LMFDB - Embedded newform 414.2.p.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.971812 - 0.235759i) q^{2} +(-0.490425 - 1.66117i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-1.22350 - 0.962173i) q^{5} +(-0.868236 - 1.49872i) q^{6} +(-1.60431 - 1.14243i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.51897 + 1.62936i) q^{9} +O(q^{10})$	\(q+(0.971812 - 0.235759i) q^{2} +(-0.490425 - 1.66117i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-1.22350 - 0.962173i) q^{5} +(-0.868236 - 1.49872i) q^{6} +(-1.60431 - 1.14243i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.51897 + 1.62936i) q^{9} +(-1.41585 - 0.646599i) q^{10} +(-0.185480 - 0.176855i) q^{11} +(-1.19710 - 1.25178i) q^{12} +(-2.11108 - 2.96460i) q^{13} +(-1.82843 - 0.731993i) q^{14} +(-0.998297 + 2.50432i) q^{15} +(0.580057 - 0.814576i) q^{16} +(2.21445 - 1.42314i) q^{17} +(-2.06383 + 2.17730i) q^{18} +(-1.36612 + 2.12573i) q^{19} +(-1.52839 - 0.294572i) q^{20} +(-1.11097 + 3.22531i) q^{21} +(-0.221947 - 0.128141i) q^{22} +(4.68783 - 1.01207i) q^{23} +(-1.45847 - 0.934268i) q^{24} +(-0.607613 - 2.50462i) q^{25} +(-2.75050 - 2.38332i) q^{26} +(3.94200 + 3.38536i) q^{27} +(-1.94946 - 0.280290i) q^{28} +(-0.238431 + 0.462491i) q^{29} +(-0.379741 + 2.66908i) q^{30} +(-7.58994 + 1.46284i) q^{31} +(0.371662 - 0.928368i) q^{32} +(-0.202822 + 0.394848i) q^{33} +(1.81651 - 1.90510i) q^{34} +(0.863670 + 2.94139i) q^{35} +(-1.49233 + 2.60249i) q^{36} +(7.03187 - 1.01103i) q^{37} +(-0.826453 + 2.38788i) q^{38} +(-3.88937 + 4.96077i) q^{39} +(-1.55475 + 0.0740619i) q^{40} +(7.67480 - 9.75931i) q^{41} +(-0.319257 + 3.39632i) q^{42} +(0.321547 - 1.66834i) q^{43} +(-0.245901 - 0.0722031i) q^{44} +(4.64969 + 0.430161i) q^{45} +(4.31708 - 2.08874i) q^{46} +(3.41128 - 1.96950i) q^{47} +(-1.63762 - 0.564085i) q^{48} +(-1.02079 - 2.94938i) q^{49} +(-1.18097 - 2.29076i) q^{50} +(-3.45010 - 2.98064i) q^{51} +(-3.23486 - 1.66769i) q^{52} +(3.83157 + 8.38996i) q^{53} +(4.62901 + 2.36057i) q^{54} +(0.0567704 + 0.394847i) q^{55} +(-1.96059 + 0.187214i) q^{56} +(4.20117 + 1.22685i) q^{57} +(-0.122673 + 0.505666i) q^{58} +(0.896384 - 0.638312i) q^{59} +(0.260223 + 2.68337i) q^{60} +(0.934917 + 0.323578i) q^{61} +(-7.03112 + 3.21100i) q^{62} +(5.90264 + 0.263737i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.269544 + 5.65841i) q^{65} +(-0.104016 + 0.431535i) q^{66} +(3.06222 + 3.21156i) q^{67} +(1.31616 - 2.27966i) q^{68} +(-3.98025 - 7.29093i) q^{69} +(1.53278 + 2.65486i) q^{70} +(-0.211410 + 0.719996i) q^{71} +(-0.836707 + 2.88096i) q^{72} +(1.36346 + 0.876244i) q^{73} +(6.59530 - 2.64036i) q^{74} +(-3.86260 + 2.23767i) q^{75} +(-0.240193 + 2.51541i) q^{76} +(0.0955246 + 0.495629i) q^{77} +(-2.61019 + 5.73789i) q^{78} +(0.106168 + 1.11184i) q^{79} +(-1.49346 + 0.438521i) q^{80} +(3.69039 - 8.20859i) q^{81} +(5.15762 - 11.2936i) q^{82} +(-0.283231 + 0.222735i) q^{83} +(0.490454 + 3.37585i) q^{84} +(-4.07870 - 0.389468i) q^{85} +(-0.0808440 - 1.69712i) q^{86} +(0.885208 + 0.169257i) q^{87} +(-0.255992 - 0.0121944i) q^{88} +(8.49393 - 9.80252i) q^{89} +(4.62003 - 0.678170i) q^{90} +7.16790i q^{91} +(3.70295 - 3.04765i) q^{92} +(6.15232 + 11.8908i) q^{93} +(2.85079 - 2.71822i) q^{94} +(3.71677 - 1.28639i) q^{95} +(-1.72445 - 0.162100i) q^{96} +(-0.454851 - 1.13616i) q^{97} +(-1.68736 - 2.62558i) q^{98} +(0.755379 + 0.143279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.971812	−	0.235759i	0.687175	−	0.166707i
$2$	0.971812	−	0.235759i	0.687175	−	0.166707i
$3$	−0.490425	−	1.66117i	−0.283147	−	0.959077i
$3$	−0.490425	−	1.66117i	−0.283147	−	0.959077i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	−1.22350	−	0.962173i	−0.547167	−	0.430297i	0.305926	−	0.952055i	$-0.401034\pi$
$5$	−1.22350	−	0.962173i	−0.547167	−	0.430297i	−0.853093	+	0.521758i	$0.825276\pi$
$6$	−0.868236	−	1.49872i	−0.354456	−	0.611851i
$7$	−1.60431	−	1.14243i	−0.606374	−	0.431797i	0.235194	−	0.971948i	$-0.424428\pi$
$7$	−1.60431	−	1.14243i	−0.606374	−	0.431797i	−0.841568	+	0.540152i	$0.818367\pi$
$8$	0.755750	−	0.654861i	0.267198	−	0.231528i
$9$	−2.51897	+	1.62936i	−0.839656	+	0.543119i
$10$	−1.41585	−	0.646599i	−0.447733	−	0.204473i
$11$	−0.185480	−	0.176855i	−0.0559244	−	0.0533238i	0.661602	−	0.749856i	$-0.269877\pi$
$11$	−0.185480	−	0.176855i	−0.0559244	−	0.0533238i	−0.717526	+	0.696532i	$0.754726\pi$
$12$	−1.19710	−	1.25178i	−0.345573	−	0.361358i
$13$	−2.11108	−	2.96460i	−0.585508	−	0.822231i	0.410466	−	0.911876i	$-0.365366\pi$
$13$	−2.11108	−	2.96460i	−0.585508	−	0.822231i	−0.995974	+	0.0896449i	$0.971427\pi$
$14$	−1.82843	−	0.731993i	−0.488668	−	0.195633i
$15$	−0.998297	+	2.50432i	−0.257759	+	0.646612i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	2.21445	−	1.42314i	0.537083	−	0.345163i	−0.243814	−	0.969822i	$-0.578399\pi$
$17$	2.21445	−	1.42314i	0.537083	−	0.345163i	0.780897	+	0.624659i	$0.214762\pi$
$18$	−2.06383	+	2.17730i	−0.486449	+	0.513194i
$19$	−1.36612	+	2.12573i	−0.313410	+	0.487675i	−0.961845	−	0.273595i	$-0.911787\pi$
$19$	−1.36612	+	2.12573i	−0.313410	+	0.487675i	0.648435	+	0.761270i	$0.275424\pi$
$20$	−1.52839	−	0.294572i	−0.341757	−	0.0658683i
$21$	−1.11097	+	3.22531i	−0.242434	+	0.703821i
$22$	−0.221947	−	0.128141i	−0.0473193	−	0.0273198i
$23$	4.68783	−	1.01207i	0.977479	−	0.211032i
$23$	4.68783	−	1.01207i	0.977479	−	0.211032i
$24$	−1.45847	−	0.934268i	−0.297710	−	0.190707i
$25$	−0.607613	−	2.50462i	−0.121523	−	0.500923i
$26$	−2.75050	−	2.38332i	−0.539418	−	0.467408i
$27$	3.94200	+	3.38536i	0.758638	+	0.651512i
$28$	−1.94946	−	0.280290i	−0.368414	−	0.0529699i
$29$	−0.238431	+	0.462491i	−0.0442754	+	0.0858824i	−0.909935	−	0.414750i	$-0.863869\pi$
$29$	−0.238431	+	0.462491i	−0.0442754	+	0.0858824i	0.865660	+	0.500633i	$0.166899\pi$
$30$	−0.379741	+	2.66908i	−0.0693309	+	0.487306i
$31$	−7.58994	+	1.46284i	−1.36319	+	0.262734i	−0.817828	−	0.575463i	$-0.804822\pi$
$31$	−7.58994	+	1.46284i	−1.36319	+	0.262734i	−0.545367	+	0.838198i	$0.683610\pi$
$32$	0.371662	−	0.928368i	0.0657013	−	0.164114i
$33$	−0.202822	+	0.394848i	−0.0353068	+	0.0687342i
$34$	1.81651	−	1.90510i	0.311529	−	0.326722i
$35$	0.863670	+	2.94139i	0.145987	+	0.497186i
$36$	−1.49233	+	2.60249i	−0.248722	+	0.433748i
$37$	7.03187	−	1.01103i	1.15603	−	0.166212i	0.462488	−	0.886626i	$-0.346957\pi$
$37$	7.03187	−	1.01103i	1.15603	−	0.166212i	0.693545	+	0.720413i	$0.256048\pi$
$38$	−0.826453	+	2.38788i	−0.134068	+	0.387365i
$39$	−3.88937	+	4.96077i	−0.622798	+	0.794359i
$40$	−1.55475	+	0.0740619i	−0.245828	+	0.0117102i
$41$	7.67480	−	9.75931i	1.19860	−	1.52415i	0.406629	−	0.913593i	$-0.366704\pi$
$41$	7.67480	−	9.75931i	1.19860	−	1.52415i	0.791974	−	0.610554i	$-0.209053\pi$
$42$	−0.319257	+	3.39632i	−0.0492625	+	0.524063i
$43$	0.321547	−	1.66834i	0.0490355	−	0.254420i	−0.949136	−	0.314866i	$-0.898040\pi$
$43$	0.321547	−	1.66834i	0.0490355	−	0.254420i	0.998171	+	0.0604463i	$0.0192524\pi$
$44$	−0.245901	−	0.0722031i	−0.0370710	−	0.0108850i
$45$	4.64969	+	0.430161i	0.693134	+	0.0641246i
$46$	4.31708	−	2.08874i	0.636518	−	0.307968i
$47$	3.41128	−	1.96950i	0.497586	−	0.287281i	−0.230130	−	0.973160i	$-0.573915\pi$
$47$	3.41128	−	1.96950i	0.497586	−	0.287281i	0.727716	+	0.685878i	$0.240582\pi$
$48$	−1.63762	−	0.564085i	−0.236370	−	0.0814186i
$49$	−1.02079	−	2.94938i	−0.145827	−	0.421340i
$50$	−1.18097	−	2.29076i	−0.167015	−	0.323963i
$51$	−3.45010	−	2.98064i	−0.483111	−	0.417372i
$52$	−3.23486	−	1.66769i	−0.448594	−	0.231266i
$53$	3.83157	+	8.38996i	0.526306	+	1.15245i	0.966996	+	0.254791i	$0.0820066\pi$
$53$	3.83157	+	8.38996i	0.526306	+	1.15245i	−0.440690	+	0.897659i	$0.645266\pi$
$54$	4.62901	+	2.36057i	0.629928	+	0.321232i
$55$	0.0567704	+	0.394847i	0.00765492	+	0.0532411i
$56$	−1.96059	+	0.187214i	−0.261995	+	0.0250175i
$57$	4.20117	+	1.22685i	0.556459	+	0.162500i
$58$	−0.122673	+	0.505666i	−0.0161078	+	0.0663972i
$59$	0.896384	−	0.638312i	0.116699	−	0.0831011i	−0.520217	−	0.854034i	$-0.674149\pi$
$59$	0.896384	−	0.638312i	0.116699	−	0.0831011i	0.636916	+	0.770933i	$0.280210\pi$
$60$	0.260223	+	2.68337i	0.0335947	+	0.346422i
$61$	0.934917	+	0.323578i	0.119704	+	0.0414299i	0.386263	−	0.922389i	$-0.373766\pi$
$61$	0.934917	+	0.323578i	0.119704	+	0.0414299i	−0.266559	+	0.963818i	$0.585887\pi$
$62$	−7.03112	+	3.21100i	−0.892953	+	0.407798i
$63$	5.90264	+	0.263737i	0.743662	+	0.0332277i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.269544	+	5.65841i	−0.0334328	+	0.701840i
$66$	−0.104016	+	0.431535i	−0.0128035	+	0.0531183i
$67$	3.06222	+	3.21156i	0.374109	+	0.392355i	0.883693	−	0.468066i	$-0.155049\pi$
$67$	3.06222	+	3.21156i	0.374109	+	0.392355i	−0.509584	+	0.860421i	$0.670201\pi$
$68$	1.31616	−	2.27966i	0.159608	−	0.276449i
$69$	−3.98025	−	7.29093i	−0.479166	−	0.877724i
$70$	1.53278	+	2.65486i	0.183203	+	0.317316i
$71$	−0.211410	+	0.719996i	−0.0250897	+	0.0854478i	−0.971086	−	0.238729i	$-0.923269\pi$
$71$	−0.211410	+	0.719996i	−0.0250897	+	0.0854478i	0.945996	+	0.324177i	$0.105087\pi$
$72$	−0.836707	+	2.88096i	−0.0986069	+	0.339524i
$73$	1.36346	+	0.876244i	0.159581	+	0.102557i	0.617994	−	0.786183i	$-0.287946\pi$
$73$	1.36346	+	0.876244i	0.159581	+	0.102557i	−0.458413	+	0.888739i	$0.651582\pi$
$74$	6.59530	−	2.64036i	0.766688	−	0.306935i
$75$	−3.86260	+	2.23767i	−0.446015	+	0.258384i
$76$	−0.240193	+	2.51541i	−0.0275520	+	0.288538i
$77$	0.0955246	+	0.495629i	0.0108860	+	0.0564821i
$78$	−2.61019	+	5.73789i	−0.295546	+	0.649688i
