i	0.335942	+	0.581869i
$353$	−0.789934	+	4.47994i	−0.0420439	+	0.238443i	−0.998587	−	0.0531495i	$-0.983074\pi$
$353$	−0.789934	+	4.47994i	−0.0420439	+	0.238443i	0.956543	+	0.291592i	$0.0941851\pi$
$354$	3.16857	−	6.39353i	0.168408	−	0.339812i
$355$	11.5044	+	4.18725i	0.610589	+	0.222236i
$356$	−4.90718	−	27.8300i	−0.260080	−	1.47499i
$357$	1.51942	−	7.32022i	0.0804164	−	0.387427i
$358$	3.48017	+	2.92021i	0.183933	+	0.154338i
$359$	−12.8431			−0.677834			−0.338917	−	0.940816i	$-0.610061\pi$
$359$	−12.8431			−0.677834			−0.338917	+	0.940816i	$0.610061\pi$
$360$	6.13810	+	1.38611i	0.323506	+	0.0730542i
$361$	−16.4448			−0.865516
$362$	−5.60424	+	2.03978i	−0.294553	+	0.107208i
$363$	6.74631	−	6.43284i	0.354089	−	0.337636i
$364$	4.75041	−	3.28155i	0.248989	−	0.172000i
$365$	9.37492	+	3.41219i	0.490706	+	0.178602i
$366$	−5.14695	−	1.51117i	−0.269035	−	0.0789903i
$367$	−26.9590	−	22.6212i	−1.40725	−	1.18082i	−0.957773	−	0.287526i	$-0.907167\pi$
$367$	−26.9590	−	22.6212i	−1.40725	−	1.18082i	−0.449473	−	0.893294i	$-0.648388\pi$
$368$	9.11599			0.475204
$369$	−1.18276	+	1.28062i	−0.0615719	+	0.0666662i
$370$	3.02789	−	5.24446i	0.157412	−	0.272646i
$371$	−25.9155	+	6.76808i	−1.34546	+	0.351381i
$372$	−13.6733	−	10.0670i	−0.708928	−	0.521952i
$373$	−14.3291	+	12.0236i	−0.741935	+	0.622557i	−0.933356	−	0.358951i	$-0.883135\pi$
$373$	−14.3291	+	12.0236i	−0.741935	+	0.622557i	0.191422	+	0.981508i	$0.438690\pi$
$374$	0.369183	+	2.09374i	0.0190900	+	0.108265i
$375$	−7.09065	+	14.3075i	−0.366160	+	0.738836i
$376$	−19.3919	−	16.2717i	−1.00006	−	0.839150i
$377$	−6.89588			−0.355156
$378$	−2.02611	−	7.28184i	−0.104212	−	0.374537i
$379$	6.10620			0.313654			0.156827	−	0.987626i	$-0.449873\pi$
$379$	6.10620			0.313654			0.156827	+	0.987626i	$0.449873\pi$
$380$	−2.14491	−	1.79979i	−0.110032	−	0.0923274i
$381$	7.98299	−	0.507486i	0.408981	−	0.0259993i
$382$	−0.0154912	−	0.0878548i	−0.000792597	−	0.00449504i
$383$	2.68591	−	2.25374i	0.137243	−	0.115161i	−0.571582	−	0.820545i	$-0.693670\pi$
$383$	2.68591	−	2.25374i	0.137243	−	0.115161i	0.708825	+	0.705384i	$0.249226\pi$
$384$	−18.3006	+	8.00959i	−0.933899	+	0.408738i
$385$	−4.54603	−	4.60409i	−0.231687	−	0.234646i
$386$	0.500105	−	0.866208i	0.0254547	−	0.0440888i
$387$	1.82492	+	1.17271i	0.0927661	+	0.0596122i
$388$	−14.2763			−0.724770
$389$	4.43673	+	3.72286i	0.224951	+	0.188757i	0.748297	−	0.663364i	$-0.230872\pi$
$389$	4.43673	+	3.72286i	0.224951	+	0.188757i	−0.523346	+	0.852121i	$0.675316\pi$
$390$	0.297766	+	1.22731i	0.0150780	+	0.0621470i
$391$	6.13571	+	2.23322i	0.310296	+	0.112939i
$392$	12.2331	+	7.27132i	0.617865	+	0.367257i
$393$	−1.03108	−	4.24984i	−0.0520113	−	0.214376i
$394$	14.0536	−	5.11509i	0.708009	−	0.257694i
$395$	9.59958			0.483007
$396$	−7.31136	−	9.60625i	−0.367409	−	0.482732i
$397$	−13.4804			−0.676563			−0.338281	−	0.941045i	$-0.609846\pi$
$397$	−13.4804			−0.676563			−0.338281	+	0.941045i	$0.609846\pi$
$398$	2.74491	+	2.30325i	0.137590	+	0.115452i
$399$	−1.48873	+	7.17236i	−0.0745299	+	0.359067i
$400$	−1.55656	−	8.82772i	−0.0778282	−	0.441386i
$401$	11.4522	+	4.16826i	0.571896	+	0.208153i	0.611748	−	0.791053i	$-0.290467\pi$
$401$	11.4522	+	4.16826i	0.571896	+	0.208153i	−0.0398524	+	0.999206i	$0.512689\pi$
$402$	−2.01371	−	3.02658i	−0.100435	−	0.150952i
$403$	1.28885	−	7.30943i	0.0642022	−	0.364109i
$404$	−11.5163	−	19.9468i	−0.572957	−	0.992391i
$405$	−9.24380	−	0.881969i	−0.459328	−	0.0438254i
$406$	−3.25309	−	7.09345i	−0.161448	−	0.352042i
$407$	−23.7779	+	8.65443i	−1.17862	+	0.428984i
$408$	−5.73318	+	0.364463i	−0.283835	+	0.0180436i
$409$	6.08583	+	34.5144i	0.300925	+	1.70663i	0.642093	+	0.766627i	$0.278067\pi$
$409$	6.08583	+	34.5144i	0.300925	+	1.70663i	−0.341168	+	0.940002i	$0.610822\pi$
$410$	0.309742	+	0.112737i	0.0152971	+	0.00556769i
$411$	7.97429	−	3.49009i	0.393343	−	0.172154i
$412$	7.83344	+	6.57304i	0.385926	+	0.323830i
$413$	−8.26432	−	18.0206i	−0.406661	−	0.886733i
$414$	6.54815	−	0.835921i	0.321824	−	0.0410833i
$415$	0.422365	−	0.731557i	0.0207331	−	0.0359107i
$416$	−5.23671	−	4.39412i	−0.256751	−	0.215439i
$417$	6.07437	+	1.78347i	0.297463	+	0.0873370i
$418$	−0.361726	−	2.05145i	−0.0176926	−	0.100340i
$419$	−24.4448	−	8.89718i	−1.19421	−	0.434656i	−0.333008	−	0.942924i	$-0.608064\pi$
$419$	−24.4448	−	8.89718i	−1.19421	−	0.434656i	−0.861199	+	0.508268i	$0.830286\pi$
$420$	6.30166	−	4.97209i	0.307489	−	0.242613i
$421$	−2.98469	+	16.9270i	−0.145465	+	0.824971i	0.821528	+	0.570168i	$0.193122\pi$
$421$	−2.98469	+	16.9270i	−0.145465	+	0.824971i	−0.966993	+	0.254803i	$0.917989\pi$
$422$	5.76335	−	9.98242i	0.280556	−	0.485936i
$423$	31.4259	+	20.1945i	1.52798	+	0.981892i
$424$	10.2907	+	17.8240i	0.499760	+	0.865609i
$425$	1.11492	−	6.32301i	0.0540814	−	0.306711i
$426$	−10.3516	+	4.53056i	−0.501537	+	0.219506i
$427$	−12.2623	+	8.47072i	−0.593415	+	0.409927i
$428$	−10.5915	+	8.88732i	−0.511959	+	0.429585i
$429$	2.34326	−	4.72823i	0.113134	−	0.228281i
$430$	0.0712254	−	0.403939i	0.00343479	−	0.0194797i
$431$	5.64058	−	9.76977i	0.271697	−	0.470593i	−0.697599	−	0.716488i	$-0.745748\pi$
$431$	5.64058	−	9.76977i	0.271697	−	0.470593i	0.969297	+	0.245895i	$0.0790818\pi$
$432$	10.1542	−	6.08012i	0.488543	−	0.292530i
$433$	−33.9521			−1.63163			−0.815817	−	0.578310i	$-0.803712\pi$
$433$	−33.9521			−1.63163			−0.815817	+	0.578310i	$0.803712\pi$
$434$	8.12686	−	2.12241i	0.390102	−	0.101879i
$435$	−9.56790	+	0.608240i	−0.458746	+	0.0291629i
$436$	20.9960	+	7.64192i	1.00553	+	0.365982i
$437$	−6.01178	−	2.18811i	−0.287582	−	0.104671i
$438$	−8.43552	+	3.69196i	−0.403065	+	0.176409i
$439$	0.164166	−	0.931032i	0.00783522	−	0.0444357i	−0.980639	−	0.195822i	$-0.937263\pi$
$439$	0.164166	−	0.931032i	0.00783522	−	0.0444357i	0.988475	+	0.151386i	$0.0483737\pi$
