LMFDB - Embedded newform 135.2.q.a.113.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03978 + 0.0909691i) q^{2} +(0.874685 + 1.49497i) q^{3} +(-0.896746 - 0.158121i) q^{4} +(2.23373 - 0.102160i) q^{5} +(0.773485 + 1.63401i) q^{6} +(-0.567627 - 0.397456i) q^{7} +(-2.93441 - 0.786273i) q^{8} +(-1.46985 + 2.61525i) q^{9} +O(q^{10})$	\(q+(1.03978 + 0.0909691i) q^{2} +(0.874685 + 1.49497i) q^{3} +(-0.896746 - 0.158121i) q^{4} +(2.23373 - 0.102160i) q^{5} +(0.773485 + 1.63401i) q^{6} +(-0.567627 - 0.397456i) q^{7} +(-2.93441 - 0.786273i) q^{8} +(-1.46985 + 2.61525i) q^{9} +(2.33189 + 0.0969768i) q^{10} +(0.597632 - 1.64198i) q^{11} +(-0.547986 - 1.47891i) q^{12} +(-0.0630233 - 0.720360i) q^{13} +(-0.554051 - 0.464904i) q^{14} +(2.10654 + 3.25000i) q^{15} +(-1.26829 - 0.461619i) q^{16} +(-2.95614 + 0.792096i) q^{17} +(-1.76623 + 2.58558i) q^{18} +(3.38781 - 1.95596i) q^{19} +(-2.01925 - 0.261588i) q^{20} +(0.0976895 - 1.19623i) q^{21} +(0.770776 - 1.65293i) q^{22} +(-4.63055 - 6.61310i) q^{23} +(-1.39123 - 5.07459i) q^{24} +(4.97913 - 0.456395i) q^{25} -0.754750i q^{26} +(-5.19537 + 0.0901428i) q^{27} +(0.446171 + 0.446171i) q^{28} +(-5.68683 + 4.77181i) q^{29} +(1.89469 + 3.57092i) q^{30} +(0.764639 - 4.33648i) q^{31} +(4.22984 + 1.97241i) q^{32} +(2.97745 - 0.542776i) q^{33} +(-3.14580 + 0.554689i) q^{34} +(-1.30853 - 0.829823i) q^{35} +(1.73161 - 2.11280i) q^{36} +(2.86540 + 10.6938i) q^{37} +(3.70052 - 1.72558i) q^{38} +(1.02179 - 0.724306i) q^{39} +(-6.63502 - 1.45655i) q^{40} +(2.71443 - 3.23493i) q^{41} +(0.210396 - 1.23493i) q^{42} +(2.74095 + 5.87799i) q^{43} +(-0.795555 + 1.37794i) q^{44} +(-3.01608 + 5.99193i) q^{45} +(-4.21317 - 7.29742i) q^{46} +(-2.32838 + 3.32527i) q^{47} +(-0.419248 - 2.29982i) q^{48} +(-2.22991 - 6.12663i) q^{49} +(5.21872 - 0.0216046i) q^{50} +(-3.76985 - 3.72650i) q^{51} +(-0.0573878 + 0.655945i) q^{52} +(-5.90884 + 5.90884i) q^{53} +(-5.41025 - 0.378889i) q^{54} +(1.16721 - 3.72880i) q^{55} +(1.35314 + 1.61261i) q^{56} +(5.88736 + 3.35382i) q^{57} +(-6.34714 + 4.44432i) q^{58} +(2.63750 - 0.959971i) q^{59} +(-1.37514 - 3.24751i) q^{60} +(1.13591 + 6.44205i) q^{61} +(1.18954 - 4.43943i) q^{62} +(1.87378 - 0.900284i) q^{63} +(6.55640 + 3.78534i) q^{64} +(-0.214369 - 1.60265i) q^{65} +(3.14527 - 0.293513i) q^{66} +(11.1831 - 0.978397i) q^{67} +(2.77616 - 0.242882i) q^{68} +(5.83610 - 12.7069i) q^{69} +(-1.28510 - 0.981870i) q^{70} +(5.58689 + 3.22559i) q^{71} +(6.36945 - 6.51852i) q^{72} +(-2.16667 + 8.08612i) q^{73} +(2.00658 + 11.3799i) q^{74} +(5.03746 + 7.04443i) q^{75} +(-3.34729 + 1.21831i) q^{76} +(-0.991847 + 0.694499i) q^{77} +(1.12833 - 0.660168i) q^{78} +(-1.04738 - 1.24822i) q^{79} +(-2.88018 - 0.901566i) q^{80} +(-4.67907 - 7.68806i) q^{81} +(3.11669 - 3.11669i) q^{82} +(0.156261 - 1.78607i) q^{83} +(-0.276752 + 1.05727i) q^{84} +(-6.52232 + 2.07133i) q^{85} +(2.31528 + 6.36117i) q^{86} +(-12.1079 - 4.32778i) q^{87} +(-3.04474 + 4.34834i) q^{88} +(2.78132 + 4.81739i) q^{89} +(-3.68115 + 5.95593i) q^{90} +(-0.250538 + 0.433944i) q^{91} +(3.10676 + 6.66246i) q^{92} +(7.15171 - 2.64995i) q^{93} +(-2.72350 + 3.24574i) q^{94} +(7.36765 - 4.71518i) q^{95} +(0.751097 + 8.04871i) q^{96} +(-4.20036 + 1.95866i) q^{97} +(-1.76129 - 6.57321i) q^{98} +(3.41576 + 3.97642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.03978	+	0.0909691i	0.735236	+	0.0643248i	0.448622	−	0.893721i	$-0.351915\pi$
$2$	1.03978	+	0.0909691i	0.735236	+	0.0643248i	0.286614	+	0.958046i	$0.407470\pi$
$3$	0.874685	+	1.49497i	0.505000	+	0.863119i
$3$	0.874685	+	1.49497i	0.505000	+	0.863119i
$4$	−0.896746	−	0.158121i	−0.448373	−	0.0790603i
$5$	2.23373	−	0.102160i	0.998956	−	0.0456872i
$5$	2.23373	−	0.102160i	0.998956	−	0.0456872i
$6$	0.773485	+	1.63401i	0.315774	+	0.667081i
$7$	−0.567627	−	0.397456i	−0.214543	−	0.150224i	0.461366	−	0.887210i	$-0.347360\pi$
$7$	−0.567627	−	0.397456i	−0.214543	−	0.150224i	−0.675908	+	0.736986i	$0.736249\pi$
$8$	−2.93441	−	0.786273i	−1.03747	−	0.277990i
$9$	−1.46985	+	2.61525i	−0.489950	+	0.871750i
$10$	2.33189	+	0.0969768i	0.737407	+	0.0306668i
$11$	0.597632	−	1.64198i	0.180193	−	0.495076i	−0.816406	−	0.577478i	$-0.804037\pi$
$11$	0.597632	−	1.64198i	0.180193	−	0.495076i	0.996599	+	0.0824022i	$0.0262592\pi$
$12$	−0.547986	−	1.47891i	−0.158190	−	0.426925i
$13$	−0.0630233	−	0.720360i	−0.0174795	−	0.199792i	−0.999913	−	0.0131795i	$-0.995805\pi$
$13$	−0.0630233	−	0.720360i	−0.0174795	−	0.199792i	0.982434	−	0.186612i	$-0.0597508\pi$
$14$	−0.554051	−	0.464904i	−0.148076	−	0.124251i
$15$	2.10654	+	3.25000i	0.543906	+	0.839146i
$16$	−1.26829	−	0.461619i	−0.317072	−	0.115405i
$17$	−2.95614	+	0.792096i	−0.716970	+	0.192112i	−0.598819	−	0.800884i	$-0.704363\pi$
$17$	−2.95614	+	0.792096i	−0.716970	+	0.192112i	−0.118151	+	0.992996i	$0.537697\pi$
$18$	−1.76623	+	2.58558i	−0.416304	+	0.609426i
$19$	3.38781	−	1.95596i	0.777218	−	0.448727i	−0.0582254	−	0.998303i	$-0.518544\pi$
$19$	3.38781	−	1.95596i	0.777218	−	0.448727i	0.835443	+	0.549576i	$0.185211\pi$
$20$	−2.01925	−	0.261588i	−0.451517	−	0.0584928i
$21$	0.0976895	−	1.19623i	0.0213176	−	0.261039i
$22$	0.770776	−	1.65293i	0.164330	−	0.352407i
$23$	−4.63055	−	6.61310i	−0.965535	−	1.37893i	−0.925091	−	0.379746i	$-0.876011\pi$
$23$	−4.63055	−	6.61310i	−0.965535	−	1.37893i	−0.0404446	−	0.999182i	$-0.512877\pi$
$24$	−1.39123	−	5.07459i	−0.283985	−	1.03585i
$25$	4.97913	−	0.456395i	0.995825	−	0.0912790i
$26$		−	0.754750i		−	0.148019i
$27$	−5.19537	+	0.0901428i	−0.999850	+	0.0173480i
$28$	0.446171	+	0.446171i	0.0843184	+	0.0843184i
$29$	−5.68683	+	4.77181i	−1.05602	+	0.886103i	−0.993713	−	0.111954i	$-0.964289\pi$
$29$	−5.68683	+	4.77181i	−1.05602	+	0.886103i	−0.0623035	+	0.998057i	$0.519845\pi$
$30$	1.89469	+	3.57092i	0.345921	+	0.651957i
$31$	0.764639	−	4.33648i	0.137333	−	0.778855i	−0.835873	−	0.548922i	$-0.815038\pi$
$31$	0.764639	−	4.33648i	0.137333	−	0.778855i	0.973207	−	0.229933i	$-0.0738506\pi$
$32$	4.22984	+	1.97241i	0.747738	+	0.348676i
$33$	2.97745	−	0.542776i	0.518307	−	0.0944852i
$34$	−3.14580	+	0.554689i	−0.539500	+	0.0951284i
$35$	−1.30853	−	0.829823i	−0.221182	−	0.140266i
$36$	1.73161	−	2.11280i	0.288601	−	0.352134i
$37$	2.86540	+	10.6938i	0.471069	+	1.75805i	0.635939	+	0.771739i	$0.280613\pi$
$37$	2.86540	+	10.6938i	0.471069	+	1.75805i	−0.164870	+	0.986315i	$0.552720\pi$
$38$	3.70052	−	1.72558i	0.600303	−	0.279926i
$39$	1.02179	−	0.724306i	0.163617	−	0.115982i
$40$	−6.63502	−	1.45655i	−1.04909	−	0.230300i
$41$	2.71443	−	3.23493i	0.423923	−	0.505212i	−0.511236	−	0.859441i	$-0.670812\pi$
$41$	2.71443	−	3.23493i	0.423923	−	0.505212i	0.935159	+	0.354229i	$0.115257\pi$
$42$	0.210396	−	1.23493i	0.0324648	−	0.190554i
$43$	2.74095	+	5.87799i	0.417991	+	0.896385i	0.996725	+	0.0808685i	$0.0257694\pi$
$43$	2.74095	+	5.87799i	0.417991	+	0.896385i	−0.578733	+	0.815517i	$0.696453\pi$
$44$	−0.795555	+	1.37794i	−0.119934	+	0.207733i
$45$	−3.01608	+	5.99193i	−0.449611	+	0.893224i
$46$	−4.21317	−	7.29742i	−0.621197	−	1.07595i
$47$	−2.32838	+	3.32527i	−0.339628	+	0.485040i	−0.952243	−	0.305342i	$-0.901229\pi$
$47$	−2.32838	+	3.32527i	−0.339628	+	0.485040i	0.612614	+	0.790382i	$0.290118\pi$
$48$	−0.419248	−	2.29982i	−0.0605132	−	0.331950i
$49$	−2.22991	−	6.12663i	−0.318559	−	0.875234i
$50$	5.21872	−	0.0216046i	0.738038	−	0.00305535i
$51$	−3.76985	−	3.72650i	−0.527885	−	0.521815i
$52$	−0.0573878	+	0.655945i	−0.00795825	+	0.0909632i
$53$	−5.90884	+	5.90884i	−0.811642	+	0.811642i	−0.984880	−	0.173238i	$-0.944577\pi$
$53$	−5.90884	+	5.90884i	−0.811642	+	0.811642i	0.173238	+	0.984880i	$0.444577\pi$
$54$	−5.41025	−	0.378889i	−0.736241	−	0.0515603i
$55$	1.16721	−	3.72880i	0.157386	−	0.502791i
$56$	1.35314	+	1.61261i	0.180821	+	0.215494i
$57$	5.88736	+	3.35382i	0.779800	+	0.444225i
$58$	−6.34714	+	4.44432i	−0.833420	+	0.583567i
$59$	2.63750	−	0.959971i	0.343373	−	0.124978i	−0.164577	−	0.986364i	$-0.552626\pi$
$59$	2.63750	−	0.959971i	0.343373	−	0.124978i	0.507950	+	0.861387i	$0.330404\pi$
$60$	−1.37514	−	3.24751i	−0.177530	−	0.419252i
$61$	1.13591	+	6.44205i	0.145438	+	0.824820i	0.967014	+	0.254722i	$0.0819838\pi$
$61$	1.13591	+	6.44205i	0.145438	+	0.824820i	−0.821576	+	0.570098i	$0.806905\pi$
$62$	1.18954	−	4.43943i	0.151072	−	0.563808i
$63$	1.87378	−	0.900284i	0.236073	−	0.113425i
$64$	6.55640	+	3.78534i	0.819551	+	0.473168i
$65$	−0.214369	−	1.60265i	−0.0265892	−	0.198785i
$66$	3.14527	−	0.293513i	0.387156	−	0.0361289i
$67$	11.1831	−	0.978397i	1.36624	−	0.119530i	0.619682	−	0.784853i	$-0.287262\pi$
$67$	11.1831	−	0.978397i	1.36624	−	0.119530i	0.746556	+	0.665323i	$0.231706\pi$
$68$	2.77616	−	0.242882i	0.336659	−	0.0294538i
$69$	5.83610	−	12.7069i	0.702584	−	1.52973i
$70$	−1.28510	−	0.981870i	−0.153598	−	0.117356i
$71$	5.58689	+	3.22559i	0.663042	+	0.382807i	0.793435	−	0.608655i	$-0.208291\pi$
$71$	5.58689	+	3.22559i	0.663042	+	0.382807i	−0.130393	+	0.991462i	$0.541624\pi$
$72$	6.36945	−	6.51852i	0.750647	−	0.768215i
$73$	−2.16667	+	8.08612i	−0.253589	+	0.946409i	0.715280	+	0.698838i	$0.246299\pi$
$73$	−2.16667	+	8.08612i	−0.253589	+	0.946409i	−0.968870	+	0.247571i	$0.920368\pi$
$74$	2.00658	+	11.3799i	0.233261	+	1.32289i
$75$	5.03746	+	7.04443i	0.581676	+	0.813420i
$76$	−3.34729	+	1.21831i	−0.383960	+	0.139750i
$77$	−0.991847	+	0.694499i	−0.113032	+	0.0791455i
$78$	1.12833	−	0.660168i	0.127758	−	0.0747494i
