LMFDB - Embedded newform 462.2.y.c.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	462.37
Dual form			462.2.y.c.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0207786 - 0.197695i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.07849 - 1.63704i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0207786 - 0.197695i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.07849 - 1.63704i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.0993921 + 0.172152i) q^{10} +(-1.70343 + 2.84575i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.44038 + 1.77304i) q^{13} +(2.56464 + 0.650113i) q^{14} +(0.0614277 + 0.189055i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(4.83838 + 2.15419i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-0.813228 - 0.903181i) q^{19} +(-0.160820 - 0.116842i) q^{20} +(2.37343 + 1.16912i) q^{21} +(0.398693 - 3.29257i) q^{22} +(-0.917325 + 1.58885i) q^{23} +(0.104528 - 0.994522i) q^{24} +(4.85209 - 1.03134i) q^{25} +(-2.95056 - 0.627161i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.60734 + 0.449223i) q^{28} +(2.77769 + 8.54885i) q^{29} +(-0.133013 - 0.147725i) q^{30} +(-0.533797 + 5.07874i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.07455 - 3.13773i) q^{33} -5.29627 q^{34} +(-0.280447 + 0.444922i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-11.3311 - 2.40850i) q^{37} +(1.11028 + 0.494327i) q^{38} +(-2.75569 - 1.22691i) q^{39} +(0.194440 + 0.0413295i) q^{40} +(-2.45021 + 7.54097i) q^{41} +(-2.64376 - 0.102689i) q^{42} +10.2293 q^{43} +(0.974986 + 3.17008i) q^{44} +(-0.0993921 - 0.172152i) q^{45} +(0.191773 - 1.82460i) q^{46} +(8.35194 + 9.27577i) q^{47} +(0.309017 + 0.951057i) q^{48} +(1.64021 + 6.80512i) q^{49} +(-4.01312 + 2.91570i) q^{50} +(-5.18053 - 1.10116i) q^{51} +(2.95056 - 0.627161i) q^{52} +(0.712498 - 6.77896i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.597987 + 0.277630i) q^{55} +(2.19920 - 1.47088i) q^{56} +(0.983238 + 0.714365i) q^{57} +(-6.01468 - 6.67998i) q^{58} +(-1.36125 + 1.51183i) q^{59} +(0.181598 + 0.0808528i) q^{60} +(0.937704 + 8.92166i) q^{61} +(-1.57806 - 4.85677i) q^{62} +(-2.56464 - 0.650113i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.299814 - 0.519293i) q^{65} +(0.294584 + 3.30352i) q^{66} +(-7.93430 - 13.7426i) q^{67} +(4.83838 - 2.15419i) q^{68} +(0.566938 - 1.74486i) q^{69} +(0.0752347 - 0.520524i) q^{70} +(-3.72712 + 2.70791i) q^{71} +(0.104528 + 0.994522i) q^{72} +(3.80537 - 4.22629i) q^{73} +(11.3311 - 2.40850i) q^{74} +(-4.53163 + 2.01761i) q^{75} -1.21535 q^{76} +(8.19917 - 3.12627i) q^{77} +3.01648 q^{78} +(7.43835 - 3.31177i) q^{79} +(-0.194440 + 0.0413295i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-0.828811 - 7.88561i) q^{82} +(-11.6002 + 8.42802i) q^{83} +(2.45696 - 0.981502i) q^{84} +(0.325338 - 1.00129i) q^{85} +(-9.34493 + 4.16063i) q^{86} +(-4.49440 - 7.78453i) q^{87} +(-2.18008 - 2.49945i) q^{88} +(3.05212 - 5.28643i) q^{89} +(0.160820 + 0.116842i) q^{90} +(-2.16976 - 7.68024i) q^{91} +(0.566938 + 1.74486i) q^{92} +(-0.533797 - 5.07874i) q^{93} +(-11.4027 - 5.07680i) q^{94} +(-0.161657 + 0.179538i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(2.40493 + 1.74728i) q^{97} +(-4.26630 - 5.54966i) q^{98} +(-0.398693 + 3.29257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.0207786	−	0.197695i	−0.00929247	−	0.0884120i	0.988893	−	0.148631i	$-0.0474867\pi$
$5$	−0.0207786	−	0.197695i	−0.00929247	−	0.0884120i	−0.998185	+	0.0602192i	$0.980820\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−2.07849	−	1.63704i	−0.785594	−	0.618743i
$7$	−2.07849	−	1.63704i	−0.785594	−	0.618743i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	0.0993921	+	0.172152i	0.0314305	+	0.0544393i
$11$	−1.70343	+	2.84575i	−0.513605	+	0.858027i
$11$	−1.70343	+	2.84575i	−0.513605	+	0.858027i
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.44038	+	1.77304i	0.676840	+	0.491753i	0.872308	−	0.488957i	$-0.162623\pi$
$13$	2.44038	+	1.77304i	0.676840	+	0.491753i	−0.195468	+	0.980710i	$0.562623\pi$
$14$	2.56464	+	0.650113i	0.685428	+	0.173750i
$15$	0.0614277	+	0.189055i	0.0158606	+	0.0488138i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	4.83838	+	2.15419i	1.17348	+	0.522467i	0.898496	−	0.438981i	$-0.144661\pi$
$17$	4.83838	+	2.15419i	1.17348	+	0.522467i	0.274984	+	0.961449i	$0.411327\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	−0.813228	−	0.903181i	−0.186567	−	0.207204i	0.642604	−	0.766198i	$-0.277854\pi$
$19$	−0.813228	−	0.903181i	−0.186567	−	0.207204i	−0.829171	+	0.558994i	$0.811187\pi$
$20$	−0.160820	−	0.116842i	−0.0359604	−	0.0261268i
$21$	2.37343	+	1.16912i	0.517924	+	0.255124i
$22$	0.398693	−	3.29257i	0.0850017	−	0.701979i
$23$	−0.917325	+	1.58885i	−0.191275	+	0.331299i	−0.945673	−	0.325119i	$-0.894596\pi$
$23$	−0.917325	+	1.58885i	−0.191275	+	0.331299i	0.754398	+	0.656418i	$0.227929\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	4.85209	−	1.03134i	0.970417	−	0.206269i
$26$	−2.95056	−	0.627161i	−0.578652	−	0.122996i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−2.60734	+	0.449223i	−0.492740	+	0.0848952i
$29$	2.77769	+	8.54885i	0.515804	+	1.58748i	0.781814	+	0.623512i	$0.214295\pi$
$29$	2.77769	+	8.54885i	0.515804	+	1.58748i	−0.266010	+	0.963970i	$0.585705\pi$
$30$	−0.133013	−	0.147725i	−0.0242847	−	0.0269708i
$31$	−0.533797	+	5.07874i	−0.0958728	+	0.912169i	0.835840	+	0.548973i	$0.184981\pi$
$31$	−0.533797	+	5.07874i	−0.0958728	+	0.912169i	−0.931713	+	0.363196i	$0.881686\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.07455	−	3.13773i	0.187054	−	0.546209i
$34$	−5.29627			−0.908303
$35$	−0.280447	+	0.444922i	−0.0474041	+	0.0752055i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−11.3311	−	2.40850i	−1.86282	−	0.395955i	−0.867911	−	0.496720i	$-0.834538\pi$
$37$	−11.3311	−	2.40850i	−1.86282	−	0.395955i	−0.994910	+	0.100765i	$0.967871\pi$
$38$	1.11028	+	0.494327i	0.180111	+	0.0801905i
$39$	−2.75569	−	1.22691i	−0.441263	−	0.196463i
$40$	0.194440	+	0.0413295i	0.0307437	+	0.00653478i
$41$	−2.45021	+	7.54097i	−0.382658	+	1.17770i	0.555506	+	0.831512i	$0.312524\pi$
$41$	−2.45021	+	7.54097i	−0.382658	+	1.17770i	−0.938165	+	0.346189i	$0.887476\pi$
$42$	−2.64376	−	0.102689i	−0.407941	−	0.0158453i
$43$	10.2293			1.55995			0.779977	−	0.625808i	$-0.215231\pi$
$43$	10.2293			1.55995			0.779977	+	0.625808i	$0.215231\pi$
$44$	0.974986	+	3.17008i	0.146985	+	0.477907i
$45$	−0.0993921	−	0.172152i	−0.0148165	−	0.0256629i
$46$	0.191773	−	1.82460i	0.0282754	−	0.269022i
$47$	8.35194	+	9.27577i	1.21826	+	1.35301i	0.916707	+	0.399560i	$0.130837\pi$
$47$	8.35194	+	9.27577i	1.21826	+	1.35301i	0.301549	+	0.953451i	$0.402496\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	1.64021	+	6.80512i	0.234315	+	0.972161i
$50$	−4.01312	+	2.91570i	−0.567540	+	0.412342i
$51$	−5.18053	−	1.10116i	−0.725420	−	0.154193i
$52$	2.95056	−	0.627161i	0.409169	−	0.0869715i
$53$	0.712498	−	6.77896i	0.0978691	−	0.931162i	−0.829876	−	0.557948i	$-0.811589\pi$
$53$	0.712498	−	6.77896i	0.0978691	−	0.931162i	0.927745	−	0.373214i	$-0.121744\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	0.597987	+	0.277630i	0.0806325	+	0.0374356i
$56$	2.19920	−	1.47088i	0.293881	−	0.196555i
$57$	0.983238	+	0.714365i	0.130233	+	0.0946199i
$58$	−6.01468	−	6.67998i	−0.789766	−	0.877124i
$59$	−1.36125	+	1.51183i	−0.177220	+	0.196823i	−0.825210	−	0.564826i	$-0.808943\pi$
$59$	−1.36125	+	1.51183i	−0.177220	+	0.196823i	0.647990	+	0.761649i	$0.275610\pi$
$60$	0.181598	+	0.0808528i	0.0234442	+	0.0104381i
$61$	0.937704	+	8.92166i	0.120061	+	1.14230i	0.874193	+	0.485579i	$0.161391\pi$
$61$	0.937704	+	8.92166i	0.120061	+	1.14230i	−0.754132	+	0.656722i	$0.771942\pi$
$62$	−1.57806	−	4.85677i	−0.200414	−	0.616811i
$63$	−2.56464	−	0.650113i	−0.323114	−	0.0819066i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.299814	−	0.519293i	0.0371873	−	0.0644103i
$66$	0.294584	+	3.30352i	0.0362608	+	0.406635i
$67$	−7.93430	−	13.7426i	−0.969329	−	1.67893i	−0.697506	−	0.716579i	$-0.745707\pi$
$67$	−7.93430	−	13.7426i	−0.969329	−	1.67893i	−0.271823	−	0.962347i	$-0.587626\pi$
$68$	4.83838	−	2.15419i	0.586740	−	0.261234i
$69$	0.566938	−	1.74486i	0.0682513	−	0.210056i
$70$	0.0752347	−	0.520524i	0.00899227	−	0.0622146i
$71$	−3.72712	+	2.70791i	−0.442328	+	0.321370i	−0.786559	−	0.617515i	$-0.788140\pi$
$71$	−3.72712	+	2.70791i	−0.442328	+	0.321370i	0.344231	+	0.938885i	$0.388140\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	3.80537	−	4.22629i	0.445385	−	0.494650i	−0.478089	−	0.878311i	$-0.658670\pi$
$73$	3.80537	−	4.22629i	0.445385	−	0.494650i	0.923474	+	0.383661i	$0.125337\pi$
$74$	11.3311	−	2.40850i	1.31721	−	0.279982i
$75$	−4.53163	+	2.01761i	−0.523267	+	0.232974i
$76$	−1.21535			−0.139410
$77$	8.19917	−	3.12627i	0.934383	−	0.356271i
$78$	3.01648			0.341549
$79$	7.43835	−	3.31177i	0.836880	−	0.372603i	0.0568789	−	0.998381i	$-0.481885\pi$
$79$	7.43835	−	3.31177i	0.836880	−	0.372603i	0.780001	+	0.625778i	$0.215218\pi$
$80$	−0.194440	+	0.0413295i	−0.0217391	+	0.00462078i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	−0.828811	−	7.88561i	−0.0915268	−	0.870820i
$83$	−11.6002	+	8.42802i	−1.27328	+	0.925095i	−0.999328	−	0.0366467i	$-0.988332\pi$