$440$	−2.48587	+	4.30565i	−0.118509	+	0.205264i
$441$	−19.2652	−	8.35767i	−0.917392	−	0.397984i
$442$	−0.576474	−	0.998482i	−0.0274201	−	0.0474930i
$443$	6.92442	−	2.52028i	0.328989	−	0.119742i	−0.172245	−	0.985054i	$-0.555102\pi$
$443$	6.92442	−	2.52028i	0.328989	−	0.119742i	0.501234	+	0.865312i	$0.332880\pi$
$444$	−7.40153	−	30.5070i	−0.351261	−	1.44780i
$445$	13.1560	−	11.0392i	0.623655	−	0.523309i
$446$	−0.568486	−	3.22404i	−0.0269186	−	0.152663i
$447$	13.9874	−	13.3374i	0.661581	−	0.630840i
$448$	−1.14360	+	4.16217i	−0.0540302	+	0.196644i
$449$	−1.91338	−	3.31406i	−0.0902978	−	0.156400i	0.817339	−	0.576158i	$-0.195449\pi$
$449$	−1.91338	−	3.31406i	−0.0902978	−	0.156400i	−0.907636	+	0.419757i	$0.862115\pi$
$450$	−1.92759	−	6.19834i	−0.0908675	−	0.292193i
$451$	−0.688655	−	1.19279i	−0.0324275	−	0.0561661i
$452$	19.4603	−	7.08295i	0.915333	−	0.333154i
$453$	0.175032	−	1.56971i	0.00822372	−	0.0737513i
$454$	−1.62903	−	9.23870i	−0.0764543	−	0.433594i
$455$	3.17058	+	1.50303i	0.148639	+	0.0704632i
$456$	5.61738	−	0.357102i	0.263058	−	0.0167228i
$457$	−8.45725	−	7.09648i	−0.395614	−	0.331959i	0.423182	−	0.906045i	$-0.360913\pi$
$457$	−8.45725	−	7.09648i	−0.395614	−	0.331959i	−0.818795	+	0.574086i	$0.805358\pi$
$458$	−6.58563	+	11.4066i	−0.307726	+	0.532997i
$459$	8.32398	−	1.60481i	0.388530	−	0.0749059i
$460$	3.50524	+	6.07126i	0.163433	+	0.283074i
$461$	25.8609	−	9.41259i	1.20446	−	0.438388i	0.339682	−	0.940540i	$-0.389680\pi$
$461$	25.8609	−	9.41259i	1.20446	−	0.438388i	0.864779	+	0.502152i	$0.167458\pi$
$462$	5.96912	+	0.179882i	0.277708	+	0.00836886i
$463$	9.38014	−	7.87087i	0.435932	−	0.365790i	−0.398253	−	0.917276i	$-0.630383\pi$
$463$	9.38014	−	7.87087i	0.435932	−	0.365790i	0.834185	+	0.551485i	$0.185939\pi$
$464$	9.36071	−	7.85457i	0.434560	−	0.364639i
$465$	1.14354	−	10.2554i	0.0530303	−	0.475582i
$466$	−12.1828	+	4.43418i	−0.564357	+	0.205409i
$467$	2.49643			0.115521			0.0577605	−	0.998330i	$-0.481604\pi$
$467$	2.49643			0.115521			0.0577605	+	0.998330i	$0.481604\pi$
$468$	5.50756	+	3.53920i	0.254587	+	0.163600i
$469$	−10.0558	−	0.944103i	−0.464335	−	0.0435946i
$470$	1.22653	−	6.95599i	0.0565756	−	0.320856i
$471$	4.64341	+	19.1388i	0.213957	+	0.881870i
$472$	−11.6697	+	9.79204i	−0.537141	+	0.450715i
$473$	−1.31291	+	1.10166i	−0.0603677	+	0.0506545i
$474$	−6.41225	+	6.11430i	−0.294524	+	0.280839i
$475$	−1.09240	+	6.19529i	−0.0501226	+	0.284259i
$476$	−4.24121	+	5.97601i	−0.194396	+	0.273910i
$477$	−18.3939	−	24.1674i	−0.842198	−	1.10655i
$478$	−11.8964			−0.544129
$479$	32.2060	−	11.7220i	1.47153	−	0.535594i	0.523016	−	0.852323i	$-0.324807\pi$
$479$	32.2060	−	11.7220i	1.47153	−	0.535594i	0.948516	+	0.316729i	$0.102585\pi$
$480$	−7.65341	−	5.63486i	−0.349329	−	0.257195i
$481$	10.5119	−	8.82049i	0.479299	−	0.402180i
$482$	10.4078	−	8.73318i	0.474062	−	0.397785i
$483$	9.64460	−	15.6000i	0.438845	−	0.709826i
$484$	−8.58593	+	3.12502i	−0.390269	+	0.142046i
$485$	−4.33806	−	7.51374i	−0.196981	−	0.341181i
$486$	6.73635	−	5.29856i	0.305567	−	0.240348i
$487$	−3.18613	+	5.51853i	−0.144377	+	0.250069i	−0.929140	−	0.369727i	$-0.879451\pi$
$487$	−3.18613	+	5.51853i	−0.144377	+	0.250069i	0.784763	+	0.619796i	$0.212785\pi$
$488$	8.77270	+	7.36117i	0.397121	+	0.333224i
$489$	11.7951	−	23.8002i	0.533394	−	1.07628i
$490$	−0.0503903	+	3.97046i	−0.00227640	+	0.179367i
$491$	4.17767	+	23.6927i	0.188535	+	1.06924i	0.921328	+	0.388786i	$0.127105\pi$
$491$	4.17767	+	23.6927i	0.188535	+	1.06924i	−0.732793	+	0.680452i	$0.761784\pi$
$492$	1.56534	−	0.685097i	0.0705708	−	0.0308866i
$493$	8.22462	−	2.99352i	0.370418	−	0.134821i
$494$	0.564830	+	0.978315i	0.0254129	+	0.0440165i
$495$	2.83419	−	6.76702i	0.127387	−	0.304155i
$496$	6.57608	+	11.3901i	0.295275	+	0.511431i
$497$	−8.31768	+	30.2724i	−0.373099	+	1.35790i
$498$	0.183826	+	0.757678i	0.00823744	+	0.0339524i
$499$	5.40595	+	30.6587i	0.242003	+	1.37247i	0.827350	+	0.561687i	$0.189847\pi$
$499$	5.40595	+	30.6587i	0.242003	+	1.37247i	−0.585346	+	0.810783i	$0.699042\pi$
$500$	11.9899	−	10.0607i	0.536204	−	0.449928i
$501$	−28.8108	+	27.4721i	−1.28717	+	1.22736i
$502$	3.58302	−	1.30411i	0.159918	−	0.0582054i
$503$	10.2647	+	17.7789i	0.457679	+	0.792724i	0.998838	−	0.0481965i	$-0.0153474\pi$
$503$	10.2647	+	17.7789i	0.457679	+	0.792724i	−0.541158	+	0.840921i	$0.682014\pi$
$504$	−2.27048	+	15.9759i	−0.101135	+	0.711622i
$505$	6.99878	−	12.1222i	0.311441	−	0.539432i
$506$	−0.905676	+	5.13634i	−0.0402622	+	0.228338i
$507$	2.17815	−	19.5339i	0.0967349	−	0.867530i
$508$	−7.36773	−	2.68163i	−0.326890	−	0.118978i
$509$	−11.3414	−	4.12792i	−0.502697	−	0.182967i	0.0782094	−	0.996937i	$-0.475080\pi$
$509$	−11.3414	−	4.12792i	−0.502697	−	0.182967i	−0.580907	+	0.813970i	$0.697302\pi$
$510$	−0.887917	−	1.33453i	−0.0393176	−	0.0590939i
$511$	−6.77809	+	24.6690i	−0.299845	+	1.09129i
$512$	21.3746			0.944635
$513$	−8.15585	+	1.57239i	−0.360090	+	0.0694228i
$514$	−6.08877	+	10.5461i	−0.268564	+	0.465167i
$515$	−1.07914	+	6.12011i	−0.0475526	+	0.269684i
$516$	−1.17780	−	1.77023i	−0.0518500	−	0.0779299i
$517$	−22.6089	+	18.9711i	−0.994337	+	0.834348i
$518$	14.0321	+	6.65200i	0.616535	+	0.292272i
$519$	29.4842	+	21.7079i	1.29421	+	0.952871i
$520$	0.468184	−	2.65520i	0.0205312	−	0.116438i
$521$	17.6721	+	30.6089i	0.774227	+	1.34100i	0.935228	+	0.354046i	$0.115194\pi$
$521$	17.6721	+	30.6089i	0.774227	+	1.34100i	−0.161001	+	0.986954i	$0.551472\pi$
$522$	6.00368	−	6.50041i	0.262774	−	0.284515i
$523$	13.0130	−	22.5391i	0.569017	−	0.985567i	−0.427646	−	0.903946i	$-0.640657\pi$
$523$	13.0130	−	22.5391i	0.569017	−	0.985567i	0.996663	−	0.0816207i	$-0.0260096\pi$
$524$	−0.744335	+	4.22134i	−0.0325164	+	0.184410i
$525$	−16.7535	−	6.67589i	−0.731185	−	0.291360i
