LMFDB - Embedded newform 288.2.bf.a.11.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.18
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.514835 + 1.31717i) q^{2} +(-0.894226 - 1.48336i) q^{3} +(-1.46989 - 1.35625i) q^{4} +(0.446317 + 3.39012i) q^{5} +(2.41422 - 0.414163i) q^{6} +(-0.836733 - 3.12273i) q^{7} +(2.54317 - 1.23785i) q^{8} +(-1.40072 + 2.65292i) q^{9} +O(q^{10})$	\(q+(-0.514835 + 1.31717i) q^{2} +(-0.894226 - 1.48336i) q^{3} +(-1.46989 - 1.35625i) q^{4} +(0.446317 + 3.39012i) q^{5} +(2.41422 - 0.414163i) q^{6} +(-0.836733 - 3.12273i) q^{7} +(2.54317 - 1.23785i) q^{8} +(-1.40072 + 2.65292i) q^{9} +(-4.69515 - 1.15747i) q^{10} +(-4.01895 + 3.08385i) q^{11} +(-0.697402 + 3.39317i) q^{12} +(-1.48486 + 1.93511i) q^{13} +(4.54395 + 0.505569i) q^{14} +(4.62966 - 3.69358i) q^{15} +(0.321150 + 3.98709i) q^{16} -1.01461 q^{17} +(-2.77321 - 3.21081i) q^{18} +(-2.17425 + 0.900605i) q^{19} +(3.94182 - 5.58842i) q^{20} +(-3.88391 + 4.03360i) q^{21} +(-1.99287 - 6.88133i) q^{22} +(-6.01199 - 1.61091i) q^{23} +(-4.11035 - 2.66552i) q^{24} +(-6.46406 + 1.73204i) q^{25} +(-1.78442 - 2.95208i) q^{26} +(5.18780 - 0.294534i) q^{27} +(-3.00531 + 5.72489i) q^{28} +(-1.52671 - 0.200995i) q^{29} +(2.48157 + 7.99965i) q^{30} +(-7.43368 + 4.29184i) q^{31} +(-5.41702 - 1.62968i) q^{32} +(8.16831 + 3.20390i) q^{33} +(0.522355 - 1.33641i) q^{34} +(10.2130 - 4.23035i) q^{35} +(5.65694 - 1.99976i) q^{36} +(3.35400 - 8.09728i) q^{37} +(-0.0668708 - 3.32753i) q^{38} +(4.19827 + 0.472162i) q^{39} +(5.33152 + 8.06918i) q^{40} +(-0.0141655 + 0.0528664i) q^{41} +(-3.31338 - 7.19242i) q^{42} +(6.95331 + 9.06173i) q^{43} +(10.0899 + 0.917801i) q^{44} +(-9.61887 - 3.56456i) q^{45} +(5.21703 - 7.08948i) q^{46} +(6.69989 + 3.86818i) q^{47} +(5.62711 - 4.04174i) q^{48} +(-2.98914 + 1.72578i) q^{49} +(1.04653 - 9.40600i) q^{50} +(0.907288 + 1.50503i) q^{51} +(4.80709 - 0.830548i) q^{52} +(-2.66169 + 6.42590i) q^{53} +(-2.28291 + 6.98486i) q^{54} +(-12.2483 - 12.2483i) q^{55} +(-5.99343 - 6.90589i) q^{56} +(3.28020 + 2.41986i) q^{57} +(1.05075 - 1.90746i) q^{58} +(9.66398 - 1.27229i) q^{59} +(-11.8145 - 0.849841i) q^{60} +(0.369438 - 2.80616i) q^{61} +(-1.82597 - 12.0010i) q^{62} +(9.45638 + 2.15429i) q^{63} +(4.93545 - 6.29614i) q^{64} +(-7.22297 - 4.17019i) q^{65} +(-8.42542 + 9.10960i) q^{66} +(-3.37411 + 4.39723i) q^{67} +(1.49136 + 1.37606i) q^{68} +(2.98652 + 10.3585i) q^{69} +(0.314107 + 15.6302i) q^{70} +(-1.30625 - 1.30625i) q^{71} +(-0.278354 + 8.48071i) q^{72} +(5.41978 - 5.41978i) q^{73} +(8.93876 + 8.58656i) q^{74} +(8.34957 + 8.03970i) q^{75} +(4.41736 + 1.62505i) q^{76} +(12.9928 + 9.96974i) q^{77} +(-2.78334 + 5.28676i) q^{78} +(2.10030 - 3.63783i) q^{79} +(-13.3734 + 2.86824i) q^{80} +(-5.07596 - 7.43200i) q^{81} +(-0.0623413 - 0.0458759i) q^{82} +(-0.791678 - 0.104226i) q^{83} +(11.1795 - 0.661383i) q^{84} +(-0.452837 - 3.43964i) q^{85} +(-15.5157 + 4.49342i) q^{86} +(1.06707 + 2.44439i) q^{87} +(-6.40354 + 12.8176i) q^{88} +(2.14845 - 2.14845i) q^{89} +(9.64728 - 10.8346i) q^{90} +(7.28526 + 3.01765i) q^{91} +(6.65216 + 10.5216i) q^{92} +(13.0137 + 7.18896i) q^{93} +(-8.54440 + 6.83343i) q^{94} +(-4.02356 - 6.96902i) q^{95} +(2.42663 + 9.49271i) q^{96} +(-1.83760 + 3.18282i) q^{97} +(-0.734236 - 4.82570i) q^{98} +(-2.55178 - 14.9816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.514835	+	1.31717i	−0.364043	+	0.931382i
$2$	−0.514835	+	1.31717i	−0.364043	+	0.931382i
$3$	−0.894226	−	1.48336i	−0.516281	−	0.856419i
$3$	−0.894226	−	1.48336i	−0.516281	−	0.856419i
$4$	−1.46989	−	1.35625i	−0.734945	−	0.678127i
$5$	0.446317	+	3.39012i	0.199599	+	1.51611i	0.738798	+	0.673927i	$0.235394\pi$
$5$	0.446317	+	3.39012i	0.199599	+	1.51611i	−0.539198	+	0.842179i	$0.681273\pi$
$6$	2.41422	−	0.414163i	0.985602	−	0.169081i
$7$	−0.836733	−	3.12273i	−0.316255	−	1.18028i	−0.922815	−	0.385243i	$-0.874118\pi$
$7$	−0.836733	−	3.12273i	−0.316255	−	1.18028i	0.606560	−	0.795038i	$-0.292549\pi$
$8$	2.54317	−	1.23785i	0.899147	−	0.437647i
$9$	−1.40072	+	2.65292i	−0.466907	+	0.884306i
$10$	−4.69515	−	1.15747i	−1.48474	−	0.366025i
$11$	−4.01895	+	3.08385i	−1.21176	+	0.929816i	−0.998882	−	0.0472633i	$-0.984950\pi$
$11$	−4.01895	+	3.08385i	−1.21176	+	0.929816i	−0.212877	+	0.977079i	$0.568283\pi$
$12$	−0.697402	+	3.39317i	−0.201323	+	0.979525i
$13$	−1.48486	+	1.93511i	−0.411827	+	0.536703i	−0.952504	−	0.304527i	$-0.901502\pi$
$13$	−1.48486	+	1.93511i	−0.411827	+	0.536703i	0.540677	+	0.841230i	$0.318168\pi$
$14$	4.54395	+	0.505569i	1.21442	+	0.135119i
$15$	4.62966	−	3.69358i	1.19537	−	0.953678i
$16$	0.321150	+	3.98709i	0.0802875	+	0.996772i
$17$	−1.01461			−0.246078			−0.123039	−	0.992402i	$-0.539264\pi$
$17$	−1.01461			−0.246078			−0.123039	+	0.992402i	$0.539264\pi$
$18$	−2.77321	−	3.21081i	−0.653653	−	0.756795i
$19$	−2.17425	+	0.900605i	−0.498808	+	0.206613i	−0.617880	−	0.786273i	$-0.712008\pi$
$19$	−2.17425	+	0.900605i	−0.498808	+	0.206613i	0.119072	+	0.992886i	$0.462008\pi$
$20$	3.94182	−	5.58842i	0.881418	−	1.24961i
$21$	−3.88391	+	4.03360i	−0.847538	+	0.880204i
$22$	−1.99287	−	6.88133i	−0.424881	−	1.46710i
$23$	−6.01199	−	1.61091i	−1.25359	−	0.335897i	−0.429866	−	0.902893i	$-0.641439\pi$
$23$	−6.01199	−	1.61091i	−1.25359	−	0.335897i	−0.823721	+	0.566995i	$0.808106\pi$
$24$	−4.11035	−	2.66552i	−0.839022	−	0.544098i
$25$	−6.46406	+	1.73204i	−1.29281	+	0.346408i
$26$	−1.78442	−	2.95208i	−0.349953	−	0.578951i
$27$	5.18780	−	0.294534i	0.998392	−	0.0566830i
$28$	−3.00531	+	5.72489i	−0.567950	+	1.08190i
$29$	−1.52671	−	0.200995i	−0.283502	−	0.0373238i	−0.0125660	−	0.999921i	$-0.504000\pi$
$29$	−1.52671	−	0.200995i	−0.283502	−	0.0373238i	−0.270936	+	0.962597i	$0.587333\pi$
$30$	2.48157	+	7.99965i	0.453071	+	1.46053i
$31$	−7.43368	+	4.29184i	−1.33513	+	0.770837i	−0.986081	−	0.166268i	$-0.946828\pi$