$79$	0.106168	+	1.11184i	0.0119448	+	0.125092i	0.999477	−	0.0323224i	$-0.0102903\pi$
$79$	0.106168	+	1.11184i	0.0119448	+	0.125092i	−0.987533	+	0.157414i	$0.949684\pi$
$80$	−1.49346	+	0.438521i	−0.166974	+	0.0490281i
$81$	3.69039	−	8.20859i	0.410044	−	0.912066i
$82$	5.15762	−	11.2936i	0.569564	−	1.24717i
$83$	−0.283231	+	0.222735i	−0.0310886	+	0.0244484i	−0.633582	−	0.773675i	$-0.718416\pi$
$83$	−0.283231	+	0.222735i	−0.0310886	+	0.0244484i	0.602494	+	0.798124i	$0.294174\pi$
$84$	0.490454	+	3.37585i	0.0535130	+	0.368335i
$85$	−4.07870	−	0.389468i	−0.442397	−	0.0422438i
$86$	−0.0808440	−	1.69712i	−0.00871763	−	0.183006i
$87$	0.885208	+	0.169257i	0.0949042	+	0.0181462i
$88$	−0.255992	−	0.0121944i	−0.0272888	−	0.00129993i
$89$	8.49393	−	9.80252i	0.900355	−	1.03906i	−0.0986791	−	0.995119i	$-0.531462\pi$
$89$	8.49393	−	9.80252i	0.900355	−	1.03906i	0.999034	−	0.0439455i	$-0.0139928\pi$
$90$	4.62003	−	0.678170i	0.486994	−	0.0714854i
$91$			7.16790i			0.751400i
$92$	3.70295	−	3.04765i	0.386059	−	0.317740i
$93$	6.15232	+	11.8908i	0.637966	+	1.23302i
$94$	2.85079	−	2.71822i	0.294037	−	0.280363i
$95$	3.71677	−	1.28639i	0.381332	−	0.131980i
$96$	−1.72445	−	0.162100i	−0.176001	−	0.0165442i
$97$	−0.454851	−	1.13616i	−0.0461831	−	0.115360i	0.903483	−	0.428624i	$-0.141002\pi$
$97$	−0.454851	−	1.13616i	−0.0461831	−	0.115360i	−0.949666	+	0.313264i	$0.898577\pi$
$98$	−1.68736	−	2.62558i	−0.170449	−	0.265224i
$99$	0.755379	+	0.143279i	0.0759184	+	0.0144001i
$100$	−1.68775	−	1.94777i	−0.168775	−	0.194777i
$101$	5.63158	+	7.16113i	0.560363	+	0.712559i	0.980856	−	0.194737i	$-0.0623852\pi$
$101$	5.63158	+	7.16113i	0.560363	+	0.712559i	−0.420493	+	0.907296i	$0.638143\pi$
$102$	−4.05556	−	2.08322i	−0.401560	−	0.206270i
$103$	−12.5845	−	3.05297i	−1.23999	−	0.300818i	−0.438447	−	0.898757i	$-0.644471\pi$
$103$	−12.5845	−	3.05297i	−1.23999	−	0.300818i	−0.801541	+	0.597939i	$0.795986\pi$
$104$	−3.53685	−	0.858029i	−0.346816	−	0.0841367i
$105$	4.46258	−	2.87723i	0.435503	−	0.280789i
$106$	5.70157	+	7.25014i	0.553786	+	0.704196i
$107$	11.7371	+	13.5454i	1.13467	+	1.30948i	0.944791	+	0.327675i	$0.106265\pi$
$107$	11.7371	+	13.5454i	1.13467	+	1.30948i	0.189882	+	0.981807i	$0.439189\pi$
$108$	5.05505	+	1.20269i	0.486422	+	0.115729i
$109$	3.22169	+	5.01305i	0.308582	+	0.480164i	0.960559	−	0.278075i	$-0.0896965\pi$
$109$	3.22169	+	5.01305i	0.308582	+	0.480164i	−0.651977	+	0.758239i	$0.726060\pi$
$110$	0.148259	+	0.370332i	0.0141359	+	0.0353098i
$111$	−5.12810	−	11.1853i	−0.486737	−	1.06166i
$112$	−1.86119	+	0.644163i	−0.175866	+	0.0608677i
$113$	−4.57754	+	4.36468i	−0.430619	+	0.410594i	−0.874143	−	0.485668i	$-0.838576\pi$
$113$	−4.57754	+	4.36468i	−0.430619	+	0.410594i	0.443524	+	0.896262i	$0.353728\pi$
$114$	4.37199	+	0.201804i	0.409474	+	0.0189007i
$115$	−6.70936	−	3.27222i	−0.625651	−	0.305136i
$116$			0.520333i			0.0483117i
$117$	10.1481	+	4.02802i	0.938195	+	0.372391i
$118$	0.720628	−	0.831649i	0.0663392	−	0.0765595i
$119$	−5.17851	−	0.246683i	−0.474714	−	0.0226134i
$120$	0.885517	+	2.54638i	0.0808363	+	0.232452i
$121$	−0.520276	−	10.9219i	−0.0472978	−	0.992903i
$122$	0.984850	+	0.0940417i	0.0891641	+	0.00851414i
$123$	−19.9758	−	7.96295i	−1.80116	−	0.717995i
$124$	−6.07590	+	4.77814i	−0.545632	+	0.429090i
$125$	−4.89945	+	10.7283i	−0.438220	+	0.959569i
$126$	5.79843	−	1.13530i	0.516565	−	0.101140i
$127$	−7.80472	+	2.29167i	−0.692557	+	0.203353i	−0.609024	−	0.793152i	$-0.708439\pi$
$127$	−7.80472	+	2.29167i	−0.692557	+	0.203353i	−0.0835329	+	0.996505i	$0.526620\pi$
$128$	−0.0950560	−	0.995472i	−0.00840185	−	0.0879881i
$129$	−2.92910	+	0.284053i	−0.257893	+	0.0250095i
$130$	1.07208	+	5.56246i	0.0940273	+	0.487860i
$131$	1.37326	−	14.3815i	0.119982	−	1.25651i	−0.712186	−	0.701991i	$-0.752295\pi$
$131$	1.37326	−	14.3815i	0.119982	−	1.25651i	0.832169	−	0.554523i	$-0.187099\pi$
$132$	0.000654391		0.443894i	5.69574e−5		0.0386360i
$133$	4.62018	−	1.84964i	0.400620	−	0.160384i
$134$	3.73305	+	2.39909i	0.322487	+	0.207250i
$135$	−1.56575	−	7.93488i	−0.134758	−	0.682925i
$136$	0.741611	−	2.52570i	0.0635926	−	0.216577i
$137$	7.28644	+	12.6205i	0.622523	+	1.07824i	0.989014	+	0.147820i	$0.0472256\pi$
$137$	7.28644	+	12.6205i	0.622523	+	1.07824i	−0.366491	+	0.930421i	$0.619441\pi$
$138$	−5.58696	−	6.14703i	−0.475593	−	0.523270i
$139$	−10.8630	+	18.8153i	−0.921392	+	1.59590i	−0.124128	+	0.992266i	$0.539613\pi$
$139$	−10.8630	+	18.8153i	−0.921392	+	1.59590i	−0.797264	+	0.603631i	$0.793720\pi$
$140$	2.11548	+	2.21866i	0.178791	+	0.187511i
$141$	−4.94465	−	4.70082i	−0.416415	−	0.395880i
$142$	−0.0357051	+	0.749543i	−0.00299631	+	0.0629002i
$143$	−0.132740	+	0.923229i	−0.0111003	+	0.0772043i
$144$	−0.133910	+	2.99701i	−0.0111592	+	0.249751i
$145$	0.736716	−	0.336447i	0.0611810	−	0.0279404i
$146$	1.53161	+	0.530095i	0.126757	+	0.0438710i
$147$	−4.39880	+	3.14215i	−0.362807	+	0.259161i
$148$	5.78690	−	4.12083i	0.475680	−	0.338730i
$149$	−2.00282	+	8.25575i	−0.164078	+	0.676337i	0.829037	+	0.559193i	$0.188889\pi$
$149$	−2.00282	+	8.25575i	−0.164078	+	0.676337i	−0.993115	+	0.117144i	$0.962626\pi$
$150$	−3.22617	+	3.08524i	−0.263416	+	0.251909i
$151$	−7.54052	+	0.720033i	−0.613639	+	0.0585954i	−0.397248	−	0.917711i	$-0.630035\pi$
$151$	−7.54052	+	0.720033i	−0.613639	+	0.0585954i	−0.216391	+	0.976307i	$0.569429\pi$
$152$	0.359609	+	2.50114i	0.0291681	+	0.202869i
$153$	−3.25933	+	7.19298i	−0.263501	+	0.581518i
$154$	0.209681	+	0.459137i	0.0168966	+	0.0369983i
$155$	10.6938	+	5.51305i	0.858948	+	0.442819i
$156$	−1.18385	+	6.19152i	−0.0947842	+	0.495719i
$157$	−9.46559	−	18.3607i	−0.755437	−	1.46534i	−0.880929	−	0.473248i	$-0.843081\pi$
$157$	−9.46559	−	18.3607i	−0.755437	−	1.46534i	0.125493	−	0.992095i	$-0.459949\pi$
$158$	0.365301	+	1.05547i	0.0290618	+	0.0839685i
$159$	12.0581	−	10.4795i	0.956266	−	0.831081i
$160$	−1.34798	+	0.778257i	−0.106567	+	0.0615266i
$161$	−8.67697	−	3.73181i	−0.683841	−	0.294108i
$162$	1.65112	−	8.84725i	0.129724	−	0.695105i
$163$	1.41372	+	0.415105i	0.110731	+	0.0325135i	0.336629	−	0.941638i	$-0.390713\pi$
$163$	1.41372	+	0.415105i	0.110731	+	0.0325135i	−0.225898	+	0.974151i	$0.572532\pi$
$164$	2.34966	−	12.1912i	0.183478	−	0.951974i
$165$	0.628066	−	0.287948i	0.0488948	−	0.0224167i
$166$	−0.222735	+	0.283231i	−0.0172876	+	0.0219830i
$167$	−15.3739	+	0.732348i	−1.18967	+	0.0566708i	−0.633058	−	0.774104i	$-0.718201\pi$
$167$	−15.3739	+	0.732348i	−1.18967	+	0.0566708i	−0.556608	+	0.830775i	$0.687898\pi$
$168$	1.27252	+	3.16506i	0.0981767	+	0.244190i
$169$	−0.0802922	+	0.231989i	−0.00617632	+	0.0178453i
$170$	−4.05554	+	0.583099i	−0.311046	+	0.0447217i
$171$	−0.0223506	−	7.58053i	−0.00170919	−	0.579698i
$172$	−0.478677	−	1.63022i	−0.0364988	−	0.124303i
$173$	6.37533	−	6.68625i	0.484707	−	0.508346i	−0.435280	−	0.900295i	$-0.643351\pi$
$173$	6.37533	−	6.68625i	0.484707	−	0.508346i	0.919987	+	0.391949i	$0.128199\pi$
$174$	0.900159	−	0.0442100i	0.0682409	−	0.00335155i
$175$	−1.88654	+	4.71235i	−0.142609	+	0.356220i
$176$	−0.251651	+	0.0485017i	−0.0189689	+	0.00365596i
$177$	−1.49995	−	1.17600i	−0.112743	−	0.0883937i
$178$	5.94347	−	11.5287i	0.445482	−	0.864114i
$179$	0.761715	+	0.109518i	0.0569333	+	0.00818577i	0.170723	−	0.985319i	$-0.445390\pi$
$179$	0.761715	+	0.109518i	0.0569333	+	0.00818577i	−0.113789	+	0.993505i	$0.536299\pi$
$180$	4.32992	−	1.74827i	0.322733	−	0.130308i
$181$	−3.80055	−	3.29319i	−0.282492	−	0.244781i	0.502076	−	0.864824i	$-0.332570\pi$
$181$	−3.80055	−	3.29319i	−0.282492	−	0.244781i	−0.784568	+	0.620043i	$0.787115\pi$
$182$	1.68990	+	6.96585i	0.125263	+	0.516343i
$183$	0.0790115	−	1.71175i	0.00584070	−	0.126536i
$184$	2.88005	−	3.83475i	0.212320	−	0.282701i
$185$	−9.57630	−	5.52888i	−0.704064	−	0.406491i
$186$	8.78225	+	10.1051i	0.643946	+	0.740944i
$187$	−0.662427	−	0.127672i	−0.0484414	−	0.00933632i
$188$	2.12959	−	3.31370i	0.155316	−	0.241676i
$189$	−2.45669	−	9.93462i	−0.178698	−	0.722638i
$190$	3.30872	−	2.12639i	0.240040	−	0.154264i
$191$	0.995436	−	1.39789i	0.0720272	−	0.101148i	−0.776991	−	0.629512i	$-0.783255\pi$
$191$	0.995436	−	1.39789i	0.0720272	−	0.101148i	0.849018	+	0.528364i	$0.177194\pi$
$192$	−1.71406	+	0.249024i	−0.123701	+	0.0179717i
$193$	17.3530	+	6.94710i	1.24910	+	0.500063i	0.899535	−	0.436849i	$-0.143906\pi$
$193$	17.3530	+	6.94710i	1.24910	+	0.500063i	0.349563	+	0.936913i	$0.386330\pi$
$194$	−0.709890	−	0.996901i	−0.0509671	−	0.0715733i
$195$	9.53178	−	2.32727i	0.682585	−	0.166659i
$196$	−2.25880	−	2.15376i	−0.161343	−	0.153840i
$197$	−16.5169	−	7.54301i	−1.17678	−	0.537417i	−0.271585	−	0.962415i	$-0.587548\pi$
$197$	−16.5169	−	7.54301i	−1.17678	−	0.537417i	−0.905194	+	0.424998i	$0.860275\pi$
$198$	0.767865	−	0.0388474i	0.0545698	−	0.00276076i
$199$	−18.5083	+	16.0375i	−1.31202	+	1.13687i	−0.330857	+	0.943681i	$0.607338\pi$
$199$	−18.5083	+	16.0375i	−1.31202	+	1.13687i	−0.981161	+	0.193190i	$0.938117\pi$
$200$	−2.09938	−	1.49496i	−0.148448	−	0.105710i
$201$	3.83316	−	6.66189i	0.270370	−	0.469893i
$202$	7.16113	+	5.63158i	0.503855	+	0.396236i
$203$	0.910880	−	0.469591i	0.0639312	−	0.0329588i
$204$	−4.43238	−	1.06837i	−0.310329	−	0.0748007i
$205$	−18.7803	+	4.55605i	−1.31167	+	0.318208i
$206$	−12.9495			−0.902236
$207$	−10.1594	+	10.1875i	−0.706131	+	0.708082i
$208$	−3.63944			−0.252349
$209$	0.629334	−	0.152675i	0.0435319	−	0.0105607i
$210$	3.65846	−	3.84822i	0.252457	−	0.265553i
$211$	10.7914	−	5.56336i	0.742911	−	0.382997i	−0.0448375	−	0.998994i	$-0.514277\pi$
