LMFDB - Embedded newform 354.2.e.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	354.19
Dual form			354.2.e.c.205.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(1.70467 - 0.375225i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(1.66436 - 1.26521i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})$	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(1.70467 - 0.375225i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(1.66436 - 1.26521i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(0.466964 - 1.68185i) q^{10} +(1.63608 + 4.10626i) q^{11} +(-0.976621 - 0.214970i) q^{12} +(0.0259109 + 0.477898i) q^{13} +(-0.338231 - 2.06312i) q^{14} +(0.979538 - 1.44471i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(-5.43699 - 4.13309i) q^{17} +(-0.856857 - 0.515554i) q^{18} +(-4.45939 + 1.50254i) q^{19} +(-1.26721 - 1.20036i) q^{20} +(0.338231 - 2.06312i) q^{21} +(4.39428 + 0.477907i) q^{22} +(7.68994 - 4.62688i) q^{23} +(-0.647386 + 0.762162i) q^{24} +(-1.77278 + 0.820177i) q^{25} +(0.434366 + 0.200959i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(-1.98122 - 0.667550i) q^{28} +(4.74762 + 8.95495i) q^{29} +(-0.817595 - 1.54215i) q^{30} +(-8.67584 - 2.92323i) q^{31} +(0.647386 + 0.762162i) q^{32} +(4.01166 + 1.85599i) q^{33} +(-6.19837 + 2.86767i) q^{34} +(2.36243 - 2.78127i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(4.22692 + 0.459705i) q^{37} +(-0.761301 + 4.64373i) q^{38} +(0.347461 + 0.329133i) q^{39} +(-1.65410 + 0.557333i) q^{40} +(0.512136 + 0.308142i) q^{41} +(-1.66436 - 1.26521i) q^{42} +(1.50287 - 3.77193i) q^{43} +(2.48056 - 3.65854i) q^{44} +(-0.282386 - 1.72248i) q^{45} +(-0.485874 - 8.96143i) q^{46} +(-10.0104 - 2.20345i) q^{47} +(0.370138 + 0.928977i) q^{48} +(-0.703373 + 2.53332i) q^{49} +(-0.105751 + 1.95045i) q^{50} +(-6.78956 + 0.738409i) q^{51} +(0.381010 - 0.289636i) q^{52} +(3.85133 + 13.8712i) q^{53} +(-0.976621 + 0.214970i) q^{54} +(4.32975 + 6.38590i) q^{55} +(-1.51781 + 1.43774i) q^{56} +(-2.20420 + 4.15756i) q^{57} +10.1356 q^{58} +(6.58392 + 3.95626i) q^{59} -1.74547 q^{60} +(-0.810416 + 1.52861i) q^{61} +(-6.64655 + 6.29594i) q^{62} +(-1.17325 - 1.73041i) q^{63} +(0.976621 - 0.214970i) q^{64} +(0.223489 + 0.804934i) q^{65} +(3.51888 - 2.67499i) q^{66} +(-7.75360 + 0.843255i) q^{67} +(-0.369747 + 6.81958i) q^{68} +(2.40096 - 8.64746i) q^{69} +(-1.35070 - 3.39001i) q^{70} +(8.30561 + 1.82820i) q^{71} +(0.0541389 + 0.998533i) q^{72} +(-0.225672 - 1.37654i) q^{73} +(2.38608 - 3.51920i) q^{74} +(-0.722998 + 1.81459i) q^{75} +(3.74619 + 2.84778i) q^{76} +(7.91831 + 4.76429i) q^{77} +(0.453547 - 0.152818i) q^{78} +(-0.882699 - 0.836137i) q^{79} +(-0.282386 + 1.72248i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(0.512136 - 0.308142i) q^{82} +(5.95093 - 7.00597i) q^{83} +(-1.89743 + 0.877844i) q^{84} +(-10.8191 - 5.00545i) q^{85} +(-2.62859 - 3.09461i) q^{86} +(9.60506 + 3.23632i) q^{87} +(-2.07046 - 3.90529i) q^{88} +(5.12276 + 9.66255i) q^{89} +(-1.65410 - 0.557333i) q^{90} +(0.647767 + 0.762611i) q^{91} +(-8.14512 - 3.76833i) q^{92} +(-8.30893 + 3.84412i) q^{93} +(-6.63570 + 7.81216i) q^{94} +(-7.03798 + 4.23461i) q^{95} +(0.994138 + 0.108119i) q^{96} +(0.0801690 - 0.489009i) q^{97} +(1.90875 + 1.80807i) q^{98} +(4.18881 - 1.41137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{19}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.468408	−	0.883512i	0.331215	−	0.624737i
$2$	0.468408	−	0.883512i	0.331215	−	0.624737i
$3$	0.725995	−	0.687699i	0.419154	−	0.397043i
$3$	0.725995	−	0.687699i	0.419154	−	0.397043i
$4$	−0.561187	−	0.827689i	−0.280594	−	0.413844i
$5$	1.70467	−	0.375225i	0.762350	−	0.167806i	0.183254	−	0.983066i	$-0.441337\pi$
$5$	1.70467	−	0.375225i	0.762350	−	0.167806i	0.579096	+	0.815260i	$0.303406\pi$
$6$	−0.267528	−	0.963550i	−0.109218	−	0.393368i
$7$	1.66436	−	1.26521i	0.629068	−	0.478205i	−0.241403	−	0.970425i	$-0.577608\pi$
$7$	1.66436	−	1.26521i	0.629068	−	0.478205i	0.870471	+	0.492220i	$0.163814\pi$
$8$	−0.994138	+	0.108119i	−0.351481	+	0.0382258i
$9$	0.0541389	−	0.998533i	0.0180463	−	0.332844i
$10$	0.466964	−	1.68185i	0.147667	−	0.531848i
$11$	1.63608	+	4.10626i	0.493297	+	1.23808i	0.939314	+	0.343058i	$0.111463\pi$
$11$	1.63608	+	4.10626i	0.493297	+	1.23808i	−0.446017	+	0.895025i	$0.647158\pi$
$12$	−0.976621	−	0.214970i	−0.281926	−	0.0620566i
$13$	0.0259109	+	0.477898i	0.00718639	+	0.132545i	0.999925	+	0.0122530i	$0.00390035\pi$
$13$	0.0259109	+	0.477898i	0.00718639	+	0.132545i	−0.992739	+	0.120292i	$0.961617\pi$
$14$	−0.338231	−	2.06312i	−0.0903960	−	0.551391i
$15$	0.979538	−	1.44471i	0.252916	−	0.373023i
$16$	−0.370138	+	0.928977i	−0.0925345	+	0.232244i
$17$	−5.43699	−	4.13309i	−1.31866	−	1.00242i	−0.998483	−	0.0550667i	$-0.982463\pi$
$17$	−5.43699	−	4.13309i	−1.31866	−	1.00242i	−0.320182	−	0.947356i	$-0.603744\pi$
$18$	−0.856857	−	0.515554i	−0.201963	−	0.121517i
$19$	−4.45939	+	1.50254i	−1.02305	+	0.344707i	−0.780317	−	0.625385i	$-0.784942\pi$
$19$	−4.45939	+	1.50254i	−1.02305	+	0.344707i	−0.242738	+	0.970092i	$0.578046\pi$
$20$	−1.26721	−	1.20036i	−0.283356	−	0.268409i
$21$	0.338231	−	2.06312i	0.0738080	−	0.450209i
$22$	4.39428	+	0.477907i	0.936864	+	0.101890i
$23$	7.68994	−	4.62688i	1.60346	−	0.964772i	0.619799	−	0.784761i	$-0.287214\pi$
$23$	7.68994	−	4.62688i	1.60346	−	0.964772i	0.983665	−	0.180011i	$-0.0576134\pi$
$24$	−0.647386	+	0.762162i	−0.132147	+	0.155576i
$25$	−1.77278	+	0.820177i	−0.354557	+	0.164035i
$26$	0.434366	+	0.200959i	0.0851861	+	0.0394113i
$27$	−0.647386	−	0.762162i	−0.124590	−	0.146678i
$28$	−1.98122	−	0.667550i	−0.374415	−	0.126155i
$29$	4.74762	+	8.95495i	0.881610	+	1.66289i	0.739620	+	0.673025i	$0.235005\pi$
$29$	4.74762	+	8.95495i	0.881610	+	1.66289i	0.141990	+	0.989868i	$0.454650\pi$
$30$	−0.817595	−	1.54215i	−0.149272	−	0.281556i
$31$	−8.67584	−	2.92323i	−1.55823	−	0.525028i	−0.597345	−	0.801984i	$-0.703778\pi$
$31$	−8.67584	−	2.92323i	−1.55823	−	0.525028i	−0.960882	+	0.276957i	$0.910674\pi$
$32$	0.647386	+	0.762162i	0.114443	+	0.134732i
$33$	4.01166	+	1.85599i	0.698340	+	0.323087i
$34$	−6.19837	+	2.86767i	−1.06301	+	0.491802i
$35$	2.36243	−	2.78127i	0.399324	−	0.470121i
$36$	−0.856857	+	0.515554i	−0.142810	+	0.0859256i
$37$	4.22692	+	0.459705i	0.694901	+	0.0755750i	0.448751	−	0.893657i	$-0.351869\pi$
$37$	4.22692	+	0.459705i	0.694901	+	0.0755750i	0.246150	+	0.969232i	$0.420835\pi$
$38$	−0.761301	+	4.64373i	−0.123499	+	0.753313i
$39$	0.347461	+	0.329133i	0.0556384	+	0.0527034i
$40$	−1.65410	+	0.557333i	−0.261537	+	0.0881220i
$41$	0.512136	+	0.308142i	0.0799821	+	0.0481237i	0.554983	−	0.831862i	$-0.312725\pi$
$41$	0.512136	+	0.308142i	0.0799821	+	0.0481237i	−0.475001	+	0.879985i	$0.657552\pi$
$42$	−1.66436	−	1.26521i	−0.256816	−	0.195226i
$43$	1.50287	−	3.77193i	0.229186	−	0.575214i	−0.768742	−	0.639560i	$-0.779117\pi$
$43$	1.50287	−	3.77193i	0.229186	−	0.575214i	0.997928	+	0.0643457i	$0.0204960\pi$
$44$	2.48056	−	3.65854i	0.373958	−	0.551546i
$45$	−0.282386	−	1.72248i	−0.0420957	−	0.256772i
$46$	−0.485874	−	8.96143i	−0.0716383	−	1.32129i
$47$	−10.0104	−	2.20345i	−1.46016	−	0.321406i	−0.587297	−	0.809371i	$-0.699808\pi$
$47$	−10.0104	−	2.20345i	−1.46016	−	0.321406i	−0.872863	+	0.487966i	$0.837739\pi$
$48$	0.370138	+	0.928977i	0.0534248	+	0.134086i
$49$	−0.703373	+	2.53332i	−0.100482	+	0.361903i
$50$	−0.105751	+	1.95045i	−0.0149554	+	0.275836i
$51$	−6.78956	+	0.738409i	−0.950729	+	0.103398i
$52$	0.381010	−	0.289636i	0.0528366	−	0.0401653i
$53$	3.85133	+	13.8712i	0.529020	+	1.90536i	0.408837	+	0.912608i	$0.365935\pi$
$53$	3.85133	+	13.8712i	0.529020	+	1.90536i	0.120184	+	0.992752i	$0.461652\pi$
$54$	−0.976621	+	0.214970i	−0.132901	+	0.0292538i
$55$	4.32975	+	6.38590i	0.583823	+	0.861074i
$56$	−1.51781	+	1.43774i	−0.202826	+	0.192127i
$57$	−2.20420	+	4.15756i	−0.291953	+	0.550683i
$58$	10.1356			1.33087
$59$	6.58392	+	3.95626i	0.857153	+	0.515062i
$59$	6.58392	+	3.95626i	0.857153	+	0.515062i
$60$	−1.74547			−0.225340
$61$	−0.810416	+	1.52861i	−0.103763	+	0.195718i	−0.929957	−	0.367667i	$-0.880157\pi$
$61$	−0.810416	+	1.52861i	−0.103763	+	0.195718i	0.826194	+	0.563385i	$0.190501\pi$
$62$	−6.64655	+	6.29594i	−0.844112	+	0.799586i
$63$	−1.17325	−	1.73041i	−0.147816	−	0.218012i
$64$	0.976621	−	0.214970i	0.122078	−	0.0268713i
$65$	0.223489	+	0.804934i	0.0277204	+	0.0998398i
$66$	3.51888	−	2.67499i	0.433145	−	0.329268i
$67$	−7.75360	+	0.843255i	−0.947253	+	0.103020i	−0.568687	−	0.822554i	$-0.692548\pi$
$67$	−7.75360	+	0.843255i	−0.947253	+	0.103020i	−0.378566	+	0.925574i	$0.623583\pi$
$68$	−0.369747	+	6.81958i	−0.0448384	+	0.826995i
$69$	2.40096	−	8.64746i	0.289041	−	1.04103i
$70$	−1.35070	−	3.39001i	−0.161440	−	0.405184i
$71$	8.30561	+	1.82820i	0.985695	+	0.216968i	0.678437	−	0.734659i	$-0.262658\pi$
$71$	8.30561	+	1.82820i	0.985695	+	0.216968i	0.307258	+	0.951626i	$0.400589\pi$
$72$	0.0541389	+	0.998533i	0.00638033	+	0.117678i
$73$	−0.225672	−	1.37654i	−0.0264129	−	0.161111i	0.970327	−	0.241798i	$-0.0777370\pi$
$73$	−0.225672	−	1.37654i	−0.0264129	−	0.161111i	−0.996740	+	0.0806864i	$0.974289\pi$
$74$	2.38608	−	3.51920i	0.277376	−	0.409099i
$75$	−0.722998	+	1.81459i	−0.0834846	+	0.209531i
$76$	3.74619	+	2.84778i	0.429718	+	0.326663i
$77$	7.91831	+	4.76429i	0.902375	+	0.542941i
$78$	0.453547	−	0.152818i	0.0513541	−	0.0173032i
