LMFDB - Embedded newform 930.2.bg.g.541.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.3
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.g.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.408047 - 3.88231i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.408047 - 3.88231i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.25100 - 1.44744i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(-3.59874 - 0.764935i) q^{13} +(-3.56620 - 1.58777i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.319207 - 0.142120i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-2.66513 + 0.566490i) q^{19} +(0.913545 - 0.406737i) q^{20} +(-2.61208 - 2.90101i) q^{21} +(-0.371981 - 3.53916i) q^{22} +(1.27744 - 0.928117i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.83957 + 3.18622i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.61208 + 2.90101i) q^{28} +(0.283390 - 0.872186i) q^{29} +1.00000 q^{30} +(4.71374 + 2.96321i) q^{31} +1.00000 q^{32} +(1.09969 - 3.38449i) q^{33} +(-0.233805 + 0.259667i) q^{34} +(3.15815 + 2.29453i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.13932 - 5.43747i) q^{37} +(-0.284805 + 2.70974i) q^{38} +(-2.97648 + 2.16254i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-5.39771 - 5.99476i) q^{41} +(-3.56620 + 1.58777i) q^{42} +(-9.44211 + 2.00698i) q^{43} +(-3.48089 - 0.739887i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-0.487940 - 1.50172i) q^{46} +(-1.30379 - 4.01265i) q^{47} +(0.913545 + 0.406737i) q^{48} +(-8.05877 - 1.71294i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(-0.319207 + 0.142120i) q^{51} +(2.46182 + 2.73413i) q^{52} +(-0.146274 - 1.39170i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.371981 + 3.53916i) q^{55} +(1.95185 + 3.38070i) q^{56} +(-1.36233 + 2.35963i) q^{57} +(-0.741926 - 0.539041i) q^{58} +(6.16411 - 6.84594i) q^{59} +(0.309017 - 0.951057i) q^{60} +4.56384 q^{61} +(4.27481 - 3.56735i) q^{62} -3.90369 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.46182 - 2.73413i) q^{65} +(-2.87902 - 2.09173i) q^{66} +(-1.34186 + 2.32417i) q^{67} +(0.174708 + 0.302603i) q^{68} +(0.165051 - 1.57036i) q^{69} +(3.15815 - 2.29453i) q^{70} +(0.746758 + 7.10493i) q^{71} +(0.669131 + 0.743145i) q^{72} +(0.290327 - 0.129262i) q^{73} +(-6.14144 + 1.30540i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(2.48911 + 1.10822i) q^{76} +(-4.29284 - 13.2120i) q^{77} +(1.13691 + 3.49906i) q^{78} +(14.9461 + 6.65444i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-7.36934 + 3.28104i) q^{82} +(-6.51855 - 7.23958i) q^{83} +(0.408047 + 3.88231i) q^{84} +(0.282684 - 0.205382i) q^{85} +(-1.00902 + 9.60017i) q^{86} +(-0.458535 - 0.794207i) q^{87} +(-1.77933 + 3.08189i) q^{88} +(4.58172 + 3.32881i) q^{89} +(0.669131 - 0.743145i) q^{90} +(-4.43816 + 13.6593i) q^{91} -1.57901 q^{92} +(5.35621 - 1.52022i) q^{93} -4.21915 q^{94} +(0.841968 - 2.59131i) q^{95} +(0.669131 - 0.743145i) q^{96} +(4.44280 + 3.22788i) q^{97} +(-4.11940 + 7.13502i) q^{98} +(-1.77933 - 3.08189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.408047	−	3.88231i	0.154227	−	1.46737i	−0.594286	−	0.804254i	$-0.702565\pi$
$7$	0.408047	−	3.88231i	0.154227	−	1.46737i	0.748513	−	0.663120i	$-0.230768\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	3.25100	−	1.44744i	0.980213	−	0.436419i	0.146858	−	0.989158i	$-0.453084\pi$
$11$	3.25100	−	1.44744i	0.980213	−	0.436419i	0.833355	+	0.552739i	$0.186417\pi$
$12$	−0.978148	+	0.207912i	−0.282367	+	0.0600189i
$13$	−3.59874	−	0.764935i	−0.998110	−	0.212155i	−0.320240	−	0.947337i	$-0.603763\pi$
$13$	−3.59874	−	0.764935i	−0.998110	−	0.212155i	−0.677870	+	0.735182i	$0.737097\pi$
$14$	−3.56620	−	1.58777i	−0.953107	−	0.424351i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.319207	−	0.142120i	−0.0774192	−	0.0344692i	0.367662	−	0.929960i	$-0.380158\pi$
$17$	−0.319207	−	0.142120i	−0.0774192	−	0.0344692i	−0.445081	+	0.895490i	$0.646825\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	−2.66513	+	0.566490i	−0.611422	+	0.129962i	−0.503207	−	0.864166i	$-0.667847\pi$
$19$	−2.66513	+	0.566490i	−0.611422	+	0.129962i	−0.108215	+	0.994128i	$0.534513\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	−2.61208	−	2.90101i	−0.570002	−	0.633052i
$22$	−0.371981	−	3.53916i	−0.0793067	−	0.754552i
$23$	1.27744	−	0.928117i	0.266365	−	0.193526i	−0.446583	−	0.894742i	$-0.647359\pi$
$23$	1.27744	−	0.928117i	0.266365	−	0.193526i	0.712949	+	0.701216i	$0.247359\pi$
$24$	−0.104528	+	0.994522i	−0.0213368	+	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.83957	+	3.18622i	−0.360769	+	0.624870i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−2.61208	+	2.90101i	−0.493637	+	0.548239i
$29$	0.283390	−	0.872186i	0.0526243	−	0.161961i	−0.921290	−	0.388875i	$-0.872864\pi$
$29$	0.283390	−	0.872186i	0.0526243	−	0.161961i	0.973915	+	0.226914i	$0.0728637\pi$
$30$	1.00000			0.182574
$31$	4.71374	+	2.96321i	0.846613	+	0.532209i
$31$	4.71374	+	2.96321i	0.846613	+	0.532209i
$32$	1.00000			0.176777
$33$	1.09969	−	3.38449i	0.191431	−	0.589163i
$34$	−0.233805	+	0.259667i	−0.0400972	+	0.0445325i
$35$	3.15815	+	2.29453i	0.533825	+	0.387847i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.13932	−	5.43747i	−0.516102	−	0.893914i	−0.999825	−	0.0186935i	$-0.994049\pi$
$37$	−3.13932	−	5.43747i	−0.516102	−	0.893914i	0.483724	−	0.875221i	$-0.339284\pi$
$38$	−0.284805	+	2.70974i	−0.0462015	+	0.439578i
$39$	−2.97648	+	2.16254i	−0.476618	+	0.346284i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	−5.39771	−	5.99476i	−0.842980	−	0.936224i	0.155689	−	0.987806i	$-0.450240\pi$
$41$	−5.39771	−	5.99476i	−0.842980	−	0.936224i	−0.998669	+	0.0515819i	$0.983574\pi$
$42$	−3.56620	+	1.58777i	−0.550277	+	0.244999i
$43$	−9.44211	+	2.00698i	−1.43991	+	0.306062i	−0.860698	−	0.509116i	$-0.829972\pi$
$43$	−9.44211	+	2.00698i	−1.43991	+	0.306062i	−0.579210	+	0.815178i	$0.696639\pi$
$44$	−3.48089	−	0.739887i	−0.524765	−	0.111542i
$45$	0.913545	+	0.406737i	0.136183	+	0.0606327i
$46$	−0.487940	−	1.50172i	−0.0719428	−	0.221417i
$47$	−1.30379	−	4.01265i	−0.190177	−	0.585305i	0.809822	−	0.586676i	$-0.199564\pi$
$47$	−1.30379	−	4.01265i	−0.190177	−	0.585305i	−0.999999	+	0.00137094i	$0.999564\pi$
$48$	0.913545	+	0.406737i	0.131859	+	0.0587074i
$49$	−8.05877	−	1.71294i	−1.15125	−	0.244706i
$50$	−0.978148	+	0.207912i	−0.138331	+	0.0294032i
$51$	−0.319207	+	0.142120i	−0.0446980	+	0.0199008i
$52$	2.46182	+	2.73413i	0.341393	+	0.379155i
$53$	−0.146274	−	1.39170i	−0.0200923	−	0.191165i	0.979872	−	0.199627i	$-0.0639731\pi$
$53$	−0.146274	−	1.39170i	−0.0200923	−	0.191165i	−0.999964	+	0.00846207i	$0.997306\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−0.371981	+	3.53916i	−0.0501579	+	0.477221i
$56$	1.95185	+	3.38070i	0.260826	+	0.451765i
$57$	−1.36233	+	2.35963i	−0.180445	+	0.312541i
$58$	−0.741926	−	0.539041i	−0.0974196	−	0.0707795i
$59$	6.16411	−	6.84594i	0.802499	−	0.891266i	−0.193457	−	0.981109i	$-0.561970\pi$
$59$	6.16411	−	6.84594i	0.802499	−	0.891266i	0.995956	+	0.0898432i	$0.0286366\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	4.56384			0.584340			0.292170	−	0.956366i	$-0.405623\pi$
$61$	4.56384			0.584340			0.292170	+	0.956366i	$0.405623\pi$
$62$	4.27481	−	3.56735i	0.542901	−	0.453054i
$63$	−3.90369			−0.491819
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	2.46182	−	2.73413i	0.305351	−	0.339127i
$66$	−2.87902	−	2.09173i	−0.354382	−	0.257474i
$67$	−1.34186	+	2.32417i	−0.163934	+	0.283942i	−0.936276	−	0.351265i	$-0.885752\pi$
$67$	−1.34186	+	2.32417i	−0.163934	+	0.283942i	0.772342	+	0.635207i	$0.219085\pi$
$68$	0.174708	+	0.302603i	0.0211865	+	0.0366960i
$69$	0.165051	−	1.57036i	0.0198698	−	0.189049i
$70$	3.15815	−	2.29453i	0.377471	−	0.274249i
$71$	0.746758	+	7.10493i	0.0886239	+	0.843200i	0.945049	+	0.326929i	$0.106014\pi$
$71$	0.746758	+	7.10493i	0.0886239	+	0.843200i	−0.856425	+	0.516271i	$0.827320\pi$
$72$	0.669131	+	0.743145i	0.0788578	+	0.0875805i
$73$	0.290327	−	0.129262i	0.0339802	−	0.0151290i	−0.389676	−	0.920952i	$-0.627413\pi$
$73$	0.290327	−	0.129262i	0.0339802	−	0.0151290i	0.423656	+	0.905823i	$0.360746\pi$
$74$	−6.14144	+	1.30540i	−0.713928	+	0.151750i
$75$	−0.978148	−	0.207912i	−0.112947	−	0.0240076i
$76$	2.48911	+	1.10822i	0.285520	+	0.127122i
$77$	−4.29284	−	13.2120i	−0.489214	−	1.50565i
$78$	1.13691	+	3.49906i	0.128730	+	0.396191i
$79$	14.9461	+	6.65444i	1.68157	+	0.748683i	0.999854	+	0.0170643i	$0.00543200\pi$
$79$	14.9461	+	6.65444i	1.68157	+	0.748683i	0.681714	+	0.731618i	$0.261235\pi$
$80$	−0.978148	−	0.207912i	−0.109360	−	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−7.36934	+	3.28104i	−0.813807	+	0.362330i
$83$	−6.51855	−	7.23958i	−0.715503	−	0.794647i	0.270260	−	0.962787i	$-0.412890\pi$
$83$	−6.51855	−	7.23958i	−0.715503	−	0.794647i	−0.985763	+	0.168140i	$0.946224\pi$
$84$	0.408047	+	3.88231i	0.0445216	+	0.423594i
$85$	0.282684	−	0.205382i	0.0306613	−	0.0222768i
$86$	−1.00902	+	9.60017i	−0.108805	+	1.03521i
$87$	−0.458535	−	0.794207i	−0.0491602	−	0.0851479i
$88$	−1.77933	+	3.08189i	−0.189677	+	0.328531i
