LMFDB - Embedded newform 690.2.n.b.89.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.20
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(1.42695 + 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.21959 + 0.270933i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(1.28454 - 0.825522i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(1.42695 + 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.21959 + 0.270933i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(1.28454 - 0.825522i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +(0.0477058 + 2.23556i) q^{10} +(-0.219473 + 1.52646i) q^{11} +(-1.64574 - 0.539952i) q^{12} +(2.39248 - 3.72277i) q^{13} +(0.999928 + 1.15398i) q^{14} +(2.90127 + 2.56567i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.0211748 + 0.0721148i) q^{17} +(-2.62065 + 1.46020i) q^{18} +(0.126511 + 0.430858i) q^{19} +(-2.20602 + 0.365373i) q^{20} +(2.64342 + 0.0830986i) q^{21} -1.54216 q^{22} +(-4.78300 + 0.350566i) q^{23} +(0.300243 - 1.70583i) q^{24} +(4.85319 + 1.20272i) q^{25} +(4.02536 + 1.83832i) q^{26} +(-1.22038 + 5.05081i) q^{27} +(-0.999928 + 1.15398i) q^{28} +(-1.07283 + 3.65371i) q^{29} +(-2.12666 + 3.23687i) q^{30} +(-2.98547 - 6.53727i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.81176 + 1.96273i) q^{33} +(-0.0743943 - 0.0106963i) q^{34} +(3.07481 - 1.48430i) q^{35} +(-1.81830 - 2.38617i) q^{36} +(-1.83669 - 2.11966i) q^{37} +(-0.408468 + 0.186541i) q^{38} +(7.06874 - 2.96343i) q^{39} +(-0.675603 - 2.13156i) q^{40} +(4.70508 + 4.07697i) q^{41} +(0.293945 + 2.62834i) q^{42} +(1.54435 - 3.38165i) q^{43} +(-0.219473 - 1.52646i) q^{44} +(1.62116 + 6.50937i) q^{45} +(-1.02769 - 4.68443i) q^{46} -7.94130 q^{47} +(1.73120 + 0.0544219i) q^{48} +(-1.93936 + 4.24660i) q^{49} +(-0.499799 + 4.97496i) q^{50} +(-0.101013 + 0.0821162i) q^{51} +(-1.24674 + 4.24601i) q^{52} +(-5.45190 - 8.48332i) q^{53} +(-5.17308 - 0.489153i) q^{54} +(-0.900709 + 3.32867i) q^{55} +(-1.28454 - 0.825522i) q^{56} +(-0.242464 + 0.739014i) q^{57} +(-3.76920 - 0.541929i) q^{58} +(0.831298 - 1.29353i) q^{59} +(-3.50658 - 1.64436i) q^{60} +(-3.72803 + 1.70254i) q^{61} +(6.04585 - 3.88544i) q^{62} +(3.69045 + 2.71372i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(6.31895 - 7.61484i) q^{65} +(-2.20059 - 1.51400i) q^{66} +(1.56866 + 10.9103i) q^{67} -0.0751593i q^{68} +(-7.16928 - 4.19541i) q^{69} +(1.90678 + 2.83228i) q^{70} +(-6.98782 + 1.00470i) q^{71} +(2.10311 - 2.13938i) q^{72} +(-3.21126 - 10.9365i) q^{73} +(1.83669 - 2.11966i) q^{74} +(5.74451 + 6.48079i) q^{75} +(-0.242773 - 0.377763i) q^{76} +(0.978209 + 2.14198i) q^{77} +(3.93925 + 6.57505i) q^{78} +(-4.68933 + 7.29674i) q^{79} +(2.01372 - 0.972079i) q^{80} +(-6.69999 + 6.00917i) q^{81} +(-3.36587 + 5.23740i) q^{82} +(3.99704 - 3.46346i) q^{83} +(-2.55975 + 0.665004i) q^{84} +(-0.0665378 + 0.154329i) q^{85} +(3.56702 + 1.04737i) q^{86} +(-5.11785 + 4.16043i) q^{87} +(1.47969 - 0.434477i) q^{88} +(3.53383 - 7.73801i) q^{89} +(-6.21240 + 2.53104i) q^{90} -6.75708i q^{91} +(4.49049 - 1.68389i) q^{92} +(2.15776 - 12.2593i) q^{93} +(-1.13017 - 7.86047i) q^{94} +(0.164070 + 0.990605i) q^{95} +(0.192507 + 1.72132i) q^{96} +(-3.14175 + 3.62578i) q^{97} +(-4.47937 - 1.31526i) q^{98} +(-4.51218 + 1.02204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	1.42695	+	0.981738i	0.823851	+	0.566807i
$3$	1.42695	+	0.981738i	0.823851	+	0.566807i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	2.21959	+	0.270933i	0.992632	+	0.121165i
$5$	2.21959	+	0.270933i	0.992632	+	0.121165i
$6$	−0.768669	+	1.55214i	−0.313808	+	0.633660i
$7$	1.28454	−	0.825522i	0.485509	−	0.312018i	−0.274888	−	0.961476i	$-0.588641\pi$
$7$	1.28454	−	0.825522i	0.485509	−	0.312018i	0.760397	+	0.649458i	$0.225004\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	1.07238	+	2.80178i	0.357461	+	0.933928i
$10$	0.0477058	+	2.23556i	0.0150859	+	0.706946i
$11$	−0.219473	+	1.52646i	−0.0661735	+	0.460246i	0.929612	+	0.368538i	$0.120142\pi$
$11$	−0.219473	+	1.52646i	−0.0661735	+	0.460246i	−0.995786	+	0.0917080i	$0.970767\pi$
$12$	−1.64574	−	0.539952i	−0.475084	−	0.155871i
$13$	2.39248	−	3.72277i	0.663555	−	1.03251i	−0.332442	−	0.943124i	$-0.607873\pi$
$13$	2.39248	−	3.72277i	0.663555	−	1.03251i	0.995997	−	0.0893875i	$-0.0284910\pi$
$14$	0.999928	+	1.15398i	0.267242	+	0.308414i
$15$	2.90127	+	2.56567i	0.749104	+	0.662452i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.0211748	+	0.0721148i	−0.00513565	+	0.0174904i	−0.962021	−	0.272976i	$-0.911992\pi$
$17$	−0.0211748	+	0.0721148i	−0.00513565	+	0.0174904i	0.956885	+	0.290466i	$0.0938103\pi$
$18$	−2.62065	+	1.46020i	−0.617693	+	0.344173i
$19$	0.126511	+	0.430858i	0.0290237	+	0.0988455i	0.972731	−	0.231936i	$-0.0745059\pi$
$19$	0.126511	+	0.430858i	0.0290237	+	0.0988455i	−0.943707	+	0.330781i	$0.892688\pi$
$20$	−2.20602	+	0.365373i	−0.493280	+	0.0817000i
$21$	2.64342	+	0.0830986i	0.576841	+	0.0181336i
$22$	−1.54216			−0.328790
$23$	−4.78300	+	0.350566i	−0.997325	+	0.0730981i
$23$	−4.78300	+	0.350566i	−0.997325	+	0.0730981i
$24$	0.300243	−	1.70583i	0.0612868	−	0.348201i
$25$	4.85319	+	1.20272i	0.970638	+	0.240544i
$26$	4.02536	+	1.83832i	0.789439	+	0.360525i
$27$	−1.22038	+	5.05081i	−0.234862	+	0.972029i
$28$	−0.999928	+	1.15398i	−0.188969	+	0.218081i
$29$	−1.07283	+	3.65371i	−0.199219	+	0.678477i	0.797912	+	0.602774i	$0.205938\pi$
$29$	−1.07283	+	3.65371i	−0.199219	+	0.678477i	−0.997130	+	0.0757023i	$0.975880\pi$
$30$	−2.12666	+	3.23687i	−0.388273	+	0.590969i
$31$	−2.98547	−	6.53727i	−0.536207	−	1.17413i	−0.962931	−	0.269747i	$-0.913060\pi$
$31$	−2.98547	−	6.53727i	−0.536207	−	1.17413i	0.426725	−	0.904382i	$-0.359667\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−1.81176	+	1.96273i	−0.315388	+	0.341667i
$34$	−0.0743943	−	0.0106963i	−0.0127585	−	0.00183440i
$35$	3.07481	−	1.48430i	0.519738	−	0.250892i
$36$	−1.81830	−	2.38617i	−0.303050	−	0.397695i
$37$	−1.83669	−	2.11966i	−0.301951	−	0.348470i	0.584415	−	0.811455i	$-0.301324\pi$
$37$	−1.83669	−	2.11966i	−0.301951	−	0.348470i	−0.886366	+	0.462985i	$0.846778\pi$
$38$	−0.408468	+	0.186541i	−0.0662622	+	0.0302609i
$39$	7.06874	−	2.96343i	1.13190	−	0.474528i
$40$	−0.675603	−	2.13156i	−0.106822	−	0.337030i
$41$	4.70508	+	4.07697i	0.734810	+	0.636716i	0.939673	−	0.342074i	$-0.111129\pi$
$41$	4.70508	+	4.07697i	0.734810	+	0.636716i	−0.204863	+	0.978791i	$0.565675\pi$
$42$	0.293945	+	2.62834i	0.0453567	+	0.405561i
$43$	1.54435	−	3.38165i	0.235511	−	0.515697i	−0.754566	−	0.656224i	$-0.772152\pi$
$43$	1.54435	−	3.38165i	0.235511	−	0.515697i	0.990077	+	0.140527i	$0.0448797\pi$
$44$	−0.219473	−	1.52646i	−0.0330867	−	0.230123i
$45$	1.62116	+	6.50937i	0.241668	+	0.970359i
$46$	−1.02769	−	4.68443i	−0.151525	−	0.690681i
$47$	−7.94130			−1.15836			−0.579179	−	0.815200i	$-0.696627\pi$
$47$	−7.94130			−1.15836			−0.579179	+	0.815200i	$0.696627\pi$
$48$	1.73120	+	0.0544219i	0.249877	+	0.00785513i
$49$	−1.93936	+	4.24660i	−0.277051	+	0.606657i
$50$	−0.499799	+	4.97496i	−0.0706823	+	0.703565i
$51$	−0.101013	+	0.0821162i	−0.0141447	+	0.0114986i
$52$	−1.24674	+	4.24601i	−0.172892	+	0.588816i
$53$	−5.45190	−	8.48332i	−0.748876	−	1.16527i	−0.981267	−	0.192652i	$-0.938291\pi$
$53$	−5.45190	−	8.48332i	−0.748876	−	1.16527i	0.232391	−	0.972622i	$-0.425345\pi$
$54$	−5.17308	−	0.489153i	−0.703967	−	0.0665653i
$55$	−0.900709	+	3.32867i	−0.121452	+	0.448838i
$56$	−1.28454	−	0.825522i	−0.171653	−	0.110315i
$57$	−0.242464	+	0.739014i	−0.0321151	+	0.0978848i
$58$	−3.76920	−	0.541929i	−0.494920	−	0.0711587i
$59$	0.831298	−	1.29353i	0.108226	−	0.168403i	−0.782916	−	0.622127i	$-0.786269\pi$
$59$	0.831298	−	1.29353i	0.108226	−	0.168403i	0.891142	+	0.453725i	$0.149905\pi$
$60$	−3.50658	−	1.64436i	−0.452697	−	0.212286i
$61$	−3.72803	+	1.70254i	−0.477326	+	0.217987i	−0.639524	−	0.768771i	$-0.720869\pi$
$61$	−3.72803	+	1.70254i	−0.477326	+	0.217987i	0.162199	+	0.986758i	$0.448141\pi$
$62$	6.04585	−	3.88544i	0.767824	−	0.493451i
$63$	3.69045	+	2.71372i	0.464953	+	0.341897i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	6.31895	−	7.61484i	0.783770	−	0.944504i
$66$	−2.20059	−	1.51400i	−0.270874	−	0.186360i
$67$	1.56866	+	10.9103i	0.191643	+	1.33290i	0.827660	+	0.561229i	$0.189671\pi$
$67$	1.56866	+	10.9103i	0.191643	+	1.33290i	−0.636018	+	0.771674i	$0.719419\pi$
$68$		−	0.0751593i		−	0.00911440i
$69$	−7.16928	−	4.19541i	−0.863079	−	0.505068i
$70$	1.90678	+	2.83228i	0.227904	+	0.338522i
$71$	−6.98782	+	1.00470i	−0.829302	+	0.119236i	−0.543876	−	0.839165i	$-0.683044\pi$
$71$	−6.98782	+	1.00470i	−0.829302	+	0.119236i	−0.285425	+	0.958401i	$0.592135\pi$
$72$	2.10311	−	2.13938i	0.247854	−	0.252128i
$73$	−3.21126	−	10.9365i	−0.375849	−	1.28002i	−0.902775	−	0.430113i	$-0.858474\pi$
$73$	−3.21126	−	10.9365i	−0.375849	−	1.28002i	0.526926	−	0.849911i	$-0.323345\pi$
$74$	1.83669	−	2.11966i	0.213511	−	0.246405i
$75$	5.74451	+	6.48079i	0.663319	+	0.748337i
$76$	−0.242773	−	0.377763i	−0.0278480	−	0.0433323i
$77$	0.978209	+	2.14198i	0.111477	+	0.244101i
$78$	3.93925	+	6.57505i	0.446032	+	0.744478i
$79$	−4.68933	+	7.29674i	−0.527591	+	0.820947i	−0.998111	−	0.0614421i	$-0.980430\pi$
$79$	−4.68933	+	7.29674i	−0.527591	+	0.820947i	0.470520	+	0.882389i	$0.344066\pi$
$80$	2.01372	−	0.972079i	0.225141	−	0.108682i