$79$	−0.882699	−	0.836137i	−0.0993114	−	0.0940728i	0.636433	−	0.771332i	$-0.280409\pi$
$79$	−0.882699	−	0.836137i	−0.0993114	−	0.0940728i	−0.735745	+	0.677259i	$0.763168\pi$
$80$	−0.282386	+	1.72248i	−0.0315718	+	0.192579i
$81$	−0.994138	−	0.108119i	−0.110460	−	0.0120132i
$82$	0.512136	−	0.308142i	0.0565559	−	0.0340286i
$83$	5.95093	−	7.00597i	0.653199	−	0.769005i	−0.331465	−	0.943468i	$-0.607543\pi$
$83$	5.95093	−	7.00597i	0.653199	−	0.769005i	0.984664	+	0.174462i	$0.0558187\pi$
$84$	−1.89743	+	0.877844i	−0.207026	+	0.0957806i
$85$	−10.8191	−	5.00545i	−1.17350	−	0.542917i
$86$	−2.62859	−	3.09461i	−0.283448	−	0.333701i
$87$	9.60506	+	3.23632i	1.02977	+	0.346970i
$88$	−2.07046	−	3.90529i	−0.220711	−	0.416306i
$89$	5.12276	+	9.66255i	0.543011	+	1.02423i	0.991459	+	0.130419i	$0.0416322\pi$
$89$	5.12276	+	9.66255i	0.543011	+	1.02423i	−0.448448	+	0.893809i	$0.648023\pi$
$90$	−1.65410	−	0.557333i	−0.174358	−	0.0587480i
$91$	0.647767	+	0.762611i	0.0679045	+	0.0799433i
$92$	−8.14512	−	3.76833i	−0.849187	−	0.392876i
$93$	−8.30893	+	3.84412i	−0.861596	+	0.398617i
$94$	−6.63570	+	7.81216i	−0.684421	+	0.805762i
$95$	−7.03798	+	4.23461i	−0.722082	+	0.434462i
$96$	0.994138	+	0.108119i	0.101464	+	0.0110349i
$97$	0.0801690	−	0.489009i	0.00813992	−	0.0496513i	−0.982444	−	0.186556i	$-0.940267\pi$
$97$	0.0801690	−	0.489009i	0.00813992	−	0.0496513i	0.990584	+	0.136905i	$0.0437155\pi$
$98$	1.90875	+	1.80807i	0.192813	+	0.182642i
$99$	4.18881	−	1.41137i	0.420991	−	0.141848i
$100$	1.67372	+	1.00704i	0.167372	+	0.100704i
$101$	−0.242401	−	0.184269i	−0.0241198	−	0.0183354i	0.593045	−	0.805169i	$-0.297926\pi$
$101$	−0.242401	−	0.184269i	−0.0241198	−	0.0183354i	−0.617165	+	0.786834i	$0.711719\pi$
$102$	−2.52789	+	6.34453i	−0.250299	+	0.628203i
$103$	−2.42805	+	3.58110i	−0.239242	+	0.352856i	−0.928288	−	0.371862i	$-0.878720\pi$
$103$	−2.42805	+	3.58110i	−0.239242	+	0.352856i	0.689046	+	0.724718i	$0.258030\pi$
$104$	−0.0774289	−	0.472295i	−0.00759252	−	0.0463123i
$105$	−0.197563	−	3.64384i	−0.0192802	−	0.355602i
$106$	14.0594	+	3.09471i	1.36557	+	0.300584i
$107$	−2.69937	−	6.77490i	−0.260958	−	0.654955i	0.738864	−	0.673855i	$-0.235363\pi$
$107$	−2.69937	−	6.77490i	−0.260958	−	0.654955i	−0.999821	+	0.0189003i	$0.993983\pi$
$108$	−0.267528	+	0.963550i	−0.0257429	+	0.0927176i
$109$	0.169602	−	3.12813i	0.0162449	−	0.299620i	−0.979109	−	0.203336i	$-0.934822\pi$
$109$	0.169602	−	3.12813i	0.0162449	−	0.299620i	0.995354	−	0.0962841i	$-0.0306957\pi$
$110$	7.67011	−	0.834174i	0.731316	−	0.0795354i
$111$	3.38486	−	2.57310i	0.321277	−	0.244228i
$112$	0.559310	+	2.01445i	0.0528498	+	0.190348i
$113$	−3.90968	+	0.860585i	−0.367792	+	0.0809571i	−0.395021	−	0.918672i	$-0.629263\pi$
$113$	−3.90968	+	0.860585i	−0.367792	+	0.0809571i	0.0272292	+	0.999629i	$0.491332\pi$
$114$	2.64079	+	3.89487i	0.247333	+	0.364788i
$115$	11.3727	−	10.7728i	1.06051	−	1.00456i
$116$	4.74762	−	8.95495i	0.440805	−	0.831446i
$117$	0.478600			0.0442466
$118$	6.57937	−	3.96382i	0.605680	−	0.364900i
$119$	−14.2783			−1.30889
$120$	−0.817595	+	1.54215i	−0.0746359	+	0.140778i
$121$	−6.19863	+	5.87165i	−0.563511	+	0.533786i
$122$	0.970936	+	1.43202i	0.0879044	+	0.129649i
$123$	0.583717	−	0.128486i	0.0526320	−	0.0115852i
$124$	2.44924	+	8.82138i	0.219949	+	0.792183i
$125$	−9.66205	+	7.34490i	−0.864200	+	0.656948i
$126$	−2.07840	+	0.226040i	−0.185159	+	0.0201372i
$127$	0.557293	−	10.2787i	0.0494517	−	0.912084i	−0.863584	−	0.504205i	$-0.831786\pi$
$127$	0.557293	−	10.2787i	0.0494517	−	0.912084i	0.913036	−	0.407879i	$-0.133732\pi$
$128$	0.267528	−	0.963550i	0.0236464	−	0.0851666i
$129$	−1.50287	−	3.77193i	−0.132321	−	0.332100i
$130$	0.815853	+	0.179583i	0.0715551	+	0.0157505i
$131$	−0.0765128	−	1.41119i	−0.00668495	−	0.123297i	−0.999971	−	0.00761271i	$-0.997577\pi$
$131$	−0.0765128	−	1.41119i	−0.00668495	−	0.123297i	0.993286	−	0.115684i	$-0.0369060\pi$
$132$	−0.715108	−	4.36196i	−0.0622421	−	0.379660i
$133$	−5.52099	+	8.14285i	−0.478730	+	0.706074i
$134$	−2.88683	+	7.24539i	−0.249384	+	0.625906i
$135$	−1.38956	−	1.05632i	−0.119594	−	0.0909132i
$136$	5.85199	+	3.52102i	0.501804	+	0.301925i
$137$	17.5249	−	5.90482i	1.49725	−	0.504483i	0.552851	−	0.833280i	$-0.313540\pi$
$137$	17.5249	−	5.90482i	1.49725	−	0.504483i	0.944401	+	0.328797i	$0.106643\pi$
$138$	−6.51551	−	6.17182i	−0.554637	−	0.525380i
$139$	−1.84546	+	11.2568i	−0.156530	+	0.954793i	0.785401	+	0.618987i	$0.212457\pi$
$139$	−1.84546	+	11.2568i	−0.156530	+	0.954793i	−0.941931	+	0.335805i	$0.890992\pi$
$140$	−3.62780	−	0.394547i	−0.306605	−	0.0333453i
$141$	−8.78278	+	5.28442i	−0.739643	+	0.445029i
$142$	5.50566	−	6.48176i	0.462025	−	0.543937i
$143$	−1.91998	+	0.888277i	−0.160557	+	0.0742815i
$144$	0.907575	+	0.419889i	0.0756313	+	0.0349908i
$145$	11.4532	+	13.4838i	0.951139	+	1.11977i
$146$	−1.32189	−	0.445397i	−0.109401	−	0.0368613i
$147$	1.23152	+	2.32289i	0.101574	+	0.191589i
$148$	−1.99160	−	3.75655i	−0.163708	−	0.308787i
$149$	−17.7144	−	5.96869i	−1.45122	−	0.488974i	−0.520234	−	0.854024i	$-0.674155\pi$
$149$	−17.7144	−	5.96869i	−1.45122	−	0.488974i	−0.930988	+	0.365050i	$0.881052\pi$
$150$	1.26455	+	1.48875i	0.103250	+	0.121556i
$151$	−13.5764	−	6.28113i	−1.10483	−	0.511151i	−0.219269	−	0.975665i	$-0.570367\pi$
$151$	−13.5764	−	6.28113i	−1.10483	−	0.511151i	−0.885566	+	0.464514i	$0.846229\pi$
$152$	4.27080	−	1.97588i	0.346407	−	0.160265i
$153$	−4.42139	+	5.20526i	−0.357448	+	0.420820i
$154$	7.91831	−	4.76429i	0.638076	−	0.383917i
$155$	−15.8863	−	1.72774i	−1.27602	−	0.138775i
$156$	0.0774289	−	0.472295i	0.00619927	−	0.0378139i
$157$	2.99247	+	2.83462i	0.238825	+	0.226227i	0.797746	−	0.602994i	$-0.206026\pi$
$157$	2.99247	+	2.83462i	0.238825	+	0.226227i	−0.558921	+	0.829221i	$0.688784\pi$
$158$	−1.15220	+	0.388222i	−0.0916642	+	0.0308853i
$159$	12.3353	+	7.42189i	0.978251	+	0.588594i
$160$	1.38956	+	1.05632i	0.109854	+	0.0835091i
$161$	6.94482	−	17.4302i	0.547329	−	1.37369i
$162$	−0.561187	+	0.827689i	−0.0440910	+	0.0650294i
$163$	−4.04844	−	24.6944i	−0.317098	−	1.93421i	−0.354842	−	0.934926i	$-0.615465\pi$
$163$	−4.04844	−	24.6944i	−0.317098	−	1.93421i	0.0377435	−	0.999287i	$-0.487983\pi$
$164$	−0.0323583	−	0.596814i	−0.00252676	−	0.0466034i
$165$	7.53495	+	1.65857i	0.586595	+	0.129119i
$166$	−3.40240	−	8.53937i	−0.264077	−	0.662784i
$167$	2.62758	−	9.46370i	0.203329	−	0.732323i	−0.789601	−	0.613620i	$-0.789713\pi$
$167$	2.62758	−	9.46370i	0.203329	−	0.732323i	0.992930	−	0.118703i	$-0.0378736\pi$
$168$	−0.113186	+	2.08759i	−0.00873248	+	0.161061i
$169$	12.6961	−	1.38078i	0.976621	−	0.106214i
$170$	−9.49013	+	7.21421i	−0.727860	+	0.553305i
$171$	1.25891	+	4.53420i	0.0962716	+	0.346739i
$172$	−3.96538	+	0.872846i	−0.302357	+	0.0665539i
$173$	−13.2205	−	19.4988i	−1.00513	−	1.48246i	−0.870868	−	0.491517i	$-0.836442\pi$
$173$	−13.2205	−	19.4988i	−1.00513	−	1.48246i	−0.134267	−	0.990945i	$-0.542868\pi$
$174$	7.35842	−	6.97027i	0.557841	−	0.528415i
$175$	−1.91285	+	3.60802i	−0.144598	+	0.272740i
$176$	−4.42019			−0.333185
$177$	7.50061	−	1.65553i	0.563781	−	0.124437i
$178$	10.9365			0.819727
$179$	3.90881	−	7.37280i	0.292158	−	0.551069i	−0.693370	−	0.720582i	$-0.743875\pi$
$179$	3.90881	−	7.37280i	0.292158	−	0.551069i	0.985528	+	0.169513i	$0.0542195\pi$
$180$	−1.26721	+	1.20036i	−0.0944520	+	0.0894697i
$181$	−9.34848	−	13.7880i	−0.694867	−	1.02485i	−0.997425	−	0.0717208i	$-0.977151\pi$
$181$	−9.34848	−	13.7880i	−0.694867	−	1.02485i	0.302558	−	0.953131i	$-0.402159\pi$
$182$	0.977195	−	0.215097i	0.0724345	−	0.0159440i
$183$	0.462863	+	1.66708i	0.0342159	+	0.123234i
$184$	−7.14461	+	5.43119i	−0.526707	+	0.400393i
$185$	7.37798	−	0.802403i	0.542440	−	0.0589939i
$186$	−0.495646	+	9.14166i	−0.0363425	+	0.670299i
$187$	8.07618	−	29.0878i	0.590589	−	2.12711i
$188$	3.79391	+	9.52200i	0.276700	+	0.694464i
$189$	−2.04178	−	0.449429i	−0.148518	−	0.0326912i
$190$	0.444682	+	8.20167i	0.0322606	+	0.595012i
$191$	1.26383	+	7.70903i	0.0914476	+	0.557806i	0.992318	+	0.123717i	$0.0394814\pi$
$191$	1.26383	+	7.70903i	0.0914476	+	0.557806i	−0.900870	+	0.434089i	$0.857070\pi$
$192$	0.561187	−	0.827689i	0.0405002	−	0.0597333i
$193$	−6.96783	+	17.4879i	−0.501555	+	1.25881i	0.432485	+	0.901641i	$0.357637\pi$
$193$	−6.96783	+	17.4879i	−0.501555	+	1.25881i	−0.934040	+	0.357168i	$0.883742\pi$
$194$	−0.394494	−	0.299886i	−0.0283230	−	0.0215306i
$195$	0.715805	+	0.430685i	0.0512598	+	0.0308420i
$196$	2.49153	−	0.839493i	0.177966	−	0.0599638i
$197$	−3.35331	−	3.17643i	−0.238914	−	0.226311i	0.558869	−	0.829256i	$-0.311235\pi$
$197$	−3.35331	−	3.17643i	−0.238914	−	0.226311i	−0.797783	+	0.602945i	$0.793994\pi$
$198$	0.715108	−	4.36196i	0.0508205	−	0.309991i
$199$	−16.3667	−	1.77999i	−1.16021	−	0.126180i	−0.492300	−	0.870426i	$-0.663844\pi$
$199$	−16.3667	−	1.77999i	−1.16021	−	0.126180i	−0.667906	+	0.744246i	$0.732809\pi$
$200$	1.67372	−	1.00704i	0.118350	−	0.0712086i
$201$	−5.04917	+	5.94435i	−0.356141	+	0.419282i
$202$	−0.276346	+	0.127851i	−0.0194437	+	0.00899560i
$203$	19.2316	+	8.89750i	1.34980	+	0.624482i
$204$	4.42139	+	5.20526i	0.309559	+	0.364441i
$205$	0.988643	+	0.333113i	0.0690498	+	0.0232656i
$206$	2.02663	+	3.82262i	0.141202	+	0.266335i
$207$	−4.20377	−	7.92916i	−0.292182	−	0.551114i
$208$	−0.453547	−	0.152818i	−0.0314478	−	0.0105960i
$209$	−13.4658	−	15.8531i	−0.931446	−	1.09658i
