LMFDB - Embedded newform 538.2.e.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(9,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([109]))

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

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

chi := DirichletCharacter("538.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.e (of order $134$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$1452$
Relative dimension:	$22$ over $\Q(\zeta_{134})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{134}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	538.49
Dual form			538.2.e.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.902417 - 0.430864i) q^{2} +(-0.405300 - 2.86221i) q^{3} +(0.628713 + 0.777638i) q^{4} +(0.0702905 + 2.99759i) q^{5} +(-0.867475 + 2.75754i) q^{6} +(-1.94113 + 2.77992i) q^{7} +(-0.232305 - 0.972643i) q^{8} +(-5.14594 + 1.48719i) q^{9} +O(q^{10})$	\(q+(-0.902417 - 0.430864i) q^{2} +(-0.405300 - 2.86221i) q^{3} +(0.628713 + 0.777638i) q^{4} +(0.0702905 + 2.99759i) q^{5} +(-0.867475 + 2.75754i) q^{6} +(-1.94113 + 2.77992i) q^{7} +(-0.232305 - 0.972643i) q^{8} +(-5.14594 + 1.48719i) q^{9} +(1.22812 - 2.73536i) q^{10} +(1.08059 - 2.94502i) q^{11} +(1.97095 - 2.11469i) q^{12} +(0.409433 + 0.183827i) q^{13} +(2.94948 - 1.67228i) q^{14} +(8.55125 - 1.41611i) q^{15} +(-0.209440 + 0.977821i) q^{16} +(7.08482 - 2.59958i) q^{17} +(5.28456 + 0.875136i) q^{18} +(0.861878 - 2.18884i) q^{19} +(-2.28684 + 1.93928i) q^{20} +(8.74346 + 4.42923i) q^{21} +(-2.24405 + 2.19204i) q^{22} +(4.82336 - 0.683005i) q^{23} +(-2.68976 + 1.05912i) q^{24} +(-3.98609 + 0.187042i) q^{25} +(-0.290275 - 0.342299i) q^{26} +(2.79021 + 6.21455i) q^{27} +(-3.38218 + 0.238276i) q^{28} +(-0.421441 + 8.98139i) q^{29} +(-8.32694 - 2.40650i) q^{30} +(6.02794 - 7.10827i) q^{31} +(0.610310 - 0.792162i) q^{32} +(-8.86723 - 1.89928i) q^{33} +(-7.51352 - 0.706683i) q^{34} +(-8.46950 - 5.62330i) q^{35} +(-4.39181 - 3.06666i) q^{36} +(7.15819 - 1.35854i) q^{37} +(-1.72087 + 1.60389i) q^{38} +(0.360209 - 1.24639i) q^{39} +(2.89925 - 0.764723i) q^{40} +(-0.866815 - 1.81549i) q^{41} +(-5.98186 - 7.76425i) q^{42} +(7.44910 + 0.349540i) q^{43} +(2.96954 - 1.01126i) q^{44} +(-4.81969 - 15.3209i) q^{45} +(-4.64696 - 1.46186i) q^{46} +(-1.49279 + 12.6762i) q^{47} +(2.88362 + 0.203152i) q^{48} +(-1.54870 - 4.22078i) q^{49} +(3.67770 + 1.54867i) q^{50} +(-10.3120 - 19.2246i) q^{51} +(0.114465 + 0.433965i) q^{52} +(-5.03580 + 3.87976i) q^{53} +(0.159695 - 6.81032i) q^{54} +(8.90390 + 3.03217i) q^{55} +(3.15480 + 1.24224i) q^{56} +(-6.61425 - 1.57974i) q^{57} +(4.25007 - 7.92338i) q^{58} +(-1.90670 + 1.54155i) q^{59} +(6.47750 + 5.75945i) q^{60} +(1.19413 - 1.62748i) q^{61} +(-8.50241 + 3.81741i) q^{62} +(5.85468 - 17.1921i) q^{63} +(-0.892068 + 0.451900i) q^{64} +(-0.522258 + 1.24023i) q^{65} +(7.18361 + 5.53451i) q^{66} +(8.10352 - 10.0230i) q^{67} +(6.47585 + 3.87503i) q^{68} +(-3.90981 - 13.5287i) q^{69} +(5.22014 + 8.72377i) q^{70} +(-5.52961 + 9.75279i) q^{71} +(2.64193 + 4.65968i) q^{72} +(-7.15333 + 11.9545i) q^{73} +(-7.04502 - 1.85823i) q^{74} +(2.15091 + 11.3332i) q^{75} +(2.24400 - 0.705924i) q^{76} +(6.08934 + 8.72063i) q^{77} +(-0.862083 + 0.969562i) q^{78} +(-4.91747 - 5.03413i) q^{79} +(-2.94583 - 0.559084i) q^{80} +(3.06433 - 1.93261i) q^{81} +2.01181i q^{82} +(3.41233 + 5.41056i) q^{83} +(2.05279 + 9.58396i) q^{84} +(8.29047 + 21.0546i) q^{85} +(-6.57159 - 3.52498i) q^{86} +(25.8775 - 2.43390i) q^{87} +(-3.11548 - 0.366890i) q^{88} +(0.872891 - 1.31470i) q^{89} +(-2.25184 + 15.9025i) q^{90} +(-1.30579 + 0.781359i) q^{91} +(3.56364 + 3.32141i) q^{92} +(-22.7885 - 14.3723i) q^{93} +(6.80882 - 10.7960i) q^{94} +(6.62182 + 2.42970i) q^{95} +(-2.51470 - 1.42578i) q^{96} +(-2.62742 - 3.58090i) q^{97} +(-0.421007 + 4.47619i) q^{98} +(-1.18088 + 16.7619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9	$ 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99}+O(q^{100}) $ 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{19}{134}\right)$

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 $

$2$	−0.902417	−	0.430864i	−0.638105	−	0.304667i
$2$	−0.902417	−	0.430864i	−0.638105	−	0.304667i
$3$	−0.405300	−	2.86221i	−0.234000	−	1.65250i	−0.662576	−	0.748994i	$-0.730537\pi$
$3$	−0.405300	−	2.86221i	−0.234000	−	1.65250i	0.428577	−	0.903505i	$-0.359015\pi$
$4$	0.628713	+	0.777638i	0.314356	+	0.388819i
$5$	0.0702905	+	2.99759i	0.0314349	+	1.34056i	0.757454	+	0.652888i	$0.226443\pi$
$5$	0.0702905	+	2.99759i	0.0314349	+	1.34056i	−0.726020	+	0.687674i	$0.758632\pi$
$6$	−0.867475	+	2.75754i	−0.354145	+	1.12576i
$7$	−1.94113	+	2.77992i	−0.733678	+	1.05071i	0.262633	+	0.964896i	$0.415409\pi$
$7$	−1.94113	+	2.77992i	−0.733678	+	1.05071i	−0.996311	+	0.0858152i	$0.972651\pi$
$8$	−0.232305	−	0.972643i	−0.0821323	−	0.343881i
$9$	−5.14594	+	1.48719i	−1.71531	+	0.495729i
$10$	1.22812	−	2.73536i	0.388366	−	0.864997i
$11$	1.08059	−	2.94502i	0.325812	−	0.887956i	−0.664274	−	0.747489i	$-0.731259\pi$
$11$	1.08059	−	2.94502i	0.325812	−	0.887956i	0.990085	−	0.140467i	$-0.0448603\pi$
$12$	1.97095	−	2.11469i	0.568964	−	0.610457i
$13$	0.409433	+	0.183827i	0.113556	+	0.0509845i	0.465574	−	0.885009i	$-0.345848\pi$
$13$	0.409433	+	0.183827i	0.113556	+	0.0509845i	−0.352018	+	0.935993i	$0.614504\pi$
$14$	2.94948	−	1.67228i	0.788280	−	0.446937i
$15$	8.55125	−	1.41611i	2.20792	−	0.365637i
$16$	−0.209440	+	0.977821i	−0.0523601	+	0.244455i
$17$	7.08482	−	2.59958i	1.71832	−	0.630491i	0.720316	−	0.693646i	$-0.243997\pi$
$17$	7.08482	−	2.59958i	1.71832	−	0.630491i	0.998004	+	0.0631543i	$0.0201160\pi$
$18$	5.28456	+	0.875136i	1.24558	+	0.206272i
$19$	0.861878	−	2.18884i	0.197728	−	0.502154i	−0.797086	−	0.603866i	$-0.793626\pi$
$19$	0.861878	−	2.18884i	0.197728	−	0.502154i	0.994814	+	0.101712i	$0.0324320\pi$
$20$	−2.28684	+	1.93928i	−0.511354	+	0.433637i
$21$	8.74346	+	4.42923i	1.90798	+	0.966537i
$22$	−2.24405	+	2.19204i	−0.478433	+	0.467345i
$23$	4.82336	−	0.683005i	1.00574	−	0.142416i	0.382094	−	0.924123i	$-0.375203\pi$
$23$	4.82336	−	0.683005i	1.00574	−	0.142416i	0.623646	+	0.781707i	$0.285651\pi$
$24$	−2.68976	+	1.05912i	−0.549045	+	0.216192i
$25$	−3.98609	+	0.187042i	−0.797217	+	0.0374085i
$26$	−0.290275	−	0.342299i	−0.0569276	−	0.0671303i
$27$	2.79021	+	6.21455i	0.536976	+	1.19599i
$28$	−3.38218	+	0.238276i	−0.639173	+	0.0450299i
$29$	−0.421441	+	8.98139i	−0.0782597	+	1.66780i	0.510790	+	0.859706i	$0.329353\pi$
$29$	−0.421441	+	8.98139i	−0.0782597	+	1.66780i	−0.589049	+	0.808097i	$0.700498\pi$
$30$	−8.32694	−	2.40650i	−1.52028	−	0.439365i
$31$	6.02794	−	7.10827i	1.08265	−	1.27668i	0.123942	−	0.992289i	$-0.460446\pi$
$31$	6.02794	−	7.10827i	1.08265	−	1.27668i	0.958707	−	0.284394i	$-0.0917924\pi$
$32$	0.610310	−	0.792162i	0.107889	−	0.140036i
$33$	−8.86723	−	1.89928i	−1.54359	−	0.330622i
$34$	−7.51352	−	0.706683i	−1.28856	−	0.121195i
$35$	−8.46950	−	5.62330i	−1.43161	−	0.950512i
$36$	−4.39181	−	3.06666i	−0.731969	−	0.511111i
$37$	7.15819	−	1.35854i	1.17680	−	0.223343i	0.439078	−	0.898449i	$-0.355305\pi$
$37$	7.15819	−	1.35854i	1.17680	−	0.223343i	0.737721	+	0.675106i	$0.235902\pi$
$38$	−1.72087	+	1.60389i	−0.279161	+	0.260186i
$39$	0.360209	−	1.24639i	0.0576796	−	0.199582i
$40$	2.89925	−	0.764723i	0.458412	−	0.120913i
$41$	−0.866815	−	1.81549i	−0.135374	−	0.283532i	0.823525	−	0.567280i	$-0.192004\pi$
$41$	−0.866815	−	1.81549i	−0.135374	−	0.283532i	−0.958899	+	0.283748i	$0.908422\pi$
$42$	−5.98186	−	7.76425i	−0.923021	−	1.19805i
$43$	7.44910	+	0.349540i	1.13598	+	0.0533044i	0.606546	−	0.795048i	$-0.292555\pi$
$43$	7.44910	+	0.349540i	1.13598	+	0.0533044i	0.529431	+	0.848353i	$0.322405\pi$
