LMFDB - Embedded newform 418.2.q.b.109.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	418.109
Dual form			418.2.q.b.395.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.64099 + 0.289351i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.95336 + 1.63906i) q^{5} +(-1.64099 + 0.289351i) q^{6} +(-0.632001 + 0.364886i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.209943 - 0.0764129i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.64099 + 0.289351i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.95336 + 1.63906i) q^{5} +(-1.64099 + 0.289351i) q^{6} +(-0.632001 + 0.364886i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.209943 - 0.0764129i) q^{9} +(-2.39615 - 0.872127i) q^{10} +(0.307307 + 3.30236i) q^{11} +(1.44307 - 0.833154i) q^{12} +(1.02841 + 5.83238i) q^{13} +(0.469088 - 0.559038i) q^{14} +(2.73118 + 3.25490i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.95288 - 5.36549i) q^{17} +0.223417 q^{18} +(3.91398 - 1.91852i) q^{19} +2.54993 q^{20} +(-1.14269 + 0.415905i) q^{21} +(-1.41825 - 2.99810i) q^{22} +(-3.05410 + 2.56269i) q^{23} +(-1.07108 + 1.27647i) q^{24} +(0.260844 + 1.47932i) q^{25} +(-2.96118 - 5.12891i) q^{26} +(-4.65160 - 2.68560i) q^{27} +(-0.249597 + 0.685761i) q^{28} +(1.30026 + 0.473257i) q^{29} +(-3.67972 - 2.12448i) q^{30} +(7.60816 - 4.39257i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.451254 + 5.50807i) q^{33} +(3.67021 + 4.37399i) q^{34} +(-1.83260 - 0.323136i) q^{35} +(-0.209943 + 0.0764129i) q^{36} -3.83234i q^{37} +(-3.02177 + 3.14148i) q^{38} +9.86847i q^{39} +(-2.39615 + 0.872127i) q^{40} +(-0.590845 + 3.35085i) q^{41} +(0.931529 - 0.781646i) q^{42} +(1.75793 - 2.09502i) q^{43} +(2.35812 + 2.33222i) q^{44} +(-0.284848 - 0.493372i) q^{45} +(1.99342 - 3.45270i) q^{46} +(11.2222 + 4.08454i) q^{47} +(0.569911 - 1.56582i) q^{48} +(-3.23372 + 5.60096i) q^{49} +(-0.751071 - 1.30089i) q^{50} +(-1.65215 - 9.36981i) q^{51} +(4.53679 + 3.80682i) q^{52} +(-4.77218 - 5.68726i) q^{53} +(5.28961 + 0.932700i) q^{54} +(-4.81249 + 6.95439i) q^{55} -0.729772i q^{56} +(6.97795 - 2.01577i) q^{57} -1.38371 q^{58} +(0.147002 + 0.403884i) q^{59} +(4.18442 + 0.737826i) q^{60} +(0.505539 + 0.602478i) q^{61} +(-5.64698 + 6.72981i) q^{62} +(0.160566 - 0.0283121i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.55079 + 13.0784i) q^{65} +(-1.45983 - 5.33023i) q^{66} +(4.10128 - 11.2682i) q^{67} +(-4.94486 - 2.85492i) q^{68} +(-5.75327 + 3.32165i) q^{69} +(1.83260 - 0.323136i) q^{70} +(-10.2630 + 12.2310i) q^{71} +(0.171147 - 0.143609i) q^{72} +(-4.70904 - 0.830330i) q^{73} +(1.31074 + 3.60122i) q^{74} +2.50303i q^{75} +(1.76508 - 3.98553i) q^{76} +(-1.39920 - 1.97496i) q^{77} +(-3.37521 - 9.27333i) q^{78} +(2.97075 - 16.8479i) q^{79} +(1.95336 - 1.63906i) q^{80} +(-6.34272 - 5.32218i) q^{81} +(-0.590845 - 3.35085i) q^{82} +(-0.285339 + 0.164741i) q^{83} +(-0.608012 + 1.05311i) q^{84} +(4.97971 - 13.6816i) q^{85} +(-0.935377 + 2.56993i) q^{86} +(1.99678 + 1.15284i) q^{87} +(-3.01358 - 1.38504i) q^{88} +(7.97707 - 1.40657i) q^{89} +(0.436413 + 0.366194i) q^{90} +(-2.77811 - 3.31082i) q^{91} +(-0.692308 + 3.92627i) q^{92} +(13.7559 - 5.00675i) q^{93} -11.9424 q^{94} +(10.7900 + 2.66770i) q^{95} +1.66631i q^{96} +(-1.26860 - 3.48546i) q^{97} +(1.12306 - 6.36918i) q^{98} +(0.187826 - 0.716788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.64099	+	0.289351i	0.947428	+	0.167057i	0.625953	−	0.779861i	$-0.284710\pi$
$3$	1.64099	+	0.289351i	0.947428	+	0.167057i	0.321475	+	0.946918i	$0.395821\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.95336	+	1.63906i	0.873569	+	0.733011i	0.964846	−	0.262814i	$-0.0846506\pi$
$5$	1.95336	+	1.63906i	0.873569	+	0.733011i	−0.0912775	+	0.995825i	$0.529095\pi$
$6$	−1.64099	+	0.289351i	−0.669933	+	0.118127i
$7$	−0.632001	+	0.364886i	−0.238874	+	0.137914i	−0.614659	−	0.788793i	$-0.710706\pi$
$7$	−0.632001	+	0.364886i	−0.238874	+	0.137914i	0.375785	+	0.926707i	$0.377373\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.209943	−	0.0764129i	−0.0699809	−	0.0254710i
$10$	−2.39615	−	0.872127i	−0.757729	−	0.275791i
$11$	0.307307	+	3.30236i	0.0926564	+	0.995698i
$11$	0.307307	+	3.30236i	0.0926564	+	0.995698i
$12$	1.44307	−	0.833154i	0.416577	−	0.240511i
$13$	1.02841	+	5.83238i	0.285228	+	1.61761i	0.704468	+	0.709736i	$0.251186\pi$
$13$	1.02841	+	5.83238i	0.285228	+	1.61761i	−0.419240	+	0.907876i	$0.637703\pi$
$14$	0.469088	−	0.559038i	0.125369	−	0.149409i
$15$	2.73118	+	3.25490i	0.705189	+	0.840411i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.95288	−	5.36549i	−0.473643	−	1.30132i	−0.914805	−	0.403896i	$-0.867656\pi$
$17$	−1.95288	−	5.36549i	−0.473643	−	1.30132i	0.441162	−	0.897427i	$-0.354566\pi$
$18$	0.223417			0.0526598
$19$	3.91398	−	1.91852i	0.897929	−	0.440140i
$19$	3.91398	−	1.91852i	0.897929	−	0.440140i
$20$	2.54993			0.570182
$21$	−1.14269	+	0.415905i	−0.249355	+	0.0907579i
$22$	−1.41825	−	2.99810i	−0.302371	−	0.639196i
$23$	−3.05410	+	2.56269i	−0.636823	+	0.534358i	−0.903041	−	0.429555i	$-0.858670\pi$
$23$	−3.05410	+	2.56269i	−0.636823	+	0.534358i	0.266218	+	0.963913i	$0.414226\pi$
$24$	−1.07108	+	1.27647i	−0.218634	+	0.260558i
$25$	0.260844	+	1.47932i	0.0521689	+	0.295864i
$26$	−2.96118	−	5.12891i	−0.580735	−	1.00586i
$27$	−4.65160	−	2.68560i	−0.895201	−	0.516845i
$28$	−0.249597	+	0.685761i	−0.0471693	+	0.129597i
$29$	1.30026	+	0.473257i	0.241453	+	0.0878816i	0.459912	−	0.887964i	$-0.347881\pi$
$29$	1.30026	+	0.473257i	0.241453	+	0.0878816i	−0.218459	+	0.975846i	$0.570103\pi$
$30$	−3.67972	−	2.12448i	−0.671821	−	0.387876i
$31$	7.60816	−	4.39257i	1.36647	−	0.788929i	0.375991	−	0.926623i	$-0.377302\pi$
$31$	7.60816	−	4.39257i	1.36647	−	0.788929i	0.990475	+	0.137694i	$0.0439691\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.451254	+	5.50807i	−0.0785532	+	0.958831i
$34$	3.67021	+	4.37399i	0.629436	+	0.750133i
$35$	−1.83260	−	0.323136i	−0.309765	−	0.0546200i
$36$	−0.209943	+	0.0764129i	−0.0349905	+	0.0127355i
$37$		−	3.83234i		−	0.630033i	−0.949086	−	0.315017i	$-0.897990\pi$
$37$		−	3.83234i		−	0.630033i	0.949086	−	0.315017i	$-0.102010\pi$
$38$	−3.02177	+	3.14148i	−0.490195	+	0.509616i
$39$			9.86847i			1.58022i
$40$	−2.39615	+	0.872127i	−0.378865	+	0.137895i
$41$	−0.590845	+	3.35085i	−0.0922745	+	0.523315i	0.903274	+	0.429064i	$0.141157\pi$
$41$	−0.590845	+	3.35085i	−0.0922745	+	0.523315i	−0.995549	+	0.0942505i	$0.969955\pi$
$42$	0.931529	−	0.781646i	0.143738	−	0.120611i
$43$	1.75793	−	2.09502i	0.268082	−	0.319488i	−0.615162	−	0.788400i	$-0.710910\pi$
$43$	1.75793	−	2.09502i	0.268082	−	0.319488i	0.883245	+	0.468912i	$0.155354\pi$
$44$	2.35812	+	2.33222i	0.355501	+	0.351595i
$45$	−0.284848	−	0.493372i	−0.0424627	−	0.0735475i
$46$	1.99342	−	3.45270i	0.293914	−	0.509074i
$47$	11.2222	+	4.08454i	1.63692	+	0.595792i	0.986497	−	0.163777i	$-0.0523676\pi$
$47$	11.2222	+	4.08454i	1.63692	+	0.595792i	0.650427	+	0.759569i	$0.274590\pi$
$48$	0.569911	−	1.56582i	0.0822596	−	0.226006i
$49$	−3.23372	+	5.60096i	−0.461960	+	0.800137i
$50$	−0.751071	−	1.30089i	−0.106218	−	0.183974i
$51$	−1.65215	−	9.36981i	−0.231347	−	1.31204i
$52$	4.53679	+	3.80682i	0.629139	+	0.527910i
$53$	−4.77218	−	5.68726i	−0.655509	−	0.781205i	0.331225	−	0.943552i	$-0.392538\pi$
$53$	−4.77218	−	5.68726i	−0.655509	−	0.781205i	−0.986734	+	0.162347i	$0.948094\pi$
$54$	5.28961	+	0.932700i	0.719824	+	0.126924i
$55$	−4.81249	+	6.95439i	−0.648916	+	0.937729i
$56$		−	0.729772i		−	0.0975198i
$57$	6.97795	−	2.01577i	0.924252	−	0.266995i
$58$	−1.38371			−0.181690
$59$	0.147002	+	0.403884i	0.0191380	+	0.0525812i	0.948894	−	0.315596i	$-0.102204\pi$
$59$	0.147002	+	0.403884i	0.0191380	+	0.0525812i	−0.929756	+	0.368177i	$0.879982\pi$
$60$	4.18442	+	0.737826i	0.540206	+	0.0952529i
$61$	0.505539	+	0.602478i	0.0647277	+	0.0771394i	0.797437	−	0.603403i	$-0.206189\pi$
$61$	0.505539	+	0.602478i	0.0647277	+	0.0771394i	−0.732709	+	0.680542i	$0.761744\pi$
$62$	−5.64698	+	6.72981i	−0.717167	+	0.854687i
$63$	0.160566	−	0.0283121i	0.0202294	−	0.00356699i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−7.55079	+	13.0784i	−0.936561	+	1.62217i
$66$	−1.45983	−	5.33023i	−0.179693	−	0.656106i
$67$	4.10128	−	11.2682i	0.501052	−	1.37663i	−0.389198	−	0.921154i	$-0.627248\pi$
$67$	4.10128	−	11.2682i	0.501052	−	1.37663i	0.890249	−	0.455474i	$-0.150530\pi$
$68$	−4.94486	−	2.85492i	−0.599653	−	0.346210i
$69$	−5.75327	+	3.32165i	−0.692612	+	0.399880i
$70$	1.83260	−	0.323136i	0.219037	−	0.0386221i
$71$	−10.2630	+	12.2310i	−1.21799	+	1.45155i	−0.363891	+	0.931441i	$0.618552\pi$
$71$	−10.2630	+	12.2310i	−1.21799	+	1.45155i	−0.854102	+	0.520106i	$0.825892\pi$
$72$	0.171147	−	0.143609i	0.0201699	−	0.0169245i
$73$	−4.70904	−	0.830330i	−0.551151	−	0.0971828i	−0.108865	−	0.994057i	$-0.534721\pi$
$73$	−4.70904	−	0.830330i	−0.551151	−	0.0971828i	−0.442287	+	0.896874i	$0.645833\pi$
$74$	1.31074	+	3.60122i	0.152370	+	0.418634i
$75$			2.50303i			0.289025i
$76$	1.76508	−	3.98553i	0.202469	−	0.457172i
$77$	−1.39920	−	1.97496i	−0.159454	−	0.225068i
$78$	−3.37521	−	9.27333i	−0.382168	−	1.05000i
$79$	2.97075	−	16.8479i	0.334235	−	1.89554i	−0.100420	−	0.994945i	$-0.532019\pi$