$79$	−1.04738	−	1.24822i	−0.117840	−	0.140436i	0.703899	−	0.710300i	$-0.251441\pi$
$79$	−1.04738	−	1.24822i	−0.117840	−	0.140436i	−0.821739	+	0.569863i	$0.806996\pi$
$80$	−2.88018	−	0.901566i	−0.322013	−	0.100798i
$81$	−4.67907	−	7.68806i	−0.519897	−	0.854229i
$82$	3.11669	−	3.11669i	0.344181	−	0.344181i
$83$	0.156261	−	1.78607i	0.0171518	−	0.196046i	−0.982784	−	0.184756i	$-0.940851\pi$
$83$	0.156261	−	1.78607i	0.0171518	−	0.196046i	0.999936	−	0.0112903i	$-0.00359389\pi$
$84$	−0.276752	+	1.05727i	−0.0301961	+	0.115358i
$85$	−6.52232	+	2.07133i	−0.707444	+	0.224667i
$86$	2.31528	+	6.36117i	0.249663	+	0.685942i
$87$	−12.1079	−	4.32778i	−1.29810	−	0.463987i
$88$	−3.04474	+	4.34834i	−0.324571	+	0.463535i
$89$	2.78132	+	4.81739i	0.294820	+	0.510643i	0.974943	−	0.222455i	$-0.0714071\pi$
$89$	2.78132	+	4.81739i	0.294820	+	0.510643i	−0.680123	+	0.733098i	$0.738074\pi$
$90$	−3.68115	+	5.95593i	−0.388027	+	0.627810i
$91$	−0.250538	+	0.433944i	−0.0262635	+	0.0454897i
$92$	3.10676	+	6.66246i	0.323902	+	0.694610i
$93$	7.15171	−	2.64995i	0.741598	−	0.274787i
$94$	−2.72350	+	3.24574i	−0.280907	+	0.334772i
$95$	7.36765	−	4.71518i	0.755905	−	0.483767i
$96$	0.751097	+	8.04871i	0.0766585	+	0.821468i
$97$	−4.20036	+	1.95866i	−0.426482	+	0.198872i	−0.623995	−	0.781429i	$-0.714491\pi$
$97$	−4.20036	+	1.95866i	−0.426482	+	0.198872i	0.197513	+	0.980300i	$0.436714\pi$
$98$	−1.76129	−	6.57321i	−0.177917	−	0.663995i
$99$	3.41576	+	3.97642i	0.343297	+	0.399646i
$100$	−4.53718	−	0.378032i	−0.453718	−	0.0378032i
$101$	11.1359	−	1.96356i	1.10806	−	0.195381i	0.410469	−	0.911875i	$-0.365365\pi$
$101$	11.1359	−	1.96356i	1.10806	−	0.195381i	0.697594	+	0.716493i	$0.254254\pi$
$102$	−3.58083	−	4.21769i	−0.354555	−	0.417613i
$103$	−4.47475	−	2.08661i	−0.440911	−	0.205600i	0.189470	−	0.981887i	$-0.439323\pi$
$103$	−4.47475	−	2.08661i	−0.440911	−	0.205600i	−0.630380	+	0.776287i	$0.717101\pi$
$104$	−0.381463	+	2.16339i	−0.0374055	+	0.212137i
$105$	0.0960055	−	2.68204i	0.00936918	−	0.261741i
$106$	−6.68142	+	5.60638i	−0.648957	+	0.544540i
$107$	−11.1511	−	11.1511i	−1.07801	−	1.07801i	−0.996688	−	0.0813251i	$-0.974085\pi$
$107$	−11.1511	−	11.1511i	−1.07801	−	1.07801i	−0.0813251	−	0.996688i	$-0.525915\pi$
$108$	4.67318	+	0.740660i	0.449677	+	0.0712700i
$109$		−	20.3152i		−	1.94584i	−0.231133	−	0.972922i	$-0.574243\pi$
$109$		−	20.3152i		−	1.94584i	0.231133	−	0.972922i	$-0.425757\pi$
$110$	1.55284	−	3.77096i	0.148058	−	0.359546i
$111$	−13.4806	+	13.6374i	−1.27952	+	1.29441i
$112$	0.536441	+	0.766117i	0.0506889	+	0.0723912i
$113$	0.0516106	−	0.110679i	0.00485512	−	0.0104118i	−0.903865	−	0.427817i	$-0.859283\pi$
$113$	0.0516106	−	0.110679i	0.00485512	−	0.0104118i	0.908720	+	0.417405i	$0.137060\pi$
$114$	5.81647	+	4.02281i	0.544763	+	0.376771i
$115$	−11.0190	−	14.2989i	−1.02753	−	1.33338i
$116$	5.85416	−	3.37990i	0.543545	−	0.313816i
$117$	1.97656	+	0.894000i	0.182733	+	0.0826503i
$118$	2.82975	−	0.758229i	0.260500	−	0.0698006i
$119$	1.99281	+	0.725323i	0.182681	+	0.0664903i
$120$	−3.62606	−	11.1931i	−0.331013	−	1.02179i
$121$	6.08755	+	5.10806i	0.553414	+	0.464369i
$122$	0.595068	+	6.80165i	0.0538749	+	0.615793i
$123$	7.21039	+	1.22844i	0.650139	+	0.110764i
$124$	−1.37137	+	3.76782i	−0.123153	+	0.338360i
$125$	11.0754	−	1.52813i	0.990615	−	0.136680i
$126$	2.03021	−	0.765643i	0.180866	−	0.0682089i
$127$	−16.0361	−	4.29687i	−1.42298	−	0.381286i	−0.536439	−	0.843939i	$-0.680231\pi$
$127$	−16.0361	−	4.29687i	−1.42298	−	0.381286i	−0.886539	+	0.462654i	$0.846897\pi$
$128$	−1.17328	−	0.821539i	−0.103704	−	0.0726144i
$129$	−6.38993	+	9.23903i	−0.562602	+	0.813451i
$130$	−0.0771050	−	1.68591i	−0.00676256	−	0.147864i
$131$	−22.1825	−	3.91138i	−1.93810	−	0.341739i	−0.938109	−	0.346341i	$-0.887424\pi$
$131$	−22.1825	−	3.91138i	−1.93810	−	0.341739i	−0.999989	+	0.00460251i	$0.998535\pi$
$132$	−2.75584	+	0.0159371i	−0.239865	+	0.00138714i
$133$	−2.70042	−	0.236256i	−0.234156	−	0.0204860i
$134$	11.7170			1.01220
$135$	−11.5959	+	0.732113i	−0.998013	+	0.0630102i
$136$	9.29735			0.797241
$137$	5.19392	+	0.454409i	0.443747	+	0.0388228i	0.306840	−	0.951761i	$-0.400728\pi$
$137$	5.19392	+	0.454409i	0.443747	+	0.0388228i	0.136907	+	0.990584i	$0.456284\pi$
$138$	7.22420	−	12.6815i	0.614965	−	1.07952i
$139$	12.7974	+	2.25653i	1.08546	+	0.191396i	0.687630	−	0.726061i	$-0.258651\pi$
$139$	12.7974	+	2.25653i	1.08546	+	0.191396i	0.397833	+	0.917458i	$0.369762\pi$
$140$	1.04221	+	0.951046i	0.0880826	+	0.0803781i
$141$	−7.00776	−	0.572284i	−0.590160	−	0.0481950i
$142$	5.51571	+	3.86214i	0.462868	+	0.324104i
$143$	−1.22048	−	0.327027i	−0.102062	−	0.0273474i
$144$	3.07144	−	2.63838i	0.255954	−	0.219865i
$145$	−12.2154	+	11.2399i	−1.01443	+	0.933425i
$146$	−2.98845	+	8.21069i	−0.247326	+	0.679522i
$147$	7.20864	−	8.69252i	0.594559	−	0.716947i
$148$	−0.878625	−	10.0427i	−0.0722225	−	0.825507i
$149$	−8.70742	−	7.30639i	−0.713340	−	0.598563i	0.212194	−	0.977227i	$-0.431939\pi$
$149$	−8.70742	−	7.30639i	−0.713340	−	0.598563i	−0.925534	+	0.378664i	$0.876383\pi$
$150$	4.59704	+	7.78291i	0.375346	+	0.635472i
$151$	−8.54652	−	3.11068i	−0.695506	−	0.253143i	−0.0300149	−	0.999549i	$-0.509555\pi$
$151$	−8.54652	−	3.11068i	−0.695506	−	0.253143i	−0.665491	+	0.746406i	$0.731778\pi$
$152$	−11.4792	+	3.07583i	−0.931083	+	0.249483i
$153$	2.27356	−	8.89532i	0.183806	−	0.719144i
$154$	−1.09448	+	0.631900i	−0.0881959	+	0.0509199i
$155$	1.26498	−	9.76466i	0.101606	−	0.784316i
$156$	−1.03081	+	0.487953i	−0.0825311	+	0.0390675i
$157$	1.41498	−	3.03444i	0.112928	−	0.242175i	−0.841718	−	0.539917i	$-0.818456\pi$
$157$	1.41498	−	3.03444i	0.112928	−	0.242175i	0.954646	+	0.297742i	$0.0962335\pi$
$158$	−0.975501	−	1.39316i	−0.0776067	−	0.110834i
$159$	−14.0019	−	3.66515i	−1.11042	−	0.290665i
$160$	9.64984	+	3.97371i	0.762887	+	0.314150i
$161$			5.59421i			0.440886i
$162$	−4.16584	−	8.41955i	−0.327299	−	0.661502i
$163$	9.97670	+	9.97670i	0.781435	+	0.781435i	0.980073	−	0.198638i	$-0.0636517\pi$
$163$	9.97670	+	9.97670i	0.781435	+	0.781435i	−0.198638	+	0.980073i	$0.563652\pi$
$164$	−2.94567	+	2.47171i	−0.230018	+	0.193008i
$165$	6.59537	−	1.51659i	0.513449	−	0.118067i
$166$	0.324953	−	1.84290i	0.0252213	−	0.143037i
$167$	−12.6150	−	5.88249i	−0.976182	−	0.455201i	−0.131995	−	0.991250i	$-0.542138\pi$
$167$	−12.6150	−	5.88249i	−0.976182	−	0.455201i	−0.844187	+	0.536049i	$0.819916\pi$
$168$	−1.22723	+	3.43343i	−0.0946826	+	0.264895i
$169$	12.2876	−	2.16663i	0.945196	−	0.166664i
$170$	−6.97021	+	1.56040i	−0.534590	+	0.119677i
$171$	0.135731	+	11.7350i	0.0103796	+	0.897394i
$172$	−1.52851	−	5.70447i	−0.116548	−	0.434962i
$173$	−2.81939	+	1.31470i	−0.214354	+	0.0999551i	−0.526830	−	0.849971i	$-0.676620\pi$
$173$	−2.81939	+	1.31470i	−0.214354	+	0.0999551i	0.312476	+	0.949926i	$0.398842\pi$
$174$	−12.1959	−	5.60139i	−0.924565	−	0.424640i
$175$	−3.00768	−	1.71992i	−0.227359	−	0.130014i
$176$	−1.51594	+	1.80663i	−0.114268	+	0.136180i
$177$	3.74211	+	3.10330i	0.281274	+	0.233258i
$178$	2.45373	+	5.26205i	0.183915	+	0.394407i
$179$	2.53650	−	4.39334i	0.189587	−	0.328374i	−0.755526	−	0.655119i	$-0.772619\pi$
$179$	2.53650	−	4.39334i	0.189587	−	0.328374i	0.945113	+	0.326745i	$0.105952\pi$
$180$	3.65211	−	4.89634i	0.272212	−	0.364951i
$181$	−4.66805	−	8.08530i	−0.346974	−	0.600976i	0.638737	−	0.769425i	$-0.279457\pi$
$181$	−4.66805	−	8.08530i	−0.346974	−	0.600976i	−0.985710	+	0.168449i	$0.946124\pi$
$182$	−0.299980	+	0.428416i	−0.0222360	+	0.0317563i
$183$	−8.63709	+	7.33291i	−0.638472	+	0.542064i
$184$	8.38822	+	23.0464i	0.618388	+	1.69901i
$185$	7.49302	+	23.5944i	0.550898	+	1.73470i
$186$	7.67728	−	2.10478i	0.562925	−	0.154330i
$187$	−0.466079	+	5.32731i	−0.0340831	+	0.389572i
$188$	2.61375	−	2.61375i	0.190628	−	0.190628i
$189$	2.98486	+	2.01377i	0.217117	+	0.146480i
$190$	8.08968	−	4.23253i	0.586887	−	0.307060i
$191$	0.729528	+	0.869417i	0.0527868	+	0.0629088i	0.791792	−	0.610791i	$-0.209148\pi$
$191$	0.729528	+	0.869417i	0.0527868	+	0.0629088i	−0.739005	+	0.673700i	$0.764704\pi$
$192$	0.0758304	+	13.1126i	0.00547259	+	0.946320i
$193$	11.2910	−	7.90607i	0.812746	−	0.569091i	−0.0916467	−	0.995792i	$-0.529213\pi$
$193$	11.2910	−	7.90607i	0.812746	−	0.569091i	0.904393	+	0.426701i	$0.140324\pi$
$194$	−4.54563	+	1.65447i	−0.326357	+	0.118784i
$195$	2.20841	−	1.72229i	0.158147	−	0.123336i
$196$	1.03092	+	5.84663i	0.0736371	+	0.417617i
$197$	0.517983	−	1.93314i	0.0369048	−	0.137730i	−0.945015	−	0.327026i	$-0.893954\pi$
$197$	0.517983	−	1.93314i	0.0369048	−	0.137730i	0.981920	+	0.189295i	$0.0606203\pi$
$198$	3.18991	+	4.44534i	0.226697	+	0.315916i
$199$	16.0030	+	9.23931i	1.13442	+	0.654957i	0.945043	−	0.326947i	$-0.106020\pi$
$199$	16.0030	+	9.23931i	1.13442	+	0.654957i	0.189377	+	0.981905i	$0.439353\pi$
$200$	−14.9697	−	2.57570i	−1.05851	−	0.182130i
$201$	11.2444	+	15.8626i	0.793118	+	1.11886i
$202$	11.7575	−	1.02865i	0.827256	−	0.0723755i
$203$	5.12458	−	0.448343i	0.359675	−	0.0314675i
$204$	2.79136	+	3.93782i	0.195435	+	0.275702i
$205$	5.73284	−	7.50329i	0.400399	−	0.524052i
$206$	−4.46295	−	2.57668i	−0.310948	−	0.179526i
$207$	24.1011	−	2.38976i	1.67515	−	0.166100i
$208$	−0.252600	+	0.942717i	−0.0175147	+	0.0653656i
$209$	−1.18697	−	6.73167i	−0.0821047	−	0.465639i
$210$	0.343808	−	2.78000i	0.0237250	−	0.191839i
$211$	15.7638	−	5.73754i	1.08522	−	0.394989i	0.263374	−	0.964694i	$-0.415165\pi$
$211$	15.7638	−	5.73754i	1.08522	−	0.394989i	0.821849	+	0.569705i	$0.192943\pi$
