LMFDB - Embedded newform 414.2.m.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	414.13
Dual form			414.2.m.a.223.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(1.72251 + 0.181502i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.09565 - 1.53862i) q^{5} +(0.734899 - 1.56841i) q^{6} +(-0.216031 - 0.890490i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.93411 + 0.625279i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(1.72251 + 0.181502i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.09565 - 1.53862i) q^{5} +(0.734899 - 1.56841i) q^{6} +(-0.216031 - 0.890490i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.93411 + 0.625279i) q^{9} +(-1.81235 + 0.532155i) q^{10} +(1.10056 + 0.212116i) q^{11} +(-1.24179 - 1.20746i) q^{12} +(1.44384 - 5.95157i) q^{13} +(-0.912170 - 0.0871017i) q^{14} +(-1.60801 - 2.84917i) q^{15} +(0.235759 + 0.971812i) q^{16} +(0.0973643 + 0.677184i) q^{17} +(1.55054 - 2.56823i) q^{18} +(-0.0447979 + 0.311576i) q^{19} +(-0.0898758 + 1.88673i) q^{20} +(-0.210490 - 1.57309i) q^{21} +(0.560408 - 0.970655i) q^{22} +(-4.24934 + 2.22330i) q^{23} +(-1.54720 + 0.778573i) q^{24} +(0.468422 - 1.35342i) q^{25} +(-5.15201 - 3.31100i) q^{26} +(4.94057 + 1.60960i) q^{27} +(-0.380653 + 0.833514i) q^{28} +(-2.17646 + 1.71159i) q^{29} +(-3.21839 + 0.587699i) q^{30} +(-0.149557 - 3.13958i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.85723 + 0.565126i) q^{33} +(0.671784 + 0.129476i) q^{34} +(-1.13344 + 1.30805i) q^{35} +(-1.91985 - 2.30525i) q^{36} +(3.35153 + 7.33883i) q^{37} +(0.279788 + 0.144241i) q^{38} +(3.56725 - 9.98962i) q^{39} +(1.75356 + 0.702020i) q^{40} +(6.04316 + 8.48642i) q^{41} +(-1.55542 - 0.315595i) q^{42} +(-0.310190 + 6.51169i) q^{43} +(-0.733978 - 0.847056i) q^{44} +(-2.25269 - 5.19959i) q^{45} +(0.711200 + 4.74280i) q^{46} +(3.87813 + 6.71711i) q^{47} +(0.229713 + 1.71675i) q^{48} +(5.47555 - 2.82284i) q^{49} +(-1.12578 - 0.885319i) q^{50} +(0.0448014 + 1.18413i) q^{51} +(-4.81395 + 3.78573i) q^{52} +(-6.68438 - 1.96271i) q^{53} +(3.13697 - 4.14239i) q^{54} +(-0.879463 - 1.92575i) q^{55} +(0.663172 + 0.632333i) q^{56} +(-0.133717 + 0.528564i) q^{57} +(0.905602 + 2.61657i) q^{58} +(-0.0387312 + 0.159652i) q^{59} +(-0.497257 + 3.23360i) q^{60} +(-0.343626 - 0.177152i) q^{61} +(-3.01582 - 0.885524i) q^{62} +(-0.0770534 - 2.74788i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-10.7392 + 4.29932i) q^{65} +(1.14149 - 1.57025i) q^{66} +(-5.37298 + 1.03556i) q^{67} +(0.342074 - 0.592489i) q^{68} +(-7.72309 + 3.05841i) q^{69} +(0.865402 + 1.49892i) q^{70} +(-7.71531 - 8.90394i) q^{71} +(-2.80639 + 1.06028i) q^{72} +(0.198413 - 1.38000i) q^{73} +(8.03138 - 0.766904i) q^{74} +(1.05251 - 2.24626i) q^{75} +(0.227817 - 0.217223i) q^{76} +(-0.0488678 - 1.02586i) q^{77} +(-8.27346 - 6.63834i) q^{78} +(6.63153 + 6.32315i) q^{79} +(1.23694 - 1.42751i) q^{80} +(8.21805 + 3.66928i) q^{81} +(9.99620 - 2.93515i) q^{82} +(-7.89833 + 11.0916i) q^{83} +(-0.806964 + 1.36665i) q^{84} +(0.935254 - 0.891763i) q^{85} +(6.05209 + 2.42289i) q^{86} +(-4.05965 + 2.55321i) q^{87} +(-1.04053 + 0.416565i) q^{88} +(4.85913 + 3.12277i) q^{89} +(-5.65040 + 0.428176i) q^{90} -5.61173 q^{91} +(4.71456 + 0.879135i) q^{92} +(0.312226 - 5.43511i) q^{93} +(7.61609 - 1.46788i) q^{94} +(0.528481 - 0.272451i) q^{95} +(1.69746 + 0.344415i) q^{96} +(14.8387 - 1.41693i) q^{97} +(-0.876710 - 6.09765i) q^{98} +(3.09654 + 1.31053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	1.72251	+	0.181502i	0.994494	+	0.104790i
$3$	1.72251	+	0.181502i	0.994494	+	0.104790i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−1.09565	−	1.53862i	−0.489989	−	0.688094i	0.493359	−	0.869826i	$-0.335769\pi$
$5$	−1.09565	−	1.53862i	−0.489989	−	0.688094i	−0.983348	+	0.181732i	$0.941830\pi$
$6$	0.734899	−	1.56841i	0.300021	−	0.640303i
$7$	−0.216031	−	0.890490i	−0.0816519	−	0.336574i	0.916304	−	0.400484i	$-0.131158\pi$
$7$	−0.216031	−	0.890490i	−0.0816519	−	0.336574i	−0.997956	+	0.0639104i	$0.979643\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	2.93411	+	0.625279i	0.978038	+	0.208426i
$10$	−1.81235	+	0.532155i	−0.573116	+	0.168282i
$11$	1.10056	+	0.212116i	0.331832	+	0.0639553i	0.352446	−	0.935832i	$-0.385350\pi$
$11$	1.10056	+	0.212116i	0.331832	+	0.0639553i	−0.0206142	+	0.999788i	$0.506562\pi$
$12$	−1.24179	−	1.20746i	−0.358474	−	0.348563i
$13$	1.44384	−	5.95157i	0.400448	−	1.65067i	−0.312845	−	0.949804i	$-0.601282\pi$
$13$	1.44384	−	5.95157i	0.400448	−	1.65067i	0.713293	−	0.700866i	$-0.247203\pi$
$14$	−0.912170	−	0.0871017i	−0.243788	−	0.0232789i
$15$	−1.60801	−	2.84917i	−0.415186	−	0.735651i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	0.0973643	+	0.677184i	0.0236143	+	0.164241i	0.998216	−	0.0597036i	$-0.0190156\pi$
$17$	0.0973643	+	0.677184i	0.0236143	+	0.164241i	−0.974602	+	0.223945i	$0.928106\pi$
$18$	1.55054	−	2.56823i	0.365467	−	0.605338i
$19$	−0.0447979	+	0.311576i	−0.0102773	+	0.0714805i	−0.994315	−	0.106482i	$-0.966041\pi$
$19$	−0.0447979	+	0.311576i	−0.0102773	+	0.0714805i	0.984037	+	0.177962i	$0.0569505\pi$
$20$	−0.0898758	+	1.88673i	−0.0200968	+	0.421885i
$21$	−0.210490	−	1.57309i	−0.0459327	−	0.343277i
$22$	0.560408	−	0.970655i	0.119479	−	0.206944i
$23$	−4.24934	+	2.22330i	−0.886049	+	0.463591i
$23$	−4.24934	+	2.22330i	−0.886049	+	0.463591i
$24$	−1.54720	+	0.778573i	−0.315821	+	0.158925i
$25$	0.468422	−	1.35342i	0.0936845	−	0.270684i
$26$	−5.15201	−	3.31100i	−1.01039	−	0.649340i
$27$	4.94057	+	1.60960i	0.950812	+	0.309768i
$28$	−0.380653	+	0.833514i	−0.0719366	+	0.157519i
$29$	−2.17646	+	1.71159i	−0.404159	+	0.317834i	−0.799462	−	0.600717i	$-0.794882\pi$
$29$	−2.17646	+	1.71159i	−0.404159	+	0.317834i	0.395303	+	0.918551i	$0.370640\pi$
$30$	−3.21839	+	0.587699i	−0.587595	+	0.107299i
$31$	−0.149557	−	3.13958i	−0.0268611	−	0.563885i	−0.971681	−	0.236295i	$-0.924067\pi$
$31$	−0.149557	−	3.13958i	−0.0268611	−	0.563885i	0.944820	−	0.327590i	$-0.106236\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	1.85723	+	0.565126i	0.323303	+	0.0983759i
$34$	0.671784	+	0.129476i	0.115210	+	0.0222049i
$35$	−1.13344	+	1.30805i	−0.191586	+	0.221102i
$36$	−1.91985	−	2.30525i	−0.319975	−	0.384209i
$37$	3.35153	+	7.33883i	0.550989	+	1.20650i	0.956319	+	0.292327i	$0.0944294\pi$
$37$	3.35153	+	7.33883i	0.550989	+	1.20650i	−0.405330	+	0.914171i	$0.632843\pi$
$38$	0.279788	+	0.144241i	0.0453876	+	0.0233989i
$39$	3.56725	−	9.98962i	0.571217	−	1.59962i
$40$	1.75356	+	0.702020i	0.277263	+	0.110999i
$41$	6.04316	+	8.48642i	0.943782	+	1.32536i	0.945591	+	0.325358i	$0.105485\pi$
$41$	6.04316	+	8.48642i	0.943782	+	1.32536i	−0.00180842	+	0.999998i	$0.500576\pi$
$42$	−1.55542	−	0.315595i	−0.240006	−	0.0486973i
$43$	−0.310190	+	6.51169i	−0.0473035	+	0.993023i	0.843073	+	0.537799i	$0.180744\pi$
$43$	−0.310190	+	6.51169i	−0.0473035	+	0.993023i	−0.890377	+	0.455224i	$0.849559\pi$
$44$	−0.733978	−	0.847056i	−0.110651	−	0.127699i
$45$	−2.25269	−	5.19959i	−0.335811	−	0.775109i
$46$	0.711200	+	4.74280i	0.104861	+	0.699288i
$47$	3.87813	+	6.71711i	0.565683	+	0.979792i	0.996986	+	0.0775845i	$0.0247207\pi$
$47$	3.87813	+	6.71711i	0.565683	+	0.979792i	−0.431303	+	0.902207i	$0.641946\pi$
$48$	0.229713	+	1.71675i	0.0331562	+	0.247792i
$49$	5.47555	−	2.82284i	0.782221	−	0.403263i
$50$	−1.12578	−	0.885319i	−0.159209	−	0.125203i
$51$	0.0448014	+	1.18413i	0.00627345	+	0.165811i
$52$	−4.81395	+	3.78573i	−0.667575	+	0.524987i
$53$	−6.68438	−	1.96271i	−0.918170	−	0.269599i	−0.211694	−	0.977336i	$-0.567898\pi$
$53$	−6.68438	−	1.96271i	−0.918170	−	0.269599i	−0.706476	+	0.707737i	$0.749716\pi$
$54$	3.13697	−	4.14239i	0.426888	−	0.563708i
$55$	−0.879463	−	1.92575i	−0.118587	−	0.259669i
$56$	0.663172	+	0.632333i	0.0886200	+	0.0844990i
$57$	−0.133717	+	0.528564i	−0.0177112	+	0.0700099i
$58$	0.905602	+	2.61657i	0.118911	+	0.343572i
$59$	−0.0387312	+	0.159652i	−0.00504237	+	0.0207849i	−0.974277	−	0.225353i	$-0.927646\pi$
$59$	−0.0387312	+	0.159652i	−0.00504237	+	0.0207849i	0.969235	+	0.246138i	$0.0791616\pi$
$60$	−0.497257	+	3.23360i	−0.0641956	+	0.417456i
$61$	−0.343626	−	0.177152i	−0.0439968	−	0.0226819i	0.436088	−	0.899904i	$-0.356364\pi$
$61$	−0.343626	−	0.177152i	−0.0439968	−	0.0226819i	−0.480085	+	0.877222i	$0.659394\pi$
$62$	−3.01582	−	0.885524i	−0.383009	−	0.112462i
$63$	−0.0770534	−	2.74788i	−0.00970781	−	0.346200i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−10.7392	+	4.29932i	−1.33203	+	0.533265i
$66$	1.14149	−	1.57025i	0.140507	−	0.193285i
$67$	−5.37298	+	1.03556i	−0.656414	+	0.126513i	−0.506573	−	0.862197i	$-0.669088\pi$
$67$	−5.37298	+	1.03556i	−0.656414	+	0.126513i	−0.149840	+	0.988710i	$0.547876\pi$
$68$	0.342074	−	0.592489i	0.0414825	−	0.0718498i
$69$	−7.72309	+	3.05841i	−0.929751	+	0.368189i
$70$	0.865402	+	1.49892i	0.103435	+	0.179155i
$71$	−7.71531	−	8.90394i	−0.915639	−	1.05670i	−0.998191	−	0.0601171i	$-0.980853\pi$
$71$	−7.71531	−	8.90394i	−0.915639	−	1.05670i	0.0825522	−	0.996587i	$-0.473693\pi$
$72$	−2.80639	+	1.06028i	−0.330736	+	0.124956i
$73$	0.198413	−	1.38000i	0.0232225	−	0.161516i	−0.974910	−	0.222599i	$-0.928546\pi$
$73$	0.198413	−	1.38000i	0.0232225	−	0.161516i	0.998133	+	0.0610822i	$0.0194552\pi$
$74$	8.03138	−	0.766904i	0.933629	−	0.0891508i
$75$	1.05251	−	2.24626i	0.121534	−	0.259376i
$76$	0.227817	−	0.217223i	0.0261324	−	0.0249172i
$77$	−0.0488678	−	1.02586i	−0.00556901	−	0.116908i
$78$	−8.27346	−	6.63834i	−0.936785	−	0.751644i
