LMFDB - Embedded newform 294.2.m.b.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([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("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.2
Character	$\chi$	$=$	294.235
Dual form			294.2.m.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0829648 - 1.10709i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-2.15873 - 1.52966i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})$	\(q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0829648 - 1.10709i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-2.15873 - 1.52966i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(-0.0829648 + 1.10709i) q^{10} +(-0.896144 - 2.28334i) q^{11} +(0.955573 - 0.294755i) q^{12} +(1.75343 - 2.19874i) q^{13} +(1.90664 + 1.83432i) q^{14} +(-0.692194 - 0.867984i) q^{15} +(0.826239 + 0.563320i) q^{16} +(-5.23495 - 4.85732i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.75130 + 6.49744i) q^{19} +(0.247041 - 1.08236i) q^{20} +(-2.64532 - 0.0478109i) q^{21} +(0.545821 + 2.39140i) q^{22} +(-1.89161 + 1.75516i) q^{23} +(-0.988831 + 0.149042i) q^{24} +(3.72539 - 0.561513i) q^{25} +(-2.06155 + 1.91284i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-1.61195 - 2.09800i) q^{28} +(1.31754 - 5.77251i) q^{29} +(0.555096 + 0.961455i) q^{30} +(4.79230 - 8.30051i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-2.02668 - 1.38177i) q^{33} +(4.45253 + 5.58330i) q^{34} +(-1.51438 + 2.51682i) q^{35} +(0.623490 - 0.781831i) q^{36} +(-7.55789 + 2.33130i) q^{37} +(-2.74101 - 6.98397i) q^{38} +(0.210163 - 2.80443i) q^{39} +(-0.405599 + 1.03345i) q^{40} +(-1.70340 - 0.820316i) q^{41} +(2.60865 + 0.441541i) q^{42} +(-5.22216 + 2.51486i) q^{43} +(-0.183305 - 2.44604i) q^{44} +(-1.06087 - 0.327235i) q^{45} +(2.13207 - 1.45362i) q^{46} +(9.22899 + 1.39105i) q^{47} +1.00000 q^{48} +(2.32025 + 6.60427i) q^{49} -3.76747 q^{50} +(-7.06155 - 1.06436i) q^{51} +(2.32362 - 1.58422i) q^{52} +(9.41380 + 2.90377i) q^{53} +(0.0747301 + 0.997204i) q^{54} +(-2.45351 + 1.18155i) q^{55} +(1.28125 + 2.31482i) q^{56} +(6.75961 + 3.25526i) q^{57} +(-2.16317 + 5.51167i) q^{58} +(-0.588835 + 7.85746i) q^{59} +(-0.405599 - 1.03345i) q^{60} +(6.94339 - 2.14175i) q^{61} +(-5.97590 + 7.49355i) q^{62} +(-2.21260 + 1.45066i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-2.57967 - 1.75879i) q^{65} +(1.79810 + 1.66839i) q^{66} +(-0.0774217 + 0.134098i) q^{67} +(-3.57065 - 6.18455i) q^{68} +(-0.574205 + 2.51576i) q^{69} +(1.87257 - 2.26300i) q^{70} +(2.31321 + 10.1348i) q^{71} +(-0.733052 + 0.680173i) q^{72} +(2.08994 - 0.315008i) q^{73} +(7.82094 - 1.17882i) q^{74} +(2.76175 - 2.56253i) q^{75} +(1.66949 + 7.31449i) q^{76} +(-1.55820 + 6.29991i) q^{77} +(-0.625793 + 2.74178i) q^{78} +(1.92214 + 3.32924i) q^{79} +(0.555096 - 0.961455i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(1.56212 + 1.06503i) q^{82} +(3.54971 + 4.45119i) q^{83} +(-2.51370 - 0.825408i) q^{84} +(-4.94317 + 6.19854i) q^{85} +(5.53865 - 1.70845i) q^{86} +(-2.16317 - 5.51167i) q^{87} +(-0.183305 + 2.44604i) q^{88} +(-4.86684 + 12.4005i) q^{89} +(1.00025 + 0.481695i) q^{90} +(-7.14852 + 2.06432i) q^{91} +(-2.32491 + 1.11962i) q^{92} +(-0.716259 - 9.55781i) q^{93} +(-8.91858 - 2.75102i) q^{94} +(6.88202 - 4.69208i) q^{95} +(-0.988831 - 0.149042i) q^{96} +8.21789 q^{97} +(-1.31002 - 6.87632i) q^{98} -2.45290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$2$	−0.988831	−	0.149042i	−0.699209	−	0.105389i
$3$	0.826239	−	0.563320i	0.477029	−	0.325233i
$3$	0.826239	−	0.563320i	0.477029	−	0.325233i
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	−0.0829648	−	1.10709i	−0.0371030	−	0.495105i	−0.984540	−	0.175162i	$-0.943955\pi$
$5$	−0.0829648	−	1.10709i	−0.0371030	−	0.495105i	0.947437	−	0.319943i	$-0.103664\pi$
$6$	−0.900969	+	0.433884i	−0.367819	+	0.177132i
$7$	−2.15873	−	1.52966i	−0.815924	−	0.578159i
$7$	−2.15873	−	1.52966i	−0.815924	−	0.578159i
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	0.365341	−	0.930874i	0.121780	−	0.310291i
$10$	−0.0829648	+	1.10709i	−0.0262358	+	0.350092i
$11$	−0.896144	−	2.28334i	−0.270197	−	0.688452i	−0.999989	−	0.00478172i	$-0.998478\pi$
$11$	−0.896144	−	2.28334i	−0.270197	−	0.688452i	0.729791	−	0.683670i	$-0.239617\pi$
$12$	0.955573	−	0.294755i	0.275850	−	0.0850885i
$13$	1.75343	−	2.19874i	0.486315	−	0.609820i	−0.476766	−	0.879030i	$-0.658191\pi$
$13$	1.75343	−	2.19874i	0.486315	−	0.609820i	0.963081	+	0.269210i	$0.0867627\pi$
$14$	1.90664	+	1.83432i	0.509570	+	0.490243i
$15$	−0.692194	−	0.867984i	−0.178724	−	0.224112i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	−5.23495	−	4.85732i	−1.26966	−	1.17807i	−0.974934	−	0.222492i	$-0.928581\pi$
$17$	−5.23495	−	4.85732i	−1.26966	−	1.17807i	−0.294727	−	0.955581i	$-0.595229\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	3.75130	+	6.49744i	0.860607	+	1.49062i	0.871344	+	0.490673i	$0.163249\pi$
$19$	3.75130	+	6.49744i	0.860607	+	1.49062i	−0.0107369	+	0.999942i	$0.503418\pi$
$20$	0.247041	−	1.08236i	0.0552401	−	0.242023i
$21$	−2.64532	−	0.0478109i	−0.577256	−	0.0104332i
$22$	0.545821	+	2.39140i	0.116369	+	0.509848i
$23$	−1.89161	+	1.75516i	−0.394427	+	0.365975i	−0.852310	−	0.523038i	$-0.824799\pi$
$23$	−1.89161	+	1.75516i	−0.394427	+	0.365975i	0.457882	+	0.889013i	$0.348608\pi$
$24$	−0.988831	+	0.149042i	−0.201844	+	0.0304231i
$25$	3.72539	−	0.561513i	0.745078	−	0.112303i
$26$	−2.06155	+	1.91284i	−0.404304	+	0.375139i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	−1.61195	−	2.09800i	−0.304630	−	0.396485i
$29$	1.31754	−	5.77251i	0.244661	−	1.07193i	−0.692057	−	0.721843i	$-0.743295\pi$
$29$	1.31754	−	5.77251i	0.244661	−	1.07193i	0.936718	−	0.350086i	$-0.113847\pi$
$30$	0.555096	+	0.961455i	0.101346	+	0.175537i
$31$	4.79230	−	8.30051i	0.860723	−	1.49082i	−0.0105089	−	0.999945i	$-0.503345\pi$
$31$	4.79230	−	8.30051i	0.860723	−	1.49082i	0.871232	−	0.490871i	$-0.163322\pi$
$32$	−0.733052	−	0.680173i	−0.129586	−	0.120239i
$33$	−2.02668	−	1.38177i	−0.352799	−	0.240535i
$34$	4.45253	+	5.58330i	0.763603	+	0.957528i
$35$	−1.51438	+	2.51682i	−0.255976	+	0.425420i
$36$	0.623490	−	0.781831i	0.103915	−	0.130305i
$37$	−7.55789	+	2.33130i	−1.24251	+	0.383264i	−0.845215	−	0.534427i	$-0.820527\pi$
$37$	−7.55789	+	2.33130i	−1.24251	+	0.383264i	−0.397295	+	0.917691i	$0.630051\pi$
$38$	−2.74101	−	6.98397i	−0.444650	−	1.13295i
$39$	0.210163	−	2.80443i	0.0336530	−	0.449068i
$40$	−0.405599	+	1.03345i	−0.0641308	+	0.163403i
$41$	−1.70340	−	0.820316i	−0.266027	−	0.128112i	0.296116	−	0.955152i	$-0.404309\pi$
$41$	−1.70340	−	0.820316i	−0.266027	−	0.128112i	−0.562143	+	0.827040i	$0.690023\pi$
$42$	2.60865	+	0.441541i	0.402523	+	0.0681313i
$43$	−5.22216	+	2.51486i	−0.796372	+	0.383512i	−0.787396	−	0.616447i	$-0.788571\pi$
$43$	−5.22216	+	2.51486i	−0.796372	+	0.383512i	−0.00897563	+	0.999960i	$0.502857\pi$
$44$	−0.183305	−	2.44604i	−0.0276343	−	0.368754i
$45$	−1.06087	−	0.327235i	−0.158145	−	0.0487813i
$46$	2.13207	−	1.45362i	0.314357	−	0.214325i
$47$	9.22899	+	1.39105i	1.34619	+	0.202905i	0.782276	−	0.622931i	$-0.214058\pi$
$47$	9.22899	+	1.39105i	1.34619	+	0.202905i	0.563910	+	0.825836i	$0.309297\pi$
$48$	1.00000			0.144338
$49$	2.32025	+	6.60427i	0.331465	+	0.943468i
$50$	−3.76747			−0.532801
$51$	−7.06155	−	1.06436i	−0.988814	−	0.149040i
$52$	2.32362	−	1.58422i	0.322228	−	0.219692i
$53$	9.41380	+	2.90377i	1.29308	+	0.398864i	0.863585	−	0.504203i	$-0.168214\pi$
$53$	9.41380	+	2.90377i	1.29308	+	0.398864i	0.429500	+	0.903067i	$0.358690\pi$
$54$	0.0747301	+	0.997204i	0.0101695	+	0.135702i
$55$	−2.45351	+	1.18155i	−0.330831	+	0.159320i
$56$	1.28125	+	2.31482i	0.171215	+	0.309331i
$57$	6.75961	+	3.25526i	0.895332	+	0.431169i
$58$	−2.16317	+	5.51167i	−0.284038	+	0.723717i
$59$	−0.588835	+	7.85746i	−0.0766598	+	1.02295i	0.817711	+	0.575628i	$0.195242\pi$
$59$	−0.588835	+	7.85746i	−0.0766598	+	1.02295i	−0.894371	+	0.447325i	$0.852377\pi$
$60$	−0.405599	−	1.03345i	−0.0523626	−	0.133418i
$61$	6.94339	−	2.14175i	0.889010	−	0.274223i	0.183582	−	0.983004i	$-0.441231\pi$
$61$	6.94339	−	2.14175i	0.889010	−	0.274223i	0.705428	+	0.708781i	$0.250755\pi$
$62$	−5.97590	+	7.49355i	−0.758941	+	0.951681i
$63$	−2.21260	+	1.45066i	−0.278761	+	0.182766i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−2.57967	−	1.75879i	−0.319969	−	0.218151i
$66$	1.79810	+	1.66839i	0.221331	+	0.205365i
$67$	−0.0774217	+	0.134098i	−0.00945856	+	0.0163827i	−0.870716	−	0.491786i	$-0.836344\pi$
$67$	−0.0774217	+	0.134098i	−0.00945856	+	0.0163827i	0.861257	+	0.508169i	$0.169677\pi$
$68$	−3.57065	−	6.18455i	−0.433005	−	0.749987i
$69$	−0.574205	+	2.51576i	−0.0691262	+	0.302862i
$70$	1.87257	−	2.26300i	0.223815	−	0.270480i
$71$	2.31321	+	10.1348i	0.274527	+	1.20278i	0.904605	+	0.426250i	$0.140166\pi$
$71$	2.31321	+	10.1348i	0.274527	+	1.20278i	−0.630078	+	0.776531i	$0.716977\pi$
$72$	−0.733052	+	0.680173i	−0.0863910	+	0.0801591i
$73$	2.08994	−	0.315008i	0.244609	−	0.0368689i	−0.0255933	−	0.999672i	$-0.508148\pi$
$73$	2.08994	−	0.315008i	0.244609	−	0.0368689i	0.270202	+	0.962804i	$0.412909\pi$
$74$	7.82094	−	1.17882i	0.909166	−	0.137035i
$75$	2.76175	−	2.56253i	0.318900	−	0.295896i
$76$	1.66949	+	7.31449i	0.191503	+	0.839030i
$77$	−1.55820	+	6.29991i	−0.177574	+	0.717942i
$78$	−0.625793	+	2.74178i	−0.0708571	+	0.310445i