$212$	6.23304	−	4.36442i	0.428087	−	0.299750i
$213$	0.0646171	+	11.1736i	0.00442749	+	0.765602i
$214$	−10.5803	−	12.6091i	−0.723251	−	0.861937i
$215$	6.72305	+	12.8498i	0.458508	+	0.876352i
$216$	15.3162	+	3.82046i	1.04214	+	0.259950i
$217$	−2.15759	+	2.15759i	−0.146467	+	0.146467i
$218$	1.84806	−	21.1234i	0.125166	−	1.43066i
$219$	−13.9836	+	3.83371i	−0.944926	+	0.259058i
$220$	−1.63629	+	3.15923i	−0.110318	+	0.212995i
$221$	0.756900	+	2.07957i	0.0509146	+	0.139887i
$222$	−15.2574	+	12.9536i	−1.02401	+	0.869389i
$223$	11.5264	−	16.4615i	0.771868	−	1.10234i	−0.220054	−	0.975488i	$-0.570623\pi$
$223$	11.5264	−	16.4615i	0.771868	−	1.10234i	0.991921	−	0.126854i	$-0.0404879\pi$
$224$	−1.61703	−	2.80077i	−0.108042	−	0.187134i
$225$	−6.12499	+	13.6925i	−0.408333	+	0.912833i
$226$	0.0637321	−	0.110387i	0.00423940	−	0.00734285i
$227$	1.96975	+	4.22414i	0.130737	+	0.280366i	0.960769	−	0.277349i	$-0.0894559\pi$
$227$	1.96975	+	4.22414i	0.130737	+	0.280366i	−0.830032	+	0.557715i	$0.811678\pi$
$228$	−4.74916	−	3.93844i	−0.314521	−	0.260830i
$229$	−15.6103	+	18.6036i	−1.03156	+	1.22936i	−0.0586205	+	0.998280i	$0.518670\pi$
$229$	−15.6103	+	18.6036i	−1.03156	+	1.22936i	−0.972935	+	0.231080i	$0.925774\pi$
$230$	−10.1566	−	15.8701i	−0.669706	−	1.04644i
$231$	−1.90581	−	0.875311i	−0.125393	−	0.0575912i
$232$	20.4394	−	9.53106i	1.34191	−	0.625745i
$233$	1.83322	+	6.84167i	0.120098	+	0.448213i	0.999618	−	0.0276501i	$-0.00880243\pi$
$233$	1.83322	+	6.84167i	0.120098	+	0.448213i	−0.879519	+	0.475863i	$0.842136\pi$
$234$	1.97386	+	1.10937i	0.129035	+	0.0725218i
$235$	−4.86126	+	7.66562i	−0.317114	+	0.500050i
$236$	−2.51696	+	0.443808i	−0.163840	+	0.0288894i
$237$	0.949922	−	2.65761i	0.0617041	−	0.172630i
$238$	2.00610	+	0.935462i	0.130036	+	0.0606370i
$239$	2.01666	−	11.4370i	0.130447	−	0.739799i	−0.847476	−	0.530833i	$-0.821879\pi$
$239$	2.01666	−	11.4370i	0.130447	−	0.739799i	0.977923	−	0.208966i	$-0.0670098\pi$
$240$	−1.17144	−	5.09435i	−0.0756159	−	0.328839i
$241$	8.02324	−	6.73230i	0.516822	−	0.433665i	−0.346700	−	0.937976i	$-0.612698\pi$
$241$	8.02324	−	6.73230i	0.516822	−	0.433665i	0.863522	+	0.504311i	$0.168253\pi$
$242$	5.86505	+	5.86505i	0.377020	+	0.377020i
$243$	7.40068	−	13.7197i	0.474754	−	0.880119i
$244$		−	5.95649i		−	0.381325i
$245$	−5.60692	−	13.4575i	−0.358213	−	0.859766i
$246$	7.38548	+	1.93323i	0.470881	+	0.123258i
$247$	−1.62250	−	2.31717i	−0.103237	−	0.147438i
$248$	−5.65342	+	12.1238i	−0.358993	+	0.769862i
$249$	2.80679	−	1.32864i	0.177873	−	0.0841992i
$250$	11.6550	−	0.581402i	0.737128	−	0.0367711i
$251$	−9.75413	+	5.63155i	−0.615675	+	0.355460i	−0.775183	−	0.631736i	$-0.782343\pi$
$251$	−9.75413	+	5.63155i	−0.615675	+	0.355460i	0.159508	+	0.987197i	$0.449009\pi$
$252$	−1.82265	+	0.511044i	−0.114816	+	0.0321928i
$253$	−13.6259	+	3.65106i	−0.856656	+	0.229540i
$254$	−16.2832	−	5.92660i	−1.02170	−	0.371868i
$255$	−8.80154	−	7.93888i	−0.551174	−	0.497152i
$256$	−12.7442	−	10.6936i	−0.796511	−	0.668352i
$257$	1.72895	+	19.7620i	0.107849	+	1.23272i	0.836551	+	0.547890i	$0.184569\pi$
$257$	1.72895	+	19.7620i	0.107849	+	1.23272i	−0.728701	+	0.684832i	$0.759876\pi$
$258$	−7.48459	+	9.02528i	−0.465970	+	0.561889i
$259$	2.62385	−	7.20897i	0.163038	−	0.447944i
$260$	−0.0611778	+	1.47107i	−0.00379408	+	0.0912318i
$261$	−4.12070	−	21.8863i	−0.255065	−	1.35473i
$262$	−22.7092	−	6.08491i	−1.40298	−	0.375927i
$263$	−13.8257	−	9.68085i	−0.852529	−	0.596947i	0.0635351	−	0.997980i	$-0.479763\pi$
$263$	−13.8257	−	9.68085i	−0.852529	−	0.596947i	−0.916064	+	0.401033i	$0.868651\pi$
$264$	−9.16382	−	0.748357i	−0.563994	−	0.0460582i
$265$	−12.5951	+	13.8024i	−0.773713	+	0.847876i
$266$	−2.78635	−	0.491310i	−0.170842	−	0.0301241i
$267$	−4.76906	+	8.37169i	−0.291862	+	0.512339i
$268$	−10.1831	−	0.890909i	−0.622034	−	0.0544209i
$269$	30.5994			1.86568			0.932838	−	0.360296i	$-0.117324\pi$
$269$	30.5994			1.86568			0.932838	+	0.360296i	$0.117324\pi$
$270$	−12.1238	−	0.293628i	−0.737828	−	0.0178696i
$271$	−5.21670			−0.316892			−0.158446	−	0.987368i	$-0.550648\pi$
$271$	−5.21670			−0.316892			−0.158446	+	0.987368i	$0.550648\pi$
$272$	4.11489	+	0.360006i	0.249502	+	0.0218286i
$273$	−0.867874	+	0.00501894i	−0.0525262	+	0.000303760i
$274$	5.35921	+	0.944973i	0.323761	+	0.0570879i
$275$	2.22629	−	8.44838i	0.134251	−	0.509457i
$276$	−7.24272	+	10.4721i	−0.435961	+	0.630344i
$277$	−9.56033	−	6.69422i	−0.574425	−	0.402216i	0.249952	−	0.968258i	$-0.419585\pi$
$277$	−9.56033	−	6.69422i	−0.574425	−	0.402216i	−0.824377	+	0.566042i	$0.808474\pi$
$278$	13.1012	+	3.51047i	0.785760	+	0.210544i
$279$	10.2171	+	8.37370i	0.611681	+	0.501320i
$280$	3.18730	+	3.46390i	0.190478	+	0.207008i
$281$	4.68215	−	12.8641i	0.279313	−	0.767407i	−0.718127	−	0.695912i	$-0.755001\pi$
$281$	4.68215	−	12.8641i	0.279313	−	0.767407i	0.997441	−	0.0714958i	$-0.0227772\pi$
$282$	−7.23447	−	1.23254i	−0.430807	−	0.0733966i
$283$	0.773481	+	8.84093i	0.0459787	+	0.525539i	0.983904	+	0.178700i	$0.0571892\pi$
$283$	0.773481	+	8.84093i	0.0459787	+	0.525539i	−0.937925	+	0.346838i	$0.887255\pi$
$284$	−4.49999	−	3.77594i	−0.267025	−	0.224061i
$285$	13.4934	+	6.89010i	0.799281	+	0.408134i
$286$	−1.23928	−	0.451062i	−0.0732804	−	0.0266719i
$287$	−2.82653	+	0.757366i	−0.166845	+	0.0447059i
$288$	−11.3756	+	8.16295i	−0.670313	+	0.481007i
$289$	−6.61106	+	3.81690i	−0.388886	+	0.224524i
$290$	−13.7238	+	10.5758i	−0.805889	+	0.621035i
$291$	−6.60212	−	4.56619i	−0.387023	−	0.267675i
$292$	3.22153	−	6.90860i	0.188526	−	0.404295i
$293$	6.47833	+	9.25201i	0.378468	+	0.540508i	0.962521	−	0.271207i	$-0.0874228\pi$
$293$	6.47833	+	9.25201i	0.378468	+	0.540508i	−0.584053	+	0.811716i	$0.698534\pi$
$294$	8.28616	−	8.38256i	0.483259	−	0.488881i
$295$	5.79340	−	2.41377i	0.337305	−	0.140535i
$296$		−	33.6331i		−	1.95488i
$297$	−2.95691	+	8.58457i	−0.171577	+	0.498127i
$298$	−8.38915	−	8.38915i	−0.485971	−	0.485971i
$299$	−4.47198	+	3.75244i	−0.258621	+	0.217009i
$300$	−3.40346	−	7.11359i	−0.196499	−	0.410703i
$301$	0.780408	−	4.42591i	0.0449820	−	0.255105i
$302$	−8.60353	−	4.01189i	−0.495078	−	0.230858i
$303$	12.6759	+	14.9303i	0.728209	+	0.857723i
$304$	−5.19963	+	0.916835i	−0.298219	+	0.0525841i
$305$	3.19543	+	14.2738i	0.182970	+	0.817314i
$306$	3.17320	−	9.04236i	0.181400	−	0.516917i
$307$	2.20847	+	8.24213i	0.126044	+	0.470403i	0.999875	−	0.0158274i	$-0.00503823\pi$
$307$	2.20847	+	8.24213i	0.126044	+	0.470403i	−0.873831	+	0.486230i	$0.838372\pi$
$308$	0.999250	−	0.465958i	0.0569376	−	0.0265504i
$309$	−0.794586	−	8.51474i	−0.0452024	−	0.484386i
$310$	2.20359	−	10.0380i	0.125155	−	0.570122i
$311$	−9.40563	+	11.2092i	−0.533344	+	0.635615i	−0.963682	−	0.267053i	$-0.913950\pi$
$311$	−9.40563	+	11.2092i	−0.533344	+	0.635615i	0.430338	+	0.902668i	$0.358394\pi$
$312$	−3.56785	+	1.32201i	−0.201990	+	0.0748439i
$313$	−3.94117	−	8.45186i	−0.222768	−	0.477727i	0.762880	−	0.646540i	$-0.223785\pi$
$313$	−3.94117	−	8.45186i	−0.222768	−	0.477727i	−0.985648	+	0.168812i	$0.946007\pi$
$314$	1.74731	−	3.02644i	0.0986067	−	0.170792i
$315$	4.09354	−	2.20242i	0.230645	−	0.124092i
$316$	0.741868	+	1.28495i	0.0417333	+	0.0722843i
$317$	13.5519	−	19.3542i	0.761152	−	1.08704i	−0.232283	−	0.972648i	$-0.574620\pi$
$317$	13.5519	−	19.3542i	0.761152	−	1.08704i	0.993436	−	0.114390i	$-0.0364914\pi$
$318$	−14.2255	−	5.08469i	−0.797726	−	0.285135i
$319$	4.43659	+	12.1894i	0.248402	+	0.682478i
$320$	15.0320	+	7.78564i	0.840312	+	0.435231i
$321$	6.91679	−	26.4241i	0.386058	−	1.47485i
$322$	−0.508900	+	5.81676i	−0.0283599	+	0.324155i
$323$	−8.46556	+	8.46556i	−0.471036	+	0.471036i
$324$	2.98030	+	7.63410i	0.165572	+	0.424116i
$325$	−0.642570	−	3.55800i	−0.0356434	−	0.197362i
$326$	9.46601	+	11.2812i	0.524274	+	0.624805i
$327$	30.3706	−	17.7694i	1.67950	−	0.982651i
$328$	−10.5088	+	7.35834i	−0.580252	+	0.406297i
$329$	2.64330	−	0.962081i	0.145730	−	0.0530413i
$330$	6.99570	−	0.976949i	0.385101	−	0.0537793i
$331$	4.01625	+	22.7773i	0.220753	+	1.25195i	0.870639	+	0.491922i	$0.163705\pi$
$331$	4.01625	+	22.7773i	0.220753	+	1.25195i	−0.649886	+	0.760032i	$0.725183\pi$
$332$	−0.422540	+	1.57694i	−0.0231899	+	0.0865458i
$333$	−32.1788	−	8.22459i	−1.76338	−	0.450705i
$334$	−12.5818	−	7.26408i	−0.688443	−	0.397473i
$335$	24.8802	−	3.32794i	1.35935	−	0.181825i
$336$	−0.676102	+	1.47207i	−0.0368844	+	0.0803081i
$337$	−12.4168	+	1.08633i	−0.676384	+	0.0591760i	−0.420172	−	0.907445i	$-0.638030\pi$
$337$	−12.4168	+	1.08633i	−0.676384	+	0.0591760i	−0.256212	+	0.966621i	$0.582475\pi$
$338$	12.9735	−	1.13503i	0.705663	−	0.0617375i
$339$	0.210605	−	0.0196534i	0.0114385	−	0.00106743i
$340$	6.17638	−	0.826146i	0.334961	−	0.0448040i
$341$	−6.66344	−	3.84714i	−0.360846	−	0.208334i
$342$	−0.926386	+	12.2141i	−0.0500932	+	0.660464i
$343$	−2.42474	+	9.04926i	−0.130924	+	0.488614i
$344$	−3.42137	−	19.4036i	−0.184468	−	1.04617i
$345$	11.7382	−	28.9800i	0.631961	−	1.56023i
$346$	−3.05115	+	1.11053i	−0.164031	+	0.0597023i
$347$	9.36840	−	6.55983i	0.502922	−	0.352150i	−0.294421	−	0.955676i	$-0.595127\pi$
$347$	9.36840	−	6.55983i	0.502922	−	0.352150i	0.797343	+	0.603526i	$0.206238\pi$
$348$	10.1734	+	5.79543i	0.545351	+	0.310667i
$349$	−15.6113	−	18.6048i	−0.835652	−	0.995891i	−0.999955	−	0.00948135i	$-0.996982\pi$
$349$	−15.6113	−	18.6048i	−0.835652	−	0.995891i	0.164303	−	0.986410i	$-0.447462\pi$
$350$	−2.97087	−	2.06195i	−0.158800	−	0.110216i