$211$	10.7914	−	5.56336i	0.742911	−	0.382997i	0.787748	+	0.615997i	$0.211247\pi$
$212$	7.25014	+	5.70157i	0.497941	+	0.391585i
$213$	1.29972	−	0.00191605i	0.0890551	−	0.000131286i
$214$	14.5997	+	10.3964i	0.998017	+	0.710685i
$215$	−1.99865	+	1.73184i	−0.136307	+	0.118110i
$216$	5.19610	−	0.0229805i	0.353550	−	0.00156363i
$217$	13.8478	+	6.32410i	0.940053	+	0.429308i
$218$	4.31275	+	4.11220i	0.292096	+	0.278513i
$219$	0.786914	−	2.69467i	0.0531747	−	0.182089i
$220$	0.231389	+	0.324940i	0.0156002	+	0.0219074i
$221$	−8.89393	−	3.56059i	−0.598270	−	0.239511i
$222$	−7.62058	−	9.66101i	−0.511460	−	0.648404i
$223$	11.9245	−	16.7456i	0.798521	−	1.12137i	−0.191644	−	0.981464i	$-0.561382\pi$
$223$	11.9245	−	16.7456i	0.798521	−	1.12137i	0.990165	−	0.139901i	$-0.0446786\pi$
$224$	−1.65686	+	1.06480i	−0.110703	+	0.0711447i
$225$	5.61147	+	5.31903i	0.374098	+	0.354602i
$226$	−3.41950	+	5.32084i	−0.227462	+	0.353937i
$227$	15.0099	+	2.89291i	0.996239	+	0.192009i	0.661212	−	0.750199i	$-0.270042\pi$
$227$	15.0099	+	2.89291i	0.996239	+	0.192009i	0.335027	+	0.942208i	$0.391255\pi$
$228$	4.29632	−	0.834620i	0.284531	−	0.0552740i
$229$	20.2096	+	11.6680i	1.33549	+	0.771046i	0.986135	−	0.165945i	$-0.0530673\pi$
$229$	20.2096	+	11.6680i	1.33549	+	0.771046i	0.349355	+	0.936990i	$0.386401\pi$
$230$	−7.29169	−	1.59819i	−0.480799	−	0.105382i
$231$	0.776476	−	0.401751i	0.0510884	−	0.0264333i
$232$	0.122673	+	0.505666i	0.00805389	+	0.0331986i
$233$	−9.88890	−	8.56878i	−0.647843	−	0.561359i	0.267738	−	0.963492i	$-0.413724\pi$
$233$	−9.88890	−	8.56878i	−0.647843	−	0.561359i	−0.915582	+	0.402132i	$0.868269\pi$
$234$	10.8117	+	1.52197i	0.706783	+	0.0994941i
$235$	−6.06871	−	0.872548i	−0.395879	−	0.0569188i
$236$	0.504246	−	0.978101i	0.0328236	−	0.0636690i
$237$	1.79489	−	0.721636i	0.116590	−	0.0468753i
$238$	−5.09070	+	0.981151i	−0.329981	+	0.0635986i
$239$	2.99744	−	7.48724i	0.193888	−	0.484309i	−0.799286	−	0.600951i	$-0.794789\pi$
$239$	2.99744	−	7.48724i	0.193888	−	0.484309i	0.993174	+	0.116642i	$0.0372130\pi$
$240$	1.46089	+	2.26584i	0.0942999	+	0.146259i
$241$	7.07502	−	7.42007i	0.455742	−	0.477969i	−0.455267	−	0.890355i	$-0.650456\pi$
$241$	7.07502	−	7.42007i	0.455742	−	0.477969i	0.911009	+	0.412386i	$0.135305\pi$
$242$	−3.08055	−	10.4914i	−0.198025	−	0.674413i
$243$	−15.4457	−	2.10468i	−0.990844	−	0.135015i
$244$	0.979259	−	0.140796i	0.0626907	−	0.00901356i
$245$	−1.58887	+	4.59075i	−0.101509	+	0.293292i
$246$	−21.2900	−	3.02902i	−1.35740	−	0.193123i
$247$	9.18591	−	0.437579i	0.584486	−	0.0278425i
$248$	−4.77814	+	6.07590i	−0.303412	+	0.385820i
$249$	0.508904	+	0.361260i	0.0322505	+	0.0228939i
$250$	−2.23205	+	11.5810i	−0.141167	+	0.732446i
$251$	−11.1650	−	3.27834i	−0.704728	−	0.206927i	−0.0903173	−	0.995913i	$-0.528788\pi$
$251$	−11.1650	−	3.27834i	−0.704728	−	0.206927i	−0.614411	+	0.788986i	$0.710606\pi$
$252$	5.36732	−	2.47033i	0.338110	−	0.155616i
$253$	−1.04849	−	0.641346i	−0.0659180	−	0.0403211i
$254$	−7.04443	+	4.06710i	−0.442007	+	0.255193i
$255$	1.35332	+	6.96641i	0.0847482	+	0.436253i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	−3.69048	−	7.15852i	−0.230206	−	0.446536i	0.745234	−	0.666803i	$-0.232338\pi$
$257$	−3.69048	−	7.15852i	−0.230206	−	0.446536i	−0.975440	+	0.220266i	$0.929307\pi$
$258$	−2.77956	+	0.966607i	−0.173048	+	0.0601783i
$259$	−12.4364	−	6.41139i	−0.772758	−	0.398385i
$260$	2.35326	+	5.15291i	0.145943	+	0.319570i
$261$	−0.152963	−	1.55349i	−0.00946820	−	0.0961585i
$262$	−2.05600	−	14.2998i	−0.127020	−	0.883446i
$263$	−20.7397	+	1.98040i	−1.27886	+	0.122117i	−0.712285	−	0.701891i	$-0.752339\pi$
$263$	−20.7397	+	1.98040i	−1.27886	+	0.122117i	−0.566579	+	0.824007i	$0.691733\pi$
$264$	0.105288	+	0.431227i	0.00648002	+	0.0265402i
$265$	3.38466	−	13.9518i	0.207918	−	0.857050i
$266$	4.05387	−	2.88675i	0.248559	−	0.176998i
$267$	−20.4493	−	9.30246i	−1.25148	−	0.569301i
$268$	4.19343	+	1.45136i	0.256154	+	0.0886559i
$269$	−18.5436	+	8.46859i	−1.13062	+	0.516339i	−0.890763	−	0.454468i	$-0.849829\pi$
$269$	−18.5436	+	8.46859i	−1.13062	+	0.516339i	−0.239861	+	0.970807i	$0.577102\pi$
$270$	−3.39233	−	7.34207i	−0.206451	−	0.446824i
$271$	2.84095	−	19.7593i	0.172576	−	1.20029i	−0.700842	−	0.713317i	$-0.747192\pi$
$271$	2.84095	−	19.7593i	0.172576	−	1.20029i	0.873417	−	0.486972i	$-0.161899\pi$
$272$	0.125251	−	2.62934i	0.00759446	−	0.159427i
$273$	11.9071	−	3.51531i	0.720650	−	0.212757i
$274$	10.0564	+	10.5469i	0.607532	+	0.637161i
$275$	−0.330254	+	0.572016i	−0.0199151	+	0.0344939i
$276$	−6.87868	−	4.65658i	−0.414048	−	0.280293i
$277$	4.99262	+	8.64747i	0.299978	+	0.519576i	0.976130	−	0.217185i	$-0.0696875\pi$
$277$	4.99262	+	8.64747i	0.299978	+	0.519576i	−0.676153	+	0.736761i	$0.736354\pi$
$278$	−6.12095	+	20.8460i	−0.367110	+	1.25026i
$279$	16.7353	−	16.0516i	1.00192	−	0.960983i
$280$	2.57892	+	1.65737i	0.154120	+	0.0990469i
$281$	11.8363	−	4.73855i	0.706096	−	0.282678i	0.00930923	−	0.999957i	$-0.497037\pi$
$281$	11.8363	−	4.73855i	0.706096	−	0.282678i	0.696787	+	0.717279i	$0.254612\pi$
$282$	−5.91353	−	3.40256i	−0.352145	−	0.202620i
$283$	−2.29846	+	24.0706i	−0.136629	+	1.43085i	0.623879	+	0.781521i	$0.285556\pi$
$283$	−2.29846	+	24.0706i	−0.136629	+	1.43085i	−0.760509	+	0.649328i	$0.775050\pi$
$284$	0.142013	+	0.736832i	0.00842690	+	0.0437229i
$285$	−3.95970	−	5.54331i	−0.234552	−	0.328357i
$286$	0.0886610	+	0.928500i	0.00524263	+	0.0549033i
$287$	−23.4621	+	6.88909i	−1.38492	+	0.406650i
$288$	0.576437	+	2.94410i	0.0339669	+	0.173483i
$289$	−4.18359	+	9.16079i	−0.246094	+	0.538870i
$290$	0.636629	−	0.500651i	0.0373842	−	0.0293992i
$291$	−1.66429	+	1.31279i	−0.0975624	+	0.0769569i
$292$	1.61341	+	0.154062i	0.0944177	+	0.00901580i
$293$	−0.394052	−	8.27216i	−0.0230207	−	0.483265i	−0.980711	−	0.195464i	$-0.937379\pi$
$293$	−0.394052	−	8.27216i	−0.0230207	−	0.483265i	0.957690	−	0.287801i	$-0.0929242\pi$
$294$	−3.53401	+	4.09064i	−0.206108	+	0.238571i
$295$	−1.71089	−	0.0814999i	−0.0996121	−	0.00474511i
$296$	4.65225	−	5.36898i	0.270407	−	0.312066i
$297$	−0.132446	−	1.32508i	−0.00768530	−	0.0768889i
$298$			8.49521i			0.492115i
$299$	−12.8968	−	11.7609i	−0.745839	−	0.680153i
$300$	−2.40786	+	3.75887i	−0.139018	+	0.217019i
$301$	−2.42182	+	2.30921i	−0.139592	+	0.133100i
$302$	−7.15821	+	2.47748i	−0.411909	+	0.142563i
$303$	9.13399	−	12.8670i	0.524734	−	0.739190i
$304$	0.939137	+	2.34585i	0.0538632	+	0.134544i
$305$	−0.832535	−	1.29545i	−0.0476708	−	0.0741773i
$306$	−1.47164	+	7.75864i	−0.0841282	+	0.443532i
$307$	8.56386	+	9.88323i	0.488766	+	0.564066i	0.945535	−	0.325519i	$-0.105539\pi$
$307$	8.56386	+	9.88323i	0.488766	+	0.564066i	−0.456770	+	0.889585i	$0.650994\pi$
$308$	0.312016	+	0.396761i	0.0177788	+	0.0226075i
$309$	1.10025	+	22.4022i	0.0625912	+	1.27442i
$310$	11.6921	+	2.83648i	0.664068	+	0.161101i
$311$	−5.01651	−	1.21699i	−0.284460	−	0.0690093i	0.0909902	−	0.995852i	$-0.470997\pi$
$311$	−5.01651	−	1.21699i	−0.284460	−	0.0690093i	−0.375450	+	0.926842i	$0.622512\pi$
$312$	0.309224	+	6.29610i	0.0175063	+	0.356446i
$313$	19.9219	+	25.3327i	1.12605	+	1.43189i	0.887528	+	0.460754i	$0.152421\pi$
$313$	19.9219	+	25.3327i	1.12605	+	1.43189i	0.238524	+	0.971137i	$0.423336\pi$
$314$	−13.5275	−	15.6115i	−0.763399	−	0.881010i
$315$	−6.96813	−	6.00204i	−0.392610	−	0.338177i
$316$	0.603840	+	0.939593i	0.0339686	+	0.0528562i
$317$	1.31335	+	3.28058i	0.0737648	+	0.184256i	0.960668	−	0.277700i	$-0.0895722\pi$
$317$	1.31335	+	3.28058i	0.0737648	+	0.184256i	−0.886903	+	0.461956i	$0.847148\pi$
$318$	9.24752	−	13.0269i	0.518575	−	0.730513i
$319$	0.126018	−	0.0436153i	0.00705565	−	0.00244199i
$320$	−1.12650	+	1.07412i	−0.0629734	+	0.0600450i
$321$	16.7450	−	26.1404i	0.934615	−	1.45901i
$322$	−9.31219	−	1.58095i	−0.518948	−	0.0881027i
$323$			6.65150i			0.370099i
$324$	−0.481241	−	8.98712i	−0.0267356	−	0.499285i
$325$	−6.14246	+	7.08877i	−0.340722	+	0.393214i
$326$	1.47173	+	0.0701072i	0.0815117	+	0.00388288i
$327$	6.74753	−	7.81031i	0.373140	−	0.431911i
$328$	−0.590757	−	12.4015i	−0.0326191	−	0.684759i
$329$	−7.72277	−	0.737436i	−0.425770	−	0.0406561i
$330$	0.542475	−	0.427903i	0.0298623	−	0.0235553i
$331$	8.86980	−	6.97528i	0.487528	−	0.383396i	−0.343920	−	0.938999i	$-0.611755\pi$
$331$	8.86980	−	6.97528i	0.487528	−	0.383396i	0.831448	+	0.555603i	$0.187512\pi$
$332$	−0.149682	+	0.327759i	−0.00821489	+	0.0179881i
$333$	−16.0657	+	14.0042i	−0.880397	+	0.767424i
$334$	−14.7679	+	4.33623i	−0.808061	+	0.237268i
$335$	−0.656553	−	6.87573i	−0.0358713	−	0.375661i
$336$	1.98284	+	2.77583i	0.108173	+	0.151434i
$337$	−2.33756	−	12.1284i	−0.127335	−	0.660677i	−0.988362	−	0.152118i	$-0.951391\pi$
$337$	−2.33756	−	12.1284i	−0.127335	−	0.660677i	0.861027	−	0.508559i	$-0.169822\pi$
$338$	−0.0233354	+	0.244379i	−0.00126928	+	0.0132925i
$339$	9.49541	+	5.46353i	0.515720	+	0.296738i
$340$	−3.80375	+	1.52279i	−0.206288	+	0.0825851i
$341$	1.66650	+	1.07099i	0.0902458	+	0.0579975i
$342$	−1.80890	−	7.36158i	−0.0978141	−	0.398069i
$343$	−5.61591	+	19.1260i	−0.303230	+	1.03271i
$344$	−0.849524	−	1.47142i	−0.0458033	−	0.0793336i
$345$	−2.14528	+	12.7502i	−0.115498	+	0.686445i
$346$	4.61927	−	8.00082i	0.248334	−	0.430127i
$347$	15.0808	+	15.8163i	0.809579	+	0.849062i	0.990933	−	0.134356i	$-0.0428966\pi$
$347$	15.0808	+	15.8163i	0.809579	+	0.849062i	−0.181354	+	0.983418i	$0.558048\pi$
$348$	0.864362	−	0.255184i	0.0463347	−	0.0136793i