$89$	4.58172	+	3.32881i	0.485661	+	0.352854i	0.803513	−	0.595287i	$-0.202962\pi$
$89$	4.58172	+	3.32881i	0.485661	+	0.352854i	−0.317852	+	0.948140i	$0.602962\pi$
$90$	0.669131	−	0.743145i	0.0705326	−	0.0783343i
$91$	−4.43816	+	13.6593i	−0.465246	+	1.43188i
$92$	−1.57901			−0.164623
$93$	5.35621	−	1.52022i	0.555413	−	0.157639i
$94$	−4.21915			−0.435172
$95$	0.841968	−	2.59131i	0.0863841	−	0.265863i
$96$	0.669131	−	0.743145i	0.0682929	−	0.0758469i
$97$	4.44280	+	3.22788i	0.451098	+	0.327742i	0.790029	−	0.613069i	$-0.210065\pi$
$97$	4.44280	+	3.22788i	0.451098	+	0.327742i	−0.338931	+	0.940811i	$0.610065\pi$
$98$	−4.11940	+	7.13502i	−0.416123	+	0.720746i
$99$	−1.77933	−	3.08189i	−0.178829	−	0.309742i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	12.7461	−	9.26059i	1.26829	−	0.921463i	0.269152	−	0.963098i	$-0.413256\pi$
$101$	12.7461	−	9.26059i	1.26829	−	0.921463i	0.999133	+	0.0416344i	$0.0132565\pi$
$102$	0.0365239	+	0.347502i	0.00361641	+	0.0344078i
$103$	8.56807	+	9.51580i	0.844237	+	0.937620i	0.998730	−	0.0503740i	$-0.0160413\pi$
$103$	8.56807	+	9.51580i	0.844237	+	0.937620i	−0.154494	+	0.987994i	$0.549375\pi$
$104$	3.36106	−	1.49644i	0.329579	−	0.146738i
$105$	3.81839	−	0.811623i	0.372636	−	0.0792063i
$106$	−1.36879	−	0.290945i	−0.132949	−	0.0282591i
$107$	6.33965	+	2.82259i	0.612877	+	0.272870i	0.689610	−	0.724181i	$-0.257782\pi$
$107$	6.33965	+	2.82259i	0.612877	+	0.272870i	−0.0767326	+	0.997052i	$0.524449\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	4.98518	+	15.3428i	0.477493	+	1.46957i	0.842565	+	0.538594i	$0.181044\pi$
$109$	4.98518	+	15.3428i	0.477493	+	1.46957i	−0.365072	+	0.930979i	$0.618956\pi$
$110$	3.25100	+	1.44744i	0.309970	+	0.138008i
$111$	−6.14144	−	1.30540i	−0.582920	−	0.123904i
$112$	3.81839	−	0.811623i	0.360804	−	0.0766912i
$113$	−0.124622	+	0.0554853i	−0.0117235	+	0.00521962i	−0.412590	−	0.910917i	$-0.635376\pi$
$113$	−0.124622	+	0.0554853i	−0.0117235	+	0.00521962i	0.400867	+	0.916136i	$0.368709\pi$
$114$	1.82316	+	2.02482i	0.170754	+	0.189642i
$115$	0.165051	+	1.57036i	0.0153911	+	0.146437i
$116$	−0.741926	+	0.539041i	−0.0688861	+	0.0500487i
$117$	−0.384574	+	3.65898i	−0.0355539	+	0.338273i
$118$	−4.60606	−	7.97793i	−0.424022	−	0.734428i
$119$	−0.682006	+	1.18127i	−0.0625194	+	0.108287i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	1.11347	−	1.23664i	0.101225	−	0.112421i
$122$	1.41030	−	4.34047i	0.127683	−	0.392968i
$123$	−8.06675			−0.727354
$124$	−2.07176	−	5.16796i	−0.186050	−	0.464096i
$125$	1.00000			0.0894427
$126$	−1.20631	+	3.71263i	−0.107466	+	0.330747i
$127$	−0.341643	+	0.379433i	−0.0303159	+	0.0336692i	−0.758112	−	0.652124i	$-0.773878\pi$
$127$	−0.341643	+	0.379433i	−0.0303159	+	0.0336692i	0.727796	+	0.685794i	$0.240545\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−4.82653	+	8.35979i	−0.424952	+	0.736038i
$130$	−1.83957	−	3.18622i	−0.161341	−	0.279450i
$131$	2.01100	−	19.1334i	0.175702	−	1.67169i	−0.451067	−	0.892490i	$-0.648957\pi$
$131$	2.01100	−	19.1334i	0.175702	−	1.67169i	0.626769	−	0.779205i	$-0.284377\pi$
$132$	−2.87902	+	2.09173i	−0.250586	+	0.182062i
$133$	1.11179	+	10.5780i	0.0964046	+	0.917228i
$134$	1.79576	+	1.99439i	0.155130	+	0.172289i
$135$	0.913545	−	0.406737i	0.0786255	−	0.0350063i
$136$	0.341780	−	0.0726477i	0.0293074	−	0.00622949i
$137$	7.85876	+	1.67043i	0.671419	+	0.142715i	0.530992	−	0.847377i	$-0.321819\pi$
$137$	7.85876	+	1.67043i	0.671419	+	0.142715i	0.140427	+	0.990091i	$0.455153\pi$
$138$	−1.44249	−	0.642240i	−0.122793	−	0.0546711i
$139$	−3.24900	−	9.99940i	−0.275577	−	0.848138i	−0.989066	−	0.147472i	$-0.952886\pi$
$139$	−3.24900	−	9.99940i	−0.275577	−	0.848138i	0.713489	−	0.700666i	$-0.247114\pi$
$140$	−1.20631	−	3.71263i	−0.101952	−	0.313775i
$141$	−3.85438	−	1.71608i	−0.324598	−	0.144520i
$142$	6.98795	+	1.48533i	0.586416	+	0.124646i
$143$	−12.8067	+	2.72214i	−1.07095	+	0.227637i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	0.613640	+	0.681516i	0.0509600	+	0.0565969i
$146$	−0.0332194	−	0.316062i	−0.00274926	−	0.0261574i
$147$	−6.66534	+	4.84265i	−0.549748	+	0.399415i
$148$	−0.656297	+	6.24425i	−0.0539473	+	0.513274i
$149$	3.97780	+	6.88975i	0.325874	+	0.564430i	0.981689	−	0.190492i	$-0.0610082\pi$
$149$	3.97780	+	6.88975i	0.325874	+	0.564430i	−0.655815	+	0.754922i	$0.727675\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	9.54629	+	6.93578i	0.776866	+	0.564426i	0.904037	−	0.427455i	$-0.140590\pi$
$151$	9.54629	+	6.93578i	0.776866	+	0.564426i	−0.127171	+	0.991881i	$0.540590\pi$
$152$	1.82316	−	2.02482i	0.147878	−	0.164235i
$153$	−0.107975	+	0.332314i	−0.00872930	+	0.0268660i
$154$	−13.8919			−1.11944
$155$	−4.92309	+	2.60061i	−0.395432	+	0.208886i
$156$	3.67913			0.294566
$157$	7.30753	−	22.4903i	0.583204	−	1.79492i	−0.0231604	−	0.999732i	$-0.507373\pi$
$157$	7.30753	−	22.4903i	0.583204	−	1.79492i	0.606365	−	0.795187i	$-0.292627\pi$
$158$	10.9473	−	12.1583i	0.870924	−	0.967259i
$159$	−1.13211	−	0.822528i	−0.0897824	−	0.0652307i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−3.08198	−	5.33814i	−0.242894	−	0.420704i
$162$	−0.104528	+	0.994522i	−0.00821253	+	0.0781370i
$163$	−7.76364	+	5.64061i	−0.608095	+	0.441807i	−0.848743	−	0.528806i	$-0.822640\pi$
$163$	−7.76364	+	5.64061i	−0.608095	+	0.441807i	0.240648	+	0.970612i	$0.422640\pi$
$164$	0.843205	+	8.02256i	0.0658432	+	0.626456i
$165$	2.38121	+	2.64460i	0.185377	+	0.205882i
$166$	−8.89959	+	3.96235i	−0.690742	+	0.307538i
$167$	18.9574	−	4.02951i	1.46697	−	0.311813i	0.595931	−	0.803035i	$-0.296783\pi$
$167$	18.9574	−	4.02951i	1.46697	−	0.311813i	0.871034	+	0.491222i	$0.163450\pi$
$168$	3.81839	+	0.811623i	0.294595	+	0.0626181i
$169$	0.489680	+	0.218019i	0.0376677	+	0.0167707i
$170$	−0.107975	−	0.332314i	−0.00828134	−	0.0254874i
$171$	0.841968	+	2.59131i	0.0643869	+	0.198163i
$172$	8.81850	+	3.92625i	0.672404	+	0.299374i
$173$	4.58827	+	0.975267i	0.348840	+	0.0741481i	0.378999	−	0.925397i	$-0.376268\pi$
$173$	4.58827	+	0.975267i	0.348840	+	0.0741481i	−0.0301597	+	0.999545i	$0.509602\pi$
$174$	−0.897031	+	0.190670i	−0.0680037	+	0.0144546i
$175$	−3.56620	+	1.58777i	−0.269579	+	0.120024i
$176$	2.38121	+	2.64460i	0.179490	+	0.199344i
$177$	−0.962929	−	9.16166i	−0.0723782	−	0.688632i
$178$	4.58172	−	3.32881i	0.343414	−	0.249505i
$179$	−1.44569	+	13.7548i	−0.108056	+	1.02808i	0.797344	+	0.603525i	$0.206238\pi$
$179$	−1.44569	+	13.7548i	−0.108056	+	1.02808i	−0.905400	+	0.424559i	$0.860429\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−1.88494	+	3.26481i	−0.140106	+	0.242671i	−0.927537	−	0.373732i	$-0.878078\pi$
$181$	−1.88494	+	3.26481i	−0.140106	+	0.242671i	0.787430	+	0.616404i	$0.211411\pi$
$182$	11.6193	+	8.44189i	0.861277	+	0.625755i
$183$	3.05380	−	3.39159i	0.225744	−	0.250714i
$184$	−0.487940	+	1.50172i	−0.0359714	+	0.110709i
$185$	6.27865			0.461615
$186$	0.209348	−	5.56383i	0.0153501	−	0.407960i
$187$	−1.24345			−0.0909303
$188$	−1.30379	+	4.01265i	−0.0950885	+	0.292652i
$189$	−2.61208	+	2.90101i	−0.190001	+	0.211017i
$190$	−2.20430	−	1.60152i	−0.159917	−	0.116186i
$191$	4.30924	−	7.46382i	0.311806	−	0.540063i	−0.666948	−	0.745105i	$-0.732400\pi$
$191$	4.30924	−	7.46382i	0.311806	−	0.540063i	0.978753	+	0.205041i	$0.0657329\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	1.82488	−	17.3625i	0.131357	−	1.24978i	−0.708004	−	0.706209i	$-0.750404\pi$
$193$	1.82488	−	17.3625i	0.131357	−	1.24978i	0.839361	−	0.543574i	$-0.182929\pi$
$194$	4.44280	−	3.22788i	0.318974	−	0.231749i
$195$	−0.384574	−	3.65898i	−0.0275399	−	0.262025i
$196$	5.51284	+	6.12263i	0.393774	+	0.437331i
$197$	20.3309	−	9.05189i	1.44851	−	0.644920i	0.476358	−	0.879252i	$-0.341957\pi$
$197$	20.3309	−	9.05189i	1.44851	−	0.644920i	0.972157	+	0.234331i	$0.0752900\pi$
$198$	−3.48089	+	0.739887i	−0.247376	+	0.0525815i
$199$	−9.42860	−	2.00411i	−0.668376	−	0.142068i	−0.138787	−	0.990322i	$-0.544320\pi$
$199$	−9.42860	−	2.00411i	−0.668376	−	0.142068i	−0.529589	+	0.848255i	$0.677654\pi$
$200$	0.913545	+	0.406737i	0.0645974	+	0.0287606i
$201$	0.829314	+	2.55236i	0.0584953	+	0.180030i
$202$	−4.86858	−	14.9840i	−0.342552	−	1.05427i
$203$	−3.27046	−	1.45610i	−0.229541	−	0.102198i
$204$	0.341780	+	0.0726477i	0.0239294	+	0.00508635i
$205$	7.89047	−	1.67717i	0.551094	−	0.117139i
$206$	11.6977	−	5.20817i	0.815020	−	0.362870i
$207$	−1.05656	−	1.17343i	−0.0734361	−	0.0815591i
$208$	−0.384574	−	3.65898i	−0.0266654	−	0.253705i
$209$	−7.84436	+	5.69926i	−0.542606	+	0.394226i
$210$	0.408047	−	3.88231i	0.0281579	−	0.267905i
$211$	−6.40630	−	11.0960i	−0.441028	−	0.763883i	0.556738	−	0.830688i	$-0.312053\pi$
$211$	−6.40630	−	11.0960i	−0.441028	−	0.763883i	−0.997766	+	0.0668051i	$0.978719\pi$
$212$	−0.699684	+	1.21189i	−0.0480545	+	0.0832328i
$213$	5.77967	+	4.19918i	0.396016	+	0.287723i
$214$	4.64351	−	5.15714i	0.317424	−	0.352535i
$215$	2.98296	−	9.18060i	0.203436	−	0.626112i
$216$	1.00000			0.0680414
$217$	13.4275	−	17.0911i	0.911520	−	1.16022i
$218$	16.1324			1.09262
$219$	0.0982064	−	0.302248i	0.00663617	−	0.0204240i
$220$	2.38121	−	2.64460i	0.160541	−	0.178299i