$31$	−7.43368	+	4.29184i	−1.33513	+	0.770837i	−0.349048	+	0.937105i	$0.613495\pi$
$32$	−5.41702	−	1.62968i	−0.957603	−	0.288090i
$33$	8.16831	+	3.20390i	1.42192	+	0.557727i
$34$	0.522355	−	1.33641i	0.0895832	−	0.229193i
$35$	10.2130	−	4.23035i	1.72631	−	0.715060i
$36$	5.65694	−	1.99976i	0.942823	−	0.333294i
$37$	3.35400	−	8.09728i	0.551394	−	1.33118i	−0.365037	−	0.930993i	$-0.618944\pi$
$37$	3.35400	−	8.09728i	0.551394	−	1.33118i	0.916432	−	0.400191i	$-0.131056\pi$
$38$	−0.0668708	−	3.32753i	−0.0108479	−	0.539797i
$39$	4.19827	+	0.472162i	0.672261	+	0.0756064i
$40$	5.33152	+	8.06918i	0.842988	+	1.27585i
$41$	−0.0141655	+	0.0528664i	−0.00221228	+	0.00825635i	−0.967023	−	0.254689i	$-0.918027\pi$
$41$	−0.0141655	+	0.0528664i	−0.00221228	+	0.00825635i	0.964811	+	0.262945i	$0.0846937\pi$
$42$	−3.31338	−	7.19242i	−0.511265	−	1.10981i
$43$	6.95331	+	9.06173i	1.06037	+	1.38190i	0.920053	+	0.391794i	$0.128146\pi$
$43$	6.95331	+	9.06173i	1.06037	+	1.38190i	0.140317	+	0.990107i	$0.455188\pi$
$44$	10.0899	+	0.917801i	1.52111	+	0.138364i
$45$	−9.61887	−	3.56456i	−1.43390	−	0.531374i
$46$	5.21703	−	7.08948i	0.769209	−	1.04529i
$47$	6.69989	+	3.86818i	0.977279	+	0.564232i	0.901447	−	0.432888i	$-0.142506\pi$
$47$	6.69989	+	3.86818i	0.977279	+	0.564232i	0.0758313	+	0.997121i	$0.475839\pi$
$48$	5.62711	−	4.04174i	0.812203	−	0.583375i
$49$	−2.98914	+	1.72578i	−0.427019	+	0.246540i
$50$	1.04653	−	9.40600i	0.148002	−	1.33021i
$51$	0.907288	+	1.50503i	0.127046	+	0.210746i
$52$	4.80709	−	0.830548i	0.666623	−	0.115176i
$53$	−2.66169	+	6.42590i	−0.365612	+	0.882665i	0.628846	+	0.777530i	$0.283528\pi$
$53$	−2.66169	+	6.42590i	−0.365612	+	0.882665i	−0.994458	+	0.105135i	$0.966472\pi$
$54$	−2.28291	+	6.98486i	−0.310665	+	0.950520i
$55$	−12.2483	−	12.2483i	−1.65157	−	1.65157i
$56$	−5.99343	−	6.90589i	−0.800906	−	0.922838i
$57$	3.28020	+	2.41986i	0.434472	+	0.320518i
$58$	1.05075	−	1.90746i	0.137970	−	0.250462i
$59$	9.66398	−	1.27229i	1.25814	−	0.165638i	0.528185	−	0.849129i	$-0.322873\pi$
$59$	9.66398	−	1.27229i	1.25814	−	0.165638i	0.729958	+	0.683492i	$0.239539\pi$
$60$	−11.8145	−	0.849841i	−1.52525	−	0.109714i
$61$	0.369438	−	2.80616i	0.0473017	−	0.359292i	−0.951383	−	0.308011i	$-0.900336\pi$
$61$	0.369438	−	2.80616i	0.0473017	−	0.359292i	0.998684	−	0.0512803i	$-0.0163302\pi$
$62$	−1.82597	−	12.0010i	−0.231899	−	1.52413i
$63$	9.45638	+	2.15429i	1.19139	+	0.271415i
$64$	4.93545	−	6.29614i	0.616931	−	0.787017i
$65$	−7.22297	−	4.17019i	−0.895900	−	0.517248i
$66$	−8.42542	+	9.10960i	−1.03710	+	1.12131i
$67$	−3.37411	+	4.39723i	−0.412214	+	0.537207i	−0.952606	−	0.304206i	$-0.901609\pi$
$67$	−3.37411	+	4.39723i	−0.412214	+	0.537207i	0.540393	+	0.841413i	$0.318276\pi$
$68$	1.49136	+	1.37606i	0.180854	+	0.166872i
$69$	2.98652	+	10.3585i	0.359534	+	1.24701i
$70$	0.314107	+	15.6302i	0.0375430	+	1.86816i
$71$	−1.30625	−	1.30625i	−0.155023	−	0.155023i	0.625334	−	0.780357i	$-0.284963\pi$