$349$	0.851924	−	17.8841i	0.0456024	−	0.957313i	−0.853911	−	0.520419i	$-0.825776\pi$
$349$	0.851924	−	17.8841i	0.0456024	−	0.957313i	0.899513	−	0.436894i	$-0.143921\pi$
$350$	−0.722383	+	5.02428i	−0.0386130	+	0.268559i
$351$	1.71434	−	18.8332i	0.0915045	−	1.00524i
$352$	−0.233123	+	0.106464i	−0.0124255	+	0.00567452i
$353$	25.0043	+	8.65408i	1.33085	+	0.460610i	0.897657	−	0.440694i	$-0.145268\pi$
$353$	25.0043	+	8.65408i	1.33085	+	0.460610i	0.433188	+	0.901304i	$0.357389\pi$
$354$	−1.73492	−	0.789224i	−0.0922102	−	0.0419468i
$355$	0.951422	−	0.677504i	0.0504962	−	0.0359582i
$356$	3.05793	−	12.6050i	0.162070	−	0.668062i
$357$	2.12989	+	8.72337i	0.112726	+	0.461690i
$358$	0.766064	−	0.0731502i	0.0404877	−	0.00386611i
$359$	2.16873	+	15.0839i	0.114461	+	0.796096i	0.963489	+	0.267748i	$0.0862794\pi$
$359$	2.16873	+	15.0839i	0.114461	+	0.796096i	−0.849028	+	0.528348i	$0.822812\pi$
$360$	3.79569	−	2.71980i	0.200051	−	0.143346i
$361$	5.24046	+	11.4750i	0.275814	+	0.603948i
$362$	−4.46981	−	2.30435i	−0.234928	−	0.121114i
$363$	−17.8880	+	6.22065i	−0.938878	+	0.326500i
$364$	3.28452	+	6.37108i	0.172156	+	0.333936i
$365$	−0.825101	−	2.38397i	−0.0431877	−	0.124783i
$366$	−0.326775	−	1.68212i	−0.0170808	−	0.0879260i
$367$	29.4194	−	16.9853i	1.53568	−	0.886625i	0.536595	−	0.843840i	$-0.319710\pi$
$367$	29.4194	−	16.9853i	1.53568	−	0.886625i	0.999084	−	0.0427851i	$-0.0136231\pi$
$368$	1.89479	−	4.40565i	0.0987730	−	0.229660i
$369$	−3.43119	+	37.0884i	−0.178621	+	1.93074i
$370$	−10.6098	−	3.11533i	−0.551579	−	0.161958i
$371$	3.43788	−	17.8374i	0.178486	−	0.926073i
$372$	10.9171	+	7.74978i	0.566024	+	0.401807i
$373$	−21.2688	+	27.0455i	−1.10126	+	1.40036i	−0.193382	+	0.981124i	$0.561946\pi$
$373$	−21.2688	+	27.0455i	−1.10126	+	1.40036i	−0.907876	+	0.419240i	$0.862297\pi$
$374$	−0.673854	+	0.0320996i	−0.0348442	+	0.00165983i
$375$	20.2243	+	2.87740i	1.04438	+	0.148588i
$376$	1.28832	−	3.72236i	0.0664401	−	0.191966i
$377$	1.87444	−	0.269504i	0.0965388	−	0.0138802i
$378$	−4.72961	−	9.07540i	−0.243265	−	0.466788i
$379$	2.96998	+	10.1148i	0.152557	+	0.519563i	0.999935	−	0.0114284i	$-0.00363786\pi$
$379$	2.96998	+	10.1148i	0.152557	+	0.519563i	−0.847377	+	0.530991i	$0.821820\pi$
$380$	2.71414	−	2.84651i	0.139232	−	0.146023i
$381$	7.63448	+	11.8411i	0.391126	+	0.606636i
$382$	0.637810	−	1.59317i	0.0326332	−	0.0815138i
$383$	24.7612	−	4.77234i	1.26524	−	0.243855i	0.487880	−	0.872911i	$-0.337771\pi$
$383$	24.7612	−	4.77234i	1.26524	−	0.243855i	0.777360	+	0.629056i	$0.216558\pi$
$384$	−1.60703	+	0.646108i	−0.0820084	+	0.0329716i
$385$	0.360006	−	0.698314i	0.0183476	−	0.0355894i
$386$	18.5017	+	2.66014i	0.941712	+	0.135398i
$387$	1.90836	+	4.72642i	0.0970074	+	0.240257i
$388$	−0.924908	−	0.801437i	−0.0469551	−	0.0406868i
$389$	−5.73554	−	23.6422i	−0.290803	−	1.19871i	−0.910381	−	0.413772i	$-0.864211\pi$
$389$	−5.73554	−	23.6422i	−0.290803	−	1.19871i	0.619577	−	0.784936i	$-0.287304\pi$
$390$	8.71442	−	4.50887i	0.441272	−	0.228315i
$391$	8.94064	−	8.91263i	0.452147	−	0.450731i
$392$	−2.70290	−	1.56052i	−0.136517	−	0.0788180i
$393$	−24.5635	+	4.77180i	−1.23907	+	0.240705i
$394$	−17.8296	−	3.43638i	−0.898244	−	0.173122i
$395$	0.939885	−	1.46249i	0.0472907	−	0.0735858i
$396$	0.737061	−	0.218783i	0.0370387	−	0.0109943i
$397$	25.2363	−	16.2184i	1.26657	−	0.813977i	0.277403	−	0.960754i	$-0.410526\pi$
$397$	25.2363	−	16.2184i	1.26657	−	0.813977i	0.989170	+	0.146777i	$0.0468899\pi$
$398$	−14.2056	+	19.9490i	−0.712062	+	0.999951i
$399$	−5.33841	−	6.76779i	−0.267255	−	0.338813i
$400$	−2.39265	−	0.957873i	−0.119633	−	0.0478936i
$401$	2.19584	+	3.08363i	0.109655	+	0.153989i	0.865756	−	0.500465i	$-0.166838\pi$
$401$	2.19584	+	3.08363i	0.109655	+	0.153989i	−0.756102	+	0.654454i	$0.772898\pi$
$402$	2.15451	−	7.37780i	0.107457	−	0.367971i
$403$	20.3597	+	19.4129i	1.01419	+	0.967028i
$404$	8.28696	+	3.78453i	0.412292	+	0.188287i
$405$	−12.4133	+	6.49243i	−0.616821	+	0.322612i
$406$	0.774493	−	0.671102i	0.0384375	−	0.0333062i
$407$	−1.48308	−	1.05610i	−0.0735135	−	0.0523487i
$408$	−4.55931	+	0.00672137i	−0.225720	+	0.000332757i
$409$	25.0430	+	19.6941i	1.23830	+	0.973809i	0.999997	+	0.00261750i	$0.000833176\pi$
$409$	25.0430	+	19.6941i	1.23830	+	0.973809i	0.238302	+	0.971191i	$0.423409\pi$
$410$	−17.1768	+	8.85524i	−0.848300	+	0.437329i
$411$	17.3913	−	18.2934i	0.857851	−	0.902348i
$412$	−12.5845	+	3.05297i	−0.619994	+	0.150409i
$413$	−2.16731			−0.106646
$414$	−7.47127	+	12.2955i	−0.367193	+	0.604292i
$415$	0.560843			0.0275307
$416$	−3.53685	+	0.858029i	−0.173408	+	0.0420684i
$417$	36.5830	+	8.81785i	1.79148	+	0.431812i
$418$	0.575600	−	0.296742i	0.0281535	−	0.0145141i
$419$	11.4132	+	8.97542i	0.557570	+	0.438478i	0.856760	−	0.515716i	$-0.172474\pi$
$419$	11.4132	+	8.97542i	0.557570	+	0.438478i	−0.299190	+	0.954194i	$0.596716\pi$
$420$	2.64808	−	4.60226i	0.129213	−	0.224567i
$421$	−9.40512	−	6.69735i	−0.458377	−	0.326409i	0.327435	−	0.944874i	$-0.393816\pi$
$421$	−9.40512	−	6.69735i	−0.458377	−	0.326409i	−0.785813	+	0.618465i	$0.787755\pi$
$422$	9.17560	−	7.95070i	0.446661	−	0.387034i
$423$	−5.38388	+	10.5193i	−0.261773	+	0.511466i
$424$	8.38996	+	3.83157i	0.407453	+	0.186077i
$425$	−4.90995	−	4.68163i	−0.238168	−	0.227092i
$426$	1.26263	−	0.308282i	0.0611745	−	0.0149363i
$427$	−1.13024	−	1.58720i	−0.0546960	−	0.0768098i
$428$	16.6392	+	6.66135i	0.804288	+	0.321988i
$429$	1.59874	−	0.232270i	0.0771879	−	0.0112141i
$430$	−1.53401	+	2.15422i	−0.0739767	+	0.103886i
$431$	25.9994	−	16.7088i	1.25235	−	0.804834i	0.265129	−	0.964213i	$-0.414585\pi$
$431$	25.9994	−	16.7088i	1.25235	−	0.804834i	0.987217	+	0.159379i	$0.0509491\pi$
$432$	5.04421	−	1.24736i	0.242690	−	0.0600136i
$433$	20.9401	−	32.5834i	1.00632	−	1.56586i	0.195380	−	0.980728i	$-0.437406\pi$
$433$	20.9401	−	32.5834i	1.00632	−	1.56586i	0.810937	−	0.585133i	$-0.198958\pi$
$434$	14.9485	+	2.88108i	0.717549	+	0.138296i
$435$	−0.920200	−	1.05881i	−0.0441202	−	0.0507660i
$436$	5.16067	+	2.97951i	0.247151	+	0.142693i
$437$	−4.25274	+	11.3476i	−0.203436	+	0.542832i
$438$	0.129439	−	2.80424i	0.00618484	−	0.133992i
$439$	5.30013	+	21.8474i	0.252962	+	1.04272i	0.946603	+	0.322401i	$0.104490\pi$
$439$	5.30013	+	21.8474i	0.252962	+	1.04272i	−0.693641	+	0.720320i	$0.743995\pi$
$440$	0.301474	+	0.261228i	0.0143722	+	0.0124536i
$441$	7.37693	+	5.76616i	0.351282	+	0.274579i
$442$	−9.48266	−	1.36340i	−0.451044	−	0.0648504i
$443$	−7.03716	+	13.6502i	−0.334345	+	0.648540i	−0.994746	−	0.102374i	$-0.967356\pi$
$443$	−7.03716	+	13.6502i	−0.334345	+	0.648540i	0.660401	+	0.750913i	$0.270386\pi$
$444$	−9.68343	−	7.59206i	−0.459555	−	0.360303i
$445$	−19.8241	+	3.82077i	−0.939751	+	0.181122i
$446$	7.64041	−	19.0848i	0.361784	−	0.903693i
$447$	14.6964	−	0.721793i	0.695117	−	0.0341397i
$448$	−1.35912	+	1.42540i	−0.0642122	+	0.0673439i
$449$	1.01246	+	3.44812i	0.0477809	+	0.162727i	0.979927	−	0.199354i	$-0.0638845\pi$
$449$	1.01246	+	3.44812i	0.0477809	+	0.162727i	−0.932147	+	0.362081i	$0.882066\pi$
$450$	6.70730	+	3.84614i	0.316185	+	0.181309i
$451$	−3.14951	+	0.452831i	−0.148305	+	0.0213230i
$452$	−2.06867	+	5.97703i	−0.0973021	+	0.281136i
$453$	4.89415	+	12.1730i	0.229947	+	0.571936i
$454$	15.2688	−	0.727342i	0.716599	−	0.0341358i
$455$	6.89676	−	8.76994i	0.323325	−	0.411141i
$456$	3.97845	−	1.82399i	0.186308	−	0.0854162i
$457$	−0.944294	+	4.89946i	−0.0441722	+	0.229187i	−0.997305	−	0.0733644i	$-0.976626\pi$
$457$	−0.944294	+	4.89946i	−0.0441722	+	0.229187i	0.953133	+	0.302552i	$0.0978385\pi$
$458$	22.3908	+	6.57453i	1.04625	+	0.307208i
$459$	13.5472	+	1.88668i	0.632330	+	0.0880627i
$460$	−7.46293	+	0.165937i	−0.347961	+	0.00773685i
$461$	−6.28220	+	3.62703i	−0.292591	+	0.168928i	−0.639110	−	0.769115i	$-0.720697\pi$
$461$	−6.28220	+	3.62703i	−0.292591	+	0.168928i	0.346519	+	0.938043i	$0.387364\pi$
$462$	0.659872	−	0.573488i	0.0307000	−	0.0266811i
$463$	1.74122	+	5.03093i	0.0809215	+	0.233807i	0.978203	−	0.207652i	$-0.0665822\pi$
$463$	1.74122	+	5.03093i	0.0809215	+	0.233807i	−0.897281	+	0.441459i	$0.854461\pi$
$464$	0.238431	+	0.462491i	0.0110689	+	0.0214706i
$465$	3.91359	−	20.4680i	0.181489	−	0.949180i
$466$	−11.6303	−	5.99584i	−0.538764	−	0.277752i
$467$	8.61545	+	18.8652i	0.398676	+	0.872978i	0.997403	+	0.0720247i	$0.0229460\pi$
$467$	8.61545	+	18.8652i	0.398676	+	0.872978i	−0.598727	+	0.800953i	$0.704327\pi$
$468$	10.8658	−	1.06989i	0.502270	−	0.0494558i
$469$	−1.24378	−	8.65071i	−0.0574326	−	0.399453i
$470$	−6.10335	+	0.582799i	−0.281527	+	0.0268825i
$471$	−25.8581	+	24.7285i	−1.19148	+	1.13943i
$472$	0.259436	−	1.06941i	0.0119415	−	0.0492236i
$473$	−0.354696	+	0.252578i	−0.0163089	+	0.0116135i
$474$	1.57416	−	1.12445i	0.0723035	−	0.0516479i
$475$	6.15420	+	2.12999i	0.282374	+	0.0977306i
$476$	−4.71588	+	2.15367i	−0.216152	+	0.0987134i
$477$	−23.3218	−	14.8911i	−1.06783	−	0.681815i
$478$	1.14776	−	7.98286i	0.0524974	−	0.365127i
$479$	−0.853941	+	17.9264i	−0.0390176	+	0.819080i	0.891542	+	0.452938i	$0.149624\pi$
$479$	−0.853941	+	17.9264i	−0.0390176	+	0.819080i	−0.930559	+	0.366141i	$0.880679\pi$
$480$	1.95390	+	1.85755i	0.0891829	+	0.0847851i
$481$	−17.8421	−	18.7123i	−0.813532	−	0.853208i
$482$	5.12624	−	8.87891i	0.233494	−	0.404423i
$483$	−1.94378	+	16.2441i	−0.0884449	+	0.739132i
$484$	−5.46716	−	9.46940i	−0.248507	−	0.430427i
$485$	−0.536674	+	1.82774i	−0.0243691	+	0.0829936i
$486$	−15.5065	+	1.59612i	−0.703390	+	0.0724014i