$526$	−10.4424	−	3.80072i	−0.455310	−	0.165719i
$527$	1.63585	+	9.27735i	0.0712586	+	0.404128i
$528$	2.20474	+	9.08730i	0.0959488	+	0.395474i
$529$	−5.34847	−	4.48790i	−0.232542	−	0.195126i
$530$	−2.87135	+	4.97332i	−0.124723	+	0.216027i
$531$	15.2521	−	16.5140i	0.661883	−	0.716645i
$532$	4.15555	−	5.85531i	0.180166	−	0.253860i
$533$	0.572169	+	0.480107i	0.0247834	+	0.0207957i
$534$	−1.75660	+	15.7534i	−0.0760155	+	0.681716i
$535$	−7.89584	−	2.87385i	−0.341367	−	0.124247i
$536$	1.34766	+	7.64298i	0.0582102	+	0.330126i
$537$	7.92802	+	11.9157i	0.342119	+	0.514201i
$538$	−0.0604006	+	0.0219840i	−0.00260405	+	0.000947798i
$539$	10.8254	−	12.5737i	0.466284	−	0.541587i
$540$	7.95381	+	4.42479i	0.342277	+	0.190413i
$541$	−19.3656	−	33.5421i	−0.832591	−	1.44209i	−0.895977	−	0.444100i	$-0.853523\pi$
$541$	−19.3656	−	33.5421i	−0.832591	−	1.44209i	0.0633866	−	0.997989i	$-0.479810\pi$
$542$	−1.74569	+	9.90033i	−0.0749840	+	0.425255i
$543$	−18.7505	+	1.19199i	−0.804663	+	0.0511531i
$544$	8.15324	+	2.96754i	0.349567	+	0.127232i
$545$	2.35793	+	13.3725i	0.101002	+	0.572813i
$546$	−3.07519	+	1.01547i	−0.131606	+	0.0434580i
$547$	−1.89965	−	1.59400i	−0.0812232	−	0.0681544i	0.601272	−	0.799044i	$-0.294661\pi$
$547$	−1.89965	−	1.59400i	−0.0812232	−	0.0681544i	−0.682495	+	0.730890i	$0.739105\pi$
$548$	−8.53209			−0.364473
$549$	−14.2168	−	9.13581i	−0.606757	−	0.389907i
$550$	5.12856			0.218683
$551$	−8.05849	+	2.93305i	−0.343303	+	0.124952i
$552$	−13.5222	−	3.97019i	−0.575542	−	0.168983i
$553$	1.98982	+	24.5359i	0.0846157	+	1.04337i
$554$	11.2946	+	4.11089i	0.479860	+	0.174655i
$555$	13.8070	−	13.1654i	0.586075	−	0.558842i
$556$	−4.75354	−	3.98870i	−0.201595	−	0.169158i
$557$	−21.0521			−0.892008			−0.446004	−	0.895031i	$-0.647153\pi$
$557$	−21.0521			−0.892008			−0.446004	+	0.895031i	$0.647153\pi$
$558$	5.76815	+	7.57866i	0.244185	+	0.320830i
$559$	0.464718	−	0.804916i	0.0196555	−	0.0340443i
$560$	−6.01584	+	1.57110i	−0.254216	+	0.0663909i
$561$	−0.742242	+	6.65651i	−0.0313375	+	0.281038i
$562$	2.10124	−	1.76315i	0.0886356	−	0.0743741i
$563$	−0.245936	−	1.39477i	−0.0103650	−	0.0587826i	0.979187	−	0.202962i	$-0.0650568\pi$
$563$	−0.245936	−	1.39477i	−0.0103650	−	0.0587826i	−0.989552	+	0.144180i	$0.953946\pi$
$564$	−20.2823	−	30.4840i	−0.854038	−	1.28361i
$565$	9.64108	+	8.08983i	0.405603	+	0.340342i
$566$	10.2112			0.429210
$567$	0.338182	−	23.8094i	0.0142023	−	0.999899i
$568$	24.1234			1.01219
$569$	−7.19666	−	6.03872i	−0.301700	−	0.253156i	0.479352	−	0.877623i	$-0.340872\pi$
$569$	−7.19666	−	6.03872i	−0.301700	−	0.253156i	−0.781051	+	0.624467i	$0.785316\pi$
$570$	0.869982	+	1.30757i	0.0364395	+	0.0547682i
$571$	−2.15721	−	12.2342i	−0.0902765	−	0.511983i	−0.996093	−	0.0883128i	$-0.971852\pi$
$571$	−2.15721	−	12.2342i	−0.0902765	−	0.511983i	0.905816	−	0.423671i	$-0.139259\pi$
$572$	−3.96232	+	3.32478i	−0.165673	+	0.139016i
$573$	0.0311450	−	0.279312i	0.00130110	−	0.0116684i
$574$	−0.223944	+	0.815050i	−0.00934726	+	0.0340195i
$575$	7.87541	−	13.6406i	0.328427	−	0.568853i
$576$	−4.85496	+	0.619773i	−0.202290	+	0.0258239i
$577$	−36.1914			−1.50667			−0.753334	−	0.657638i	$-0.771556\pi$
$577$	−36.1914			−1.50667			−0.753334	+	0.657638i	$0.771556\pi$
$578$	−6.03887	−	5.06722i	−0.251184	−	0.210768i
$579$	2.28045	−	2.17449i	0.0947723	−	0.0903687i
$580$	8.83049	+	3.21403i	0.366666	+	0.133456i
$581$	1.95736	+	0.927898i	0.0812050	+	0.0384957i
$582$	7.68345	+	2.25591i	0.318489	+	0.0935104i
$583$	22.5485	−	8.20700i	0.933865	−	0.339899i
$584$	19.6581			0.813460
$585$	−0.189159	+	3.97411i	−0.00782076	+	0.164309i
$586$	7.94796			0.328327
$587$	−1.87391	−	1.57240i	−0.0773445	−	0.0648997i	0.603296	−	0.797518i	$-0.293854\pi$
$587$	−1.87391	−	1.57240i	−0.0773445	−	0.0648997i	−0.680640	+	0.732618i	$0.738298\pi$
$588$	14.0145	+	15.0760i	0.577950	+	0.621723i
$589$	−1.60281	−	9.08996i	−0.0660425	−	0.374545i
$590$	−3.99423	−	1.45378i	−0.164440	−	0.0598512i
$591$	47.0201	−	2.98911i	1.93415	−	0.122956i
$592$	−4.22241	+	23.9465i	−0.173540	+	0.984194i
$593$	8.91340	+	15.4385i	0.366029	+	0.633981i	0.988941	−	0.148311i	$-0.0473836\pi$
$593$	8.91340	+	15.4385i	0.366029	+	0.633981i	−0.622911	+	0.782292i	$0.714050\pi$
$594$	2.41698	+	6.32537i	0.0991701	+	0.259533i
$595$	−4.43397	−	0.416289i	−0.181775	−	0.0170662i
$596$	−17.8015	+	6.47923i	−0.729179	+	0.265400i
$597$	6.25305	+	9.39827i	0.255920	+	0.384646i
$598$	−0.491147	−	2.78543i	−0.0200845	−	0.113905i
$599$	7.01957	+	2.55491i	0.286812	+	0.104391i	0.481420	−	0.876490i	$-0.340121\pi$
$599$	7.01957	+	2.55491i	0.286812	+	0.104391i	−0.194608	+	0.980881i	$0.562344\pi$
$600$	−1.53572	+	13.7725i	−0.0626954	+	0.562259i
$601$	11.8770	+	9.96601i	0.484474	+	0.406522i	0.852041	−	0.523475i	$-0.175365\pi$
$601$	11.8770	+	9.96601i	0.484474	+	0.406522i	−0.367567	+	0.929997i	$0.619809\pi$
$602$	1.04721	+	0.0983181i	0.0426809	+	0.00400715i
$603$	−3.40086	−	10.9358i	−0.138494	−	0.445339i
$604$	−0.774066	+	1.34072i	−0.0314963	+	0.0545532i
$605$	−4.25368	−	3.56926i	−0.172937	−	0.145111i
$606$	3.04608	+	12.5551i	0.123738	+	0.510015i
$607$	−8.09650	−	45.9175i	−0.328627	−	1.86374i	−0.482856	−	0.875700i	$-0.660400\pi$
$607$	−8.09650	−	45.9175i	−0.328627	−	1.86374i	0.154229	−	0.988035i	$-0.450711\pi$
$608$	−7.98856	−	2.90760i	−0.323979	−	0.117919i
$609$	−3.53787	−	24.3288i	−0.143362	−	0.985855i
$610$	−0.554870	+	3.14682i	−0.0224660	+	0.127411i
$611$	8.00264	−	13.8610i	0.323752	−	0.560755i
$612$	−8.10516	−	1.83031i	−0.327632	−	0.0739858i
$613$	−6.49695	−	11.2531i	−0.262409	−	0.454507i	0.704472	−	0.709732i	$-0.251184\pi$
$613$	−6.49695	−	11.2531i	−0.262409	−	0.454507i	−0.966882	+	0.255225i	$0.917850\pi$
$614$	0.774696	−	4.39352i	0.0312642	−	0.177308i
$615$	0.836221	+	0.615672i	0.0337197	+	0.0248263i