$210$	−3.31191	−	1.53225i	−0.228544	−	0.105736i
$211$	11.1865	−	5.17541i	0.770108	−	0.356290i	0.00482876	−	0.999988i	$-0.498463\pi$
$211$	11.1865	−	5.17541i	0.770108	−	0.356290i	0.765279	+	0.643698i	$0.222601\pi$
$212$	9.31975	−	10.9721i	0.640083	−	0.753564i
$213$	7.28709	−	4.38450i	0.499303	−	0.300421i
$214$	−7.25012	−	0.788498i	−0.495608	−	0.0539006i
$215$	1.14657	−	6.99380i	0.0781958	−	0.476973i
$216$	0.725995	+	0.687699i	0.0493977	+	0.0467920i
$217$	−18.1382	+	6.11148i	−1.23130	+	0.414874i
$218$	−2.68430	−	1.61509i	−0.181803	−	0.109388i
$219$	−1.11048	−	0.844164i	−0.0750392	−	0.0570433i
$220$	2.85574	−	7.16737i	0.192534	−	0.483224i
$221$	1.83432	−	2.70542i	0.123390	−	0.181986i
$222$	−0.687871	−	4.19583i	−0.0461669	−	0.281606i
$223$	0.827444	+	15.2613i	0.0554098	+	1.02197i	0.885587	+	0.464474i	$0.153756\pi$
$223$	0.827444	+	15.2613i	0.0554098	+	1.02197i	−0.830177	+	0.557500i	$0.811761\pi$
$224$	2.04178	+	0.449429i	0.136422	+	0.0300288i
$225$	0.722998	+	1.81459i	0.0481999	+	0.120973i
$226$	−1.07099	+	3.85735i	−0.0712411	+	0.256587i
$227$	0.215878	−	3.98164i	0.0143283	−	0.264271i	−0.982588	−	0.185798i	$-0.940513\pi$
$227$	0.215878	−	3.98164i	0.0143283	−	0.264271i	0.996916	−	0.0784725i	$-0.0250043\pi$
$228$	4.67814	−	0.508778i	0.309817	−	0.0336947i
$229$	8.01067	−	6.08955i	0.529360	−	0.402409i	−0.306067	−	0.952010i	$-0.599013\pi$
$229$	8.01067	−	6.08955i	0.529360	−	0.402409i	0.835427	+	0.549601i	$0.185220\pi$
$230$	−4.19081	−	15.0939i	−0.276334	−	0.995264i
$231$	9.02506	−	1.98656i	0.593805	−	0.130706i
$232$	−5.68799	−	8.38915i	−0.373435	−	0.550775i
$233$	−2.43404	+	2.30564i	−0.159459	+	0.151048i	−0.763269	−	0.646080i	$-0.776407\pi$
$233$	−2.43404	+	2.30564i	−0.159459	+	0.151048i	0.603810	+	0.797128i	$0.293648\pi$
$234$	0.224180	−	0.422849i	0.0146551	−	0.0276425i
$235$	−17.8911			−1.16709
$236$	−0.420255	−	7.66964i	−0.0273563	−	0.499251i
$237$	−1.21585			−0.0789777
$238$	−6.68810	+	12.6151i	−0.433525	+	0.817715i
$239$	4.74080	−	4.49072i	0.306657	−	0.290481i	−0.518859	−	0.854860i	$-0.673643\pi$
$239$	4.74080	−	4.49072i	0.306657	−	0.290481i	0.825516	+	0.564379i	$0.190884\pi$
$240$	0.979538	+	1.44471i	0.0632289	+	0.0932556i
$241$	−6.13025	+	1.34937i	−0.394884	+	0.0869205i	−0.407973	−	0.912994i	$-0.633764\pi$
$241$	−6.13025	+	1.34937i	−0.394884	+	0.0869205i	0.0130895	+	0.999914i	$0.495833\pi$
$242$	2.28418	+	8.22689i	0.146833	+	0.528845i
$243$	−0.796093	+	0.605174i	−0.0510694	+	0.0388219i
$244$	1.72001	−	0.187062i	0.110112	−	0.0119754i
$245$	−0.248450	+	4.58239i	−0.0158729	+	0.292758i
$246$	0.159899	−	0.575905i	0.0101948	−	0.0367184i
$247$	−0.833610	−	2.09220i	−0.0530413	−	0.133124i
$248$	8.94104	+	1.96807i	0.567757	+	0.124973i
$249$	−0.497657	−	9.17875i	−0.0315378	−	0.581680i
$250$	1.96352	+	11.9770i	0.124184	+	0.757489i
$251$	−5.37387	+	7.92586i	−0.339195	+	0.500276i	−0.958584	−	0.284808i	$-0.908070\pi$
$251$	−5.37387	+	7.92586i	−0.339195	+	0.500276i	0.619389	+	0.785084i	$0.287380\pi$
$252$	−0.773832	+	1.94217i	−0.0487468	+	0.122345i
$253$	31.5805	+	24.0069i	1.98545	+	1.50930i
$254$	−8.82028	−	5.30699i	−0.553434	−	0.332990i
$255$	−11.2969	+	3.80636i	−0.707437	+	0.238363i
$256$	−0.725995	−	0.687699i	−0.0453747	−	0.0429812i
$257$	−0.204701	+	1.24862i	−0.0127689	+	0.0778869i	−0.992442	−	0.122713i	$-0.960841\pi$
$257$	−0.204701	+	1.24862i	−0.0127689	+	0.0778869i	0.979673	+	0.200599i	$0.0642890\pi$
$258$	−4.03650	−	0.438996i	−0.251302	−	0.0273307i
$259$	7.61672	−	4.58283i	0.473280	−	0.284763i
$260$	0.540816	−	0.636698i	0.0335400	−	0.0394863i
$261$	9.19885	−	4.25584i	0.569395	−	0.263430i
$262$	−1.28265	−	0.593416i	−0.0792422	−	0.0366613i
$263$	−10.0972	−	11.8874i	−0.622622	−	0.733007i	0.356945	−	0.934125i	$-0.383818\pi$
$263$	−10.0972	−	11.8874i	−0.622622	−	0.733007i	−0.979567	+	0.201118i	$0.935542\pi$
$264$	−4.18881	−	1.41137i	−0.257803	−	0.0868641i
$265$	11.7701	+	22.2007i	0.723029	+	1.36378i
$266$	4.60823	+	8.69204i	0.282549	+	0.532943i
$267$	10.3640	+	3.49205i	0.634268	+	0.213710i
$268$	5.04917	+	5.94435i	0.308427	+	0.363109i
$269$	−9.81600	−	4.54137i	−0.598492	−	0.276892i	0.0971622	−	0.995269i	$-0.469023\pi$
$269$	−9.81600	−	4.54137i	−0.598492	−	0.276892i	−0.695654	+	0.718377i	$0.744886\pi$
$270$	−1.58415	+	0.732906i	−0.0964083	+	0.0446032i
$271$	13.6358	−	16.0533i	0.828314	−	0.975167i	−0.171636	−	0.985160i	$-0.554905\pi$
$271$	13.6358	−	16.0533i	0.828314	−	0.975167i	0.999950	+	0.00999383i	$0.00318119\pi$
$272$	5.85199	−	3.52102i	0.354829	−	0.213493i
$273$	0.994723	+	0.108183i	0.0602034	+	0.00654751i
$274$	2.99182	−	18.2493i	0.180743	−	1.10248i
$275$	−6.26828	−	5.93763i	−0.377991	−	0.358052i
$276$	−8.50480	+	2.86560i	−0.511929	+	0.172489i
$277$	7.97110	+	4.79605i	0.478937	+	0.288167i	0.734479	−	0.678631i	$-0.237426\pi$
$277$	7.97110	+	4.79605i	0.478937	+	0.288167i	−0.255542	+	0.966798i	$0.582254\pi$
$278$	9.08112	+	6.90329i	0.544649	+	0.414032i
$279$	−3.38865	+	8.50486i	−0.202873	+	0.509173i
$280$	−2.04788	+	3.02039i	−0.122384	+	0.180503i
$281$	0.496851	+	3.03066i	0.0296397	+	0.180794i	0.997497	−	0.0707048i	$-0.0225248\pi$
$281$	0.496851	+	3.03066i	0.0296397	+	0.180794i	−0.967858	+	0.251499i	$0.919077\pi$
$282$	0.554923	+	10.2350i	0.0330452	+	0.609483i
$283$	7.31126	+	1.60933i	0.434609	+	0.0956647i	0.426886	−	0.904305i	$-0.359611\pi$
$283$	7.31126	+	1.60933i	0.434609	+	0.0956647i	0.00772317	+	0.999970i	$0.497542\pi$
$284$	−3.14782	−	7.90043i	−0.186789	−	0.468804i
$285$	−2.19740	+	7.91433i	−0.130163	+	0.468804i
$286$	−0.114531	+	2.11240i	−0.00677237	+	0.124909i
$287$	1.24224	−	0.135102i	0.0733272	−	0.00797481i
$288$	0.796093	−	0.605174i	0.0469102	−	0.0356602i
$289$	7.93044	+	28.5629i	0.466497	+	1.68017i
$290$	17.2779	−	3.80315i	1.01459	−	0.223328i
$291$	−0.278089	−	0.410150i	−0.0163019	−	0.0240434i
$292$	−1.01270	+	0.959280i	−0.0592637	+	0.0561376i
$293$	−11.2475	+	21.2150i	−0.657084	+	1.23939i	0.301197	+	0.953562i	$0.402614\pi$
$293$	−11.2475	+	21.2150i	−0.657084	+	1.23939i	−0.958281	+	0.285829i	$0.907731\pi$
$294$	2.62915			0.153335
$295$	12.7079	+	4.27365i	0.739881	+	0.248822i
$296$	−4.25184			−0.247133
$297$	2.07046	−	3.90529i	0.120140	−	0.226608i
$298$	−13.5710	+	12.8551i	−0.786146	+	0.744677i
$299$	2.41043	+	3.55512i	0.139399	+	0.205598i
$300$	1.90765	−	0.419906i	0.110138	−	0.0242433i
$301$	−2.27097	−	8.17929i	−0.130897	−	0.471447i
$302$	−11.9088	+	9.05281i	−0.685273	+	0.520931i
$303$	−0.302704	+	0.0329210i	−0.0173899	+	0.00189126i
$304$	0.254763	−	4.69882i	0.0146116	−	0.269496i
$305$	−0.807916	+	2.90985i	−0.0462612	+	0.166618i
$306$	2.52789	+	6.34453i	0.144510	+	0.362693i
$307$	−18.3177	−	4.03204i	−1.04545	−	0.230120i	−0.341138	−	0.940013i	$-0.610812\pi$
$307$	−18.3177	−	4.03204i	−1.04545	−	0.230120i	−0.704310	+	0.709893i	$0.748743\pi$
$308$	−0.500303	−	9.22755i	−0.0285074	−	0.525789i
$309$	0.699970	+	4.26963i	0.0398199	+	0.242891i
$310$	−8.96775	+	13.2264i	−0.509334	+	0.751211i
$311$	1.67120	−	4.19439i	0.0947650	−	0.237842i	−0.873951	−	0.486014i	$-0.838450\pi$
$311$	1.67120	−	4.19439i	0.0947650	−	0.237842i	0.968716	+	0.248172i	$0.0798297\pi$
$312$	−0.381010	−	0.289636i	−0.0215705	−	0.0163974i
$313$	14.9986	+	9.02437i	0.847772	+	0.510087i	0.871936	−	0.489621i	$-0.162865\pi$
$313$	14.9986	+	9.02437i	0.847772	+	0.510087i	−0.0241637	+	0.999708i	$0.507692\pi$
$314$	3.90612	−	1.31612i	0.220435	−	0.0742732i
$315$	−2.64929	−	2.50955i	−0.149271	−	0.141397i
$316$	−0.196702	+	1.19983i	−0.0110654	+	0.0674957i
$317$	4.09481	+	0.445338i	0.229988	+	0.0250126i	0.222387	−	0.974958i	$-0.428615\pi$
$317$	4.09481	+	0.445338i	0.229988	+	0.0250126i	0.00760049	+	0.999971i	$0.497581\pi$
$318$	12.3353	−	7.42189i	0.691728	−	0.416199i
$319$	−29.0038	+	34.1460i	−1.62390	+	1.91181i
$320$	1.58415	−	0.732906i	0.0885567	−	0.0409707i
$321$	−6.61883	−	3.06220i	−0.369427	−	0.170915i
$322$	−12.1468	−	14.3003i	−0.676913	−	0.796924i
$323$	30.4558	+	10.2618i	1.69461	+	0.570980i
$324$	0.468408	+	0.883512i	0.0260227	+	0.0490840i
$325$	−0.437896	−	0.825959i	−0.0242901	−	0.0458159i
$326$	−23.7141	−	7.99022i	−1.31340	−	0.442537i
$327$	−2.02808	−	2.38764i	−0.112153	−	0.132037i
$328$	−0.542449	−	0.250964i	−0.0299518	−	0.0138572i
$329$	−19.4486	+	8.99790i	−1.07224	+	0.496070i
$330$	4.99480	−	5.88033i	0.274955	−	0.323702i
$331$	−3.61103	+	2.17269i	−0.198480	+	0.119422i	−0.611325	−	0.791380i	$-0.709363\pi$
$331$	−3.61103	+	2.17269i	−0.198480	+	0.119422i	0.412844	+	0.910802i	$0.364535\pi$
$332$	−9.13835	−	0.993855i	−0.501532	−	0.0545449i
$333$	0.687871	−	4.19583i	0.0376951	−	0.229930i
$334$	−7.13051	−	6.75438i	−0.390164	−	0.369583i
$335$	−12.9009	+	4.34682i	−0.704851	+	0.237492i
$336$	1.79139	+	1.07785i	0.0977286	+	0.0588013i
$337$	−1.52782	−	1.16142i	−0.0832257	−	0.0632666i	0.562734	−	0.826638i	$-0.309750\pi$
$337$	−1.52782	−	1.16142i	−0.0832257	−	0.0632666i	−0.645960	+	0.763371i	$0.723543\pi$
$338$	4.72701	−	11.8639i	0.257116	−	0.645312i
$339$	−2.24658	+	3.31346i	−0.122018	+	0.179963i
$340$	1.92858	+	11.7638i	0.104592	+	0.637984i
$341$	−2.19085	−	40.4079i	−0.118641	−	2.18821i
$342$	4.59571	+	1.01159i	0.248507	+	0.0547006i
$343$	7.45135	+	18.7015i	0.402335	+	1.00978i
$344$	−1.08625	+	3.91231i	−0.0585665	+	0.210938i
$345$	0.848081	−	15.6419i	0.0456592	−	0.842134i
$346$	−23.4200	+	2.54707i	−1.25907	+	0.136932i
$347$	−8.12127	+	6.17363i	−0.435973	+	0.331418i	−0.800031	−	0.599958i	$-0.795184\pi$
