LMFDB - Embedded newform 418.2.u.b.93.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			93.9
Character	$\chi$	$=$	418.93
Dual form			418.2.u.b.9.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.990268 - 0.139173i) q^{2} +(0.530296 + 2.12690i) q^{3} +(0.961262 - 0.275637i) q^{4} +(0.0547010 + 1.56643i) q^{5} +(0.821143 + 2.03240i) q^{6} +(2.87167 + 1.27855i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-1.59366 + 0.847362i) q^{9} +O(q^{10})$	\(q+(0.990268 - 0.139173i) q^{2} +(0.530296 + 2.12690i) q^{3} +(0.961262 - 0.275637i) q^{4} +(0.0547010 + 1.56643i) q^{5} +(0.821143 + 2.03240i) q^{6} +(2.87167 + 1.27855i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-1.59366 + 0.847362i) q^{9} +(0.272174 + 1.54358i) q^{10} +(-1.49853 - 2.95879i) q^{11} +(1.09601 + 1.89834i) q^{12} +(-2.34165 - 1.46322i) q^{13} +(3.02167 + 0.866449i) q^{14} +(-3.30264 + 0.947017i) q^{15} +(0.848048 - 0.529919i) q^{16} +(-6.27809 - 3.33812i) q^{17} +(-1.46022 + 1.06091i) q^{18} +(2.16967 + 3.78055i) q^{19} +(0.484349 + 1.49067i) q^{20} +(-1.19652 + 6.78578i) q^{21} +(-1.89573 - 2.72144i) q^{22} +(-1.39052 - 0.506108i) q^{23} +(1.34954 + 1.72733i) q^{24} +(2.53710 - 0.177411i) q^{25} +(-2.52250 - 1.12309i) q^{26} +(1.75287 + 1.94675i) q^{27} +(3.11285 + 0.437482i) q^{28} +(1.22673 + 1.18464i) q^{29} +(-3.13870 + 1.39744i) q^{30} +(3.78193 - 4.20026i) q^{31} +(0.766044 - 0.642788i) q^{32} +(5.49839 - 4.75625i) q^{33} +(-6.68156 - 2.43189i) q^{34} +(-1.84568 + 4.56822i) q^{35} +(-1.29836 + 1.25381i) q^{36} +(2.62851 - 1.90972i) q^{37} +(2.67471 + 3.44179i) q^{38} +(1.87037 - 5.75639i) q^{39} +(0.687097 + 1.40876i) q^{40} +(0.410003 + 1.64443i) q^{41} +(-0.240474 + 6.88626i) q^{42} +(-11.8872 + 4.32658i) q^{43} +(-2.25603 - 2.43112i) q^{44} +(-1.41451 - 2.45000i) q^{45} +(-1.44743 - 0.307660i) q^{46} +(3.83207 - 7.85691i) q^{47} +(1.57680 + 1.52270i) q^{48} +(1.92790 + 2.14115i) q^{49} +(2.48772 - 0.528781i) q^{50} +(3.77060 - 15.1231i) q^{51} +(-2.65425 - 0.761095i) q^{52} +(0.0190311 - 0.544981i) q^{53} +(2.00674 + 1.68386i) q^{54} +(4.55277 - 2.50919i) q^{55} +3.14344 q^{56} +(-6.89028 + 6.61949i) q^{57} +(1.37966 + 1.00238i) q^{58} +(-2.51772 - 5.16209i) q^{59} +(-2.91367 + 1.82066i) q^{60} +(-4.73404 + 6.05929i) q^{61} +(3.16056 - 4.68573i) q^{62} +(-5.65986 + 0.395776i) q^{63} +(0.669131 - 0.743145i) q^{64} +(2.16395 - 3.74807i) q^{65} +(4.78294 - 5.47519i) q^{66} +(-0.957384 - 5.42960i) q^{67} +(-6.95499 - 1.47833i) q^{68} +(0.339055 - 3.22589i) q^{69} +(-1.19195 + 4.78063i) q^{70} +(-0.319354 - 9.14512i) q^{71} +(-1.11122 + 1.42230i) q^{72} +(6.81009 + 0.476208i) q^{73} +(2.33715 - 2.25696i) q^{74} +(1.72275 + 5.30209i) q^{75} +(3.12768 + 3.03605i) q^{76} +(-0.520313 - 10.4126i) q^{77} +(1.05103 - 5.96068i) q^{78} +(-2.27548 + 5.63200i) q^{79} +(0.876472 + 1.29942i) q^{80} +(-6.23893 + 9.24959i) q^{81} +(0.634874 + 1.57137i) q^{82} +(10.5529 - 2.24308i) q^{83} +(0.720249 + 6.85271i) q^{84} +(4.88552 - 10.0168i) q^{85} +(-11.1694 + 5.93886i) q^{86} +(-1.86908 + 3.23735i) q^{87} +(-2.57242 - 2.09348i) q^{88} +(-6.95620 + 5.83694i) q^{89} +(-1.74172 - 2.22930i) q^{90} +(-4.85364 - 7.19581i) q^{91} +(-1.47616 - 0.103223i) q^{92} +(10.9391 + 5.81642i) q^{93} +(2.70131 - 8.31376i) q^{94} +(-5.80329 + 3.60545i) q^{95} +(1.77338 + 1.28843i) q^{96} +(16.6004 - 2.33303i) q^{97} +(2.20713 + 1.85200i) q^{98} +(4.89530 + 3.44550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.990268	−	0.139173i	0.700225	−	0.0984102i
$2$	0.990268	−	0.139173i	0.700225	−	0.0984102i
$3$	0.530296	+	2.12690i	0.306167	+	1.22797i	0.904414	+	0.426656i	$0.140309\pi$
$3$	0.530296	+	2.12690i	0.306167	+	1.22797i	−0.598247	+	0.801312i	$0.704136\pi$
$4$	0.961262	−	0.275637i	0.480631	−	0.137819i
$5$	0.0547010	+	1.56643i	0.0244630	+	0.700530i	0.948232	+	0.317579i	$0.102870\pi$
$5$	0.0547010	+	1.56643i	0.0244630	+	0.700530i	−0.923769	+	0.382951i	$0.874908\pi$
$6$	0.821143	+	2.03240i	0.335230	+	0.829724i
$7$	2.87167	+	1.27855i	1.08539	+	0.483247i	0.869884	−	0.493256i	$-0.164193\pi$
$7$	2.87167	+	1.27855i	1.08539	+	0.483247i	0.215506	+	0.976503i	$0.430860\pi$
$8$	0.913545	−	0.406737i	0.322987	−	0.143803i
$9$	−1.59366	+	0.847362i	−0.531219	+	0.282454i
$10$	0.272174	+	1.54358i	0.0860690	+	0.488121i
$11$	−1.49853	−	2.95879i	−0.451822	−	0.892108i
$11$	−1.49853	−	2.95879i	−0.451822	−	0.892108i
$12$	1.09601	+	1.89834i	0.316390	+	0.548004i
$13$	−2.34165	−	1.46322i	−0.649456	−	0.405825i	0.164803	−	0.986326i	$-0.447301\pi$
$13$	−2.34165	−	1.46322i	−0.649456	−	0.405825i	−0.814259	+	0.580501i	$0.802857\pi$
$14$	3.02167	+	0.866449i	0.807574	+	0.231568i
$15$	−3.30264	+	0.947017i	−0.852738	+	0.244519i
$16$	0.848048	−	0.529919i	0.212012	−	0.132480i
$17$	−6.27809	−	3.33812i	−1.52266	−	0.809612i	−0.523558	−	0.851990i	$-0.675396\pi$
$17$	−6.27809	−	3.33812i	−1.52266	−	0.809612i	−0.999102	+	0.0423779i	$0.986507\pi$
$18$	−1.46022	+	1.06091i	−0.344176	+	0.250059i
$19$	2.16967	+	3.78055i	0.497757	+	0.867317i
$19$	2.16967	+	3.78055i	0.497757	+	0.867317i
$20$	0.484349	+	1.49067i	0.108304	+	0.333325i
$21$	−1.19652	+	6.78578i	−0.261101	+	1.48078i
$22$	−1.89573	−	2.72144i	−0.404170	−	0.580213i
$23$	−1.39052	−	0.506108i	−0.289944	−	0.105531i	0.192954	−	0.981208i	$-0.438193\pi$
$23$	−1.39052	−	0.506108i	−0.289944	−	0.105531i	−0.482897	+	0.875677i	$0.660416\pi$
$24$	1.34954	+	1.72733i	0.275473	+	0.352590i
$25$	2.53710	−	0.177411i	0.507420	−	0.0354823i
$26$	−2.52250	−	1.12309i	−0.494703	−	0.220256i
$27$	1.75287	+	1.94675i	0.337339	+	0.374653i
$28$	3.11285	+	0.437482i	0.588273	+	0.0826763i
$29$	1.22673	+	1.18464i	0.227798	+	0.219982i	0.799794	−	0.600274i	$-0.204942\pi$
$29$	1.22673	+	1.18464i	0.227798	+	0.219982i	−0.571996	+	0.820256i	$0.693831\pi$
$30$	−3.13870	+	1.39744i	−0.573046	+	0.255136i
$31$	3.78193	−	4.20026i	0.679255	−	0.754389i	−0.300676	−	0.953726i	$-0.597212\pi$
$31$	3.78193	−	4.20026i	0.679255	−	0.754389i	0.979931	+	0.199337i	$0.0638790\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	5.49839	−	4.75625i	0.957147	−	0.827957i
$34$	−6.68156	−	2.43189i	−1.14588	−	0.417066i
$35$	−1.84568	+	4.56822i	−0.311977	+	0.772170i
$36$	−1.29836	+	1.25381i	−0.216393	+	0.208968i
$37$	2.62851	−	1.90972i	0.432124	−	0.313957i	−0.350374	−	0.936610i	$-0.613945\pi$
$37$	2.62851	−	1.90972i	0.432124	−	0.313957i	0.782498	+	0.622654i	$0.213945\pi$
$38$	2.67471	+	3.44179i	0.433895	+	0.558333i
$39$	1.87037	−	5.75639i	0.299498	−	0.921761i
$40$	0.687097	+	1.40876i	0.108640	+	0.222744i
$41$	0.410003	+	1.64443i	0.0640317	+	0.256817i	0.993777	−	0.111385i	$-0.0355288\pi$
$41$	0.410003	+	1.64443i	0.0640317	+	0.256817i	−0.929746	+	0.368203i	$0.879973\pi$
$42$	−0.240474	+	6.88626i	−0.0371059	+	1.06257i
$43$	−11.8872	+	4.32658i	−1.81278	+	0.659798i	−0.816143	+	0.577850i	$0.803892\pi$
$43$	−11.8872	+	4.32658i	−1.81278	+	0.659798i	−0.996637	+	0.0819482i	$0.973886\pi$
$44$	−2.25603	−	2.43112i	−0.340109	−	0.366505i
$45$	−1.41451	−	2.45000i	−0.210863	−	0.365225i
$46$	−1.44743	−	0.307660i	−0.213411	−	0.0453620i
$47$	3.83207	−	7.85691i	0.558965	−	1.14605i	−0.412959	−	0.910750i	$-0.635505\pi$
$47$	3.83207	−	7.85691i	0.558965	−	1.14605i	0.971923	−	0.235298i	$-0.0756065\pi$
$48$	1.57680	+	1.52270i	0.227592	+	0.219783i
$49$	1.92790	+	2.14115i	0.275414	+	0.305878i
$50$	2.48772	−	0.528781i	0.351817	−	0.0747809i
$51$	3.77060	−	15.1231i	0.527990	−	2.11765i
$52$	−2.65425	−	0.761095i	−0.368079	−	0.105545i
$53$	0.0190311	−	0.544981i	0.00261413	−	0.0748589i	−0.997383	−	0.0723044i	$-0.976965\pi$
$53$	0.0190311	−	0.544981i	0.00261413	−	0.0748589i	0.999997	−	0.00255442i	$-0.000813098\pi$
$54$	2.00674	+	1.68386i	0.273083	+	0.229144i
$55$	4.55277	−	2.50919i	0.613895	−	0.338339i
$56$	3.14344			0.420059
$57$	−6.89028	+	6.61949i	−0.912640	+	0.876773i
$58$	1.37966	+	1.00238i	0.181158	+	0.131619i
$59$	−2.51772	−	5.16209i	−0.327779	−	0.672047i	0.669728	−	0.742606i	$-0.266411\pi$
$59$	−2.51772	−	5.16209i	−0.327779	−	0.672047i	−0.997508	+	0.0705593i	$0.977522\pi$
$60$	−2.91367	+	1.82066i	−0.376153	+	0.235047i
$61$	−4.73404	+	6.05929i	−0.606131	+	0.775812i	−0.988988	−	0.147995i	$-0.952718\pi$
$61$	−4.73404	+	6.05929i	−0.606131	+	0.775812i	0.382857	+	0.923808i	$0.374940\pi$
$62$	3.16056	−	4.68573i	0.401392	−	0.595088i
$63$	−5.65986	+	0.395776i	−0.713075	+	0.0498630i
$64$	0.669131	−	0.743145i	0.0836413	−	0.0928931i
$65$	2.16395	−	3.74807i	0.268405	−	0.464891i
$66$	4.78294	−	5.47519i	0.588739	−	0.673949i
$67$	−0.957384	−	5.42960i	−0.116963	−	0.663331i	−0.985760	−	0.168161i	$-0.946217\pi$
$67$	−0.957384	−	5.42960i	−0.116963	−	0.663331i	0.868796	−	0.495169i	$-0.164894\pi$
$68$	−6.95499	−	1.47833i	−0.843417	−	0.179274i
$69$	0.339055	−	3.22589i	0.0408174	−	0.388352i
$70$	−1.19195	+	4.78063i	−0.142465	+	0.571395i
$71$	−0.319354	−	9.14512i	−0.0379004	−	1.08533i	−0.858175	−	0.513356i	$-0.828402\pi$
$71$	−0.319354	−	9.14512i	−0.0379004	−	1.08533i	0.820275	−	0.571969i	$-0.193820\pi$
$72$	−1.11122	+	1.42230i	−0.130959	+	0.167620i
$73$	6.81009	+	0.476208i	0.797060	+	0.0557359i	0.462478	−	0.886631i	$-0.346960\pi$
$73$	6.81009	+	0.476208i	0.797060	+	0.0557359i	0.334582	+	0.942367i	$0.391405\pi$
$74$	2.33715	−	2.25696i	0.271688	−	0.262366i
$75$	1.72275	+	5.30209i	0.198926	+	0.612232i
$76$	3.12768	+	3.03605i	0.358770	+	0.348259i
$77$	−0.520313	−	10.4126i	−0.0592952	−	1.18663i
