LMFDB - Embedded newform 189.2.bd.a.185.15

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			185.15
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.892534 - 0.157378i) q^{2} +(-1.71459 - 0.245341i) q^{3} +(-1.10754 + 0.403110i) q^{4} +(-1.14226 + 0.415747i) q^{5} +(-1.56894 + 0.0508626i) q^{6} +(-1.98483 + 1.74942i) q^{7} +(-2.49483 + 1.44039i) q^{8} +(2.87962 + 0.841317i) q^{9} +O(q^{10})$	\(q+(0.892534 - 0.157378i) q^{2} +(-1.71459 - 0.245341i) q^{3} +(-1.10754 + 0.403110i) q^{4} +(-1.14226 + 0.415747i) q^{5} +(-1.56894 + 0.0508626i) q^{6} +(-1.98483 + 1.74942i) q^{7} +(-2.49483 + 1.44039i) q^{8} +(2.87962 + 0.841317i) q^{9} +(-0.954073 + 0.550834i) q^{10} +(-1.22714 + 3.37155i) q^{11} +(1.99787 - 0.419444i) q^{12} +(-0.206055 - 0.566132i) q^{13} +(-1.49621 + 1.87378i) q^{14} +(2.06050 - 0.432592i) q^{15} +(-0.194293 + 0.163031i) q^{16} +(-3.97470 - 6.88437i) q^{17} +(2.70256 + 0.297716i) q^{18} +(1.22523 + 0.707386i) q^{19} +(1.09750 - 0.920911i) q^{20} +(3.83236 - 2.51257i) q^{21} +(-0.564660 + 3.20235i) q^{22} +(1.00502 + 0.177213i) q^{23} +(4.63100 - 1.85759i) q^{24} +(-2.69832 + 2.26416i) q^{25} +(-0.273008 - 0.472864i) q^{26} +(-4.73094 - 2.14900i) q^{27} +(1.49306 - 2.73765i) q^{28} +(-0.413325 + 1.13560i) q^{29} +(1.77098 - 0.710380i) q^{30} +(2.83760 + 7.79623i) q^{31} +(3.55571 - 4.23753i) q^{32} +(2.93123 - 5.47975i) q^{33} +(-4.63100 - 5.51901i) q^{34} +(1.53987 - 2.82347i) q^{35} +(-3.52842 + 0.229013i) q^{36} +8.45042 q^{37} +(1.20488 + 0.438542i) q^{38} +(0.214404 + 1.02124i) q^{39} +(2.25090 - 2.68252i) q^{40} +(-6.73814 + 2.45248i) q^{41} +(3.02509 - 2.84568i) q^{42} +(1.41438 + 8.02135i) q^{43} -4.22879i q^{44} +(-3.63903 + 0.236192i) q^{45} +0.924908 q^{46} +(-0.296592 - 0.107951i) q^{47} +(0.373131 - 0.231863i) q^{48} +(0.879076 - 6.94458i) q^{49} +(-2.05201 + 2.44549i) q^{50} +(5.12594 + 12.7790i) q^{51} +(0.456428 + 0.543949i) q^{52} +(-5.74259 - 3.31549i) q^{53} +(-4.56073 - 1.17351i) q^{54} -4.36136i q^{55} +(2.43197 - 7.22344i) q^{56} +(-1.92721 - 1.51347i) q^{57} +(-0.190188 + 1.07861i) q^{58} +(-0.763827 - 0.640927i) q^{59} +(-2.10769 + 1.30972i) q^{60} +(-4.19127 + 11.5154i) q^{61} +(3.75960 + 6.51182i) q^{62} +(-7.18735 + 3.36778i) q^{63} +(2.76033 - 4.78103i) q^{64} +(0.470736 + 0.561001i) q^{65} +(1.75383 - 5.35217i) q^{66} +(-1.79273 + 10.1671i) q^{67} +(7.17729 + 6.02246i) q^{68} +(-1.67972 - 0.550421i) q^{69} +(0.930030 - 2.76238i) q^{70} +(-0.952881 - 0.550146i) q^{71} +(-8.39599 + 2.04883i) q^{72} -0.933127i q^{73} +(7.54228 - 1.32991i) q^{74} +(5.18199 - 3.22009i) q^{75} +(-1.64214 - 0.289554i) q^{76} +(-3.46258 - 8.83874i) q^{77} +(0.352083 + 0.877746i) q^{78} +(-2.33590 - 13.2476i) q^{79} +(0.154153 - 0.267000i) q^{80} +(7.58437 + 4.84534i) q^{81} +(-5.62805 + 3.24936i) q^{82} +(5.66119 + 2.06050i) q^{83} +(-3.23164 + 4.32763i) q^{84} +(7.40228 + 6.21125i) q^{85} +(2.52476 + 6.93673i) q^{86} +(0.987292 - 1.84568i) q^{87} +(-1.79484 - 10.1790i) q^{88} +(-2.96167 + 5.12977i) q^{89} +(-3.21079 + 0.783513i) q^{90} +(1.39939 + 0.763198i) q^{91} +(-1.18454 + 0.208866i) q^{92} +(-2.95257 - 14.0635i) q^{93} +(-0.281708 - 0.0496727i) q^{94} +(-1.69362 - 0.298631i) q^{95} +(-7.13622 + 6.39326i) q^{96} +(8.29293 - 1.46227i) q^{97} +(-0.308318 - 6.33662i) q^{98} +(-6.37025 + 8.67636i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.892534	−	0.157378i	0.631117	−	0.111283i	0.151066	−	0.988524i	$-0.451729\pi$
$2$	0.892534	−	0.157378i	0.631117	−	0.111283i	0.480051	+	0.877241i	$0.340618\pi$
$3$	−1.71459	−	0.245341i	−0.989917	−	0.141648i
$3$	−1.71459	−	0.245341i	−0.989917	−	0.141648i
$4$	−1.10754	+	0.403110i	−0.553768	+	0.201555i
$5$	−1.14226	+	0.415747i	−0.510832	+	0.185928i	−0.584560	−	0.811351i	$-0.698733\pi$
$5$	−1.14226	+	0.415747i	−0.510832	+	0.185928i	0.0737273	+	0.997278i	$0.476511\pi$
$6$	−1.56894	+	0.0508626i	−0.640516	+	0.0207646i
$7$	−1.98483	+	1.74942i	−0.750194	+	0.661218i
$7$	−1.98483	+	1.74942i	−0.750194	+	0.661218i
$8$	−2.49483	+	1.44039i	−0.882057	+	0.509256i
$9$	2.87962	+	0.841317i	0.959872	+	0.280439i
$10$	−0.954073	+	0.550834i	−0.301704	+	0.174189i
$11$	−1.22714	+	3.37155i	−0.369998	+	1.01656i	0.605364	+	0.795949i	$0.293028\pi$
$11$	−1.22714	+	3.37155i	−0.369998	+	1.01656i	−0.975362	+	0.220612i	$0.929195\pi$
$12$	1.99787	−	0.419444i	0.576735	−	0.121083i
$13$	−0.206055	−	0.566132i	−0.0571495	−	0.157017i	0.907833	−	0.419333i	$-0.137736\pi$
$13$	−0.206055	−	0.566132i	−0.0571495	−	0.157017i	−0.964982	+	0.262316i	$0.915514\pi$
$14$	−1.49621	+	1.87378i	−0.399878	+	0.500789i
$15$	2.06050	−	0.432592i	0.532018	−	0.111695i
$16$	−0.194293	+	0.163031i	−0.0485733	+	0.0407578i
$17$	−3.97470	−	6.88437i	−0.964005	−	1.66971i	−0.712264	−	0.701911i	$-0.752330\pi$
$17$	−3.97470	−	6.88437i	−0.964005	−	1.66971i	−0.251741	−	0.967795i	$-0.581003\pi$
$18$	2.70256	+	0.297716i	0.636999	+	0.0701724i
$19$	1.22523	+	0.707386i	0.281087	+	0.162286i	0.633915	−	0.773402i	$-0.281447\pi$
$19$	1.22523	+	0.707386i	0.281087	+	0.162286i	−0.352829	+	0.935688i	$0.614780\pi$
$20$	1.09750	−	0.920911i	0.245408	−	0.205922i
$21$	3.83236	−	2.51257i	0.836290	−	0.548287i
$22$	−0.564660	+	3.20235i	−0.120386	+	0.682743i
$23$	1.00502	+	0.177213i	0.209562	+	0.0369515i	0.277444	−	0.960742i	$-0.410513\pi$
$23$	1.00502	+	0.177213i	0.209562	+	0.0369515i	−0.0678814	+	0.997693i	$0.521624\pi$
$24$	4.63100	−	1.85759i	0.945299	−	0.379180i
$25$	−2.69832	+	2.26416i	−0.539664	+	0.452832i
$26$	−0.273008	−	0.472864i	−0.0535413	−	0.0927362i
$27$	−4.73094	−	2.14900i	−0.910470	−	0.413575i
$28$	1.49306	−	2.73765i	0.282162	−	0.517367i
$29$	−0.413325	+	1.13560i	−0.0767526	+	0.210876i	−0.972135	−	0.234422i	$-0.924680\pi$
$29$	−0.413325	+	1.13560i	−0.0767526	+	0.210876i	0.895382	+	0.445298i	$0.146902\pi$
$30$	1.77098	−	0.710380i	0.323336	−	0.129697i
$31$	2.83760	+	7.79623i	0.509647	+	1.40024i	0.881602	+	0.471994i	$0.156466\pi$
$31$	2.83760	+	7.79623i	0.509647	+	1.40024i	−0.371954	+	0.928251i	$0.621312\pi$
$32$	3.55571	−	4.23753i	0.628567	−	0.749097i
$33$	2.93123	−	5.47975i	0.510261	−	0.953902i
$34$	−4.63100	−	5.51901i	−0.794209	−	0.946502i
$35$	1.53987	−	2.82347i	0.260285	−	0.477253i
$36$	−3.52842	+	0.229013i	−0.588071	+	0.0381689i
$37$	8.45042			1.38924			0.694620	−	0.719377i	$-0.255573\pi$
$37$	8.45042			1.38924			0.694620	+	0.719377i	$0.255573\pi$
$38$	1.20488	+	0.438542i	0.195458	+	0.0711409i
$39$	0.214404	+	1.02124i	0.0343321	+	0.163529i
$40$	2.25090	−	2.68252i	0.355899	−	0.424144i
$41$	−6.73814	+	2.45248i	−1.05232	+	0.383013i	−0.809538	−	0.587067i	$-0.800282\pi$
$41$	−6.73814	+	2.45248i	−1.05232	+	0.383013i	−0.242782	+	0.970081i	$0.578060\pi$
$42$	3.02509	−	2.84568i	0.466781	−	0.439098i
$43$	1.41438	+	8.02135i	0.215691	+	1.22324i	0.879703	+	0.475523i	$0.157741\pi$
$43$	1.41438	+	8.02135i	0.215691	+	1.22324i	−0.664012	+	0.747722i	$0.731148\pi$
$44$		−	4.22879i		−	0.637515i
$45$	−3.63903	+	0.236192i	−0.542475	+	0.0352095i
$46$	0.924908			0.136370
$47$	−0.296592	−	0.107951i	−0.0432625	−	0.0157462i	0.320298	−	0.947317i	$-0.396217\pi$
$47$	−0.296592	−	0.107951i	−0.0432625	−	0.0157462i	−0.363561	+	0.931570i	$0.618439\pi$
$48$	0.373131	−	0.231863i	0.0538568	−	0.0334666i
$49$	0.879076	−	6.94458i	0.125582	−	0.992083i
$50$	−2.05201	+	2.44549i	−0.290198	+	0.345845i
$51$	5.12594	+	12.7790i	0.717775	+	1.78942i
$52$	0.456428	+	0.543949i	0.0632951	+	0.0754322i
$53$	−5.74259	−	3.31549i	−0.788806	−	0.455417i	0.0507361	−	0.998712i	$-0.483843\pi$
$53$	−5.74259	−	3.31549i	−0.788806	−	0.455417i	−0.839542	+	0.543295i	$0.817177\pi$
$54$	−4.56073	−	1.17351i	−0.620636	−	0.159694i
$55$		−	4.36136i		−	0.588085i
$56$	2.43197	−	7.22344i	0.324985	−	0.965273i
$57$	−1.92721	−	1.51347i	−0.255265	−	0.200465i
$58$	−0.190188	+	1.07861i	−0.0249729	+	0.141629i
$59$	−0.763827	−	0.640927i	−0.0994418	−	0.0834416i	0.591711	−	0.806150i	$-0.298453\pi$
$59$	−0.763827	−	0.640927i	−0.0994418	−	0.0834416i	−0.691153	+	0.722708i	$0.742897\pi$
$60$	−2.10769	+	1.30972i	−0.272102	+	0.169084i
$61$	−4.19127	+	11.5154i	−0.536637	+	1.47440i	0.314399	+	0.949291i	$0.398197\pi$
$61$	−4.19127	+	11.5154i	−0.536637	+	1.47440i	−0.851036	+	0.525107i	$0.824025\pi$
$62$	3.75960	+	6.51182i	0.477470	+	0.827003i
$63$	−7.18735	+	3.36778i	−0.905521	+	0.424301i
$64$	2.76033	−	4.78103i	0.345041	−	0.597629i
$65$	0.470736	+	0.561001i	0.0583876	+	0.0695836i
$66$	1.75383	−	5.35217i	0.215881	−	0.658807i
$67$	−1.79273	+	10.1671i	−0.219017	+	1.24211i	0.654781	+	0.755818i	$0.272761\pi$
$67$	−1.79273	+	10.1671i	−0.219017	+	1.24211i	−0.873798	+	0.486289i	$0.838350\pi$
$68$	7.17729	+	6.02246i	0.870374	+	0.730330i
$69$	−1.67972	−	0.550421i	−0.202215	−	0.0662629i
$70$	0.930030	−	2.76238i	0.111160	−	0.330168i
$71$	−0.952881	−	0.550146i	−0.113086	−	0.0652904i	0.442390	−	0.896823i	$-0.354131\pi$
$71$	−0.952881	−	0.550146i	−0.113086	−	0.0652904i	−0.555476	+	0.831532i	$0.687464\pi$
$72$	−8.39599	+	2.04883i	−0.989477	+	0.241457i
$73$		−	0.933127i		−	0.109214i	−0.998508	−	0.0546071i	$-0.982609\pi$
$73$		−	0.933127i		−	0.109214i	0.998508	−	0.0546071i	$-0.0173906\pi$
$74$	7.54228	−	1.32991i	0.876772	−	0.154599i
$75$	5.18199	−	3.22009i	0.598365	−	0.371824i
$76$	−1.64214	−	0.289554i	−0.188366	−	0.0332141i
$77$	−3.46258	−	8.83874i	−0.394598	−	1.00727i
$78$	0.352083	+	0.877746i	0.0398655	+	0.0993851i