$347$	−8.12127	+	6.17363i	−0.435973	+	0.331418i	0.364059	+	0.931376i	$0.381391\pi$
$348$	−2.71157	−	9.76619i	−0.145355	−	0.523523i
$349$	26.7523	−	5.88863i	1.43202	−	0.315211i	0.569815	−	0.821773i	$-0.307015\pi$
$349$	26.7523	−	5.88863i	1.43202	−	0.315211i	0.862203	+	0.506562i	$0.169084\pi$
$350$	2.29173	+	3.38005i	0.122498	+	0.180671i
$351$	0.347461	−	0.329133i	0.0185461	−	0.0175678i
$352$	−2.07046	+	3.90529i	−0.110356	+	0.208153i
$353$	4.01319			0.213601			0.106800	−	0.994280i	$-0.465939\pi$
$353$	4.01319			0.213601			0.106800	+	0.994280i	$0.465939\pi$
$354$	2.05067	−	7.40235i	0.108992	−	0.393430i
$355$	14.8443			0.787853
$356$	5.12276	−	9.66255i	0.271506	−	0.512114i
$357$	−10.3660	+	9.81921i	−0.548628	+	0.519688i
$358$	−4.68304	−	6.90697i	−0.247506	−	0.365045i
$359$	17.3215	−	3.81276i	0.914195	−	0.201230i	0.267127	−	0.963661i	$-0.413926\pi$
$359$	17.3215	−	3.81276i	0.914195	−	0.201230i	0.647068	+	0.762432i	$0.275995\pi$
$360$	0.466964	+	1.68185i	0.0246112	+	0.0886414i
$361$	2.50278	−	1.90256i	0.131725	−	0.100135i
$362$	−16.5607	+	1.80109i	−0.870413	+	0.0946631i
$363$	−0.462244	+	8.52558i	−0.0242615	+	0.447477i
$364$	0.267686	−	0.964117i	0.0140305	−	0.0505335i
$365$	−0.901206	−	2.26186i	−0.0471713	−	0.118391i
$366$	1.68970	+	0.371931i	0.0883219	+	0.0194411i
$367$	−0.506438	−	9.34070i	−0.0264359	−	0.487581i	−0.981534	−	0.191290i	$-0.938733\pi$
$367$	−0.506438	−	9.34070i	−0.0264359	−	0.487581i	0.955098	−	0.296291i	$-0.0957498\pi$
$368$	1.45193	+	8.85636i	0.0756869	+	0.461670i
$369$	0.335416	−	0.494702i	0.0174611	−	0.0257532i
$370$	2.74697	−	6.89438i	0.142808	−	0.358422i
$371$	23.9600	+	18.2139i	1.24394	+	0.945620i
$372$	7.84460	+	4.71994i	0.406723	+	0.244717i
$373$	−7.60831	+	2.56354i	−0.393943	+	0.132735i	−0.509300	−	0.860589i	$-0.670096\pi$
$373$	−7.60831	+	2.56354i	−0.393943	+	0.132735i	0.115357	+	0.993324i	$0.463199\pi$
$374$	−21.9164	−	20.7604i	−1.13327	−	1.07349i
$375$	−1.96352	+	11.9770i	−0.101396	+	0.618487i
$376$	10.1899	+	1.10822i	0.525504	+	0.0571520i
$377$	−4.15654	+	2.50091i	−0.214073	+	0.128803i
$378$	−1.35346	+	1.59342i	−0.0696146	+	0.0819567i
$379$	22.8603	−	10.5763i	1.17425	−	0.543267i	0.266936	−	0.963714i	$-0.413989\pi$
$379$	22.8603	−	10.5763i	1.17425	−	0.543267i	0.907317	+	0.420447i	$0.138127\pi$
$380$	7.45457	+	3.44885i	0.382411	+	0.176922i
$381$	−6.66404	−	7.84551i	−0.341409	−	0.401938i
$382$	7.40301	+	2.49437i	0.378771	+	0.127623i
$383$	14.0199	+	26.4444i	0.716385	+	1.35125i	0.927515	+	0.373787i	$0.121941\pi$
$383$	14.0199	+	26.4444i	0.716385	+	1.35125i	−0.211130	+	0.977458i	$0.567714\pi$
$384$	−0.468408	−	0.883512i	−0.0239034	−	0.0450865i
$385$	15.2858	+	5.15037i	0.779034	+	0.262487i
$386$	12.1870	+	14.3477i	0.620302	+	0.730277i
$387$	−3.68503	−	1.70488i	−0.187321	−	0.0866638i
$388$	−0.449737	+	0.208071i	−0.0228319	+	0.0105632i
$389$	−11.0699	+	13.0325i	−0.561267	+	0.660775i	−0.967463	−	0.253011i	$-0.918579\pi$
$389$	−11.0699	+	13.0325i	−0.561267	+	0.660775i	0.406196	+	0.913786i	$0.366855\pi$
$390$	0.715805	−	0.430685i	0.0362462	−	0.0218086i
$391$	−60.9335	−	6.62692i	−3.08154	−	0.335138i
$392$	0.425350	−	2.59452i	0.0214834	−	0.131043i
$393$	−1.02603	−	0.971903i	−0.0517562	−	0.0490260i
$394$	−4.37713	+	1.47483i	−0.220517	+	0.0743007i
$395$	−1.81845	−	1.09412i	−0.0914960	−	0.0550513i
$396$	−3.51888	−	2.67499i	−0.176831	−	0.134423i
$397$	−7.77958	+	19.5253i	−0.390446	+	0.979945i	0.594033	+	0.804441i	$0.297535\pi$
$397$	−7.77958	+	19.5253i	−0.390446	+	0.979945i	−0.984479	+	0.175504i	$0.943844\pi$
$398$	−9.23895	+	13.6264i	−0.463107	+	0.683031i
$399$	1.59162	+	9.70845i	0.0796806	+	0.486030i
$400$	−0.105751	−	1.95045i	−0.00528753	−	0.0975227i
$401$	−15.3796	−	3.38530i	−0.768020	−	0.169054i	−0.186355	−	0.982482i	$-0.559668\pi$
$401$	−15.3796	−	3.38530i	−0.768020	−	0.169054i	−0.581665	+	0.813428i	$0.697599\pi$
$402$	2.88683	+	7.24539i	0.143982	+	0.361367i
$403$	1.17221	−	4.22191i	0.0583918	−	0.210308i
$404$	−0.0164847	+	0.304042i	−0.000820144	+	0.0151267i
$405$	−1.73524	+	0.188719i	−0.0862249	+	0.00937752i
$406$	16.8693	−	12.8237i	0.837210	−	0.636431i
$407$	5.02792	+	18.1089i	0.249225	+	0.897626i
$408$	6.66992	−	1.46816i	0.330210	−	0.0726848i
$409$	−7.45867	−	11.0007i	−0.368807	−	0.543950i	0.597324	−	0.802000i	$-0.296231\pi$
$409$	−7.45867	−	11.0007i	−0.368807	−	0.543950i	−0.966132	+	0.258050i	$0.916920\pi$
$410$	0.757398	−	0.717445i	0.0374052	−	0.0354321i
$411$	8.66224	−	16.3387i	0.427277	−	0.805930i
$412$	4.32662			0.213157
$413$	15.9635	−	1.74542i	0.785513	−	0.0858863i
$414$	−8.97459			−0.441077
$415$	7.51552	−	14.1758i	0.368923	−	0.695862i
$416$	−0.347461	+	0.329133i	−0.0170357	+	0.0161371i
$417$	6.40152	+	9.44154i	0.313484	+	0.462354i
$418$	−20.3139	+	4.47143i	−0.993585	+	0.218705i
$419$	−6.36226	−	22.9148i	−0.310817	−	1.11946i	−0.939711	−	0.341970i	$-0.888906\pi$
$419$	−6.36226	−	22.9148i	−0.310817	−	1.11946i	0.628894	−	0.777491i	$-0.283508\pi$
$420$	−2.90509	+	2.20839i	−0.141754	+	0.107759i
$421$	−12.5289	+	1.36260i	−0.610621	+	0.0664091i	−0.408205	−	0.912890i	$-0.633845\pi$
$421$	−12.5289	+	1.36260i	−0.610621	+	0.0664091i	−0.202417	+	0.979299i	$0.564880\pi$
$422$	0.667298	−	12.3076i	0.0324835	−	0.599124i
$423$	−2.74216	+	9.87638i	−0.133329	+	0.480206i
$424$	−5.32849	−	13.3735i	−0.258775	−	0.649475i
$425$	13.0285	+	2.86779i	0.631974	+	0.139108i
$426$	−0.460421	−	8.49197i	−0.0223075	−	0.411437i
$427$	0.585189	+	3.56949i	0.0283193	+	0.172740i
$428$	−4.09266	+	6.03623i	−0.197826	+	0.291772i
$429$	−0.783029	+	1.96525i	−0.0378050	+	0.0948834i
$430$	−5.64204	−	4.28897i	−0.272083	−	0.206832i
$431$	−8.00585	−	4.81696i	−0.385628	−	0.232025i	0.309517	−	0.950894i	$-0.399832\pi$
$431$	−8.00585	−	4.81696i	−0.385628	−	0.232025i	−0.695146	+	0.718869i	$0.744660\pi$
$432$	0.947653	−	0.319302i	0.0455940	−	0.0153624i
$433$	−8.27204	−	7.83569i	−0.397529	−	0.376559i	0.462659	−	0.886536i	$-0.346895\pi$
$433$	−8.27204	−	7.83569i	−0.397529	−	0.376559i	−0.860188	+	0.509977i	$0.829654\pi$
$434$	−3.09653	+	18.8880i	−0.148638	+	0.906653i
$435$	17.5878	+	1.91279i	0.843269	+	0.0917111i
$436$	−2.68430	+	1.61509i	−0.128554	+	0.0773487i
$437$	−27.3404	+	32.1876i	−1.30787	+	1.53974i
$438$	−1.26599	+	0.585708i	−0.0604912	+	0.0279862i
$439$	18.9766	+	8.77951i	0.905704	+	0.419023i	0.816736	−	0.577011i	$-0.195781\pi$
$439$	18.9766	+	8.77951i	0.905704	+	0.419023i	0.0889678	+	0.996035i	$0.471643\pi$
$440$	−4.99480	−	5.88033i	−0.238118	−	0.280334i
$441$	2.49153	+	0.839493i	0.118644	+	0.0399758i
$442$	−1.53106	−	2.88789i	−0.0728251	−	0.137363i
$443$	10.7633	+	20.3017i	0.511378	+	0.964561i	0.995959	+	0.0898143i	$0.0286273\pi$
$443$	10.7633	+	20.3017i	0.511378	+	0.964561i	−0.484581	+	0.874747i	$0.661028\pi$
$444$	−4.02927	−	1.35762i	−0.191221	−	0.0644298i
$445$	12.3582	+	14.5492i	0.585836	+	0.689700i
$446$	13.8711	+	6.41747i	0.656817	+	0.303876i
$447$	−16.9653	+	7.84896i	−0.802429	+	0.371243i
$448$	1.35346	−	1.59342i	0.0639451	−	0.0752820i
$449$	18.8895	−	11.3654i	0.891451	−	0.536369i	0.00541565	−	0.999985i	$-0.498276\pi$
$449$	18.8895	−	11.3654i	0.891451	−	0.536369i	0.886036	+	0.463617i	$0.153449\pi$
$450$	1.94187	+	0.211191i	0.0915406	+	0.00995564i
$451$	−0.427413	+	2.60711i	−0.0201261	+	0.122764i
$452$	2.90636	+	2.75305i	0.136704	+	0.129493i
$453$	−14.1760	+	4.77644i	−0.666045	+	0.224417i
$454$	−3.41671	−	2.05576i	−0.160354	−	0.0964817i
$455$	1.39038	+	1.05694i	0.0651819	+	0.0495500i
$456$	1.74177	−	4.37151i	0.0815657	−	0.204715i
$457$	16.5429	−	24.3989i	0.773843	−	1.14133i	−0.212586	−	0.977142i	$-0.568189\pi$
$457$	16.5429	−	24.3989i	0.773843	−	1.14133i	0.986429	−	0.164190i	$-0.0525011\pi$
$458$	−1.62793	−	9.92992i	−0.0760681	−	0.463995i
$459$	0.369747	+	6.81958i	0.0172583	+	0.318311i
$460$	−15.2987	−	3.36749i	−0.713304	−	0.157010i
$461$	−3.48849	−	8.75544i	−0.162475	−	0.407782i	0.825088	−	0.565004i	$-0.191125\pi$
$461$	−3.48849	−	8.75544i	−0.162475	−	0.407782i	−0.987563	+	0.157222i	$0.949746\pi$
$462$	2.47226	−	8.90427i	0.115020	−	0.414264i
$463$	0.302031	−	5.57063i	0.0140366	−	0.258889i	−0.983089	−	0.183127i	$-0.941378\pi$
$463$	0.302031	−	5.57063i	0.0140366	−	0.258889i	0.997126	−	0.0757625i	$-0.0241391\pi$
$464$	−10.0762	+	1.09585i	−0.467777	+	0.0508738i
$465$	−12.7215	+	9.67066i	−0.589947	+	0.448466i
$466$	0.896940	+	3.23049i	0.0415500	+	0.149649i
$467$	10.1768	−	2.24008i	0.470926	−	0.103659i	0.0268343	−	0.999640i	$-0.491457\pi$
$467$	10.1768	−	2.24008i	0.470926	−	0.103659i	0.444092	+	0.895981i	$0.353526\pi$
$468$	−0.268584	−	0.396132i	−0.0124153	−	0.0183112i
$469$	−11.8379	+	11.2134i	−0.546622	+	0.517788i
$470$	−8.38034	+	15.8070i	−0.386556	+	0.729123i
$471$	4.12188			0.189926
$472$	−6.97307	−	3.22122i	−0.320962	−	0.148269i
$473$	17.9473			0.825219
$474$	−0.569513	+	1.07422i	−0.0261586	+	0.0493403i
$475$	6.67319	−	6.32118i	0.306187	−	0.290036i
$476$	8.01282	+	11.8180i	0.367267	+	0.541678i
$477$	14.0594	−	3.09471i	0.643735	−	0.141697i
$478$	−1.74698	−	6.29205i	−0.0799049	−	0.287792i
$479$	−31.5808	+	24.0071i	−1.44296	+	1.09691i	−0.465684	+	0.884951i	$0.654192\pi$
$479$	−31.5808	+	24.0071i	−1.44296	+	1.09691i	−0.977278	+	0.211961i	$0.932015\pi$
$480$	1.73524	−	0.188719i	0.0792026	−	0.00861380i
$481$	−0.110169	+	2.03195i	−0.00502327	+	0.0926488i
$482$	−1.67927	+	6.04820i	−0.0764889	+	0.275488i
$483$	−6.94482	−	17.4302i	−0.316000	−	0.793101i