$83$	−11.6002	+	8.42802i	−1.27328	+	0.925095i	−0.273956	+	0.961742i	$0.588332\pi$
$84$	2.45696	−	0.981502i	0.268076	−	0.107091i
$85$	0.325338	−	1.00129i	0.0352878	−	0.108605i
$86$	−9.34493	+	4.16063i	−1.00769	+	0.448652i
$87$	−4.49440	−	7.78453i	−0.481850	−	0.834589i
$88$	−2.18008	−	2.49945i	−0.232397	−	0.266442i
$89$	3.05212	−	5.28643i	0.323524	−	0.560360i	−0.657688	−	0.753290i	$-0.728466\pi$
$89$	3.05212	−	5.28643i	0.323524	−	0.560360i	0.981213	+	0.192930i	$0.0617989\pi$
$90$	0.160820	+	0.116842i	0.0169519	+	0.0123163i
$91$	−2.16976	−	7.68024i	−0.227453	−	0.805108i
$92$	0.566938	+	1.74486i	0.0591074	+	0.181914i
$93$	−0.533797	−	5.07874i	−0.0553522	−	0.526641i
$94$	−11.4027	−	5.07680i	−1.17610	−	0.523632i
$95$	−0.161657	+	0.179538i	−0.0165856	+	0.0184202i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	2.40493	+	1.74728i	0.244184	+	0.177410i	0.703145	−	0.711046i	$-0.251778\pi$
$97$	2.40493	+	1.74728i	0.244184	+	0.177410i	−0.458962	+	0.888456i	$0.651778\pi$
$98$	−4.26630	−	5.54966i	−0.430961	−	0.560600i
$99$	−0.398693	+	3.29257i	−0.0400702	+	0.330916i
$100$	2.48024	−	4.29591i	0.248024	−	0.429591i
$101$	1.00058	−	9.51991i	0.0995617	−	0.947266i	−0.824716	−	0.565546i	$-0.808665\pi$
$101$	1.00058	−	9.51991i	0.0995617	−	0.947266i	0.924278	−	0.381720i	$-0.124668\pi$
$102$	5.18053	−	1.10116i	0.512949	−	0.109031i
$103$	4.39633	+	0.934469i	0.433183	+	0.0920760i	0.419342	−	0.907828i	$-0.362261\pi$
$103$	4.39633	+	0.934469i	0.433183	+	0.0920760i	0.0138412	+	0.999904i	$0.495594\pi$
$104$	−2.44038	+	1.77304i	−0.239299	+	0.173861i
$105$	0.181814	−	0.493508i	0.0177432	−	0.0481614i
$106$	2.10635	+	6.48269i	0.204587	+	0.629654i
$107$	−9.16212	−	10.1756i	−0.885735	−	0.983709i	0.114217	−	0.993456i	$-0.463564\pi$
$107$	−9.16212	−	10.1756i	−0.885735	−	0.983709i	−0.999952	+	0.00974697i	$0.996897\pi$
$108$	−0.104528	+	0.994522i	−0.0100583	+	0.0956979i
$109$	5.32085	+	9.21598i	0.509645	+	0.882731i	0.999938	+	0.0111731i	$0.00355659\pi$
$109$	5.32085	+	9.21598i	0.509645	+	0.882731i	−0.490293	+	0.871558i	$0.663110\pi$
$110$	−0.659210	−	0.0104046i	−0.0628532	−	0.000992044i
$111$	11.5842			1.09953
$112$	−1.41081	+	2.23822i	−0.133309	+	0.211492i
$113$	3.72863	−	11.4755i	0.350760	−	1.07953i	−0.607667	−	0.794192i	$-0.707895\pi$
$113$	3.72863	−	11.4755i	0.350760	−	1.07953i	0.958427	−	0.285337i	$-0.0921054\pi$
$114$	−1.18879	−	0.252685i	−0.111341	−	0.0236662i
$115$	0.333169	+	0.148337i	0.0310682	+	0.0138325i
$116$	8.21167	+	3.65607i	0.762435	+	0.339458i
$117$	2.95056	+	0.627161i	0.272779	+	0.0579810i
$118$	0.628653	−	1.93479i	0.0578722	−	0.178112i
$119$	−6.53002	−	12.3981i	−0.598606	−	1.13653i
$120$	−0.198784			−0.0181464
$121$	−5.19662	−	9.69511i	−0.472420	−	0.881374i
$122$	−4.48540	−	7.76894i	−0.406089	−	0.703367i
$123$	0.828811	−	7.88561i	0.0747313	−	0.711021i
$124$	3.41706	+	3.79503i	0.306861	+	0.340804i
$125$	−0.611849	−	1.88308i	−0.0547255	−	0.168428i
$126$	2.60734	−	0.449223i	0.232280	−	0.0400200i
$127$	−2.08407	+	1.51416i	−0.184931	+	0.134360i	−0.676399	−	0.736535i	$-0.736460\pi$
$127$	−2.08407	+	1.51416i	−0.184931	+	0.134360i	0.491468	+	0.870896i	$0.336460\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	−10.0058	+	2.12679i	−0.880959	+	0.187254i
$130$	−0.0626781	+	0.596343i	−0.00549724	+	0.0523027i
$131$	7.65259	−	13.2547i	0.668610	−	1.15807i	−0.309683	−	0.950840i	$-0.600223\pi$
$131$	7.65259	−	13.2547i	0.668610	−	1.15807i	0.978293	−	0.207227i	$-0.0664437\pi$
$132$	−1.61278	−	2.89809i	−0.140374	−	0.252247i
$133$	0.211740	+	3.20853i	0.0183602	+	0.278215i
$134$	12.8380	+	9.32733i	1.10903	+	0.805758i
$135$	0.133013	+	0.147725i	0.0114479	+	0.0127142i
$136$	−3.54390	+	3.93590i	−0.303887	+	0.337500i
$137$	0.0982329	+	0.0437361i	0.00839260	+	0.00373663i	0.410929	−	0.911668i	$-0.365205\pi$
$137$	0.0982329	+	0.0437361i	0.00839260	+	0.00373663i	−0.402536	+	0.915404i	$0.631871\pi$
$138$	0.191773	+	1.82460i	0.0163248	+	0.155320i
$139$	5.76941	+	17.7564i	0.489355	+	1.50608i	0.825573	+	0.564296i	$0.190852\pi$
$139$	5.76941	+	17.7564i	0.489355	+	1.50608i	−0.336218	+	0.941784i	$0.609148\pi$
$140$	0.142986	+	0.506123i	0.0120845	+	0.0427752i
$141$	−10.0980	−	7.33661i	−0.850403	−	0.617854i
$142$	2.30349	−	3.98976i	0.193305	−	0.334813i
$143$	−9.20266	+	3.92446i	−0.769565	+	0.328180i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.63235	−	0.726769i	0.135559	−	0.0603549i
$146$	−1.75739	+	5.40869i	−0.145443	+	0.447627i
$147$	−3.01923	−	6.31540i	−0.249022	−	0.520885i
$148$	−9.37185	+	6.80905i	−0.770361	+	0.559700i
$149$	2.10494	+	20.0271i	0.172443	+	1.64069i	0.648459	+	0.761250i	$0.275414\pi$
$149$	2.10494	+	20.0271i	0.172443	+	1.64069i	−0.476016	+	0.879437i	$0.657919\pi$
$150$	3.31921	−	3.68636i	0.271013	−	0.300990i
$151$	1.81706	−	0.386228i	0.147870	−	0.0314308i	−0.133382	−	0.991065i	$-0.542584\pi$
$151$	1.81706	−	0.386228i	0.147870	−	0.0314308i	0.281252	+	0.959634i	$0.409250\pi$
$152$	1.11028	−	0.494327i	0.0900554	−	0.0400952i
$153$	5.29627			0.428178
$154$	−6.21875	+	6.19089i	−0.501121	+	0.498876i
$155$	1.01513			0.0815375
$156$	−2.75569	+	1.22691i	−0.220632	+	0.0982315i
$157$	11.0346	−	2.34547i	0.880656	−	0.187189i	0.254674	−	0.967027i	$-0.418032\pi$
$157$	11.0346	−	2.34547i	0.880656	−	0.187189i	0.625982	+	0.779838i	$0.284698\pi$
$158$	−5.44826	+	6.05090i	−0.433440	+	0.481384i
$159$	0.712498	+	6.77896i	0.0565047	+	0.537607i
$160$	0.160820	−	0.116842i	0.0127139	−	0.00923720i
$161$	4.50766	−	1.80071i	0.355253	−	0.141916i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	−3.80116	+	1.69239i	−0.297730	+	0.132558i	−0.550165	−	0.835056i	$-0.685435\pi$
$163$	−3.80116	+	1.69239i	−0.297730	+	0.132558i	0.252435	+	0.967614i	$0.418769\pi$
$164$	3.96452	+	6.86675i	0.309577	+	0.536203i
$165$	−0.642642	−	0.147235i	−0.0500296	−	0.0114622i
$166$	7.16930	−	12.4176i	0.556446	−	0.963792i
$167$	−0.0624349	−	0.0453616i	−0.00483136	−	0.00351019i	0.585367	−	0.810768i	$-0.300950\pi$
$167$	−0.0624349	−	0.0453616i	−0.00483136	−	0.00351019i	−0.590198	+	0.807258i	$0.700950\pi$
$168$	−1.84533	+	1.89598i	−0.142370	+	0.146278i
$169$	−1.20544	−	3.70995i	−0.0927259	−	0.285381i
$170$	0.110049	+	1.04705i	0.00844038	+	0.0803049i
$171$	−1.11028	−	0.494327i	−0.0849050	−	0.0378021i
$172$	6.84474	−	7.60185i	0.521906	−	0.579636i
$173$	2.55232	+	2.83464i	0.194049	+	0.215514i	0.832316	−	0.554302i	$-0.187015\pi$
$173$	2.55232	+	2.83464i	0.194049	+	0.215514i	−0.638266	+	0.769816i	$0.720348\pi$
$174$	7.27209	+	5.28348i	0.551296	+	0.400540i
$175$	−11.7733	−	5.79942i	−0.889981	−	0.438395i
$176$	3.00822	+	1.39664i	0.226753	+	0.105276i
$177$	1.01718	−	1.76181i	0.0764560	−	0.132426i
$178$	−0.638067	+	6.07080i	−0.0478252	+	0.455026i
$179$	−3.64272	+	0.774283i	−0.272269	+	0.0578726i	−0.342023	−	0.939692i	$-0.611112\pi$
$179$	−3.64272	+	0.774283i	−0.272269	+	0.0578726i	0.0697535	+	0.997564i	$0.477779\pi$
$180$	−0.194440	−	0.0413295i	−0.0144927	−	0.00308052i
$181$	−11.4390	+	8.31089i	−0.850251	+	0.617743i	−0.925215	−	0.379443i	$-0.876116\pi$
$181$	−11.4390	+	8.31089i	−0.850251	+	0.617743i	0.0749645	+	0.997186i	$0.476116\pi$
$182$	5.10601	+	6.13372i	0.378483	+	0.454662i
$183$	−2.77213	−	8.53174i	−0.204922	−	0.630684i
$184$	−1.22762	−	1.36341i	−0.0905013	−	0.100512i
$185$	−0.240704	+	2.29015i	−0.0176969	+	0.168375i
$186$	2.55336	+	4.42254i	0.187221	+	0.324277i
$187$	−14.3722	+	10.0993i	−1.05100	+	0.738536i
$188$	12.4818			0.910328
$189$	2.64376	+	0.102689i	0.192305	+	0.00746953i
$190$	0.0746561	−	0.229768i	0.00541612	−	0.0166691i
$191$	−18.8290	−	4.00222i	−1.36242	−	0.289591i	−0.532005	−	0.846741i	$-0.678561\pi$
$191$	−18.8290	−	4.00222i	−1.36242	−	0.289591i	−0.830411	+	0.557151i	$0.811895\pi$
$192$	0.913545	+	0.406737i	0.0659295	+	0.0293537i
$193$	−5.85469	−	2.60668i	−0.421430	−	0.187633i	0.185054	−	0.982728i	$-0.440754\pi$
$193$	−5.85469	−	2.60668i	−0.421430	−	0.187633i	−0.606484	+	0.795096i	$0.707421\pi$
$194$	−2.90770	−	0.618050i	−0.208760	−	0.0443734i
$195$	−0.185295	+	0.570280i	−0.0132693	+	0.0408386i
$196$	6.15471	+	3.33461i	0.439622	+	0.238186i
$197$	−6.03278			−0.429818			−0.214909	−	0.976634i	$-0.568945\pi$
$197$	−6.03278			−0.429818			−0.214909	+	0.976634i	$0.568945\pi$
$198$	−0.974986	−	3.17008i	−0.0692892	−	0.225288i
$199$	5.88026	+	10.1849i	0.416841	+	0.721989i	0.995620	−	0.0934952i	$-0.0298040\pi$
$199$	5.88026	+	10.1849i	0.416841	+	0.721989i	−0.578779	+	0.815484i	$0.696471\pi$
$200$	−0.518512	+	4.93331i	−0.0366643	+	0.348838i
$201$	10.6182	+	11.7927i	0.748947	+	0.831790i
$202$	2.95802	+	9.10384i	0.208125	+	0.640544i
$203$	8.22141	−	22.3159i	0.577030	−	1.56627i
$204$	−4.28477	+	3.11307i	−0.299994	+	0.217958i
$205$	1.54173	+	0.327704i	0.107679	+	0.0228878i
$206$	−4.39633	+	0.934469i	−0.306307	+	0.0651076i
$207$	−0.191773	+	1.82460i	−0.0133292	+	0.126818i
$208$	1.50824	−	2.61234i	0.104577	−	0.181134i
$209$	3.95551	−	0.775735i	0.273608	−	0.0536587i
$210$	0.0346325	+	0.524792i	0.00238987	+	0.0362141i
$211$	3.66754	+	2.66462i	0.252484	+	0.183440i	0.706827	−	0.707387i	$-0.250126\pi$
$211$	3.66754	+	2.66462i	0.252484	+	0.183440i	−0.454343	+	0.890827i	$0.650126\pi$
$212$	−4.56100	−	5.06550i	−0.313251	−	0.347900i
$213$	3.08267	−	3.42365i	0.211221	−	0.234585i
$214$	12.5088	+	5.56927i	0.855083	+	0.380707i