$71$	−1.30625	−	1.30625i	−0.155023	−	0.155023i	−0.780357	+	0.625334i	$0.784963\pi$
$72$	−0.278354	+	8.48071i	−0.0328043	+	0.999462i
$73$	5.41978	−	5.41978i	0.634337	−	0.634337i	−0.314816	−	0.949153i	$-0.601943\pi$
$73$	5.41978	−	5.41978i	0.634337	−	0.634337i	0.949153	+	0.314816i	$0.101943\pi$
$74$	8.93876	+	8.58656i	1.03911	+	0.998168i
$75$	8.34957	+	8.03970i	0.964126	+	0.928345i
$76$	4.41736	+	1.62505i	0.506706	+	0.186406i
$77$	12.9928	+	9.96974i	1.48067	+	1.13616i
$78$	−2.78334	+	5.28676i	−0.315151	+	0.598608i
$79$	2.10030	−	3.63783i	0.236302	−	0.409287i	−0.723348	−	0.690484i	$-0.757398\pi$
$79$	2.10030	−	3.63783i	0.236302	−	0.409287i	0.959650	+	0.281196i	$0.0907311\pi$
$80$	−13.3734	+	2.86824i	−1.49519	+	0.320679i
$81$	−5.07596	−	7.43200i	−0.563996	−	0.825778i
$82$	−0.0623413	−	0.0458759i	−0.00688445	−	0.00506615i
$83$	−0.791678	−	0.104226i	−0.0868979	−	0.0114403i	0.0869518	−	0.996213i	$-0.472287\pi$
$83$	−0.791678	−	0.104226i	−0.0868979	−	0.0114403i	−0.173850	+	0.984772i	$0.555621\pi$
$84$	11.1795	−	0.661383i	1.21978	−	0.0721628i
$85$	−0.452837	−	3.43964i	−0.0491170	−	0.373081i
$86$	−15.5157	+	4.49342i	−1.67310	+	0.484537i
$87$	1.06707	+	2.44439i	0.114402	+	0.262066i
$88$	−6.40354	+	12.8176i	−0.682619	+	1.36636i
$89$	2.14845	−	2.14845i	0.227735	−	0.227735i	−0.584011	−	0.811746i	$-0.698517\pi$
$89$	2.14845	−	2.14845i	0.227735	−	0.227735i	0.811746	+	0.584011i	$0.198517\pi$
$90$	9.64728	−	10.8346i	1.01691	−	1.14206i
$91$	7.28526	+	3.01765i	0.763703	+	0.316336i
$92$	6.65216	+	10.5216i	0.693536	+	1.09696i
$93$	13.0137	+	7.18896i	1.34946	+	0.745461i
$94$	−8.54440	+	6.83343i	−0.881288	+	0.704815i
$95$	−4.02356	−	6.96902i	−0.412809	−	0.715006i
$96$	2.42663	+	9.49271i	0.247667	+	0.968845i
$97$	−1.83760	+	3.18282i	−0.186580	+	0.323166i	−0.944108	−	0.329637i	$-0.893074\pi$
$97$	−1.83760	+	3.18282i	−0.186580	+	0.323166i	0.757528	+	0.652803i	$0.226407\pi$
$98$	−0.734236	−	4.82570i	−0.0741691	−	0.487469i
$99$	−2.55178	−	14.9816i	−0.256463	−	1.50570i
$100$	11.8505	+	6.22100i	1.18505	+	0.622100i
$101$	−10.1712	+	7.80465i	−1.01207	+	0.776592i	−0.974883	−	0.222716i	$-0.928508\pi$
$101$	−10.1712	+	7.80465i	−1.01207	+	0.776592i	−0.0371908	+	0.999308i	$0.511841\pi$
$102$	−2.44949	+	0.420213i	−0.242535	+	0.0416073i
$103$	−12.4857	−	3.34554i	−1.23025	−	0.329646i	−0.415575	−	0.909559i	$-0.636420\pi$
$103$	−12.4857	−	3.34554i	−1.23025	−	0.329646i	−0.814678	+	0.579913i	$0.803086\pi$
$104$	−1.38088	+	6.75936i	−0.135407	+	0.662810i
$105$	−15.4078	−	11.3666i	−1.50365	−	1.10927i
$106$	−7.09369	−	6.81419i	−0.689000	−	0.661853i
$107$	−9.38865	−	3.88891i	−0.907636	−	0.375955i	−0.120484	−	0.992715i	$-0.538445\pi$
$107$	−9.38865	−	3.88891i	−0.907636	−	0.375955i	−0.787151	+	0.616760i	$0.788445\pi$
$108$	−8.02495	−	6.60304i	−0.772201	−	0.635378i
$109$	−2.54524	−	6.14476i	−0.243790	−	0.588561i	0.753863	−	0.657031i	$-0.228188\pi$