$44$	2.96954	−	1.01126i	0.447675	−	0.152453i
$45$	−4.81969	−	15.3209i	−0.718477	−	2.28390i
$46$	−4.64696	−	1.46186i	−0.685157	−	0.215539i
$47$	−1.49279	+	12.6762i	−0.217746	+	1.84901i	0.253912	+	0.967227i	$0.418283\pi$
$47$	−1.49279	+	12.6762i	−0.217746	+	1.84901i	−0.471657	+	0.881782i	$0.656344\pi$
$48$	2.88362	+	0.203152i	0.416215	+	0.0293225i
$49$	−1.54870	−	4.22078i	−0.221243	−	0.602969i
$50$	3.67770	+	1.54867i	0.520106	+	0.219015i
$51$	−10.3120	−	19.2246i	−1.44397	−	2.69199i
$52$	0.114465	+	0.433965i	0.0158734	+	0.0601801i
$53$	−5.03580	+	3.87976i	−0.691721	+	0.532926i	−0.894929	−	0.446209i	$-0.852774\pi$
$53$	−5.03580	+	3.87976i	−0.691721	+	0.532926i	0.203208	+	0.979136i	$0.434863\pi$
$54$	0.159695	−	6.81032i	0.0217318	−	0.926767i
$55$	8.90390	+	3.03217i	1.20060	+	0.408858i
$56$	3.15480	+	1.24224i	0.421578	+	0.166001i
$57$	−6.61425	−	1.57974i	−0.876078	−	0.209242i
$58$	4.25007	−	7.92338i	0.558062	−	1.04039i
$59$	−1.90670	+	1.54155i	−0.248232	+	0.200693i	−0.744769	−	0.667322i	$-0.767440\pi$
$59$	−1.90670	+	1.54155i	−0.248232	+	0.200693i	0.496537	+	0.868015i	$0.334605\pi$
$60$	6.47750	+	5.75945i	0.836241	+	0.743541i
$61$	1.19413	−	1.62748i	0.152893	−	0.208378i	−0.723045	−	0.690801i	$-0.757258\pi$
$61$	1.19413	−	1.62748i	0.152893	−	0.208378i	0.875938	+	0.482423i	$0.160243\pi$
$62$	−8.50241	+	3.81741i	−1.07981	+	0.484811i
$63$	5.85468	−	17.1921i	0.737620	−	2.16601i
$64$	−0.892068	+	0.451900i	−0.111509	+	0.0564875i
$65$	−0.522258	+	1.24023i	−0.0647782	+	0.153832i
$66$	7.18361	+	5.53451i	0.884241	+	0.681251i
$67$	8.10352	−	10.0230i	0.990003	−	1.22451i	0.0155580	−	0.999879i	$-0.495048\pi$
$67$	8.10352	−	10.0230i	0.990003	−	1.22451i	0.974445	−	0.224628i	$-0.0721167\pi$
$68$	6.47585	+	3.87503i	0.785312	+	0.469916i
$69$	−3.90981	−	13.5287i	−0.470686	−	1.62866i
$70$	5.22014	+	8.72377i	0.623926	+	1.04269i
$71$	−5.52961	+	9.75279i	−0.656244	+	1.15744i	0.321353	+	0.946959i	$0.395862\pi$
$71$	−5.52961	+	9.75279i	−0.656244	+	1.15744i	−0.977597	+	0.210484i	$0.932496\pi$
$72$	2.64193	+	4.65968i	0.311355	+	0.549149i
$73$	−7.15333	+	11.9545i	−0.837234	+	1.39916i	0.0783019	+	0.996930i	$0.475050\pi$
$73$	−7.15333	+	11.9545i	−0.837234	+	1.39916i	−0.915536	+	0.402235i	$0.868233\pi$
$74$	−7.04502	−	1.85823i	−0.818967	−	0.216015i
$75$	2.15091	+	11.3332i	0.248366	+	1.30865i
$76$	2.24400	−	0.705924i	0.257404	−	0.0809750i
$77$	6.08934	+	8.72063i	0.693944	+	0.993808i
$78$	−0.862083	+	0.969562i	−0.0976117	+	0.109781i
$79$	−4.91747	−	5.03413i	−0.553259	−	0.566384i	0.380275	−	0.924873i	$-0.375829\pi$
$79$	−4.91747	−	5.03413i	−0.553259	−	0.566384i	−0.933534	+	0.358489i	$0.883292\pi$
$80$	−2.94583	−	0.559084i	−0.329353	−	0.0625075i
$81$	3.06433	−	1.93261i	0.340481	−	0.214734i
$82$			2.01181i			0.222167i
$83$	3.41233	+	5.41056i	0.374552	+	0.593886i	0.979271	−	0.202553i	$-0.0649238\pi$
$83$	3.41233	+	5.41056i	0.374552	+	0.593886i	−0.604720	+	0.796438i	$0.706715\pi$
$84$	2.05279	+	9.58396i	0.223978	+	1.04570i
$85$	8.29047	+	21.0546i	0.899228	+	2.28370i
$86$	−6.57159	−	3.52498i	−0.708633	−	0.380108i
$87$	25.8775	−	2.43390i	2.77436	−	0.260941i
$88$	−3.11548	−	0.366890i	−0.332111	−	0.0391106i
$89$	0.872891	−	1.31470i	0.0925263	−	0.139358i	−0.783912	−	0.620872i	$-0.786779\pi$
$89$	0.872891	−	1.31470i	0.0925263	−	0.139358i	0.876438	+	0.481514i	$0.159913\pi$
$90$	−2.25184	+	15.9025i	−0.237365	+	1.67627i
$91$	−1.30579	+	0.781359i	−0.136884	+	0.0819087i
$92$	3.56364	+	3.32141i	0.371535	+	0.346281i
$93$	−22.7885	−	14.3723i	−2.36306	−	1.49033i
$94$	6.80882	−	10.7960i	0.702276	−	1.11352i
$95$	6.62182	+	2.42970i	0.679385	+	0.249282i
$96$	−2.51470	−	1.42578i	−0.256655	−	0.145518i
$97$	−2.62742	−	3.58090i	−0.266774	−	0.363585i	0.652103	−	0.758131i	$-0.273887\pi$
$97$	−2.62742	−	3.58090i	−0.266774	−	0.363585i	−0.918876	+	0.394546i	$0.870902\pi$
$98$	−0.421007	+	4.47619i	−0.0425281	+	0.452163i
$99$	−1.18088	+	16.7619i	−0.118683	+	1.68464i
$100$	−2.65156	−	2.98213i	−0.265156	−	0.298213i
$101$	1.71984	−	7.20081i	0.171130	−	0.716507i	−0.818696	−	0.574227i	$-0.805303\pi$
$101$	1.71984	−	7.20081i	0.171130	−	0.716507i	0.989826	−	0.142280i	$-0.0454435\pi$
$102$	1.02255	+	21.7917i	0.101248	+	2.15770i
$103$	−1.23576	−	10.4935i	−0.121763	−	1.03396i	−0.908852	−	0.417120i	$-0.863040\pi$
$103$	−1.23576	−	10.4935i	−0.121763	−	1.03396i	0.787089	−	0.616840i	$-0.211587\pi$
$104$	0.0836846	−	0.440936i	0.00820595	−	0.0432373i
$105$	−12.6624	+	26.5206i	−1.23573	+	2.58815i
$106$	6.21604	−	1.33142i	0.603756	−	0.129319i
$107$	14.9964	−	1.76603i	1.44976	−	0.170729i	0.644932	−	0.764240i	$-0.276886\pi$
$107$	14.9964	−	1.76603i	1.44976	−	0.170729i	0.804826	+	0.593511i	$0.202259\pi$
$108$	−3.07843	+	6.07694i	−0.296222	+	0.584754i
$109$	−0.468841	−	0.344003i	−0.0449068	−	0.0329495i	0.568889	−	0.822414i	$-0.307373\pi$
$109$	−0.468841	−	0.344003i	−0.0449068	−	0.0329495i	−0.613796	+	0.789465i	$0.710358\pi$
$110$	−6.72858	−	6.57265i	−0.641545	−	0.626678i
$111$	−6.78965	−	19.9376i	−0.644445	−	1.89240i
$112$	−2.31171	−	2.48031i	−0.218437	−	0.234367i
$113$	−3.44393	+	1.45023i	−0.323978	+	0.136426i	−0.544039	−	0.839060i	$-0.683106\pi$
$113$	−3.44393	+	1.45023i	−0.323978	+	0.136426i	0.220061	+	0.975486i	$0.429374\pi$
$114$	5.28816	+	4.27543i	0.495281	+	0.400430i
$115$	2.38640	+	14.4104i	0.222533	+	1.34378i
$116$	−7.24923	+	5.31899i	−0.673075	+	0.493856i
$117$	−2.38030	−	0.337060i	−0.220059	−	0.0311612i
$118$	2.38484	−	0.569594i	0.219542	−	0.0524353i
$119$	−6.52592	+	24.7413i	−0.598230	+	2.26804i
$120$	−3.36387	−	7.98834i	−0.307078	−	0.729232i
$121$	0.884095	+	0.749727i	0.0803723	+	0.0681570i
$122$	−1.77883	+	0.954158i	−0.161048	+	0.0863854i
$123$	−4.84500	+	3.21683i	−0.436859	+	0.290052i
$124$	9.31750	+	0.218486i	0.836736	+	0.0196206i
$125$	0.212725	+	3.01950i	0.0190267	+	0.270072i
$126$	−12.6908	+	12.9919i	−1.13059	+	1.15741i
$127$	1.11465	−	0.778322i	0.0989088	−	0.0690649i	−0.522012	−	0.852938i	$-0.674818\pi$
$127$	1.11465	−	0.778322i	0.0989088	−	0.0690649i	0.620921	+	0.783873i	$0.286759\pi$
$128$	0.999725	−	0.0234426i	0.0883641	−	0.00207205i
$129$	−2.01866	−	21.4626i	−0.177733	−	1.88968i
$130$	1.00567	−	0.894185i	0.0882028	−	0.0784252i
$131$	1.74375	−	10.5297i	0.152352	−	0.919987i	−0.796586	−	0.604525i	$-0.793363\pi$
$131$	1.74375	−	10.5297i	0.152352	−	0.919987i	0.948938	−	0.315462i	$-0.102160\pi$
$132$	−4.09799	−	8.08959i	−0.356685	−	0.704109i
$133$	4.41178	+	6.64477i	0.382550	+	0.576175i
$134$	−11.6313	+	5.55343i	−1.00479	+	0.479743i
$135$	−18.4325	+	8.80072i	−1.58642	+	0.757445i
$136$	−4.17431	−	6.28710i	−0.357944	−	0.539114i
$137$	−2.93155	−	5.78700i	−0.250459	−	0.494416i	0.731902	−	0.681410i	$-0.238633\pi$
$137$	−2.93155	−	5.78700i	−0.250459	−	0.494416i	−0.982361	+	0.186994i	$0.940126\pi$
$138$	−2.30073	+	13.8931i	−0.195851	+	1.18266i
$139$	2.01182	−	1.78880i	0.170640	−	0.151724i	−0.574807	−	0.818289i	$-0.694923\pi$
$139$	2.01182	−	1.78880i	0.170640	−	0.151724i	0.745447	+	0.666565i	$0.232236\pi$
$140$	−0.951989	−	10.1216i	−0.0804577	−	0.855435i
$141$	36.8869	−	0.864962i	3.10644	−	0.0728430i
$142$	9.19214	−	6.41858i	0.771387	−	0.538635i
$143$	0.983805	−	1.00714i	0.0822699	−	0.0842217i
$144$	−0.376437	−	5.34329i	−0.0313697	−	0.445274i
$145$	−26.9521	−	0.632001i	−2.23825	−	0.0524848i
$146$	11.6060	−	7.70581i	0.960523	−	0.637737i
$147$	−11.4531	+	6.14340i	−0.944635	+	0.506699i
$148$	5.55690	+	4.71234i	0.456774	+	0.387352i
$149$	−7.93917	−	18.8535i	−0.650403	−	1.54454i	−0.828174	−	0.560471i	$-0.810620\pi$
$149$	−7.93917	−	18.8535i	−0.650403	−	1.54454i	0.177772	−	0.984072i	$-0.443111\pi$
$150$	2.94205	−	11.1540i	0.240218	−	0.910724i
$151$	−10.5446	+	2.51847i	−0.858110	+	0.204950i	−0.637537	−	0.770420i	$-0.720047\pi$