$79$	2.97075	−	16.8479i	0.334235	−	1.89554i	0.434656	−	0.900597i	$-0.356870\pi$
$80$	1.95336	−	1.63906i	0.218392	−	0.183253i
$81$	−6.34272	−	5.32218i	−0.704747	−	0.591353i
$82$	−0.590845	−	3.35085i	−0.0652479	−	0.370039i
$83$	−0.285339	+	0.164741i	−0.0313200	+	0.0180826i	−0.515578	−	0.856842i	$-0.672423\pi$
$83$	−0.285339	+	0.164741i	−0.0313200	+	0.0180826i	0.484258	+	0.874925i	$0.339090\pi$
$84$	−0.608012	+	1.05311i	−0.0663396	+	0.114904i
$85$	4.97971	−	13.6816i	0.540125	−	1.48398i
$86$	−0.935377	+	2.56993i	−0.100864	+	0.277122i
$87$	1.99678	+	1.15284i	0.214078	+	0.123598i
$88$	−3.01358	−	1.38504i	−0.321249	−	0.147646i
$89$	7.97707	−	1.40657i	0.845568	−	0.149096i	0.265952	−	0.963986i	$-0.414314\pi$
$89$	7.97707	−	1.40657i	0.845568	−	0.149096i	0.579616	+	0.814890i	$0.303203\pi$
$90$	0.436413	+	0.366194i	0.0460019	+	0.0386002i
$91$	−2.77811	−	3.31082i	−0.291225	−	0.347068i
$92$	−0.692308	+	3.92627i	−0.0721781	+	0.409342i
$93$	13.7559	−	5.00675i	1.42642	−	0.519176i
$94$	−11.9424			−1.23177
$95$	10.7900	+	2.66770i	1.10703	+	0.273700i
$96$			1.66631i			0.170067i
$97$	−1.26860	−	3.48546i	−0.128807	−	0.353895i	0.858479	−	0.512849i	$-0.171410\pi$
$97$	−1.26860	−	3.48546i	−0.128807	−	0.353895i	−0.987286	+	0.158954i	$0.949188\pi$
$98$	1.12306	−	6.36918i	0.113446	−	0.643384i
$99$	0.187826	−	0.716788i	0.0188772	−	0.0720399i
$100$	1.15071	+	0.965559i	0.115071	+	0.0965559i
$101$	12.7053	−	2.24029i	1.26423	−	0.222918i	0.498958	−	0.866626i	$-0.333716\pi$
$101$	12.7053	−	2.24029i	1.26423	−	0.222918i	0.765271	+	0.643708i	$0.222605\pi$
$102$	4.75717	+	8.23967i	0.471031	+	0.815849i
$103$	−3.72289	−	2.14941i	−0.366827	−	0.211788i	0.305244	−	0.952274i	$-0.401262\pi$
$103$	−3.72289	−	2.14941i	−0.366827	−	0.211788i	−0.672071	+	0.740486i	$0.734595\pi$
$104$	−5.56519	−	2.02556i	−0.545712	−	0.198623i
$105$	−2.91378	−	1.06053i	−0.284356	−	0.103497i
$106$	6.42954	+	3.71209i	0.624492	+	0.360550i
$107$	−3.13260	−	5.42581i	−0.302839	−	0.524533i	0.673939	−	0.738787i	$-0.264601\pi$
$107$	−3.13260	−	5.42581i	−0.302839	−	0.524533i	−0.976778	+	0.214254i	$0.931268\pi$
$108$	−5.28961	+	0.932700i	−0.508992	+	0.0897491i
$109$	−12.8325	−	10.7677i	−1.22913	−	1.03136i	−0.998295	−	0.0583667i	$-0.981411\pi$
$109$	−12.8325	−	10.7677i	−1.22913	−	1.03136i	−0.230832	−	0.972994i	$-0.574145\pi$
$110$	2.14372	−	8.18095i	0.204396	−	0.780023i
$111$	1.10889	−	6.28885i	0.105252	−	0.596911i
$112$	0.249597	+	0.685761i	0.0235847	+	0.0647983i
$113$		−	11.8399i		−	1.11380i	−0.830578	−	0.556902i	$-0.811990\pi$
$113$		−	11.8399i		−	1.11380i	0.830578	−	0.556902i	$-0.188010\pi$
$114$	−5.86769	+	4.28080i	−0.549560	+	0.400934i
$115$	−10.1662			−0.948000
$116$	1.30026	−	0.473257i	0.120726	−	0.0439408i
$117$	0.229763	−	1.30305i	0.0212416	−	0.120467i
$118$	−0.276273	−	0.329249i	−0.0254330	−	0.0303098i
$119$	3.19201	+	2.67842i	0.292611	+	0.245530i
$120$	−4.18442	+	0.737826i	−0.381983	+	0.0673540i
$121$	−10.8111	+	2.02967i	−0.982830	+	0.184516i
$122$	−0.681111	−	0.393240i	−0.0616649	−	0.0356022i
$123$	−1.93915	+	5.32776i	−0.174847	+	0.480388i
$124$	3.00470	−	8.25534i	0.269830	−	0.741351i
$125$	4.45965	−	7.72433i	0.398883	−	0.690885i
$126$	−0.141199	+	0.0815215i	−0.0125790	+	0.00726251i
$127$	0.643184	+	3.64768i	0.0570733	+	0.323679i	0.999955	−	0.00944787i	$-0.00300740\pi$
$127$	0.643184	+	3.64768i	0.0570733	+	0.323679i	−0.942882	+	0.333127i	$0.891896\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	3.49096	−	2.92926i	0.307361	−	0.257907i
$130$	2.62236	−	14.8722i	0.229996	−	1.30437i
$131$	2.21377	+	6.08227i	0.193418	+	0.531411i	0.998054	−	0.0623574i	$-0.0198619\pi$
$131$	2.21377	+	6.08227i	0.193418	+	0.531411i	−0.804636	+	0.593768i	$0.797640\pi$
$132$	3.19484	+	4.50948i	0.278075	+	0.392500i
$133$	−1.77360	+	2.64067i	−0.153791	+	0.228975i
$134$			11.9914i			1.03590i
$135$	−4.68438	−	12.8702i	−0.403167	−	1.10769i
$136$	5.62309	+	0.991503i	0.482176	+	0.0850207i
$137$	−10.4339	+	8.75505i	−0.891426	+	0.747995i	−0.968496	−	0.249031i	$-0.919888\pi$
$137$	−10.4339	+	8.75505i	−0.891426	+	0.747995i	0.0770700	+	0.997026i	$0.475443\pi$
$138$	4.27023	−	5.08907i	0.363506	−	0.433210i
$139$	−0.195936	+	0.0345488i	−0.0166191	+	0.00293039i	−0.181952	−	0.983308i	$-0.558241\pi$
$139$	−0.195936	+	0.0345488i	−0.0166191	+	0.00293039i	0.165332	+	0.986238i	$0.447130\pi$
$140$	−1.61156	+	0.930433i	−0.136201	+	0.0786360i
$141$	17.2337	+	9.94987i	1.45134	+	0.837930i
$142$	5.46082	−	15.0035i	0.458262	−	1.25906i
$143$	−18.9446	+	5.18849i	−1.58422	+	0.433883i
$144$	−0.111708	+	0.193484i	−0.00930902	+	0.0161237i
$145$	1.76418	+	3.05565i	0.146507	+	0.253758i
$146$	4.70904	−	0.830330i	0.389723	−	0.0687186i
$147$	−6.92715	+	8.25546i	−0.571342	+	0.680899i
$148$	−2.46338	−	2.93575i	−0.202489	−	0.241317i
$149$	−16.7619	−	2.95557i	−1.37319	−	0.242130i	−0.562106	−	0.827065i	$-0.690009\pi$
$149$	−16.7619	−	2.95557i	−1.37319	−	0.242130i	−0.811080	+	0.584936i	$0.801120\pi$
$150$	−0.856088	−	2.35208i	−0.0698993	−	0.192047i
$151$	15.9976			1.30187			0.650933	−	0.759135i	$-0.274378\pi$
$151$	15.9976			1.30187			0.650933	+	0.759135i	$0.274378\pi$
$152$	−0.295502	+	4.34887i	−0.0239683	+	0.352740i
$153$			1.27567i			0.103132i
$154$	1.99030	+	1.37730i	0.160383	+	0.110986i
$155$	22.0612	+	3.88998i	1.77200	+	0.312451i
$156$	6.34333	+	7.55968i	0.507873	+	0.605259i
$157$	−0.125760	−	0.105525i	−0.0100367	−	0.00842180i	0.637755	−	0.770239i	$-0.279863\pi$
$157$	−0.125760	−	0.105525i	−0.0100367	−	0.00842180i	−0.647792	+	0.761817i	$0.724307\pi$
$158$	2.97075	+	16.8479i	0.236340	+	1.34035i
$159$	−6.18549	−	10.7136i	−0.490542	−	0.849643i
$160$	−1.27496	+	2.20830i	−0.100795	+	0.174582i
$161$	0.995102	−	2.73402i	0.0784250	−	0.215471i
$162$	7.78050	+	2.83187i	0.611294	+	0.222493i
$163$	−3.83252	+	6.63811i	−0.300186	+	0.519937i	−0.976178	−	0.216972i	$-0.930382\pi$
$163$	−3.83252	+	6.63811i	−0.300186	+	0.519937i	0.675992	+	0.736909i	$0.263715\pi$
$164$	1.70127	+	2.94669i	0.132847	+	0.230098i
$165$	−9.90953	+	10.0196i	−0.771456	+	0.780025i
$166$	0.211787	−	0.252397i	0.0164378	−	0.0195898i
$167$	11.9711	−	10.0450i	0.926354	−	0.777303i	−0.0488052	−	0.998808i	$-0.515541\pi$
$167$	11.9711	−	10.0450i	0.926354	−	0.777303i	0.975159	+	0.221505i	$0.0710969\pi$
$168$	0.211160	−	1.19755i	0.0162914	−	0.0923930i
$169$	−20.7430	+	7.54985i	−1.59562	+	0.580757i
$170$			14.5597i			1.11668i
$171$	−0.968313	+	0.103701i	−0.0740487	+	0.00793024i
$172$		−	2.73486i		−	0.208531i
$173$	−19.1437	+	6.96773i	−1.45547	+	0.529747i	−0.944113	−	0.329623i	$-0.893078\pi$
$173$	−19.1437	+	6.96773i	−1.45547	+	0.529747i	−0.511355	+	0.859370i	$0.670856\pi$
$174$	−2.27066	−	0.400378i	−0.172138	−	0.0303526i
$175$	−0.704637	−	0.839754i	−0.0532656	−	0.0634794i
$176$	3.30555	+	0.270810i	0.249165	+	0.0204131i
$177$	0.124364	+	0.705306i	0.00934780	+	0.0530140i
$178$	−7.01492	+	4.05006i	−0.525790	+	0.303565i
$179$	18.5306	+	10.6986i	1.38504	+	0.799654i	0.992751	−	0.120188i	$-0.0383496\pi$
$179$	18.5306	+	10.6986i	1.38504	+	0.799654i	0.392290	+	0.919842i	$0.371683\pi$
$180$	−0.535340	−	0.194848i	−0.0399019	−	0.0145231i
$181$	3.78048	−	10.3868i	0.281001	−	0.772044i	−0.716243	−	0.697851i	$-0.754140\pi$
$181$	3.78048	−	10.3868i	0.281001	−	0.772044i	0.997244	−	0.0741929i	$-0.0236381\pi$
$182$	3.74293	+	2.16098i	0.277445	+	0.160183i
$183$	0.655259	+	1.13494i	0.0484381	+	0.0838973i
$184$	−0.692308	−	3.92627i	−0.0510376	−	0.289449i
$185$	6.28145	−	7.48594i	0.461822	−	0.550378i
$186$	−11.2139	+	9.40961i	−0.822246	+	0.689946i
$187$	17.1186	−	8.09796i	1.25184	−	0.592181i
$188$	11.2222	−	4.08454i	0.818462	−	0.297896i
$189$	3.91975			0.285120
$190$	−11.0517	+	1.18358i	−0.801774	+	0.0858658i
$191$	−4.53072			−0.327831			−0.163916	−	0.986474i	$-0.552413\pi$
$191$	−4.53072			−0.327831			−0.163916	+	0.986474i	$0.552413\pi$
$192$	−0.569911	−	1.56582i	−0.0411298	−	0.113003i
$193$	0.874967	−	4.96218i	0.0629815	−	0.357186i	−0.936988	−	0.349362i	$-0.886398\pi$
$193$	0.874967	−	4.96218i	0.0629815	−	0.357186i	0.999969	−	0.00782395i	$-0.00249047\pi$
$194$	2.38420	+	2.84137i	0.171175	+	0.203999i
$195$	−16.1750	+	19.2767i	−1.15832	+	1.38043i
$196$	1.12306	+	6.36918i	0.0802184	+	0.454941i
$197$	−19.0550	+	11.0014i	−1.35761	+	0.783819i	−0.989302	−	0.145883i	$-0.953398\pi$
$197$	−19.0550	+	11.0014i	−1.35761	+	0.783819i	−0.368312	+	0.929702i	$0.620064\pi$
$198$	0.0686573	+	0.737801i	0.00487927	+	0.0524332i
$199$	16.6746	+	6.06906i	1.18203	+	0.430224i	0.856919	−	0.515451i	$-0.172376\pi$
$199$	16.6746	+	6.06906i	1.18203	+	0.430224i	0.325112	+	0.945675i	$0.394598\pi$
$200$	−1.41155	−	0.513763i	−0.0998118	−	0.0363285i
$201$	9.99065	−	17.3043i	0.704686	−	1.22055i
$202$	−11.1729	+	6.45067i	−0.786122	+	0.453868i
$203$	−0.994451	+	0.175349i	−0.0697968	+	0.0123071i
$204$	−7.28841	−	6.11571i	−0.510291	−	0.428185i
$205$	−6.64639	+	5.57698i	−0.464204	+	0.389513i
$206$	4.23351	+	0.746483i	0.294963	+	0.0520099i
$207$	0.837009	−	0.304646i	0.0581761	−	0.0211744i
$208$	5.92235			0.410641
$209$	7.53844	+	12.3358i	0.521445	+	0.853285i
$210$	3.10078			0.213974
$211$	6.99041	−	2.54430i	0.481240	−	0.175157i	−0.0899974	−	0.995942i	$-0.528686\pi$