$215$	−0.212551	−	2.02228i	−0.0144958	−	0.137919i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	9.42358	−	9.68224i	0.639715	−	0.657273i
$218$	−8.60932	−	6.25503i	−0.583096	−	0.423644i
$219$	−2.84352	+	4.92512i	−0.192147	+	0.332809i
$220$	0.606451	−	0.258620i	0.0408869	−	0.0174361i
$221$	7.98804	+	13.8357i	0.537334	+	0.930689i
$222$	−10.5827	+	4.71174i	−0.710266	+	0.316231i
$223$	1.13650	−	3.49777i	0.0761054	−	0.234228i	−0.905766	−	0.423779i	$-0.860703\pi$
$223$	1.13650	−	3.49777i	0.0761054	−	0.234228i	0.981871	+	0.189551i	$0.0607032\pi$
$224$	0.378474	−	2.61854i	0.0252879	−	0.174959i
$225$	4.01312	−	2.91570i	0.267541	−	0.194380i
$226$	1.26125	+	12.0000i	0.0838972	+	0.798228i
$227$	−5.35423	+	5.94648i	−0.355373	+	0.394682i	−0.894151	−	0.447766i	$-0.852220\pi$
$227$	−5.35423	+	5.94648i	−0.355373	+	0.394682i	0.538778	+	0.842448i	$0.318886\pi$
$228$	1.18879	−	0.252685i	0.0787296	−	0.0167345i
$229$	−15.2411	+	6.78580i	−1.00716	+	0.448418i	−0.842941	−	0.538005i	$-0.819178\pi$
$229$	−15.2411	+	6.78580i	−1.00716	+	0.448418i	−0.164222	+	0.986423i	$0.552511\pi$
$230$	−0.364699			−0.0240476
$231$	−7.37001	+	4.76266i	−0.484911	+	0.313360i
$232$	−8.98880			−0.590143
$233$	−6.98064	+	3.10798i	−0.457317	+	0.203611i	−0.622448	−	0.782661i	$-0.713862\pi$
$233$	−6.98064	+	3.10798i	−0.457317	+	0.203611i	0.165131	+	0.986272i	$0.447195\pi$
$234$	−2.95056	+	0.627161i	−0.192884	+	0.0409988i
$235$	1.66023	−	1.84388i	0.108302	−	0.120281i
$236$	0.212649	+	2.02322i	0.0138423	+	0.131700i
$237$	−6.58725	+	4.78592i	−0.427888	+	0.310879i
$238$	11.0082	+	8.67020i	0.713557	+	0.562006i
$239$	−1.36952	+	4.21495i	−0.0885869	+	0.272643i	−0.985529	−	0.169505i	$-0.945783\pi$
$239$	−1.36952	+	4.21495i	−0.0885869	+	0.272643i	0.896942	+	0.442147i	$0.145783\pi$
$240$	0.181598	−	0.0808528i	0.0117221	−	0.00521903i
$241$	3.70370	+	6.41499i	0.238576	+	0.413226i	0.960306	−	0.278949i	$-0.0899860\pi$
$241$	3.70370	+	6.41499i	0.238576	+	0.413226i	−0.721730	+	0.692175i	$0.756653\pi$
$242$	8.69070	+	6.74327i	0.558660	+	0.433474i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	7.25753	+	5.27290i	0.464616	+	0.337563i
$245$	1.31126	−	0.465662i	0.0837733	−	0.0297501i
$246$	2.45021	+	7.54097i	0.156220	+	0.480795i
$247$	−0.383209	−	3.64599i	−0.0243830	−	0.231989i
$248$	−4.66522	−	2.07709i	−0.296242	−	0.131895i
$249$	9.59440	−	10.6557i	0.608020	−	0.675275i
$250$	1.32487	+	1.47142i	0.0837921	+	0.0930606i
$251$	−13.5473	−	9.84267i	−0.855096	−	0.621264i	0.0714503	−	0.997444i	$-0.477237\pi$
$251$	−13.5473	−	9.84267i	−0.855096	−	0.621264i	−0.926546	+	0.376180i	$0.877237\pi$
$252$	−2.19920	+	1.47088i	−0.138537	+	0.0926570i
$253$	−2.95888	−	5.31699i	−0.186023	−	0.334276i
$254$	1.28802	−	2.23092i	0.0808178	−	0.139981i
$255$	−0.110049	+	1.04705i	−0.00689154	+	0.0655686i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	3.98346	+	0.846711i	0.248481	+	0.0528164i	0.330468	−	0.943817i	$-0.392793\pi$
$257$	3.98346	+	0.846711i	0.248481	+	0.0528164i	−0.0819870	+	0.996633i	$0.526127\pi$
$258$	8.27568	−	6.01263i	0.515221	−	0.374330i
$259$	19.6087	+	23.5555i	1.21843	+	1.46367i
$260$	−0.185295	−	0.570280i	−0.0114915	−	0.0353672i
$261$	6.01468	+	6.67998i	0.372299	+	0.413480i
$262$	−1.59983	+	15.2213i	−0.0988377	+	0.940377i
$263$	3.91003	+	6.77237i	0.241103	+	0.417602i	0.961029	−	0.276449i	$-0.0891576\pi$
$263$	3.91003	+	6.77237i	0.241103	+	0.417602i	−0.719926	+	0.694051i	$0.755824\pi$
$264$	2.65211	+	1.99157i	0.163226	+	0.122572i
$265$	−1.35497			−0.0832353
$266$	−1.49846	−	2.84502i	−0.0918766	−	0.174439i
$267$	−1.88632	+	5.80548i	−0.115441	+	0.355290i
$268$	−15.5218	−	3.29927i	−0.948146	−	0.201535i
$269$	−6.55597	−	2.91891i	−0.399725	−	0.177969i	0.197021	−	0.980399i	$-0.436873\pi$
$269$	−6.55597	−	2.91891i	−0.399725	−	0.177969i	−0.596746	+	0.802430i	$0.703540\pi$
$270$	−0.181598	−	0.0808528i	−0.0110517	−	0.00492054i
$271$	23.3986	+	4.97352i	1.42136	+	0.302120i	0.853538	−	0.521031i	$-0.174452\pi$
$271$	23.3986	+	4.97352i	1.42136	+	0.302120i	0.567824	+	0.823150i	$0.307786\pi$
$272$	1.63664	−	5.03705i	0.0992357	−	0.305416i
$273$	3.71916	+	7.06129i	0.225094	+	0.427368i
$274$	−0.107529			−0.00649608
$275$	−5.33027	+	15.5647i	−0.321427	+	0.938585i
$276$	−0.917325	−	1.58885i	−0.0552165	−	0.0956377i
$277$	−0.677223	+	6.44335i	−0.0406904	+	0.387143i	0.955157	+	0.296101i	$0.0956865\pi$
$277$	−0.677223	+	6.44335i	−0.0406904	+	0.387143i	−0.995847	+	0.0910423i	$0.970980\pi$
$278$	−12.4928	−	13.8747i	−0.749269	−	0.832147i
$279$	1.57806	+	4.85677i	0.0944761	+	0.290767i
$280$	−0.336483	−	0.404209i	−0.0201087	−	0.0241561i
$281$	10.8720	−	7.89900i	0.648572	−	0.471215i	−0.214213	−	0.976787i	$-0.568719\pi$
$281$	10.8720	−	7.89900i	0.648572	−	0.471215i	0.862784	+	0.505572i	$0.168719\pi$
$282$	12.2090	+	2.59511i	0.727037	+	0.154536i
$283$	−10.5106	+	2.23410i	−0.624790	+	0.132803i	−0.509418	−	0.860519i	$-0.670139\pi$
$283$	−10.5106	+	2.23410i	−0.624790	+	0.132803i	−0.115372	+	0.993322i	$0.536806\pi$
$284$	−0.481561	+	4.58174i	−0.0285754	+	0.271876i
$285$	0.120796	−	0.209225i	0.00715534	−	0.0123934i
$286$	6.81083	−	7.32823i	0.402733	−	0.433328i
$287$	17.4376	−	11.6627i	1.02931	−	0.688428i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	7.39422	+	8.21211i	0.434954	+	0.483065i
$290$	−1.19562	+	1.32787i	−0.0702094	+	0.0779754i
$291$	−2.71566	−	1.20909i	−0.159195	−	0.0708780i
$292$	−0.594457	−	5.65588i	−0.0347880	−	0.330985i
$293$	−5.84780	−	17.9977i	−0.341632	−	1.05144i	−0.963362	−	0.268204i	$-0.913570\pi$
$293$	−5.84780	−	17.9977i	−0.341632	−	1.05144i	0.621730	−	0.783231i	$-0.286430\pi$
$294$	5.32691	+	4.54137i	0.310672	+	0.264858i
$295$	0.327166	+	0.237700i	0.0190483	+	0.0138394i
$296$	5.79212	−	10.0322i	0.336660	−	0.583113i
$297$	−0.294584	−	3.30352i	−0.0170935	−	0.191689i
$298$	−10.0687	−	17.4395i	−0.583266	−	1.01025i
$299$	−5.05572	+	2.25095i	−0.292380	+	0.130176i
$300$	−1.53287	+	4.71770i	−0.0885005	+	0.272377i
$301$	−21.2615	−	16.7458i	−1.22549	−	0.965210i
$302$	−1.50287	+	1.09190i	−0.0864806	+	0.0628318i
$303$	1.00058	+	9.51991i	0.0574820	+	0.546904i
$304$	−0.813228	+	0.903181i	−0.0466418	+	0.0518010i
$305$	1.74428	−	0.370759i	0.0998774	−	0.0212296i
$306$	−4.83838	+	2.15419i	−0.276592	+	0.123147i
$307$	29.8221			1.70204			0.851020	−	0.525134i	$-0.175985\pi$
$307$	29.8221			1.70204			0.851020	+	0.525134i	$0.175985\pi$
$308$	3.16305	−	8.18506i	0.180231	−	0.466387i
$309$	−4.49455			−0.255686
$310$	−0.927371	+	0.412892i	−0.0526711	+	0.0234507i
$311$	−14.6680	+	3.11778i	−0.831747	+	0.176793i	−0.604058	−	0.796941i	$-0.706450\pi$
$311$	−14.6680	+	3.11778i	−0.831747	+	0.176793i	−0.227689	+	0.973734i	$0.573117\pi$
$312$	2.01842	−	2.24168i	0.114270	−	0.126910i
$313$	0.728586	+	6.93203i	0.0411821	+	0.391822i	0.995626	+	0.0934305i	$0.0297833\pi$
$313$	0.728586	+	6.93203i	0.0411821	+	0.391822i	−0.954444	+	0.298391i	$0.903550\pi$
$314$	−9.12660	+	6.63087i	−0.515044	+	0.374201i
$315$	−0.0752347	+	0.520524i	−0.00423900	+	0.0293282i
$316$	2.51611	−	7.74378i	0.141542	−	0.435622i
$317$	10.0736	−	4.48504i	0.565788	−	0.251905i	−0.103850	−	0.994593i	$-0.533116\pi$
$317$	10.0736	−	4.48504i	0.565788	−	0.251905i	0.669638	+	0.742688i	$0.266449\pi$
$318$	−3.40815	−	5.90309i	−0.191120	−	0.331029i
$319$	−29.0595	−	6.65779i	−1.62702	−	0.372765i
$320$	−0.0993921	+	0.172152i	−0.00555619	+	0.00962360i
$321$	11.0775	+	8.04829i	0.618287	+	0.449212i
$322$	−3.38554	+	3.47846i	−0.188669	+	0.193847i
$323$	−1.98909	−	6.12178i	−0.110676	−	0.340625i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	13.6695	+	6.08607i	0.758250	+	0.337595i
$326$	2.78418	−	3.09214i	0.154201	−	0.171258i
$327$	−7.12069	−	7.90832i	−0.393775	−	0.437331i
$328$	−6.41473	−	4.66057i	−0.354194	−	0.257337i
$329$	−2.17459	−	32.9520i	−0.119889	−	1.81670i
$330$	0.646968	−	0.126880i	0.0356144	−	0.00698453i
$331$	1.80744	−	3.13058i	0.0993459	−	0.172072i	−0.812068	−	0.583563i	$-0.801658\pi$
$331$	1.80744	−	3.13058i	0.0993459	−	0.172072i	0.911414	+	0.411490i	$0.134992\pi$
$332$	−1.49879	+	14.2601i	−0.0822569	+	0.782622i
$333$	−11.3311	+	2.40850i	−0.620940	+	0.131985i
$334$	0.0754873	+	0.0160453i	0.00413048	+	0.000877961i
$335$	−2.55198	+	1.85412i	−0.139430	+	0.101302i
$336$	0.914629	−	2.48263i	0.0498971	−	0.135439i
$337$	4.70391	+	14.4772i	0.256239	+	0.788621i	0.993583	+	0.113104i	$0.0360794\pi$
$337$	4.70391	+	14.4772i	0.256239	+	0.788621i	−0.737345	+	0.675517i	$0.763921\pi$
$338$	2.61019	+	2.89891i	0.141976	+	0.157680i
$339$	−1.26125	+	12.0000i	−0.0685018	+	0.651751i
$340$	−0.526407	−	0.911764i	−0.0285484	−	0.0494474i
$341$	−13.5435	−	10.1704i	−0.733424	−	0.550756i
$342$	1.21535			0.0657186
$343$	7.73111	−	16.8294i	0.417441	−	0.908704i
$344$	−3.16103	+	9.72864i	−0.170431	+	0.524533i
$345$	−0.356730	−	0.0758252i	−0.0192057	−	0.00408229i
$346$	−3.48461	−	1.55145i	−0.187334	−	0.0834064i
$347$	2.26637	+	1.00905i	0.121665	+	0.0541687i	0.466666	−	0.884433i	$-0.345455\pi$
$347$	2.26637	+	1.00905i	0.121665	+	0.0541687i	−0.345001	+	0.938602i	$0.612122\pi$
$348$	−8.79237	−	1.86888i	−0.471320	−	0.100182i
$349$	−4.67412	+	14.3855i	−0.250200	+	0.770036i	0.744538	+	0.667581i	$0.232670\pi$
$349$	−4.67412	+	14.3855i	−0.250200	+	0.770036i	−0.994738	+	0.102456i	$0.967330\pi$
$350$	13.1143	+	0.509387i	0.700990	+	0.0272279i
$351$	−3.01648			−0.161008
$352$	−3.31621	−	0.0523414i	−0.176755	−	0.00278981i