$79$	1.92214	+	3.32924i	0.216257	+	0.374569i	0.953661	−	0.300884i	$-0.0972817\pi$
$79$	1.92214	+	3.32924i	0.216257	+	0.374569i	−0.737403	+	0.675453i	$0.763948\pi$
$80$	0.555096	−	0.961455i	0.0620617	−	0.107494i
$81$	−0.733052	−	0.680173i	−0.0814502	−	0.0755747i
$82$	1.56212	+	1.06503i	0.172507	+	0.117613i
$83$	3.54971	+	4.45119i	0.389631	+	0.488582i	0.937501	−	0.347981i	$-0.113133\pi$
$83$	3.54971	+	4.45119i	0.389631	+	0.488582i	−0.547870	+	0.836563i	$0.684561\pi$
$84$	−2.51370	−	0.825408i	−0.274267	−	0.0900594i
$85$	−4.94317	+	6.19854i	−0.536162	+	0.672326i
$86$	5.53865	−	1.70845i	0.597248	−	0.184227i
$87$	−2.16317	−	5.51167i	−0.231916	−	0.590913i
$88$	−0.183305	+	2.44604i	−0.0195404	+	0.260748i
$89$	−4.86684	+	12.4005i	−0.515884	+	1.31445i	0.401286	+	0.915953i	$0.368563\pi$
$89$	−4.86684	+	12.4005i	−0.515884	+	1.31445i	−0.917169	+	0.398497i	$0.869532\pi$
$90$	1.00025	+	0.481695i	0.105436	+	0.0507751i
$91$	−7.14852	+	2.06432i	−0.749369	+	0.216399i
$92$	−2.32491	+	1.11962i	−0.242389	+	0.116728i
$93$	−0.716259	−	9.55781i	−0.0742726	−	0.991098i
$94$	−8.91858	−	2.75102i	−0.919882	−	0.283746i
$95$	6.88202	−	4.69208i	0.706080	−	0.481397i
$96$	−0.988831	−	0.149042i	−0.100922	−	0.0152116i
$97$	8.21789			0.834400			0.417200	−	0.908815i	$-0.363011\pi$
$97$	8.21789			0.834400			0.417200	+	0.908815i	$0.363011\pi$
$98$	−1.31002	−	6.87632i	−0.132332	−	0.694614i
$99$	−2.45290			−0.246525
$100$	3.72539	+	0.561513i	0.372539	+	0.0561513i
$101$	5.80665	−	3.95891i	0.577784	−	0.393926i	−0.238872	−	0.971051i	$-0.576778\pi$
$101$	5.80665	−	3.95891i	0.577784	−	0.393926i	0.816656	+	0.577125i	$0.195825\pi$
$102$	6.82404	+	2.10494i	0.675681	+	0.208420i
$103$	0.413381	+	5.51619i	0.0407317	+	0.543526i	0.979824	+	0.199862i	$0.0640493\pi$
$103$	0.413381	+	5.51619i	0.0407317	+	0.543526i	−0.939092	+	0.343665i	$0.888332\pi$
$104$	−2.53379	+	1.22021i	−0.248458	+	0.119651i
$105$	0.166538	+	2.93257i	0.0162524	+	0.286189i
$106$	−8.87587	−	4.27439i	−0.862101	−	0.415166i
$107$	0.312678	−	0.796691i	0.0302277	−	0.0770190i	−0.914963	−	0.403538i	$-0.867780\pi$
$107$	0.312678	−	0.796691i	0.0302277	−	0.0770190i	0.945191	+	0.326519i	$0.105876\pi$
$108$	0.0747301	−	0.997204i	0.00719091	−	0.0959560i
$109$	−6.44419	−	16.4195i	−0.617241	−	1.57271i	−0.806793	−	0.590834i	$-0.798799\pi$
$109$	−6.44419	−	16.4195i	−0.617241	−	1.57271i	0.189551	−	0.981871i	$-0.439297\pi$
$110$	2.60220	−	0.802674i	0.248110	−	0.0765319i
$111$	−4.93136	+	6.18372i	−0.468064	+	0.586933i
$112$	−0.921938	−	2.47993i	−0.0871149	−	0.234331i
$113$	−8.33784	−	10.4553i	−0.784358	−	0.983553i	−0.999975	−	0.00707552i	$-0.997748\pi$
$113$	−8.33784	−	10.4553i	−0.784358	−	0.983553i	0.215617	−	0.976478i	$-0.430824\pi$
$114$	−6.19894	−	4.22636i	−0.580584	−	0.395835i
$115$	2.10005	+	1.94856i	0.195831	+	0.181704i
$116$	2.96048	−	5.12770i	0.274874	−	0.476095i
$117$	−1.40614	−	2.43551i	−0.129998	−	0.225163i
$118$	1.75335	−	7.68193i	0.161409	−	0.707179i
$119$	3.87078	+	18.4934i	0.354834	+	1.69529i
$120$	0.247041	+	1.08236i	0.0225517	+	0.0988053i
$121$	3.65302	−	3.38950i	0.332092	−	0.308137i
$122$	−7.18505	+	1.08297i	−0.650504	+	0.0980477i
$123$	−1.86952	+	0.281784i	−0.168569	+	0.0254077i
$124$	7.02601	−	6.51919i	0.630955	−	0.585440i
$125$	−2.16593	−	9.48954i	−0.193726	−	0.848771i
$126$	2.40409	−	1.10468i	0.214174	−	0.0984132i
$127$	−0.905000	+	3.96506i	−0.0803057	+	0.351842i	−0.999077	−	0.0429470i	$-0.986325\pi$
$127$	−0.905000	+	3.96506i	−0.0803057	+	0.351842i	0.918772	+	0.394789i	$0.129182\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−2.89808	+	5.01962i	−0.255162	+	0.441953i
$130$	2.28872	+	2.12362i	0.200734	+	0.186254i
$131$	6.35805	+	4.33485i	0.555506	+	0.378737i	0.808289	−	0.588785i	$-0.200394\pi$
$131$	6.35805	+	4.33485i	0.555506	+	0.378737i	−0.252784	+	0.967523i	$0.581346\pi$
$132$	−1.52936	−	1.91775i	−0.133113	−	0.166919i
$133$	1.84085	−	19.7645i	0.159622	−	1.71380i
$134$	0.0965432	−	0.121061i	0.00834006	−	0.0104581i
$135$	−1.06087	+	0.327235i	−0.0913052	+	0.0281639i
$136$	2.60901	+	6.64766i	0.223721	+	0.570032i
$137$	0.298165	−	3.97873i	0.0254739	−	0.339926i	−0.969876	−	0.243600i	$-0.921672\pi$
$137$	0.298165	−	3.97873i	0.0254739	−	0.339926i	0.995350	−	0.0963262i	$-0.0307092\pi$
$138$	0.942746	−	2.40208i	0.0802519	−	0.204478i
$139$	9.61286	+	4.62931i	0.815352	+	0.392653i	0.794601	−	0.607132i	$-0.207680\pi$
$139$	9.61286	+	4.62931i	0.815352	+	0.392653i	0.0207508	+	0.999785i	$0.493394\pi$
$140$	−2.18894	+	1.95863i	−0.184999	+	0.165535i
$141$	8.40895	−	4.04954i	0.708162	−	0.341033i
$142$	−0.776853	−	10.3664i	−0.0651921	−	0.869928i
$143$	−6.59178	−	2.03330i	−0.551233	−	0.170033i
$144$	0.826239	−	0.563320i	0.0688532	−	0.0469433i
$145$	−6.49999	−	0.979716i	−0.539795	−	0.0813610i
$146$	−2.11355			−0.174918
$147$	5.63740	+	4.14966i	0.464965	+	0.342258i
$148$	−7.90928			−0.650139
$149$	−6.54521	−	0.986532i	−0.536205	−	0.0808198i	−0.124643	−	0.992202i	$-0.539778\pi$
$149$	−6.54521	−	0.986532i	−0.536205	−	0.0808198i	−0.411562	+	0.911382i	$0.635017\pi$
$150$	−3.11283	+	2.12229i	−0.254162	+	0.173284i
$151$	−15.2987	−	4.71902i	−1.24499	−	0.384029i	−0.398863	−	0.917010i	$-0.630595\pi$
$151$	−15.2987	−	4.71902i	−1.24499	−	0.384029i	−0.846127	+	0.532982i	$0.821071\pi$
$152$	−0.560670	−	7.48162i	−0.0454763	−	0.606839i
$153$	−6.43410	+	3.09850i	−0.520166	+	0.250499i
$154$	2.47975	−	5.99731i	0.199824	−	0.483277i
$155$	−9.58699	−	4.61685i	−0.770046	−	0.370835i
$156$	1.02744	−	2.61789i	0.0822614	−	0.209599i
$157$	0.791544	−	10.5624i	0.0631721	−	0.842973i	−0.872164	−	0.489213i	$-0.837284\pi$
$157$	0.791544	−	10.5624i	0.0631721	−	0.842973i	0.935336	−	0.353760i	$-0.115097\pi$
$158$	−1.40447	−	3.57853i	−0.111734	−	0.284693i
$159$	9.41380	−	2.90377i	0.746563	−	0.230284i
$160$	−0.692194	+	0.867984i	−0.0547227	+	0.0686201i
$161$	6.76827	−	0.895386i	0.533415	−	0.0705663i
$162$	0.623490	+	0.781831i	0.0489860	+	0.0614265i
$163$	−18.2155	−	12.4191i	−1.42675	−	0.972740i	−0.997581	−	0.0695139i	$-0.977855\pi$
$163$	−18.2155	−	12.4191i	−1.42675	−	0.972740i	−0.429166	−	0.903226i	$-0.641192\pi$
$164$	−1.38593	−	1.28596i	−0.108223	−	0.100416i
$165$	−1.36159	+	2.35835i	−0.106000	+	0.183597i
$166$	−2.84664	−	4.93053i	−0.220942	−	0.382684i
$167$	0.0900139	−	0.394377i	0.00696549	−	0.0305178i	−0.971326	−	0.237753i	$-0.923589\pi$
$167$	0.0900139	−	0.394377i	0.00696549	−	0.0305178i	0.978291	+	0.207235i	$0.0664464\pi$
$168$	2.36261	+	1.19084i	0.182279	+	0.0918751i
$169$	1.13286	+	4.96339i	0.0871431	+	0.381799i
$170$	5.81180	−	5.39256i	0.445745	−	0.413591i
$171$	7.41880	−	1.11820i	0.567330	−	0.0855112i
$172$	−5.73142	+	0.863873i	−0.437017	+	0.0658697i
$173$	15.5826	−	14.4586i	1.18472	−	1.09926i	0.191688	−	0.981456i	$-0.438604\pi$
$173$	15.5826	−	14.4586i	1.18472	−	1.09926i	0.993036	−	0.117808i	$-0.0375867\pi$
$174$	1.31754	+	5.77251i	0.0998823	+	0.437613i
$175$	−8.90105	−	4.48645i	−0.672856	−	0.339143i
$176$	0.545821	−	2.39140i	0.0411428	−	0.180258i
$177$	3.93974	+	6.82384i	0.296129	+	0.512911i
$178$	6.66068	−	11.5366i	0.499239	−	0.864707i
$179$	10.8591	+	10.0758i	0.811646	+	0.753097i	0.972256	−	0.233921i	$-0.0751556\pi$
$179$	10.8591	+	10.0758i	0.811646	+	0.753097i	−0.160610	+	0.987018i	$0.551346\pi$
$180$	−0.917284	−	0.625394i	−0.0683703	−	0.0466141i
$181$	6.30962	+	7.91202i	0.468991	+	0.588096i	0.958924	−	0.283665i	$-0.0915502\pi$
$181$	6.30962	+	7.91202i	0.468991	+	0.588096i	−0.489933	+	0.871760i	$0.662979\pi$
$182$	7.37635	−	0.975829i	0.546772	−	0.0723333i
$183$	4.53041	−	5.68095i	0.334897	−	0.419948i
$184$	2.46581	−	0.760603i	0.181782	−	0.0560724i
$185$	3.20800	+	8.17384i	0.235857	+	0.600953i
$186$	−0.716259	+	9.55781i	−0.0525186	+	0.700812i
$187$	−6.39964	+	16.3060i	−0.467988	+	1.19241i
$188$	8.40895	+	4.04954i	0.613286	+	0.295343i
$189$	−1.01095	+	2.44499i	−0.0735358	+	0.177847i
$190$	−7.50447	+	3.61396i	−0.544431	+	0.262184i
$191$	−0.367143	−	4.89918i	−0.0265655	−	0.354492i	−0.994608	−	0.103706i	$-0.966930\pi$
$191$	−0.367143	−	4.89918i	−0.0265655	−	0.354492i	0.968042	−	0.250786i	$-0.0806891\pi$
$192$	0.955573	+	0.294755i	0.0689625	+	0.0212721i
$193$	−11.5189	+	7.85347i	−0.829151	+	0.565305i	−0.901850	−	0.432048i	$-0.857791\pi$
$193$	−11.5189	+	7.85347i	−0.829151	+	0.565305i	0.0726996	+	0.997354i	$0.476839\pi$
$194$	−8.12610	−	1.22481i	−0.583420	−	0.0879365i
$195$	−3.12218			−0.223584
$196$	0.270526	+	6.99477i	0.0193233	+	0.499626i
$197$	12.4524			0.887197			0.443598	−	0.896226i	$-0.353702\pi$
$197$	12.4524			0.887197			0.443598	+	0.896226i	$0.353702\pi$
$198$	2.42550	+	0.365585i	0.172373	+	0.0259810i
$199$	12.1522	−	8.28521i	0.861444	−	0.587323i	−0.0499985	−	0.998749i	$-0.515922\pi$
$199$	12.1522	−	8.28521i	0.861444	−	0.587323i	0.911443	+	0.411426i	$0.134969\pi$
$200$	−3.60009	−	1.11048i	−0.254565	−	0.0785229i
$201$	0.0115715	+	0.154410i	0.000816188	+	0.0108913i
$202$	−6.33184	+	3.04926i	−0.445507	+	0.214545i
$203$	−11.6742	+	10.4459i	−0.819369	+	0.733160i
$204$	−6.43410	−	3.09850i	−0.450477	−	0.216938i
$205$	−0.766840	+	1.95388i	−0.0535584	+	0.136465i
$206$	0.413381	−	5.51619i	0.0288016	−	0.384331i
$207$	0.942746	+	2.40208i	0.0655254	+	0.166956i
$208$	2.68735	−	0.828937i	0.186334	−	0.0574764i
$209$	11.4741	−	14.3881i	0.793683	−	0.995247i
$210$	0.272399	−	2.92464i	0.0187973	−	0.201819i