$79$	6.63153	+	6.32315i	0.746106	+	0.711410i	0.964393	−	0.264474i	$-0.0851984\pi$
$79$	6.63153	+	6.32315i	0.746106	+	0.711410i	−0.218287	+	0.975885i	$0.570047\pi$
$80$	1.23694	−	1.42751i	0.138295	−	0.159600i
$81$	8.21805	+	3.66928i	0.913117	+	0.407698i
$82$	9.99620	−	2.93515i	1.10390	−	0.324133i
$83$	−7.89833	+	11.0916i	−0.866954	+	1.21747i	0.107797	+	0.994173i	$0.465620\pi$
$83$	−7.89833	+	11.0916i	−0.866954	+	1.21747i	−0.974751	+	0.223293i	$0.928319\pi$
$84$	−0.806964	+	1.36665i	−0.0880470	+	0.149114i
$85$	0.935254	−	0.891763i	0.101443	−	0.0967253i
$86$	6.05209	+	2.42289i	0.652614	+	0.261267i
$87$	−4.05965	+	2.55321i	−0.435240	+	0.273732i
$88$	−1.04053	+	0.416565i	−0.110921	+	0.0444060i
$89$	4.85913	+	3.12277i	0.515067	+	0.331013i	0.772218	−	0.635358i	$-0.219147\pi$
$89$	4.85913	+	3.12277i	0.515067	+	0.331013i	−0.257151	+	0.966371i	$0.582784\pi$
$90$	−5.65040	+	0.428176i	−0.595604	+	0.0451338i
$91$	−5.61173			−0.588269
$92$	4.71456	+	0.879135i	0.491527	+	0.0916562i
$93$	0.312226	−	5.43511i	0.0323763	−	0.563595i
$94$	7.61609	−	1.46788i	0.785540	−	0.151400i
$95$	0.528481	−	0.272451i	0.0542210	−	0.0279529i
$96$	1.69746	+	0.344415i	0.173247	+	0.0351518i
$97$	14.8387	−	1.41693i	1.50665	−	0.143867i	0.691185	−	0.722678i	$-0.257089\pi$
$97$	14.8387	−	1.41693i	1.50665	−	0.143867i	0.815462	+	0.578811i	$0.196483\pi$
$98$	−0.876710	−	6.09765i	−0.0885611	−	0.615956i
$99$	3.09654	+	1.31053i	0.311214	+	0.131713i
$100$	−1.20483	+	0.774299i	−0.120483	+	0.0774299i
$101$	−0.976540	+	1.37136i	−0.0971694	+	0.136455i	−0.860298	−	0.509791i	$-0.829723\pi$
$101$	−0.976540	+	1.37136i	−0.0971694	+	0.136455i	0.763129	+	0.646246i	$0.223662\pi$
$102$	1.13366	+	0.344954i	0.112249	+	0.0341555i
$103$	4.15406	+	12.0024i	0.409311	+	1.18263i	0.941795	+	0.336187i	$0.109138\pi$
$103$	4.15406	+	12.0024i	0.409311	+	1.18263i	−0.532484	+	0.846440i	$0.678741\pi$
$104$	2.00303	+	5.78738i	0.196413	+	0.567499i
$105$	−2.18977	+	2.04742i	−0.213700	+	0.199808i
$106$	−4.04101	+	5.67481i	−0.392498	+	0.551186i
$107$	10.7010	−	6.87712i	1.03451	−	0.664836i	0.0908836	−	0.995862i	$-0.471031\pi$
$107$	10.7010	−	6.87712i	1.03451	−	0.664836i	0.943622	+	0.331025i	$0.107395\pi$
$108$	−2.88856	−	4.31929i	−0.277952	−	0.415623i
$109$	−1.38004	−	9.59836i	−0.132183	−	0.919356i	−0.942700	−	0.333641i	$-0.891723\pi$
$109$	−1.38004	−	9.59836i	−0.132183	−	0.919356i	0.810517	−	0.585715i	$-0.199186\pi$
$110$	−2.10748	+	0.201240i	−0.200941	+	0.0191875i
$111$	4.44105	+	13.2496i	0.421526	+	1.25759i
$112$	0.814457	−	0.419882i	0.0769590	−	0.0396751i
$113$	−14.5348	+	2.80135i	−1.36732	+	0.263528i	−0.819504	−	0.573074i	$-0.805751\pi$
$113$	−14.5348	+	2.80135i	−1.36732	+	0.263528i	−0.547811	+	0.836602i	$0.684539\pi$
$114$	0.455759	+	0.299239i	0.0426857	+	0.0280263i
$115$	8.07662	+	4.10218i	0.753149	+	0.382530i
$116$	2.76885			0.257081
$117$	7.95778	−	16.5598i	0.735697	−	1.53095i
$118$	0.138204	+	0.0888181i	0.0127227	+	0.00817636i
$119$	0.581992	−	0.232994i	0.0533511	−	0.0213586i
$120$	2.89312	+	1.52752i	0.264104	+	0.139442i
$121$	−9.04581	−	3.62139i	−0.822346	−	0.329218i
$122$	−0.279798	+	0.266786i	−0.0253317	+	0.0241537i
$123$	8.86912	+	15.7148i	0.799702	+	1.41696i
$124$	−1.82320	+	2.56032i	−0.163728	+	0.229924i
$125$	−11.6574	+	3.42292i	−1.04267	+	0.306155i
$126$	−2.62195	−	0.825928i	−0.233582	−	0.0735795i
$127$	0.745471	−	0.860320i	0.0661499	−	0.0763410i	−0.721710	−	0.692195i	$-0.756644\pi$
$127$	0.745471	−	0.860320i	0.0661499	−	0.0763410i	0.787860	+	0.615854i	$0.211189\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	−1.71619	+	11.1602i	−0.151102	+	0.982599i
$130$	0.550418	+	11.5547i	0.0482749	+	1.01341i
$131$	2.88785	−	2.75356i	0.252313	−	0.240580i	−0.553358	−	0.832944i	$-0.686654\pi$
$131$	2.88785	−	2.75356i	0.252313	−	0.240580i	0.805671	+	0.592364i	$0.201805\pi$
$132$	−1.11055	−	1.59228i	−0.0966606	−	0.138591i
$133$	0.287133	−	0.0274179i	0.0248976	−	0.00237743i
$134$	−0.778727	+	5.41617i	−0.0672718	+	0.467885i
$135$	−2.93656	−	9.36523i	−0.252739	−	0.806031i
$136$	−0.448021	−	0.517044i	−0.0384175	−	0.0443362i
$137$	0.439449	+	0.761148i	0.0375447	+	0.0650293i	0.884187	−	0.467133i	$-0.154713\pi$
$137$	0.439449	+	0.761148i	0.0375447	+	0.0650293i	−0.846642	+	0.532162i	$0.821380\pi$
$138$	0.364224	+	8.29863i	0.0310048	+	0.706427i
$139$	0.980651	−	1.69854i	0.0831777	−	0.144068i	−0.821436	−	0.570301i	$-0.806826\pi$
$139$	0.980651	−	1.69854i	0.0831777	−	0.144068i	0.904613	+	0.426233i	$0.140160\pi$
$140$	1.69953	−	0.327557i	0.143636	−	0.0276836i
$141$	5.46096	+	12.2742i	0.459896	+	1.03368i
$142$	−10.9377	+	4.37878i	−0.917869	+	0.367459i
$143$	2.85145	−	6.24381i	0.238451	−	0.522134i
$144$	0.0840901	+	2.99882i	0.00700750	+	0.249902i
$145$	5.01813	+	1.47346i	0.416733	+	0.122364i
$146$	−1.23920	−	0.638853i	−0.102557	−	0.0528719i
$147$	9.94406	−	3.86856i	0.820172	−	0.319074i
$148$	1.90208	−	7.84049i	0.156350	−	0.644485i
$149$	−5.17431	−	14.9502i	−0.423896	−	1.22477i	−0.931679	−	0.363282i	$-0.881656\pi$
$149$	−5.17431	−	14.9502i	−0.423896	−	1.22477i	0.507784	−	0.861485i	$-0.330465\pi$
$150$	−1.77848	−	1.72931i	−0.145212	−	0.141197i
$151$	9.60679	+	9.16005i	0.781789	+	0.745434i	0.971662	−	0.236374i	$-0.0759591\pi$
$151$	9.60679	+	9.16005i	0.781789	+	0.745434i	−0.189873	+	0.981809i	$0.560808\pi$
$152$	−0.130764	−	0.286334i	−0.0106064	−	0.0232248i
$153$	−0.137751	+	2.04781i	−0.0111365	+	0.165556i
$154$	−0.985424	−	0.289346i	−0.0794077	−	0.0233162i
$155$	−4.66677	+	3.66999i	−0.374844	+	0.294781i
$156$	−8.97922	+	5.64724i	−0.718913	+	0.452141i
$157$	−7.23029	−	5.68596i	−0.577040	−	0.453789i	0.286493	−	0.958082i	$-0.407511\pi$
$157$	−7.23029	−	5.68596i	−0.577040	−	0.453789i	−0.863532	+	0.504293i	$0.831753\pi$
$158$	8.14435	−	4.19870i	0.647929	−	0.334031i
$159$	−11.1577	−	4.59403i	−0.884864	−	0.364330i
$160$	−0.944433	−	1.63581i	−0.0746640	−	0.129322i
$161$	2.89782	+	3.30370i	0.228380	+	0.260368i
$162$	6.15534	−	6.56596i	0.483609	−	0.515871i
$163$	0.0679811	+	0.0784544i	0.00532469	+	0.00614502i	0.758406	−	0.651783i	$-0.225979\pi$
$163$	0.0679811	+	0.0784544i	0.00532469	+	0.00614502i	−0.753081	+	0.657928i	$0.771433\pi$
$164$	0.495718	−	10.4064i	0.0387091	−	0.812604i
$165$	−1.16536	−	3.47677i	−0.0907231	−	0.270666i
$166$	7.89833	+	11.0916i	0.613029	+	0.860879i
$167$	12.5323	+	5.01716i	0.969775	+	0.388239i	0.801827	−	0.597557i	$-0.203862\pi$
$167$	12.5323	+	5.01716i	0.969775	+	0.388239i	0.167948	+	0.985796i	$0.446286\pi$
$168$	1.02755	+	1.20957i	0.0792775	+	0.0933203i
$169$	−21.7817	−	11.2293i	−1.67552	−	0.863789i
$170$	−0.536825	−	1.17548i	−0.0411726	−	0.0901555i
$171$	−0.326264	+	0.886189i	−0.0249500	+	0.0677685i
$172$	4.26908	−	4.92678i	0.325514	−	0.375664i
$173$	−2.86901	−	0.552957i	−0.218127	−	0.0420406i	0.0790167	−	0.996873i	$-0.474822\pi$
$173$	−2.86901	−	0.552957i	−0.218127	−	0.0420406i	−0.297144	+	0.954833i	$0.596034\pi$
$174$	1.08500	+	4.67144i	0.0822537	+	0.354141i
$175$	−1.30640	−	0.124746i	−0.0987545	−	0.00942991i
$176$	0.0533306	+	1.11955i	0.00401994	+	0.0843890i
$177$	−0.0956921	+	0.267973i	−0.00719266	+	0.0201421i
$178$	4.54029	−	3.57052i	0.340309	−	0.267622i
$179$	−2.81613	+	6.16646i	−0.210487	+	0.460903i	−0.985200	−	0.171411i	$-0.945167\pi$
$179$	−2.81613	+	6.16646i	−0.210487	+	0.460903i	0.774712	+	0.632314i	$0.217895\pi$
$180$	−1.44344	+	5.47967i	−0.107587	+	0.408431i
$181$	−14.5329	−	9.33971i	−1.08022	−	0.694215i	−0.125612	−	0.992079i	$-0.540089\pi$
$181$	−14.5329	−	9.33971i	−1.08022	−	0.694215i	−0.954608	+	0.297864i	$0.903726\pi$
$182$	−1.83542	+	5.30309i	−0.136050	+	0.393091i
$183$	−0.559748	−	0.367515i	−0.0413778	−	0.0271675i
$184$	2.37277	−	4.16773i	0.174923	−	0.307249i
$185$	7.61960	−	13.1975i	0.560204	−	0.970303i
$186$	−5.03407	−	2.07271i	−0.369116	−	0.151978i
$187$	−0.0364860	+	0.765935i	−0.00266812	+	0.0560107i
$188$	1.10383	−	7.67731i	0.0805051	−	0.559925i
$189$	0.366019	−	4.74725i	0.0266240	−	0.345311i
$190$	−0.0846172	−	0.588525i	−0.00613877	−	0.0426961i
$191$	−2.11725	−	8.72742i	−0.153199	−	0.631494i	−0.995687	−	0.0927789i	$-0.970425\pi$
$191$	−2.11725	−	8.72742i	−0.153199	−	0.631494i	0.842488	−	0.538715i	$-0.181090\pi$
$192$	0.880658	−	1.49146i	0.0635560	−	0.107637i
$193$	−13.2391	−	1.26418i	−0.952970	−	0.0909976i	−0.393026	−	0.919528i	$-0.628572\pi$
$193$	−13.2391	−	1.26418i	−0.952970	−	0.0909976i	−0.559945	+	0.828530i	$0.689178\pi$
$194$	3.51428	−	14.4861i	0.252311	−	1.04004i
$195$	−19.2787	+	5.45646i	−1.38058	+	0.390745i
$196$	−6.04903	−	1.16586i	−0.432074	−	0.0832754i
$197$	9.08446	−	2.66744i	0.647241	−	0.190047i	0.0583964	−	0.998293i	$-0.481401\pi$
$197$	9.08446	−	2.66744i	0.647241	−	0.190047i	0.588844	+	0.808246i	$0.299583\pi$
$198$	2.25123	−	2.49760i	0.159988	−	0.177497i
$199$	−14.9998	+	9.63978i	−1.06331	+	0.683346i	−0.950643	−	0.310288i	$-0.899575\pi$
$199$	−14.9998	+	9.63978i	−1.06331	+	0.683346i	−0.112664	+	0.993633i	$0.535938\pi$
$200$	0.337651	+	1.39182i	0.0238755	+	0.0984162i
$201$	−9.44299	+	0.808556i	−0.666057	+	0.0570312i
$202$	0.976540	+	1.37136i	0.0687091	+	0.0964885i
$203$	1.99434	+	1.56836i	0.139975	+	0.110077i
$204$	0.696765	−	0.958484i	0.0487833	−	0.0671073i
$205$	6.43624	−	18.5963i	0.449526	−	1.29882i
$206$	12.7009			0.884914
$207$	−13.8582	+	3.86640i	−0.963215	+	0.268733i
$208$	6.12421			0.424637
$209$	−0.115393	+	0.333406i	−0.00798190	+	0.0230622i
$210$	1.21861	+	2.73898i	0.0840922	+	0.189008i
$211$	−1.59951	−	1.25787i	−0.110115	−	0.0865950i	0.561584	−	0.827420i	$-0.310192\pi$