$221$	1.04003	+	0.755626i	0.0699600	+	0.0508289i
$222$	−3.13932	+	5.43747i	−0.210698	+	0.364939i
$223$	0.279126	+	0.483460i	0.0186916	+	0.0323749i	0.875220	−	0.483725i	$-0.160717\pi$
$223$	0.279126	+	0.483460i	0.0186916	+	0.0323749i	−0.856528	+	0.516100i	$0.827383\pi$
$224$	0.408047	−	3.88231i	0.0272638	−	0.259398i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	0.0142593	+	0.135669i	0.000948517	+	0.00902454i
$227$	−3.21688	−	3.57271i	−0.213512	−	0.237129i	0.626870	−	0.779124i	$-0.284336\pi$
$227$	−3.21688	−	3.57271i	−0.213512	−	0.237129i	−0.840382	+	0.541995i	$0.817669\pi$
$228$	2.48911	−	1.10822i	0.164845	−	0.0733938i
$229$	−15.2539	+	3.24232i	−1.00801	+	0.214258i	−0.682190	−	0.731175i	$-0.738972\pi$
$229$	−15.2539	+	3.24232i	−1.00801	+	0.214258i	−0.325816	+	0.945433i	$0.605639\pi$
$230$	1.54450	+	0.328294i	0.101841	+	0.0216471i
$231$	−12.6909	−	5.65035i	−0.834999	−	0.371766i
$232$	0.283390	+	0.872186i	0.0186055	+	0.0572618i
$233$	8.67929	+	26.7121i	0.568599	+	1.74997i	0.657007	+	0.753885i	$0.271822\pi$
$233$	8.67929	+	26.7121i	0.568599	+	1.74997i	−0.0884072	+	0.996084i	$0.528178\pi$
$234$	3.36106	+	1.49644i	0.219719	+	0.0978252i
$235$	4.12695	+	0.877210i	0.269212	+	0.0572229i
$236$	−9.01081	+	1.91531i	−0.586554	+	0.124676i
$237$	14.9461	−	6.65444i	0.970854	−	0.432252i
$238$	0.912702	+	1.01366i	0.0591617	+	0.0657057i
$239$	2.88524	+	27.4513i	0.186631	+	1.77567i	0.541443	+	0.840737i	$0.317878\pi$
$239$	2.88524	+	27.4513i	0.186631	+	1.77567i	−0.354812	+	0.934938i	$0.615455\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	−1.70191	+	16.1926i	−0.109630	+	1.04306i	0.791991	+	0.610532i	$0.209045\pi$
$241$	−1.70191	+	16.1926i	−0.109630	+	1.04306i	−0.901621	+	0.432527i	$0.857622\pi$
$242$	−0.832029	−	1.44112i	−0.0534848	−	0.0926385i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.69222	−	2.68256i	−0.236370	−	0.171733i
$245$	5.51284	−	6.12263i	0.352202	−	0.391160i
$246$	−2.49276	+	7.67193i	−0.158933	+	0.489144i
$247$	10.0244			0.637838
$248$	−5.55523	+	0.373377i	−0.352758	+	0.0237095i
$249$	−9.74181			−0.617362
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	16.2387	−	18.0349i	1.02498	−	1.13836i	0.0346812	−	0.999398i	$-0.488958\pi$
$251$	16.2387	−	18.0349i	1.02498	−	1.13836i	0.990298	−	0.138957i	$-0.0443749\pi$
$252$	3.15815	+	2.29453i	0.198945	+	0.144542i
$253$	2.80957	−	4.86632i	0.176636	−	0.305943i
$254$	0.255289	+	0.442173i	0.0160182	+	0.0277444i
$255$	0.0365239	−	0.347502i	0.00228722	−	0.0217614i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	0.0172527	+	0.164149i	0.00107620	+	0.0102393i	0.995047	−	0.0994074i	$-0.0316947\pi$
$257$	0.0172527	+	0.164149i	0.00107620	+	0.0102393i	−0.993971	+	0.109647i	$0.965028\pi$
$258$	6.45915	+	7.17362i	0.402129	+	0.446610i
$259$	−22.3909	+	9.96908i	−1.39130	+	0.619448i
$260$	−3.59874	+	0.764935i	−0.223184	+	0.0474392i
$261$	−0.897031	−	0.190670i	−0.0555248	−	0.0118022i
$262$	−17.5755	−	7.82513i	−1.08582	−	0.483438i
$263$	−6.00127	−	18.4700i	−0.370054	−	1.13891i	−0.946755	−	0.321954i	$-0.895660\pi$
$263$	−6.00127	−	18.4700i	−0.370054	−	1.13891i	0.576701	−	0.816955i	$-0.304340\pi$
$264$	1.09969	+	3.38449i	0.0676810	+	0.208301i
$265$	1.27839	+	0.569174i	0.0785307	+	0.0349641i
$266$	10.4038	+	2.21140i	0.637900	+	0.135590i
$267$	5.53956	−	1.17747i	0.339016	−	0.0720600i
$268$	2.45170	−	1.09157i	0.149761	−	0.0666780i
$269$	7.12792	+	7.91635i	0.434597	+	0.482669i	0.920165	−	0.391530i	$-0.128054\pi$
$269$	7.12792	+	7.91635i	0.434597	+	0.482669i	−0.485569	+	0.874199i	$0.661387\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	−20.7782	+	15.0962i	−1.26219	+	0.917031i	−0.998863	−	0.0476768i	$-0.984818\pi$
$271$	−20.7782	+	15.0962i	−1.26219	+	0.917031i	−0.263322	+	0.964708i	$0.584818\pi$
$272$	0.0365239	−	0.347502i	0.00221459	−	0.0210704i
$273$	7.18110	+	12.4380i	0.434620	+	0.752784i
$274$	4.01716	−	6.95793i	0.242686	−	0.420344i
$275$	−2.87902	−	2.09173i	−0.173611	−	0.126136i
$276$	−1.05656	+	1.17343i	−0.0635975	+	0.0706322i
$277$	−2.17831	+	6.70414i	−0.130882	+	0.402813i	−0.994927	−	0.100602i	$-0.967923\pi$
$277$	−2.17831	+	6.70414i	−0.130882	+	0.402813i	0.864045	+	0.503415i	$0.167923\pi$
$278$	−10.5140			−0.630587
$279$	2.45426	−	4.99766i	0.146933	−	0.299202i
$280$	−3.90369			−0.233290
$281$	−1.42437	+	4.38376i	−0.0849707	+	0.261513i	−0.984510	−	0.175326i	$-0.943902\pi$
$281$	−1.42437	+	4.38376i	−0.0849707	+	0.261513i	0.899540	+	0.436839i	$0.143902\pi$
$282$	−2.82316	+	3.13544i	−0.168117	+	0.186713i
$283$	−3.04438	−	2.21187i	−0.180970	−	0.131482i	0.493612	−	0.869682i	$-0.335676\pi$
$283$	−3.04438	−	2.21187i	−0.180970	−	0.131482i	−0.674582	+	0.738200i	$0.735676\pi$
$284$	3.57203	−	6.18694i	0.211961	−	0.367127i
$285$	−1.36233	−	2.35963i	−0.0806976	−	0.139772i
$286$	−1.36857	+	13.0211i	−0.0809251	+	0.769951i
$287$	−25.4760	+	18.5094i	−1.50380	+	1.09258i
$288$	−0.104528	−	0.994522i	−0.00615940	−	0.0586028i
$289$	−11.2935	−	12.5427i	−0.664325	−	0.737808i
$290$	0.837786	−	0.373006i	0.0491965	−	0.0219037i
$291$	5.37160	−	1.14177i	0.314889	−	0.0669317i
$292$	−0.310858	−	0.0660748i	−0.0181916	−	0.00386674i
$293$	−8.77662	−	3.90760i	−0.512735	−	0.228284i	0.134025	−	0.990978i	$-0.457210\pi$
$293$	−8.77662	−	3.90760i	−0.512735	−	0.228284i	−0.646760	+	0.762693i	$0.723877\pi$
$294$	2.54593	+	7.83557i	0.148482	+	0.456980i
$295$	2.84670	+	8.76125i	0.165741	+	0.510100i
$296$	5.73583	+	2.55376i	0.333388	+	0.148434i
$297$	−3.48089	−	0.739887i	−0.201982	−	0.0429326i
$298$	7.78175	−	1.65406i	0.450785	−	0.0958172i
$299$	−5.30713	+	2.36289i	−0.306919	+	0.136649i
$300$	0.669131	+	0.743145i	0.0386323	+	0.0429055i
$301$	3.93890	+	37.4761i	0.227034	+	2.16009i
$302$	9.54629	−	6.93578i	0.549327	−	0.399110i
$303$	1.64685	−	15.6687i	0.0946092	−	0.900146i
$304$	−1.36233	−	2.35963i	−0.0781352	−	0.135334i
$305$	−2.28192	+	3.95240i	−0.130662	+	0.226314i
$306$	0.282684	+	0.205382i	0.0161599	+	0.0117409i
$307$	16.5789	−	18.4127i	0.946208	−	1.05087i	−0.0524265	−	0.998625i	$-0.516696\pi$
$307$	16.5789	−	18.4127i	0.946208	−	1.05087i	0.998634	−	0.0522454i	$-0.0166378\pi$
$308$	−4.29284	+	13.2120i	−0.244607	+	0.752823i
$309$	12.8048			0.728438
$310$	0.952012	+	5.48577i	0.0540706	+	0.311571i
$311$	18.1428			1.02879			0.514393	−	0.857555i	$-0.328017\pi$
$311$	18.1428			1.02879			0.514393	+	0.857555i	$0.328017\pi$
$312$	1.13691	−	3.49906i	0.0643651	−	0.198095i
$313$	7.23936	−	8.04012i	0.409193	−	0.454454i	−0.502957	−	0.864311i	$-0.667755\pi$
$313$	7.23936	−	8.04012i	0.409193	−	0.454454i	0.912150	+	0.409857i	$0.134421\pi$
$314$	−19.1314	−	13.8997i	−1.07965	−	0.784408i
$315$	1.95185	−	3.38070i	0.109974	−	0.190481i
$316$	−8.18028	−	14.1687i	−0.460177	−	0.797049i
$317$	−2.46052	+	23.4103i	−0.138197	+	1.31485i	0.677135	+	0.735859i	$0.263221\pi$
$317$	−2.46052	+	23.4103i	−0.138197	+	1.31485i	−0.815332	+	0.578994i	$0.803445\pi$
$318$	−1.13211	+	0.822528i	−0.0634857	+	0.0461251i
$319$	−0.341133	−	3.24566i	−0.0190998	−	0.181722i
$320$	0.669131	+	0.743145i	0.0374055	+	0.0415431i
$321$	6.33965	−	2.82259i	0.353845	−	0.157542i
$322$	−6.02926	+	1.28156i	−0.335997	+	0.0714184i
$323$	0.931238	+	0.197941i	0.0518154	+	0.0110137i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	1.13691	+	3.49906i	0.0630647	+	0.194093i
$326$	2.96545	+	9.12670i	0.164241	+	0.505481i
$327$	14.7377	+	6.56163i	0.814994	+	0.362859i
$328$	7.89047	+	1.67717i	0.435678	+	0.0926063i
$329$	−16.1103	+	3.42436i	−0.888191	+	0.188791i
$330$	3.25100	−	1.44744i	0.178962	−	0.0796788i
$331$	5.68955	+	6.31888i	0.312726	+	0.347317i	0.878933	−	0.476946i	$-0.158256\pi$
$331$	5.68955	+	6.31888i	0.312726	+	0.347317i	−0.566207	+	0.824263i	$0.691590\pi$
$332$	1.01830	+	9.68845i	0.0558863	+	0.531723i
$333$	−5.07953	+	3.69050i	−0.278357	+	0.202238i
$334$	2.02586	−	19.2747i	0.110850	−	1.05467i
$335$	−1.34186	−	2.32417i	−0.0733135	−	0.126983i
$336$	1.95185	−	3.38070i	0.106482	−	0.184432i
$337$	9.13874	+	6.63969i	0.497819	+	0.361687i	0.808183	−	0.588931i	$-0.200451\pi$
$337$	9.13874	+	6.63969i	0.497819	+	0.361687i	−0.310364	+	0.950618i	$0.600451\pi$
$338$	0.358668	−	0.398341i	0.0195090	−	0.0216669i
$339$	−0.0421548	+	0.129739i	−0.00228953	+	0.00704646i
$340$	−0.349416			−0.0189497
$341$	19.6134	+	2.81056i	1.06213	+	0.152200i
$342$	2.72467			0.147333
$343$	−1.49438	+	4.59924i	−0.0806891	+	0.248336i
$344$	6.45915	−	7.17362i	0.348254	−	0.386775i
$345$	1.27744	+	0.928117i	0.0687752	+	0.0499681i
$346$	2.34539	−	4.06233i	0.126089	−	0.218392i
$347$	−4.29383	−	7.43714i	−0.230505	−	0.399246i	0.727452	−	0.686159i	$-0.240704\pi$
$347$	−4.29383	−	7.43714i	−0.230505	−	0.399246i	−0.957957	+	0.286912i	$0.907371\pi$
$348$	−0.0958600	+	0.912047i	−0.00513864	+	0.0488909i
$349$	15.7185	−	11.4201i	0.841390	−	0.611306i	−0.0813685	−	0.996684i	$-0.525929\pi$
$349$	15.7185	−	11.4201i	0.841390	−	0.611306i	0.922759	+	0.385378i	$0.125929\pi$
$350$	0.408047	+	3.88231i	0.0218110	+	0.207518i
$351$	2.46182	+	2.73413i	0.131402	+	0.145937i
$352$	3.25100	−	1.44744i	0.173279	−	0.0771487i
$353$	0.749837	−	0.159383i	0.0399098	−	0.00848309i	−0.187914	−	0.982186i	$-0.560172\pi$