$353$	4.53782	+	7.85974i	0.241524	+	0.418332i	0.961149	−	0.276032i	$-0.0890194\pi$
$353$	4.53782	+	7.85974i	0.241524	+	0.418332i	−0.719625	+	0.694363i	$0.755686\pi$
$354$	−0.212649	+	2.02322i	−0.0113022	+	0.107533i
$355$	0.612786	+	0.680568i	0.0325233	+	0.0361208i
$356$	−1.88632	−	5.80548i	−0.0999745	−	0.307690i
$357$	8.96503	+	10.7695i	0.474480	+	0.569981i
$358$	3.01286	−	2.18897i	0.159234	−	0.115691i
$359$	−11.7010	−	2.48711i	−0.617553	−	0.131265i	−0.111496	−	0.993765i	$-0.535564\pi$
$359$	−11.7010	−	2.48711i	−0.617553	−	0.131265i	−0.506057	+	0.862500i	$0.668897\pi$
$360$	0.194440	−	0.0413295i	0.0102479	−	0.00217826i
$361$	1.83164	−	17.4269i	0.0964023	−	0.917207i
$362$	7.06966	−	12.2450i	0.371573	−	0.643584i
$363$	7.09879	+	8.40281i	0.372590	+	0.441033i
$364$	−7.15938	−	3.52663i	−0.375254	−	0.184846i
$365$	−0.914588	−	0.664487i	−0.0478717	−	0.0347808i
$366$	6.00264	+	6.66660i	0.313763	+	0.348469i
$367$	9.26633	−	10.2913i	0.483699	−	0.537202i	−0.451056	−	0.892496i	$-0.648953\pi$
$367$	9.26633	−	10.2913i	0.483699	−	0.537202i	0.934755	+	0.355294i	$0.115619\pi$
$368$	1.67604	+	0.746219i	0.0873694	+	0.0388994i
$369$	0.828811	+	7.88561i	0.0431462	+	0.410508i
$370$	−0.711593	−	2.19006i	−0.0369940	−	0.113856i
$371$	−12.5783	+	12.9236i	−0.653035	+	0.670959i
$372$	−4.13142	−	3.00165i	−0.214204	−	0.155628i
$373$	11.4181	−	19.7767i	0.591204	−	1.02400i	−0.402866	−	0.915259i	$-0.631986\pi$
$373$	11.4181	−	19.7767i	0.591204	−	1.02400i	0.994071	−	0.108737i	$-0.0346807\pi$
$374$	9.02185	−	15.0719i	0.466509	−	0.779348i
$375$	0.989993	+	1.71472i	0.0511230	+	0.0885477i
$376$	−11.4027	+	5.07680i	−0.588048	+	0.261816i
$377$	−8.37884	+	25.7874i	−0.431532	+	1.32812i
$378$	−2.45696	+	0.981502i	−0.126372	+	0.0504830i
$379$	−10.5515	+	7.66615i	−0.541996	+	0.393783i	−0.824826	−	0.565387i	$-0.808727\pi$
$379$	−10.5515	+	7.66615i	−0.541996	+	0.393783i	0.282829	+	0.959170i	$0.408727\pi$
$380$	0.0252533	+	0.240269i	0.00129547	+	0.0123255i
$381$	1.72371	−	1.91438i	0.0883084	−	0.0980765i
$382$	18.8290	−	4.00222i	0.963374	−	0.204771i
$383$	12.6789	−	5.64500i	0.647860	−	0.288446i	−0.0563782	−	0.998409i	$-0.517955\pi$
$383$	12.6789	−	5.64500i	0.647860	−	0.288446i	0.704238	+	0.709963i	$0.251289\pi$
$384$	−1.00000			−0.0510310
$385$	−0.788415	−	1.55598i	−0.0401814	−	0.0793000i
$386$	6.40876			0.326197
$387$	9.34493	−	4.16063i	0.475030	−	0.211497i
$388$	2.90770	−	0.618050i	0.147616	−	0.0313767i
$389$	−9.71598	+	10.7907i	−0.492620	+	0.547110i	−0.937274	−	0.348592i	$-0.886660\pi$
$389$	−9.71598	+	10.7907i	−0.492620	+	0.547110i	0.444655	+	0.895702i	$0.353326\pi$
$390$	−0.0626781	−	0.596343i	−0.00317383	−	0.0301970i
$391$	−7.86106	+	5.71139i	−0.397551	+	0.288837i
$392$	−6.97891	−	0.542970i	−0.352488	−	0.0274241i
$393$	−4.72956	+	14.5561i	−0.238575	+	0.734258i
$394$	5.51122	−	2.45375i	0.277651	−	0.123618i
$395$	−0.809279	−	1.40171i	−0.0407193	−	0.0705278i
$396$	2.18008	+	2.49945i	0.109553	+	0.125602i
$397$	−16.7364	+	28.9882i	−0.839974	+	1.45488i	0.0499407	+	0.998752i	$0.484097\pi$
$397$	−16.7364	+	28.9882i	−0.839974	+	1.45488i	−0.889915	+	0.456126i	$0.849237\pi$
$398$	−9.51446	−	6.91266i	−0.476917	−	0.346500i
$399$	−0.874205	−	3.09440i	−0.0437650	−	0.154914i
$400$	−1.53287	−	4.71770i	−0.0766437	−	0.235885i
$401$	−3.94313	−	37.5164i	−0.196911	−	1.87348i	−0.432511	−	0.901629i	$-0.642372\pi$
$401$	−3.94313	−	37.5164i	−0.196911	−	1.87348i	0.235600	−	0.971850i	$-0.424294\pi$
$402$	−14.4967	−	6.45434i	−0.723029	−	0.321913i
$403$	−10.3075	+	11.4476i	−0.513452	+	0.570246i
$404$	−6.40515	−	7.11364i	−0.318668	−	0.353917i
$405$	−0.160820	−	0.116842i	−0.00799120	−	0.00580594i
$406$	1.56604	+	23.7305i	0.0777213	+	1.17773i
$407$	26.1558	−	28.1428i	1.29649	−	1.39499i
$408$	2.64814	−	4.58671i	0.131102	−	0.227076i
$409$	3.84562	−	36.5886i	0.190154	−	1.80919i	−0.318178	−	0.948031i	$-0.603071\pi$
$409$	3.84562	−	36.5886i	0.190154	−	1.80919i	0.508332	−	0.861161i	$-0.330262\pi$
$410$	−1.54173	+	0.327704i	−0.0761404	+	0.0161841i
$411$	−0.105180	−	0.0223566i	−0.00518812	−	0.00110277i
$412$	3.63617	−	2.64183i	0.179141	−	0.130154i
$413$	5.30427	−	0.913883i	0.261006	−	0.0449692i
$414$	−0.566938	−	1.74486i	−0.0278635	−	0.0857550i
$415$	1.90721	+	2.11818i	0.0936215	+	0.103977i
$416$	−0.315308	+	2.99995i	−0.0154592	+	0.147085i
$417$	−9.33510	−	16.1689i	−0.457142	−	0.791793i
$418$	−3.29802	+	2.31752i	−0.161311	+	0.113354i
$419$	−3.14325			−0.153558			−0.0767790	−	0.997048i	$-0.524464\pi$
$419$	−3.14325			−0.153558			−0.0767790	+	0.997048i	$0.524464\pi$
$420$	−0.245090	−	0.465335i	−0.0119592	−	0.0227060i
$421$	10.1649	−	31.2844i	0.495408	−	1.52471i	−0.320911	−	0.947109i	$-0.603989\pi$
$421$	10.1649	−	31.2844i	0.495408	−	1.52471i	0.816319	−	0.577601i	$-0.196011\pi$
$422$	−4.43426	−	0.942531i	−0.215856	−	0.0458817i
$423$	11.4027	+	5.07680i	0.554417	+	0.246842i
$424$	6.22700	+	2.77244i	0.302410	+	0.134642i
$425$	25.6980	+	5.46227i	1.24653	+	0.264959i
$426$	−1.42364	+	4.38150i	−0.0689753	+	0.212284i
$427$	12.6561	−	20.0786i	0.612471	−	0.971671i
$428$	−13.6926			−0.661855
$429$	8.18562	−	5.75204i	0.395206	−	0.277711i
$430$	1.01671	+	1.76100i	0.0490302	+	0.0849228i
$431$	0.955162	−	9.08776i	0.0460085	−	0.437742i	−0.947135	−	0.320837i	$-0.896036\pi$
$431$	0.955162	−	9.08776i	0.0460085	−	0.437742i	0.993143	−	0.116905i	$-0.0372974\pi$
$432$	0.669131	+	0.743145i	0.0321936	+	0.0357546i
$433$	−7.54891	−	23.2332i	−0.362778	−	1.11651i	−0.951361	−	0.308078i	$-0.900314\pi$
$433$	−7.54891	−	23.2332i	−0.362778	−	1.11651i	0.588584	−	0.808436i	$-0.299686\pi$
$434$	−4.67075	+	12.6781i	−0.224203	+	0.608568i
$435$	−1.44558	+	1.05027i	−0.0693101	+	0.0503567i
$436$	10.4092	+	2.21253i	0.498508	+	0.105961i
$437$	2.18102	−	0.463589i	0.104332	−	0.0221765i
$438$	0.594457	−	5.65588i	0.0284043	−	0.270248i
$439$	2.79719	−	4.84488i	0.133503	−	0.231233i	−0.791522	−	0.611141i	$-0.790711\pi$
$439$	2.79719	−	4.84488i	0.133503	−	0.231233i	0.925024	+	0.379908i	$0.124044\pi$
$440$	−0.448830	+	0.482927i	−0.0213971	+	0.0230226i
$441$	4.26630	+	5.54966i	0.203157	+	0.264269i
$442$	−12.9249	−	9.39050i	−0.614776	−	0.446661i
$443$	20.8157	+	23.1181i	0.988982	+	1.09838i	0.995147	+	0.0983951i	$0.0313709\pi$
$443$	20.8157	+	23.1181i	0.988982	+	1.09838i	−0.00616516	+	0.999981i	$0.501962\pi$
$444$	7.75137	−	8.60877i	0.367864	−	0.408554i
$445$	−1.10852	−	0.493545i	−0.0525489	−	0.0233963i
$446$	0.384432	+	3.65763i	0.0182034	+	0.173194i
$447$	−6.22281	−	19.1519i	−0.294329	−	0.905851i
$448$	0.719303	+	2.54610i	0.0339839	+	0.120292i
$449$	−6.82734	−	4.96035i	−0.322202	−	0.234094i	0.414912	−	0.909861i	$-0.363812\pi$
$449$	−6.82734	−	4.96035i	−0.322202	−	0.234094i	−0.737115	+	0.675768i	$0.763812\pi$
$450$	−2.48024	+	4.29591i	−0.116920	+	0.202511i
$451$	−17.2860	−	19.8182i	−0.813964	−	0.933204i
$452$	−6.03305	−	10.4496i	−0.283771	−	0.491506i
$453$	−1.69705	+	0.755575i	−0.0797343	+	0.0355000i
$454$	2.47268	−	7.61014i	0.116049	−	0.357162i
$455$	−1.47326	+	0.588536i	−0.0690675	+	0.0275910i
$456$	−0.983238	+	0.714365i	−0.0460444	+	0.0334532i
$457$	−1.61559	−	15.3713i	−0.0755742	−	0.719040i	−0.965051	−	0.262061i	$-0.915598\pi$
$457$	−1.61559	−	15.3713i	−0.0755742	−	0.719040i	0.889477	−	0.456980i	$-0.151069\pi$
$458$	11.1635	−	12.3983i	0.521634	−	0.579333i
$459$	−5.18053	+	1.10116i	−0.241807	+	0.0513976i
$460$	0.333169	−	0.148337i	0.0155341	−	0.00691623i
$461$	−11.5956			−0.540061			−0.270031	−	0.962852i	$-0.587034\pi$
$461$	−11.5956			−0.540061			−0.270031	+	0.962852i	$0.587034\pi$
$462$	4.79570	−	7.34856i	0.223116	−	0.341886i
$463$	6.42606			0.298644			0.149322	−	0.988789i	$-0.452291\pi$
$463$	6.42606			0.298644			0.149322	+	0.988789i	$0.452291\pi$
$464$	8.21167	−	3.65607i	0.381217	−	0.169729i
$465$	−0.992951	+	0.211058i	−0.0460470	+	0.00978759i
$466$	5.11300	−	5.67856i	0.236855	−	0.263054i
$467$	−1.79713	−	17.0986i	−0.0831615	−	0.791228i	−0.954030	−	0.299712i	$-0.903109\pi$
$467$	−1.79713	−	17.0986i	−0.0831615	−	0.791228i	0.870868	−	0.491516i	$-0.163557\pi$
$468$	2.44038	−	1.77304i	0.112807	−	0.0819588i
$469$	−6.00586	+	41.5526i	−0.277325	+	1.91872i
$470$	−0.766727	+	2.35974i	−0.0353665	+	0.108847i
$471$	−10.3058	+	4.58844i	−0.474866	+	0.211424i
$472$	−1.01718	−	1.76181i	−0.0468196	−	0.0810939i
$473$	−17.4249	+	29.1101i	−0.801200	+	1.33848i
$474$	4.07115	−	7.05143i	0.186994	−	0.323883i
$475$	−4.87734	−	3.54359i	−0.223788	−	0.162591i
$476$	−13.5830	−	3.44318i	−0.622576	−	0.157818i
$477$	−2.10635	−	6.48269i	−0.0964433	−	0.296822i
$478$	−0.463256	−	4.40758i	−0.0211888	−	0.201598i
$479$	24.3574	+	10.8446i	1.11292	+	0.495503i	0.879033	−	0.476761i	$-0.158189\pi$
$479$	24.3574	+	10.8446i	1.11292	+	0.495503i	0.233886	+	0.972264i	$0.424856\pi$
$480$	−0.133013	+	0.147725i	−0.00607116	+	0.00674271i
$481$	−23.3818	−	25.9681i	−1.06612	−	1.18405i
$482$	−5.99271	−	4.35396i	−0.272961	−	0.198317i
$483$	−4.03477	+	2.69856i	−0.183588	+	0.122789i
$484$	−10.6821	−	2.62545i	−0.485549	−	0.119339i
$485$	0.295458	−	0.511749i	0.0134161	−	0.0232373i
$486$	0.104528	−	0.994522i	0.00474151	−	0.0451124i
$487$	−0.112841	+	0.0239851i	−0.00511331	+	0.00108687i	−0.210468	−	0.977601i	$-0.567499\pi$
$487$	−0.112841	+	0.0239851i	−0.00511331	+	0.00108687i	0.205354	+	0.978688i	$0.434165\pi$