$151$	−10.5446	+	2.51847i	−0.858110	+	0.204950i	−0.220573	+	0.975370i	$0.570793\pi$
$152$	−2.32918	−	0.329820i	−0.188921	−	0.0267519i
$153$	−32.5920	+	23.9138i	−2.63491	+	1.93331i
$154$	−1.73772	−	10.4933i	−0.140029	−	0.845576i
$155$	21.7314	+	17.5696i	1.74551	+	1.41123i
$156$	1.19571	−	0.503509i	0.0957332	−	0.0403130i
$157$	1.38195	+	1.48273i	0.110292	+	0.118335i	0.784280	−	0.620406i	$-0.213032\pi$
$157$	1.38195	+	1.48273i	0.110292	+	0.118335i	−0.673989	+	0.738742i	$0.735420\pi$
$158$	2.26858	+	6.66165i	0.180479	+	0.529972i
$159$	13.1457	+	12.8411i	1.04252	+	1.01836i
$160$	2.41748	+	1.77378i	0.191118	+	0.140229i
$161$	−7.46407	+	14.7344i	−0.588251	+	1.16123i
$162$	−3.59799	+	0.423712i	−0.282685	+	0.0332900i
$163$	−18.8439	+	4.03619i	−1.47597	+	0.316139i	−0.875387	−	0.483423i	$-0.839393\pi$
$163$	−18.8439	+	4.03619i	−1.47597	+	0.316139i	−0.600583	+	0.799562i	$0.705065\pi$
$164$	0.866815	−	1.81549i	0.0676869	−	0.141766i
$165$	5.06997	−	26.7138i	0.394697	−	2.07967i
$166$	−0.748131	−	6.35283i	−0.0580662	−	0.493075i
$167$	0.479035	+	10.2088i	0.0370688	+	0.789978i	0.936024	+	0.351937i	$0.114477\pi$
$167$	0.479035	+	10.2088i	0.0370688	+	0.789978i	−0.898955	+	0.438041i	$0.855672\pi$
$168$	2.27690	−	9.53320i	0.175667	−	0.735502i
$169$	−8.50429	−	9.56455i	−0.654176	−	0.735734i
$170$	1.59021	−	22.5721i	0.121964	−	1.73120i
$171$	−1.17996	+	12.5454i	−0.0902335	+	0.959372i
$172$	4.41153	+	6.01246i	0.336376	+	0.458446i
$173$	6.04711	+	3.42857i	0.459753	+	0.260669i	0.705561	−	0.708649i	$-0.250695\pi$
$173$	6.04711	+	3.42857i	0.459753	+	0.260669i	−0.245808	+	0.969319i	$0.579053\pi$
$174$	−24.4010	−	8.95327i	−1.84983	−	0.678746i
$175$	7.21755	−	11.4441i	0.545595	−	0.865091i
$176$	2.65338	+	1.67343i	0.200006	+	0.126140i
$177$	5.18504	+	4.83260i	0.389731	+	0.363241i
$178$	−1.35417	+	0.810309i	−0.101499	+	0.0607352i
$179$	0.273297	−	1.93001i	0.0204272	−	0.144256i	−0.977278	−	0.211960i	$-0.932015\pi$
$179$	0.273297	−	1.93001i	0.0204272	−	0.144256i	0.997705	+	0.0677044i	$0.0215675\pi$
$180$	8.88389	−	13.3804i	0.662166	−	0.997316i
$181$	14.6896	+	1.72990i	1.09187	+	0.128583i	0.643636	−	0.765332i	$-0.277425\pi$
$181$	14.6896	+	1.72990i	1.09187	+	0.128583i	0.448237	+	0.893915i	$0.352052\pi$
$182$	1.51502	−	0.142495i	0.112301	−	0.0105624i
$183$	−5.14218	−	2.75825i	−0.380121	−	0.203896i
$184$	−1.78481	−	4.53274i	−0.131578	−	0.334158i
$185$	4.57550	+	21.3618i	0.336397	+	1.57055i
$186$	14.3723	+	22.7885i	1.05383	+	1.67094i
$187$		−	23.6740i		−	1.73121i
$188$	−10.7960	+	6.80882i	−0.787379	+	0.496584i
$189$	−22.6921	−	4.30670i	−1.65061	−	0.313267i
$190$	−4.92878	−	5.04571i	−0.357571	−	0.366054i
$191$	0.158405	−	0.178154i	0.0114618	−	0.0128908i	−0.741555	−	0.670892i	$-0.765911\pi$
$191$	0.158405	−	0.178154i	0.0114618	−	0.0128908i	0.753017	+	0.658001i	$0.228598\pi$
$192$	1.65499	+	2.37014i	0.119439	+	0.171050i
$193$	13.2527	−	4.16907i	0.953949	−	0.300096i	0.217097	−	0.976150i	$-0.430341\pi$
$193$	13.2527	−	4.16907i	0.953949	−	0.300096i	0.736852	+	0.676054i	$0.236311\pi$
$194$	0.828146	+	4.36352i	0.0594574	+	0.313283i
$195$	3.76148	+	0.992149i	0.269365	+	0.0710493i
$196$	2.30855	−	3.85799i	0.164896	−	0.275571i
$197$	5.52614	+	9.74667i	0.393721	+	0.694422i	0.994471	−	0.105016i	$-0.0334893\pi$
$197$	5.52614	+	9.74667i	0.393721	+	0.694422i	−0.600749	+	0.799437i	$0.705131\pi$
$198$	8.28776	−	14.6175i	0.588986	−	1.03882i
$199$	−13.7579	−	22.9919i	−0.975273	−	1.62985i	−0.756411	−	0.654096i	$-0.773049\pi$
$199$	−13.7579	−	22.9919i	−0.975273	−	1.62985i	−0.218862	−	0.975756i	$-0.570234\pi$
$200$	1.10791	+	3.83359i	0.0783414	+	0.271076i
$201$	−31.9724	−	19.1317i	−2.25516	−	1.34944i
$202$	−4.65458	+	5.75712i	−0.327495	+	0.405069i
$203$	−24.1495	−	18.6056i	−1.69496	−	1.30586i
$204$	8.46650	−	20.1058i	0.592773	−	1.40769i
$205$	5.38116	−	2.72597i	0.375837	−	0.190390i
$206$	−3.40612	+	10.0020i	−0.237316	+	0.696872i
$207$	−23.8050	+	10.6879i	−1.65456	+	0.742864i
$208$	−0.265502	+	0.361852i	−0.0184092	+	0.0250899i
$209$	−5.51483	−	4.90349i	−0.381469	−	0.339182i
$210$	22.8536	−	18.4769i	1.57705	−	1.27503i
$211$	−0.809512	+	1.50917i	−0.0557291	+	0.103895i	−0.907562	−	0.419919i	$-0.862059\pi$
$211$	−0.809512	+	1.50917i	−0.0557291	+	0.103895i	0.851833	+	0.523814i	$0.175491\pi$
$212$	−6.18312	−	1.47677i	−0.424659	−	0.101425i
$213$	30.1557	+	11.8741i	2.06624	+	0.813601i
$214$	−14.2939	−	4.86771i	−0.977113	−	0.332750i
$215$	−0.524177	+	22.3539i	−0.0357486	+	1.52452i
$216$	5.39636	−	4.15755i	0.367176	−	0.282885i
$217$	8.05943	+	30.5553i	0.547109	+	2.07423i
$218$	0.274871	+	0.512440i	0.0186166	+	0.0347068i
$219$	37.1155	+	15.6292i	2.50803	+	1.05613i
$220$	3.24007	+	8.83037i	0.218445	+	0.595344i
$221$	3.37863	+	0.238026i	0.227271	+	0.0160114i
$222$	−2.46332	+	20.9175i	−0.165327	+	1.40389i
$223$	0.602404	+	0.189506i	0.0403399	+	0.0126903i	0.320188	−	0.947354i	$-0.396254\pi$
$223$	0.602404	+	0.189506i	0.0403399	+	0.0126903i	−0.279848	+	0.960044i	$0.590284\pi$
$224$	1.01746	+	3.23430i	0.0679817	+	0.216101i
$225$	20.2340	−	6.89057i	1.34893	−	0.459371i
$226$	3.73271	+	0.175153i	0.248296	+	0.0116510i
$227$	7.13119	+	9.25605i	0.473314	+	0.614346i	0.966839	−	0.255386i	$-0.0822024\pi$
$227$	7.13119	+	9.25605i	0.473314	+	0.614346i	−0.493525	+	0.869731i	$0.664292\pi$
$228$	−2.93000	−	6.13669i	−0.194044	−	0.406412i
$229$	14.0028	−	3.69346i	0.925332	−	0.244071i	0.238715	−	0.971090i	$-0.423274\pi$
$229$	14.0028	−	3.69346i	0.925332	−	0.244071i	0.686617	+	0.727019i	$0.259095\pi$
$230$	4.05540	−	14.0324i	0.267405	−	0.925271i
$231$	22.4923	−	20.9635i	1.47988	−	1.37929i
$232$	8.83359	−	1.67651i	0.579954	−	0.110069i
$233$	4.74442	+	3.31288i	0.310817	+	0.217034i	0.717539	−	0.696518i	$-0.245268\pi$
$233$	4.74442	+	3.31288i	0.310817	+	0.217034i	−0.406722	+	0.913552i	$0.633328\pi$
$234$	2.00280	+	1.32976i	0.130927	+	0.0869288i
$235$	−38.1029	−	3.58376i	−2.48556	−	0.233778i
$236$	−2.39754	−	0.513530i	−0.156066	−	0.0334280i
$237$	−12.4157	+	16.1152i	−0.806487	+	1.04679i
$238$	16.5492	−	19.5152i	1.07273	−	1.26498i
$239$	−16.2960	−	4.70957i	−1.05410	−	0.304637i	−0.294923	−	0.955521i	$-0.595294\pi$
$239$	−16.2960	−	4.70957i	−1.05410	−	0.304637i	−0.759177	+	0.650884i	$0.774398\pi$
$240$	−0.406275	+	8.65818i	−0.0262249	+	0.558883i
$241$	1.61888	−	0.114051i	0.104281	−	0.00734664i	−0.0180396	−	0.999837i	$-0.505742\pi$
$241$	1.61888	−	0.114051i	0.104281	−	0.00734664i	0.122321	+	0.992491i	$0.460966\pi$
$242$	−0.474792	−	1.05749i	−0.0305208	−	0.0679781i
$243$	6.44425	+	7.59920i	0.413399	+	0.487489i
$244$	2.01636	−	0.0946152i	0.129084	−	0.00605712i
$245$	12.5433	−	4.93905i	0.801362	−	0.315544i
$246$	5.75822	−	0.815385i	0.367131	−	0.0519870i
$247$	0.755249	−	0.737747i	0.0480554	−	0.0469417i
$248$	−8.31413	−	4.21174i	−0.527948	−	0.267446i
$249$	14.1031	−	11.9597i	0.893751	−	0.757916i
$250$	1.10902	−	2.81650i	0.0701409	−	0.178131i
$251$	−2.06831	−	0.342517i	−0.130551	−	0.0216195i	0.0977440	−	0.995212i	$-0.468837\pi$
$251$	−2.06831	−	0.342517i	−0.130551	−	0.0216195i	−0.228295	+	0.973592i	$0.573315\pi$
$252$	17.0502	−	6.25610i	1.07406	−	0.394097i
$253$	3.20064	−	14.9429i	0.201222	−	0.939454i
$254$	−1.34123	+	0.222110i	−0.0841560	+	0.0139364i
$255$	56.9027	−	32.2625i	3.56339	−	2.02036i
$256$	−0.912270	−	0.409590i	−0.0570168	−	0.0255994i
$257$	−3.18681	+	3.41922i	−0.198788	+	0.213285i	−0.823110	−	0.567881i	$-0.807763\pi$
$257$	−3.18681	+	3.41922i	−0.198788	+	0.213285i	0.624322	+	0.781167i	$0.285375\pi$
$258$	−7.42578	+	20.2380i	−0.462309	+	1.25996i
$259$	−10.1183	+	22.5363i	−0.628723	+	1.40034i
$260$	−1.29280	+	0.373622i	−0.0801762	+	0.0231711i
$261$	−11.1883	−	46.8445i	−0.692539	−	2.89960i
$262$	−6.11047	+	8.75089i	−0.377506	+	0.540632i