$109$	−2.54524	−	6.14476i	−0.243790	−	0.588561i	−0.997653	+	0.0684705i	$0.978188\pi$
$110$	22.4391	−	9.82731i	2.13948	−	0.936997i
$111$	−15.0104	+	2.26560i	−1.42473	+	0.215041i
$112$	12.1819	−	4.33899i	1.15108	−	0.409996i
$113$	3.26269	+	5.65114i	0.306928	+	0.531615i	0.977689	−	0.210059i	$-0.0673656\pi$
$113$	3.26269	+	5.65114i	0.306928	+	0.531615i	−0.670761	+	0.741674i	$0.734032\pi$
$114$	−4.87613	+	3.07476i	−0.456692	+	0.287977i
$115$	2.77791	−	21.1003i	0.259041	−	1.96762i
$116$	1.97149	+	2.36604i	0.183048	+	0.219682i
$117$	−3.05382	−	6.64977i	−0.282325	−	0.614772i
$118$	−3.29954	+	13.3842i	−0.303747	+	1.23211i
$119$	0.848955	+	3.16834i	0.0778236	+	0.290442i
$120$	7.20192	−	15.1242i	0.657442	−	1.38065i
$121$	3.79483	−	14.1625i	0.344985	−	1.28750i
$122$	3.50600	+	1.93132i	0.317418	+	0.174854i
$123$	0.0910872	−	0.0262619i	0.00821305	−	0.00236796i
$124$	16.7475	+	3.77343i	1.50397	+	0.338864i
$125$	−2.21416	−	5.34546i	−0.198041	−	0.478112i
$126$	−7.70604	+	11.3466i	−0.686509	+	1.01083i
$127$			0.275503i			0.0244470i	0.999925	+	0.0122235i	$0.00389095\pi$
$127$			0.275503i			0.0244470i	−0.999925	+	0.0122235i	$0.996109\pi$
$128$	5.75216	+	9.74231i	0.508424	+	0.861107i
$129$	7.22399	−	18.4175i	0.636037	−	1.62157i
$130$	9.21150	−	7.36695i	0.807902	−	0.646124i
$131$	−8.22613	−	6.31213i	−0.718720	−	0.551493i	0.183369	−	0.983044i	$-0.441300\pi$
$131$	−8.22613	−	6.31213i	−0.718720	−	0.551493i	−0.902089	+	0.431551i	$0.857966\pi$
$132$	−7.66122	−	15.7877i	−0.666823	−	1.37414i
$133$	4.63161	+	6.03604i	0.401612	+	0.523391i
$134$	−4.05480	−	6.70814i	−0.350281	−	0.579495i
$135$	3.31391	+	17.4558i	0.285216	+	1.50235i
$136$	−2.58032	+	1.25593i	−0.221261	+	0.107695i
$137$	5.50255	−	1.47440i	0.470115	−	0.125967i	−0.0159812	−	0.999872i	$-0.505087\pi$
$137$	5.50255	−	1.47440i	0.470115	−	0.125967i	0.486096	+	0.873905i	$0.338421\pi$
$138$	−15.1815	−	1.39914i	−1.29233	−	0.119103i
$139$	5.38055	−	0.708363i	0.456372	−	0.0600825i	0.101164	−	0.994870i	$-0.467743\pi$
$139$	5.38055	−	0.708363i	0.456372	−	0.0600825i	0.355208	+	0.934787i	$0.384410\pi$
$140$	−20.7494	−	7.63323i	−1.75364	−	0.645126i
$141$	−0.253300	−	13.3974i	−0.0213317	−	1.12826i
$142$	2.39305	−	1.04805i	0.200821	−	0.0879505i
$143$		−	12.3562i		−	1.03328i
$144$	−11.0273	−	4.73281i	−0.918938	−	0.394401i
$145$		−	5.26542i		−	0.437270i
$146$	4.34849	+	9.92908i	0.359884	+	0.821736i
$147$	5.23291	+	2.89073i	0.431604	+	0.238424i
$148$	−15.9120	+	7.35322i	−1.30796	+	0.604431i
$149$	−19.9620	+	2.62804i	−1.63535	+	0.215298i	−0.891490	−	0.453041i	$-0.850339\pi$
$149$	−19.9620	+	2.62804i	−1.63535	+	0.215298i	−0.743857	+	0.668338i	$0.767006\pi$
$150$	−14.8883	+	6.85871i	−1.21563	+	0.560011i
$151$	3.36494	−	0.901632i	0.273835	−	0.0733738i	−0.119288	−	0.992860i	$-0.538061\pi$
$151$	3.36494	−	0.901632i	0.273835	−	0.0733738i	0.393123	+	0.919486i	$0.371395\pi$
$152$	−4.41468	+	4.98180i	−0.358078	+	0.404077i
$153$	1.42118	−	2.69167i	0.114896	−	0.217609i