$211$	−1.59951	−	1.25787i	−0.110115	−	0.0865950i	−0.671698	+	0.740825i	$0.734435\pi$
$212$	4.04101	+	5.67481i	0.277538	+	0.389747i
$213$	−11.6737	−	16.7375i	−0.799866	−	1.14684i
$214$	−2.99893	−	12.3617i	−0.205002	−	0.845032i
$215$	10.3589	−	6.65726i	0.706471	−	0.454021i
$216$	−5.02648	+	1.31699i	−0.342009	+	0.0896098i
$217$	−2.76345	+	0.811423i	−0.187595	+	0.0550830i
$218$	−9.52183	−	1.83518i	−0.644899	−	0.124294i
$219$	0.592242	−	2.34105i	0.0400200	−	0.158194i
$220$	−0.499118	+	2.05739i	−0.0336505	+	0.138709i
$221$	4.17089	+	0.398272i	0.280564	+	0.0267906i
$222$	13.9734	+	0.136707i	0.937831	+	0.00917519i
$223$	−3.66184	−	15.0943i	−0.245215	−	1.01079i	−0.952664	−	0.304025i	$-0.901669\pi$
$223$	−3.66184	−	15.0943i	−0.245215	−	1.01079i	0.707449	−	0.706764i	$-0.249846\pi$
$224$	−0.130406	−	0.906993i	−0.00871311	−	0.0606010i
$225$	2.22067	−	3.67819i	0.148045	−	0.245213i
$226$	−2.10658	+	14.6516i	−0.140128	+	0.974609i
$227$	0.0552352	−	1.15953i	0.00366609	−	0.0769607i	−0.996293	−	0.0860269i	$-0.972583\pi$
$227$	0.0552352	−	1.15953i	0.00366609	−	0.0769607i	0.999959	+	0.00906627i	$0.00288592\pi$
$228$	0.431845	−	0.332821i	0.0285996	−	0.0220416i
$229$	11.6303	−	20.1443i	0.768551	−	1.33117i	−0.169797	−	0.985479i	$-0.554311\pi$
$229$	11.6303	−	20.1443i	0.768551	−	1.33117i	0.938348	−	0.345691i	$-0.112356\pi$
$230$	6.51817	−	6.29072i	0.429795	−	0.414798i
$231$	0.102020	−	1.77593i	0.00671244	−	0.116848i
$232$	0.905602	−	2.61657i	0.0594557	−	0.171786i
$233$	−14.2939	−	9.18616i	−0.936427	−	0.601805i	−0.0190477	−	0.999819i	$-0.506063\pi$
$233$	−14.2939	−	9.18616i	−0.936427	−	0.601805i	−0.917380	+	0.398013i	$0.869700\pi$
$234$	−13.0463	−	12.9363i	−0.852863	−	0.845671i
$235$	6.08605	−	13.3266i	0.397010	−	0.869330i
$236$	0.129135	−	0.101553i	0.00840598	−	0.00661054i
$237$	10.2752	+	12.0954i	0.667449	+	0.785678i
$238$	−0.0298290	−	0.626188i	−0.00193353	−	0.0405897i
$239$	26.6008	+	2.54007i	1.72066	+	0.164303i	0.908152	−	0.418642i	$-0.137494\pi$
$239$	26.6008	+	2.54007i	1.72066	+	0.164303i	0.812512	+	0.582945i	$0.198100\pi$
$240$	2.38975	−	2.23440i	0.154258	−	0.144230i
$241$	−18.6581	−	3.59606i	−1.20188	−	0.231643i	−0.451267	−	0.892389i	$-0.649028\pi$
$241$	−18.6581	−	3.59606i	−1.20188	−	0.231643i	−0.750610	+	0.660746i	$0.770240\pi$
$242$	−6.38081	+	7.36385i	−0.410174	+	0.473366i
$243$	13.4897	+	7.81198i	0.865367	+	0.501139i
$244$	0.160601	+	0.351666i	0.0102814	+	0.0225131i
$245$	−10.3426	−	5.33196i	−0.660762	−	0.340647i
$246$	17.7513	−	3.24151i	1.13178	−	0.206671i
$247$	1.78969	+	0.716483i	0.113875	+	0.0455887i
$248$	1.82320	+	2.56032i	0.115773	+	0.162581i
$249$	−15.6181	+	17.6720i	−0.989759	+	1.11992i
$250$	−0.578098	+	12.1358i	−0.0365621	+	0.767534i
$251$	−1.91817	−	2.21369i	−0.121074	−	0.139727i	0.691977	−	0.721920i	$-0.256740\pi$
$251$	−1.91817	−	2.21369i	−0.121074	−	0.139727i	−0.813050	+	0.582193i	$0.802195\pi$
$252$	−1.63806	+	2.20761i	−0.103188	+	0.139066i
$253$	−5.14826	+	1.54553i	−0.323668	+	0.0971666i
$254$	−0.569183	−	0.985854i	−0.0357137	−	0.0618580i
$255$	1.77285	−	1.36632i	0.111020	−	0.0855626i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−6.25388	−	4.91811i	−0.390107	−	0.306783i	0.403772	−	0.914860i	$-0.367699\pi$
$257$	−6.25388	−	4.91811i	−0.390107	−	0.306783i	−0.793878	+	0.608077i	$0.791941\pi$
$258$	9.98506	+	5.27194i	0.621643	+	0.328216i
$259$	5.81113	−	4.56992i	0.361086	−	0.283961i
$260$	11.0992	+	3.25903i	0.688345	+	0.202116i
$261$	−7.45621	+	3.66110i	−0.461528	+	0.226616i
$262$	−1.65759	−	3.62963i	−0.102407	−	0.224239i
$263$	0.540964	+	0.515808i	0.0333573	+	0.0318061i	0.706574	−	0.707639i	$-0.250240\pi$
$263$	0.540964	+	0.515808i	0.0333573	+	0.0318061i	−0.673217	+	0.739445i	$0.735088\pi$
$264$	−1.86793	+	0.528682i	−0.114963	+	0.0325381i
$265$	4.30386	+	12.4352i	0.264384	+	0.763888i
$266$	0.0680021	−	0.280309i	0.00416948	−	0.0171868i
$267$	7.80314	+	6.26097i	0.477544	+	0.383165i
$268$	4.86358	+	2.50735i	0.297091	+	0.153161i
$269$	−23.2572	−	6.82892i	−1.41801	−	0.416367i	−0.519184	−	0.854663i	$-0.673764\pi$
$269$	−23.2572	−	6.82892i	−1.41801	−	0.416367i	−0.898831	+	0.438296i	$0.855582\pi$
$270$	−9.81061	−	0.288017i	−0.597054	−	0.0175282i
$271$	−1.60500	+	3.51447i	−0.0974970	+	0.213489i	−0.952096	−	0.305801i	$-0.901076\pi$
$271$	−1.60500	+	3.51447i	−0.0974970	+	0.213489i	0.854599	+	0.519289i	$0.173803\pi$
$272$	−0.635141	+	0.254272i	−0.0385111	+	0.0154175i
$273$	−9.66629	−	1.01854i	−0.585030	−	0.0616448i
$274$	0.863015	−	0.166333i	0.0521366	−	0.0100485i
$275$	0.802609	−	1.39016i	0.0483991	−	0.0838298i
$276$	7.96134	+	2.37003i	0.479217	+	0.142659i
$277$	4.13088	+	7.15490i	0.248201	+	0.429896i	0.963027	−	0.269406i	$-0.0868274\pi$
$277$	4.13088	+	7.15490i	0.248201	+	0.429896i	−0.714826	+	0.699302i	$0.753494\pi$
$278$	−1.28438	−	1.48225i	−0.0770320	−	0.0888996i
$279$	1.52430	−	9.30540i	0.0912573	−	0.557099i
$280$	0.246319	−	1.71319i	0.0147204	−	0.102383i
$281$	−8.52057	+	0.813616i	−0.508295	+	0.0485363i	−0.346053	−	0.938215i	$-0.612478\pi$
$281$	−8.52057	+	0.813616i	−0.508295	+	0.0485363i	−0.162241	+	0.986751i	$0.551872\pi$
$282$	13.3852	−	1.14611i	0.797080	−	0.0682500i
$283$	−23.9621	+	22.8478i	−1.42440	+	1.35816i	−0.589483	+	0.807781i	$0.700669\pi$
$283$	−23.9621	+	22.8478i	−1.42440	+	1.35816i	−0.834915	+	0.550380i	$0.814483\pi$
$284$	0.560591	+	11.7683i	0.0332650	+	0.698318i
$285$	0.959767	−	0.373381i	0.0568517	−	0.0221172i
$286$	−4.96779	−	4.73678i	−0.293751	−	0.280091i
$287$	6.25157	−	7.21470i	0.369018	−	0.425870i
$288$	2.86139	+	0.901353i	0.168609	+	0.0531127i
$289$	15.8623	−	4.65759i	0.933075	−	0.273976i
$290$	3.03369	−	4.26022i	0.178144	−	0.250169i
$291$	25.8171	+	0.252580i	1.51343	+	0.0148065i
$292$	−1.00902	+	0.962099i	−0.0590484	+	0.0563026i
$293$	27.6536	+	11.0708i	1.61554	+	0.646766i	0.990956	−	0.134190i	$-0.0428431\pi$
$293$	27.6536	+	11.0708i	1.61554	+	0.646766i	0.624587	+	0.780955i	$0.285267\pi$
$294$	−0.403411	−	10.6624i	−0.0235274	−	0.621845i
$295$	0.288080	−	0.115330i	0.0167727	−	0.00671477i
$296$	−6.78716	−	4.36184i	−0.394496	−	0.253527i
$297$	5.09597	+	2.81944i	0.295698	+	0.163600i
$298$	−15.8203			−0.916444
$299$	7.09680	+	28.5004i	0.410419	+	1.64822i
$300$	−2.21588	+	1.11506i	−0.127934	+	0.0643781i
$301$	5.86560	−	1.13050i	0.338088	−	0.0651610i
$302$	11.7983	−	6.08246i	0.678918	−	0.350006i
$303$	−1.93101	+	2.18494i	−0.110934	+	0.125522i
$304$	−0.313355	+	0.0299218i	−0.0179721	+	0.00171613i
$305$	0.103924	+	0.722808i	0.00595067	+	0.0413879i
$306$	1.89013	+	0.799949i	0.108052	+	0.0457301i
$307$	−21.3087	+	13.6943i	−1.21615	+	0.781575i	−0.981678	−	0.190547i	$-0.938974\pi$
$307$	−21.3087	+	13.6943i	−1.21615	+	0.781575i	−0.234476	+	0.972122i	$0.575338\pi$
$308$	−0.595733	+	0.836590i	−0.0339450	+	0.0476692i
$309$	4.97697	+	21.4282i	0.283130	+	1.21901i
$310$	1.94179	+	5.61044i	0.110286	+	0.318651i
$311$	1.49046	+	4.30639i	0.0845160	+	0.244193i	0.979338	−	0.202230i	$-0.0648189\pi$
$311$	1.49046	+	4.30639i	0.0845160	+	0.244193i	−0.894822	+	0.446423i	$0.852698\pi$
$312$	2.39983	+	10.3324i	0.135864	+	0.584957i
$313$	−7.74725	+	10.8795i	−0.437900	+	0.614945i	−0.973268	−	0.229674i	$-0.926234\pi$
$313$	−7.74725	+	10.8795i	−0.437900	+	0.614945i	0.535367	+	0.844620i	$0.320173\pi$
$314$	−7.73804	+	4.97293i	−0.436683	+	0.280639i
$315$	−4.14353	+	3.12927i	−0.233461	+	0.176314i
$316$	−1.30402	−	9.06968i	−0.0733570	−	0.510209i
$317$	13.1818	−	1.25871i	0.740362	−	0.0706960i	0.281942	−	0.959431i	$-0.409021\pi$
$317$	13.1818	−	1.25871i	0.740362	−	0.0706960i	0.458420	+	0.888735i	$0.348415\pi$
$318$	−7.99069	+	9.04149i	−0.448096	+	0.507021i
$319$	−2.75839	+	1.42205i	−0.154440	+	0.0796193i
$320$	−1.85473	+	0.357470i	−0.103683	+	0.0199832i
$321$	19.6809	−	9.90369i	1.09848	−	0.552770i
$322$	4.06978	−	1.65791i	0.226800	−	0.0923915i
$323$	−0.215356			−0.0119827
$324$	−4.19163	−	7.96431i	−0.232868	−	0.442462i
$325$	−7.37864	−	4.74197i	−0.409293	−	0.263037i
$326$	0.0963739	−	0.0385823i	0.00533766	−	0.00213688i
$327$	−0.635012	−	16.7838i	−0.0351163	−	0.928146i
$328$	−9.67193	−	3.87206i	−0.534043	−	0.213799i
$329$	5.14373	−	4.90453i	0.283583	−	0.270396i
$330$	−3.66670	−	0.0358728i	−0.201845	−	0.00197473i
$331$	20.7606	−	29.1542i	1.14110	−	1.60246i	0.423697	−	0.905804i	$-0.360732\pi$
$331$	20.7606	−	29.1542i	1.14110	−	1.60246i	0.717408	−	0.696653i	$-0.245328\pi$
$332$	13.0649	−	3.83620i	0.717030	−	0.210539i
$333$	5.24496	+	23.6286i	0.287422	+	1.29484i
$334$	8.84011	−	10.2020i	0.483710	−	0.558231i
$335$	7.48023	+	7.13239i	0.408689	+	0.389684i
$336$	1.47912	−	0.575427i	0.0806928	−	0.0313921i
$337$	−1.21823	−	25.5737i	−0.0663611	−	1.39309i	−0.749114	−	0.662441i	$-0.769521\pi$
$337$	−1.21823	−	25.5737i	−0.0663611	−	1.39309i	0.682753	−	0.730649i	$-0.260782\pi$
$338$	−17.7358	+	16.9110i	−0.964698	+	0.919838i
$339$	−25.5448	+	2.18727i	−1.38740	+	0.118796i
$340$	−1.28641	+	0.122837i	−0.0697654	+	0.00666179i
$341$	0.501358	−	3.48702i	0.0271501	−	0.188833i
$342$	0.730738	+	0.598164i	0.0395138	+	0.0323450i
$343$	−7.89703	−	9.11365i	−0.426399	−	0.492091i
$344$	−3.25953	−	5.64568i	−0.175742	−	0.304395i
$345$	13.1675	+	8.53199i	0.708917	+	0.459347i
$346$	−1.46091	+	2.53037i	−0.0785389	+	0.136033i
$347$	4.33090	−	0.834712i	0.232495	−	0.0448097i	−0.0716729	−	0.997428i	$-0.522834\pi$
$347$	4.33090	−	0.834712i	0.232495	−	0.0448097i	0.304168	+	0.952618i	$0.401622\pi$
$348$	4.76938	+	0.502551i	0.255666	+	0.0269396i
$349$	20.1548	−	8.06877i	1.07886	−	0.431911i	0.236948	−	0.971522i	$-0.423853\pi$