$263$	−2.20603	+	7.01256i	−0.136030	+	0.432413i	−0.997103	−	0.0760687i	$-0.975763\pi$
$263$	−2.20603	+	7.01256i	−0.136030	+	0.432413i	0.861073	+	0.508482i	$0.169793\pi$
$264$	0.212586	+	9.06586i	0.0130837	+	0.557965i
$265$	−11.9839	−	14.8226i	−0.736165	−	0.910542i
$266$	−1.11828	−	7.89724i	−0.0685659	−	0.484211i
$267$	−4.11673	−	1.96555i	−0.251940	−	0.120290i
$268$	12.8891			0.787325
$269$	−11.4103	−	11.7816i	−0.695698	−	0.718334i
$269$	−11.4103	−	11.7816i	−0.695698	−	0.718334i
$270$	20.4258			1.24307
$271$	8.34229	+	3.98307i	0.506758	+	0.241954i	0.666910	−	0.745138i	$-0.267616\pi$
$271$	8.34229	+	3.98307i	0.506758	+	0.241954i	−0.160152	+	0.987092i	$0.551199\pi$
$272$	1.05808	+	7.47214i	0.0641556	+	0.453065i
$273$	2.76565	+	3.42076i	0.167385	+	0.207034i
$274$	0.152076	+	6.48538i	0.00918724	+	0.391796i
$275$	−3.75650	+	11.9412i	−0.226526	+	0.720082i
$276$	8.06225	−	11.5461i	0.485290	−	0.694991i
$277$	2.62090	+	10.9735i	0.157474	+	0.659332i	0.993808	+	0.111111i	$0.0354410\pi$
$277$	2.62090	+	10.9735i	0.157474	+	0.659332i	−0.836334	+	0.548221i	$0.815305\pi$
$278$	−2.58623	+	0.747425i	−0.155112	+	0.0448276i
$279$	−20.4481	+	45.5434i	−1.22419	+	2.72661i
$280$	−3.50196	+	9.54412i	−0.209282	+	0.570370i
$281$	5.90638	−	6.33713i	0.352345	−	0.378041i	−0.530516	−	0.847675i	$-0.678002\pi$
$281$	5.90638	−	6.33713i	0.352345	−	0.378041i	0.882862	+	0.469633i	$0.155614\pi$
$282$	−33.6601	−	15.1127i	−2.00443	−	0.899947i
$283$	0.481144	−	0.272797i	0.0286010	−	0.0162161i	−0.478850	−	0.877897i	$-0.658946\pi$
$283$	0.481144	−	0.272797i	0.0286010	−	0.0162161i	0.507451	+	0.861681i	$0.330588\pi$
$284$	−11.0607	+	1.83168i	−0.656330	+	0.108690i
$285$	4.27050	−	19.9378i	0.252962	−	1.18101i
$286$	−1.32174	+	0.484979i	−0.0781564	+	0.0286774i
$287$	6.72952	+	1.11442i	0.397231	+	0.0657824i
$288$	−1.96253	+	4.98407i	−0.115643	+	0.293689i
$289$	30.4711	−	25.8400i	1.79242	−	1.52000i
$290$	24.0498	+	12.1830i	1.41225	+	0.715412i
$291$	−9.18440	+	8.97156i	−0.538399	+	0.525922i
$292$	−13.7936	+	1.95323i	−0.807212	+	0.114304i
$293$	−9.53005	+	3.75255i	−0.556752	+	0.219227i	−0.627975	−	0.778234i	$-0.716116\pi$
$293$	−9.53005	+	3.75255i	−0.556752	+	0.219227i	0.0712229	+	0.997460i	$0.477310\pi$
$294$	12.9824	−	0.609186i	0.757151	−	0.0355284i
$295$	−4.75496	−	5.60715i	−0.276844	−	0.326461i
$296$	−2.98426	−	6.64676i	−0.173457	−	0.386335i
$297$	21.3171	−	1.50179i	1.23694	−	0.0871430i
$298$	−0.958863	+	20.4345i	−0.0555455	+	1.18374i
$299$	2.10040	+	0.607019i	0.121469	+	0.0351048i
$300$	−7.46083	+	8.79797i	−0.430751	+	0.507951i
$301$	−15.4314	+	20.0294i	−0.889449	+	1.15448i
$302$	10.6008	+	2.27059i	0.610006	+	0.130658i
$303$	−21.3073	−	2.00405i	−1.22407	−	0.115130i
$304$	1.95978	+	1.30119i	0.112401	+	0.0746286i
$305$	4.96245	+	3.46512i	0.284149	+	0.198412i
$306$	39.7151	−	7.53747i	2.27036	−	0.430889i
$307$	−6.15645	+	5.73799i	−0.351367	+	0.327484i	−0.837537	−	0.546380i	$-0.816005\pi$
$307$	−6.15645	+	5.73799i	−0.351367	+	0.327484i	0.486170	+	0.873864i	$0.338394\pi$
$308$	−2.95304	+	10.2181i	−0.168265	+	0.582229i
$309$	−29.5339	+	7.79003i	−1.68013	+	0.443159i
$310$	−12.0407	−	25.2184i	−0.683863	−	1.43231i
$311$	−20.1672	−	26.1763i	−1.14358	−	1.48432i	−0.848767	−	0.528767i	$-0.822654\pi$
$311$	−20.1672	−	26.1763i	−1.14358	−	1.48432i	−0.294809	−	0.955556i	$-0.595256\pi$
$312$	−1.29597	−	0.0608119i	−0.0733699	−	0.00344280i
$313$	−10.7141	+	3.64862i	−0.605596	+	0.206232i	−0.608225	−	0.793764i	$-0.708118\pi$
$313$	−10.7141	+	3.64862i	−0.605596	+	0.206232i	0.00262932	+	0.999997i	$0.499163\pi$
$314$	−0.608239	−	1.93348i	−0.0343249	−	0.109112i
$315$	51.9465	+	16.3415i	2.92685	+	0.920738i
$316$	0.823053	−	6.98904i	0.0463004	−	0.393164i
$317$	25.0849	+	1.76724i	1.40891	+	0.0992583i	0.754212	−	0.656631i	$-0.228019\pi$
$317$	25.0849	+	1.76724i	1.40891	+	0.0992583i	0.654699	+	0.755890i	$0.272795\pi$
$318$	−6.33017	−	17.2520i	−0.354978	−	0.967445i
$319$	25.9950	+	10.9464i	1.45544	+	0.612881i
$320$	−1.41731	−	2.64229i	−0.0792303	−	0.147708i
$321$	−11.1328	−	42.2072i	−0.621372	−	2.35577i
$322$	13.0842	−	10.0805i	0.729154	−	0.561766i
$323$	0.416174	−	17.7481i	0.0231566	−	0.987528i
$324$	3.42945	+	1.16788i	0.190525	+	0.0648822i
$325$	−1.66642	−	0.656169i	−0.0924363	−	0.0363977i
$326$	18.7441	+	4.47683i	1.03814	+	0.247949i
$327$	−0.794589	+	1.48135i	−0.0439409	+	0.0819186i
$328$	−1.56446	+	1.26485i	−0.0863827	+	0.0698396i
$329$	−32.3410	−	28.7559i	−1.78302	−	1.58537i
$330$	−16.0852	+	21.9225i	−0.885463	+	1.20680i
$331$	−5.45914	+	2.45104i	−0.300061	+	0.134721i	−0.554044	−	0.832487i	$-0.686916\pi$
$331$	−5.45914	+	2.45104i	−0.300061	+	0.134721i	0.253983	+	0.967209i	$0.418259\pi$
$332$	−2.06208	+	6.05524i	−0.113171	+	0.332325i
$333$	−34.8152	+	17.6365i	−1.90786	+	0.966477i
$334$	3.96630	−	9.41897i	0.217026	−	0.515383i
$335$	30.6145	+	23.5865i	1.67265	+	1.28867i
$336$	−6.16223	+	7.62189i	−0.336177	+	0.415808i
$337$	−9.79745	−	5.86261i	−0.533701	−	0.319357i	0.221164	−	0.975237i	$-0.429014\pi$
$337$	−9.79745	−	5.86261i	−0.533701	−	0.319357i	−0.754865	+	0.655880i	$0.772298\pi$
$338$	3.55340	+	12.2954i	0.193279	+	0.668782i
$339$	5.54669	+	9.26948i	0.301255	+	0.503449i
$340$	−11.1605	+	19.6843i	−0.605265	+	1.06753i
$341$	−14.4202	−	25.4335i	−0.780899	−	1.37730i
$342$	6.47018	−	10.8128i	0.349867	−	0.584689i
$343$	−8.20941	−	2.16536i	−0.443266	−	0.116918i
$344$	−1.39049	−	7.32652i	−0.0749701	−	0.395019i
$345$	40.2785	−	12.6709i	2.16852	−	0.682180i
$346$	−3.97977	−	5.69948i	−0.213954	−	0.306406i
$347$	−4.65451	+	5.23481i	−0.249867	+	0.281019i	−0.858919	−	0.512111i	$-0.828864\pi$
$347$	−4.65451	+	5.23481i	−0.249867	+	0.281019i	0.609052	+	0.793130i	$0.291550\pi$
$348$	18.1622	+	18.5931i	0.973596	+	0.996693i
$349$	−13.9123	−	2.64040i	−0.744710	−	0.141337i	−0.199806	−	0.979836i	$-0.564031\pi$
$349$	−13.9123	−	2.64040i	−0.744710	−	0.141337i	−0.544905	+	0.838498i	$0.683434\pi$
$350$	−11.4441	+	7.21755i	−0.611712	+	0.385794i
$351$			3.05736i			0.163190i
$352$	−1.67343	−	2.65338i	−0.0891943	−	0.141426i
$353$	−4.71152	−	21.9969i	−0.250769	−	1.17077i	−0.908619	−	0.417626i	$-0.862862\pi$
$353$	−4.71152	−	21.9969i	−0.250769	−	1.17077i	0.657850	−	0.753149i	$-0.271466\pi$
$354$	−2.59687	−	6.59507i	−0.138022	−	0.350524i
$355$	−29.6235	−	15.8900i	−1.57225	−	0.843352i
$356$	1.57116	−	0.147775i	0.0832711	−	0.00783205i
$357$	73.4600	+	8.65090i	3.88791	+	0.457854i
$358$	−1.07820	+	1.62392i	−0.0569847	+	0.0858270i
$359$	−0.310329	+	2.19154i	−0.0163786	+	0.115665i	−0.996621	−	0.0821331i	$-0.973827\pi$
$359$	−0.310329	+	2.19154i	−0.0163786	+	0.115665i	0.980243	+	0.197798i	$0.0633790\pi$
$360$	−13.7821	+	8.24696i	−0.726381	+	0.434653i
$361$	9.85091	+	9.18132i	0.518469	+	0.483228i
$362$	−12.5108	−	7.89033i	−0.657555	−	0.414706i
$363$	1.78756	−	2.83433i	0.0938224	−	0.148764i
$364$	−1.42858	−	0.524179i	−0.0748779	−	0.0274744i
$365$	−36.3374	−	20.6025i	−1.90199	−	1.07838i
$366$	3.45196	+	4.70467i	0.180437	+	0.245917i
$367$	1.76090	−	18.7221i	0.0919184	−	0.977286i	−0.821485	−	0.570230i	$-0.806854\pi$
$367$	1.76090	−	18.7221i	0.0919184	−	0.977286i	0.913403	−	0.407056i	$-0.133445\pi$
$368$	−0.342349	+	4.85943i	−0.0178462	+	0.253315i
$369$	7.16055	+	8.05329i	0.372764	+	0.419237i
$370$	5.07502	−	21.2487i	0.263838	−	1.10467i
$371$	−1.01028	−	21.5303i	−0.0524512	−	1.11780i
$372$	−3.15103	−	26.7572i	−0.163373	−	1.38730i
$373$	1.23683	−	6.51689i	0.0640407	−	0.337432i	−0.935847	−	0.352406i	$-0.885364\pi$
$373$	1.23683	−	6.51689i	0.0640407	−	0.337432i	0.999888	+	0.0149741i	$0.00476658\pi$
$374$	−10.2003	+	21.3638i	−0.527443	+	1.10470i
$375$	8.55622	−	1.83266i	0.441841	−	0.0946383i
$376$	12.6762	−	1.49279i	0.653724	−	0.0769848i
$377$	−1.82358	+	3.59981i	−0.0939189	+	0.185400i