$616$	−11.5202	−	5.46123i	−0.464163	−	0.220039i
$617$	13.8356	−	11.6094i	0.556999	−	0.467378i	−0.320304	−	0.947315i	$-0.603785\pi$
$617$	13.8356	−	11.6094i	0.556999	−	0.467378i	0.877303	+	0.479937i	$0.159341\pi$
$618$	−3.17727	−	4.77540i	−0.127809	−	0.192095i
$619$	−1.40277	+	7.95549i	−0.0563820	+	0.319758i	−0.999934	−	0.0114654i	$-0.996350\pi$
$619$	−1.40277	+	7.95549i	−0.0563820	+	0.319758i	0.943552	+	0.331224i	$0.107461\pi$
$620$	−5.05722	+	8.75935i	−0.203103	+	0.351784i
$621$	20.5353	+	3.28468i	0.824053	+	0.131810i
$622$	−6.49360			−0.260370
$623$	30.9425	+	31.3377i	1.23968	+	1.25552i
$624$	−2.80900	−	4.22190i	−0.112450	−	0.169011i
$625$	−9.55241	−	3.47679i	−0.382096	−	0.139072i
$626$	−7.32394	−	2.66570i	−0.292723	−	0.106543i
$627$	0.727250	−	6.52206i	0.0290436	−	0.260466i
$628$	3.35206	−	19.0105i	0.133762	−	0.758600i
$629$	−8.70834	+	15.0833i	−0.347224	+	0.601410i
$630$	−4.17720	+	1.68018i	−0.166424	+	0.0669401i
$631$	23.6861	+	41.0255i	0.942927	+	1.63320i	0.759849	+	0.650100i	$0.225273\pi$
$631$	23.6861	+	41.0255i	0.942927	+	1.63320i	0.183078	+	0.983098i	$0.441394\pi$
$632$	17.7746	−	6.46941i	0.707034	−	0.257339i
$633$	26.2806	−	25.0594i	1.04456	−	0.996022i
$634$	−11.0959	+	9.31057i	−0.440675	+	0.369770i
$635$	−0.827422	−	4.69254i	−0.0328352	−	0.186218i
$636$	7.01887	+	28.9298i	0.278316	+	1.14714i
$637$	−3.18445	+	8.41534i	−0.126172	+	0.333428i
$638$	3.49561	+	6.05458i	0.138393	+	0.239703i
$639$	−35.3112	+	4.50774i	−1.39689	+	0.178324i
$640$	5.94987	+	10.3055i	0.235189	+	0.407360i
$641$	−31.6131	+	11.5062i	−1.24864	+	0.454468i	−0.879942	−	0.475081i	$-0.842419\pi$
$641$	−31.6131	+	11.5062i	−1.24864	+	0.454468i	−0.368699	+	0.929549i	$0.620197\pi$
$642$	7.10465	−	3.10948i	0.280398	−	0.122721i
$643$	−0.447675	−	2.53889i	−0.0176546	−	0.100124i	0.974707	−	0.223486i	$-0.0717436\pi$
$643$	−0.447675	−	2.53889i	−0.0176546	−	0.100124i	−0.992362	+	0.123362i	$0.960632\pi$
$644$	−14.7912	+	10.2176i	−0.582853	+	0.402631i
$645$	0.573792	−	1.15780i	0.0225930	−	0.0455882i
$646$	−1.09835	−	0.921628i	−0.0432141	−	0.0362610i
$647$	−13.2070	+	22.8753i	−0.519223	+	0.899320i	0.480528	+	0.876980i	$0.340445\pi$
$647$	−13.2070	+	22.8753i	−0.519223	+	0.899320i	−0.999750	+	0.0223405i	$0.992888\pi$
$648$	−17.7102	+	4.59659i	−0.695722	+	0.180571i
$649$	8.88044	+	15.3814i	0.348588	+	0.603771i
$650$	−2.61348	+	0.951231i	−0.102509	+	0.0373103i
$651$	26.4491	+	0.797055i	1.03662	+	0.0312390i
$652$	−19.9449	+	16.7358i	−0.781102	+	0.655423i
$653$	−17.6334	+	14.7962i	−0.690049	+	0.579020i	−0.918923	−	0.394436i	$-0.870940\pi$
$653$	−17.6334	+	14.7962i	−0.690049	+	0.579020i	0.228875	+	0.973456i	$0.426495\pi$
$654$	−10.0924	−	7.43058i	−0.394644	−	0.290559i
$655$	−2.44790	+	0.890962i	−0.0956473	+	0.0348128i
$656$	−1.32353			−0.0516754
$657$	−28.7751	+	3.67336i	−1.12262	+	0.143312i
$658$	18.0333	+	1.69308i	0.703011	+	0.0660030i
$659$	4.87327	−	27.6377i	0.189836	−	1.07661i	−0.729748	−	0.683716i	$-0.760363\pi$
$659$	4.87327	−	27.6377i	0.189836	−	1.07661i	0.919583	−	0.392895i	$-0.128526\pi$
$660$	−5.20439	+	4.96257i	−0.202581	+	0.193168i
$661$	15.8929	−	13.3357i	0.618161	−	0.518699i	−0.279064	−	0.960273i	$-0.590024\pi$
$661$	15.8929	−	13.3357i	0.618161	−	0.518699i	0.897225	+	0.441574i	$0.145580\pi$
$662$	11.5091	−	9.65726i	0.447313	−	0.375340i
$663$	−0.856387	−	3.52978i	−0.0332593	−	0.137085i
$664$	0.289034	−	1.63919i	0.0112167	−	0.0636130i
$665$	4.34442	+	0.407881i	0.168469	+	0.0158169i
$666$	−0.837165	+	17.5883i	−0.0324395	+	0.681533i
$667$	21.4714			0.831377
$668$	36.6671	−	13.3457i	1.41869	−	0.516362i
$669$	1.14294	−	10.2500i	0.0441886	−	0.396288i
$670$	−1.65885	+	1.39194i	−0.0640869	+	0.0537753i
$671$	10.2280	−	8.58233i	0.394848	−	0.331317i
$672$	12.8159	−	20.7296i	0.494385	−	0.799662i
$673$	−5.18042	+	1.88552i	−0.199691	+	0.0726815i	−0.439929	−	0.898032i	$-0.644997\pi$
$673$	−5.18042	+	1.88552i	−0.199691	+	0.0726815i	0.240239	+	0.970714i	$0.422774\pi$
$674$	−0.833079	−	1.44294i	−0.0320890	−	0.0555798i
$675$	−0.325612	−	20.4468i	−0.0125328	−	0.786997i
$676$	−9.63270	+	16.6843i	−0.370488	+	0.641705i
$677$	−24.2758	−	20.3698i	−0.932993	−	0.782874i	0.0433590	−	0.999060i	$-0.486194\pi$
$677$	−24.2758	−	20.3698i	−0.932993	−	0.782874i	−0.976352	+	0.216185i	$0.930639\pi$
$678$	−11.5927	+	0.736956i	−0.445213	+	0.0283026i
$679$	18.3054	−	12.6452i	0.702497	−	0.485280i
$680$	0.594233	+	3.37006i	0.0227878	+	0.129236i
$681$	3.27517	−	29.3721i	0.125505	−	1.12554i
$682$	−7.07102	+	2.57364i	−0.270763	+	0.0985498i
$683$	−18.4846	−	32.0163i	−0.707294	−	1.22507i	−0.965857	−	0.259075i	$-0.916582\pi$
$683$	−18.4846	−	32.0163i	−0.707294	−	1.22507i	0.258563	−	0.965994i	$-0.416751\pi$
$684$	7.94145	+	1.79334i	0.303649	+	0.0685701i
$685$	−2.59259	−	4.49050i	−0.0990579	−	0.171573i
$686$	−10.1587	+	0.694211i	−0.387861	+	0.0265051i
$687$	−30.0301	+	28.6347i	−1.14572	+	1.09248i
$688$	0.285993	+	1.62195i	0.0109034	+	0.0618361i
$689$	−9.96839	+	8.36447i	−0.379765	+	0.318661i
$690$	−0.927141	−	3.82141i	−0.0352957	−	0.145479i
$691$	1.68363	−	0.612792i	0.0640484	−	0.0233117i	−0.309797	−	0.950803i	$-0.600261\pi$
$691$	1.68363	−	0.612792i	0.0640484	−	0.0233117i	0.373846	+	0.927491i	$0.378039\pi$
$692$	−17.9440	−	31.0798i	−0.682127	−	1.18148i
$693$	17.8835	+	5.84132i	0.679339	+	0.221893i
$694$	−2.49561	+	4.32251i	−0.0947319	+	0.164080i
$695$	0.654851	−	3.71385i	0.0248399	−	0.140874i
$696$	−17.3060	+	7.57428i	−0.655982	+	0.287102i
$697$	−0.890833	−	0.324237i	−0.0337427	−	0.0122813i
$698$	3.25933	+	1.18630i	0.123368	+	0.0449021i
$699$	−40.7609	+	2.59121i	−1.54172	+	0.0980085i
$700$	12.4201	+	12.5788i	0.469437	+	0.475432i
$701$	28.5094			1.07678			0.538392	−	0.842694i	$-0.319032\pi$
$701$	28.5094			1.07678			0.538392	+	0.842694i	$0.319032\pi$