$349$	20.1548	−	8.06877i	1.07886	−	0.431911i	0.841915	+	0.539611i	$0.181429\pi$
$350$	−0.545166	+	1.19375i	−0.0291404	+	0.0638085i
$351$	16.7130	−	27.0801i	0.892075	−	1.44543i
$352$	1.07541	+	0.315770i	0.0573198	+	0.0168306i
$353$	−2.47936	−	1.27820i	−0.131963	−	0.0680316i	0.390981	−	0.920399i	$-0.372136\pi$
$353$	−2.47936	−	1.27820i	−0.131963	−	0.0680316i	−0.522944	+	0.852367i	$0.675166\pi$
$354$	0.221937	+	0.178075i	0.0117958	+	0.00946456i
$355$	−5.24655	+	21.6266i	−0.278458	+	1.14782i
$356$	−1.88916	−	5.45838i	−0.100126	−	0.289294i
$357$	1.04478	−	0.295704i	0.0552955	−	0.0156503i
$358$	4.90624	+	4.67809i	0.259303	+	0.247245i
$359$	15.1616	+	33.1992i	0.800197	+	1.75219i	0.644825	+	0.764330i	$0.276930\pi$
$359$	15.1616	+	33.1992i	0.800197	+	1.75219i	0.155372	+	0.987856i	$0.450342\pi$
$360$	4.70619	+	3.15627i	0.248038	+	0.166350i
$361$	18.1353	+	5.32500i	0.954489	+	0.280263i
$362$	−13.5793	+	10.6789i	−0.713711	+	0.561268i
$363$	−14.9242	−	7.87974i	−0.783320	−	0.413579i
$364$	4.41112	+	3.46894i	0.231205	+	0.181822i
$365$	−2.34069	+	1.20671i	−0.122517	+	0.0631620i
$366$	−0.530378	+	0.408760i	−0.0277233	+	0.0213662i
$367$	−9.10821	−	15.7759i	−0.475445	−	0.823495i	0.524159	−	0.851620i	$-0.324380\pi$
$367$	−9.10821	−	15.7759i	−0.475445	−	0.823495i	−0.999604	+	0.0281254i	$0.991046\pi$
$368$	−3.16245	−	3.60540i	−0.164854	−	0.187944i
$369$	12.4249	+	28.6788i	0.646816	+	1.49296i
$370$	−9.97956	−	11.5170i	−0.518813	−	0.598742i
$371$	−0.303744	+	6.37638i	−0.0157696	+	0.331045i
$372$	−3.60519	+	4.07928i	−0.186920	+	0.211501i
$373$	−15.6173	−	21.9314i	−0.808634	−	1.13557i	−0.988402	−	0.151858i	$-0.951474\pi$
$373$	−15.6173	−	21.9314i	−0.808634	−	1.13557i	0.179769	−	0.983709i	$-0.442465\pi$
$374$	0.711876	+	0.284992i	0.0368102	+	0.0147366i
$375$	−20.7013	+	3.78019i	−1.06901	+	0.195208i
$376$	−6.89403	−	3.55412i	−0.355533	−	0.183290i
$377$	7.04420	+	15.4246i	0.362795	+	0.794409i
$378$	−4.36644	−	1.89856i	−0.224585	−	0.0976514i
$379$	−6.32289	+	7.29700i	−0.324785	+	0.374822i	−0.894536	−	0.446995i	$-0.852494\pi$
$379$	−6.32289	+	7.29700i	−0.324785	+	0.374822i	0.569751	+	0.821817i	$0.307040\pi$
$380$	−0.583832	−	0.112524i	−0.0299500	−	0.00577238i
$381$	1.44023	−	1.34661i	0.0737855	−	0.0689889i
$382$	−8.93991	−	0.853658i	−0.457405	−	0.0436769i
$383$	0.796851	+	16.7280i	0.0407172	+	0.854759i	0.923178	+	0.384373i	$0.125582\pi$
$383$	0.796851	+	16.7280i	0.0407172	+	0.854759i	−0.882461	+	0.470386i	$0.844115\pi$
$384$	−1.12139	−	1.32003i	−0.0572258	−	0.0673625i
$385$	−1.52487	+	1.19917i	−0.0777148	+	0.0611156i
$386$	−5.52473	+	12.0975i	−0.281201	+	0.615745i
$387$	−4.98175	+	18.9121i	−0.253237	+	0.961355i
$388$	−12.5399	−	8.05892i	−0.636619	−	0.409130i
$389$	7.09341	−	20.4951i	0.359650	−	1.03914i	−0.609524	−	0.792767i	$-0.708640\pi$
$389$	7.09341	−	20.4951i	0.359650	−	1.03914i	0.969175	−	0.246374i	$-0.0792392\pi$
$390$	−1.14910	+	20.0030i	−0.0581867	+	1.01289i
$391$	−1.91932	−	2.66112i	−0.0970642	−	0.134578i
$392$	−3.08018	+	5.33503i	−0.155573	+	0.269460i
$393$	5.47415	−	4.21890i	0.276134	−	0.212815i
$394$	0.450504	−	9.45725i	0.0226961	−	0.476450i
$395$	2.46312	−	17.1314i	0.123933	−	0.861974i
$396$	−1.62393	−	2.94430i	−0.0816055	−	0.147957i
$397$	3.83393	+	26.6656i	0.192420	+	1.33831i	0.825579	+	0.564286i	$0.190849\pi$
$397$	3.83393	+	26.6656i	0.192420	+	1.33831i	−0.633159	+	0.774021i	$0.718242\pi$
$398$	4.20365	+	17.3277i	0.210710	+	0.868558i
$399$	0.499567	+	0.00488747i	0.0250097	+	0.000244680i
$400$	1.42570	+	0.136138i	0.0712851	+	0.00680690i
$401$	0.804819	−	3.31751i	0.0401908	−	0.165669i	−0.948179	−	0.317735i	$-0.897078\pi$
$401$	0.804819	−	3.31751i	0.0401908	−	0.165669i	0.988370	+	0.152067i	$0.0485928\pi$
$402$	−2.32441	+	9.18809i	−0.115931	+	0.458260i
$403$	−18.9014	−	3.64294i	−0.941544	−	0.181468i
$404$	1.61533	−	0.474304i	0.0803657	−	0.0235975i
$405$	−3.35846	−	16.6647i	−0.166883	−	0.828078i
$406$	2.13439	−	1.37169i	0.105928	−	0.0680757i
$407$	2.13189	+	8.78775i	0.105674	+	0.435593i
$408$	−0.677879	−	0.971933i	−0.0335600	−	0.0481178i
$409$	11.1883	+	15.7118i	0.553226	+	0.776897i	0.992603	−	0.121406i	$-0.0387402\pi$
$409$	11.1883	+	15.7118i	0.553226	+	0.776897i	−0.439377	+	0.898303i	$0.644801\pi$
$410$	−15.4684	−	12.1645i	−0.763931	−	0.600762i
$411$	0.618808	+	1.39085i	0.0305235	+	0.0686055i
$412$	4.15406	−	12.0024i	0.204656	−	0.591314i
$413$	0.150536			0.00740738
$414$	−0.878836	+	14.3606i	−0.0431924	+	0.705786i
$415$	25.7197			1.26253
$416$	2.00303	−	5.78738i	0.0982067	−	0.283750i
$417$	1.99747	−	2.74776i	0.0978167	−	0.134559i
$418$	0.277328	+	0.218093i	0.0135645	+	0.0106673i
$419$	−18.8205	−	26.4297i	−0.919441	−	1.29117i	−0.956461	−	0.291859i	$-0.905726\pi$
$419$	−18.8205	−	26.4297i	−0.919441	−	1.29117i	0.0370207	−	0.999314i	$-0.488213\pi$
$420$	2.98691	−	0.255754i	0.145746	−	0.0124795i
$421$	7.16527	+	29.5356i	0.349214	+	1.43948i	0.827594	+	0.561327i	$0.189709\pi$
$421$	7.16527	+	29.5356i	0.349214	+	1.43948i	−0.478381	+	0.878153i	$0.658776\pi$
$422$	−1.71183	+	1.10013i	−0.0833306	+	0.0535533i
$423$	7.17880	+	22.1337i	0.349045	+	1.07618i
$424$	6.68438	−	1.96271i	0.324622	−	0.0953177i
$425$	0.962120	+	0.185433i	0.0466697	+	0.00899485i
$426$	−19.6350	+	5.55731i	−0.951321	+	0.269252i
$427$	−0.0835180	+	0.344266i	−0.00404172	+	0.0166602i
$428$	−12.6627	−	1.20914i	−0.612075	−	0.0584461i
$429$	6.04493	−	10.2375i	0.291852	−	0.494272i
$430$	−2.90305	−	11.9665i	−0.139998	−	0.577078i
$431$	0.699960	+	4.86833i	0.0337159	+	0.234499i	0.999710	−	0.0240633i	$-0.00766032\pi$
$431$	0.699960	+	4.86833i	0.0337159	+	0.234499i	−0.965995	+	0.258562i	$0.916751\pi$
$432$	−0.399445	+	5.18078i	−0.0192183	+	0.249260i
$433$	−0.760004	+	5.28594i	−0.0365235	+	0.254026i	−0.999900	−	0.0141252i	$-0.995504\pi$
$433$	−0.760004	+	5.28594i	−0.0365235	+	0.254026i	0.963377	+	0.268151i	$0.0864128\pi$
$434$	−0.137042	+	2.87686i	−0.00657821	+	0.138094i
$435$	8.37637	+	3.44885i	0.401616	+	0.165360i
$436$	−4.84853	+	8.39790i	−0.232203	+	0.402187i
$437$	−0.502367	−	1.42359i	−0.0240315	−	0.0680997i
$438$	−2.01859	−	1.32535i	−0.0964520	−	0.0633277i
$439$	−3.80854	+	11.0041i	−0.181772	+	0.525195i	−0.998668	−	0.0515888i	$-0.983571\pi$
$439$	−3.80854	+	11.0041i	−0.181772	+	0.525195i	0.816896	+	0.576784i	$0.195693\pi$
$440$	1.78099	+	1.14457i	0.0849055	+	0.0545655i
$441$	17.8309	−	4.85879i	0.849092	−	0.231371i
$442$	1.74053	−	3.81123i	0.0827886	−	0.181282i
$443$	22.3450	−	17.5723i	1.06164	−	0.834884i	0.0749016	−	0.997191i	$-0.476136\pi$
$443$	22.3450	−	17.5723i	1.06164	−	0.834884i	0.986740	+	0.162306i	$0.0518933\pi$
$444$	4.69943	−	13.1601i	0.223025	−	0.624552i
$445$	−0.519128	−	10.8978i	−0.0246090	−	0.516607i
$446$	−15.4618	−	1.47642i	−0.732137	−	0.0699106i
$447$	−6.19934	−	26.6910i	−0.293218	−	1.26244i
$448$	−0.899760	−	0.173415i	−0.0425097	−	0.00819307i
$449$	−14.7401	+	17.0109i	−0.695627	+	0.802796i	−0.988155	−	0.153461i	$-0.950958\pi$
$449$	−14.7401	+	17.0109i	−0.695627	+	0.802796i	0.292528	+	0.956257i	$0.405504\pi$
$450$	−2.74958	−	3.30155i	−0.129616	−	0.155637i
$451$	4.85076	+	10.6217i	0.228413	+	0.500155i
$452$	13.1568	+	6.78279i	0.618842	+	0.319035i
$453$	14.8853	+	17.5220i	0.699371	+	0.823254i
$454$	−1.07769	−	0.431442i	−0.0505785	−	0.0202486i
$455$	6.14849	+	8.63435i	0.288246	+	0.404784i
$456$	−0.173273	−	0.516949i	−0.00811427	−	0.0242083i
$457$	−1.52671	+	32.0496i	−0.0714165	+	1.49922i	0.624461	+	0.781056i	$0.285319\pi$
$457$	−1.52671	+	32.0496i	−0.0714165	+	1.49922i	−0.695877	+	0.718161i	$0.744984\pi$
$458$	−15.2324	−	17.5792i	−0.711765	−	0.821421i
$459$	−0.608960	+	3.50239i	−0.0284238	+	0.163477i
$460$	−3.81285	−	8.21717i	−0.177775	−	0.383127i
$461$	−8.55050	−	14.8099i	−0.398236	−	0.689766i	0.595272	−	0.803524i	$-0.297044\pi$
$461$	−8.55050	−	14.8099i	−0.398236	−	0.689766i	−0.993508	+	0.113759i	$0.963711\pi$
$462$	−1.64489	−	0.677260i	−0.0765272	−	0.0315090i
$463$	−28.9590	+	14.9294i	−1.34584	+	0.693829i	−0.972289	−	0.233781i	$-0.924890\pi$
$463$	−28.9590	+	14.9294i	−1.34584	+	0.693829i	−0.373551	+	0.927610i	$0.621860\pi$
$464$	−2.17646	−	1.71159i	−0.101040	−	0.0794585i
$465$	−8.70469	+	5.47458i	−0.403670	+	0.253878i
$466$	−13.3560	+	10.5033i	−0.618706	+	0.486556i
$467$	28.1489	+	8.26528i	1.30258	+	0.382471i	0.858176	−	0.513356i	$-0.171598\pi$
$467$	28.1489	+	8.26528i	1.30258	+	0.382471i	0.444402	+	0.895827i	$0.353416\pi$
$468$	−16.4918	+	8.09771i	−0.762335	+	0.374317i
$469$	2.08288	+	4.56087i	0.0961785	+	0.210601i
$470$	−10.6031	−	10.1100i	−0.489084	−	0.466340i
$471$	−11.4223	−	11.1065i	−0.526310	−	0.511759i
$472$	−0.0537317	−	0.155247i	−0.00247320	−	0.00714585i
$473$	−1.72261	+	7.10071i	−0.0792059	+	0.326491i
$474$	14.7908	−	5.75411i	0.679365	−	0.264295i
$475$	0.400708	+	0.206580i	0.0183858	+	0.00947852i
$476$	−0.601504	−	0.176617i	−0.0275699	−	0.00809525i
$477$	−18.3855	−	9.93842i	−0.841814	−	0.455049i
$478$	11.1006	−	24.3070i	0.507731	−	1.11178i
$479$	−9.59442	+	3.84103i	−0.438380	+	0.175501i	−0.580345	−	0.814371i	$-0.697082\pi$
$479$	−9.59442	+	3.84103i	−0.438380	+	0.175501i	0.141965	+	0.989872i	$0.454658\pi$
$480$	−1.32990	−	2.98912i	−0.0607012	−	0.136434i
$481$	48.5167	−	9.35083i	2.21217	−	0.426361i
$482$	−9.50077	+	16.4558i	−0.432748	+	0.749542i
$483$	4.39191	+	6.21662i	0.199839	+	0.282866i
$484$	4.87189	+	8.43835i	0.221449	+	0.383562i
$485$	−18.4382	−	21.2788i	−0.837235	−	0.966221i
$486$	11.7944	−	10.1928i	0.535004	−	0.462353i