$487$	−6.74615	−	4.33549i	−0.305697	−	0.196460i	0.378794	−	0.925481i	$-0.376339\pi$
$487$	−6.74615	−	4.33549i	−0.305697	−	0.196460i	−0.684491	+	0.729021i	$0.739975\pi$
$488$	0.918462	−	0.367697i	0.0415768	−	0.0166448i
$489$	−0.00376218	−	2.55200i	−0.000170132	−	0.115406i
$490$	−0.461776	+	4.83594i	−0.0208609	+	0.218465i
$491$	5.79159	+	30.0496i	0.261371	+	1.35612i	0.840909	+	0.541176i	$0.182021\pi$
$491$	5.79159	+	30.0496i	0.261371	+	1.35612i	−0.579539	+	0.814945i	$0.696767\pi$
$492$	−21.4040	+	2.07568i	−0.964967	+	0.0935789i
$493$	0.130197	+	1.36348i	0.00586378	+	0.0614082i
$494$	8.82381	−	2.59090i	0.397002	−	0.116570i
$495$	−0.786349	−	0.902107i	−0.0353437	−	0.0405467i
$496$	−3.21100	+	7.03112i	−0.144178	+	0.315707i
$497$	1.16171	−	0.913580i	0.0521099	−	0.0409797i
$498$	0.579729	+	0.231097i	0.0259783	+	0.0103557i
$499$	−17.2384	−	1.64607i	−0.771697	−	0.0736881i	−0.298223	−	0.954496i	$-0.596394\pi$
$499$	−17.2384	−	1.64607i	−0.771697	−	0.0736881i	−0.473474	+	0.880808i	$0.657000\pi$
$500$	0.561187	+	11.7808i	0.0250970	+	0.526852i
$501$	8.75628	+	25.1795i	0.391202	+	1.12494i
$502$	−11.6232	−	0.553680i	−0.518767	−	0.0247119i
$503$	14.7508	−	17.0233i	0.657706	−	0.759033i	−0.324695	−	0.945819i	$-0.605262\pi$
$503$	14.7508	−	17.0233i	0.657706	−	0.759033i	0.982401	+	0.186786i	$0.0598071\pi$
$504$	4.63363	−	3.66609i	0.206398	−	0.163300i
$505$		−	14.1802i		−	0.631011i
$506$	−1.17014	−	0.376076i	−0.0520189	−	0.0167186i
$507$	0.424750	+	0.0196058i	0.0188638	+	0.000870724i
$508$	−5.88700	+	5.61325i	−0.261194	+	0.249048i
$509$	−19.7605	+	6.83917i	−0.875868	+	0.303141i	−0.727761	−	0.685831i	$-0.759439\pi$
$509$	−19.7605	+	6.83917i	−0.875868	+	0.303141i	−0.148106	+	0.988971i	$0.547318\pi$
$510$	2.95756	+	6.45098i	0.130963	+	0.285654i
$511$	−1.18638	−	2.96343i	−0.0524822	−	0.131094i
$512$	−0.540641	−	0.841254i	−0.0238932	−	0.0371785i
$513$	−12.5816	+	3.75481i	−0.555491	+	0.165779i
$514$	−5.27413	−	6.08667i	−0.232632	−	0.268472i
$515$	12.4597	+	15.8438i	0.549039	+	0.698160i
$516$	−2.47332	+	1.59467i	−0.108882	+	0.0702013i
$517$	−0.981041	−	0.237998i	−0.0431461	−	0.0104671i
$518$	−13.5973	−	3.29868i	−0.597433	−	0.144936i
$519$	−14.2336	−	7.31140i	−0.624786	−	0.320935i
$520$	3.50177	+	4.45286i	0.153563	+	0.195271i
$521$	−18.7589	−	21.6490i	−0.821843	−	0.948458i	0.177521	−	0.984117i	$-0.443192\pi$
$521$	−18.7589	−	21.6490i	−0.821843	−	0.948458i	−0.999364	+	0.0356593i	$0.988647\pi$
$522$	−0.514900	−	1.47363i	−0.0225366	−	0.0644992i
$523$	−0.739143	−	1.15013i	−0.0323205	−	0.0502916i	0.824717	−	0.565545i	$-0.191334\pi$
$523$	−0.739143	−	1.15013i	−0.0323205	−	0.0502916i	−0.857038	+	0.515253i	$0.827698\pi$
$524$	−5.36936	−	13.4120i	−0.234562	−	0.585906i
$525$	8.75321	+	0.822810i	0.382021	+	0.0359104i
$526$	−19.6882	+	6.81414i	−0.858445	+	0.297111i
$527$	−14.7257	+	14.0410i	−0.641463	+	0.611634i
$528$	0.203985	+	0.394248i	0.00887733	+	0.0171575i
$529$	20.9514	−	9.48886i	0.910931	−	0.412559i
$530$		−	14.3565i		−	0.623605i
$531$	−1.21792	+	3.06842i	−0.0528534	+	0.133158i
$532$	3.25902	−	3.76111i	0.141297	−	0.163065i
$533$	−45.1345	−	2.15002i	−1.95499	−	0.0931278i
$534$	−22.0660	−	4.21914i	−0.954888	−	0.182580i
$535$	−1.32742	−	27.8660i	−0.0573894	−	1.20475i
$536$	4.41739	+	0.421810i	0.190802	+	0.0182194i
$537$	−0.191636	−	1.31905i	−0.00826969	−	0.0569211i
$538$	−16.0244	+	12.6017i	−0.690859	+	0.543298i
$539$	−0.332276	+	0.727584i	−0.0143122	+	0.0313392i
$540$	−5.02766	−	6.33533i	−0.216356	−	0.272629i
$541$	14.7178	−	4.32153i	0.632767	−	0.185797i	0.0504075	−	0.998729i	$-0.483948\pi$
$541$	14.7178	−	4.32153i	0.632767	−	0.185797i	0.582359	+	0.812932i	$0.302130\pi$
$542$	−1.89755	−	19.8720i	−0.0815068	−	0.853578i
$543$	−3.60667	+	7.92841i	−0.154777	+	0.340241i
$544$	−0.498171	−	2.58475i	−0.0213589	−	0.110820i
$545$	0.881674	−	9.23331i	0.0377668	−	0.395512i
$546$	10.7427	−	6.22343i	0.459745	−	0.266338i
$547$	20.6604	−	8.27118i	0.883375	−	0.353650i	0.114784	−	0.993390i	$-0.463382\pi$
$547$	20.6604	−	8.27118i	0.883375	−	0.353650i	0.768591	+	0.639740i	$0.220958\pi$
$548$	12.2595	+	7.87870i	0.523700	+	0.336561i
$549$	−2.88225	+	0.708231i	−0.123011	+	0.0302266i
$550$	−0.186086	+	0.633752i	−0.00793475	+	0.0270233i
$551$	−0.657404	−	1.13866i	−0.0280063	−	0.0485084i
$552$	−7.78261	−	2.90360i	−0.331250	−	0.123586i
$553$	1.09987	−	1.90503i	0.0467712	−	0.0810100i
$554$	6.89061	+	7.22666i	0.292754	+	0.307031i
$555$	−4.48795	+	18.6194i	−0.190503	+	0.790348i
$556$	−1.03377	+	21.7015i	−0.0438416	+	0.920348i
$557$	5.24190	−	36.4582i	0.222106	−	1.54478i	−0.507945	−	0.861390i	$-0.669595\pi$
$557$	5.24190	−	36.4582i	0.222106	−	1.54478i	0.730051	−	0.683393i	$-0.239496\pi$
$558$	12.4793	−	19.5446i	0.528290	−	0.827389i
$559$	−5.62478	+	2.56875i	−0.237903	+	0.108647i
$560$	2.89696	+	1.00265i	0.122419	+	0.0423697i
$561$	0.112785	+	1.16302i	0.00476179	+	0.0491026i
$562$	10.3855	−	7.39549i	0.438087	−	0.311960i
$563$	0.404420	−	1.66704i	0.0170443	−	0.0702574i	−0.962654	−	0.270734i	$-0.912734\pi$
$563$	0.404420	−	1.66704i	0.0170443	−	0.0702574i	0.979699	+	0.200476i	$0.0642489\pi$
$564$	−6.54902	−	1.91248i	−0.275763	−	0.0805301i
$565$	9.80021	−	0.935806i	0.412298	−	0.0393697i
$566$	3.44118	+	23.9340i	0.144644	+	1.00602i
$567$	−15.2983	+	8.95316i	−0.642467	+	0.375997i
$568$	0.311724	+	0.682581i	0.0130797	+	0.0286405i
$569$	−14.8861	−	7.67432i	−0.624058	−	0.321724i	0.117034	−	0.993128i	$-0.462661\pi$
$569$	−14.8861	−	7.67432i	−0.624058	−	0.321724i	−0.741092	+	0.671404i	$0.765692\pi$
$570$	−5.15497	−	4.45352i	−0.215918	−	0.186537i
$571$	−15.3883	−	29.8491i	−0.643979	−	1.24915i	−0.954396	−	0.298545i	$-0.903499\pi$
$571$	−15.3883	−	29.8491i	−0.643979	−	1.24915i	0.310416	−	0.950601i	$-0.399532\pi$
$572$	0.305064	+	0.881424i	0.0127554	+	0.0368542i
$573$	−2.81032	−	0.968026i	−0.117403	−	0.0404399i
$574$	−21.1766	+	12.2263i	−0.883893	+	0.510316i
$575$	−5.38324	−	11.1263i	−0.224497	−	0.463997i
$576$	1.25429	+	2.72521i	0.0522619	+	0.113550i
$577$	−45.9368	−	13.4883i	−1.91238	−	0.561524i	−0.979553	−	0.201188i	$-0.935520\pi$
$577$	−45.9368	−	13.4883i	−1.91238	−	0.561524i	−0.932823	−	0.360336i	$-0.882662\pi$
$578$	−1.90592	+	9.88888i	−0.0792760	+	0.411323i
$579$	3.02997	−	32.2333i	0.125921	−	1.33957i
$580$	0.500651	−	0.636629i	0.0207884	−	0.0264346i
$581$	0.708850	−	0.0337667i	0.0294081	−	0.00140088i
$582$	−1.30787	+	1.66815i	−0.0542131	+	0.0691471i
$583$	0.773127	−	2.23380i	0.0320197	−	0.0925147i
$584$	1.60425	−	0.230657i	0.0663845	−	0.00954464i
$585$	−8.54060	−	14.6925i	−0.353110	−	0.607462i
$586$	−2.33318	−	7.94608i	−0.0963828	−	0.328250i
$587$	23.4384	−	24.5814i	0.967404	−	1.01458i	−0.0324813	−	0.999472i	$-0.510341\pi$
$587$	23.4384	−	24.5814i	0.967404	−	1.01458i	0.999886	−	0.0151122i	$-0.00481056\pi$
$588$	−2.46999	+	4.80850i	−0.101861	+	0.198299i
$589$	7.25918	−	18.1326i	0.299109	−	0.747139i
$590$	−1.68188	+	0.324156i	−0.0692419	+	0.0133453i
$591$	−4.42993	+	31.1366i	−0.182223	+	1.28079i
$592$	3.25533	−	6.31445i	0.133793	−	0.259522i
$593$	15.0837	+	2.16870i	0.619412	+	0.0890580i	0.444875	−	0.895593i	$-0.353248\pi$
$593$	15.0837	+	2.16870i	0.619412	+	0.0890580i	0.174537	+	0.984651i	$0.444157\pi$
$594$	−0.441112	−	1.25650i	−0.0180990	−	0.0515549i
$595$	6.09857	+	5.28444i	0.250017	+	0.216641i
$596$	2.00282	+	8.25575i	0.0820388	+	0.338169i
$597$	35.7180	+	22.8802i	1.46184	+	0.936425i
$598$	−15.3060	−	8.38889i	−0.625908	−	0.343047i
$599$	0.437594	+	0.252645i	0.0178796	+	0.0103228i	0.508913	−	0.860818i	$-0.330047\pi$
$599$	0.437594	+	0.252645i	0.0178796	+	0.0103228i	−0.491034	+	0.871141i	$0.663381\pi$
$600$	−1.45380	+	4.22059i	−0.0593510	+	0.172305i
$601$	−31.5506	−	6.08087i	−1.28697	−	0.248044i	−0.500538	−	0.865715i	$-0.666864\pi$
$601$	−31.5506	−	6.08087i	−1.28697	−	0.248044i	−0.786437	+	0.617671i	$0.788076\pi$
$602$	−1.80914	+	2.81508i	−0.0737351	+	0.114734i
$603$	−12.9464	−	3.10037i	−0.527218	−	0.126257i
$604$	−6.37235	+	4.09526i	−0.259287	+	0.166634i
$605$	−9.87223	+	13.8636i	−0.401363	+	0.563636i
$606$	5.84301	−	14.6577i	0.237356	−	0.595429i
$607$	−21.6382	−	8.66262i	−0.878266	−	0.351605i	−0.111679	−	0.993744i	$-0.535623\pi$
$607$	−21.6382	−	8.66262i	−0.878266	−	0.351605i	−0.766588	+	0.642140i	$0.778047\pi$
$608$	1.46572	+	2.05832i	0.0594428	+	0.0834757i
$609$	−1.22679	−	1.28283i	−0.0497120	−	0.0519828i
$610$	−1.11448	−	1.06266i	−0.0451240	−	0.0430257i
$611$	−13.0403	−	5.95529i	−0.527552	−	0.240925i
$612$	0.399009	+	7.88688i	0.0161290	+	0.318808i
$613$	9.98834	−	8.65495i	0.403425	−	0.349570i	−0.429392	−	0.903118i	$-0.641272\pi$
$613$	9.98834	−	8.65495i	0.403425	−	0.349570i	0.832817	+	0.553548i	$0.186727\pi$
$614$	10.6525	+	7.58563i	0.429901	+	0.306131i
$615$	16.7787	+	28.9628i	0.676582	+	1.16789i
$616$	0.396761	+	0.312016i	0.0159859	+	0.0125715i
$617$	−4.53923	+	2.34014i	−0.182743	+	0.0942104i	−0.547170	−	0.837021i	$-0.684295\pi$
$617$	−4.53923	+	2.34014i	−0.182743	+	0.0942104i	0.364428	+	0.931232i	$0.381265\pi$
$618$	6.35077	+	21.5114i	0.255465	+	0.865314i
$619$	−19.7362	+	4.78796i	−0.793266	+	0.192444i	−0.611862	−	0.790965i	$-0.709579\pi$
$619$	−19.7362	+	4.78796i	−0.793266	+	0.192444i	−0.181404	+	0.983409i	$0.558064\pi$
$620$	12.0313			0.483188
$621$	21.9056	+	11.8804i	0.879043	+	0.476742i
$622$	−5.16202			−0.206978
$623$	−24.8256	+	6.02263i	−0.994617	+	0.241291i
$624$	1.78487	+	6.04572i	0.0714519	+	0.242022i
$625$	4.86315	−	2.50713i	0.194526	−	0.100285i
$626$	25.3327	+	19.9219i	1.01250	+	0.796239i
$627$	−0.562259	−	0.970555i	−0.0224545	−	0.0387602i