$78$	1.05103	−	5.96068i	0.119006	−	0.674914i
$79$	−2.27548	+	5.63200i	−0.256011	+	0.633649i	−0.999379	−	0.0352331i	$-0.988783\pi$
$79$	−2.27548	+	5.63200i	−0.256011	+	0.633649i	0.743368	+	0.668882i	$0.233227\pi$
$80$	0.876472	+	1.29942i	0.0979925	+	0.145280i
$81$	−6.23893	+	9.24959i	−0.693214	+	1.02773i
$82$	0.634874	+	1.57137i	0.0701101	+	0.173529i
$83$	10.5529	−	2.24308i	1.15833	−	0.246210i	0.411615	−	0.911358i	$-0.364965\pi$
$83$	10.5529	−	2.24308i	1.15833	−	0.246210i	0.746712	+	0.665148i	$0.231631\pi$
$84$	0.720249	+	6.85271i	0.0785856	+	0.747692i
$85$	4.88552	−	10.0168i	0.529909	−	1.08647i
$86$	−11.1694	+	5.93886i	−1.20442	+	0.640403i
$87$	−1.86908	+	3.23735i	−0.200387	+	0.347080i
$88$	−2.57242	−	2.09348i	−0.274221	−	0.223166i
$89$	−6.95620	+	5.83694i	−0.737356	+	0.618715i	−0.932126	−	0.362134i	$-0.882048\pi$
$89$	−6.95620	+	5.83694i	−0.737356	+	0.618715i	0.194770	+	0.980849i	$0.437604\pi$
$90$	−1.74172	−	2.22930i	−0.183593	−	0.234989i
$91$	−4.85364	−	7.19581i	−0.508799	−	0.754326i
$92$	−1.47616	−	0.103223i	−0.153900	−	0.0107617i
$93$	10.9391	+	5.81642i	1.13433	+	0.603134i
$94$	2.70131	−	8.31376i	0.278618	−	0.857499i
$95$	−5.80329	+	3.60545i	−0.595405	+	0.369911i
$96$	1.77338	+	1.28843i	0.180995	+	0.131500i
$97$	16.6004	−	2.33303i	1.68551	−	0.236883i	0.769676	−	0.638434i	$-0.220418\pi$
$97$	16.6004	−	2.33303i	1.68551	−	0.236883i	0.915837	+	0.401551i	$0.131529\pi$
$98$	2.20713	+	1.85200i	0.222953	+	0.187080i
$99$	4.89530	+	3.44550i	0.491996	+	0.346285i
$100$	2.38992	−	0.869859i	0.238992	−	0.0869859i
$101$	2.89320	+	1.80787i	0.287884	+	0.179890i	0.666172	−	0.745798i	$-0.267932\pi$
$101$	2.89320	+	1.80787i	0.287884	+	0.179890i	−0.378288	+	0.925688i	$0.623487\pi$
$102$	1.62918	−	15.5007i	0.161313	−	1.53479i
$103$	0.642686	+	6.11475i	0.0633257	+	0.602504i	0.979461	+	0.201634i	$0.0646252\pi$
$103$	0.642686	+	6.11475i	0.0633257	+	0.602504i	−0.916135	+	0.400869i	$0.868708\pi$
$104$	−2.73435	−	0.384287i	−0.268125	−	0.0376825i
$105$	−10.6949	−	1.50307i	−1.04372	−	0.146685i
$106$	−0.0570007	−	0.542326i	−0.00553640	−	0.0526753i
$107$	1.02051	−	9.70947i	0.0986561	−	0.938650i	−0.827489	−	0.561482i	$-0.810231\pi$
$107$	1.02051	−	9.70947i	0.0986561	−	0.938650i	0.926145	−	0.377168i	$-0.123102\pi$
$108$	2.22156	+	1.38819i	0.213770	+	0.133578i
$109$	−14.1253	+	5.14119i	−1.35296	+	0.492436i	−0.913870	−	0.406008i	$-0.866921\pi$
$109$	−14.1253	+	5.14119i	−1.35296	+	0.492436i	−0.439088	+	0.898444i	$0.644698\pi$
$110$	4.15925	−	3.11839i	0.396569	−	0.297327i
$111$	5.45568	+	4.57786i	0.517830	+	0.434511i
$112$	3.11285	−	0.437482i	0.294136	−	0.0413382i
$113$	8.04520	+	5.84518i	0.756829	+	0.549868i	0.897936	−	0.440126i	$-0.145066\pi$
$113$	8.04520	+	5.84518i	0.756829	+	0.549868i	−0.141107	+	0.989994i	$0.545066\pi$
$114$	−5.90197	+	7.51401i	−0.552770	+	0.703752i
$115$	0.716722	−	2.20584i	0.0668347	−	0.205696i
$116$	1.50574	+	0.800616i	0.139804	+	0.0743353i
$117$	4.97166	+	0.347652i	0.459630	+	0.0321405i
$118$	−3.21164	−	4.76145i	−0.295656	−	0.438327i
$119$	−13.7607	−	17.6128i	−1.26144	−	1.61457i
$120$	−2.63193	+	2.20845i	−0.240261	+	0.201603i
$121$	−6.50885	+	8.86763i	−0.591713	+	0.806149i
$122$	−3.84467	+	6.65917i	−0.348080	+	0.602893i
$123$	−3.28012	+	1.74407i	−0.295759	+	0.157258i
$124$	2.47768	−	5.07999i	0.222502	−	0.456197i
$125$	1.23587	+	11.7585i	0.110539	+	1.05171i
$126$	−5.54969	+	1.17962i	−0.494406	+	0.105089i
$127$	−7.01465	−	17.3619i	−0.622450	−	1.54062i	−0.827262	−	0.561816i	$-0.810103\pi$
$127$	−7.01465	−	17.3619i	−0.622450	−	1.54062i	0.204813	−	0.978801i	$-0.434342\pi$
$128$	0.559193	−	0.829038i	0.0494261	−	0.0732773i
$129$	−15.5060	−	22.9885i	−1.36522	−	2.02403i
$130$	1.62126	−	4.01276i	0.142194	−	0.351942i
$131$	2.30975	−	13.0993i	0.201804	−	1.14449i	−0.700587	−	0.713567i	$-0.747078\pi$
$131$	2.30975	−	13.0993i	0.201804	−	1.14449i	0.902390	−	0.430919i	$-0.141811\pi$
$132$	3.97439	−	6.08756i	0.345926	−	0.529854i
$133$	1.39697	+	13.6305i	0.121133	+	1.18192i
$134$	−1.70372	−	5.24351i	−0.147179	−	0.452971i
$135$	−2.95358	+	2.85223i	−0.254203	+	0.245481i
$136$	−7.09305	−	0.495994i	−0.608224	−	0.0425312i
$137$	−4.58241	+	5.86522i	−0.391502	+	0.501100i	−0.942869	−	0.333163i	$-0.891884\pi$
$137$	−4.58241	+	5.86522i	−0.391502	+	0.501100i	0.551367	+	0.834263i	$0.314106\pi$
$138$	−0.113202	−	3.24168i	−0.00963640	−	0.275950i
$139$	−3.89145	+	15.6078i	−0.330069	+	1.32383i	0.544430	+	0.838806i	$0.316746\pi$
$139$	−3.89145	+	15.6078i	−0.330069	+	1.32383i	−0.874499	+	0.485027i	$0.838810\pi$
$140$	−0.515010	+	4.89999i	−0.0435263	+	0.414125i
$141$	18.7430	+	3.98395i	1.57845	+	0.335509i
$142$	−1.58900	−	9.01167i	−0.133346	−	0.756243i
$143$	−0.820350	+	9.12111i	−0.0686011	+	0.762746i
$144$	−0.902464	+	1.56311i	−0.0752053	+	0.130259i
$145$	−1.78856	+	1.98639i	−0.148531	+	0.164961i
$146$	6.81009	−	0.476208i	0.563607	−	0.0394112i
$147$	−3.53165	+	5.23589i	−0.291286	+	0.431849i
$148$	2.00029	−	2.56026i	0.164423	−	0.210452i
$149$	−18.6037	+	11.6249i	−1.52407	+	0.952347i	−0.529500	+	0.848310i	$0.677621\pi$
$149$	−18.6037	+	11.6249i	−1.52407	+	0.952347i	−0.994573	+	0.104037i	$0.966824\pi$
$150$	2.44389	+	5.01073i	0.199543	+	0.409124i
$151$	−5.64590	−	4.10199i	−0.459457	−	0.333815i	0.333861	−	0.942622i	$-0.391648\pi$
$151$	−5.64590	−	4.10199i	−0.459457	−	0.333815i	−0.793318	+	0.608807i	$0.791648\pi$
$152$	3.51978	+	2.57121i	0.285492	+	0.208553i
$153$	12.8337			1.03754
$154$	−1.96440	−	10.2389i	−0.158296	−	0.825071i
$155$	6.78630	+	5.69438i	0.545089	+	0.457384i
$156$	0.211234	−	6.04894i	0.0169122	−	0.484303i
$157$	19.8888	+	5.70302i	1.58730	+	0.455150i	0.949166	−	0.314776i	$-0.101929\pi$
$157$	19.8888	+	5.70302i	1.58730	+	0.455150i	0.638132	+	0.769927i	$0.279707\pi$
$158$	−1.46951	+	5.89387i	−0.116908	+	0.468891i
$159$	1.16921	−	0.248524i	0.0927246	−	0.0197092i
$160$	1.04879	+	1.16480i	0.0829139	+	0.0920852i
$161$	−3.34604	−	3.23123i	−0.263705	−	0.254657i
$162$	−4.89092	+	10.0279i	−0.384267	+	0.787863i
$163$	−11.3942	−	2.42191i	−0.892461	−	0.189698i	−0.261215	−	0.965281i	$-0.584123\pi$
$163$	−11.3942	−	2.42191i	−0.892461	−	0.189698i	−0.631246	+	0.775582i	$0.717456\pi$
$164$	0.847387	+	1.46772i	0.0661698	+	0.114610i
$165$	7.75111	+	8.35268i	0.603423	+	0.650256i
$166$	10.1380	−	3.68992i	0.786860	−	0.286394i
$167$	−0.178758	+	5.11897i	−0.0138327	+	0.396118i	0.972652	+	0.232266i	$0.0746140\pi$
$167$	−0.178758	+	5.11897i	−0.0138327	+	0.396118i	−0.986485	+	0.163852i	$0.947608\pi$
$168$	1.66695	+	6.68578i	0.128608	+	0.515819i
$169$	−2.35654	−	4.83162i	−0.181272	−	0.371663i
$170$	3.44390	−	10.5992i	0.264135	−	0.812925i
$171$	−6.66120	−	4.18639i	−0.509395	−	0.320141i
$172$	−10.2341	+	7.43553i	−0.780345	+	0.566954i
$173$	−7.15161	+	6.90623i	−0.543727	+	0.525071i	−0.915001	−	0.403452i	$-0.867810\pi$
$173$	−7.15161	+	6.90623i	−0.543727	+	0.525071i	0.371274	+	0.928523i	$0.378921\pi$
$174$	−1.40034	+	3.46597i	−0.106160	+	0.262754i
$175$	7.51255	+	2.73435i	0.567896	+	0.206697i
$176$	−2.83874	−	1.71510i	−0.213978	−	0.129280i
$177$	9.64412	−	8.09238i	0.724897	−	0.608261i
$178$	−6.07616	+	6.74825i	−0.455427	+	0.505803i
$179$	2.11434	−	0.941364i	0.158033	−	0.0703609i	−0.326196	−	0.945302i	$-0.605767\pi$
$179$	2.11434	−	0.941364i	0.158033	−	0.0703609i	0.484229	+	0.874941i	$0.339100\pi$
$180$	−2.03503	−	1.96520i	−0.151682	−	0.146478i
$181$	−4.29641	−	0.603822i	−0.319350	−	0.0448817i	−0.0223230	−	0.999751i	$-0.507106\pi$
$181$	−4.29641	−	0.603822i	−0.319350	−	0.0448817i	−0.297027	+	0.954869i	$0.595995\pi$
$182$	−5.80787	−	6.45029i	−0.430508	−	0.478127i
$183$	−15.3980	−	6.85561i	−1.13825	−	0.506781i
$184$	−1.47616	+	0.103223i	−0.108824	+	0.00760970i
$185$	3.13523	+	4.01292i	0.230507	+	0.295036i
$186$	11.6421	+	4.23738i	0.853641	+	0.310700i
$187$	−0.468911	+	23.5778i	−0.0342901	+	1.72418i
$188$	1.51796	−	8.60880i	0.110709	−	0.627861i
$189$	2.54463	+	7.83157i	0.185095	+	0.569663i
$190$	−5.24503	+	4.37802i	−0.380514	+	0.317615i
$191$	−17.1919	+	12.4907i	−1.24396	+	0.903792i	−0.997856	−	0.0654503i	$-0.979152\pi$
$191$	−17.1919	+	12.4907i	−1.24396	+	0.903792i	−0.246107	+	0.969243i	$0.579152\pi$
$192$	1.93543	+	1.02909i	0.139678	+	0.0742681i
$193$	15.8074	−	9.87757i	1.13784	−	0.711003i	0.175942	−	0.984401i	$-0.443703\pi$
$193$	15.8074	−	9.87757i	1.13784	−	0.711003i	0.961901	+	0.273397i	$0.0881474\pi$
$194$	16.1141	−	4.62065i	1.15693	−	0.331743i
$195$	9.11932	+	2.61492i	0.653048	+	0.187258i
$196$	2.44339	+	1.52680i	0.174528	+	0.109057i
$197$	−6.44641	−	11.1655i	−0.459287	−	0.795509i	0.539636	−	0.841898i	$-0.318562\pi$
$197$	−6.44641	−	11.1655i	−0.459287	−	0.795509i	−0.998923	+	0.0463893i	$0.985229\pi$
$198$	5.32718	+	2.73067i	0.378586	+	0.194060i
$199$	1.23750	+	7.01824i	0.0877244	+	0.497510i	0.996735	+	0.0807377i	$0.0257276\pi$
$199$	1.23750	+	7.01824i	0.0877244	+	0.497510i	−0.909011	+	0.416772i	$0.863161\pi$
$200$	2.24560	−	1.19401i	0.158788	−	0.0844289i
$201$	11.0405	−	4.91556i	0.778738	−	0.346717i
$202$	3.11665	+	1.38762i	0.219287	+	0.0976328i
$203$	2.00815	+	4.97034i	0.140944	+	0.348849i
$204$	−0.543945	−	15.5765i	−0.0380838	−	1.09058i
$205$	−2.55347	+	0.732194i	−0.178342	+	0.0511387i
$206$	1.48744	+	5.96579i	0.103635	+	0.415656i
$207$	2.64487	−	0.371712i	0.183831	−	0.0258358i
$208$	−2.76122			−0.191456
$209$	7.93452	−	12.0848i	0.548842	−	0.835926i
$210$	−10.8000			−0.745272
$211$	17.9135	−	2.51758i	1.23322	−	0.173317i	0.507707	−	0.861530i	$-0.330493\pi$