$211$	−10.2868	−	12.8992i	−0.708172	−	0.888019i	0.289432	−	0.957198i	$-0.406533\pi$
$211$	−10.2868	−	12.8992i	−0.708172	−	0.888019i	−0.997604	+	0.0691791i	$0.977962\pi$
$212$	8.13967	+	5.54953i	0.559035	+	0.381143i
$213$	7.62041	+	7.07070i	0.522142	+	0.484477i
$214$	−0.427926	+	0.741190i	−0.0292524	+	0.0506667i
$215$	3.21743	+	5.57275i	0.219427	+	0.380058i
$216$	−0.222521	+	0.974928i	−0.0151406	+	0.0663354i
$217$	−23.0423	+	10.5880i	−1.56421	+	0.718758i
$218$	3.92501	+	17.1966i	0.265835	+	1.16470i
$219$	1.54934	−	1.43758i	0.104695	−	0.0971424i
$220$	−2.69277	+	0.405870i	−0.181547	+	0.0273638i
$221$	−19.8591	+	2.99328i	−1.33587	+	0.201350i
$222$	5.79791	−	5.37968i	0.389130	−	0.361060i
$223$	−1.96162	−	8.59441i	−0.131360	−	0.575524i	−0.997172	−	0.0751551i	$-0.976055\pi$
$223$	−1.96162	−	8.59441i	−0.131360	−	0.575524i	0.865812	−	0.500369i	$-0.166802\pi$
$224$	0.542027	+	2.58963i	0.0362157	+	0.173027i
$225$	0.838341	−	3.67301i	0.0558894	−	0.244868i
$226$	6.68643	+	11.5812i	0.444774	+	0.770372i
$227$	−10.3726	+	17.9659i	−0.688456	+	1.19244i	0.283882	+	0.958859i	$0.408378\pi$
$227$	−10.3726	+	17.9659i	−0.688456	+	1.19244i	−0.972337	+	0.233581i	$0.924956\pi$
$228$	5.49979	+	5.10306i	0.364233	+	0.337959i
$229$	1.39436	+	0.950661i	0.0921422	+	0.0628215i	0.608515	−	0.793543i	$-0.291766\pi$
$229$	1.39436	+	0.950661i	0.0921422	+	0.0628215i	−0.516373	+	0.856364i	$0.672718\pi$
$230$	−1.78618	−	2.23979i	−0.117777	−	0.147688i
$231$	2.26142	+	6.08300i	0.148790	+	0.400232i
$232$	−3.69166	+	4.62919i	−0.242369	+	0.303921i
$233$	−8.52316	+	2.62905i	−0.558371	+	0.172235i	−0.561080	−	0.827762i	$-0.689614\pi$
$233$	−8.52316	+	2.62905i	−0.558371	+	0.172235i	0.00270908	+	0.999996i	$0.499138\pi$
$234$	1.02744	+	2.61789i	0.0671662	+	0.171137i
$235$	0.774330	−	10.3327i	0.0505117	−	0.674032i
$236$	−2.87870	+	7.33481i	−0.187387	+	0.477455i
$237$	3.46357	+	1.66797i	0.224983	+	0.108346i
$238$	−1.07125	−	18.8637i	−0.0694389	−	1.22275i
$239$	−16.0232	+	7.71638i	−1.03646	+	0.499131i	−0.873154	−	0.487445i	$-0.837929\pi$
$239$	−16.0232	+	7.71638i	−1.03646	+	0.499131i	−0.163302	+	0.986576i	$0.552215\pi$
$240$	−0.0829648	−	1.10709i	−0.00535536	−	0.0714623i
$241$	16.3106	+	5.03116i	1.05066	+	0.324085i	0.771546	−	0.636173i	$-0.219484\pi$
$241$	16.3106	+	5.03116i	1.05066	+	0.324085i	0.279112	+	0.960258i	$0.409960\pi$
$242$	−4.11740	+	2.80719i	−0.264676	+	0.180453i
$243$	−0.988831	−	0.149042i	−0.0634335	−	0.00956107i
$244$	7.26621			0.465171
$245$	7.11902	−	3.11665i	0.454817	−	0.199115i
$246$	1.89063			0.120542
$247$	20.8638	+	3.14471i	1.32753	+	0.200093i
$248$	−7.91917	+	5.39920i	−0.502868	+	0.342850i
$249$	5.44035	+	1.67813i	0.344768	+	0.106347i
$250$	0.727392	+	9.70637i	0.0460043	+	0.613885i
$251$	1.73431	−	0.835198i	0.109468	−	0.0527172i	−0.378348	−	0.925663i	$-0.623508\pi$
$251$	1.73431	−	0.835198i	0.109468	−	0.0527172i	0.487817	+	0.872946i	$0.337793\pi$
$252$	−2.54189	+	0.734035i	−0.160124	+	0.0462398i
$253$	5.70276	+	2.74631i	0.358530	+	0.172659i
$254$	1.48585	−	3.78589i	0.0932308	−	0.237548i
$255$	−0.592477	+	7.90606i	−0.0371024	+	0.495097i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	−0.923604	+	0.284894i	−0.0576128	+	0.0177712i	−0.323428	−	0.946253i	$-0.604835\pi$
$257$	−0.923604	+	0.284894i	−0.0576128	+	0.0177712i	0.265815	+	0.964024i	$0.414359\pi$
$258$	3.61385	−	4.53162i	0.224988	−	0.282126i
$259$	19.8816	+	6.52839i	1.23538	+	0.405654i
$260$	−1.94665	−	2.44102i	−0.120726	−	0.151386i
$261$	−4.89213	−	3.33540i	−0.302815	−	0.206456i
$262$	−5.64096	−	5.23405i	−0.348500	−	0.323361i
$263$	5.36643	−	9.29493i	0.330908	−	0.573150i	−0.651782	−	0.758406i	$-0.725978\pi$
$263$	5.36643	−	9.29493i	0.330908	−	0.573150i	0.982690	+	0.185257i	$0.0593117\pi$
$264$	1.22645	+	2.12427i	0.0754827	+	0.130740i
$265$	2.43372	−	10.6628i	0.149502	−	0.655012i
$266$	−4.76603	+	19.2693i	−0.292224	+	1.18148i
$267$	2.96428	+	12.9874i	0.181411	+	0.794814i
$268$	−0.113508	+	0.105320i	−0.00693362	+	0.00643346i
$269$	2.13176	−	0.321311i	0.129975	−	0.0195906i	−0.0837323	−	0.996488i	$-0.526684\pi$
$269$	2.13176	−	0.321311i	0.129975	−	0.0195906i	0.213708	+	0.976898i	$0.431446\pi$
$270$	1.09779	−	0.165466i	0.0668095	−	0.0100699i
$271$	−12.8115	+	11.8873i	−0.778242	+	0.722103i	−0.965555	−	0.260197i	$-0.916212\pi$
$271$	−12.8115	+	11.8873i	−0.778242	+	0.722103i	0.187314	+	0.982300i	$0.440022\pi$
$272$	−1.58909	−	6.96226i	−0.0963528	−	0.422149i
$273$	−4.74352	+	5.73253i	−0.287091	+	0.346948i
$274$	−0.887833	+	3.88985i	−0.0536360	+	0.234994i
$275$	−4.62061	−	8.00313i	−0.278633	−	0.482607i
$276$	−1.29023	+	2.23474i	−0.0776626	+	0.134516i
$277$	−8.17162	−	7.58216i	−0.490985	−	0.455568i	0.395405	−	0.918507i	$-0.370604\pi$
$277$	−8.17162	−	7.58216i	−0.490985	−	0.455568i	−0.886390	+	0.462939i	$0.846795\pi$
$278$	−8.81553	−	6.01032i	−0.528720	−	0.360475i
$279$	−5.97590	−	7.49355i	−0.357768	−	0.448627i
$280$	2.45641	−	1.61051i	0.146799	−	0.0962464i
$281$	9.33790	−	11.7094i	0.557053	−	0.698522i	−0.420957	−	0.907080i	$-0.638306\pi$
$281$	9.33790	−	11.7094i	0.557053	−	0.698522i	0.978010	+	0.208559i	$0.0668772\pi$
$282$	−8.91858	+	2.75102i	−0.531094	+	0.163821i
$283$	−5.57666	−	14.2091i	−0.331498	−	0.844643i	−0.995309	−	0.0967428i	$-0.969158\pi$
$283$	−5.57666	−	14.2091i	−0.331498	−	0.844643i	0.663812	−	0.747900i	$-0.268938\pi$
$284$	−0.776853	+	10.3664i	−0.0460977	+	0.615132i
$285$	3.04305	−	7.75356i	0.180254	−	0.459281i
$286$	6.21511	+	2.99304i	0.367507	+	0.176982i
$287$	2.42238	+	4.37648i	0.142989	+	0.258335i
$288$	−0.900969	+	0.433884i	−0.0530901	+	0.0255668i
$289$	2.54069	+	33.9032i	0.149453	+	1.99431i
$290$	6.28137	+	1.93755i	0.368855	+	0.113777i
$291$	6.78994	−	4.62930i	0.398033	−	0.271375i
$292$	2.08994	+	0.315008i	0.122304	+	0.0184344i
$293$	−3.57910			−0.209093			−0.104547	−	0.994520i	$-0.533339\pi$
$293$	−3.57910			−0.209093			−0.104547	+	0.994520i	$0.533339\pi$
$294$	−4.95596	−	4.94353i	−0.289038	−	0.288312i
$295$	8.74775			0.509314
$296$	7.82094	+	1.17882i	0.454583	+	0.0685174i
$297$	−2.02668	+	1.38177i	−0.117600	+	0.0801782i
$298$	6.32507	+	1.95103i	0.366402	+	0.113020i
$299$	0.542315	+	7.23670i	0.0313629	+	0.418509i
$300$	3.39437	−	1.63464i	0.195974	−	0.0943763i
$301$	15.1201	+	2.55924i	0.871510	+	0.147512i
$302$	14.4245	+	6.94647i	0.830036	+	0.399724i
$303$	2.56755	−	6.54201i	0.147502	−	0.375829i
$304$	−0.560670	+	7.48162i	−0.0321566	+	0.429100i
$305$	−2.94717	−	7.50926i	−0.168754	−	0.429979i
$306$	6.82404	−	2.10494i	0.390104	−	0.120331i
$307$	−4.38233	+	5.49527i	−0.250113	+	0.313631i	−0.891000	−	0.454004i	$-0.849995\pi$
$307$	−4.38233	+	5.49527i	−0.250113	+	0.313631i	0.640887	+	0.767635i	$0.278567\pi$
$308$	−3.34591	+	5.56074i	−0.190651	+	0.316852i
$309$	3.44893	+	4.32482i	0.196203	+	0.246031i
$310$	8.79181	+	5.99415i	0.499341	+	0.340445i
$311$	10.7864	+	10.0083i	0.611641	+	0.567520i	0.923975	−	0.382452i	$-0.124920\pi$
$311$	10.7864	+	10.0083i	0.611641	+	0.567520i	−0.312334	+	0.949972i	$0.601111\pi$
$312$	−1.40614	+	2.43551i	−0.0796073	+	0.137884i
$313$	−13.7671	−	23.8454i	−0.778165	−	1.34782i	−0.932998	−	0.359880i	$-0.882817\pi$
$313$	−13.7671	−	23.8454i	−0.778165	−	1.34782i	0.154834	−	0.987941i	$-0.450516\pi$
$314$	−2.35695	+	10.3265i	−0.133010	+	0.582756i
$315$	1.78957	+	2.32919i	0.100831	+	0.131235i
$316$	0.855431	+	3.74789i	0.0481218	+	0.210835i
$317$	3.44450	−	3.19603i	0.193463	−	0.179507i	−0.577494	−	0.816395i	$-0.695969\pi$
$317$	3.44450	−	3.19603i	0.193463	−	0.179507i	0.770956	+	0.636888i	$0.219779\pi$
$318$	−9.74144	+	1.46829i	−0.546273	+	0.0823374i
$319$	−14.3613	+	2.16462i	−0.804078	+	0.121195i
$320$	0.813829	−	0.755123i	0.0454944	−	0.0422127i
$321$	−0.190445	−	0.834395i	−0.0106296	−	0.0465714i
$322$	−6.82613	−	0.123374i	−0.380405	−	0.00687535i
$323$	11.9223	−	52.2350i	0.663375	−	2.90644i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	5.29761	−	9.17573i	0.293859	−	0.508978i
$326$	16.1611	+	14.9953i	0.895078	+	0.830511i
$327$	−14.5739	−	9.93631i	−0.805938	−	0.549479i
$328$	1.17879	+	1.47816i	0.0650879	+	0.0816176i
$329$	−17.7951	−	17.1202i	−0.981075	−	0.943865i
$330$	1.69788	−	2.12907i	0.0934652	−	0.117202i
$331$	13.3985	−	4.13290i	0.736449	−	0.227164i	0.0962325	−	0.995359i	$-0.469321\pi$
$331$	13.3985	−	4.13290i	0.736449	−	0.227164i	0.640217	+	0.768194i	$0.278845\pi$
$332$	2.07999	+	5.29973i	0.114154	+	0.290861i
$333$	−0.591061	+	7.88716i	−0.0323900	+	0.432214i
$334$	−0.147787	+	0.376556i	−0.00808657	+	0.0206042i
$335$	0.154882	+	0.0745872i	0.00846210	+	0.00407513i
$336$	−2.15873	−	1.52966i	−0.117769	−	0.0834500i
$337$	0.524871	−	0.252765i	0.0285915	−	0.0137690i	−0.419533	−	0.907740i	$-0.637806\pi$
$337$	0.524871	−	0.252765i	0.0285915	−	0.0137690i	0.448125	+	0.893971i	$0.352092\pi$
$338$	−0.380453	−	5.07679i	−0.0206939	−	0.276141i
$339$	−12.7787	−	3.94172i	−0.694046	−	0.214085i
$340$	−6.55061	+	4.46613i	−0.355257	+	0.242210i
$341$	−23.2475	−	3.50399i	−1.25892	−	0.189752i
$342$	−7.50260			−0.405694
$343$	5.09352	−	17.8061i	0.275024	−	0.961437i
$344$	5.79616			0.312508
$345$	2.83281	+	0.426977i	0.152513	+	0.0229877i
$346$	−17.5635	+	11.9746i	−0.944220	+	0.643758i
$347$	8.74461	+	2.69735i	0.469435	+	0.144802i	0.520443	−	0.853897i	$-0.325767\pi$
$347$	8.74461	+	2.69735i	0.469435	+	0.144802i	−0.0510073	+	0.998698i	$0.516243\pi$
$348$	−0.442474	−	5.90441i	−0.0237191	−	0.316509i