$628$	−16.8267	−	11.9822i	−0.671459	−	0.478144i
$629$	14.1329	−	12.2462i	0.563516	−	0.488289i
$630$	−8.18674	−	4.19005i	−0.326168	−	0.166936i
$631$	2.90538	+	1.32684i	0.115662	+	0.0528209i	0.472405	−	0.881381i	$-0.343386\pi$
$631$	2.90538	+	1.32684i	0.115662	+	0.0528209i	−0.356744	+	0.934202i	$0.616113\pi$
$632$	0.808336	+	0.770746i	0.0321539	+	0.0306586i
$633$	−14.5340	−	15.1979i	−0.577677	−	0.604064i
$634$	2.04975	+	2.87847i	0.0814060	+	0.114319i
$635$	11.7541	+	4.70562i	0.466446	+	0.186737i
$636$	5.91563	−	14.8399i	0.234570	−	0.588440i
$637$	−6.58875	+	9.25261i	−0.261056	+	0.366602i
$638$	0.112183	−	0.0720957i	0.00444137	−	0.00285430i
$639$	−0.640596	−	2.15811i	−0.0253416	−	0.0853735i
$640$	−0.841515	+	1.30942i	−0.0332638	+	0.0517595i
$641$	36.3081	+	6.99782i	1.43409	+	0.276397i	0.846338	−	0.532647i	$-0.178803\pi$
$641$	36.3081	+	6.99782i	1.43409	+	0.276397i	0.587748	+	0.809044i	$0.300015\pi$
$642$	10.1102	−	29.3513i	0.399016	−	1.15840i
$643$	−3.77274	−	2.17819i	−0.148782	−	0.0858995i	0.423761	−	0.905774i	$-0.360710\pi$
$643$	−3.77274	−	2.17819i	−0.148782	−	0.0858995i	−0.572543	+	0.819875i	$0.694043\pi$
$644$	−9.42241	+	0.659049i	−0.371295	+	0.0259702i
$645$	3.85707	+	2.47076i	0.151872	+	0.0972860i
$646$	1.56815	+	6.46401i	0.0616981	+	0.254323i
$647$	16.7532	+	14.5167i	0.658635	+	0.570711i	0.918737	−	0.394871i	$-0.129211\pi$
$647$	16.7532	+	14.5167i	0.658635	+	0.570711i	−0.260101	+	0.965581i	$0.583756\pi$
$648$	−2.58647	−	8.62033i	−0.101606	−	0.338639i
$649$	−0.279150	−	0.0401357i	−0.0109576	−	0.00157547i
$650$	−4.29807	+	8.33709i	−0.168584	+	0.327008i
$651$	3.71408	−	26.1051i	0.145566	−	1.02314i
$652$	1.44677	−	0.278843i	0.0566601	−	0.0109203i
$653$	−12.3194	+	30.7724i	−0.482095	+	1.20422i	0.465587	+	0.885002i	$0.345843\pi$
$653$	−12.3194	+	30.7724i	−0.482095	+	1.20422i	−0.947683	+	0.319214i	$0.896581\pi$
$654$	4.71598	−	9.18094i	0.184410	−	0.359003i
$655$	−15.5176	+	16.2744i	−0.606324	+	0.635894i
$656$	−3.49787	−	11.9127i	−0.136569	−	0.465111i
$657$	−4.86223	+	0.0143359i	−0.189694	+	0.000559296i
$658$	−7.67894	+	1.10406i	−0.299356	+	0.0430409i
$659$	14.6093	−	42.2107i	0.569096	−	1.64430i	−0.181392	−	0.983411i	$-0.558060\pi$
$659$	14.6093	−	42.2107i	0.569096	−	1.64430i	0.750488	−	0.660884i	$-0.229819\pi$
$660$	0.426302	−	0.543734i	0.0165938	−	0.0211648i
$661$	−1.23676	+	0.0589142i	−0.0481044	+	0.00229150i	−0.0716203	−	0.997432i	$-0.522817\pi$
$661$	−1.23676	+	0.0589142i	−0.0481044	+	0.00229150i	0.0235159	+	0.999723i	$0.492514\pi$
$662$	6.97528	−	8.86980i	0.271102	−	0.344734i
$663$	−1.55294	+	16.5205i	−0.0603114	+	0.641604i
$664$	−0.0681910	+	0.353809i	−0.00264633	+	0.0137304i
$665$	−7.43247	−	2.18237i	−0.288219	−	0.0846287i
$666$	−12.3113	+	17.3971i	−0.477051	+	0.674123i
$667$	−0.649646	+	2.40939i	−0.0251544	+	0.0932918i
$668$	−13.3293	+	7.69566i	−0.515725	+	0.297754i
$669$	−33.6653	−	11.5961i	−1.30157	−	0.448332i
$670$	−2.25906	−	6.52713i	−0.0872752	−	0.252165i
$671$	−0.116182	−	0.225362i	−0.00448517	−	0.00870001i
$672$	2.58137	+	2.23012i	0.0995786	+	0.0860286i
$673$	−22.2090	−	11.4495i	−0.856094	−	0.441347i	−0.0264568	−	0.999650i	$-0.508422\pi$
$673$	−22.2090	−	11.4495i	−0.856094	−	0.441347i	−0.829637	+	0.558303i	$0.811453\pi$
$674$	−5.13105	−	11.2354i	−0.197641	−	0.432773i
$675$	6.08380	−	11.9302i	0.234166	−	0.459193i
$676$	0.0349370	+	0.242992i	0.00134373	+	0.00934585i
$677$	−30.4299	+	2.90571i	−1.16952	+	0.111675i	−0.661686	−	0.749781i	$-0.730159\pi$
$677$	−30.4299	+	2.90571i	−1.16952	+	0.111675i	−0.507831	+	0.861456i	$0.669553\pi$
$678$	10.5158	+	3.07089i	0.403858	+	0.117937i
$679$	−0.568259	+	2.34240i	−0.0218078	+	0.0898929i
$680$	−3.33752	+	2.37664i	−0.127988	+	0.0911399i
$681$	−2.55558	−	26.3527i	−0.0979302	−	1.00984i
$682$	1.87202	+	0.647911i	0.0716832	+	0.0248098i
$683$	32.0143	−	14.6204i	1.22499	−	0.559436i	0.305369	−	0.952234i	$-0.401220\pi$
$683$	32.0143	−	14.6204i	1.22499	−	0.559436i	0.919625	+	0.392798i	$0.128493\pi$
$684$	−3.49347	−	6.72761i	−0.133576	−	0.257236i
$685$	3.22811	−	22.4520i	0.123340	−	0.857848i
$686$	−0.948473	+	19.9109i	−0.0362129	+	0.760201i
$687$	9.47129	−	39.2939i	0.361352	−	1.49916i
$688$	−1.17248	−	1.22966i	−0.0447003	−	0.0468803i
$689$	16.7841	−	29.0709i	0.639424	−	1.10751i
$690$	0.921151	+	12.8965i	0.0350676	+	0.490962i
$691$	1.22017	+	2.11339i	0.0464174	+	0.0803973i	0.888301	−	0.459262i	$-0.151886\pi$
$691$	1.22017	+	2.11339i	0.0464174	+	0.0803973i	−0.841883	+	0.539660i	$0.818553\pi$
$692$	2.60280	−	8.86432i	0.0989436	−	0.336971i
$693$	−1.04818	−	1.09283i	−0.0398170	−	0.0415132i
$694$	18.3845	+	11.8150i	0.697866	+	0.448491i
$695$	31.3946	−	12.5685i	1.19086	−	0.476750i
$696$	0.779835	−	0.451772i	0.0295596	−	0.0171244i
$697$	3.10661	−	32.5339i	0.117671	−	1.23231i
$698$	−3.38842	−	17.5808i	−0.128254	−	0.665443i
$699$	−9.38444	+	20.6295i	−0.354952	+	0.780279i
$700$	0.482499	+	5.05296i	0.0182368	+	0.190984i
$701$	15.2347	−	4.47332i	0.575408	−	0.168955i	0.0189350	−	0.999821i	$-0.493972\pi$
$701$	15.2347	−	4.47332i	0.575408	−	0.168955i	0.556473	+	0.830866i	$0.312154\pi$
$702$	−2.77408	−	18.7065i	−0.104701	−	0.706031i
$703$	−7.45722	+	16.3290i	−0.281254	+	0.615861i
$704$	−0.201452	+	0.158423i	−0.00759249	+	0.00597080i
$705$	1.52679	+	10.5091i	0.0575023	+	0.395794i
$706$	26.3398	+	2.51514i	0.991310	+	0.0946586i
$707$	−0.853748	−	17.9224i	−0.0321085	−	0.674040i
$708$	−1.87209	−	0.357954i	−0.0703573	−	0.0134527i
$709$	−45.7311	−	2.17844i	−1.71747	−	0.0818131i	−0.834430	−	0.551114i	$-0.814203\pi$
$709$	−45.7311	−	2.17844i	−1.71747	−	0.0818131i	−0.883039	+	0.469300i	$0.844506\pi$
$710$	0.764875	−	0.882713i	0.0287052	−	0.0331276i
$711$	−2.07901	−	2.62770i	−0.0779691	−	0.0985465i
$712$		−	12.9706i		−	0.486093i
$713$	−34.0998	+	14.5391i	−1.27705	+	0.544495i
$714$	4.12646	+	7.97533i	0.154429	+	0.298469i
$715$	1.05071	−	1.00185i	0.0392945	−	0.0374672i
$716$	0.727224	−	0.251695i	0.0271776	−	0.00940627i
$717$	−13.9076	−	1.30733i	−0.519388	−	0.0488230i
$718$	5.66376	+	14.1474i	0.211370	+	0.527976i
$719$	−2.59438	−	4.03693i	−0.0967539	−	0.150552i	0.789502	−	0.613748i	$-0.210339\pi$
$719$	−2.59438	−	4.03693i	−0.0967539	−	0.150552i	−0.886256	+	0.463196i	$0.846703\pi$
$720$	3.04748	−	3.53800i	0.113573	−	0.131854i
$721$	16.7017	+	19.2748i	0.622004	+	0.717831i
$722$	7.79808	+	9.91606i	0.290214	+	0.369038i
$723$	−15.7958	−	8.11383i	−0.587451	−	0.301757i
$724$	−4.88709	−	1.18559i	−0.181627	−	0.0440623i
$725$	1.30324	+	0.316162i	0.0484010	+	0.0117419i
$726$	−15.9172	+	10.2626i	−0.590743	+	0.380879i
$727$	13.6408	+	17.3457i	0.505910	+	0.643317i	0.970183	−	0.242375i	$-0.0779266\pi$
$727$	13.6408	+	17.3457i	0.505910	+	0.643317i	−0.464272	+	0.885692i	$0.653684\pi$
$728$	4.69398	+	5.41714i	0.173970	+	0.200772i
$729$	4.07874	+	26.6901i	0.151064	+	0.988524i
$730$	−1.36389	−	2.12225i	−0.0504797	−	0.0785479i
$731$	−1.66224	−	4.15207i	−0.0614802	−	0.153570i
$732$	−0.714139	−	1.55767i	−0.0263953	−	0.0575730i
$733$	−12.2999	+	4.25704i	−0.454307	+	0.157237i	−0.544632	−	0.838675i	$-0.683331\pi$
$733$	−12.2999	+	4.25704i	−0.454307	+	0.157237i	0.0903249	+	0.995912i	$0.471209\pi$
$734$	24.5857	−	23.4424i	0.907473	−	0.865274i
$735$	8.40524	+	0.387972i	0.310032	+	0.0143106i
$736$	0.802711	−	4.72818i	0.0295883	−	0.174283i
$737$		−	1.13725i		−	0.0418911i
$738$	5.40944	+	36.8518i	0.199124	+	1.35654i
$739$	−19.8678	+	22.9286i	−0.730848	+	0.843444i	−0.992567	−	0.121701i	$-0.961165\pi$
$739$	−19.8678	+	22.9286i	−0.730848	+	0.843444i	0.261719	+	0.965144i	$0.415711\pi$
$740$	−11.0452	−	0.526149i	−0.406031	−	0.0193416i
$741$	−5.23189	−	15.0448i	−0.192198	−	0.552683i
$742$	−0.864359	−	18.1451i	−0.0317316	−	0.666129i
$743$	0.129460	+	0.0123620i	0.00474944	+	0.000453517i	0.0974305	−	0.995242i	$-0.468938\pi$
$743$	0.129460	+	0.0123620i	0.00474944	+	0.000453517i	−0.0926811	+	0.995696i	$0.529544\pi$
$744$	12.4364	+	4.95753i	0.455941	+	0.181752i
$745$	10.3939	−	8.17386i	0.380804	−	0.299467i
$746$	−14.2931	+	31.2974i	−0.523306	+	1.14588i
$747$	0.350534	−	1.02255i	0.0128254	−	0.0374130i
$748$	−0.647291	+	0.190062i	−0.0236673	+	0.00694935i
$749$	−3.35545	−	35.1399i	−0.122606	−	1.28398i
$750$	20.3326	−	1.97178i	0.742442	−	0.0719993i
$751$	−3.81445	−	19.7913i	−0.139191	−	0.722193i	−0.982718	−	0.185107i	$-0.940737\pi$
$751$	−3.81445	−	19.7913i	−0.139191	−	0.722193i	0.843527	−	0.537087i	$-0.180475\pi$
$752$	0.374426	−	3.92117i	0.0136539	−	0.142990i
$753$	0.0297122	+	20.1547i	0.00108277	+	0.734479i
$754$	1.75807	−	0.703825i	0.0640251	−	0.0256318i
$755$	9.91864	+	6.37432i	0.360976	+	0.231985i
$756$	−6.73590	−	7.70453i	−0.244982	−	0.280211i
$757$	13.1388	−	44.7465i	0.477536	−	1.62634i	−0.270528	−	0.962712i	$-0.587198\pi$
$757$	13.1388	−	44.7465i	0.477536	−	1.62634i	0.748064	−	0.663626i	$-0.230984\pi$
$758$	5.27091	+	9.12949i	0.191448	+	0.331598i
$759$	−0.551179	+	2.05625i	−0.0200065	+	0.0746372i
$760$	1.96654	−	3.40615i	0.0713340	−	0.123554i
$761$	−20.7517	−	21.7637i	−0.752247	−	0.788934i	0.230660	−	0.973034i	$-0.425911\pi$
$761$	−20.7517	−	21.7637i	−0.752247	−	0.788934i	−0.982908	+	0.184100i	$0.941063\pi$
$762$	10.2109	+	9.70739i	0.369902	+	0.351662i
$763$	0.558439	−	11.7231i	0.0202168	−	0.424404i
$764$	0.244227	−	1.69863i	0.00883581	−	0.0614544i
$765$	10.9087	−	5.66459i	0.394404	−	0.204804i
$766$	22.9381	−	10.4755i	0.828788	−	0.378495i
$767$	−3.78468	−	1.30989i	−0.136657	−	0.0472973i
$768$	−1.40940	+	1.00677i	−0.0508575	+	0.0363286i