$211$	17.9135	−	2.51758i	1.23322	−	0.173317i	0.725509	+	0.688213i	$0.241604\pi$
$212$	−0.131923	−	0.529115i	−0.00906052	−	0.0363398i
$213$	19.2814	−	5.52886i	1.32114	−	0.378831i
$214$	−0.340722	−	9.75700i	−0.0232913	−	0.666975i
$215$	−7.42754	−	18.3838i	−0.506554	−	1.25377i
$216$	2.39314	+	1.06549i	0.162832	+	0.0724977i
$217$	16.2307	−	7.22638i	1.10181	−	0.490559i
$218$	−13.2723	+	7.05701i	−0.898914	+	0.477961i
$219$	2.59852	+	14.7369i	0.175591	+	0.995829i
$220$	3.68478	−	3.66690i	0.248428	−	0.247222i
$221$	9.81665	+	17.0029i	0.660339	+	1.14374i
$222$	6.03970	+	3.77403i	0.405358	+	0.253296i
$223$	−4.33983	−	1.24443i	−0.290616	−	0.0833329i	0.127162	−	0.991882i	$-0.459413\pi$
$223$	−4.33983	−	1.24443i	−0.290616	−	0.0833329i	−0.417778	+	0.908549i	$0.637191\pi$
$224$	3.02167	−	0.866449i	0.201894	−	0.0578920i
$225$	−3.89294	+	2.43258i	−0.259529	+	0.162172i
$226$	8.78040	+	4.66862i	0.584063	+	0.310552i
$227$	12.3653	−	8.98391i	0.820713	−	0.596283i	−0.0962033	−	0.995362i	$-0.530670\pi$
$227$	12.3653	−	8.98391i	0.820713	−	0.596283i	0.916917	+	0.399078i	$0.130670\pi$
$228$	−4.79878	+	8.26228i	−0.317807	+	0.547183i
$229$	1.29890	+	3.99760i	0.0858336	+	0.264169i	0.984757	−	0.173938i	$-0.0556492\pi$
$229$	1.29890	+	3.99760i	0.0858336	+	0.264169i	−0.898923	+	0.438107i	$0.855649\pi$
$230$	0.402753	−	2.28412i	0.0265567	−	0.150611i
$231$	21.8707	−	6.62842i	1.43899	−	0.436118i
$232$	1.60251	+	0.583266i	0.105210	+	0.0382933i
$233$	0.519732	+	0.665227i	0.0340488	+	0.0435805i	0.804734	−	0.593636i	$-0.202308\pi$
$233$	0.519732	+	0.665227i	0.0340488	+	0.0435805i	−0.770685	+	0.637216i	$0.780086\pi$
$234$	4.97166	−	0.347652i	0.325008	−	0.0227267i
$235$	12.5169	+	5.57290i	0.816515	+	0.363536i
$236$	−3.84305	−	4.26814i	−0.250161	−	0.277832i
$237$	−13.1854	−	1.85309i	−0.856483	−	0.120371i
$238$	−16.0780	−	15.5263i	−1.04218	−	1.00642i
$239$	−24.0154	+	10.6923i	−1.55343	+	0.691630i	−0.990832	−	0.135102i	$-0.956864\pi$
$239$	−24.0154	+	10.6923i	−1.55343	+	0.691630i	−0.562596	+	0.826732i	$0.690197\pi$
$240$	−2.29896	+	2.55325i	−0.148397	+	0.164812i
$241$	3.57373	−	2.99871i	0.230204	−	0.193164i	−0.520388	−	0.853930i	$-0.674213\pi$
$241$	3.57373	−	2.99871i	0.230204	−	0.193164i	0.750592	+	0.660766i	$0.229768\pi$
$242$	−5.21137	+	9.68719i	−0.334999	+	0.622716i
$243$	−15.5965	−	5.67668i	−1.00052	−	0.364159i
$244$	−2.88048	+	7.12944i	−0.184404	+	0.456416i
$245$	−3.24851	+	3.13705i	−0.207539	+	0.200418i
$246$	−3.00547	+	2.18360i	−0.191622	+	0.139222i
$247$	0.451175	−	12.0274i	0.0287076	−	0.765286i
$248$	1.74657	−	5.37538i	0.110907	−	0.341337i
$249$	10.3670	+	21.2554i	0.656979	+	1.34701i
$250$	2.86031	+	11.4721i	0.180902	+	0.725557i
$251$	−0.664129	+	19.0182i	−0.0419194	+	1.20042i	0.778123	+	0.628112i	$0.216172\pi$
$251$	−0.664129	+	19.0182i	−0.0419194	+	1.20042i	−0.820042	+	0.572303i	$0.806050\pi$
$252$	−5.33151	+	1.94051i	−0.335854	+	0.122241i
$253$	0.586264	+	4.87267i	0.0368581	+	0.306342i
$254$	−9.36269	−	16.2167i	−0.587468	−	1.01752i
$255$	23.8955	+	5.07915i	1.49640	+	0.318069i
$256$	0.438371	−	0.898794i	0.0273982	−	0.0561746i
$257$	−4.29362	−	4.14630i	−0.267829	−	0.258639i	0.548601	−	0.836085i	$-0.315161\pi$
$257$	−4.29362	−	4.14630i	−0.267829	−	0.258639i	−0.816429	+	0.577445i	$0.804050\pi$
$258$	−18.5544	−	20.6068i	−1.15515	−	1.28292i
$259$	9.98989	−	2.12342i	0.620742	−	0.131943i
$260$	1.04701	−	4.19934i	0.0649330	−	0.260432i
$261$	−2.95881	−	0.848424i	−0.183145	−	0.0525161i
$262$	0.464210	−	13.2932i	0.0286790	−	0.821258i
$263$	−5.84983	−	4.90859i	−0.360716	−	0.302677i	0.444360	−	0.895848i	$-0.353431\pi$
$263$	−5.84983	−	4.90859i	−0.360716	−	0.302677i	−0.805076	+	0.593172i	$0.797876\pi$
$264$	3.08849	−	6.58145i	0.190083	−	0.405060i
$265$	0.854717			0.0525048
$266$	3.28038	+	13.3035i	0.201133	+	0.815687i
$267$	−16.1035	−	11.6998i	−0.985515	−	0.716019i
$268$	−2.41690	−	4.95537i	−0.147635	−	0.302697i
$269$	−20.1363	+	12.5825i	−1.22773	+	0.767171i	−0.979483	−	0.201526i	$-0.935410\pi$
$269$	−20.1363	+	12.5825i	−1.22773	+	0.767171i	−0.248247	+	0.968697i	$0.579854\pi$
$270$	−2.52788	+	3.23554i	−0.153842	+	0.196908i
$271$	−2.74502	+	4.06965i	−0.166748	+	0.247214i	−0.903145	−	0.429336i	$-0.858748\pi$
$271$	−2.74502	+	4.06965i	−0.166748	+	0.247214i	0.736397	+	0.676550i	$0.236526\pi$
$272$	−7.09305	+	0.495994i	−0.430079	+	0.0300741i
$273$	12.7309	−	14.1391i	0.770511	−	0.855739i
$274$	−3.72154	+	6.44589i	−0.224826	+	0.389411i
$275$	−4.32683	−	7.24089i	−0.260918	−	0.436642i
$276$	−0.563256	−	3.19438i	−0.0339040	−	0.192279i
$277$	8.46976	+	1.80030i	0.508898	+	0.108170i	0.455203	−	0.890388i	$-0.349567\pi$
$277$	8.46976	+	1.80030i	0.508898	+	0.108170i	0.0536953	+	0.998557i	$0.482900\pi$
$278$	−1.68140	+	15.9975i	−0.100844	+	0.959464i
$279$	−2.46796	+	9.89844i	−0.147753	+	0.592604i
$280$	0.171949	+	4.92398i	0.0102759	+	0.294264i
$281$	3.30034	−	4.22424i	0.196882	−	0.251997i	−0.679431	−	0.733739i	$-0.737773\pi$
$281$	3.30034	−	4.22424i	0.196882	−	0.251997i	0.876313	+	0.481742i	$0.159996\pi$
$282$	19.1151	+	1.33665i	1.13828	+	0.0795966i
$283$	−20.7776	+	20.0647i	−1.23510	+	1.19272i	−0.261312	+	0.965254i	$0.584155\pi$
$283$	−20.7776	+	20.0647i	−1.23510	+	1.19272i	−0.973786	+	0.227466i	$0.926956\pi$
$284$	−2.82772	−	8.70282i	−0.167794	−	0.516418i
$285$	−10.7459	−	10.4311i	−0.636532	−	0.617883i
$286$	0.457047	+	9.14651i	0.0270257	+	0.540845i
$287$	−0.925096	+	5.24648i	−0.0546067	+	0.309690i
$288$	−0.676138	+	1.67350i	−0.0398418	+	0.0986119i
$289$	18.7650	+	27.8203i	1.10383	+	1.63649i
$290$	−1.49470	+	2.21598i	−0.0877716	+	0.130127i
$291$	13.7652	+	34.0702i	0.806933	+	1.99723i
$292$	6.67754	−	1.41935i	0.390773	−	0.0830614i
$293$	1.68052	+	15.9890i	0.0981768	+	0.934090i	0.927122	+	0.374760i	$0.122275\pi$
$293$	1.68052	+	15.9890i	0.0981768	+	0.934090i	−0.828945	+	0.559330i	$0.811059\pi$
$294$	−2.76859	+	5.67645i	−0.161467	+	0.331057i
$295$	7.94834	−	4.22621i	0.462770	−	0.246059i
$296$	1.62451	−	2.81373i	0.0944226	−	0.163545i
$297$	3.13332	−	8.10362i	0.181814	−	0.470219i
$298$	−16.8048	+	14.1009i	−0.973474	+	0.816842i
$299$	2.51556	+	3.21977i	0.145479	+	0.186204i
$300$	3.11747	+	4.62184i	0.179987	+	0.266842i
$301$	−39.6679	−	2.77385i	−2.28642	−	0.159882i
$302$	−6.16184	−	3.27631i	−0.354574	−	0.188530i
$303$	−2.31091	+	7.11226i	−0.132759	+	0.408589i
$304$	3.84337	+	2.05633i	0.220432	+	0.117939i
$305$	−9.75042	−	7.08410i	−0.558308	−	0.405634i
$306$	12.7088	−	1.78611i	0.726514	−	0.102105i
$307$	21.6889	+	18.1991i	1.23785	+	1.03868i	0.997689	+	0.0679464i	$0.0216447\pi$
$307$	21.6889	+	18.1991i	1.23785	+	1.03868i	0.240161	+	0.970733i	$0.422800\pi$
$308$	−3.37026	−	9.86583i	−0.192038	−	0.562158i
$309$	−12.6647	+	4.60956i	−0.720467	+	0.262228i
$310$	7.51276	+	4.69449i	0.426696	+	0.266629i
$311$	1.02419	−	9.74448i	0.0580763	−	0.552559i	−0.926338	−	0.376693i	$-0.877061\pi$
$311$	1.02419	−	9.74448i	0.0580763	−	0.552559i	0.984414	−	0.175865i	$-0.0562723\pi$
$312$	−0.632672	−	6.01947i	−0.0358180	−	0.340786i
$313$	−12.7533	−	1.79236i	−0.720857	−	0.101310i	−0.230801	−	0.973001i	$-0.574135\pi$
$313$	−12.7533	−	1.79236i	−0.720857	−	0.101310i	−0.490056	+	0.871691i	$0.663024\pi$
$314$	20.4889	+	2.87953i	1.15626	+	0.162501i
$315$	−0.929556	−	8.84413i	−0.0523745	−	0.498310i
$316$	−0.634938	+	6.04103i	−0.0357180	+	0.339835i
$317$	−18.7718	−	11.7299i	−1.05433	−	0.658818i	−0.112069	−	0.993700i	$-0.535748\pi$
$317$	−18.7718	−	11.7299i	−1.05433	−	0.658818i	−0.942260	+	0.334883i	$0.891303\pi$
$318$	1.12325	−	0.408828i	0.0629885	−	0.0229260i
$319$	1.66681	−	5.40485i	0.0933235	−	0.302613i
$320$	1.20069	+	1.00750i	0.0671205	+	0.0563208i
$321$	21.1923	−	2.97838i	1.18284	−	0.166237i
$322$	−3.76317	−	2.73411i	−0.209714	−	0.152366i
$323$	−1.00149	−	30.9772i	−0.0557242	−	1.72362i
$324$	−3.44771	+	10.6110i	−0.191539	+	0.589498i
$325$	−6.20059	−	3.29691i	−0.343947	−	0.182880i
$326$	−11.6204	−	0.812574i	−0.643592	−	0.0450043i
$327$	−18.4254	−	27.3168i	−1.01893	−	1.51062i
$328$	1.04341	+	1.33550i	0.0576125	+	0.0737407i
$329$	21.0499	−	17.6630i	1.16052	−	0.973791i
$330$	8.83815	+	7.19265i	0.486524	+	0.395942i
$331$	−9.08835	+	15.7415i	−0.499541	+	0.865230i	−1.00000		0.000530140i	$-0.999831\pi$
$331$	−9.08835	+	15.7415i	−0.499541	+	0.865230i	0.500459	+	0.865760i	$0.333165\pi$
$332$	9.52578	−	5.06495i	0.522795	−	0.277975i
$333$	−2.57071	+	5.27074i	−0.140874	+	0.288835i
$334$	0.535404	+	5.09403i	0.0292960	+	0.278733i
$335$	8.45273	−	1.79668i	0.461822	−	0.0981632i
$336$	2.58121	+	6.38872i	0.140817	+	0.348533i
$337$	−10.1079	+	14.9856i	−0.550613	+	0.816317i	−0.996909	−	0.0785681i	$-0.974965\pi$
$337$	−10.1079	+	14.9856i	−0.550613	+	0.816317i	0.446296	+	0.894886i	$0.352743\pi$
$338$	−3.00604	−	4.45663i	−0.163507	−	0.242409i
$339$	−8.16579	+	20.2110i	−0.443505	+	1.09771i
$340$	1.93526	−	10.9754i	0.104954	−	0.595224i
$341$	−18.0950	−	4.89573i	−0.979899	−	0.265119i
$342$	−7.17901	−	3.21859i	−0.388196	−	0.174041i
$343$	−4.00090	−	12.3135i	−0.216028	−	0.664867i
$344$	−9.09971	+	8.78749i	−0.490623	+	0.473790i
$345$	5.07169	+	0.354647i	0.273050	+	0.0190935i
$346$	−6.12085	+	7.83433i	−0.329059	+	0.421176i
$347$	0.221462	+	6.34183i	0.0118887	+	0.340448i	0.990732	+	0.135834i	$0.0433715\pi$
$347$	0.221462	+	6.34183i	0.0118887	+	0.340448i	−0.978843	+	0.204613i	$0.934406\pi$
$348$	−0.904344	+	3.62713i	−0.0484779	+	0.194434i