$349$	−1.69572	+	0.816617i	−0.0907700	+	0.0437125i	−0.478718	−	0.877969i	$-0.658898\pi$
$349$	−1.69572	+	0.816617i	−0.0907700	+	0.0437125i	0.387948	+	0.921681i	$0.373184\pi$
$350$	8.13296	+	5.76297i	0.434725	+	0.308044i
$351$	−2.53379	−	1.22021i	−0.135243	−	0.0651298i
$352$	−0.896144	+	2.28334i	−0.0477646	+	0.121702i
$353$	−2.42652	+	32.3797i	−0.129151	+	1.72340i	0.437311	+	0.899310i	$0.355931\pi$
$353$	−2.42652	+	32.3797i	−0.129151	+	1.72340i	−0.566462	+	0.824088i	$0.691688\pi$
$354$	−2.87870	−	7.33481i	−0.153001	−	0.389841i
$355$	11.0282	−	3.40176i	0.585317	−	0.180546i
$356$	−8.30573	+	10.4151i	−0.440203	+	0.551997i
$357$	13.6159	+	13.0995i	0.720629	+	0.693297i
$358$	−9.23608	−	11.5817i	−0.488142	−	0.612111i
$359$	−20.7800	−	14.1676i	−1.09673	−	0.747735i	−0.126993	−	0.991904i	$-0.540533\pi$
$359$	−20.7800	−	14.1676i	−1.09673	−	0.747735i	−0.969733	+	0.244168i	$0.921485\pi$
$360$	0.813829	+	0.755123i	0.0428925	+	0.0397985i
$361$	−18.6445	+	32.2932i	−0.981289	+	1.69964i
$362$	−5.05992	−	8.76405i	−0.265944	−	0.460628i
$363$	1.10889	−	4.85836i	0.0582016	−	0.254998i
$364$	−7.43940	−	0.134458i	−0.389931	−	0.00704751i
$365$	−0.522133	−	2.28761i	−0.0273297	−	0.119739i
$366$	−5.32651	+	4.94228i	−0.278421	+	0.258337i
$367$	30.2467	−	4.55895i	1.57886	−	0.237975i	0.699679	−	0.714457i	$-0.253326\pi$
$367$	30.2467	−	4.55895i	1.57886	−	0.237975i	0.879184	+	0.476482i	$0.158088\pi$
$368$	−2.55163	+	0.384597i	−0.133013	+	0.0200485i
$369$	−1.38593	+	1.28596i	−0.0721488	+	0.0669443i
$370$	−1.95392	−	8.56067i	−0.101579	−	0.445048i
$371$	−15.8801	−	20.6684i	−0.824452	−	1.07305i
$372$	2.13278	−	9.34430i	0.110579	−	0.484479i
$373$	9.14041	+	15.8317i	0.473273	+	0.819732i	0.999532	−	0.0305919i	$-0.00973922\pi$
$373$	9.14041	+	15.8317i	0.473273	+	0.819732i	−0.526259	+	0.850324i	$0.676406\pi$
$374$	8.75844	−	15.1701i	0.452888	−	0.784426i
$375$	−7.13522	−	6.62052i	−0.368461	−	0.341882i
$376$	−7.71148	−	5.25760i	−0.397689	−	0.271140i
$377$	−10.3820	−	13.0186i	−0.534701	−	0.670494i
$378$	1.36407	−	2.26701i	0.0701599	−	0.116602i
$379$	−7.90209	+	9.90891i	−0.405903	+	0.508986i	−0.942204	−	0.335041i	$-0.891250\pi$
$379$	−7.90209	+	9.90891i	−0.405903	+	0.508986i	0.536301	+	0.844027i	$0.319821\pi$
$380$	7.95928	−	2.45511i	0.408303	−	0.125945i
$381$	1.48585	+	3.78589i	0.0761226	+	0.193957i
$382$	−0.367143	+	4.89918i	−0.0187847	+	0.250664i
$383$	−3.16173	+	8.05595i	−0.161557	+	0.411640i	−0.988613	−	0.150479i	$-0.951918\pi$
$383$	−3.16173	+	8.05595i	−0.161557	+	0.411640i	0.827057	+	0.562119i	$0.190014\pi$
$384$	−0.900969	−	0.433884i	−0.0459774	−	0.0221415i
$385$	7.10384	+	1.20240i	0.362045	+	0.0612800i
$386$	12.5608	−	6.04895i	0.639327	−	0.307883i
$387$	0.433148	+	5.77995i	0.0220181	+	0.293811i
$388$	7.85279	+	2.42227i	0.398665	+	0.122972i
$389$	1.34991	−	0.920353i	0.0684432	−	0.0466638i	−0.528615	−	0.848862i	$-0.677288\pi$
$389$	1.34991	−	0.920353i	0.0684432	−	0.0466638i	0.597058	+	0.802198i	$0.296336\pi$
$390$	3.08731	+	0.465337i	0.156332	+	0.0235633i
$391$	18.4278			0.931935
$392$	0.775012	−	6.95696i	0.0391440	−	0.351380i
$393$	7.69518			0.388170
$394$	−12.3133	−	1.85593i	−0.620336	−	0.0935006i
$395$	3.52629	−	2.40419i	0.177427	−	0.120968i
$396$	−2.34392	−	0.723004i	−0.117786	−	0.0363323i
$397$	2.17303	+	28.9971i	0.109061	+	1.45532i	0.736385	+	0.676563i	$0.236531\pi$
$397$	2.17303	+	28.9971i	0.109061	+	1.45532i	−0.627324	+	0.778759i	$0.715850\pi$
$398$	−13.2513	+	6.38148i	−0.664227	+	0.319875i
$399$	−9.61274	−	17.3672i	−0.481239	−	0.869445i
$400$	3.39437	+	1.63464i	0.169719	+	0.0817322i
$401$	−13.7061	+	34.9226i	−0.684451	+	1.74395i	−0.0163665	+	0.999866i	$0.505210\pi$
$401$	−13.7061	+	34.9226i	−0.684451	+	1.74395i	−0.668084	+	0.744086i	$0.732885\pi$
$402$	0.0115715	−	0.154410i	0.000577132	−	0.00770129i
$403$	−9.84765	−	25.0914i	−0.490547	−	1.24989i
$404$	6.71559	−	2.07149i	0.334113	−	0.103060i
$405$	−0.692194	+	0.867984i	−0.0343954	+	0.0431305i
$406$	13.1007	−	8.58929i	0.650177	−	0.426279i
$407$	12.0961	+	15.1680i	0.599582	+	0.751852i
$408$	5.90043	+	4.02284i	0.292115	+	0.199160i
$409$	−0.884112	−	0.820336i	−0.0437165	−	0.0405630i	0.658012	−	0.753007i	$-0.271398\pi$
$409$	−0.884112	−	0.820336i	−0.0437165	−	0.0405630i	−0.701729	+	0.712444i	$0.747588\pi$
$410$	1.04948	−	1.81776i	0.0518303	−	0.0897728i
$411$	−1.99494	−	3.45534i	−0.0984033	−	0.170439i
$412$	−1.23091	+	5.39297i	−0.0606426	+	0.265692i
$413$	13.2904	−	16.0614i	0.653978	−	0.790331i
$414$	−0.574205	−	2.51576i	−0.0282207	−	0.123643i
$415$	4.63336	−	4.29913i	0.227443	−	0.211036i
$416$	−2.78088	+	0.419150i	−0.136344	+	0.0205505i
$417$	10.5503	−	1.59020i	0.516650	−	0.0778725i
$418$	−13.4904	+	12.5173i	−0.659838	+	0.612240i
$419$	−3.75160	−	16.4368i	−0.183278	−	0.802992i	−0.980056	−	0.198721i	$-0.936321\pi$
$419$	−3.75160	−	16.4368i	−0.183278	−	0.802992i	0.796778	−	0.604272i	$-0.206536\pi$
$420$	−0.705251	+	2.85137i	−0.0344127	+	0.139133i
$421$	3.66576	−	16.0607i	0.178658	−	0.782753i	−0.803592	−	0.595180i	$-0.797081\pi$
$421$	3.66576	−	16.0607i	0.178658	−	0.782753i	0.982251	−	0.187573i	$-0.0600621\pi$
$422$	8.24936	+	14.2883i	0.401573	+	0.695544i
$423$	4.66662	−	8.08282i	0.226899	−	0.393000i
$424$	−7.22164	−	6.70070i	−0.350714	−	0.325415i
$425$	−22.2297	−	15.1559i	−1.07830	−	0.735171i
$426$	−6.48146	−	8.12749i	−0.314028	−	0.393778i
$427$	−18.2651	−	5.99759i	−0.883909	−	0.290244i
$428$	0.533615	−	0.669133i	0.0257933	−	0.0323437i
$429$	−6.59178	+	2.03330i	−0.318254	+	0.0981685i
$430$	−2.35092	−	5.99004i	−0.113371	−	0.288865i
$431$	−2.57822	+	34.4039i	−0.124188	+	1.65718i	0.492753	+	0.870169i	$0.335991\pi$
$431$	−2.57822	+	34.4039i	−0.124188	+	1.65718i	−0.616941	+	0.787009i	$0.711628\pi$
$432$	0.365341	−	0.930874i	0.0175775	−	0.0447867i
$433$	−16.4970	−	7.94454i	−0.792796	−	0.381790i	−0.00676457	−	0.999977i	$-0.502153\pi$
$433$	−16.4970	−	7.94454i	−0.792796	−	0.381790i	−0.786031	+	0.618187i	$0.787868\pi$
$434$	24.3630	−	7.03544i	1.16946	−	0.337712i
$435$	−5.92244	+	2.85210i	−0.283959	+	0.136747i
$436$	−1.31815	−	17.5895i	−0.0631280	−	0.842385i
$437$	−18.5000	−	5.70650i	−0.884975	−	0.272979i
$438$	−1.74629	+	1.19060i	−0.0834412	+	0.0568892i
$439$	−7.83165	−	1.18043i	−0.373784	−	0.0563389i	−0.0405361	−	0.999178i	$-0.512907\pi$
$439$	−7.83165	−	1.18043i	−0.373784	−	0.0563389i	−0.333248	+	0.942839i	$0.608145\pi$
$440$	2.72319			0.129823
$441$	6.99543	+	0.252950i	0.333116	+	0.0120452i
$442$	20.0834			0.955271
$443$	32.1324	+	4.84318i	1.52666	+	0.230106i	0.858071	−	0.513531i	$-0.171663\pi$
$443$	32.1324	+	4.84318i	1.52666	+	0.230106i	0.668584	+	0.743637i	$0.266901\pi$
$444$	−6.53495	+	4.45546i	−0.310135	+	0.211447i
$445$	14.1322	+	4.35921i	0.669932	+	0.206647i
$446$	0.658778	+	8.79078i	0.0311940	+	0.416255i
$447$	−5.96364	+	2.87194i	−0.282070	+	0.135838i
$448$	−0.150008	−	2.64150i	−0.00708720	−	0.124799i
$449$	17.1470	+	8.25755i	0.809216	+	0.389698i	0.792279	−	0.610159i	$-0.208894\pi$
$449$	17.1470	+	8.25755i	0.809216	+	0.389698i	0.0169367	+	0.999857i	$0.494609\pi$
$450$	−1.37641	+	3.50704i	−0.0648847	+	0.165323i
$451$	−0.346563	+	4.62456i	−0.0163190	+	0.217762i
$452$	−4.88565	−	12.4484i	−0.229802	−	0.585525i
$453$	−15.2987	+	4.71902i	−0.718795	+	0.221719i
$454$	12.9345	−	16.2193i	0.607044	−	0.761209i
$455$	2.87846	+	7.74278i	0.134944	+	0.362987i
$456$	−4.67779	−	5.86577i	−0.219058	−	0.274690i
$457$	20.7034	+	14.1153i	0.968464	+	0.660287i	0.940669	−	0.339326i	$-0.110199\pi$
$457$	20.7034	+	14.1153i	0.968464	+	0.660287i	0.0277950	+	0.999614i	$0.491151\pi$
$458$	−1.23710	−	1.14786i	−0.0578060	−	0.0536361i
$459$	−3.57065	+	6.18455i	−0.166664	+	0.288670i
$460$	1.43240	+	2.48099i	0.0667861	+	0.115677i
$461$	6.27621	−	27.4979i	0.292312	−	1.28070i	−0.588986	−	0.808143i	$-0.700473\pi$
$461$	6.27621	−	27.4979i	0.292312	−	1.28070i	0.881298	−	0.472560i	$-0.156670\pi$
$462$	−1.32954	−	6.35210i	−0.0618556	−	0.295527i
$463$	3.80824	+	16.6850i	0.176984	+	0.775417i	0.983012	+	0.183540i	$0.0587556\pi$
$463$	3.80824	+	16.6850i	0.176984	+	0.775417i	−0.806028	+	0.591877i	$0.798387\pi$
$464$	4.34037	−	4.02728i	0.201497	−	0.186962i
$465$	−10.5219	+	1.58592i	−0.487942	+	0.0735454i
$466$	8.81980	−	1.32937i	0.408569	−	0.0615819i
$467$	28.6108	−	26.5469i	1.32395	−	1.22845i	0.369801	−	0.929111i	$-0.379426\pi$
$467$	28.6108	−	26.5469i	1.32395	−	1.22845i	0.954148	−	0.299334i	$-0.0967646\pi$
$468$	−0.625793	−	2.74178i	−0.0289273	−	0.126739i
$469$	0.372258	−	0.171053i	0.0171893	−	0.00789850i
$470$	−2.30569	+	10.1019i	−0.106354	+	0.465966i
$471$	−5.29602	−	9.17297i	−0.244028	−	0.422668i
$472$	3.93974	−	6.82384i	0.181341	−	0.314093i
$473$	10.4221	+	9.67027i	0.479208	+	0.444640i
$474$	−3.17629	−	2.16556i	−0.145892	−	0.0994673i
$475$	17.6235	+	22.0991i	0.808620	+	1.01398i
$476$	−1.75221	+	18.8127i	−0.0803122	+	0.862279i
$477$	6.14229	−	7.70219i	0.281236	−	0.352659i
$478$	16.9943	−	5.24205i	0.777302	−	0.239766i
$479$	−3.59410	−	9.15762i	−0.164219	−	0.418422i	0.824950	−	0.565206i	$-0.191203\pi$
$479$	−3.59410	−	9.15762i	−0.164219	−	0.418422i	−0.989169	+	0.146783i	$0.953108\pi$
$480$	−0.0829648	+	1.10709i	−0.00378681	+	0.0505314i
$481$	−8.12635	+	20.7056i	−0.370530	+	0.944094i
$482$	−15.3786	−	7.40593i	−0.700475	−	0.337331i
$483$	5.08782	−	4.55251i	0.231504	−	0.207146i
$484$	4.48980	−	2.16217i	0.204082	−	0.0982806i
$485$	−0.681796	−	9.09793i	−0.0309588	−	0.413116i