$484$	8.33849	+	1.83544i	0.379022	+	0.0834291i
$485$	−0.0468273	−	0.863679i	−0.00212632	−	0.0392176i
$486$	0.161782	+	0.986827i	0.00733858	+	0.0447634i
$487$	19.2286	−	28.3601i	0.871331	−	1.28512i	−0.0860509	−	0.996291i	$-0.527425\pi$
$487$	19.2286	−	28.3601i	0.871331	−	1.28512i	0.957382	−	0.288826i	$-0.0932649\pi$
$488$	0.640394	−	1.60727i	0.0289893	−	0.0727575i
$489$	−19.9215	−	15.1439i	−0.900880	−	0.684831i
$490$	3.93222	+	2.36594i	0.177640	+	0.106882i
$491$	−23.8983	+	8.05228i	−1.07852	+	0.363394i	−0.801821	−	0.597564i	$-0.796136\pi$
$491$	−23.8983	+	8.05228i	−1.07852	+	0.363394i	−0.276694	+	0.960958i	$0.589239\pi$
$492$	−0.433921	−	0.411032i	−0.0195627	−	0.0185307i
$493$	11.1989	−	68.3104i	0.504374	−	3.07654i
$494$	−2.23896	−	0.243501i	−0.100735	−	0.0109556i
$495$	6.61094	−	3.97767i	0.297140	−	0.178783i
$496$	5.92687	−	6.97766i	0.266125	−	0.313306i
$497$	16.1366	−	7.46557i	0.723824	−	0.334877i
$498$	−8.34264	−	3.85972i	−0.373843	−	0.172958i
$499$	4.89266	+	5.76008i	0.219025	+	0.257857i	0.860691	−	0.509128i	$-0.170032\pi$
$499$	4.89266	+	5.76008i	0.219025	+	0.257857i	−0.641665	+	0.766985i	$0.721756\pi$
$500$	11.5015	+	3.87531i	0.514363	+	0.173309i
$501$	−4.60057	−	8.67759i	−0.205538	−	0.387686i
$502$	4.48543	+	8.46041i	0.200194	+	0.377607i
$503$	−8.83724	−	2.97761i	−0.394033	−	0.132765i	0.115308	−	0.993330i	$-0.463214\pi$
$503$	−8.83724	−	2.97761i	−0.394033	−	0.132765i	−0.509341	+	0.860565i	$0.670111\pi$
$504$	1.35346	+	1.59342i	0.0602880	+	0.0709765i
$505$	−0.482356	−	0.223162i	−0.0214645	−	0.00993056i
$506$	36.0030	−	16.6568i	1.60053	−	0.740483i
$507$	8.26773	−	9.73353i	0.367183	−	0.432281i
$508$	−8.82028	+	5.30699i	−0.391337	+	0.235459i
$509$	24.1795	+	2.62968i	1.07174	+	0.116558i	0.626936	−	0.779071i	$-0.284309\pi$
$509$	24.1795	+	2.62968i	1.07174	+	0.116558i	0.444801	+	0.895629i	$0.353274\pi$
$510$	−1.92858	+	11.7638i	−0.0853992	+	0.520912i
$511$	−2.11721	−	2.00552i	−0.0936597	−	0.0887192i
$512$	−0.947653	+	0.319302i	−0.0418807	+	0.0141113i
$513$	4.03213	+	2.42605i	0.178023	+	0.107113i
$514$	1.00729	+	0.765721i	0.0444296	+	0.0337745i
$515$	−2.79529	+	7.01564i	−0.123175	+	0.309146i
$516$	−2.27859	+	3.36067i	−0.100309	+	0.147945i
$517$	−7.32985	−	44.7101i	−0.322366	−	1.96635i
$518$	−0.481248	−	8.87611i	−0.0211448	−	0.389994i
$519$	−23.0073	−	5.06429i	−1.00991	−	0.222298i
$520$	−0.309208	−	0.776052i	−0.0135596	−	0.0340321i
$521$	7.70181	−	27.7394i	0.337422	−	1.21529i	−0.579085	−	0.815267i	$-0.696590\pi$
$521$	7.70181	−	27.7394i	0.337422	−	1.21529i	0.916507	−	0.400018i	$-0.130996\pi$
$522$	0.548732	−	10.1208i	0.0240173	−	0.442974i
$523$	32.8448	−	3.57209i	1.43620	−	0.156196i	0.643333	−	0.765587i	$-0.277551\pi$
$523$	32.8448	−	3.57209i	1.43620	−	0.156196i	0.792870	+	0.609390i	$0.208586\pi$
$524$	−1.12509	+	0.855273i	−0.0491499	+	0.0373628i
$525$	1.09251	+	3.93487i	0.0476811	+	0.171732i
$526$	−15.2323	+	3.35288i	−0.664159	+	0.146192i
$527$	35.0885	+	51.7517i	1.52848	+	2.25434i
$528$	−3.20904	+	3.03976i	−0.139656	+	0.132289i
$529$	26.9537	−	50.8401i	1.17190	−	2.21044i
$530$	25.1278			1.09148
$531$	4.30691	−	6.36008i	0.186904	−	0.276004i
$532$	9.83805			0.426534
$533$	−0.133990	+	0.252733i	−0.00580377	+	0.0109471i
$534$	7.93987	−	7.52104i	0.343592	−	0.325467i
$535$	−7.14364	−	10.5361i	−0.308846	−	0.455514i
$536$	7.61698	−	1.67662i	0.329003	−	0.0724191i
$537$	−2.23249	−	8.04071i	−0.0963392	−	0.346982i
$538$	−8.61025	+	6.54534i	−0.371214	+	0.282190i
$539$	−11.5532	+	1.25649i	−0.497633	+	0.0541209i
$540$	−0.0944981	+	1.74291i	−0.00406655	+	0.0750031i
$541$	0.642797	−	2.31514i	0.0276360	−	0.0995358i	−0.948446	−	0.316939i	$-0.897345\pi$
$541$	0.642797	−	2.31514i	0.0276360	−	0.0995358i	0.976082	+	0.217403i	$0.0697587\pi$
$542$	−7.79615	−	19.5669i	−0.334873	−	0.840468i
$543$	−16.2689	−	3.58106i	−0.698167	−	0.153678i
$544$	−0.369747	−	6.81958i	−0.0158528	−	0.292387i
$545$	−0.884638	−	5.39605i	−0.0378937	−	0.231142i
$546$	0.561517	−	0.828176i	0.0240307	−	0.0354427i
$547$	−6.20346	+	15.5695i	−0.265241	+	0.665704i	−0.999919	−	0.0127113i	$-0.995954\pi$
$547$	−6.20346	+	15.5695i	−0.265241	+	0.665704i	0.734678	+	0.678416i	$0.237333\pi$
$548$	−14.7221	−	11.1914i	−0.628897	−	0.478075i
$549$	1.48249	+	0.891984i	0.0632711	+	0.0380690i
$550$	−8.18208	+	2.75686i	−0.348885	+	0.117553i
$551$	−34.6267	−	32.8001i	−1.47515	−	1.39733i
$552$	−1.45193	+	8.85636i	−0.0617981	+	0.376952i
$553$	−2.52702	−	0.274830i	−0.107460	−	0.0116869i
$554$	7.97110	−	4.79605i	0.338660	−	0.203765i
$555$	4.80456	−	5.65637i	0.203942	−	0.240100i
$556$	10.3528	−	4.78972i	0.439057	−	0.203129i
$557$	0.274564	+	0.127027i	0.0116336	+	0.00538230i	0.425697	−	0.904866i	$-0.360029\pi$
$557$	0.274564	+	0.127027i	0.0116336	+	0.00538230i	−0.414064	+	0.910248i	$0.635891\pi$
$558$	5.92687	+	6.97766i	0.250905	+	0.295388i
$559$	1.84154	+	0.620487i	0.0778888	+	0.0262438i
$560$	1.70931	+	3.22410i	0.0722316	+	0.136243i
$561$	−14.1404	−	26.6716i	−0.597007	−	1.12607i
$562$	2.91035	+	0.980612i	0.122766	+	0.0413646i
$563$	6.95835	+	8.19200i	0.293259	+	0.345252i	0.888985	−	0.457936i	$-0.151411\pi$
$563$	6.95835	+	8.19200i	0.293259	+	0.345252i	−0.595726	+	0.803188i	$0.703135\pi$
$564$	9.30264	+	4.30386i	0.391712	+	0.181225i
$565$	−6.34178	+	2.93402i	−0.266801	+	0.123435i
$566$	4.84652	−	5.70576i	0.203714	−	0.239831i
$567$	−1.79139	+	1.07785i	−0.0752315	+	0.0452653i
$568$	−8.45459	−	0.919492i	−0.354747	−	0.0385810i
$569$	4.81279	−	29.3567i	0.201763	−	1.23070i	−0.670592	−	0.741826i	$-0.733960\pi$
$569$	4.81279	−	29.3567i	0.201763	−	1.23070i	0.872355	−	0.488873i	$-0.162592\pi$
$570$	5.96312	+	5.64857i	0.249768	+	0.236593i
$571$	−8.62962	+	2.90766i	−0.361138	+	0.121682i	−0.494021	−	0.869450i	$-0.664473\pi$
$571$	−8.62962	+	2.90766i	−0.361138	+	0.121682i	0.132882	+	0.991132i	$0.457577\pi$
$572$	1.81268	+	1.09066i	0.0757922	+	0.0456026i
$573$	6.21903	+	4.72759i	0.259804	+	0.197498i
$574$	0.462512	−	1.16082i	0.0193049	−	0.0484516i
$575$	−9.83774	+	14.5096i	−0.410262	+	0.605091i
$576$	−0.161782	−	0.986827i	−0.00674092	−	0.0411178i
$577$	−0.694259	−	12.8049i	−0.0289024	−	0.533073i	−0.976754	−	0.214362i	$-0.931233\pi$
$577$	−0.694259	−	12.8049i	−0.0289024	−	0.533073i	0.947852	−	0.318711i	$-0.103250\pi$
$578$	28.9503	+	6.37245i	1.20417	+	0.265059i
$579$	6.96783	+	17.4879i	0.289573	+	0.726774i
$580$	4.73297	−	17.0466i	0.196526	−	0.707823i
$581$	1.04043	−	19.1896i	0.0431644	−	0.796120i
$582$	−0.492632	+	0.0535770i	−0.0204203	+	0.00222084i
$583$	−50.6577	+	38.5090i	−2.09803	+	1.59488i
$584$	0.373178	+	1.34407i	0.0154422	+	0.0556179i
$585$	0.815853	−	0.179583i	0.0337314	−	0.00742484i
$586$	13.4753	+	19.8745i	0.556658	+	0.821009i
$587$	33.8997	−	32.1115i	1.39919	−	1.32538i	0.515832	−	0.856690i	$-0.327483\pi$
$587$	33.8997	−	32.1115i	1.39919	−	1.32538i	0.883360	−	0.468695i	$-0.155276\pi$
$588$	1.23152	−	2.32289i	0.0507869	−	0.0957943i
$589$	43.0813			1.77513
$590$	9.72830	−	9.22574i	0.400508	−	0.379818i
$591$	−4.61892			−0.189997
$592$	−1.99160	+	3.75655i	−0.0818542	+	0.154393i
$593$	−2.10826	+	1.99705i	−0.0865760	+	0.0820091i	−0.729764	−	0.683699i	$-0.760370\pi$
$593$	−2.10826	+	1.99705i	−0.0865760	+	0.0820091i	0.643188	+	0.765708i	$0.277611\pi$
$594$	−2.48056	−	3.65854i	−0.101778	−	0.150112i
$595$	−24.3398	+	5.35760i	−0.997835	+	0.219640i
$596$	5.00089	+	18.0116i	0.204845	+	0.737783i
$597$	−13.1063	+	9.96312i	−0.536403	+	0.407763i
$598$	4.27006	−	0.464397i	0.174616	−	0.0189906i
$599$	−1.68832	+	31.1392i	−0.0689829	+	1.27231i	0.735166	+	0.677887i	$0.237104\pi$
$599$	−1.68832	+	31.1392i	−0.0689829	+	1.27231i	−0.804149	+	0.594428i	$0.797379\pi$
$600$	0.522568	−	1.88212i	0.0213338	−	0.0768372i
$601$	2.07180	+	5.19982i	0.0845103	+	0.212105i	0.965159	−	0.261666i	$-0.0842718\pi$
$601$	2.07180	+	5.19982i	0.0845103	+	0.212105i	−0.880648	+	0.473771i	$0.842893\pi$
$602$	−8.29025	−	1.82482i	−0.337885	−	0.0743742i
$603$	0.422247	+	7.78788i	0.0171952	+	0.317147i
$604$	2.42010	+	14.7620i	0.0984724	+	0.600655i
$605$	−8.36340	+	12.3351i	−0.340020	+	0.501493i
$606$	−0.112703	+	0.282863i	−0.00457824	+	0.0114905i
$607$	−26.6020	−	20.2223i	−1.07974	−	0.820797i	−0.0951128	−	0.995467i	$-0.530321\pi$
$607$	−26.6020	−	20.2223i	−1.07974	−	0.820797i	−0.984627	+	0.174670i	$0.944114\pi$
$608$	−4.03213	−	2.42605i	−0.163525	−	0.0983895i
$609$	20.0809	−	6.76604i	0.813719	−	0.274174i
$610$	2.19245	+	2.07680i	0.0887699	+	0.0840873i
$611$	0.793645	−	4.84102i	0.0321074	−	0.195847i
$612$	6.78956	+	0.738409i	0.274452	+	0.0298484i
$613$	−7.61265	+	4.58038i	−0.307472	+	0.185000i	−0.660924	−	0.750453i	$-0.729835\pi$
$613$	−7.61265	+	4.58038i	−0.307472	+	0.185000i	0.353452	+	0.935453i	$0.385008\pi$
$614$	−12.1425	+	14.2953i	−0.490033	+	0.576911i
$615$	0.946832	−	0.438051i	0.0381799	−	0.0176639i
$616$	−8.38700	−	3.88024i	−0.337922	−	0.156339i
$617$	−25.1561	−	29.6160i	−1.01274	−	1.19230i	−0.981240	−	0.192792i	$-0.938246\pi$
$617$	−25.1561	−	29.6160i	−1.01274	−	1.19230i	−0.0315049	−	0.999504i	$-0.510030\pi$
$618$	4.10014	+	1.38150i	0.164932	+	0.0555720i
$619$	7.79541	+	14.7037i	0.313324	+	0.590992i	0.989294	−	0.145938i	$-0.0466199\pi$
$619$	7.79541	+	14.7037i	0.313324	+	0.590992i	−0.675970	+	0.736929i	$0.736275\pi$
$620$	7.48515	+	14.1185i	0.300611	+	0.567012i
$621$	−8.50480	−	2.86560i	−0.341286	−	0.114993i
$622$	−2.92299	−	3.44121i	−0.117201	−	0.137980i