$211$	6.99041	−	2.54430i	0.481240	−	0.175157i	0.571237	+	0.820785i	$0.306464\pi$
$212$	−7.31140	−	1.28920i	−0.502149	−	0.0885424i
$213$	−20.3805	+	17.1013i	−1.39645	+	1.17176i
$214$	4.79941	+	4.02719i	0.328081	+	0.275293i
$215$	6.86775	−	1.21097i	0.468377	−	0.0825875i
$216$	4.65160	−	2.68560i	0.316501	−	0.182732i
$217$	−3.20557	+	5.55222i	−0.217609	+	0.376909i
$218$	15.7413	+	5.72938i	1.06614	+	0.388043i
$219$	−7.48724	−	2.72513i	−0.505941	−	0.184147i
$220$	0.783610	+	8.42078i	0.0528310	+	0.567729i
$221$	29.2852	−	16.9078i	1.96994	−	1.13734i
$222$	1.10889	+	6.28885i	0.0744241	+	0.422080i
$223$	−2.47274	+	2.94689i	−0.165587	+	0.197338i	−0.842457	−	0.538764i	$-0.818891\pi$
$223$	−2.47274	+	2.94689i	−0.165587	+	0.197338i	0.676870	+	0.736102i	$0.263336\pi$
$224$	−0.469088	−	0.559038i	−0.0313423	−	0.0373523i
$225$	0.0582769	−	0.330505i	0.00388513	−	0.0220337i
$226$	4.04948	+	11.1259i	0.269368	+	0.740081i
$227$	−6.32853			−0.420039			−0.210019	−	0.977697i	$-0.567353\pi$
$227$	−6.32853			−0.420039			−0.210019	+	0.977697i	$0.567353\pi$
$228$	4.04971	−	6.02951i	0.268198	−	0.399314i
$229$	13.1901			0.871624			0.435812	−	0.900038i	$-0.356461\pi$
$229$	13.1901			0.871624			0.435812	+	0.900038i	$0.356461\pi$
$230$	9.55307	−	3.47703i	0.629911	−	0.229269i
$231$	−1.72462	−	3.64576i	−0.113472	−	0.239873i
$232$	−1.05998	+	0.889432i	−0.0695913	+	0.0583940i
$233$	−19.2589	+	22.9518i	−1.26169	+	1.50362i	−0.483868	+	0.875141i	$0.660769\pi$
$233$	−19.2589	+	22.9518i	−1.26169	+	1.50362i	−0.777823	+	0.628484i	$0.783676\pi$
$234$	0.229763	+	1.30305i	0.0150201	+	0.0851830i
$235$	15.2261	+	26.3725i	0.993244	+	1.72035i
$236$	0.372221	+	0.214902i	0.0242295	+	0.0139889i
$237$	9.74995	−	26.7878i	0.633327	−	1.74005i
$238$	−3.91558	−	1.42516i	−0.253810	−	0.0923791i
$239$	0.202081	+	0.116671i	0.0130715	+	0.00754684i	0.506522	−	0.862227i	$-0.330931\pi$
$239$	0.202081	+	0.116671i	0.0130715	+	0.00754684i	−0.493450	+	0.869774i	$0.664264\pi$
$240$	3.67972	−	2.12448i	0.237525	−	0.137135i
$241$	2.39677	+	13.5927i	0.154389	+	0.875585i	0.959342	+	0.282246i	$0.0910795\pi$
$241$	2.39677	+	13.5927i	0.154389	+	0.875585i	−0.804953	+	0.593339i	$0.797809\pi$
$242$	9.46495	−	5.60489i	0.608430	−	0.360296i
$243$	1.48925	+	1.77482i	0.0955353	+	0.113855i
$244$	0.774531	+	0.136571i	0.0495843	+	0.00874304i
$245$	−15.4969	+	5.64043i	−0.990063	+	0.360354i
$246$		−	5.66968i		−	0.361486i
$247$	15.2147	+	20.8548i	0.968090	+	1.32696i
$248$			8.78515i			0.557857i
$249$	−0.515908	+	0.187775i	−0.0326943	+	0.0118998i
$250$	−1.54882	+	8.78379i	−0.0979559	+	0.555535i
$251$	−0.371005	+	0.311310i	−0.0234176	+	0.0196497i	−0.654421	−	0.756130i	$-0.727088\pi$
$251$	−0.371005	+	0.311310i	−0.0234176	+	0.0196497i	0.631004	+	0.775780i	$0.282643\pi$
$252$	0.104802	−	0.124898i	0.00660191	−	0.00786785i
$253$	−9.40147	−	9.29819i	−0.591065	−	0.584572i
$254$	−1.85197	−	3.20771i	−0.116203	−	0.201270i
$255$	12.1305	−	21.0106i	0.759639	−	1.31573i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−1.44861	+	3.98002i	−0.0903617	+	0.248267i	−0.976638	−	0.214889i	$-0.931061\pi$
$257$	−1.44861	+	3.98002i	−0.0903617	+	0.248267i	0.886277	+	0.463156i	$0.153283\pi$
$258$	−2.27856	+	3.94658i	−0.141857	+	0.245703i
$259$	1.39837	+	2.42204i	0.0868903	+	0.150498i
$260$	2.62236	+	14.8722i	0.162632	+	0.922332i
$261$	−0.236818	−	0.198714i	−0.0146587	−	0.0123001i
$262$	−4.16052	−	4.95832i	−0.257038	−	0.306326i
$263$	−16.8558	−	2.97213i	−1.03937	−	0.183269i	−0.372184	−	0.928159i	$-0.621391\pi$
$263$	−16.8558	−	2.97213i	−1.03937	−	0.183269i	−0.667188	+	0.744890i	$0.732502\pi$
$264$	−4.54450	−	3.14483i	−0.279695	−	0.193551i
$265$		−	18.9312i		−	1.16293i
$266$	0.763477	−	3.08802i	0.0468118	−	0.189339i
$267$	13.4973			0.826022
$268$	−4.10128	−	11.2682i	−0.250526	−	0.688314i
$269$	−7.71717	−	1.36075i	−0.470524	−	0.0829661i	−0.0666417	−	0.997777i	$-0.521228\pi$
$269$	−7.71717	−	1.36075i	−0.470524	−	0.0829661i	−0.403883	+	0.914811i	$0.632340\pi$
$270$	8.80375	+	10.4919i	0.535779	+	0.638516i
$271$	5.20256	−	6.20017i	0.316033	−	0.376633i	−0.584520	−	0.811379i	$-0.698717\pi$
$271$	5.20256	−	6.20017i	0.316033	−	0.376633i	0.900553	+	0.434746i	$0.143162\pi$
$272$	−5.62309	+	0.991503i	−0.340950	+	0.0601187i
$273$	−3.60086	−	6.23688i	−0.217934	−	0.377473i
$274$	6.81022	−	11.7957i	0.411421	−	0.712601i
$275$	−4.80509	+	1.31601i	−0.289758	+	0.0793582i
$276$	−2.27214	+	6.24266i	−0.136767	+	0.375764i
$277$	5.28997	+	3.05417i	0.317844	+	0.183507i	0.650431	−	0.759565i	$-0.274588\pi$
$277$	5.28997	+	3.05417i	0.317844	+	0.183507i	−0.332587	+	0.943072i	$0.607922\pi$
$278$	0.172303	−	0.0994792i	0.0103341	−	0.00596637i
$279$	−1.93293	+	0.340827i	−0.115721	+	0.0204048i
$280$	1.19614	−	1.42551i	0.0714832	−	0.0851903i
$281$	−12.9720	+	10.8848i	−0.773845	+	0.649333i	−0.941690	−	0.336480i	$-0.890763\pi$
$281$	−12.9720	+	10.8848i	−0.773845	+	0.649333i	0.167846	+	0.985813i	$0.446319\pi$
$282$	−19.5974	−	3.45555i	−1.16701	−	0.205775i
$283$	3.61836	+	9.94136i	0.215089	+	0.590952i	0.999574	−	0.0291959i	$-0.00929467\pi$
$283$	3.61836	+	9.94136i	0.215089	+	0.590952i	−0.784485	+	0.620148i	$0.787072\pi$
$284$			15.9664i			0.947430i
$285$	16.9344	+	7.49978i	1.00311	+	0.444249i
$286$	16.0275	−	11.3550i	0.947726	−	0.671436i
$287$	−0.849263	−	2.33333i	−0.0501304	−	0.137732i
$288$	0.0387959	−	0.220022i	0.00228607	−	0.0129649i
$289$	−11.9520	+	10.0289i	−0.703060	+	0.589937i
$290$	−2.70288	−	2.26799i	−0.158719	−	0.133181i
$291$	−1.07325	−	6.08669i	−0.0629149	−	0.356808i
$292$	−4.14106	+	2.39084i	−0.242337	+	0.139913i
$293$	16.3908	−	28.3898i	0.957564	−	1.65855i	0.229174	−	0.973386i	$-0.426398\pi$
$293$	16.3908	−	28.3898i	0.957564	−	1.65855i	0.728390	−	0.685163i	$-0.240269\pi$
$294$	3.68586	−	10.1268i	0.214964	−	0.590608i
$295$	−0.374844	+	1.02988i	−0.0218243	+	0.0599617i
$296$	3.31891	+	1.91617i	0.192908	+	0.111375i
$297$	7.43935	−	16.1866i	0.431675	−	0.939239i
$298$	16.7619	−	2.95557i	0.970989	−	0.171212i
$299$	−18.0874	−	15.1772i	−1.04602	−	0.877718i
$300$	1.60892	+	1.91743i	0.0928909	+	0.110703i
$301$	−0.346571	+	1.96550i	−0.0199760	+	0.113290i
$302$	−15.0328	+	5.47150i	−0.865041	+	0.314849i
$303$	21.4976			1.23501
$304$	−1.20972	−	4.18767i	−0.0693822	−	0.240179i
$305$			2.00547i			0.114833i
$306$	−0.436305	−	1.19874i	−0.0249419	−	0.0685274i
$307$	−2.12723	+	12.0641i	−0.121408	+	0.688537i	0.861969	+	0.506961i	$0.169231\pi$
$307$	−2.12723	+	12.0641i	−0.121408	+	0.688537i	−0.983377	+	0.181576i	$0.941880\pi$
$308$	−2.34133	−	0.613518i	−0.133410	−	0.0349584i
$309$	−5.48730	−	4.60439i	−0.312162	−	0.261935i
$310$	−22.0612	+	3.88998i	−1.25299	+	0.220936i
$311$	−0.628382	−	1.08839i	−0.0356323	−	0.0617170i	0.847659	−	0.530541i	$-0.178011\pi$
$311$	−0.628382	−	1.08839i	−0.0356323	−	0.0617170i	−0.883292	+	0.468824i	$0.844678\pi$
$312$	−8.54634	−	4.93423i	−0.483841	−	0.279346i
$313$	−17.1379	−	6.23767i	−0.968689	−	0.352574i	−0.191256	−	0.981540i	$-0.561256\pi$
$313$	−17.1379	−	6.23767i	−0.968689	−	0.352574i	−0.777433	+	0.628966i	$0.783478\pi$
$314$	0.154267	+	0.0561486i	0.00870579	+	0.00316865i
$315$	0.360049	+	0.207874i	0.0202864	+	0.0117124i
$316$	−8.55393	−	14.8158i	−0.481196	−	0.833456i
$317$	−7.75282	+	1.36703i	−0.435442	+	0.0767801i	−0.387072	−	0.922049i	$-0.626514\pi$
$317$	−7.75282	+	1.36703i	−0.435442	+	0.0767801i	−0.0483694	+	0.998830i	$0.515402\pi$
$318$	9.47673	+	7.95192i	0.531428	+	0.445921i
$319$	−1.16328	+	4.43936i	−0.0651314	+	0.248557i
$320$	0.442791	−	2.51119i	0.0247528	−	0.140380i
$321$	−3.57060	−	9.81015i	−0.199292	−	0.547549i
$322$			2.90948i			0.162139i
$323$	−17.9374	−	17.2538i	−0.998061	−	0.960027i
$324$	−8.27984			−0.459991
$325$	−8.35971	+	3.04269i	−0.463713	+	0.168778i
$326$	1.33102	−	7.54858i	0.0737183	−	0.418077i
$327$	−17.9423	−	21.3828i	−0.992214	−	1.18247i
$328$	−2.60650	−	2.18711i	−0.143920	−	0.120763i
$329$	−8.58283	+	1.51338i	−0.473186	+	0.0834355i
$330$	5.88501	−	12.8046i	0.323959	−	0.704870i
$331$	−13.3505	−	7.70793i	−0.733811	−	0.423666i	0.0860038	−	0.996295i	$-0.472590\pi$
$331$	−13.3505	−	7.70793i	−0.733811	−	0.423666i	−0.819815	+	0.572629i	$0.805924\pi$
$332$	−0.112689	+	0.309611i	−0.00618463	+	0.0169921i
$333$	−0.292841	+	0.804573i	−0.0160476	+	0.0440903i
$334$	−7.81360	+	13.5336i	−0.427541	+	0.740523i
$335$	26.4806	−	15.2886i	1.44679	−	0.835303i
$336$	0.211160	+	1.19755i	0.0115197	+	0.0653317i
$337$	−5.87431	−	4.92913i	−0.319994	−	0.268507i	0.468614	−	0.883403i	$-0.344753\pi$
$337$	−5.87431	−	4.92913i	−0.319994	−	0.268507i	−0.788608	+	0.614896i	$0.789198\pi$
$338$	16.9099	−	14.1891i	0.919776	−	0.771784i
$339$	3.42589	−	19.4292i	0.186069	−	1.05525i
$340$	−4.97971	−	13.6816i	−0.270062	−	0.741991i
$341$	16.8439	+	23.7750i	0.912147	+	1.28749i
$342$	0.874449	−	0.428630i	0.0472848	−	0.0231776i
$343$		−	9.82815i		−	0.530670i
$344$	0.935377	+	2.56993i	0.0504321	+	0.138561i
$345$	−16.6826	−	2.94159i	−0.898161	−	0.158370i
$346$	15.6061	−	13.0950i	0.838988	−	0.703994i
$347$	6.51799	−	7.76784i	0.349904	−	0.417000i	−0.562172	−	0.827020i	$-0.690034\pi$
$347$	6.51799	−	7.76784i	0.349904	−	0.417000i	0.912076	+	0.410021i	$0.134479\pi$
$348$	2.27066	−	0.400378i	0.121720	−	0.0214625i
$349$	−3.58836	+	2.07174i	−0.192080	+	0.110898i	−0.592956	−	0.805235i	$-0.702039\pi$