$349$	2.04364	−	19.4440i	0.109394	−	1.04081i	−0.792801	−	0.609481i	$-0.791378\pi$
$349$	2.04364	−	19.4440i	0.109394	−	1.04081i	0.902194	−	0.431330i	$-0.141956\pi$
$350$	7.81999	+	1.66219i	0.417996	+	0.0888478i
$351$	−1.25606	−	7.12344i	−0.0670433	−	0.380221i
$352$	−3.04981	−	1.30333i	−0.162555	−	0.0694677i
$353$	−2.84689	+	4.93095i	−0.151524	+	0.262448i	−0.931788	−	0.363003i	$-0.881752\pi$
$353$	−2.84689	+	4.93095i	−0.151524	+	0.262448i	0.780264	+	0.625451i	$0.215085\pi$
$354$	8.42403	−	9.35583i	0.447732	−	0.497257i
$355$	14.3077	−	1.00049i	0.759376	−	0.0531007i
$356$	−5.07785	+	7.52822i	−0.269125	+	0.398995i
$357$	30.1636	−	38.6076i	1.59642	−	2.04333i
$358$	1.96275	−	1.22646i	0.103735	−	0.0648205i
$359$	−13.6100	−	27.9045i	−0.718306	−	1.47275i	−0.874503	−	0.485019i	$-0.838813\pi$
$359$	−13.6100	−	27.9045i	−0.718306	−	1.47275i	0.156198	−	0.987726i	$-0.450076\pi$
$360$	−2.28873	−	1.66286i	−0.120626	−	0.0876402i
$361$	−9.58504	+	16.4051i	−0.504476	+	0.863426i
$362$	−4.33864			−0.228034
$363$	−22.3122	−	9.14120i	−1.17109	−	0.479789i
$364$	−6.64905	−	5.57922i	−0.348505	−	0.292430i
$365$	−0.373428	+	10.6936i	−0.0195461	+	0.559728i
$366$	−16.2022	−	4.64591i	−0.846904	−	0.242846i
$367$	3.03430	−	12.1699i	0.158389	−	0.635265i	−0.837639	−	0.546225i	$-0.816064\pi$
$367$	3.03430	−	12.1699i	0.158389	−	0.635265i	0.996028	−	0.0890404i	$-0.0283800\pi$
$368$	−1.44743	+	0.307660i	−0.0754523	+	0.0160379i
$369$	−2.04683	−	2.27324i	−0.106554	−	0.118340i
$370$	3.66321	+	3.53752i	0.190441	+	0.183907i
$371$	0.751437	−	1.54067i	0.0390127	−	0.0799878i
$372$	12.1185	+	2.57588i	0.628317	+	0.133553i
$373$	5.68720	+	9.85052i	0.294472	+	0.510040i	0.974862	−	0.222810i	$-0.0715229\pi$
$373$	5.68720	+	9.85052i	0.294472	+	0.510040i	−0.680390	+	0.732850i	$0.738190\pi$
$374$	2.81704	+	23.4136i	0.145666	+	1.21069i
$375$	−24.3538	+	8.86406i	−1.25762	+	0.457738i
$376$	0.305078	−	8.73628i	0.0157332	−	0.450539i
$377$	−1.13918	−	4.56899i	−0.0586706	−	0.235315i
$378$	3.60981	+	7.40121i	0.185669	+	0.380677i
$379$	10.3462	−	31.8422i	0.531447	−	1.63563i	−0.219757	−	0.975555i	$-0.570526\pi$
$379$	10.3462	−	31.8422i	0.531447	−	1.63563i	0.751204	−	0.660071i	$-0.229474\pi$
$380$	−4.58468	+	5.06538i	−0.235189	+	0.259848i
$381$	33.2072	−	24.1264i	1.70125	−	1.23603i
$382$	−15.2862	+	14.7618i	−0.782112	+	0.755277i
$383$	7.81820	−	19.3507i	0.399491	−	0.988776i	−0.584633	−	0.811298i	$-0.698762\pi$
$383$	7.81820	−	19.3507i	0.399491	−	0.988776i	0.984125	−	0.177478i	$-0.0567939\pi$
$384$	2.05982	+	0.749713i	0.105115	+	0.0382586i
$385$	16.2822	−	1.38462i	0.829817	−	0.0705665i
$386$	14.2789	−	11.9814i	0.726776	−	0.609838i
$387$	15.2779	−	16.9678i	0.776620	−	0.862524i
$388$	15.3142	−	6.81834i	0.777462	−	0.346149i
$389$	7.27704	+	7.02736i	0.368961	+	0.356301i	0.855906	−	0.517131i	$-0.173000\pi$
$389$	7.27704	+	7.02736i	0.368961	+	0.356301i	−0.486945	+	0.873432i	$0.661889\pi$
$390$	9.39449	+	1.32031i	0.475709	+	0.0668565i
$391$	7.04036	+	7.81912i	0.356046	+	0.395430i
$392$	2.63211	+	1.17189i	0.132941	+	0.0591893i
$393$	29.0857	−	2.03387i	1.46718	−	0.102595i
$394$	−7.93761	−	10.1597i	−0.399891	−	0.511837i
$395$	−8.94662	−	3.25630i	−0.450153	−	0.163842i
$396$	5.65537	+	1.96270i	0.284193	+	0.0986292i
$397$	−2.11483	+	11.9938i	−0.106140	+	0.601950i	0.884619	+	0.466315i	$0.154419\pi$
$397$	−2.11483	+	11.9938i	−0.106140	+	0.601950i	−0.990759	+	0.135635i	$0.956692\pi$
$398$	2.20221	+	6.77771i	0.110387	+	0.339736i
$399$	−28.2500	+	10.1994i	−1.41427	+	0.510610i
$400$	2.05757	−	1.49491i	0.102879	−	0.0747456i
$401$	−8.20989	−	4.36528i	−0.409982	−	0.217992i	0.251652	−	0.967818i	$-0.419026\pi$
$401$	−8.20989	−	4.36528i	−0.409982	−	0.217992i	−0.661635	+	0.749826i	$0.730137\pi$
$402$	10.2490	−	6.40426i	0.511172	−	0.319416i
$403$	−15.0019	+	4.30171i	−0.747296	+	0.214284i
$404$	3.27944	+	0.940364i	0.163158	+	0.0467849i
$405$	−14.8301	−	9.26690i	−0.736915	−	0.460476i
$406$	2.68034	+	4.64249i	0.133023	+	0.230403i
$407$	−9.58935	−	4.91543i	−0.475326	−	0.243649i
$408$	−2.70649	−	15.3492i	−0.133991	−	0.759901i
$409$	4.01572	−	2.13520i	0.198565	−	0.105579i	−0.367212	−	0.930137i	$-0.619688\pi$
$409$	4.01572	−	2.13520i	0.198565	−	0.105579i	0.565776	+	0.824559i	$0.308577\pi$
$410$	−2.42671	+	1.08044i	−0.119847	+	0.0533592i
$411$	−14.9048	−	6.63604i	−0.735199	−	0.327332i
$412$	2.30324	+	5.70072i	0.113473	+	0.280854i
$413$	−0.630071	−	18.0429i	−0.0310038	−	0.887831i
$414$	2.56740	−	0.736190i	0.126181	−	0.0361817i
$415$	4.09089	+	16.4076i	0.200814	+	0.805420i
$416$	−2.73435	+	0.384287i	−0.134062	+	0.0188412i
$417$	−35.2598			−1.72668
$418$	6.17542	−	13.0715i	0.302050	−	0.639348i
$419$	17.5666			0.858184			0.429092	−	0.903261i	$-0.358834\pi$
$419$	17.5666			0.858184			0.429092	+	0.903261i	$0.358834\pi$
$420$	−10.6949	+	1.50307i	−0.521858	+	0.0733424i
$421$	1.67852	+	6.73219i	0.0818063	+	0.328107i	0.997230	−	0.0743854i	$-0.0236995\pi$
$421$	1.67852	+	6.73219i	0.0818063	+	0.328107i	−0.915423	+	0.402493i	$0.868144\pi$
$422$	17.3888	−	4.98615i	0.846473	−	0.242722i
$423$	0.550643	+	15.7684i	0.0267732	+	0.766684i
$424$	−0.204278	−	0.505605i	−0.00992061	−	0.0245544i
$425$	−16.5204	−	7.35534i	−0.801355	−	0.356786i
$426$	18.3243	−	8.15851i	0.887815	−	0.395281i
$427$	−21.3417	+	11.3476i	−1.03280	+	0.549148i
$428$	−1.69532	−	9.61463i	−0.0819463	−	0.464741i
$429$	−19.8347	+	3.09209i	−0.957630	+	0.149287i
$430$	−9.91379	−	17.1712i	−0.478086	−	0.828068i
$431$	16.8051	+	10.5010i	0.809474	+	0.505816i	0.870411	−	0.492326i	$-0.163853\pi$
$431$	16.8051	+	10.5010i	0.809474	+	0.505816i	−0.0609367	+	0.998142i	$0.519409\pi$
$432$	2.51814	+	0.722064i	0.121154	+	0.0347403i
$433$	11.4735	−	3.28998i	0.551382	−	0.158106i	0.0116332	−	0.999932i	$-0.496297\pi$
$433$	11.4735	−	3.28998i	0.551382	−	0.158106i	0.539749	+	0.841826i	$0.318519\pi$
$434$	15.0670	−	9.41493i	0.723241	−	0.451931i
$435$	−5.17333	−	2.75071i	−0.248042	−	0.131886i
$436$	−12.1610	+	8.83548i	−0.582406	+	0.423143i
$437$	−1.10361	−	6.35502i	−0.0527929	−	0.304002i
$438$	4.62421	+	14.2319i	0.220953	+	0.680025i
$439$	2.79408	−	15.8460i	0.133354	−	0.756289i	−0.842638	−	0.538481i	$-0.818998\pi$
$439$	2.79408	−	15.8460i	0.133354	−	0.756289i	0.975992	−	0.217808i	$-0.0698906\pi$
$440$	3.13858	−	4.14404i	0.149626	−	0.197559i
$441$	−4.88673	−	1.77863i	−0.232702	−	0.0846965i
$442$	12.0875	+	15.4712i	0.574942	+	0.735892i
$443$	34.6708	−	2.42442i	1.64726	−	0.115188i	0.784274	−	0.620415i	$-0.213036\pi$
$443$	34.6708	−	2.42442i	1.64726	−	0.115188i	0.862986	+	0.505227i	$0.168591\pi$
$444$	6.50617	+	2.89673i	0.308769	+	0.137473i
$445$	−9.52369	−	10.5771i	−0.451466	−	0.501404i
$446$	−4.47078	−	0.628328i	−0.211698	−	0.0297522i
$447$	−34.5904	−	33.4036i	−1.63607	−	1.57994i
$448$	2.87167	−	1.27855i	0.135674	−	0.0604059i
$449$	10.0974	−	11.2142i	0.476524	−	0.529233i	−0.456175	−	0.889890i	$-0.650781\pi$
$449$	10.0974	−	11.2142i	0.476524	−	0.529233i	0.932699	+	0.360657i	$0.117448\pi$
$450$	−3.51650	+	2.95069i	−0.165769	+	0.139097i
$451$	4.25113	−	3.67734i	0.200178	−	0.173159i
$452$	9.34469	+	3.40119i	0.439537	+	0.159979i
$453$	5.73052	−	14.1835i	0.269244	−	0.666401i
$454$	10.9946	−	10.6174i	0.516004	−	0.498299i
$455$	11.0063	−	7.99651i	0.515981	−	0.374882i
$456$	−3.60220	+	8.84974i	−0.168688	+	0.414427i
$457$	7.35842	−	22.6469i	0.344212	−	1.05938i	−0.617792	−	0.786342i	$-0.711972\pi$
$457$	7.35842	−	22.6469i	0.344212	−	1.05938i	0.962004	−	0.273035i	$-0.0880275\pi$
$458$	1.84261	+	3.77792i	0.0860997	+	0.176531i
$459$	−4.50614	−	18.0732i	−0.210329	−	0.843583i
$460$	0.0809445	−	2.31795i	0.00377406	−	0.108075i
$461$	−3.57793	+	1.30226i	−0.166641	+	0.0606523i	−0.423993	−	0.905665i	$-0.639372\pi$
$461$	−3.57793	+	1.30226i	−0.166641	+	0.0606523i	0.257353	+	0.966318i	$0.417150\pi$
$462$	20.7353	−	9.60773i	0.964695	−	0.446992i
$463$	2.85805	+	4.95030i	0.132825	+	0.230060i	0.924765	−	0.380540i	$-0.124262\pi$
$463$	2.85805	+	4.95030i	0.132825	+	0.230060i	−0.791939	+	0.610600i	$0.790928\pi$
$464$	1.66809	+	0.354563i	0.0774391	+	0.0164602i
$465$	−8.51264	+	17.4535i	−0.394764	+	0.809387i
$466$	0.607256	+	0.586420i	0.0281306	+	0.0271654i
$467$	−5.86550	−	6.51430i	−0.271423	−	0.301446i	0.591988	−	0.805947i	$-0.298343\pi$
$467$	−5.86550	−	6.51430i	−0.271423	−	0.301446i	−0.863411	+	0.504501i	$0.831677\pi$
$468$	4.87489	−	1.03619i	0.225342	−	0.0478979i
$469$	4.19272	−	16.8161i	0.193602	−	0.776495i
$470$	13.1707	+	3.77664i	0.607520	+	0.174203i
$471$	−1.58281	+	45.3258i	−0.0729321	+	2.08850i
$472$	−4.39966	−	3.69175i	−0.202511	−	0.169927i
$473$	30.6147	+	28.6882i	1.40767	+	1.31908i
$474$	−13.3150			−0.611577
$475$	6.17539	+	9.20670i	0.283346	+	0.422432i
$476$	−18.0823	−	13.1376i	−0.828803	−	0.602161i
$477$	0.431467	+	0.884638i	0.0197555	+	0.0405048i
$478$	−22.2936	+	13.9306i	−1.01969	+	0.637170i
$479$	−2.50593	+	3.20744i	−0.114499	+	0.146552i	−0.841846	−	0.539718i	$-0.818531\pi$
$479$	−2.50593	+	3.20744i	−0.114499	+	0.146552i	0.727347	+	0.686270i	$0.240753\pi$
$480$	−1.92124	+	2.84835i	−0.0876922	+	0.130009i
$481$	−8.94939	+	0.625802i	−0.408057	+	0.0285341i
$482$	3.12161	−	3.46690i	0.142185	−	0.157913i
$483$	5.09812	−	8.83020i	0.231973	−	0.401788i
$484$	−3.81245	+	10.3182i	−0.173293	+	0.469009i
$485$	4.56259	+	25.8758i	0.207177	+	1.17496i
$486$	−16.2348	−	3.45081i	−0.736426	−	0.156532i
$487$	1.92380	−	18.3038i	0.0871758	−	0.829422i	−0.860342	−	0.509718i	$-0.829750\pi$