$79$	−2.33590	−	13.2476i	−0.262810	−	1.49047i	−0.775200	−	0.631716i	$-0.782351\pi$
$79$	−2.33590	−	13.2476i	−0.262810	−	1.49047i	0.512390	−	0.858753i	$-0.328760\pi$
$80$	0.154153	−	0.267000i	0.0172348	−	0.0298516i
$81$	7.58437	+	4.84534i	0.842708	+	0.538371i
$82$	−5.62805	+	3.24936i	−0.621514	+	0.358831i
$83$	5.66119	+	2.06050i	0.621396	+	0.226170i	0.633482	−	0.773757i	$-0.281625\pi$
$83$	5.66119	+	2.06050i	0.621396	+	0.226170i	−0.0120862	+	0.999927i	$0.503847\pi$
$84$	−3.23164	+	4.32763i	−0.352601	+	0.472183i
$85$	7.40228	+	6.21125i	0.802890	+	0.673705i
$86$	2.52476	+	6.93673i	0.272252	+	0.748007i
$87$	0.987292	−	1.84568i	0.105849	−	0.197878i
$88$	−1.79484	−	10.1790i	−0.191330	−	1.08509i
$89$	−2.96167	+	5.12977i	−0.313937	+	0.543754i	−0.979211	−	0.202845i	$-0.934981\pi$
$89$	−2.96167	+	5.12977i	−0.313937	+	0.543754i	0.665274	+	0.746599i	$0.268315\pi$
$90$	−3.21079	+	0.783513i	−0.338447	+	0.0825895i
$91$	1.39939	+	0.763198i	0.146696	+	0.0800049i
$92$	−1.18454	+	0.208866i	−0.123497	+	0.0217758i
$93$	−2.95257	−	14.0635i	−0.306167	−	1.45832i
$94$	−0.281708	−	0.0496727i	−0.0290559	−	0.00512335i
$95$	−1.69362	−	0.298631i	−0.173762	−	0.0306389i
$96$	−7.13622	+	6.39326i	−0.728337	+	0.652509i
$97$	8.29293	−	1.46227i	0.842019	−	0.148471i	0.264029	−	0.964515i	$-0.414948\pi$
$97$	8.29293	−	1.46227i	0.842019	−	0.148471i	0.577990	+	0.816044i	$0.303837\pi$
$98$	−0.308318	−	6.33662i	−0.0311448	−	0.640095i
$99$	−6.37025	+	8.67636i	−0.640234	+	0.872007i
$100$	2.07578	−	3.59536i	0.207578	−	0.359536i
$101$	0.430556	+	2.44180i	0.0428419	+	0.242968i	0.998707	−	0.0508377i	$-0.0161891\pi$
$101$	0.430556	+	2.44180i	0.0428419	+	0.242968i	−0.955865	+	0.293806i	$0.905078\pi$
$102$	6.58621	+	10.5990i	0.652132	+	1.04946i
$103$	−3.26796	−	8.97865i	−0.322002	−	0.884693i	−0.990068	−	0.140591i	$-0.955100\pi$
$103$	−3.26796	−	8.97865i	−0.322002	−	0.884693i	0.668066	−	0.744102i	$-0.267122\pi$
$104$	1.32953	+	1.11561i	0.130371	+	0.109394i
$105$	−3.33295	+	4.46329i	−0.325262	+	0.435573i
$106$	−5.64724	−	2.05543i	−0.548509	−	0.199641i
$107$	−10.6429	+	6.14467i	−1.02889	+	0.594028i	−0.916666	−	0.399655i	$-0.869130\pi$
$107$	−10.6429	+	6.14467i	−1.02889	+	0.594028i	−0.112221	+	0.993683i	$0.535797\pi$
$108$	6.10598	+	0.473004i	0.587548	+	0.0455149i
$109$	−4.67103	+	8.09046i	−0.447404	+	0.774926i	−0.998216	−	0.0597033i	$-0.980985\pi$
$109$	−4.67103	+	8.09046i	−0.447404	+	0.774926i	0.550813	+	0.834629i	$0.314318\pi$
$110$	−0.686381	−	3.89266i	−0.0654438	−	0.371150i
$111$	−14.4890	−	2.07323i	−1.37523	−	0.196783i
$112$	0.100428	−	0.663489i	0.00948960	−	0.0626938i
$113$	3.90833	+	0.689145i	0.367665	+	0.0648293i	0.354428	−	0.935083i	$-0.384675\pi$
$113$	3.90833	+	0.689145i	0.367665	+	0.0648293i	0.0132365	+	0.999912i	$0.495787\pi$
$114$	−1.95829	−	1.04753i	−0.183410	−	0.0981098i
$115$	−1.22167	+	0.215414i	−0.113921	+	0.0200874i
$116$		−	1.42434i		−	0.132246i
$117$	−0.117063	−	1.80360i	−0.0108225	−	0.166743i
$118$	−0.782609	−	0.451839i	−0.0720450	−	0.0415952i
$119$	19.9327	+	6.71089i	1.82723	+	0.615186i
$120$	−4.51750	+	4.04717i	−0.412389	+	0.369455i
$121$	−1.43499	−	1.20410i	−0.130454	−	0.109464i
$122$	−1.92858	+	10.9375i	−0.174605	+	0.990236i
$123$	12.1548	−	2.55185i	1.09596	−	0.230093i
$124$	−6.28549	−	7.49075i	−0.564453	−	0.672689i
$125$	5.17976	−	8.97161i	0.463292	−	0.802445i
$126$	−5.88494	+	4.13699i	−0.524272	+	0.368552i
$127$	−7.34765	−	12.7265i	−0.651998	−	1.12929i	−0.982637	−	0.185537i	$-0.940598\pi$
$127$	−7.34765	−	12.7265i	−0.651998	−	1.12929i	0.330639	−	0.943757i	$-0.392736\pi$
$128$	−2.07265	+	5.69456i	−0.183198	+	0.503333i
$129$	−0.457111	−	14.1003i	−0.0402464	−	1.24146i
$130$	0.508437	+	0.426629i	0.0445928	+	0.0374178i
$131$	−3.07983	+	17.4666i	−0.269086	+	1.52606i	0.488055	+	0.872813i	$0.337706\pi$
$131$	−3.07983	+	17.4666i	−0.269086	+	1.52606i	−0.757141	+	0.653251i	$0.773405\pi$
$132$	−1.03750	+	7.25063i	−0.0903025	+	0.631087i
$133$	−3.66938	+	0.739398i	−0.318176	+	0.0641139i
$134$			9.35660i			0.808287i
$135$	6.29739	+	0.487832i	0.541993	+	0.0419859i
$136$	19.8324	+	11.4503i	1.70062	+	0.981851i
$137$	−2.14849	−	2.56047i	−0.183558	−	0.218756i	0.666417	−	0.745580i	$-0.267827\pi$
$137$	−2.14849	−	2.56047i	−0.183558	−	0.218756i	−0.849975	+	0.526824i	$0.823383\pi$
$138$	−1.58583	−	0.226918i	−0.134995	−	0.0193165i
$139$	−2.56143	+	3.05259i	−0.217257	+	0.258917i	−0.863655	−	0.504084i	$-0.831830\pi$
$139$	−2.56143	+	3.05259i	−0.217257	+	0.258917i	0.646397	+	0.763001i	$0.276275\pi$
$140$	−0.567288	+	3.74783i	−0.0479446	+	0.316750i
$141$	0.482049	+	0.257857i	0.0405958	+	0.0217155i
$142$	−0.937059	−	0.341062i	−0.0786363	−	0.0286213i
$143$	2.16160			0.180762
$144$	−0.696651	+	0.306005i	−0.0580542	+	0.0255005i
$145$		−	1.46899i		−	0.121993i
$146$	−0.146853	−	0.832847i	−0.0121537	−	0.0689269i
$147$	−3.21104	+	11.6914i	−0.264842	+	0.964292i
$148$	−9.35915	+	3.40645i	−0.769317	+	0.280009i
$149$	9.04723	−	10.7821i	0.741178	−	0.883302i	−0.255325	−	0.966855i	$-0.582183\pi$
$149$	9.04723	−	10.7821i	0.741178	−	0.883302i	0.996503	+	0.0835536i	$0.0266270\pi$
$150$	4.11833	−	3.68957i	0.336260	−	0.301252i
$151$	−12.4056	−	4.51528i	−1.00956	−	0.367449i	−0.216294	−	0.976328i	$-0.569397\pi$
$151$	−12.4056	−	4.51528i	−1.00956	−	0.367449i	−0.793263	+	0.608880i	$0.791619\pi$
$152$	−4.07566			−0.330580
$153$	−5.65365	−	23.1683i	−0.457071	−	1.87305i
$154$	−4.48149	−	7.34393i	−0.361129	−	0.591791i
$155$	−6.48252	−	7.72557i	−0.520689	−	0.620533i
$156$	−0.649132	−	1.04463i	−0.0519721	−	0.0836372i
$157$	3.21248	−	3.82848i	0.256384	−	0.305546i	−0.622464	−	0.782648i	$-0.713868\pi$
$157$	3.21248	−	3.82848i	0.256384	−	0.305546i	0.878848	+	0.477102i	$0.158313\pi$
$158$	−4.16975	−	11.4563i	−0.331727	−	0.911413i
$159$	9.03275	+	7.09359i	0.716344	+	0.562558i
$160$	−2.29979	+	6.31863i	−0.181815	+	0.499531i
$161$	−2.30482	+	1.40647i	−0.181645	+	0.110845i
$162$	7.53185	+	3.13102i	0.591758	+	0.245996i
$163$	−1.07224	−	1.85718i	−0.0839847	−	0.145466i	0.820973	−	0.570966i	$-0.193431\pi$
$163$	−1.07224	−	1.85718i	−0.0839847	−	0.145466i	−0.904958	+	0.425501i	$0.860098\pi$
$164$	6.47412	−	5.43243i	0.505543	−	0.424201i
$165$	−1.07002	+	7.47793i	−0.0833010	+	0.582156i
$166$	5.37708	+	0.948123i	0.417342	+	0.0735886i
$167$	−2.40447	+	13.6365i	−0.186064	+	1.05522i	0.738517	+	0.674235i	$0.235526\pi$
$167$	−2.40447	+	13.6365i	−0.186064	+	1.05522i	−0.924581	+	0.380986i	$0.875585\pi$
$168$	−5.94202	+	11.7886i	−0.458437	+	0.909507i
$169$	9.68053	−	8.12293i	0.744656	−	0.624841i
$170$	7.58430	+	4.37880i	0.581689	+	0.335838i
$171$	2.93305	+	3.06781i	0.224296	+	0.234601i
$172$	−4.79997	−	8.31379i	−0.365994	−	0.633921i
$173$	−2.77181	+	2.32582i	−0.210737	+	0.176829i	−0.742046	−	0.670349i	$-0.766145\pi$
$173$	−2.77181	+	2.32582i	−0.210737	+	0.176829i	0.531310	+	0.847178i	$0.321700\pi$
$174$	0.590722	−	1.80271i	0.0447825	−	0.136663i
$175$	1.39474	−	9.21445i	0.105432	−	0.696547i
$176$	−0.311243	−	0.855133i	−0.0234608	−	0.0644581i
$177$	1.15240	+	1.28632i	0.0866198	+	0.0966860i
$178$	−1.83608	+	5.04459i	−0.137620	+	0.378108i
$179$	21.1818	−	12.2293i	1.58320	−	0.914063i	0.588815	−	0.808268i	$-0.299595\pi$
$179$	21.1818	−	12.2293i	1.58320	−	0.914063i	0.994388	−	0.105795i	$-0.0337387\pi$
$180$	3.93515	−	1.72852i	0.293309	−	0.128837i
$181$	13.8640	−	8.00438i	1.03050	−	0.594961i	0.113374	−	0.993552i	$-0.463834\pi$
$181$	13.8640	−	8.00438i	1.03050	−	0.594961i	0.917129	+	0.398591i	$0.130501\pi$
$182$	1.36911	+	0.460948i	0.101485	+	0.0341677i
$183$	10.0115	−	18.7159i	0.740071	−	1.38352i
$184$	−2.76263	+	1.00551i	−0.203664	+	0.0741275i
$185$	−9.65254	+	3.51324i	−0.709669	+	0.258298i
$186$	−4.84855	−	12.0875i	−0.355513	−	0.886297i
$187$	28.0886	−	4.95277i	2.05404	−	0.362182i
$188$	0.372003			0.0271311
$189$	13.1496	−	4.01100i	0.956492	−	0.291757i
$190$	−1.55861			−0.113073
$191$	−6.32951	+	1.11606i	−0.457987	+	0.0807555i	−0.397882	−	0.917437i	$-0.630255\pi$
$191$	−6.32951	+	1.11606i	−0.457987	+	0.0807555i	−0.0601052	+	0.998192i	$0.519144\pi$
$192$	−5.90581	+	7.52027i	−0.426215	+	0.542729i
$193$	1.28770	−	0.468686i	0.0926910	−	0.0337368i	−0.295258	−	0.955417i	$-0.595406\pi$
$193$	1.28770	−	0.468686i	0.0926910	−	0.0337368i	0.387949	+	0.921681i	$0.373184\pi$
$194$	7.17159	−	2.61024i	0.514890	−	0.187405i
$195$	−0.669481	−	1.07738i	−0.0479425	−	0.0771525i
$196$	1.82582	+	8.04575i	0.130416	+	0.574696i
$197$	19.2475	−	11.1125i	1.37132	−	0.791734i	0.380229	−	0.924892i	$-0.375845\pi$
$197$	19.2475	−	11.1125i	1.37132	−	0.791734i	0.991095	+	0.133158i	$0.0425118\pi$
$198$	−4.32020	+	8.74647i	−0.307023	+	0.621585i
$199$	−11.5230	+	6.65279i	−0.816841	+	0.471603i	−0.849326	−	0.527869i	$-0.822991\pi$
$199$	−11.5230	+	6.65279i	−0.816841	+	0.471603i	0.0324848	+	0.999472i	$0.489658\pi$
$200$	3.47058	−	9.53534i	0.245407	−	0.674251i
$201$	5.56820	−	16.9925i	0.392750	−	1.19856i
$202$	0.768571	+	2.11163i	0.0540765	+	0.148574i
$203$	−1.16626	−	2.97705i	−0.0818556	−	0.208948i
$204$	−10.8285	−	12.0869i	−0.758148	−	0.846253i
$205$	6.67707	−	5.60272i	0.466347	−	0.391311i
$206$	−4.32981	−	7.49944i	−0.301672	−	0.522511i
$207$	2.74499	+	1.35585i	0.190790	+	0.0942381i
$208$	0.132332	+	0.0764022i	0.00917561	+	0.00529754i
$209$	−3.88852	+	3.26286i	−0.268975	+	0.225697i
$210$	−2.27234	+	4.50817i	−0.156807	+	0.311093i