$769$	−9.20678	+	6.55612i	−0.332005	+	0.236420i	−0.733887	−	0.679272i	$-0.762296\pi$
$769$	−9.20678	+	6.55612i	−0.332005	+	0.236420i	0.401882	+	0.915692i	$0.368356\pi$
$770$	0.185224	−	0.763505i	0.00667502	−	0.0275148i
$771$	−10.0816	+	9.64122i	−0.363081	+	0.347220i
$772$	18.6073	−	1.77678i	0.669692	−	0.0639479i
$773$	4.13673	+	28.7716i	0.148788	+	1.03484i	0.918208	+	0.396100i	$0.129636\pi$
$773$	4.13673	+	28.7716i	0.148788	+	1.03484i	−0.769420	+	0.638744i	$0.779454\pi$
$774$	2.96886	+	4.14328i	0.106714	+	0.148927i
$775$	8.27561	+	18.1211i	0.297269	+	0.650928i
$776$	−1.08778	−	0.560791i	−0.0390491	−	0.0201312i
$777$	−4.55131	+	23.8032i	−0.163277	+	0.853936i
$778$	−11.1477	−	21.6236i	−0.399665	−	0.775243i
$779$	10.2609	+	29.6469i	0.367635	+	1.06221i
$780$	7.40576	−	6.43627i	0.265169	−	0.230455i
$781$	0.166547	−	0.0961562i	0.00595953	−	0.00344074i
$782$	6.58738	−	10.7692i	0.235564	−	0.385107i
$783$	−2.50559	+	1.01597i	−0.0895425	+	0.0363077i
$784$	−2.99461	−	0.879297i	−0.106950	−	0.0314035i
$785$	−6.08498	+	31.5719i	−0.217182	+	1.12685i
$786$	−22.7461	+	10.4284i	−0.811327	+	0.371967i
$787$	−27.5295	+	35.0066i	−0.981321	+	1.24785i	−0.0125429	+	0.999921i	$0.503993\pi$
$787$	−27.5295	+	35.0066i	−0.981321	+	1.24785i	−0.968778	+	0.247930i	$0.920250\pi$
$788$	−18.1372	+	0.863981i	−0.646111	+	0.0307780i
$789$	13.4610	+	33.4809i	0.479225	+	1.19195i
$790$	0.568596	−	1.64285i	0.0202297	−	0.0584500i
$791$	12.3301	−	1.77281i	0.438409	−	0.0630338i
$792$	0.664705	−	0.386385i	0.0236193	−	0.0137296i
$793$	−1.01441	−	3.45475i	−0.0360226	−	0.122682i
$794$	20.7013	−	21.7109i	0.734661	−	0.770490i
$795$	−24.8362	+	1.21979i	−0.880848	+	0.0432616i
$796$	−9.10201	+	22.7357i	−0.322612	+	0.805846i
$797$	25.3414	−	4.88414i	0.897637	−	0.173005i	0.280493	−	0.959856i	$-0.409502\pi$
$797$	25.3414	−	4.88414i	0.897637	−	0.173005i	0.617143	+	0.786851i	$0.288290\pi$
$798$	−6.78350	−	5.31843i	−0.240133	−	0.188271i
$799$	4.75123	−	9.21610i	0.168086	−	0.326042i
$800$	−2.55103	−	0.366783i	−0.0901926	−	0.0129677i
$801$	−5.42414	+	38.5319i	−0.191653	+	1.36146i
$802$	2.86093	+	2.47901i	0.101023	+	0.0875370i
$803$	−0.0979271	−	0.403661i	−0.00345577	−	0.0142449i
$804$	0.354394	−	7.67778i	0.0124985	−	0.270774i
$805$	7.02564	+	12.9146i	0.247621	+	0.455181i
$806$	24.3626	+	14.0657i	0.858135	+	0.495445i
$807$	23.1620	+	26.6509i	0.815341	+	0.938156i
$808$	8.94560	+	1.72412i	0.314705	+	0.0606545i
$809$	13.2028	−	20.5439i	0.464185	−	0.722285i	−0.527700	−	0.849431i	$-0.676945\pi$
$809$	13.2028	−	20.5439i	0.464185	−	0.722285i	0.991884	+	0.127146i	$0.0405816\pi$
$810$	−10.5327	+	9.23597i	−0.370082	+	0.324519i
$811$	17.5449	−	11.2754i	0.616084	−	0.395933i	−0.195050	−	0.980793i	$-0.562487\pi$
$811$	17.5449	−	11.2754i	0.616084	−	0.395933i	0.811134	+	0.584860i	$0.198851\pi$
$812$	0.594443	−	0.834779i	0.0208609	−	0.0292950i
$813$	−34.2167	+	4.97112i	−1.20003	+	0.174345i
$814$	−1.69026	−	0.676677i	−0.0592435	−	0.0237175i
$815$	−1.33028	−	1.86812i	−0.0465978	−	0.0654375i
$816$	−4.42921	+	1.08143i	−0.155053	+	0.0378577i
$817$	3.10717	+	2.96268i	0.108706	+	0.103651i
$818$	28.9802	+	13.2348i	1.01327	+	0.462744i
$819$	−11.6791	−	18.0557i	−0.408100	−	0.630918i
$820$	−14.6049	+	12.6552i	−0.510025	+	0.441939i
$821$	3.58673	+	2.55410i	0.125178	+	0.0891388i	0.640931	−	0.767598i	$-0.278548\pi$
$821$	3.58673	+	2.55410i	0.125178	+	0.0891388i	−0.515753	+	0.856737i	$0.672488\pi$
$822$	12.5883	−	21.8779i	0.439066	−	0.763080i
$823$	43.6275	+	34.3090i	1.52076	+	1.19594i	0.917075	+	0.398714i	$0.130543\pi$
$823$	43.6275	+	34.3090i	1.52076	+	1.19594i	0.603684	+	0.797224i	$0.293699\pi$
$824$	−11.5100	+	5.93382i	−0.400970	+	0.206714i
$825$	1.11218	+	0.268077i	0.0387212	+	0.00933323i
$826$	−2.10621	+	0.510962i	−0.0732845	+	0.0177786i
$827$	−31.5391			−1.09672			−0.548362	−	0.836241i	$-0.684748\pi$
$827$	−31.5391			−1.09672			−0.548362	+	0.836241i	$0.684748\pi$
$828$	−4.36189	+	13.7104i	−0.151586	+	0.476468i
$829$	−20.9491			−0.727592			−0.363796	−	0.931479i	$-0.618519\pi$
$829$	−20.9491			−0.727592			−0.363796	+	0.931479i	$0.618519\pi$
$830$	0.545034	−	0.132224i	0.0189184	−	0.00458956i
$831$	11.9164	−	12.5345i	0.413376	−	0.434818i
$832$	−3.23486	+	1.66769i	−0.112149	+	0.0578166i
$833$	−6.45788	−	5.07853i	−0.223752	−	0.175961i
$834$	37.6307	−	0.0554754i	1.30304	−	0.00192095i
$835$	19.5146	+	13.8963i	0.675331	+	0.480901i
$836$	0.489415	−	0.424080i	0.0169268	−	0.0146671i
$837$	−34.8718	−	19.9281i	−1.20535	−	0.688817i
$838$	13.2075	+	6.03166i	0.456245	+	0.208360i
$839$	−20.8411	−	19.8719i	−0.719514	−	0.686055i	0.239026	−	0.971013i	$-0.423172\pi$
$839$	−20.8411	−	19.8719i	−0.719514	−	0.686055i	−0.958540	+	0.284958i	$0.908020\pi$
$840$	1.48841	−	5.09684i	0.0513550	−	0.175858i
$841$	16.6646	+	23.4022i	0.574641	+	0.806971i
$842$	−10.7190	−	4.29123i	−0.369400	−	0.147885i
$843$	−13.6764	−	17.3382i	−0.471039	−	0.597161i
$844$	7.04251	−	9.88982i	0.242413	−	0.340422i
$845$	0.321451	−	0.206584i	0.0110583	−	0.00710671i
$846$	−2.75209	+	11.4921i	−0.0946190	+	0.395106i
$847$	−11.6428	+	18.1166i	−0.400052	+	0.622494i
$848$	9.05679	+	1.74555i	0.311011	+	0.0599425i
$849$	41.1126	−	7.98667i	1.41098	−	0.274102i
$850$	−5.87529	−	3.39210i	−0.201521	−	0.116348i
$851$	31.9410	−	11.8563i	1.09492	−	0.406429i
$852$	1.15436	−	0.597268i	0.0395476	−	0.0204621i
$853$	1.52806	+	6.29876i	0.0523199	+	0.215666i	0.991970	−	0.126470i	$-0.0403648\pi$
$853$	1.52806	+	6.29876i	0.0523199	+	0.215666i	−0.939651	+	0.342136i	$0.888850\pi$
$854$	−1.47257	−	1.27599i	−0.0503904	−	0.0436635i
$855$	−7.26644	+	9.29631i	−0.248507	+	0.317927i
$856$	17.7407	+	2.55072i	0.606364	+	0.0871820i
$857$	−19.0049	+	36.8644i	−0.649195	+	1.25926i	0.302772	+	0.953063i	$0.402088\pi$
$857$	−19.0049	+	36.8644i	−0.649195	+	1.25926i	−0.951967	+	0.306200i	$0.900942\pi$
$858$	1.49891	−	0.602640i	0.0511721	−	0.0205738i
$859$	−44.0266	+	8.48543i	−1.50217	+	0.289519i	−0.872988	−	0.487741i	$-0.837821\pi$
$859$	−44.0266	+	8.48543i	−1.50217	+	0.289519i	−0.629179	+	0.777260i	$0.716609\pi$
$860$	−0.982895	+	2.45515i	−0.0335165	+	0.0837201i
$861$	22.9503	+	35.5959i	0.782146	+	1.21311i
$862$	21.3273	−	22.3674i	0.726409	−	0.761836i
$863$	8.34914	+	28.4345i	0.284208	+	0.967923i	0.970601	+	0.240693i	$0.0773746\pi$
$863$	8.34914	+	28.4345i	0.284208	+	0.967923i	−0.686393	+	0.727230i	$0.740807\pi$
$864$	4.60795	−	2.40142i	0.156766	−	0.0816979i
$865$	−14.2336	+	2.04648i	−0.483956	+	0.0695823i
$866$	12.6680	−	36.6018i	0.430476	−	1.24378i
$867$	17.2694	+	2.45698i	0.586498	+	0.0834434i
$868$	15.2063	−	0.724367i	0.516136	−	0.0245866i
$869$	0.176942	−	0.225000i	0.00600236	−	0.00763262i
$870$	−1.14388	−	0.812018i	−0.0387813	−	0.0275300i
$871$	3.05640	−	15.8581i	0.103562	−	0.537331i
$872$	5.71765	+	1.67885i	0.193624	+	0.0568531i
$873$	2.99697	+	2.12084i	0.101432	+	0.0717797i
$874$	−1.45756	+	12.0304i	−0.0493026	+	0.406934i
$875$	20.1166	−	11.6143i	0.680064	−	0.392635i
$876$	−0.535333	−	2.75570i	−0.0180872	−	0.0931066i
$877$	8.17429	+	23.6181i	0.276026	+	0.797525i	0.994760	+	0.102240i	$0.0326009\pi$
$877$	8.17429	+	23.6181i	0.276026	+	0.797525i	−0.718734	+	0.695286i	$0.755278\pi$
$878$	10.3015	+	19.9820i	0.347658	+	0.674362i
$879$	−13.5482	+	4.71146i	−0.456970	+	0.158914i
$880$	0.354563	+	0.182790i	0.0119523	+	0.00616184i
$881$	18.7713	+	41.1034i	0.632421	+	1.38481i	0.906131	+	0.422997i	$0.139022\pi$
$881$	18.7713	+	41.1034i	0.632421	+	1.38481i	−0.273710	+	0.961812i	$0.588251\pi$
$882$	8.52841	+	3.86445i	0.287166	+	0.130123i
$883$	−6.88197	−	47.8651i	−0.231597	−	1.61079i	−0.691199	−	0.722665i	$-0.742917\pi$
$883$	−6.88197	−	47.8651i	−0.231597	−	1.61079i	0.459602	−	0.888125i	$-0.347992\pi$
$884$	−9.53679	+	0.910653i	−0.320757	+	0.0306286i
$885$	0.703679	+	2.88205i	0.0236539	+	0.0968792i
$886$	−3.62064	+	14.9245i	−0.121638	+	0.501398i
$887$	−22.6112	+	16.1014i	−0.759210	+	0.540631i	−0.892826	−	0.450402i	$-0.851281\pi$
$887$	−22.6112	+	16.1014i	−0.759210	+	0.540631i	0.133616	+	0.991033i	$0.457341\pi$
$888$	−11.2004	−	5.09510i	−0.375860	−	0.170980i
$889$	15.1393	+	5.23976i	0.507755	+	0.175736i
$890$	−18.3645	+	8.38677i	−0.615578	+	0.281125i
$891$	−2.13623	+	0.869867i	−0.0715663	+	0.0291416i
$892$	2.92562	−	20.3482i	0.0979571	−	0.681307i
$893$	−0.473597	+	9.94202i	−0.0158483	+	0.332697i
$894$	14.1120	−	4.16626i	0.471976	−	0.139341i
$895$	−0.826585	−	0.866897i	−0.0276297	−	0.0289772i
$896$	−0.984754	+	1.70564i	−0.0328983	+	0.0569816i
$897$	−13.2120	+	27.1916i	−0.441137	+	0.907900i
$898$	1.79685	+	3.11223i	0.0599615	+	0.103856i
$899$	1.13312	−	3.85907i	0.0377918	−	0.128707i
$900$	7.42499	+	2.15642i	0.247500	+	0.0718805i
$901$	20.4249	+	13.1263i	0.680453	+	0.437301i
$902$	−2.95397	+	1.18259i	−0.0983564	+	0.0393760i
$903$	5.02370	+	2.89057i	0.167178	+	0.0961921i
$904$	−0.601219	+	6.29626i	−0.0199963	+	0.209410i
$905$	1.48136	+	7.68601i	0.0492420	+	0.255492i
$906$	7.62608	+	10.6760i	0.253360	+	0.354686i
$907$	0.761075	+	7.97034i	0.0252711	+	0.264651i	0.999273	+	0.0381129i	$0.0121347\pi$
$907$	0.761075	+	7.97034i	0.0252711	+	0.264651i	−0.974002	+	0.226538i	$0.927259\pi$
$908$	14.6669	−	4.30659i	0.486738	−	0.142919i
$909$	−25.8538	−	8.86281i	−0.857516	−	0.293961i
$910$	4.63476	−	10.1487i	0.153641	−	0.336426i
$911$	−16.0361	+	12.6110i	−0.531301	+	0.417819i	−0.847438	−	0.530894i	$-0.821856\pi$
$911$	−16.0361	+	12.6110i	−0.531301	+	0.417819i	0.316138	+	0.948713i	$0.397614\pi$
$912$	3.43628	−	2.71053i	0.113787	−	0.0897546i
$913$	0.0919256	+	0.00877783i	0.00304229	+	0.000290504i