$487$	−3.20976	+	22.3244i	−0.145448	+	1.01161i	0.778102	+	0.628138i	$0.216183\pi$
$487$	−3.20976	+	22.3244i	−0.145448	+	1.01161i	−0.923550	+	0.383477i	$0.874727\pi$
$488$	0.384852	−	0.0367489i	0.0174214	−	0.00166355i
$489$	0.102859	+	0.147478i	0.00465144	+	0.00666916i
$490$	−8.42143	+	8.02982i	−0.380442	+	0.362750i
$491$	−0.876057	−	18.3907i	−0.0395359	−	0.829961i	−0.928353	−	0.371699i	$-0.878775\pi$
$491$	−0.876057	−	18.3907i	−0.0395359	−	0.829961i	0.888817	−	0.458262i	$-0.151528\pi$
$492$	2.74267	−	17.8352i	0.123649	−	0.804074i
$493$	−1.37097	−	1.30722i	−0.0617454	−	0.0588741i
$494$	1.26243	−	1.45692i	0.0567992	−	0.0655498i
$495$	−1.37631	−	6.20029i	−0.0618605	−	0.278683i
$496$	3.01582	−	0.885524i	0.135414	−	0.0397612i
$497$	−6.26213	+	8.79393i	−0.280895	+	0.394462i
$498$	11.5918	+	20.5391i	0.519442	+	0.920378i
$499$	7.81703	−	7.45352i	0.349938	−	0.333666i	−0.494640	−	0.869098i	$-0.664700\pi$
$499$	7.81703	−	7.45352i	0.349938	−	0.333666i	0.844578	+	0.535433i	$0.179851\pi$
$500$	11.2792	+	4.51553i	0.504423	+	0.201940i
$501$	20.6764	+	10.9168i	0.923752	+	0.487725i
$502$	−2.71931	+	1.08865i	−0.121369	+	0.0485887i
$503$	−21.5800	−	13.8686i	−0.962203	−	0.618370i	−0.0375959	−	0.999293i	$-0.511970\pi$
$503$	−21.5800	−	13.8686i	−0.962203	−	0.618370i	−0.924607	+	0.380923i	$0.875606\pi$
$504$	1.55044	+	2.27000i	0.0690619	+	0.101114i
$505$	3.17995			0.141506
$506$	−0.223305	+	5.37060i	−0.00992712	+	0.238752i
$507$	−35.4812	−	23.2960i	−1.57578	−	1.03461i
$508$	−1.11779	+	0.215437i	−0.0495941	+	0.00955848i
$509$	−24.3772	+	12.5673i	−1.08050	+	0.557037i	−0.904117	−	0.427284i	$-0.859470\pi$
$509$	−24.3772	+	12.5673i	−1.08050	+	0.557037i	−0.176384	+	0.984321i	$0.556440\pi$
$510$	−0.711337	−	2.12222i	−0.0314985	−	0.0939736i
$511$	−1.27174	+	0.121436i	−0.0562583	+	0.00537201i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−0.722840	+	1.46726i	−0.0319142	+	0.0647809i
$514$	−6.69306	+	4.30137i	−0.295218	+	0.189725i
$515$	13.9157	−	19.5419i	0.613200	−	0.861120i
$516$	8.24778	−	7.71161i	0.363088	−	0.339485i
$517$	2.84331	+	8.21521i	0.125049	+	0.361304i
$518$	−2.41794	−	6.98619i	−0.106238	−	0.306956i
$519$	−4.84156	−	1.47321i	−0.212521	−	0.0646667i
$520$	6.70998	−	9.42285i	0.294252	−	0.413219i
$521$	−5.62228	+	3.61322i	−0.246316	+	0.158298i	−0.657974	−	0.753041i	$-0.728586\pi$
$521$	−5.62228	+	3.61322i	−0.246316	+	0.158298i	0.411658	+	0.911339i	$0.364950\pi$
$522$	1.02106	+	8.24356i	0.0446904	+	0.360811i
$523$	5.16121	+	35.8970i	0.225684	+	1.56967i	0.715986	+	0.698114i	$0.245977\pi$
$523$	5.16121	+	35.8970i	0.225684	+	1.56967i	−0.490302	+	0.871552i	$0.663114\pi$
$524$	−3.97214	+	0.379294i	−0.173524	+	0.0165695i
$525$	−2.22765	−	0.451990i	−0.0972226	−	0.0197265i
$526$	0.664371	−	0.342507i	0.0289680	−	0.0149340i
$527$	2.11151	−	0.406960i	0.0919788	−	0.0177275i
$528$	−0.111337	+	1.93811i	−0.00484532	+	0.0843456i
$529$	13.1138	−	18.8952i	0.570167	−	0.821529i
$530$	13.1589			0.571587
$531$	−0.213469	+	0.444220i	−0.00926376	+	0.0192775i
$532$	−0.242650	−	0.155942i	−0.0105202	−	0.00676094i
$533$	59.2329	−	23.7133i	2.56566	−	1.02714i
$534$	8.46877	−	5.32621i	0.366480	−	0.230488i
$535$	−22.3059	−	8.92992i	−0.964366	−	0.386074i
$536$	3.96017	−	3.77602i	0.171053	−	0.163099i
$537$	−5.97004	+	10.1107i	−0.257626	+	0.436308i
$538$	−14.0600	+	19.7445i	−0.606170	+	0.851247i
$539$	6.62494	−	1.94526i	0.285356	−	0.0837882i
$540$	−3.48091	+	9.17683i	−0.149795	+	0.394908i
$541$	−24.9585	+	28.8037i	−1.07305	+	1.23837i	−0.103201	+	0.994660i	$0.532909\pi$
$541$	−24.9585	+	28.8037i	−1.07305	+	1.23837i	−0.969849	+	0.243706i	$0.921637\pi$
$542$	2.79623	+	2.66620i	0.120108	+	0.114523i
$543$	−23.3379	−	18.7255i	−1.00153	−	0.803590i
$544$	0.0325530	+	0.683372i	0.00139570	+	0.0292994i
$545$	−13.2562	+	12.6398i	−0.567835	+	0.541429i
$546$	−4.12405	+	8.80152i	−0.176493	+	0.376670i
$547$	19.5981	−	1.87140i	0.837956	−	0.0800151i	0.332751	−	0.943015i	$-0.392023\pi$
$547$	19.5981	−	1.87140i	0.837956	−	0.0800151i	0.505205	+	0.863000i	$0.331417\pi$
$548$	0.125080	−	0.869952i	0.00534316	−	0.0371625i
$549$	−0.897469	−	0.734645i	−0.0383031	−	0.0313539i
$550$	−1.05119	−	1.21314i	−0.0448231	−	0.0517286i
$551$	−0.435789	−	0.754809i	−0.0185653	−	0.0321560i
$552$	4.84358	−	6.74832i	0.206156	−	0.287227i
$553$	4.19809	−	7.27131i	0.178521	−	0.309207i
$554$	8.11246	−	1.56355i	0.344666	−	0.0664288i
$555$	15.5203	−	21.3500i	0.658798	−	0.906257i
$556$	−1.82081	+	0.728942i	−0.0772195	+	0.0309140i
$557$	−12.2186	+	26.7551i	−0.517720	+	1.13365i	0.452575	+	0.891726i	$0.350505\pi$
$557$	−12.2186	+	26.7551i	−0.517720	+	1.13365i	−0.970295	+	0.241923i	$0.922222\pi$
$558$	−8.29506	−	4.48396i	−0.351158	−	0.189821i
$559$	38.3069	+	11.2479i	1.62021	+	0.475737i
$560$	−1.53840	−	0.793100i	−0.0650093	−	0.0335146i
$561$	−0.201866	+	1.31271i	−0.00852280	+	0.0554227i
$562$	−2.01794	+	8.31805i	−0.0851216	+	0.350876i
$563$	−11.2123	−	32.3958i	−0.472542	−	1.36532i	−0.889725	−	0.456497i	$-0.849104\pi$
$563$	−11.2123	−	32.3958i	−0.472542	−	1.36532i	0.417183	−	0.908823i	$-0.363017\pi$
$564$	3.29481	−	13.0239i	0.138736	−	0.548406i
$565$	20.2352	+	19.2942i	0.851302	+	0.811715i
$566$	13.7540	+	30.1170i	0.578122	+	1.26591i
$567$	1.49211	−	8.11077i	0.0626626	−	0.340620i
$568$	11.3044	+	3.31926i	0.474321	+	0.139273i
$569$	−0.765151	+	0.601722i	−0.0320768	+	0.0252255i	−0.634069	−	0.773277i	$-0.718616\pi$
$569$	−0.765151	+	0.601722i	−0.0320768	+	0.0252255i	0.601992	+	0.798502i	$0.294374\pi$
$570$	−0.0389359	−	1.02910i	−0.00163084	−	0.0431043i
$571$	19.0864	+	15.0097i	0.798741	+	0.628137i	0.931800	−	0.362971i	$-0.118238\pi$
$571$	19.0864	+	15.0097i	0.798741	+	0.628137i	−0.133059	+	0.991108i	$0.542480\pi$
$572$	−6.10106	+	3.14532i	−0.255098	+	0.131512i
$573$	−2.06295	−	15.4174i	−0.0861810	−	0.644071i
$574$	−4.77321	−	8.26743i	−0.199230	−	0.345076i
$575$	1.01857	+	6.79258i	0.0424773	+	0.283270i
$576$	1.78765	−	2.40921i	0.0744854	−	0.100384i
$577$	−9.18783	−	10.6033i	−0.382494	−	0.441422i	0.531556	−	0.847023i	$-0.321608\pi$
$577$	−9.18783	−	10.6033i	−0.382494	−	0.441422i	−0.914050	+	0.405601i	$0.867062\pi$
$578$	0.786621	−	16.5132i	0.0327191	−	0.686859i
$579$	−22.5751	−	4.58049i	−0.938188	−	0.190359i
$580$	−3.03369	−	4.26022i	−0.125967	−	0.176896i
$581$	11.5833	+	4.63725i	0.480555	+	0.192385i
$582$	8.68265	−	24.3146i	0.359907	−	1.00787i
$583$	−6.94025	−	3.57795i	−0.287436	−	0.148183i
$584$	0.579166	+	1.26820i	0.0239661	+	0.0524783i
$585$	−34.1982	+	5.89971i	−1.41392	+	0.243923i
$586$	19.5066	−	22.5118i	0.805809	−	0.929953i
$587$	−40.3492	−	7.77667i	−1.66539	−	0.320977i	−0.732398	−	0.680877i	$-0.761599\pi$
$587$	−40.3492	−	7.77667i	−1.66539	−	0.320977i	−0.932991	+	0.359900i	$0.882811\pi$
$588$	−10.2079	−	3.10611i	−0.420968	−	0.128094i
$589$	0.984917	+	0.0940482i	0.0405828	+	0.00387519i
$590$	−0.0147651	−	0.309957i	−0.000607868	−	0.0127607i
$591$	16.1323	−	2.94585i	0.663592	−	0.121176i
$592$	−6.34181	+	4.98726i	−0.260647	+	0.204975i
$593$	7.12822	−	15.6086i	0.292721	−	0.640969i	−0.704944	−	0.709263i	$-0.749028\pi$
$593$	7.12822	−	15.6086i	0.292721	−	0.640969i	0.997665	+	0.0682931i	$0.0217553\pi$
$594$	4.33110	−	3.89355i	0.177707	−	0.159754i
$595$	−0.996150	−	0.640186i	−0.0408382	−	0.0262451i
$596$	−5.17431	+	14.9502i	−0.211948	+	0.612383i
$597$	−27.5870	+	13.8822i	−1.12906	+	0.568159i
$598$	29.2540	+	2.61508i	1.19629	+	0.106938i
$599$	4.16023	−	7.20573i	0.169982	−	0.294418i	−0.768431	−	0.639933i	$-0.778962\pi$
$599$	4.16023	−	7.20573i	0.169982	−	0.294418i	0.938413	+	0.345515i	$0.112296\pi$
$600$	0.328991	+	2.45871i	0.0134310	+	0.100376i
$601$	−1.26555	+	26.5671i	−0.0516228	+	1.08370i	0.813317	+	0.581821i	$0.197660\pi$
$601$	−1.26555	+	26.5671i	−0.0516228	+	1.08370i	−0.864940	+	0.501876i	$0.832644\pi$
$602$	0.850125	−	5.91275i	0.0346485	−	0.240986i
$603$	−16.4124	−	0.321170i	−0.668366	−	0.0130791i
$604$	−1.88908	−	13.1388i	−0.0768654	−	0.534611i
$605$	4.33907	+	17.8859i	0.176408	+	0.727164i
$606$	1.43320	+	2.53943i	0.0582198	+	0.103157i
$607$	−21.6398	−	2.06635i	−0.878332	−	0.0838705i	−0.353860	−	0.935298i	$-0.615131\pi$
$607$	−21.6398	−	2.06635i	−0.878332	−	0.0838705i	−0.524472	+	0.851428i	$0.675737\pi$
$608$	−0.0742122	+	0.305907i	−0.00300970	+	0.0124062i
$609$	3.15061	+	3.06350i	0.127669	+	0.124139i
$610$	0.717044	+	0.138199i	0.0290323	+	0.00559551i
$611$	45.5768	−	13.3826i	1.84384	−	0.541400i
$612$	1.37415	−	1.52454i	0.0555469	−	0.0616258i
$613$	26.4766	−	17.0155i	1.06938	−	0.687248i	0.117298	−	0.993097i	$-0.462577\pi$
$613$	26.4766	−	17.0155i	1.06938	−	0.687248i	0.952080	+	0.305849i	$0.0989403\pi$
$614$	5.97172	+	24.6157i	0.240999	+	0.993411i
$615$	14.4618	−	30.8642i	0.583155	−	1.24456i
$616$	0.595733	+	0.836590i	0.0240028	+	0.0337072i
$617$	3.31911	+	2.61018i	0.133622	+	0.105082i	0.682733	−	0.730668i	$-0.260791\pi$
$617$	3.31911	+	2.61018i	0.133622	+	0.105082i	−0.549111	+	0.835750i	$0.685034\pi$
$618$	21.8775	+	2.30524i	0.880041	+	0.0927302i
$619$	12.2320	−	35.3422i	0.491647	−	1.42052i	−0.377519	−	0.926002i	$-0.623223\pi$
$619$	12.2320	−	35.3422i	0.491647	−	1.42052i	0.869166	−	0.494520i	$-0.164656\pi$
$620$	5.93697			0.238434
$621$	−24.5728	+	4.14463i	−0.986072	+	0.166318i
$622$	4.55702			0.182720
$623$	1.73108	−	5.00162i	0.0693542	−	0.200386i
$624$	10.5490	+	1.11155i	0.422299	+	0.0444978i
$625$	12.4101	+	9.75944i	0.496405	+	0.390377i
$626$	7.74725	+	10.8795i	0.309642	+	0.434832i
$627$	−0.259280	+	0.553353i	−0.0103546	+	0.0220988i
$628$	2.16856	+	8.93894i	0.0865351	+	0.356702i