$211$	−2.63818	+	14.9619i	−0.181620	+	1.03002i	0.748602	+	0.663019i	$0.230725\pi$
$211$	−2.63818	+	14.9619i	−0.181620	+	1.03002i	−0.930222	+	0.366997i	$0.880386\pi$
$212$	7.69664	+	1.35713i	0.528608	+	0.0932078i
$213$	1.49882	+	1.17705i	0.102698	+	0.0806505i
$214$	−8.53210	+	7.15928i	−0.583242	+	0.489398i
$215$	−4.95044	−	8.57441i	−0.337617	−	0.584770i
$216$	14.8983	−	1.45302i	1.01370	−	0.0988654i
$217$	−19.2710	−	10.5100i	−1.30820	−	0.713467i
$218$	−2.89579	+	7.95612i	−0.196128	+	0.538857i
$219$	−0.228934	+	1.59993i	−0.0154700	+	0.108113i
$220$	1.75811	+	4.83036i	0.118532	+	0.325663i
$221$	−3.07846	+	3.66877i	−0.207080	+	0.246788i
$222$	−13.2582	+	0.429810i	−0.889830	+	0.0288470i
$223$	4.53645	+	5.40633i	0.303783	+	0.362035i	0.896242	−	0.443566i	$-0.146287\pi$
$223$	4.53645	+	5.40633i	0.303783	+	0.362035i	−0.592458	+	0.805601i	$0.701842\pi$
$224$	0.355741	+	14.6312i	0.0237689	+	0.977588i
$225$	−9.67500	+	4.24976i	−0.645000	+	0.283318i
$226$	3.59677			0.239254
$227$	−16.1249	−	5.86897i	−1.07024	−	0.389537i	−0.253976	−	0.967210i	$-0.581739\pi$
$227$	−16.1249	−	5.86897i	−1.07024	−	0.389537i	−0.816268	+	0.577673i	$0.803961\pi$
$228$	2.74455	+	0.899350i	0.181763	+	0.0595609i
$229$	5.74182	−	6.84283i	0.379430	−	0.452187i	−0.542204	−	0.840247i	$-0.682410\pi$
$229$	5.74182	−	6.84283i	0.379430	−	0.452187i	0.921634	+	0.388060i	$0.126855\pi$
$230$	−1.05648	+	0.384528i	−0.0696623	+	0.0253550i
$231$	3.76839	+	16.0043i	0.247942	+	1.05301i
$232$	−0.604535	−	3.42849i	−0.0396897	−	0.225091i
$233$			8.54612i			0.559875i	0.960018	+	0.279937i	$0.0903137\pi$
$233$			8.54612i			0.559875i	−0.960018	+	0.279937i	$0.909686\pi$
$234$	−0.388330	−	1.59135i	−0.0253859	−	0.104030i
$235$	0.383665			0.0250275
$236$	1.10433	+	0.401944i	0.0718858	+	0.0261643i
$237$	0.754937	+	23.2872i	0.0490384	+	1.51267i
$238$	18.8468	+	2.85273i	1.22165	+	0.184915i
$239$	8.54791	−	10.1870i	0.552919	−	0.658943i	−0.415113	−	0.909770i	$-0.636258\pi$
$239$	8.54791	−	10.1870i	0.552919	−	0.658943i	0.968032	+	0.250827i	$0.0807025\pi$
$240$	−0.329814	+	0.419975i	−0.0212894	+	0.0271093i
$241$	8.98273	+	10.7052i	0.578629	+	0.689583i	0.973378	−	0.229206i	$-0.0736130\pi$
$241$	8.98273	+	10.7052i	0.578629	+	0.689583i	−0.394749	+	0.918789i	$0.629169\pi$
$242$	−1.47027	−	0.848864i	−0.0945128	−	0.0545670i
$243$	−11.8153	−	10.1685i	−0.757952	−	0.652310i
$244$		−	14.4433i		−	0.924637i
$245$	1.88306	+	8.29797i	0.120304	+	0.530138i
$246$	10.4470	−	4.19051i	0.666075	−	0.267177i
$247$	0.148009	−	0.839402i	0.00941761	−	0.0534099i
$248$	−18.3090	−	15.3631i	−1.16262	−	0.975555i
$249$	−9.20107	−	4.92183i	−0.583094	−	0.311908i
$250$	3.21118	−	8.82264i	0.203093	−	0.557993i
$251$	12.8062	+	22.1810i	0.808322	+	1.40005i	0.914025	+	0.405657i	$0.132957\pi$
$251$	12.8062	+	22.1810i	0.808322	+	1.40005i	−0.105704	+	0.994398i	$0.533709\pi$
$252$	6.60267	−	6.62724i	0.415929	−	0.417477i
$253$	−1.83079	+	3.17103i	−0.115101	+	0.199361i
$254$	−8.56089	−	10.2025i	−0.537158	−	0.640160i
$255$	−11.1680	−	12.4658i	−0.699366	−	0.780639i
$256$	−2.87102	+	16.2824i	−0.179439	+	1.01765i
$257$	−9.14993	−	7.67771i	−0.570757	−	0.478922i	0.311140	−	0.950364i	$-0.399289\pi$
$257$	−9.14993	−	7.67771i	−0.570757	−	0.478922i	−0.881897	+	0.471442i	$0.843734\pi$
$258$	−2.62706	−	12.5131i	−0.163554	−	0.779029i
$259$	−16.7726	+	14.7833i	−1.04220	+	0.918590i
$260$	−0.747503	−	0.431571i	−0.0463582	−	0.0267649i
$261$	−2.14562	+	2.92236i	−0.132810	+	0.180889i
$262$			16.0742i			0.993069i
$263$	−14.0094	+	2.47023i	−0.863854	+	0.152321i	−0.587982	−	0.808874i	$-0.700078\pi$
$263$	−14.0094	+	2.47023i	−0.863854	+	0.152321i	−0.275872	+	0.961195i	$0.588966\pi$
$264$	0.580071	+	17.8932i	0.0357009	+	1.10125i
$265$	7.93792	+	1.39967i	0.487622	+	0.0859810i
$266$	−3.15868	+	1.23742i	−0.193671	+	0.0758709i
$267$	6.33659	−	8.06881i	0.387793	−	0.493803i
$268$	−2.11294	−	11.9831i	−0.129068	−	0.731984i
$269$	−15.2108	+	26.3459i	−0.927421	+	1.60634i	−0.139801	+	0.990180i	$0.544646\pi$
$269$	−15.2108	+	26.3459i	−0.927421	+	1.60634i	−0.787620	+	0.616161i	$0.788687\pi$
$270$	5.69740	−	0.555662i	0.346733	−	0.0338165i
$271$	−11.2849	+	6.51534i	−0.685509	+	0.395779i	−0.801927	−	0.597421i	$-0.796192\pi$
$271$	−11.2849	+	6.51534i	−0.685509	+	0.395779i	0.116418	+	0.993200i	$0.462859\pi$
$272$	1.89463	+	0.689587i	0.114879	+	0.0418124i
$273$	−2.21212	−	1.65190i	−0.133884	−	0.0999773i
$274$	−2.32056	−	1.94718i	−0.140190	−	0.117634i
$275$	−4.32250	−	11.8760i	−0.260657	−	0.716148i
$276$	2.08224	−	0.0675030i	0.125336	−	0.00406321i
$277$	3.11459	+	17.6637i	0.187138	+	1.06131i	0.923178	+	0.384373i	$0.125582\pi$
$277$	3.11459	+	17.6637i	0.187138	+	1.06131i	−0.736040	+	0.676938i	$0.763307\pi$
$278$	−1.80575	+	3.12765i	−0.108302	+	0.187584i
$279$	1.61208	+	24.8375i	0.0965129	+	1.48698i
$280$	0.225197	+	9.26210i	0.0134581	+	0.553516i
$281$	−9.46609	+	1.66913i	−0.564700	+	0.0995718i	−0.448708	−	0.893678i	$-0.648116\pi$
$281$	−9.46609	+	1.66913i	−0.564700	+	0.0995718i	−0.115992	+	0.993250i	$0.537005\pi$
$282$	0.470826	+	0.154283i	0.0280373	+	0.00918740i
$283$	−13.1374	−	2.31648i	−0.780939	−	0.137701i	−0.231054	−	0.972941i	$-0.574217\pi$
$283$	−13.1374	−	2.31648i	−0.780939	−	0.137701i	−0.549885	+	0.835240i	$0.685328\pi$
$284$	1.27712	+	0.225191i	0.0757832	+	0.0133626i
$285$	2.83059	+	0.927543i	0.167670	+	0.0549429i
$286$	1.92930	−	0.340188i	0.114082	−	0.0201158i
$287$	9.08362	−	16.6556i	0.536189	−	0.983147i
$288$	13.8042	−	9.21098i	0.813420	−	0.542762i
$289$	−23.0964	+	40.0042i	−1.35861	+	2.35319i
$290$	−0.231186	−	1.31112i	−0.0135757	−	0.0769916i
$291$	−14.5777	+	0.472588i	−0.854560	+	0.0277036i
$292$	0.376153	+	1.03347i	0.0220127	+	0.0604794i
$293$	−1.25235	−	1.05085i	−0.0731631	−	0.0613911i	0.605473	−	0.795866i	$-0.292984\pi$
$293$	−1.25235	−	1.05085i	−0.0731631	−	0.0613911i	−0.678636	+	0.734475i	$0.737429\pi$
$294$	−1.02600	+	10.9403i	−0.0598373	+	0.638053i
$295$	1.13895	+	0.414544i	0.0663122	+	0.0241357i
$296$	−21.0824	+	12.1719i	−1.22539	+	0.707479i
$297$	13.0510	−	13.3135i	0.757296	−	0.772526i
$298$	6.37810	−	11.0472i	0.369473	−	0.639947i
$299$	−0.106765	−	0.605493i	−0.00617436	−	0.0350165i
$300$	−4.44120	+	5.65528i	−0.256413	+	0.326508i
$301$	−16.8400	−	13.4467i	−0.970641	−	0.775052i
$302$	−11.7831	−	2.07767i	−0.678039	−	0.119556i
$303$	−0.139151	−	4.29232i	−0.00799399	−	0.246587i
$304$	−0.353380	+	0.0623104i	−0.0202677	+	0.00357375i
$305$		−	14.8961i		−	0.852946i
$306$	−8.69225	−	19.7888i	−0.496903	−	1.13125i
$307$	9.99990	+	5.77344i	0.570724	+	0.329508i	0.757439	−	0.652906i	$-0.226451\pi$
$307$	9.99990	+	5.77344i	0.570724	+	0.329508i	−0.186714	+	0.982414i	$0.559784\pi$
$308$	7.39792	+	8.39342i	0.421536	+	0.478260i
$309$	3.40037	+	16.1964i	0.193440	+	0.921384i
$310$	−7.00170	−	5.87513i	−0.397670	−	0.333685i
$311$	4.17791	−	23.6941i	0.236908	−	1.34357i	−0.601651	−	0.798759i	$-0.705490\pi$
$311$	4.17791	−	23.6941i	0.236908	−	1.34357i	0.838559	−	0.544811i	$-0.183399\pi$
$312$	−2.00589	−	2.23899i	−0.113561	−	0.126758i
$313$	20.8975	+	24.9047i	1.18120	+	1.40770i	0.892960	+	0.450136i	$0.148624\pi$
$313$	20.8975	+	24.9047i	1.18120	+	1.40770i	0.288236	+	0.957559i	$0.406931\pi$
$314$	2.26473	−	3.92262i	0.127806	−	0.221366i
$315$	6.80965	−	6.83499i	0.383680	−	0.385108i
$316$	7.92734	+	13.7305i	0.445947	+	0.772404i
$317$	1.72725	−	4.74558i	0.0970120	−	0.266538i	−0.881688	−	0.471832i	$-0.843593\pi$
$317$	1.72725	−	4.74558i	0.0970120	−	0.266538i	0.978700	+	0.205294i	$0.0658150\pi$
$318$	9.17840	+	4.90971i	0.514699	+	0.275323i
$319$	−3.32153	−	2.78709i	−0.185970	−	0.156047i
$320$	−1.16530	+	6.60877i	−0.0651425	+	0.369441i
$321$	19.7557	−	7.92444i	1.10266	−	0.442299i
$322$	−1.83578	+	1.61805i	−0.102304	+	0.0901704i
$323$		−	11.2466i		−	0.625776i
$324$	−10.3532	−	2.30905i	−0.575177	−	0.128281i
$325$	1.83782	+	1.06106i	0.101944	+	0.0588572i
$326$	−1.24929	−	1.48885i	−0.0691920	−	0.0824598i
$327$	9.99381	−	12.7258i	0.552659	−	0.703738i
$328$	13.2780	−	15.8241i	0.733155	−	0.873740i
$329$	0.777536	−	0.304600i	0.0428669	−	0.0167932i
$330$	0.221830	+	6.84270i	0.0122113	+	0.376678i
$331$	−11.5066	−	4.18808i	−0.632463	−	0.230198i	0.00584016	−	0.999983i	$-0.498141\pi$
$331$	−11.5066	−	4.18808i	−0.632463	−	0.230198i	−0.638303	+	0.769785i	$0.720363\pi$
$332$	−7.10058			−0.389695
$333$	24.3339	+	7.10948i	1.33349	+	0.389597i
$334$			12.5494i			0.686673i
$335$	−2.17918	−	12.3587i	−0.119061	−	0.675230i
$336$	−0.334974	+	1.11297i	−0.0182744	+	0.0607175i
$337$	16.9278	−	6.16122i	0.922116	−	0.335623i	0.163036	−	0.986620i	$-0.447871\pi$
$337$	16.9278	−	6.16122i	0.922116	−	0.335623i	0.759080	+	0.650997i	$0.225649\pi$
$338$	7.36183	−	8.77349i	0.400431	−	0.477215i
$339$	−6.53210	−	2.14047i	−0.354775	−	0.116255i
$340$	−10.7021	−	3.89525i	−0.580404	−	0.211250i
$341$	−29.7675			−1.61200
$342$	3.10065	+	2.27652i	0.167664	+	0.123100i
$343$	10.4042	+	15.3217i	0.561772	+	0.827292i
$344$	−15.0825	−	17.9747i	−0.813196	−	0.969130i
$345$	2.14751	−	0.0696191i	0.115618	−	0.00374817i
$346$	−2.10790	+	2.51210i	−0.113321	+	0.135051i
$347$	3.91300	+	10.7509i	0.210061	+	0.577137i	0.999318	−	0.0369254i	$-0.0117564\pi$
$347$	3.91300	+	10.7509i	0.210061	+	0.577137i	−0.789257	+	0.614063i	$0.789534\pi$
$348$	−0.349448	+	2.44215i	−0.0187324	+	0.130913i
$349$	−2.98735	+	8.20768i	−0.159909	+	0.439347i	−0.993610	−	0.112870i	$-0.963996\pi$