$488$	−8.77477	−	1.86513i	−0.397215	−	0.0844307i
$489$	3.36623	−	2.44571i	0.152226	−	0.110599i
$490$	−1.00849	+	0.958741i	−0.0455591	+	0.0433115i
$491$	0.0245808	+	0.0756520i	0.00110932	+	0.00341413i	0.951610	−	0.307309i	$-0.0994287\pi$
$491$	0.0245808	+	0.0756520i	0.00110932	+	0.00341413i	−0.950500	+	0.310724i	$0.899429\pi$
$492$	−5.30557	−	5.89243i	−0.239193	−	0.265651i
$493$	−4.97630	+	47.3463i	−0.224121	+	2.13237i
$494$	1.83304	+	3.17491i	0.0824722	+	0.142846i
$495$	0.659210	+	0.0104046i	0.0296293	+	0.000467654i
$496$	5.10671			0.229298
$497$	12.1797	+	0.473086i	0.546336	+	0.0212208i
$498$	−4.43087	+	13.6368i	−0.198552	+	0.611081i
$499$	43.2919	+	9.20197i	1.93801	+	0.411937i	0.997365	+	0.0725464i	$0.0231125\pi$
$499$	43.2919	+	9.20197i	1.93801	+	0.411937i	0.940646	+	0.339390i	$0.110221\pi$
$500$	−1.80881	−	0.805333i	−0.0808923	−	0.0360156i
$501$	0.0705018	+	0.0313894i	0.00314979	+	0.00140238i
$502$	16.3794	+	3.48155i	0.731049	+	0.155389i
$503$	7.12513	−	21.9289i	0.317694	−	0.977761i	−0.656937	−	0.753945i	$-0.728148\pi$
$503$	7.12513	−	21.9289i	0.317694	−	0.977761i	0.974631	−	0.223816i	$-0.0718515\pi$
$504$	1.41081	−	2.23822i	0.0628425	−	0.0996981i
$505$	−1.90283			−0.0846748
$506$	4.86568	+	3.65382i	0.216306	+	0.162432i
$507$	1.95044	+	3.37826i	0.0866219	+	0.150034i
$508$	−0.269270	+	2.56194i	−0.0119469	+	0.113668i
$509$	26.8858	+	29.8597i	1.19169	+	1.32351i	0.933996	+	0.357284i	$0.116297\pi$
$509$	26.8858	+	29.8597i	1.19169	+	1.32351i	0.257697	+	0.966226i	$0.417036\pi$
$510$	−0.325338	−	1.00129i	−0.0144062	−	0.0443377i
$511$	−14.8280	+	2.55475i	−0.655953	+	0.113015i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	1.18879	+	0.252685i	0.0524864	+	0.0111563i
$514$	−3.98346	+	0.846711i	−0.175703	+	0.0373468i
$515$	0.0933904	−	0.888551i	0.00411527	−	0.0391542i
$516$	−5.11465	+	8.85883i	−0.225160	+	0.389988i
$517$	−40.6235	+	7.96689i	−1.78662	+	0.350383i
$518$	−27.4943	−	13.5434i	−1.20803	−	0.595064i
$519$	−3.08590	−	2.24204i	−0.135456	−	0.0984146i
$520$	0.401229	+	0.445610i	0.0175951	+	0.0195413i
$521$	0.0616627	−	0.0684833i	0.00270149	−	0.00300031i	−0.741793	−	0.670629i	$-0.766024\pi$
$521$	0.0616627	−	0.0684833i	0.00270149	−	0.00300031i	0.744494	+	0.667629i	$0.232691\pi$
$522$	−8.21167	−	3.65607i	−0.359415	−	0.160022i
$523$	−1.84598	−	17.5633i	−0.0807189	−	0.767989i	−0.957759	−	0.287572i	$-0.907152\pi$
$523$	−1.84598	−	17.5633i	−0.0807189	−	0.767989i	0.877040	−	0.480417i	$-0.159515\pi$
$524$	−4.72956	−	14.5561i	−0.206612	−	0.635886i
$525$	12.7218	+	3.22488i	0.555226	+	0.140745i
$526$	−6.32656	−	4.59651i	−0.275851	−	0.200417i
$527$	−13.5233	+	23.4230i	−0.589083	+	1.02032i
$528$	−3.23286	−	0.740677i	−0.140692	−	0.0322338i
$529$	9.81703	+	17.0036i	0.426827	+	0.739287i
$530$	1.23783	−	0.551117i	0.0537679	−	0.0239390i
$531$	−0.628653	+	1.93479i	−0.0272812	+	0.0839629i
$532$	2.52609	+	1.98957i	0.109520	+	0.0862590i
$533$	−19.3499	+	14.0585i	−0.838136	+	0.608942i
$534$	−0.638067	−	6.07080i	−0.0276119	−	0.262709i
$535$	−1.82128	+	2.02274i	−0.0787410	+	0.0874507i
$536$	15.5218	−	3.29927i	0.670441	−	0.142507i
$537$	3.40213	−	1.51473i	0.146813	−	0.0653653i
$538$	7.17640			0.309397
$539$	−22.1597	−	6.92446i	−0.954485	−	0.298258i
$540$	0.198784			0.00855431
$541$	1.43484	−	0.638830i	0.0616884	−	0.0274655i	−0.375661	−	0.926757i	$-0.622584\pi$
$541$	1.43484	−	0.638830i	0.0616884	−	0.0274655i	0.437349	+	0.899292i	$0.355917\pi$
$542$	−23.3986	+	4.97352i	−1.00505	+	0.213631i
$543$	9.46105	−	10.5076i	0.406013	−	0.450923i
$544$	0.553611	+	5.26726i	0.0237359	+	0.225832i
$545$	1.71140	−	1.24340i	0.0733081	−	0.0532615i
$546$	−6.26970	−	4.93809i	−0.268318	−	0.211331i
$547$	4.61840	−	14.2140i	0.197469	−	0.607746i	−0.802470	−	0.596692i	$-0.796481\pi$
$547$	4.61840	−	14.2140i	0.197469	−	0.607746i	0.999939	−	0.0110540i	$-0.00351868\pi$
$548$	0.0982329	−	0.0437361i	0.00419630	−	0.00186831i
$549$	4.48540	+	7.76894i	0.191432	+	0.331570i
$550$	−1.46128	−	16.3870i	−0.0623091	−	0.698746i
$551$	5.46227	−	9.46092i	0.232700	−	0.403049i
$552$	1.48426	+	1.07838i	0.0631744	+	0.0458989i
$553$	−20.8820	−	5.29341i	−0.887993	−	0.225099i
$554$	−2.00207	−	6.16174i	−0.0850599	−	0.261787i
$555$	−0.240704	−	2.29015i	−0.0102173	−	0.0972114i
$556$	17.0561	+	7.59386i	0.723339	+	0.322051i
$557$	−11.4680	+	12.7365i	−0.485914	+	0.539662i	−0.935384	−	0.353633i	$-0.884946\pi$
$557$	−11.4680	+	12.7365i	−0.485914	+	0.539662i	0.449470	+	0.893295i	$0.351613\pi$
$558$	−3.41706	−	3.79503i	−0.144656	−	0.160656i
$559$	24.9634	+	18.1370i	1.05584	+	0.767112i
$560$	0.471799	+	0.232403i	0.0199372	+	0.00982083i
$561$	11.9583	−	12.8668i	0.504881	−	0.543236i
$562$	−6.71929	+	11.6382i	−0.283436	+	0.490926i
$563$	−3.11673	+	29.6537i	−0.131355	+	1.24976i	0.708016	+	0.706197i	$0.249591\pi$
$563$	−3.11673	+	29.6537i	−0.131355	+	1.24976i	−0.839370	+	0.543560i	$0.817076\pi$
$564$	−12.2090	+	2.59511i	−0.514093	+	0.109274i
$565$	−2.34614	−	0.498687i	−0.0987027	−	0.0209799i
$566$	8.69321	−	6.31599i	0.365403	−	0.265481i
$567$	−2.60734	+	0.449223i	−0.109498	+	0.0188656i
$568$	−1.42364	−	4.38150i	−0.0597344	−	0.183844i
$569$	16.2160	+	18.0097i	0.679811	+	0.755007i	0.980027	−	0.198865i	$-0.0637254\pi$
$569$	16.2160	+	18.0097i	0.679811	+	0.755007i	−0.300216	+	0.953871i	$0.597059\pi$
$570$	−0.0252533	+	0.240269i	−0.00105774	+	0.0100638i
$571$	−10.3686	−	17.9589i	−0.433912	−	0.751557i	0.563294	−	0.826256i	$-0.309534\pi$
$571$	−10.3686	−	17.9589i	−0.433912	−	0.751557i	−0.997206	+	0.0746992i	$0.976200\pi$
$572$	−3.24134	+	9.46489i	−0.135527	+	0.395747i
$573$	19.2496			0.804164
$574$	−11.1864	+	17.7469i	−0.466910	+	0.740742i
$575$	−2.81229	+	8.65533i	−0.117280	+	0.360952i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	−12.5963	−	5.60822i	−0.524390	−	0.233473i	0.127430	−	0.991848i	$-0.459327\pi$
$577$	−12.5963	−	5.60822i	−0.524390	−	0.233473i	−0.651819	+	0.758374i	$0.725994\pi$
$578$	−10.0951	−	4.49464i	−0.419902	−	0.186952i
$579$	6.26871	+	1.33246i	0.260519	+	0.0553750i
$580$	0.552161	−	1.69938i	0.0229272	−	0.0705628i
$581$	37.9078	+	1.47242i	1.57268	+	0.0610861i
$582$	2.97266			0.123221
$583$	18.0776	+	13.5751i	0.748696	+	0.562224i
$584$	2.84352	+	4.92512i	0.117666	+	0.203803i
$585$	0.0626781	−	0.596343i	0.00259142	−	0.0246557i
$586$	12.6625	+	14.0632i	0.523085	+	0.580945i
$587$	6.60838	+	20.3385i	0.272757	+	0.839459i	0.989804	+	0.142435i	$0.0454931\pi$
$587$	6.60838	+	20.3385i	0.272757	+	0.839459i	−0.717047	+	0.697025i	$0.754507\pi$
$588$	−6.71351	−	1.98210i	−0.276861	−	0.0817405i
$589$	5.02112	−	3.64806i	0.206892	−	0.150316i
$590$	−0.395562	−	0.0840793i	−0.0162850	−	0.00346149i
$591$	5.90095	−	1.25428i	0.242732	−	0.0515944i
$592$	−1.21088	+	11.5208i	−0.0497670	+	0.473501i
$593$	−9.66820	+	16.7458i	−0.397026	+	0.687668i	−0.993357	−	0.115070i	$-0.963291\pi$
$593$	−9.66820	+	16.7458i	−0.397026	+	0.687668i	0.596332	+	0.802738i	$0.296624\pi$
$594$	1.61278	+	2.89809i	0.0661730	+	0.118910i
$595$	−2.31535	+	1.54857i	−0.0949203	+	0.0634851i
$596$	16.2915	+	11.8365i	0.667327	+	0.484842i
$597$	−7.86933	−	8.73977i	−0.322070	−	0.357695i
$598$	3.70309	−	4.11269i	0.151430	−	0.168181i
$599$	21.1973	+	9.43766i	0.866100	+	0.385613i	0.791185	−	0.611577i	$-0.209465\pi$
$599$	21.1973	+	9.43766i	0.866100	+	0.385613i	0.0749153	+	0.997190i	$0.476131\pi$
$600$	−0.518512	−	4.93331i	−0.0211682	−	0.201402i
$601$	2.44973	+	7.53949i	0.0999266	+	0.307542i	0.988506	−	0.151180i	$-0.0483073\pi$
$601$	2.44973	+	7.53949i	0.0999266	+	0.307542i	−0.888580	+	0.458722i	$0.848307\pi$
$602$	26.2344	+	6.65020i	1.06924	+	0.271042i
$603$	−12.8380	−	9.32733i	−0.522802	−	0.379838i
$604$	0.928826	−	1.60877i	0.0377934	−	0.0654601i
$605$	−1.80870	+	1.22880i	−0.0735340	+	0.0499577i
$606$	−4.78617	−	8.28989i	−0.194425	−	0.336754i
$607$	−22.2189	+	9.89247i	−0.901836	+	0.401523i	−0.804654	−	0.593744i	$-0.797649\pi$
$607$	−22.2189	+	9.89247i	−0.901836	+	0.401523i	−0.0971814	+	0.995267i	$0.530983\pi$
$608$	0.375564	−	1.15587i	0.0152311	−	0.0468766i
$609$	−3.40203	+	23.5375i	−0.137857	+	0.953789i
$610$	−1.44268	+	1.04817i	−0.0584125	+	0.0424391i
$611$	3.93560	+	37.4447i	0.159217	+	1.51485i
$612$	3.54390	−	3.93590i	0.143254	−	0.159099i
$613$	−30.6201	+	6.50851i	−1.23673	+	0.262876i	−0.779461	−	0.626450i	$-0.784507\pi$
$613$	−30.6201	+	6.50851i	−1.23673	+	0.262876i	−0.457273	+	0.889326i	$0.651174\pi$
$614$	−27.2439	+	12.1298i	−1.09947	+	0.489517i
$615$	−1.57617			−0.0635572
$616$	0.439574	+	8.76395i	0.0177109	+	0.353110i
$617$	48.1719			1.93933			0.969664	−	0.244442i	$-0.0786047\pi$
$617$	48.1719			1.93933			0.969664	+	0.244442i	$0.0786047\pi$
$618$	4.10597	−	1.82810i	0.165167	−	0.0735369i
$619$	41.8668	−	8.89905i	1.68277	−	0.357683i	0.735351	−	0.677687i	$-0.237017\pi$
$619$	41.8668	−	8.89905i	1.68277	−	0.357683i	0.947416	+	0.320004i	$0.103684\pi$
$620$	0.679257	−	0.754391i	0.0272796	−	0.0302971i
$621$	−0.191773	−	1.82460i	−0.00769559	−	0.0732186i
$622$	12.1318	−	8.81426i	0.486440	−	0.353420i
$623$	−14.9979	+	5.99133i	−0.600878	+	0.240037i
$624$	−0.932142	+	2.86884i	−0.0373156	+	0.114845i
$625$	22.2986	−	9.92797i	0.891943	−	0.397119i
$626$	−3.48511	−	6.03638i	−0.139293	−	0.241262i
$627$	−3.70779	+	1.58118i	−0.148075	+	0.0631463i
$628$	5.64055	−	9.76972i	0.225083	−	0.389854i
$629$	−49.6359	−	36.0626i	−1.97911	−	1.43791i