$629$	−4.64342	+	2.98414i	−0.185145	+	0.118986i
$630$	1.60194	+	4.93912i	0.0638230	+	0.196779i
$631$	34.2097	−	10.0449i	1.36187	−	0.399880i	0.482447	−	0.875925i	$-0.339748\pi$
$631$	34.2097	−	10.0449i	1.36187	−	0.399880i	0.879421	+	0.476045i	$0.157930\pi$
$632$	−8.99735	−	1.73410i	−0.357896	−	0.0689787i
$633$	−2.52687	−	2.45700i	−0.100434	−	0.0976572i
$634$	3.12186	−	12.8685i	0.123985	−	0.511072i
$635$	−2.14048	−	0.204391i	−0.0849425	−	0.00811103i
$636$	5.93071	+	10.5084i	0.235168	+	0.416685i
$637$	−8.89455	−	36.6638i	−0.352415	−	1.45267i
$638$	0.441656	+	3.07178i	0.0174853	+	0.121613i
$639$	−17.0702	−	30.9494i	−0.675285	−	1.22434i
$640$	−0.268814	+	1.86964i	−0.0106258	+	0.0739040i
$641$	1.72036	−	36.1149i	0.0679502	−	1.42645i	−0.665343	−	0.746538i	$-0.731715\pi$
$641$	1.72036	−	36.1149i	0.0679502	−	1.42645i	0.733293	−	0.679913i	$-0.237982\pi$
$642$	−2.92202	−	21.8376i	−0.115323	−	0.861861i
$643$	5.59585	−	9.69229i	0.220679	−	0.382227i	−0.734336	−	0.678787i	$-0.762506\pi$
$643$	5.59585	−	9.69229i	0.220679	−	0.382227i	0.955014	+	0.296560i	$0.0958394\pi$
$644$	−0.235629	−	4.38819i	−0.00928508	−	0.172919i
$645$	19.0517	−	9.58707i	0.750158	−	0.377490i
$646$	−0.0704360	+	0.203512i	−0.00277127	+	0.00800706i
$647$	−3.40499	−	2.18826i	−0.133864	−	0.0860292i	0.471995	−	0.881601i	$-0.343534\pi$
$647$	−3.40499	−	2.18826i	−0.133864	−	0.0860292i	−0.605859	+	0.795572i	$0.707170\pi$
$648$	−8.89723	+	1.35622i	−0.349516	+	0.0532773i
$649$	−0.0764907	+	0.167491i	−0.00300252	+	0.00657461i
$650$	−6.89448	+	5.42188i	−0.270424	+	0.212664i
$651$	−4.90736	+	0.896117i	−0.192335	+	0.0351216i
$652$	−0.00493948	−	0.103692i	−0.000193445	−	0.00406091i
$653$	−34.5886	−	3.30282i	−1.35356	−	0.129249i	−0.607070	−	0.794648i	$-0.707655\pi$
$653$	−34.5886	−	3.30282i	−1.35356	−	0.129249i	−0.746488	+	0.665399i	$0.768261\pi$
$654$	−16.0684	−	4.88936i	−0.628324	−	0.191189i
$655$	−7.40077	−	1.42638i	−0.289172	−	0.0557334i
$656$	−6.82248	+	7.87356i	−0.266373	+	0.307411i
$657$	1.44505	−	3.92500i	0.0563768	−	0.153129i
$658$	−2.95244	−	6.46494i	−0.115098	−	0.252030i
$659$	8.89083	+	4.58354i	0.346338	+	0.178549i	0.622615	−	0.782529i	$-0.286070\pi$
$659$	8.89083	+	4.58354i	0.346338	+	0.178549i	−0.276277	+	0.961078i	$0.589101\pi$
$660$	−1.23316	+	3.45330i	−0.0480007	+	0.134420i
$661$	−2.62820	−	1.05217i	−0.102225	−	0.0409248i	0.319986	−	0.947422i	$-0.396322\pi$
$661$	−2.62820	−	1.05217i	−0.102225	−	0.0409248i	−0.422211	+	0.906497i	$0.638746\pi$
$662$	−20.7606	−	29.1542i	−0.806883	−	1.13311i
$663$	7.11213	+	1.44305i	0.276212	+	0.0560435i
$664$	0.647898	−	13.6010i	0.0251433	−	0.527823i
$665$	−0.356783	−	0.411750i	−0.0138355	−	0.0159670i
$666$	24.0445	+	2.77167i	0.931707	+	0.107400i
$667$	5.44316	−	12.1121i	0.210760	−	0.468981i
$668$	−6.74961	−	11.6907i	−0.261150	−	0.452326i
$669$	−3.56793	−	26.6648i	−0.137944	−	1.03092i
$670$	9.18666	−	4.73605i	0.354912	−	0.182970i
$671$	−0.340605	−	0.267855i	−0.0131489	−	0.0103404i
$672$	−0.0600052	−	1.58598i	−0.00231475	−	0.0611804i
$673$	−39.1946	+	30.8229i	−1.51084	+	1.18814i	−0.584530	+	0.811372i	$0.698721\pi$
$673$	−39.1946	+	30.8229i	−1.51084	+	1.18814i	−0.926309	+	0.376765i	$0.877036\pi$
$674$	−24.5656	−	7.21312i	−0.946233	−	0.277839i
$675$	4.49273	−	5.93268i	0.172925	−	0.228349i
$676$	10.1801	+	22.2914i	0.391543	+	0.857360i
$677$	−14.6399	−	13.9591i	−0.562657	−	0.536492i	0.354481	−	0.935063i	$-0.384658\pi$
$677$	−14.6399	−	13.9591i	−0.562657	−	0.536492i	−0.917137	+	0.398571i	$0.869506\pi$
$678$	−6.28791	+	24.8552i	−0.241486	+	0.954559i
$679$	−4.46738	−	12.9077i	−0.171442	−	0.495350i
$680$	−0.304662	+	1.25584i	−0.0116833	+	0.0481591i
$681$	0.305600	−	1.98728i	0.0117106	−	0.0761528i
$682$	−3.13126	−	1.61428i	−0.119902	−	0.0618138i
$683$	−48.4824	−	14.2357i	−1.85513	−	0.544714i	−0.999638	−	0.0268933i	$-0.991439\pi$
$683$	−48.4824	−	14.2357i	−1.85513	−	0.544714i	−0.855489	−	0.517821i	$-0.826743\pi$
$684$	0.804266	−	0.494908i	0.0307519	−	0.0189233i
$685$	0.689639	−	1.51010i	0.0263497	−	0.0576979i
$686$	−11.1953	+	4.48191i	−0.427438	+	0.171120i
$687$	23.6896	−	32.5879i	0.903814	−	1.24330i
$688$	−6.40126	+	1.23374i	−0.244046	+	0.0470360i
$689$	−21.3324	+	36.9488i	−0.812699	+	1.40764i
$690$	12.3694	−	9.65280i	0.470896	−	0.367476i
$691$	16.1349	+	27.9465i	0.613802	+	1.06314i	0.990593	+	0.136838i	$0.0436939\pi$
$691$	16.1349	+	27.9465i	0.613802	+	1.06314i	−0.376792	+	0.926298i	$0.622973\pi$
$692$	1.91338	+	2.20816i	0.0727359	+	0.0839417i
$693$	0.498066	−	3.04055i	0.0189200	−	0.115501i
$694$	0.627694	−	4.36571i	0.0238270	−	0.165720i
$695$	−3.68786	+	0.352148i	−0.139888	+	0.0133577i
$696$	2.03482	−	4.34270i	0.0771298	−	0.164610i
$697$	−5.15848	+	4.91860i	−0.195391	+	0.186305i
$698$	−1.03300	−	21.6854i	−0.0390997	−	0.820803i
$699$	−22.9542	−	18.4177i	−0.868208	−	0.696620i
$700$	0.949786	+	0.905619i	0.0358985	+	0.0342292i
$701$	25.5221	−	29.4540i	0.963956	−	1.11246i	−0.0296504	−	0.999560i	$-0.509439\pi$
$701$	25.5221	−	29.4540i	0.963956	−	1.11246i	0.993606	−	0.112904i	$-0.0360152\pi$
$702$	−20.1245	−	24.6509i	−0.759549	−	0.930387i
$703$	−2.43675	+	0.715494i	−0.0919037	+	0.0269853i
$704$	0.650137	−	0.912990i	0.0245030	−	0.0344096i
$705$	12.9021	−	21.8506i	0.485921	−	0.822942i
$706$	−2.01882	+	1.92494i	−0.0759791	+	0.0724459i
$707$	1.43214	+	0.573344i	0.0538613	+	0.0215628i
$708$	0.240869	−	0.151488i	0.00905242	−	0.00569328i
$709$	29.8278	−	11.9412i	1.12021	−	0.448463i	0.263703	−	0.964604i	$-0.415056\pi$
$709$	29.8278	−	11.9412i	1.12021	−	0.448463i	0.856504	+	0.516141i	$0.172632\pi$
$710$	18.7211	+	12.0314i	0.702592	+	0.451529i
$711$	15.5039	+	22.6994i	0.581443	+	0.851295i
$712$	−5.77606			−0.216467
$713$	7.61575	+	13.0086i	0.285212	+	0.487177i
$714$	0.0622733	−	1.08403i	0.00233052	−	0.0405689i
$715$	−12.7311	+	2.45371i	−0.476115	+	0.0917637i
$716$	6.02547	−	3.10635i	0.225183	−	0.116090i
$717$	45.3593	+	9.20340i	1.69397	+	0.343707i
$718$	36.3321	−	3.46930i	1.35590	−	0.129473i
$719$	5.39157	+	37.4992i	0.201072	+	1.39848i	0.801112	+	0.598515i	$0.204242\pi$
$719$	5.39157	+	37.4992i	0.201072	+	1.39848i	−0.600040	+	0.799970i	$0.704849\pi$
$720$	4.52193	−	3.41504i	0.168522	−	0.127271i
$721$	9.79058	−	6.29202i	0.364620	−	0.234327i
$722$	10.9636	−	15.3962i	0.408023	−	0.572988i
$723$	−31.4862	−	9.58076i	−1.17099	−	0.356312i
$724$	5.65018	+	16.3251i	0.209987	+	0.606719i
$725$	1.29699	+	3.74741i	0.0481691	+	0.139175i
$726$	−12.3276	+	11.5262i	−0.457520	+	0.427778i
$727$	−18.0376	+	25.3303i	−0.668978	+	0.939448i	−0.999991	−	0.00417823i	$-0.998670\pi$
$727$	−18.0376	+	25.3303i	−0.668978	+	0.939448i	0.331014	+	0.943626i	$0.392609\pi$
$728$	4.72089	−	3.03393i	0.174968	−	0.112445i
$729$	21.8184	+	15.9047i	0.808088	+	0.589062i
$730$	0.374776	+	2.60663i	0.0138711	+	0.0964756i
$731$	−4.43981	+	0.423950i	−0.164212	+	0.0156804i
$732$	0.212809	+	0.634900i	0.00786564	+	0.0234666i
$733$	30.5588	−	15.7542i	1.12872	−	0.581893i	0.210350	−	0.977626i	$-0.432540\pi$
$733$	30.5588	−	15.7542i	1.12872	−	0.581893i	0.918366	+	0.395733i	$0.129509\pi$
$734$	−17.8872	+	3.44748i	−0.660230	+	0.127249i
$735$	−16.8475	−	11.0616i	−0.621428	−	0.408013i
$736$	−4.44144	+	1.80931i	−0.163714	+	0.0666921i
$737$	−6.13295			−0.225910
$738$	31.1653	−	2.36165i	1.14721	−	0.0869334i
$739$	11.2051	+	7.20111i	0.412188	+	0.264897i	0.730260	−	0.683169i	$-0.239399\pi$
$739$	11.2051	+	7.20111i	0.412188	+	0.264897i	−0.318072	+	0.948067i	$0.603035\pi$
$740$	−14.1476	+	5.66384i	−0.520076	+	0.208207i
$741$	2.95272	+	1.55898i	0.108471	+	0.0572707i
$742$	5.92634	+	2.37255i	0.217563	+	0.0870990i
$743$	−15.5318	+	14.8095i	−0.569806	+	0.543308i	−0.919263	−	0.393644i	$-0.871214\pi$
$743$	−15.5318	+	14.8095i	−0.569806	+	0.543308i	0.349458	+	0.936952i	$0.386366\pi$
$744$	2.67578	+	4.74111i	0.0980990	+	0.173818i
$745$	−17.3335	+	24.3415i	−0.635050	+	0.891802i
$746$	−25.8332	+	7.58530i	−0.945819	+	0.277717i
$747$	−30.1100	+	27.6055i	−1.10167	+	1.01003i
$748$	0.502149	−	0.579511i	0.0183604	−	0.0211890i
$749$	−8.43575	−	8.04347i	−0.308236	−	0.293902i
$750$	−3.19845	+	20.7991i	−0.116791	+	0.759477i
$751$	−0.627915	−	13.1815i	−0.0229129	−	0.481002i	−0.980938	−	0.194319i	$-0.937750\pi$
$751$	−0.627915	−	13.1815i	−0.0229129	−	0.481002i	0.958026	−	0.286683i	$-0.0925526\pi$
$752$	−5.61347	+	5.35243i	−0.204702	+	0.195183i
$753$	−2.90229	−	4.16126i	−0.105765	−	0.151645i
$754$	16.8802	−	1.61187i	0.614742	−	0.0587007i
$755$	3.56821	−	24.8174i	0.129860	−	0.903199i
$756$	−3.22226	+	3.50533i	−0.117193	+	0.127488i
$757$	−16.4409	−	18.9739i	−0.597556	−	0.689617i	0.373728	−	0.927538i	$-0.378079\pi$
$757$	−16.4409	−	18.9739i	−0.597556	−	0.689617i	−0.971284	+	0.237921i	$0.923534\pi$
$758$	4.82766	+	8.36175i	0.175349	+	0.303713i
$759$	−9.14847	+	1.72778i	−0.332068	+	0.0627144i
$760$	−0.297289	+	0.514919i	−0.0107838	+	0.0186781i
$761$	−10.1492	+	1.95610i	−0.367908	+	0.0709085i	−0.369855	−	0.929090i	$-0.620593\pi$
$761$	−10.1492	+	1.95610i	−0.367908	+	0.0709085i	0.00194651	+	0.999998i	$0.499380\pi$
$762$	−0.801492	−	1.80146i	−0.0290350	−	0.0652598i
$763$	−8.24911	+	3.30245i	−0.298638	+	0.119557i
$764$	−3.73066	+	8.16901i	−0.134971	+	0.295545i
$765$	3.30174	−	2.03174i	0.119375	−	0.0734577i
$766$	16.0686	+	4.71815i	0.580580	+	0.170474i
$767$	0.894260	+	0.461023i	0.0322898	+	0.0166466i
$768$	−1.61420	+	0.627977i	−0.0582475	+	0.0226602i
$769$	1.14470	−	4.71850i	0.0412788	−	0.170153i	−0.947441	−	0.319930i	$-0.896340\pi$