$623$	20.7513	+	9.60056i	0.831382	+	0.384638i
$624$	−0.434366	+	0.200959i	−0.0173885	+	0.00804479i
$625$	−7.39182	+	8.70233i	−0.295673	+	0.348093i
$626$	14.9986	−	9.02437i	0.599465	−	0.360686i
$627$	−20.6783	−	2.24890i	−0.825811	−	0.0898123i
$628$	0.666847	−	4.06758i	0.0266101	−	0.162314i
$629$	−21.0817	−	19.9697i	−0.840583	−	0.796242i
$630$	−3.45817	+	1.16519i	−0.137777	+	0.0464223i
$631$	−25.2008	−	15.1628i	−1.00323	−	0.603622i	−0.0836351	−	0.996496i	$-0.526653\pi$
$631$	−25.2008	−	15.1628i	−1.00323	−	0.603622i	−0.919592	+	0.392875i	$0.871481\pi$
$632$	0.967927	+	0.735799i	0.0385021	+	0.0292685i
$633$	4.56220	−	11.4503i	0.181331	−	0.455107i
$634$	2.31151	−	3.40922i	0.0918016	−	0.135397i
$635$	−2.90682	−	17.7308i	−0.115354	−	0.703625i
$636$	−0.779381	−	14.3748i	−0.0309045	−	0.570000i
$637$	−1.22889	−	0.270500i	−0.0486905	−	0.0107176i
$638$	16.5827	+	41.6195i	0.656516	+	1.64773i
$639$	2.27518	−	8.19445i	0.0900047	−	0.324168i
$640$	0.0944981	−	1.74291i	0.00373536	−	0.0688947i
$641$	31.2010	−	3.39331i	1.23236	−	0.134028i	0.531336	−	0.847161i	$-0.321690\pi$
$641$	31.2010	−	3.39331i	1.23236	−	0.134028i	0.701028	+	0.713134i	$0.252725\pi$
$642$	−5.80580	+	4.41346i	−0.229137	+	0.174185i
$643$	−3.15256	−	11.3545i	−0.124325	−	0.447778i	0.875015	−	0.484095i	$-0.160851\pi$
$643$	−3.15256	−	11.3545i	−0.124325	−	0.447778i	−0.999340	+	0.0363172i	$0.988437\pi$
$644$	−18.3241	+	4.03344i	−0.722072	+	0.158940i
$645$	−3.97722	−	5.86596i	−0.156603	−	0.230972i
$646$	23.3322	−	22.1014i	0.917992	−	0.869568i
$647$	−23.2320	+	43.8201i	−0.913343	+	1.72275i	−0.260130	+	0.965574i	$0.583765\pi$
$647$	−23.2320	+	43.8201i	−0.913343	+	1.72275i	−0.653213	+	0.757174i	$0.726579\pi$
$648$	1.00000			0.0392837
$649$	−5.47360	+	33.5080i	−0.214857	+	1.31531i
$650$	−0.934858			−0.0366682
$651$	−8.96540	+	16.9105i	−0.351382	+	0.662776i
$652$	−18.1673	+	17.2090i	−0.711488	+	0.673957i
$653$	18.9681	+	27.9758i	0.742278	+	1.09478i	0.991973	+	0.126454i	$0.0403595\pi$
$653$	18.9681	+	27.9758i	0.742278	+	1.09478i	−0.249694	+	0.968325i	$0.580330\pi$
$654$	−3.05948	+	0.673443i	−0.119635	+	0.0263337i
$655$	−0.659945	−	2.37691i	−0.0257862	−	0.0928734i
$656$	−0.475817	+	0.361707i	−0.0185776	+	0.0141223i
$657$	−1.38673	+	0.150816i	−0.0541017	+	0.00588391i
$658$	−1.16015	+	21.3978i	−0.0452275	+	0.834173i
$659$	6.68760	−	24.0866i	0.260512	−	0.938280i	−0.711371	−	0.702817i	$-0.751925\pi$
$659$	6.68760	−	24.0866i	0.260512	−	0.938280i	0.971883	−	0.235463i	$-0.0756607\pi$
$660$	−2.85574	−	7.16737i	−0.111160	−	0.278989i
$661$	22.8193	+	5.02291i	0.887568	+	0.195369i	0.635278	−	0.772283i	$-0.280885\pi$
$661$	22.8193	+	5.02291i	0.887568	+	0.195369i	0.252290	+	0.967652i	$0.418816\pi$
$662$	0.228156	+	4.20810i	0.00886755	+	0.163552i
$663$	−0.528808	−	3.22558i	−0.0205372	−	0.125271i
$664$	−5.15856	+	7.60831i	−0.200191	+	0.295260i
$665$	−6.35604	+	15.9525i	−0.246477	+	0.618610i
$666$	−3.38486	−	2.57310i	−0.131161	−	0.0997058i
$667$	77.9424	+	46.8964i	3.01794	+	1.81584i
$668$	−9.30757	+	3.13609i	−0.360121	+	0.121339i
$669$	11.0959	+	10.5106i	0.428993	+	0.406364i
$670$	−2.20242	+	13.4342i	−0.0850870	+	0.519008i
$671$	−7.60275	−	0.826849i	−0.293501	−	0.0319202i
$672$	1.79139	−	1.07785i	0.0691045	−	0.0415788i
$673$	−15.2286	+	17.9285i	−0.587021	+	0.691094i	−0.972840	−	0.231480i	$-0.925643\pi$
$673$	−15.2286	+	17.9285i	−0.587021	+	0.691094i	0.385819	+	0.922575i	$0.373919\pi$
$674$	−1.74177	+	0.805830i	−0.0670906	+	0.0310394i
$675$	1.77278	+	0.820177i	0.0682345	+	0.0315686i
$676$	−8.26773	−	9.73353i	−0.317990	−	0.374366i
$677$	23.2592	+	7.83693i	0.893923	+	0.301198i	0.728517	−	0.685028i	$-0.240210\pi$
$677$	23.2592	+	7.83693i	0.893923	+	0.301198i	0.165406	+	0.986226i	$0.447107\pi$
$678$	1.87517	+	3.53694i	0.0720153	+	0.135835i
$679$	−0.485270	−	0.915317i	−0.0186230	−	0.0351266i
$680$	11.2969	+	3.80636i	0.433215	+	0.145967i
$681$	−2.58144	−	3.03911i	−0.0989211	−	0.116459i
$682$	−36.7271	−	16.9917i	−1.40635	−	0.650648i
$683$	16.3678	−	7.57255i	0.626296	−	0.289756i	−0.0809549	−	0.996718i	$-0.525797\pi$
$683$	16.3678	−	7.57255i	0.626296	−	0.289756i	0.707251	+	0.706962i	$0.249935\pi$
$684$	3.04642	−	3.58652i	0.116483	−	0.137134i
$685$	27.6584	−	16.6415i	1.05677	−	0.635840i
$686$	20.0132	+	2.17657i	0.764109	+	0.0831019i
$687$	1.62793	−	9.92992i	0.0621093	−	0.378850i
$688$	2.94776	+	2.79227i	0.112382	+	0.106454i
$689$	−6.52924	+	2.19996i	−0.248744	+	0.0838117i
$690$	−13.4226	−	8.07611i	−0.510989	−	0.307452i
$691$	−19.8055	−	15.0558i	−0.753439	−	0.572749i	0.156409	−	0.987692i	$-0.450008\pi$
$691$	−19.8055	−	15.0558i	−0.753439	−	0.572749i	−0.909847	+	0.414943i	$0.863801\pi$
$692$	−8.71974	+	21.8849i	−0.331475	+	0.831939i
$693$	5.18599	−	7.64876i	0.196999	−	0.290552i
$694$	1.65040	+	10.0670i	0.0626485	+	0.382139i
$695$	1.07795	+	19.8816i	0.0408890	+	0.754153i
$696$	−9.89867	−	2.17886i	−0.375208	−	0.0825895i
$697$	−1.51090	−	3.79207i	−0.0572294	−	0.143635i
$698$	7.32833	−	26.3943i	0.277381	−	0.999038i
$699$	−0.181511	+	3.34778i	−0.00686538	+	0.126624i
$700$	4.05978	−	0.441528i	0.153445	−	0.0166882i
$701$	−2.67158	+	2.03088i	−0.100904	+	0.0767054i	−0.654410	−	0.756140i	$-0.727083\pi$
$701$	−2.67158	+	2.03088i	−0.100904	+	0.0767054i	0.553506	+	0.832845i	$0.313290\pi$
$702$	−0.128039	−	0.461155i	−0.00483252	−	0.0174052i
$703$	−19.5402	+	4.30113i	−0.736973	+	0.162220i
$704$	2.48056	+	3.65854i	0.0934894	+	0.137887i
$705$	−12.9889	+	12.3037i	−0.489189	+	0.463384i
$706$	1.87981	−	3.54570i	0.0707477	−	0.133444i
$707$	−0.636581			−0.0239411
$708$	−5.57951	−	5.27912i	−0.209691	−	0.198401i
$709$	−12.6554			−0.475283			−0.237642	−	0.971353i	$-0.576374\pi$
$709$	−12.6554			−0.475283			−0.237642	+	0.971353i	$0.576374\pi$
$710$	6.95319	−	13.1151i	0.260948	−	0.492201i
$711$	−0.882699	+	0.836137i	−0.0331038	+	0.0313576i
$712$	−6.13743	−	9.05204i	−0.230010	−	0.339239i
$713$	−80.2422	+	17.6626i	−3.00509	+	0.661471i
$714$	3.81986	+	13.7579i	0.142955	+	0.514876i
$715$	−2.93962	+	2.23464i	−0.109936	+	0.0835708i
$716$	−8.29596	+	0.902240i	−0.310035	+	0.0337183i
$717$	0.353531	−	6.52049i	0.0132028	−	0.243512i
$718$	4.74493	−	17.0897i	0.177079	−	0.637782i
$719$	3.24814	+	8.15223i	0.121135	+	0.304027i	0.977023	−	0.213136i	$-0.0683676\pi$
$719$	3.24814	+	8.15223i	0.121135	+	0.304027i	−0.855887	+	0.517162i	$0.826988\pi$
$720$	1.70467	+	0.375225i	0.0635292	+	0.0139838i
$721$	0.489713	+	9.03222i	0.0182379	+	0.336378i
$722$	−0.508614	−	3.10241i	−0.0189287	−	0.115460i
$723$	−3.52257	+	5.19540i	−0.131006	+	0.193219i
$724$	−6.16591	+	15.4753i	−0.229154	+	0.575134i
$725$	−15.7611	−	11.9813i	−0.585354	−	0.444975i
$726$	7.31594	+	4.40185i	0.271520	+	0.163368i
$727$	20.0244	−	6.74699i	0.742663	−	0.250232i	0.0775637	−	0.996987i	$-0.475286\pi$
$727$	20.0244	−	6.74699i	0.742663	−	0.250232i	0.665099	+	0.746755i	$0.268389\pi$
$728$	−0.726423	−	0.688104i	−0.0269230	−	0.0255028i
$729$	−0.161782	+	0.986827i	−0.00599193	+	0.0365491i
$730$	−2.42051	−	0.263246i	−0.0895871	−	0.00974318i
$731$	−23.7609	+	14.2964i	−0.878827	+	0.528773i
$732$	1.12007	−	1.31865i	0.0413991	−	0.0487388i
$733$	−13.8070	+	6.38780i	−0.509973	+	0.235939i	−0.657963	−	0.753050i	$-0.728582\pi$
$733$	−13.8070	+	6.38780i	−0.509973	+	0.235939i	0.147990	+	0.988989i	$0.452720\pi$
$734$	−8.48984	−	3.92782i	−0.313366	−	0.144978i
$735$	2.97093	+	3.49765i	0.109585	+	0.129013i
$736$	8.50480	+	2.86560i	0.313491	+	0.105627i
$737$	−16.1481	−	30.4586i	−0.594825	−	1.12196i
$738$	−0.279963	−	0.528067i	−0.0103056	−	0.0194384i
$739$	−43.0714	−	14.5125i	−1.58441	−	0.533849i	−0.616977	−	0.786981i	$-0.711643\pi$
$739$	−43.0714	−	14.5125i	−1.58441	−	0.533849i	−0.967432	+	0.253132i	$0.918539\pi$
$740$	−4.80456	−	5.65637i	−0.176619	−	0.207932i
$741$	−2.04400	−	0.945657i	−0.0750884	−	0.0347396i
$742$	27.3153	−	12.6374i	1.00278	−	0.463934i
$743$	5.23251	−	6.16018i	0.191962	−	0.225995i	−0.657758	−	0.753229i	$-0.728495\pi$
$743$	5.23251	−	6.16018i	0.191962	−	0.225995i	0.849720	+	0.527234i	$0.176771\pi$
$744$	7.84460	−	4.71994i	0.287597	−	0.173041i
$745$	−32.4368	−	3.52771i	−1.18839	−	0.129245i
$746$	−1.29888	+	7.92281i	−0.0475553	+	0.290075i
$747$	−6.67352	−	6.32149i	−0.244171	−	0.231291i
$748$	−28.6079	+	9.63912i	−1.04601	+	0.352441i
$749$	−13.0644	−	7.86059i	−0.477363	−	0.287220i
$750$	9.66205	+	7.34490i	0.352808	+	0.268198i
$751$	0.608430	−	1.52704i	0.0222019	−	0.0557226i	−0.917458	−	0.397833i	$-0.869762\pi$
$751$	0.608430	−	1.52704i	0.0222019	−	0.0557226i	0.939660	+	0.342110i	$0.111142\pi$
$752$	5.75216	−	8.48381i	0.209760	−	0.309373i
$753$	1.54921	+	9.44974i	0.0564562	+	0.344368i
$754$	0.262623	+	4.84380i	0.00956417	+	0.176401i
$755$	−25.5001	−	5.61300i	−0.928045	−	0.204278i
$756$	0.773832	+	1.94217i	0.0281440	+	0.0706361i
$757$	2.21026	−	7.96064i	0.0803333	−	0.289334i	−0.912461	−	0.409163i	$-0.865821\pi$
$757$	2.21026	−	7.96064i	0.0803333	−	0.289334i	0.992795	+	0.119829i	$0.0382345\pi$
$758$	1.36367	−	25.1513i	0.0495306	−	0.913538i
$759$	39.4369	−	4.28902i	1.43147	−	0.155681i
$760$	6.53888	−	4.97073i	0.237190	−	0.180307i
$761$	13.1301	+	47.2903i	0.475965	+	1.71427i	0.678150	+	0.734923i	$0.262782\pi$
$761$	13.1301	+	47.2903i	0.475965	+	1.71427i	−0.202185	+	0.979347i	$0.564804\pi$
$762$	−10.0531	+	2.21285i	−0.364185	+	0.0801632i
$763$	−3.67547	−	5.42091i	−0.133061	−	0.196250i
$764$	5.67143	−	5.37227i	0.205185	−	0.194362i