$81$	−6.69999	+	6.00917i	−0.744444	+	0.667685i
$82$	−3.36587	+	5.23740i	−0.371699	+	0.578374i
$83$	3.99704	−	3.46346i	0.438732	−	0.380164i	−0.407301	−	0.913294i	$-0.633530\pi$
$83$	3.99704	−	3.46346i	0.438732	−	0.380164i	0.846033	+	0.533130i	$0.178984\pi$
$84$	−2.55975	+	0.665004i	−0.279292	+	0.0725579i
$85$	−0.0665378	+	0.154329i	−0.00721703	+	0.0167393i
$86$	3.56702	+	1.04737i	0.384641	+	0.112941i
$87$	−5.11785	+	4.16043i	−0.548691	+	0.446045i
$88$	1.47969	−	0.434477i	0.157736	−	0.0463154i
$89$	3.53383	−	7.73801i	0.374585	−	0.820227i	−0.624642	−	0.780912i	$-0.714755\pi$
$89$	3.53383	−	7.73801i	0.374585	−	0.820227i	0.999227	−	0.0393158i	$-0.0125178\pi$
$90$	−6.21240	+	2.53104i	−0.654844	+	0.266795i
$91$		−	6.75708i		−	0.708335i
$92$	4.49049	−	1.68389i	0.468166	−	0.175558i
$93$	2.15776	−	12.2593i	0.223749	−	1.27123i
$94$	−1.13017	−	7.86047i	−0.116568	−	0.810746i
$95$	0.164070	+	0.990605i	0.0168332	+	0.101634i
$96$	0.192507	+	1.72132i	0.0196476	+	0.175681i
$97$	−3.14175	+	3.62578i	−0.318997	+	0.368142i	−0.892489	−	0.451069i	$-0.851043\pi$
$97$	−3.14175	+	3.62578i	−0.318997	+	0.368142i	0.573492	+	0.819211i	$0.305588\pi$
$98$	−4.47937	−	1.31526i	−0.452485	−	0.132862i
$99$	−4.51218	+	1.02204i	−0.453492	+	0.102719i
$100$	−4.99545	+	0.213298i	−0.499545	+	0.0213298i
$101$	2.20987	−	1.91486i	0.219890	−	0.190536i	−0.537949	−	0.842978i	$-0.680801\pi$
$101$	2.20987	−	1.91486i	0.219890	−	0.190536i	0.757839	+	0.652441i	$0.226255\pi$
$102$	−0.0956561	−	0.0882987i	−0.00947136	−	0.00874288i
$103$	2.47829	−	17.2369i	0.244193	−	1.69840i	−0.386435	−	0.922317i	$-0.626294\pi$
$103$	2.47829	−	17.2369i	0.244193	−	1.69840i	0.630628	−	0.776085i	$-0.282797\pi$
$104$	−4.38022	−	0.629781i	−0.429516	−	0.0617551i
$105$	5.84480	+	0.900634i	0.570394	+	0.0878929i
$106$	7.62109	−	6.60371i	0.740226	−	0.641409i
$107$	15.6615	−	7.15239i	1.51406	−	0.691447i	0.526714	−	0.850042i	$-0.323424\pi$
$107$	15.6615	−	7.15239i	1.51406	−	0.691447i	0.987344	+	0.158595i	$0.0506964\pi$
$108$	−0.252032	−	5.19004i	−0.0242518	−	0.499412i
$109$	−4.09077	+	13.9319i	−0.391824	+	1.33443i	0.493617	+	0.869679i	$0.335675\pi$
$109$	−4.09077	+	13.9319i	−0.391824	+	1.33443i	−0.885441	+	0.464752i	$0.846144\pi$
$110$	−3.42297	−	0.417823i	−0.326368	−	0.0398378i
$111$	−0.539926	−	4.82780i	−0.0512475	−	0.458235i
$112$	0.634310	−	1.38895i	0.0599367	−	0.131243i
$113$	9.61164	−	1.38195i	0.904187	−	0.130003i	0.325491	−	0.945545i	$-0.394471\pi$
$113$	9.61164	−	1.38195i	0.904187	−	0.130003i	0.578697	+	0.815543i	$0.303561\pi$
$114$	−0.765998	−	0.134823i	−0.0717423	−	0.0126273i
$115$	−10.7113	−	0.517759i	−0.998834	−	0.0482813i
$116$		−	3.80796i		−	0.353560i
$117$	12.9961	+	2.71098i	1.20149	+	0.250630i
$118$	1.39866	+	0.638749i	0.128758	+	0.0588016i
$119$	0.0323325	+	0.110114i	0.00296391	+	0.0100942i
$120$	1.12858	−	3.70490i	0.103025	−	0.338210i
$121$	8.27250	+	2.42902i	0.752045	+	0.220820i
$122$	−2.21576	−	3.44779i	−0.200605	−	0.312148i
$123$	2.71140	+	10.4368i	0.244479	+	0.941055i
$124$	4.70630	+	5.43136i	0.422638	+	0.487751i
$125$	10.4463	+	3.98444i	0.934341	+	0.356380i
$126$	−2.16089	+	4.03909i	−0.192508	+	0.359831i
$127$	−9.56945	−	1.37588i	−0.849151	−	0.122090i	−0.296018	−	0.955182i	$-0.595659\pi$
$127$	−9.56945	−	1.37588i	−0.849151	−	0.122090i	−0.553133	+	0.833093i	$0.686568\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	5.52361	−	3.30931i	0.486327	−	0.291369i
$130$	8.43661	+	5.17093i	0.739940	+	0.453521i
$131$	−8.43094	−	13.1188i	−0.736615	−	1.14620i	−0.984154	−	0.177317i	$-0.943258\pi$
$131$	−8.43094	−	13.1188i	−0.736615	−	1.14620i	0.247539	−	0.968878i	$-0.420378\pi$
$132$	1.18541	−	2.39366i	0.103177	−	0.208341i
$133$	0.518191	+	0.449015i	0.0449328	+	0.0389345i
$134$	−10.5760	+	3.10539i	−0.913627	+	0.268265i
$135$	−4.07718	+	10.8801i	−0.350908	+	0.936410i
$136$	0.0743943	−	0.0106963i	0.00637925	−	0.000917198i
$137$			5.79820i			0.495373i	0.968840	+	0.247687i	$0.0796703\pi$
$137$			5.79820i			0.495373i	−0.968840	+	0.247687i	$0.920330\pi$
$138$	3.13241	−	7.69337i	0.266649	−	0.654903i
$139$	−7.74202			−0.656669			−0.328335	−	0.944561i	$-0.606487\pi$
$139$	−7.74202			−0.656669			−0.328335	+	0.944561i	$0.606487\pi$
$140$	−2.53208	+	2.29045i	−0.214000	+	0.193578i
$141$	−11.3319	−	7.79628i	−0.954315	−	0.656565i
$142$	−1.98894	−	6.77371i	−0.166908	−	0.568437i
$143$	5.15760	+	4.46908i	0.431300	+	0.373723i
$144$	2.41690	+	1.77724i	0.201409	+	0.148103i
$145$	−3.37115	+	7.81908i	−0.279958	+	0.649339i
$146$	10.3682	−	4.73500i	0.858079	−	0.391872i
$147$	−6.93641	+	4.15575i	−0.572106	+	0.342761i
$148$	2.35947	+	1.51634i	0.193947	+	0.124642i
$149$	0.816379	−	5.67804i	0.0668804	−	0.465163i	−0.928668	−	0.370912i	$-0.879045\pi$
$149$	0.816379	−	5.67804i	0.0668804	−	0.465163i	0.995548	−	0.0942513i	$-0.0300457\pi$
$150$	−5.59729	+	6.60835i	−0.457017	+	0.539570i
$151$	7.53875	+	4.84486i	0.613495	+	0.394269i	0.810166	−	0.586200i	$-0.199377\pi$
$151$	7.53875	+	4.84486i	0.613495	+	0.394269i	−0.196671	+	0.980469i	$0.563013\pi$
$152$	0.339367	−	0.294063i	0.0275263	−	0.0238517i
$153$	−0.224758	+	0.0180074i	−0.0181706	+	0.00145581i
$154$	−1.98096	+	1.27309i	−0.159631	+	0.102588i
$155$	−4.85537	−	15.3189i	−0.389993	−	1.23045i
$156$	−5.94751	+	4.83488i	−0.476182	+	0.387100i
$157$	17.0227	−	4.99833i	1.35856	−	0.398910i	0.480306	−	0.877101i	$-0.340526\pi$
$157$	17.0227	−	4.99833i	1.35856	−	0.398910i	0.878256	+	0.478191i	$0.158707\pi$
$158$	−7.88983	−	3.60316i	−0.627681	−	0.286652i
$159$	0.548799	−	17.4576i	0.0435226	−	1.38448i
$160$	1.24877	+	1.85488i	0.0987237	+	0.146641i
$161$	−5.85454	+	4.39879i	−0.461403	+	0.346673i
$162$	−6.90151	−	5.77660i	−0.542234	−	0.453853i
$163$	8.41298	−	1.20960i	0.658956	−	0.0947435i	0.195279	−	0.980748i	$-0.437439\pi$
$163$	8.41298	−	1.20960i	0.658956	−	0.0947435i	0.463677	+	0.886004i	$0.346530\pi$
$164$	−5.66311	−	2.58625i	−0.442214	−	0.201953i
$165$	−4.55315	+	3.86559i	−0.354462	+	0.300936i
$166$	3.99704	+	3.46346i	0.310231	+	0.268816i
$167$	−11.7390	−	3.44687i	−0.908387	−	0.266727i	−0.206025	−	0.978547i	$-0.566053\pi$
$167$	−11.7390	−	3.44687i	−0.908387	−	0.266727i	−0.702362	+	0.711820i	$0.747871\pi$
$168$	−1.02253	−	2.43906i	−0.0788896	−	0.188177i
$169$	−2.73467	−	5.98810i	−0.210359	−	0.460623i
$170$	−0.162227	−	0.0438972i	−0.0124422	−	0.00336677i
$171$	−1.07150	+	0.816501i	−0.0819398	+	0.0624394i
$172$	−0.529070	+	3.67977i	−0.0403412	+	0.280580i
$173$	2.39213	−	16.6376i	0.181870	−	1.26494i	−0.670465	−	0.741941i	$-0.733905\pi$
$173$	2.39213	−	16.6376i	0.181870	−	1.26494i	0.852335	−	0.522995i	$-0.175186\pi$
$174$	−4.84643	−	4.47367i	−0.367407	−	0.339148i
$175$	7.22698	−	2.46147i	0.546308	−	0.186070i
$176$	0.640637	+	1.40280i	0.0482898	+	0.105740i
$177$	2.45612	−	1.02968i	0.184614	−	0.0773956i
$178$	8.16216	+	2.39663i	0.611780	+	0.179635i
$179$	8.11150	+	7.02865i	0.606282	+	0.525346i	0.903012	−	0.429615i	$-0.141351\pi$
$179$	8.11150	+	7.02865i	0.606282	+	0.525346i	−0.296730	+	0.954961i	$0.595896\pi$
$180$	−3.38939	−	5.78896i	−0.252630	−	0.431483i
$181$	4.56732	+	2.08583i	0.339486	+	0.155038i	0.577861	−	0.816135i	$-0.303887\pi$
$181$	4.56732	+	2.08583i	0.339486	+	0.155038i	−0.238375	+	0.971173i	$0.576615\pi$
$182$	6.68830	−	0.961633i	0.495770	−	0.0712810i
$183$	−6.99116	−	1.23051i	−0.516802	−	0.0909622i
$184$	2.30582	+	4.20514i	0.169987	+	0.310007i
$185$	−3.50243	−	5.20240i	−0.257504	−	0.382488i
$186$	12.4416	+	0.391115i	0.912264	+	0.0286780i
$187$	−0.105433	−	0.0481498i	−0.00771005	−	0.00352106i
$188$	7.61963	−	2.23732i	0.555718	−	0.163174i
$189$	2.60193	+	7.49540i	0.189263	+	0.545210i
$190$	−0.957172	+	0.303378i	−0.0694406	+	0.0220093i
$191$	7.60228	−	4.88569i	0.550082	−	0.353516i	−0.235889	−	0.971780i	$-0.575800\pi$
$191$	7.60228	−	4.88569i	0.550082	−	0.353516i	0.785970	+	0.618264i	$0.212164\pi$
$192$	−1.67640	+	0.435517i	−0.120984	+	0.0314307i
$193$	13.6079	−	11.7913i	0.979515	−	0.848755i	−0.00898712	−	0.999960i	$-0.502861\pi$
$193$	13.6079	−	11.7913i	0.979515	−	0.848755i	0.988502	+	0.151205i	$0.0483153\pi$
$194$	−4.03599	−	2.59377i	−0.289767	−	0.186222i
$195$	16.4926	−	4.66245i	1.18106	−	0.333885i
$196$	0.664394	−	4.62096i	0.0474567	−	0.330069i
$197$	1.21200	+	0.778906i	0.0863515	+	0.0554947i	0.583104	−	0.812397i	$-0.301838\pi$
$197$	1.21200	+	0.778906i	0.0863515	+	0.0554947i	−0.496753	+	0.867892i	$0.665474\pi$
$198$	−1.65379	−	4.32081i	−0.117530	−	0.307066i
$199$	−10.6391	+	4.85870i	−0.754183	+	0.344424i	−0.755130	−	0.655576i	$-0.772426\pi$
$199$	−10.6391	+	4.85870i	−0.754183	+	0.344424i	0.000946248		1.00000i	$0.499699\pi$
$200$	−0.922054	−	4.91425i	−0.0651990	−	0.347490i
$201$	−8.47264	+	17.1085i	−0.597614	+	1.20674i
$202$	2.20987	+	1.91486i	0.155486	+	0.134729i
$203$	1.63813	+	5.57896i	0.114974	+	0.391566i
$204$	0.0737867	−	0.107249i	0.00516610	−	0.00750891i
$205$	9.33878	+	10.3240i	0.652248	+	0.721059i
$206$	17.4141			1.21330
$207$	−6.11142	−	13.0250i	−0.424773	−	0.905300i
$208$		−	4.42527i		−	0.306837i
$209$	−0.685455	+	0.0985535i	−0.0474139	+	0.00681709i
$210$	−0.0596655	+	5.91348i	−0.00411731	+	0.408069i
$211$	−24.0656	+	7.06631i	−1.65675	+	0.486465i	−0.970540	−	0.240941i	$-0.922544\pi$
$211$	−24.0656	+	7.06631i	−1.65675	+	0.486465i	−0.686207	+	0.727406i	$0.740726\pi$
$212$	7.62109	+	6.60371i	0.523419	+	0.453545i
$213$	−10.9576	−	5.42655i	−0.750804	−	0.371821i
$214$	9.30845	+	14.4842i	0.636313	+	0.990122i