$486$	0.955573	+	0.294755i	0.0433457	+	0.0133704i
$487$	32.4699	−	22.1376i	1.47135	−	1.00315i	0.479255	−	0.877676i	$-0.340907\pi$
$487$	32.4699	−	22.1376i	1.47135	−	1.00315i	0.992097	−	0.125475i	$-0.0400454\pi$
$488$	−7.18505	−	1.08297i	−0.325252	−	0.0490238i
$489$	−22.0463			−0.996967
$490$	−7.50401	+	2.02080i	−0.338997	+	0.0912905i
$491$	−4.38795			−0.198025			−0.0990127	−	0.995086i	$-0.531568\pi$
$491$	−4.38795			−0.198025			−0.0990127	+	0.995086i	$0.531568\pi$
$492$	−1.86952	−	0.281784i	−0.0842844	−	0.0127038i
$493$	−34.9362	+	23.8191i	−1.57345	+	1.07276i
$494$	−20.1621	−	6.21918i	−0.907135	−	0.279814i
$495$	0.203504	+	2.71557i	0.00914683	+	0.122056i
$496$	8.63543	−	4.15861i	0.387742	−	0.186727i
$497$	10.5093	−	25.4168i	0.471405	−	1.14010i
$498$	−5.12948	−	2.47023i	−0.229857	−	0.110693i
$499$	−4.67159	+	11.9030i	−0.209129	+	0.532852i	−0.996497	−	0.0836317i	$-0.973348\pi$
$499$	−4.67159	+	11.9030i	−0.209129	+	0.532852i	0.787368	+	0.616484i	$0.211443\pi$
$500$	0.727392	−	9.70637i	0.0325299	−	0.434082i
$501$	−0.147787	−	0.376556i	−0.00660265	−	0.0168233i
$502$	−1.83941	+	0.567384i	−0.0820971	+	0.0253236i
$503$	−6.82581	+	8.55929i	−0.304348	+	0.381640i	−0.910361	−	0.413814i	$-0.864196\pi$
$503$	−6.82581	+	8.55929i	−0.304348	+	0.381640i	0.606014	+	0.795454i	$0.292768\pi$
$504$	2.62290	−	0.346988i	0.116833	−	0.0154561i
$505$	−4.86461	−	6.10003i	−0.216472	−	0.271448i
$506$	−5.22975	−	3.56558i	−0.232491	−	0.158510i
$507$	3.73199	+	3.46278i	0.165743	+	0.153787i
$508$	−2.03352	+	3.52215i	−0.0902227	+	0.156270i
$509$	−15.1279	−	26.2023i	−0.670533	−	1.16140i	−0.977753	−	0.209759i	$-0.932732\pi$
$509$	−15.1279	−	26.2023i	−0.670533	−	1.16140i	0.307220	−	0.951639i	$-0.400601\pi$
$510$	1.76420	−	7.72945i	0.0781199	−	0.342266i
$511$	−4.99348	−	2.51689i	−0.220898	−	0.111341i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	5.49979	−	5.10306i	0.242822	−	0.225306i
$514$	0.955750	−	0.144056i	0.0421563	−	0.00635404i
$515$	6.07261	−	0.915299i	0.267591	−	0.0403329i
$516$	−4.24889	+	3.94239i	−0.187047	+	0.173554i
$517$	−5.09427	−	22.3195i	−0.224046	−	0.981609i
$518$	−18.6865	−	9.41866i	−0.821038	−	0.413832i
$519$	4.73017	−	20.7242i	0.207631	−	0.909692i
$520$	1.56109	+	2.70389i	0.0684584	+	0.118573i
$521$	−16.5143	+	28.6037i	−0.723507	+	1.25315i	0.236079	+	0.971734i	$0.424138\pi$
$521$	−16.5143	+	28.6037i	−0.723507	+	1.25315i	−0.959586	+	0.281416i	$0.909196\pi$
$522$	4.34037	+	4.02728i	0.189973	+	0.176269i
$523$	−26.0027	−	17.7283i	−1.13702	−	0.775205i	−0.159738	−	0.987159i	$-0.551065\pi$
$523$	−26.0027	−	17.7283i	−1.13702	−	0.775205i	−0.977280	+	0.211954i	$0.932017\pi$
$524$	4.79786	+	6.01633i	0.209596	+	0.262825i
$525$	−9.88170	+	1.30727i	−0.431273	+	0.0570538i
$526$	−6.69183	+	8.39128i	−0.291777	+	0.365877i
$527$	−65.4057	+	20.1750i	−2.84912	+	0.878837i
$528$	−0.896144	−	2.28334i	−0.0389996	−	0.0993695i
$529$	−1.22118	+	16.2956i	−0.0530949	+	0.708502i
$530$	−3.99575	+	10.1810i	−0.173564	+	0.442234i
$531$	7.09917	+	3.41878i	0.308078	+	0.148363i
$532$	7.58475	−	18.3438i	0.328841	−	0.795304i
$533$	−4.79046	+	2.30697i	−0.207498	+	0.0999258i
$534$	−0.995506	−	13.2841i	−0.0430798	−	0.574859i
$535$	−0.907949	−	0.280065i	−0.0392540	−	0.0121083i
$536$	0.127938	−	0.0872263i	0.00552606	−	0.00376760i
$537$	14.6481	+	2.20784i	0.632111	+	0.0952754i
$538$	−2.15583			−0.0929446
$539$	13.0005	−	11.2163i	0.559971	−	0.483120i
$540$	−1.11019			−0.0477751
$541$	31.7454	+	4.78486i	1.36484	+	0.205717i	0.790281	−	0.612744i	$-0.209934\pi$
$541$	31.7454	+	4.78486i	1.36484	+	0.205717i	0.574562	+	0.818461i	$0.305172\pi$
$542$	14.4401	−	9.84509i	0.620255	−	0.422883i
$543$	9.67025	+	2.98288i	0.414990	+	0.128008i
$544$	0.533671	+	7.12134i	0.0228809	+	0.305325i
$545$	−17.6432	+	8.49653i	−0.755753	+	0.363951i
$546$	5.54492	−	4.96151i	0.237301	−	0.212333i
$547$	6.17146	+	2.97202i	0.263873	+	0.127074i	0.561143	−	0.827719i	$-0.310362\pi$
$547$	6.17146	+	2.97202i	0.263873	+	0.127074i	−0.297270	+	0.954793i	$0.596076\pi$
$548$	1.45767	−	3.71408i	0.0622685	−	0.158658i
$549$	0.543004	−	7.24589i	0.0231749	−	0.309247i
$550$	3.37620	+	8.60241i	0.143961	+	0.366808i
$551$	42.4490	−	13.0938i	1.80839	−	0.557814i
$552$	1.60889	−	2.01748i	0.0684788	−	0.0858697i
$553$	0.943239	−	10.1272i	0.0401106	−	0.430651i
$554$	6.95029	+	8.71539i	0.295290	+	0.370281i
$555$	7.25506	+	4.94642i	0.307960	+	0.209964i
$556$	7.82127	+	7.25708i	0.331696	+	0.307769i
$557$	−5.79956	+	10.0451i	−0.245735	+	0.425626i	−0.962338	−	0.271856i	$-0.912363\pi$
$557$	−5.79956	+	10.0451i	−0.245735	+	0.425626i	0.716603	+	0.697481i	$0.245696\pi$
$558$	4.79230	+	8.30051i	0.202874	+	0.351389i
$559$	−3.62720	+	15.8918i	−0.153414	+	0.672151i
$560$	−2.66901	+	1.22641i	−0.112786	+	0.0518254i
$561$	3.89787	+	17.0777i	0.164568	+	0.721021i
$562$	−10.9788	+	10.1868i	−0.463113	+	0.429706i
$563$	−3.66347	+	0.552179i	−0.154397	+	0.0232716i	−0.225786	−	0.974177i	$-0.572495\pi$
$563$	−3.66347	+	0.552179i	−0.154397	+	0.0232716i	0.0713890	+	0.997449i	$0.477257\pi$
$564$	9.22899	−	1.39105i	0.388611	−	0.0585736i
$565$	−10.8832	+	10.0981i	−0.457860	+	0.424832i
$566$	3.39661	+	14.8815i	0.142770	+	0.625518i
$567$	0.542027	+	2.58963i	0.0227630	+	0.108754i
$568$	2.31321	−	10.1348i	0.0970599	−	0.425247i
$569$	−0.453693	−	0.785819i	−0.0190198	−	0.0329432i	0.856359	−	0.516381i	$-0.172721\pi$
$569$	−0.453693	−	0.785819i	−0.0190198	−	0.0329432i	−0.875379	+	0.483438i	$0.839388\pi$
$570$	−4.16467	+	7.21341i	−0.174439	+	0.302137i
$571$	−15.1092	−	14.0193i	−0.632299	−	0.586688i	0.297515	−	0.954717i	$-0.403842\pi$
$571$	−15.1092	−	14.0193i	−0.632299	−	0.586688i	−0.929814	+	0.368029i	$0.880033\pi$
$572$	−5.69961	−	3.88593i	−0.238312	−	0.162479i
$573$	−3.06315	−	3.84107i	−0.127965	−	0.160463i
$574$	−1.74305	−	4.68863i	−0.0727534	−	0.195700i
$575$	−6.06144	+	7.60080i	−0.252779	+	0.316975i
$576$	0.955573	−	0.294755i	0.0398155	−	0.0122815i
$577$	6.66218	+	16.9750i	0.277350	+	0.706677i	0.999882	+	0.0153395i	$0.00488291\pi$
$577$	6.66218	+	16.9750i	0.277350	+	0.706677i	−0.722532	+	0.691337i	$0.757022\pi$
$578$	2.54069	−	33.9032i	0.105679	−	1.41019i
$579$	−5.09337	+	12.9777i	−0.211673	+	0.539334i
$580$	−5.92244	−	2.85210i	−0.245916	−	0.118427i
$581$	−0.854038	−	15.0388i	−0.0354314	−	0.623914i
$582$	−7.40406	+	3.56561i	−0.306908	+	0.147799i
$583$	−1.80583	−	24.0971i	−0.0747896	−	0.997998i
$584$	−2.01965	−	0.622979i	−0.0835736	−	0.0257790i
$585$	−2.57967	+	1.75879i	−0.106656	+	0.0727170i
$586$	3.53912	+	0.533437i	0.146200	+	0.0220361i
$587$	−37.1325			−1.53262			−0.766312	−	0.642468i	$-0.777910\pi$
$587$	−37.1325			−1.53262			−0.766312	+	0.642468i	$0.777910\pi$
$588$	4.16381	+	5.62696i	0.171713	+	0.232052i
$589$	71.9095			2.96298
$590$	−8.65005	−	1.30378i	−0.356117	−	0.0536760i
$591$	10.2887	−	7.01469i	0.423219	−	0.288546i
$592$	−7.55789	−	2.33130i	−0.310627	−	0.0958159i
$593$	1.50754	+	20.1167i	0.0619071	+	0.826093i	0.938592	+	0.345028i	$0.112131\pi$
$593$	1.50754	+	20.1167i	0.0619071	+	0.826093i	−0.876685	+	0.481064i	$0.840250\pi$
$594$	2.20998	−	1.06427i	0.0906767	−	0.0436676i
$595$	20.1527	−	5.81960i	0.826179	−	0.238580i
$596$	−5.96364	−	2.87194i	−0.244280	−	0.117639i
$597$	5.37337	−	13.6911i	0.219917	−	0.560340i
$598$	0.542315	−	7.23670i	0.0221769	−	0.295931i
$599$	15.8390	+	40.3570i	0.647162	+	1.64894i	0.755754	+	0.654856i	$0.227271\pi$
$599$	15.8390	+	40.3570i	0.647162	+	1.64894i	−0.108592	+	0.994086i	$0.534634\pi$
$600$	−3.60009	+	1.11048i	−0.146973	+	0.0453352i
$601$	−6.27570	+	7.86947i	−0.255991	+	0.321003i	−0.893175	−	0.449709i	$-0.851528\pi$
$601$	−6.27570	+	7.86947i	−0.255991	+	0.321003i	0.637184	+	0.770712i	$0.280099\pi$
$602$	−14.5698	−	4.78420i	−0.593822	−	0.194989i
$603$	0.0965432	+	0.121061i	0.00393154	+	0.00493000i
$604$	−13.2281	−	9.01874i	−0.538242	−	0.366967i
$605$	−4.05555	−	3.76300i	−0.164882	−	0.152988i
$606$	−3.51391	+	6.08627i	−0.142743	+	0.247238i
$607$	20.1310	+	34.8680i	0.817093	+	1.41525i	0.907815	+	0.419371i	$0.137749\pi$
$607$	20.1310	+	34.8680i	0.817093	+	1.41525i	−0.0907216	+	0.995876i	$0.528917\pi$
$608$	1.66949	−	7.31449i	0.0677066	−	0.296642i
$609$	−3.76130	+	15.2071i	−0.152415	+	0.616224i
$610$	1.79505	+	7.86464i	0.0726795	+	0.318430i
$611$	19.2410	−	17.8530i	0.778406	−	0.722255i
$612$	−7.06155	+	1.06436i	−0.285446	+	0.0430241i
$613$	−34.3924	+	5.18382i	−1.38910	+	0.209372i	−0.800634	−	0.599153i	$-0.795504\pi$
$613$	−34.3924	+	5.18382i	−1.38910	+	0.209372i	−0.588461	+	0.808526i	$0.700266\pi$
$614$	5.15241	−	4.78074i	0.207934	−	0.192935i
$615$	0.467065	+	2.04634i	0.0188339	+	0.0825165i
$616$	4.13732	−	4.99995i	0.166698	−	0.201454i
$617$	−9.56905	+	41.9248i	−0.385236	+	1.68783i	0.295536	+	0.955332i	$0.404502\pi$
$617$	−9.56905	+	41.9248i	−0.385236	+	1.68783i	−0.680772	+	0.732496i	$0.738355\pi$
$618$	−2.76583	−	4.79056i	−0.111258	−	0.192704i
$619$	−9.56757	+	16.5715i	−0.384553	+	0.666065i	−0.991707	−	0.128519i	$-0.958978\pi$
$619$	−9.56757	+	16.5715i	−0.384553	+	0.666065i	0.607154	+	0.794584i	$0.292311\pi$
$620$	−7.80023	−	7.23756i	−0.313265	−	0.290667i
$621$	2.13207	+	1.45362i	0.0855571	+	0.0583319i
$622$	−9.17427	−	11.5042i	−0.367855	−	0.461275i
$623$	29.4748	−	19.3247i	1.18088	−	0.774229i
$624$	1.75343	−	2.19874i	0.0701935	−	0.0880199i
$625$	7.67440	−	2.36724i	0.306976	−	0.0946896i
$626$	10.0594	+	25.6309i	0.402055	+	1.02442i