$349$	−3.58836	+	2.07174i	−0.192080	+	0.110898i	0.400876	+	0.916132i	$0.368706\pi$
$350$	0.949355	+	0.548111i	0.0507452	+	0.0292977i
$351$	10.8797	−	29.8918i	0.580717	−	1.59551i
$352$	−3.19882	+	0.876086i	−0.170498	+	0.0466955i
$353$	−12.9615	+	22.4500i	−0.689873	+	1.19489i	0.282006	+	0.959413i	$0.409000\pi$
$353$	−12.9615	+	22.4500i	−0.689873	+	1.19489i	−0.971879	+	0.235482i	$0.924333\pi$
$354$	−0.358093	−	0.620235i	−0.0190324	−	0.0329651i
$355$	−40.0946	+	7.06976i	−2.12800	+	0.375224i
$356$	5.20666	−	6.20506i	0.275953	−	0.328867i
$357$	4.46307	+	5.31888i	0.236211	+	0.281505i
$358$	−21.0722	−	3.71560i	−1.11370	−	0.196376i
$359$	4.78460	+	13.1456i	0.252522	+	0.693798i	0.999578	+	0.0290372i	$0.00924413\pi$
$359$	4.78460	+	13.1456i	0.252522	+	0.693798i	−0.747057	+	0.664760i	$0.768534\pi$
$360$	0.569696			0.0300256
$361$	11.6385	−	15.0181i	0.612554	−	0.790428i
$362$			11.0534i			0.580953i
$363$	−18.3283	+	0.202463i	−0.961985	+	0.0106266i
$364$	−4.25631	−	0.750501i	−0.223091	−	0.0393370i
$365$	−7.83748	−	9.34034i	−0.410232	−	0.488896i
$366$	−1.00391	−	0.842384i	−0.0524754	−	0.0440321i
$367$	3.69925	+	20.9795i	0.193099	+	1.09512i	0.915100	+	0.403228i	$0.132112\pi$
$367$	3.69925	+	20.9795i	0.193099	+	1.09512i	−0.722000	+	0.691893i	$0.756777\pi$
$368$	1.99342	+	3.45270i	0.103914	+	0.179985i
$369$	0.380092	−	0.658339i	0.0197868	−	0.0342717i
$370$	−3.34229	+	9.18287i	−0.173757	+	0.477395i
$371$	5.09122	+	1.85305i	0.264323	+	0.0962057i
$372$	7.31938	−	12.6775i	0.379492	−	0.657300i
$373$	14.1481	+	24.5053i	0.732563	+	1.26884i	0.955784	+	0.294069i	$0.0950094\pi$
$373$	14.1481	+	24.5053i	0.732563	+	1.26884i	−0.223221	+	0.974768i	$0.571657\pi$
$374$	−13.3166	+	13.4645i	−0.688585	+	0.696233i
$375$	9.55330	−	11.3852i	0.493330	−	0.587928i
$376$	−9.14841	+	7.67643i	−0.471793	+	0.395882i
$377$	−1.42302	+	8.07032i	−0.0732890	+	0.415643i
$378$	−3.68336	+	1.34063i	−0.189452	+	0.0689548i
$379$			4.54532i			0.233477i	0.993163	+	0.116739i	$0.0372440\pi$
$379$			4.54532i			0.233477i	−0.993163	+	0.116739i	$0.962756\pi$
$380$	9.98038	−	4.89210i	0.511983	−	0.250959i
$381$			6.17192i			0.316197i
$382$	4.25748	−	1.54960i	0.217832	−	0.0792843i
$383$	15.0968	+	2.66197i	0.771410	+	0.136020i	0.545481	−	0.838123i	$-0.316347\pi$
$383$	15.0968	+	2.66197i	0.771410	+	0.136020i	0.225929	+	0.974144i	$0.427458\pi$
$384$	1.07108	+	1.27647i	0.0546584	+	0.0651394i
$385$	0.503942	−	6.15119i	0.0256833	−	0.313494i
$386$	0.874967	+	4.96218i	0.0445346	+	0.252568i
$387$	−0.529152	+	0.305506i	−0.0268983	+	0.0155298i
$388$	−3.21222	−	1.85458i	−0.163076	−	0.0941518i
$389$	20.3379	+	7.40239i	1.03117	+	0.375316i	0.801527	−	0.597959i	$-0.204021\pi$
$389$	20.3379	+	7.40239i	1.03117	+	0.375316i	0.229645	+	0.973274i	$0.426243\pi$
$390$	8.60656	−	23.6463i	0.435810	−	1.19738i
$391$	19.7144	+	11.3821i	0.996999	+	0.575618i
$392$	−3.23372	−	5.60096i	−0.163327	−	0.282891i
$393$	1.87286	+	10.6215i	0.0944734	+	0.535785i
$394$	14.1432	−	16.8552i	0.712522	−	0.849151i
$395$	33.4178	−	28.0409i	1.68143	−	1.41089i
$396$	−0.316860	−	0.669824i	−0.0159228	−	0.0336599i
$397$	1.46705	−	0.533963i	0.0736292	−	0.0267988i	−0.304943	−	0.952371i	$-0.598637\pi$
$397$	1.46705	−	0.533963i	0.0736292	−	0.0267988i	0.378572	+	0.925572i	$0.376415\pi$
$398$	−17.7447			−0.889464
$399$	−3.67454	+	3.82012i	−0.183957	+	0.191245i
$400$	1.50214			0.0751071
$401$	−6.46916	−	17.7739i	−0.323055	−	0.887585i	−0.989821	−	0.142318i	$-0.954544\pi$
$401$	−6.46916	−	17.7739i	−0.323055	−	0.887585i	0.666766	−	0.745267i	$-0.267678\pi$
$402$	−3.46971	+	19.6777i	−0.173054	+	0.981436i
$403$	33.4434	+	39.8563i	1.66594	+	1.98538i
$404$	8.29282	−	9.88300i	0.412583	−	0.491698i
$405$	−3.66623	−	20.7922i	−0.182177	−	1.03318i
$406$	0.874506	−	0.504896i	0.0434010	−	0.0250576i
$407$	12.6558	−	1.17770i	0.627323	−	0.0583766i
$408$	8.94056	+	3.25410i	0.442624	+	0.161102i
$409$	19.6766	+	7.16170i	0.972945	+	0.354123i	0.779094	−	0.626908i	$-0.215680\pi$
$409$	19.6766	+	7.16170i	0.972945	+	0.354123i	0.193852	+	0.981031i	$0.437902\pi$
$410$	4.33812	−	7.51385i	0.214245	−	0.371082i
$411$	−19.6552	+	11.3479i	−0.969519	+	0.559752i
$412$	−4.23351	+	0.746483i	−0.208570	+	0.0367766i
$413$	−0.240277	−	0.201616i	−0.0118232	−	0.00992088i
$414$	−0.682336	+	0.572548i	−0.0335350	+	0.0281392i
$415$	−0.827390	−	0.145891i	−0.0406150	−	0.00716152i
$416$	−5.56519	+	2.02556i	−0.272856	+	0.0993115i
$417$	−0.331526			−0.0162349
$418$	−11.3029	−	9.01356i	−0.552843	−	0.440868i
$419$	−7.71582			−0.376943			−0.188471	−	0.982079i	$-0.560353\pi$
$419$	−7.71582			−0.376943			−0.188471	+	0.982079i	$0.560353\pi$
$420$	−2.91378	+	1.06053i	−0.142178	+	0.0517485i
$421$	−8.43170	−	1.48674i	−0.410936	−	0.0724591i	−0.0356413	−	0.999365i	$-0.511347\pi$
$421$	−8.43170	−	1.48674i	−0.410936	−	0.0724591i	−0.375295	+	0.926906i	$0.622458\pi$
$422$	−5.69864	+	4.78172i	−0.277405	+	0.232771i
$423$	−2.04391	−	1.71504i	−0.0993781	−	0.0833882i
$424$	7.31140	−	1.28920i	0.355073	−	0.0626089i
$425$	7.42789	−	4.28849i	0.360306	−	0.208023i
$426$	13.3025	−	23.0405i	0.644506	−	1.11632i
$427$	−0.539337	−	0.196303i	−0.0261003	−	0.00949975i
$428$	−5.88735	−	2.14282i	−0.284576	−	0.103577i
$429$	−32.5892	+	3.03264i	−1.57342	+	0.146417i
$430$	−6.03940	+	3.48685i	−0.291246	+	0.168151i
$431$	1.49517	+	8.47954i	0.0720199	+	0.408445i	0.999410	+	0.0343492i	$0.0109358\pi$
$431$	1.49517	+	8.47954i	0.0720199	+	0.408445i	−0.927390	+	0.374096i	$0.877953\pi$
$432$	−3.45254	+	4.11458i	−0.166111	+	0.197963i
$433$	2.07509	+	2.47299i	0.0997224	+	0.118844i	0.813597	−	0.581429i	$-0.197506\pi$
$433$	2.07509	+	2.47299i	0.0997224	+	0.118844i	−0.713875	+	0.700273i	$0.753062\pi$
$434$	1.11328	−	6.31375i	0.0534394	−	0.303070i
$435$	2.01085	+	5.52477i	0.0964130	+	0.264893i
$436$	−16.7516			−0.802256
$437$	−7.03710	+	15.8897i	−0.336630	+	0.760107i
$438$	7.96776			0.380714
$439$	16.1949	−	5.89446i	0.772941	−	0.281327i	0.0747148	−	0.997205i	$-0.476195\pi$
$439$	16.1949	−	5.89446i	0.772941	−	0.281327i	0.698226	+	0.715878i	$0.253973\pi$
$440$	−3.61643	−	7.64493i	−0.172406	−	0.364458i
$441$	1.10688	−	0.928784i	0.0527086	−	0.0442278i
$442$	−21.7363	+	25.9043i	−1.03389	+	1.23214i
$443$	−2.35651	−	13.3644i	−0.111961	−	0.634963i	−0.988210	−	0.153104i	$-0.951073\pi$
$443$	−2.35651	−	13.3644i	−0.111961	−	0.634963i	0.876249	−	0.481859i	$-0.160038\pi$
$444$	−3.19293	−	5.53032i	−0.151530	−	0.262457i
$445$	17.8875	+	10.3274i	0.847951	+	0.489565i
$446$	1.31571	−	3.61490i	0.0623009	−	0.171170i
$447$	−26.6509	−	9.70014i	−1.26054	−	0.458801i
$448$	0.632001	+	0.364886i	0.0298592	+	0.0172392i
$449$	−23.9745	+	13.8417i	−1.13143	+	0.653231i	−0.944294	−	0.329104i	$-0.893253\pi$
$449$	−23.9745	+	13.8417i	−1.13143	+	0.653231i	−0.187135	+	0.982334i	$0.559920\pi$
$450$	0.0582769	+	0.330505i	0.00274720	+	0.0155801i
$451$	−11.2473	−	0.921444i	−0.529613	−	0.0433891i
$452$	−7.61054	−	9.06989i	−0.357970	−	0.426612i
$453$	26.2519	+	4.62892i	1.23342	+	0.217486i
$454$	5.94687	−	2.16448i	0.279100	−	0.101584i
$455$		−	11.0207i		−	0.516659i
$456$	−1.74327	+	7.05096i	−0.0816360	+	0.330192i
$457$		−	27.4765i		−	1.28530i	−0.766162	−	0.642648i	$-0.777836\pi$
$457$		−	27.4765i		−	1.28530i	0.766162	−	0.642648i	$-0.222164\pi$
$458$	−12.3946	+	4.51127i	−0.579162	+	0.210798i
$459$	−5.32557	+	30.2028i	−0.248576	+	1.40975i
$460$	−7.78773	+	6.53468i	−0.363105	+	0.304681i
$461$	5.47728	−	6.52757i	0.255102	−	0.304019i	−0.623260	−	0.782015i	$-0.714192\pi$
$461$	5.47728	−	6.52757i	0.255102	−	0.304019i	0.878362	+	0.477996i	$0.158637\pi$
$462$	2.86754	+	2.83604i	0.133410	+	0.131944i
$463$	16.2030	+	28.0643i	0.753015	+	1.30426i	0.946355	+	0.323129i	$0.104735\pi$
$463$	16.2030	+	28.0643i	0.753015	+	1.30426i	−0.193340	+	0.981132i	$0.561932\pi$
$464$	0.691855	−	1.19833i	0.0321186	−	0.0556310i
$465$	35.0767	+	12.7669i	1.62664	+	0.592049i
$466$	10.2474	−	28.1546i	0.474703	−	1.30424i
$467$	−4.05400	+	7.02174i	−0.187597	+	0.324927i	−0.944449	−	0.328659i	$-0.893403\pi$
$467$	−4.05400	+	7.02174i	−0.187597	+	0.324927i	0.756852	+	0.653587i	$0.226737\pi$
$468$	−0.661576	−	1.14588i	−0.0305813	−	0.0529685i
$469$	1.51959	+	8.61800i	0.0701680	+	0.397942i
$470$	−23.3278	−	19.5744i	−1.07603	−	0.902898i
$471$	−0.175837	−	0.209554i	−0.00810214	−	0.00965575i
$472$	−0.423274	−	0.0746347i	−0.0194828	−	0.00343534i
$473$	7.45874	+	5.16151i	0.342953	+	0.237326i
$474$			28.5070i			1.30937i
$475$	3.85905	+	5.28960i	0.177066	+	0.242704i
$476$	4.16688			0.190989
$477$	0.567304	+	1.55866i	0.0259751	+	0.0713659i
$478$	−0.229798	−	0.0405195i	−0.0105107	−	0.00185332i
$479$	19.6986	+	23.4759i	0.900054	+	1.07264i	0.997004	+	0.0773535i	$0.0246470\pi$
$479$	19.6986	+	23.4759i	0.900054	+	1.07264i	−0.0969495	+	0.995289i	$0.530909\pi$
$480$	−2.73118	+	3.25490i	−0.124661	+	0.148565i
$481$	22.3517	−	3.94120i	1.01915	−	0.179703i
$482$	−6.90121	−	11.9533i	−0.314342	−	0.544456i
$483$	2.42405	−	4.19857i	0.110298	−	0.191042i
$484$	−6.97715	+	8.50408i	−0.317143	+	0.386549i
$485$	3.23485	−	8.88768i	0.146887	−	0.403569i
$486$	−2.00646	−	1.15843i	−0.0910148	−	0.0525474i
$487$	−20.8831	+	12.0569i	−0.946304	+	0.546349i	−0.891931	−	0.452172i	$-0.850649\pi$