$351$	0.392365	+	3.73686i	0.0209429	+	0.199459i
$352$	5.76654	−	5.76654i	0.307358	−	0.307358i
$353$	−2.92059	+	33.3825i	−0.155447	+	1.77677i	0.373024	+	0.927822i	$0.378321\pi$
$353$	−2.92059	+	33.3825i	−0.155447	+	1.77677i	−0.528472	+	0.848951i	$0.677235\pi$
$354$	3.60867	+	3.56717i	0.191799	+	0.189593i
$355$	12.8091	+	6.63436i	0.679839	+	0.352115i
$356$	−1.73241	−	4.75976i	−0.0918177	−	0.252267i
$357$	0.658747	+	3.61361i	0.0348646	+	0.191253i
$358$	3.03706	−	4.33737i	0.160514	−	0.229237i
$359$	9.34241	+	16.1815i	0.493073	+	0.854028i	0.999968	−	0.00797981i	$-0.00254008\pi$
$359$	9.34241	+	16.1815i	0.493073	+	0.854028i	−0.506895	+	0.862008i	$0.669207\pi$
$360$	13.5617	−	15.2113i	0.714765	−	0.801707i
$361$	−1.84847	+	3.20165i	−0.0972881	+	0.168508i
$362$	−4.11824	−	8.83159i	−0.216450	−	0.464178i
$363$	−2.31169	+	13.5686i	−0.121332	+	0.712169i
$364$	0.293285	−	0.349523i	0.0153723	−	0.0183200i
$365$	−4.01368	+	18.2836i	−0.210086	+	0.957006i
$366$	−9.64775	+	6.83891i	−0.504296	+	0.357476i
$367$	−6.45312	+	3.00914i	−0.336850	+	0.157076i	−0.583682	−	0.811983i	$-0.698388\pi$
$367$	−6.45312	+	3.00914i	−0.336850	+	0.157076i	0.246831	+	0.969058i	$0.420611\pi$
$368$	2.82013	+	10.5249i	0.147009	+	0.548647i
$369$	4.47035	+	11.8538i	0.232717	+	0.617084i
$370$	5.64474	+	25.2147i	0.293456	+	1.31085i
$371$	5.70252	−	1.00551i	0.296060	−	0.0522034i
$372$	−6.83228	+	1.24550i	−0.354237	+	0.0645760i
$373$	−9.36399	−	4.36650i	−0.484849	−	0.226089i	0.164794	−	0.986328i	$-0.447304\pi$
$373$	−9.36399	−	4.36650i	−0.484849	−	0.226089i	−0.649643	+	0.760239i	$0.725082\pi$
$374$	−0.969241	+	5.49684i	−0.0501183	+	0.284235i
$375$	11.9720	+	15.2207i	0.618232	+	0.785996i
$376$	9.44698	−	7.92696i	0.487191	−	0.408802i
$377$	3.79582	+	3.79582i	0.195495	+	0.195495i
$378$	2.92041	+	2.36541i	0.150210	+	0.121663i
$379$			5.45309i			0.280106i	0.990144	+	0.140053i	$0.0447273\pi$
$379$			5.45309i			0.280106i	−0.990144	+	0.140053i	$0.955273\pi$
$380$	−7.35248	+	3.06334i	−0.377174	+	0.157146i
$381$	−7.60290	−	27.7319i	−0.389508	−	1.42075i
$382$	0.679459	+	0.970368i	0.0347641	+	0.0496483i
$383$	−1.88914	+	4.05128i	−0.0965307	+	0.207011i	−0.948643	−	0.316348i	$-0.897543\pi$
$383$	−1.88914	+	4.05128i	−0.0965307	+	0.207011i	0.852113	+	0.523359i	$0.175321\pi$
$384$	0.201923	−	2.47260i	0.0103044	−	0.126179i
$385$	−2.14457	+	1.65265i	−0.109298	+	0.0842270i
$386$	12.4594	−	7.19344i	0.634167	−	0.366137i
$387$	−19.4012	−	1.47149i	−0.986219	−	0.0748003i
$388$	4.07636	−	1.09226i	0.206946	−	0.0554510i
$389$	−9.10172	−	3.31276i	−0.461476	−	0.167963i	0.100811	−	0.994906i	$-0.467856\pi$
$389$	−9.10172	−	3.31276i	−0.461476	−	0.167963i	−0.562287	+	0.826942i	$0.690078\pi$
$390$	2.45294	−	1.58991i	0.124209	−	0.0805082i
$391$	18.9268	+	15.8814i	0.957168	+	0.803159i
$392$	1.72627	+	19.7314i	0.0871899	+	0.996586i
$393$	−13.5554	−	36.5834i	−0.683778	−	1.84539i
$394$	0.714445	−	1.96292i	0.0359932	−	0.0988906i
$395$	−2.46710	−	2.68120i	−0.124133	−	0.134906i
$396$	−2.43432	−	4.10595i	−0.122329	−	0.206332i
$397$	−0.981728	−	0.263053i	−0.0492715	−	0.0132023i	0.234099	−	0.972213i	$-0.424786\pi$
$397$	−0.981728	−	0.263053i	−0.0492715	−	0.0132023i	−0.283371	+	0.959010i	$0.591453\pi$
$398$	15.7991	+	11.0626i	0.791936	+	0.554520i
$399$	−2.00882	−	4.24369i	−0.100567	−	0.212450i
$400$	−6.52565	−	1.71962i	−0.326282	−	0.0859810i
$401$	8.07342	+	1.42356i	0.403168	+	0.0710893i	0.371555	−	0.928411i	$-0.378825\pi$
$401$	8.07342	+	1.42356i	0.403168	+	0.0710893i	0.0316124	+	0.999500i	$0.489936\pi$
$402$	10.2487	+	17.5165i	0.511159	+	0.873646i
$403$	−3.17202	−	0.277515i	−0.158009	−	0.0138240i
$404$	−10.2965			−0.512272
$405$	−11.2372	−	16.6951i	−0.558382	−	0.829584i
$406$	5.36923			0.266470
$407$	19.2715	+	1.68604i	0.955253	+	0.0835738i
$408$	8.13225	+	13.8992i	0.402606	+	0.688114i
$409$	−28.0740	−	4.95021i	−1.38817	−	0.244772i	−0.570897	−	0.821021i	$-0.693405\pi$
$409$	−28.0740	−	4.95021i	−1.38817	−	0.244772i	−0.817274	+	0.576249i	$0.804516\pi$
$410$	6.64346	−	7.28026i	0.328097	−	0.359547i
$411$	3.86372	+	8.16221i	0.190583	+	0.402612i
$412$	3.68278	+	2.57871i	0.181438	+	0.127044i
$413$	−1.87866	−	0.503386i	−0.0924429	−	0.0247700i
$414$	25.2773	−	0.292368i	1.24231	−	0.0143691i
$415$	0.166580	−	4.00556i	0.00817710	−	0.196625i
$416$	1.15426	−	3.17132i	0.0565925	−	0.155487i
$417$	7.82028	+	21.1055i	0.382961	+	1.03354i
$418$	−0.621820	−	7.10744i	−0.0304142	−	0.347636i
$419$	−19.6956	−	16.5265i	−0.962192	−	0.807375i	0.0191165	−	0.999817i	$-0.493915\pi$
$419$	−19.6956	−	16.5265i	−0.962192	−	0.807375i	−0.981308	+	0.192443i	$0.938359\pi$
$420$	−0.510179	+	2.38993i	−0.0248942	+	0.116617i
$421$	−12.0396	−	4.38206i	−0.586775	−	0.213569i	0.0315356	−	0.999503i	$-0.489960\pi$
$421$	−12.0396	−	4.38206i	−0.586775	−	0.213569i	−0.618310	+	0.785934i	$0.712182\pi$
$422$	16.9128	−	4.53177i	0.823303	−	0.220603i
$423$	−5.27404	−	10.9769i	−0.256432	−	0.533717i
$424$	21.9849	−	12.6930i	1.06768	−	0.616427i
$425$	−14.3575	+	5.29312i	−0.696441	+	0.256754i
$426$	−0.949263	+	11.6240i	−0.0459920	+	0.563183i
$427$	1.91566	−	4.10815i	0.0927054	−	0.198807i
$428$	8.23645	+	11.7629i	0.398124	+	0.568580i
$429$	−0.578643	−	2.11062i	−0.0279371	−	0.101902i
$430$	5.82156	+	13.9726i	0.280741	+	0.673819i
$431$			5.16823i			0.248945i	0.992223	+	0.124473i	$0.0397239\pi$
$431$			5.16823i			0.248945i	−0.992223	+	0.124473i	$0.960276\pi$
$432$	6.63084	+	2.28396i	0.319026	+	0.109887i
$433$	−2.74947	−	2.74947i	−0.132131	−	0.132131i	0.637948	−	0.770079i	$-0.279783\pi$
$433$	−2.74947	−	2.74947i	−0.132131	−	0.132131i	−0.770079	+	0.637948i	$0.779783\pi$
$434$	−2.43970	+	2.04715i	−0.117109	+	0.0982663i
$435$	−27.4879	−	8.43017i	−1.31794	−	0.404196i
$436$	−3.21225	+	18.2176i	−0.153839	+	0.872464i
$437$	−28.6224	−	13.3468i	−1.36919	−	0.638465i
$438$	−14.8887	+	2.71414i	−0.711408	+	0.129687i
$439$	−31.6512	+	5.58095i	−1.51063	+	0.266364i	−0.866742	−	0.498757i	$-0.833790\pi$
$439$	−31.6512	+	5.58095i	−1.51063	+	0.266364i	−0.643886	+	0.765122i	$0.722679\pi$
$440$	−6.35692	+	10.0241i	−0.303054	+	0.477880i
$441$	19.3003	+	3.17346i	0.919063	+	0.151117i
$442$	0.597834	+	2.23115i	0.0284361	+	0.106125i
$443$	13.9035	−	6.48333i	0.660577	−	0.308032i	−0.0632661	−	0.997997i	$-0.520152\pi$
$443$	13.9035	−	6.48333i	0.660577	−	0.308032i	0.723843	+	0.689965i	$0.242374\pi$
$444$	14.2450	−	10.0977i	0.676039	−	0.479218i
$445$	6.70488	+	10.4766i	0.317842	+	0.496640i
$446$	13.4825	−	16.0678i	0.638413	−	0.760831i
$447$	3.30656	−	19.4081i	0.156395	−	0.917972i
$448$	−2.21708	−	4.75455i	−0.104747	−	0.224631i
$449$	−1.37821	+	2.38713i	−0.0650416	+	0.112655i	−0.896712	−	0.442614i	$-0.854051\pi$
$449$	−1.37821	+	2.38713i	−0.0650416	+	0.112655i	0.831671	+	0.555269i	$0.187385\pi$
$450$	−7.61424	+	13.6800i	−0.358939	+	0.644882i
$451$	−3.68947	−	6.39034i	−0.173730	−	0.300910i
$452$	−0.0637823	+	0.0910905i	−0.00300007	+	0.00428454i
$453$	−2.82515	−	15.4976i	−0.132737	−	0.728142i
$454$	1.66384	+	4.57137i	0.0780879	+	0.214545i
$455$	−0.515303	+	0.994911i	−0.0241578	+	0.0466421i
$456$	−14.6389	−	14.4706i	−0.685530	−	0.677647i
$457$	−2.98806	+	34.1536i	−0.139775	+	1.59764i	0.525335	+	0.850895i	$0.323940\pi$
$457$	−2.98806	+	34.1536i	−0.139775	+	1.59764i	−0.665111	+	0.746745i	$0.731616\pi$
$458$	−17.9236	+	17.9236i	−0.837515	+	0.837515i
$459$	15.2869	−	4.38171i	0.713529	−	0.204521i
$460$	7.62030	+	14.5648i	0.355298	+	0.679086i
$461$	−1.95614	−	2.33124i	−0.0911067	−	0.108577i	0.718565	−	0.695460i	$-0.244799\pi$
$461$	−1.95614	−	2.33124i	−0.0911067	−	0.108577i	−0.809672	+	0.586883i	$0.800355\pi$
$462$	−1.90200	−	1.08350i	−0.0884889	−	0.0504090i
$463$	22.0633	−	15.4489i	1.02537	−	0.717970i	0.0653361	−	0.997863i	$-0.479188\pi$
$463$	22.0633	−	15.4489i	1.02537	−	0.717970i	0.960031	+	0.279894i	$0.0902992\pi$
$464$	9.41529	−	3.42689i	0.437094	−	0.159089i
$465$	15.7043	−	6.64989i	0.728269	−	0.308381i
$466$	1.28377	+	7.28061i	0.0594694	+	0.337268i
$467$	4.45355	−	16.6209i	0.206086	−	0.769122i	−0.783030	−	0.621983i	$-0.786327\pi$
$467$	4.45355	−	16.6209i	0.206086	−	0.769122i	0.989116	−	0.147138i	$-0.0470062\pi$
$468$	−1.63111	−	1.11423i	−0.0753981	−	0.0515051i
$469$	−6.73671	−	3.88944i	−0.311073	−	0.179598i
$470$	−5.75198	+	7.52834i	−0.265319	+	0.347257i
$471$	5.77406	−	0.538829i	0.266055	−	0.0248279i
$472$	−8.49431	+	0.743156i	−0.390982	+	0.0342065i
$473$	11.2896	−	0.987714i	0.519098	−	0.0454152i
$474$	1.22947	−	2.67692i	0.0564715	−	0.122955i
$475$	15.9757	−	11.2851i	0.733014	−	0.517797i
$476$	−1.67236	−	0.965535i	−0.0766523	−	0.0442552i
$477$	−6.76799	−	24.1382i	−0.309885	−	1.10521i
$478$	3.13729	−	11.7085i	0.143497	−	0.535536i
$479$	6.03903	+	34.2490i	0.275930	+	1.56488i	0.735991	+	0.676991i	$0.236717\pi$
$479$	6.03903	+	34.2490i	0.275930	+	1.56488i	−0.460061	+	0.887888i	$0.652172\pi$
$480$	2.50000	+	17.9019i	0.114109	+	0.817108i
$481$	7.52282	−	2.73808i	0.343011	−	0.124846i
$482$	8.95484	−	6.27025i	0.407882	−	0.285602i
$483$	−8.36316	+	4.89318i	−0.380537	+	0.222647i
$484$	−4.65130	−	5.54320i	−0.211423	−	0.251964i
$485$	−9.18238	+	4.80423i	−0.416951	+	0.218149i
$486$	8.94315	−	13.5922i	0.405670	−	0.616557i
$487$	−10.1713	+	10.1713i	−0.460908	+	0.460908i	−0.898953	−	0.438045i	$-0.855671\pi$
$487$	−10.1713	+	10.1713i	−0.460908	+	0.460908i	0.438045	+	0.898953i	$0.355671\pi$
$488$	1.73199	−	19.7968i	0.0784036	−	0.896157i
$489$	−6.18836	+	23.6413i	−0.279847	+	1.06910i