$154$	−19.8210	+	11.9810i	−1.59722	+	0.965458i
$155$	−17.8676	−	23.2855i	−1.43516	−	1.87034i
$156$	−5.53062	−	6.38795i	−0.442804	−	0.511445i
$157$	12.7960	+	9.81875i	1.02124	+	0.783621i	0.976531	−	0.215379i	$-0.0690987\pi$
$157$	12.7960	+	9.81875i	1.02124	+	0.783621i	0.0447047	+	0.999000i	$0.485765\pi$
$158$	3.71034	+	4.63934i	0.295179	+	0.369086i
$159$	11.9121	−	1.79795i	0.944690	−	0.142587i
$160$	3.10710	−	19.0917i	0.245638	−	1.50933i
$161$			20.1217i			1.58581i
$162$	12.4025	−	2.85967i	0.974433	−	0.224677i
$163$	8.29456	+	20.0248i	0.649680	+	1.56847i	0.813237	+	0.581932i	$0.197703\pi$
$163$	8.29456	+	20.0248i	0.649680	+	1.56847i	−0.163557	+	0.986534i	$0.552297\pi$
$164$	0.0925221	−	0.0584958i	0.00722476	−	0.00456775i
$165$	−7.21593	+	29.1215i	−0.561760	+	2.26710i
$166$	0.544868	−	0.989117i	0.0422899	−	0.0767704i
$167$	−0.109632	+	0.409151i	−0.00848355	+	0.0316610i	−0.970038	−	0.242954i	$-0.921884\pi$
$167$	−0.109632	+	0.409151i	−0.00848355	+	0.0316610i	0.961554	+	0.274615i	$0.0885503\pi$
$168$	−4.88444	+	15.0658i	−0.376843	+	1.16235i
$169$	1.82481	+	6.81029i	0.140370	+	0.523868i
$170$	4.76373	+	1.17438i	0.365362	+	0.0900710i
$171$	0.656289	−	7.02961i	0.0501877	−	0.537568i
$172$	2.06941	−	22.7502i	0.157791	−	1.73469i
$173$	−0.0441519	+	0.335367i	−0.00335680	+	0.0254975i	−0.993041	−	0.117767i	$-0.962427\pi$
$173$	−0.0441519	+	0.335367i	−0.00335680	+	0.0254975i	0.989684	+	0.143264i	$0.0457598\pi$
$174$	−3.76906	+	0.147060i	−0.285731	+	0.0111486i
$175$	10.8174	+	18.7363i	0.817717	+	1.41633i
$176$	−13.5863	−	15.0335i	−1.02410	−	1.13319i
$177$	−10.5290	−	13.1975i	−0.791411	−	0.991982i
$178$	1.72378	+	3.93597i	0.129203	+	0.295014i
$179$	7.10685	+	17.1574i	0.531191	+	1.28241i	0.930735	+	0.365694i	$0.119168\pi$
$179$	7.10685	+	17.1574i	0.531191	+	1.28241i	−0.399544	+	0.916714i	$0.630832\pi$
$180$	9.30423	+	18.2851i	0.693496	+	1.36289i
$181$	−7.23422	−	2.99651i	−0.537716	−	0.222729i	0.0972632	−	0.995259i	$-0.468991\pi$
$181$	−7.23422	−	2.99651i	−0.537716	−	0.222729i	−0.634979	+	0.772530i	$0.718991\pi$
$182$	−7.72548	+	8.04235i	−0.572651	+	0.596139i
$183$	−4.49291	+	1.96133i	−0.332125	+	0.144986i
$184$	−17.2836	+	3.34513i	−1.27416	+	0.246607i
$185$	28.9477	+	7.75650i	2.12827	+	0.570269i
$186$	−16.1690	+	13.4402i	−1.18557	+	0.985484i
$187$	4.07766	−	3.12890i	0.298188	−	0.228808i
$188$	−4.60186	−	14.7725i	−0.335625	−	1.07740i
$189$	−5.26055	−	15.9536i	−0.382649	−	1.16046i
$190$	11.2509	−	1.71183i	0.816224	−	0.124190i
$191$	−6.34290	+	10.9862i	−0.458956	+	0.794935i	−0.998906	−	0.0467619i	$-0.985110\pi$
$191$	−6.34290	+	10.9862i	−0.458956	+	0.794935i	0.539950	+	0.841697i	$0.318443\pi$
$192$	−13.7529	−	1.69088i	−0.992527	−	0.122029i
$193$	−6.52683	−	11.3048i	−0.469812	−	0.813738i	0.529592	−	0.848252i	$-0.322345\pi$
$193$	−6.52683	−	11.3048i	−0.469812	−	0.813738i	−0.999404	+	0.0345143i	$0.989012\pi$
$194$	−3.24626	−	4.05906i	−0.233068	−	0.291424i