$215$	4.34403	−	7.08748i	0.296260	−	0.483362i
$216$	5.10134	−	0.988086i	0.347102	−	0.0672307i
$217$	−9.23161	−	5.93279i	−0.626682	−	0.402744i
$218$	−14.3722	−	2.06642i	−0.973411	−	0.139955i
$219$	6.15450	−	18.7585i	0.415883	−	1.26758i
$220$	−0.0735700	−	3.44759i	−0.00496009	−	0.232437i
$221$	0.217807	+	0.251362i	0.0146513	+	0.0169084i
$222$	4.70182	−	1.22150i	0.315566	−	0.0819816i
$223$	−0.982571	−	1.52891i	−0.0657978	−	0.102383i	0.806796	−	0.590831i	$-0.201200\pi$
$223$	−0.982571	−	1.52891i	−0.0657978	−	0.102383i	−0.872593	+	0.488447i	$0.837563\pi$
$224$	1.46508	+	0.430186i	0.0978898	+	0.0287430i
$225$	1.83471	+	14.8874i	0.122314	+	0.992491i
$226$	2.73576	+	9.31714i	0.181980	+	0.619767i
$227$	12.1334	+	5.54114i	0.805323	+	0.367778i	0.775159	−	0.631766i	$-0.217670\pi$
$227$	12.1334	+	5.54114i	0.805323	+	0.367778i	0.0301638	+	0.999545i	$0.490397\pi$
$228$	0.0244380	−	0.777389i	0.00161845	−	0.0514838i
$229$		−	20.2203i		−	1.33619i	−0.744075	−	0.668096i	$-0.767110\pi$
$229$		−	20.2203i		−	1.33619i	0.744075	−	0.668096i	$-0.232890\pi$
$230$	−1.01189	−	10.6760i	−0.0667219	−	0.703952i
$231$	−0.707005	+	4.01685i	−0.0465175	+	0.264289i
$232$	3.76920	−	0.541929i	0.247460	−	0.0355794i
$233$	5.44463	−	11.9221i	0.356690	−	0.781042i	−0.643193	−	0.765704i	$-0.722391\pi$
$233$	5.44463	−	11.9221i	0.356690	−	0.781042i	0.999882	−	0.0153372i	$-0.00488217\pi$
$234$	−0.833853	+	13.2496i	−0.0545107	+	0.866153i
$235$	−17.6265	−	2.15156i	−1.14982	−	0.140352i
$236$	−0.433197	+	1.47533i	−0.0281987	+	0.0960359i
$237$	−13.8549	+	5.80840i	−0.899975	+	0.377296i
$238$	−0.104392	+	0.0476743i	−0.00676674	+	0.00309027i
$239$	6.31658	−	5.47335i	0.408585	−	0.354041i	−0.426188	−	0.904634i	$-0.640144\pi$
$239$	6.31658	−	5.47335i	0.408585	−	0.354041i	0.834774	+	0.550593i	$0.185598\pi$
$240$	3.82781	+	0.589833i	0.247084	+	0.0380735i
$241$	18.7450	+	2.69512i	1.20747	+	0.173608i	0.716512	−	0.697575i	$-0.245738\pi$
$241$	18.7450	+	2.69512i	1.20747	+	0.173608i	0.490958	+	0.871183i	$0.336647\pi$
$242$	−1.22700	+	8.53398i	−0.0788746	+	0.548585i
$243$	−15.4600	+	1.99716i	−0.991759	+	0.128118i
$244$	3.09736	−	2.68388i	0.198288	−	0.171818i
$245$	−5.45513	+	8.90029i	−0.348515	+	0.568618i
$246$	−9.94470	+	4.16912i	−0.634051	+	0.265813i
$247$	1.90666	+	0.559846i	0.121318	+	0.0356221i
$248$	−4.70630	+	5.43136i	−0.298850	+	0.344892i
$249$	9.10379	−	1.01814i	0.576929	−	0.0645219i
$250$	−2.45723	+	10.9070i	−0.155409	+	0.689817i
$251$	0.108126	+	0.752035i	0.00682487	+	0.0474680i	0.992949	−	0.118540i	$-0.0378214\pi$
$251$	0.108126	+	0.752035i	0.00682487	+	0.0474680i	−0.986124	+	0.166008i	$0.946912\pi$
$252$	−4.30550	−	1.56408i	−0.271221	−	0.0985275i
$253$	0.514611	−	7.37802i	0.0323533	−	0.463852i
$254$		−	9.66786i		−	0.606615i
$255$	−0.246456	+	0.154897i	−0.0154337	+	0.00970001i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−25.5672	+	7.50720i	−1.59484	+	0.468286i	−0.954103	−	0.299477i	$-0.903188\pi$
$257$	−25.5672	+	7.50720i	−1.59484	+	0.468286i	−0.640733	+	0.767764i	$0.721370\pi$
$258$	4.06172	+	4.99642i	0.252871	+	0.311064i
$259$	−4.10912	−	1.20655i	−0.255329	−	0.0749712i
$260$	−3.91765	+	9.08664i	−0.242962	+	0.563529i
$261$	−11.3874	+	0.912346i	−0.704861	+	0.0564728i
$262$	11.7854	−	10.2121i	0.728106	−	0.630907i
$263$	−9.89708	+	15.4002i	−0.610280	+	0.949614i	0.389314	+	0.921105i	$0.372712\pi$
$263$	−9.89708	+	15.4002i	−0.610280	+	0.949614i	−0.999594	+	0.0285088i	$0.990924\pi$
$264$	2.53799	+	0.832693i	0.156203	+	0.0512487i
$265$	−9.80259	−	20.3066i	−0.602168	−	1.24743i
$266$	−0.370698	+	0.576818i	−0.0227290	+	0.0353670i
$267$	12.6393	−	7.57247i	0.773513	−	0.463428i
$268$	−4.57890	−	10.0264i	−0.279701	−	0.612460i
$269$	−4.11521	−	6.40339i	−0.250909	−	0.390422i	0.692837	−	0.721095i	$-0.256361\pi$
$269$	−4.11521	−	6.40339i	−0.250909	−	0.390422i	−0.943745	+	0.330673i	$0.892724\pi$
$270$	−11.3496	−	2.48728i	−0.690715	−	0.151371i
$271$	−6.62768	+	7.64875i	−0.402603	+	0.464628i	−0.920459	−	0.390839i	$-0.872185\pi$
$271$	−6.62768	+	7.64875i	−0.402603	+	0.464628i	0.517856	+	0.855468i	$0.326730\pi$
$272$	0.0211748	+	0.0721148i	0.00128391	+	0.00437260i
$273$	6.63368	−	9.64203i	0.401489	−	0.583562i
$274$	−5.73918	+	0.825169i	−0.346716	+	0.0498503i
$275$	−2.90106	+	7.14426i	−0.174940	+	0.430815i
$276$	8.06085	+	2.00565i	0.485206	+	0.120726i
$277$			2.53450i			0.152283i	0.997097	+	0.0761416i	$0.0242601\pi$
$277$			2.53450i			0.152283i	−0.997097	+	0.0761416i	$0.975740\pi$
$278$	−1.10180	−	7.66321i	−0.0660818	−	0.459609i
$279$	15.1145	−	15.3751i	0.904879	−	0.920483i
$280$	−2.62749	−	2.18035i	−0.157022	−	0.130301i
$281$	−11.1025	+	12.8130i	−0.662319	+	0.764357i	−0.983154	−	0.182778i	$-0.941491\pi$
$281$	−11.1025	+	12.8130i	−0.662319	+	0.764357i	0.320835	+	0.947135i	$0.396036\pi$
$282$	6.10423	−	12.3260i	0.363502	−	0.734005i
$283$	−25.1660	+	16.1732i	−1.49596	+	0.961397i	−0.500552	+	0.865706i	$0.666870\pi$
$283$	−25.1660	+	16.1732i	−1.49596	+	0.961397i	−0.995411	+	0.0956910i	$0.969494\pi$
$284$	6.42171	−	2.93270i	0.381058	−	0.174023i
$285$	−0.738394	+	1.57462i	−0.0437387	+	0.0932724i
$286$	−3.68959	+	5.74112i	−0.218170	+	0.339479i
$287$	9.40948	+	1.35288i	0.555424	+	0.0798579i
$288$	−1.41519	+	2.64523i	−0.0833907	+	0.155872i
$289$	14.2966	+	9.18784i	0.840974	+	0.540461i
$290$	−8.21926	−	2.22406i	−0.482652	−	0.130601i
$291$	−8.04269	+	2.08943i	−0.471471	+	0.122485i
$292$	6.16236	+	9.58881i	0.360625	+	0.561143i
$293$	−6.18090	+	21.0502i	−0.361092	+	1.22977i	0.556031	+	0.831162i	$0.312324\pi$
$293$	−6.18090	+	21.0502i	−0.361092	+	1.22977i	−0.917123	+	0.398604i	$0.869495\pi$
$294$	−5.10061	−	6.27439i	−0.297473	−	0.365930i
$295$	2.19560	−	2.64587i	0.127833	−	0.154049i
$296$	−1.16512	+	2.55125i	−0.0677211	+	0.148289i
$297$	−7.44204	−	2.97138i	−0.431831	−	0.172417i
$298$	5.73643			0.332302
$299$	−10.1382	+	18.6447i	−0.586305	+	1.07825i
$300$	−7.33767	−	4.59985i	−0.423640	−	0.265573i
$301$	−0.807855	−	5.61875i	−0.0465640	−	0.323859i
$302$	−3.72267	+	8.15151i	−0.214216	+	0.469067i
$303$	5.03327	−	0.562905i	0.289154	−	0.0323380i
$304$	0.339367	+	0.294063i	0.0194640	+	0.0168657i
$305$	−8.73599	+	2.76889i	−0.500221	+	0.158546i
$306$	−0.0498104	−	0.219907i	−0.00284747	−	0.0125713i
$307$	−22.8416	+	10.4314i	−1.30364	+	0.595351i	−0.941575	−	0.336803i	$-0.890654\pi$
$307$	−22.8416	+	10.4314i	−1.30364	+	0.595351i	−0.362061	+	0.932154i	$0.617927\pi$
$308$	−1.54205	−	1.77962i	−0.0878665	−	0.101403i
$309$	20.4585	−	22.1632i	1.16384	−	1.26082i
$310$	14.4720	−	6.98606i	0.821956	−	0.396782i
$311$	−27.2890	−	3.92357i	−1.54742	−	0.222485i	−0.684948	−	0.728592i	$-0.740175\pi$
$311$	−27.2890	−	3.92357i	−1.54742	−	0.222485i	−0.862471	+	0.506106i	$0.831084\pi$
$312$	−5.63209	−	5.19890i	−0.318854	−	0.294330i
$313$	−0.0716998	−	0.0827460i	−0.00405271	−	0.00467708i	0.753720	−	0.657196i	$-0.228258\pi$
$313$	−0.0716998	−	0.0827460i	−0.00405271	−	0.00467708i	−0.757772	+	0.652519i	$0.773712\pi$
$314$	7.37004	+	16.1381i	0.415915	+	0.910727i
$315$	7.45606	+	7.02322i	0.420101	+	0.395714i
$316$	2.44365	−	8.32231i	0.137466	−	0.468166i
$317$	12.0872	−	13.9494i	0.678887	−	0.783478i	−0.306852	−	0.951757i	$-0.599276\pi$
$317$	12.0872	−	13.9494i	0.678887	−	0.783478i	0.985739	+	0.168280i	$0.0538212\pi$
$318$	17.3580	−	1.94127i	0.973390	−	0.108861i
$319$	−5.34180	−	2.43952i	−0.299083	−	0.136587i
$320$	−1.65828	+	1.50003i	−0.0927008	+	0.0838544i
$321$	29.3700	+	5.16941i	1.63927	+	0.288529i
$322$	−5.18720	−	5.16894i	−0.289071	−	0.288054i
$323$	−0.0337501			−0.00187790
$324$	4.73562	−	7.65336i	0.263090	−	0.425187i
$325$	16.0886	−	15.1898i	0.892436	−	0.842580i
$326$	2.39458	+	8.15521i	0.132624	+	0.451675i
$327$	−19.5148	+	15.8640i	−1.07917	+	0.877284i
$328$	1.75399	−	5.97353i	0.0968477	−	0.329833i
$329$	−10.2009	+	6.55572i	−0.562394	+	0.361429i
$330$	−4.47422	−	3.95667i	−0.246298	−	0.217808i
$331$	−0.680280	−	0.785085i	−0.0373916	−	0.0431522i	0.736746	−	0.676170i	$-0.236361\pi$
$331$	−0.680280	−	0.785085i	−0.0373916	−	0.0431522i	−0.774137	+	0.633018i	$0.781816\pi$
$332$	−2.85936	+	4.44926i	−0.156928	+	0.244185i
$333$	3.96919	−	7.41910i	0.217510	−	0.406564i
$334$	1.74116	−	12.1100i	0.0952718	−	0.662630i
$335$	0.525836	+	24.6414i	0.0287295	+	1.34630i
$336$	2.26871	−	1.35923i	0.123768	−	0.0741522i
$337$	11.5204	+	25.2263i	0.627559	+	1.37416i	0.909892	+	0.414846i	$0.136164\pi$
$337$	11.5204	+	25.2263i	0.627559	+	1.37416i	−0.282333	+	0.959316i	$0.591108\pi$
$338$	5.53796	−	3.55903i	0.301225	−	0.193586i
$339$	15.0721	+	7.46414i	0.818602	+	0.405397i
$340$	0.0203631	−	0.166823i	0.00110435	−	0.00904725i
$341$	10.6341	−	3.12247i	0.575871	−	0.169091i
$342$	−0.960681	−	0.944395i	−0.0519477	−	0.0510670i
$343$	2.53562	+	17.6356i	0.136911	+	0.952234i
$344$	−3.71761			−0.200440
$345$	−14.7762	−	11.2545i	−0.795524	−	0.605922i
$346$	16.8087			0.903643
$347$	2.24184	+	15.5924i	0.120348	+	0.837042i	0.957162	+	0.289554i	$0.0935069\pi$
$347$	2.24184	+	15.5924i	0.120348	+	0.837042i	−0.836813	+	0.547488i	$0.815584\pi$
$348$	3.73841	−	5.43377i	0.200400	−	0.291281i
$349$	−12.5921	+	3.69737i	−0.674038	+	0.197916i	−0.600801	−	0.799399i	$-0.705151\pi$
$349$	−12.5921	+	3.69737i	−0.674038	+	0.197916i	−0.0732379	+	0.997315i	$0.523333\pi$
$350$	3.46492	+	6.80311i	0.185208	+	0.363642i
$351$	15.8833	+	16.6272i	0.847787	+	0.887492i