$769$	1.14470	−	4.71850i	0.0412788	−	0.170153i	0.988720	+	0.149777i	$0.0478556\pi$
$770$	0.634483	+	1.83322i	0.0228652	+	0.0660646i
$771$	−9.87976	−	9.60661i	−0.355811	−	0.345973i
$772$	9.62516	+	9.17757i	0.346417	+	0.330308i
$773$	−8.21675	−	17.9922i	−0.295536	−	0.647134i	0.702370	−	0.711812i	$-0.252125\pi$
$773$	−8.21675	−	17.9922i	−0.295536	−	0.647134i	−0.997906	+	0.0646783i	$0.979398\pi$
$774$	16.2426	+	10.8933i	0.583827	+	0.391551i
$775$	−4.31922	−	1.26824i	−0.155151	−	0.0455564i
$776$	−11.7171	+	9.21443i	−0.420619	+	0.330779i
$777$	10.8392	−	6.81702i	0.388854	−	0.244559i
$778$	−17.0478	−	13.4066i	−0.611194	−	0.480649i
$779$	−2.91489	+	1.50273i	−0.104437	+	0.0538409i
$780$	18.5271	+	7.62825i	0.663375	+	0.273135i
$781$	−6.60251	−	11.4359i	−0.236256	−	0.409208i
$782$	−3.14250	+	0.943393i	−0.112376	+	0.0337357i
$783$	−13.5079	+	4.95299i	−0.482734	+	0.177005i
$784$	4.03418	+	4.65569i	0.144078	+	0.166275i
$785$	−0.826698	+	17.3545i	−0.0295061	+	0.619409i
$786$	−2.19645	−	6.55294i	−0.0783447	−	0.233736i
$787$	14.0971	+	19.7967i	0.502509	+	0.705675i	0.985448	−	0.169979i	$-0.0543701\pi$
$787$	14.0971	+	19.7967i	0.502509	+	0.705675i	−0.482939	+	0.875654i	$0.660431\pi$
$788$	−8.78977	−	3.51889i	−0.313122	−	0.125355i
$789$	0.838198	+	0.986673i	0.0298407	+	0.0351265i
$790$	−15.3836	−	7.93078i	−0.547323	−	0.282165i
$791$	5.63452	+	12.3379i	0.200341	+	0.438685i
$792$	−3.31350	+	0.571628i	−0.117740	+	0.0203119i
$793$	−1.55047	+	1.78934i	−0.0550588	+	0.0635413i
$794$	26.4530	+	5.09839i	0.938781	+	0.180935i
$795$	5.15646	+	22.2010i	0.182881	+	0.787387i
$796$	17.7495	+	1.69488i	0.629116	+	0.0600733i
$797$	2.02689	+	42.5496i	0.0717960	+	1.50718i	0.691516	+	0.722361i	$0.256943\pi$
$797$	2.02689	+	42.5496i	0.0717960	+	1.50718i	−0.619720	+	0.784823i	$0.712754\pi$
$798$	0.168011	−	0.470493i	0.00594753	−	0.0166553i
$799$	−4.17113	+	3.28021i	−0.147564	+	0.116046i
$800$	0.594952	−	1.30276i	0.0210347	−	0.0460596i
$801$	12.3046	+	12.2009i	0.434763	+	0.431097i
$802$	−2.87182	−	1.84561i	−0.101407	−	0.0651706i
$803$	0.511085	−	1.47668i	0.0180358	−	0.0521110i
$804$	7.92251	+	5.20170i	0.279405	+	0.183450i
$805$	1.90816	−	8.07835i	0.0672536	−	0.284724i
$806$	−9.62461	+	16.6703i	−0.339013	+	0.587187i
$807$	−38.8214	−	15.9841i	−1.36658	−	0.562668i
$808$	0.0801054	−	1.68162i	0.00281810	−	0.0591591i
$809$	−7.13772	+	49.6439i	−0.250949	+	1.74539i	0.341594	+	0.939848i	$0.389033\pi$
$809$	−7.13772	+	49.6439i	−0.250949	+	1.74539i	−0.592543	+	0.805539i	$0.701876\pi$
$810$	−16.8466	−	2.27676i	−0.591931	−	0.0799971i
$811$	1.89580	+	13.1856i	0.0665705	+	0.463008i	0.995653	+	0.0931362i	$0.0296892\pi$
$811$	1.89580	+	13.1856i	0.0665705	+	0.463008i	−0.929083	+	0.369871i	$0.879402\pi$
$812$	−0.598156	−	2.46563i	−0.0209912	−	0.0865267i
$813$	−3.40252	+	5.76241i	−0.119332	+	0.202096i
$814$	9.00170	+	0.859558i	0.315510	+	0.0301275i
$815$	0.0462284	−	0.190556i	0.00161931	−	0.00667488i
$816$	−1.14019	+	0.322708i	−0.0399146	+	0.0112970i
$817$	−2.01499	−	0.388357i	−0.0704956	−	0.0135869i
$818$	18.5070	−	5.43414i	0.647081	−	0.190000i
$819$	−16.4655	−	3.50890i	−0.575350	−	0.122611i
$820$	−16.5547	+	10.6391i	−0.578115	+	0.371532i
$821$	3.62671	+	14.9495i	0.126573	+	0.521742i	0.999430	+	0.0337649i	$0.0107498\pi$
$821$	3.62671	+	14.9495i	0.126573	+	0.521742i	−0.872857	+	0.487977i	$0.837735\pi$
$822$	1.51675	−	0.129871i	0.0529026	−	0.00452979i
$823$	−1.48268	−	2.08213i	−0.0516829	−	0.0725785i	0.787926	−	0.615770i	$-0.211155\pi$
$823$	−1.48268	−	2.08213i	−0.0516829	−	0.0725785i	−0.839609	+	0.543192i	$0.817216\pi$
$824$	−9.98358	−	7.85117i	−0.347794	−	0.273509i
$825$	1.63482	−	2.24890i	0.0569172	−	0.0782965i
$826$	0.0492354	−	0.142256i	0.00171312	−	0.00494973i
$827$	−7.95118			−0.276490			−0.138245	−	0.990398i	$-0.544146\pi$
$827$	−7.95118			−0.276490			−0.138245	+	0.990398i	$0.544146\pi$
$828$	13.2834	+	5.52740i	0.461629	+	0.192091i
$829$	−28.3971			−0.986272			−0.493136	−	0.869952i	$-0.664150\pi$
$829$	−28.3971			−0.986272			−0.493136	+	0.869952i	$0.664150\pi$
$830$	8.41208	−	24.3051i	0.291988	−	0.843643i
$831$	5.81688	+	13.0742i	0.201785	+	0.453538i
$832$	−4.81395	−	3.78573i	−0.166894	−	0.131247i
$833$	2.44470	+	3.43311i	0.0847040	+	0.118950i
$834$	−1.94333	−	2.78632i	−0.0672920	−	0.0964823i
$835$	−6.01144	−	24.7795i	−0.208034	−	0.857529i
$836$	0.296803	−	0.190744i	0.0102651	−	0.00659701i
$837$	4.31457	−	15.7520i	0.149133	−	0.544469i
$838$	−31.1316	+	9.14107i	−1.07542	+	0.315773i
$839$	5.31007	+	1.02343i	0.183324	+	0.0353328i	0.280087	−	0.959975i	$-0.409637\pi$
$839$	5.31007	+	1.02343i	0.183324	+	0.0353328i	−0.0967628	+	0.995307i	$0.530849\pi$
$840$	0.735235	−	2.90628i	0.0253680	−	0.100276i
$841$	−5.02956	+	20.7321i	−0.173433	+	0.714900i
$842$	30.2547	+	2.88898i	1.04265	+	0.0995607i
$843$	−14.8245	−	0.145034i	−0.510582	−	0.00499524i
$844$	0.479736	+	1.97750i	0.0165132	+	0.0680683i
$845$	6.58752	+	45.8172i	0.226618	+	1.57616i
$846$	23.2643	+	0.455252i	0.799843	+	0.0156519i
$847$	−1.27065	+	8.83753i	−0.0436599	+	0.303661i
$848$	0.331483	−	6.95869i	0.0113832	−	0.238962i
$849$	−45.4219	+	35.0065i	−1.55888	+	1.20142i
$850$	0.489914	−	0.848555i	0.0168039	−	0.0291052i
$851$	−30.5583	−	23.7338i	−1.04752	−	0.813583i
$852$	−1.17033	+	20.3728i	−0.0400950	+	0.697959i
$853$	−5.12855	+	14.8180i	−0.175598	+	0.507358i	−0.998114	−	0.0613841i	$-0.980449\pi$
$853$	−5.12855	+	14.8180i	−0.175598	+	0.507358i	0.822516	+	0.568742i	$0.192570\pi$
$854$	0.298015	+	0.191523i	0.0101979	+	0.00655378i
$855$	1.72098	−	0.468954i	0.0588564	−	0.0160379i
$856$	−5.28421	+	11.5708i	−0.180611	+	0.395482i
$857$	18.1647	−	14.2849i	0.620494	−	0.487962i	−0.257727	−	0.966218i	$-0.582973\pi$
$857$	18.1647	−	14.2849i	0.620494	−	0.487962i	0.878220	+	0.478256i	$0.158731\pi$
$858$	−7.69735	−	9.06083i	−0.262783	−	0.309332i
$859$	0.0579719	+	1.21698i	0.00197798	+	0.0415228i	0.999641	−	0.0268102i	$-0.00853498\pi$
$859$	0.0579719	+	1.21698i	0.00197798	+	0.0415228i	−0.997663	+	0.0683331i	$0.978232\pi$
$860$	−12.2579	−	1.17049i	−0.417991	−	0.0399133i
$861$	12.0779	−	11.2927i	0.411614	−	0.384856i
$862$	4.82951	+	0.930812i	0.164494	+	0.0317036i
$863$	4.99265	−	5.76183i	0.169952	−	0.196135i	−0.664384	−	0.747391i	$-0.731306\pi$
$863$	4.99265	−	5.76183i	0.169952	−	0.196135i	0.834336	+	0.551257i	$0.185851\pi$
$864$	4.76519	+	2.07194i	0.162115	+	0.0704889i
$865$	2.29264	+	5.02018i	0.0779521	+	0.170691i
$866$	4.74665	+	2.44707i	0.161298	+	0.0831547i
$867$	28.1684	−	5.14373i	0.956648	−	0.174690i
$868$	2.67381	+	1.07043i	0.0907550	+	0.0363328i
$869$	5.95717	+	8.36567i	0.202083	+	0.283786i
$870$	5.99881	−	6.78767i	0.203379	−	0.230124i
$871$	−1.59451	+	33.4729i	−0.0540279	+	1.13418i
$872$	6.35023	+	7.32855i	0.215046	+	0.248176i
$873$	44.4246	+	5.12093i	1.50354	+	0.173317i
$874$	−1.50960	+	0.00912521i	−0.0510631	+	0.000308665i
$875$	5.56643	+	9.64134i	0.188180	+	0.325937i
$876$	−1.91267	+	1.47409i	−0.0646233	+	0.0498049i
$877$	8.76770	−	4.52006i	0.296064	−	0.152632i	−0.303795	−	0.952738i	$-0.598254\pi$
$877$	8.76770	−	4.52006i	0.296064	−	0.152632i	0.599859	+	0.800106i	$0.295223\pi$
$878$	9.15320	+	7.19816i	0.308906	+	0.242926i
$879$	45.6244	+	24.0889i	1.53887	+	0.812498i
$880$	1.66413	−	1.30869i	0.0560978	−	0.0441158i
$881$	34.9682	+	10.2676i	1.17811	+	0.345924i	0.811445	−	0.584429i	$-0.198682\pi$
$881$	34.9682	+	10.2676i	1.17811	+	0.345924i	0.366664	+	0.930353i	$0.380500\pi$
$882$	1.24037	−	18.4394i	0.0417654	−	0.620887i
$883$	−20.0439	−	43.8899i	−0.674529	−	1.47701i	−0.868338	−	0.495974i	$-0.834811\pi$
$883$	−20.0439	−	43.8899i	−0.674529	−	1.47701i	0.193808	−	0.981039i	$-0.437916\pi$
$884$	−3.03234	−	2.89133i	−0.101989	−	0.0972461i
$885$	0.517155	−	0.146370i	0.0173840	−	0.00492019i
$886$	−9.29750	−	26.8634i	−0.312356	−	0.902492i
$887$	1.22811	−	5.06234i	0.0412359	−	0.169977i	−0.947470	−	0.319844i	$-0.896369\pi$
$887$	1.22811	−	5.06234i	0.0412359	−	0.169977i	0.988706	+	0.149867i	$0.0478846\pi$
$888$	−10.8993	−	8.74522i	−0.365757	−	0.293471i
$889$	−0.927150	−	0.477979i	−0.0310956	−	0.0160309i
$890$	−10.4683	−	3.07376i	−0.350897	−	0.103033i
$891$	8.26616	+	5.78145i	0.276927	+	0.193686i
$892$	−6.45228	+	14.1285i	−0.216038	+	0.473058i
$893$	−2.26662	+	0.907419i	−0.0758497	+	0.0303656i
$894$	−27.2507	−	2.87141i	−0.911399	−	0.0960343i
$895$	12.5733	−	2.42331i	0.420281	−	0.0810025i
$896$	−0.458160	+	0.793556i	−0.0153060	+	0.0265108i
$897$	7.05147	+	50.3804i	0.235442	+	1.68215i
$898$	11.2544	+	19.4931i	0.375563	+	0.650494i
$899$	5.69917	+	6.57720i	0.190078	+	0.219362i
$900$	−4.01927	+	1.51852i	−0.133976	+	0.0506175i
$901$	0.678296	−	4.71765i	0.0225973	−	0.157168i
$902$	11.6240	−	1.10996i	0.387038	−	0.0369576i
$903$	10.3088	−	0.882689i	0.343054	−	0.0293740i
$904$	10.7129	−	10.2147i	0.356306	−	0.339737i
$905$	1.55263	+	32.5937i	0.0516111	+	1.08345i
$906$	21.4268	−	8.33571i	0.711857	−	0.276935i
$907$	8.62293	+	8.22195i	0.286320	+	0.273005i	0.819604	−	0.572931i	$-0.194194\pi$
$907$	8.62293	+	8.22195i	0.286320	+	0.273005i	−0.533284	+	0.845936i	$0.679042\pi$
$908$	−0.760191	+	0.877307i	−0.0252278	+	0.0291145i
$909$	−3.72276	+	3.41311i	−0.123476	+	0.113206i
$910$	10.1704	−	2.98631i	0.337147	−	0.0989952i
$911$	28.9010	−	40.5858i	0.957534	−	1.34467i	0.0188751	−	0.999822i	$-0.493991\pi$
$911$	28.9010	−	40.5858i	0.957534	−	1.34467i	0.938659	−	0.344847i	$-0.112069\pi$
$912$	−0.545189	−	0.00533381i	−0.0180530	−	0.000176620i
$913$	−11.0453	+	10.5317i	−0.365546	+	0.348548i
$914$	29.7876	+	11.9251i	0.985285	+	0.394449i