$490$	−4.60576	−	14.5029i	−0.208067	−	0.655173i
$491$	10.0702	+	27.6677i	0.454462	+	1.24863i	0.929553	+	0.368688i	$0.120193\pi$
$491$	10.0702	+	27.6677i	0.454462	+	1.24863i	−0.475091	+	0.879937i	$0.657585\pi$
$492$	−6.27165	−	2.24171i	−0.282748	−	0.101064i
$493$	13.0313	−	18.6107i	0.586902	−	0.838183i
$494$	−1.47626	−	2.55695i	−0.0664199	−	0.115043i
$495$	8.03613	+	8.53332i	0.361197	+	0.383544i
$496$	−2.97158	+	5.14694i	−0.133428	+	0.231104i
$497$	−1.88923	−	4.05148i	−0.0847438	−	0.181734i
$498$	3.03931	−	1.12617i	0.136195	−	0.0504647i
$499$	11.3613	−	13.5399i	0.508604	−	0.606130i	−0.449243	−	0.893410i	$-0.648306\pi$
$499$	11.3613	−	13.5399i	0.508604	−	0.606130i	0.957847	+	0.287279i	$0.0927507\pi$
$500$	−10.1735	−	0.380905i	−0.454971	−	0.0170346i
$501$	−2.24006	−	24.0044i	−0.100079	−	1.07244i
$502$	−10.6545	+	4.96826i	−0.475532	+	0.221744i
$503$	−3.36375	−	12.5537i	−0.149982	−	0.559742i	−0.999483	−	0.0321541i	$-0.989763\pi$
$503$	−3.36375	−	12.5537i	−0.149982	−	0.559742i	0.849501	−	0.527588i	$-0.176903\pi$
$504$	−6.20630	+	1.16851i	−0.276450	+	0.0520494i
$505$	24.6740	−	5.52370i	1.09798	−	0.245802i
$506$	−14.5001	+	2.55677i	−0.644610	+	0.113662i
$507$	13.9868	+	16.4744i	0.621175	+	0.731652i
$508$	13.7009	+	6.38885i	0.607880	+	0.283459i
$509$	−0.0644329	+	0.365417i	−0.00285594	+	0.0161968i	−0.986202	−	0.165544i	$-0.947062\pi$
$509$	−0.0644329	+	0.365417i	−0.00285594	+	0.0161968i	0.983346	+	0.181741i	$0.0581732\pi$
$510$	−8.42949	−	9.05537i	−0.373264	−	0.400978i
$511$	4.44374	−	3.72874i	0.196579	−	0.164950i
$512$	−10.2528	−	10.2528i	−0.453113	−	0.453113i
$513$	−17.4246	+	10.4673i	−0.769317	+	0.462143i
$514$			20.7055i			0.913279i
$515$	−10.2086	−	4.20379i	−0.449843	−	0.185241i
$516$	7.19103	−	7.27468i	0.316567	−	0.320250i
$517$	4.06851	+	5.81043i	0.178933	+	0.255542i
$518$	3.38403	−	7.25707i	0.148686	−	0.318857i
$519$	−4.43152	−	3.06494i	−0.194522	−	0.134536i
$520$	−0.631076	+	4.87140i	−0.0276745	+	0.213625i
$521$	−2.40696	+	1.38966i	−0.105451	+	0.0608820i	−0.551798	−	0.833978i	$-0.686058\pi$
$521$	−2.40696	+	1.38966i	−0.105451	+	0.0608820i	0.446347	+	0.894860i	$0.352725\pi$
$522$	−2.29365	−	23.1318i	−0.100390	−	1.01245i
$523$	14.6842	−	3.93462i	0.642096	−	0.172049i	0.0769434	−	0.997035i	$-0.475484\pi$
$523$	14.6842	−	3.93462i	0.642096	−	0.172049i	0.565153	+	0.824986i	$0.308817\pi$
$524$	19.2736	+	7.01503i	0.841973	+	0.306453i
$525$	−0.0595462	−	6.00078i	−0.00259881	−	0.261895i
$526$	−13.4950	−	11.3237i	−0.588411	−	0.493736i
$527$	1.17453	+	13.4249i	0.0511633	+	0.584799i
$528$	−4.02681	−	0.686049i	−0.175245	−	0.0298565i
$529$	−14.4247	+	39.6316i	−0.627162	+	1.72311i
$530$	−14.3518	+	13.2057i	−0.623401	+	0.573620i
$531$	−1.36617	+	8.30874i	−0.0592866	+	0.360569i
$532$	2.38424	+	0.638854i	0.103370	+	0.0276978i
$533$	−2.50139	−	1.75149i	−0.108347	−	0.0758655i
$534$	−5.72034	+	8.27089i	−0.247544	+	0.357916i
$535$	−26.0477	−	23.7693i	−1.12614	−	1.02764i
$536$	−33.5852	−	5.92198i	−1.45066	−	0.255790i
$537$	8.78654	−	0.0508127i	0.379167	−	0.00219273i
$538$	31.8166	+	2.78359i	1.37171	+	0.120009i
$539$	−11.3925			−0.490709
$540$	10.5143	+	1.17702i	0.452464	+	0.0506511i
$541$	−16.6575			−0.716163			−0.358081	−	0.933690i	$-0.616569\pi$
$541$	−16.6575			−0.716163			−0.358081	+	0.933690i	$0.616569\pi$
$542$	−5.42423	−	0.474558i	−0.232990	−	0.0203840i
$543$	8.00418	−	14.0507i	0.343492	−	0.602972i
$544$	−14.0664	−	2.48028i	−0.603090	−	0.106341i
$545$	−2.07540	−	45.3788i	−0.0889002	−	1.94381i
$546$	−0.902856	−	0.0737311i	−0.0386387	−	0.00315540i
$547$	0.317541	+	0.222344i	0.0135771	+	0.00950676i	0.580345	−	0.814371i	$-0.302918\pi$
$547$	0.317541	+	0.222344i	0.0135771	+	0.00950676i	−0.566768	+	0.823877i	$0.691806\pi$
$548$	−4.58578	−	1.22876i	−0.195895	−	0.0524899i
$549$	−18.5172	−	6.49817i	−0.790294	−	0.277335i
$550$	3.08340	−	8.58195i	0.131477	−	0.365935i
$551$	−9.93246	+	27.2892i	−0.423137	+	1.16256i
$552$	−27.1166	+	32.6985i	−1.15416	+	1.39174i
$553$	0.0984086	+	1.12482i	0.00418476	+	0.0478320i
$554$	−9.33168	−	7.83021i	−0.396465	−	0.332674i
$555$	−28.7188	+	31.8395i	−1.21905	+	1.35151i
$556$	−11.1192	−	4.04707i	−0.471561	−	0.171634i
$557$	12.2853	−	3.29185i	0.520546	−	0.139480i	0.0110271	−	0.999939i	$-0.496490\pi$
$557$	12.2853	−	3.29185i	0.520546	−	0.139480i	0.509519	+	0.860459i	$0.329823\pi$
$558$	9.86178	+	9.63626i	0.417482	+	0.407935i
$559$	4.06152	−	2.34492i	0.171784	−	0.0991797i
$560$	1.27653	+	1.65650i	0.0539433	+	0.0699998i
$561$	−8.37183	+	3.96295i	−0.353459	+	0.167316i
$562$	6.03864	−	12.9499i	0.254725	−	0.546259i
$563$	−16.7779	−	23.9613i	−0.707102	−	1.00985i	−0.998580	−	0.0532691i	$-0.983036\pi$
$563$	−16.7779	−	23.9613i	−0.707102	−	1.00985i	0.291478	−	0.956578i	$-0.405853\pi$
$564$	6.19369	+	1.62126i	0.260801	+	0.0682675i
$565$	0.103977	−	0.252500i	0.00437436	−	0.0106228i
$566$			9.26299i			0.389353i
$567$	−0.399701	+	6.22368i	−0.0167859	+	0.261370i
$568$	−13.8580	−	13.8580i	−0.581470	−	0.581470i
$569$	−3.92124	+	3.29031i	−0.164387	+	0.137937i	−0.721270	−	0.692654i	$-0.756441\pi$
$569$	−3.92124	+	3.29031i	−0.164387	+	0.137937i	0.556884	+	0.830591i	$0.311997\pi$
$570$	13.4034	+	8.39168i	0.561407	+	0.351489i
$571$	1.16063	−	6.58228i	0.0485710	−	0.275460i	−0.950844	−	0.309671i	$-0.899781\pi$
$571$	1.16063	−	6.58228i	0.0485710	−	0.275460i	0.999415	+	0.0342116i	$0.0108920\pi$
$572$	1.04275	+	0.486243i	0.0435997	+	0.0203309i
$573$	−0.661643	+	1.85109i	−0.0276405	+	0.0773302i
$574$	−3.00787	+	0.530368i	−0.125546	+	0.0221372i
$575$	−26.0743	−	30.8141i	−1.08737	−	1.28504i
$576$	−19.5366	+	11.5828i	−0.814023	+	0.482615i
$577$	−11.9622	−	44.6435i	−0.497992	−	1.85853i	−0.512580	−	0.858640i	$-0.671310\pi$
$577$	−11.9622	−	44.6435i	−0.497992	−	1.85853i	0.0145873	−	0.999894i	$-0.495357\pi$
$578$	−7.22128	+	3.36734i	−0.300366	+	0.140063i
$579$	21.6954	+	9.96440i	0.901630	+	0.414106i
$580$	12.7313	−	8.14786i	0.528640	−	0.338321i
$581$	−0.798581	+	0.951712i	−0.0331307	+	0.0394837i
$582$	−6.44938	−	5.34842i	−0.267335	−	0.221699i
$583$	6.17089	+	13.2335i	0.255572	+	0.548076i
$584$	12.7158	−	22.0244i	0.526183	−	0.911376i
$585$	4.50643	+	1.79503i	0.186318	+	0.0742155i
$586$	5.89440	+	10.2094i	0.243495	+	0.421746i
$587$	1.01832	−	1.45431i	0.0420306	−	0.0600260i	−0.797587	−	0.603204i	$-0.793890\pi$
$587$	1.01832	−	1.45431i	0.0420306	−	0.0600260i	0.839617	+	0.543178i	$0.182779\pi$
$588$	−7.83879	+	6.65515i	−0.323266	+	0.274454i
$589$	−5.89151	−	16.1868i	−0.242755	−	0.666965i
$590$	6.24344	−	1.98277i	0.257039	−	0.0816293i
$591$	3.34305	−	0.916521i	0.137515	−	0.0377006i
$592$	1.30232	−	14.8856i	0.0535250	−	0.611794i
$593$	27.8118	−	27.8118i	1.14209	−	1.14209i	0.154028	−	0.988066i	$-0.450775\pi$
$593$	27.8118	−	27.8118i	1.14209	−	1.14209i	0.988066	−	0.154028i	$-0.0492246\pi$
$594$	−3.85547	+	8.65708i	−0.158192	+	0.355204i
$595$	4.52550	+	1.41659i	0.185528	+	0.0580747i
$596$	6.65306	+	7.92880i	0.272520	+	0.324776i
$597$	0.185088	+	32.0054i	0.00757514	+	1.30989i
$598$	−4.99124	+	3.49490i	−0.204107	+	0.142917i
$599$	37.7245	−	13.7306i	1.54138	−	0.561017i	0.575005	−	0.818150i	$-0.305000\pi$
$599$	37.7245	−	13.7306i	1.54138	−	0.561017i	0.966376	+	0.257133i	$0.0827779\pi$
$600$	−9.24315	−	24.6321i	−0.377350	−	1.00560i
$601$	3.13840	+	17.7988i	0.128018	+	0.726027i	0.979469	+	0.201593i	$0.0646119\pi$
$601$	3.13840	+	17.7988i	0.128018	+	0.726027i	−0.851451	+	0.524434i	$0.824277\pi$
$602$	1.21407	−	4.53099i	0.0494820	−	0.184669i
$603$	−13.8788	+	30.6848i	−0.565188	+	1.24958i
$604$	7.17219	+	4.14087i	0.291832	+	0.168490i
$605$	14.1198	+	10.7881i	0.574052	+	0.438601i
$606$	11.8219	+	16.6773i	0.480233	+	0.677471i
$607$	−14.2779	+	1.24916i	−0.579522	+	0.0507016i	−0.373149	−	0.927772i	$-0.621722\pi$
$607$	−14.2779	+	1.24916i	−0.579522	+	0.0507016i	−0.206374	+	0.978473i	$0.566166\pi$
$608$	18.1879	−	1.59123i	0.737616	−	0.0645330i
$609$	5.15265	+	7.26892i	0.208796	+	0.294552i
$610$	2.02408	+	15.1323i	0.0819525	+	0.612688i
$611$	2.54213	+	1.46770i	0.102844	+	0.0593767i
$612$	−3.44534	+	7.61735i	−0.139270	+	0.307913i
$613$	7.34062	−	27.3956i	0.296485	−	1.10650i	−0.643546	−	0.765408i	$-0.722537\pi$
$613$	7.34062	−	27.3956i	0.296485	−	1.10650i	0.940031	−	0.341090i	$-0.110796\pi$
$614$	1.54655	+	8.77091i	0.0624136	+	0.353965i
$615$	16.2316	+	2.00739i	0.654521	+	0.0809457i
$616$	3.45655	−	1.25808i	0.139269	−	0.0506896i
$617$	19.2569	−	13.4838i	0.775255	−	0.542839i	−0.117666	−	0.993053i	$-0.537541\pi$
$617$	19.2569	−	13.4838i	0.775255	−	0.542839i	0.892921	+	0.450214i	$0.148652\pi$
$618$	−0.0516178	−	8.92574i	−0.00207637	−	0.359046i
$619$	5.35313	+	6.37961i	0.215160	+	0.256418i	0.862820	−	0.505512i	$-0.168696\pi$
$619$	5.35313	+	6.37961i	0.215160	+	0.256418i	−0.647659	+	0.761930i	$0.724252\pi$
$620$	−2.67836	+	8.55640i	−0.107566	+	0.343633i
$621$	24.6535	+	33.9401i	0.989312	+	1.36197i
$622$	−10.7995	+	10.7995i	−0.433020	+	0.433020i
$623$	0.335951	−	3.83994i	0.0134596	−	0.153844i
$624$	−1.63028	+	0.446952i	−0.0652633	+	0.0178924i
$625$	24.5834	−	4.54490i	0.983336	−	0.181796i
$626$	−3.32909	−	9.14661i	−0.133057	−	0.365572i
$627$	9.02539	−	7.66258i	0.360439	−	0.306014i
$628$	−1.74869	+	2.49739i	−0.0697803	+	0.0996566i
$629$	−16.9411	−	29.3428i	−0.675485	−	1.16997i
$630$	4.45674	−	1.91765i	0.177561	−	0.0764009i
$631$	10.7788	−	18.6694i	0.429097	−	0.743218i	−0.567696	−	0.823238i	$-0.692165\pi$
$631$	10.7788	−	18.6694i	0.429097	−	0.743218i	0.996793	+	0.0800204i	$0.0254985\pi$