$352$	−1.29735	+	0.833756i	−0.0691489	+	0.0444393i
$353$	12.3316	+	27.0025i	0.656346	+	1.43720i	0.885888	+	0.463899i	$0.153550\pi$
$353$	12.3316	+	27.0025i	0.656346	+	1.43720i	−0.229542	+	0.973299i	$0.573723\pi$
$354$	1.36874	+	2.28459i	0.0727479	+	0.121424i
$355$	−15.7823	+	0.336787i	−0.837639	+	0.0178748i
$356$	−1.21064	+	8.42016i	−0.0641636	+	0.446268i
$357$	−0.0619665	+	0.188870i	−0.00327962	+	0.00999606i
$358$	−5.80273	+	9.02922i	−0.306684	+	0.477209i
$359$	24.6651	+	28.4650i	1.30177	+	1.50233i	0.734015	+	0.679133i	$0.237644\pi$
$359$	24.6651	+	28.4650i	1.30177	+	1.50233i	0.567759	+	0.823195i	$0.307810\pi$
$360$	5.24767	−	4.17874i	0.276577	−	0.220239i
$361$	15.8142	−	10.1632i	0.832325	−	0.534903i
$362$	−1.41460	+	4.81768i	−0.0743496	+	0.253211i
$363$	9.41979	+	11.5875i	0.494411	+	0.608187i
$364$	1.90369	+	6.48337i	0.0997805	+	0.339821i
$365$	−4.16462	−	25.1447i	−0.217986	−	1.31613i
$366$	0.223043	−	7.09512i	0.0116586	−	0.370868i
$367$	2.24178			0.117020			0.0585101	−	0.998287i	$-0.481365\pi$
$367$	2.24178			0.117020			0.0585101	+	0.998287i	$0.481365\pi$
$368$	−3.83419	+	2.88080i	−0.199871	+	0.150172i
$369$	−6.37716	+	17.5547i	−0.331982	+	0.913861i
$370$	4.65100	−	4.20716i	0.241794	−	0.218720i
$371$	−14.0063	−	6.39648i	−0.727173	−	0.332089i
$372$	1.38349	+	12.3706i	0.0717308	+	0.641388i
$373$	0.540194	−	0.623417i	0.0279702	−	0.0322793i	−0.741592	−	0.670851i	$-0.765929\pi$
$373$	0.540194	−	0.623417i	0.0279702	−	0.0322793i	0.769562	+	0.638572i	$0.220474\pi$
$374$	0.0326550	−	0.111213i	0.00168855	−	0.00575067i
$375$	10.9946	+	15.9411i	0.567760	+	0.823194i
$376$	3.29894	+	7.22366i	0.170130	+	0.372532i
$377$	11.0352	+	12.7353i	0.568342	+	0.655902i
$378$	−7.04881	+	3.64215i	−0.362552	+	0.187332i
$379$	−4.45047	−	0.639881i	−0.228605	−	0.0328685i	0.0270602	−	0.999634i	$-0.491385\pi$
$379$	−4.45047	−	0.639881i	−0.228605	−	0.0328685i	−0.255665	+	0.966765i	$0.582295\pi$
$380$	−0.436510	−	0.904255i	−0.0223925	−	0.0463873i
$381$	−12.3044	−	11.3580i	−0.630373	−	0.581888i
$382$	5.91788	+	6.82959i	0.302785	+	0.349432i
$383$	−27.1518	+	12.3998i	−1.38739	+	0.633601i	−0.962410	−	0.271601i	$-0.912447\pi$
$383$	−27.1518	+	12.3998i	−1.38739	+	0.633601i	−0.424982	+	0.905202i	$0.639720\pi$
$384$	−0.669661	−	1.59736i	−0.0341735	−	0.0815149i
$385$	1.59089	+	5.01935i	0.0810795	+	0.255810i
$386$	13.6079	+	11.7913i	0.692622	+	0.600160i
$387$	11.1308	+	0.700509i	0.565810	+	0.0356089i
$388$	1.99299	−	4.36404i	0.101179	−	0.221551i
$389$	3.02213	+	21.0194i	0.153228	+	1.06572i	0.910763	+	0.412929i	$0.135494\pi$
$389$	3.02213	+	21.0194i	0.153228	+	1.06572i	−0.757535	+	0.652795i	$0.773597\pi$
$390$	6.96214	+	15.6612i	0.352542	+	0.793036i
$391$	0.0759982	−	0.352348i	0.00384339	−	0.0178190i
$392$	4.66848			0.235794
$393$	0.848675	−	26.9969i	0.0428100	−	1.36181i
$394$	−0.598492	+	1.31051i	−0.0301516	+	0.0660228i
$395$	−12.3853	+	14.9253i	−0.623174	+	0.750973i
$396$	4.04147	−	2.25187i	0.203091	−	0.113161i
$397$	10.0165	−	34.1130i	0.502712	−	1.71208i	−0.182028	−	0.983293i	$-0.558266\pi$
$397$	10.0165	−	34.1130i	0.502712	−	1.71208i	0.684740	−	0.728787i	$-0.259916\pi$
$398$	−6.32334	−	9.83931i	−0.316960	−	0.493200i
$399$	0.298618	+	1.14945i	0.0149496	+	0.0575445i
$400$	4.73300	−	1.61204i	0.236650	−	0.0806019i
$401$	−11.4322	−	7.34702i	−0.570896	−	0.366893i	0.223118	−	0.974791i	$-0.428376\pi$
$401$	−11.4322	−	7.34702i	−0.570896	−	0.366893i	−0.794015	+	0.607898i	$0.792013\pi$
$402$	−18.1401	−	5.95161i	−0.904747	−	0.296839i
$403$	−31.4795	−	4.52606i	−1.56810	−	0.225459i
$404$	−1.58088	+	2.45989i	−0.0786515	+	0.122384i
$405$	−16.4993	+	11.5227i	−0.819859	+	0.572566i
$406$	−5.28905	+	2.41543i	−0.262491	+	0.119876i
$407$	3.63869	−	2.33844i	0.180363	−	0.115912i
$408$	0.116658	+	0.0577726i	0.00577543	+	0.00286017i
$409$	−22.8084	+	26.3222i	−1.12780	+	1.30155i	−0.179650	+	0.983731i	$0.557496\pi$
$409$	−22.8084	+	26.3222i	−1.12780	+	1.30155i	−0.948151	+	0.317821i	$0.897049\pi$
$410$	−8.88986	+	10.7130i	−0.439039	+	0.529076i
$411$	−5.69231	+	8.27374i	−0.280781	+	0.408114i
$412$	2.47829	+	17.2369i	0.122097	+	0.849201i
$413$		−	2.34784i		−	0.115529i
$414$	12.0227	−	7.90286i	0.590882	−	0.388404i
$415$	9.81017	−	6.60453i	0.481562	−	0.324204i
$416$	4.38022	−	0.629781i	0.214758	−	0.0308776i
$417$	−11.0475	−	7.60063i	−0.540998	−	0.372204i
$418$	−0.195101	−	0.664452i	−0.00954269	−	0.0324994i
$419$	20.7734	−	23.9738i	1.01485	−	1.17119i	0.0296855	−	0.999559i	$-0.490549\pi$
$419$	20.7734	−	23.9738i	1.01485	−	1.17119i	0.985161	−	0.171635i	$-0.0549051\pi$
$420$	−5.86178	+	0.782518i	−0.286026	+	0.0381830i
$421$	−2.78229	−	4.32932i	−0.135600	−	0.210998i	0.766812	−	0.641872i	$-0.221842\pi$
$421$	−2.78229	−	4.32932i	−0.135600	−	0.210998i	−0.902412	+	0.430874i	$0.858206\pi$
$422$	−10.4193	−	22.8150i	−0.507203	−	1.11062i
$423$	−8.51611	−	22.2498i	−0.414068	−	1.08182i
$424$	−5.45190	+	8.48332i	−0.264768	+	0.411987i
$425$	−0.189499	+	0.324519i	−0.00919207	+	0.0157415i
$426$	3.81188	−	11.6184i	0.184686	−	0.562912i
$427$	−3.38331	+	5.26454i	−0.163730	+	0.254769i
$428$	−13.0121	+	11.2750i	−0.628962	+	0.544999i
$429$	2.97217	+	11.4406i	0.143498	+	0.552356i
$430$	7.63356	+	3.29116i	0.368123	+	0.158714i
$431$	1.19289	+	0.350265i	0.0574597	+	0.0168717i	0.310336	−	0.950627i	$-0.399558\pi$
$431$	1.19289	+	0.350265i	0.0574597	+	0.0168717i	−0.252876	+	0.967499i	$0.581377\pi$
$432$	1.70403	+	4.90880i	0.0819849	+	0.236175i
$433$	−10.5570	+	3.09981i	−0.507337	+	0.148968i	−0.525377	−	0.850870i	$-0.676076\pi$
$433$	−10.5570	+	3.09981i	−0.507337	+	0.148968i	0.0180399	+	0.999837i	$0.494257\pi$
$434$	4.55861	−	9.98197i	0.218820	−	0.479150i
$435$	−12.4868	+	7.84787i	−0.598694	+	0.376277i
$436$		−	14.5200i		−	0.695383i
$437$	−0.756147	−	2.01644i	−0.0361714	−	0.0964595i
$438$	19.4435	+	3.42224i	0.929045	+	0.163521i
$439$	2.39759	+	16.6756i	0.114431	+	0.795884i	0.963520	+	0.267635i	$0.0862421\pi$
$439$	2.39759	+	16.6756i	0.114431	+	0.795884i	−0.849090	+	0.528249i	$0.822849\pi$
$440$	3.40203	−	0.563465i	0.162186	−	0.0268621i
$441$	−13.9778	−	0.879682i	−0.665609	−	0.0418896i
$442$	−0.217807	+	0.251362i	−0.0103600	+	0.0119561i
$443$	−4.83376	−	1.41932i	−0.229659	−	0.0674339i	0.164878	−	0.986314i	$-0.447277\pi$
$443$	−4.83376	−	1.41932i	−0.229659	−	0.0674339i	−0.394537	+	0.918880i	$0.629095\pi$
$444$	1.87820	+	4.48013i	0.0891356	+	0.212617i
$445$	9.94015	−	16.2178i	0.471208	−	0.768798i
$446$	1.37351	−	1.19016i	0.0650377	−	0.0563555i
$447$	6.73928	−	7.30082i	0.318757	−	0.345317i
$448$	−0.217305	+	1.51139i	−0.0102667	+	0.0714065i
$449$	5.24080	+	0.753513i	0.247328	+	0.0355605i	0.264864	−	0.964286i	$-0.414673\pi$
$449$	5.24080	+	0.753513i	0.247328	+	0.0355605i	−0.0175355	+	0.999846i	$0.505582\pi$
$450$	−14.4747	+	3.93473i	−0.682346	+	0.185485i
$451$	−7.25599	+	6.28735i	−0.341671	+	0.296060i
$452$	−8.83297	+	4.03388i	−0.415468	+	0.189738i
$453$	6.00105	+	14.3145i	0.281954	+	0.672552i
$454$	−3.75798	+	12.7985i	−0.176371	+	0.600663i
$455$	1.83072	−	14.9980i	0.0858253	−	0.703116i
$456$	0.772954	−	0.0864446i	0.0361969	−	0.00404814i
$457$	0.00287378	−	0.00629269i	0.000134430	−	0.000294360i	−0.909565	−	0.415562i	$-0.863585\pi$
$457$	0.00287378	−	0.00629269i	0.000134430	−	0.000294360i	0.909699	+	0.415268i	$0.136312\pi$
$458$	20.0144	−	2.87764i	0.935213	−	0.134463i
$459$	−0.338397	−	0.194957i	−0.0157950	−	0.00909983i
$460$	10.4233	−	2.52094i	0.485988	−	0.117539i
$461$			16.6775i			0.776748i	0.921502	+	0.388374i	$0.126963\pi$
$461$			16.6775i			0.776748i	−0.921502	+	0.388374i	$0.873037\pi$
$462$	−4.07658	−	0.128151i	−0.189660	−	0.00596215i
$463$	−10.4491	−	4.77196i	−0.485613	−	0.221772i	0.157536	−	0.987513i	$-0.449645\pi$
$463$	−10.4491	−	4.77196i	−0.485613	−	0.221772i	−0.643149	+	0.765741i	$0.722372\pi$
$464$	1.07283	+	3.65371i	0.0498047	+	0.169619i
$465$	8.11081	−	26.6261i	0.376130	−	1.23476i
$466$	12.5756	+	3.69252i	0.582553	+	0.171053i
$467$	10.7050	+	16.6573i	0.495368	+	0.770807i	0.995462	−	0.0951638i	$-0.0303375\pi$
$467$	10.7050	+	16.6573i	0.495368	+	0.770807i	−0.500094	+	0.865971i	$0.666701\pi$
$468$	−13.2334	+	1.06025i	−0.611714	+	0.0490099i
$469$	11.0217	+	12.7197i	0.508934	+	0.587341i
$470$	−0.378846	−	17.7533i	−0.0174749	−	0.818897i
$471$	29.1977	+	9.57949i	1.34536	+	0.441400i
$472$	−1.52197	−	0.218826i	−0.0700541	−	0.0100723i
$473$	4.82303	+	3.09957i	0.221763	+	0.142519i
$474$	−7.72104	−	12.8873i	−0.354639	−	0.591933i
$475$	0.0957810	+	2.24319i	0.00439473	+	0.102925i
$476$	−0.0620456	−	0.0965448i	−0.00284386	−	0.00442513i
$477$	17.9219	−	24.3724i	0.820588	−	1.11594i
$478$	6.31658	+	5.47335i	0.288914	+	0.250345i
$479$	28.4605	−	8.35677i	1.30039	−	0.381830i	0.443015	−	0.896514i	$-0.353909\pi$
$479$	28.4605	−	8.35677i	1.30039	−	0.381830i	0.857380	+	0.514684i	$0.172091\pi$
$480$	−0.0390754	+	3.87279i	−0.00178354	+	0.176768i
$481$	−12.2853	+	1.76635i	−0.560159	+	0.0805388i
$482$			18.9377i			0.862590i
$483$	−12.6726	+	0.529231i	−0.576623	+	0.0240809i
$484$	−8.62174			−0.391897
$485$	−7.95576	+	7.19654i	−0.361252	+	0.326778i
$486$	−4.17702	−	15.0184i	−0.189473	−	0.681249i
$487$	1.79475	+	6.11234i	0.0813277	+	0.276977i	0.990110	−	0.140294i	$-0.0448048\pi$
$487$	1.79475	+	6.11234i	0.0813277	+	0.276977i	−0.908782	+	0.417271i	$0.862987\pi$
$488$	3.09736	+	2.68388i	0.140211	+	0.121493i
$489$	13.1924	+	6.53329i	0.596582	+	0.295446i