$487$	−20.8831	+	12.0569i	−0.946304	+	0.546349i	−0.0543730	+	0.998521i	$0.517316\pi$
$488$	−0.774531	+	0.136571i	−0.0350614	+	0.00618227i
$489$	−8.20988	+	9.78415i	−0.371264	+	0.442455i
$490$	12.6332	−	10.6005i	0.570711	−	0.478883i
$491$	14.8258	+	2.61419i	0.669080	+	0.117977i	0.497862	−	0.867256i	$-0.334119\pi$
$491$	14.8258	+	2.61419i	0.669080	+	0.117977i	0.171218	+	0.985233i	$0.445230\pi$
$492$	1.93915	+	5.32776i	0.0874234	+	0.240194i
$493$		−	7.90076i		−	0.355832i
$494$	−21.4299	−	14.3934i	−0.964178	−	0.647589i
$495$	1.54175	−	1.09229i	0.0692967	−	0.0490946i
$496$	−3.00470	−	8.25534i	−0.134915	−	0.370676i
$497$	2.02332	−	11.4748i	0.0907581	−	0.514715i
$498$	0.420572	−	0.352902i	0.0188463	−	0.0158139i
$499$	−30.6434	−	25.7129i	−1.37179	−	1.15107i	−0.972141	−	0.234398i	$-0.924688\pi$
$499$	−30.6434	−	25.7129i	−1.37179	−	1.15107i	−0.399648	−	0.916669i	$-0.630868\pi$
$500$	−1.54882	−	8.78379i	−0.0692653	−	0.392823i
$501$	22.5511	−	13.0199i	1.00751	−	0.581685i
$502$	0.242156	−	0.419427i	0.0108080	−	0.0187199i
$503$	1.36972	−	3.76327i	0.0610727	−	0.167796i	−0.905403	−	0.424552i	$-0.860432\pi$
$503$	1.36972	−	3.76327i	0.0610727	−	0.167796i	0.966476	+	0.256756i	$0.0826538\pi$
$504$	−0.0557640	+	0.153210i	−0.00248393	+	0.00682453i
$505$	28.4901	+	16.4488i	1.26779	+	0.731960i
$506$	12.0147	+	5.52195i	0.534117	+	0.245480i
$507$	−36.2237	+	6.38722i	−1.60875	+	0.283666i
$508$	2.83739	+	2.38085i	0.125889	+	0.105633i
$509$	1.77532	+	2.11575i	0.0786898	+	0.0937788i	0.803953	−	0.594693i	$-0.202726\pi$
$509$	1.77532	+	2.11575i	0.0786898	+	0.0937788i	−0.725263	+	0.688472i	$0.758282\pi$
$510$	−4.21287	+	23.8923i	−0.186549	+	1.05797i
$511$	3.27909	−	1.19349i	0.145058	−	0.0527970i
$512$	1.00000			0.0441942
$513$	−23.3587	−	1.58720i	−1.03131	−	0.0700766i
$514$		−	4.23545i		−	0.186818i
$515$	−3.74912	−	10.3006i	−0.165206	−	0.453900i
$516$	0.791335	−	4.48789i	0.0348366	−	0.197568i
$517$	−10.0400	+	38.3149i	−0.441557	+	1.68509i
$518$	−2.14242	−	1.79771i	−0.0941327	−	0.0789867i
$519$	−33.4308	+	5.89475i	−1.46745	+	0.258751i
$520$	−7.55079	−	13.0784i	−0.331124	−	0.573524i
$521$	19.2596	+	11.1195i	0.843779	+	0.487156i	0.858547	−	0.512735i	$-0.171368\pi$
$521$	19.2596	+	11.1195i	0.843779	+	0.487156i	−0.0147682	+	0.999891i	$0.504701\pi$
$522$	0.290500	+	0.105733i	0.0127148	+	0.00462782i
$523$	−33.8949	−	12.3368i	−1.48212	−	0.539448i	−0.530760	−	0.847522i	$-0.678093\pi$
$523$	−33.8949	−	12.3368i	−1.48212	−	0.539448i	−0.951363	+	0.308074i	$0.900316\pi$
$524$	5.60545	+	3.23631i	0.244875	+	0.141379i
$525$	−0.913321	−	1.58192i	−0.0398606	−	0.0690406i
$526$	16.8558	−	2.97213i	0.734947	−	0.129591i
$527$	−38.4261	−	32.2434i	−1.67387	−	1.40454i
$528$	5.34603	+	1.40086i	0.232656	+	0.0609648i
$529$	−1.23379	+	6.99716i	−0.0536430	+	0.304224i
$530$	6.47484	+	17.7895i	0.281249	+	0.772725i
$531$		−	0.0960253i		−	0.00416714i
$532$	0.338732	+	3.16291i	0.0146859	+	0.137130i
$533$	−20.1511			−0.872839
$534$	−12.6833	+	4.61635i	−0.548861	+	0.199769i
$535$	2.77417	−	15.7331i	0.119938	−	0.680201i
$536$	7.70789	+	9.18591i	0.332930	+	0.396771i
$537$	27.3129	+	22.9183i	1.17864	+	0.988996i
$538$	7.71717	−	1.36075i	0.332711	−	0.0586659i
$539$	−19.4901	−	8.95768i	−0.839499	−	0.385834i
$540$	−11.8613	−	6.84810i	−0.510427	−	0.294695i
$541$	5.99359	−	16.4672i	0.257684	−	0.707982i	−0.741625	−	0.670815i	$-0.765944\pi$
$541$	5.99359	−	16.4672i	0.257684	−	0.707982i	0.999309	−	0.0371671i	$-0.0118334\pi$
$542$	−2.76822	+	7.60563i	−0.118905	+	0.326690i
$543$	9.20918	−	15.9508i	0.395204	−	0.684513i
$544$	4.94486	−	2.85492i	0.212009	−	0.122404i
$545$	−7.41745	−	42.0664i	−0.317729	−	1.80193i
$546$	5.51684	+	4.62918i	0.236099	+	0.198111i
$547$	−35.6076	+	29.8783i	−1.52247	+	1.27750i	−0.689322	+	0.724455i	$0.742091\pi$
$547$	−35.6076	+	29.8783i	−1.52247	+	1.27750i	−0.833149	+	0.553049i	$0.813464\pi$
$548$	−2.36517	+	13.4135i	−0.101035	+	0.572997i
$549$	−0.0600972	−	0.165116i	−0.00256489	−	0.00704697i
$550$	4.06521	−	2.88008i	0.173341	−	0.122807i
$551$	5.99716	−	0.642265i	0.255488	−	0.0273614i
$552$		−	6.64331i		−	0.282758i
$553$	4.27006	+	11.7319i	0.181581	+	0.498891i
$554$	−6.01554	−	1.06070i	−0.255576	−	0.0450649i
$555$	12.4739	−	10.4668i	0.529487	−	0.444292i
$556$	−0.127888	+	0.152411i	−0.00542366	+	0.00646367i
$557$	16.0039	−	2.82192i	0.678108	−	0.119569i	0.176022	−	0.984386i	$-0.443677\pi$
$557$	16.0039	−	2.82192i	0.678108	−	0.119569i	0.502086	+	0.864818i	$0.332566\pi$
$558$	1.69979	−	0.981373i	0.0719578	−	0.0415448i
$559$	14.0268	+	8.09840i	0.593272	+	0.342526i
$560$	−0.636454	+	1.74864i	−0.0268951	+	0.0738936i
$561$	30.4347	−	8.33539i	1.28496	−	0.351920i
$562$	8.46687	−	14.6651i	0.357154	−	0.618608i
$563$	−15.4211	−	26.7101i	−0.649921	−	1.12570i	−0.983141	−	0.182847i	$-0.941469\pi$
$563$	−15.4211	−	26.7101i	−0.649921	−	1.12570i	0.333220	−	0.942849i	$-0.391865\pi$
$564$	19.5974	−	3.45555i	0.825200	−	0.145505i
$565$	19.4063	−	23.1276i	0.816431	−	0.972984i
$566$	−6.80029	−	8.10427i	−0.285837	−	0.340648i
$567$	5.95059	+	1.04925i	0.249901	+	0.0440644i
$568$	−5.46082	−	15.0035i	−0.229131	−	0.629532i
$569$	22.7747			0.954764			0.477382	−	0.878696i	$-0.341586\pi$
$569$	22.7747			0.954764			0.477382	+	0.878696i	$0.341586\pi$
$570$	−18.4782	−	1.25558i	−0.773967	−	0.0525903i
$571$			41.7992i			1.74924i	0.484808	+	0.874621i	$0.338890\pi$
$571$			41.7992i			1.74924i	−0.484808	+	0.874621i	$0.661110\pi$
$572$	−11.1773	+	16.1519i	−0.467346	+	0.675347i
$573$	−7.43488	−	1.31097i	−0.310597	−	0.0547666i
$574$	1.59609	+	1.90215i	0.0666196	+	0.0793941i
$575$	−4.58769	−	3.84953i	−0.191320	−	0.160536i
$576$	0.0387959	+	0.220022i	0.00161649	+	0.00916760i
$577$	7.81608	+	13.5378i	0.325388	+	0.563588i	0.981591	−	0.190996i	$-0.0611719\pi$
$577$	7.81608	+	13.5378i	0.325388	+	0.563588i	−0.656203	+	0.754584i	$0.727839\pi$
$578$	7.80112	−	13.5119i	0.324484	−	0.562023i
$579$	2.87163	−	7.88974i	0.119341	−	0.327886i
$580$	3.31558	+	1.20677i	0.137672	+	0.0501085i
$581$	0.120223	−	0.208232i	0.00498769	−	0.00863894i
$582$	3.09029	+	5.35255i	0.128097	+	0.221870i
$583$	17.3148	−	17.5072i	0.717107	−	0.725073i
$584$	3.07361	−	3.66298i	0.127187	−	0.151575i
$585$	2.58459	−	2.16873i	0.106860	−	0.0896659i
$586$	−5.69248	+	32.2837i	−0.235154	+	1.33363i
$587$	12.8307	−	4.67000i	0.529580	−	0.192751i	−0.0633708	−	0.997990i	$-0.520185\pi$
$587$	12.8307	−	4.67000i	0.529580	−	0.192751i	0.592951	+	0.805239i	$0.297963\pi$
$588$			10.7767i			0.444425i
$589$	21.3510	−	31.7889i	0.879751	−	1.30984i
$590$		−	1.09597i		−	0.0451204i
$591$	−34.4524	+	12.5397i	−1.41718	+	0.515813i
$592$	−3.77412	−	0.665479i	−0.155115	−	0.0273510i
$593$	14.7699	+	17.6021i	0.606526	+	0.722830i	0.978691	−	0.205337i	$-0.0658290\pi$
$593$	14.7699	+	17.6021i	0.606526	+	0.722830i	−0.372165	+	0.928167i	$0.621385\pi$
$594$	−1.45458	+	17.7548i	−0.0596821	+	0.728488i
$595$	1.84505	+	10.4638i	0.0756399	+	0.428975i
$596$	−14.7401	+	8.51022i	−0.603780	+	0.348592i
$597$	25.6068	+	14.7841i	1.04802	+	0.605073i
$598$	22.1875	+	8.07560i	0.907316	+	0.330236i
$599$	−5.56255	+	15.2830i	−0.227280	+	0.624446i	−0.999946	−	0.0103663i	$-0.996700\pi$
$599$	−5.56255	+	15.2830i	−0.227280	+	0.624446i	0.772667	+	0.634812i	$0.218922\pi$
$600$	−2.16769	−	1.25152i	−0.0884956	−	0.0510929i
$601$	−13.9873	−	24.2267i	−0.570554	−	0.988228i	−0.996509	−	0.0834840i	$-0.973395\pi$
$601$	−13.9873	−	24.2267i	−0.570554	−	0.988228i	0.425955	−	0.904744i	$-0.359938\pi$
$602$	−0.346571	−	1.96550i	−0.0141252	−	0.0801079i
$603$	−1.72207	+	2.05228i	−0.0701281	+	0.0835755i
$604$	12.2549	−	10.2831i	0.498643	−	0.418411i
$605$	−24.4448	−	13.7554i	−0.993821	−	0.559238i
$606$	−20.2012	+	7.35262i	−0.820616	+	0.298680i
$607$	7.35323			0.298458			0.149229	−	0.988803i	$-0.452321\pi$
$607$	7.35323			0.298458			0.149229	+	0.988803i	$0.452321\pi$
$608$	2.56903	+	3.52137i	0.104188	+	0.142811i
$609$	−1.68263			−0.0681834
$610$	−0.685910	−	1.88452i	−0.0277717	−	0.0763021i
$611$	−12.2816	+	69.6526i	−0.496862	+	2.81784i
$612$	0.819986	+	0.977221i	0.0331460	+	0.0395018i
$613$	−17.7997	+	21.2129i	−0.718925	+	0.856781i	−0.994526	−	0.104491i	$-0.966679\pi$
$613$	−17.7997	+	21.2129i	−0.718925	+	0.856781i	0.275601	+	0.961272i	$0.411123\pi$
$614$	−2.12723	−	12.0641i	−0.0858482	−	0.486869i
$615$	−12.5204	+	7.22865i	−0.504871	+	0.291487i
$616$	2.40997	−	0.224264i	0.0971003	−	0.00903584i
$617$	−20.1724	−	7.34215i	−0.812110	−	0.295584i	−0.0976149	−	0.995224i	$-0.531121\pi$
$617$	−20.1724	−	7.34215i	−0.812110	−	0.295584i	−0.714495	+	0.699640i	$0.753344\pi$
$618$	6.73117	+	2.44995i	0.270767	+	0.0985513i
$619$	−7.86103	+	13.6157i	−0.315961	+	0.547261i	−0.979641	−	0.200755i	$-0.935660\pi$
$619$	−7.86103	+	13.6157i	−0.315961	+	0.547261i	0.663680	+	0.748017i	$0.268994\pi$
$620$	19.4003	−	11.2008i	0.779134	−	0.449833i
$621$	21.0888	−	3.71853i	0.846265	−	0.149219i
$622$	0.962738	+	0.807833i	0.0386023	+	0.0323911i
$623$	−4.52828	+	3.79968i	−0.181422	+	0.152231i
$624$	9.71854	+	1.71364i	0.389053	+	0.0686006i
$625$	28.4297	−	10.3476i	1.13719	−	0.413903i
$626$	18.2377			0.728926
$627$	8.80115	+	22.4242i	0.351484	+	0.895537i
$628$	−0.164167			−0.00655099
$629$	−20.5624	+	7.48410i	−0.819877	+	0.298411i