$632$	2.09201	+	4.48633i	0.0832158	+	0.178457i
$633$	22.3658	+	18.5478i	0.888960	+	0.737208i
$634$	15.8517	−	18.8913i	0.629550	−	0.750269i
$635$	−36.2594	−	7.95982i	−1.43891	−	0.315876i
$636$	11.9766	+	5.50069i	0.474904	+	0.218117i
$637$	−4.27285	+	1.99246i	−0.169296	+	0.0789442i
$638$	3.50422	+	13.0779i	0.138734	+	0.517761i
$639$	−16.6476	+	9.86998i	−0.658570	+	0.390450i
$640$	−2.70472	−	1.71524i	−0.106913	−	0.0678007i
$641$	−4.89330	+	0.862821i	−0.193274	+	0.0340794i	−0.269447	−	0.963015i	$-0.586841\pi$
$641$	−4.89330	+	0.862821i	−0.193274	+	0.0340794i	0.0761733	+	0.997095i	$0.475730\pi$
$642$	9.59572	−	26.8461i	0.378713	−	1.05953i
$643$	−20.7326	−	9.66776i	−0.817613	−	0.381259i	−0.0316243	−	0.999500i	$-0.510068\pi$
$643$	−20.7326	−	9.66776i	−0.817613	−	0.381259i	−0.785989	+	0.618241i	$0.787846\pi$
$644$	0.884560	−	5.01659i	0.0348566	−	0.197681i
$645$	−13.3295	+	21.2903i	−0.524850	+	0.838305i
$646$	−9.57243	+	8.03223i	−0.376622	+	0.316024i
$647$	−8.15287	−	8.15287i	−0.320522	−	0.320522i	0.528445	−	0.848967i	$-0.322775\pi$
$647$	−8.15287	−	8.15287i	−0.320522	−	0.320522i	−0.848967	+	0.528445i	$0.822775\pi$
$648$	7.68542	+	26.2390i	0.301912	+	1.03076i
$649$		−	4.90443i		−	0.192516i
$650$	−0.344464	−	3.75799i	−0.0135110	−	0.147401i
$651$	−5.11274	−	1.33831i	−0.200384	−	0.0524527i
$652$	−7.36905	−	10.5241i	−0.288594	−	0.412155i
$653$	−15.6937	+	33.6553i	−0.614142	+	1.31703i	0.315625	+	0.948884i	$0.397786\pi$
$653$	−15.6937	+	33.6553i	−0.614142	+	1.31703i	−0.929767	+	0.368148i	$0.879992\pi$
$654$	33.1952	−	15.7135i	1.29804	−	0.614447i
$655$	−49.9495	−	6.47082i	−1.95169	−	0.252836i
$656$	−4.93599	+	2.84980i	−0.192718	+	0.111266i
$657$	−17.9626	−	17.5518i	−0.700786	−	0.684760i
$658$	2.83597	−	0.759896i	0.110558	−	0.0296238i
$659$	17.4051	+	6.33493i	0.678005	+	0.246774i	0.657991	−	0.753026i	$-0.271407\pi$
$659$	17.4051	+	6.33493i	0.678005	+	0.246774i	0.0200144	+	0.999800i	$0.493629\pi$
$660$	−6.15418	+	0.317135i	−0.239551	+	0.0123445i
$661$	32.6452	+	27.3925i	1.26975	+	1.06545i	0.994572	+	0.104053i	$0.0331813\pi$
$661$	32.6452	+	27.3925i	1.26975	+	1.06545i	0.275178	+	0.961393i	$0.411263\pi$
$662$	2.10399	+	24.0488i	0.0817740	+	0.934682i
$663$	−2.44683	+	2.95051i	−0.0950271	+	0.114588i
$664$	−1.86287	+	5.11819i	−0.0722933	+	0.198624i
$665$	−6.05616	−	0.251859i	−0.234848	−	0.00976668i
$666$	−32.7107	−	11.4790i	−1.26751	−	0.444804i
$667$	57.8896	+	15.5115i	2.24149	+	0.600607i
$668$	10.3824	+	7.26980i	0.401705	+	0.281277i
$669$	34.6914	+	2.83305i	1.34125	+	0.109532i
$670$	26.1727	−	1.19701i	1.01114	−	0.0462444i
$671$	11.2566	+	1.98484i	0.434555	+	0.0766238i
$672$	2.77267	−	4.86719i	0.106958	−	0.187756i
$673$	9.45392	+	0.827111i	0.364422	+	0.0318828i	0.267896	−	0.963448i	$-0.413672\pi$
$673$	9.45392	+	0.827111i	0.364422	+	0.0318828i	0.0965254	+	0.995331i	$0.469227\pi$
$674$	−13.0095			−0.501109
$675$	−25.8273	+	2.81997i	−0.994092	+	0.108541i
$676$	−11.3614			−0.436977
$677$	−10.7923	−	0.944208i	−0.414783	−	0.0362888i	−0.122146	−	0.992512i	$-0.538977\pi$
$677$	−10.7923	−	0.944208i	−0.414783	−	0.0362888i	−0.292638	+	0.956223i	$0.594533\pi$
$678$	0.220771	−	0.00127672i	0.00847865	−	4.90322e-5i
$679$	3.16272	+	0.557672i	0.121374	+	0.0214015i
$680$	20.7678	−	0.949814i	0.796408	−	0.0364237i
$681$	−4.59204	+	6.63950i	−0.175967	+	0.254426i
$682$	−6.57855	−	4.60635i	−0.251906	−	0.176386i
$683$	−2.18859	−	0.586431i	−0.0837441	−	0.0224392i	0.216704	−	0.976237i	$-0.430469\pi$
$683$	−2.18859	−	0.586431i	−0.0837441	−	0.0224392i	−0.300448	+	0.953798i	$0.597136\pi$
$684$	1.73382	−	10.5447i	0.0662943	−	0.403188i
$685$	11.6483	+	0.484420i	0.445057	+	0.0185087i
$686$	−3.34440	+	9.18868i	−0.127690	+	0.350825i
$687$	−41.4658	−	7.06454i	−1.58202	−	0.269529i
$688$	−0.762924	−	8.72026i	−0.0290862	−	0.332457i
$689$	4.62889	+	3.88410i	0.176347	+	0.147972i
$690$	14.8414	−	29.0651i	0.565002	−	1.10649i
$691$	7.28698	+	2.65224i	0.277210	+	0.100896i	0.476884	−	0.878966i	$-0.341766\pi$
$691$	7.28698	+	2.65224i	0.277210	+	0.100896i	−0.199674	+	0.979862i	$0.563988\pi$
$692$	2.73616	−	0.733152i	0.104013	−	0.0278703i
$693$	−0.358421	−	3.61474i	−0.0136153	−	0.137313i
$694$	10.3378	−	5.96855i	0.392419	−	0.226563i
$695$	28.8165	+	3.73311i	1.09307	+	0.141605i
$696$	32.1267	+	22.2196i	1.21776	+	0.842231i
$697$	−5.46187	+	11.7130i	−0.206883	+	0.443662i
$698$	−14.5398	−	20.7650i	−0.550341	−	0.785969i
$699$	−8.62458	+	8.72492i	−0.326212	+	0.330007i
$700$	2.42517	+	2.01791i	0.0916629	+	0.0762699i
$701$		−	3.06270i		−	0.115677i	−0.998326	−	0.0578383i	$-0.981579\pi$
$701$		−	3.06270i		−	0.115677i	0.998326	−	0.0578383i	$-0.0184208\pi$
$702$	0.0680353	+	3.92120i	0.00256783	+	0.147996i
$703$	30.6241	+	30.6241i	1.15501	+	1.15501i
$704$	10.1338	−	8.50324i	0.381931	−	0.320478i
$705$	−15.7119	−	0.562419i	−0.591745	−	0.0211819i
$706$	−6.07355	+	34.4448i	−0.228581	+	1.29635i
$707$	−7.10146	−	3.31146i	−0.267078	−	0.124540i
$708$	−2.86502	−	3.37458i	−0.107674	−	0.126824i
$709$	45.6222	−	8.04442i	1.71338	−	0.302114i	0.771041	−	0.636785i	$-0.219736\pi$
$709$	45.6222	−	8.04442i	1.71338	−	0.302114i	0.942335	+	0.334671i	$0.108625\pi$
$710$	12.7152	+	8.06351i	0.477192	+	0.302618i
$711$	4.80392	−	0.904469i	0.180161	−	0.0339203i
$712$	−4.37376	−	16.3231i	−0.163914	−	0.611734i
$713$	−32.2183	+	15.0236i	−1.20658	+	0.562640i
$714$	0.356226	+	3.81729i	0.0133314	+	0.142859i
$715$	−2.75964	−	0.605807i	−0.103205	−	0.0226559i
$716$	−2.96927	+	3.53864i	−0.110967	+	0.132245i
$717$	18.8619	−	6.98896i	0.704411	−	0.261008i
$718$	8.24204	+	17.6751i	0.307590	+	0.659629i
$719$	−25.2485	+	43.7317i	−0.941610	+	1.63092i	−0.179211	+	0.983811i	$0.557354\pi$
$719$	−25.2485	+	43.7317i	−0.941610	+	1.63092i	−0.762400	+	0.647106i	$0.775979\pi$
$720$	6.59125	−	6.20722i	0.245641	−	0.231329i
$721$	1.71065	+	2.96294i	0.0637080	+	0.110346i
$722$	−2.21326	+	3.16086i	−0.0823690	+	0.117635i
$723$	17.0824	+	6.10583i	0.635300	+	0.227078i
$724$	2.90761	+	7.98858i	0.108060	+	0.296893i
$725$	−26.1376	+	26.3549i	−0.970726	+	0.978796i
$726$	−3.63798	+	13.8981i	−0.135018	+	0.515808i
$727$	−0.922993	+	10.5499i	−0.0342319	+	0.391273i	0.959680	+	0.281095i	$0.0906976\pi$
$727$	−0.922993	+	10.5499i	−0.0342319	+	0.391273i	−0.993912	+	0.110178i	$0.964858\pi$
$728$	1.07638	−	1.07638i	0.0398933	−	0.0398933i
$729$	26.9837	−	0.936651i	0.999398	−	0.0346908i
$730$	−5.83659	+	18.6458i	−0.216022	+	0.690112i
$731$	−12.7586	−	15.2051i	−0.471893	−	0.562380i
$732$	8.90476	−	5.21006i	0.329129	−	0.192569i
$733$	−23.8946	+	16.7312i	−0.882569	+	0.617981i	−0.924518	−	0.381139i	$-0.875532\pi$
$733$	−23.8946	+	16.7312i	−0.882569	+	0.617981i	0.0419494	+	0.999120i	$0.486643\pi$
$734$	−6.98357	+	2.54181i	−0.257768	+	0.0938200i
$735$	15.2142	−	20.1532i	0.561183	−	0.743362i
$736$	−6.54274	−	37.1057i	−0.241169	−	1.36774i
$737$	5.07689	−	18.9472i	0.187010	−	0.697929i
$738$	3.56986	+	12.7320i	0.131408	+	0.468672i
$739$	5.54415	+	3.20092i	0.203945	+	0.117748i	0.598494	−	0.801127i	$-0.295766\pi$
$739$	5.54415	+	3.20092i	0.203945	+	0.117748i	−0.394549	+	0.918875i	$0.629099\pi$
$740$	−2.98858	−	22.3430i	−0.109862	−	0.821346i
$741$	2.04492	−	4.45239i	0.0751220	−	0.163563i
$742$	6.02085	−	0.526756i	0.221032	−	0.0193378i
$743$	29.7334	−	2.60134i	1.09081	−	0.0954338i	0.472473	−	0.881345i	$-0.343361\pi$
$743$	29.7334	−	2.60134i	1.09081	−	0.0954338i	0.618339	+	0.785911i	$0.287806\pi$
$744$	−23.0696	+	2.15283i	−0.845774	+	0.0789267i
$745$	−20.1965	−	15.4310i	−0.739941	−	0.565347i
$746$	−9.33928	−	5.39204i	−0.341935	−	0.197416i
$747$	4.44133	+	3.03391i	0.162500	+	0.111005i
$748$	1.26031	−	4.70355i	0.0460816	−	0.171979i
$749$	1.89758	+	10.7617i	0.0693359	+	0.393224i
$750$	11.0637	+	16.9153i	0.403987	+	0.617660i
$751$	−9.53000	+	3.46864i	−0.347755	+	0.126572i	−0.509991	−	0.860180i	$-0.670351\pi$
$751$	−9.53000	+	3.46864i	−0.347755	+	0.126572i	0.162237	+	0.986752i	$0.448129\pi$
$752$	4.48806	−	3.14257i	0.163663	−	0.114598i
$753$	−16.9508	−	9.65627i	−0.617721	−	0.351894i
$754$	3.60152	+	4.29213i	0.131160	+	0.156310i
$755$	−19.4084	−	6.07531i	−0.706345	−	0.221103i
$756$	−2.35824	−	2.27780i	−0.0857685	−	0.0828430i
$757$	6.39851	−	6.39851i	0.232558	−	0.232558i	−0.581202	−	0.813760i	$-0.697417\pi$
$757$	6.39851	−	6.39851i	0.232558	−	0.232558i	0.813760	+	0.581202i	$0.197417\pi$
$758$	−0.496062	+	5.67002i	−0.0180178	+	0.205944i
$759$	−17.3766	−	17.1768i	−0.630732	−	0.623479i
$760$	−25.3271	+	8.04329i	−0.918712	+	0.291761i
$761$	9.16585	+	25.1830i	0.332262	+	0.912882i	0.987522	+	0.157479i	$0.0503367\pi$
$761$	9.16585	+	25.1830i	0.332262	+	0.912882i	−0.655260	+	0.755403i	$0.727441\pi$
$762$	−5.38260	−	29.5267i	−0.194991	−	1.06964i
$763$	−8.07441	+	11.5315i	−0.292313	+	0.417467i
$764$	−0.516728	−	0.895000i	−0.0186946	−	0.0323800i
$765$	4.16978	−	20.1020i	0.150759	−	0.726791i
$766$	−2.33284	+	4.04059i	−0.0842888	+	0.145993i
$767$	−0.857749	−	1.83945i	−0.0309715	−	0.0664186i
$768$	4.83948	−	28.4057i	0.174630	−	1.02500i
$769$	−8.41448	+	10.0280i	−0.303434	+	0.361619i	−0.896117	−	0.443817i	$-0.853624\pi$
$769$	−8.41448	+	10.0280i	−0.303434	+	0.361619i	0.592684	+	0.805435i	$0.298068\pi$
$770$	−2.38023	+	1.52331i	−0.0857774	+	0.0548962i
$771$	−28.0313	+	19.8703i	−1.00952	+	0.715611i
$772$	−11.3753	+	5.30439i	−0.409406	+	0.190909i
$773$	−3.35520	−	12.5218i	−0.120678	−	0.450377i	0.878971	−	0.476876i	$-0.158231\pi$
$773$	−3.35520	−	12.5218i	−0.120678	−	0.450377i	−0.999649	+	0.0264987i	$0.991564\pi$