$490$	−9.58604	−	4.13296i	−0.433053	−	0.186708i
$491$	−16.0080	+	7.31060i	−0.722430	+	0.329923i	−0.742473	−	0.669876i	$-0.766347\pi$
$491$	−16.0080	+	7.31060i	−0.722430	+	0.329923i	0.0200427	+	0.999799i	$0.493620\pi$
$492$	−5.54196	−	9.25015i	−0.249851	−	0.417029i
$493$	−0.240769	−	0.154733i	−0.0108437	−	0.00696883i
$494$	−0.282801	+	1.96693i	−0.0127238	+	0.0884962i
$495$	−10.2921	+	1.04601i	−0.462596	+	0.0470147i
$496$	−6.04585	−	3.88544i	−0.271467	−	0.174461i
$497$	−8.14671	+	7.05917i	−0.365430	+	0.316647i
$498$	2.30338	+	8.86623i	0.103217	+	0.397305i
$499$	−17.5745	+	11.2945i	−0.786744	+	0.505610i	−0.871266	−	0.490812i	$-0.836700\pi$
$499$	−17.5745	+	11.2945i	−0.786744	+	0.505610i	0.0845214	+	0.996422i	$0.473064\pi$
$500$	−11.1457	−	0.879997i	−0.498449	−	0.0393546i
$501$	−13.3670	−	16.4431i	−0.597193	−	0.734623i
$502$	−0.728992	+	0.214051i	−0.0325365	+	0.00955358i
$503$	18.9156	+	8.63845i	0.843403	+	0.385169i	0.789779	−	0.613392i	$-0.210195\pi$
$503$	18.9156	+	8.63845i	0.843403	+	0.385169i	0.0536243	+	0.998561i	$0.482923\pi$
$504$	0.935419	−	4.48427i	0.0416669	−	0.199745i
$505$	5.42381	−	3.65149i	0.241357	−	0.162489i
$506$	7.37616	−	0.540629i	0.327910	−	0.0240339i
$507$	1.97650	−	11.2295i	0.0877792	−	0.498718i
$508$	9.56945	−	1.37588i	0.424576	−	0.0610448i
$509$	−32.2664	−	14.7356i	−1.43018	−	0.653142i	−0.458340	−	0.888777i	$-0.651556\pi$
$509$	−32.2664	−	14.7356i	−1.43018	−	0.653142i	−0.971842	+	0.235635i	$0.924283\pi$
$510$	−0.188395	−	0.221904i	−0.00834225	−	0.00982606i
$511$	−13.1533	−	11.3974i	−0.581869	−	0.504192i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	−2.33057	+	0.113174i	−0.102897	+	0.00499676i
$514$	−11.0694	−	24.2386i	−0.488249	−	1.06912i
$515$	10.1708	−	37.5874i	0.448181	−	1.65630i
$516$	−4.36752	+	4.73144i	−0.192269	+	0.208290i
$517$	1.74290	−	12.1221i	0.0766526	−	0.533130i
$518$	0.609478	−	4.23901i	0.0267789	−	0.186251i
$519$	19.7473	−	21.3927i	0.866808	−	0.939034i
$520$	−9.55169	−	2.58461i	−0.418869	−	0.113342i
$521$	−14.1015	−	30.8780i	−0.617799	−	1.35279i	−0.917109	−	0.398636i	$-0.869484\pi$
$521$	−14.1015	−	30.8780i	−0.617799	−	1.35279i	0.299310	−	0.954156i	$-0.403243\pi$
$522$	−2.52365	−	11.1416i	−0.110457	−	0.487656i
$523$	30.1696	+	8.85861i	1.31923	+	0.387360i	0.864214	−	0.503125i	$-0.167816\pi$
$523$	30.1696	+	8.85861i	1.31923	+	0.387360i	0.455013	+	0.890485i	$0.349635\pi$
$524$	11.7854	+	10.2121i	0.514849	+	0.446119i
$525$	12.7291	+	3.58259i	0.555542	+	0.156357i
$526$	−16.6519	−	7.60467i	−0.726057	−	0.331579i
$527$	0.534651	−	0.0768712i	0.0232898	−	0.00334856i
$528$	−0.463023	+	2.63067i	−0.0201505	+	0.114485i
$529$	22.7542	−	3.35351i	0.989313	−	0.145805i
$530$	18.7049	−	12.5927i	0.812488	−	0.546994i
$531$	4.51565	+	0.941965i	0.195962	+	0.0408778i
$532$	−0.623702	−	0.284835i	−0.0270409	−	0.0123492i
$533$	26.4345	−	7.76186i	1.14500	−	0.336203i
$534$	9.29415	+	11.4330i	0.402197	+	0.494753i
$535$	36.7001	−	11.6322i	1.58668	−	0.502902i
$536$	9.27270	−	5.95920i	0.400520	−	0.257398i
$537$	4.67442	+	17.9929i	0.201716	+	0.776452i
$538$	5.75256	−	4.98462i	0.248010	−	0.214902i
$539$	−6.05665	−	3.89237i	−0.260878	−	0.167656i
$540$	0.846744	−	11.5881i	0.0364381	−	0.498670i
$541$	1.63207	−	11.3513i	0.0701682	−	0.488030i	−0.924188	−	0.381938i	$-0.875257\pi$
$541$	1.63207	−	11.3513i	0.0701682	−	0.488030i	0.994356	−	0.106093i	$-0.0338340\pi$
$542$	−8.51411	−	5.47169i	−0.365713	−	0.235029i
$543$	4.46961	+	7.46028i	0.191809	+	0.320151i
$544$	−0.0683673	+	0.0312223i	−0.00293122	+	0.00133864i
$545$	−12.8544	+	29.8148i	−0.550624	+	1.27712i
$546$	10.4880	+	5.19396i	0.448843	+	0.222281i
$547$	−23.7002	−	20.5363i	−1.01335	−	0.878070i	−0.0207813	−	0.999784i	$-0.506615\pi$
$547$	−23.7002	−	20.5363i	−1.01335	−	0.878070i	−0.992565	+	0.121714i	$0.961161\pi$
$548$	−1.63354	−	5.56333i	−0.0697814	−	0.237654i
$549$	−8.76801	−	8.61937i	−0.374210	−	0.367866i
$550$	−7.48441	−	1.85479i	−0.319136	−	0.0790886i
$551$	−1.70995			−0.0728464
$552$	−0.838056	+	8.26424i	−0.0356700	+	0.351749i
$553$			13.2441i			0.563195i
$554$	−2.50870	+	0.360697i	−0.106584	+	0.0153245i
$555$	0.109595	−	10.8620i	0.00465206	−	0.461068i
$556$	7.42841	−	2.18118i	0.315035	−	0.0925026i
$557$	−5.71257	−	4.94997i	−0.242049	−	0.209737i	0.525385	−	0.850865i	$-0.323921\pi$
$557$	−5.71257	−	4.94997i	−0.242049	−	0.209737i	−0.767434	+	0.641128i	$0.778467\pi$
$558$	17.3696	+	12.7725i	0.735315	+	0.540703i
$559$	−8.89430	−	13.8398i	−0.376189	−	0.585361i
$560$	1.78422	−	2.91104i	0.0753972	−	0.123014i
$561$	−0.103178	−	0.172215i	−0.00435617	−	0.00727094i
$562$	−14.2626	−	9.16601i	−0.601631	−	0.386645i
$563$	−27.3594	−	3.93368i	−1.15306	−	0.165785i	−0.460847	−	0.887479i	$-0.652454\pi$
$563$	−27.3594	−	3.93368i	−1.15306	−	0.165785i	−0.692212	+	0.721694i	$0.743364\pi$
$564$	13.0693	+	4.28792i	0.550317	+	0.180554i
$565$	21.7084	−	0.463246i	0.913277	−	0.0194889i
$566$	−19.5901	−	22.6082i	−0.823433	−	0.950292i
$567$	−3.64569	+	13.2500i	−0.153105	+	0.556447i
$568$	3.81675	+	5.93898i	0.160147	+	0.249194i
$569$	−15.1019	−	4.43431i	−0.633104	−	0.185896i	−0.0505935	−	0.998719i	$-0.516111\pi$
$569$	−15.1019	−	4.43431i	−0.633104	−	0.185896i	−0.582510	+	0.812823i	$0.697929\pi$
$570$	−1.66368	−	0.506787i	−0.0696837	−	0.0212270i
$571$	−7.62777	−	25.9778i	−0.319212	−	1.08714i	−0.950277	−	0.311406i	$-0.899200\pi$
$571$	−7.62777	−	25.9778i	−0.319212	−	1.08714i	0.631065	−	0.775730i	$-0.282618\pi$
$572$	−6.20776	−	2.83499i	−0.259560	−	0.118537i
$573$	15.6445	+	0.491803i	0.653560	+	0.0205454i
$574$			9.50624i			0.396783i
$575$	−23.6345	−	4.05126i	−0.985625	−	0.168949i
$576$	−2.81971	−	1.02433i	−0.117488	−	0.0426803i
$577$	8.64026	−	1.24228i	0.359699	−	0.0517169i	0.0399034	−	0.999204i	$-0.487295\pi$
$577$	8.64026	−	1.24228i	0.359699	−	0.0517169i	0.319795	+	0.947487i	$0.396386\pi$
$578$	−7.05971	+	15.4586i	−0.293645	+	0.642993i
$579$	30.9937	−	3.46624i	1.28805	−	0.144052i
$580$	1.03170	−	8.45212i	0.0428391	−	0.350955i
$581$	2.27519	−	7.74858i	0.0943907	−	0.321465i
$582$	−3.21276	−	7.66347i	−0.133173	−	0.317661i
$583$	14.1460	−	6.46028i	0.585869	−	0.267557i
$584$	−8.61422	+	7.46426i	−0.356459	+	0.308873i
$585$	28.1115	+	9.53833i	1.16227	+	0.394361i
$586$	−21.7156	−	3.12223i	−0.897062	−	0.128978i
$587$	−2.03095	+	14.1256i	−0.0838264	+	0.583025i	0.904008	+	0.427516i	$0.140611\pi$
$587$	−2.03095	+	14.1256i	−0.0838264	+	0.583025i	−0.987834	+	0.155510i	$0.950298\pi$
$588$	5.48463	−	5.94163i	0.226182	−	0.245029i
$589$	2.43894	−	2.11335i	0.100495	−	0.0870791i
$590$	2.93141	+	1.79671i	0.120684	+	0.0739693i
$591$	0.964786	+	2.30133i	0.0396860	+	0.0946640i
$592$	−2.69110	−	0.790178i	−0.110603	−	0.0324761i
$593$	30.9210	−	35.6848i	1.26977	−	1.46540i	0.449658	−	0.893201i	$-0.351546\pi$
$593$	30.9210	−	35.6848i	1.26977	−	1.46540i	0.820117	−	0.572196i	$-0.193909\pi$
$594$	1.88202	−	7.78917i	0.0772203	−	0.319593i
$595$	0.0419314	+	0.253169i	0.00171902	+	0.0103789i
$596$	0.816379	+	5.67804i	0.0334402	+	0.232582i
$597$	−19.9514	−	3.51164i	−0.816556	−	0.143722i
$598$	−19.8978	−	7.38154i	−0.813681	−	0.301854i
$599$		−	10.1000i		−	0.412676i	−0.978481	−	0.206338i	$-0.933845\pi$
$599$		−	10.1000i		−	0.412676i	0.978481	−	0.206338i	$-0.0661546\pi$
$600$	3.50877	−	7.91761i	0.143245	−	0.323235i
$601$	−2.79191	+	6.11343i	−0.113884	+	0.249372i	−0.957988	−	0.286808i	$-0.907406\pi$
$601$	−2.79191	+	6.11343i	−0.113884	+	0.249372i	0.844104	+	0.536180i	$0.180133\pi$
$602$	5.44659	−	1.59926i	0.221987	−	0.0651811i
$603$	−28.8861	+	16.0951i	−1.17633	+	0.655441i
$604$	−8.59833	−	2.52470i	−0.349861	−	0.102728i
$605$	17.7035	+	7.63274i	0.719749	+	0.310315i
$606$	1.27348	+	4.90193i	0.0517318	+	0.199127i
$607$	27.5224	−	23.8483i	1.11710	−	0.967972i	0.117415	−	0.993083i	$-0.462539\pi$
$607$	27.5224	−	23.8483i	1.11710	−	0.967972i	0.999685	+	0.0251109i	$0.00799388\pi$
$608$	−0.242773	+	0.377763i	−0.00984576	+	0.0153203i
$609$	−3.13954	+	9.56913i	−0.127221	+	0.387761i
$610$	−3.98397	−	8.25301i	−0.161306	−	0.334155i
$611$	−18.9994	+	29.5637i	−0.768634	+	1.19602i
$612$	0.210580	−	0.0805995i	0.00851219	−	0.00325804i
$613$	20.2525	+	44.3468i	0.817992	+	1.79115i	0.568288	+	0.822829i	$0.307606\pi$
$613$	20.2525	+	44.3468i	0.817992	+	1.79115i	0.249703	+	0.968322i	$0.419667\pi$
$614$	−13.5759	−	21.1245i	−0.547879	−	0.852516i
$615$	3.19054	+	23.9001i	0.128655	+	0.963744i
$616$	1.54205	−	1.77962i	0.0621310	−	0.0717030i
$617$	−3.58628	−	12.2137i	−0.144378	−	0.491707i	0.855271	−	0.518180i	$-0.173390\pi$
$617$	−3.58628	−	12.2137i	−0.144378	−	0.491707i	−0.999650	+	0.0264735i	$0.991572\pi$
$618$	24.8491	+	17.0961i	0.999579	+	0.687707i
$619$	−20.2238	+	2.90775i	−0.812864	+	0.116872i	−0.536196	−	0.844093i	$-0.680139\pi$
$619$	−20.2238	+	2.90775i	−0.812864	+	0.116872i	−0.276668	+	0.960966i	$0.589230\pi$
$620$	8.97454	+	13.3305i	0.360426	+	0.535366i
$621$	4.06644	−	24.5859i	0.163180	−	0.986596i
$622$		−	27.5697i		−	1.10544i
$623$	−1.84856	−	12.8570i	−0.0740610	−	0.515105i
$624$	4.34445	−	6.31464i	0.173917	−	0.252788i
$625$	22.1069	+	11.6741i	0.884277	+	0.466963i
$626$	0.0716998	−	0.0827460i	0.00286570	−	0.00330719i
$627$	−1.07486	−	0.532306i	−0.0429260	−	0.0212582i
$628$	−14.9250	+	9.59172i	−0.595572	+	0.382751i
$629$	0.191750	−	0.0875694i	0.00764559	−	0.00349162i
$630$	−5.89063	+	8.37968i	−0.234688	+	0.333854i
$631$	−17.6051	+	27.3940i	−0.700847	+	1.09054i	0.290193	+	0.956968i	$0.406281\pi$