$487$	1.92380	−	18.3038i	0.0871758	−	0.829422i	0.947517	−	0.319704i	$-0.103584\pi$
$488$	−1.86022	+	7.46094i	−0.0842083	+	0.337741i
$489$	−0.891130	−	25.5186i	−0.0402983	−	1.15399i
$490$	−2.78030	+	3.55862i	−0.125601	+	0.160762i
$491$	−17.7812	−	1.24338i	−0.802453	−	0.0561130i	−0.337361	−	0.941375i	$-0.609534\pi$
$491$	−17.7812	−	1.24338i	−0.802453	−	0.0561130i	−0.465092	+	0.885262i	$0.653979\pi$
$492$	−2.67233	+	2.58064i	−0.120478	+	0.116344i
$493$	−3.74705	−	11.5322i	−0.168759	−	0.519386i
$494$	−1.22711	−	11.9732i	−0.0552102	−	0.538698i
$495$	−5.12936	+	7.85663i	−0.230548	+	0.353129i
$496$	0.981461	−	5.56614i	0.0440689	−	0.249927i
$497$	10.7754	−	26.6701i	0.483344	−	1.19632i
$498$	13.2242	+	19.6057i	0.592593	+	0.878555i
$499$	2.95413	−	4.37968i	0.132245	−	0.196061i	−0.757099	−	0.653300i	$-0.773384\pi$
$499$	2.95413	−	4.37968i	0.132245	−	0.196061i	0.889344	+	0.457239i	$0.151162\pi$
$500$	4.42907	+	10.9623i	0.198074	+	0.490251i
$501$	−10.9823	+	2.33437i	−0.490655	+	0.104292i
$502$	1.98915	+	18.9255i	0.0887801	+	0.844686i
$503$	−13.1486	+	26.9585i	−0.586265	+	1.20202i	0.375161	+	0.926959i	$0.377587\pi$
$503$	−13.1486	+	26.9585i	−0.586265	+	1.20202i	−0.961427	+	0.275062i	$0.911302\pi$
$504$	−5.00956	+	2.66363i	−0.223143	+	0.118648i
$505$	−2.67365	+	4.63090i	−0.118976	+	0.206072i
$506$	1.25870	+	4.74366i	0.0559562	+	0.210881i
$507$	9.02672	−	7.57432i	0.400891	−	0.336387i
$508$	−11.5285	−	14.7558i	−0.511494	−	0.654683i
$509$	8.33453	+	12.3565i	0.369422	+	0.547690i	0.967215	−	0.253960i	$-0.0817333\pi$
$509$	8.33453	+	12.3565i	0.369422	+	0.547690i	−0.597793	+	0.801651i	$0.703956\pi$
$510$	24.3698	+	1.70411i	1.07912	+	0.0754591i
$511$	18.9475	+	10.0746i	0.838188	+	0.445672i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−3.55665	+	10.8506i	−0.157030	+	0.479066i
$514$	−4.82889	−	3.50839i	−0.212993	−	0.154749i
$515$	−9.54318	+	1.34121i	−0.420523	+	0.0591006i
$516$	−21.2418	−	17.8240i	−0.935117	−	0.784656i
$517$	−28.9894	+	0.435493i	−1.27495	+	0.0191530i
$518$	9.59715	−	3.49308i	0.421675	−	0.153477i
$519$	−18.4814	−	11.5484i	−0.811241	−	0.506920i
$520$	0.452389	−	4.30419i	0.0198386	−	0.188751i
$521$	0.768166	+	7.30861i	0.0336540	+	0.320196i	0.998378	+	0.0569328i	$0.0181321\pi$
$521$	0.768166	+	7.30861i	0.0336540	+	0.320196i	−0.964724	+	0.263263i	$0.915201\pi$
$522$	−3.04809	−	0.428381i	−0.133411	−	0.0187497i
$523$	33.1019	+	4.65217i	1.44745	+	0.203425i	0.818716	−	0.574199i	$-0.194686\pi$
$523$	33.1019	+	4.65217i	1.44745	+	0.203425i	0.628729	+	0.777624i	$0.283575\pi$
$524$	−1.39037	−	13.2285i	−0.0607385	−	0.577888i
$525$	−1.83181	+	17.4285i	−0.0799466	+	0.760641i
$526$	−6.47604	−	4.04668i	−0.282369	−	0.176444i
$527$	−37.7642	+	13.7451i	−1.64504	+	0.598744i
$528$	2.14247	−	6.94723i	0.0932390	−	0.302339i
$529$	−15.9416	−	13.3766i	−0.693114	−	0.581592i
$530$	0.846399	−	0.118954i	0.0367652	−	0.00516701i
$531$	8.38654	+	6.09318i	0.363945	+	0.264421i
$532$	5.09994	+	12.7174i	0.221110	+	0.551371i
$533$	1.44609	−	4.45061i	0.0626371	−	0.192777i
$534$	−17.5750	−	9.34481i	−0.760546	−	0.404390i
$535$	15.2651	+	1.06744i	0.659966	+	0.0461493i
$536$	−3.08303	−	4.57078i	−0.133167	−	0.197428i
$537$	3.12342	+	3.99779i	0.134785	+	0.172517i
$538$	−18.1892	+	15.2625i	−0.784190	+	0.658014i
$539$	3.44620	−	8.91280i	0.148438	−	0.383902i
$540$	−2.05298	+	3.55586i	−0.0883461	+	0.153020i
$541$	−36.0099	+	19.1468i	−1.54819	+	0.823186i	−0.999914	−	0.0131122i	$-0.995826\pi$
$541$	−36.0099	+	19.1468i	−1.54819	+	0.823186i	−0.548274	+	0.836299i	$0.684715\pi$
$542$	−2.15192	+	4.41208i	−0.0924327	+	0.189515i
$543$	−0.994103	−	9.45826i	−0.0426610	−	0.405893i
$544$	−6.95499	+	1.47833i	−0.298193	+	0.0633828i
$545$	−8.82599	−	21.8451i	−0.378064	−	0.935741i
$546$	10.6392	−	15.7733i	0.455318	−	0.675036i
$547$	17.6792	+	26.2104i	0.755907	+	1.12068i	0.988956	+	0.148213i	$0.0473520\pi$
$547$	17.6792	+	26.2104i	0.755907	+	1.12068i	−0.233049	+	0.972465i	$0.574870\pi$
$548$	−2.78822	+	6.90110i	−0.119107	+	0.294800i
$549$	2.41001	−	13.6679i	0.102857	−	0.583330i
$550$	−5.29246	−	6.56824i	−0.225671	−	0.280071i
$551$	−1.81698	+	7.20799i	−0.0774060	+	0.307071i
$552$	−1.00235	−	3.08490i	−0.0426627	−	0.131302i
$553$	−13.7352	+	13.2639i	−0.584081	+	0.564040i
$554$	8.63788	+	0.604020i	0.366988	+	0.0256623i
$555$	−6.87248	+	8.79637i	−0.291721	+	0.373385i
$556$	0.561379	+	16.0758i	0.0238078	+	0.681765i
$557$	−2.66554	+	10.6909i	−0.112942	+	0.452987i	−0.999962	−	0.00874511i	$-0.997216\pi$
$557$	−2.66554	+	10.6909i	−0.112942	+	0.452987i	0.887019	+	0.461732i	$0.152772\pi$
$558$	−1.06634	+	10.1456i	−0.0451419	+	0.429497i
$559$	34.1664	+	7.26228i	1.44508	+	0.307162i
$560$	0.855562	+	4.85213i	0.0361541	+	0.205040i
$561$	−50.3963	+	11.5059i	−2.12773	+	0.485779i
$562$	2.68032	−	4.64245i	0.113063	−	0.195830i
$563$	22.2589	−	24.7210i	0.938099	−	1.04186i	−0.0609450	−	0.998141i	$-0.519411\pi$
$563$	22.2589	−	24.7210i	0.938099	−	1.04186i	0.999044	−	0.0437231i	$-0.0139219\pi$
$564$	19.1151	−	1.33665i	0.804889	−	0.0562833i
$565$	−8.71600	+	12.9220i	−0.366685	+	0.543633i
$566$	−17.7829	+	22.7611i	−0.747471	+	0.956719i
$567$	−29.7422	+	18.5850i	−1.24906	+	0.780497i
$568$	−4.01140	−	8.22459i	−0.168315	−	0.345096i
$569$	−18.5522	−	13.4790i	−0.777750	−	0.565069i	0.126553	−	0.991960i	$-0.459609\pi$
$569$	−18.5522	−	13.4790i	−0.777750	−	0.565069i	−0.904303	+	0.426891i	$0.859609\pi$
$570$	−12.0930	−	8.83401i	−0.506522	−	0.370016i
$571$	29.2044			1.22217			0.611083	−	0.791566i	$-0.290734\pi$
$571$	29.2044			1.22217			0.611083	+	0.791566i	$0.290734\pi$
$572$	1.72555	+	8.99389i	0.0721488	+	0.376054i
$573$	−35.6832	−	29.9418i	−1.49069	−	1.25084i
$574$	−0.185924	+	5.32417i	−0.00776033	+	0.222227i
$575$	−3.61768	−	1.03735i	−0.150868	−	0.0432607i
$576$	−0.436651	+	1.75131i	−0.0181938	+	0.0729714i
$577$	−7.44130	+	1.58170i	−0.309785	+	0.0658469i	−0.360181	−	0.932882i	$-0.617285\pi$
$577$	−7.44130	+	1.58170i	−0.309785	+	0.0658469i	0.0503958	+	0.998729i	$0.483952\pi$
$578$	22.4543	+	24.9380i	0.933974	+	1.03728i
$579$	29.3912	+	28.3828i	1.22146	+	1.17955i
$580$	−1.17175	+	2.40243i	−0.0486541	+	0.0997557i
$581$	33.1723	+	7.05098i	1.37622	+	0.292524i
$582$	18.3729	+	31.8229i	0.761583	+	1.31910i
$583$	−1.64100	+	0.760358i	−0.0679633	+	0.0314908i
$584$	6.41502	−	2.33487i	0.265455	−	0.0966178i
$585$	−0.272619	+	7.80679i	−0.0112714	+	0.322771i
$586$	3.88940	+	15.5996i	0.160670	+	0.644412i
$587$	13.9864	+	28.6764i	0.577282	+	1.18360i	0.965103	+	0.261869i	$0.0843388\pi$
$587$	13.9864	+	28.6764i	0.577282	+	1.18360i	−0.387822	+	0.921734i	$0.626772\pi$
$588$	−1.95164	+	6.00652i	−0.0804841	+	0.247705i
$589$	24.0848	+	5.18457i	0.992398	+	0.213627i
$590$	7.28282	−	5.29128i	0.299829	−	0.217838i
$591$	20.3294	−	19.6319i	0.836241	−	0.807548i
$592$	1.21710	−	3.01243i	0.0500226	−	0.123810i
$593$	18.5091	+	6.73675i	0.760076	+	0.276645i	0.692839	−	0.721092i	$-0.256359\pi$
$593$	18.5091	+	6.73675i	0.760076	+	0.276645i	0.0672369	+	0.997737i	$0.478582\pi$
$594$	1.97502	−	8.46083i	0.0810361	−	0.347152i
$595$	26.8366	−	22.5186i	1.10019	−	0.923172i
$596$	−14.6788	+	16.3024i	−0.601266	+	0.667773i
$597$	−14.2709	+	6.35380i	−0.584068	+	0.260044i
$598$	2.93918	+	2.83834i	0.120192	+	0.116068i
$599$	41.0820	+	5.77370i	1.67856	+	0.235907i	0.913148	−	0.407628i	$-0.133644\pi$
$599$	41.0820	+	5.77370i	1.67856	+	0.235907i	0.765417	+	0.643535i	$0.222533\pi$
$600$	3.73037	+	4.14299i	0.152292	+	0.169137i
$601$	−3.03684	−	1.35209i	−0.123875	−	0.0551528i	0.343863	−	0.939020i	$-0.388264\pi$
$601$	−3.03684	−	1.35209i	−0.123875	−	0.0551528i	−0.467738	+	0.883867i	$0.654931\pi$
$602$	−39.6679	+	2.77385i	−1.61674	+	0.113054i
$603$	6.12657	+	7.84166i	0.249493	+	0.319337i
$604$	−6.55785	−	2.38686i	−0.266835	−	0.0971200i
$605$	−14.2466	−	9.71060i	−0.579206	−	0.394792i
$606$	−1.29859	+	7.36467i	−0.0527516	+	0.299169i
$607$	−13.7055	−	42.1812i	−0.556290	−	1.71208i	−0.692513	−	0.721406i	$-0.743496\pi$
$607$	−13.7055	−	42.1812i	−0.556290	−	1.71208i	0.136223	−	0.990678i	$-0.456504\pi$
$608$	4.09215	+	1.50143i	0.165959	+	0.0608909i
$609$	−9.50651	+	6.90688i	−0.385223	+	0.279881i
$610$	−10.6414	−	5.65816i	−0.430860	−	0.229092i
$611$	−20.4698	+	12.7909i	−0.828118	+	0.517465i
$612$	12.3365	−	3.53745i	0.498675	−	0.142993i
$613$	43.4460	+	12.4579i	1.75477	+	0.503171i	0.989992	−	0.141127i	$-0.0450725\pi$
$613$	43.4460	+	12.4579i	1.75477	+	0.503171i	0.764775	+	0.644298i	$0.222850\pi$
$614$	24.0106	+	15.0035i	0.968991	+	0.605492i
$615$	−2.91140	−	5.04269i	−0.117399	−	0.203341i
$616$	−4.71052	−	9.30076i	−0.189792	−	0.374738i
$617$	2.51314	+	14.2528i	0.101175	+	0.573794i	0.992679	+	0.120781i	$0.0385399\pi$
$617$	2.51314	+	14.2528i	0.101175	+	0.573794i	−0.891504	+	0.453013i	$0.850349\pi$
$618$	−11.8999	+	6.32728i	−0.478683	+	0.254520i
$619$	−1.21843	+	0.542480i	−0.0489729	+	0.0218041i	−0.431077	−	0.902315i	$-0.641866\pi$
$619$	−1.21843	+	0.542480i	−0.0489729	+	0.0218041i	0.382104	+	0.924119i	$0.375200\pi$
$620$	8.09299	+	3.60323i	0.325022	+	0.144709i
$621$	−1.45213	−	3.59414i	−0.0582719	−	0.144228i
$622$	−0.341951	−	9.79218i	−0.0137110	−	0.392631i
$623$	−27.4388	+	7.86794i	−1.09931	+	0.315222i
$624$	−1.46426	−	5.87284i	−0.0586175	−	0.235102i
$625$	−5.75857	+	0.809314i	−0.230343	+	0.0323725i
$626$	−12.8786			−0.514733
$627$	29.9109	+	10.4674i	1.19453	+	0.418028i
$628$	20.6903			0.825633