$349$	−2.98735	+	8.20768i	−0.159909	+	0.439347i	0.833701	+	0.552217i	$0.186218\pi$
$350$	−0.205299	−	8.44371i	−0.0109737	−	0.451335i
$351$	−0.241782	+	3.12115i	−0.0129054	+	0.166595i
$352$	9.92369	+	17.1883i	0.528934	+	0.916141i
$353$	−17.0490	+	14.3058i	−0.907428	+	0.761422i	−0.971628	−	0.236515i	$-0.923995\pi$
$353$	−17.0490	+	14.3058i	−0.907428	+	0.761422i	0.0642000	+	0.997937i	$0.479550\pi$
$354$	1.23100	+	0.966724i	0.0654267	+	0.0513808i
$355$	1.31716	+	0.232250i	0.0699074	+	0.0123266i
$356$	1.21230	−	6.87529i	0.0642517	−	0.364389i
$357$	−32.5299	−	16.3967i	−1.72167	−	0.867807i
$358$	16.9809	−	14.2486i	0.897466	−	0.753063i
$359$	22.7063	+	13.1095i	1.19839	+	0.691891i	0.960196	−	0.279326i	$-0.0901110\pi$
$359$	22.7063	+	13.1095i	1.19839	+	0.691891i	0.238195	+	0.971217i	$0.423444\pi$
$360$	8.73858	−	5.83090i	0.460564	−	0.307316i
$361$	−8.49921	−	14.7211i	−0.447327	−	0.774793i
$362$	11.1144	−	9.32606i	0.584158	−	0.490167i
$363$	2.16500	+	2.41659i	0.113633	+	0.126838i
$364$	−1.85752	−	0.281163i	−0.0973607	−	0.0147369i
$365$	0.387945	+	1.06587i	0.0203060	+	0.0557902i
$366$	5.99014	−	18.2801i	0.313109	−	0.955519i
$367$	6.11382	−	16.7976i	0.319139	−	0.876827i	−0.671584	−	0.740929i	$-0.734386\pi$
$367$	6.11382	−	16.7976i	0.319139	−	0.876827i	0.990723	−	0.135898i	$-0.0433921\pi$
$368$	−0.224161	+	0.129419i	−0.0116852	+	0.00674644i
$369$	−21.4666	+	1.39329i	−1.11750	+	0.0725319i
$370$	−8.06231	+	4.65478i	−0.419140	+	0.241990i
$371$	17.1982	−	3.46552i	0.892887	−	0.179921i
$372$	8.93922	+	14.3856i	0.463477	+	0.745860i
$373$	−10.0649	+	3.66333i	−0.521141	+	0.189680i	−0.589179	−	0.808003i	$-0.700549\pi$
$373$	−10.0649	+	3.66333i	−0.521141	+	0.189680i	0.0680373	+	0.997683i	$0.478326\pi$
$374$	24.2905	−	8.84103i	1.25603	−	0.457159i
$375$	−11.0823	+	14.1118i	−0.572285	+	0.728730i
$376$	0.895441	−	0.157890i	0.0461788	−	0.00814258i
$377$	0.728069			0.0374974
$378$	11.1052	−	5.64941i	0.571191	−	0.290574i
$379$	13.1823			0.677127			0.338564	−	0.940944i	$-0.390059\pi$
$379$	13.1823			0.677127			0.338564	+	0.940944i	$0.390059\pi$
$380$	1.99613	−	0.351971i	0.102399	−	0.0180557i
$381$	9.47584	+	23.6234i	0.485462	+	1.21026i
$382$	−5.47366	+	1.99225i	−0.280057	+	0.101932i
$383$	14.9561	−	5.44356i	0.764219	−	0.278153i	0.0696426	−	0.997572i	$-0.477814\pi$
$383$	14.9561	−	5.44356i	0.764219	−	0.278153i	0.694576	+	0.719419i	$0.255592\pi$
$384$	4.95085	−	9.25531i	0.252647	−	0.472308i
$385$	7.62984	+	8.65654i	0.388852	+	0.441178i
$386$	1.07556	−	0.620974i	0.0547445	−	0.0316067i
$387$	−2.67563	+	24.2883i	−0.136010	+	1.23465i
$388$	−8.59527	+	4.96248i	−0.436359	+	0.251932i
$389$	−8.53902	+	23.4608i	−0.432945	+	1.18951i	0.511051	+	0.859551i	$0.329257\pi$
$389$	−8.53902	+	23.4608i	−0.432945	+	1.18951i	−0.943996	+	0.329957i	$0.892966\pi$
$390$	−0.767089	−	0.856233i	−0.0388431	−	0.0433570i
$391$	−2.77467	−	7.62333i	−0.140321	−	0.385529i
$392$	7.80978	+	18.5918i	0.394454	+	0.939028i
$393$	9.56591	−	29.1924i	0.482537	−	1.47256i
$394$	15.4301	−	12.9474i	0.777359	−	0.652281i
$395$	8.17584	+	14.1610i	0.411371	+	0.712516i
$396$	3.55776	−	12.1773i	0.178784	−	0.611932i
$397$	−18.6785	−	10.7840i	−0.937446	−	0.541235i	−0.0482875	−	0.998833i	$-0.515376\pi$
$397$	−18.6785	−	10.7840i	−0.937446	−	0.541235i	−0.889159	+	0.457599i	$0.848710\pi$
$398$	−9.23763	+	7.75129i	−0.463041	+	0.388537i
$399$	6.47288	−	0.367511i	0.324049	−	0.0183986i
$400$	0.155136	−	0.879821i	0.00775681	−	0.0439911i
$401$	9.32277	+	1.64386i	0.465557	+	0.0820903i	0.401506	−	0.915856i	$-0.368487\pi$
$401$	9.32277	+	1.64386i	0.465557	+	0.0820903i	0.0640509	+	0.997947i	$0.479598\pi$
$402$	2.29556	−	16.0427i	0.114492	−	0.800137i
$403$	3.82900	−	3.21291i	0.190736	−	0.160046i
$404$	−1.46117	−	2.53083i	−0.0726961	−	0.125913i
$405$	−10.6777	−	2.38144i	−0.530581	−	0.118335i
$406$	−1.50945	−	2.47357i	−0.0749128	−	0.122761i
$407$	−10.3699	+	28.4910i	−0.514016	+	1.41225i
$408$	−31.1952	−	24.4982i	−1.54439	−	1.21284i
$409$	−4.45219	−	12.2323i	−0.220146	−	0.604847i	0.779625	−	0.626247i	$-0.215410\pi$
$409$	−4.45219	−	12.2323i	−0.220146	−	0.604847i	−0.999771	+	0.0213999i	$0.993188\pi$
$410$	5.07776	−	6.05144i	0.250773	−	0.298859i
$411$	3.05559	+	4.91726i	0.150721	+	0.242551i
$412$	7.23878	+	8.62684i	0.356629	+	0.425014i
$413$	2.63731	−	0.0641233i	0.129774	−	0.00315530i
$414$	2.66338	+	0.778141i	0.130898	+	0.0382435i
$415$	−7.32317			−0.359480
$416$	−3.13168	−	1.13984i	−0.153543	−	0.0558851i
$417$	5.14071	−	4.60551i	0.251742	−	0.225533i
$418$	−2.95714	+	3.52418i	−0.144638	+	0.172373i
$419$	−11.0177	+	4.01012i	−0.538251	+	0.195907i	−0.596819	−	0.802376i	$-0.703569\pi$
$419$	−11.0177	+	4.01012i	−0.538251	+	0.195907i	0.0585680	+	0.998283i	$0.481347\pi$
$420$	1.89216	−	6.28680i	0.0923280	−	0.306765i
$421$	−2.93922	−	16.6692i	−0.143249	−	0.812405i	−0.968756	−	0.248014i	$-0.920222\pi$
$421$	−2.93922	−	16.6692i	−0.143249	−	0.812405i	0.825508	−	0.564391i	$-0.190889\pi$
$422$			13.7691i			0.670272i
$423$	−0.763251	−	0.560385i	−0.0371106	−	0.0272469i
$424$	19.1024			0.927696
$425$	26.3123	+	9.57690i	1.27633	+	0.464548i
$426$	1.52299	+	0.814679i	0.0737893	+	0.0394713i
$427$	−11.8263	−	30.1884i	−0.572316	−	1.46092i
$428$	9.31041	−	11.0957i	0.450036	−	0.536332i
$429$	−3.70626	−	0.530330i	−0.178940	−	0.0256046i
$430$	−5.76785	−	6.87386i	−0.278151	−	0.331487i
$431$	−1.64280	−	0.948469i	−0.0791307	−	0.0456861i	0.459913	−	0.887964i	$-0.347881\pi$
$431$	−1.64280	−	0.948469i	−0.0791307	−	0.0456861i	−0.539043	+	0.842278i	$0.681214\pi$
$432$	1.26954	−	0.353756i	0.0610810	−	0.0170201i
$433$		−	8.59518i		−	0.413058i	−0.978440	−	0.206529i	$-0.933783\pi$
$433$		−	8.59518i		−	0.413058i	0.978440	−	0.206529i	$-0.0662168\pi$
$434$	−18.8541	−	6.34773i	−0.905024	−	0.304701i
$435$	−0.360403	+	2.51871i	−0.0172800	+	0.120763i
$436$	1.91199	−	10.8434i	0.0915676	−	0.519306i
$437$	1.10603	+	0.928067i	0.0529085	+	0.0443955i
$438$	0.0474613	+	1.46402i	0.00226779	+	0.0699535i
$439$	5.95017	−	16.3480i	0.283986	−	0.780246i	−0.712891	−	0.701275i	$-0.752614\pi$
$439$	5.95017	−	16.3480i	0.283986	−	0.780246i	0.996877	−	0.0789705i	$-0.0251633\pi$
$440$	6.28207	+	10.8809i	0.299486	+	0.518725i
$441$	8.37400	−	19.2581i	0.398762	−	0.917055i
$442$	−2.17025	+	3.75898i	−0.103228	+	0.178796i
$443$	−19.6774	−	23.4506i	−0.934901	−	1.11417i	−0.993264	−	0.115876i	$-0.963032\pi$
$443$	−19.6774	−	23.4506i	−0.934901	−	1.11417i	0.0583624	−	0.998295i	$-0.481412\pi$
$444$	16.8828	−	3.54447i	0.801223	−	0.168213i
$445$	1.25030	−	7.09081i	0.0592700	−	0.336137i
$446$	4.89977	+	4.11140i	0.232011	+	0.194680i
$447$	−18.1575	+	16.2671i	−0.858823	+	0.769409i
$448$	2.88524	+	14.3185i	0.136315	+	0.676485i
$449$	23.7529	+	13.7137i	1.12097	+	0.647191i	0.941648	−	0.336600i	$-0.109277\pi$
$449$	23.7529	+	13.7137i	1.12097	+	0.647191i	0.179320	+	0.983791i	$0.442610\pi$
$450$	−7.96644	+	5.31569i	−0.375542	+	0.250584i
$451$		−	25.7275i		−	1.21146i
$452$	−4.60642	+	0.812237i	−0.216668	+	0.0382044i
$453$	20.1628	+	10.7855i	0.947329	+	0.506745i
$454$	−15.3156	−	2.70056i	−0.718798	−	0.126743i
$455$	−1.91575	−	0.289977i	−0.0898120	−	0.0135943i
$456$	6.98807	+	0.999926i	0.327246	+	0.0468258i
$457$	3.98175	+	22.5816i	0.186259	+	1.05632i	0.924328	+	0.381600i	$0.124627\pi$
$457$	3.98175	+	22.5816i	0.186259	+	1.05632i	−0.738069	+	0.674725i	$0.764262\pi$
$458$	4.04785	−	7.01109i	0.189144	−	0.327607i
$459$	4.00953	+	41.1112i	0.187149	+	1.91891i
$460$	1.26621	−	0.731047i	0.0590374	−	0.0340852i
$461$	28.3324	+	10.3121i	1.31957	+	0.480284i	0.903321	−	0.428966i	$-0.141122\pi$
$461$	28.3324	+	10.3121i	1.31957	+	0.480284i	0.416250	+	0.909250i	$0.363344\pi$
$462$	5.88214	+	13.6913i	0.273662	+	0.636977i
$463$	−22.9581	−	19.2641i	−1.06695	−	0.895279i	−0.0721787	−	0.997392i	$-0.522995\pi$
$463$	−22.9581	−	19.2641i	−1.06695	−	0.895279i	−0.994773	+	0.102113i	$0.967440\pi$
$464$	−0.104832	−	0.288025i	−0.00486672	−	0.0133712i
$465$	9.21945	+	14.8366i	0.427542	+	0.688031i
$466$	1.34497	+	7.62769i	0.0623045	+	0.353346i
$467$	−1.17552	+	2.03607i	−0.0543967	+	0.0942179i	−0.891942	−	0.452151i	$-0.850657\pi$
$467$	−1.17552	+	2.03607i	−0.0543967	+	0.0942179i	0.837545	+	0.546369i	$0.183990\pi$
$468$	0.856702	+	1.95037i	0.0396011	+	0.0901557i
$469$	−14.2282	−	23.3161i	−0.656998	−	1.07664i
$470$	0.342434	−	0.0603803i	0.0157953	−	0.00278514i
$471$	−6.44736	+	5.77612i	−0.297079	+	0.266149i
$472$	2.82881	+	0.498795i	0.130207	+	0.0229589i
$473$	−28.7800	−	5.07470i	−1.32331	−	0.233335i
$474$	4.33869	+	20.6658i	0.199283	+	0.949212i
$475$	−4.90769	+	0.865359i	−0.225180	+	0.0397054i
$476$	−24.7815	+	0.602533i	−1.13586	+	0.0276171i
$477$	−13.7471	−	14.3787i	−0.629436	−	0.658354i
$478$	6.02609	−	10.4375i	0.275627	−	0.477400i
$479$	3.25239	+	18.4452i	0.148606	+	0.842784i	0.964401	+	0.264444i	$0.0851883\pi$
$479$	3.25239	+	18.4452i	0.148606	+	0.842784i	−0.815796	+	0.578340i	$0.803701\pi$
$480$	5.49341	−	10.2696i	0.250739	−	0.468741i
$481$	−1.74125	−	4.78405i	−0.0793943	−	0.218134i
$482$	9.70215	+	8.14107i	0.441921	+	0.370816i
$483$	4.29688	−	1.84605i	0.195515	−	0.0839981i
$484$	2.07469	+	0.755125i	0.0943040	+	0.0343239i
$485$	−8.86472	+	5.11805i	−0.402526	+	0.232398i
$486$	−12.1458	−	7.21627i	−0.550947	−	0.327337i
$487$	0.370050	−	0.640946i	0.0167686	−	0.0290440i	−0.857519	−	0.514452i	$-0.827995\pi$