$631$	−17.6051	+	27.3940i	−0.700847	+	1.09054i	−0.991039	+	0.133570i	$0.957356\pi$
$632$	8.58537	+	1.23439i	0.341508	+	0.0491014i
$633$	−41.2778	−	13.5429i	−1.64064	−	0.538280i
$634$	15.5276	+	9.97900i	0.616681	+	0.396317i
$635$	−20.8675	−	5.64657i	−0.828102	−	0.224077i
$636$	4.39181	+	16.9051i	0.174147	+	0.670330i
$637$	11.1692	+	17.3797i	0.442542	+	0.688608i
$638$	1.65447	−	5.63461i	0.0655011	−	0.223076i
$639$	−10.3086	−	18.5009i	−0.407800	−	0.731886i
$640$	−1.72076	−	1.42793i	−0.0680191	−	0.0564437i
$641$	9.15806	−	20.0534i	0.361722	−	0.792060i	−0.638035	−	0.770007i	$-0.720253\pi$
$641$	9.15806	−	20.0534i	0.361722	−	0.792060i	0.999757	−	0.0220528i	$-0.00702020\pi$
$642$	−0.937007	+	29.8068i	−0.0369807	+	1.17638i
$643$	1.63341			0.0644152			0.0322076	−	0.999481i	$-0.489746\pi$
$643$	1.63341			0.0644152			0.0322076	+	0.999481i	$0.489746\pi$
$644$	4.37811	−	5.87002i	0.172522	−	0.231311i
$645$	13.1568	−	5.84880i	0.518047	−	0.230296i
$646$	−0.00480313	−	0.0334065i	−0.000188977	−	0.00131436i
$647$	7.93010	−	17.3645i	0.311765	−	0.682669i	−0.687279	−	0.726393i	$-0.741195\pi$
$647$	7.93010	−	17.3645i	0.311765	−	0.682669i	0.999044	+	0.0437243i	$0.0139223\pi$
$648$	8.24941	+	3.59823i	0.324067	+	0.141352i
$649$	1.79207	+	1.55284i	0.0703450	+	0.0609543i
$650$	17.3249	+	13.7631i	0.679537	+	0.539834i
$651$	−7.34861	−	17.5288i	−0.288015	−	0.687009i
$652$	−7.73141	+	3.53082i	−0.302785	+	0.138277i
$653$	13.9775	+	16.1309i	0.546983	+	0.631252i	0.960177	−	0.279391i	$-0.0901325\pi$
$653$	13.9775	+	16.1309i	0.546983	+	0.631252i	−0.413195	+	0.910643i	$0.635587\pi$
$654$	−18.4798	−	17.0584i	−0.722618	−	0.667038i
$655$	−15.1589	−	31.4026i	−0.592309	−	1.22700i
$656$	6.16234	+	0.886011i	0.240599	+	0.0345929i
$657$	27.1981	−	20.7254i	1.06110	−	0.808575i
$658$	−7.94073	−	9.16409i	−0.309562	−	0.357253i
$659$	8.73973	+	19.1373i	0.340452	+	0.745485i	0.999981	−	0.00619385i	$-0.00197158\pi$
$659$	8.73973	+	19.1373i	0.340452	+	0.745485i	−0.659529	+	0.751679i	$0.729244\pi$
$660$	3.27965	−	4.99178i	0.127660	−	0.194305i
$661$	2.85263	−	9.71516i	0.110954	−	0.377876i	−0.885230	−	0.465154i	$-0.845999\pi$
$661$	2.85263	−	9.71516i	0.110954	−	0.377876i	0.996184	+	0.0872785i	$0.0278170\pi$
$662$	0.680280	−	0.785085i	0.0264398	−	0.0305132i
$663$	0.0640277	+	0.572511i	0.00248663	+	0.0222345i
$664$	−4.81090	−	2.19707i	−0.186699	−	0.0852627i
$665$	1.02852	+	1.13703i	0.0398843	+	0.0440919i
$666$	7.90846	+	2.87294i	0.306447	+	0.111324i
$667$	3.85046	−	17.8518i	0.149090	−	0.691224i
$668$	12.2345			0.473368
$669$	0.0989075	−	3.14631i	0.00382398	−	0.121643i
$670$	−24.3158	+	4.02732i	−0.939400	+	0.155589i
$671$	−1.78066	−	6.06437i	−0.0687416	−	0.234112i
$672$	1.66827	+	2.05218i	0.0643549	+	0.0791646i
$673$	1.67119	−	5.69154i	0.0644196	−	0.219393i	−0.920992	−	0.389582i	$-0.872620\pi$
$673$	1.67119	−	5.69154i	0.0644196	−	0.219393i	0.985411	+	0.170189i	$0.0544378\pi$
$674$	−23.3300	+	14.9933i	−0.898637	+	0.577519i
$675$	−11.9975	+	23.0448i	−0.461782	+	0.886993i
$676$	4.31094	+	4.97509i	0.165805	+	0.191350i
$677$	9.44586	−	14.6980i	0.363034	−	0.564892i	−0.610905	−	0.791704i	$-0.709194\pi$
$677$	9.44586	−	14.6980i	0.363034	−	0.564892i	0.973938	+	0.226813i	$0.0728305\pi$
$678$	−5.24319	+	15.9809i	−0.201364	+	0.613743i
$679$	−1.04254	+	7.25103i	−0.0400090	+	0.278269i
$680$	0.168023	−	0.00358553i	0.00644339	−	0.000137499i
$681$	11.8738	+	19.8188i	0.455006	+	0.759457i
$682$	4.60408	+	10.0815i	0.176299	+	0.386042i
$683$	14.1226	−	9.07606i	0.540387	−	0.347286i	−0.241803	−	0.970325i	$-0.577739\pi$
$683$	14.1226	−	9.07606i	0.540387	−	0.347286i	0.782190	+	0.623040i	$0.214103\pi$
$684$	0.798063	−	1.08530i	0.0305147	−	0.0414976i
$685$	−1.57092	+	12.8696i	−0.0600219	+	0.491724i
$686$	−17.0953	+	5.01962i	−0.652700	+	0.191650i
$687$	19.8510	−	28.8533i	0.757362	−	1.10082i
$688$	−0.529070	−	3.67977i	−0.0201706	−	0.140290i
$689$	−44.6250			−1.70008
$690$	9.03708	−	16.2275i	0.344036	−	0.617770i
$691$	48.2189			1.83433			0.917166	−	0.398505i	$-0.130471\pi$
$691$	48.2189			1.83433			0.917166	+	0.398505i	$0.130471\pi$
$692$	2.39213	+	16.6376i	0.0909352	+	0.632468i
$693$	−4.95235	+	5.03775i	−0.188124	+	0.191368i
$694$	−15.1146	+	4.43805i	−0.573743	+	0.168466i
$695$	−17.1841	−	2.09757i	−0.651831	−	0.0795653i
$696$	5.91049	+	2.92706i	0.224037	+	0.110950i
$697$	−0.393639	+	0.252977i	−0.0149102	+	0.00958217i
$698$	−5.45177	−	11.9377i	−0.206353	−	0.451849i
$699$	19.4736	−	11.6670i	0.736559	−	0.441288i
$700$	−6.24076	+	4.39784i	−0.235878	+	0.166223i
$701$	−2.27772	+	15.8419i	−0.0860282	+	0.598340i	0.900513	+	0.434829i	$0.143191\pi$
$701$	−2.27772	+	15.8419i	−0.0860282	+	0.598340i	−0.986542	+	0.163511i	$0.947718\pi$
$702$	−14.1975	+	18.0879i	−0.535850	+	0.682684i
$703$	0.680908	−	1.05951i	0.0256809	−	0.0399603i
$704$	−1.00990	−	1.16549i	−0.0380621	−	0.0439260i
$705$	−23.0398	−	20.3747i	−0.867731	−	0.767357i
$706$	−24.9727	+	16.0490i	−0.939859	+	0.604011i
$707$	1.25790	−	4.28401i	0.0473081	−	0.161117i
$708$	−2.06654	+	1.67994i	−0.0776653	+	0.0631361i
$709$	8.89931	+	30.3083i	0.334220	+	1.13825i	0.939589	+	0.342305i	$0.111208\pi$
$709$	8.89931	+	30.3083i	0.334220	+	1.13825i	−0.605368	+	0.795945i	$0.706974\pi$
$710$	−2.57942	−	15.5738i	−0.0968039	−	0.584473i
$711$	−25.4726	−	5.31360i	−0.955299	−	0.199275i
$712$	−8.50675			−0.318804
$713$	16.5713	+	30.2212i	0.620599	+	1.13179i
$714$	−0.195766	−	0.0344568i	−0.00732637	−	0.00128951i
$715$	10.2369	+	11.3169i	0.382840	+	0.423228i
$716$	−9.76313	−	4.45867i	−0.364865	−	0.166628i
$717$	14.3868	−	1.60898i	0.537286	−	0.0600884i
$718$	−24.6651	+	28.4650i	−0.920494	+	1.06231i
$719$	1.32460	−	4.51118i	0.0493993	−	0.168239i	−0.931099	−	0.364767i	$-0.881149\pi$
$719$	1.32460	−	4.51118i	0.0493993	−	0.168239i	0.980498	+	0.196528i	$0.0629668\pi$
$720$	4.88303	+	4.59956i	0.181980	+	0.171416i
$721$	−11.0460	−	24.1873i	−0.411374	−	0.900782i
$722$	12.3103	+	14.2069i	0.458142	+	0.528724i
$723$	24.1023	+	22.2484i	0.896373	+	0.827429i
$724$	−4.96996	−	0.714572i	−0.184707	−	0.0265569i
$725$	−9.60102	+	16.4418i	−0.356573	+	0.610634i
$726$	−10.1290	+	10.9730i	−0.375922	+	0.407246i
$727$	−23.5744	−	27.2063i	−0.874325	−	1.00902i	−0.999857	−	0.0169347i	$-0.994609\pi$
$727$	−23.5744	−	27.2063i	−0.874325	−	1.00902i	0.125532	−	0.992090i	$-0.459936\pi$
$728$	−6.14646	+	2.80699i	−0.227803	+	0.104034i
$729$	−24.0213	−	12.3278i	−0.889680	−	0.456586i
$730$	24.2961	−	7.70069i	0.899238	−	0.285015i
$731$	0.211166	+	0.182976i	0.00781025	+	0.00676762i
$732$	7.05465	−	0.788969i	0.260747	−	0.0291611i
$733$	0.546364	−	1.19637i	0.0201804	−	0.0441889i	−0.899273	−	0.437387i	$-0.855904\pi$
$733$	0.546364	−	1.19637i	0.0201804	−	0.0441889i	0.919454	+	0.393198i	$0.128631\pi$
$734$	0.319039	+	2.21897i	0.0117760	+	0.0819036i
$735$	−16.5219	+	7.34477i	−0.609421	+	0.270916i
$736$	−3.39714	−	3.38518i	−0.125220	−	0.124779i
$737$	−16.9985			−0.626146
$738$	−18.2836	−	3.81396i	−0.673028	−	0.140394i
$739$	−4.76050	+	10.4240i	−0.175118	+	0.383455i	−0.976756	−	0.214355i	$-0.931235\pi$
$739$	−4.76050	+	10.4240i	−0.175118	+	0.383455i	0.801638	+	0.597810i	$0.203962\pi$
$740$	4.82624	+	4.00492i	0.177416	+	0.147224i
$741$	2.17109	+	2.67071i	0.0797570	+	0.0981111i
$742$	4.33806	−	14.7741i	0.159255	−	0.542374i
$743$	22.8197	+	35.5081i	0.837173	+	1.30267i	0.951008	+	0.309167i	$0.100050\pi$
$743$	22.8197	+	35.5081i	0.837173	+	1.30267i	−0.113835	+	0.993500i	$0.536313\pi$
$744$	−12.0478	+	3.12994i	−0.441695	+	0.114749i
$745$	3.35040	−	12.3818i	0.122749	−	0.453633i
$746$	0.693949	+	0.445974i	0.0254073	+	0.0163283i
$747$	13.9902	+	7.48470i	0.511875	+	0.273851i
$748$	0.114728	+	0.0164954i	0.00419487	+	0.000603131i
$749$	14.2134	−	22.1164i	0.519345	−	0.808117i
$750$	−14.2141	+	13.1514i	−0.519027	+	0.480220i
$751$	15.7618	−	7.19819i	0.575158	−	0.262666i	−0.106529	−	0.994310i	$-0.533974\pi$
$751$	15.7618	−	7.19819i	0.575158	−	0.262666i	0.681687	+	0.731644i	$0.261247\pi$
$752$	−6.68065	+	4.29339i	−0.243618	+	0.156564i
$753$	−0.584010	+	1.17927i	−0.0212825	+	0.0429749i
$754$	−11.0352	+	12.7353i	−0.401879	+	0.463793i
$755$	15.4203	+	12.7961i	0.561203	+	0.465698i
$756$	−4.60823	−	6.45874i	−0.167600	−	0.234902i
$757$	4.35875	+	30.3158i	0.158422	+	1.10185i	0.901543	+	0.432689i	$0.142435\pi$
$757$	4.35875	+	30.3158i	0.158422	+	1.10185i	−0.743122	+	0.669156i	$0.766656\pi$
$758$		−	4.49623i		−	0.163311i
$759$	7.97761	−	10.0229i	0.289569	−	0.363807i
$760$	0.832929	−	0.560755i	0.0302135	−	0.0203407i
$761$	3.43249	−	0.493518i	0.124428	−	0.0178900i	−0.0798196	−	0.996809i	$-0.525434\pi$
$761$	3.43249	−	0.493518i	0.124428	−	0.0178900i	0.204247	+	0.978919i	$0.434525\pi$
$762$	9.49130	−	13.7956i	0.343833	−	0.499761i
$763$	6.24632	+	21.2730i	0.226132	+	0.770135i
$764$	−5.91788	+	6.82959i	−0.214101	+	0.247086i
$765$	−0.503749	−	0.0209252i	−0.0182131	−	0.000756553i
$766$	−16.1377	−	25.1108i	−0.583079	−	0.907288i
$767$	−2.82663	−	6.18947i	−0.102064	−	0.223489i
$768$	1.48580	−	0.890172i	0.0536141	−	0.0321213i
$769$	9.85737	−	15.3384i	0.355466	−	0.553115i	−0.616763	−	0.787149i	$-0.711556\pi$
$769$	9.85737	−	15.3384i	0.355466	−	0.553115i	0.972228	+	0.234034i	$0.0751926\pi$
$770$	−4.74186	+	2.28903i	−0.170885	+	0.0824909i
$771$	−43.8532	−	14.3878i	−1.57934	−	0.518166i
$772$	−9.73466	+	15.1474i	−0.350358	+	0.545168i