$630$	−0.409432	−	0.0721939i	−0.0163122	−	0.00287628i
$631$	5.97300	−	5.01194i	0.237781	−	0.199522i	−0.516108	−	0.856523i	$-0.672620\pi$
$631$	5.97300	−	5.01194i	0.237781	−	0.199522i	0.753890	+	0.657001i	$0.228175\pi$
$632$	13.1054	+	10.9967i	0.521304	+	0.437426i
$633$	12.2074	−	2.15250i	0.485201	−	0.0855541i
$634$	6.81771	−	3.93621i	0.270766	−	0.156327i
$635$	−4.72240	+	8.17944i	−0.187403	+	0.324591i
$636$	−11.6249	−	4.23113i	−0.460958	−	0.167775i
$637$	−35.9925	−	13.1002i	−1.42608	−	0.519049i
$638$	−0.425223	−	4.56950i	−0.0168347	−	0.180908i
$639$	3.08924	−	1.78358i	0.122209	−	0.0705572i
$640$	0.442791	+	2.51119i	0.0175028	+	0.0992635i
$641$	23.2577	−	27.7174i	0.918622	−	1.09477i	−0.0765926	−	0.997062i	$-0.524404\pi$
$641$	23.2577	−	27.7174i	0.918622	−	1.09477i	0.995215	−	0.0977091i	$-0.0311515\pi$
$642$	6.71054	+	7.99730i	0.264844	+	0.315628i
$643$	1.14604	−	6.49951i	0.0451954	−	0.256316i	−0.953836	−	0.300329i	$-0.902903\pi$
$643$	1.14604	−	6.49951i	0.0451954	−	0.256316i	0.999031	+	0.0440136i	$0.0140145\pi$
$644$	−0.995102	−	2.73402i	−0.0392125	−	0.107735i
$645$	11.6203			0.457550
$646$	22.7568	+	10.0783i	0.895353	+	0.396527i
$647$	−25.7923			−1.01400			−0.507001	−	0.861946i	$-0.669246\pi$
$647$	−25.7923			−1.01400			−0.507001	+	0.861946i	$0.669246\pi$
$648$	7.78050	−	2.83187i	0.305647	−	0.111246i
$649$	−1.28859	+	0.609568i	−0.0505817	+	0.0239276i
$650$	6.81490	−	5.71838i	0.267302	−	0.224293i
$651$	−6.86687	+	8.18362i	−0.269134	+	0.320741i
$652$	1.33102	+	7.54858i	0.0521267	+	0.295625i
$653$	−5.89683	−	10.2136i	−0.230761	−	0.399689i	0.727271	−	0.686350i	$-0.240788\pi$
$653$	−5.89683	−	10.2136i	−0.230761	−	0.399689i	−0.958032	+	0.286661i	$0.907455\pi$
$654$	24.1736	+	13.9567i	0.945264	+	0.545749i
$655$	−5.64495	+	15.5094i	−0.220566	+	0.606001i
$656$	3.19734	+	1.16374i	0.124835	+	0.0454363i
$657$	0.925181	+	0.534153i	0.0360947	+	0.0208393i
$658$	7.54761	−	4.35761i	0.294236	−	0.169878i
$659$	−1.14841	−	6.51294i	−0.0447356	−	0.253708i	0.954236	−	0.299056i	$-0.0966716\pi$
$659$	−1.14841	−	6.51294i	−0.0447356	−	0.253708i	−0.998971	+	0.0453474i	$0.985561\pi$
$660$	−1.15067	+	14.0452i	−0.0447896	+	0.546708i
$661$	12.9701	+	15.4572i	0.504480	+	0.601216i	0.956839	−	0.290620i	$-0.0938616\pi$
$661$	12.9701	+	15.4572i	0.504480	+	0.601216i	−0.452358	+	0.891836i	$0.649417\pi$
$662$	15.1816	+	2.67693i	0.590052	+	0.104042i
$663$	52.9492	−	19.2719i	2.05638	−	0.748460i
$664$		−	0.329481i		−	0.0127864i
$665$	−7.79269	+	2.25113i	−0.302188	+	0.0872950i
$666$		−	0.856209i		−	0.0331774i
$667$	−5.18394	+	1.88680i	−0.200723	+	0.0730571i
$668$	2.71364	−	15.3898i	0.104994	−	0.595449i
$669$	−4.91043	+	4.12034i	−0.189848	+	0.159302i
$670$	−19.6546	+	23.4234i	−0.759323	+	0.904926i
$671$	−1.83424	+	1.85462i	−0.0708101	+	0.0715967i
$672$	−0.608012	−	1.05311i	−0.0234546	−	0.0406245i
$673$	−5.96613	+	10.3336i	−0.229977	+	0.398332i	−0.957801	−	0.287432i	$-0.907199\pi$
$673$	−5.96613	+	10.3336i	−0.229977	+	0.398332i	0.727824	+	0.685764i	$0.240532\pi$
$674$	7.20590	+	2.62273i	0.277561	+	0.101024i
$675$	2.75953	−	7.58174i	0.106214	−	0.291821i
$676$	−11.0371	+	19.1169i	−0.424505	+	0.735265i
$677$	7.60791	+	13.1773i	0.292396	+	0.506445i	0.974376	−	0.224926i	$-0.0722142\pi$
$677$	7.60791	+	13.1773i	0.292396	+	0.506445i	−0.681980	+	0.731371i	$0.738881\pi$
$678$	3.42589	+	19.4292i	0.131571	+	0.746174i
$679$	2.07355	+	1.73992i	0.0795757	+	0.0667719i
$680$	9.35879	+	11.1534i	0.358893	+	0.427712i
$681$	−10.3851	−	1.83117i	−0.397957	−	0.0701705i
$682$	−23.9596	−	16.5802i	−0.917460	−	0.634890i
$683$		−	28.4068i		−	1.08696i	−0.839424	−	0.543478i	$-0.817107\pi$
$683$		−	28.4068i		−	1.08696i	0.839424	−	0.543478i	$-0.182893\pi$
$684$	−0.675113	+	0.701859i	−0.0258136	+	0.0268363i
$685$	−34.7312			−1.32701
$686$	3.36143	+	9.23544i	0.128340	+	0.352611i
$687$	21.6448	+	3.81657i	0.825801	+	0.145611i
$688$	−1.75793	−	2.09502i	−0.0670206	−	0.0798720i
$689$	28.2625	−	33.6820i	1.07672	−	1.28318i
$690$	16.6826	−	2.94159i	0.635096	−	0.111985i
$691$	−12.3393	−	21.3724i	−0.469410	−	0.813043i	0.529978	−	0.848011i	$-0.322200\pi$
$691$	−12.3393	−	21.3724i	−0.469410	−	0.813043i	−0.999388	+	0.0349687i	$0.988867\pi$
$692$	−10.1861	+	17.6429i	−0.387219	+	0.670683i
$693$	0.142840	+	0.521546i	0.00542603	+	0.0198119i
$694$	−3.46815	+	9.52867i	−0.131649	+	0.361703i
$695$	−0.439361	−	0.253665i	−0.0166659	−	0.00962206i
$696$	−1.99678	+	1.15284i	−0.0756879	+	0.0436984i
$697$	19.1328	−	3.37363i	0.724707	−	0.127785i
$698$	2.66338	−	3.17409i	0.100810	−	0.120141i
$699$	−38.2448	+	32.0912i	−1.44655	+	1.21380i
$700$	−1.07957	−	0.190357i	−0.0408038	−	0.00719481i
$701$	−10.2037	−	28.0346i	−0.385390	−	1.05885i	−0.969053	−	0.246854i	$-0.920603\pi$
$701$	−10.2037	−	28.0346i	−0.385390	−	1.05885i	0.583662	−	0.811996i	$-0.301619\pi$
$702$			31.8102i			1.20060i
$703$	−7.35244	−	14.9997i	−0.277303	−	0.565725i
$704$	2.70627	−	1.91731i	0.101996	−	0.0722615i
$705$	17.3551	+	47.6827i	0.653631	+	1.79584i
$706$	4.50149	−	25.5292i	0.169416	−	0.960805i
$707$	−7.21233	+	6.05187i	−0.271248	+	0.227604i
$708$	0.548630	+	0.460356i	0.0206188	+	0.0173012i
$709$	−3.30357	−	18.7355i	−0.124068	−	0.703627i	−0.981857	−	0.189624i	$-0.939273\pi$
$709$	−3.30357	−	18.7355i	−0.124068	−	0.703627i	0.857788	−	0.514003i	$-0.171838\pi$
$710$	35.2586	−	20.3566i	1.32323	−	0.763969i
$711$	−1.91109	+	3.31010i	−0.0716714	+	0.124139i
$712$	−2.77041	+	7.61163i	−0.103825	+	0.285258i
$713$	−11.9792	+	32.9127i	−0.448626	+	1.23259i
$714$	−6.01308	−	3.47165i	−0.225034	−	0.129923i
$715$	−45.5098	−	20.9164i	−1.70197	−	0.782227i
$716$	21.0722	−	3.71560i	0.787505	−	0.138858i
$717$	0.297854	+	0.249929i	0.0111236	+	0.00933378i
$718$	−8.99211	−	10.7164i	−0.335583	−	0.399932i
$719$	8.91354	−	50.5512i	0.332419	−	1.88524i	−0.118943	−	0.992901i	$-0.537951\pi$
$719$	8.91354	−	50.5512i	0.332419	−	1.88524i	0.451362	−	0.892341i	$-0.350938\pi$
$720$	−0.535340	+	0.194848i	−0.0199509	+	0.00726154i
$721$	3.13716			0.116834
$722$	−5.80014	+	18.0930i	−0.215859	+	0.673354i
$723$			22.9991i			0.855346i
$724$	−3.78048	−	10.3868i	−0.140501	−	0.386022i
$725$	−0.360933	+	2.04695i	−0.0134047	+	0.0760219i
$726$	17.1537	−	6.45889i	0.636633	−	0.239712i
$727$	−24.5260	−	20.5798i	−0.909620	−	0.763262i	0.0624264	−	0.998050i	$-0.480116\pi$
$727$	−24.5260	−	20.5798i	−0.909620	−	0.763262i	−0.972047	+	0.234788i	$0.924561\pi$
$728$	4.25631	−	0.750501i	0.157749	−	0.0278154i
$729$	14.3501	+	24.8550i	0.531483	+	0.920556i
$730$	10.5594	+	6.09648i	0.390821	+	0.225641i
$731$	−14.6739	−	5.34085i	−0.542732	−	0.197538i
$732$	1.23148	+	0.448223i	0.0455169	+	0.0165668i
$733$	28.9057	+	16.6887i	1.06765	+	0.616411i	0.927540	−	0.373725i	$-0.121919\pi$
$733$	28.9057	+	16.6887i	1.06765	+	0.616411i	0.140115	+	0.990135i	$0.455253\pi$
$734$	−10.6516	−	18.4491i	−0.393157	−	0.680967i
$735$	−27.0624	+	4.77184i	−0.998213	+	0.176012i
$736$	−3.05410	−	2.56269i	−0.112576	−	0.0944621i
$737$	38.4719	+	10.0811i	1.41713	+	0.371343i
$738$	−0.132005	+	0.748635i	−0.00485915	+	0.0275576i
$739$	0.515946	+	1.41755i	0.0189794	+	0.0521454i	0.948821	−	0.315816i	$-0.102278\pi$
$739$	0.515946	+	1.41755i	0.0189794	+	0.0521454i	−0.929841	+	0.367961i	$0.880056\pi$
$740$		−	9.77221i		−	0.359233i
$741$	18.9329	+	38.6250i	0.695517	+	1.41893i
$742$	−5.41796			−0.198900
$743$	4.91909	−	1.79040i	0.180464	−	0.0656835i	−0.250208	−	0.968192i	$-0.580499\pi$
$743$	4.91909	−	1.79040i	0.180464	−	0.0656835i	0.430672	+	0.902509i	$0.358277\pi$
$744$	−2.54199	+	14.4164i	−0.0931940	+	0.528530i
$745$	−27.8976	−	33.2470i	−1.02209	−	1.21808i
$746$	−21.6762	−	18.1885i	−0.793623	−	0.665928i
$747$	0.0724932	−	0.0127825i	0.00265239	−	0.000467688i
$748$	7.90837	−	17.2070i	0.289159	−	0.629152i
$749$	3.95961	+	2.28608i	0.144681	+	0.0835315i
$750$	−5.08320	+	13.9660i	−0.185612	+	0.509966i
$751$	10.0266	−	27.5480i	0.365877	−	1.00524i	−0.611036	−	0.791603i	$-0.709247\pi$
$751$	10.0266	−	27.5480i	0.365877	−	1.00524i	0.976913	−	0.213637i	$-0.0685308\pi$
$752$	5.97120	−	10.3424i	0.217747	−	0.377150i
$753$	−0.698894	+	0.403507i	−0.0254691	+	0.0147046i
$754$	−1.42302	−	8.07032i	−0.0518232	−	0.293904i
$755$	31.2490	+	26.2211i	1.13727	+	0.954282i
$756$	3.00271	−	2.51957i	0.109207	−	0.0916358i
$757$	−8.23951	+	46.7286i	−0.299470	+	1.69838i	0.348987	+	0.937128i	$0.386526\pi$
$757$	−8.23951	+	46.7286i	−0.299470	+	1.69838i	−0.648457	+	0.761251i	$0.724585\pi$
$758$	−1.55459	−	4.27121i	−0.0564653	−	0.155137i
$759$	−12.7373	−	17.9786i	−0.462335	−	0.652581i
$760$	−7.70530	+	8.01056i	−0.279500	+	0.290574i
$761$		−	17.6603i		−	0.640186i	−0.947386	−	0.320093i	$-0.896286\pi$
$761$		−	17.6603i		−	0.640186i	0.947386	−	0.320093i	$-0.103714\pi$
$762$	−2.11092	−	5.79971i	−0.0764706	−	0.210101i
$763$	12.0391	+	2.12282i	0.435845	+	0.0768513i
$764$	−3.47073	+	2.91229i	−0.125567	+	0.105363i
$765$	−2.09091	+	2.49185i	−0.0755969	+	0.0900929i
$766$	−15.0968	+	2.66197i	−0.545469	+	0.0961809i
$767$	−2.20443	+	1.27273i	−0.0795972	+	0.0459555i
$768$	−1.44307	−	0.833154i	−0.0520721	−	0.0300639i
$769$	−9.95163	+	27.3419i	−0.358865	+	0.985973i	0.620559	+	0.784160i	$0.286906\pi$
$769$	−9.95163	+	27.3419i	−0.358865	+	0.985973i	−0.979424	+	0.201813i	$0.935317\pi$