$353$	0.749837	−	0.159383i	0.0399098	−	0.00848309i	0.227823	+	0.973702i	$0.426839\pi$
$354$	−9.01081	−	1.91531i	−0.478919	−	0.101797i
$355$	−6.52643	−	2.90575i	−0.346387	−	0.154221i
$356$	−1.75006	−	5.38613i	−0.0927530	−	0.285465i
$357$	0.421503	+	1.29725i	0.0223083	+	0.0686579i
$358$	12.6349	+	5.62541i	0.667774	+	0.297312i
$359$	−9.32021	−	1.98107i	−0.491902	−	0.104557i	−0.0447191	−	0.999000i	$-0.514239\pi$
$359$	−9.32021	−	1.98107i	−0.491902	−	0.104557i	−0.447183	+	0.894443i	$0.647573\pi$
$360$	−0.978148	+	0.207912i	−0.0515529	+	0.0109579i
$361$	−10.5754	+	4.70846i	−0.556599	+	0.247814i
$362$	2.52254	+	2.80157i	0.132582	+	0.147247i
$363$	−0.173941	−	1.65494i	−0.00912956	−	0.0868619i
$364$	11.6193	−	8.44189i	0.609015	−	0.442475i
$365$	−0.0332194	+	0.316062i	−0.00173878	+	0.0165434i
$366$	−2.28192	−	3.95240i	−0.119278	−	0.206595i
$367$	−9.71602	+	16.8286i	−0.507172	+	0.878448i	0.492793	+	0.870146i	$0.335976\pi$
$367$	−9.71602	+	16.8286i	−0.507172	+	0.878448i	−0.999966	+	0.00830184i	$0.997357\pi$
$368$	1.27744	+	0.928117i	0.0665913	+	0.0483814i
$369$	−5.39771	+	5.99476i	−0.280993	+	0.312075i
$370$	1.94021	−	5.97135i	0.100867	−	0.310436i
$371$	−5.46270			−0.283609
$372$	−5.22682	−	1.91842i	−0.270998	−	0.0994654i
$373$	24.3384			1.26019			0.630096	−	0.776517i	$-0.283015\pi$
$373$	24.3384			1.26019			0.630096	+	0.776517i	$0.283015\pi$
$374$	−0.384248	+	1.18259i	−0.0198690	+	0.0611505i
$375$	0.669131	−	0.743145i	0.0345538	−	0.0383758i
$376$	3.41336	+	2.47995i	0.176031	+	0.127894i
$377$	−1.68701	+	2.92199i	−0.0868856	+	0.150490i
$378$	1.95185	+	3.38070i	0.100392	+	0.173884i
$379$	−1.58640	+	15.0936i	−0.0814879	+	0.775305i	0.875116	+	0.483913i	$0.160785\pi$
$379$	−1.58640	+	15.0936i	−0.0814879	+	0.775305i	−0.956604	+	0.291392i	$0.905882\pi$
$380$	−2.20430	+	1.60152i	−0.113078	+	0.0821562i
$381$	0.0533699	+	0.507780i	0.00273422	+	0.0260144i
$382$	−5.76689	−	6.40478i	−0.295060	−	0.327697i
$383$	−10.3658	+	4.61517i	−0.529670	+	0.235824i	−0.654105	−	0.756404i	$-0.726955\pi$
$383$	−10.3658	+	4.61517i	−0.529670	+	0.235824i	0.124436	+	0.992228i	$0.460288\pi$
$384$	−0.978148	+	0.207912i	−0.0499159	+	0.0106099i
$385$	13.5883	+	2.88829i	0.692526	+	0.147201i
$386$	−15.9488	−	7.10088i	−0.811775	−	0.361425i
$387$	2.98296	+	9.18060i	0.151632	+	0.466676i
$388$	−1.69700	−	5.22283i	−0.0861521	−	0.265149i
$389$	7.14275	+	3.18016i	0.362152	+	0.161240i	0.579743	−	0.814800i	$-0.303153\pi$
$389$	7.14275	+	3.18016i	0.362152	+	0.161240i	−0.217591	+	0.976040i	$0.569820\pi$
$390$	−3.59874	−	0.764935i	−0.182229	−	0.0387340i
$391$	−0.539674	+	0.114711i	−0.0272925	+	0.00580119i
$392$	7.52653	−	3.35103i	0.380147	−	0.169252i
$393$	−12.8733	−	14.2972i	−0.649371	−	0.721200i
$394$	−2.32627	−	22.1330i	−0.117196	−	1.11504i
$395$	−13.2360	+	9.61649i	−0.665974	+	0.483858i
$396$	−0.371981	+	3.53916i	−0.0186928	+	0.177850i
$397$	−15.2487	−	26.4115i	−0.765309	−	1.32555i	−0.940083	−	0.340946i	$-0.889253\pi$
$397$	−15.2487	−	26.4115i	−0.765309	−	1.32555i	0.174774	−	0.984609i	$-0.444081\pi$
$398$	−4.81962	+	8.34783i	−0.241586	+	0.418439i
$399$	8.60491	+	6.25183i	0.430784	+	0.312983i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	3.56308	−	10.9660i	0.177932	−	0.547617i	−0.821824	−	0.569742i	$-0.807043\pi$
$401$	3.56308	−	10.9660i	0.177932	−	0.547617i	0.999755	+	0.0221248i	$0.00704312\pi$
$402$	2.68372			0.133852
$403$	−14.6968	−	14.2695i	−0.732102	−	0.710816i
$404$	−15.7551			−0.783843
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	−2.39546	+	2.66043i	−0.118885	+	0.132035i
$407$	−18.0763	−	13.1332i	−0.896010	−	0.650990i
$408$	0.174708	−	0.302603i	0.00864934	−	0.0149811i
$409$	−1.36192	−	2.35891i	−0.0673426	−	0.116641i	0.830388	−	0.557185i	$-0.188119\pi$
$409$	−1.36192	−	2.35891i	−0.0673426	−	0.116641i	−0.897731	+	0.440545i	$0.854785\pi$
$410$	0.843205	−	8.02256i	0.0416429	−	0.396206i
$411$	6.49991	−	4.72246i	0.320617	−	0.232942i
$412$	−1.33846	−	12.7346i	−0.0659414	−	0.627390i
$413$	−24.0628	−	26.7244i	−1.18405	−	1.31502i
$414$	−1.44249	+	0.642240i	−0.0708947	+	0.0315644i
$415$	9.52893	−	2.02544i	0.467757	−	0.0994248i
$416$	−3.59874	−	0.764935i	−0.176443	−	0.0375040i
$417$	−9.60501	−	4.27643i	−0.470359	−	0.209418i
$418$	2.99628	+	9.22160i	0.146553	+	0.451043i
$419$	10.7131	+	32.9717i	0.523372	+	1.61077i	0.767514	+	0.641032i	$0.221494\pi$
$419$	10.7131	+	32.9717i	0.523372	+	1.61077i	−0.244142	+	0.969739i	$0.578506\pi$
$420$	−3.56620	−	1.58777i	−0.174013	−	0.0774755i
$421$	−27.1368	−	5.76810i	−1.32257	−	0.281120i	−0.508084	−	0.861308i	$-0.669646\pi$
$421$	−27.1368	−	5.76810i	−1.32257	−	0.281120i	−0.814483	+	0.580187i	$0.802979\pi$
$422$	−12.5326	+	2.66389i	−0.610078	+	0.129676i
$423$	−3.85438	+	1.71608i	−0.187406	+	0.0834387i
$424$	0.936360	+	1.03993i	0.0454737	+	0.0505036i
$425$	0.0365239	+	0.347502i	0.00177167	+	0.0168563i
$426$	5.77967	−	4.19918i	0.280026	−	0.203451i
$427$	1.86226	−	17.7182i	0.0901211	−	0.857445i
$428$	−3.46981	−	6.00988i	−0.167719	−	0.290498i
$429$	−6.54639	+	11.3387i	−0.316063	+	0.547437i
$430$	−7.80948	−	5.67392i	−0.376607	−	0.273621i
$431$	−11.6371	+	12.9243i	−0.560539	+	0.622542i	−0.955084	−	0.296335i	$-0.904236\pi$
$431$	−11.6371	+	12.9243i	−0.560539	+	0.622542i	0.394545	+	0.918877i	$0.370902\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	5.44967			0.261895			0.130947	−	0.991389i	$-0.458198\pi$
$433$	5.44967			0.261895			0.130947	+	0.991389i	$0.458198\pi$
$434$	−12.1052	−	18.0518i	−0.581070	−	0.866513i
$435$	0.917071			0.0439702
$436$	4.98518	−	15.3428i	0.238747	−	0.734787i
$437$	−2.87878	+	3.19721i	−0.137711	+	0.152943i
$438$	−0.257108	−	0.186800i	−0.0122851	−	0.00892563i
$439$	−7.88467	+	13.6567i	−0.376315	+	0.651796i	−0.990523	−	0.137348i	$-0.956142\pi$
$439$	−7.88467	+	13.6567i	−0.376315	+	0.651796i	0.614208	+	0.789144i	$0.289476\pi$
$440$	−1.77933	−	3.08189i	−0.0848262	−	0.146923i
$441$	−0.861190	+	8.19368i	−0.0410090	+	0.390175i
$442$	1.04003	−	0.755626i	0.0494692	−	0.0359415i
$443$	−1.61396	−	15.3558i	−0.0766816	−	0.729577i	−0.963545	−	0.267545i	$-0.913787\pi$
$443$	−1.61396	−	15.3558i	−0.0766816	−	0.729577i	0.886864	−	0.462031i	$-0.152879\pi$
$444$	4.20124	+	4.66594i	0.199382	+	0.221436i
$445$	−5.17370	+	2.30348i	−0.245257	+	0.109195i
$446$	0.546052	−	0.116067i	0.0258563	−	0.00549593i
$447$	7.78175	+	1.65406i	0.368064	+	0.0782344i
$448$	−3.56620	−	1.58777i	−0.168487	−	0.0750153i
$449$	−7.38907	−	22.7412i	−0.348712	−	1.07322i	−0.959567	−	0.281481i	$-0.909174\pi$
$449$	−7.38907	−	22.7412i	−0.348712	−	1.07322i	0.610855	−	0.791742i	$-0.290826\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	−26.2250	−	11.6761i	−1.23489	−	0.549806i
$452$	0.133435	+	0.0283624i	0.00627625	+	0.00133406i
$453$	11.5420	−	2.45333i	0.542291	−	0.115267i
$454$	−4.39192	+	1.95541i	−0.206123	+	0.0917719i
$455$	−9.61019	−	10.6732i	−0.450533	−	0.500367i
$456$	−0.284805	−	2.70974i	−0.0133372	−	0.126895i
$457$	12.5333	−	9.10598i	0.586283	−	0.425960i	−0.254701	−	0.967020i	$-0.581977\pi$
$457$	12.5333	−	9.10598i	0.586283	−	0.425960i	0.840984	+	0.541060i	$0.181977\pi$
$458$	−1.63009	+	15.5093i	−0.0761691	+	0.724700i
$459$	0.174708	+	0.302603i	0.00815467	+	0.0141243i
$460$	0.789503	−	1.36746i	0.0368108	−	0.0637581i
$461$	−29.9609	−	21.7679i	−1.39542	−	1.01383i	−0.995246	−	0.0973925i	$-0.968950\pi$
$461$	−29.9609	−	21.7679i	−1.39542	−	1.01383i	−0.400174	−	0.916439i	$-0.631050\pi$
$462$	−9.29550	+	10.3237i	−0.432466	+	0.480302i
$463$	−11.8366	+	36.4294i	−0.550094	+	1.69302i	0.158465	+	0.987365i	$0.449345\pi$
$463$	−11.8366	+	36.4294i	−0.550094	+	1.69302i	−0.708559	+	0.705651i	$0.750655\pi$
$464$	0.917071			0.0425739
$465$	−1.36156	+	5.39872i	−0.0631407	+	0.250360i
$466$	28.0868			1.30110
$467$	−3.26146	+	10.0377i	−0.150922	+	0.464491i	−0.997725	−	0.0674160i	$-0.978525\pi$
$467$	−3.26146	+	10.0377i	−0.150922	+	0.464491i	0.846803	+	0.531907i	$0.178525\pi$
$468$	2.46182	−	2.73413i	0.113798	−	0.126385i
$469$	8.47558	+	6.15787i	0.391366	+	0.284344i
$470$	2.10957	−	3.65389i	0.0973074	−	0.168541i
$471$	−11.8238	−	20.4795i	−0.544813	−	0.943644i
$472$	−0.962929	+	9.16166i	−0.0443224	+	0.421699i
$473$	−27.7913	+	20.1916i	−1.27784	+	0.928409i
$474$	−1.71014	−	16.2709i	−0.0785495	−	0.747349i
$475$	1.82316	+	2.02482i	0.0836522	+	0.0929052i
$476$	1.24609	−	0.554794i	0.0571143	−	0.0254289i
$477$	−1.36879	+	0.290945i	−0.0626725	+	0.0133215i
$478$	26.9993	+	5.73888i	1.23492	+	0.262490i
$479$	−7.92955	−	3.53046i	−0.362310	−	0.161311i	0.217504	−	0.976059i	$-0.430208\pi$
$479$	−7.92955	−	3.53046i	−0.362310	−	0.161311i	−0.579815	+	0.814748i	$0.696875\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	7.13829	+	21.9694i	0.325478	+	1.00172i
$482$	14.8742	+	6.62241i	0.677501	+	0.301643i
$483$	−6.02926	−	1.28156i	−0.274341	−	0.0583129i
$484$	−1.62769	+	0.345977i	−0.0739861	+	0.0157262i
$485$	−5.01683	+	2.23364i	−0.227802	+	0.101424i
$486$	0.669131	+	0.743145i	0.0303524	+	0.0337097i
$487$	2.43700	+	23.1865i	0.110431	+	1.05068i	0.899663	+	0.436586i	$0.143813\pi$
$487$	2.43700	+	23.1865i	0.110431	+	1.05068i	−0.789231	+	0.614096i	$0.789521\pi$