$773$	−17.7827	+	15.4088i	−0.639599	+	0.554216i	−0.913141	−	0.407644i	$-0.866350\pi$
$773$	−17.7827	+	15.4088i	−0.639599	+	0.554216i	0.273542	+	0.961860i	$0.411805\pi$
$774$	0.890699	+	11.1172i	0.0320155	+	0.399599i
$775$	−6.62654	−	35.3173i	−0.238032	−	1.26864i
$776$	4.60325	+	1.35164i	0.165247	+	0.0485209i
$777$	−4.67901	−	5.75577i	−0.167859	−	0.206487i
$778$	−20.3753	+	5.98273i	−0.730491	+	0.214491i
$779$	−1.16135	+	2.54300i	−0.0416097	+	0.0911125i
$780$	−14.5110	+	9.12009i	−0.519577	+	0.326552i
$781$		−	10.8872i		−	0.389573i
$782$	0.359578	+	0.0250802i	0.0128585	+	0.000896867i
$783$	−17.1449	−	9.87755i	−0.612710	−	0.352995i
$784$	0.664394	+	4.62096i	0.0237284	+	0.165034i
$785$	39.1378	−	6.48223i	1.39689	−	0.231361i
$786$	26.8429	−	3.00202i	0.957453	−	0.107078i
$787$	−7.44282	+	8.58948i	−0.265308	+	0.306182i	−0.872735	−	0.488193i	$-0.837656\pi$
$787$	−7.44282	+	8.58948i	−0.265308	+	0.306182i	0.607427	+	0.794375i	$0.292202\pi$
$788$	−1.38235	−	0.405894i	−0.0492442	−	0.0144594i
$789$	−29.2416	+	12.2589i	−1.04103	+	0.436430i
$790$	−16.5360	−	10.1352i	−0.588325	−	0.360593i
$791$	11.2057	−	9.70978i	0.398428	−	0.345240i
$792$	2.80411	+	3.67986i	0.0996397	+	0.130758i
$793$	−2.58109	+	17.9519i	−0.0916573	+	0.637490i
$794$	35.1912	+	5.05974i	1.24889	+	0.179563i
$795$	5.94796	−	38.6002i	0.210952	−	1.36901i
$796$	8.83925	−	7.65926i	0.313299	−	0.271475i
$797$	−0.0605070	+	0.0276326i	−0.00214327	+	0.000978797i	−0.416486	−	0.909142i	$-0.636739\pi$
$797$	−0.0605070	+	0.0276326i	−0.00214327	+	0.000978797i	0.414343	+	0.910121i	$0.364011\pi$
$798$	−1.09525	+	0.459163i	−0.0387715	+	0.0162542i
$799$	0.168156	−	0.572685i	0.00594892	−	0.0202602i
$800$	2.26921	+	4.45541i	0.0802286	+	0.157523i
$801$	25.4699	+	1.60293i	0.899933	+	0.0566366i
$802$	5.64527	−	12.3614i	0.199341	−	0.436497i
$803$	17.3990	−	2.50160i	0.613998	−	0.0882796i
$804$	3.30942	−	18.8025i	0.116714	−	0.663112i
$805$	−14.1865	+	8.17733i	−0.500008	+	0.288213i
$806$		−	31.8032i		−	1.12022i
$807$	0.414245	−	13.1774i	0.0145821	−	0.463866i
$808$	−2.65983	−	1.21471i	−0.0935727	−	0.0427332i
$809$	−7.33430	−	24.9783i	−0.257860	−	0.878192i	−0.982055	−	0.188596i	$-0.939606\pi$
$809$	−7.33430	−	24.9783i	−0.257860	−	0.878192i	0.724194	−	0.689596i	$-0.242212\pi$
$810$	−13.7535	−	14.6916i	−0.483248	−	0.516209i
$811$	6.79938	+	1.99648i	0.238758	+	0.0701058i	0.398923	−	0.916985i	$-0.369384\pi$
$811$	6.79938	+	1.99648i	0.238758	+	0.0701058i	−0.160164	+	0.987090i	$0.551202\pi$
$812$	−3.14355	−	4.89146i	−0.110317	−	0.171657i
$813$	−16.9664	+	4.40775i	−0.595039	+	0.154587i
$814$	2.83248	+	3.26886i	0.0992784	+	0.114573i
$815$	19.0011	−	0.405475i	0.665580	−	0.0142032i
$816$	−0.0405824	+	0.123692i	−0.00142067	+	0.00433010i
$817$	1.65239	+	0.237578i	0.0578098	+	0.00831179i
$818$	−29.3003	−	18.8302i	−1.02446	−	0.658381i
$819$	18.9319	−	7.24617i	0.661534	−	0.253202i
$820$	−11.8691	−	7.27476i	−0.414487	−	0.254046i
$821$	9.24040	+	14.3784i	0.322492	+	0.501808i	0.964212	−	0.265131i	$-0.0854152\pi$
$821$	9.24040	+	14.3784i	0.322492	+	0.501808i	−0.641720	+	0.766939i	$0.721779\pi$
$822$	−8.99963	−	4.45689i	−0.313898	−	0.155452i
$823$	30.6957	+	26.5979i	1.06998	+	0.927146i	0.997531	−	0.0702259i	$-0.0223720\pi$
$823$	30.6957	+	26.5979i	1.06998	+	0.927146i	0.0724524	+	0.997372i	$0.476917\pi$
$824$	−16.7087	+	4.90613i	−0.582077	+	0.170913i
$825$	−11.1535	+	7.34644i	−0.388313	+	0.255770i
$826$	2.32394	−	0.334132i	0.0808601	−	0.0116259i
$827$		−	44.5089i		−	1.54773i	−0.633353	−	0.773863i	$-0.718322\pi$
$827$		−	44.5089i		−	1.54773i	0.633353	−	0.773863i	$-0.281678\pi$
$828$	9.53343	+	10.7756i	0.331310	+	0.374478i
$829$	51.9310			1.80364			0.901819	−	0.432114i	$-0.142232\pi$
$829$	51.9310			1.80364			0.901819	+	0.432114i	$0.142232\pi$
$830$	7.93344	+	8.77040i	0.275374	+	0.304425i
$831$	−2.48821	+	3.61661i	−0.0863151	+	0.125459i
$832$	1.24674	+	4.24601i	0.0432230	+	0.147204i
$833$	−0.265177	−	0.229777i	−0.00918784	−	0.00796131i
$834$	5.95104	−	12.0167i	0.206068	−	0.416105i
$835$	−25.1218	−	10.8311i	−0.869377	−	0.374826i
$836$	0.629923	−	0.287676i	0.0217864	−	0.00994949i
$837$	36.6619	−	7.10110i	1.26722	−	0.245450i
$838$	26.6861	+	17.1501i	0.921856	+	0.592441i
$839$	6.23375	−	43.3567i	0.215213	−	1.49684i	−0.540170	−	0.841556i	$-0.681640\pi$
$839$	6.23375	−	43.3567i	0.215213	−	1.49684i	0.755383	−	0.655284i	$-0.227451\pi$
$840$	−1.60877	−	5.69075i	−0.0555079	−	0.196350i
$841$	12.1977	+	7.83900i	0.420611	+	0.270310i
$842$	3.88930	−	3.37009i	0.134034	−	0.116141i
$843$	−28.4217	+	7.38373i	−0.978894	+	0.254309i
$844$	21.1000	−	13.5601i	0.726292	−	0.466760i
$845$	−4.44749	−	14.0321i	−0.152998	−	0.482717i
$846$	20.8114	−	11.5959i	0.715510	−	0.398676i
$847$	12.6315	−	3.70895i	0.434025	−	0.127441i
$848$	−9.17286	−	4.18911i	−0.314997	−	0.143854i
$849$	−51.7885	−	1.62803i	−1.77738	−	0.0558737i
$850$	−0.348185	−	0.141387i	−0.0119426	−	0.00484952i
$851$	9.52799	+	9.49445i	0.326615	+	0.325465i
$852$	12.0426	+	2.11962i	0.412573	+	0.0726169i
$853$	−17.9827	+	2.58552i	−0.615716	+	0.0885266i	−0.443114	−	0.896465i	$-0.646126\pi$
$853$	−17.9827	+	2.58552i	−0.615716	+	0.0885266i	−0.172602	+	0.984992i	$0.555217\pi$
$854$	−5.69245	−	2.59966i	−0.194792	−	0.0889584i
$855$	−2.59952	+	1.52200i	−0.0889016	+	0.0520512i
$856$	−13.0121	−	11.2750i	−0.444744	−	0.385373i
$857$	−25.3086	−	7.43126i	−0.864524	−	0.253847i	−0.180739	−	0.983531i	$-0.557849\pi$
$857$	−25.3086	−	7.43126i	−0.864524	−	0.253847i	−0.683785	+	0.729684i	$0.739667\pi$
$858$	−10.9011	+	4.57008i	−0.372159	+	0.156020i
$859$	−10.1772	−	22.2851i	−0.347243	−	0.760356i	−0.999996	−	0.00278543i	$-0.999113\pi$
$859$	−10.1772	−	22.2851i	−0.347243	−	0.760356i	0.652753	−	0.757571i	$-0.273614\pi$
$860$	−2.17129	+	8.02424i	−0.0740404	+	0.273624i
$861$	12.0987	+	11.1681i	0.412323	+	0.380609i
$862$	−0.176934	+	1.23060i	−0.00602638	+	0.0419144i
$863$	7.03675	−	48.9417i	0.239534	−	1.66599i	−0.414894	−	0.909870i	$-0.636181\pi$
$863$	7.03675	−	48.9417i	0.239534	−	1.66599i	0.654428	−	0.756125i	$-0.272910\pi$
$864$	−4.61633	+	2.38528i	−0.157051	+	0.0811487i
$865$	9.81725	−	36.2807i	0.333796	−	1.23358i
$866$	−4.57068	−	10.0084i	−0.155318	−	0.340099i
$867$	11.3804	+	27.1461i	0.386500	+	0.921929i
$868$	10.5291	+	3.09163i	0.357382	+	0.104937i
$869$	−10.1090	−	8.75953i	−0.342926	−	0.297147i
$870$	−9.54504	−	11.2428i	−0.323607	−	0.381166i
$871$	44.3695	+	20.2629i	1.50340	+	0.686581i
$872$	14.3722	−	2.06642i	0.486705	−	0.0699777i
$873$	−13.5278	−	4.91430i	−0.457847	−	0.166324i
$874$	1.88831	−	1.03542i	0.0638729	−	0.0350236i
$875$	16.7078	−	3.50544i	0.564828	−	0.118506i
$876$	−0.620315	+	19.7326i	−0.0209585	+	0.666703i
$877$	−47.5272	−	21.7049i	−1.60488	−	0.732924i	−0.606799	−	0.794856i	$-0.707547\pi$
$877$	−47.5272	−	21.7049i	−1.60488	−	0.732924i	−0.998080	+	0.0619321i	$0.980274\pi$
$878$	−16.1647	+	4.74637i	−0.545531	+	0.160182i
$879$	−29.4856	+	23.9696i	−0.994525	+	0.808475i
$880$	1.04189	+	3.28721i	0.0351221	+	0.110812i
$881$	34.2308	−	21.9988i	1.15327	−	0.741159i	0.182980	−	0.983117i	$-0.441426\pi$
$881$	34.2308	−	21.9988i	1.15327	−	0.741159i	0.970287	+	0.241957i	$0.0777894\pi$
$882$	−1.11852	−	13.9607i	−0.0376625	−	0.470081i
$883$	−36.7387	+	31.8343i	−1.23636	+	1.07131i	−0.241459	+	0.970411i	$0.577626\pi$
$883$	−36.7387	+	31.8343i	−1.23636	+	1.07131i	−0.994897	+	0.100897i	$0.967829\pi$
$884$	−0.279801	−	0.179817i	−0.00941072	−	0.00604790i
$885$	5.73057	−	1.62003i	0.192631	−	0.0544567i
$886$	0.716958	−	4.98655i	0.0240867	−	0.167526i
$887$	6.38475	+	4.10323i	0.214379	+	0.137773i	0.643424	−	0.765510i	$-0.277513\pi$
$887$	6.38475	+	4.10323i	0.214379	+	0.137773i	−0.429045	+	0.903283i	$0.641150\pi$
$888$	−4.16723	+	2.49667i	−0.139843	+	0.0837829i
$889$	−13.4281	+	6.13242i	−0.450365	+	0.205675i
$890$	17.4674	+	7.53094i	0.585507	+	0.252438i
$891$	−7.70232	−	11.5462i	−0.258037	−	0.386811i
$892$	1.37351	+	1.19016i	0.0459886	+	0.0398494i
$893$	−1.00466	−	3.42157i	−0.0336198	−	0.114499i
$894$	8.18561	+	5.63167i	0.273768	+	0.188351i
$895$	16.0999	+	17.7984i	0.538162	+	0.594936i
$896$	−1.52693			−0.0510112
$897$	−32.7709	+	16.6521i	−1.09419	+	0.555999i
$898$			5.29469i			0.176686i
$899$	27.0882	−	3.89469i	0.903441	−	0.129895i
$900$	−5.95465	−	13.7674i	−0.198488	−	0.458914i
$901$	0.727216	−	0.213530i	0.0242271	−	0.00711371i
$902$	−7.25599	−	6.28735i	−0.241598	−	0.209346i
$903$	4.36337	−	8.81079i	0.145204	−	0.293205i
$904$	−5.24988	−	8.16898i	−0.174609	−	0.271696i
$905$	9.57248	+	5.86712i	0.318200	+	0.195030i
$906$	−13.3147	+	7.97713i	−0.442352	+	0.265022i
$907$	37.3108	+	23.9782i	1.23888	+	0.796183i	0.985251	−	0.171118i	$-0.0547379\pi$
$907$	37.3108	+	23.9782i	1.23888	+	0.796183i	0.253634	+	0.967300i	$0.418374\pi$
$908$	−13.2030	−	1.89831i	−0.438158	−	0.0629976i
$909$	7.73486	+	4.13812i	0.256549	+	0.137253i
$910$	15.1059	−	0.322352i	0.500754	−	0.0106859i
$911$	13.9887	+	16.1438i	0.463465	+	0.534867i	0.938582	−	0.345055i	$-0.112140\pi$
$911$	13.9887	+	16.1438i	0.463465	+	0.534867i	−0.475117	+	0.879922i	$0.657594\pi$
$912$	0.195568	+	0.752784i	0.00647589	+	0.0249272i
$913$	4.40960	+	6.86148i	0.145937	+	0.227082i
$914$	0.00663762	+	0.00194898i	0.000219553	+	6.44666e-5i
$915$	−15.1842	−	4.62538i	−0.501973	−	0.152910i
$916$	5.69670	+	19.4012i	0.188224	+	0.641033i
$917$	−21.6597	−	9.89166i	−0.715267	−	0.326651i
$918$	0.144814	−	0.362698i	0.00477958	−	0.0119708i