$630$	−0.142986	−	0.506123i	−0.00569670	−	0.0201644i
$631$	11.9327	+	36.7250i	0.475032	+	1.46200i	0.845914	+	0.533319i	$0.179055\pi$
$631$	11.9327	+	36.7250i	0.475032	+	1.46200i	−0.370882	+	0.928680i	$0.620945\pi$
$632$	0.851101	+	8.09769i	0.0338550	+	0.322109i
$633$	−4.14140	−	1.84387i	−0.164606	−	0.0732872i
$634$	−7.37843	+	8.19458i	−0.293035	+	0.325448i
$635$	0.342647	+	0.380548i	0.0135975	+	0.0151016i
$636$	5.51450	+	4.00652i	0.218664	+	0.158869i
$637$	−8.06303	+	19.5152i	−0.319469	+	0.773222i
$638$	29.2552	−	5.73738i	1.15822	−	0.227145i
$639$	−2.30349	+	3.98976i	−0.0911247	+	0.157833i
$640$	0.0207786	−	0.197695i	0.000821346	−	0.00781459i
$641$	−6.39685	+	1.35969i	−0.252660	+	0.0537046i	−0.332500	−	0.943103i	$-0.607892\pi$
$641$	−6.39685	+	1.35969i	−0.252660	+	0.0537046i	0.0798403	+	0.996808i	$0.474559\pi$
$642$	−13.3934	−	2.84685i	−0.528594	−	0.112356i
$643$	35.2374	−	25.6015i	1.38963	−	1.00962i	0.393721	−	0.919230i	$-0.371188\pi$
$643$	35.2374	−	25.6015i	1.38963	−	1.00962i	0.995906	−	0.0903935i	$-0.0288125\pi$
$644$	1.67802	−	4.55476i	0.0661234	−	0.179483i
$645$	0.628362	+	1.93390i	0.0247417	+	0.0761472i
$646$	4.30707	+	4.78349i	0.169460	+	0.188204i
$647$	0.893653	−	8.50254i	0.0351331	−	0.334269i	−0.962811	−	0.270176i	$-0.912918\pi$
$647$	0.893653	−	8.50254i	0.0351331	−	0.334269i	0.997944	−	0.0640928i	$-0.0204154\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−1.98348	−	6.44909i	−0.0778582	−	0.253149i
$650$	−14.9632			−0.586904
$651$	−7.20460	+	11.4299i	−0.282371	+	0.447974i
$652$	−1.28579	+	3.95724i	−0.0503552	+	0.154978i
$653$	−12.8800	−	2.73772i	−0.504032	−	0.107135i	−0.0511235	−	0.998692i	$-0.516280\pi$
$653$	−12.8800	−	2.73772i	−0.504032	−	0.107135i	−0.452908	+	0.891557i	$0.649614\pi$
$654$	9.72168	+	4.32837i	0.380148	+	0.169253i
$655$	−2.77940	−	1.23747i	−0.108600	−	0.0483518i
$656$	7.75578	+	1.64854i	0.302812	+	0.0643647i
$657$	1.75739	−	5.40869i	0.0685623	−	0.211013i
$658$	15.3894	+	29.2187i	0.599941	+	1.13906i
$659$	−34.8138			−1.35615			−0.678076	−	0.734992i	$-0.737186\pi$
$659$	−34.8138			−1.35615			−0.678076	+	0.734992i	$0.737186\pi$
$660$	−0.539428	+	0.379057i	−0.0209972	+	0.0147548i
$661$	−22.9262	−	39.7093i	−0.891726	−	1.54451i	−0.837805	−	0.545969i	$-0.816161\pi$
$661$	−22.9262	−	39.7093i	−0.891726	−	1.54451i	−0.0539208	−	0.998545i	$-0.517172\pi$
$662$	−0.377858	+	3.59508i	−0.0146859	+	0.139727i
$663$	−10.6901	−	11.8725i	−0.415168	−	0.461091i
$664$	−4.43087	−	13.6368i	−0.171951	−	0.529211i
$665$	0.629912	−	0.108529i	0.0244269	−	0.00420857i
$666$	9.37185	−	6.80905i	0.363152	−	0.263845i
$667$	−16.1309	−	3.42873i	−0.624592	−	0.132761i
$668$	−0.0754873	+	0.0160453i	−0.00292069	+	0.000620812i
$669$	−0.384432	+	3.65763i	−0.0148630	+	0.141412i
$670$	1.57721	−	2.73181i	0.0609330	−	0.105539i
$671$	−26.9861	−	12.5290i	−1.04179	−	0.483676i
$672$	0.174221	+	2.64001i	0.00672074	+	0.101841i
$673$	16.7084	+	12.1393i	0.644061	+	0.467938i	0.861243	−	0.508194i	$-0.169687\pi$
$673$	16.7084	+	12.1393i	0.644061	+	0.467938i	−0.217182	+	0.976131i	$0.569687\pi$
$674$	−10.1856	−	11.3123i	−0.392336	−	0.435733i
$675$	−3.31921	+	3.68636i	−0.127757	+	0.141888i
$676$	−3.56363	−	1.58663i	−0.137063	−	0.0610242i
$677$	−3.71547	−	35.3503i	−0.142797	−	1.35862i	−0.797766	−	0.602967i	$-0.793985\pi$
$677$	−3.71547	−	35.3503i	−0.142797	−	1.35862i	0.654969	−	0.755656i	$-0.272682\pi$
$678$	−3.72863	−	11.4755i	−0.143197	−	0.440716i
$679$	−2.13824	−	7.56867i	−0.0820581	−	0.290459i
$680$	0.851745	+	0.618829i	0.0326629	+	0.0237310i
$681$	4.00089	−	6.92974i	0.153314	−	0.265548i
$682$	16.5093	+	3.78243i	0.632174	+	0.144837i
$683$	5.17401	+	8.96164i	0.197978	+	0.342908i	0.947873	−	0.318649i	$-0.103229\pi$
$683$	5.17401	+	8.96164i	0.197978	+	0.342908i	−0.749895	+	0.661557i	$0.769896\pi$
$684$	−1.11028	+	0.494327i	−0.0424525	+	0.0189011i
$685$	0.00660527	−	0.0203289i	0.000252375	−	0.000776729i
$686$	−0.217569	+	18.5190i	−0.00830681	+	0.707058i
$687$	13.4972	−	9.80632i	0.514952	−	0.374135i
$688$	−1.06925	−	10.1733i	−0.0407649	−	0.387852i
$689$	13.7581	−	15.2800i	0.524143	−	0.582120i
$690$	0.356730	−	0.0758252i	0.0135805	−	0.00288662i
$691$	−9.36219	+	4.16831i	−0.356154	+	0.158570i	−0.577011	−	0.816736i	$-0.695781\pi$
$691$	−9.36219	+	4.16831i	−0.356154	+	0.158570i	0.220857	+	0.975306i	$0.429115\pi$
$692$	3.81438			0.145001
$693$	6.21875	−	6.19089i	0.236231	−	0.235173i
$694$	−2.48085			−0.0941716
$695$	3.39048	−	1.50954i	0.128608	−	0.0572601i
$696$	8.79237	−	1.86888i	0.333274	−	0.0708396i
$697$	−28.0997	+	31.2079i	−1.06435	+	1.18208i
$698$	−1.58107	−	15.0429i	−0.0598445	−	0.569383i
$699$	6.18191	−	4.49142i	0.233821	−	0.169881i
$700$	−12.1877	+	4.86873i	−0.460652	+	0.184021i
$701$	4.53177	−	13.9473i	0.171162	−	0.526784i	−0.828275	−	0.560322i	$-0.810677\pi$
$701$	4.53177	−	13.9473i	0.171162	−	0.526784i	0.999437	+	0.0335380i	$0.0106775\pi$
$702$	2.75569	−	1.22691i	0.104007	−	0.0463068i
$703$	7.03945	+	12.1927i	0.265498	+	0.459856i
$704$	3.05080	−	1.30101i	0.114981	−	0.0490336i
$705$	−1.24059	+	2.14877i	−0.0467233	+	0.0809272i
$706$	−7.34235	−	5.33453i	−0.276333	−	0.200768i
$707$	−17.6642	+	18.1490i	−0.664329	+	0.682563i
$708$	−0.628653	−	1.93479i	−0.0236262	−	0.0727140i
$709$	1.17894	+	11.2169i	0.0442761	+	0.421259i	0.994099	+	0.108472i	$0.0345958\pi$
$709$	1.17894	+	11.2169i	0.0442761	+	0.421259i	−0.949823	+	0.312787i	$0.898738\pi$
$710$	−0.836620	−	0.372487i	−0.0313978	−	0.0139792i
$711$	5.44826	−	6.05090i	0.204326	−	0.226927i
$712$	4.08454	+	4.53634i	0.153074	+	0.170006i
$713$	−7.57970	−	5.50698i	−0.283862	−	0.206238i
$714$	−12.5703	−	6.19200i	−0.470432	−	0.231730i
$715$	0.967065	+	1.73778i	0.0361662	+	0.0649892i
$716$	−1.86205	+	3.22516i	−0.0695880	+	0.120530i
$717$	0.463256	−	4.40758i	0.0173006	−	0.164604i
$718$	11.7010	−	2.48711i	0.436676	−	0.0928183i
$719$	46.1752	+	9.81483i	1.72204	+	0.366031i	0.959675	−	0.281112i	$-0.0907034\pi$
$719$	46.1752	+	9.81483i	1.72204	+	0.366031i	0.762368	+	0.647144i	$0.224037\pi$
$720$	−0.160820	+	0.116842i	−0.00599340	+	0.00435446i
$721$	−7.60795	−	9.13925i	−0.283335	−	0.340363i
$722$	5.41488	+	16.6653i	0.201521	+	0.620218i
$723$	−4.95652	−	5.50477i	−0.184335	−	0.204725i
$724$	−1.47796	+	14.0619i	−0.0549280	+	0.522605i
$725$	22.2944	+	38.6150i	0.827993	+	1.43413i
$726$	−9.90280	−	4.78901i	−0.367527	−	0.177737i
$727$	−15.1418			−0.561579			−0.280789	−	0.959769i	$-0.590596\pi$
$727$	−15.1418			−0.561579			−0.280789	+	0.959769i	$0.590596\pi$
$728$	7.97483	+	0.309759i	0.295567	+	0.0114804i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	1.10579	+	0.235043i	0.0409271	+	0.00869932i
$731$	49.4933	+	22.0358i	1.83058	+	0.815025i
$732$	−8.19523	−	3.64875i	−0.302905	−	0.134862i
$733$	−46.8357	−	9.95523i	−1.72992	−	0.367705i	−0.767873	−	0.640603i	$-0.778685\pi$
$733$	−46.8357	−	9.95523i	−1.72992	−	0.367705i	−0.962043	+	0.272898i	$0.912018\pi$
$734$	−4.27937	+	13.1705i	−0.157954	+	0.486133i
$735$	−1.18579	+	0.728112i	−0.0437385	+	0.0268568i
$736$	−1.83465			−0.0676261
$737$	52.6236	+	0.830585i	1.93842	+	0.0305950i
$738$	−3.96452	−	6.86675i	−0.145936	−	0.252769i
$739$	0.322939	−	3.07256i	0.0118795	−	0.113026i	−0.986975	−	0.160873i	$-0.948569\pi$
$739$	0.322939	−	3.07256i	0.0118795	−	0.113026i	0.998855	+	0.0478466i	$0.0152359\pi$
$740$	1.54085	+	1.71129i	0.0566428	+	0.0629082i
$741$	1.13288	+	3.48664i	0.0416173	+	0.128085i
$742$	6.23439	−	16.9224i	0.228872	−	0.621239i
$743$	22.4187	−	16.2882i	0.822463	−	0.597555i	−0.0949537	−	0.995482i	$-0.530270\pi$
$743$	22.4187	−	16.2882i	0.822463	−	0.597555i	0.917417	+	0.397927i	$0.130270\pi$
$744$	4.99512	+	1.06175i	0.183130	+	0.0389255i
$745$	3.91553	−	0.832272i	0.143454	−	0.0304921i
$746$	−2.38702	+	22.7110i	−0.0873951	+	0.831509i
$747$	−7.16930	+	12.4176i	−0.262311	+	0.454336i
$748$	−2.11159	+	17.4384i	−0.0772073	+	0.637610i
$749$	2.38554	+	36.1485i	0.0871657	+	1.32084i
$750$	−1.60184	−	1.16381i	−0.0584910	−	0.0424962i
$751$	−19.4020	−	21.5481i	−0.707988	−	0.786300i	0.276639	−	0.960974i	$-0.410780\pi$
$751$	−19.4020	−	21.5481i	−0.707988	−	0.786300i	−0.984626	+	0.174674i	$0.944113\pi$
$752$	8.35194	−	9.27577i	0.304564	−	0.338253i
$753$	15.2976	+	6.81095i	0.557477	+	0.248205i
$754$	−2.83424	−	26.9660i	−0.103217	−	0.982042i
$755$	−0.114111	−	0.351198i	−0.00415293	−	0.0127814i
$756$	1.84533	−	1.89598i	0.0671141	−	0.0689562i
$757$	−23.3657	−	16.9762i	−0.849242	−	0.617010i	0.0756951	−	0.997131i	$-0.475882\pi$
$757$	−23.3657	−	16.9762i	−0.849242	−	0.617010i	−0.924937	+	0.380121i	$0.875882\pi$
$758$	6.52121	−	11.2951i	0.236861	−	0.410256i
$759$	3.99969	+	4.58561i	0.145179	+	0.166447i
$760$	−0.120796	−	0.209225i	−0.00438174	−	0.00758939i
$761$	11.2325	−	5.00105i	0.407179	−	0.181288i	−0.192918	−	0.981215i	$-0.561795\pi$
$761$	11.2325	−	5.00105i	0.407179	−	0.181288i	0.600097	+	0.799927i	$0.295129\pi$
$762$	−0.796042	+	2.44997i	−0.0288376	+	0.0887529i
$763$	4.02761	−	27.8657i	0.145809	−	1.00881i
$764$	−15.5733	+	11.3146i	−0.563421	+	0.409349i
$765$	−0.110049	−	1.04705i	−0.00397883	−	0.0378561i
$766$	−9.28670	+	10.3139i	−0.335542	+	0.372657i
$767$	−6.00251	+	1.27587i	−0.216738	+	0.0460691i
$768$	0.913545	−	0.406737i	0.0329647	−	0.0146768i
$769$	37.1716			1.34044			0.670222	−	0.742161i	$-0.266199\pi$