$488$	−3.69222	+	2.68256i	−0.167139	+	0.121434i
$489$	−1.00310	+	9.54381i	−0.0453615	+	0.431586i
$490$	−4.11940	−	7.13502i	−0.186096	−	0.322327i
$491$	8.58789	−	14.8747i	0.387566	−	0.671284i	−0.604555	−	0.796563i	$-0.706649\pi$
$491$	8.58789	−	14.8747i	0.387566	−	0.671284i	0.992122	+	0.125279i	$0.0399825\pi$
$492$	6.52613	+	4.74151i	0.294221	+	0.213764i
$493$	−0.214416	+	0.238133i	−0.00965680	+	0.0107250i
$494$	3.09771	−	9.53378i	0.139373	−	0.428945i
$495$	3.55866			0.159950
$496$	−1.36156	+	5.39872i	−0.0611357	+	0.242410i
$497$	27.8882			1.25096
$498$	−3.01039	+	9.26502i	−0.134899	+	0.415175i
$499$	−22.3261	+	24.7957i	−0.999455	+	1.11001i	−0.00552560	+	0.999985i	$0.501759\pi$
$499$	−22.3261	+	24.7957i	−0.999455	+	1.11001i	−0.993929	+	0.110022i	$0.964908\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	9.69045	−	16.7843i	0.432937	−	0.749869i
$502$	−12.1342	−	21.0171i	−0.541576	−	0.938037i
$503$	0.218679	−	2.08059i	0.00975042	−	0.0927690i	−0.988564	−	0.150799i	$-0.951815\pi$
$503$	0.218679	−	2.08059i	0.00975042	−	0.0927690i	0.998315	+	0.0580302i	$0.0184820\pi$
$504$	3.15815	−	2.29453i	0.140675	−	0.102207i
$505$	1.64685	+	15.6687i	0.0732839	+	0.697250i
$506$	−3.75994	−	4.17584i	−0.167150	−	0.185639i
$507$	0.489680	−	0.218019i	0.0217474	−	0.00968259i
$508$	0.499420	−	0.106155i	0.0221582	−	0.00470987i
$509$	31.6609	+	6.72974i	1.40335	+	0.298290i	0.846528	−	0.532344i	$-0.178689\pi$
$509$	31.6609	+	6.72974i	1.40335	+	0.298290i	0.556818	+	0.830634i	$0.312022\pi$
$510$	−0.319207	−	0.142120i	−0.0141347	−	0.00629319i
$511$	−0.383367	−	1.17988i	−0.0169592	−	0.0521950i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	2.48911	+	1.10822i	0.109897	+	0.0489292i
$514$	0.161446	+	0.0343164i	0.00712108	+	0.00151363i
$515$	−12.5250	+	2.66226i	−0.551916	+	0.117313i
$516$	8.81850	−	3.92625i	0.388213	−	0.172844i
$517$	−10.0467	−	11.1580i	−0.441852	−	0.490726i
$518$	2.56198	+	24.3756i	0.112567	+	1.07100i
$519$	3.79492	−	2.75717i	0.166578	−	0.121026i
$520$	−0.384574	+	3.65898i	−0.0168647	+	0.160457i
$521$	−0.966712	−	1.67439i	−0.0423524	−	0.0733566i	0.844072	−	0.536230i	$-0.180152\pi$
$521$	−0.966712	−	1.67439i	−0.0423524	−	0.0733566i	−0.886425	+	0.462873i	$0.846819\pi$
$522$	−0.458535	+	0.794207i	−0.0200695	+	0.0347615i
$523$	−14.1269	−	10.2638i	−0.617726	−	0.448804i	0.234401	−	0.972140i	$-0.424687\pi$
$523$	−14.1269	−	10.2638i	−0.617726	−	0.448804i	−0.852126	+	0.523336i	$0.824687\pi$
$524$	−12.8733	+	14.2972i	−0.562372	+	0.624577i
$525$	−1.20631	+	3.71263i	−0.0526476	+	0.162033i
$526$	−19.4205			−0.846774
$527$	−1.08353	−	1.61580i	−0.0471992	−	0.0703853i
$528$	3.55866			0.154871
$529$	−6.33693	+	19.5031i	−0.275519	+	0.847959i
$530$	0.936360	−	1.03993i	0.0406729	−	0.0451718i
$531$	−7.45276	−	5.41475i	−0.323422	−	0.234980i
$532$	5.31813	−	9.21127i	0.230570	−	0.399359i
$533$	14.8393	+	25.7024i	0.642762	+	1.11330i
$534$	0.591978	−	5.63229i	0.0256174	−	0.243733i
$535$	−5.61426	+	4.07900i	−0.242726	+	0.176351i
$536$	−0.280525	−	2.66901i	−0.0121168	−	0.115284i
$537$	9.25448	+	10.2781i	0.399360	+	0.443534i
$538$	9.73155	−	4.33276i	0.419557	−	0.186799i
$539$	−28.6784	+	6.09579i	−1.23527	+	0.262564i
$540$	−0.978148	−	0.207912i	−0.0420928	−	0.00894709i
$541$	−26.2770	−	11.6993i	−1.12973	−	0.502990i	−0.245203	−	0.969472i	$-0.578855\pi$
$541$	−26.2770	−	11.6993i	−1.12973	−	0.502990i	−0.884531	+	0.466481i	$0.845521\pi$
$542$	7.93656	+	24.4262i	0.340905	+	1.04920i
$543$	1.16496	+	3.58537i	0.0499931	+	0.153863i
$544$	−0.319207	−	0.142120i	−0.0136859	−	0.00609336i
$545$	−15.7798	−	3.35411i	−0.675934	−	0.143674i
$546$	14.0484	−	2.98607i	0.601214	−	0.127792i
$547$	−30.8809	+	13.7491i	−1.32037	+	0.587868i	−0.941323	−	0.337508i	$-0.890416\pi$
$547$	−30.8809	+	13.7491i	−1.32037	+	0.587868i	−0.379051	+	0.925376i	$0.623749\pi$
$548$	−5.37601	−	5.97067i	−0.229652	−	0.255054i
$549$	−0.477051	−	4.53884i	−0.0203600	−	0.193713i
$550$	−2.87902	+	2.09173i	−0.122762	+	0.0891916i
$551$	−0.261187	+	2.48502i	−0.0111269	+	0.105866i
$552$	0.789503	+	1.36746i	0.0336035	+	0.0582030i
$553$	31.9333	−	55.3101i	1.35794	−	2.35202i
$554$	5.70288	+	4.14339i	0.242292	+	0.176036i
$555$	4.20124	−	4.66594i	0.178333	−	0.198058i
$556$	−3.24900	+	9.99940i	−0.137788	+	0.424069i
$557$	−10.3854			−0.440044			−0.220022	−	0.975495i	$-0.570613\pi$
$557$	−10.3854			−0.440044			−0.220022	+	0.975495i	$0.570613\pi$
$558$	−3.99465	−	3.87850i	−0.169107	−	0.164190i
$559$	35.5149			1.50212
$560$	−1.20631	+	3.71263i	−0.0509758	+	0.156887i
$561$	−0.832032	+	0.924065i	−0.0351284	+	0.0390141i
$562$	3.72905	+	2.70931i	0.157300	+	0.114285i
$563$	−6.30621	+	10.9227i	−0.265775	+	0.460336i	−0.967766	−	0.251850i	$-0.918961\pi$
$563$	−6.30621	+	10.9227i	−0.265775	+	0.460336i	0.701991	+	0.712185i	$0.252294\pi$
$564$	2.10957	+	3.65389i	0.0888291	+	0.153856i
$565$	0.0142593	−	0.135669i	0.000599895	−	0.00570762i
$566$	−3.04438	+	2.21187i	−0.127965	+	0.0929719i
$567$	0.408047	+	3.88231i	0.0171364	+	0.163042i
$568$	−4.78031	−	5.30907i	−0.200577	−	0.222764i
$569$	33.5648	−	14.9440i	1.40711	−	0.626485i	0.444105	−	0.895975i	$-0.353522\pi$
$569$	33.5648	−	14.9440i	1.40711	−	0.626485i	0.963003	+	0.269489i	$0.0868549\pi$
$570$	−2.66513	+	0.566490i	−0.111630	+	0.0237277i
$571$	−33.7761	−	7.17933i	−1.41349	−	0.300446i	−0.563005	−	0.826453i	$-0.690355\pi$
$571$	−33.7761	−	7.17933i	−1.41349	−	0.300446i	−0.850480	+	0.526008i	$0.823688\pi$
$572$	11.9609	+	5.32531i	0.500108	+	0.222663i
$573$	−2.66326	−	8.19666i	−0.111259	−	0.342420i
$574$	9.73097	+	29.9489i	0.406163	+	1.25004i
$575$	−1.44249	−	0.642240i	−0.0601562	−	0.0267833i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	20.1226	−	4.27720i	0.837716	−	0.178062i	0.230973	−	0.972960i	$-0.425809\pi$
$577$	20.1226	−	4.27720i	0.837716	−	0.178062i	0.606743	+	0.794898i	$0.292476\pi$
$578$	−15.4187	+	6.86486i	−0.641335	+	0.285541i
$579$	−11.6818	−	12.9740i	−0.485479	−	0.539179i
$580$	−0.0958600	−	0.912047i	−0.00398037	−	0.0378707i
$581$	−30.7661	+	22.3529i	−1.27639	+	0.927355i
$582$	0.574029	−	5.46152i	0.0237943	−	0.226387i
$583$	−2.48994	−	4.31270i	−0.103123	−	0.178614i
$584$	−0.158901	+	0.275225i	−0.00657538	+	0.0113889i
$585$	−2.97648	−	2.16254i	−0.123062	−	0.0894100i
$586$	−6.42847	+	7.13954i	−0.265558	+	0.294932i
$587$	−11.2971	+	34.7689i	−0.466281	+	1.43506i	0.391084	+	0.920355i	$0.372100\pi$
$587$	−11.2971	+	34.7689i	−0.466281	+	1.43506i	−0.857365	+	0.514709i	$0.827900\pi$
$588$	8.23881			0.339763
$589$	−14.2413	−	5.22705i	−0.586804	−	0.215377i
$590$	9.21212			0.379257
$591$	6.87715	−	21.1657i	0.282888	−	0.870640i
$592$	4.20124	−	4.66594i	0.172670	−	0.191769i
$593$	−2.54721	−	1.85066i	−0.104601	−	0.0759974i	0.534255	−	0.845323i	$-0.320592\pi$
$593$	−2.54721	−	1.85066i	−0.104601	−	0.0759974i	−0.638856	+	0.769326i	$0.720592\pi$
$594$	−1.77933	+	3.08189i	−0.0730068	+	0.126451i
$595$	−0.682006	−	1.18127i	−0.0279595	−	0.0484273i
$596$	0.831586	−	7.91201i	0.0340631	−	0.324089i
$597$	−7.79831	+	5.66580i	−0.319164	+	0.231886i
$598$	0.607245	+	5.77755i	0.0248321	+	0.236262i
$599$	−18.2683	−	20.2890i	−0.746422	−	0.828985i	0.243604	−	0.969875i	$-0.421670\pi$
$599$	−18.2683	−	20.2890i	−0.746422	−	0.828985i	−0.990025	+	0.140890i	$0.955004\pi$
$600$	0.913545	−	0.406737i	0.0372953	−	0.0166050i
$601$	20.1516	−	4.28336i	0.822002	−	0.174722i	0.222334	−	0.974971i	$-0.428632\pi$
$601$	20.1516	−	4.28336i	0.822002	−	0.174722i	0.599668	+	0.800249i	$0.295299\pi$
$602$	36.8591	+	7.83464i	1.50226	+	0.319316i
$603$	2.45170	+	1.09157i	0.0998408	+	0.0444520i
$604$	−3.64636	−	11.2223i	−0.148368	−	0.456630i
$605$	0.514222	+	1.58261i	0.0209061	+	0.0643424i
$606$	−14.3930	−	6.40816i	−0.584674	−	0.260314i
$607$	−26.6224	−	5.65877i	−1.08057	−	0.229682i	−0.366969	−	0.930233i	$-0.619604\pi$
$607$	−26.6224	−	5.65877i	−1.08057	−	0.229682i	−0.713602	+	0.700551i	$0.752938\pi$
$608$	−2.66513	+	0.566490i	−0.108085	+	0.0229742i
$609$	−3.27046	+	1.45610i	−0.132526	+	0.0590042i
$610$	3.05380	+	3.39159i	0.123645	+	0.137322i
$611$	1.62257	+	15.4378i	0.0656423	+	0.624545i
$612$	0.282684	−	0.205382i	0.0114268	−	0.00830206i
$613$	3.34475	−	31.8232i	0.135093	−	1.28533i	−0.691438	−	0.722436i	$-0.743022\pi$
$613$	3.34475	−	31.8232i	0.135093	−	1.28533i	0.826531	−	0.562891i	$-0.190311\pi$
$614$	−12.3884	−	21.4573i	−0.499955	−	0.865947i
$615$	4.03337	−	6.98601i	0.162641	−	0.281703i
$616$	11.2388	+	8.16546i	0.452824	+	0.328996i
$617$	1.41137	−	1.56748i	0.0568194	−	0.0631044i	−0.714065	−	0.700079i	$-0.753148\pi$
$617$	1.41137	−	1.56748i	0.0568194	−	0.0631044i	0.770884	+	0.636975i	$0.219815\pi$
$618$	3.95689	−	12.1781i	0.159170	−	0.489874i
$619$	18.3298			0.736738			0.368369	−	0.929680i	$-0.379916\pi$
$619$	18.3298			0.736738			0.368369	+	0.929680i	$0.379916\pi$
$620$	5.51147	+	0.789779i	0.221346	+	0.0317183i
$621$	−1.57901			−0.0633634
$622$	5.60645	−	17.2549i	0.224798	−	0.691857i
$623$	14.7930	−	16.4293i	0.592670	−	0.658227i
$624$	−2.97648	−	2.16254i	−0.119155	−	0.0865709i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.40952	−	9.36957i	−0.216208	−	0.374483i
$627$	−1.01352	+	9.64304i	−0.0404763	+	0.385106i