$195$	0.273077	+	14.4434i	0.0195554	+	1.03431i
$196$	6.73429	+	1.51732i	0.481021	+	0.108380i
$197$	11.3643	+	4.70723i	0.809670	+	0.335376i	0.748822	−	0.662771i	$-0.230620\pi$
$197$	11.3643	+	4.70723i	0.809670	+	0.335376i	0.0608475	+	0.998147i	$0.480620\pi$
$198$	21.0471	+	4.35191i	1.49575	+	0.309277i
$199$	1.17092	−	1.17092i	0.0830040	−	0.0830040i	−0.664386	−	0.747390i	$-0.731307\pi$
$199$	1.17092	−	1.17092i	0.0830040	−	0.0830040i	0.747390	+	0.664386i	$0.231307\pi$
$200$	−14.2952	+	12.4064i	−1.01082	+	0.877267i
$201$	9.53990	+	1.07291i	0.672893	+	0.0756774i
$202$	−5.04357	−	17.4154i	−0.354865	−	1.22534i
$203$	0.649794	+	4.93567i	0.0456066	+	0.346416i
$204$	0.707589	−	3.44274i	0.0495411	−	0.241040i
$205$	−0.185546	−	0.0244276i	−0.0129591	−	0.00170609i
$206$	10.8347	−	14.7234i	0.754892	−	1.02583i
$207$	12.6947	−	13.6929i	0.882345	−	0.951722i
$208$	−8.19232	−	5.29882i	−0.568035	−	0.367407i
$209$	5.96089	−	10.3246i	0.412323	−	0.714165i
$210$	22.9043	−	14.4428i	1.58055	−	0.996651i
$211$	−4.69013	−	3.59886i	−0.322882	−	0.247756i	0.434583	−	0.900632i	$-0.356896\pi$
$211$	−4.69013	−	3.59886i	−0.322882	−	0.247756i	−0.757465	+	0.652876i	$0.773562\pi$
$212$	12.6275	−	5.83543i	0.867263	−	0.400779i
$213$	−0.769556	+	3.10571i	−0.0527291	+	0.212800i
$214$	9.95597	−	10.3643i	0.680576	−	0.708491i
$215$	−27.6169	+	27.6169i	−1.88346	+	1.88346i
$216$	12.8289	−	7.17077i	0.872894	−	0.487909i
$217$	19.6223	+	19.6223i	1.33205	+	1.33205i
$218$	9.40409	−	0.188987i	0.636925	−	0.0127998i
$219$	−12.8860	−	3.19298i	−0.870755	−	0.215762i
$220$	1.39185	+	34.6156i	0.0938382	+	2.33378i
$221$	1.50655	−	1.96338i	0.101342	−	0.132071i
$222$	4.74371	−	20.9377i	0.318377	−	1.40525i
$223$	−11.2323	−	6.48494i	−0.752167	−	0.434264i	0.0743092	−	0.997235i	$-0.476325\pi$
$223$	−11.2323	−	6.48494i	−0.752167	−	0.434264i	−0.826476	+	0.562971i	$0.809658\pi$
$224$	−0.556456	+	18.2795i	−0.0371798	+	1.22135i
$225$	4.45938	−	19.5747i	0.297292	−	1.30498i
$226$	−9.12328	+	1.38812i	−0.606872	+	0.0923363i
$227$	1.36356	−	10.3573i	0.0905026	−	0.687435i	−0.884706	−	0.466149i	$-0.845641\pi$
$227$	1.36356	−	10.3573i	0.0905026	−	0.687435i	0.975209	−	0.221286i	$-0.0710256\pi$
$228$	−1.53958	−	8.00570i	−0.101961	−	0.530191i
$229$	−6.91549	+	0.910442i	−0.456989	+	0.0601637i	−0.355507	−	0.934674i	$-0.615692\pi$
$229$	−6.91549	+	0.910442i	−0.456989	+	0.0601637i	−0.101482	+	0.994837i	$0.532358\pi$
$230$	26.3626	+	14.5222i	1.73830	+	0.957564i
$231$	3.17021	−	28.1882i	0.208585	−	1.85465i
$232$	−4.13148	+	1.37867i	−0.271245	+	0.0905143i
$233$	15.4948	+	15.4948i	1.01510	+	1.01510i	0.999884	+	0.0152134i	$0.00484277\pi$
$233$	15.4948	+	15.4948i	1.01510	+	1.01510i	0.0152134	+	0.999884i	$0.495157\pi$
$234$	10.3311	−	0.598866i	0.675366	−	0.0391491i
$235$	−10.1233	+	24.4398i	−0.660372	+	1.59428i
$236$	−15.9305	−	11.2367i	−1.03699	−	0.731447i
$237$	−7.27435	+	0.137534i	−0.472520	+	0.00893380i