$702$	−2.40489	−	2.77507i	−0.0907667	−	0.104738i
$703$	8.53245	−	14.7786i	0.321807	−	0.557387i
$704$	0.671491	−	3.80821i	0.0253078	−	0.143527i
$705$	9.88092	−	19.9377i	0.372137	−	0.750897i
$706$	−1.91592	+	1.60764i	−0.0721065	+	0.0605045i
$707$	32.4343	+	15.3757i	1.21982	+	0.578262i
$708$	−20.1855	+	8.83455i	−0.758618	+	0.332023i
$709$	−2.65241	+	15.0426i	−0.0996133	+	0.564935i	0.893622	+	0.448819i	$0.148155\pi$
$709$	−2.65241	+	15.0426i	−0.0996133	+	0.564935i	−0.993236	+	0.116115i	$0.962956\pi$
$710$	3.36550	+	5.82921i	0.126305	+	0.218767i
$711$	−24.8091	+	12.7912i	−0.930413	+	0.479706i
$712$	16.9200	−	29.3064i	0.634105	−	1.09830i
$713$	−4.01304	+	22.7591i	−0.150290	+	0.852335i
$714$	3.22692	−	2.54608i	0.120764	−	0.0952846i
$715$	−2.95387	−	1.07512i	−0.110468	−	0.0402072i
$716$	−2.43602	−	13.8154i	−0.0910385	−	0.516305i
$717$	−35.9599	−	10.5580i	−1.34295	−	0.394297i
$718$	−5.40913	−	4.53880i	−0.201867	−	0.169386i
$719$	9.14943	−	15.8473i	0.341216	−	0.591004i	−0.643443	−	0.765494i	$-0.722495\pi$
$719$	9.14943	−	15.8473i	0.341216	−	0.591004i	0.984659	+	0.174491i	$0.0558278\pi$
$720$	−4.26983	−	5.61005i	−0.159127	−	0.209074i
$721$	−15.8663	−	1.48962i	−0.590891	−	0.0554765i
$722$	−6.92604	−	5.81164i	−0.257760	−	0.216287i
$723$	39.2109	−	17.1613i	1.45827	−	0.638237i
$724$	17.3054	+	6.29865i	0.643150	+	0.234088i
$725$	−3.66627	−	20.7925i	−0.136162	−	0.772212i
$726$	5.11472	−	0.325147i	0.189825	−	0.0120673i
$727$	6.03585	−	2.19687i	0.223857	−	0.0814773i	−0.227657	−	0.973741i	$-0.573106\pi$
$727$	6.03585	−	2.19687i	0.223857	−	0.0814773i	0.451514	+	0.892264i	$0.350884\pi$
$728$	6.88357	+	0.646272i	0.255122	+	0.0239524i
$729$	25.0648	−	10.0377i	0.928326	−	0.371768i
$730$	2.74255	+	4.75023i	0.101506	+	0.175814i
$731$	−0.204847	+	1.16175i	−0.00757655	+	0.0429688i
$732$	9.17550	+	13.7907i	0.339136	+	0.509718i
$733$	−36.8456	−	13.4107i	−1.36092	−	0.495335i	−0.444582	−	0.895738i	$-0.646648\pi$
$733$	−36.8456	−	13.4107i	−1.36092	−	0.495335i	−0.916339	+	0.400403i	$0.868870\pi$
$734$	−3.35986	−	19.0547i	−0.124015	−	0.703323i
$735$	−3.67610	+	11.9570i	−0.135595	+	0.441041i
$736$	16.3053	+	13.6818i	0.601022	+	0.504318i
$737$	9.04836			0.333301
$738$	−0.950714	+	0.121366i	−0.0349963	+	0.00446754i
$739$	10.0709			0.370466			0.185233	−	0.982695i	$-0.440696\pi$
$739$	10.0709			0.370466			0.185233	+	0.982695i	$0.440696\pi$
$740$	−17.5720	+	6.39567i	−0.645958	+	0.235110i
$741$	0.839090	+	3.45849i	0.0308247	+	0.127051i
$742$	−13.3067	−	6.30809i	−0.488503	−	0.231577i
$743$	−12.3507	−	4.49527i	−0.453101	−	0.164915i	0.105381	−	0.994432i	$-0.466394\pi$
$743$	−12.3507	−	4.49527i	−0.453101	−	0.164915i	−0.558482	+	0.829516i	$0.688616\pi$
$744$	−4.79400	−	19.7595i	−0.175757	−	0.724418i
$745$	−8.81931	−	7.40028i	−0.323115	−	0.271125i
$746$	−10.2841			−0.376529
$747$	−0.116777	+	2.45342i	−0.00427267	+	0.0897659i
$748$	3.28251	−	5.68547i	0.120020	−	0.207882i
$749$	5.70871	−	20.7769i	0.208592	−	0.759173i
$750$	−8.04267	+	3.52002i	−0.293677	+	0.128533i
$751$	−12.8284	+	10.7643i	−0.468116	+	0.392796i	−0.846107	−	0.533014i	$-0.821059\pi$
$751$	−12.8284	+	10.7643i	−0.468116	+	0.392796i	0.377991	+	0.925809i	$0.376615\pi$
$752$	4.92491	+	27.9306i	0.179593	+	1.01852i
$753$	11.9880	−	0.762086i	0.436866	−	0.0277720i
$754$	−2.90433	−	2.43702i	−0.105769	−	0.0887511i
$755$	−0.940843			−0.0342408
$756$	−9.66078	+	21.2466i	−0.351359	+	0.772731i
$757$	32.8223			1.19295			0.596473	−	0.802633i	$-0.296568\pi$
$757$	32.8223			1.19295			0.596473	+	0.802633i	$0.296568\pi$
$758$	2.57174	+	2.15795i	0.0934098	+	0.0783801i
$759$	−7.29613	+	14.7221i	−0.264833	+	0.534379i
$760$	−0.582231	−	3.30199i	−0.0211197	−	0.119776i
$761$	−27.0490	+	22.6968i	−0.980524	+	0.822757i	−0.984168	−	0.177236i	$-0.943284\pi$
$761$	−27.0490	+	22.6968i	−0.980524	+	0.822757i	0.00364434	+	0.999993i	$0.498840\pi$
$762$	3.54153	+	2.60747i	0.128296	+	0.0944587i
$763$	−33.6904	+	8.79857i	−1.21967	+	0.318530i
$764$	−0.137736	+	0.238566i	−0.00498313	+	0.00863103i
$765$	−1.49956	−	4.82197i	−0.0542167	−	0.174339i
$766$	1.92770			0.0696506
$767$	−7.37831	−	6.19113i	−0.266415	−	0.223549i
$768$	−5.11563	−	1.50198i	−0.184594	−	0.0541980i
$769$	−9.00688	−	3.27824i	−0.324797	−	0.118216i	0.174476	−	0.984661i	$-0.444177\pi$
$769$	−9.00688	−	3.27824i	−0.324797	−	0.118216i	−0.499272	+	0.866445i	$0.666399\pi$
$770$	−0.287548	−	3.54568i	−0.0103625	−	0.127777i
$771$	−27.7645	+	26.4744i	−0.999912	+	0.953451i
$772$	−2.90230	+	1.05635i	−0.104456	+	0.0380189i
$773$	−18.9585			−0.681890			−0.340945	−	0.940083i	$-0.610747\pi$
$773$	−18.9585			−0.681890			−0.340945	+	0.940083i	$0.610747\pi$
$774$	0.354163	+	1.13884i	0.0127301	+	0.0409348i
$775$	22.7246			0.816293
$776$	−13.0960	−	10.9889i	−0.470121	−	0.394478i
$777$	36.5120	+	32.5608i	1.30986	+	1.16811i
$778$	0.552945	+	3.13591i	0.0198240	+	0.112428i
$779$	0.872840	+	0.317688i	0.0312727	+	0.0113823i
$780$	1.73168	−	3.49419i	0.0620042	−	0.125112i
$781$	4.88390	−	27.6980i	0.174760	−	0.991111i
$782$	1.79495	+	3.10894i	0.0641871	+	0.111175i
$783$	23.9167	−	14.3209i	0.854715	−	0.511786i
$784$	−5.26259	−	15.0504i	−0.187950	−	0.537516i
$785$	11.0239	−	4.01238i	0.393461	−	0.143208i
$786$	1.06764	−	2.15429i	0.0380816	−	0.0768409i
$787$	−4.89985	−	27.7884i	−0.174661	−	0.990551i	−0.938535	−	0.345185i	$-0.887816\pi$
$787$	−4.89985	−	27.7884i	−0.174661	−	0.990551i	0.763874	−	0.645366i	$-0.223295\pi$
$788$	−43.3962	−	15.7949i	−1.54593	−	0.562671i
$789$	−28.1917	−	20.7563i	−1.00365	−	0.738942i
$790$	4.04305	+	3.39252i	0.143845	+	0.120700i
$791$	−18.6786	+	26.3188i	−0.664136	+	0.935790i
$792$	0.687305	−	14.4398i	0.0244223	−	0.513097i
$793$	−3.62031	+	6.27057i	−0.128561	+	0.222674i
$794$	−5.67753	−	4.76401i	−0.201488	−	0.169069i