$765$	−5.58384	+	10.5322i	−0.201884	+	0.380794i
$766$	29.9310			1.08145
$767$	−1.72010	+	3.24895i	−0.0621090	+	0.117313i
$768$	−1.00000			−0.0360844
$769$	−14.9461	+	28.1913i	−0.538970	+	1.01660i	0.453165	+	0.891427i	$0.350295\pi$
$769$	−14.9461	+	28.1913i	−0.538970	+	1.01660i	−0.992134	+	0.125178i	$0.960050\pi$
$770$	11.7104	−	11.0927i	0.422013	−	0.399752i
$771$	0.710064	+	1.04727i	0.0255723	+	0.0377164i
$772$	18.3848	−	4.04681i	0.661684	−	0.145648i
$773$	11.6541	+	41.9744i	0.419170	+	1.50972i	0.808433	+	0.588588i	$0.200316\pi$
$773$	11.6541	+	41.9744i	0.419170	+	1.50972i	−0.389262	+	0.921127i	$0.627270\pi$
$774$	−3.23238	+	2.45719i	−0.116186	+	0.0883220i
$775$	17.7780	−	1.93347i	0.638603	−	0.0694523i
$776$	−0.0268278	+	0.494810i	−0.000963063	+	0.0177627i
$777$	2.37810	−	8.56513i	0.0853138	−	0.307272i
$778$	6.32914	+	15.8850i	0.226911	+	0.569503i
$779$	−2.74681	−	0.604619i	−0.0984147	−	0.0216627i
$780$	−0.0452268	−	0.834159i	−0.00161938	−	0.0298677i
$781$	6.08159	+	37.0961i	0.217616	+	1.32740i
$782$	−34.3967	+	50.7314i	−1.23002	+	1.81415i
$783$	3.75158	−	9.41577i	0.134071	−	0.336492i
$784$	−2.09305	−	1.59110i	−0.0747518	−	0.0568248i
$785$	6.16478	+	3.70923i	0.220030	+	0.132388i
$786$	−1.33929	+	0.451258i	−0.0477708	+	0.0160959i
$787$	24.5396	+	23.2451i	0.874742	+	0.828600i	0.986266	−	0.165162i	$-0.0528147\pi$
$787$	24.5396	+	23.2451i	0.874742	+	0.828600i	−0.111525	+	0.993762i	$0.535573\pi$
$788$	−0.747258	+	4.55807i	−0.0266199	+	0.162374i
$789$	−15.5055	−	1.68632i	−0.552010	−	0.0600347i
$790$	−1.81845	+	1.09412i	−0.0646975	+	0.0389272i
$791$	−5.41828	+	6.37889i	−0.192652	+	0.226807i
$792$	−4.01166	+	1.85599i	−0.142548	+	0.0659498i
$793$	−0.751516	−	0.347689i	−0.0266871	−	0.0123468i
$794$	13.6068	+	16.0192i	0.482887	+	0.568498i
$795$	23.8124	+	8.02334i	0.844539	+	0.284558i
$796$	7.71151	+	14.5455i	0.273327	+	0.515550i
$797$	7.02189	+	13.2447i	0.248728	+	0.469151i	0.976167	−	0.217022i	$-0.0696342\pi$
$797$	7.02189	+	13.2447i	0.248728	+	0.469151i	−0.727439	+	0.686173i	$0.759289\pi$
$798$	9.32306	+	3.14131i	0.330033	+	0.111201i
$799$	45.3192	+	53.3539i	1.60328	+	1.88752i
$800$	−1.77278	−	0.820177i	−0.0626774	−	0.0289976i
$801$	9.92572	−	4.59213i	0.350708	−	0.162255i
$802$	−10.1949	+	12.0024i	−0.359994	+	0.423818i
$803$	5.28319	−	3.17879i	0.186440	−	0.112177i
$804$	7.75360	+	0.843255i	0.273448	+	0.0297393i
$805$	5.29835	−	32.3185i	0.186742	−	1.13908i
$806$	−3.18104	−	3.01324i	−0.112047	−	0.106137i
$807$	−10.2495	+	3.45345i	−0.360798	+	0.121567i
$808$	0.260903	+	0.156980i	0.00917855	+	0.00552255i
$809$	−39.7704	−	30.2327i	−1.39825	−	1.06292i	−0.988581	−	0.150693i	$-0.951850\pi$
$809$	−39.7704	−	30.2327i	−1.39825	−	1.06292i	−0.409673	−	0.912232i	$-0.634357\pi$
$810$	−0.646067	+	1.62151i	−0.0227005	+	0.0569739i
$811$	18.3754	−	27.1017i	0.645247	−	0.951668i	−0.354614	−	0.935013i	$-0.615388\pi$
$811$	18.3754	−	27.1017i	0.645247	−	0.951668i	0.999861	−	0.0166554i	$-0.00530182\pi$
$812$	−3.42818	−	20.9110i	−0.120306	−	0.733832i
$813$	−1.14032	−	21.0319i	−0.0399927	−	0.737621i
$814$	18.3546	+	4.04015i	0.643327	+	0.141607i
$815$	−16.1672	−	40.5766i	−0.566312	−	1.42134i
$816$	1.82711	−	6.58066i	0.0639617	−	0.230369i
$817$	−1.03441	+	19.0787i	−0.0361896	+	0.667478i
$818$	−13.2130	+	1.43700i	−0.461980	+	0.0502434i
$819$	0.796562	−	0.605530i	0.0278341	−	0.0211589i
$820$	−0.279100	−	1.00523i	−0.00974659	−	0.0351041i
$821$	49.6517	−	10.9292i	1.73286	−	0.381431i	0.767233	−	0.641369i	$-0.221633\pi$
$821$	49.6517	−	10.9292i	1.73286	−	0.381431i	0.965625	+	0.259938i	$0.0837021\pi$
$822$	−10.3780	−	15.3064i	−0.361974	−	0.533872i
$823$	−32.6900	+	30.9656i	−1.13950	+	1.07939i	−0.143537	+	0.989645i	$0.545848\pi$
$823$	−32.6900	+	30.9656i	−1.13950	+	1.07939i	−0.995964	+	0.0897481i	$0.971394\pi$
$824$	2.02663	−	3.82262i	0.0706009	−	0.133167i
$825$	−8.63405			−0.300599
$826$	5.93534	−	14.9215i	0.206517	−	0.519186i
$827$	25.7553			0.895598			0.447799	−	0.894134i	$-0.352208\pi$
$827$	25.7553			0.895598			0.447799	+	0.894134i	$0.352208\pi$
$828$	−4.20377	+	7.92916i	−0.146091	+	0.275557i
$829$	−12.5901	+	11.9259i	−0.437271	+	0.414205i	−0.874409	−	0.485189i	$-0.838751\pi$
$829$	−12.5901	+	11.9259i	−0.437271	+	0.414205i	0.437138	+	0.899394i	$0.355992\pi$
$830$	−9.00414	−	13.2801i	−0.312538	−	0.460959i
$831$	9.08523	−	1.99981i	0.315163	−	0.0693727i
$832$	0.128039	+	0.461155i	0.00443896	+	0.0159877i
$833$	14.2947	−	10.8665i	0.495282	−	0.376503i
$834$	11.3402	−	1.23333i	0.392680	−	0.0427066i
$835$	0.928132	−	17.1184i	0.0321193	−	0.592406i
$836$	−5.56464	+	20.0420i	−0.192457	+	0.693168i
$837$	3.38865	+	8.50486i	0.117129	+	0.293971i
$838$	−23.2256	−	5.11235i	−0.802316	−	0.176603i
$839$	1.06622	+	19.6654i	0.0368102	+	0.678923i	0.957466	+	0.288547i	$0.0931723\pi$
$839$	1.06622	+	19.6654i	0.0368102	+	0.678923i	−0.920655	+	0.390376i	$0.872345\pi$
$840$	0.590373	+	3.60112i	0.0203698	+	0.124250i
$841$	−41.3769	+	61.0264i	−1.42679	+	2.10436i
$842$	−4.66477	+	11.7077i	−0.160759	+	0.403474i
$843$	2.44489	+	1.85856i	0.0842066	+	0.0640122i
$844$	−10.5613	−	6.35454i	−0.363536	−	0.218732i
$845$	21.1245	−	7.11766i	0.726704	−	0.244855i
$846$	7.44145	+	7.04891i	0.255842	+	0.242347i
$847$	−2.88785	+	17.6151i	−0.0992277	+	0.605262i
$848$	−14.3116	−	1.55648i	−0.491461	−	0.0534496i
$849$	6.41467	−	3.85958i	0.220151	−	0.132460i
$850$	8.63638	−	10.1675i	0.296225	−	0.348743i
$851$	34.6317	−	16.0223i	1.18716	−	0.549239i
$852$	−7.71842	−	3.57092i	−0.264429	−	0.122338i
$853$	−24.6167	−	28.9811i	−0.842861	−	0.992293i	−0.999989	−	0.00471473i	$-0.998499\pi$
$853$	−24.6167	−	28.9811i	−0.842861	−	0.992293i	0.157128	−	0.987578i	$-0.449777\pi$
$854$	3.42780	+	1.15496i	0.117297	+	0.0395219i
$855$	3.84738	+	7.25692i	0.131577	+	0.248181i
$856$	3.41604	+	6.44334i	0.116758	+	0.220229i
$857$	−7.22969	−	2.43596i	−0.246961	−	0.0832110i	0.193099	−	0.981179i	$-0.438146\pi$
$857$	−7.22969	−	2.43596i	−0.246961	−	0.0832110i	−0.440060	+	0.897968i	$0.645043\pi$
$858$	1.36955	+	1.61236i	0.0467556	+	0.0550450i
$859$	−21.9089	−	10.1361i	−0.747523	−	0.345841i	0.00886809	−	0.999961i	$-0.497177\pi$
$859$	−21.9089	−	10.1361i	−0.747523	−	0.345841i	−0.756391	+	0.654120i	$0.773039\pi$
$860$	−6.43213	+	2.97582i	−0.219334	+	0.101475i
$861$	0.808952	−	0.952372i	0.0275690	−	0.0324568i
$862$	−8.00585	+	4.81696i	−0.272680	+	0.164066i
$863$	23.7591	+	2.58396i	0.808771	+	0.0879591i	0.503155	−	0.864196i	$-0.332172\pi$
$863$	23.7591	+	2.58396i	0.808771	+	0.0879591i	0.305615	+	0.952155i	$0.401138\pi$
$864$	0.161782	−	0.986827i	0.00550394	−	0.0335725i
$865$	−29.8529	−	28.2782i	−1.01503	−	0.961488i
$866$	−10.7976	+	3.63814i	−0.366918	+	0.123629i
$867$	25.4001	+	15.2828i	0.862634	+	0.519030i
$868$	15.2373	+	11.5831i	0.517189	+	0.393157i
$869$	1.98922	−	4.99258i	0.0674798	−	0.169362i
$870$	9.92823	−	14.6430i	0.336599	−	0.496446i
$871$	−0.603892	−	3.68358i	−0.0204621	−	0.124813i
$872$	0.169602	+	3.12813i	0.00574346	+	0.105932i
$873$	−0.483952	−	0.106526i	−0.0163793	−	0.00360535i
$874$	15.6316	+	39.2325i	0.528748	+	1.32706i
$875$	−6.78826	+	24.4491i	−0.229485	+	0.826530i
$876$	−0.0755190	+	1.39287i	−0.00255155	+	0.0470606i
$877$	−17.3177	+	1.88341i	−0.584777	+	0.0635983i	−0.395725	−	0.918369i	$-0.629507\pi$
$877$	−17.3177	+	1.88341i	−0.584777	+	0.0635983i	−0.189051	+	0.981967i	$0.560541\pi$
$878$	16.6456	−	12.6537i	0.561762	−	0.427040i
$879$	6.42391	+	23.1368i	0.216673	+	0.780386i
$880$	−7.53495	+	1.65857i	−0.254003	+	0.0559103i
$881$	1.18049	+	1.74110i	0.0397719	+	0.0586591i	0.847055	−	0.531505i	$-0.178373\pi$
$881$	1.18049	+	1.74110i	0.0397719	+	0.0586591i	−0.807283	+	0.590164i	$0.799063\pi$
$882$	1.90875	−	1.80807i	0.0642711	−	0.0608808i
$883$	−12.0785	+	22.7825i	−0.406474	+	0.766692i	−0.999252	−	0.0386744i	$-0.987686\pi$
$883$	−12.0785	+	22.7825i	−0.406474	+	0.766692i	0.592778	+	0.805366i	$0.298031\pi$
$884$	−3.26864			−0.109936
$885$	12.1648	−	5.63654i	0.408917	−	0.189470i
$886$	22.9784			0.771973
$887$	−11.0280	+	20.8009i	−0.370282	+	0.698427i	−0.996710	−	0.0810531i	$-0.974172\pi$
$887$	−11.0280	+	20.8009i	−0.370282	+	0.698427i	0.626427	+	0.779480i	$0.284517\pi$
$888$	−3.08682	+	2.92399i	−0.103587	+	0.0981226i
$889$	−12.0772	−	17.8125i	−0.405055	−	0.597411i
$890$	18.6431	−	4.10366i	0.624919	−	0.137555i
$891$	−1.18253	−	4.25908i	−0.0396161	−	0.142684i
$892$	12.1673	−	9.24932i	0.407390	−	0.309690i
$893$	47.9509	−	5.21497i	1.60461	−	0.174512i
$894$	−1.01202	+	18.6655i	−0.0338469	+	0.624269i
$895$	3.89676	−	14.0349i	0.130254	−	0.469134i
$896$	−0.773832	−	1.94217i	−0.0258519	−	0.0648834i
$897$	4.19482	+	0.923349i	0.140061	+	0.0308297i
$898$	−1.19350	−	22.0128i	−0.0398276	−	0.734576i
$899$	−15.0122	−	91.5701i	−0.500684	−	3.05403i
$900$	1.09618	−	1.61674i	0.0365392	−	0.0538914i
$901$	36.3915	−	91.3357i	1.21238	−	3.04283i
$902$	2.10320	+	1.59881i	0.0700291	+	0.0532347i
$903$	−7.27361	−	4.37639i	−0.242051	−	0.145637i
$904$	3.79371	−	1.27825i	0.126177	−	0.0425140i
$905$	−21.1096	−	19.9961i	−0.701708	−	0.664693i
$906$	−2.42010	+	14.7620i	−0.0804024	+	0.490433i
$907$	6.34424	+	0.689977i	0.210657	+	0.0229103i	0.212839	−	0.977087i	$-0.431729\pi$
$907$	6.34424	+	0.689977i	0.210657	+	0.0229103i	−0.00218203	+	0.999998i	$0.500695\pi$
$908$	−3.41671	+	2.05576i	−0.113387	+	0.0682229i
$909$	−0.197122	+	0.232070i	−0.00653812	+	0.00769727i
$910$	1.58508	−	0.733337i	0.0525450	−	0.0243099i