$915$	0.0478198	+	1.26391i	0.00158087	+	0.0417836i
$916$	−21.5944	+	8.64509i	−0.713499	+	0.285642i
$917$	−3.07588	−	1.97675i	−0.101575	−	0.0652780i
$918$	3.11059	+	1.72099i	0.102665	+	0.0568010i
$919$	−22.2667			−0.734510			−0.367255	−	0.930120i	$-0.619702\pi$
$919$	−22.2667			−0.734510			−0.367255	+	0.930120i	$0.619702\pi$
$920$	−9.01229	+	0.915575i	−0.297126	+	0.0301856i
$921$	−39.1902	+	19.7211i	−1.29136	+	0.649831i
$922$	−16.7920	+	3.23639i	−0.553014	+	0.106585i
$923$	−64.1321	+	33.0624i	−2.11094	+	1.08826i
$924$	−1.17800	+	1.33291i	−0.0387534	+	0.0438496i
$925$	11.5024	−	1.09835i	0.378198	−	0.0361135i
$926$	4.63674	+	32.2492i	0.152373	+	1.05978i
$927$	4.68365	+	37.8137i	0.153831	+	1.24197i
$928$	−2.32930	+	1.49695i	−0.0764632	+	0.0491399i
$929$	11.4580	−	16.0906i	0.375926	−	0.527914i	−0.582661	−	0.812716i	$-0.697988\pi$
$929$	11.4580	−	16.0906i	0.375926	−	0.527914i	0.958587	+	0.284801i	$0.0919277\pi$
$930$	2.32646	+	10.0165i	0.0762876	+	0.328454i
$931$	0.634237	+	1.83251i	0.0207863	+	0.0600580i
$932$	5.55729	+	16.0567i	0.182035	+	0.525956i
$933$	1.78571	+	7.68834i	0.0584617	+	0.251705i
$934$	17.0173	−	23.8975i	0.556823	−	0.781949i
$935$	1.21846	−	0.783058i	0.0398480	−	0.0256087i
$936$	2.25840	+	18.2333i	0.0738180	+	0.595974i
$937$	−3.20864	−	22.3166i	−0.104822	−	0.729051i	−0.972665	−	0.232213i	$-0.925403\pi$
$937$	−3.20864	−	22.3166i	−0.104822	−	0.729051i	0.867843	−	0.496838i	$-0.165506\pi$
$938$	4.99127	−	0.476608i	0.162971	−	0.0155618i
$939$	−15.3194	+	17.3339i	−0.499930	+	0.565672i
$940$	−13.0219	+	6.71326i	−0.424728	+	0.218962i
$941$	−11.4209	+	2.20120i	−0.372311	+	0.0717570i	−0.371975	−	0.928243i	$-0.621319\pi$
$941$	−11.4209	+	2.20120i	−0.372311	+	0.0717570i	−0.000336171		1.00000i	$0.500107\pi$
$942$	−14.2315	+	7.16148i	−0.463687	+	0.233334i
$943$	−44.5473	−	22.6260i	−1.45066	−	0.736803i
$944$	−0.164283			−0.00534695
$945$	−7.70526	+	4.63815i	−0.250652	+	0.150879i
$946$	6.14677	+	3.95029i	0.199849	+	0.128435i
$947$	−3.92528	+	1.57144i	−0.127554	+	0.0510651i	−0.434562	−	0.900642i	$-0.643097\pi$
$947$	−3.92528	+	1.57144i	−0.127554	+	0.0510651i	0.307007	+	0.951707i	$0.400672\pi$
$948$	−0.600035	−	15.8593i	−0.0194882	−	0.515087i
$949$	−7.92667	−	3.17336i	−0.257311	−	0.103012i
$950$	0.326277	−	0.311104i	0.0105858	−	0.0100936i
$951$	22.9343	+	0.224375i	0.743694	+	0.00727587i
$952$	−0.363636	+	0.510656i	−0.0117855	+	0.0165504i
$953$	−1.47235	+	0.432321i	−0.0476941	+	0.0140043i	−0.305493	−	0.952194i	$-0.598821\pi$
$953$	−1.47235	+	0.432321i	−0.0476941	+	0.0140043i	0.257798	+	0.966199i	$0.417003\pi$
$954$	−15.4051	+	14.1238i	−0.498759	+	0.457274i
$955$	−11.1085	+	12.8198i	−0.359461	+	0.414841i
$956$	−19.3395	−	18.4402i	−0.625483	−	0.596397i
$957$	−5.00946	+	1.94884i	−0.161933	+	0.0629972i
$958$	0.491745	+	10.3230i	0.0158876	+	0.333521i
$959$	0.582860	−	0.555756i	0.0188215	−	0.0179463i
$960$	−3.25968	+	0.279110i	−0.105206	+	0.00900825i
$961$	21.0250	−	2.00765i	0.678227	−	0.0647629i
$962$	7.03172	−	48.9067i	0.226712	−	1.57681i
$963$	35.6981	−	13.4871i	1.15036	−	0.434617i
$964$	12.4434	+	14.3604i	0.400774	+	0.462517i
$965$	12.5603	+	21.7551i	0.404330	+	0.700321i
$966$	7.31117	−	2.11710i	0.235233	−	0.0681165i
$967$	−27.1005	+	46.9394i	−0.871493	+	1.50947i	−0.0110398	+	0.999939i	$0.503514\pi$
$967$	−27.1005	+	46.9394i	−0.871493	+	1.50947i	−0.860453	+	0.509530i	$0.829819\pi$
$968$	9.56769	−	1.84402i	0.307517	−	0.0592691i
$969$	−0.370954	−	0.0390875i	−0.0119168	−	0.00125567i
$970$	−26.1390	+	10.4645i	−0.839274	+	0.335994i
$971$	16.3414	−	35.7827i	0.524421	−	1.14832i	−0.443318	−	0.896364i	$-0.646199\pi$
$971$	16.3414	−	35.7827i	0.524421	−	1.14832i	0.967739	−	0.251957i	$-0.0810740\pi$
$972$	−5.77460	−	14.4794i	−0.185220	−	0.464428i
$973$	−1.72438	−	0.506324i	−0.0552811	−	0.0162320i
$974$	20.0468	+	10.3348i	0.642340	+	0.331149i
$975$	−11.8491	−	9.50734i	−0.379476	−	0.304479i
$976$	0.0911450	−	0.375705i	0.00291748	−	0.0120260i
$977$	−9.40939	−	27.1867i	−0.301033	−	0.869778i	−0.989503	−	0.144513i	$-0.953838\pi$
$977$	−9.40939	−	27.1867i	−0.301033	−	0.869778i	0.688470	−	0.725265i	$-0.258283\pi$
$978$	0.173008	−	0.0489665i	0.00553219	−	0.00156578i
$979$	4.68538	+	4.46750i	0.149745	+	0.142782i
$980$	4.83381	+	10.5846i	0.154410	+	0.338111i
$981$	1.95247	−	29.0256i	0.0623377	−	0.926716i
$982$	−17.6658	−	5.18713i	−0.563737	−	0.165528i
$983$	5.95192	−	4.68064i	0.189837	−	0.149289i	−0.518717	−	0.854946i	$-0.673590\pi$
$983$	5.95192	−	4.68064i	0.189837	−	0.149289i	0.708554	+	0.705657i	$0.249348\pi$
$984$	−15.9573	−	8.42515i	−0.508699	−	0.268584i
$985$	−14.0576	−	11.0550i	−0.447911	−	0.352241i
$986$	−1.68372	+	0.868019i	−0.0536206	+	0.0276434i
$987$	9.75033	−	7.51454i	0.310356	−	0.239190i
$988$	−0.963889	−	1.66951i	−0.0306654	−	0.0531140i
$989$	−13.1594	−	28.3600i	−0.418443	−	0.901797i
$990$	−6.30943	−	0.727304i	−0.200527	−	0.0231152i
$991$	−16.5541	−	19.1045i	−0.525858	−	0.606873i	0.429229	−	0.903195i	$-0.358785\pi$
$991$	−16.5541	−	19.1045i	−0.525858	−	0.606873i	−0.955088	+	0.296322i	$0.904240\pi$
$992$	0.149557	−	3.13958i	0.00474842	−	0.0996817i
$993$	41.0519	−	46.4504i	1.30274	−	1.47406i
$994$	6.26213	+	8.79393i	0.198623	+	0.278927i
$995$	31.2665	+	12.5172i	0.991215	+	0.396823i
$996$	23.2008	−	4.23661i	0.735144	−	0.134242i
$997$	1.29714	+	0.668722i	0.0410809	+	0.0211787i	0.478645	−	0.878009i	$-0.341128\pi$
$997$	1.29714	+	0.668722i	0.0410809	+	0.0211787i	−0.437564	+	0.899187i	$0.644159\pi$
$998$	−4.48689	−	9.82491i	−0.142030	−	0.311002i
$999$	4.74588	+	41.6526i	0.150153	+	1.31783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.13.12	✓	240
9.7	even	3	inner	414.2.m.a.151.9	yes	240
23.16	even	11	inner	414.2.m.a.85.9	yes	240
207.16	even	33	inner	414.2.m.a.223.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.12	✓	240	1.1	even	1	trivial
414.2.m.a.85.9	yes	240	23.16	even	11	inner
414.2.m.a.151.9	yes	240	9.7	even	3	inner
414.2.m.a.223.12	yes	240	207.16	even	33	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.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(1.72251 + 0.181502i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.09565 - 1.53862i) q^{5} +(0.734899 - 1.56841i) q^{6} +(-0.216031 - 0.890490i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.93411 + 0.625279i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(1.72251 + 0.181502i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.09565 - 1.53862i) q^{5} +(0.734899 - 1.56841i) q^{6} +(-0.216031 - 0.890490i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(2.93411 + 0.625279i) q^{9} +(-1.81235 + 0.532155i) q^{10} +(1.10056 + 0.212116i) q^{11} +(-1.24179 - 1.20746i) q^{12} +(1.44384 - 5.95157i) q^{13} +(-0.912170 - 0.0871017i) q^{14} +(-1.60801 - 2.84917i) q^{15} +(0.235759 + 0.971812i) q^{16} +(0.0973643 + 0.677184i) q^{17} +(1.55054 - 2.56823i) q^{18} +(-0.0447979 + 0.311576i) q^{19} +(-0.0898758 + 1.88673i) q^{20} +(-0.210490 - 1.57309i) q^{21} +(0.560408 - 0.970655i) q^{22} +(-4.24934 + 2.22330i) q^{23} +(-1.54720 + 0.778573i) q^{24} +(0.468422 - 1.35342i) q^{25} +(-5.15201 - 3.31100i) q^{26} +(4.94057 + 1.60960i) q^{27} +(-0.380653 + 0.833514i) q^{28} +(-2.17646 + 1.71159i) q^{29} +(-3.21839 + 0.587699i) q^{30} +(-0.149557 - 3.13958i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.85723 + 0.565126i) q^{33} +(0.671784 + 0.129476i) q^{34} +(-1.13344 + 1.30805i) q^{35} +(-1.91985 - 2.30525i) q^{36} +(3.35153 + 7.33883i) q^{37} +(0.279788 + 0.144241i) q^{38} +(3.56725 - 9.98962i) q^{39} +(1.75356 + 0.702020i) q^{40} +(6.04316 + 8.48642i) q^{41} +(-1.55542 - 0.315595i) q^{42} +(-0.310190 + 6.51169i) q^{43} +(-0.733978 - 0.847056i) q^{44} +(-2.25269 - 5.19959i) q^{45} +(0.711200 + 4.74280i) q^{46} +(3.87813 + 6.71711i) q^{47} +(0.229713 + 1.71675i) q^{48} +(5.47555 - 2.82284i) q^{49} +(-1.12578 - 0.885319i) q^{50} +(0.0448014 + 1.18413i) q^{51} +(-4.81395 + 3.78573i) q^{52} +(-6.68438 - 1.96271i) q^{53} +(3.13697 - 4.14239i) q^{54} +(-0.879463 - 1.92575i) q^{55} +(0.663172 + 0.632333i) q^{56} +(-0.133717 + 0.528564i) q^{57} +(0.905602 + 2.61657i) q^{58} +(-0.0387312 + 0.159652i) q^{59} +(-0.497257 + 3.23360i) q^{60} +(-0.343626 - 0.177152i) q^{61} +(-3.01582 - 0.885524i) q^{62} +(-0.0770534 - 2.74788i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-10.7392 + 4.29932i) q^{65} +(1.14149 - 1.57025i) q^{66} +(-5.37298 + 1.03556i) q^{67} +(0.342074 - 0.592489i) q^{68} +(-7.72309 + 3.05841i) q^{69} +(0.865402 + 1.49892i) q^{70} +(-7.71531 - 8.90394i) q^{71} +(-2.80639 + 1.06028i) q^{72} +(0.198413 - 1.38000i) q^{73} +(8.03138 - 0.766904i) q^{74} +(1.05251 - 2.24626i) q^{75} +(0.227817 - 0.217223i) q^{76} +(-0.0488678 - 1.02586i) q^{77} +(-8.27346 - 6.63834i) q^{78} +(6.63153 + 6.32315i) q^{79} +(1.23694 - 1.42751i) q^{80} +(8.21805 + 3.66928i) q^{81} +(9.99620 - 2.93515i) q^{82} +(-7.89833 + 11.0916i) q^{83} +(-0.806964 + 1.36665i) q^{84} +(0.935254 - 0.891763i) q^{85} +(6.05209 + 2.42289i) q^{86} +(-4.05965 + 2.55321i) q^{87} +(-1.04053 + 0.416565i) q^{88} +(4.85913 + 3.12277i) q^{89} +(-5.65040 + 0.428176i) q^{90} -5.61173 q^{91} +(4.71456 + 0.879135i) q^{92} +(0.312226 - 5.43511i) q^{93} +(7.61609 - 1.46788i) q^{94} +(0.528481 - 0.272451i) q^{95} +(1.69746 + 0.344415i) q^{96} +(14.8387 - 1.41693i) q^{97} +(-0.876710 - 6.09765i) q^{98} +(3.09654 + 1.31053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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