$628$	−19.1314	+	13.8997i	−0.763424	+	0.554660i
$629$	0.229321	+	2.18184i	0.00914362	+	0.0869957i
$630$	−2.61208	−	2.90101i	−0.104068	−	0.115579i
$631$	−14.9401	+	6.65176i	−0.594756	+	0.264802i	−0.681962	−	0.731388i	$-0.738873\pi$
$631$	−14.9401	+	6.65176i	−0.594756	+	0.264802i	0.0872056	+	0.996190i	$0.472206\pi$
$632$	−16.0030	+	3.40155i	−0.636567	+	0.135306i
$633$	−12.5326	−	2.66389i	−0.498127	−	0.105880i
$634$	21.5042	+	9.57427i	0.854039	+	0.380243i
$635$	−0.157777	−	0.485588i	−0.00626119	−	0.0192700i
$636$	0.432429	+	1.33088i	0.0171469	+	0.0527728i
$637$	27.6911	+	12.3289i	1.09716	+	0.488488i
$638$	−3.19223	−	0.678529i	−0.126381	−	0.0268632i
$639$	6.98795	−	1.48533i	0.276439	−	0.0587589i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−26.5750	−	29.5146i	−1.04965	−	1.16575i	−0.985822	−	0.167794i	$-0.946336\pi$
$641$	−26.5750	−	29.5146i	−1.04965	−	1.16575i	−0.0638284	−	0.997961i	$-0.520331\pi$
$642$	−0.725387	−	6.90160i	−0.0286287	−	0.272384i
$643$	−25.9926	+	18.8847i	−1.02505	+	0.744740i	−0.967311	−	0.253592i	$-0.918388\pi$
$643$	−25.9926	+	18.8847i	−1.02505	+	0.744740i	−0.0577356	+	0.998332i	$0.518388\pi$
$644$	−0.644309	+	6.13019i	−0.0253893	+	0.241563i
$645$	−4.82653	−	8.35979i	−0.190044	−	0.329166i
$646$	0.476021	−	0.824493i	0.0187288	−	0.0324392i
$647$	−0.326781	−	0.237420i	−0.0128471	−	0.00933395i	0.581343	−	0.813658i	$-0.302527\pi$
$647$	−0.326781	−	0.237420i	−0.0128471	−	0.00933395i	−0.594190	+	0.804325i	$0.702527\pi$
$648$	0.669131	−	0.743145i	0.0262859	−	0.0291935i
$649$	10.1304	−	31.1783i	0.397655	−	1.22386i
$650$	3.67913			0.144307
$651$	−3.71636	−	21.4148i	−0.145656	−	0.839310i
$652$	9.59638			0.375823
$653$	−10.5051	+	32.3314i	−0.411097	+	1.26523i	0.504598	+	0.863354i	$0.331641\pi$
$653$	−10.5051	+	32.3314i	−0.411097	+	1.26523i	−0.915695	+	0.401873i	$0.868359\pi$
$654$	10.7947	−	11.9887i	0.422105	−	0.468795i
$655$	15.5645	+	11.3083i	0.608156	+	0.441851i
$656$	4.03337	−	6.98601i	0.157477	−	0.272758i
$657$	−0.158901	−	0.275225i	−0.00619933	−	0.0107375i
$658$	−1.72161	+	16.3800i	−0.0671153	+	0.638560i
$659$	−5.09396	+	3.70098i	−0.198432	+	0.144170i	−0.682565	−	0.730825i	$-0.739135\pi$
$659$	−5.09396	+	3.70098i	−0.198432	+	0.144170i	0.484132	+	0.874995i	$0.339135\pi$
$660$	−0.371981	−	3.53916i	−0.0144793	−	0.137762i
$661$	16.5245	+	18.3523i	0.642729	+	0.713823i	0.973191	−	0.229996i	$-0.0738714\pi$
$661$	16.5245	+	18.3523i	0.642729	+	0.713823i	−0.330463	+	0.943819i	$0.607205\pi$
$662$	7.76778	−	3.45844i	0.301903	−	0.134416i
$663$	1.25746	−	0.267280i	0.0488355	−	0.0103803i
$664$	9.52893	+	2.02544i	0.369794	+	0.0786022i
$665$	−9.71670	−	4.32616i	−0.376798	−	0.167761i
$666$	1.94021	+	5.97135i	0.0751816	+	0.231385i
$667$	−0.447475	−	1.37719i	−0.0173263	−	0.0533249i
$668$	−17.7053	−	7.88292i	−0.685040	−	0.304999i
$669$	0.546052	+	0.116067i	0.0211116	+	0.00448741i
$670$	−2.62507	+	0.557976i	−0.101415	+	0.0215565i
$671$	14.8370	−	6.60587i	0.572777	−	0.255017i
$672$	−2.61208	−	2.90101i	−0.100763	−	0.111909i
$673$	−0.879548	−	8.36834i	−0.0339041	−	0.322576i	−0.998308	−	0.0581432i	$-0.981482\pi$
$673$	−0.879548	−	8.36834i	−0.0339041	−	0.322576i	0.964404	−	0.264433i	$-0.0851847\pi$
$674$	9.13874	−	6.63969i	0.352011	−	0.255751i
$675$	−0.104528	+	0.994522i	−0.00402330	+	0.0382792i
$676$	−0.268011	−	0.464208i	−0.0103081	−	0.0178542i
$677$	0.818171	−	1.41711i	0.0314449	−	0.0544641i	−0.849875	−	0.526985i	$-0.823322\pi$
$677$	0.818171	−	1.41711i	0.0314449	−	0.0544641i	0.881320	+	0.472521i	$0.156656\pi$
$678$	0.110363	+	0.0801832i	0.00423845	+	0.00307942i
$679$	14.3445	−	15.9312i	0.550492	−	0.611383i
$680$	−0.107975	+	0.332314i	−0.00414067	+	0.0127437i
$681$	−4.80755			−0.184226
$682$	8.73388	−	17.7850i	0.334438	−	0.681022i
$683$	6.61634			0.253167			0.126584	−	0.991956i	$-0.459599\pi$
$683$	6.61634			0.253167			0.126584	+	0.991956i	$0.459599\pi$
$684$	0.841968	−	2.59131i	0.0321935	−	0.0990813i
$685$	−5.37601	+	5.97067i	−0.205407	+	0.228128i
$686$	3.91235	+	2.84249i	0.149374	+	0.108527i
$687$	−7.79735	+	13.5054i	−0.297487	+	0.515263i
$688$	−4.82653	−	8.35979i	−0.184010	−	0.318714i
$689$	−0.538161	+	5.12026i	−0.0205023	+	0.195066i
$690$	1.27744	−	0.928117i	0.0486314	−	0.0353328i
$691$	−2.84038	−	27.0244i	−0.108053	−	1.02806i	−0.905407	−	0.424544i	$-0.860434\pi$
$691$	−2.84038	−	27.0244i	−0.108053	−	1.02806i	0.797354	−	0.603512i	$-0.206232\pi$
$692$	−3.13874	−	3.48592i	−0.119317	−	0.132515i
$693$	−12.6909	+	5.65035i	−0.482087	+	0.214639i
$694$	−8.40000	+	1.78548i	−0.318860	+	0.0677757i
$695$	10.2842	+	2.18598i	0.390103	+	0.0829190i
$696$	0.837786	+	0.373006i	0.0317562	+	0.0141388i
$697$	0.871011	+	2.68070i	0.0329919	+	0.101539i
$698$	−6.00392	−	18.4782i	−0.227252	−	0.699409i
$699$	25.6586	+	11.4239i	0.970496	+	0.432093i
$700$	3.81839	+	0.811623i	0.144321	+	0.0306765i
$701$	−40.9666	+	8.70771i	−1.54729	+	0.328886i	−0.900866	−	0.434096i	$-0.857068\pi$
$701$	−40.9666	+	8.70771i	−1.54729	+	0.328886i	−0.646420	+	0.762982i	$0.723734\pi$
$702$	3.36106	−	1.49644i	0.126855	−	0.0564794i
$703$	11.4470	+	12.7131i	0.431730	+	0.479485i
$704$	−0.371981	−	3.53916i	−0.0140196	−	0.133387i
$705$	3.41336	−	2.47995i	0.128555	−	0.0934004i
$706$	0.0801304	−	0.762389i	0.00301575	−	0.0286929i
$707$	−30.7514	−	53.2631i	−1.15653	−	2.00316i
$708$	−4.60606	+	7.97793i	−0.173106	+	0.299829i
$709$	33.6190	+	24.4256i	1.26259	+	0.917323i	0.998882	−	0.0472800i	$-0.0150553\pi$
$709$	33.6190	+	24.4256i	1.26259	+	0.917323i	0.263706	+	0.964603i	$0.415055\pi$
$710$	−4.78031	+	5.30907i	−0.179402	+	0.199246i
$711$	5.05569	−	15.5598i	0.189603	−	0.583539i
$712$	−5.66332			−0.212242
$713$	8.77175	−	0.589566i	0.328504	−	0.0220794i
$714$	1.36401			0.0510469
$715$	4.04589	−	12.4520i	0.151308	−	0.465678i
$716$	9.25448	−	10.2781i	0.345856	−	0.384112i
$717$	22.3309	+	16.2243i	0.833962	+	0.605909i
$718$	−4.76421	+	8.25186i	−0.177799	+	0.307957i
$719$	21.7688	+	37.7047i	0.811839	+	1.40615i	0.911576	+	0.411132i	$0.134867\pi$
$719$	21.7688	+	37.7047i	0.811839	+	1.40615i	−0.0997368	+	0.995014i	$0.531800\pi$
$720$	−0.104528	+	0.994522i	−0.00389555	+	0.0370636i
$721$	40.4394	−	29.3810i	1.50604	−	1.09420i
$722$	1.21004	+	11.5128i	0.0450331	+	0.428461i
$723$	10.8947	+	12.0998i	0.405177	+	0.449995i
$724$	3.44396	−	1.53335i	0.127994	−	0.0569864i
$725$	−0.897031	+	0.190670i	−0.0333149	+	0.00708130i
$726$	−1.62769	−	0.345977i	−0.0604094	−	0.0128404i
$727$	36.6939	+	16.3372i	1.36090	+	0.605913i	0.951840	−	0.306594i	$-0.0991895\pi$
$727$	36.6939	+	16.3372i	1.36090	+	0.605913i	0.409062	+	0.912507i	$0.365856\pi$
$728$	−4.43816	−	13.6593i	−0.164489	−	0.506246i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.290327	+	0.129262i	0.0107455	+	0.00478420i
$731$	3.29922	+	0.701272i	0.122026	+	0.0259375i
$732$	−4.46411	+	0.948876i	−0.164998	+	0.0350715i
$733$	11.7860	−	5.24748i	0.435327	−	0.193820i	−0.177359	−	0.984146i	$-0.556756\pi$
$733$	11.7860	−	5.24748i	0.435327	−	0.193820i	0.612687	+	0.790326i	$0.290089\pi$
$734$	13.0026	+	14.4408i	0.479934	+	0.533021i
$735$	−0.861190	−	8.19368i	−0.0317655	−	0.302228i
$736$	1.27744	−	0.928117i	0.0470872	−	0.0342108i
$737$	−0.998292	+	9.49811i	−0.0367725	+	0.349867i
$738$	4.03337	+	6.98601i	0.148471	+	0.257158i
$739$	18.3537	−	31.7895i	0.675152	−	1.16940i	−0.301273	−	0.953538i	$-0.597411\pi$
$739$	18.3537	−	31.7895i	0.675152	−	1.16940i	0.976425	−	0.215859i	$-0.0692552\pi$
$740$	−5.07953	−	3.69050i	−0.186727	−	0.135665i
$741$	6.70764	−	7.44959i	0.246411	−	0.273667i
$742$	−1.68807	+	5.19534i	−0.0619709	+	0.190727i
$743$	33.7524			1.23825			0.619127	−	0.785291i	$-0.287486\pi$
$743$	33.7524			1.23825			0.619127	+	0.785291i	$0.287486\pi$
$744$	−3.43970	+	4.37818i	−0.126106	+	0.160512i
$745$	−7.95560			−0.291470
$746$	7.52097	−	23.1472i	0.275362	−	0.847477i
$747$	−6.51855	+	7.23958i	−0.238501	+	0.264882i
$748$	1.00597	+	0.730883i	0.0367821	+	0.0267237i
$749$	13.5451	−	23.4607i	0.494925	−	0.857236i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−2.60745	+	24.8083i	−0.0951473	+	0.905266i	0.837975	+	0.545708i	$0.183739\pi$
$751$	−2.60745	+	24.8083i	−0.0951473	+	0.905266i	−0.933123	+	0.359558i	$0.882927\pi$
$752$	3.41336	−	2.47995i	0.124472	−	0.0904345i
$753$	−2.53674	−	24.1355i	−0.0924439	−	0.879545i
$754$	2.25766	+	2.50739i	0.0822193	+	0.0913137i
$755$	−10.7797	+	4.79944i	−0.392314	+	0.174669i
$756$	3.81839	−	0.811623i	0.138873	−	0.0295184i
$757$	20.5940	+	4.37740i	0.748503	+	0.159099i	0.566343	−	0.824170i	$-0.308358\pi$
$757$	20.5940	+	4.37740i	0.748503	+	0.159099i	0.182160	+	0.983269i	$0.441691\pi$
$758$	13.8646	+	6.17293i	0.503586	+	0.224211i
$759$	−1.73641	−	5.34413i	−0.0630278	−	0.193979i
$760$	0.841968	+	2.59131i	0.0305414	+	0.0939967i
$761$	5.48996	+	2.44429i	0.199011	+	0.0886054i	0.503822	−	0.863807i	$-0.331927\pi$
$761$	5.48996	+	2.44429i	0.199011	+	0.0886054i	−0.304811	+	0.952413i	$0.598593\pi$
$762$	0.499420	+	0.106155i	0.0180921	+	0.00384559i
$763$	61.5996	−	13.0934i	2.23006	−	0.474013i
$764$	−7.87337	+	3.50545i	−0.284849	+	0.126823i
$765$	−0.233805	−	0.259667i	−0.00845324	−	0.00938827i