$914$	0.237416	+	4.98398i	0.00785303	+	0.164855i
$915$	−1.74367	+	2.01830i	−0.0576438	+	0.0667230i
$916$	23.3096	+	1.11038i	0.770172	+	0.0366878i
$917$	−18.6329	+	21.5035i	−0.615313	+	0.710109i
$918$	13.6101	−	1.36038i	0.449201	−	0.0448992i
$919$			52.7582i			1.74033i	0.492758	+	0.870166i	$0.335989\pi$
$919$			52.7582i			1.74033i	−0.492758	+	0.870166i	$0.664011\pi$
$920$	−7.21344	+	1.92071i	−0.237820	+	0.0633240i
$921$	12.2178	−	19.0730i	0.402590	−	0.628477i
$922$	−5.25001	+	5.00588i	−0.172900	+	0.164860i
$923$	2.58080	−	0.893224i	0.0849481	−	0.0294008i
$924$	0.506066	−	0.712892i	0.0166484	−	0.0234524i
$925$	−6.80490	−	16.9978i	−0.223744	−	0.558885i
$926$	2.87823	+	4.47861i	0.0945844	+	0.147176i
$927$	36.6743	−	12.8143i	1.20454	−	0.420877i
$928$	0.340746	+	0.393242i	0.0111855	+	0.0129088i
$929$	−35.6503	−	45.3330i	−1.16965	−	1.48733i	−0.839467	−	0.543410i	$-0.817133\pi$
$929$	−35.6503	−	45.3330i	−1.16965	−	1.48733i	−0.330181	−	0.943918i	$-0.607110\pi$
$930$	−1.02223	−	20.8137i	−0.0335204	−	0.682508i
$931$	7.66410	+	1.85929i	0.251181	+	0.0609358i
$932$	−12.7160	−	3.08488i	−0.416528	−	0.101049i
$933$	0.438590	+	8.93012i	0.0143588	+	0.292359i
$934$	12.8202	+	16.3023i	0.419491	+	0.533426i
$935$	0.687638	+	0.793577i	0.0224882	+	0.0259527i
$936$	10.3072	−	3.60143i	0.336903	−	0.117717i
$937$	−25.2118	−	39.2303i	−0.823632	−	1.28160i	−0.956871	−	0.290513i	$-0.906174\pi$
$937$	−25.2118	−	39.2303i	−0.823632	−	1.28160i	0.133239	−	0.991084i	$-0.457462\pi$
$938$	−3.24821	−	8.11363i	−0.106058	−	0.264919i
$939$	32.3118	−	45.5174i	1.05446	−	1.48540i
$940$	−5.79391	+	2.00529i	−0.188976	+	0.0654054i
$941$	−34.4835	+	32.8799i	−1.12413	+	1.07185i	−0.127333	+	0.991860i	$0.540642\pi$
$941$	−34.4835	+	32.8799i	−1.12413	+	1.07185i	−0.996795	+	0.0799942i	$0.974510\pi$
$942$	−19.2992	+	30.1277i	−0.628802	+	0.981613i
$943$	26.1010	−	53.5174i	0.849965	−	1.74277i
$944$		−	1.10043i		−	0.0358159i
$945$	−6.55306	+	14.5188i	−0.213171	+	0.472296i
$946$	−0.285150	+	0.329081i	−0.00927102	+	0.0106993i
$947$	6.47119	+	0.308261i	0.210285	+	0.0100171i	0.152460	−	0.988310i	$-0.451280\pi$
$947$	6.47119	+	0.308261i	0.210285	+	0.0100171i	0.0578251	+	0.998327i	$0.481583\pi$
$948$	1.26468	−	1.46388i	0.0410751	−	0.0475446i
$949$	−0.280667	−	5.89193i	−0.00911085	−	0.191260i
$950$	6.48289	+	0.619041i	0.210333	+	0.0200843i
$951$	4.80550	−	3.79056i	0.155829	−	0.122917i
$952$	−4.07520	+	3.20477i	−0.132078	+	0.103867i
$953$	14.0981	−	30.8706i	0.456683	−	0.999997i	−0.531548	−	0.847028i	$-0.678389\pi$
$953$	14.0981	−	30.8706i	0.456683	−	0.999997i	0.988231	−	0.152969i	$-0.0488833\pi$
$954$	−26.1751	−	8.97297i	−0.847451	−	0.290511i
$955$	−2.56293	+	0.752545i	−0.0829346	+	0.0243518i
$956$	−0.766622	−	8.02843i	−0.0247943	−	0.259658i
$957$	−0.134255	−	0.187947i	−0.00433984	−	0.00607547i
$958$	3.39645	+	17.6224i	0.109734	+	0.569355i
$959$	2.72824	−	28.5715i	0.0880996	−	0.922621i
$960$	2.33676	+	1.34454i	0.0754184	+	0.0433947i
$961$	26.6879	−	10.6842i	0.860901	−	0.344653i
$962$	−21.7508	−	13.9784i	−0.701274	−	0.450681i
$963$	−51.6357	−	14.9964i	−1.66394	−	0.483252i
$964$	2.88846	−	9.83719i	0.0930310	−	0.316834i
$965$	−14.5472	−	25.1964i	−0.468289	−	0.811101i
$966$	1.94070	+	16.2445i	0.0624411	+	0.522657i
$967$	18.3098	−	31.7135i	0.588803	−	1.01984i	−0.405587	−	0.914056i	$-0.632933\pi$
$967$	18.3098	−	31.7135i	0.588803	−	1.01984i	0.994390	−	0.105780i	$-0.0337338\pi$
$968$	−7.54554	−	7.91354i	−0.242523	−	0.254351i
$969$	11.0493	−	3.26206i	0.354954	−	0.104792i
$970$	−0.0906391	+	1.90275i	−0.00291024	+	0.0610936i
$971$	7.79256	−	54.1984i	0.250075	−	1.73931i	−0.347663	−	0.937620i	$-0.613025\pi$
$971$	7.79256	−	54.1984i	0.250075	−	1.73931i	0.597738	−	0.801691i	$-0.296066\pi$
$972$	−14.6931	+	5.20693i	−0.471282	+	0.167012i
$973$	38.9229	−	17.7755i	1.24781	−	0.569856i
$974$	−7.57812	−	2.62281i	−0.242819	−	0.0840403i
$975$	14.7881	+	6.72715i	0.473597	+	0.215441i
$976$	0.805884	−	0.573867i	0.0257957	−	0.0183690i
$977$	−11.5365	+	47.5541i	−0.369086	+	1.52139i	0.420238	+	0.907414i	$0.361947\pi$
$977$	−11.5365	+	47.5541i	−0.369086	+	1.52139i	−0.789323	+	0.613978i	$0.789568\pi$
$978$	−0.605313	−	2.47918i	−0.0193558	−	0.0792754i
$979$	−3.30908	+	0.315979i	−0.105759	+	0.0100987i
$980$	0.691356	+	4.80849i	0.0220846	+	0.153601i
$981$	−16.2834	−	7.37843i	−0.519889	−	0.235575i
$982$	12.7128	+	27.8372i	0.405682	+	0.888319i
$983$	35.8046	+	18.4585i	1.14199	+	0.588736i	0.922162	−	0.386803i	$-0.126421\pi$
$983$	35.8046	+	18.4585i	1.14199	+	0.588736i	0.219826	+	0.975539i	$0.429451\pi$
$984$	−20.3113	+	7.06336i	−0.647501	+	0.225172i
$985$	12.9508	+	25.1210i	0.412646	+	0.800421i
$986$	0.447980	+	1.29435i	0.0142666	+	0.0412206i
$987$	2.56243	+	13.1905i	0.0815631	+	0.419858i
$988$	7.96425	−	4.59816i	0.253377	−	0.146287i
$989$	−0.181132	−	8.14634i	−0.00575967	−	0.259038i
$990$	−0.976862	−	0.691289i	−0.0310467	−	0.0219706i
$991$	37.7925	+	11.0969i	1.20052	+	0.352504i	0.820051	−	0.572290i	$-0.193945\pi$
$991$	37.7925	+	11.0969i	1.20052	+	0.352504i	0.380467	+	0.924794i	$0.375763\pi$
$992$	−1.46284	+	7.58994i	−0.0464453	+	0.240981i
$993$	−15.9371	−	11.3134i	−0.505748	−	0.359019i
$994$	0.913580	−	1.16171i	0.0289770	−	0.0368473i
$995$	38.0758	−	1.81378i	1.20708	−	0.0575005i
$996$	0.617871	+	0.0879069i	0.0195780	+	0.00278544i
$997$	−4.94845	+	14.2976i	−0.156719	+	0.452809i	−0.995838	−	0.0911378i	$-0.970950\pi$
$997$	−4.94845	+	14.2976i	−0.156719	+	0.452809i	0.839119	+	0.543947i	$0.183071\pi$
$998$	−17.1406	+	2.46444i	−0.542575	+	0.0780105i
$999$	31.1423	+	19.8199i	0.985300	+	0.627074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.17	✓	480
9.2	odd	6	inner	414.2.p.a.281.24	yes	480
23.14	odd	22	inner	414.2.p.a.221.24	yes	480
207.83	even	66	inner	414.2.p.a.83.17	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.17	✓	480	1.1	even	1	trivial
414.2.p.a.83.17	yes	480	207.83	even	66	inner
414.2.p.a.221.24	yes	480	23.14	odd	22	inner
414.2.p.a.281.24	yes	480	9.2	odd	6	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.971812 - 0.235759i) q^{2} +(-0.490425 - 1.66117i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-1.22350 - 0.962173i) q^{5} +(-0.868236 - 1.49872i) q^{6} +(-1.60431 - 1.14243i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.51897 + 1.62936i) q^{9} +O(q^{10})\)	\(q+(0.971812 - 0.235759i) q^{2} +(-0.490425 - 1.66117i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-1.22350 - 0.962173i) q^{5} +(-0.868236 - 1.49872i) q^{6} +(-1.60431 - 1.14243i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-2.51897 + 1.62936i) q^{9} +(-1.41585 - 0.646599i) q^{10} +(-0.185480 - 0.176855i) q^{11} +(-1.19710 - 1.25178i) q^{12} +(-2.11108 - 2.96460i) q^{13} +(-1.82843 - 0.731993i) q^{14} +(-0.998297 + 2.50432i) q^{15} +(0.580057 - 0.814576i) q^{16} +(2.21445 - 1.42314i) q^{17} +(-2.06383 + 2.17730i) q^{18} +(-1.36612 + 2.12573i) q^{19} +(-1.52839 - 0.294572i) q^{20} +(-1.11097 + 3.22531i) q^{21} +(-0.221947 - 0.128141i) q^{22} +(4.68783 - 1.01207i) q^{23} +(-1.45847 - 0.934268i) q^{24} +(-0.607613 - 2.50462i) q^{25} +(-2.75050 - 2.38332i) q^{26} +(3.94200 + 3.38536i) q^{27} +(-1.94946 - 0.280290i) q^{28} +(-0.238431 + 0.462491i) q^{29} +(-0.379741 + 2.66908i) q^{30} +(-7.58994 + 1.46284i) q^{31} +(0.371662 - 0.928368i) q^{32} +(-0.202822 + 0.394848i) q^{33} +(1.81651 - 1.90510i) q^{34} +(0.863670 + 2.94139i) q^{35} +(-1.49233 + 2.60249i) q^{36} +(7.03187 - 1.01103i) q^{37} +(-0.826453 + 2.38788i) q^{38} +(-3.88937 + 4.96077i) q^{39} +(-1.55475 + 0.0740619i) q^{40} +(7.67480 - 9.75931i) q^{41} +(-0.319257 + 3.39632i) q^{42} +(0.321547 - 1.66834i) q^{43} +(-0.245901 - 0.0722031i) q^{44} +(4.64969 + 0.430161i) q^{45} +(4.31708 - 2.08874i) q^{46} +(3.41128 - 1.96950i) q^{47} +(-1.63762 - 0.564085i) q^{48} +(-1.02079 - 2.94938i) q^{49} +(-1.18097 - 2.29076i) q^{50} +(-3.45010 - 2.98064i) q^{51} +(-3.23486 - 1.66769i) q^{52} +(3.83157 + 8.38996i) q^{53} +(4.62901 + 2.36057i) q^{54} +(0.0567704 + 0.394847i) q^{55} +(-1.96059 + 0.187214i) q^{56} +(4.20117 + 1.22685i) q^{57} +(-0.122673 + 0.505666i) q^{58} +(0.896384 - 0.638312i) q^{59} +(0.260223 + 2.68337i) q^{60} +(0.934917 + 0.323578i) q^{61} +(-7.03112 + 3.21100i) q^{62} +(5.90264 + 0.263737i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.269544 + 5.65841i) q^{65} +(-0.104016 + 0.431535i) q^{66} +(3.06222 + 3.21156i) q^{67} +(1.31616 - 2.27966i) q^{68} +(-3.98025 - 7.29093i) q^{69} +(1.53278 + 2.65486i) q^{70} +(-0.211410 + 0.719996i) q^{71} +(-0.836707 + 2.88096i) q^{72} +(1.36346 + 0.876244i) q^{73} +(6.59530 - 2.64036i) q^{74} +(-3.86260 + 2.23767i) q^{75} +(-0.240193 + 2.51541i) q^{76} +(0.0955246 + 0.495629i) q^{77} +(-2.61019 + 5.73789i) q^{78} +(0.106168 + 1.11184i) q^{79} +(-1.49346 + 0.438521i) q^{80} +(3.69039 - 8.20859i) q^{81} +(5.15762 - 11.2936i) q^{82} +(-0.283231 + 0.222735i) q^{83} +(0.490454 + 3.37585i) q^{84} +(-4.07870 - 0.389468i) q^{85} +(-0.0808440 - 1.69712i) q^{86} +(0.885208 + 0.169257i) q^{87} +(-0.255992 - 0.0121944i) q^{88} +(8.49393 - 9.80252i) q^{89} +(4.62003 - 0.678170i) q^{90} +7.16790i q^{91} +(3.70295 - 3.04765i) q^{92} +(6.15232 + 11.8908i) q^{93} +(2.85079 - 2.71822i) q^{94} +(3.71677 - 1.28639i) q^{95} +(-1.72445 - 0.162100i) q^{96} +(-0.454851 - 1.13616i) q^{97} +(-1.68736 - 2.62558i) q^{98} +(0.755379 + 0.143279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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