$911$	−6.44884	−	2.98355i	−0.213660	−	0.0988495i	0.310140	−	0.950691i	$-0.399624\pi$
$911$	−6.44884	−	2.98355i	−0.213660	−	0.0988495i	−0.523800	+	0.851841i	$0.675486\pi$
$912$	−3.04642	−	3.58652i	−0.100877	−	0.118762i
$913$	38.5045	+	12.9737i	1.27431	+	0.429366i
$914$	−13.8079	−	26.0445i	−0.456725	−	0.861475i
$915$	1.41456	+	2.66814i	0.0467639	+	0.0882061i
$916$	−9.53574	−	3.21296i	−0.315070	−	0.106159i
$917$	−1.91280	−	2.25193i	−0.0631664	−	0.0743652i
$918$	6.19837	+	2.86767i	0.204577	+	0.0946473i
$919$	28.8079	−	13.3279i	0.950283	−	0.439648i	0.117393	−	0.993086i	$-0.462546\pi$
$919$	28.8079	−	13.3279i	0.950283	−	0.439648i	0.832891	+	0.553438i	$0.186684\pi$
$920$	−10.1413	+	11.9392i	−0.334347	+	0.393624i
$921$	−16.0714	+	9.66985i	−0.529571	+	0.318632i
$922$	−9.36957	−	1.01900i	−0.308571	−	0.0335591i
$923$	−0.658489	+	4.01661i	−0.0216744	+	0.132208i
$924$	−6.70900	−	6.35510i	−0.220710	−	0.209068i
$925$	−7.87045	+	2.65186i	−0.258779	+	0.0871927i
$926$	−4.78024	−	2.87618i	−0.157089	−	0.0945171i
$927$	3.44440	+	2.61836i	0.113129	+	0.0859983i
$928$	−3.75158	+	9.41577i	−0.123152	+	0.309088i
$929$	18.3238	−	27.0256i	0.601184	−	0.886680i	−0.398349	−	0.917234i	$-0.630417\pi$
$929$	18.3238	−	27.0256i	0.601184	−	0.886680i	0.999533	+	0.0305537i	$0.00972705\pi$
$930$	2.58527	+	15.7694i	0.0847743	+	0.517101i
$931$	−0.669810	−	12.3539i	−0.0219521	−	0.404883i
$932$	3.27431	+	0.720730i	0.107254	+	0.0236083i
$933$	−1.67120	−	4.19439i	−0.0547126	−	0.137318i
$934$	2.78776	−	10.0406i	0.0912183	−	0.328539i
$935$	2.85272	−	52.6153i	0.0932939	−	1.72071i
$936$	−0.475794	+	0.0517458i	−0.0155518	+	0.00169136i
$937$	7.47584	−	5.68298i	0.244225	−	0.185655i	−0.475900	−	0.879499i	$-0.657878\pi$
$937$	7.47584	−	5.68298i	0.244225	−	0.185655i	0.720125	+	0.693844i	$0.244084\pi$
$938$	4.36224	+	15.7114i	0.142432	+	0.512994i
$939$	17.0950	−	3.76289i	0.557874	−	0.122797i
$940$	10.0403	+	14.8083i	0.327477	+	0.482992i
$941$	−23.0862	+	21.8684i	−0.752588	+	0.712889i	−0.964408	−	0.264420i	$-0.914820\pi$
$941$	−23.0862	+	21.8684i	−0.752588	+	0.712889i	0.211820	+	0.977309i	$0.432061\pi$
$942$	1.93073	−	3.64173i	0.0629064	−	0.118654i
$943$	5.36403			0.174677
$944$	−6.11224	+	4.65194i	−0.198936	+	0.151408i
$945$	−3.64919			−0.118708
$946$	8.40668	−	15.8567i	0.273325	−	0.515545i
$947$	15.1635	−	14.3636i	0.492747	−	0.466755i	−0.400515	−	0.916290i	$-0.631169\pi$
$947$	15.1635	−	14.3636i	0.492747	−	0.466755i	0.893263	+	0.449535i	$0.148410\pi$
$948$	0.682317	+	1.00634i	0.0221606	+	0.0326845i
$949$	0.651996	−	0.143515i	0.0211647	−	0.00465870i
$950$	−2.45906	−	8.85674i	−0.0797825	−	0.287350i
$951$	3.27907	−	2.49269i	0.106331	−	0.0808309i
$952$	14.1946	−	1.54376i	0.460051	−	0.0500336i
$953$	−1.63223	+	30.1047i	−0.0528731	+	0.975187i	0.844954	+	0.534839i	$0.179628\pi$
$953$	−1.63223	+	30.1047i	−0.0528731	+	0.975187i	−0.897827	+	0.440348i	$0.854855\pi$
$954$	3.85133	−	13.8712i	0.124691	−	0.449097i
$955$	5.04704	+	12.6671i	0.163318	+	0.409898i
$956$	−6.37740	−	1.40377i	−0.206260	−	0.0454012i
$957$	2.42550	+	44.7357i	0.0784053	+	1.44610i
$958$	6.41784	+	39.1471i	0.207351	+	1.26479i
$959$	21.6968	−	32.0004i	0.700627	−	1.03335i
$960$	0.646067	−	1.62151i	0.0208517	−	0.0523339i
$961$	42.0461	+	31.9626i	1.35632	+	1.03105i
$962$	1.74365	+	1.04912i	0.0562174	+	0.0338249i
$963$	−6.91111	+	2.32862i	−0.222707	+	0.0750389i
$964$	4.55707	+	4.31669i	0.146773	+	0.139031i
$965$	−5.31591	+	32.4256i	−0.171125	+	1.04382i
$966$	−18.6528	−	2.02861i	−0.600144	−	0.0652696i
$967$	−9.52792	+	5.73276i	−0.306397	+	0.184353i	−0.660445	−	0.750874i	$-0.729633\pi$
$967$	−9.52792	+	5.73276i	−0.306397	+	0.184353i	0.354048	+	0.935227i	$0.384805\pi$
$968$	5.52745	−	6.50742i	0.177659	−	0.209156i
$969$	29.1678	−	13.4945i	0.937005	−	0.433505i
$970$	−0.785005	−	0.363182i	−0.0252050	−	0.0116611i
$971$	20.4179	+	24.0378i	0.655241	+	0.771410i	0.984981	−	0.172662i	$-0.0552369\pi$
$971$	20.4179	+	24.0378i	0.655241	+	0.771410i	−0.329740	+	0.944072i	$0.606961\pi$
$972$	0.947653	+	0.319302i	0.0303960	+	0.0102416i
$973$	11.1708	+	21.0703i	0.358118	+	0.675483i
$974$	−16.0496	−	30.2728i	−0.514263	−	0.970002i
$975$	−0.885921	−	0.298502i	−0.0283722	−	0.00955971i
$976$	−1.12007	−	1.31865i	−0.0358527	−	0.0422090i
$977$	42.8422	+	19.8209i	1.37064	+	0.634127i	0.960599	−	0.277939i	$-0.0896515\pi$
$977$	42.8422	+	19.8209i	1.37064	+	0.634127i	0.410043	+	0.912066i	$0.365514\pi$
$978$	−22.7112	+	10.5073i	−0.726224	+	0.335987i
$979$	−31.2956	+	36.8441i	−1.00021	+	1.17754i
$980$	3.93222	−	2.36594i	0.125610	−	0.0755771i
$981$	−3.11436	−	0.338707i	−0.0994338	−	0.0108141i
$982$	−4.07989	+	24.8862i	−0.130194	+	0.794151i
$983$	−28.0503	−	26.5707i	−0.894667	−	0.847473i	0.0943104	−	0.995543i	$-0.469935\pi$
$983$	−28.0503	−	26.5707i	−0.894667	−	0.847473i	−0.988977	+	0.148070i	$0.952694\pi$
$984$	−0.566404	+	0.190844i	−0.0180563	+	0.00608387i
$985$	−6.90815	−	4.15650i	−0.220112	−	0.132437i
$986$	−55.1074	−	41.8915i	−1.75498	−	1.33410i
$987$	−7.93177	+	19.9072i	−0.252471	+	0.633655i
$988$	−1.26388	+	1.86409i	−0.0402095	+	0.0593045i
$989$	−5.89527	−	35.9595i	−0.187459	−	1.14345i
$990$	−0.417700	−	7.70402i	−0.0132754	−	0.244850i
$991$	0.248220	+	0.0546374i	0.00788498	+	0.00173561i	0.218911	−	0.975745i	$-0.429750\pi$
$991$	0.248220	+	0.0546374i	0.00788498	+	0.00173561i	−0.211026	+	0.977480i	$0.567681\pi$
$992$	−3.38865	−	8.50486i	−0.107590	−	0.270030i
$993$	−1.12744	+	4.06067i	−0.0357782	+	0.128861i
$994$	0.962583	−	17.7538i	0.0305313	−	0.563116i
$995$	−28.5677	+	3.10692i	−0.905656	+	0.0984961i
$996$	−7.31787	+	5.56290i	−0.231876	+	0.176267i
$997$	9.72828	+	35.0381i	0.308098	+	1.10967i	0.941823	+	0.336109i	$0.109111\pi$
$997$	9.72828	+	35.0381i	0.308098	+	1.10967i	−0.633725	+	0.773558i	$0.718475\pi$
$998$	7.38086	−	1.62465i	0.233637	−	0.0514274i
$999$	−2.38608	−	3.51920i	−0.0754922	−	0.111343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.19.2	✓	84
59.28	even	29	inner	354.2.e.c.205.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.19.2	✓	84	1.1	even	1	trivial
354.2.e.c.205.2	yes	84	59.28	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(1.70467 - 0.375225i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(1.66436 - 1.26521i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +O(q^{10})\)	\(q+(0.468408 - 0.883512i) q^{2} +(0.725995 - 0.687699i) q^{3} +(-0.561187 - 0.827689i) q^{4} +(1.70467 - 0.375225i) q^{5} +(-0.267528 - 0.963550i) q^{6} +(1.66436 - 1.26521i) q^{7} +(-0.994138 + 0.108119i) q^{8} +(0.0541389 - 0.998533i) q^{9} +(0.466964 - 1.68185i) q^{10} +(1.63608 + 4.10626i) q^{11} +(-0.976621 - 0.214970i) q^{12} +(0.0259109 + 0.477898i) q^{13} +(-0.338231 - 2.06312i) q^{14} +(0.979538 - 1.44471i) q^{15} +(-0.370138 + 0.928977i) q^{16} +(-5.43699 - 4.13309i) q^{17} +(-0.856857 - 0.515554i) q^{18} +(-4.45939 + 1.50254i) q^{19} +(-1.26721 - 1.20036i) q^{20} +(0.338231 - 2.06312i) q^{21} +(4.39428 + 0.477907i) q^{22} +(7.68994 - 4.62688i) q^{23} +(-0.647386 + 0.762162i) q^{24} +(-1.77278 + 0.820177i) q^{25} +(0.434366 + 0.200959i) q^{26} +(-0.647386 - 0.762162i) q^{27} +(-1.98122 - 0.667550i) q^{28} +(4.74762 + 8.95495i) q^{29} +(-0.817595 - 1.54215i) q^{30} +(-8.67584 - 2.92323i) q^{31} +(0.647386 + 0.762162i) q^{32} +(4.01166 + 1.85599i) q^{33} +(-6.19837 + 2.86767i) q^{34} +(2.36243 - 2.78127i) q^{35} +(-0.856857 + 0.515554i) q^{36} +(4.22692 + 0.459705i) q^{37} +(-0.761301 + 4.64373i) q^{38} +(0.347461 + 0.329133i) q^{39} +(-1.65410 + 0.557333i) q^{40} +(0.512136 + 0.308142i) q^{41} +(-1.66436 - 1.26521i) q^{42} +(1.50287 - 3.77193i) q^{43} +(2.48056 - 3.65854i) q^{44} +(-0.282386 - 1.72248i) q^{45} +(-0.485874 - 8.96143i) q^{46} +(-10.0104 - 2.20345i) q^{47} +(0.370138 + 0.928977i) q^{48} +(-0.703373 + 2.53332i) q^{49} +(-0.105751 + 1.95045i) q^{50} +(-6.78956 + 0.738409i) q^{51} +(0.381010 - 0.289636i) q^{52} +(3.85133 + 13.8712i) q^{53} +(-0.976621 + 0.214970i) q^{54} +(4.32975 + 6.38590i) q^{55} +(-1.51781 + 1.43774i) q^{56} +(-2.20420 + 4.15756i) q^{57} +10.1356 q^{58} +(6.58392 + 3.95626i) q^{59} -1.74547 q^{60} +(-0.810416 + 1.52861i) q^{61} +(-6.64655 + 6.29594i) q^{62} +(-1.17325 - 1.73041i) q^{63} +(0.976621 - 0.214970i) q^{64} +(0.223489 + 0.804934i) q^{65} +(3.51888 - 2.67499i) q^{66} +(-7.75360 + 0.843255i) q^{67} +(-0.369747 + 6.81958i) q^{68} +(2.40096 - 8.64746i) q^{69} +(-1.35070 - 3.39001i) q^{70} +(8.30561 + 1.82820i) q^{71} +(0.0541389 + 0.998533i) q^{72} +(-0.225672 - 1.37654i) q^{73} +(2.38608 - 3.51920i) q^{74} +(-0.722998 + 1.81459i) q^{75} +(3.74619 + 2.84778i) q^{76} +(7.91831 + 4.76429i) q^{77} +(0.453547 - 0.152818i) q^{78} +(-0.882699 - 0.836137i) q^{79} +(-0.282386 + 1.72248i) q^{80} +(-0.994138 - 0.108119i) q^{81} +(0.512136 - 0.308142i) q^{82} +(5.95093 - 7.00597i) q^{83} +(-1.89743 + 0.877844i) q^{84} +(-10.8191 - 5.00545i) q^{85} +(-2.62859 - 3.09461i) q^{86} +(9.60506 + 3.23632i) q^{87} +(-2.07046 - 3.90529i) q^{88} +(5.12276 + 9.66255i) q^{89} +(-1.65410 - 0.557333i) q^{90} +(0.647767 + 0.762611i) q^{91} +(-8.14512 - 3.76833i) q^{92} +(-8.30893 + 3.84412i) q^{93} +(-6.63570 + 7.81216i) q^{94} +(-7.03798 + 4.23461i) q^{95} +(0.994138 + 0.108119i) q^{96} +(0.0801690 - 0.489009i) q^{97} +(1.90875 + 1.80807i) q^{98} +(4.18881 - 1.41137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more