$795$	−13.0932	+	12.4848i	−0.464367	+	0.442790i
$796$	−1.92136	−	10.8966i	−0.0681009	−	0.386219i
$797$	−19.4848	−	7.09189i	−0.690188	−	0.251208i	−0.0269721	−	0.999636i	$-0.508587\pi$
$797$	−19.4848	−	7.09189i	−0.690188	−	0.251208i	−0.663216	+	0.748428i	$0.730809\pi$
$798$	−3.16174	+	2.49465i	−0.111924	+	0.0883098i
$799$	−3.52755	+	20.0057i	−0.124796	+	0.707753i
$800$	10.4650	−	18.1259i	0.369993	−	0.640847i
$801$	−19.2909	+	46.0596i	−0.681609	+	1.62744i
$802$	3.35024	+	5.80278i	0.118301	+	0.204903i
$803$	3.97989	−	22.5711i	0.140447	−	0.796517i
$804$	−1.24399	+	11.1563i	−0.0438722	+	0.393451i
$805$	−9.87211	−	4.67993i	−0.347946	−	0.164946i
$806$	3.12600	−	2.62302i	0.110109	−	0.0923920i
$807$	−0.202087	+	0.0128468i	−0.00711379	+	0.000452230i
$808$	4.78942	−	27.1622i	0.168491	−	0.955561i
$809$	−7.19695	+	12.4655i	−0.253031	+	0.438263i	−0.964359	−	0.264598i	$-0.914761\pi$
$809$	−7.19695	+	12.4655i	−0.253031	+	0.438263i	0.711328	+	0.702861i	$0.248094\pi$
$810$	−3.58151	−	3.63824i	−0.125841	−	0.127835i
$811$	−2.71283			−0.0952604			−0.0476302	−	0.998865i	$-0.515167\pi$
$811$	−2.71283			−0.0952604			−0.0476302	+	0.998865i	$0.515167\pi$
$812$	−6.38446	+	23.2364i	−0.224051	+	0.815436i
$813$	−14.0633	+	28.3769i	−0.493222	+	0.995223i
$814$	−13.0730	−	4.75818i	−0.458208	−	0.166774i
$815$	−14.8687	−	5.41176i	−0.520827	−	0.189566i
$816$	5.18300	+	3.81601i	0.181441	+	0.133587i
$817$	0.200710	−	1.13828i	0.00702195	−	0.0398234i
$818$	−9.63434	+	16.6872i	−0.336857	+	0.583453i
$819$	−10.1968	+	0.340282i	−0.356304	+	0.0118904i
$820$	−0.508920	−	0.881475i	−0.0177723	−	0.0307825i
$821$	19.2631	−	7.01119i	0.672286	−	0.244692i	0.0167544	−	0.999860i	$-0.494667\pi$
$821$	19.2631	−	7.01119i	0.672286	−	0.244692i	0.655532	+	0.755167i	$0.272444\pi$
$822$	4.59193	+	1.34822i	0.160162	+	0.0470245i
$823$	28.0860	−	23.5670i	0.979018	−	0.821494i	−0.00492296	−	0.999988i	$-0.501567\pi$
$823$	28.0860	−	23.5670i	0.979018	−	0.821494i	0.983941	+	0.178494i	$0.0571226\pi$
$824$	2.12637	+	12.0592i	0.0740756	+	0.420104i
$825$	15.5024	+	4.55159i	0.539724	+	0.158466i
$826$	2.88784	−	10.5103i	0.100481	−	0.365701i
$827$	−17.8474	−	30.9126i	−0.620615	−	1.07494i	−0.989371	−	0.145410i	$-0.953550\pi$
$827$	−17.8474	−	30.9126i	−0.620615	−	1.07494i	0.368757	−	0.929526i	$-0.379784\pi$
$828$	−17.1487	−	11.0199i	−0.595958	−	0.382967i
$829$	17.8654	+	30.9438i	0.620491	+	1.07472i	0.989394	+	0.145254i	$0.0464001\pi$
$829$	17.8654	+	30.9438i	0.620491	+	1.07472i	−0.368903	+	0.929468i	$0.620267\pi$
$830$	0.436421	−	0.158844i	0.0151484	−	0.00551357i
$831$	30.4923	+	22.4501i	1.05777	+	0.778786i
$832$	0.364148	+	2.06519i	0.0126246	+	0.0715975i
$833$	0.144925	−	11.4192i	0.00502134	−	0.395653i
$834$	1.92805	+	2.89784i	0.0667630	+	0.100344i
$835$	18.1658	+	15.2429i	0.628653	+	0.527502i
$836$	−3.21621	+	5.57064i	−0.111235	+	0.192665i
$837$	10.7096	+	28.0276i	0.370179	+	0.968777i
$838$	−7.15111	−	12.3861i	−0.247031	−	0.427870i
$839$	37.8898	−	13.7908i	1.30810	−	0.476110i	0.408474	−	0.912770i	$-0.366061\pi$
$839$	37.8898	−	13.7908i	1.30810	−	0.476110i	0.899627	+	0.436660i	$0.143839\pi$
$840$	9.60783	+	0.289536i	0.331502	+	0.00998993i
$841$	−0.167454	+	0.140511i	−0.00577429	+	0.00484521i
$842$	−7.23910	+	6.07433i	−0.249476	+	0.209335i
$843$	7.91633	−	3.46472i	0.272653	−	0.119331i
$844$	−33.4469	+	12.1737i	−1.15129	+	0.419035i
$845$	−11.7081			−0.402771
$846$	6.09882	+	19.6113i	0.209682	+	0.674251i
$847$	8.24108	−	11.6120i	0.283167	−	0.398991i
$848$	4.00411	−	22.7085i	0.137502	−	0.779812i
$849$	30.8660	+	9.06244i	1.05932	+	0.311022i
$850$	2.70413	−	2.26904i	0.0927511	−	0.0778274i
$851$	−32.7303	+	27.4640i	−1.12198	+	0.941455i
$852$	33.4790	+	9.82964i	1.14697	+	0.336758i
$853$	2.42652	−	13.7615i	0.0830825	−	0.471184i	−0.914671	−	0.404198i	$-0.867551\pi$
$853$	2.42652	−	13.7615i	0.0830825	−	0.471184i	0.997754	−	0.0669859i	$-0.0213383\pi$
$854$	−8.15808	−	0.765931i	−0.279164	−	0.0262096i
$855$	1.46927	+	4.72458i	0.0502480	+	0.161577i
$856$	−16.5567			−0.565895
$857$	48.6923	−	17.7225i	1.66330	−	0.605390i	0.672421	−	0.740169i	$-0.265255\pi$
$857$	48.6923	−	17.7225i	1.66330	−	0.605390i	0.990876	+	0.134779i	$0.0430323\pi$
$858$	2.65788	−	1.16327i	0.0907385	−	0.0397133i
$859$	4.43850	−	3.72435i	0.151440	−	0.127073i	−0.563920	−	0.825830i	$-0.690707\pi$
$859$	4.43850	−	3.72435i	0.151440	−	0.127073i	0.715360	+	0.698756i	$0.246263\pi$
$860$	−0.970249	+	0.814135i	−0.0330852	+	0.0277618i
$861$	−1.40028	+	2.26494i	−0.0477215	+	0.0771890i
$862$	5.82830	−	2.12133i	0.198513	−	0.0722527i
$863$	21.3837	+	37.0376i	0.727908	+	1.26077i	0.957766	+	0.287550i	$0.0928406\pi$
$863$	21.3837	+	37.0376i	0.727908	+	1.26077i	−0.229858	+	0.973224i	$0.573826\pi$
$864$	27.2877	+	4.36475i	0.928346	+	0.148492i
$865$	10.9050	−	18.8881i	0.370782	−	0.642214i
$866$	−14.2996	−	11.9988i	−0.485919	−	0.407735i
$867$	−13.7569	−	20.6764i	−0.467208	−	0.702208i
$868$	−23.4366	−	11.1103i	−0.795490	−	0.377107i
$869$	−3.82950	−	21.7182i	−0.129907	−	0.736738i
$870$	−4.24466	−	3.12515i	−0.143907	−	0.105953i
$871$	−4.61099	+	1.67826i	−0.156237	+	0.0568658i
$872$	13.3780	+	23.1713i	0.453036	+	0.784681i
$873$	21.2231	+	13.6381i	0.718292	+	0.461580i
$874$	−1.75869	−	3.04614i	−0.0594886	−	0.103037i
$875$	−6.46242	+	23.5201i	−0.218470	+	0.795124i
$876$	27.2821	+	8.01018i	0.921776	+	0.270639i
$877$	1.10772	+	6.28218i	0.0374050	+	0.212134i	0.997782	−	0.0665710i	$-0.0212059\pi$
$877$	1.10772	+	6.28218i	0.0374050	+	0.212134i	−0.960377	+	0.278705i	$0.910095\pi$
$878$	0.398171	−	0.334105i	0.0134376	−	0.0112755i
$879$	24.0247	+	7.05380i	0.810334	+	0.237919i
$880$	5.23427	−	1.90512i	0.176447	−	0.0642215i
$881$	−14.6076	−	25.3011i	−0.492142	−	0.852416i	0.507817	−	0.861465i	$-0.330453\pi$