$769$	37.1716			1.34044			0.670222	+	0.742161i	$0.266199\pi$
$770$	1.35313	+	1.10078i	0.0487633	+	0.0396693i
$771$	−4.07245			−0.146666
$772$	−5.85469	+	2.60668i	−0.210715	+	0.0938163i
$773$	38.7542	−	8.23746i	1.39389	−	0.296281i	0.551063	−	0.834464i	$-0.314222\pi$
$773$	38.7542	−	8.23746i	1.39389	−	0.296281i	0.842828	+	0.538183i	$0.180889\pi$
$774$	−6.84474	+	7.60185i	−0.246029	+	0.273243i
$775$	2.64789	+	25.1930i	0.0951151	+	0.904960i
$776$	−2.40493	+	1.74728i	−0.0863319	+	0.0627238i
$777$	−24.0777	−	18.9639i	−0.863782	−	0.680325i
$778$	4.48702	−	13.8096i	0.160867	−	0.495099i
$779$	8.80344	−	3.91954i	0.315416	−	0.140432i
$780$	0.299814	+	0.519293i	0.0107351	+	0.0185937i
$781$	−1.35714	−	15.2192i	−0.0485624	−	0.544587i
$782$	4.85840	−	8.41500i	0.173736	−	0.300920i
$783$	−7.27209	−	5.28348i	−0.259883	−	0.188816i
$784$	6.59640	−	2.34255i	0.235586	−	0.0836625i
$785$	−0.692972	−	2.13275i	−0.0247332	−	0.0761211i
$786$	−1.59983	−	15.2213i	−0.0570639	−	0.542927i
$787$	−14.9678	−	6.66407i	−0.533543	−	0.237549i	0.122237	−	0.992501i	$-0.460993\pi$
$787$	−14.9678	−	6.66407i	−0.533543	−	0.237549i	−0.655780	+	0.754952i	$0.727660\pi$
$788$	−4.03672	+	4.48323i	−0.143802	+	0.159708i
$789$	−5.23264	−	5.81143i	−0.186287	−	0.206893i
$790$	1.30944	+	0.951365i	0.0465878	+	0.0338480i
$791$	−26.5358	+	17.7478i	−0.943505	+	0.631041i
$792$	−3.00822	−	1.39664i	−0.106892	−	0.0496275i
$793$	−13.5301	+	23.4348i	−0.480468	+	0.832195i
$794$	3.49885	−	33.2894i	0.124170	−	1.18140i
$795$	1.32536	−	0.281715i	0.0470058	−	0.00999139i
$796$	11.5035	+	2.44515i	0.407732	+	0.0866660i
$797$	−14.4178	+	10.4752i	−0.510706	+	0.371050i	−0.813091	−	0.582136i	$-0.802217\pi$
$797$	−14.4178	+	10.4752i	−0.510706	+	0.371050i	0.302385	+	0.953186i	$0.402217\pi$
$798$	2.05723	+	2.47130i	0.0728252	+	0.0874831i
$799$	20.4282	+	62.8714i	0.722696	+	2.22423i
$800$	3.31921	+	3.68636i	0.117352	+	0.130332i
$801$	0.638067	−	6.07080i	0.0225450	−	0.214501i
$802$	18.8615	+	32.6691i	0.666023	+	1.15359i
$803$	5.54478	+	18.0284i	0.195671	+	0.636207i
$804$	15.8686			0.559642
$805$	−0.449655	−	0.853726i	−0.0158483	−	0.0300899i
$806$	4.76018	−	14.6503i	0.167670	−	0.516036i
$807$	7.01958	+	1.49206i	0.247101	+	0.0525229i
$808$	8.74477	+	3.89342i	0.307640	+	0.136970i
$809$	−13.5235	−	6.02103i	−0.475459	−	0.211688i	0.154994	−	0.987915i	$-0.450464\pi$
$809$	−13.5235	−	6.02103i	−0.475459	−	0.211688i	−0.630453	+	0.776227i	$0.717131\pi$
$810$	0.194440	+	0.0413295i	0.00683193	+	0.00145217i
$811$	13.7265	−	42.2459i	0.482004	−	1.48345i	−0.354270	−	0.935143i	$-0.615271\pi$
$811$	13.7265	−	42.2459i	0.482004	−	1.48345i	0.836274	−	0.548312i	$-0.184729\pi$
$812$	−11.0827	−	21.0419i	−0.388927	−	0.738427i
$813$	−23.9213			−0.838957
$814$	−12.4478	+	36.3482i	−0.436295	+	1.27400i
$815$	0.413559	+	0.716306i	0.0144864	+	0.0250911i
$816$	−0.553611	+	5.26726i	−0.0193803	+	0.184391i
$817$	−8.31875	−	9.23891i	−0.291036	−	0.323228i
$818$	11.3688	+	34.9895i	0.397501	+	1.22338i
$819$	−5.10601	−	6.13372i	−0.178418	−	0.214330i
$820$	1.27515	−	0.926448i	0.0445301	−	0.0323530i
$821$	−31.4139	−	6.67724i	−1.09635	−	0.233037i	−0.375983	−	0.926627i	$-0.622695\pi$
$821$	−31.4139	−	6.67724i	−1.09635	−	0.233037i	−0.720371	+	0.693589i	$0.756028\pi$
$822$	0.105180	−	0.0223566i	0.00366856	−	0.000779776i
$823$	1.06123	−	10.0970i	0.0369923	−	0.351958i	−0.960332	−	0.278858i	$-0.910044\pi$
$823$	1.06123	−	10.0970i	0.0369923	−	0.351958i	0.997325	−	0.0730999i	$-0.0232892\pi$
$824$	−2.24727	+	3.89239i	−0.0782875	+	0.135598i
$825$	1.97771	−	16.3328i	0.0688551	−	0.568634i
$826$	−4.47398	+	2.99231i	−0.155670	+	0.104116i
$827$	7.29128	+	5.29742i	0.253542	+	0.184209i	0.707295	−	0.706918i	$-0.249915\pi$
$827$	7.29128	+	5.29742i	0.253542	+	0.184209i	−0.453753	+	0.891128i	$0.649915\pi$
$828$	1.22762	+	1.36341i	0.0426627	+	0.0473818i
$829$	4.18750	−	4.65069i	0.145438	−	0.161525i	−0.666024	−	0.745930i	$-0.732005\pi$
$829$	4.18750	−	4.65069i	0.145438	−	0.161525i	0.811462	+	0.584405i	$0.198672\pi$
$830$	−2.60387	−	1.15932i	−0.0903815	−	0.0402405i
$831$	−0.677223	−	6.44335i	−0.0234926	−	0.223517i
$832$	−0.932142	−	2.86884i	−0.0323162	−	0.0994591i
$833$	−6.72356	+	36.4591i	−0.232958	+	1.26323i
$834$	15.1045	+	10.9741i	0.523027	+	0.380001i
$835$	−0.00767046	+	0.0132856i	−0.000265447	+	0.000459768i
$836$	2.07027	−	3.45858i	0.0716017	−	0.119618i
$837$	−2.55336	−	4.42254i	−0.0882569	−	0.152865i
$838$	2.87150	−	1.27848i	0.0991945	−	0.0441642i
$839$	13.7893	−	42.4390i	0.476059	−	1.46516i	−0.368466	−	0.929641i	$-0.620117\pi$
$839$	13.7893	−	42.4390i	0.476059	−	1.46516i	0.844524	−	0.535517i	$-0.179883\pi$
$840$	0.413170	+	0.325417i	0.0142557	+	0.0112280i
$841$	−41.9058	+	30.4464i	−1.44503	+	1.04987i
$842$	3.43840	+	32.7142i	0.118495	+	1.12741i
$843$	−8.99217	+	9.98681i	−0.309707	+	0.343964i
$844$	4.43426	−	0.942531i	0.152633	−	0.0324432i
$845$	−0.708392	+	0.315397i	−0.0243694	+	0.0108500i
$846$	−12.4818			−0.429133
$847$	−5.07017	+	28.6582i	−0.174213	+	0.984708i
$848$	−6.81630			−0.234073
$849$	9.81641	−	4.37055i	0.336898	−	0.149997i
$850$	−25.6980	+	5.46227i	−0.881433	+	0.187354i
$851$	14.2210	−	15.7941i	0.487491	−	0.541414i
$852$	−0.481561	−	4.58174i	−0.0164980	−	0.156968i
$853$	19.1546	−	13.9166i	0.655839	−	0.476495i	−0.209416	−	0.977827i	$-0.567156\pi$
$853$	19.1546	−	13.9166i	0.655839	−	0.476495i	0.865255	+	0.501331i	$0.167156\pi$
$854$	−3.39522	+	23.4904i	−0.116182	+	0.803825i
$855$	−0.0746561	+	0.229768i	−0.00255318	+	0.00785789i
$856$	12.5088	−	5.56927i	0.427542	−	0.190354i
$857$	−20.5063	−	35.5180i	−0.700483	−	1.21327i	−0.968297	−	0.249802i	$-0.919635\pi$
$857$	−20.5063	−	35.5180i	−0.700483	−	1.21327i	0.267814	−	0.963471i	$-0.413699\pi$
$858$	−5.13837	+	8.58414i	−0.175421	+	0.293058i
$859$	11.4255	−	19.7895i	0.389832	−	0.675209i	−0.602595	−	0.798047i	$-0.705866\pi$
$859$	11.4255	−	19.7895i	0.389832	−	0.675209i	0.992427	+	0.122839i	$0.0391997\pi$
$860$	−1.64507	−	1.19522i	−0.0560965	−	0.0407565i
$861$	−14.6317	+	15.0333i	−0.498648	+	0.512334i
$862$	2.82374	+	8.69058i	0.0961770	+	0.296002i
$863$	1.16594	+	11.0932i	0.0396892	+	0.377617i	0.996279	+	0.0861813i	$0.0274664\pi$
$863$	1.16594	+	11.0932i	0.0396892	+	0.377617i	−0.956590	+	0.291436i	$0.905867\pi$
$864$	−0.913545	−	0.406737i	−0.0310794	−	0.0138375i
$865$	0.507361	−	0.563481i	0.0172508	−	0.0191589i
$866$	16.3461	+	18.1541i	0.555461	+	0.616902i
$867$	−8.94003	−	6.49531i	−0.303619	−	0.220592i
$868$	−0.889699	−	13.4818i	−0.0301984	−	0.457601i
$869$	−3.24628	+	26.8091i	−0.110122	+	0.909436i
$870$	0.893415	−	1.54744i	0.0302896	−	0.0524631i
$871$	5.00349	−	47.6050i	0.169537	−	1.61303i
$872$	−10.4092	+	2.21253i	−0.352498	+	0.0749258i
$873$	2.90770	+	0.618050i	0.0984106	+	0.0209178i
$874$	−1.80390	+	1.31061i	−0.0610178	+	0.0443320i
$875$	−1.81095	+	4.91557i	−0.0612214	+	0.166177i
$876$	1.75739	+	5.40869i	0.0593767	+	0.182743i
$877$	14.1692	+	15.7365i	0.478460	+	0.531384i	0.933256	−	0.359212i	$-0.116954\pi$
$877$	14.1692	+	15.7365i	0.478460	+	0.531384i	−0.454796	+	0.890596i	$0.650288\pi$
$878$	−0.584772	+	5.56374i	−0.0197351	+	0.187767i
$879$	9.46194	+	16.3886i	0.319143	+	0.552772i
$880$	0.213603	−	0.623731i	0.00720054	−	0.0210260i
$881$	−1.19162			−0.0401466			−0.0200733	−	0.999799i	$-0.506390\pi$
$881$	−1.19162			−0.0401466			−0.0200733	+	0.999799i	$0.506390\pi$
$882$	−6.15471	−	3.33461i	−0.207240	−	0.112282i
$883$	9.39002	−	28.8995i	0.315999	−	0.972546i	−0.659342	−	0.751843i	$-0.729165\pi$
$883$	9.39002	−	28.8995i	0.315999	−	0.972546i	0.975341	−	0.220703i	$-0.0708350\pi$
$884$	15.6270	+	3.32161i	0.525591	+	0.111718i
$885$	−0.369437	−	0.164484i	−0.0124185	−	0.00552907i
$886$	−28.4191	−	12.6530i	−0.954757	−	0.425085i
$887$	−33.4948	−	7.11953i	−1.12464	−	0.239051i	−0.392202	−	0.919879i	$-0.628287\pi$
$887$	−33.4948	−	7.11953i	−1.12464	−	0.239051i	−0.732443	+	0.680829i	$0.761620\pi$
$888$	−3.57973	+	11.0173i	−0.120128	+	0.369715i
$889$	6.81045	+	0.264532i	0.228415	+	0.00887211i
$890$	1.21343			0.0406742
$891$	0.974986	+	3.17008i	0.0326633	+	0.106202i
$892$	−1.83889	−	3.18505i	−0.0615705	−	0.106643i
$893$	1.58567	−	15.0866i	0.0530624	−	0.504855i
$894$	13.4746	+	14.9650i	0.450657	+	0.500506i
$895$	0.228763	+	0.704059i	0.00764669	+	0.0235341i
$896$	−1.69271	−	2.03341i	−0.0565494	−	0.0679314i
$897$	4.47724	−	3.25291i	0.149491	−	0.108611i
$898$	8.25464	+	1.75458i	0.275461	+	0.0585511i
$899$	−44.9001	+	9.54382i	−1.49750	+	0.318304i
$900$	0.518512	−	4.93331i	0.0172837	−	0.164444i
$901$	18.0505	−	31.2644i	0.601349	−	1.04157i
$902$	23.8523	+	11.0740i	0.794195	+	0.368725i
$903$	24.2785	+	11.9593i	0.807937	+	0.397981i
$904$	9.76168	+	7.09228i	0.324669	+	0.235886i
$905$	1.88071	+	2.08874i	0.0625168	+	0.0694320i
$906$	1.24301	−	1.38050i	0.0412963	−	0.0458642i
$907$	4.14736	+	1.84652i	0.137711	+	0.0613128i	0.474435	−	0.880290i	$-0.342652\pi$
$907$	4.14736	+	1.84652i	0.137711	+	0.0613128i	−0.336724	+	0.941603i	$0.609319\pi$
$908$	0.836413	+	7.95794i	0.0277574	+	0.264094i
$909$	−2.95802	−	9.10384i	−0.0981112	−	0.301955i
$910$	1.10651	−	1.13688i	0.0366805	−	0.0376873i
$911$	−3.89712	−	2.83142i	−0.129117	−	0.0938093i	0.521352	−	0.853342i	$-0.325428\pi$
$911$	−3.89712	−	2.83142i	−0.129117	−	0.0938093i	−0.650469	+	0.759532i	$0.725428\pi$
$912$	0.607675	−	1.05252i	0.0201221	−	0.0348525i