$378$	18.6222	+	13.6637i	0.957820	+	0.702783i
$379$	−2.99685	−	2.92740i	−0.153938	−	0.150371i	0.617744	−	0.786379i	$-0.288047\pi$
$379$	−2.99685	−	2.92740i	−0.153938	−	0.150371i	−0.771682	+	0.636009i	$0.780584\pi$
$380$	2.27380	+	6.67696i	0.116643	+	0.342521i
$381$	−2.67949	−	2.87490i	−0.137274	−	0.147286i
$382$	−0.219707	+	0.0925181i	−0.0112412	+	0.00473364i
$383$	29.2438	+	23.6434i	1.49429	+	1.20812i	0.921477	+	0.388432i	$0.126983\pi$
$383$	29.2438	+	23.6434i	1.49429	+	1.20812i	0.572812	+	0.819687i	$0.305853\pi$
$384$	−0.472286	−	2.85193i	−0.0241012	−	0.145537i
$385$	−25.7128	+	18.8663i	−1.31045	+	0.961516i
$386$	−13.7557	−	1.94786i	−0.700149	−	0.0991436i
$387$	−38.8525	+	9.27950i	−1.97498	+	0.471703i
$388$	1.13275	−	4.29453i	0.0575067	−	0.218022i
$389$	−4.19569	−	9.96371i	−0.212730	−	0.505180i	0.779966	−	0.625822i	$-0.215236\pi$
$389$	−4.19569	−	9.96371i	−0.212730	−	0.505180i	−0.992696	+	0.120642i	$0.961505\pi$
$390$	−2.96694	−	2.51602i	−0.150237	−	0.127404i
$391$	32.3971	−	17.3777i	1.63839	−	0.878827i
$392$	−3.74554	+	2.48685i	−0.189178	+	0.125605i
$393$	−30.8451	−	0.723287i	−1.55593	−	0.0364850i
$394$	−0.787394	−	11.1766i	−0.0396683	−	0.563068i
$395$	14.7446	−	15.0944i	0.741882	−	0.759482i
$396$	−13.7772	+	9.62015i	−0.692328	+	0.483431i
$397$	−33.8438	+	0.793604i	−1.69857	+	0.0398298i	−0.861653	−	0.507498i	$-0.830570\pi$
$397$	−33.8438	+	0.793604i	−1.69857	+	0.0398298i	−0.836918	+	0.547328i	$0.815645\pi$
$398$	2.50901	+	26.6761i	0.125765	+	1.33715i
$399$	17.2307	−	15.3206i	0.862612	−	0.766989i
$400$	0.651953	−	3.93686i	0.0325976	−	0.196843i
$401$	13.9518	+	27.5415i	0.696721	+	1.37535i	0.916591	+	0.399825i	$0.130929\pi$
$401$	13.9518	+	27.5415i	0.696721	+	1.37535i	−0.219870	+	0.975529i	$0.570563\pi$
$402$	20.6093	+	31.0405i	1.02790	+	1.54816i
$403$	3.77473	−	1.80226i	0.188033	−	0.0897772i
$404$	6.68090	−	3.18983i	0.332387	−	0.158700i
$405$	6.00856	+	9.04975i	0.298568	+	0.449686i
$406$	13.7764	+	27.1952i	0.683712	+	1.34967i
$407$	3.73417	−	22.5490i	0.185096	−	1.11771i
$408$	−16.3032	+	14.4959i	−0.807127	+	0.717655i
$409$	0.536730	+	5.70657i	0.0265396	+	0.282171i	0.998829	+	0.0483892i	$0.0154088\pi$
$409$	0.536730	+	5.70657i	0.0265396	+	0.282171i	−0.972289	+	0.233782i	$0.924890\pi$
$410$	−6.03057	+	0.141411i	−0.297829	+	0.00698379i
$411$	−15.3755	+	10.7362i	−0.758415	+	0.529577i
$412$	7.38324	−	7.55840i	0.363746	−	0.372375i
$413$	−0.584233	−	8.29283i	−0.0287482	−	0.408064i
$414$	26.0871	+	0.611716i	1.28211	+	0.0300642i
$415$	−15.9788	+	10.6091i	−0.784366	+	0.520778i
$416$	0.395502	−	0.212146i	0.0193911	−	0.0104013i
$417$	−5.93532	−	5.03325i	−0.290654	−	0.246479i
$418$	2.86394	+	6.80114i	0.140080	+	0.332655i
$419$	−8.79178	+	33.3318i	−0.429507	+	1.62837i	0.306840	+	0.951761i	$0.400728\pi$
$419$	−8.79178	+	33.3318i	−0.429507	+	1.62837i	−0.736347	+	0.676604i	$0.763451\pi$
$420$	−28.5845	+	6.82709i	−1.39478	+	0.333128i
$421$	−4.12766	−	0.584491i	−0.201170	−	0.0284863i	0.0388947	−	0.999243i	$-0.487616\pi$
$421$	−4.12766	−	0.584491i	−0.201170	−	0.0284863i	−0.240064	+	0.970757i	$0.577169\pi$
$422$	1.38076	−	1.01311i	0.0672145	−	0.0493174i
$423$	−11.1700	−	67.4509i	−0.543106	−	3.27958i
$424$	4.94347	+	3.99675i	0.240076	+	0.194099i
$425$	−27.7545	+	11.6873i	−1.34629	+	0.566918i
$426$	−22.0969	−	23.7084i	−1.07060	−	1.14868i
$427$	2.20630	+	6.47875i	0.106770	+	0.313529i
$428$	10.8018	+	10.5514i	0.522123	+	0.510023i
$429$	−3.28140	−	2.40767i	−0.158427	−	0.116243i
$430$	10.1045	−	19.9467i	0.487283	−	0.961915i
$431$	−26.4300	+	3.11249i	−1.27309	+	0.149923i	−0.726318	−	0.687359i	$-0.758770\pi$
$431$	−26.4300	+	3.11249i	−1.27309	+	0.149923i	−0.546771	+	0.837282i	$0.684143\pi$
$432$	−6.66111	+	1.42675i	−0.320483	+	0.0686444i
$433$	−4.47628	+	9.37529i	−0.215116	+	0.450548i	−0.981405	−	0.191949i	$-0.938519\pi$
$433$	−4.47628	+	9.37529i	−0.215116	+	0.450548i	0.766289	+	0.642497i	$0.222101\pi$
$434$	5.89219	−	31.0461i	0.282834	−	1.49026i
$435$	9.11477	+	77.3989i	0.437020	+	3.71099i
$436$	−0.0272565	−	0.580867i	−0.00130535	−	0.0278185i
$437$	2.66216	−	11.1462i	0.127348	−	0.533196i
$438$	−26.7596	−	30.0958i	−1.27862	−	1.43803i
$439$	1.26512	−	17.9576i	0.0603807	−	0.857067i	−0.870598	−	0.491995i	$-0.836268\pi$
$439$	1.26512	−	17.9576i	0.0603807	−	0.857067i	0.930979	−	0.365073i	$-0.118956\pi$
$440$	0.880795	−	9.36471i	0.0419903	−	0.446445i
$441$	14.2466	+	19.4167i	0.678411	+	0.924604i
$442$	−2.94638	−	1.67053i	−0.140145	−	0.0794589i
$443$	−31.5254	−	11.5674i	−1.49782	−	0.549584i	−0.541191	−	0.840900i	$-0.682026\pi$
$443$	−31.5254	−	11.5674i	−1.49782	−	0.549584i	−0.956627	+	0.291316i	$0.905907\pi$
$444$	11.2355	−	17.8149i	0.533214	−	0.845460i
$445$	4.00228	+	2.52416i	0.189726	+	0.119656i
$446$	−0.461968	−	0.430567i	−0.0218748	−	0.0203879i
$447$	−50.7451	+	30.3649i	−2.40016	+	1.43621i
$448$	0.475374	−	3.35708i	0.0224593	−	0.158607i
$449$	7.35739	−	11.0813i	0.347217	−	0.522958i	−0.617388	−	0.786659i	$-0.711809\pi$
$449$	7.35739	−	11.0813i	0.347217	−	0.522958i	0.964604	+	0.263701i	$0.0849433\pi$
$450$	−21.2284	−	2.49993i	−1.00072	−	0.117848i
$451$	−6.28332	+	0.590977i	−0.295870	+	0.0278280i
$452$	−3.29299	−	1.76635i	−0.154889	−	0.0830822i
$453$	11.4821	+	29.1603i	0.539478	+	1.37007i
$454$	−2.44721	−	11.4254i	−0.114853	−	0.536220i
$455$	−2.43398	−	3.85929i	−0.114107	−	0.180926i
$456$			6.80028i			0.318452i
$457$	−31.8380	+	20.0796i	−1.48932	+	0.939285i	−0.491670	+	0.870782i	$0.663613\pi$
$457$	−31.8380	+	20.0796i	−1.48932	+	0.939285i	−0.997651	+	0.0685033i	$0.978178\pi$
$458$	−14.2278	−	2.70026i	−0.664819	−	0.126175i
$459$	35.9234	+	36.7756i	1.67676	+	1.71654i
$460$	−9.70573	+	10.9158i	−0.452532	+	0.508951i
$461$	15.2292	+	21.8100i	0.709296	+	1.01579i	0.998290	+	0.0584617i	$0.0186196\pi$
$461$	15.2292	+	21.8100i	0.709296	+	1.01579i	−0.288994	+	0.957331i	$0.593321\pi$
$462$	−29.3298	+	9.22666i	−1.36455	+	0.429263i
$463$	6.05793	+	31.9194i	0.281536	+	1.48342i	0.785050	+	0.619432i	$0.212637\pi$
$463$	6.05793	+	31.9194i	0.281536	+	1.48342i	−0.503515	+	0.863987i	$0.667960\pi$
$464$	−8.69393	−	2.29316i	−0.403606	−	0.106457i
$465$	41.4803	−	69.3208i	1.92360	−	3.21468i
$466$	−2.85405	−	5.03380i	−0.132211	−	0.233186i
$467$	13.0012	−	22.9307i	0.601623	−	1.06111i	−0.388573	−	0.921418i	$-0.627032\pi$
$467$	13.0012	−	22.9307i	0.601623	−	1.06111i	0.990196	−	0.139688i	$-0.0446100\pi$
$468$	−1.23442	−	2.06293i	−0.0570610	−	0.0953589i
$469$	12.1332	+	41.9831i	0.560260	+	1.93860i
$470$	32.8406	+	19.6512i	1.51482	+	0.906441i
$471$	3.68380	−	4.55639i	0.169741	−	0.209947i
$472$	1.94232	+	1.49643i	0.0894024	+	0.0688788i
$473$	9.07886	−	21.5600i	0.417447	−	0.991331i
$474$	18.1476	−	9.19314i	0.833547	−	0.422255i
$475$	−3.02611	+	8.88611i	−0.138848	+	0.407723i
$476$	−23.3427	+	10.4804i	−1.06991	+	0.480369i
$477$	20.1440	−	27.4542i	0.922331	−	1.25704i
$478$	12.6766	+	11.2713i	0.579814	+	0.515539i
$479$	−15.5683	+	12.5869i	−0.711335	+	0.575108i	−0.914767	−	0.403981i	$-0.867626\pi$
$479$	−15.5683	+	12.5869i	−0.711335	+	0.575108i	0.203432	+	0.979089i	$0.434790\pi$
$480$	4.09713	−	7.63824i	0.187007	−	0.348636i
$481$	3.18054	+	0.759637i	0.145020	+	0.0346365i
$482$	−1.51004	−	0.594595i	−0.0687806	−	0.0270831i
$483$	45.1980	+	15.3919i	2.05658	+	0.700357i
$484$	−0.0271743	+	1.15887i	−0.00123520	+	0.0526758i
$485$	10.5494	−	8.12761i	0.479022	−	0.369056i
$486$	−2.54118	−	9.63424i	−0.115270	−	0.437018i
$487$	−16.7790	−	31.2810i	−0.760329	−	1.41748i	−0.903859	−	0.427830i	$-0.859278\pi$
$487$	−16.7790	−	31.2810i	−0.760329	−	1.41748i	0.143530	−	0.989646i	$-0.454154\pi$
$488$	−1.86036	−	0.783393i	−0.0842146	−	0.0354625i
$489$	19.1899	+	52.2995i	0.867797	+	2.36506i