$627$	1.37527	−	18.3516i	0.0549228	−	0.732894i
$628$	3.86970	−	9.85985i	0.154418	−	0.393451i
$629$	50.8891	+	24.5069i	2.02908	+	0.977153i
$630$	−1.42244	−	2.56990i	−0.0566713	−	0.102387i
$631$	−33.2331	+	16.0042i	−1.32299	+	0.637117i	−0.956071	−	0.293136i	$-0.905301\pi$
$631$	−33.2331	+	16.0042i	−1.32299	+	0.637117i	−0.366917	+	0.930254i	$0.619587\pi$
$632$	−0.287283	−	3.83352i	−0.0114275	−	0.152489i
$633$	−15.7657	−	4.86309i	−0.626632	−	0.193290i
$634$	−3.88238	+	2.64696i	−0.154189	+	0.105124i
$635$	4.46476	+	0.672954i	0.177179	+	0.0267054i
$636$	9.85147			0.390636
$637$	18.5895	+	6.47853i	0.736541	+	0.256689i
$638$	14.5235			0.574991
$639$	10.2793	+	1.54936i	0.406645	+	0.0612918i
$640$	−0.917284	+	0.625394i	−0.0362588	+	0.0247209i
$641$	−28.6071	−	8.82411i	−1.12991	−	0.348531i	−0.327233	−	0.944944i	$-0.606116\pi$
$641$	−28.6071	−	8.82411i	−1.12991	−	0.348531i	−0.802678	+	0.596412i	$0.796592\pi$
$642$	0.0639580	+	0.853460i	0.00252422	+	0.0336834i
$643$	−0.598326	+	0.288139i	−0.0235957	+	0.0113631i	−0.445644	−	0.895210i	$-0.647025\pi$
$643$	−0.598326	+	0.288139i	−0.0235957	+	0.0113631i	0.422049	+	0.906573i	$0.361311\pi$
$644$	6.73150	+	1.13938i	0.265258	+	0.0448978i
$645$	5.79760	+	2.79198i	0.228280	+	0.109934i
$646$	−19.5744	+	49.8747i	−0.770143	+	1.96229i
$647$	1.99857	−	26.6691i	0.0785720	−	1.04847i	−0.809002	−	0.587806i	$-0.799992\pi$
$647$	1.99857	−	26.6691i	0.0785720	−	1.04847i	0.887574	−	0.460665i	$-0.152389\pi$
$648$	0.365341	+	0.930874i	0.0143520	+	0.0365682i
$649$	18.4689	−	5.69690i	0.724968	−	0.223623i
$650$	−6.60601	+	8.28368i	−0.259109	+	0.324913i
$651$	−13.0740	+	21.7284i	−0.512412	+	0.851602i
$652$	−13.7456	−	17.2365i	−0.538320	−	0.675032i
$653$	29.5217	+	20.1275i	1.15527	+	0.787652i	0.980415	−	0.196942i	$-0.0631011\pi$
$653$	29.5217	+	20.1275i	1.15527	+	0.787652i	0.174857	+	0.984594i	$0.444054\pi$
$654$	12.9302	+	11.9975i	0.505610	+	0.469138i
$655$	4.27156	−	7.39857i	0.166904	−	0.289086i
$656$	−0.945317	−	1.63734i	−0.0369084	−	0.0639273i
$657$	0.470308	−	2.06056i	0.0183485	−	0.0803899i
$658$	15.0447	+	19.5812i	0.586504	+	0.763353i
$659$	2.51175	+	11.0047i	0.0978440	+	0.428682i	0.999996	−	0.00273531i	$-0.000870676\pi$
$659$	2.51175	+	11.0047i	0.0978440	+	0.428682i	−0.902152	+	0.431418i	$0.858014\pi$
$660$	−1.99624	+	1.85224i	−0.0777035	+	0.0720983i
$661$	12.3978	−	1.86866i	0.482217	−	0.0726825i	0.0965647	−	0.995327i	$-0.469215\pi$
$661$	12.3978	−	1.86866i	0.482217	−	0.0726825i	0.385652	+	0.922644i	$0.373976\pi$
$662$	−13.8648	+	2.08979i	−0.538872	+	0.0812220i
$663$	−14.7222	+	13.6602i	−0.571763	+	0.530518i
$664$	−1.26688	−	5.55055i	−0.0491643	−	0.215403i
$665$	−22.0337	−	0.398232i	−0.854432	−	0.0154428i
$666$	1.75998	−	7.71098i	0.0681979	−	0.298794i
$667$	7.63939	+	13.2318i	0.295798	+	0.512338i
$668$	0.202260	−	0.350324i	0.00782566	−	0.0135544i
$669$	−6.46217	−	5.99601i	−0.249842	−	0.231819i
$670$	−0.142035	−	0.0968381i	−0.00548730	−	0.00374118i
$671$	−11.1126	−	13.9348i	−0.428998	−	0.537946i
$672$	1.90664	+	1.83432i	0.0735501	+	0.0707605i
$673$	−18.8233	+	23.6037i	−0.725586	+	0.909857i	−0.998640	−	0.0521423i	$-0.983395\pi$
$673$	−18.8233	+	23.6037i	−0.725586	+	0.909857i	0.273053	+	0.961999i	$0.411966\pi$
$674$	−0.556681	+	0.171713i	−0.0214426	+	0.00661415i
$675$	−1.37641	−	3.50704i	−0.0529781	−	0.134986i
$676$	−0.380453	+	5.07679i	−0.0146328	+	0.195261i
$677$	−15.3346	+	39.0718i	−0.589355	+	1.50165i	0.255582	+	0.966787i	$0.417733\pi$
$677$	−15.3346	+	39.0718i	−0.589355	+	1.50165i	−0.844937	+	0.534865i	$0.820362\pi$
$678$	12.0485	+	5.80226i	0.462721	+	0.222835i
$679$	−17.7402	−	12.5706i	−0.680807	−	0.482416i
$680$	7.14309	−	3.43993i	0.273925	−	0.131915i
$681$	1.55030	+	20.6873i	0.0594074	+	0.792737i
$682$	22.4656	+	6.92971i	0.860251	+	0.265352i
$683$	−20.8432	+	14.2106i	−0.797542	+	0.543755i	−0.892139	−	0.451761i	$-0.850796\pi$
$683$	−20.8432	+	14.2106i	−0.797542	+	0.543755i	0.0945975	+	0.995516i	$0.469844\pi$
$684$	7.41880	+	1.11820i	0.283665	+	0.0427556i
$685$	−4.42954			−0.169244
$686$	−7.69049	+	16.8480i	−0.293624	+	0.643261i
$687$	1.68760			0.0643861
$688$	−5.73142	−	0.863873i	−0.218508	−	0.0329348i
$689$	22.8911	−	15.6069i	0.872081	−	0.594575i
$690$	−2.73753	−	0.844416i	−0.104216	−	0.0321464i
$691$	0.186734	+	2.49180i	0.00710371	+	0.0947924i	0.999629	−	0.0272494i	$-0.00867483\pi$
$691$	0.186734	+	2.49180i	0.00710371	+	0.0947924i	−0.992525	+	0.122042i	$0.961056\pi$
$692$	19.1521	−	9.22315i	0.728052	−	0.350611i
$693$	5.29515	+	3.75211i	0.201146	+	0.142531i
$694$	−8.24492	−	3.97054i	−0.312973	−	0.150720i
$695$	4.32752	−	11.0264i	0.164152	−	0.418253i
$696$	−0.442474	+	5.90441i	−0.0167719	+	0.223806i
$697$	4.93269	+	12.5683i	0.186839	+	0.476058i
$698$	1.79849	−	0.554762i	0.0680740	−	0.0209980i
$699$	−5.56117	+	6.97348i	−0.210343	+	0.263761i
$700$	−7.18320	−	6.91076i	−0.271499	−	0.261202i
$701$	−20.6777	−	25.9290i	−0.780986	−	0.979325i	−0.999994	−	0.00360188i	$-0.998853\pi$
$701$	−20.6777	−	25.9290i	−0.780986	−	0.979325i	0.219008	−	0.975723i	$-0.429718\pi$
$702$	2.32362	+	1.58422i	0.0876995	+	0.0597925i
$703$	−43.4994	−	40.3616i	−1.64061	−	1.52226i
$704$	1.22645	−	2.12427i	0.0462235	−	0.0800615i
$705$	−5.18084	−	8.97349i	−0.195122	−	0.337961i
$706$	7.22537	−	31.6564i	0.271930	−	1.19140i
$707$	−18.5908	−	0.336006i	−0.699180	−	0.0126368i
$708$	1.75335	+	7.68193i	0.0658950	+	0.288705i
$709$	2.45190	−	2.27503i	0.0920831	−	0.0854406i	−0.632788	−	0.774325i	$-0.718090\pi$
$709$	2.45190	−	2.27503i	0.0920831	−	0.0854406i	0.724871	+	0.688884i	$0.241899\pi$
$710$	−11.4121	+	1.72009i	−0.428287	+	0.0645538i
$711$	3.80134	−	0.572959i	0.142561	−	0.0214877i
$712$	9.76524	−	9.06082i	0.365968	−	0.339569i
$713$	5.50353	+	24.1126i	0.206109	+	0.903022i
$714$	−11.5114	−	14.9825i	−0.430804	−	0.560706i
$715$	−1.70415	+	7.46638i	−0.0637317	+	0.279227i
$716$	7.40676	+	12.8289i	0.276804	+	0.479438i
$717$	−8.89222	+	15.4018i	−0.332086	+	0.575190i
$718$	18.4363	+	17.1064i	0.688038	+	0.638406i
$719$	−1.34882	−	0.919608i	−0.0503024	−	0.0342956i	0.537908	−	0.843004i	$-0.319215\pi$
$719$	−1.34882	−	0.919608i	−0.0503024	−	0.0342956i	−0.588210	+	0.808708i	$0.700167\pi$
$720$	−0.692194	−	0.867984i	−0.0257965	−	0.0323478i
$721$	7.54554	−	12.5403i	0.281011	−	0.467026i
$722$	23.2493	−	29.1537i	0.865249	−	1.08499i
$723$	16.3106	−	5.03116i	0.606598	−	0.187111i
$724$	3.69720	+	9.42030i	0.137405	+	0.350103i
$725$	1.66701	−	22.2447i	0.0619111	−	0.826147i
$726$	−1.82060	+	4.63882i	−0.0675689	+	0.172163i
$727$	−23.4527	−	11.2942i	−0.869812	−	0.418880i	−0.0549193	−	0.998491i	$-0.517490\pi$
$727$	−23.4527	−	11.2942i	−0.869812	−	0.418880i	−0.814893	+	0.579611i	$0.803204\pi$
$728$	7.33627	+	1.24174i	0.271900	+	0.0460220i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	0.175350	+	2.33988i	0.00648999	+	0.0866030i
$731$	39.5532	+	12.2006i	1.46293	+	0.451254i
$732$	6.00362	−	4.09320i	0.221900	−	0.151289i
$733$	6.32588	+	0.953473i	0.233652	+	0.0352173i	0.264824	−	0.964297i	$-0.414686\pi$
$733$	6.32588	+	0.953473i	0.233652	+	0.0352173i	−0.0311725	+	0.999514i	$0.509924\pi$
$734$	−30.5883			−1.12904
$735$	4.12634	−	6.58538i	0.152202	−	0.242905i
$736$	2.58046			0.0951169
$737$	0.375572	+	0.0566084i	0.0138344	+	0.00208520i
$738$	1.56212	−	1.06503i	0.0575023	−	0.0392044i
$739$	49.7132	+	15.3345i	1.82873	+	0.564088i	0.999990	+	0.00445210i	$0.00141715\pi$
$739$	49.7132	+	15.3345i	1.82873	+	0.564088i	0.828739	+	0.559636i	$0.189059\pi$
$740$	0.656192	+	8.75627i	0.0241221	+	0.321887i
$741$	19.0100	−	9.15472i	0.698349	−	0.336307i
$742$	12.6222	+	22.8044i	0.463377	+	0.837175i
$743$	−0.613550	−	0.295470i	−0.0225090	−	0.0108397i	0.422595	−	0.906318i	$-0.361119\pi$
$743$	−0.613550	−	0.295470i	−0.0225090	−	0.0108397i	−0.445104	+	0.895479i	$0.646833\pi$
$744$	−3.50165	+	8.92206i	−0.128377	+	0.327099i
$745$	−0.549156	+	7.32797i	−0.0201195	+	0.268476i
$746$	−6.67874	−	17.0171i	−0.244526	−	0.623042i
$747$	5.44035	−	1.67813i	0.199052	−	0.0613994i
$748$	−10.9216	+	13.6953i	−0.399333	+	0.500748i
$749$	−1.89366	+	1.24155i	−0.0691928	+	0.0453652i
$750$	6.06879	+	7.61002i	0.221601	+	0.277879i
$751$	−28.0846	−	19.1478i	−1.02482	−	0.698712i	−0.0705065	−	0.997511i	$-0.522462\pi$
$751$	−28.0846	−	19.1478i	−1.02482	−	0.698712i	−0.954316	+	0.298799i	$0.903414\pi$
$752$	6.84174	+	6.34821i	0.249493	+	0.231495i
$753$	0.962467	−	1.66704i	0.0350743	−	0.0607504i
$754$	8.32573	+	14.4206i	0.303205	+	0.525167i
$755$	−3.95512	+	17.3285i	−0.143942	+	0.630649i
$756$	−1.68671	+	2.03838i	−0.0613450	+	0.0741353i
$757$	−1.62172	−	7.10524i	−0.0589426	−	0.258244i	0.936868	−	0.349683i	$-0.113711\pi$
$757$	−1.62172	−	7.10524i	−0.0589426	−	0.258244i	−0.995811	+	0.0914385i	$0.970854\pi$
$758$	9.29067	−	8.62049i	0.337452	−	0.313110i
$759$	6.25889	−	0.943376i	0.227183	−	0.0342424i
$760$	−8.23630	+	1.24142i	−0.298762	+	0.0450311i
$761$	24.1909	−	22.4459i	0.876920	−	0.813663i	−0.106630	−	0.994299i	$-0.534006\pi$
$761$	24.1909	−	22.4459i	0.876920	−	0.813663i	0.983550	+	0.180636i	$0.0578157\pi$
$762$	−0.905000	−	3.96506i	−0.0327847	−	0.143639i
$763$	−11.2051	+	45.3028i	−0.405651	+	1.64007i
$764$	1.09323	−	4.78974i	0.0395516	−	0.173287i
$765$	3.96411	+	6.86605i	0.143323	+	0.248242i
$766$	4.32709	−	7.49474i	0.156344	−	0.270796i
$767$	16.2440	+	15.0722i	0.586537	+	0.544226i