$913$	−4.22392	−	47.3678i	−0.139791	−	1.56765i
$914$	7.72800	+	13.3853i	0.255619	+	0.442746i
$915$	−1.62908	+	0.725314i	−0.0538558	+	0.0239781i
$916$	−5.15549	+	15.8670i	−0.170342	+	0.524259i
$917$	−37.6042	+	15.0221i	−1.24180	+	0.496072i
$918$	4.28477	−	3.11307i	0.141419	−	0.102747i
$919$	3.33336	+	31.7148i	0.109958	+	1.04618i	0.900823	+	0.434186i	$0.142964\pi$
$919$	3.33336	+	31.7148i	0.109958	+	1.04618i	−0.790866	+	0.611990i	$0.790369\pi$
$920$	−0.244031	+	0.271024i	−0.00804548	+	0.00893541i
$921$	−29.1705	+	6.20037i	−0.961199	+	0.204309i
$922$	10.5931	−	4.71636i	0.348866	−	0.155325i
$923$	−13.8968			−0.457420
$924$	−1.39216	+	8.66383i	−0.0457987	+	0.285019i
$925$	−57.4635			−1.88939
$926$	−5.87050	+	2.61371i	−0.192916	+	0.0858919i
$927$	4.39633	−	0.934469i	0.144394	−	0.0306920i
$928$	−6.01468	+	6.67998i	−0.197442	+	0.219281i
$929$	−2.21983	−	21.1203i	−0.0728302	−	0.692933i	−0.968635	−	0.248486i	$-0.920067\pi$
$929$	−2.21983	−	21.1203i	−0.0728302	−	0.692933i	0.895805	−	0.444447i	$-0.146600\pi$
$930$	0.821261	−	0.596681i	0.0269302	−	0.0195659i
$931$	4.81240	−	7.01552i	0.157720	−	0.229924i
$932$	−2.36128	+	7.26727i	−0.0773463	+	0.238047i
$933$	13.6993	−	6.09931i	0.448494	−	0.199682i
$934$	8.59639	+	14.8894i	0.281282	+	0.487195i
$935$	2.29522	+	2.63146i	0.0750618	+	0.0860578i
$936$	−1.50824	+	2.61234i	−0.0492983	+	0.0853872i
$937$	−14.1346	−	10.2694i	−0.461758	−	0.335487i	0.332463	−	0.943116i	$-0.392120\pi$
$937$	−14.1346	−	10.2694i	−0.461758	−	0.335487i	−0.794220	+	0.607630i	$0.792120\pi$
$938$	−11.4143	−	40.4030i	−0.372691	−	1.31920i
$939$	−2.15391	−	6.62907i	−0.0702904	−	0.216331i
$940$	−0.259354	−	2.46759i	−0.00845919	−	0.0804839i
$941$	−43.6821	−	19.4485i	−1.42400	−	0.634004i	−0.457156	−	0.889387i	$-0.651132\pi$
$941$	−43.6821	−	19.4485i	−1.42400	−	0.634004i	−0.966840	+	0.255383i	$0.917798\pi$
$942$	7.54853	−	8.38349i	0.245944	−	0.273149i
$943$	−9.73385	−	10.8105i	−0.316978	−	0.352040i
$944$	1.64583	+	1.19577i	0.0535673	+	0.0389189i
$945$	−0.0346325	−	0.524792i	−0.00112659	−	0.0170715i
$946$	4.07835	−	33.6807i	0.132599	−	1.09506i
$947$	−2.00809	+	3.47811i	−0.0652541	+	0.113023i	−0.896807	−	0.442423i	$-0.854119\pi$
$947$	−2.00809	+	3.47811i	−0.0652541	+	0.113023i	0.831553	+	0.555446i	$0.187452\pi$
$948$	−0.851101	+	8.09769i	−0.0276425	+	0.263001i
$949$	16.7799	−	3.56668i	0.544700	−	0.115779i
$950$	5.89698	+	1.25344i	0.191323	+	0.0406670i
$951$	−8.92094	+	6.48144i	−0.289281	+	0.210175i
$952$	13.8092	−	2.37921i	0.447557	−	0.0771106i
$953$	−3.30817	−	10.1815i	−0.107162	−	0.329811i	0.883070	−	0.469242i	$-0.155473\pi$
$953$	−3.30817	−	10.1815i	−0.107162	−	0.329811i	−0.990232	+	0.139431i	$0.955473\pi$
$954$	4.56100	+	5.06550i	0.147668	+	0.164002i
$955$	−0.399980	+	3.80556i	−0.0129431	+	0.123145i
$956$	2.21593	+	3.83811i	0.0716683	+	0.124133i
$957$	29.8088	+	0.470486i	0.963580	+	0.0152087i
$958$	−26.6625			−0.861427
$959$	−0.132578	−	0.251716i	−0.00428117	−	0.00812833i
$960$	0.0614277	−	0.189055i	0.00198257	−	0.00610172i
$961$	4.81392	+	1.02323i	0.155288	+	0.0330074i
$962$	31.9226	+	14.2128i	1.02922	+	0.458240i
$963$	−12.5088	−	5.56927i	−0.403090	−	0.179467i
$964$	7.24553	+	1.54008i	0.233363	+	0.0496028i
$965$	−0.393675	+	1.21161i	−0.0126728	+	0.0390030i
$966$	2.58834	−	4.10634i	0.0832785	−	0.132119i
$967$	−16.7236			−0.537796			−0.268898	−	0.963169i	$-0.586659\pi$
$967$	−16.7236			−0.537796			−0.268898	+	0.963169i	$0.586659\pi$
$968$	10.8264	−	1.94633i	0.347975	−	0.0625573i
$969$	3.21841	+	5.57445i	0.103390	+	0.179077i
$970$	−0.0617676	+	0.587680i	−0.00198324	+	0.0188693i
$971$	8.34642	+	9.26964i	0.267849	+	0.297477i	0.862033	−	0.506853i	$-0.169191\pi$
$971$	8.34642	+	9.26964i	0.267849	+	0.297477i	−0.594183	+	0.804330i	$0.702525\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	17.0763	−	46.3512i	0.547442	−	1.48595i
$974$	0.0933297	−	0.0678080i	0.00299048	−	0.00217271i
$975$	−14.6362	−	3.11102i	−0.468734	−	0.0996324i
$976$	8.77477	−	1.86513i	0.280873	−	0.0597015i
$977$	1.75733	−	16.7199i	0.0562219	−	0.534916i	−0.929772	−	0.368136i	$-0.879996\pi$
$977$	1.75733	−	16.7199i	0.0562219	−	0.534916i	0.985994	−	0.166780i	$-0.0533371\pi$
$978$	−2.08044	+	3.60344i	−0.0665253	+	0.115225i
$979$	9.84478	+	17.6907i	0.314641	+	0.565396i
$980$	0.531349	−	1.28604i	0.0169733	−	0.0410812i
$981$	8.60932	+	6.25503i	0.274874	+	0.199708i
$982$	−0.0532261	−	0.0591136i	−0.00169851	−	0.00188639i
$983$	27.3160	−	30.3375i	0.871244	−	0.967615i	−0.128465	−	0.991714i	$-0.541005\pi$
$983$	27.3160	−	30.3375i	0.871244	−	0.967615i	0.999710	+	0.0240991i	$0.00767172\pi$
$984$	7.24354	+	3.22503i	0.230916	+	0.102810i
$985$	0.125353	+	1.19265i	0.00399407	+	0.0380010i
$986$	−14.7114	−	45.2770i	−0.468507	−	1.44191i
$987$	8.97818	+	31.7798i	0.285779	+	1.01156i
$988$	−2.96592	−	2.15486i	−0.0943583	−	0.0685553i
$989$	−9.38359	+	16.2529i	−0.298381	+	0.516811i
$990$	−0.606451	+	0.258620i	−0.0192743	+	0.00821948i
$991$	−4.13214	−	7.15707i	−0.131262	−	0.227352i	0.792902	−	0.609350i	$-0.208569\pi$
$991$	−4.13214	−	7.15707i	−0.131262	−	0.227352i	−0.924163	+	0.381998i	$0.875236\pi$
$992$	−4.66522	+	2.07709i	−0.148121	+	0.0659476i
$993$	−1.11706	+	3.43795i	−0.0354488	+	0.109100i
$994$	−11.3192	+	4.52176i	−0.359022	+	0.143422i
$995$	1.89132	−	1.37413i	0.0599590	−	0.0435628i
$996$	−1.49879	−	14.2601i	−0.0474911	−	0.451847i
$997$	22.8771	−	25.4076i	0.724524	−	0.804666i	−0.262552	−	0.964918i	$-0.584564\pi$
$997$	22.8771	−	25.4076i	0.724524	−	0.804666i	0.987076	+	0.160252i	$0.0512308\pi$
$998$	−43.2919	+	9.20197i	−1.37038	+	0.291283i
$999$	10.5827	−	4.71174i	0.334823	−	0.149073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.c.37.3	yes	40
7.4	even	3	inner	462.2.y.c.235.3	yes	40
11.3	even	5	inner	462.2.y.c.289.3	yes	40
77.25	even	15	inner	462.2.y.c.25.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.c.25.3	✓	40	77.25	even	15	inner
462.2.y.c.37.3	yes	40	1.1	even	1	trivial
462.2.y.c.235.3	yes	40	7.4	even	3	inner
462.2.y.c.289.3	yes	40	11.3	even	5	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0207786 - 0.197695i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.07849 - 1.63704i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.0207786 - 0.197695i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-2.07849 - 1.63704i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.0993921 + 0.172152i) q^{10} +(-1.70343 + 2.84575i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.44038 + 1.77304i) q^{13} +(2.56464 + 0.650113i) q^{14} +(0.0614277 + 0.189055i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(4.83838 + 2.15419i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-0.813228 - 0.903181i) q^{19} +(-0.160820 - 0.116842i) q^{20} +(2.37343 + 1.16912i) q^{21} +(0.398693 - 3.29257i) q^{22} +(-0.917325 + 1.58885i) q^{23} +(0.104528 - 0.994522i) q^{24} +(4.85209 - 1.03134i) q^{25} +(-2.95056 - 0.627161i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.60734 + 0.449223i) q^{28} +(2.77769 + 8.54885i) q^{29} +(-0.133013 - 0.147725i) q^{30} +(-0.533797 + 5.07874i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.07455 - 3.13773i) q^{33} -5.29627 q^{34} +(-0.280447 + 0.444922i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-11.3311 - 2.40850i) q^{37} +(1.11028 + 0.494327i) q^{38} +(-2.75569 - 1.22691i) q^{39} +(0.194440 + 0.0413295i) q^{40} +(-2.45021 + 7.54097i) q^{41} +(-2.64376 - 0.102689i) q^{42} +10.2293 q^{43} +(0.974986 + 3.17008i) q^{44} +(-0.0993921 - 0.172152i) q^{45} +(0.191773 - 1.82460i) q^{46} +(8.35194 + 9.27577i) q^{47} +(0.309017 + 0.951057i) q^{48} +(1.64021 + 6.80512i) q^{49} +(-4.01312 + 2.91570i) q^{50} +(-5.18053 - 1.10116i) q^{51} +(2.95056 - 0.627161i) q^{52} +(0.712498 - 6.77896i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.597987 + 0.277630i) q^{55} +(2.19920 - 1.47088i) q^{56} +(0.983238 + 0.714365i) q^{57} +(-6.01468 - 6.67998i) q^{58} +(-1.36125 + 1.51183i) q^{59} +(0.181598 + 0.0808528i) q^{60} +(0.937704 + 8.92166i) q^{61} +(-1.57806 - 4.85677i) q^{62} +(-2.56464 - 0.650113i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.299814 - 0.519293i) q^{65} +(0.294584 + 3.30352i) q^{66} +(-7.93430 - 13.7426i) q^{67} +(4.83838 - 2.15419i) q^{68} +(0.566938 - 1.74486i) q^{69} +(0.0752347 - 0.520524i) q^{70} +(-3.72712 + 2.70791i) q^{71} +(0.104528 + 0.994522i) q^{72} +(3.80537 - 4.22629i) q^{73} +(11.3311 - 2.40850i) q^{74} +(-4.53163 + 2.01761i) q^{75} -1.21535 q^{76} +(8.19917 - 3.12627i) q^{77} +3.01648 q^{78} +(7.43835 - 3.31177i) q^{79} +(-0.194440 + 0.0413295i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-0.828811 - 7.88561i) q^{82} +(-11.6002 + 8.42802i) q^{83} +(2.45696 - 0.981502i) q^{84} +(0.325338 - 1.00129i) q^{85} +(-9.34493 + 4.16063i) q^{86} +(-4.49440 - 7.78453i) q^{87} +(-2.18008 - 2.49945i) q^{88} +(3.05212 - 5.28643i) q^{89} +(0.160820 + 0.116842i) q^{90} +(-2.16976 - 7.68024i) q^{91} +(0.566938 + 1.74486i) q^{92} +(-0.533797 - 5.07874i) q^{93} +(-11.4027 - 5.07680i) q^{94} +(-0.161657 + 0.179538i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(2.40493 + 1.74728i) q^{97} +(-4.26630 - 5.54966i) q^{98} +(-0.398693 + 3.29257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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