$881$	−14.6076	−	25.3011i	−0.492142	−	0.852416i	−0.999959	+	0.00904961i	$0.997119\pi$
$882$	−5.16030	−	10.3284i	−0.173756	−	0.347774i
$883$	0.969889	−	1.67990i	0.0326394	−	0.0565331i	−0.849244	−	0.528000i	$-0.822942\pi$
$883$	0.969889	−	1.67990i	0.0326394	−	0.0565331i	0.881884	+	0.471467i	$0.156275\pi$
$884$	−0.618222	+	3.50611i	−0.0207931	+	0.117923i
$885$	−10.7833	−	7.93929i	−0.362478	−	0.266876i
$886$	3.80702	+	1.38564i	0.127899	+	0.0465516i
$887$	−46.6814	−	16.9906i	−1.56741	−	0.570489i	−0.594989	−	0.803734i	$-0.702844\pi$
$887$	−46.6814	−	16.9906i	−1.56741	−	0.570489i	−0.972418	+	0.233244i	$0.925066\pi$
$888$	16.6925	−	33.6820i	0.560162	−	1.13029i
$889$	11.8223	−	3.08751i	0.396508	−	0.103552i
$890$	9.44219			0.316503
$891$	1.69220	+	21.2651i	0.0566907	+	0.712407i
$892$	−5.05457	+	8.75477i	−0.169239	+	0.293131i
$893$	3.45630	−	19.6017i	0.115661	−	0.655945i
$894$	10.6045	−	0.674140i	0.354669	−	0.0225466i
$895$	6.53092	−	5.48009i	0.218305	−	0.183179i
$896$	−25.1068	+	17.3436i	−0.838760	+	0.579409i
$897$	0.987450	−	8.85556i	0.0329700	−	0.295679i
$898$	0.365345	−	2.07197i	0.0121917	−	0.0691426i
$899$	15.4890	+	26.8278i	0.516588	+	0.894758i
$900$	−7.74324	+	18.4880i	−0.258108	+	0.616268i
$901$	8.25812	−	14.3035i	0.275118	−	0.476518i
$902$	0.131494	−	0.745737i	0.00437826	−	0.0248303i
$903$	3.07818	+	1.22658i	0.102436	+	0.0408181i
$904$	23.3033	+	8.48173i	0.775058	+	0.282098i
$905$	1.94346	+	11.0219i	0.0646027	+	0.366380i
$906$	0.628456	−	0.599255i	0.0208791	−	0.0199089i
$907$	6.74502	+	5.65974i	0.223965	+	0.187929i	0.747865	−	0.663851i	$-0.231079\pi$
$907$	6.74502	+	5.65974i	0.223965	+	0.187929i	−0.523900	+	0.851780i	$0.675524\pi$
$908$	−14.4842	+	25.0873i	−0.480675	+	0.832553i
$909$	−1.93506	+	40.6542i	−0.0641817	+	1.34842i
$910$	0.804174	+	1.75352i	0.0266581	+	0.0581287i
$911$	−14.2492	−	11.9565i	−0.472097	−	0.396137i	0.375462	−	0.926838i	$-0.377484\pi$
$911$	−14.2492	−	11.9565i	−0.472097	−	0.396137i	−0.847559	+	0.530701i	$0.821929\pi$
$912$	−5.07831	−	3.73893i	−0.168160	−	0.123808i
$913$	−1.82357	−	0.663726i	−0.0603514	−	0.0219661i
$914$	−1.05402	−	5.97763i	−0.0348638	−	0.197722i
$915$	−4.47003	+	9.01962i	−0.147775	+	0.298179i
$916$	38.2188	−	13.9105i	1.26279	−	0.459617i
$917$	−2.78464	−	6.07198i	−0.0919571	−	0.200515i
$918$	4.07294	+	2.26582i	0.134427	+	0.0747832i
$919$	−0.718907	−	1.24518i	−0.0237145	−	0.0410748i	0.853925	−	0.520397i	$-0.174216\pi$
$919$	−0.718907	−	1.24518i	−0.0237145	−	0.0410748i	−0.877639	+	0.479322i	$0.840883\pi$
$920$	−1.45777	+	8.26740i	−0.0480611	+	0.272568i
$921$	6.24095	−	12.5930i	0.205646	−	0.414953i
$922$	14.2182	+	5.17501i	0.468253	+	0.170430i
$923$	2.64853	+	15.0206i	0.0871775	+	0.494408i
$924$	−13.7628	−	12.2734i	−0.452762	−	0.403766i
$925$	32.1843	+	27.0058i	1.05821	+	0.887946i
$926$	6.73221			0.221234
$927$	−5.36594	−	17.2547i	−0.176241	−	0.566718i
$928$	28.5316			0.936597
$929$	41.8295	−	15.2247i	1.37238	−	0.499506i	0.452522	−	0.891753i	$-0.350524\pi$
$929$	41.8295	−	15.2247i	1.37238	−	0.499506i	0.919860	+	0.392247i	$0.128302\pi$
$930$	4.10590	−	3.91512i	0.134638	−	0.128382i
$931$	−0.141998	+	11.1886i	−0.00465378	+	0.366691i
$932$	37.6194	+	13.6923i	1.23226	+	0.448507i
$933$	−19.6285	−	5.76305i	−0.642609	−	0.188674i
$934$	1.05142	+	0.882244i	0.0344034	+	0.0288679i
$935$	3.98974			0.130479
$936$	2.32801	+	7.48592i	0.0760933	+	0.244685i
$937$	15.3093	−	26.5166i	0.500134	−	0.866258i	−0.499866	−	0.866103i	$-0.666617\pi$
$937$	15.3093	−	26.5166i	0.500134	−	0.866258i	1.00000		0.000155200i	$-4.94016e-5\pi$
$938$	−3.90155	−	3.95138i	−0.127390	−	0.129017i
$939$	−19.7727	−	14.5577i	−0.645256	−	0.475073i
$940$	−16.7081	+	14.0197i	−0.544957	+	0.457273i
$941$	−8.02298	−	45.5006i	−0.261542	−	1.48328i	−0.778706	−	0.627390i	$-0.784123\pi$
$941$	−8.02298	−	45.5006i	−0.261542	−	1.48328i	0.517164	−	0.855886i	$-0.326988\pi$
$942$	−4.80805	+	9.70166i	−0.156655	+	0.316097i
$943$	−1.78154	−	1.49489i	−0.0580149	−	0.0486803i
$944$	17.0674			0.555497
$945$	−14.1178	+	1.37152i	−0.459252	+	0.0446157i
$946$	−0.942288			−0.0306364
$947$	−21.3343	−	17.9016i	−0.693273	−	0.581725i	0.226578	−	0.973993i	$-0.427246\pi$
$947$	−21.3343	−	17.9016i	−0.693273	−	0.581725i	−0.919851	+	0.392268i	$0.871691\pi$
$948$	27.3041	−	1.73575i	0.886797	−	0.0563745i
$949$	2.15829	+	12.2403i	0.0700611	+	0.397336i
$950$	−2.64952	+	2.22321i	−0.0859617	+	0.0721304i
$951$	−41.8033	+	18.2960i	−1.35556	+	0.593287i
$952$	−8.49048	+	2.21737i	−0.275178	+	0.0718655i
$953$	2.14809	−	3.72060i	0.0695834	−	0.120522i	−0.829135	−	0.559049i	$-0.811166\pi$
$953$	2.14809	−	3.72060i	0.0695834	−	0.120522i	0.898718	+	0.438527i	$0.144500\pi$
$954$	0.793884	−	16.6790i	0.0257029	−	0.540002i
$955$	−0.167412			−0.00541734
$956$	28.1407	+	23.6128i	0.910134	+	0.763693i
$957$	5.19295	+	21.4039i	0.167864	+	0.691888i
$958$	17.7068	+	6.44474i	0.572080	+	0.208220i
$959$	10.9400	−	7.55729i	0.353272	−	0.244038i
$960$	0.687406	+	2.83329i	0.0221859	+	0.0914441i
$961$	−2.20116	+	0.801156i	−0.0710051	+	0.0258437i
$962$	7.54445			0.243243
$963$	24.2352	−	3.09382i	0.780970	−	0.0996968i
$964$	−41.9536			−1.35124
$965$	−1.43787	−	1.20651i	−0.0462866	−	0.0388391i
$966$	9.57510	−	3.16182i	0.308074	−	0.101730i
$967$	−1.62683	−	9.22623i	−0.0523154	−	0.296695i	0.947413	−	0.320014i	$-0.103688\pi$
$967$	−1.62683	−	9.22623i	−0.0523154	−	0.296695i	−0.999728	+	0.0233190i	$0.992577\pi$
$968$	−10.2815	−	3.74216i	−0.330460	−	0.120278i
$969$	−2.50211	−	3.76064i	−0.0803793	−	0.120809i
$970$	0.828319	−	4.69763i	0.0265957	−	0.150832i
$971$	23.7496	+	41.1355i	0.762160	+	1.32010i	0.941735	+	0.336355i	$0.109194\pi$
$971$	23.7496	+	41.1355i	0.762160	+	1.32010i	−0.179575	+	0.983744i	$0.557472\pi$
$972$	−26.4516	−	0.837168i	−0.848437	−	0.0268522i
$973$	9.62809	+	0.903944i	0.308662	+	0.0289791i