$768$	0.826239	+	0.563320i	0.0298143	+	0.0203271i
$769$	−10.8866	−	13.6513i	−0.392579	−	0.492279i	0.545786	−	0.837925i	$-0.316231\pi$
$769$	−10.8866	−	13.6513i	−0.392579	−	0.492279i	−0.938365	+	0.345646i	$0.887660\pi$
$770$	−6.84528	−	2.24774i	−0.246687	−	0.0810030i
$771$	−0.602631	+	0.755675i	−0.0217032	+	0.0272150i
$772$	−13.3220	+	4.10930i	−0.479470	+	0.147897i
$773$	0.959671	+	2.44520i	0.0345170	+	0.0879478i	0.947093	−	0.320959i	$-0.104005\pi$
$773$	0.959671	+	2.44520i	0.0345170	+	0.0879478i	−0.912576	+	0.408907i	$0.865910\pi$
$774$	0.433148	−	5.77995i	0.0155692	−	0.207756i
$775$	13.1924	−	33.6136i	0.473884	−	1.20744i
$776$	−7.40406	−	3.56561i	−0.265790	−	0.127998i
$777$	20.1045	−	5.80569i	0.721245	−	0.208278i
$778$	−1.47200	+	0.708880i	−0.0527739	+	0.0254146i
$779$	−1.06002	−	14.1450i	−0.0379792	−	0.506798i
$780$	−2.98347	−	0.920280i	−0.106825	−	0.0329513i
$781$	21.0682	−	14.3641i	0.753881	−	0.513987i
$782$	−18.2220	−	2.74653i	−0.651618	−	0.0982155i
$783$	−5.92096			−0.211598
$784$	−1.80324	+	6.76375i	−0.0644013	+	0.241563i
$785$	−11.7592			−0.419704
$786$	−7.60923	−	1.14691i	−0.271412	−	0.0409088i
$787$	0.848699	−	0.578633i	0.0302529	−	0.0206260i	−0.548099	−	0.836413i	$-0.684648\pi$
$787$	0.848699	−	0.578633i	0.0302529	−	0.0206260i	0.578352	+	0.815787i	$0.303696\pi$
$788$	11.8992	+	3.67041i	0.423891	+	0.130753i
$789$	−0.802067	−	10.7028i	−0.0285544	−	0.381031i
$790$	−3.84523	+	1.85177i	−0.136807	+	0.0658829i
$791$	2.00603	+	35.3243i	0.0713263	+	1.25599i
$792$	2.20998	+	1.06427i	0.0785283	+	0.0378173i
$793$	7.46562	−	19.0221i	0.265112	−	0.675495i
$794$	2.17303	−	28.9971i	0.0771179	−	1.02907i
$795$	−3.99575	−	10.1810i	−0.141715	−	0.361083i
$796$	14.0544	−	4.33521i	0.498145	−	0.153657i
$797$	4.44287	−	5.57119i	0.157375	−	0.197342i	−0.696893	−	0.717175i	$-0.745435\pi$
$797$	4.44287	−	5.57119i	0.157375	−	0.197342i	0.854267	+	0.519834i	$0.174006\pi$
$798$	6.91693	+	18.6059i	0.244857	+	0.658641i
$799$	−41.5565	−	52.1102i	−1.47016	−	1.84353i
$800$	−3.11283	−	2.12229i	−0.110055	−	0.0750344i
$801$	9.76524	+	9.06082i	0.345038	+	0.320148i
$802$	18.7580	−	32.4898i	0.662367	−	1.14725i
$803$	−2.59216	−	4.48974i	−0.0914752	−	0.158440i
$804$	−0.0344559	+	0.150961i	−0.00121517	+	0.00532399i
$805$	−1.55280	−	7.41879i	−0.0547290	−	0.261478i
$806$	5.99798	+	26.2789i	0.211270	+	0.925634i
$807$	1.58034	−	1.46634i	0.0556306	−	0.0516176i
$808$	−6.94932	+	1.04744i	−0.244476	+	0.0368489i
$809$	−47.1247	+	7.10291i	−1.65682	+	0.249725i	−0.909790	−	0.415068i	$-0.863758\pi$
$809$	−47.1247	+	7.10291i	−1.65682	+	0.249725i	−0.747027	+	0.664793i	$0.768520\pi$
$810$	0.813829	−	0.755123i	0.0285950	−	0.0265323i
$811$	−2.47996	−	10.8654i	−0.0870831	−	0.381536i	0.912540	−	0.408987i	$-0.134118\pi$
$811$	−2.47996	−	10.8654i	−0.0870831	−	0.381536i	−0.999623	+	0.0274513i	$0.991261\pi$
$812$	−14.2346	+	6.54080i	−0.499535	+	0.229537i
$813$	−3.88898	+	17.0387i	−0.136392	+	0.597574i
$814$	−9.70032	−	16.8015i	−0.339996	−	0.588891i
$815$	−12.2378	+	21.1965i	−0.428672	+	0.742481i
$816$	−5.23495	−	4.85732i	−0.183260	−	0.170040i
$817$	−35.9300	−	24.4967i	−1.25703	−	0.857030i
$818$	0.751973	+	0.942944i	0.0262921	+	0.0329693i
$819$	−0.690029	+	7.40855i	−0.0241116	+	0.258876i
$820$	−1.30869	+	1.64104i	−0.0457013	+	0.0573076i
$821$	−9.83768	+	3.03452i	−0.343337	+	0.105906i	−0.461628	−	0.887073i	$-0.652735\pi$
$821$	−9.83768	+	3.03452i	−0.343337	+	0.105906i	0.118291	+	0.992979i	$0.462258\pi$
$822$	1.45767	+	3.71408i	0.0508420	+	0.129543i
$823$	1.23089	−	16.4251i	0.0429061	−	0.572542i	−0.933777	−	0.357856i	$-0.883508\pi$
$823$	1.23089	−	16.4251i	0.0429061	−	0.572542i	0.976683	−	0.214687i	$-0.0688730\pi$
$824$	2.02094	−	5.14927i	0.0704028	−	0.179383i
$825$	−8.32605	−	4.00961i	−0.289876	−	0.139597i
$826$	−15.5358	+	13.9012i	−0.540560	+	0.483685i
$827$	2.91100	−	1.40187i	0.101225	−	0.0487476i	−0.382586	−	0.923920i	$-0.624966\pi$
$827$	2.91100	−	1.40187i	0.101225	−	0.0487476i	0.483811	+	0.875172i	$0.339252\pi$
$828$	0.192838	+	2.57324i	0.00670157	+	0.0894263i
$829$	−27.1786	−	8.38349i	−0.943952	−	0.291171i	−0.215684	−	0.976463i	$-0.569198\pi$
$829$	−27.1786	−	8.38349i	−0.943952	−	0.291171i	−0.728268	+	0.685292i	$0.759674\pi$
$830$	−5.22236	+	3.56055i	−0.181271	+	0.123588i
$831$	−11.0229	−	1.66143i	−0.382380	−	0.0576345i
$832$	2.81229			0.0974986
$833$	19.9327	−	45.8432i	0.690627	−	1.58837i
$834$	−10.6695			−0.369453
$835$	−0.444078	−	0.0669340i	−0.0153680	−	0.00231635i
$836$	15.2054	−	10.3668i	0.525888	−	0.358544i
$837$	−9.15879	−	2.82511i	−0.316574	−	0.0976502i
$838$	1.25992	+	16.8124i	0.0435231	+	0.580775i
$839$	−15.6822	+	7.55214i	−0.541409	+	0.260729i	−0.684541	−	0.728975i	$-0.739997\pi$
$839$	−15.6822	+	7.55214i	−0.541409	+	0.260729i	0.143131	+	0.989704i	$0.454283\pi$
$840$	1.12235	−	2.71441i	0.0387247	−	0.0936561i
$841$	−5.45787	−	2.62837i	−0.188203	−	0.0906336i
$842$	−6.01855	+	15.3350i	−0.207413	+	0.528479i
$843$	1.11922	−	14.9350i	0.0385480	−	0.514387i
$844$	−6.02766	−	15.3582i	−0.207481	−	0.528652i
$845$	5.40092	−	1.66596i	0.185797	−	0.0573109i
$846$	−5.81918	+	7.29702i	−0.200067	+	0.250877i
$847$	−13.0707	+	1.72914i	−0.449114	+	0.0594141i
$848$	6.14229	+	7.70219i	0.210927	+	0.264494i
$849$	−12.6119	−	8.59866i	−0.432840	−	0.295105i
$850$	19.7225	+	18.2998i	0.676477	+	0.627679i
$851$	10.2048	−	17.6752i	0.349815	−	0.605898i
$852$	5.19773	+	9.00272i	0.178071	+	0.308428i
$853$	−3.31494	+	14.5237i	−0.113502	+	0.497283i	0.885938	+	0.463804i	$0.153516\pi$
$853$	−3.31494	+	14.5237i	−0.113502	+	0.497283i	−0.999439	+	0.0334787i	$0.989341\pi$
$854$	17.1672	+	8.65287i	0.587449	+	0.296095i
$855$	−1.85345	−	8.12050i	−0.0633867	−	0.277715i
$856$	−0.627384	+	0.582128i	−0.0214436	+	0.0198967i
$857$	26.2016	−	3.94925i	0.895028	−	0.134904i	0.314609	−	0.949221i	$-0.398127\pi$
$857$	26.2016	−	3.94925i	0.895028	−	0.134904i	0.580420	+	0.814318i	$0.302889\pi$
$858$	6.82121	−	1.02813i	0.232872	−	0.0350998i
$859$	22.3290	−	20.7182i	0.761854	−	0.706897i	−0.200200	−	0.979755i	$-0.564159\pi$
$859$	22.3290	−	20.7182i	0.761854	−	0.706897i	0.962054	+	0.272858i	$0.0879688\pi$
$860$	1.43189	+	6.27352i	0.0488270	+	0.213925i
$861$	4.46682	+	2.25144i	0.152229	+	0.0767288i
$862$	7.67706	−	33.6354i	0.261482	−	1.14563i
$863$	−6.75965	−	11.7081i	−0.230101	−	0.398547i	0.727737	−	0.685857i	$-0.240572\pi$
$863$	−6.75965	−	11.7081i	−0.230101	−	0.398547i	−0.957838	+	0.287310i	$0.907239\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−17.2997	−	16.0518i	−0.588208	−	0.545777i
$866$	15.1287	+	10.3146i	0.514094	+	0.350503i
$867$	21.1976	+	26.5809i	0.719907	+	0.902735i
$868$	−25.1395	+	3.32574i	−0.853289	+	0.112883i
$869$	5.87926	−	7.37236i	0.199440	−	0.250090i
$870$	6.28137	−	1.93755i	0.212958	−	0.0656890i
$871$	0.159093	+	0.405362i	0.00539066	+	0.0137352i
$872$	−1.31815	+	17.5895i	−0.0446382	+	0.595656i
$873$	3.00233	−	7.64982i	0.101614	−	0.258907i
$874$	17.4429	+	8.40004i	0.590014	+	0.284136i
$875$	−9.84016	+	23.7985i	−0.332658	+	0.804537i
$876$	1.90424	−	0.917034i	0.0643383	−	0.0309837i
$877$	−1.04781	−	13.9821i	−0.0353821	−	0.472141i	−0.986549	−	0.163465i	$-0.947733\pi$
$877$	−1.04781	−	13.9821i	−0.0353821	−	0.472141i	0.951167	−	0.308677i	$-0.0998861\pi$
$878$	7.56824	+	2.33449i	0.255416	+	0.0787853i
$879$	−2.95719	+	2.01618i	−0.0997436	+	0.0680040i
$880$	−2.69277	−	0.405870i	−0.0907733	−	0.0136819i
$881$	57.1541			1.92557			0.962786	−	0.270266i	$-0.0871116\pi$
$881$	57.1541			1.92557			0.962786	+	0.270266i	$0.0871116\pi$
$882$	−6.87959	−	1.29274i	−0.231648	−	0.0435288i
$883$	16.4973			0.555179			0.277590	−	0.960700i	$-0.410464\pi$
$883$	16.4973			0.555179			0.277590	+	0.960700i	$0.410464\pi$
$884$	−19.8591	−	2.99328i	−0.667934	−	0.100675i
$885$	7.22773	−	4.92778i	0.242958	−	0.165646i
$886$	−31.0516	−	9.57816i	−1.04320	−	0.321785i
$887$	−0.413071	−	5.51205i	−0.0138696	−	0.185076i	−0.999836	−	0.0181306i	$-0.994229\pi$
$887$	−0.413071	−	5.51205i	−0.0138696	−	0.185076i	0.985966	−	0.166946i	$-0.0533905\pi$
$888$	7.12602	−	3.43171i	0.239133	−	0.115161i
$889$	8.01887	−	7.17516i	0.268944	−	0.240647i
$890$	−13.3247	−	6.41682i	−0.446644	−	0.215092i
$891$	−0.896144	+	2.28334i	−0.0300219	+	0.0764947i
$892$	0.658778	−	8.79078i	0.0220575	−	0.294337i
$893$	25.5825	+	65.1830i	0.856084	+	2.18127i
$894$	6.32507	−	1.95103i	0.211542	−	0.0652521i
$895$	10.2538	−	12.8579i	0.342748	−	0.429792i
$896$	−0.245362	+	2.63435i	−0.00819697	+	0.0880074i
$897$	4.52466	+	5.67374i	0.151074	+	0.189441i
$898$	−15.7247	−	10.7209i	−0.524741	−	0.357763i
$899$	−41.6008	−	38.5999i	−1.38746	−	1.28738i
$900$	1.88374	−	3.26273i	0.0627912	−	0.108758i
$901$	−35.1762	−	60.9269i	−1.17189	−	2.02977i
$902$	1.03195	−	4.52126i	0.0343601	−	0.150541i
$903$	13.9345	−	6.40293i	0.463712	−	0.213076i
$904$	2.97574	+	13.0376i	0.0989716	+	0.433623i
$905$	8.23582	−	7.64173i	0.273768	−	0.254020i
$906$	15.8312	−	2.38616i	0.525955	−	0.0792749i
$907$	18.0329	−	2.71802i	0.598771	−	0.0902502i	0.157339	−	0.987545i	$-0.449709\pi$
$907$	18.0329	−	2.71802i	0.598771	−	0.0902502i	0.441432	+	0.897294i	$0.354470\pi$
$908$	−15.2074	+	14.1104i	−0.504674	+	0.468269i
$909$	−1.56384	−	6.85161i	−0.0518692	−	0.227254i
$910$	−1.69231	−	8.08531i	−0.0560994	−	0.268026i
$911$	4.60182	−	20.1619i	0.152465	−	0.667993i	−0.839699	−	0.543052i	$-0.817269\pi$
$911$	4.60182	−	20.1619i	0.152465	−	0.667993i	0.992164	−	0.124941i	$-0.0398741\pi$