$487$	0.370050	−	0.640946i	0.0167686	−	0.0290440i	0.874288	+	0.485408i	$0.161329\pi$
$488$	−6.13021	−	34.7661i	−0.277502	−	1.57379i
$489$	1.38281	+	3.44737i	0.0625330	+	0.155895i
$490$	2.98661	+	7.10986i	0.134921	+	0.321191i
$491$	13.6257	+	2.40259i	0.614921	+	0.108427i	0.472429	−	0.881369i	$-0.343377\pi$
$491$	13.6257	+	2.40259i	0.614921	+	0.108427i	0.142492	+	0.989796i	$0.454488\pi$
$492$	−12.4332	+	7.72600i	−0.560533	+	0.348315i
$493$	9.46075	−	1.66819i	0.426091	−	0.0751313i
$494$		−	0.772488i		−	0.0347559i
$495$	3.66929	−	12.5590i	0.164922	−	0.564487i
$496$	−1.82236	−	1.05214i	−0.0818262	−	0.0472424i
$497$	2.85374	−	0.575042i	0.128008	−	0.0257942i
$498$	−8.98685	−	2.94486i	−0.402710	−	0.131962i
$499$	1.83412	+	1.53901i	0.0821066	+	0.0688956i	0.682917	−	0.730496i	$-0.260711\pi$
$499$	1.83412	+	1.53901i	0.0821066	+	0.0688956i	−0.600811	+	0.799391i	$0.705155\pi$
$500$	−2.12023	+	12.0244i	−0.0948195	+	0.537748i
$501$	7.46826	−	22.7910i	0.333657	−	1.01823i
$502$	14.9208	+	17.7819i	0.665947	+	0.793645i
$503$	−0.926534	+	1.60480i	−0.0413121	+	0.0715547i	−0.885942	−	0.463796i	$-0.846487\pi$
$503$	−0.926534	+	1.60480i	−0.0413121	+	0.0715547i	0.844630	+	0.535350i	$0.179820\pi$
$504$	13.0803	−	18.7547i	0.582644	−	0.835400i
$505$	−1.50698	−	2.61016i	−0.0670596	−	0.116151i
$506$	−1.13500	+	3.11837i	−0.0504567	+	0.138629i
$507$	−18.5910	+	11.5524i	−0.825655	+	0.513062i
$508$	13.2680	+	11.1332i	0.588671	+	0.493954i
$509$	−0.923884	+	5.23961i	−0.0409505	+	0.232242i	−0.998413	−	0.0563160i	$-0.982065\pi$
$509$	−0.923884	+	5.23961i	−0.0409505	+	0.232242i	0.957463	+	0.288558i	$0.0931757\pi$
$510$	−11.9296	−	9.36856i	−0.528253	−	0.414847i
$511$	1.63243	+	1.85210i	0.0722144	+	0.0819319i
$512$			2.86433i			0.126587i
$513$	−4.27631	−	5.97962i	−0.188804	−	0.264007i
$514$	−9.37492	−	5.41261i	−0.413510	−	0.238740i
$515$	7.46570	+	8.89728i	0.328978	+	0.392061i
$516$	6.19025	+	15.4323i	0.272510	+	0.679371i
$517$	0.727924	−	0.867506i	0.0320140	−	0.0381529i
$518$	−12.6436	+	15.8342i	−0.555526	+	0.695716i
$519$	5.32313	−	3.30779i	0.233659	−	0.145196i
$520$	−1.98247	−	0.721560i	−0.0869371	−	0.0316425i
$521$	24.4240			1.07004			0.535018	−	0.844841i	$-0.320305\pi$
$521$	24.4240			1.07004			0.535018	+	0.844841i	$0.320305\pi$
$522$	−1.45512	+	2.94598i	−0.0636890	+	0.128942i
$523$			30.7392i			1.34413i	0.740492	+	0.672065i	$0.234593\pi$
$523$			30.7392i			1.34413i	−0.740492	+	0.672065i	$0.765407\pi$
$524$	−3.62994	−	20.5864i	−0.158575	−	0.899322i
$525$	−4.65208	+	15.4568i	−0.203033	+	0.674589i
$526$	−12.1151	+	4.40952i	−0.528242	+	0.192264i
$527$	42.3936	−	50.5227i	1.84669	−	2.20080i
$528$	0.323854	+	1.54256i	0.0140939	+	0.0671313i
$529$	−20.6343	−	7.51026i	−0.897142	−	0.326533i
$530$	7.30513			0.317315
$531$	−1.66031	−	2.48824i	−0.0720511	−	0.107981i
$532$	3.76592	−	2.29808i	0.163273	−	0.0996342i
$533$	2.77686	+	3.30933i	0.120279	+	0.143343i
$534$	4.38576	−	8.19892i	0.189791	−	0.354802i
$535$	9.60227	−	11.4435i	0.415142	−	0.494747i
$536$	−10.1720	−	27.9474i	−0.439365	−	1.20715i
$537$	−39.3184	+	15.7715i	−1.69671	+	0.680589i
$538$	−9.42992	+	25.9085i	−0.406553	+	1.11699i
$539$	22.3353	+	11.4859i	0.962048	+	0.494731i
$540$	−7.17124	+	1.99825i	−0.308601	+	0.0859910i
$541$	14.3316	+	24.8231i	0.616166	+	1.06723i	0.990179	+	0.139807i	$0.0446481\pi$
$541$	14.3316	+	24.8231i	0.616166	+	1.06723i	−0.374013	+	0.927423i	$0.622019\pi$
$542$	−9.04679	+	7.59115i	−0.388593	+	0.326068i
$543$	−25.7348	+	10.3228i	−1.10439	+	0.442994i
$544$	−43.3056	−	7.63595i	−1.85671	−	0.327389i
$545$	1.97193	−	11.1833i	0.0844680	−	0.479042i
$546$	−2.23437	−	1.12623i	−0.0956221	−	0.0481983i
$547$	−28.4534	+	23.8752i	−1.21658	+	1.02083i	−0.217582	+	0.976042i	$0.569817\pi$
$547$	−28.4534	+	23.8752i	−1.21658	+	1.02083i	−0.998996	+	0.0447884i	$0.985739\pi$
$548$	3.41169	+	1.96974i	0.145740	+	0.0841430i
$549$	−21.7574	+	29.6338i	−0.928582	+	1.26474i
$550$	−5.72699	−	9.91944i	−0.244200	−	0.422966i
$551$	−1.30973	+	1.09899i	−0.0557962	+	0.0468186i
$552$	4.98346	−	1.04625i	0.212110	−	0.0445316i
$553$	27.8119	+	22.2077i	1.18268	+	0.944366i
$554$	5.55975	+	15.2753i	0.236211	+	0.648985i
$555$	17.4121	−	3.65559i	0.739101	−	0.155171i
$556$	1.60634	−	4.41339i	0.0681242	−	0.187170i
$557$	20.8533	−	12.0396i	0.883581	−	0.510136i	0.0117433	−	0.999931i	$-0.496262\pi$
$557$	20.8533	−	12.0396i	0.883581	−	0.510136i	0.871837	+	0.489795i	$0.162929\pi$
$558$	5.34770	+	21.9146i	0.226386	+	0.927718i
$559$	4.24971	−	2.45357i	0.179743	−	0.103775i
$560$	0.161129	+	0.799627i	0.00680893	+	0.0337904i
$561$	−49.3754	+	1.60068i	−2.08463	+	0.0675806i
$562$	−8.18612	+	2.97950i	−0.345311	+	0.125683i
$563$	5.49200	−	1.99893i	0.231460	−	0.0842447i	−0.223686	−	0.974661i	$-0.571809\pi$
$563$	5.49200	−	1.99893i	0.231460	−	0.0842447i	0.455147	+	0.890417i	$0.349587\pi$
$564$	−0.637832	−	0.0912677i	−0.0268576	−	0.00384306i
$565$	−4.75083	+	0.837699i	−0.199869	+	0.0352423i
$566$	−12.0902			−0.508187
$567$	−23.5302	+	3.65107i	−0.988175	+	0.153331i
$568$	3.16971			0.132998
$569$	−14.3012	+	2.52168i	−0.599536	+	0.105714i	−0.465176	−	0.885218i	$-0.654009\pi$
$569$	−14.3012	+	2.52168i	−0.599536	+	0.105714i	−0.134360	+	0.990933i	$0.542898\pi$
$570$	2.67237	+	0.382391i	0.111933	+	0.0160166i
$571$	37.5999	−	13.6852i	1.57351	−	0.572710i	0.599728	−	0.800204i	$-0.295276\pi$
$571$	37.5999	−	13.6852i	1.57351	−	0.572710i	0.973779	+	0.227494i	$0.0730533\pi$
$572$	−2.39406	+	0.871365i	−0.100101	+	0.0364336i
$573$	11.1263	−	0.360699i	0.464808	−	0.0150684i
$574$	5.48622	−	16.2952i	0.228991	−	0.680149i
$575$	−3.11312	+	1.79736i	−0.129826	+	0.0749550i
$576$	11.9711	−	11.4452i	0.498794	−	0.476884i
$577$	10.4145	−	6.01282i	0.433561	−	0.250317i	−0.267301	−	0.963613i	$-0.586132\pi$
$577$	10.4145	−	6.01282i	0.433561	−	0.250317i	0.700863	+	0.713296i	$0.252799\pi$
$578$	−14.3186	+	39.3399i	−0.595573	+	1.63632i
$579$	−2.32287	+	0.487676i	−0.0965351	+	0.0202671i
$580$	0.592164	+	1.62696i	0.0245883	+	0.0675557i
$581$	−14.8412	+	5.81404i	−0.615715	+	0.241207i
$582$	−12.9367	+	2.71601i	−0.536244	+	0.112582i
$583$	18.2253	−	15.2929i	0.754816	−	0.633366i
$584$	1.34407	+	2.32800i	0.0556180	+	0.0963332i
$585$	0.883558	+	2.01151i	0.0365306	+	0.0831655i
$586$	−1.28314	−	0.740824i	−0.0530062	−	0.0306032i
$587$	−13.0785	+	10.9742i	−0.539807	+	0.452952i	−0.871472	−	0.490445i	$-0.836834\pi$
$587$	−13.0785	+	10.9742i	−0.539807	+	0.452952i	0.331665	+	0.943397i	$0.392390\pi$
$588$	−1.15658	−	14.2431i	−0.0476966	−	0.587375i
$589$	−2.03824	+	11.5594i	−0.0839843	+	0.476299i
$590$	1.08179	+	0.190749i	0.0445366	+	0.00785301i
$591$	−35.7278	+	14.3312i	−1.46964	+	0.589506i
$592$	−1.64186	+	1.37768i	−0.0674800	+	0.0566224i
$593$	−8.82192	−	15.2800i	−0.362273	−	0.627475i	0.626062	−	0.779774i	$-0.284666\pi$
$593$	−8.82192	−	15.2800i	−0.362273	−	0.627475i	−0.988335	+	0.152299i	$0.951332\pi$
$594$	9.55322	−	13.9367i	0.391973	−	0.571828i
$595$	−25.5583	+	0.621421i	−1.04779	+	0.0254758i
$596$	−5.67378	+	15.5886i	−0.232407	+	0.638533i
$597$	21.3893	−	8.57972i	0.875407	−	0.351145i
$598$	−0.190582	−	0.523620i	−0.00779348	−	0.0214124i
$599$	9.65598	−	11.5076i	0.394533	−	0.470186i	−0.531812	−	0.846862i	$-0.678489\pi$
$599$	9.65598	−	11.5076i	0.394533	−	0.470186i	0.926345	+	0.376677i	$0.122933\pi$
$600$	−8.29002	+	15.4977i	−0.338439	+	0.632691i
$601$	−4.19281	−	4.99680i	−0.171028	−	0.203824i	0.673721	−	0.738986i	$-0.264695\pi$
$601$	−4.19281	−	4.99680i	−0.171028	−	0.203824i	−0.844749	+	0.535162i	$0.820251\pi$
$602$	−17.1465	−	9.35135i	−0.698838	−	0.381132i
$603$	−13.7161	+	27.7690i	−0.558564	+	1.13084i
$604$	15.5599			0.633122
$605$	2.13973	+	0.778797i	0.0869923	+	0.0316626i
$606$	−0.799711	−	3.80914i	−0.0324861	−	0.154736i
$607$	20.8219	−	24.8146i	0.845136	−	1.00719i	−0.154679	−	0.987965i	$-0.549434\pi$
$607$	20.8219	−	24.8146i	0.845136	−	1.00719i	0.999815	−	0.0192294i	$-0.00612128\pi$
$608$	7.35413	−	2.67669i	0.298250	−	0.108554i
$609$	1.26927	+	5.39055i	0.0514332	+	0.218436i
$610$	−2.34431	−	13.2952i	−0.0949183	−	0.538308i
$611$			0.190154i			0.00769283i
$612$	15.6010	+	23.3807i	0.630634	+	0.945110i
$613$	3.85405			0.155663			0.0778317	−	0.996967i	$-0.475200\pi$
$613$	3.85405			0.155663			0.0778317	+	0.996967i	$0.475200\pi$
$614$	9.83386	+	3.57923i	0.396862	+	0.144446i
$615$	−12.8230	+	7.96820i	−0.517073	+	0.321309i
$616$	21.3698	+	17.0637i	0.861015	+	0.687516i
$617$	−20.8477	+	24.8453i	−0.839295	+	1.00023i	0.160617	+	0.987017i	$0.448652\pi$
$617$	−20.8477	+	24.8453i	−0.839295	+	1.00023i	−0.999913	+	0.0132165i	$0.995793\pi$
$618$	5.58391	+	13.9207i	0.224618	+	0.559974i
$619$	−12.0752	−	14.3907i	−0.485344	−	0.578410i	0.466683	−	0.884425i	$-0.345449\pi$
$619$	−12.0752	−	14.3907i	−0.485344	−	0.578410i	−0.952027	+	0.306015i	$0.901004\pi$
$620$	10.2939	+	5.94318i	0.413413	+	0.238684i
$621$	−4.37388	−	2.99818i	−0.175518	−	0.120313i
$622$		−	21.8053i		−	0.874313i
$623$	−3.09570	−	15.3629i	−0.124026	−	0.615502i
$624$	−0.208151	−	0.163465i	−0.00833271	−	0.00654383i
$625$	0.871603	−	4.94311i	0.0348641	−	0.197724i
$626$	22.5712	+	18.9395i	0.902125	+	0.756973i
$627$	7.46772	−	4.64044i	0.298232	−	0.185321i
$628$	−2.01464	+	5.53517i	−0.0803928	+	0.220877i
$629$	−33.5878	−	58.1758i	−1.33923	−	2.31962i
$630$	5.00217	−	7.17215i	0.199291	−	0.285745i