$770$	1.63028	+	5.95258i	0.0587512	+	0.214516i
$771$	−3.52878	+	6.11203i	−0.127086	+	0.220119i
$772$	−2.51937	−	4.36367i	−0.0906740	−	0.157052i
$773$	4.74157	−	0.836066i	0.170542	−	0.0300712i	−0.0877249	−	0.996145i	$-0.527960\pi$
$773$	4.74157	−	0.836066i	0.170542	−	0.0300712i	0.258267	+	0.966074i	$0.416849\pi$
$774$	0.392751	−	0.468063i	0.0141172	−	0.0168242i
$775$	8.48257	+	10.1091i	0.304703	+	0.363131i
$776$	3.65280	+	0.644087i	0.131128	+	0.0231214i
$777$	1.59389	+	4.37918i	0.0571805	+	0.157102i
$778$	−21.6431			−0.775944
$779$	4.11613	+	14.2487i	0.147475	+	0.510513i
$780$			25.1639i			0.901012i
$781$	−43.5449	−	30.1334i	−1.55816	−	1.07826i
$782$	−22.4184	−	3.95296i	−0.801679	−	0.141358i
$783$	−4.77732	−	5.69339i	−0.170728	−	0.203465i
$784$	4.95434	+	4.15719i	0.176941	+	0.148471i
$785$	−0.0726918	−	0.412256i	−0.00259448	−	0.0147140i
$786$	−5.39269	−	9.34042i	−0.192351	−	0.333162i
$787$	2.14015	−	3.70685i	0.0762881	−	0.132135i	−0.825358	−	0.564610i	$-0.809026\pi$
$787$	2.14015	−	3.70685i	0.0762881	−	0.132135i	0.901646	+	0.432476i	$0.142360\pi$
$788$	−7.52542	+	20.6759i	−0.268082	+	0.736549i
$789$	−26.8002	−	9.75449i	−0.954114	−	0.347269i
$790$	−21.8119	+	37.7793i	−0.776033	+	1.34413i
$791$	4.32021	+	7.48282i	0.153609	+	0.266059i
$792$	0.526844	+	0.521056i	0.0187206	+	0.0185149i
$793$	−2.99398	+	3.56809i	−0.106319	+	0.126707i
$794$	−1.19595	+	1.00352i	−0.0424427	+	0.0356137i
$795$	5.47776	−	31.0659i	0.194276	−	1.10179i
$796$	16.6746	−	6.06906i	0.591016	−	0.215112i
$797$			21.0476i			0.745544i	0.927923	+	0.372772i	$0.121593\pi$
$797$			21.0476i			0.745544i	−0.927923	+	0.372772i	$0.878407\pi$
$798$	2.14638	−	4.84651i	0.0759811	−	0.171565i
$799$		−	68.1892i		−	2.41236i
$800$	−1.41155	+	0.513763i	−0.0499059	+	0.0181643i
$801$	−1.78221	−	0.314252i	−0.0629713	−	0.0111035i
$802$	12.1580	+	14.4894i	0.429316	+	0.511638i
$803$	1.29493	−	15.8061i	0.0456971	−	0.557785i
$804$	−3.46971	−	19.6777i	−0.122367	−	0.693980i
$805$	6.42502	−	3.70949i	0.226452	−	0.130742i
$806$	−45.0582	−	26.0144i	−1.58711	−	0.916317i
$807$	−12.2701	−	4.46595i	−0.431928	−	0.157209i
$808$	−4.41252	+	12.1233i	−0.155232	+	0.426496i
$809$	23.3345	+	13.4722i	0.820397	+	0.473657i	0.850553	−	0.525889i	$-0.176267\pi$
$809$	23.3345	+	13.4722i	0.820397	+	0.473657i	−0.0301562	+	0.999545i	$0.509600\pi$
$810$	10.5565	+	18.2844i	0.370918	+	0.642448i
$811$	1.50504	+	8.53550i	0.0528491	+	0.299722i	0.999763	−	0.0217649i	$-0.00692852\pi$
$811$	1.50504	+	8.53550i	0.0528491	+	0.299722i	−0.946914	+	0.321487i	$0.895817\pi$
$812$	−0.649082	+	0.773546i	−0.0227783	+	0.0271461i
$813$	10.3314	−	8.66907i	0.362338	−	0.304037i
$814$	−11.4897	+	5.43521i	−0.402715	+	0.190504i
$815$	−18.3666	+	6.68488i	−0.643353	+	0.234161i
$816$	−9.51435			−0.333069
$817$	2.86117	−	11.5725i	0.100100	−	0.404871i
$818$	−20.9394			−0.732129
$819$	0.330254	+	0.907366i	0.0115400	+	0.0317059i
$820$	−1.50661	+	8.54443i	−0.0526132	+	0.298384i
$821$	3.94584	+	4.70247i	0.137711	+	0.164118i	0.830492	−	0.557030i	$-0.188059\pi$
$821$	3.94584	+	4.70247i	0.137711	+	0.164118i	−0.692781	+	0.721148i	$0.743615\pi$
$822$	14.5886	−	17.3860i	0.508837	−	0.606408i
$823$	6.42376	+	36.4310i	0.223918	+	1.26990i	0.864742	+	0.502216i	$0.167482\pi$
$823$	6.42376	+	36.4310i	0.223918	+	1.26990i	−0.640824	+	0.767688i	$0.721407\pi$
$824$	3.72289	−	2.14941i	0.129693	−	0.0748783i
$825$	−8.26591	+	0.769198i	−0.287782	+	0.0267800i
$826$	0.294743	+	0.107278i	0.0102554	+	0.00373267i
$827$	−7.08697	−	2.57945i	−0.246438	−	0.0896962i	0.215848	−	0.976427i	$-0.430748\pi$
$827$	−7.08697	−	2.57945i	−0.246438	−	0.0896962i	−0.462286	+	0.886731i	$0.652971\pi$
$828$	0.445363	−	0.771391i	0.0154774	−	0.0268077i
$829$	34.0847	−	19.6788i	1.18381	−	0.683473i	0.226917	−	0.973914i	$-0.427136\pi$
$829$	34.0847	−	19.6788i	1.18381	−	0.683473i	0.956893	+	0.290442i	$0.0938022\pi$
$830$	0.827390	−	0.145891i	0.0287191	−	0.00506396i
$831$	7.79708	+	6.54253i	0.270478	+	0.226958i
$832$	4.53679	−	3.80682i	0.157285	−	0.131978i
$833$	36.3670	+	6.41248i	1.26004	+	0.222179i
$834$	0.311533	−	0.113389i	0.0107875	−	0.00392633i
$835$	39.8483			1.37901
$836$	13.7041	+	4.60415i	0.473965	+	0.159238i
$837$	−47.1868			−1.63102
$838$	7.25050	−	2.63897i	0.250464	−	0.0911616i
$839$	−17.4121	−	3.07022i	−0.601132	−	0.105996i	−0.135203	−	0.990818i	$-0.543169\pi$
$839$	−17.4121	−	3.07022i	−0.601132	−	0.105996i	−0.465929	+	0.884822i	$0.654280\pi$
$840$	2.37533	−	1.99314i	0.0819568	−	0.0687699i
$841$	−20.7486	−	17.4101i	−0.715468	−	0.600349i
$842$	8.43170	−	1.48674i	0.290576	−	0.0512363i
$843$	−24.4365	+	14.1084i	−0.841638	+	0.485920i
$844$	3.71952	−	6.44240i	0.128031	−	0.221757i
$845$	−52.8933	−	19.2516i	−1.81958	−	0.662274i
$846$	2.50722	+	0.912554i	0.0862001	+	0.0313743i
$847$	6.09204	−	5.22758i	0.209325	−	0.179622i
$848$	−6.42954	+	3.71209i	−0.220791	+	0.127474i
$849$	3.06116	+	17.3607i	0.105059	+	0.595817i
$850$	−5.51318	+	6.57036i	−0.189101	+	0.225361i
$851$	9.82111	+	11.7043i	0.336663	+	0.401220i
$852$	−4.61989	+	26.2007i	−0.158275	+	0.897622i
$853$	7.10482	+	19.5203i	0.243264	+	0.668364i	0.999895	+	0.0145205i	$0.00462218\pi$
$853$	7.10482	+	19.5203i	0.243264	+	0.668364i	−0.756630	+	0.653843i	$0.773156\pi$
$854$	0.573950			0.0196402
$855$	−2.06144	−	1.38456i	−0.0704996	−	0.0473510i
$856$	6.26519			0.214140
$857$	40.6258	−	14.7866i	1.38775	−	0.505100i	0.463231	−	0.886237i	$-0.346690\pi$
$857$	40.6258	−	14.7866i	1.38775	−	0.505100i	0.924518	+	0.381138i	$0.124468\pi$
$858$	29.5866	−	13.9959i	1.01007	−	0.477813i
$859$	−24.1498	+	20.2641i	−0.823982	+	0.691403i	−0.953901	−	0.300122i	$-0.902973\pi$
$859$	−24.1498	+	20.2641i	−0.823982	+	0.691403i	0.129919	+	0.991525i	$0.458528\pi$
$860$	4.48261	−	5.34216i	0.152856	−	0.182166i
$861$	−0.718482	−	4.07471i	−0.0244858	−	0.138866i
$862$	−4.30518	−	7.45678i	−0.146635	−	0.253979i
$863$	−27.9521	−	16.1381i	−0.951499	−	0.549348i	−0.0579527	−	0.998319i	$-0.518457\pi$
$863$	−27.9521	−	16.1381i	−0.951499	−	0.549348i	−0.893546	+	0.448971i	$0.851791\pi$
$864$	1.83706	−	5.04728i	0.0624981	−	0.171712i
$865$	−48.8150	−	17.7672i	−1.65976	−	0.604104i
$866$	−2.79576	−	1.61413i	−0.0950037	−	0.0548504i
$867$	−22.5151	+	12.9991i	−0.764651	+	0.441472i
$868$	1.11328	+	6.31375i	0.0377873	+	0.214303i
$869$	56.5509	+	4.63299i	1.91836	+	0.157163i
$870$	−3.77917	−	4.50384i	−0.128126	−	0.152694i
$871$	69.9381	+	12.3320i	2.36976	+	0.417853i
$872$	15.7413	−	5.72938i	0.533069	−	0.194021i
$873$			0.828685i			0.0280467i
$874$	1.17812	−	17.3383i	0.0398504	−	0.586475i
$875$			6.50905i			0.220046i
$876$	−7.48724	+	2.72513i	−0.252970	+	0.0920737i
$877$	5.15575	−	29.2397i	0.174097	−	0.987355i	−0.765083	−	0.643932i	$-0.777302\pi$
$877$	5.15575	−	29.2397i	0.174097	−	0.987355i	0.939181	−	0.343424i	$-0.111587\pi$
$878$	−13.2022	+	11.0780i	−0.445553	+	0.373863i
$879$	35.1119	−	41.8447i	1.18429	−	1.41139i
$880$	6.01305	+	5.94700i	0.202700	+	0.200473i
$881$	−12.7202	−	22.0320i	−0.428554	−	0.742278i	0.568191	−	0.822897i	$-0.307644\pi$
$881$	−12.7202	−	22.0320i	−0.428554	−	0.742278i	−0.996745	+	0.0806191i	$0.974310\pi$
$882$	−0.722466	+	1.25135i	−0.0243267	+	0.0421351i
$883$	−7.44540	−	2.70990i	−0.250558	−	0.0911955i	0.213688	−	0.976902i	$-0.431452\pi$
$883$	−7.44540	−	2.70990i	−0.250558	−	0.0911955i	−0.464246	+	0.885706i	$0.653675\pi$
$884$	11.5656	−	31.7763i	0.388995	−	1.06875i
$885$	−0.913112	+	1.58156i	−0.0306939	+	0.0531635i
$886$	6.78530	+	11.7525i	0.227957	+	0.394832i
$887$	−8.44123	−	47.8726i	−0.283429	−	1.60740i	−0.710844	−	0.703349i	$-0.751687\pi$
$887$	−8.44123	−	47.8726i	−0.283429	−	1.60740i	0.427416	−	0.904055i	$-0.359424\pi$
$888$	4.89186	+	4.10475i	0.164160	+	0.137747i
$889$	−1.73748	−	2.07065i	−0.0582731	−	0.0694472i
$890$	−20.3410	−	3.58666i	−0.681831	−	0.120225i
$891$	15.6266	−	22.5815i	0.523510	−	0.756508i
$892$			3.84689i			0.128804i
$893$	51.7598	−	5.54320i	1.73207	−	0.185496i
$894$	28.3613			0.948544
$895$	18.6612	+	51.2711i	0.623774	+	1.71380i
$896$	−0.718685	−	0.126724i	−0.0240096	−	0.00423354i
$897$	−25.2898	−	30.1393i	−0.844403	−	1.00632i
$898$	17.7946	−	21.2067i	0.593812	−	0.707678i
$899$	11.9714	−	2.11088i	0.399269	−	0.0704019i
$900$	−0.167802	−	0.290641i	−0.00559339	−	0.00968804i
$901$	−21.1955	+	36.7116i	−0.706123	+	1.22304i
$902$	10.8841	−	2.98092i	0.362402	−	0.0992538i
$903$	−1.13744	+	3.12509i	−0.0378517	+	0.103997i
$904$	10.2537	+	5.91995i	0.341031	+	0.196895i
$905$	24.4092	−	14.0927i	0.811391	−	0.468457i
$906$	−26.2519	+	4.62892i	−0.872162	+	0.153786i
$907$	26.1574	−	31.1731i	0.868541	−	1.03509i	−0.130506	−	0.991447i	$-0.541660\pi$
$907$	26.1574	−	31.1731i	0.868541	−	1.03509i	0.999047	−	0.0436395i	$-0.0138953\pi$
$908$	−4.84793	+	4.06790i	−0.160884	+	0.134998i
$909$	−2.83858	−	0.500519i	−0.0941499	−	0.0166012i
$910$	3.76930	+	10.3561i	0.124951	+	0.343301i
$911$		−	24.2858i		−	0.804626i	−0.915502	−	0.402313i	$-0.868206\pi$
$911$		−	24.2858i		−	0.804626i	0.915502	−	0.402313i	$-0.131794\pi$
$912$	−0.773436	−	7.22197i	−0.0256110	−	0.239143i
$913$	−0.631719	−	0.891666i	−0.0209068	−	0.0295098i
$914$	9.39751	+	25.8195i	0.310842	+	0.854032i
$915$	−0.580285	+	3.29096i	−0.0191836	+	0.108796i