$629$	−22.8769	+	3.21514i	−0.912161	+	0.128196i
$630$	−2.15137	−	8.62869i	−0.0857128	−	0.343775i
$631$	20.5222	−	5.88464i	0.816975	−	0.234264i	0.158976	−	0.987282i	$-0.449181\pi$
$631$	20.5222	−	5.88464i	0.816975	−	0.234264i	0.657999	+	0.753018i	$0.271403\pi$
$632$	0.211990	+	6.07061i	0.00843252	+	0.241476i
$633$	14.8541	+	36.7652i	0.590398	+	1.46129i
$634$	−20.2216	−	9.00323i	−0.803102	−	0.357564i
$635$	26.8125	−	11.9377i	1.06402	−	0.473733i
$636$	1.05542	−	0.561175i	0.0418500	−	0.0222520i
$637$	−1.38148	−	7.83476i	−0.0547362	−	0.310424i
$638$	0.898380	−	5.58422i	0.0355672	−	0.221081i
$639$	8.25817	+	14.3036i	0.326688	+	0.565840i
$640$	1.32922	+	0.830589i	0.0525420	+	0.0328319i
$641$	−10.6018	−	3.04001i	−0.418745	−	0.120073i	0.0596469	−	0.998220i	$-0.481003\pi$
$641$	−10.6018	−	3.04001i	−0.418745	−	0.120073i	−0.478392	+	0.878146i	$0.658780\pi$
$642$	20.5715	−	5.89879i	0.811893	−	0.232806i
$643$	14.7726	−	9.23095i	0.582575	−	0.364033i	−0.206392	−	0.978469i	$-0.566172\pi$
$643$	14.7726	−	9.23095i	0.582575	−	0.364033i	0.788966	+	0.614436i	$0.210617\pi$
$644$	−4.10707	−	2.18377i	−0.161841	−	0.0860524i
$645$	35.1618	−	25.5465i	1.38449	−	1.00589i
$646$	−5.30293	−	30.5364i	−0.208641	−	1.20144i
$647$	−3.51006	−	10.8029i	−0.137995	−	0.424704i	0.858049	−	0.513568i	$-0.171676\pi$
$647$	−3.51006	−	10.8029i	−0.137995	−	0.424704i	−0.996044	+	0.0888637i	$0.971676\pi$
$648$	−1.93740	+	10.9875i	−0.0761081	+	0.431631i
$649$	−11.5007	+	15.1849i	−0.451440	+	0.596060i
$650$	−6.59908	−	2.40187i	−0.258837	−	0.0942091i
$651$	23.9769	+	30.6890i	0.939729	+	1.20280i
$652$	−11.6204	+	0.812574i	−0.455088	+	0.0318229i
$653$	22.3759	+	9.96240i	0.875637	+	0.389859i	0.794802	−	0.606869i	$-0.207575\pi$
$653$	22.3759	+	9.96240i	0.875637	+	0.389859i	0.0808349	+	0.996728i	$0.474241\pi$
$654$	−22.0478	−	24.4866i	−0.862138	−	0.957502i
$655$	20.6454	+	2.90153i	0.806684	+	0.113372i
$656$	1.21912	+	1.17729i	0.0475986	+	0.0459654i
$657$	−11.2565	+	5.01170i	−0.439156	+	0.195525i
$658$	18.3868	−	20.4207i	0.716794	−	0.796080i
$659$	10.8915	−	9.13906i	0.424273	−	0.356007i	−0.405513	−	0.914089i	$-0.632907\pi$
$659$	10.8915	−	9.13906i	0.424273	−	0.356007i	0.829786	+	0.558082i	$0.188463\pi$
$660$	9.75316	+	5.89262i	0.379641	+	0.229370i
$661$	13.6246	+	4.95895i	0.529936	+	0.192881i	0.593110	−	0.805122i	$-0.297900\pi$
$661$	13.6246	+	4.95895i	0.529936	+	0.192881i	−0.0631739	+	0.998003i	$0.520122\pi$
$662$	−6.80911	+	16.8531i	−0.264644	+	0.655016i
$663$	−30.9578	+	29.8956i	−1.20230	+	1.16105i
$664$	8.72817	−	6.34139i	0.338719	−	0.246094i
$665$	−21.2749	+	2.93386i	−0.825005	+	0.113770i
$666$	−1.81215	+	5.57722i	−0.0702193	+	0.216113i
$667$	−1.10624	−	2.26813i	−0.0428337	−	0.0878222i
$668$	1.23915	+	4.96994i	0.0479440	+	0.192293i
$669$	0.345377	−	9.89030i	0.0133530	−	0.382381i
$670$	8.12041	−	2.95559i	0.313719	−	0.114184i
$671$	25.0222	+	4.92701i	0.965972	+	0.190205i
$672$	3.44523	+	5.96731i	0.132903	+	0.230194i
$673$	−25.0841	−	5.33180i	−0.966922	−	0.205526i	−0.302721	−	0.953079i	$-0.597895\pi$
$673$	−25.0841	−	5.33180i	−0.966922	−	0.205526i	−0.664202	+	0.747554i	$0.731228\pi$
$674$	−7.92395	+	16.2465i	−0.305219	+	0.625792i
$675$	4.79257	+	4.62813i	0.184466	+	0.178137i
$676$	−3.59703	−	3.99490i	−0.138347	−	0.153650i
$677$	−18.3901	+	3.90894i	−0.706790	+	0.150233i	−0.547263	−	0.836961i	$-0.684330\pi$
$677$	−18.3901	+	3.90894i	−0.706790	+	0.150233i	−0.159527	+	0.987194i	$0.550997\pi$
$678$	−5.27349	+	21.1508i	−0.202527	+	0.812291i
$679$	50.6537	+	14.5247i	1.94391	+	0.557408i
$680$	0.388945	−	11.1379i	0.0149153	−	0.427120i
$681$	25.6652	+	21.5356i	0.983492	+	0.825247i
$682$	−18.6002	−	2.32975i	−0.712240	−	0.0892109i
$683$	0.0139498			0.000533773			0.000266887	−	1.00000i	$-0.499915\pi$
$683$	0.0139498			0.000533773			0.000266887		1.00000i	$0.499915\pi$
$684$	−7.55709	−	2.18814i	−0.288952	−	0.0836657i
$685$	−9.43814	−	6.85721i	−0.360613	−	0.262001i
$686$	−5.67568	−	11.6369i	−0.216698	−	0.444297i
$687$	−7.81369	+	4.88254i	−0.298111	+	0.186280i
$688$	−7.78817	+	9.96840i	−0.296921	+	0.380042i
$689$	−0.841993	+	1.24831i	−0.0320774	+	0.0475566i
$690$	5.07169	−	0.354647i	0.193076	−	0.0135012i
$691$	−9.98325	+	11.0875i	−0.379781	+	0.421789i	−0.902483	−	0.430726i	$-0.858257\pi$
$691$	−9.98325	+	11.0875i	−0.379781	+	0.421789i	0.522702	+	0.852516i	$0.324924\pi$
$692$	−4.97095	+	8.60995i	−0.188967	+	0.327301i
$693$	9.65245	+	16.1532i	0.366666	+	0.613610i
$694$	1.10192	+	6.24929i	0.0418283	+	0.237220i
$695$	−24.6614	−	5.24194i	−0.935460	−	0.198838i
$696$	−0.390745	+	3.71769i	−0.0148111	+	0.140919i
$697$	2.91527	−	11.6925i	0.110424	−	0.442886i
$698$	−0.682322	−	19.5392i	−0.0258263	−	0.739568i
$699$	−1.13926	+	1.45819i	−0.0430908	+	0.0551537i
$700$	7.97522	+	0.557682i	0.301435	+	0.0210784i
$701$	24.3191	−	23.4847i	0.918520	−	0.887004i	−0.0753952	−	0.997154i	$-0.524022\pi$
$701$	24.3191	−	23.4847i	0.918520	−	0.887004i	0.993915	+	0.110149i	$0.0351329\pi$
$702$	−2.23522	−	6.87931i	−0.0843631	−	0.259643i
$703$	12.9228	+	5.79372i	0.487392	+	0.218514i
$704$	−3.20152	−	0.866194i	−0.120662	−	0.0326459i
$705$	−5.21532	+	29.5776i	−0.196420	+	1.11396i
$706$	−2.13292	+	5.27917i	−0.0802737	+	0.198684i
$707$	5.99687	+	8.89072i	0.225535	+	0.334370i
$708$	7.03996	−	10.4372i	0.264578	−	0.392253i
$709$	11.2133	+	27.7538i	0.421123	+	1.04232i	0.977415	+	0.211330i	$0.0677793\pi$
$709$	11.2133	+	27.7538i	0.421123	+	1.04232i	−0.556292	+	0.830987i	$0.687776\pi$
$710$	14.0293	−	2.98201i	0.526509	−	0.111913i
$711$	−1.14602	−	10.9036i	−0.0429790	−	0.408918i
$712$	−3.98070	+	8.16165i	−0.149183	+	0.305871i
$713$	−7.38464	+	3.92648i	−0.276557	+	0.147048i
$714$	24.4969	−	42.4298i	0.916772	−	1.58790i
$715$	−14.3325	−	0.786089i	−0.536004	−	0.0293981i
$716$	1.77296	−	1.48769i	0.0662585	−	0.0555975i
$717$	−35.4769	−	45.4083i	−1.32491	−	1.69580i
$718$	−17.3611	−	25.7388i	−0.647909	−	0.960565i
$719$	−46.3533	−	3.24134i	−1.72869	−	0.120882i	−0.829517	−	0.558482i	$-0.811384\pi$
$719$	−46.3533	−	3.24134i	−1.72869	−	0.120882i	−0.899169	+	0.437601i	$0.855828\pi$
$720$	−2.49788	−	1.32814i	−0.0930904	−	0.0494970i
$721$	−5.97243	+	18.3813i	−0.222425	+	0.684554i
$722$	−7.20861	+	17.5794i	−0.268277	+	0.654238i
$723$	8.27310	+	6.01076i	0.307680	+	0.223543i
$724$	−4.29641	+	0.603822i	−0.159675	+	0.0224409i
$725$	3.32251	+	2.78792i	0.123395	+	0.103541i
$726$	−23.3673	−	5.94698i	−0.867241	−	0.220713i
$727$	11.3647	−	4.13641i	0.421493	−	0.153411i	−0.122561	−	0.992461i	$-0.539111\pi$
$727$	11.3647	−	4.13641i	0.421493	−	0.153411i	0.544054	+	0.839050i	$0.316889\pi$
$728$	−7.36082	−	4.59955i	−0.272810	−	0.170471i
$729$	0.304272	−	2.89495i	0.0112693	−	0.107221i
$730$	1.11847	+	10.6415i	0.0413963	+	0.393859i
$731$	89.0714	+	12.5182i	3.29443	+	0.463001i
$732$	−16.6911	−	2.34579i	−0.616922	−	0.0867027i
$733$	0.203067	+	1.93205i	0.00750045	+	0.0713620i	0.997632	−	0.0687802i	$-0.0219107\pi$
$733$	0.203067	+	1.93205i	0.00750045	+	0.0713620i	−0.990131	+	0.140142i	$0.955244\pi$
$734$	1.31105	−	12.4738i	0.0483917	−	0.460416i
$735$	−8.39486	−	5.24569i	−0.309649	−	0.193490i
$736$	−1.39052	+	0.506108i	−0.0512553	+	0.0186554i
$737$	−14.6304	+	10.9691i	−0.538916	+	0.404051i
$738$	−2.34329	−	1.96625i	−0.0862576	−	0.0723787i
$739$	14.6009	−	2.05203i	0.537104	−	0.0754850i	0.134594	−	0.990901i	$-0.457027\pi$
$739$	14.6009	−	2.05203i	0.537104	−	0.0754850i	0.402509	+	0.915416i	$0.368138\pi$
$740$	4.11989	+	2.99328i	0.151450	+	0.110035i
$741$	25.8204	−	5.41849i	0.948536	−	0.199053i
$742$	0.529704	−	1.63026i	0.0194460	−	0.0598487i
$743$	34.6278	+	18.4119i	1.27037	+	0.675468i	0.961283	−	0.275565i	$-0.0888648\pi$
$743$	34.6278	+	18.4119i	1.27037	+	0.675468i	0.309089	+	0.951033i	$0.399976\pi$
$744$	12.3591	+	0.864233i	0.453107	+	0.0316843i
$745$	−19.2272	−	28.5055i	−0.704431	−	1.04436i
$746$	7.00278	+	8.96315i	0.256390	+	0.328164i
$747$	−14.9169	+	12.5168i	−0.545782	+	0.457965i
$748$	6.04817	+	22.7937i	0.221143	+	0.833419i
$749$	15.3446	−	26.5776i	0.560680	−	0.971126i
$750$	−22.8832	+	12.1672i	−0.835575	+	0.444283i
$751$	3.53787	−	7.25371i	0.129099	−	0.264692i	−0.824447	−	0.565939i	$-0.808514\pi$
$751$	3.53787	−	7.25371i	0.129099	−	0.264692i	0.953546	+	0.301247i	$0.0974028\pi$
$752$	−0.913747	−	8.69372i	−0.0333209	−	0.317027i
$753$	−40.8019	+	8.67272i	−1.48691	+	0.316052i
$754$	−1.76397	−	4.36598i	−0.0642400	−	0.159000i
$755$	6.11665	−	9.06830i	0.222608	−	0.330029i
$756$	4.60473	+	6.82679i	0.167472	+	0.248288i
$757$	8.44307	−	20.8973i	0.306869	−	0.759527i	−0.692408	−	0.721506i	$-0.743450\pi$
$757$	8.44307	−	20.8973i	0.306869	−	0.759527i	0.999277	−	0.0380208i	$-0.0121053\pi$
$758$	5.81390	−	32.9722i	0.211170	−	1.19761i
$759$	−10.0528	+	3.83089i	−0.364894	+	0.139052i
$760$	−3.83510	+	5.65415i	−0.139114	+	0.205097i
$761$	0.309190	+	0.951588i	0.0112081	+	0.0344950i	0.956504	−	0.291719i	$-0.0942271\pi$
$761$	0.309190	+	0.951588i	0.0112081	+	0.0344950i	−0.945296	+	0.326214i	$0.894227\pi$
$762$	29.5262	−	28.5132i	1.06962	−	1.03292i
$763$	−47.1365	−	3.29610i	−1.70646	−	0.119327i
$764$	−13.0830	+	16.7455i	−0.473328	+	0.605832i
$765$	0.702017	+	20.1031i	0.0253815	+	0.726830i
$766$	5.04901	−	20.2505i	0.182428	−	0.731680i
$767$	−1.65768	+	15.7718i	−0.0598554	+	0.569486i
$768$	2.14411	+	0.455745i	0.0773690	+	0.0164453i
$769$	5.35598	+	30.3753i	0.193142	+	1.09536i	0.915041	+	0.403362i	$0.132158\pi$