$631$	3.17557	−	5.50025i	0.126417	−	0.218961i	−0.795869	−	0.605469i	$-0.792985\pi$
$631$	3.17557	−	5.50025i	0.126417	−	0.218961i	0.922286	+	0.386508i	$0.126319\pi$
$632$	24.9094	+	29.6859i	0.990843	+	1.18084i
$633$	8.19415	−	25.0061i	0.325688	−	0.993905i
$634$	0.794779	−	4.50742i	0.0315647	−	0.179012i
$635$	13.6839	+	11.4822i	0.543029	+	0.455655i
$636$	−12.8636	−	4.21521i	−0.510075	−	0.167144i
$637$	−4.11269	+	0.933295i	−0.162951	+	0.0369785i
$638$	−3.40320	−	1.96484i	−0.134734	−	0.0777888i
$639$	−2.28108	−	2.38589i	−0.0902383	−	0.0943842i
$640$		−	7.36635i		−	0.291180i
$641$	29.8979	−	5.27182i	1.18090	−	0.208224i	0.451473	−	0.892285i	$-0.350899\pi$
$641$	29.8979	−	5.27182i	1.18090	−	0.208224i	0.729425	+	0.684061i	$0.239788\pi$
$642$	16.3855	−	10.1819i	0.646684	−	0.401849i
$643$	3.55310	+	0.626507i	0.140121	+	0.0247070i	0.243268	−	0.969959i	$-0.421780\pi$
$643$	3.55310	+	0.626507i	0.140121	+	0.0247070i	−0.103148	+	0.994666i	$0.532892\pi$
$644$	1.98571	−	2.48681i	0.0782479	−	0.0979942i
$645$	6.38430	+	15.9161i	0.251382	+	0.626697i
$646$	−1.76996	−	10.0379i	−0.0696382	−	0.394938i
$647$	4.12557	−	7.14569i	0.162193	−	0.280926i	−0.773462	−	0.633843i	$-0.781477\pi$
$647$	4.12557	−	7.14569i	0.162193	−	0.280926i	0.935655	+	0.352917i	$0.114810\pi$
$648$	−25.9009	−	1.16384i	−1.01749	−	0.0457201i
$649$	3.09824	−	1.78877i	0.121617	−	0.0702155i
$650$	1.80730	+	0.657804i	0.0708882	+	0.0258012i
$651$	30.4633	+	22.7483i	1.19395	+	0.891577i
$652$	1.93620	+	1.62466i	0.0758274	+	0.0636268i
$653$	13.5899	+	37.3379i	0.531814	+	1.46115i	0.856910	+	0.515466i	$0.172381\pi$
$653$	13.5899	+	37.3379i	0.531814	+	1.46115i	−0.325096	+	0.945681i	$0.605397\pi$
$654$	6.91705	−	12.9310i	0.270478	−	0.505642i
$655$	−3.74373	−	21.2318i	−0.146280	−	0.829594i
$656$	0.909343	−	1.57503i	0.0355039	−	0.0614945i
$657$	0.785056	−	2.68705i	0.0306279	−	0.104832i
$658$	0.646040	−	0.394233i	0.0251852	−	0.0153688i
$659$	28.1991	−	4.97227i	1.09848	−	0.193692i	0.405107	−	0.914269i	$-0.367234\pi$
$659$	28.1991	−	4.97227i	1.09848	−	0.193692i	0.693375	+	0.720577i	$0.256123\pi$
$660$	−1.82934	−	8.71342i	−0.0712071	−	0.339169i
$661$	−0.279751	−	0.0493277i	−0.0108811	−	0.00191862i	0.168205	−	0.985752i	$-0.446203\pi$
$661$	−0.279751	−	0.0493277i	−0.0108811	−	0.00191862i	−0.179086	+	0.983833i	$0.557314\pi$
$662$	−10.9292	−	1.92711i	−0.424775	−	0.0748992i
$663$	6.17839	−	5.53514i	0.239949	−	0.214967i
$664$	−17.0917	+	3.01372i	−0.663285	+	0.116955i
$665$	3.88397	−	2.37012i	0.150614	−	0.0919092i
$666$	22.8377	+	2.51583i	0.884944	+	0.0974863i
$667$	−0.616645	+	1.06806i	−0.0238766	+	0.0413555i
$668$	−2.83395	−	16.0721i	−0.109649	−	0.621850i
$669$	−6.45175	−	10.3826i	−0.249439	−	0.401415i
$670$	−3.88998	−	10.6876i	−0.150283	−	0.412899i
$671$	−33.6815	−	28.2622i	−1.30026	−	1.09105i
$672$	2.97969	−	25.1737i	0.114944	−	0.971098i
$673$	−4.12151	−	1.50011i	−0.158873	−	0.0578249i	0.261360	−	0.965241i	$-0.415829\pi$
$673$	−4.12151	−	1.50011i	−0.158873	−	0.0578249i	−0.420232	+	0.907417i	$0.638051\pi$
$674$	14.1390	−	8.16315i	0.544614	−	0.314433i
$675$	17.6313	−	4.91291i	0.678628	−	0.189098i
$676$	−7.44711	+	12.8988i	−0.286427	+	0.496106i
$677$	−8.81436	−	49.9887i	−0.338763	−	1.92122i	−0.386345	−	0.922354i	$-0.626263\pi$
$677$	−8.81436	−	49.9887i	−0.338763	−	1.92122i	0.0475818	−	0.998867i	$-0.484849\pi$
$678$	−6.16698	−	0.882437i	−0.236841	−	0.0338898i
$679$	−13.9019	+	17.4101i	−0.533506	+	0.668140i
$680$	−27.4141	−	4.83385i	−1.05128	−	0.185370i
$681$	26.2076	+	14.0189i	1.00428	+	0.537207i
$682$	−26.5685	+	4.68475i	−1.01736	+	0.179388i
$683$			40.5678i			1.55229i	0.630557	+	0.776143i	$0.282826\pi$
$683$			40.5678i			1.55229i	−0.630557	+	0.776143i	$0.717174\pi$
$684$	−4.48513	−	2.21536i	−0.171493	−	0.0847066i
$685$	3.51864	+	2.03149i	0.134440	+	0.0776191i
$686$	11.6974	+	12.0377i	0.446607	+	0.459602i
$687$	−11.5237	+	10.3239i	−0.439655	+	0.393882i
$688$	−1.58254	−	1.32791i	−0.0603336	−	0.0506259i
$689$	−0.693713	+	3.93424i	−0.0264284	+	0.149883i
$690$	1.90577	−	0.400108i	0.0725514	−	0.0152318i
$691$	2.07608	+	2.47418i	0.0789780	+	0.0941223i	0.804086	−	0.594512i	$-0.202655\pi$
$691$	2.07608	+	2.47418i	0.0789780	+	0.0941223i	−0.725109	+	0.688635i	$0.758210\pi$
$692$	2.13232	−	3.69328i	0.0810585	−	0.140397i
$693$	−2.53473	−	28.3653i	−0.0962863	−	1.07751i
$694$	5.18443	+	8.97970i	0.196798	+	0.340865i
$695$	1.65670	−	4.55175i	0.0628422	−	0.172658i
$696$	0.195379	+	6.02676i	0.00740581	+	0.228444i
$697$	43.6658	+	36.6400i	1.65396	+	1.38784i
$698$	−1.37460	+	7.79577i	−0.0520296	+	0.295074i
$699$	2.09671	−	14.6531i	0.0793050	−	0.554230i
$700$	2.16972	+	10.7676i	0.0820076	+	0.406976i
$701$			6.55534i			0.247592i	0.992308	+	0.123796i	$0.0395068\pi$
$701$			6.55534i			0.247592i	−0.992308	+	0.123796i	$0.960493\pi$
$702$	0.275401	+	2.82378i	0.0103943	+	0.106577i
$703$	10.3537	+	5.97771i	0.390497	+	0.225454i
$704$	12.7322	+	15.1736i	0.479862	+	0.571877i
$705$	−0.657827	−	0.0941288i	−0.0247752	−	0.00354509i
$706$	−12.9654	+	15.4516i	−0.487959	+	0.581527i
$707$	−5.12631	−	4.09333i	−0.192795	−	0.153946i
$708$	−1.79486	−	0.960105i	−0.0674549	−	0.0360830i
$709$	9.22465	+	3.35750i	0.346439	+	0.126094i	0.509379	−	0.860543i	$-0.329875\pi$
$709$	9.22465	+	3.35750i	0.346439	+	0.126094i	−0.162939	+	0.986636i	$0.552098\pi$
$710$	1.21216			0.0454915
$711$	4.41890	−	40.1132i	0.165722	−	1.50436i
$712$		−	17.0639i		−	0.639496i
$713$	1.47026	+	8.33826i	0.0550617	+	0.312270i
$714$	−31.6145	−	9.51514i	−1.18314	−	0.356095i
$715$	−2.46911	+	0.898681i	−0.0923393	+	0.0336088i
$716$	−18.5299	+	22.0830i	−0.692494	+	0.825282i
$717$	−17.1554	+	15.3694i	−0.640681	+	0.573979i
$718$	22.3292	+	8.12718i	0.833320	+	0.303304i
$719$	−11.8461			−0.441784			−0.220892	−	0.975298i	$-0.570897\pi$
$719$	−11.8461			−0.441784			−0.220892	+	0.975298i	$0.570897\pi$
$720$	0.668533	−	0.639167i	0.0249147	−	0.0238204i
$721$	22.1938	+	12.1040i	0.826539	+	0.450778i
$722$	−9.90260	−	11.8015i	−0.368537	−	0.439205i
$723$	−12.7752	−	20.5588i	−0.475116	−	0.764591i
$724$	−12.1282	+	14.4539i	−0.450742	+	0.537174i
$725$	−1.45590	−	4.00005i	−0.0540707	−	0.148558i
$726$	2.31265	+	1.81617i	0.0858306	+	0.0674044i
$727$	15.4099	−	42.3383i	0.571521	−	1.57024i	−0.230580	−	0.973053i	$-0.574062\pi$
$727$	15.4099	−	42.3383i	0.571521	−	1.57024i	0.802101	−	0.597188i	$-0.203716\pi$
$728$	−4.59054	+	0.111614i	−0.170137	+	0.00413668i
$729$	17.7636	+	20.3336i	0.657911	+	0.753095i
$730$	0.513998	+	0.890271i	0.0190239	+	0.0329504i
$731$	49.6002	−	41.6196i	1.83453	−	1.53935i
$732$	−3.54353	+	24.7643i	−0.130973	+	0.915314i
$733$	4.22098	+	0.744273i	0.155906	+	0.0274904i	0.251056	−	0.967973i	$-0.419222\pi$
$733$	4.22098	+	0.744273i	0.155906	+	0.0274904i	−0.0951505	+	0.995463i	$0.530333\pi$
$734$	2.81322	−	15.9546i	0.103838	−	0.588895i
$735$	−1.19284	−	14.6896i	−0.0439985	−	0.541833i
$736$	4.32452	−	3.62871i	0.159404	−	0.133756i
$737$	−32.0789	−	18.5208i	−1.18164	−	0.682221i
$738$	−18.9404	+	4.62192i	−0.697204	+	0.170135i
$739$	−6.26410	−	10.8497i	−0.230429	−	0.399114i	0.727506	−	0.686102i	$-0.240679\pi$
$739$	−6.26410	−	10.8497i	−0.230429	−	0.399114i	−0.957934	+	0.286988i	$0.907346\pi$
$740$	9.27432	−	7.78208i	0.340931	−	0.286075i
$741$	−0.459715	+	1.40292i	−0.0168880	+	0.0515374i
$742$	14.8046	−	5.79971i	0.543494	−	0.212914i
$743$	−5.70379	−	15.6710i	−0.209252	−	0.574914i	0.790020	−	0.613081i	$-0.210070\pi$
$743$	−5.70379	−	15.6710i	−0.209252	−	0.574914i	−0.999271	+	0.0381673i	$0.987848\pi$
$744$	27.6231	+	30.8332i	1.01271	+	1.13040i
$745$	−5.85164	+	16.0772i	−0.214387	+	0.589025i
$746$	−8.40674	+	4.85363i	−0.307793	+	0.177704i
$747$	14.5685	+	10.6963i	0.533034	+	0.391357i
$748$	−29.1126	+	16.8082i	−1.06446	+	0.614567i
$749$	10.3747	−	30.8150i	0.379083	−	1.12595i
$750$	−7.67040	+	14.3394i	−0.280084	+	0.523599i
$751$	−47.2397	+	17.1939i	−1.72380	+	0.627413i	−0.998159	−	0.0606582i	$-0.980680\pi$
$751$	−47.2397	+	17.1939i	−1.72380	+	0.627413i	−0.725644	+	0.688071i	$0.758458\pi$
$752$	0.0752253	−	0.0273798i	0.00274318	−	0.000998437i
$753$	−16.5155	−	41.1732i	−0.601857	−	1.50043i
$754$	0.649826	−	0.114582i	0.0236653	−	0.00417282i
$755$	16.0476			0.584033
$756$	−12.9468	+	9.74307i	−0.470870	+	0.354352i
$757$	8.96036			0.325670			0.162835	−	0.986653i	$-0.447936\pi$
$757$	8.96036			0.325670			0.162835	+	0.986653i	$0.447936\pi$
$758$	11.7656	−	2.07459i	0.427346	−	0.0753527i
$759$	3.91704	−	4.98783i	0.142179	−	0.181047i
$760$	4.65545	−	1.69444i	0.168871	−	0.0614639i
$761$	−26.8181	+	9.76100i	−0.972156	+	0.353836i	−0.778786	−	0.627290i	$-0.784164\pi$
$761$	−26.8181	+	9.76100i	−0.972156	+	0.353836i	−0.193370	+	0.981126i	$0.561942\pi$
$762$	12.1753	+	19.5934i	0.441065	+	0.709792i
$763$	−4.88241	−	24.2297i	−0.176755	−	0.877176i
$764$	6.56027	−	3.78757i	0.237342	−	0.137030i
$765$	16.0901	+	24.1137i	0.581738	+	0.871832i
$766$	12.4921	−	7.21231i	0.451358	−	0.260591i
$767$	−0.205459	+	0.564494i	−0.00741869	+	0.0203827i
$768$	8.91734	−	27.2131i	0.321777	−	0.981969i
$769$	0.460020	+	1.26389i	0.0165887	+	0.0455772i	0.947711	−	0.319131i	$-0.103391\pi$
$769$	0.460020	+	1.26389i	0.0165887	+	0.0455772i	−0.931122	+	0.364708i	$0.881169\pi$
$770$	8.17223	+	6.52549i	0.294507	+	0.235162i
$771$	13.8047	+	15.4089i	0.497164	+	0.554940i
$772$	−1.23725	+	1.03817i	−0.0445295	+	0.0373647i