$912$	3.75130	+	6.49744i	0.124218	+	0.215152i
$913$	6.98252	−	12.0941i	0.231088	−	0.400256i
$914$	−18.3684	−	17.0434i	−0.607572	−	0.563744i
$915$	−6.66518	−	4.54424i	−0.220344	−	0.150228i
$916$	1.05220	+	1.31942i	0.0347658	+	0.0435949i
$917$	−7.09447	−	19.0835i	−0.234280	−	0.630191i
$918$	4.45253	−	5.58330i	0.146955	−	0.184276i
$919$	−38.3618	+	11.8330i	−1.26544	+	0.390336i	−0.853604	−	0.520922i	$-0.825588\pi$
$919$	−38.3618	+	11.8330i	−1.26544	+	0.390336i	−0.411835	+	0.911259i	$0.635112\pi$
$920$	−1.04663	−	2.66677i	−0.0345064	−	0.0879208i
$921$	−0.525256	+	7.00906i	−0.0173078	+	0.230956i
$922$	−10.3045	+	26.2553i	−0.339359	+	0.864673i
$923$	26.3398	+	12.6846i	0.866986	+	0.417519i
$924$	0.367954	+	6.47931i	0.0121048	+	0.213154i
$925$	−26.8471	+	12.9289i	−0.882726	+	0.425098i
$926$	−1.27894	−	17.0662i	−0.0420284	−	0.560830i
$927$	5.28590	+	1.63048i	0.173612	+	0.0535521i
$928$	−4.89213	+	3.33540i	−0.160592	+	0.109490i
$929$	32.1796	+	4.85030i	1.05578	+	0.159133i	0.653917	−	0.756567i	$-0.273125\pi$
$929$	32.1796	+	4.85030i	1.05578	+	0.159133i	0.401863	+	0.915700i	$0.368363\pi$
$930$	10.6408			0.348924
$931$	−34.2069	+	39.8503i	−1.12109	+	1.30604i
$932$	−8.91942			−0.292165
$933$	14.5500	+	2.19307i	0.476347	+	0.0717978i
$934$	−32.2478	+	21.9862i	−1.05518	+	0.719411i
$935$	18.5831	+	5.73214i	0.607734	+	0.187461i
$936$	0.210163	+	2.80443i	0.00686938	+	0.0916655i
$937$	−8.00970	+	3.85727i	−0.261665	+	0.126011i	−0.560117	−	0.828413i	$-0.689244\pi$
$937$	−8.00970	+	3.85727i	−0.261665	+	0.126011i	0.298452	+	0.954425i	$0.403530\pi$
$938$	−0.393594	+	0.113660i	−0.0128513	+	0.00371114i
$939$	−24.8075	−	11.9467i	−0.809563	−	0.389865i
$940$	3.78555	−	9.64542i	0.123471	−	0.314599i
$941$	0.841953	−	11.2351i	0.0274469	−	0.366253i	−0.966521	−	0.256586i	$-0.917402\pi$
$941$	0.841953	−	11.2351i	0.0274469	−	0.366253i	0.993968	−	0.109667i	$-0.0349786\pi$
$942$	3.86970	+	9.85985i	0.126082	+	0.321251i
$943$	4.66195	−	1.43802i	0.151814	−	0.0468284i
$944$	−4.91278	+	6.16043i	−0.159897	+	0.200505i
$945$	2.79069	+	0.916362i	0.0907813	+	0.0298093i
$946$	−8.86439	−	11.1156i	−0.288206	−	0.361399i
$947$	−24.3608	−	16.6089i	−0.791620	−	0.539717i	0.0986655	−	0.995121i	$-0.468543\pi$
$947$	−24.3608	−	16.6089i	−0.791620	−	0.539717i	−0.890285	+	0.455404i	$0.849495\pi$
$948$	2.81805	+	2.61477i	0.0915261	+	0.0849238i
$949$	2.97195	−	5.14757i	0.0964737	−	0.167097i
$950$	−14.1329	−	24.4789i	−0.458532	−	0.794201i
$951$	1.04559	−	4.58104i	0.0339057	−	0.148551i
$952$	4.53652	−	18.3414i	0.147030	−	0.594449i
$953$	11.9858	+	52.5133i	0.388259	+	1.70107i	0.670651	+	0.741773i	$0.266015\pi$
$953$	11.9858	+	52.5133i	0.388259	+	1.70107i	−0.282393	+	0.959299i	$0.591128\pi$
$954$	−7.22164	+	6.70070i	−0.233809	+	0.216943i
$955$	−5.39337	+	0.812919i	−0.174525	+	0.0263054i
$956$	−17.5858	+	2.65063i	−0.568765	+	0.0857276i
$957$	−10.6465	+	9.87849i	−0.344152	+	0.319326i
$958$	2.18909	+	9.59101i	0.0707261	+	0.309871i
$959$	−6.72978	+	8.13292i	−0.217316	+	0.262626i
$960$	0.247041	−	1.08236i	0.00797322	−	0.0349330i
$961$	−30.4323	−	52.7104i	−0.981689	−	1.70033i
$962$	11.1216	−	19.2632i	0.358575	−	0.621069i
$963$	−0.627384	−	0.582128i	−0.0202172	−	0.0187588i
$964$	14.1030	+	9.61527i	0.454228	+	0.309687i
$965$	9.65016	+	12.1009i	0.310650	+	0.389542i
$966$	−5.70951	+	3.74336i	−0.183701	+	0.120441i
$967$	−9.36942	+	11.7489i	−0.301300	+	0.377819i	−0.909316	−	0.416106i	$-0.863394\pi$
$967$	−9.36942	+	11.7489i	−0.301300	+	0.377819i	0.608016	+	0.793925i	$0.291966\pi$
$968$	−4.76191	+	1.46885i	−0.153053	+	0.0472107i
$969$	−19.5744	−	49.8747i	−0.628819	−	1.60221i
$970$	−0.681796	+	9.09793i	−0.0218911	+	0.292117i
$971$	3.19052	−	8.12930i	0.102389	−	0.260882i	−0.870495	−	0.492177i	$-0.836201\pi$
$971$	3.19052	−	8.12930i	0.102389	−	0.260882i	0.972884	+	0.231295i	$0.0742964\pi$
$972$	−0.900969	−	0.433884i	−0.0288986	−	0.0139168i
$973$	−13.6703	−	24.6979i	−0.438250	−	0.791778i
$974$	−35.4067	+	17.0510i	−1.13450	+	0.546348i
$975$	−0.791782	−	10.5656i	−0.0253573	−	0.338370i
$976$	6.94339	+	2.14175i	0.222252	+	0.0685558i
$977$	43.4647	−	29.6338i	1.39056	−	0.948068i	0.390943	−	0.920415i	$-0.372149\pi$
$977$	43.4647	−	29.6338i	1.39056	−	0.948068i	0.999618	−	0.0276531i	$-0.00880337\pi$
$978$	21.8000	+	3.28583i	0.697088	+	0.105069i
$979$	32.6759			1.04433
$980$	7.72139	−	0.879816i	0.246651	−	0.0281047i
$981$	−17.6388			−0.563165
$982$	4.33894	+	0.653990i	0.138461	+	0.0208697i
$983$	−2.32922	+	1.58804i	−0.0742907	+	0.0506505i	−0.599896	−	0.800078i	$-0.704791\pi$
$983$	−2.32922	+	1.58804i	−0.0742907	+	0.0506505i	0.525605	+	0.850729i	$0.323839\pi$
$984$	1.80664	+	0.557274i	0.0575936	+	0.0177653i
$985$	−1.03311	−	13.7859i	−0.0329177	−	0.439256i
$986$	38.0960	−	18.3461i	1.21322	−	0.584258i
$987$	−24.3471	−	4.12101i	−0.774977	−	0.131173i
$988$	19.0100	+	9.15472i	0.604788	+	0.291250i
$989$	5.46431	−	13.9228i	0.173755	−	0.442720i
$990$	0.203504	−	2.71557i	0.00646778	−	0.0863066i
$991$	12.3434	+	31.4506i	0.392103	+	0.999061i	0.981542	+	0.191248i	$0.0612536\pi$
$991$	12.3434	+	31.4506i	0.392103	+	0.999061i	−0.589439	+	0.807813i	$0.700651\pi$
$992$	−9.15879	+	2.82511i	−0.290792	+	0.0896974i
$993$	8.74223	−	10.9624i	0.277426	−	0.347882i
$994$	−14.1801	+	23.5666i	−0.449765	+	0.747486i
$995$	−10.1807	−	12.7661i	−0.322749	−	0.404714i
$996$	4.70402	+	3.20714i	0.149052	+	0.101622i
$997$	−25.5048	−	23.6650i	−0.807746	−	0.749478i	0.163759	−	0.986500i	$-0.447638\pi$
$997$	−25.5048	−	23.6650i	−0.807746	−	0.749478i	−0.971504	+	0.237022i	$0.923829\pi$
$998$	6.39346	−	11.0738i	0.202381	−	0.350535i
$999$	3.95464	+	6.84964i	0.125119	+	0.216713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.235.2	✓	24
3.2	odd	2		882.2.z.a.235.1		24
49.44	even	21	inner	294.2.m.b.289.2	yes	24
147.44	odd	42		882.2.z.a.289.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.235.2	✓	24	1.1	even	1	trivial
294.2.m.b.289.2	yes	24	49.44	even	21	inner
882.2.z.a.235.1		24	3.2	odd	2
882.2.z.a.289.1		24	147.44	odd	42

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0829648 - 1.10709i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-2.15873 - 1.52966i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})\)	\(q+(-0.988831 - 0.149042i) q^{2} +(0.826239 - 0.563320i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.0829648 - 1.10709i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(-2.15873 - 1.52966i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(-0.0829648 + 1.10709i) q^{10} +(-0.896144 - 2.28334i) q^{11} +(0.955573 - 0.294755i) q^{12} +(1.75343 - 2.19874i) q^{13} +(1.90664 + 1.83432i) q^{14} +(-0.692194 - 0.867984i) q^{15} +(0.826239 + 0.563320i) q^{16} +(-5.23495 - 4.85732i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.75130 + 6.49744i) q^{19} +(0.247041 - 1.08236i) q^{20} +(-2.64532 - 0.0478109i) q^{21} +(0.545821 + 2.39140i) q^{22} +(-1.89161 + 1.75516i) q^{23} +(-0.988831 + 0.149042i) q^{24} +(3.72539 - 0.561513i) q^{25} +(-2.06155 + 1.91284i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-1.61195 - 2.09800i) q^{28} +(1.31754 - 5.77251i) q^{29} +(0.555096 + 0.961455i) q^{30} +(4.79230 - 8.30051i) q^{31} +(-0.733052 - 0.680173i) q^{32} +(-2.02668 - 1.38177i) q^{33} +(4.45253 + 5.58330i) q^{34} +(-1.51438 + 2.51682i) q^{35} +(0.623490 - 0.781831i) q^{36} +(-7.55789 + 2.33130i) q^{37} +(-2.74101 - 6.98397i) q^{38} +(0.210163 - 2.80443i) q^{39} +(-0.405599 + 1.03345i) q^{40} +(-1.70340 - 0.820316i) q^{41} +(2.60865 + 0.441541i) q^{42} +(-5.22216 + 2.51486i) q^{43} +(-0.183305 - 2.44604i) q^{44} +(-1.06087 - 0.327235i) q^{45} +(2.13207 - 1.45362i) q^{46} +(9.22899 + 1.39105i) q^{47} +1.00000 q^{48} +(2.32025 + 6.60427i) q^{49} -3.76747 q^{50} +(-7.06155 - 1.06436i) q^{51} +(2.32362 - 1.58422i) q^{52} +(9.41380 + 2.90377i) q^{53} +(0.0747301 + 0.997204i) q^{54} +(-2.45351 + 1.18155i) q^{55} +(1.28125 + 2.31482i) q^{56} +(6.75961 + 3.25526i) q^{57} +(-2.16317 + 5.51167i) q^{58} +(-0.588835 + 7.85746i) q^{59} +(-0.405599 - 1.03345i) q^{60} +(6.94339 - 2.14175i) q^{61} +(-5.97590 + 7.49355i) q^{62} +(-2.21260 + 1.45066i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-2.57967 - 1.75879i) q^{65} +(1.79810 + 1.66839i) q^{66} +(-0.0774217 + 0.134098i) q^{67} +(-3.57065 - 6.18455i) q^{68} +(-0.574205 + 2.51576i) q^{69} +(1.87257 - 2.26300i) q^{70} +(2.31321 + 10.1348i) q^{71} +(-0.733052 + 0.680173i) q^{72} +(2.08994 - 0.315008i) q^{73} +(7.82094 - 1.17882i) q^{74} +(2.76175 - 2.56253i) q^{75} +(1.66949 + 7.31449i) q^{76} +(-1.55820 + 6.29991i) q^{77} +(-0.625793 + 2.74178i) q^{78} +(1.92214 + 3.32924i) q^{79} +(0.555096 - 0.961455i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(1.56212 + 1.06503i) q^{82} +(3.54971 + 4.45119i) q^{83} +(-2.51370 - 0.825408i) q^{84} +(-4.94317 + 6.19854i) q^{85} +(5.53865 - 1.70845i) q^{86} +(-2.16317 - 5.51167i) q^{87} +(-0.183305 + 2.44604i) q^{88} +(-4.86684 + 12.4005i) q^{89} +(1.00025 + 0.481695i) q^{90} +(-7.14852 + 2.06432i) q^{91} +(-2.32491 + 1.11962i) q^{92} +(-0.716259 - 9.55781i) q^{93} +(-8.91858 - 2.75102i) q^{94} +(6.88202 - 4.69208i) q^{95} +(-0.988831 - 0.149042i) q^{96} +8.21789 q^{97} +(-1.31002 - 6.87632i) q^{98} -2.45290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

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