$769$	5.35598	+	30.3753i	0.193142	+	1.09536i	−0.721899	+	0.691998i	$0.756731\pi$
$770$	15.9310	−	3.63718i	0.574115	−	0.131075i
$771$	6.54188	−	11.3309i	0.235600	−	0.408072i
$772$	12.4724	−	13.8520i	0.448893	−	0.498546i
$773$	17.8211	−	1.24617i	0.640981	−	0.0448217i	0.254432	−	0.967091i	$-0.418112\pi$
$773$	17.8211	−	1.24617i	0.640981	−	0.0448217i	0.386549	+	0.922269i	$0.373667\pi$
$774$	12.7678	−	18.9290i	0.458928	−	0.680388i
$775$	8.84997	−	11.3274i	0.317900	−	0.406894i
$776$	14.2163	−	8.88331i	0.510334	−	0.318892i
$777$	9.81391	+	20.1215i	0.352072	+	0.721854i
$778$	8.18424	+	5.94620i	0.293419	+	0.213182i
$779$	−5.32728	+	5.11792i	−0.190870	+	0.183368i
$780$	9.48682			0.339683
$781$	−26.5799	+	14.6491i	−0.951103	+	0.524186i
$782$	8.06006	+	6.76319i	0.288227	+	0.241851i
$783$	−0.155909	+	4.46466i	−0.00557174	+	0.159554i
$784$	2.76959	+	0.794166i	0.0989138	+	0.0283631i
$785$	−7.84546	+	31.4664i	−0.280016	+	1.12308i
$786$	28.5196	−	6.06202i	1.01726	−	0.216225i
$787$	−36.0672	−	40.0566i	−1.28566	−	1.42786i	−0.849140	−	0.528168i	$-0.822879\pi$
$787$	−36.0672	−	40.0566i	−1.28566	−	1.42786i	−0.436515	−	0.899697i	$-0.643787\pi$
$788$	−9.27431	−	8.95610i	−0.330384	−	0.319048i
$789$	7.33795	−	15.0450i	0.261238	−	0.535617i
$790$	−9.31274	−	1.97948i	−0.331332	−	0.0704269i
$791$	15.6298	+	27.0716i	0.555732	+	0.962557i
$792$	5.87349	+	1.15652i	0.208705	+	0.0410952i
$793$	19.9515	−	7.26176i	0.708499	−	0.257873i
$794$	−0.425034	+	12.1714i	−0.0150839	+	0.431946i
$795$	0.453253	+	1.81790i	0.0160752	+	0.0644742i
$796$	3.12406	+	6.40526i	0.110729	+	0.227029i
$797$	−1.47286	+	4.53299i	−0.0521713	+	0.160567i	−0.973748	−	0.227631i	$-0.926902\pi$
$797$	−1.47286	+	4.53299i	−0.0521713	+	0.160567i	0.921576	+	0.388197i	$0.126902\pi$
$798$	−26.5556	+	14.0318i	−0.940057	+	0.496721i
$799$	−50.2853	+	36.5344i	−1.77897	+	1.29250i
$800$	1.82949	−	1.76672i	0.0646824	−	0.0624631i
$801$	6.13978	−	15.1965i	0.216939	−	0.536942i
$802$	−8.73752	−	3.18020i	−0.308533	−	0.112297i
$803$	−8.79609	−	20.8632i	−0.310407	−	0.736247i
$804$	9.25792	−	7.76832i	0.326502	−	0.273967i
$805$	4.87847	−	5.41809i	0.171944	−	0.190963i
$806$	−14.2572	+	6.34771i	−0.502188	+	0.223588i
$807$	−37.4400	−	36.1554i	−1.31795	−	1.27273i
$808$	3.37840	+	0.474803i	0.118852	+	0.0167035i
$809$	12.4325	+	13.8077i	0.437104	+	0.485453i	0.920939	−	0.389706i	$-0.127423\pi$
$809$	12.4325	+	13.8077i	0.437104	+	0.485453i	−0.483836	+	0.875159i	$0.660757\pi$
$810$	−15.9755	−	7.11275i	−0.561322	−	0.249917i
$811$	−0.0692481	+	0.00484230i	−0.00243163	+	0.000170036i	−0.0709722	−	0.997478i	$-0.522610\pi$
$811$	−0.0692481	+	0.00484230i	−0.00243163	+	0.000170036i	0.0685406	+	0.997648i	$0.478166\pi$
$812$	3.30036	+	4.22427i	0.115820	+	0.148243i
$813$	−10.1114	−	3.68026i	−0.354623	−	0.129072i
$814$	−10.1801	−	3.53301i	−0.356813	−	0.123832i
$815$	3.17048	−	17.9807i	0.111057	−	0.629836i
$816$	−4.81635	−	14.8232i	−0.168606	−	0.518916i
$817$	−42.1482	−	35.5528i	−1.47458	−	1.24383i
$818$	3.67948	−	2.67330i	0.128650	−	0.0934696i
$819$	13.8325	+	7.35486i	0.483346	+	0.257000i
$820$	−2.25273	+	1.40766i	−0.0786687	+	0.0491576i
$821$	25.7229	−	7.37594i	0.897737	−	0.257422i	0.205128	−	0.978735i	$-0.434239\pi$
$821$	25.7229	−	7.37594i	0.897737	−	0.257422i	0.692609	+	0.721313i	$0.256461\pi$
$822$	−15.6833	−	4.49711i	−0.547018	−	0.156855i
$823$	−1.44276	−	0.901538i	−0.0502915	−	0.0314256i	0.504540	−	0.863388i	$-0.331662\pi$
$823$	−1.44276	−	0.901538i	−0.0502915	−	0.0314256i	−0.554832	+	0.831962i	$0.687217\pi$
$824$	3.07421	+	5.32469i	0.107095	+	0.185494i
$825$	13.1062	−	13.0426i	0.456298	−	0.454084i
$826$	−3.13502	−	17.7796i	−0.109081	−	0.618631i
$827$	1.17535	−	0.624946i	0.0408710	−	0.0217315i	−0.448910	−	0.893577i	$-0.648188\pi$
$827$	1.17535	−	0.624946i	0.0408710	−	0.0217315i	0.489781	+	0.871845i	$0.337077\pi$
$828$	2.43995	−	1.08634i	0.0847943	−	0.0377529i
$829$	−42.7135	−	19.0173i	−1.48350	−	0.660497i	−0.504324	−	0.863514i	$-0.668258\pi$
$829$	−42.7135	−	19.0173i	−1.48350	−	0.660497i	−0.979175	+	0.203018i	$0.934925\pi$
$830$	6.33458	+	15.6786i	0.219876	+	0.544213i
$831$	0.662413	+	18.9690i	0.0229789	+	0.658029i
$832$	−2.65425	+	0.761095i	−0.0920197	+	0.0263862i
$833$	−4.95611	−	19.8779i	−0.171719	−	0.688727i
$834$	−34.9167	+	4.90722i	−1.20907	+	0.169923i
$835$	−8.02830			−0.277831
$836$	4.29612	−	13.8037i	0.148584	−	0.477413i
$837$	14.8061			0.511773
$838$	17.3956	−	2.44480i	0.600922	−	0.0844541i
$839$	3.50148	+	14.0437i	0.120885	+	0.484842i	0.999967	+	0.00817105i	$0.00260095\pi$
$839$	3.50148	+	14.0437i	0.120885	+	0.484842i	−0.879082	+	0.476670i	$0.841843\pi$
$840$	−10.3816	+	2.97689i	−0.358201	+	0.102712i
$841$	−0.910589	−	26.0759i	−0.0313996	−	0.899168i
$842$	2.59913	+	6.43307i	0.0895719	+	0.221698i
$843$	10.7347	+	4.77940i	0.369723	+	0.164611i
$844$	16.5256	−	7.35768i	0.568835	−	0.253262i
$845$	7.43950	−	3.95565i	0.255927	−	0.136079i
$846$	2.73982	+	15.5383i	0.0941968	+	0.534217i
$847$	−30.0290	+	17.1431i	−1.03181	+	0.589042i
$848$	−0.272656	−	0.472255i	−0.00936306	−	0.0162173i
$849$	−53.6938	−	33.5516i	−1.84277	−	1.15149i
$850$	−17.3832	−	4.98457i	−0.596240	−	0.170969i
$851$	−4.62152	+	1.32520i	−0.158424	+	0.0454273i
$852$	17.0105	−	10.6294i	0.582771	−	0.364156i
$853$	−42.5145	−	22.6054i	−1.45567	−	0.773993i	−0.462059	−	0.886849i	$-0.652889\pi$
$853$	−42.5145	−	22.6054i	−1.45567	−	0.773993i	−0.993611	+	0.112856i	$0.964000\pi$
$854$	−19.5547	+	14.2073i	−0.669149	+	0.486165i
$855$	6.19333	−	10.6633i	0.211807	−	0.364678i
$856$	−3.01692	−	9.28512i	−0.103116	−	0.317359i
$857$	4.49792	−	25.5090i	0.153646	−	0.871371i	−0.806367	−	0.591416i	$-0.798569\pi$
$857$	4.49792	−	25.5090i	0.153646	−	0.871371i	0.960013	−	0.279955i	$-0.0903196\pi$
$858$	−19.2114	+	5.82246i	−0.655865	+	0.198775i
$859$	3.88217	+	1.41299i	0.132458	+	0.0482107i	0.407399	−	0.913250i	$-0.366436\pi$
$859$	3.88217	+	1.41299i	0.132458	+	0.0482107i	−0.274941	+	0.961461i	$0.588658\pi$
$860$	−12.2071	−	15.6244i	−0.416258	−	0.532786i
$861$	−11.6493	+	0.814601i	−0.397008	+	0.0277615i
$862$	18.1030	+	8.05999i	0.616592	+	0.274524i
$863$	21.4419	+	23.8136i	0.729889	+	0.810624i	0.987830	−	0.155536i	$-0.0497106\pi$
$863$	21.4419	+	23.8136i	0.729889	+	0.810624i	−0.257941	+	0.966161i	$0.583044\pi$
$864$	2.59412	+	0.364580i	0.0882538	+	0.0124033i
$865$	−11.2093	−	10.8247i	−0.381129	−	0.368052i
$866$	10.9040	−	4.85477i	0.370532	−	0.164972i
$867$	−49.2201	+	54.6644i	−1.67160	+	1.85650i
$868$	13.6101	−	11.4202i	0.461957	−	0.387628i
$869$	20.0737	−	1.70704i	0.680955	−	0.0579075i
$870$	−5.50580	−	2.00395i	−0.186664	−	0.0679402i
$871$	−5.70285	+	14.1151i	−0.193234	+	0.478271i
$872$	−10.8130	+	10.4420i	−0.366174	+	0.353610i
$873$	−24.4784	+	17.7846i	−0.828467	+	0.601917i
$874$	−1.97732	−	6.13958i	−0.0668838	−	0.207674i
$875$	−11.4848	+	35.3467i	−0.388258	+	1.19494i
$876$	6.55990	+	13.4498i	0.221639	+	0.454426i
$877$	−1.37859	−	5.52921i	−0.0465516	−	0.186708i	0.942519	−	0.334154i	$-0.108450\pi$
$877$	−1.37859	−	5.52921i	−0.0465516	−	0.186708i	−0.989070	+	0.147446i	$0.952895\pi$
$878$	0.561549	−	16.0807i	0.0189514	−	0.542696i
$879$	−33.1159	+	12.0532i	−1.11697	+	0.406545i
$880$	2.53130	−	4.54051i	0.0853302	−	0.153061i
$881$	4.49193	+	7.78025i	0.151337	+	0.262123i	0.931719	−	0.363179i	$-0.118309\pi$
$881$	4.49193	+	7.78025i	0.151337	+	0.262123i	−0.780382	+	0.625303i	$0.784975\pi$
$882$	−5.08671	−	1.08121i	−0.171279	−	0.0364064i
$883$	25.5124	−	52.3082i	0.858562	−	1.76031i	0.247194	−	0.968966i	$-0.420491\pi$
$883$	25.5124	−	52.3082i	0.858562	−	1.76031i	0.611367	−	0.791347i	$-0.290620\pi$
$884$	14.1230	+	13.6384i	0.475008	+	0.458710i
$885$	13.2037	+	14.6642i	0.443838	+	0.492932i
$886$	33.9960	−	7.22607i	1.14212	−	0.242765i
$887$	−10.4730	+	42.0051i	−0.351651	+	1.41039i	0.490637	+	0.871364i	$0.336764\pi$
$887$	−10.4730	+	42.0051i	−0.351651	+	1.41039i	−0.842287	+	0.539029i	$0.818791\pi$
$888$	6.84600	+	1.96306i	0.229737	+	0.0658759i
$889$	2.05426	−	58.8262i	0.0688976	−	1.97297i
$890$	−10.9031	−	9.14875i	−0.365471	−	0.306667i
$891$	36.7168	+	4.59892i	1.23006	+	0.154069i
$892$	−4.51472			−0.151164
$893$	38.0177	−	2.55960i	1.27221	−	0.0856538i
$894$	−38.9027	−	28.2645i	−1.30110	−	0.945305i
$895$	1.59024	+	3.26048i	0.0531559	+	0.108986i
$896$	2.66579	−	1.66577i	0.0890577	−	0.0556494i
$897$	−5.51414	+	7.05778i	−0.184112	+	0.235652i
$898$	8.43837	−	12.5104i	0.281592	−	0.417477i
$899$	9.61521	−	0.672361i	0.320685	−	0.0224245i
$900$	−3.07162	+	3.41138i	−0.102387	+	0.113713i
$901$	−1.93869	+	3.35791i	−0.0645871	+	0.111868i
$902$	3.69797	−	4.23319i	0.123129	−	0.140950i
$903$	−15.1360	−	85.8407i	−0.503695	−	2.85660i
$904$	9.72710	+	2.06756i	0.323519	+	0.0687660i
$905$	0.710828	−	6.76307i	0.0236287	−	0.224812i
$906$	3.70079	−	14.8430i	0.122950	−	0.493127i
$907$	0.845692	+	24.2174i	0.0280807	+	0.804127i	0.928987	+	0.370113i	$0.120681\pi$
$907$	0.845692	+	24.2174i	0.0280807	+	0.804127i	−0.900906	+	0.434014i	$0.857097\pi$
$908$	9.40998	−	12.0442i	0.312281	−	0.399702i
$909$	−6.14269	−	0.429539i	−0.203740	−	0.0142469i
$910$	9.78624	−	9.45047i	0.324411	−	0.313280i
$911$	−15.8473	−	48.7731i	−0.525045	−	1.61592i	−0.764226	−	0.644949i	$-0.776879\pi$
$911$	−15.8473	−	48.7731i	−0.525045	−	1.61592i	0.239181	−	0.970975i	$-0.423121\pi$
$912$	−2.33549	+	9.26494i	−0.0773359	+	0.306793i
$913$	−22.4505	−	27.8624i	−0.743004	−	0.922109i