$919$			21.6511i			0.714203i	0.934066	+	0.357101i	$0.116235\pi$
$919$			21.6511i			0.714203i	−0.934066	+	0.357101i	$0.883765\pi$
$920$	3.97866	+	9.95843i	0.131173	+	0.328320i
$921$	−42.8347	−	7.53933i	−1.41145	−	0.248429i
$922$	−16.5077	+	2.37345i	−0.543654	+	0.0781656i
$923$	−12.9780	+	28.4178i	−0.427175	+	0.935382i
$924$	−0.453310	−	4.05332i	−0.0149128	−	0.133345i
$925$	−6.36447	−	12.4961i	−0.209262	−	0.410870i
$926$	3.23632	−	11.0219i	0.106352	−	0.362202i
$927$	50.9517	−	11.5409i	1.67347	−	0.379053i
$928$	−3.46384	+	1.58188i	−0.113706	+	0.0519278i
$929$	−38.7294	+	33.5593i	−1.27067	+	1.10104i	−0.280697	+	0.959796i	$0.590566\pi$
$929$	−38.7294	+	33.5593i	−1.27067	+	1.10104i	−0.989974	+	0.141247i	$0.954889\pi$
$930$	27.5094	+	4.23896i	0.902068	+	0.139001i
$931$	−2.07503	−	0.298344i	−0.0680063	−	0.00977784i
$932$	−1.86525	+	12.9731i	−0.0610982	+	0.424948i
$933$	−35.0882	−	32.3894i	−1.14874	−	1.06038i
$934$	−14.9643	+	12.9666i	−0.489646	+	0.424280i
$935$	−0.220974	−	0.135438i	−0.00722662	−	0.00442931i
$936$	−2.93276	−	12.9478i	−0.0958604	−	0.423212i
$937$	29.9994	+	8.80862i	0.980038	+	0.287765i	0.732240	−	0.681047i	$-0.238475\pi$
$937$	29.9994	+	8.80862i	0.980038	+	0.287765i	0.247798	+	0.968812i	$0.420293\pi$
$938$	−11.0217	+	12.7197i	−0.359871	+	0.415313i
$939$	−0.0210773	−	0.188465i	−0.000687832	−	0.00615032i
$940$	17.5186	−	2.90154i	0.571395	−	0.0946379i
$941$	5.01522	+	34.8816i	0.163492	+	1.13711i	0.891988	+	0.452059i	$0.149310\pi$
$941$	5.01522	+	34.8816i	0.163492	+	1.13711i	−0.728496	+	0.685050i	$0.759780\pi$
$942$	−5.32672	+	30.2638i	−0.173554	+	0.986047i
$943$	−23.9337	−	17.8507i	−0.779387	−	0.581300i
$944$		−	1.53762i		−	0.0500451i
$945$	3.74448	+	17.3417i	0.121808	+	0.564125i
$946$	−2.38164	+	5.21506i	−0.0774337	+	0.169556i
$947$	−6.41880	+	1.88473i	−0.208583	+	0.0612455i	−0.384355	−	0.923185i	$-0.625576\pi$
$947$	−6.41880	+	1.88473i	−0.208583	+	0.0612455i	0.175772	+	0.984431i	$0.443758\pi$
$948$	11.6573	−	9.47651i	0.378611	−	0.307783i
$949$	−48.3971	−	14.2107i	−1.57104	−	0.461298i
$950$	−2.20673	+	0.414046i	−0.0715957	+	0.0134334i
$951$	30.9426	−	8.03865i	1.00338	−	0.260671i
$952$	0.0867321	−	0.0751538i	0.00281101	−	0.00243575i
$953$	5.53049	−	8.60562i	0.179150	−	0.278763i	−0.740051	−	0.672550i	$-0.765199\pi$
$953$	5.53049	−	8.60562i	0.179150	−	0.278763i	0.919202	+	0.393787i	$0.128835\pi$
$954$	26.6749	+	14.2709i	0.863632	+	0.462039i
$955$	18.1977	−	8.78453i	0.588863	−	0.284261i
$956$	−4.51869	+	7.03122i	−0.146145	+	0.227406i
$957$	−5.22752	−	8.72532i	−0.168982	−	0.282050i
$958$	12.3221	+	26.9816i	0.398108	+	0.871734i
$959$	4.78654	+	7.44800i	0.154565	+	0.240508i
$960$	−3.83893	+	0.512477i	−0.123901	+	0.0165401i
$961$	−13.5222	+	15.6054i	−0.436200	+	0.503402i
$962$	−3.49675	−	11.9088i	−0.112740	−	0.383956i
$963$	36.8346	+	36.2102i	1.18698	+	1.16686i
$964$	−18.7450	+	2.69512i	−0.603735	+	0.0868040i
$965$	33.3986	−	22.4850i	1.07514	−	0.723819i
$966$	−2.32734	−	12.4683i	−0.0748811	−	0.401161i
$967$		−	31.1218i		−	1.00081i	−0.865791	−	0.500405i	$-0.833184\pi$
$967$		−	31.1218i		−	1.00081i	0.865791	−	0.500405i	$-0.166816\pi$
$968$	−1.22700	−	8.53398i	−0.0394373	−	0.274293i
$969$	−0.0481597	−	0.0331337i	−0.00154711	−	0.00106441i
$970$	−8.25551	−	6.85060i	−0.265069	−	0.219960i
$971$	−8.80728	+	10.1641i	−0.282639	+	0.326183i	−0.879262	−	0.476339i	$-0.841963\pi$
$971$	−8.80728	+	10.1641i	−0.282639	+	0.326183i	0.596623	+	0.802522i	$0.296509\pi$
$972$	14.2711	−	6.27184i	0.457745	−	0.201169i
$973$	−9.94491	+	6.39120i	−0.318819	+	0.204893i
$974$	−5.79471	+	2.64635i	−0.185674	+	0.0847947i
$975$	37.8701	−	5.88035i	1.21281	−	0.188322i
$976$	−2.21576	+	3.44779i	−0.0709247	+	0.110361i
$977$	−24.0519	−	3.45814i	−0.769489	−	0.110636i	−0.253620	−	0.967304i	$-0.581621\pi$
$977$	−24.0519	−	3.45814i	−0.769489	−	0.110636i	−0.515868	+	0.856668i	$0.672531\pi$
$978$	−4.58932	+	13.9879i	−0.146750	+	0.447285i
$979$	11.0362	+	7.09255i	0.352719	+	0.226679i
$980$	2.72666	−	10.0766i	0.0870998	−	0.321887i
$981$	−43.4210	+	3.47885i	−1.38632	+	0.111071i
$982$	−9.51436	−	14.8046i	−0.303615	−	0.472435i
$983$	−1.10412	+	3.76028i	−0.0352159	+	0.119934i	−0.975225	−	0.221215i	$-0.928998\pi$
$983$	−1.10412	+	3.76028i	−0.0352159	+	0.119934i	0.940009	+	0.341149i	$0.110816\pi$
$984$	8.36729	−	6.80198i	0.266739	−	0.216839i
$985$	2.47912	+	2.05723i	0.0789913	+	0.0655486i
$986$	0.118893	−	0.260340i	0.00378633	−	0.00829090i
$987$	−20.9922	−	0.659911i	−0.668189	−	0.0210052i
$988$	−1.98715			−0.0632198
$989$	−6.20113	+	16.7158i	−0.197185	+	0.531533i
$990$	−2.50009	−	10.0385i	−0.0794580	−	0.319044i
$991$	4.35773	+	30.3087i	0.138428	+	0.962787i	0.934088	+	0.357043i	$0.116215\pi$
$991$	4.35773	+	30.3087i	0.138428	+	0.962787i	−0.795660	+	0.605743i	$0.792876\pi$
$992$	2.98547	−	6.53727i	0.0947888	−	0.207559i
$993$	−0.199979	−	1.78813i	−0.00634615	−	0.0567447i
$994$	−8.14671	−	7.05917i	−0.258398	−	0.223903i
$995$	−24.9308	+	7.90186i	−0.790359	+	0.250506i
$996$	−8.44818	+	3.54173i	−0.267691	+	0.112224i
$997$	−42.5816	+	19.4464i	−1.34857	+	0.615873i	−0.953114	−	0.302611i	$-0.902142\pi$
$997$	−42.5816	+	19.4464i	−1.34857	+	0.615873i	−0.395459	+	0.918484i	$0.629415\pi$
$998$	−13.6806	−	15.7883i	−0.433052	−	0.499769i
$999$	12.9475	−	6.69000i	0.409639	−	0.211662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.b.89.20	yes	240
3.2	odd	2		690.2.n.a.89.23	yes	240
5.4	even	2		690.2.n.a.89.5	✓	240
15.14	odd	2	inner	690.2.n.b.89.2	yes	240
23.15	odd	22	inner	690.2.n.b.659.2	yes	240
69.38	even	22		690.2.n.a.659.5	yes	240
115.84	odd	22		690.2.n.a.659.23	yes	240
345.314	even	22	inner	690.2.n.b.659.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.5	✓	240	5.4	even	2
690.2.n.a.89.23	yes	240	3.2	odd	2
690.2.n.a.659.5	yes	240	69.38	even	22
690.2.n.a.659.23	yes	240	115.84	odd	22
690.2.n.b.89.2	yes	240	15.14	odd	2	inner
690.2.n.b.89.20	yes	240	1.1	even	1	trivial
690.2.n.b.659.2	yes	240	23.15	odd	22	inner
690.2.n.b.659.20	yes	240	345.314	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(1.42695 + 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.21959 + 0.270933i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(1.28454 - 0.825522i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(1.42695 + 0.981738i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.21959 + 0.270933i) q^{5} +(-0.768669 + 1.55214i) q^{6} +(1.28454 - 0.825522i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.07238 + 2.80178i) q^{9} +(0.0477058 + 2.23556i) q^{10} +(-0.219473 + 1.52646i) q^{11} +(-1.64574 - 0.539952i) q^{12} +(2.39248 - 3.72277i) q^{13} +(0.999928 + 1.15398i) q^{14} +(2.90127 + 2.56567i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.0211748 + 0.0721148i) q^{17} +(-2.62065 + 1.46020i) q^{18} +(0.126511 + 0.430858i) q^{19} +(-2.20602 + 0.365373i) q^{20} +(2.64342 + 0.0830986i) q^{21} -1.54216 q^{22} +(-4.78300 + 0.350566i) q^{23} +(0.300243 - 1.70583i) q^{24} +(4.85319 + 1.20272i) q^{25} +(4.02536 + 1.83832i) q^{26} +(-1.22038 + 5.05081i) q^{27} +(-0.999928 + 1.15398i) q^{28} +(-1.07283 + 3.65371i) q^{29} +(-2.12666 + 3.23687i) q^{30} +(-2.98547 - 6.53727i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.81176 + 1.96273i) q^{33} +(-0.0743943 - 0.0106963i) q^{34} +(3.07481 - 1.48430i) q^{35} +(-1.81830 - 2.38617i) q^{36} +(-1.83669 - 2.11966i) q^{37} +(-0.408468 + 0.186541i) q^{38} +(7.06874 - 2.96343i) q^{39} +(-0.675603 - 2.13156i) q^{40} +(4.70508 + 4.07697i) q^{41} +(0.293945 + 2.62834i) q^{42} +(1.54435 - 3.38165i) q^{43} +(-0.219473 - 1.52646i) q^{44} +(1.62116 + 6.50937i) q^{45} +(-1.02769 - 4.68443i) q^{46} -7.94130 q^{47} +(1.73120 + 0.0544219i) q^{48} +(-1.93936 + 4.24660i) q^{49} +(-0.499799 + 4.97496i) q^{50} +(-0.101013 + 0.0821162i) q^{51} +(-1.24674 + 4.24601i) q^{52} +(-5.45190 - 8.48332i) q^{53} +(-5.17308 - 0.489153i) q^{54} +(-0.900709 + 3.32867i) q^{55} +(-1.28454 - 0.825522i) q^{56} +(-0.242464 + 0.739014i) q^{57} +(-3.76920 - 0.541929i) q^{58} +(0.831298 - 1.29353i) q^{59} +(-3.50658 - 1.64436i) q^{60} +(-3.72803 + 1.70254i) q^{61} +(6.04585 - 3.88544i) q^{62} +(3.69045 + 2.71372i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(6.31895 - 7.61484i) q^{65} +(-2.20059 - 1.51400i) q^{66} +(1.56866 + 10.9103i) q^{67} -0.0751593i q^{68} +(-7.16928 - 4.19541i) q^{69} +(1.90678 + 2.83228i) q^{70} +(-6.98782 + 1.00470i) q^{71} +(2.10311 - 2.13938i) q^{72} +(-3.21126 - 10.9365i) q^{73} +(1.83669 - 2.11966i) q^{74} +(5.74451 + 6.48079i) q^{75} +(-0.242773 - 0.377763i) q^{76} +(0.978209 + 2.14198i) q^{77} +(3.93925 + 6.57505i) q^{78} +(-4.68933 + 7.29674i) q^{79} +(2.01372 - 0.972079i) q^{80} +(-6.69999 + 6.00917i) q^{81} +(-3.36587 + 5.23740i) q^{82} +(3.99704 - 3.46346i) q^{83} +(-2.55975 + 0.665004i) q^{84} +(-0.0665378 + 0.154329i) q^{85} +(3.56702 + 1.04737i) q^{86} +(-5.11785 + 4.16043i) q^{87} +(1.47969 - 0.434477i) q^{88} +(3.53383 - 7.73801i) q^{89} +(-6.21240 + 2.53104i) q^{90} -6.75708i q^{91} +(4.49049 - 1.68389i) q^{92} +(2.15776 - 12.2593i) q^{93} +(-1.13017 - 7.86047i) q^{94} +(0.164070 + 0.990605i) q^{95} +(0.192507 + 1.72132i) q^{96} +(-3.14175 + 3.62578i) q^{97} +(-4.47937 - 1.31526i) q^{98} +(-4.51218 + 1.02204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Introduction

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