$916$	10.1042	−	8.47841i	0.333852	−	0.280135i
$917$	−3.61844	−	3.03623i	−0.119491	−	0.100265i
$918$	−5.32557	−	30.2028i	−0.175770	−	0.996840i
$919$	−3.81705	+	2.20377i	−0.125913	+	0.0726958i	−0.561633	−	0.827386i	$-0.689827\pi$
$919$	−3.81705	+	2.20377i	−0.125913	+	0.0726958i	0.435721	+	0.900082i	$0.356494\pi$
$920$	5.08308	−	8.80416i	0.167584	−	0.290264i
$921$	−6.98155	+	19.1817i	−0.230050	+	0.632057i
$922$	−2.91440	+	8.00725i	−0.0959806	+	0.263705i
$923$	−81.8901	−	47.2793i	−2.69545	−	1.55622i
$924$	−3.66459	−	1.68425i	−0.120556	−	0.0554076i
$925$	5.66927	−	0.999645i	0.186404	−	0.0328681i
$926$	−24.8244	−	20.8301i	−0.815779	−	0.684520i
$927$	0.617351	+	0.735730i	0.0202765	+	0.0241646i
$928$	−0.240279	+	1.36269i	−0.00788754	+	0.0447324i
$929$	−49.8927	+	18.1595i	−1.63693	+	0.595792i	−0.986498	−	0.163775i	$-0.947633\pi$
$929$	−49.8927	+	18.1595i	−1.63693	+	0.595792i	−0.650428	+	0.759568i	$0.725411\pi$
$930$	−37.3278			−1.22403
$931$	−1.91114	+	28.1260i	−0.0626350	+	0.921794i
$932$			29.9615i			0.981421i
$933$	−0.716244	−	1.96786i	−0.0234488	−	0.0644250i
$934$	1.40794	−	7.98483i	0.0460692	−	0.261272i
$935$	46.7119	+	12.2403i	1.52764	+	0.400301i
$936$	1.01359	+	0.850505i	0.0331303	+	0.0277996i
$937$	−27.4113	+	4.83335i	−0.895489	+	0.157899i	−0.602407	−	0.798189i	$-0.705792\pi$
$937$	−27.4113	+	4.83335i	−0.895489	+	0.157899i	−0.293081	+	0.956088i	$0.594681\pi$
$938$	−4.37547	−	7.57854i	−0.142864	−	0.247448i
$939$	−26.3182	−	15.1948i	−0.858863	−	0.495865i
$940$	28.6158	+	10.4153i	0.933344	+	0.339710i
$941$	−5.25434	−	1.91242i	−0.171287	−	0.0623432i	0.254953	−	0.966953i	$-0.417940\pi$
$941$	−5.25434	−	1.91242i	−0.171287	−	0.0623432i	−0.426240	+	0.904610i	$0.640162\pi$
$942$	0.236904	+	0.136777i	0.00771876	+	0.00445643i
$943$	−6.78269	−	11.7480i	−0.220875	−	0.382567i
$944$	0.423274	−	0.0746347i	0.0137764	−	0.00242915i
$945$	7.65669	+	6.42472i	0.249072	+	0.208996i
$946$	−8.77426	−	2.29919i	−0.285276	−	0.0747532i
$947$	−0.0268596	+	0.152328i	−0.000872820	+	0.00495001i	−0.985241	−	0.171173i	$-0.945244\pi$
$947$	−0.0268596	+	0.152328i	−0.000872820	+	0.00495001i	0.984368	+	0.176123i	$0.0563555\pi$
$948$	−9.74995	−	26.7878i	−0.316664	−	0.870026i
$949$		−	28.3188i		−	0.919267i
$950$	−5.43548	−	3.65073i	−0.176350	−	0.118445i
$951$	−13.1179			−0.425376
$952$	−3.91558	+	1.42516i	−0.126905	+	0.0461896i
$953$	−1.28548	+	7.29033i	−0.0416408	+	0.236157i	−0.998524	−	0.0543170i	$-0.982702\pi$
$953$	−1.28548	+	7.29033i	−0.0416408	+	0.236157i	0.956883	+	0.290474i	$0.0938130\pi$
$954$	−1.06618	−	1.27063i	−0.0345189	−	0.0411381i
$955$	−8.85013	−	7.42614i	−0.286383	−	0.240304i
$956$	0.229798	−	0.0405195i	0.00743219	−	0.00131050i
$957$	−3.19348	+	6.94837i	−0.103230	+	0.224609i
$958$	−26.5399	−	15.3228i	−0.857466	−	0.495058i
$959$	3.39962	−	9.34037i	0.109779	−	0.301616i
$960$	1.45323	−	3.99273i	0.0469029	−	0.128865i
$961$	23.0894	−	39.9920i	0.744819	−	1.29006i
$962$	−19.6557	+	11.3482i	−0.633726	+	0.365882i
$963$	0.243064	+	1.37848i	0.00783261	+	0.0444210i
$964$	10.5733	+	8.87203i	0.340542	+	0.285749i
$965$	9.84246	−	8.25880i	0.316840	−	0.265860i
$966$	−0.841863	+	4.77444i	−0.0270865	+	0.153615i
$967$	−17.2311	−	47.3420i	−0.554114	−	1.52242i	−0.828042	−	0.560666i	$-0.810545\pi$
$967$	−17.2311	−	47.3420i	−0.554114	−	1.52242i	0.273928	−	0.961750i	$-0.411677\pi$
$968$	3.64782	−	10.3775i	0.117245	−	0.333547i
$969$	−24.4427	−	33.5036i	−0.785212	−	1.07629i
$970$			9.45807i			0.303680i
$971$	0.198730	+	0.546006i	0.00637755	+	0.0175222i	0.942841	−	0.333244i	$-0.108143\pi$
$971$	0.198730	+	0.546006i	0.00637755	+	0.0175222i	−0.936463	+	0.350766i	$0.885921\pi$
$972$	2.28166	+	0.402318i	0.0731843	+	0.0129044i
$973$	0.111225	−	0.0933291i	0.00356572	−	0.00299199i
$974$	15.5000	−	18.4722i	0.496652	−	0.591887i
$975$	−14.5986	+	2.57413i	−0.467531	+	0.0824382i
$976$	0.681111	−	0.393240i	0.0218018	−	0.0125873i
$977$	−23.0816	−	13.3262i	−0.738447	−	0.426343i	0.0830573	−	0.996545i	$-0.473532\pi$
$977$	−23.0816	−	13.3262i	−0.738447	−	0.426343i	−0.821504	+	0.570202i	$0.806865\pi$
$978$	4.36839	−	12.0020i	0.139686	−	0.383783i
$979$	7.09641	+	25.9109i	0.226802	+	0.828116i
$980$	−8.24575	+	14.2821i	−0.263401	+	0.456224i
$981$	1.87129	+	3.24117i	0.0597457	+	0.103483i
$982$	−14.8258	+	2.61419i	−0.473111	+	0.0834222i
$983$	−12.8568	+	15.3221i	−0.410068	+	0.488700i	−0.931062	−	0.364860i	$-0.881117\pi$
$983$	−12.8568	+	15.3221i	−0.410068	+	0.488700i	0.520994	+	0.853560i	$0.325561\pi$
$984$	−3.64440	−	4.34323i	−0.116179	−	0.138457i
$985$	−55.2533	−	9.74265i	−1.76052	−	0.310427i
$986$	2.70222	+	7.42429i	0.0860562	+	0.236437i
$987$	−14.5223			−0.462249
$988$	25.0604	+	6.19588i	0.797277	+	0.197117i
$989$			10.9034i			0.346709i
$990$	−1.07519	+	1.55372i	−0.0341718	+	0.0493806i
$991$	−4.40651	−	0.776987i	−0.139977	−	0.0246818i	0.103220	−	0.994659i	$-0.467085\pi$
$991$	−4.40651	−	0.776987i	−0.139977	−	0.0246818i	−0.243198	+	0.969977i	$0.578196\pi$
$992$	5.64698	+	6.72981i	0.179292	+	0.213672i
$993$	−19.6778	−	16.5116i	−0.624457	−	0.523981i
$994$	2.02332	+	11.4748i	0.0641757	+	0.363958i
$995$	22.6239	+	39.1858i	0.717227	+	1.24227i
$996$	−0.274509	+	0.475463i	−0.00869814	+	0.0150656i
$997$	3.75948	−	10.3291i	0.119064	−	0.327126i	−0.865816	−	0.500362i	$-0.833200\pi$
$997$	3.75948	−	10.3291i	0.119064	−	0.327126i	0.984880	+	0.173236i	$0.0554224\pi$
$998$	37.5897	+	13.6815i	1.18988	+	0.433082i
$999$	−10.2922	+	17.8265i	−0.325629	+	0.564006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.b.109.8	yes	60
11.10	odd	2		418.2.q.a.109.8	✓	60
19.15	odd	18		418.2.q.a.395.8	yes	60
209.186	even	18	inner	418.2.q.b.395.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.109.8	✓	60	11.10	odd	2
418.2.q.a.395.8	yes	60	19.15	odd	18
418.2.q.b.109.8	yes	60	1.1	even	1	trivial
418.2.q.b.395.8	yes	60	209.186	even	18	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.64099 + 0.289351i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.95336 + 1.63906i) q^{5} +(-1.64099 + 0.289351i) q^{6} +(-0.632001 + 0.364886i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.209943 - 0.0764129i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.64099 + 0.289351i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.95336 + 1.63906i) q^{5} +(-1.64099 + 0.289351i) q^{6} +(-0.632001 + 0.364886i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.209943 - 0.0764129i) q^{9} +(-2.39615 - 0.872127i) q^{10} +(0.307307 + 3.30236i) q^{11} +(1.44307 - 0.833154i) q^{12} +(1.02841 + 5.83238i) q^{13} +(0.469088 - 0.559038i) q^{14} +(2.73118 + 3.25490i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.95288 - 5.36549i) q^{17} +0.223417 q^{18} +(3.91398 - 1.91852i) q^{19} +2.54993 q^{20} +(-1.14269 + 0.415905i) q^{21} +(-1.41825 - 2.99810i) q^{22} +(-3.05410 + 2.56269i) q^{23} +(-1.07108 + 1.27647i) q^{24} +(0.260844 + 1.47932i) q^{25} +(-2.96118 - 5.12891i) q^{26} +(-4.65160 - 2.68560i) q^{27} +(-0.249597 + 0.685761i) q^{28} +(1.30026 + 0.473257i) q^{29} +(-3.67972 - 2.12448i) q^{30} +(7.60816 - 4.39257i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.451254 + 5.50807i) q^{33} +(3.67021 + 4.37399i) q^{34} +(-1.83260 - 0.323136i) q^{35} +(-0.209943 + 0.0764129i) q^{36} -3.83234i q^{37} +(-3.02177 + 3.14148i) q^{38} +9.86847i q^{39} +(-2.39615 + 0.872127i) q^{40} +(-0.590845 + 3.35085i) q^{41} +(0.931529 - 0.781646i) q^{42} +(1.75793 - 2.09502i) q^{43} +(2.35812 + 2.33222i) q^{44} +(-0.284848 - 0.493372i) q^{45} +(1.99342 - 3.45270i) q^{46} +(11.2222 + 4.08454i) q^{47} +(0.569911 - 1.56582i) q^{48} +(-3.23372 + 5.60096i) q^{49} +(-0.751071 - 1.30089i) q^{50} +(-1.65215 - 9.36981i) q^{51} +(4.53679 + 3.80682i) q^{52} +(-4.77218 - 5.68726i) q^{53} +(5.28961 + 0.932700i) q^{54} +(-4.81249 + 6.95439i) q^{55} -0.729772i q^{56} +(6.97795 - 2.01577i) q^{57} -1.38371 q^{58} +(0.147002 + 0.403884i) q^{59} +(4.18442 + 0.737826i) q^{60} +(0.505539 + 0.602478i) q^{61} +(-5.64698 + 6.72981i) q^{62} +(0.160566 - 0.0283121i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.55079 + 13.0784i) q^{65} +(-1.45983 - 5.33023i) q^{66} +(4.10128 - 11.2682i) q^{67} +(-4.94486 - 2.85492i) q^{68} +(-5.75327 + 3.32165i) q^{69} +(1.83260 - 0.323136i) q^{70} +(-10.2630 + 12.2310i) q^{71} +(0.171147 - 0.143609i) q^{72} +(-4.70904 - 0.830330i) q^{73} +(1.31074 + 3.60122i) q^{74} +2.50303i q^{75} +(1.76508 - 3.98553i) q^{76} +(-1.39920 - 1.97496i) q^{77} +(-3.37521 - 9.27333i) q^{78} +(2.97075 - 16.8479i) q^{79} +(1.95336 - 1.63906i) q^{80} +(-6.34272 - 5.32218i) q^{81} +(-0.590845 - 3.35085i) q^{82} +(-0.285339 + 0.164741i) q^{83} +(-0.608012 + 1.05311i) q^{84} +(4.97971 - 13.6816i) q^{85} +(-0.935377 + 2.56993i) q^{86} +(1.99678 + 1.15284i) q^{87} +(-3.01358 - 1.38504i) q^{88} +(7.97707 - 1.40657i) q^{89} +(0.436413 + 0.366194i) q^{90} +(-2.77811 - 3.31082i) q^{91} +(-0.692308 + 3.92627i) q^{92} +(13.7559 - 5.00675i) q^{93} -11.9424 q^{94} +(10.7900 + 2.66770i) q^{95} +1.66631i q^{96} +(-1.26860 - 3.48546i) q^{97} +(1.12306 - 6.36918i) q^{98} +(0.187826 - 0.716788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Introduction

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