$490$	−13.4474	−	0.947371i	−0.607489	−	0.0427979i
$491$	−1.45734	+	12.3752i	−0.0657690	+	0.558484i	0.920187	+	0.391479i	$0.128036\pi$
$491$	−1.45734	+	12.3752i	−0.0657690	+	0.558484i	−0.985956	+	0.167005i	$0.946590\pi$
$492$	−5.54764	−	1.74519i	−0.250107	−	0.0786793i
$493$	20.3620	+	64.7271i	0.917060	+	2.91516i
$494$	−0.999418	+	0.340346i	−0.0449660	+	0.0153129i
$495$	−50.3284	−	2.36160i	−2.26209	−	0.106146i
$496$	5.68813	+	7.38300i	0.255405	+	0.331507i
$497$	−16.3783	−	34.3033i	−0.734667	−	1.53871i
$498$	−17.8799	+	4.71611i	−0.801219	+	0.211334i
$499$	−6.31194	+	21.8405i	−0.282561	+	0.977714i	0.685723	+	0.727863i	$0.259486\pi$
$499$	−6.31194	+	21.8405i	−0.282561	+	0.977714i	−0.968284	+	0.249851i	$0.919618\pi$
$500$	−2.21433	+	2.06382i	−0.0990279	+	0.0922968i
$501$	29.0255	−	5.50871i	1.29677	−	0.246111i
$502$	1.71890	+	1.20025i	0.0767183	+	0.0535699i
$503$	17.0708	+	11.3341i	0.761149	+	0.505364i	0.872617	−	0.488404i	$-0.162421\pi$
$503$	17.0708	+	11.3341i	0.761149	+	0.505364i	−0.111468	+	0.993768i	$0.535555\pi$
$504$	−18.0819	−	1.70069i	−0.805431	−	0.0757546i
$505$	21.7059	+	4.64921i	0.965902	+	0.206887i
$506$	−9.32667	+	12.1057i	−0.414621	+	0.538165i
$507$	−23.9290	+	28.2176i	−1.06272	+	1.25319i
$508$	1.30604	+	0.377450i	0.0579464	+	0.0167466i
$509$	−1.97893	+	42.1733i	−0.0877147	+	1.86930i	0.308609	+	0.951189i	$0.400137\pi$
$509$	−1.97893	+	42.1733i	−0.0877147	+	1.86930i	−0.396323	+	0.918111i	$0.629714\pi$
$510$	−65.2507	+	4.59694i	−2.88935	+	0.203556i
$511$	−19.3469	−	43.0909i	−0.855857	−	1.90623i
$512$	0.646770	+	0.762685i	0.0285835	+	0.0337062i
$513$	16.0075	−	0.751133i	0.706748	−	0.0331633i
$514$	4.34905	−	1.71248i	0.191829	−	0.0755344i
$515$	31.3685	−	4.44188i	1.38226	−	0.195733i
$516$	15.4210	−	15.0636i	0.678870	−	0.663138i
$517$	35.7184	+	18.0941i	1.57090	+	0.795777i
$518$	18.8410	−	15.9775i	0.827827	−	0.702012i
$519$	7.36241	−	18.6977i	0.323174	−	0.820739i
$520$	1.32763	+	0.219858i	0.0582203	+	0.00964142i
$521$	−10.7861	+	3.95766i	−0.472547	+	0.173388i	−0.569652	−	0.821886i	$-0.692922\pi$
$521$	−10.7861	+	3.95766i	−0.472547	+	0.173388i	0.0971055	+	0.995274i	$0.469042\pi$
$522$	−10.0871	+	47.0939i	−0.441499	+	2.06124i
$523$	38.9559	−	6.45120i	1.70342	−	0.282091i	0.769260	−	0.638936i	$-0.220625\pi$
$523$	38.9559	−	6.45120i	1.70342	−	0.282091i	0.934164	+	0.356845i	$0.116148\pi$
$524$	9.28464	−	5.26417i	0.405601	−	0.229967i
$525$	−35.6807	−	16.0199i	−1.55723	−	0.699165i
$526$	5.01222	−	5.37775i	0.218543	−	0.234481i
$527$	24.2283	−	66.0309i	1.05540	−	2.87635i
$528$	3.71431	−	8.27279i	0.161645	−	0.360027i
$529$	0.702536	−	0.203034i	0.0305451	−	0.00882759i
$530$	4.42797	+	18.5396i	0.192339	+	0.805307i
$531$	7.51921	−	10.7684i	0.326306	−	0.467307i
$532$	−2.39348	+	7.60842i	−0.103771	+	0.329867i
$533$	−0.0211666	−	0.902665i	−0.000916828	−	0.0390988i
$534$	2.86812	+	3.54750i	0.124116	+	0.153515i
$535$	6.34793	+	44.8289i	0.274445	+	1.93812i
$536$	−11.6313	−	5.55343i	−0.502396	−	0.239872i
$537$	−5.63488			−0.243163
$538$	5.22060	+	15.5482i	0.225076	+	0.670329i
$539$	−14.1038			−0.607494
$540$	−18.4325	−	8.80072i	−0.793211	−	0.378723i
$541$	4.43864	+	31.3455i	0.190832	+	1.34765i	0.820883	+	0.571096i	$0.193482\pi$
$541$	4.43864	+	31.3455i	0.190832	+	1.34765i	−0.630051	+	0.776553i	$0.716966\pi$
$542$	−5.81206	−	7.18878i	−0.249650	−	0.308785i
$543$	−1.00235	−	42.7460i	−0.0430151	−	1.83441i
$544$	2.26464	−	7.19888i	0.0970958	−	0.308649i
$545$	0.998224	−	1.42957i	0.0427592	−	0.0612361i
$546$	−1.02189	−	4.27857i	−0.0437329	−	0.183106i
$547$	−0.678610	+	0.196120i	−0.0290153	+	0.00838547i	−0.292116	−	0.956383i	$-0.594359\pi$
$547$	−0.678610	+	0.196120i	−0.0290153	+	0.00838547i	0.263101	+	0.964768i	$0.415255\pi$
$548$	2.65708	−	5.91804i	0.113505	−	0.252806i
$549$	−3.72457	+	10.1508i	−0.158961	+	0.433227i
$550$	8.53497	−	9.15741i	0.363932	−	0.390473i
$551$	19.2956	+	8.66333i	0.822020	+	0.369070i
$552$	−12.2503	+	6.94563i	−0.521407	+	0.295626i
$553$	23.5399	−	3.89827i	1.00102	−	0.165771i
$554$	2.36293	−	11.0319i	0.100391	−	0.468701i
$555$	59.2876	−	21.7540i	2.51662	−	0.923405i
$556$	2.65589	+	0.439822i	0.112635	+	0.0186526i
$557$	−5.32200	+	13.5159i	−0.225501	+	0.572685i	−0.998060	−	0.0622571i	$-0.980170\pi$
$557$	−5.32200	+	13.5159i	−0.225501	+	0.572685i	0.772560	+	0.634942i	$0.218976\pi$
$558$	38.0757	−	32.2888i	1.61187	−	1.36690i
$559$	2.98565	+	1.51246i	0.126280	+	0.0639702i
$560$	7.27244	−	7.10391i	0.307317	−	0.300195i
$561$	−67.7600	+	9.59506i	−2.86083	+	0.405104i
$562$	−8.06046	+	3.17389i	−0.340010	+	0.133882i
$563$	26.7686	−	1.25609i	1.12816	−	0.0529377i	0.525397	−	0.850857i	$-0.323917\pi$
$563$	26.7686	−	1.25609i	1.12816	−	0.0529377i	0.602764	+	0.797919i	$0.294066\pi$
$564$	23.8639	+	28.1408i	1.00485	+	1.18494i
$565$	−4.58926	−	10.2215i	−0.193072	−	0.430023i
$566$	−0.551731	+	0.0388696i	−0.0231910	+	0.00163381i
$567$	−0.575757	+	12.2700i	−0.0241795	+	0.515293i
$568$	10.7705	+	3.11271i	0.451922	+	0.130606i
$569$	−16.8309	+	19.8473i	−0.705587	+	0.832044i	−0.992023	−	0.126056i	$-0.959768\pi$
$569$	−16.8309	+	19.8473i	−0.705587	+	0.832044i	0.286436	+	0.958099i	$0.407529\pi$
$570$	−12.4443	+	16.1522i	−0.521232	+	0.676542i
$571$	29.3410	+	6.28457i	1.22788	+	0.263001i	0.776953	−	0.629558i	$-0.216764\pi$
$571$	29.3410	+	6.28457i	1.22788	+	0.263001i	0.450930	+	0.892559i	$0.351092\pi$
$572$	1.40172	+	0.131839i	0.0586091	+	0.00551246i
$573$	−0.574116	−	0.381183i	−0.0239840	−	0.0159241i
$574$	−5.59266	−	3.90518i	−0.233433	−	0.162999i
$575$	−19.0986	+	3.62469i	−0.796466	+	0.151160i
$576$	3.91847	−	3.65213i	0.163270	−	0.152172i
$577$	−1.15784	+	4.00635i	−0.0482017	+	0.166787i	−0.981160	−	0.193199i	$-0.938114\pi$
$577$	−1.15784	+	4.00635i	−0.0482017	+	0.166787i	0.932958	+	0.359985i	$0.117218\pi$
$578$	−38.6312	+	10.1896i	−1.60685	+	0.423831i
$579$	−17.3041	−	36.2423i	−0.719133	−	1.50618i
$580$	−16.4537	−	21.3563i	−0.683202	−	0.886774i
$581$	−21.6647	−	1.01659i	−0.898803	−	0.0421753i
$582$	12.1537	−	4.13886i	0.503786	−	0.171561i
$583$	5.98431	+	19.0230i	0.247845	+	0.787851i
$584$	13.2892	+	4.18055i	0.549911	+	0.172992i
$585$	0.843053	−	7.15886i	0.0348559	−	0.295983i
$586$	10.2169	+	0.719786i	0.422057	+	0.0297341i
$587$	3.94799	+	10.7597i	0.162951	+	0.444101i	0.993636	−	0.112642i	$-0.0359314\pi$
$587$	3.94799	+	10.7597i	0.162951	+	0.444101i	−0.830685	+	0.556743i	$0.812051\pi$
$588$	−11.9780	−	5.04392i	−0.493966	−	0.208008i
$589$	−10.3635	−	19.3207i	−0.427022	−	0.796094i
$590$	1.87504	+	7.10873i	0.0771941	+	0.292662i
$591$	25.6573	−	19.7673i	1.05540	−	0.813119i
$592$	−0.170802	+	7.28396i	−0.00701991	+	0.299369i
$593$	8.80306	+	2.99783i	0.361498	+	0.123106i	0.497182	−	0.867646i	$-0.334368\pi$
$593$	8.80306	+	2.99783i	0.361498	+	0.123106i	−0.135684	+	0.990752i	$0.543323\pi$
$594$	−19.8839	−	7.82950i	−0.815848	−	0.321248i
$595$	−74.6231	−	17.8229i	−3.05925	−	0.730669i
$596$	9.66976	−	18.0273i	0.396089	−	0.738426i
$597$	−60.2316	+	48.6967i	−2.46512	+	1.99302i
$598$	−1.63389	−	1.45277i	−0.0668148	−	0.0594082i
$599$	−7.23836	+	9.86514i	−0.295752	+	0.403079i	−0.928532	−	0.371252i	$-0.878928\pi$
$599$	−7.23836	+	9.86514i	−0.295752	+	0.403079i	0.632780	+	0.774331i	$0.281914\pi$
$600$	10.5235	−	4.72484i	0.429620	−	0.192891i
$601$	4.83496	−	14.1978i	0.197222	−	0.579138i	−0.802627	−	0.596481i	$-0.796565\pi$
$601$	4.83496	−	14.1978i	0.197222	−	0.579138i	0.999850	+	0.0173422i	$0.00552046\pi$
$602$	22.5555	−	11.4261i	0.919292	−	0.465691i
$603$	−26.7941	+	63.6294i	−1.09114	+	2.59119i
$604$	−8.58800	−	6.61650i	−0.349441	−	0.269222i
$605$	−2.18523	+	2.70285i	−0.0888422	+	0.109886i
$606$	18.3646	+	10.9890i	0.746011	+	0.446399i
$607$	−6.38610	−	22.0971i	−0.259204	−	0.896892i	−0.979197	−	0.202911i	$-0.934960\pi$