$774$	−20.0392	−	3.29494i	−0.720293	−	0.118434i
$775$	1.82808	−	21.9409i	0.0656667	−	0.788139i
$776$	13.8656	−	2.44488i	0.497747	−	0.0877662i
$777$	13.0722	−	2.38301i	0.468963	−	0.0854901i
$778$	−9.16244	−	4.27252i	−0.328489	−	0.153177i
$779$	2.86861	−	16.2687i	0.102778	−	0.582886i
$780$	−2.25271	+	1.19526i	−0.0806600	+	0.0427973i
$781$	8.63526	−	7.24584i	0.308994	−	0.259277i
$782$	18.2350	+	18.2350i	0.652082	+	0.652082i
$783$	29.1150	−	25.3040i	1.04049	−	0.904290i
$784$			8.79971i			0.314275i
$785$	2.85070	−	6.92269i	0.101746	−	0.247081i
$786$	−10.7667	−	39.2718i	−0.384034	−	1.40078i
$787$	−7.17412	−	10.2457i	−0.255730	−	0.365220i	0.670673	−	0.741753i	$-0.266005\pi$
$787$	−7.17412	−	10.2457i	−0.255730	−	0.365220i	−0.926403	+	0.376533i	$0.877116\pi$
$788$	−0.770169	+	1.65163i	−0.0274361	+	0.0588370i
$789$	2.37942	−	29.1367i	0.0847098	−	1.03729i
$790$	−2.32133	−	3.01229i	−0.0825893	−	0.107172i
$791$	−0.0732857	+	0.0423115i	−0.00260574	+	0.00150443i
$792$	−6.89669	−	14.3542i	−0.245063	−	0.510054i
$793$	4.56900	−	1.22426i	0.162250	−	0.0434748i
$794$	−0.996853	−	0.362825i	−0.0353770	−	0.0128762i
$795$	−31.6509	−	6.75653i	−1.12254	−	0.239629i
$796$	−12.8897	−	10.8157i	−0.456862	−	0.383353i
$797$	0.571540	+	6.53273i	0.0202450	+	0.231401i	0.999575	+	0.0291347i	$0.00927517\pi$
$797$	0.571540	+	6.53273i	0.0202450	+	0.231401i	−0.979331	+	0.202267i	$0.935169\pi$
$798$	−1.70269	−	4.59525i	−0.0602747	−	0.162670i
$799$	4.24908	−	11.6743i	0.150322	−	0.413006i
$800$	21.9611	+	7.89039i	0.776443	+	0.278967i
$801$	−16.6868	+	0.193007i	−0.589600	+	0.00681957i
$802$	8.26509	+	2.21462i	0.291851	+	0.0782011i
$803$	11.9824	+	8.39015i	0.422849	+	0.296082i
$804$	−7.57516	−	16.0027i	−0.267155	−	0.564372i
$805$	0.571503	+	12.4960i	0.0201429	+	0.440425i
$806$	−3.27296	−	0.577111i	−0.115285	−	0.0203279i
$807$	26.7648	+	45.7450i	0.942166	+	1.61030i
$808$	−34.2212	−	2.99397i	−1.20390	−	0.105327i
$809$	−21.1375			−0.743156			−0.371578	−	0.928402i	$-0.621183\pi$
$809$	−21.1375			−0.743156			−0.371578	+	0.928402i	$0.621183\pi$
$810$	−10.1655	−	18.3814i	−0.357180	−	0.645858i
$811$	−48.6371			−1.70788			−0.853940	−	0.520371i	$-0.825794\pi$
$811$	−48.6371			−1.70788			−0.853940	+	0.520371i	$0.825794\pi$
$812$	−4.66634	−	0.408252i	−0.163756	−	0.0143268i
$813$	−4.56297	−	7.79879i	−0.160030	−	0.273516i
$814$	19.8848	+	3.50622i	0.696961	+	0.122893i
$815$	23.3045	+	21.2661i	0.816321	+	0.744918i
$816$	3.06104	+	6.46651i	0.107158	+	0.226373i
$817$	20.7829	+	14.5524i	0.727103	+	0.509123i
$818$	−28.7405	−	7.70100i	−1.00489	−	0.269259i
$819$	−0.766620	−	1.29305i	−0.0267879	−	0.0451829i
$820$	−6.32732	+	5.82206i	−0.220960	+	0.203315i
$821$	8.00089	−	21.9823i	0.279233	−	0.767186i	−0.718217	−	0.695819i	$-0.755042\pi$
$821$	8.00089	−	21.9823i	0.279233	−	0.767186i	0.997450	−	0.0713672i	$-0.0227362\pi$
$822$	3.27492	+	8.83839i	0.114226	+	0.308274i
$823$	−0.292711	−	3.34570i	−0.0102033	−	0.116624i	0.989385	−	0.145318i	$-0.0464206\pi$
$823$	−0.292711	−	3.34570i	−0.0102033	−	0.116624i	−0.999588	+	0.0286943i	$0.990865\pi$
$824$	11.4901	+	9.64136i	0.400277	+	0.335873i
$825$	14.5774	−	4.06144i	0.507518	−	0.141401i
$826$	−1.90760	−	0.694311i	−0.0663740	−	0.0241582i
$827$	−20.9358	+	5.60974i	−0.728010	+	0.195070i	−0.603743	−	0.797179i	$-0.706325\pi$
$827$	−20.9358	+	5.60974i	−0.728010	+	0.195070i	−0.124267	+	0.992249i	$0.539658\pi$
$828$	−21.9905	−	1.66788i	−0.764222	−	0.0579628i
$829$	−4.62453	+	2.66997i	−0.160617	+	0.0927320i	−0.578154	−	0.815928i	$-0.696227\pi$
$829$	−4.62453	+	2.66997i	−0.160617	+	0.0927320i	0.417537	+	0.908660i	$0.362893\pi$
$830$	0.537589	−	4.14975i	0.0186600	−	0.144040i
$831$	1.64535	−	20.1477i	0.0570765	−	0.698916i
$832$	2.31360	−	4.96154i	0.0802097	−	0.172010i
$833$	11.4448	+	16.3449i	0.396540	+	0.566317i
$834$	6.21143	+	22.6565i	0.215084	+	0.784529i
$835$	−28.7796	−	11.8512i	−0.995959	−	0.410127i
$836$			6.22428i			0.215271i
$837$	−3.58168	+	22.5986i	−0.123801	+	0.781120i
$838$	−18.9757	−	18.9757i	−0.655504	−	0.655504i
$839$	0.256169	−	0.214952i	0.00884395	−	0.00742095i	−0.638355	−	0.769742i	$-0.720385\pi$
$839$	0.256169	−	0.214952i	0.00884395	−	0.00742095i	0.647199	+	0.762321i	$0.275940\pi$
$840$	−2.39054	+	7.79473i	−0.0824814	+	0.268944i
$841$	4.53398	−	25.7135i	0.156344	−	0.886673i
$842$	−12.1199	−	5.65161i	−0.417680	−	0.194767i
$843$	23.3268	−	4.25238i	0.803417	−	0.146460i
$844$	−15.0433	+	2.65254i	−0.517813	+	0.0913043i
$845$	27.2258	−	6.09496i	0.936595	−	0.209673i
$846$	−4.48528	−	11.8934i	−0.154207	−	0.408903i
$847$	−1.42522	−	5.31901i	−0.0489713	−	0.182763i
$848$	10.2217	−	4.76648i	0.351016	−	0.163682i
$849$	−12.5403	+	8.88936i	−0.430383	+	0.305082i
$850$	−15.4102	+	4.19759i	−0.528565	+	0.143976i
$851$	57.4510	−	68.4675i	1.96940	−	2.34703i
$852$	1.70883	−	10.0301i	0.0585435	−	0.343625i
$853$	7.30797	+	15.6720i	0.250220	+	0.536598i	0.990794	−	0.135376i	$-0.0432242\pi$
$853$	7.30797	+	15.6720i	0.250220	+	0.536598i	−0.740574	+	0.671974i	$0.765446\pi$
$854$	2.36558	−	4.09731i	0.0809486	−	0.140207i
$855$	1.50203	+	26.1989i	0.0513682	+	0.895983i
$856$	23.9540	+	41.4895i	0.818731	+	1.41808i
$857$	−6.28056	+	8.96957i	−0.214540	+	0.306395i	−0.911969	−	0.410259i	$-0.865438\pi$
$857$	−6.28056	+	8.96957i	−0.214540	+	0.306395i	0.697429	+	0.716654i	$0.254327\pi$
$858$	−0.409660	−	2.24723i	−0.0139856	−	0.0767190i
$859$	−9.19021	−	25.2499i	−0.313566	−	0.861515i	−0.991930	−	0.126789i	$-0.959533\pi$
$859$	−9.19021	−	25.2499i	−0.313566	−	0.861515i	0.678364	−	0.734726i	$-0.262689\pi$
$860$	−3.99704	−	12.5861i	−0.136298	−	0.429183i
$861$	−3.60456	−	3.56311i	−0.122843	−	0.121430i
$862$	−0.470149	+	5.37383i	−0.0160133	+	0.183033i
$863$	14.0569	−	14.0569i	0.478502	−	0.478502i	−0.426150	−	0.904652i	$-0.640131\pi$
$863$	14.0569	−	14.0569i	0.478502	−	0.478502i	0.904652	+	0.426150i	$0.140131\pi$
$864$	−22.1534	−	9.86610i	−0.753674	−	0.335652i
$865$	−6.16346	+	3.22473i	−0.209564	+	0.109644i
$866$	−2.60873	−	3.10897i	−0.0886484	−	0.105647i
$867$	−11.4887	−	6.54473i	−0.390178	−	0.222271i
$868$	2.27597	−	1.59365i	0.0772515	−	0.0540921i
$869$	−2.67551	+	0.973806i	−0.0907605	+	0.0330341i
$870$	−27.8145	−	11.2661i	−0.943001	−	0.381956i
$871$	−1.40960	−	7.99422i	−0.0477623	−	0.270874i
$872$	−15.9733	+	59.6132i	−0.540924	+	2.01876i
$873$	1.05152	−	13.8639i	0.0355884	−	0.469223i
$874$	−28.5469	−	16.4815i	−0.965612	−	0.557496i
$875$	−6.89407	−	3.53459i	−0.233062	−	0.119491i
$876$	13.1460	−	1.22677i	0.444161	−	0.0414486i
$877$	−31.0262	+	2.71444i	−1.04768	+	0.0916602i	−0.597974	−	0.801516i	$-0.704027\pi$
$877$	−31.0262	+	2.71444i	−1.04768	+	0.0916602i	−0.449708	+	0.893176i	$0.648472\pi$
$878$	−33.4180	+	2.92369i	−1.12780	+	0.0986699i
$879$	−8.16495	+	17.7775i	−0.275397	+	0.599620i
$880$	−3.20164	+	4.19039i	−0.107927	+	0.141258i
$881$	−10.7039	−	6.17988i	−0.360623	−	0.208206i	0.308731	−	0.951149i	$-0.400096\pi$
$881$	−10.7039	−	6.17988i	−0.360623	−	0.208206i	−0.669354	+	0.742944i	$0.733429\pi$
$882$	19.7794	+	5.05544i	0.666008	+	0.170225i
$883$	−9.26338	+	34.5714i	−0.311738	+	1.16342i	0.615251	+	0.788331i	$0.289055\pi$
$883$	−9.26338	+	34.5714i	−0.311738	+	1.16342i	−0.926989	+	0.375089i	$0.877612\pi$
$884$	−0.349925	−	1.98452i	−0.0117693	−	0.0667468i
$885$	8.67590	+	6.54965i	0.291637	+	0.220164i
$886$	15.0464	−	5.47645i	0.505494	−	0.183985i
$887$	1.91991	−	1.34433i	0.0644642	−	0.0451383i	−0.540900	−	0.841087i	$-0.681916\pi$
$887$	1.91991	−	1.34433i	0.0644642	−	0.0451383i	0.605364	+	0.795949i	$0.293027\pi$
$888$	50.2803	−	29.4184i	1.68730	−	0.987215i
$889$	7.39472	+	8.81269i	0.248011	+	0.295568i
$890$	6.01856	+	11.5033i	0.201742	+	0.385593i
$891$	−15.4200	+	3.08832i	−0.516590	+	0.103463i
$892$	−12.9392	+	12.9392i	−0.433236	+	0.433236i
$893$	−1.38403	+	15.8196i	−0.0463149	+	0.529382i
$894$	5.20364	−	19.8794i	0.174036	−	0.664866i
$895$	5.21703	−	10.0727i	0.174386	−	0.336693i
$896$	0.339458	+	0.932655i	0.0113405	+	0.0311578i
$897$	−9.52135	−	3.40326i	−0.317909	−	0.113632i
$898$	−1.65019	+	2.35671i	−0.0550675	+	0.0786446i
$899$	16.3445	+	28.3095i	0.545120	+	0.944175i
$900$	7.65763	−	11.3102i	0.255254	−	0.377007i
$901$	12.7870	−	22.1478i	0.425997	−	0.737849i
$902$	−3.25491	−	6.98019i	−0.108377	−	0.232415i
$903$	7.29921	−	2.70460i	0.242902	−	0.0900034i
$904$	−0.238471	+	0.284198i	−0.00793142	+	0.00945230i
$905$	−11.2532	−	17.5835i	−0.374068	−	0.584496i
$906$	−1.52774	−	16.3711i	−0.0507556	−	0.543895i
$907$	50.7113	−	23.6471i	1.68384	−	0.785188i	0.685472	−	0.728099i	$-0.259596\pi$
$907$	50.7113	−	23.6471i	1.68384	−	0.785188i	0.998369	−	0.0570890i	$-0.0181819\pi$
$908$	−1.09844	−	4.09944i	−0.0364530	−	0.136045i
$909$	−11.2329	+	32.0093i	−0.372572	+	1.06168i
$910$	−0.626309	+	0.987613i	−0.0207619	+	0.0327391i
$911$	−26.4465	+	4.66323i	−0.876211	+	0.154500i	−0.593625	−	0.804742i	$-0.702304\pi$
$911$	−26.4465	+	4.66323i	−0.876211	+	0.154500i	−0.282587	+	0.959242i	$0.591192\pi$
$912$	−5.91868	−	6.97133i	−0.195987	−	0.230844i
$913$	−2.83930	−	1.32399i	−0.0939671	−	0.0438176i
$914$	−6.21385	+	35.2405i	−0.205536	+	1.16565i
$915$	−18.5438	+	17.2621i	−0.613040	+	0.570668i
$916$	16.9401	−	14.2144i	0.559715	−	0.469657i
$917$	11.0368	+	11.0368i	0.364467	+	0.364467i
$918$	16.2936	−	3.16539i	0.537768	−	0.104473i
$919$			30.8687i			1.01826i	0.860688	+	0.509132i	$0.170033\pi$
$919$			30.8687i			1.01826i	−0.860688	+	0.509132i	$0.829967\pi$