$766$	1.18607	+	11.2847i	0.0428543	+	0.407732i
$767$	−27.4197	+	19.9216i	−0.990068	+	0.719327i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	−10.1624	−	17.6017i	−0.366464	−	0.634735i	0.622546	−	0.782583i	$-0.286098\pi$
$769$	−10.1624	−	17.6017i	−0.366464	−	0.634735i	−0.989010	+	0.147849i	$0.952765\pi$
$770$	6.94595	−	12.0307i	0.250315	−	0.433558i
$771$	0.133531	+	0.0970157i	0.00480899	+	0.00349393i
$772$	−11.6818	+	12.9740i	−0.420437	+	0.466943i
$773$	0.941830	−	2.89866i	0.0338753	−	0.104257i	−0.932689	−	0.360681i	$-0.882544\pi$
$773$	0.941830	−	2.89866i	0.0338753	−	0.104257i	0.966564	+	0.256424i	$0.0825443\pi$
$774$	9.65305			0.346972
$775$	0.209348	−	5.56383i	0.00751999	−	0.199859i
$776$	−5.49160			−0.197137
$777$	−7.57398	+	23.3103i	−0.271715	+	0.836253i
$778$	5.23174	−	5.81044i	0.187567	−	0.208314i
$779$	17.7815	+	12.9190i	0.637090	+	0.462873i
$780$	−1.83957	+	3.18622i	−0.0658671	+	0.114085i
$781$	12.7116	+	22.0172i	0.454858	+	0.787838i
$782$	−0.0576715	+	0.548708i	−0.00206233	+	0.0196218i
$783$	−0.741926	+	0.539041i	−0.0265143	+	0.0192637i
$784$	−0.861190	−	8.19368i	−0.0307568	−	0.292631i
$785$	15.8234	+	17.5736i	0.564760	+	0.627230i
$786$	−17.5755	+	7.82513i	−0.626898	+	0.279113i
$787$	−32.7643	+	6.96427i	−1.16792	+	0.248250i	−0.750755	−	0.660580i	$-0.770310\pi$
$787$	−32.7643	+	6.96427i	−1.16792	+	0.248250i	−0.417167	+	0.908830i	$0.636977\pi$
$788$	−21.7686	−	4.62706i	−0.775474	−	0.164832i
$789$	−17.7415	−	7.89903i	−0.631615	−	0.281213i
$790$	5.05569	+	15.5598i	0.179873	+	0.553593i
$791$	0.164559	+	0.506462i	0.00585106	+	0.0180077i
$792$	3.25100	+	1.44744i	0.115519	+	0.0514324i
$793$	−16.4241	−	3.49104i	−0.583235	−	0.123970i
$794$	−29.8309	+	6.34076i	−1.05866	+	0.225025i
$795$	1.27839	−	0.569174i	0.0453397	−	0.0201865i
$796$	6.44991	+	7.16335i	0.228611	+	0.253898i
$797$	−4.66397	−	44.3747i	−0.165206	−	1.57183i	−0.692036	−	0.721863i	$-0.743286\pi$
$797$	−4.66397	−	44.3747i	−0.165206	−	1.57183i	0.526830	−	0.849971i	$-0.323381\pi$
$798$	8.60491	−	6.25183i	0.304611	−	0.221313i
$799$	−0.154100	+	1.46616i	−0.00545166	+	0.0518691i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	2.83166	−	4.90458i	0.100052	−	0.173295i
$802$	−9.32826	−	6.77738i	−0.329392	−	0.239317i
$803$	0.756754	−	0.840460i	0.0267053	−	0.0296592i
$804$	0.829314	−	2.55236i	0.0292476	−	0.0900150i
$805$	6.16395			0.217251
$806$	−18.1127	+	9.56800i	−0.637993	+	0.337019i
$807$	10.6525			0.374986
$808$	−4.86858	+	14.9840i	−0.171276	+	0.527134i
$809$	−4.00629	+	4.44943i	−0.140854	+	0.156434i	−0.809444	−	0.587197i	$-0.800231\pi$
$809$	−4.00629	+	4.44943i	−0.140854	+	0.156434i	0.668590	+	0.743631i	$0.266898\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	11.4724	−	19.8708i	0.402852	−	0.697760i	−0.591217	−	0.806512i	$-0.701352\pi$
$811$	11.4724	−	19.8708i	0.402852	−	0.697760i	0.994069	+	0.108753i	$0.0346857\pi$
$812$	1.78998	+	3.10034i	0.0628160	+	0.108801i
$813$	−2.68463	+	25.5426i	−0.0941541	+	0.895817i
$814$	−18.0763	+	13.1332i	−0.633575	+	0.460319i
$815$	−1.00310	−	9.54381i	−0.0351369	−	0.334305i
$816$	−0.233805	−	0.259667i	−0.00818481	−	0.00909015i
$817$	24.0275	−	10.6977i	0.840615	−	0.374266i
$818$	−2.66432	+	0.566318i	−0.0931557	+	0.0198009i
$819$	14.0484	+	2.98607i	0.490889	+	0.104342i
$820$	−7.36934	−	3.28104i	−0.257348	−	0.114579i
$821$	4.66993	+	14.3726i	0.162982	+	0.501606i	0.998882	−	0.0472753i	$-0.0150538\pi$
$821$	4.66993	+	14.3726i	0.162982	+	0.501606i	−0.835900	+	0.548881i	$0.815054\pi$
$822$	−2.48274	−	7.64110i	−0.0865956	−	0.266514i
$823$	−4.52731	−	2.01569i	−0.157812	−	0.0702625i	0.326311	−	0.945263i	$-0.394194\pi$
$823$	−4.52731	−	2.01569i	−0.157812	−	0.0702625i	−0.484123	+	0.875000i	$0.660861\pi$
$824$	−12.5250	−	2.66226i	−0.436328	−	0.0927443i
$825$	−3.48089	+	0.739887i	−0.121189	+	0.0257596i
$826$	−32.8523	+	14.6268i	−1.14308	+	0.508930i
$827$	29.4989	+	32.7618i	1.02578	+	1.13924i	0.990169	+	0.139874i	$0.0446699\pi$
$827$	29.4989	+	32.7618i	1.02578	+	1.13924i	0.0356073	+	0.999366i	$0.488663\pi$
$828$	0.165051	+	1.57036i	0.00573592	+	0.0545737i
$829$	31.3208	−	22.7559i	1.08781	−	0.790344i	0.108786	−	0.994065i	$-0.465304\pi$
$829$	31.3208	−	22.7559i	1.08781	−	0.790344i	0.979029	+	0.203722i	$0.0653037\pi$
$830$	1.01830	−	9.68845i	0.0353456	−	0.336291i
$831$	3.52457	+	6.10474i	0.122266	+	0.211771i
$832$	−1.83957	+	3.18622i	−0.0637755	+	0.110462i
$833$	2.32898	+	1.69210i	0.0806942	+	0.0586278i
$834$	−7.03524	+	7.81342i	−0.243610	+	0.270557i
$835$	−5.98903	+	18.4323i	−0.207259	+	0.637877i
$836$	9.69616			0.335349
$837$	−2.07176	−	5.16796i	−0.0716106	−	0.178631i
$838$	34.6685			1.19760
$839$	10.0086	−	30.8034i	0.345536	−	1.06345i	−0.615760	−	0.787934i	$-0.711151\pi$
$839$	10.0086	−	30.8034i	0.345536	−	1.06345i	0.961296	−	0.275517i	$-0.0888492\pi$
$840$	−2.61208	+	2.90101i	−0.0901253	+	0.100094i
$841$	22.7811	+	16.5514i	0.785555	+	0.570739i
$842$	−13.8715	+	24.0262i	−0.478044	+	0.827997i
$843$	2.30468	+	3.99182i	0.0793773	+	0.137486i
$844$	−1.33928	+	12.7424i	−0.0461000	+	0.438612i
$845$	−0.433650	+	0.315065i	−0.0149180	+	0.0108386i
$846$	0.441021	+	4.19603i	0.0151626	+	0.144263i
$847$	−4.34665	−	4.82744i	−0.149353	−	0.165873i
$848$	1.27839	−	0.569174i	0.0439000	−	0.0195455i
$849$	−3.68083	+	0.782384i	−0.126326	+	0.0268514i
$850$	0.341780	+	0.0726477i	0.0117230	+	0.00249179i
$851$	−9.05691	−	4.03240i	−0.310467	−	0.138229i
$852$	−2.20764	−	6.79441i	−0.0756324	−	0.232773i
$853$	7.82734	+	24.0901i	0.268003	+	0.824828i	0.990986	+	0.133963i	$0.0427703\pi$
$853$	7.82734	+	24.0901i	0.268003	+	0.824828i	−0.722983	+	0.690865i	$0.757230\pi$
$854$	−16.2756	−	7.24635i	−0.556938	−	0.247965i
$855$	−2.66513	−	0.566490i	−0.0911454	−	0.0193735i
$856$	−6.78796	+	1.44283i	−0.232008	+	0.0493148i
$857$	−35.7877	+	15.9337i	−1.22248	+	0.544284i	−0.913522	−	0.406790i	$-0.866648\pi$
$857$	−35.7877	+	15.9337i	−1.22248	+	0.544284i	−0.308961	+	0.951075i	$0.599981\pi$
$858$	8.76078	+	9.72983i	0.299088	+	0.332171i
$859$	3.36802	+	32.0446i	0.114915	+	1.09335i	0.888254	+	0.459353i	$0.151919\pi$
$859$	3.36802	+	32.0446i	0.114915	+	1.09335i	−0.773338	+	0.633994i	$0.781415\pi$
$860$	−7.80948	+	5.67392i	−0.266301	+	0.193479i
$861$	−3.29161	+	31.3176i	−0.112178	+	1.06730i
$862$	8.69568	+	15.0614i	0.296176	+	0.512992i
$863$	15.8614	−	27.4727i	0.539928	−	0.935183i	−0.458979	−	0.888447i	$-0.651785\pi$
$863$	15.8614	−	27.4727i	0.539928	−	0.935183i	0.998907	−	0.0467357i	$-0.0148819\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−3.13874	+	3.48592i	−0.106720	+	0.118525i
$866$	1.68404	−	5.18295i	0.0572261	−	0.176124i
$867$	−16.8779			−0.573204
$868$	−20.9090	+	5.93445i	−0.709697	+	0.201428i
$869$	58.2216			1.97503
$870$	0.283390	−	0.872186i	0.00960784	−	0.0295699i
$871$	6.60683	−	7.33762i	0.223864	−	0.248626i
$872$	−13.0514	−	9.48237i	−0.441975	−	0.321114i
$873$	2.74580	−	4.75587i	0.0929313	−	0.160962i
$874$	2.15113	+	3.72587i	0.0727632	+	0.126029i
$875$	0.408047	−	3.88231i	0.0137945	−	0.131246i
$876$	−0.257108	+	0.186800i	−0.00868686	+	0.00631137i
$877$	−5.46885	−	52.0326i	−0.184670	−	1.75702i	−0.558487	−	0.829513i	$-0.688618\pi$
$877$	−5.46885	−	52.0326i	−0.184670	−	1.75702i	0.373817	−	0.927502i	$-0.378049\pi$
$878$	10.5518	+	11.7189i	0.356104	+	0.395494i
$879$	−8.77662	+	3.90760i	−0.296028	+	0.131800i
$880$	−3.48089	+	0.739887i	−0.117341	+	0.0249416i
$881$	29.9661	+	6.36949i	1.00958	+	0.214593i	0.682878	−	0.730533i	$-0.260728\pi$
$881$	29.9661	+	6.36949i	1.00958	+	0.214593i	0.326705	+	0.945126i	$0.394062\pi$
$882$	7.52653	+	3.35103i	0.253431	+	0.112835i
$883$	−0.648058	−	1.99452i	−0.0218089	−	0.0671209i	0.939560	−	0.342385i	$-0.111235\pi$
$883$	−0.648058	−	1.99452i	−0.0218089	−	0.0671209i	−0.961369	+	0.275264i	$0.911235\pi$
$884$	−0.397256	−	1.22263i	−0.0133612	−	0.0411215i
$885$	8.41569	+	3.74691i	0.282890	+	0.125951i
$886$	−15.1030	−	3.21024i	−0.507395	−	0.107850i
$887$	−51.3181	+	10.9080i	−1.72309	+	0.366255i	−0.959992	−	0.280026i	$-0.909657\pi$
$887$	−51.3181	+	10.9080i	−1.72309	+	0.366255i	−0.763100	+	0.646280i	$0.776324\pi$
$888$	5.73583	−	2.55376i	0.192482	−	0.0856985i
$889$	1.33367	+	1.48119i	0.0447298	+	0.0496775i
$890$	0.591978	+	5.63229i	0.0198431	+	0.188795i
$891$	−2.87902	+	2.09173i	−0.0964507	+	0.0700755i
$892$	0.0583532	−	0.555193i	0.00195381	−	0.0185892i
$893$	5.74788	+	9.95562i	0.192346	+	0.333152i
$894$	3.97780	−	6.88975i	0.133037	−	0.230428i
$895$	−11.1892	−	8.12942i	−0.374013	−	0.271737i
$896$	−2.61208	+	2.90101i	−0.0872635	+	0.0969159i
$897$	−1.79520	+	5.52504i	−0.0599398	+	0.184476i
$898$	−23.9115			−0.797938
$899$	3.92030	−	3.27151i	0.130749	−	0.109111i
$900$	1.00000			0.0333333
$901$	−0.151097	+	0.465030i	−0.00503379	+	0.0154924i
$902$	−19.2086	+	21.3333i	−0.639576	+	0.710322i
$903$	30.4858	+	22.1492i	1.01450	+	0.737081i
$904$	0.0682079	−	0.118140i	0.00226856	−	0.00392926i
$905$	−1.88494	−	3.26481i	−0.0626575	−	0.108526i
$906$	1.23342	−	11.7352i	0.0409777	−	0.389877i
$907$	−22.2111	+	16.1373i	−0.737508	+	0.535831i	−0.891930	−	0.452174i	$-0.850648\pi$
$907$	−22.2111	+	16.1373i	−0.737508	+	0.535831i	0.154422	+	0.988005i	$0.450648\pi$