$607$	−6.38610	−	22.0971i	−0.259204	−	0.896892i	0.719994	−	0.693981i	$-0.244145\pi$
$608$	−1.20790	−	2.01862i	−0.0489870	−	0.0818658i
$609$	−43.4655	+	76.6618i	−1.76131	+	3.10649i
$610$	−2.98521	−	5.26513i	−0.120867	−	0.213179i
$611$	−2.94142	+	4.91563i	−0.118997	+	0.198865i
$612$	−39.0872	−	10.3099i	−1.58001	−	0.416752i
$613$	−4.90030	−	25.8198i	−0.197921	−	1.04285i	−0.931636	−	0.363393i	$-0.881618\pi$
$613$	−4.90030	−	25.8198i	−0.197921	−	1.04285i	0.733715	−	0.679458i	$-0.237785\pi$
$614$	8.02798	−	2.52546i	0.323983	−	0.101919i
$615$	−9.98328	−	14.2972i	−0.402565	−	0.576519i
$616$	7.06747	−	7.94860i	0.284757	−	0.320258i
$617$	−7.49026	−	7.66796i	−0.301547	−	0.308700i	0.547723	−	0.836660i	$-0.315495\pi$
$617$	−7.49026	−	7.66796i	−0.301547	−	0.308700i	−0.849270	+	0.527959i	$0.822957\pi$
$618$	30.0083	+	5.69524i	1.20711	+	0.229096i
$619$	3.59861	−	2.26957i	0.144641	−	0.0912219i	−0.459176	−	0.888346i	$-0.651855\pi$
$619$	3.59861	−	2.26957i	0.144641	−	0.0912219i	0.603816	+	0.797124i	$0.293646\pi$
$620$			27.9454i			1.12231i
$621$	17.7027	+	28.0693i	0.710387	+	1.12638i
$622$	6.92077	+	32.3113i	0.277498	+	1.29556i
$623$	1.96036	+	4.97857i	0.0785402	+	0.199462i
$624$	1.14330	+	0.613265i	0.0457688	+	0.0245502i
$625$	−28.9009	+	2.71827i	−1.15604	+	0.108731i
$626$	11.2406	+	1.32374i	0.449266	+	0.0529071i
$627$	−11.7997	+	17.7720i	−0.471234	+	0.709746i
$628$	−0.284180	+	2.00687i	−0.0113400	+	0.0800829i
$629$	47.1828	−	28.2333i	1.88130	−	1.12574i
$630$	−39.8364	−	37.1287i	−1.58712	−	1.47924i
$631$	−22.9937	−	14.5016i	−0.915364	−	0.577302i	−0.00907421	−	0.999959i	$-0.502888\pi$
$631$	−22.9937	−	14.5016i	−0.915364	−	0.577302i	−0.906290	+	0.422657i	$0.861097\pi$
$632$	−3.75406	+	5.95240i	−0.149328	+	0.236774i
$633$	4.64765	+	1.70533i	0.184728	+	0.0677809i
$634$	−21.8756	−	12.4030i	−0.868792	−	0.492585i
$635$	2.41144	+	3.28654i	0.0956950	+	0.130422i
$636$	−1.72082	+	18.2960i	−0.0682350	+	0.725482i
$637$	0.141804	−	2.01282i	0.00561848	−	0.0797509i
$638$	−18.7419	−	21.0785i	−0.741998	−	0.834506i
$639$	13.9508	−	58.4109i	0.551886	−	2.31070i
$640$	0.140542	+	2.99512i	0.00555542	+	0.118392i
$641$	0.183878	+	1.56142i	0.00726274	+	0.0616723i	0.996290	−	0.0860628i	$-0.0274286\pi$
$641$	0.183878	+	1.56142i	0.00726274	+	0.0616723i	−0.989027	+	0.147735i	$0.952802\pi$
$642$	−8.13911	+	42.8852i	−0.321225	+	1.69254i
$643$	20.6549	−	43.2604i	0.814550	−	1.70602i	0.112778	−	0.993620i	$-0.464025\pi$
$643$	20.6549	−	43.2604i	0.814550	−	1.70602i	0.701771	−	0.712402i	$-0.252393\pi$
$644$	−16.1507	+	3.45934i	−0.636428	+	0.136317i
$645$	64.1941	−	7.55972i	2.52764	−	0.297664i
$646$	−8.02255	+	15.8368i	−0.315643	+	0.623092i
$647$	−11.1827	−	8.20512i	−0.439639	−	0.322577i	0.349341	−	0.936996i	$-0.386405\pi$
$647$	−11.1827	−	8.20512i	−0.439639	−	0.322577i	−0.788980	+	0.614419i	$0.789390\pi$
$648$	−2.59160	−	2.53154i	−0.101808	−	0.0994483i
$649$	2.47952	+	7.28107i	0.0973298	+	0.285807i
$650$	1.22109	+	1.31014i	0.0478949	+	0.0513878i
$651$	84.1892	−	35.4518i	3.29964	−	1.38947i
$652$	−14.9861	−	12.1161i	−0.586901	−	0.474505i
$653$	0.344289	+	2.07901i	0.0134731	+	0.0813580i	0.992461	−	0.122559i	$-0.0391102\pi$
$653$	0.344289	+	2.07901i	0.0134731	+	0.0813580i	−0.978988	+	0.203917i	$0.934633\pi$
$654$	1.35531	−	0.994432i	0.0529968	−	0.0388854i
$655$	31.6864	+	4.48690i	1.23809	+	0.175318i
$656$	1.95677	−	0.467354i	0.0763991	−	0.0182471i
$657$	19.0321	−	72.1554i	0.742513	−	2.81505i
$658$	16.7952	+	39.8844i	0.654746	+	1.55486i
$659$	−23.9109	−	20.2769i	−0.931437	−	0.789874i	0.0464693	−	0.998920i	$-0.485203\pi$
$659$	−23.9109	−	20.2769i	−0.931437	−	0.789874i	−0.977906	+	0.209046i	$0.932964\pi$
$660$	23.9612	−	12.8527i	0.932689	−	0.500291i
$661$	20.1395	−	13.3716i	0.783336	−	0.520095i	−0.0965218	−	0.995331i	$-0.530772\pi$
$661$	20.1395	−	13.3716i	0.783336	−	0.520095i	0.879858	+	0.475236i	$0.157637\pi$
$662$	5.98248	+	0.140283i	0.232516	+	0.00545227i
$663$	−0.688077	−	9.76684i	−0.0267227	−	0.379312i
$664$	4.46984	−	4.57588i	0.173463	−	0.177579i
$665$	−19.6082	+	13.6918i	−0.760373	+	0.530944i
$666$	39.0168	−	0.914906i	1.51187	−	0.0354519i
$667$	4.10157	+	43.6083i	0.158813	+	1.68852i
$668$	−7.63755	+	6.79090i	−0.295506	+	0.262748i
$669$	0.298252	−	1.80101i	0.0115311	−	0.0696312i
$670$	−17.4645	−	34.4755i	−0.674711	−	1.33191i
$671$	−3.50258	−	5.27539i	−0.135216	−	0.203654i
$672$	8.84489	−	4.22304i	0.341199	−	0.162907i
$673$	2.17205	−	1.03706i	0.0837264	−	0.0399756i	−0.388537	−	0.921433i	$-0.627019\pi$
$673$	2.17205	−	1.03706i	0.0837264	−	0.0399756i	0.472263	+	0.881458i	$0.343437\pi$
$674$	6.31540	+	9.51188i	0.243260	+	0.366384i
$675$	−12.2844	−	24.2499i	−0.472827	−	0.933378i
$676$	2.09100	−	12.6266i	0.0804230	−	0.485639i
$677$	5.92436	−	5.26763i	0.227692	−	0.202451i	−0.542870	−	0.839817i	$-0.682662\pi$
$677$	5.92436	−	5.26763i	0.227692	−	0.202451i	0.770562	+	0.637365i	$0.219976\pi$
$678$	−1.01154	−	10.7548i	−0.0388480	−	0.413036i
$679$	15.0548	−	0.353019i	0.577749	−	0.0135476i
$680$	18.5527	−	12.9548i	0.711464	−	0.496793i
$681$	23.6025	−	24.1625i	0.904451	−	0.925908i
$682$	2.05467	+	29.1648i	0.0786775	+	1.11678i
$683$	−41.0524	−	0.962637i	−1.57082	−	0.0368343i	−0.770908	−	0.636946i	$-0.780197\pi$
$683$	−41.0524	−	0.962637i	−1.57082	−	0.0368343i	−0.799916	+	0.600112i	$0.795123\pi$
$684$	−10.4976	+	6.96989i	−0.401387	+	0.266500i
$685$	17.1410	−	9.19435i	0.654923	−	0.351298i
$686$	6.47533	+	5.49119i	0.247229	+	0.209655i
$687$	−16.2468	−	38.5821i	−0.619854	−	1.47200i
$688$	−1.90193	+	7.21068i	−0.0725104	+	0.274905i
$689$	−2.77503	+	0.662786i	−0.105720	+	0.0252501i
$690$	−41.8075	−	5.92009i	−1.59158	−	0.225374i
$691$	14.7743	−	10.8404i	0.562040	−	0.412386i	−0.273454	−	0.961885i	$-0.588166\pi$
$691$	14.7743	−	10.8404i	0.562040	−	0.412386i	0.835495	+	0.549499i	$0.185181\pi$
$692$	1.13571	+	6.85805i	0.0431732	+	0.260704i
$693$	−44.3046	−	35.8199i	−1.68299	−	1.36068i
$694$	6.45580	−	2.71852i	0.245059	−	0.103194i
$695$	5.50350	+	5.90486i	0.208759	+	0.223984i
$696$	−8.37879	−	24.6041i	−0.317597	−	0.932617i
$697$	−10.8607	−	10.6091i	−0.411380	−	0.401846i
$698$	11.4171	+	8.37706i	0.432143	+	0.317077i
$699$	7.55925	−	14.9223i	0.285917	−	0.564411i
$700$	13.4371	−	1.58240i	0.507875	−	0.0598091i
$701$	−32.5017	+	6.96157i	−1.22757	+	0.262935i	−0.776825	−	0.629716i	$-0.783171\pi$
$701$	−32.5017	+	6.96157i	−1.22757	+	0.262935i	−0.450748	+	0.892651i	$0.648843\pi$
$702$	1.31731	−	2.75901i	0.0497185	−	0.104132i
$703$	3.19585	−	16.8390i	0.120534	−	0.635096i
$704$	0.366890	+	3.11548i	0.0138277	+	0.117419i
$705$	5.18560	+	110.511i	0.195301	+	4.16209i
$706$	−5.22589	+	21.8804i	−0.196679	+	0.823478i
$707$	16.6792	+	18.7587i	0.627288	+	0.705494i
$708$	−0.498112	+	7.07040i	−0.0187202	+	0.265722i
$709$	−3.50156	+	37.2290i	−0.131504	+	1.39816i	0.643131	+	0.765756i	$0.277635\pi$
$709$	−3.50156	+	37.2290i	−0.131504	+	1.39816i	−0.774635	+	0.632408i	$0.782067\pi$
$710$	19.8864	+	27.1031i	0.746322	+	1.01716i
$711$	32.7917	+	18.5922i	1.22979	+	0.697260i
$712$	−1.48151	−	0.543600i	−0.0555219	−	0.0203723i
$713$	24.2199	−	38.4029i	0.907043	−	1.43820i
$714$	−62.5642	−	39.4580i	−2.34141	−	1.47668i
$715$	3.08816	+	2.87825i	0.115491	+	0.107640i
$716$	1.67268	−	1.00090i	0.0625109	−	0.0374053i
$717$	−6.87505	+	48.5514i	−0.256753	+	1.81318i
$718$	1.22430	−	1.84397i	0.0456905	−	0.0688163i
$719$	−40.8600	−	4.81182i	−1.52382	−	0.179451i	−0.686892	−	0.726760i	$-0.741025\pi$
$719$	−40.8600	−	4.81182i	−1.52382	−	0.179451i	−0.836930	+	0.547309i	$0.815652\pi$
$720$	15.9905	−	1.50398i	0.595932	−	0.0560502i
$721$	31.5700	+	16.9340i	1.17573	+	0.630656i
$722$	−4.93373	−	12.5298i	−0.183614	−	0.466310i
$723$	−0.982568	−	4.58735i	−0.0365421	−	0.170605i