$920$	21.0915	+	50.6227i	0.695365	+	1.66898i
$921$	−10.3900	+	10.5109i	−0.342362	+	0.346345i
$922$	−1.82189	−	2.60193i	−0.0600008	−	0.0856900i
$923$	1.97148	−	4.22786i	0.0648921	−	0.139162i
$924$	1.57062	+	1.08628i	0.0516696	+	0.0357360i
$925$	19.1478	+	51.9382i	0.629576	+	1.70772i
$926$	24.3463	−	14.0564i	0.800070	−	0.461921i
$927$	12.0342	−	8.63559i	0.395256	−	0.283630i
$928$	−33.4663	+	8.96728i	−1.09859	+	0.294365i
$929$	−14.1178	−	5.13847i	−0.463191	−	0.168588i	0.0998747	−	0.995000i	$-0.468156\pi$
$929$	−14.1178	−	5.13847i	−0.463191	−	0.168588i	−0.563065	+	0.826412i	$0.690378\pi$
$930$	16.9340	−	5.48583i	0.555287	−	0.179887i
$931$	−19.5380	−	16.3943i	−0.640331	−	0.537301i
$932$	−0.562125	−	6.42512i	−0.0184130	−	0.210462i
$933$	−24.9843	−	4.25659i	−0.817950	−	0.139354i
$934$	6.14270	−	16.8769i	0.200995	−	0.552230i
$935$	−0.496860	+	11.9474i	−0.0162491	+	0.390722i
$936$	−5.09710	−	4.17748i	−0.166604	−	0.136545i
$937$	44.9601	+	12.0470i	1.46878	+	0.393559i	0.902514	−	0.430660i	$-0.141719\pi$
$937$	44.9601	+	12.0470i	1.46878	+	0.393559i	0.566270	+	0.824220i	$0.308386\pi$
$938$	−6.65089	−	4.65700i	−0.217159	−	0.152057i
$939$	9.18797	−	13.2846i	0.299838	−	0.433528i
$940$	5.57141	−	6.10545i	0.181719	−	0.199138i
$941$	−13.0261	−	2.29686i	−0.424640	−	0.0748755i	−0.0427555	−	0.999086i	$-0.513614\pi$
$941$	−13.0261	−	2.29686i	−0.424640	−	0.0748755i	−0.381884	+	0.924210i	$0.624725\pi$
$942$	6.05277	−	0.0350033i	0.197210	−	0.00114047i
$943$	−33.9623	−	2.97131i	−1.10596	−	0.0967593i
$944$	−3.78825			−0.123297
$945$	6.87310	+	4.19328i	0.223582	+	0.136408i
$946$	11.8286			0.384581
$947$	−33.5777	−	2.93767i	−1.09113	−	0.0954614i	−0.472640	−	0.881255i	$-0.656699\pi$
$947$	−33.5777	−	2.93767i	−1.09113	−	0.0954614i	−0.618488	+	0.785794i	$0.712255\pi$
$948$	−1.27206	+	2.23300i	−0.0413146	+	0.0725244i
$949$	5.96147	+	1.05117i	0.193517	+	0.0341223i
$950$	17.6378	−	10.2808i	0.572246	−	0.333552i
$951$	40.7875	+	3.33089i	1.32263	+	0.108011i
$952$	−5.27742	−	3.69529i	−0.171042	−	0.119765i
$953$	37.8969	+	10.1544i	1.22760	+	0.328935i	0.813645	−	0.581362i	$-0.197480\pi$
$953$	37.8969	+	10.1544i	1.22760	+	0.328935i	0.413956	+	0.910297i	$0.364147\pi$
$954$	−4.84139	−	25.7141i	−0.156746	−	0.832526i
$955$	1.71839	+	1.86752i	0.0556058	+	0.0604314i
$956$	−3.61686	+	9.93723i	−0.116977	+	0.321393i
$957$	−14.3422	+	17.2945i	−0.463617	+	0.559051i
$958$	3.16367	+	36.1609i	0.102213	+	1.16830i
$959$	−2.76760	−	2.32229i	−0.0893705	−	0.0749908i
$960$	1.50896	+	29.2823i	0.0487016	+	0.945081i
$961$	10.9101	+	3.97094i	0.351938	+	0.128095i
$962$	8.07116	−	2.16266i	0.260225	−	0.0697270i
$963$	45.5532	−	12.7724i	1.46793	−	0.411585i
$964$	−8.25932	+	4.76852i	−0.266015	+	0.153584i
$965$	24.4135	−	18.8135i	0.785897	−	0.605629i
$966$	−9.14099	+	4.32704i	−0.294106	+	0.139220i
$967$	−10.7806	+	23.1190i	−0.346680	+	0.743457i	−0.999906	−	0.0137056i	$-0.995637\pi$
$967$	−10.7806	+	23.1190i	−0.346680	+	0.743457i	0.653226	+	0.757163i	$0.273415\pi$
$968$	−13.8471	−	19.7756i	−0.445061	−	0.635613i
$969$	−20.0604	−	5.25103i	−0.644434	−	0.168687i
$970$	−9.98470	+	4.16003i	−0.320590	+	0.133571i
$971$			23.0327i			0.739156i	0.929200	+	0.369578i	$0.120498\pi$
$971$			23.0327i			0.739156i	−0.929200	+	0.369578i	$0.879502\pi$
$972$	−8.80589	+	11.1329i	−0.282449	+	0.357087i
$973$	−6.36728	−	6.36728i	−0.204126	−	0.204126i
$974$	−11.5013	+	9.65070i	−0.368524	+	0.309228i
$975$	4.75704	−	4.07275i	0.152347	−	0.130432i
$976$	1.53312	−	8.69473i	0.0490738	−	0.278312i
$977$	−0.251362	−	0.117212i	−0.00804177	−	0.00374994i	0.418593	−	0.908174i	$-0.362523\pi$
$977$	−0.251362	−	0.117212i	−0.00804177	−	0.00374994i	−0.426635	+	0.904424i	$0.640301\pi$
$978$	−8.58517	+	24.0188i	−0.274523	+	0.768038i
$979$	9.57227	−	1.68785i	0.305931	−	0.0539439i
$980$	2.90009	+	12.9545i	0.0926399	+	0.413816i
$981$	53.1294	+	29.8603i	1.69629	+	0.953367i
$982$	7.95391	+	29.6844i	0.253820	+	0.947268i
$983$	7.55984	−	3.52521i	0.241122	−	0.112437i	−0.298302	−	0.954472i	$-0.596420\pi$
$983$	7.55984	−	3.52521i	0.241122	−	0.112437i	0.539423	+	0.842035i	$0.318642\pi$
$984$	−20.1924	−	9.27408i	−0.643709	−	0.295647i
$985$	0.959547	−	4.37104i	0.0305737	−	0.139273i
$986$	15.2427	−	18.1656i	0.485427	−	0.578510i
$987$	3.75033	+	3.11012i	0.119374	+	0.0989963i
$988$	1.08858	+	2.33447i	0.0346324	+	0.0742694i
$989$	26.1797	−	45.3445i	0.832465	−	1.44187i
$990$	7.57954	+	9.60382i	0.240894	+	0.305229i
$991$	−3.48806	−	6.04150i	−0.110802	−	0.191914i	0.805292	−	0.592878i	$-0.202009\pi$
$991$	−3.48806	−	6.04150i	−0.110802	−	0.191914i	−0.916094	+	0.400964i	$0.868675\pi$
$992$	11.7876	−	16.8345i	0.374257	−	0.534494i
$993$	−30.5383	+	25.9271i	−0.969105	+	0.822773i
$994$	−1.59583	−	4.38451i	−0.0506167	−	0.139068i
$995$	36.6902	+	19.0033i	1.16316	+	0.602445i
$996$	−2.72706	+	0.747643i	−0.0864103	+	0.0236900i
$997$	4.81022	−	54.9810i	0.152341	−	1.74127i	−0.407980	−	0.912991i	$-0.633767\pi$
$997$	4.81022	−	54.9810i	0.152341	−	1.74127i	0.560321	−	0.828276i	$-0.310678\pi$
$998$	13.0450	−	13.0450i	0.412933	−	0.412933i
$999$	−15.8508	−	55.3001i	−0.501497	−	1.74962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.11	yes	192
3.2	odd	2		405.2.r.a.368.6		192
5.2	odd	4	inner	135.2.q.a.32.6	✓	192
5.3	odd	4		675.2.ba.b.32.11		192
5.4	even	2		675.2.ba.b.518.6		192
15.2	even	4		405.2.r.a.287.11		192
27.11	odd	18	inner	135.2.q.a.38.6	yes	192
27.16	even	9		405.2.r.a.278.11		192
135.38	even	36		675.2.ba.b.632.6		192
135.92	even	36	inner	135.2.q.a.92.11	yes	192
135.97	odd	36		405.2.r.a.197.6		192
135.119	odd	18		675.2.ba.b.443.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.6	✓	192	5.2	odd	4	inner
135.2.q.a.38.6	yes	192	27.11	odd	18	inner
135.2.q.a.92.11	yes	192	135.92	even	36	inner
135.2.q.a.113.11	yes	192	1.1	even	1	trivial
405.2.r.a.197.6		192	135.97	odd	36
405.2.r.a.278.11		192	27.16	even	9
405.2.r.a.287.11		192	15.2	even	4
405.2.r.a.368.6		192	3.2	odd	2
675.2.ba.b.32.11		192	5.3	odd	4
675.2.ba.b.443.11		192	135.119	odd	18
675.2.ba.b.518.6		192	5.4	even	2
675.2.ba.b.632.6		192	135.38	even	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03978 + 0.0909691i) q^{2} +(0.874685 + 1.49497i) q^{3} +(-0.896746 - 0.158121i) q^{4} +(2.23373 - 0.102160i) q^{5} +(0.773485 + 1.63401i) q^{6} +(-0.567627 - 0.397456i) q^{7} +(-2.93441 - 0.786273i) q^{8} +(-1.46985 + 2.61525i) q^{9} +O(q^{10})\)	\(q+(1.03978 + 0.0909691i) q^{2} +(0.874685 + 1.49497i) q^{3} +(-0.896746 - 0.158121i) q^{4} +(2.23373 - 0.102160i) q^{5} +(0.773485 + 1.63401i) q^{6} +(-0.567627 - 0.397456i) q^{7} +(-2.93441 - 0.786273i) q^{8} +(-1.46985 + 2.61525i) q^{9} +(2.33189 + 0.0969768i) q^{10} +(0.597632 - 1.64198i) q^{11} +(-0.547986 - 1.47891i) q^{12} +(-0.0630233 - 0.720360i) q^{13} +(-0.554051 - 0.464904i) q^{14} +(2.10654 + 3.25000i) q^{15} +(-1.26829 - 0.461619i) q^{16} +(-2.95614 + 0.792096i) q^{17} +(-1.76623 + 2.58558i) q^{18} +(3.38781 - 1.95596i) q^{19} +(-2.01925 - 0.261588i) q^{20} +(0.0976895 - 1.19623i) q^{21} +(0.770776 - 1.65293i) q^{22} +(-4.63055 - 6.61310i) q^{23} +(-1.39123 - 5.07459i) q^{24} +(4.97913 - 0.456395i) q^{25} -0.754750i q^{26} +(-5.19537 + 0.0901428i) q^{27} +(0.446171 + 0.446171i) q^{28} +(-5.68683 + 4.77181i) q^{29} +(1.89469 + 3.57092i) q^{30} +(0.764639 - 4.33648i) q^{31} +(4.22984 + 1.97241i) q^{32} +(2.97745 - 0.542776i) q^{33} +(-3.14580 + 0.554689i) q^{34} +(-1.30853 - 0.829823i) q^{35} +(1.73161 - 2.11280i) q^{36} +(2.86540 + 10.6938i) q^{37} +(3.70052 - 1.72558i) q^{38} +(1.02179 - 0.724306i) q^{39} +(-6.63502 - 1.45655i) q^{40} +(2.71443 - 3.23493i) q^{41} +(0.210396 - 1.23493i) q^{42} +(2.74095 + 5.87799i) q^{43} +(-0.795555 + 1.37794i) q^{44} +(-3.01608 + 5.99193i) q^{45} +(-4.21317 - 7.29742i) q^{46} +(-2.32838 + 3.32527i) q^{47} +(-0.419248 - 2.29982i) q^{48} +(-2.22991 - 6.12663i) q^{49} +(5.21872 - 0.0216046i) q^{50} +(-3.76985 - 3.72650i) q^{51} +(-0.0573878 + 0.655945i) q^{52} +(-5.90884 + 5.90884i) q^{53} +(-5.41025 - 0.378889i) q^{54} +(1.16721 - 3.72880i) q^{55} +(1.35314 + 1.61261i) q^{56} +(5.88736 + 3.35382i) q^{57} +(-6.34714 + 4.44432i) q^{58} +(2.63750 - 0.959971i) q^{59} +(-1.37514 - 3.24751i) q^{60} +(1.13591 + 6.44205i) q^{61} +(1.18954 - 4.43943i) q^{62} +(1.87378 - 0.900284i) q^{63} +(6.55640 + 3.78534i) q^{64} +(-0.214369 - 1.60265i) q^{65} +(3.14527 - 0.293513i) q^{66} +(11.1831 - 0.978397i) q^{67} +(2.77616 - 0.242882i) q^{68} +(5.83610 - 12.7069i) q^{69} +(-1.28510 - 0.981870i) q^{70} +(5.58689 + 3.22559i) q^{71} +(6.36945 - 6.51852i) q^{72} +(-2.16667 + 8.08612i) q^{73} +(2.00658 + 11.3799i) q^{74} +(5.03746 + 7.04443i) q^{75} +(-3.34729 + 1.21831i) q^{76} +(-0.991847 + 0.694499i) q^{77} +(1.12833 - 0.660168i) q^{78} +(-1.04738 - 1.24822i) q^{79} +(-2.88018 - 0.901566i) q^{80} +(-4.67907 - 7.68806i) q^{81} +(3.11669 - 3.11669i) q^{82} +(0.156261 - 1.78607i) q^{83} +(-0.276752 + 1.05727i) q^{84} +(-6.52232 + 2.07133i) q^{85} +(2.31528 + 6.36117i) q^{86} +(-12.1079 - 4.32778i) q^{87} +(-3.04474 + 4.34834i) q^{88} +(2.78132 + 4.81739i) q^{89} +(-3.68115 + 5.95593i) q^{90} +(-0.250538 + 0.433944i) q^{91} +(3.10676 + 6.66246i) q^{92} +(7.15171 - 2.64995i) q^{93} +(-2.72350 + 3.24574i) q^{94} +(7.36765 - 4.71518i) q^{95} +(0.751097 + 8.04871i) q^{96} +(-4.20036 + 1.95866i) q^{97} +(-1.76129 - 6.57321i) q^{98} +(3.41576 + 3.97642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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