$914$	4.13497	−	23.4506i	0.136773	−	0.775677i
$915$	9.89657	−	24.4949i	0.327170	−	0.809775i
$916$	2.35047	+	3.48471i	0.0776616	+	0.115138i
$917$	23.3809	−	34.6636i	0.772106	−	1.14469i
$918$	−6.97759	−	17.2701i	−0.230295	−	0.569999i
$919$	13.0748	−	2.77913i	0.431297	−	0.0916751i	0.0128528	−	0.999917i	$-0.495909\pi$
$919$	13.0748	−	2.77913i	0.431297	−	0.0916751i	0.418445	+	0.908242i	$0.362575\pi$
$920$	−0.242439	−	2.30665i	−0.00799298	−	0.0760482i
$921$	−27.2062	+	55.7811i	−0.896476	+	1.83805i
$922$	−3.36187	+	1.78754i	−0.110717	+	0.0588694i
$923$	−12.6335	+	21.8819i	−0.415838	+	0.720252i
$924$	19.1964	−	12.4000i	0.631516	−	0.407931i
$925$	6.32998	−	5.31149i	0.208129	−	0.174641i
$926$	3.51919	+	4.50436i	0.115648	+	0.148022i
$927$	−6.20562	−	9.20022i	−0.203819	−	0.302175i
$928$	1.70120	+	0.118960i	0.0558447	+	0.00390504i
$929$	45.9670	+	24.4411i	1.50813	+	0.801885i	0.998294	−	0.0583883i	$-0.0185962\pi$
$929$	45.9670	+	24.4411i	1.50813	+	0.801885i	0.509833	+	0.860274i	$0.329707\pi$
$930$	−6.00074	+	18.4684i	−0.196772	+	0.605602i
$931$	−3.91180	+	11.9341i	−0.128204	+	0.391124i
$932$	0.682960	+	0.496200i	0.0223711	+	0.0162536i
$933$	21.2687	−	2.98912i	0.696305	−	0.0978593i
$934$	−6.71503	−	5.63458i	−0.219723	−	0.184369i
$935$	−36.9586	+	0.555212i	−1.20868	+	0.0181574i
$936$	4.68324	−	1.70456i	0.153076	−	0.0557153i
$937$	−38.2360	−	23.8925i	−1.24911	−	0.780533i	−0.266079	−	0.963951i	$-0.585728\pi$
$937$	−38.2360	−	23.8925i	−1.24911	−	0.780533i	−0.983035	+	0.183418i	$0.941284\pi$
$938$	1.81157	−	17.2359i	0.0591499	−	0.562774i
$939$	−2.95085	−	28.0754i	−0.0962973	−	0.916207i
$940$	13.5681	+	1.90688i	0.442544	+	0.0621955i
$941$	−0.133406	−	0.0187491i	−0.00434893	−	0.000611202i	0.136998	−	0.990571i	$-0.456255\pi$
$941$	−0.133406	−	0.0187491i	−0.00434893	−	0.000611202i	−0.141347	+	0.989960i	$0.545143\pi$
$942$	4.74072	+	45.1050i	0.154461	+	1.46960i
$943$	0.262143	−	2.49412i	0.00853655	−	0.0812199i
$944$	−4.87064	−	3.04351i	−0.158526	−	0.0990579i
$945$	−12.1284	+	4.41439i	−0.394538	+	0.143600i
$946$	34.3094	+	24.1482i	1.11549	+	0.785127i
$947$	−3.98148	−	3.34086i	−0.129381	−	0.108563i	0.575801	−	0.817590i	$-0.304690\pi$
$947$	−3.98148	−	3.34086i	−0.129381	−	0.108563i	−0.705182	+	0.709026i	$0.749135\pi$
$948$	−13.1854	+	1.85309i	−0.428241	+	0.0601854i
$949$	−15.2500	−	11.0798i	−0.495037	−	0.359665i
$950$	7.39662	+	8.25765i	0.239978	+	0.267914i
$951$	14.9938	−	46.1461i	0.486207	−	1.49639i
$952$	−19.7348	−	10.4932i	−0.639607	−	0.340085i
$953$	24.5314	+	1.71540i	0.794651	+	0.0555674i	0.461310	−	0.887239i	$-0.347380\pi$
$953$	24.5314	+	1.71540i	0.794651	+	0.0555674i	0.333341	+	0.942806i	$0.391824\pi$
$954$	0.550386	+	0.815981i	0.0178194	+	0.0264183i
$955$	−20.5062	−	26.2467i	−0.663565	−	0.849324i
$956$	−20.1379	+	16.8977i	−0.651306	+	0.546510i
$957$	12.3795	+	0.678974i	0.400172	+	0.0219481i
$958$	−2.03515	+	3.52498i	−0.0657527	+	0.113887i
$959$	−20.6582	+	10.9842i	−0.667087	+	0.354697i
$960$	−1.50613	+	3.08802i	−0.0486101	+	0.0996654i
$961$	−0.0987987	−	0.940007i	−0.00318705	−	0.0303228i
$962$	−8.77520	+	1.86523i	−0.282924	+	0.0601373i
$963$	6.60110	+	16.3383i	0.212717	+	0.526494i
$964$	2.60873	−	3.86760i	0.0840215	−	0.124567i
$965$	16.3372	+	24.2209i	0.525914	+	0.779700i
$966$	3.81958	−	9.45379i	0.122893	−	0.304171i
$967$	−7.66268	+	43.4572i	−0.246415	+	1.39749i	0.570768	+	0.821111i	$0.306645\pi$
$967$	−7.66268	+	43.4572i	−0.246415	+	1.39749i	−0.817183	+	0.576378i	$0.804466\pi$
$968$	−2.33933	+	10.7484i	−0.0751890	+	0.345466i
$969$	65.3544	−	18.5572i	2.09949	−	0.596142i
$970$	8.11940	+	24.9889i	0.260698	+	0.802346i
$971$	−21.3419	+	20.6096i	−0.684893	+	0.661393i	−0.953339	−	0.301901i	$-0.902379\pi$
$971$	−21.3419	+	20.6096i	−0.684893	+	0.661393i	0.268447	+	0.963295i	$0.413490\pi$
$972$	−16.5571	−	1.15778i	−0.531068	−	0.0371359i
$973$	−31.1303	+	39.8450i	−0.997992	+	1.27737i
$974$	−0.642311	−	18.3934i	−0.0205810	−	0.589362i
$975$	3.72406	−	14.9364i	0.119265	−	0.478347i
$976$	−0.803756	+	7.64722i	−0.0257276	+	0.244782i
$977$	32.3870	+	6.88408i	1.03615	+	0.220241i	0.694431	−	0.719560i	$-0.255656\pi$
$977$	32.3870	+	6.88408i	1.03615	+	0.220241i	0.341723	+	0.939801i	$0.388990\pi$
$978$	−4.43396	−	25.1463i	−0.141783	−	0.804089i
$979$	27.6943	+	11.8351i	0.885114	+	0.378252i
$980$	−2.25798	+	3.91093i	−0.0721284	+	0.124930i
$981$	18.1544	−	20.1625i	0.579626	−	0.643740i
$982$	−17.7812	+	1.24338i	−0.567420	+	0.0396779i
$983$	20.1293	−	29.8429i	0.642025	−	0.951841i	−0.357813	−	0.933793i	$-0.616477\pi$
$983$	20.1293	−	29.8429i	0.642025	−	0.951841i	0.999837	−	0.0180471i	$-0.00574489\pi$
$984$	−2.28716	+	2.92744i	−0.0729121	+	0.0933233i
$985$	17.1374	−	10.7086i	0.546042	−	0.341205i
$986$	−5.31556	−	10.8985i	−0.169282	−	0.347080i
$987$	48.7301	+	35.4045i	1.55110	+	1.12694i
$988$	−2.88151	−	11.6859i	−0.0916730	−	0.371777i
$989$	18.7191			0.595233
$990$	−3.98601	+	8.49404i	−0.126684	+	0.269958i
$991$	25.2137	+	21.1568i	0.800939	+	0.672068i	0.948427	−	0.316996i	$-0.102674\pi$
$991$	25.2137	+	21.1568i	0.800939	+	0.672068i	−0.147487	+	0.989064i	$0.547119\pi$
$992$	0.197252	−	5.64856i	0.00626276	−	0.179342i
$993$	−38.3001	−	10.9824i	−1.21542	−	0.348515i
$994$	6.95879	−	27.9102i	0.220719	−	0.885257i
$995$	−10.9259	+	2.32237i	−0.346375	+	0.0736242i
$996$	15.8241	+	17.5745i	0.501407	+	0.556869i
$997$	−32.4399	−	31.3268i	−1.02738	−	0.992130i	−0.0274088	−	0.999624i	$-0.508726\pi$
$997$	−32.4399	−	31.3268i	−1.02738	−	0.992130i	−0.999972	+	0.00749424i	$0.997614\pi$
$998$	2.31585	−	4.74819i	0.0733069	−	0.150301i
$999$	8.32518	+	1.76957i	0.263397	+	0.0559868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.93.9	yes	264
11.9	even	5	inner	418.2.u.b.207.9	yes	264
19.9	even	9	inner	418.2.u.b.313.9	yes	264
209.9	even	45	inner	418.2.u.b.9.9	✓	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.9.9	✓	264	209.9	even	45	inner
418.2.u.b.93.9	yes	264	1.1	even	1	trivial
418.2.u.b.207.9	yes	264	11.9	even	5	inner
418.2.u.b.313.9	yes	264	19.9	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.990268 - 0.139173i) q^{2} +(0.530296 + 2.12690i) q^{3} +(0.961262 - 0.275637i) q^{4} +(0.0547010 + 1.56643i) q^{5} +(0.821143 + 2.03240i) q^{6} +(2.87167 + 1.27855i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-1.59366 + 0.847362i) q^{9} +O(q^{10})\)	\(q+(0.990268 - 0.139173i) q^{2} +(0.530296 + 2.12690i) q^{3} +(0.961262 - 0.275637i) q^{4} +(0.0547010 + 1.56643i) q^{5} +(0.821143 + 2.03240i) q^{6} +(2.87167 + 1.27855i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-1.59366 + 0.847362i) q^{9} +(0.272174 + 1.54358i) q^{10} +(-1.49853 - 2.95879i) q^{11} +(1.09601 + 1.89834i) q^{12} +(-2.34165 - 1.46322i) q^{13} +(3.02167 + 0.866449i) q^{14} +(-3.30264 + 0.947017i) q^{15} +(0.848048 - 0.529919i) q^{16} +(-6.27809 - 3.33812i) q^{17} +(-1.46022 + 1.06091i) q^{18} +(2.16967 + 3.78055i) q^{19} +(0.484349 + 1.49067i) q^{20} +(-1.19652 + 6.78578i) q^{21} +(-1.89573 - 2.72144i) q^{22} +(-1.39052 - 0.506108i) q^{23} +(1.34954 + 1.72733i) q^{24} +(2.53710 - 0.177411i) q^{25} +(-2.52250 - 1.12309i) q^{26} +(1.75287 + 1.94675i) q^{27} +(3.11285 + 0.437482i) q^{28} +(1.22673 + 1.18464i) q^{29} +(-3.13870 + 1.39744i) q^{30} +(3.78193 - 4.20026i) q^{31} +(0.766044 - 0.642788i) q^{32} +(5.49839 - 4.75625i) q^{33} +(-6.68156 - 2.43189i) q^{34} +(-1.84568 + 4.56822i) q^{35} +(-1.29836 + 1.25381i) q^{36} +(2.62851 - 1.90972i) q^{37} +(2.67471 + 3.44179i) q^{38} +(1.87037 - 5.75639i) q^{39} +(0.687097 + 1.40876i) q^{40} +(0.410003 + 1.64443i) q^{41} +(-0.240474 + 6.88626i) q^{42} +(-11.8872 + 4.32658i) q^{43} +(-2.25603 - 2.43112i) q^{44} +(-1.41451 - 2.45000i) q^{45} +(-1.44743 - 0.307660i) q^{46} +(3.83207 - 7.85691i) q^{47} +(1.57680 + 1.52270i) q^{48} +(1.92790 + 2.14115i) q^{49} +(2.48772 - 0.528781i) q^{50} +(3.77060 - 15.1231i) q^{51} +(-2.65425 - 0.761095i) q^{52} +(0.0190311 - 0.544981i) q^{53} +(2.00674 + 1.68386i) q^{54} +(4.55277 - 2.50919i) q^{55} +3.14344 q^{56} +(-6.89028 + 6.61949i) q^{57} +(1.37966 + 1.00238i) q^{58} +(-2.51772 - 5.16209i) q^{59} +(-2.91367 + 1.82066i) q^{60} +(-4.73404 + 6.05929i) q^{61} +(3.16056 - 4.68573i) q^{62} +(-5.65986 + 0.395776i) q^{63} +(0.669131 - 0.743145i) q^{64} +(2.16395 - 3.74807i) q^{65} +(4.78294 - 5.47519i) q^{66} +(-0.957384 - 5.42960i) q^{67} +(-6.95499 - 1.47833i) q^{68} +(0.339055 - 3.22589i) q^{69} +(-1.19195 + 4.78063i) q^{70} +(-0.319354 - 9.14512i) q^{71} +(-1.11122 + 1.42230i) q^{72} +(6.81009 + 0.476208i) q^{73} +(2.33715 - 2.25696i) q^{74} +(1.72275 + 5.30209i) q^{75} +(3.12768 + 3.03605i) q^{76} +(-0.520313 - 10.4126i) q^{77} +(1.05103 - 5.96068i) q^{78} +(-2.27548 + 5.63200i) q^{79} +(0.876472 + 1.29942i) q^{80} +(-6.23893 + 9.24959i) q^{81} +(0.634874 + 1.57137i) q^{82} +(10.5529 - 2.24308i) q^{83} +(0.720249 + 6.85271i) q^{84} +(4.88552 - 10.0168i) q^{85} +(-11.1694 + 5.93886i) q^{86} +(-1.86908 + 3.23735i) q^{87} +(-2.57242 - 2.09348i) q^{88} +(-6.95620 + 5.83694i) q^{89} +(-1.74172 - 2.22930i) q^{90} +(-4.85364 - 7.19581i) q^{91} +(-1.47616 - 0.103223i) q^{92} +(10.9391 + 5.81642i) q^{93} +(2.70131 - 8.31376i) q^{94} +(-5.80329 + 3.60545i) q^{95} +(1.77338 + 1.28843i) q^{96} +(16.6004 - 2.33303i) q^{97} +(2.20713 + 1.85200i) q^{98} +(4.89530 + 3.44550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

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