$724$	7.89033	+	12.5108i	0.293242	+	0.464961i
$725$		−	35.8794i		−	1.33253i
$726$	−2.83433	+	1.78756i	−0.105192	+	0.0663424i
$727$	−40.1912	−	7.62783i	−1.49061	−	0.282900i	−0.623817	−	0.781570i	$-0.714419\pi$
$727$	−40.1912	−	7.62783i	−1.49061	−	0.282900i	−0.866792	+	0.498670i	$0.833822\pi$
$728$	1.06332	+	1.08855i	0.0394094	+	0.0403444i
$729$	26.3605	−	29.6470i	0.976316	−	1.09804i
$730$	23.9146	+	34.2485i	0.885120	+	1.26759i
$731$	53.6842	−	16.8881i	1.98558	−	0.624630i
$732$	−1.08804	−	5.73290i	−0.0402150	−	0.211894i
$733$	−1.04933	−	0.276777i	−0.0387579	−	0.0102230i	0.235613	−	0.971847i	$-0.424290\pi$
$733$	−1.04933	−	0.276777i	−0.0387579	−	0.0102230i	−0.274371	+	0.961624i	$0.588469\pi$
$734$	−9.65575	+	16.1364i	−0.356400	+	0.595607i
$735$	−19.2204	−	33.8998i	−0.708956	−	1.25041i
$736$	2.40269	−	4.23773i	0.0885645	−	0.156205i
$737$	−20.7613	−	34.6958i	−0.764754	−	1.27804i
$738$	−2.99194	−	10.3526i	−0.110135	−	0.381086i
$739$	−8.89118	−	5.32032i	−0.327067	−	0.195711i	0.340530	−	0.940234i	$-0.389394\pi$
$739$	−8.89118	−	5.32032i	−0.327067	−	0.195711i	−0.667597	+	0.744523i	$0.732677\pi$
$740$	−13.7351	+	16.9885i	−0.504911	+	0.624510i
$741$	−2.41769	−	1.86268i	−0.0888161	−	0.0684271i
$742$	−8.36491	+	19.8646i	−0.307086	+	0.729251i
$743$	23.6829	−	11.9972i	0.868840	−	0.440133i	0.0397246	−	0.999211i	$-0.487352\pi$
$743$	23.6829	−	11.9972i	0.868840	−	0.440133i	0.829116	+	0.559077i	$0.188844\pi$
$744$	−8.68518	+	25.5038i	−0.318414	+	0.935016i
$745$	55.9571	−	25.1236i	2.05011	−	0.920457i
$746$	−3.92403	+	5.34805i	−0.143669	+	0.195806i
$747$	−25.6062	−	22.7676i	−0.936880	−	0.833024i
$748$	18.4098	−	14.8841i	0.673129	−	0.544218i
$749$	−24.2006	+	45.1169i	−0.884269	+	1.64854i
$750$	−8.51091	−	2.03274i	−0.310774	−	0.0742252i
$751$	−33.2184	−	13.0801i	−1.21216	−	0.477298i	−0.328083	−	0.944649i	$-0.606403\pi$
$751$	−33.2184	−	13.0801i	−1.21216	−	0.477298i	−0.884072	+	0.467350i	$0.845209\pi$
$752$	−12.0824	−	4.11458i	−0.440599	−	0.150043i
$753$	−0.142072	+	6.05877i	−0.00517740	+	0.220794i
$754$	3.19665	−	2.46281i	0.116415	−	0.0896904i
$755$	−8.29053	−	31.4314i	−0.301723	−	1.14391i
$756$	−10.9178	−	20.3539i	−0.397076	−	0.740265i
$757$	−12.4973	−	5.26259i	−0.454224	−	0.191272i	0.149012	−	0.988835i	$-0.452391\pi$
$757$	−12.4973	−	5.26259i	−0.454224	−	0.191272i	−0.603235	+	0.797563i	$0.706122\pi$
$758$	1.44310	+	3.93298i	0.0524157	+	0.142852i
$759$	−44.0671	−	3.10454i	−1.59953	−	0.112688i
$760$	0.824945	−	7.00510i	0.0299239	−	0.254102i
$761$	48.0109	+	15.1034i	1.74039	+	0.547499i	0.993129	−	0.117027i	$-0.0373362\pi$
$761$	48.0109	+	15.1034i	1.74039	+	0.547499i	0.747266	+	0.664525i	$0.231366\pi$
$762$	1.17933	+	3.74885i	0.0427225	+	0.135807i
$763$	1.86638	−	0.635585i	0.0675675	−	0.0230097i
$764$	0.238130	+	0.0111740i	0.00861525	+	0.000404261i
$765$	−73.9745	−	96.0164i	−2.67455	−	3.47148i
$766$	−16.2030	−	33.9363i	−0.585440	−	1.22617i
$767$	−1.06405	+	0.280659i	−0.0384205	+	0.0101340i

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.e (of order \(134\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.902417 - 0.430864i) q^{2} +(-0.405300 - 2.86221i) q^{3} +(0.628713 + 0.777638i) q^{4} +(0.0702905 + 2.99759i) q^{5} +(-0.867475 + 2.75754i) q^{6} +(-1.94113 + 2.77992i) q^{7} +(-0.232305 - 0.972643i) q^{8} +(-5.14594 + 1.48719i) q^{9} +O(q^{10})\)	\(q+(-0.902417 - 0.430864i) q^{2} +(-0.405300 - 2.86221i) q^{3} +(0.628713 + 0.777638i) q^{4} +(0.0702905 + 2.99759i) q^{5} +(-0.867475 + 2.75754i) q^{6} +(-1.94113 + 2.77992i) q^{7} +(-0.232305 - 0.972643i) q^{8} +(-5.14594 + 1.48719i) q^{9} +(1.22812 - 2.73536i) q^{10} +(1.08059 - 2.94502i) q^{11} +(1.97095 - 2.11469i) q^{12} +(0.409433 + 0.183827i) q^{13} +(2.94948 - 1.67228i) q^{14} +(8.55125 - 1.41611i) q^{15} +(-0.209440 + 0.977821i) q^{16} +(7.08482 - 2.59958i) q^{17} +(5.28456 + 0.875136i) q^{18} +(0.861878 - 2.18884i) q^{19} +(-2.28684 + 1.93928i) q^{20} +(8.74346 + 4.42923i) q^{21} +(-2.24405 + 2.19204i) q^{22} +(4.82336 - 0.683005i) q^{23} +(-2.68976 + 1.05912i) q^{24} +(-3.98609 + 0.187042i) q^{25} +(-0.290275 - 0.342299i) q^{26} +(2.79021 + 6.21455i) q^{27} +(-3.38218 + 0.238276i) q^{28} +(-0.421441 + 8.98139i) q^{29} +(-8.32694 - 2.40650i) q^{30} +(6.02794 - 7.10827i) q^{31} +(0.610310 - 0.792162i) q^{32} +(-8.86723 - 1.89928i) q^{33} +(-7.51352 - 0.706683i) q^{34} +(-8.46950 - 5.62330i) q^{35} +(-4.39181 - 3.06666i) q^{36} +(7.15819 - 1.35854i) q^{37} +(-1.72087 + 1.60389i) q^{38} +(0.360209 - 1.24639i) q^{39} +(2.89925 - 0.764723i) q^{40} +(-0.866815 - 1.81549i) q^{41} +(-5.98186 - 7.76425i) q^{42} +(7.44910 + 0.349540i) q^{43} +(2.96954 - 1.01126i) q^{44} +(-4.81969 - 15.3209i) q^{45} +(-4.64696 - 1.46186i) q^{46} +(-1.49279 + 12.6762i) q^{47} +(2.88362 + 0.203152i) q^{48} +(-1.54870 - 4.22078i) q^{49} +(3.67770 + 1.54867i) q^{50} +(-10.3120 - 19.2246i) q^{51} +(0.114465 + 0.433965i) q^{52} +(-5.03580 + 3.87976i) q^{53} +(0.159695 - 6.81032i) q^{54} +(8.90390 + 3.03217i) q^{55} +(3.15480 + 1.24224i) q^{56} +(-6.61425 - 1.57974i) q^{57} +(4.25007 - 7.92338i) q^{58} +(-1.90670 + 1.54155i) q^{59} +(6.47750 + 5.75945i) q^{60} +(1.19413 - 1.62748i) q^{61} +(-8.50241 + 3.81741i) q^{62} +(5.85468 - 17.1921i) q^{63} +(-0.892068 + 0.451900i) q^{64} +(-0.522258 + 1.24023i) q^{65} +(7.18361 + 5.53451i) q^{66} +(8.10352 - 10.0230i) q^{67} +(6.47585 + 3.87503i) q^{68} +(-3.90981 - 13.5287i) q^{69} +(5.22014 + 8.72377i) q^{70} +(-5.52961 + 9.75279i) q^{71} +(2.64193 + 4.65968i) q^{72} +(-7.15333 + 11.9545i) q^{73} +(-7.04502 - 1.85823i) q^{74} +(2.15091 + 11.3332i) q^{75} +(2.24400 - 0.705924i) q^{76} +(6.08934 + 8.72063i) q^{77} +(-0.862083 + 0.969562i) q^{78} +(-4.91747 - 5.03413i) q^{79} +(-2.94583 - 0.559084i) q^{80} +(3.06433 - 1.93261i) q^{81} +2.01181i q^{82} +(3.41233 + 5.41056i) q^{83} +(2.05279 + 9.58396i) q^{84} +(8.29047 + 21.0546i) q^{85} +(-6.57159 - 3.52498i) q^{86} +(25.8775 - 2.43390i) q^{87} +(-3.11548 - 0.366890i) q^{88} +(0.872891 - 1.31470i) q^{89} +(-2.25184 + 15.9025i) q^{90} +(-1.30579 + 0.781359i) q^{91} +(3.56364 + 3.32141i) q^{92} +(-22.7885 - 14.3723i) q^{93} +(6.80882 - 10.7960i) q^{94} +(6.62182 + 2.42970i) q^{95} +(-2.51470 - 1.42578i) q^{96} +(-2.62742 - 3.58090i) q^{97} +(-0.421007 + 4.47619i) q^{98} +(-1.18088 + 16.7619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9	\( 1452 q + 22 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} + 2 q^{11} - 10 q^{13} + 12 q^{14} - 22 q^{16} + 2 q^{20} + 12 q^{21} - 4 q^{23} - 2 q^{24} - 24 q^{25} - 8 q^{30} - 12 q^{34} - 20 q^{36} - 396 q^{37} - 2 q^{38} + 24 q^{41} + 14 q^{43} - 2 q^{44} - 42 q^{45} - 402 q^{47} + 22 q^{49} + 12 q^{51} + 10 q^{52} - 10 q^{53} - 8 q^{54} - 4 q^{55} - 12 q^{56} + 16 q^{57} - 18 q^{58} - 268 q^{60} - 2 q^{61} + 4 q^{62} + 22 q^{64} + 16 q^{65} + 40 q^{66} + 6 q^{67} - 106 q^{73} + 40 q^{78} + 40 q^{79} - 2 q^{80} - 14 q^{81} - 402 q^{83} - 12 q^{84} - 100 q^{87} + 4 q^{92} - 340 q^{93} + 2 q^{96} - 64 q^{97} + 18 q^{99}+O(q^{100}) \) 1452 * q + 22 * q^4 - 2 * q^5 + 2 * q^6 + 20 * q^9 + 2 * q^11 - 10 * q^13 + 12 * q^14 - 22 * q^16 + 2 * q^20 + 12 * q^21 - 4 * q^23 - 2 * q^24 - 24 * q^25 - 8 * q^30 - 12 * q^34 - 20 * q^36 - 396 * q^37 - 2 * q^38 + 24 * q^41 + 14 * q^43 - 2 * q^44 - 42 * q^45 - 402 * q^47 + 22 * q^49 + 12 * q^51 + 10 * q^52 - 10 * q^53 - 8 * q^54 - 4 * q^55 - 12 * q^56 + 16 * q^57 - 18 * q^58 - 268 * q^60 - 2 * q^61 + 4 * q^62 + 22 * q^64 + 16 * q^65 + 40 * q^66 + 6 * q^67 - 106 * q^73 + 40 * q^78 + 40 * q^79 - 2 * q^80 - 14 * q^81 - 402 * q^83 - 12 * q^84 - 100 * q^87 + 4 * q^92 - 340 * q^93 + 2 * q^96 - 64 * q^97 + 18 * q^99

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