$908$	0.502526	+	4.78122i	0.0166769	+	0.158670i
$909$	−10.5422	−	11.7083i	−0.349662	−	0.388339i
$910$	−13.1205	+	5.84163i	−0.434941	+	0.193648i
$911$	50.7814	−	10.7939i	1.68246	−	0.357619i	0.735145	−	0.677910i	$-0.237114\pi$
$911$	50.7814	−	10.7939i	1.68246	−	0.357619i	0.947319	+	0.320291i	$0.103781\pi$
$912$	−2.66513	−	0.566490i	−0.0882511	−	0.0187584i
$913$	−31.6706	−	14.1007i	−1.04814	−	0.466664i
$914$	−4.78730	−	14.7338i	−0.158350	−	0.487350i
$915$	1.41030	+	4.34047i	0.0466232	+	0.143491i
$916$	14.2465	+	6.34293i	0.470716	+	0.209576i
$917$	−73.4612	−	15.6147i	−2.42590	−	0.515642i
$918$	0.341780	−	0.0726477i	0.0112804	−	0.00239773i
$919$	46.6814	−	20.7839i	1.53988	−	0.685598i	0.551024	−	0.834489i	$-0.314237\pi$
$919$	46.6814	−	20.7839i	1.53988	−	0.685598i	0.988854	+	0.148891i	$0.0475705\pi$
$920$	−1.05656	−	1.17343i	−0.0348338	−	0.0386869i
$921$	−2.58988	−	24.6410i	−0.0853394	−	0.811950i
$922$	−29.9609	+	21.7679i	−0.986711	+	0.716887i
$923$	2.74742	−	26.1400i	0.0904325	−	0.860408i
$924$	6.94595	+	12.0307i	0.228505	+	0.395783i
$925$	−3.13932	+	5.43747i	−0.103220	+	0.178783i
$926$	30.9887	+	22.5146i	1.01835	+	0.739875i
$927$	8.56807	−	9.51580i	0.281412	−	0.312540i
$928$	0.283390	−	0.872186i	0.00930275	−	0.0286309i
$929$	42.5073			1.39462			0.697309	−	0.716771i	$-0.254381\pi$
$929$	42.5073			1.39462			0.697309	+	0.716771i	$0.254381\pi$
$930$	4.71374	+	2.96321i	0.154570	+	0.0971676i
$931$	22.4480			0.735704
$932$	8.67929	−	26.7121i	0.284300	−	0.874985i
$933$	12.1399	−	13.4828i	0.397443	−	0.441406i
$934$	8.53862	+	6.20367i	0.279392	+	0.202990i
$935$	0.621726	−	1.07686i	0.0203326	−	0.0352171i
$936$	−1.83957	−	3.18622i	−0.0601281	−	0.104145i
$937$	0.669291	−	6.36788i	0.0218648	−	0.208030i	−0.978135	−	0.207970i	$-0.933314\pi$
$937$	0.669291	−	6.36788i	0.0218648	−	0.208030i	1.00000		5.95812e-5i	$-1.89653e-5\pi$
$938$	8.47558	−	6.15787i	0.276738	−	0.201062i
$939$	−1.13090	−	10.7598i	−0.0369055	−	0.351132i
$940$	−2.82316	−	3.13544i	−0.0920813	−	0.102267i
$941$	−41.0781	+	18.2891i	−1.33911	+	0.596209i	−0.946263	−	0.323397i	$-0.895175\pi$
$941$	−41.0781	+	18.2891i	−1.33911	+	0.596209i	−0.392843	+	0.919606i	$0.628508\pi$
$942$	−23.1309	+	4.91663i	−0.753646	+	0.160192i
$943$	−12.4591	−	2.64826i	−0.405724	−	0.0862393i
$944$	8.41569	+	3.74691i	0.273907	+	0.121951i
$945$	−1.20631	−	3.71263i	−0.0392412	−	0.120772i
$946$	10.6153	+	32.6706i	0.345134	+	1.06221i
$947$	27.9433	+	12.4412i	0.908035	+	0.404283i	0.806967	−	0.590596i	$-0.201107\pi$
$947$	27.9433	+	12.4412i	0.908035	+	0.404283i	0.101068	+	0.994880i	$0.467774\pi$
$948$	−16.0030	−	3.40155i	−0.519754	−	0.110477i
$949$	−1.14369	+	0.243098i	−0.0371256	+	0.00789130i
$950$	2.48911	−	1.10822i	0.0807573	−	0.0359555i
$951$	15.7508	+	17.4931i	0.510755	+	0.567251i
$952$	−0.142578	−	1.35654i	−0.00462098	−	0.0439657i
$953$	12.7697	−	9.27770i	0.413650	−	0.300534i	−0.361428	−	0.932400i	$-0.617711\pi$
$953$	12.7697	−	9.27770i	0.413650	−	0.300534i	0.775078	+	0.631866i	$0.217711\pi$
$954$	−0.146274	+	1.39170i	−0.00473579	+	0.0450580i
$955$	4.30924	+	7.46382i	0.139444	+	0.241524i
$956$	13.8012	−	23.9044i	0.446364	−	0.773125i
$957$	−2.64026	−	1.91826i	−0.0853475	−	0.0620086i
$958$	−5.80803	+	6.45048i	−0.187649	+	0.208405i
$959$	9.69187	−	29.8285i	0.312967	−	0.963212i
$960$	1.00000			0.0322749
$961$	13.4387	+	27.9357i	0.433507	+	0.901150i
$962$	23.1000			0.744773
$963$	2.14446	−	6.59996i	0.0691042	−	0.212681i
$964$	10.8947	−	12.0998i	0.350894	−	0.389707i
$965$	14.1240	+	10.2617i	0.454666	+	0.330335i
$966$	−3.08198	+	5.33814i	−0.0991610	+	0.171752i
$967$	23.3440	+	40.4330i	0.750692	+	1.30024i	0.947488	+	0.319792i	$0.103613\pi$
$967$	23.3440	+	40.4330i	0.750692	+	1.30024i	−0.196796	+	0.980445i	$0.563054\pi$
$968$	−0.173941	+	1.65494i	−0.00559069	+	0.0531918i
$969$	0.770218	−	0.559596i	0.0247430	−	0.0179768i
$970$	0.574029	+	5.46152i	0.0184310	+	0.175359i
$971$	−31.4133	−	34.8880i	−1.00810	−	1.11961i	−0.992807	−	0.119726i	$-0.961798\pi$
$971$	−31.4133	−	34.8880i	−1.00810	−	1.11961i	−0.0152934	−	0.999883i	$-0.504868\pi$
$972$	0.913545	−	0.406737i	0.0293020	−	0.0130461i
$973$	−40.1465	+	8.53340i	−1.28704	+	0.273568i
$974$	22.8048	+	4.84730i	0.730712	+	0.155318i
$975$	3.36106	+	1.49644i	0.107640	+	0.0479244i
$976$	1.41030	+	4.34047i	0.0451427	+	0.138935i
$977$	−2.87360	−	8.84405i	−0.0919348	−	0.282946i	0.894508	−	0.447052i	$-0.147526\pi$
$977$	−2.87360	−	8.84405i	−0.0919348	−	0.282946i	−0.986443	+	0.164106i	$0.947526\pi$
$978$	8.76673	+	3.90320i	0.280329	+	0.124811i
$979$	19.7134	+	4.19021i	0.630043	+	0.133920i
$980$	−8.05877	+	1.71294i	−0.257428	+	0.0547180i
$981$	14.7377	−	6.56163i	0.470537	−	0.209497i
$982$	−11.4928	−	12.7641i	−0.366751	−	0.407319i
$983$	−0.271911	−	2.58706i	−0.00867262	−	0.0825145i	0.989329	−	0.145696i	$-0.0465421\pi$
$983$	−0.271911	−	2.58706i	−0.00867262	−	0.0825145i	−0.998002	+	0.0631812i	$0.979875\pi$
$984$	6.52613	−	4.74151i	0.208046	−	0.151154i
$985$	−2.32627	+	22.1330i	−0.0741212	+	0.705216i
$986$	0.160220	+	0.277509i	0.00510243	+	0.00883767i
$987$	−8.23512	+	14.2637i	−0.262127	+	0.454017i
$988$	−8.10992	−	5.89220i	−0.258011	−	0.187456i
$989$	−10.1990	+	11.3272i	−0.324311	+	0.360184i
$990$	1.09969	−	3.38449i	0.0349503	−	0.107566i
$991$	46.8255			1.48746			0.743731	−	0.668479i	$-0.233054\pi$
$991$	46.8255			1.48746			0.743731	+	0.668479i	$0.233054\pi$
$992$	4.71374	+	2.96321i	0.149661	+	0.0940821i
$993$	8.50289			0.269831
$994$	8.61793	−	26.5233i	0.273344	−	0.841267i
$995$	6.44991	−	7.16335i	0.204476	−	0.227094i
$996$	7.88129	+	5.72610i	0.249728	+	0.181438i
$997$	−14.6130	+	25.3105i	−0.462799	+	0.801592i	−0.999099	−	0.0424355i	$-0.986488\pi$
$997$	−14.6130	+	25.3105i	−0.462799	+	0.801592i	0.536300	+	0.844028i	$0.319822\pi$
$998$	16.6829	+	28.8957i	0.528089	+	0.914677i
$999$	−0.656297	+	6.24425i	−0.0207643	+	0.197559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.g.541.3	yes	24
31.20	even	15	inner	930.2.bg.g.361.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.g.361.3	✓	24	31.20	even	15	inner
930.2.bg.g.541.3	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.408047 - 3.88231i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.408047 - 3.88231i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.25100 - 1.44744i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(-3.59874 - 0.764935i) q^{13} +(-3.56620 - 1.58777i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.319207 - 0.142120i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-2.66513 + 0.566490i) q^{19} +(0.913545 - 0.406737i) q^{20} +(-2.61208 - 2.90101i) q^{21} +(-0.371981 - 3.53916i) q^{22} +(1.27744 - 0.928117i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.83957 + 3.18622i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.61208 + 2.90101i) q^{28} +(0.283390 - 0.872186i) q^{29} +1.00000 q^{30} +(4.71374 + 2.96321i) q^{31} +1.00000 q^{32} +(1.09969 - 3.38449i) q^{33} +(-0.233805 + 0.259667i) q^{34} +(3.15815 + 2.29453i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.13932 - 5.43747i) q^{37} +(-0.284805 + 2.70974i) q^{38} +(-2.97648 + 2.16254i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-5.39771 - 5.99476i) q^{41} +(-3.56620 + 1.58777i) q^{42} +(-9.44211 + 2.00698i) q^{43} +(-3.48089 - 0.739887i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-0.487940 - 1.50172i) q^{46} +(-1.30379 - 4.01265i) q^{47} +(0.913545 + 0.406737i) q^{48} +(-8.05877 - 1.71294i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(-0.319207 + 0.142120i) q^{51} +(2.46182 + 2.73413i) q^{52} +(-0.146274 - 1.39170i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.371981 + 3.53916i) q^{55} +(1.95185 + 3.38070i) q^{56} +(-1.36233 + 2.35963i) q^{57} +(-0.741926 - 0.539041i) q^{58} +(6.16411 - 6.84594i) q^{59} +(0.309017 - 0.951057i) q^{60} +4.56384 q^{61} +(4.27481 - 3.56735i) q^{62} -3.90369 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.46182 - 2.73413i) q^{65} +(-2.87902 - 2.09173i) q^{66} +(-1.34186 + 2.32417i) q^{67} +(0.174708 + 0.302603i) q^{68} +(0.165051 - 1.57036i) q^{69} +(3.15815 - 2.29453i) q^{70} +(0.746758 + 7.10493i) q^{71} +(0.669131 + 0.743145i) q^{72} +(0.290327 - 0.129262i) q^{73} +(-6.14144 + 1.30540i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(2.48911 + 1.10822i) q^{76} +(-4.29284 - 13.2120i) q^{77} +(1.13691 + 3.49906i) q^{78} +(14.9461 + 6.65444i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-7.36934 + 3.28104i) q^{82} +(-6.51855 - 7.23958i) q^{83} +(0.408047 + 3.88231i) q^{84} +(0.282684 - 0.205382i) q^{85} +(-1.00902 + 9.60017i) q^{86} +(-0.458535 - 0.794207i) q^{87} +(-1.77933 + 3.08189i) q^{88} +(4.58172 + 3.32881i) q^{89} +(0.669131 - 0.743145i) q^{90} +(-4.43816 + 13.6593i) q^{91} -1.57901 q^{92} +(5.35621 - 1.52022i) q^{93} -4.21915 q^{94} +(0.841968 - 2.59131i) q^{95} +(0.669131 - 0.743145i) q^{96} +(4.44280 + 3.22788i) q^{97} +(-4.11940 + 7.13502i) q^{98} +(-1.77933 - 3.08189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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