$773$	8.35543	+	14.4720i	0.300524	+	0.520523i	0.976255	−	0.216626i	$-0.0695051\pi$
$773$	8.35543	+	14.4720i	0.300524	+	0.520523i	−0.675731	+	0.737148i	$0.736172\pi$
$774$	1.43436	+	22.0992i	0.0515569	+	0.794341i
$775$	−25.3086	−	14.6120i	−0.909113	−	0.524877i
$776$	−18.5832	+	15.5932i	−0.667100	+	0.559763i
$777$	32.3851	−	21.2323i	1.16181	−	0.761703i
$778$	−3.92916	+	22.2834i	−0.140867	+	0.798897i
$779$	−9.99061	−	1.76161i	−0.357951	−	0.0631164i
$780$	1.17578	+	0.923359i	0.0420995	+	0.0330616i
$781$	3.02417	−	2.53758i	0.108213	−	0.0908018i
$782$	−3.67623	−	6.36741i	−0.131462	−	0.227698i
$783$	4.39582	−	4.48423i	0.157094	−	0.160253i
$784$	0.961386	+	1.49260i	0.0343352	+	0.0533072i
$785$	−2.07779	+	5.70869i	−0.0741596	+	0.203752i
$786$	3.94367	−	27.5606i	0.140666	−	0.983056i
$787$	4.47731	+	12.3013i	0.159599	+	0.438495i	0.993557	−	0.113333i	$-0.0361528\pi$
$787$	4.47731	+	12.3013i	0.159599	+	0.438495i	−0.833958	+	0.551828i	$0.813931\pi$
$788$	−16.8377	+	20.0664i	−0.599818	+	0.714835i
$789$	24.6263	−	0.798348i	0.876720	−	0.0284220i
$790$	9.52584	+	11.3524i	0.338914	+	0.403902i
$791$	−8.96297	+	5.46947i	−0.318686	+	0.194472i
$792$	3.39535	−	30.8217i	0.120649	−	1.09520i
$793$	7.38288			0.262174
$794$	−18.3683	−	6.68553i	−0.651868	−	0.237261i
$795$	−13.2669	−	4.34735i	−0.470527	−	0.154185i
$796$	10.0803	−	12.0132i	0.357287	−	0.425798i
$797$	−28.9247	+	10.5277i	−1.02457	+	0.372912i	−0.799010	−	0.601318i	$-0.794642\pi$
$797$	−28.9247	+	10.5277i	−1.02457	+	0.372912i	−0.225557	+	0.974230i	$0.572420\pi$
$798$	5.71942	−	1.34670i	0.202465	−	0.0476728i
$799$	0.435691	+	2.47093i	0.0154136	+	0.0874151i
$800$			19.4849i			0.688896i
$801$	−12.8442	+	12.2800i	−0.453829	+	0.433894i
$802$	8.57959			0.302956
$803$	3.14609	+	1.14508i	0.111023	+	0.0404091i
$804$	0.682878	+	21.0644i	0.0240832	+	0.742885i
$805$	2.04796	−	2.56477i	0.0721810	−	0.0903963i
$806$	2.91187	−	3.47023i	0.102566	−	0.122234i
$807$	32.5441	−	41.4406i	1.14560	−	1.45878i
$808$	−4.59132	−	5.47172i	−0.161522	−	0.192495i
$809$	48.9190	+	28.2434i	1.71990	+	0.992985i	0.919069	+	0.394097i	$0.128942\pi$
$809$	48.9190	+	28.2434i	1.71990	+	0.992985i	0.800832	+	0.598889i	$0.204391\pi$
$810$	−9.90502	−	0.445076i	−0.348027	−	0.0156384i
$811$			0.658409i			0.0231199i	0.999933	+	0.0115599i	$0.00367972\pi$
$811$			0.658409i			0.0231199i	−0.999933	+	0.0115599i	$0.996320\pi$
$812$	2.49176	+	2.82706i	0.0874436	+	0.0992104i
$813$	20.9474	−	8.40247i	0.734658	−	0.294687i
$814$	−4.77162	+	27.0612i	−0.167245	+	0.948494i
$815$	1.99690	+	1.67559i	0.0699482	+	0.0586935i
$816$	−3.07932	−	1.64719i	−0.107798	−	0.0576631i
$817$	−3.94125	+	10.8285i	−0.137887	+	0.378841i
$818$	−5.89881	−	10.2170i	−0.206247	−	0.357231i
$819$	3.38760	+	3.37504i	0.118372	+	0.117934i
$820$	−5.13658	+	8.89682i	−0.179377	+	0.310690i
$821$	−26.7252	−	31.8499i	−0.932718	−	1.11157i	−0.993547	−	0.113421i	$-0.963819\pi$
$821$	−26.7252	−	31.8499i	−0.932718	−	1.11157i	0.0608295	−	0.998148i	$-0.480625\pi$
$822$	3.50108	+	3.90794i	0.122114	+	0.136305i
$823$	−5.29377	+	30.0224i	−0.184529	+	1.04652i	0.742030	+	0.670367i	$0.233863\pi$
$823$	−5.29377	+	30.0224i	−0.184529	+	1.04652i	−0.926559	+	0.376150i	$0.877248\pi$
$824$	21.0858	+	17.6931i	0.734559	+	0.616369i
$825$	4.49764	+	21.4229i	0.156588	+	0.745849i
$826$	2.34380	−	0.472287i	0.0815512	−	0.0164330i
$827$	−36.1773	−	20.8870i	−1.25801	−	0.726311i	−0.285321	−	0.958432i	$-0.592100\pi$
$827$	−36.1773	−	20.8870i	−1.25801	−	0.726311i	−0.972687	+	0.232121i	$0.925433\pi$
$828$	−3.58674	−	0.395118i	−0.124648	−	0.0137313i
$829$		−	43.6190i		−	1.51495i	−0.652864	−	0.757475i	$-0.726433\pi$
$829$		−	43.6190i		−	1.51495i	0.652864	−	0.757475i	$-0.273567\pi$
$830$	−6.53618	+	1.15250i	−0.226874	+	0.0400040i
$831$	−1.00660	−	31.0501i	−0.0349185	−	1.07712i
$832$	−3.27548	−	0.577555i	−0.113557	−	0.0200231i
$833$	−51.3032	+	21.5507i	−1.77755	+	0.746688i
$834$	3.86346	−	4.91960i	0.133781	−	0.170352i
$835$	−2.92279	−	16.5760i	−0.101147	−	0.573635i
$836$	2.99139	−	5.18124i	0.103459	−	0.179197i
$837$	3.32960	−	42.9815i	0.115088	−	1.48566i
$838$	−9.20258	+	5.31311i	−0.317898	+	0.183538i
$839$	8.50951	+	3.09721i	0.293781	+	0.106928i	0.484706	−	0.874677i	$-0.338927\pi$
$839$	8.50951	+	3.09721i	0.293781	+	0.106928i	−0.190925	+	0.981605i	$0.561149\pi$
$840$	1.88625	−	15.9359i	0.0650819	−	0.549842i
$841$	21.0965	+	17.7021i	0.727467	+	0.610417i
$842$	−5.24671	−	14.4152i	−0.180814	−	0.496781i
$843$	16.6399	−	0.539442i	0.573110	−	0.0185794i
$844$	−3.10940	−	17.6343i	−0.107030	−	0.606997i
$845$	−7.68056	+	13.3031i	−0.264219	+	0.457641i
$846$	−0.769420	−	0.380044i	−0.0264532	−	0.0130662i
$847$	4.95468	−	0.120467i	0.170245	−	0.00413931i
$848$	1.65628	−	0.292046i	0.0568767	−	0.0100289i
$849$	21.9569	+	7.19496i	0.753560	+	0.246930i
$850$	24.9918	+	4.40673i	0.857212	+	0.151150i
$851$	8.49288	+	1.49752i	0.291132	+	0.0513344i
$852$	−2.13449	−	0.699440i	−0.0731263	−	0.0239624i
$853$	−49.6962	+	8.76279i	−1.70157	+	0.300032i	−0.938241	−	0.345982i	$-0.887546\pi$
$853$	−49.6962	+	8.76279i	−1.70157	+	0.300032i	−0.763325	+	0.646014i	$0.776435\pi$
$854$	−15.3064	−	25.0830i	−0.523773	−	0.858321i
$855$	−4.62573	−	2.28481i	−0.158197	−	0.0781389i
$856$	17.7015	−	30.6599i	0.605025	−	1.04793i
$857$	2.67909	+	15.1938i	0.0915158	+	0.519012i	0.995759	+	0.0919951i	$0.0293244\pi$
$857$	2.67909	+	15.1938i	0.0915158	+	0.519012i	−0.904244	+	0.427017i	$0.859564\pi$
$858$	−3.39142	+	0.109945i	−0.115781	+	0.00375346i
$859$	−1.57769	−	4.33468i	−0.0538303	−	0.147897i	0.909863	−	0.414908i	$-0.136186\pi$
$859$	−1.57769	−	4.33468i	−0.0538303	−	0.147897i	−0.963694	+	0.267011i	$0.913964\pi$
$860$	8.93923	+	7.50090i	0.304825	+	0.255779i
$861$	−19.6610	+	26.3288i	−0.670044	+	0.897284i
$862$	−1.61552	−	0.588001i	−0.0550248	−	0.0200274i
$863$	27.5293	−	15.8941i	0.937108	−	0.541040i	0.0480557	−	0.998845i	$-0.484698\pi$
$863$	27.5293	−	15.8941i	0.937108	−	0.541040i	0.889053	+	0.457805i	$0.151364\pi$
$864$	−25.9283	+	12.4063i	−0.882100	+	0.422071i
$865$	2.19916	−	3.80906i	0.0747737	−	0.129512i
$866$	−1.35269	−	7.67149i	−0.0459663	−	0.260688i
$867$	49.4155	−	62.9241i	1.67824	−	2.13701i
$868$	25.5801	+	3.87190i	0.868244	+	0.131421i
$869$	47.5314	+	8.38106i	1.61239	+	0.284308i
$870$	0.0747165	+	2.30475i	0.00253313	+	0.0781383i
$871$	6.12532	−	1.08006i	0.207548	−	0.0365964i
$872$		−	26.9125i		−	0.911372i
$873$	25.1107	+	2.76622i	0.849868	+	0.0936222i
$874$	1.13322	+	0.654267i	0.0383319	+	0.0221309i
$875$	5.41416	+	26.8687i	0.183032	+	0.908327i
$876$	−0.391394	−	1.86426i	−0.0132240	−	0.0629877i
$877$	−14.8121	−	12.4288i	−0.500167	−	0.419690i	0.357486	−	0.933919i	$-0.383634\pi$
$877$	−14.8121	−	12.4288i	−0.500167	−	0.419690i	−0.857653	+	0.514228i	$0.828078\pi$
$878$	2.73792	−	15.5275i	0.0924004	−	0.524029i
$879$	1.88945	+	2.10902i	0.0637295	+	0.0711355i
$880$	0.711038	+	0.847382i	0.0239691	+	0.0285652i
$881$	−0.310834	+	0.538380i	−0.0104723	+	0.0181385i	−0.871214	−	0.490903i	$-0.836667\pi$
$881$	−0.310834	+	0.538380i	−0.0104723	+	0.0181385i	0.860742	+	0.509042i	$0.170000\pi$
$882$	4.44327	−	18.5064i	0.149613	−	0.623144i
$883$	−1.97025	−	3.41257i	−0.0663041	−	0.114842i	0.830968	−	0.556321i	$-0.187787\pi$
$883$	−1.97025	−	3.41257i	−0.0663041	−	0.114842i	−0.897272	+	0.441479i	$0.854454\pi$
$884$	1.93059	−	5.30425i	0.0649328	−	0.178401i
$885$	−1.85112	−	0.990202i	−0.0622248	−	0.0332853i
$886$	−21.2533	−	17.8337i	−0.714020	−	0.599134i
$887$	−8.69367	+	49.3042i	−0.291905	+	1.65547i	0.387618	+	0.921820i	$0.373298\pi$
$887$	−8.69367	+	49.3042i	−0.291905	+	1.65547i	−0.679523	+	0.733654i	$0.737813\pi$
$888$	39.1339	−	15.6974i	1.31325	−	0.526772i
$889$	36.8478	+	12.4058i	1.23583	+	0.416077i
$890$		−	6.52556i		−	0.218737i
$891$	−25.6434	+	19.6252i	−0.859087	+	0.657468i
$892$	−7.20364	−	4.15902i	−0.241196	−	0.139254i
$893$	−0.287031	−	0.342070i	−0.00960512	−	0.0114469i
$894$	−13.6461	+	17.3766i	−0.456395	+	0.581159i
$895$	−19.1107	+	22.7753i	−0.638802	+	0.761294i
$896$	−5.84831	−	14.9286i	−0.195378	−	0.498731i
$897$	0.0345051	+	1.06436i	0.00115209	+	0.0355381i
$898$	23.3585	+	8.50179i	0.779482	+	0.283708i
$899$	−10.0263			−0.334395
$900$	9.00229	−	8.60686i	0.300076	−	0.286895i
$901$			52.7122i			1.75610i
$902$	−4.04894	−	22.9627i	−0.134815	−	0.764574i
$903$	25.5746	+	27.1870i	0.851070	+	0.904726i
$904$	−10.7433	+	3.91024i	−0.357316	+	0.130053i
$905$	−12.5084	+	14.9070i	−0.415794	+	0.495524i
$906$	19.6933	+	6.45321i	0.654267	+	0.214394i
$907$	21.0519	+	7.66226i	0.699016	+	0.254421i	0.666991	−	0.745066i	$-0.267582\pi$
$907$	21.0519	+	7.66226i	0.699016	+	0.254421i	0.0320254	+	0.999487i	$0.489804\pi$
$908$	20.2247			0.671181
$909$	−0.814496	+	7.39369i	−0.0270151	+	0.245233i
$910$	−1.75551	+	0.0426833i	−0.0581946	+	0.00141494i
$911$	−24.0775	−	28.6944i	−0.797723	−	0.950689i	0.201864	−	0.979413i	$-0.435300\pi$
$911$	−24.0775	−	28.6944i	−0.797723	−	0.950689i	−0.999587	+	0.0287243i	$0.990855\pi$
$912$	0.621188	−	0.0201380i	0.0205696	−	0.000666835i
$913$	−13.8942	+	16.5584i	−0.459830	+	0.548005i
$914$	7.10770	+	19.5282i	0.235102	+	0.645937i
$915$	−3.65462	+	25.5406i	−0.120818	+	0.844346i
$916$	−3.60086	+	9.89327i	−0.118976	+	0.326883i
$917$	−24.4434	−	40.0561i	−0.807193	−	1.32277i
$918$	10.0486	+	36.0621i	0.331654	+	1.19023i