$974$	−3.29216	+	1.19825i	−0.105488	+	0.0383944i
$975$	−8.74413	+	0.555872i	−0.280036	+	0.0178022i
$976$	−2.22798	−	12.6355i	−0.0713159	−	0.404453i
$977$	−3.92342	−	1.42801i	−0.125521	−	0.0456860i	0.278496	−	0.960437i	$-0.410164\pi$
$977$	−3.92342	−	1.42801i	−0.125521	−	0.0456860i	−0.404017	+	0.914751i	$0.632386\pi$
$978$	13.3788	−	5.85547i	0.427807	−	0.187237i
$979$	−30.2234	−	25.3605i	−0.965945	−	0.810524i
$980$	8.00005	−	9.29202i	0.255552	−	0.296823i
$981$	−23.9122	−	31.4178i	−0.763458	−	1.00309i
$982$	−6.61357	+	11.4550i	−0.211047	+	0.365545i
$983$	−23.1499	−	19.4251i	−0.738367	−	0.619563i	0.194032	−	0.980995i	$-0.437843\pi$
$983$	−23.1499	−	19.4251i	−0.738367	−	0.619563i	−0.932398	+	0.361432i	$0.882288\pi$
$984$	1.96326	+	0.576425i	0.0625865	+	0.0183758i
$985$	−4.87355	−	27.6393i	−0.155284	−	0.880660i
$986$	4.52187	+	1.64583i	0.144006	+	0.0524138i
$987$	53.0076	+	21.1223i	1.68725	+	0.672329i
$988$	0.605735	−	3.43530i	0.0192710	−	0.109291i
$989$	−1.44698	+	2.50624i	−0.0460111	+	0.0796936i
$990$	3.58515	−	1.84845i	0.113944	−	0.0587475i
$991$	17.2373	+	29.8559i	0.547562	+	0.948405i	0.998441	+	0.0558198i	$0.0177772\pi$
$991$	17.2373	+	29.8559i	0.547562	+	0.948405i	−0.450879	+	0.892585i	$0.648889\pi$
$992$	−5.33260	+	30.2427i	−0.169310	+	0.960207i
$993$	43.3599	−	18.9772i	1.37598	−	0.602224i
$994$	−14.2015	+	9.81028i	−0.450444	+	0.311163i
$995$	5.15112	−	4.32231i	0.163302	−	0.137026i
$996$	1.06906	−	2.15714i	0.0338744	−	0.0683516i
$997$	−9.45178	+	53.6037i	−0.299341	+	1.69765i	0.349675	+	0.936871i	$0.386292\pi$
$997$	−9.45178	+	53.6037i	−0.299341	+	1.69765i	−0.649015	+	0.760775i	$0.724819\pi$
$998$	−8.55803	+	14.8229i	−0.270900	+	0.469212i
$999$	−18.1401	+	52.4221i	−0.573928	+	1.65856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.88.14	yes	132
3.2	odd	2		567.2.w.a.424.9		132
7.2	even	3		189.2.u.a.142.14	yes	132
21.2	odd	6		567.2.u.a.100.9		132
27.4	even	9		189.2.u.a.4.14	✓	132
27.23	odd	18		567.2.u.a.550.9		132
189.23	odd	18		567.2.w.a.226.9		132
189.58	even	9	inner	189.2.w.a.58.14	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.14	✓	132	27.4	even	9
189.2.u.a.142.14	yes	132	7.2	even	3
189.2.w.a.58.14	yes	132	189.58	even	9	inner
189.2.w.a.88.14	yes	132	1.1	even	1	trivial
567.2.u.a.100.9		132	21.2	odd	6
567.2.u.a.550.9		132	27.23	odd	18
567.2.w.a.226.9		132	189.23	odd	18
567.2.w.a.424.9		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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.421169 + 0.353403i) q^{2} +(0.959445 + 1.44204i) q^{3} +(-0.294807 - 1.67193i) q^{4} +(0.790369 - 0.663198i) q^{5} +(-0.105531 + 0.946411i) q^{6} +(1.85892 + 1.88266i) q^{7} +(1.01650 - 1.76063i) q^{8} +(-1.15893 + 2.76711i) q^{9} +O(q^{10})\)	\(q+(0.421169 + 0.353403i) q^{2} +(0.959445 + 1.44204i) q^{3} +(-0.294807 - 1.67193i) q^{4} +(0.790369 - 0.663198i) q^{5} +(-0.105531 + 0.946411i) q^{6} +(1.85892 + 1.88266i) q^{7} +(1.01650 - 1.76063i) q^{8} +(-1.15893 + 2.76711i) q^{9} +0.567255 q^{10} +(-1.81572 - 1.52357i) q^{11} +(2.12813 - 2.02925i) q^{12} +(1.20787 + 0.439628i) q^{13} +(0.117582 + 1.44987i) q^{14} +(1.71467 + 0.503438i) q^{15} +(-2.14035 + 0.779023i) q^{16} -1.63145 q^{17} +(-1.46601 + 0.755850i) q^{18} +1.59850 q^{19} +(-1.34183 - 1.12593i) q^{20} +(-0.931333 + 4.48694i) q^{21} +(-0.226291 - 1.28336i) q^{22} +(-3.76089 - 1.36885i) q^{23} +(3.51416 - 0.223398i) q^{24} +(-0.683390 + 3.87570i) q^{25} +(0.353351 + 0.612021i) q^{26} +(-5.10220 + 0.983669i) q^{27} +(2.59966 - 3.66301i) q^{28} +(-5.04129 + 1.83488i) q^{29} +(0.544250 + 0.818001i) q^{30} +(-1.00269 - 5.68657i) q^{31} +(-4.99754 - 1.81896i) q^{32} +(0.454958 - 4.08012i) q^{33} +(-0.687116 - 0.576559i) q^{34} +(2.71781 + 0.255165i) q^{35} +(4.96807 + 1.12189i) q^{36} +(5.33779 - 9.24533i) q^{37} +(0.673238 + 0.564913i) q^{38} +(0.524924 + 2.16359i) q^{39} +(-0.364236 - 2.06569i) q^{40} +(0.546038 + 0.198741i) q^{41} +(-1.97794 + 1.56062i) q^{42} +(0.125561 - 0.712095i) q^{43} +(-2.01202 + 3.48492i) q^{44} +(0.919158 + 2.95564i) q^{45} +(-1.10021 - 1.90563i) q^{46} +(2.16222 - 12.2626i) q^{47} +(-3.17693 - 2.33903i) q^{48} +(-0.0888318 + 6.99944i) q^{49} +(-1.65750 + 1.39081i) q^{50} +(-1.56529 - 2.35261i) q^{51} +(0.378940 - 2.14908i) q^{52} +(-5.06183 + 8.76735i) q^{53} +(-2.49652 - 1.38884i) q^{54} -2.44552 q^{55} +(5.20425 - 1.35914i) q^{56} +(1.53367 + 2.30509i) q^{57} +(-2.77169 - 1.00881i) q^{58} +(-7.04133 - 2.56284i) q^{59} +(0.336217 - 3.01523i) q^{60} +(-0.978166 + 5.54746i) q^{61} +(1.58734 - 2.74936i) q^{62} +(-7.36389 + 2.96196i) q^{63} +(0.815727 + 1.41288i) q^{64} +(1.24622 - 0.453588i) q^{65} +(1.63354 - 1.55763i) q^{66} +(-2.92434 + 2.45382i) q^{67} +(0.480962 + 2.72767i) q^{68} +(-1.63444 - 6.73668i) q^{69} +(1.05448 + 1.06795i) q^{70} +(5.93296 + 10.2762i) q^{71} +(3.69379 + 4.85320i) q^{72} +(4.83477 + 8.37407i) q^{73} +(5.51543 - 2.00745i) q^{74} +(-6.24456 + 2.73305i) q^{75} +(-0.471248 - 2.67258i) q^{76} +(-0.506912 - 6.25059i) q^{77} +(-0.543536 + 1.09674i) q^{78} +(7.12739 + 5.98059i) q^{79} +(-1.17502 + 2.03519i) q^{80} +(-6.31376 - 6.41377i) q^{81} +(0.159738 + 0.276675i) q^{82} +(0.769357 - 0.280023i) q^{83} +(7.77642 + 0.234345i) q^{84} +(-1.28945 + 1.08198i) q^{85} +(0.304539 - 0.255538i) q^{86} +(-7.48280 - 5.50925i) q^{87} +(-4.52812 + 1.64810i) q^{88} +16.6454 q^{89} +(-0.657409 + 1.56965i) q^{90} +(1.41766 + 3.09124i) q^{91} +(-1.17989 + 6.69150i) q^{92} +(7.23820 - 6.90187i) q^{93} +(5.24428 - 4.40047i) q^{94} +(1.26340 - 1.06012i) q^{95} +(-2.17187 - 8.95182i) q^{96} +(1.46022 - 8.28134i) q^{97} +(-2.51103 + 2.91655i) q^{98} +(6.32018 - 3.25858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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