$919$	6.76771	+	11.7220i	0.223246	+	0.386674i	0.955792	−	0.294044i	$-0.0950012\pi$
$919$	6.76771	+	11.7220i	0.223246	+	0.386674i	−0.732546	+	0.680718i	$0.761668\pi$
$920$	2.73759	−	2.29711i	0.0902556	−	0.0757334i
$921$	−15.7292	−	12.3525i	−0.518296	−	0.407027i
$922$	26.9105	+	4.74505i	0.886250	+	0.156270i
$923$	−0.115109	+	0.652818i	−0.00378887	+	0.0214878i
$924$	−10.6251	−	16.2063i	−0.349541	−	0.533147i
$925$	−22.8019	+	19.1331i	−0.749722	+	0.629092i
$926$	−23.5226	−	13.5808i	−0.773000	−	0.446292i
$927$	−1.85658	−	28.6045i	−0.0609781	−	0.939494i
$928$	3.34248	+	5.78935i	0.109722	+	0.190045i
$929$	−28.4979	+	23.9126i	−0.934986	+	0.784547i	−0.976706	−	0.214583i	$-0.931161\pi$
$929$	−28.4979	+	23.9126i	−0.934986	+	0.784547i	0.0417195	+	0.999129i	$0.486716\pi$
$930$	10.5636	+	11.7912i	0.346395	+	0.386649i
$931$	5.98957	−	7.88686i	0.196300	−	0.258481i
$932$	−3.44503	−	9.46514i	−0.112846	−	0.310041i
$933$	−12.9765	+	39.6006i	−0.424833	+	1.29647i
$934$	−0.728762	+	2.00226i	−0.0238458	+	0.0655159i
$935$	−30.0252	+	17.3351i	−0.981930	+	0.566917i
$936$	2.88995	+	4.33107i	0.0944609	+	0.141565i
$937$	−42.3336	+	24.4413i	−1.38298	+	0.798463i	−0.992511	−	0.122153i	$-0.961020\pi$
$937$	−42.3336	+	24.4413i	−1.38298	+	0.798463i	−0.390468	+	0.920617i	$0.627687\pi$
$938$	−16.3686	−	18.5712i	−0.534454	−	0.606372i
$939$	−29.7204	−	47.8282i	−0.969890	−	1.56082i
$940$	−0.424923	+	0.154659i	−0.0138595	+	0.00504443i
$941$	30.0578	−	10.9401i	0.979856	−	0.356638i	0.198072	−	0.980188i	$-0.436532\pi$
$941$	30.0578	−	10.9401i	0.979856	−	0.356638i	0.781784	+	0.623549i	$0.214310\pi$
$942$	−4.84545	+	6.17005i	−0.157873	+	0.201031i
$943$	−7.20661	+	1.27072i	−0.234679	+	0.0413803i
$944$	0.252898			0.00823112
$945$	−13.3526	+	10.0485i	−0.434362	+	0.326878i
$946$	−26.4858			−0.861128
$947$	−34.1040	+	6.01346i	−1.10823	+	0.195411i	−0.697669	−	0.716421i	$-0.745779\pi$
$947$	−34.1040	+	6.01346i	−1.10823	+	0.195411i	−0.410564	+	0.911832i	$0.634668\pi$
$948$	−10.2234	−	25.4871i	−0.332042	−	0.827783i
$949$	−0.528273	+	0.192276i	−0.0171485	+	0.00624154i
$950$	−4.24409	+	1.54472i	−0.137697	+	0.0501174i
$951$	−4.12580	+	7.71294i	−0.133788	+	0.250109i
$952$	−59.3952	+	11.9684i	−1.92501	+	0.387898i
$953$	−43.1385	+	24.9060i	−1.39739	+	0.806786i	−0.994119	−	0.108293i	$-0.965461\pi$
$953$	−43.1385	+	24.9060i	−1.39739	+	0.806786i	−0.403275	+	0.915079i	$0.632128\pi$
$954$	−14.5326	−	10.6700i	−0.470511	−	0.345453i
$955$	6.76592	−	3.90631i	0.218940	−	0.126405i
$956$	−5.36064	+	14.7282i	−0.173376	+	0.476345i
$957$	5.01126	+	5.59362i	0.161991	+	0.180816i
$958$	5.80574	+	15.9511i	0.187575	+	0.515358i
$959$	8.74372	+	1.32349i	0.282349	+	0.0427376i
$960$	3.61942	−	11.0454i	0.116816	−	0.356489i
$961$	−28.9819	+	24.3187i	−0.934901	+	0.784475i
$962$	−2.30703	−	3.99589i	−0.0743816	−	0.128833i
$963$	−35.8170	+	8.74025i	−1.15419	+	0.281651i
$964$	−14.2641	−	8.23537i	−0.459415	−	0.265243i
$965$	−1.27603	+	1.07072i	−0.0410770	+	0.0344677i
$966$	3.54458	−	2.32389i	0.114045	−	0.0747701i
$967$	−0.0919287	+	0.521354i	−0.00295623	+	0.0167656i	−0.986250	−	0.165259i	$-0.947154\pi$
$967$	−0.0919287	+	0.521354i	−0.00295623	+	0.0167656i	0.983294	+	0.182025i	$0.0582651\pi$
$968$	5.31444	+	0.937079i	0.170813	+	0.0301189i
$969$	−2.75925	+	19.2832i	−0.0886398	+	0.619467i
$970$	−7.10659	+	5.96314i	−0.228179	+	0.191465i
$971$	9.94776	+	17.2300i	0.319239	+	0.552938i	0.980329	−	0.197368i	$-0.0632395\pi$
$971$	9.94776	+	17.2300i	0.319239	+	0.552938i	−0.661091	+	0.750306i	$0.729906\pi$
$972$	17.1849	+	6.49913i	0.551206	+	0.208460i
$973$	−0.256265	−	10.5399i	−0.00821547	−	0.337893i
$974$	0.229412	−	0.630304i	0.00735083	−	0.0201962i
$975$	−2.89077	−	2.27018i	−0.0925788	−	0.0727039i
$976$	−1.06304	−	2.92068i	−0.0340271	−	0.0934886i
$977$	−31.6302	+	37.6954i	−1.01194	+	1.20598i	−0.0335032	+	0.999439i	$0.510666\pi$
$977$	−31.6302	+	37.6954i	−1.01194	+	1.20598i	−0.978437	+	0.206545i	$0.933778\pi$
$978$	1.77675	+	2.85926i	0.0568141	+	0.0914292i
$979$	−13.6609	−	16.2804i	−0.436603	−	0.520324i
$980$	−5.43056	−	8.43122i	−0.173473	−	0.269325i
$981$	−20.2574	+	19.3676i	−0.646769	+	0.618360i
$982$	12.5395			0.400153
$983$	25.6891	+	9.35008i	0.819356	+	0.298221i	0.717483	−	0.696576i	$-0.245294\pi$
$983$	25.6891	+	9.35008i	0.819356	+	0.298221i	0.101873	+	0.994797i	$0.467516\pi$
$984$	−26.6486	+	23.8742i	−0.849526	+	0.761081i
$985$	−17.3655	+	20.6954i	−0.553311	+	0.659411i
$986$	8.18150	−	2.97782i	0.260552	−	0.0948332i
$987$	−1.40788	+	0.331502i	−0.0448134	+	0.0105518i
$988$	0.174446	+	0.989333i	0.00554987	+	0.0314749i
$989$			8.31230i			0.264316i
$990$	1.29845	−	11.7868i	0.0412674	−	0.374610i
$991$	44.3720			1.40952			0.704761	−	0.709445i	$-0.251054\pi$
$991$	44.3720			1.40952			0.704761	+	0.709445i	$0.251054\pi$
$992$	43.1265	+	15.6968i	1.36927	+	0.498372i
$993$	18.7016	+	10.0039i	0.593479	+	0.317463i
$994$	2.45656	−	0.962360i	0.0779174	−	0.0305242i
$995$	10.3963	−	12.3898i	0.329585	−	0.392784i
$996$	12.1746	+	1.74206i	0.385766	+	0.0551994i
$997$	−16.9190	−	20.1633i	−0.535830	−	0.638577i	0.428418	−	0.903581i	$-0.359071\pi$
$997$	−16.9190	−	20.1633i	−0.535830	−	0.638577i	−0.964247	+	0.265004i	$0.914627\pi$
$998$	1.87922	+	1.08497i	0.0594857	+	0.0343441i
$999$	−39.9784	−	18.1599i	−1.26486	−	0.574555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.15	yes	132
3.2	odd	2		567.2.bd.a.17.8		132
7.5	odd	6		189.2.ba.a.131.8	yes	132
21.5	even	6		567.2.ba.a.341.15		132
27.7	even	9		567.2.ba.a.143.15		132
27.20	odd	18		189.2.ba.a.101.8	✓	132
189.47	even	18	inner	189.2.bd.a.47.15	yes	132
189.61	odd	18		567.2.bd.a.467.8		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.8	✓	132	27.20	odd	18
189.2.ba.a.131.8	yes	132	7.5	odd	6
189.2.bd.a.47.15	yes	132	189.47	even	18	inner
189.2.bd.a.185.15	yes	132	1.1	even	1	trivial
567.2.ba.a.143.15		132	27.7	even	9
567.2.ba.a.341.15		132	21.5	even	6
567.2.bd.a.17.8		132	3.2	odd	2
567.2.bd.a.467.8		132	189.61	odd	18

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)

\(f(q)\)	\(=\)	\(q+(0.892534 - 0.157378i) q^{2} +(-1.71459 - 0.245341i) q^{3} +(-1.10754 + 0.403110i) q^{4} +(-1.14226 + 0.415747i) q^{5} +(-1.56894 + 0.0508626i) q^{6} +(-1.98483 + 1.74942i) q^{7} +(-2.49483 + 1.44039i) q^{8} +(2.87962 + 0.841317i) q^{9} +O(q^{10})\)	\(q+(0.892534 - 0.157378i) q^{2} +(-1.71459 - 0.245341i) q^{3} +(-1.10754 + 0.403110i) q^{4} +(-1.14226 + 0.415747i) q^{5} +(-1.56894 + 0.0508626i) q^{6} +(-1.98483 + 1.74942i) q^{7} +(-2.49483 + 1.44039i) q^{8} +(2.87962 + 0.841317i) q^{9} +(-0.954073 + 0.550834i) q^{10} +(-1.22714 + 3.37155i) q^{11} +(1.99787 - 0.419444i) q^{12} +(-0.206055 - 0.566132i) q^{13} +(-1.49621 + 1.87378i) q^{14} +(2.06050 - 0.432592i) q^{15} +(-0.194293 + 0.163031i) q^{16} +(-3.97470 - 6.88437i) q^{17} +(2.70256 + 0.297716i) q^{18} +(1.22523 + 0.707386i) q^{19} +(1.09750 - 0.920911i) q^{20} +(3.83236 - 2.51257i) q^{21} +(-0.564660 + 3.20235i) q^{22} +(1.00502 + 0.177213i) q^{23} +(4.63100 - 1.85759i) q^{24} +(-2.69832 + 2.26416i) q^{25} +(-0.273008 - 0.472864i) q^{26} +(-4.73094 - 2.14900i) q^{27} +(1.49306 - 2.73765i) q^{28} +(-0.413325 + 1.13560i) q^{29} +(1.77098 - 0.710380i) q^{30} +(2.83760 + 7.79623i) q^{31} +(3.55571 - 4.23753i) q^{32} +(2.93123 - 5.47975i) q^{33} +(-4.63100 - 5.51901i) q^{34} +(1.53987 - 2.82347i) q^{35} +(-3.52842 + 0.229013i) q^{36} +8.45042 q^{37} +(1.20488 + 0.438542i) q^{38} +(0.214404 + 1.02124i) q^{39} +(2.25090 - 2.68252i) q^{40} +(-6.73814 + 2.45248i) q^{41} +(3.02509 - 2.84568i) q^{42} +(1.41438 + 8.02135i) q^{43} -4.22879i q^{44} +(-3.63903 + 0.236192i) q^{45} +0.924908 q^{46} +(-0.296592 - 0.107951i) q^{47} +(0.373131 - 0.231863i) q^{48} +(0.879076 - 6.94458i) q^{49} +(-2.05201 + 2.44549i) q^{50} +(5.12594 + 12.7790i) q^{51} +(0.456428 + 0.543949i) q^{52} +(-5.74259 - 3.31549i) q^{53} +(-4.56073 - 1.17351i) q^{54} -4.36136i q^{55} +(2.43197 - 7.22344i) q^{56} +(-1.92721 - 1.51347i) q^{57} +(-0.190188 + 1.07861i) q^{58} +(-0.763827 - 0.640927i) q^{59} +(-2.10769 + 1.30972i) q^{60} +(-4.19127 + 11.5154i) q^{61} +(3.75960 + 6.51182i) q^{62} +(-7.18735 + 3.36778i) q^{63} +(2.76033 - 4.78103i) q^{64} +(0.470736 + 0.561001i) q^{65} +(1.75383 - 5.35217i) q^{66} +(-1.79273 + 10.1671i) q^{67} +(7.17729 + 6.02246i) q^{68} +(-1.67972 - 0.550421i) q^{69} +(0.930030 - 2.76238i) q^{70} +(-0.952881 - 0.550146i) q^{71} +(-8.39599 + 2.04883i) q^{72} -0.933127i q^{73} +(7.54228 - 1.32991i) q^{74} +(5.18199 - 3.22009i) q^{75} +(-1.64214 - 0.289554i) q^{76} +(-3.46258 - 8.83874i) q^{77} +(0.352083 + 0.877746i) q^{78} +(-2.33590 - 13.2476i) q^{79} +(0.154153 - 0.267000i) q^{80} +(7.58437 + 4.84534i) q^{81} +(-5.62805 + 3.24936i) q^{82} +(5.66119 + 2.06050i) q^{83} +(-3.23164 + 4.32763i) q^{84} +(7.40228 + 6.21125i) q^{85} +(2.52476 + 6.93673i) q^{86} +(0.987292 - 1.84568i) q^{87} +(-1.79484 - 10.1790i) q^{88} +(-2.96167 + 5.12977i) q^{89} +(-3.21079 + 0.783513i) q^{90} +(1.39939 + 0.763198i) q^{91} +(-1.18454 + 0.208866i) q^{92} +(-2.95257 - 14.0635i) q^{93} +(-0.281708 - 0.0496727i) q^{94} +(-1.69362 - 0.298631i) q^{95} +(-7.13622 + 6.39326i) q^{96} +(8.29293 - 1.46227i) q^{97} +(-0.308318 - 6.33662i) q^{98} +(-6.37025 + 8.67636i) 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

Modular forms

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