$238$	−4.61033	−	0.512954i	−0.298843	−	0.0332499i
$239$	5.67906	−	3.27881i	0.367348	−	0.212089i	−0.304951	−	0.952368i	$-0.598640\pi$
$239$	5.67906	−	3.27881i	0.367348	−	0.212089i	0.672299	+	0.740279i	$0.265307\pi$
$240$	16.2134	+	17.2727i	1.04657	+	1.11495i
$241$	−2.05215	−	1.18481i	−0.132191	−	0.0763204i	0.432446	−	0.901660i	$-0.357651\pi$
$241$	−2.05215	−	1.18481i	−0.132191	−	0.0763204i	−0.564637	+	0.825339i	$0.690984\pi$
$242$	16.7008	+	12.2898i	1.07357	+	0.790019i
$243$	−6.48528	+	14.1754i	−0.416031	+	0.909350i
$244$	−4.34890	+	3.62369i	−0.278410	+	0.231983i
$245$	−7.18469	−	9.36327i	−0.459013	−	0.598198i
$246$	−0.0123034	+	0.133498i	−0.000784434	+	0.00851153i
$247$	1.48570	−	5.54470i	0.0945326	−	0.352801i
$248$	−13.5925	+	20.1167i	−0.863123	+	1.27741i
$249$	0.553333	+	1.26755i	0.0350661	+	0.0803274i
$250$	8.18082	−	0.164403i	0.517400	−	0.0103978i
$251$	−7.77865	+	18.7793i	−0.490984	+	1.18534i	0.463236	+	0.886235i	$0.346688\pi$
$251$	−7.77865	+	18.7793i	−0.490984	+	1.18534i	−0.954220	+	0.299105i	$0.903312\pi$
$252$	−10.9781	−	15.9918i	−0.691553	−	1.00739i
$253$	29.1297	−	12.0659i	1.83137	−	0.758578i
$254$	−0.362886	−	0.141839i	−0.0227695	−	0.00889976i
$255$	−4.69729	+	3.74753i	−0.294155	+	0.234680i
$256$	−15.7937	+	2.56091i	−0.987108	+	0.160057i
$257$	−2.40382	+	1.38785i	−0.149946	+	0.0865716i	−0.573096	−	0.819488i	$-0.694258\pi$
$257$	−2.40382	+	1.38785i	−0.149946	+	0.0865716i	0.423150	+	0.906060i	$0.360924\pi$
$258$	20.5399	+	18.9972i	1.27876	+	1.18272i
$259$	−28.0920	−	3.69838i	−1.74555	−	0.229806i
$260$	4.96114	+	15.9259i	0.307677	+	0.987682i
$261$	2.67171	−	3.76869i	0.165375	−	0.233276i
$262$	12.5493	−	7.58553i	0.775296	−	0.468635i
$263$	8.05543	−	2.15845i	0.496719	−	0.133095i	−0.00175789	−	0.999998i	$-0.500560\pi$
$263$	8.05543	−	2.15845i	0.496719	−	0.133095i	0.498477	+	0.866903i	$0.333893\pi$
$264$	24.7394	−	1.96309i	1.52260	−	0.120820i
$265$	−22.9725	−	6.15546i	−1.41119	−	0.378127i
$266$	−10.3350	+	2.99307i	−0.633681	+	0.183517i
$267$	−5.10812	−	1.26573i	−0.312612	−	0.0774612i
$268$	10.9233	−	1.88729i	0.667249	−	0.115284i
$269$	−23.4254	+	9.70312i	−1.42827	+	0.591610i	−0.956924	−	0.290338i	$-0.906232\pi$
$269$	−23.4254	+	9.70312i	−1.42827	+	0.591610i	−0.471348	+	0.881947i	$0.656232\pi$
$270$	−24.6984	−	4.62186i	−1.50310	−	0.281278i
$271$	−6.47623			−0.393403			−0.196702	−	0.980463i	$-0.563023\pi$
$271$	−6.47623			−0.393403			−0.196702	+	0.980463i	$0.563023\pi$
$272$	−0.325841	−	4.04533i	−0.0197570	−	0.245284i
$273$	−2.03840	−	13.5051i	−0.123369	−	0.817368i
$274$	−0.890862	+	8.00689i	−0.0538189	+	0.483714i
$275$	20.6374	−	26.8952i	1.24448	−	1.62184i
$276$	9.65886	−	19.2763i	0.581395	−	1.16030i
$277$	−2.32424	+	1.78346i	−0.139650	+	0.107157i	−0.676224	−	0.736696i	$-0.736385\pi$
$277$	−2.32424	+	1.78346i	−0.139650	+	0.107157i	0.536574	+	0.843853i	$0.319718\pi$
$278$	−1.83706	+	7.45180i	−0.110180	+	0.446930i
$279$	−0.973387	−	25.7326i	−0.0582752	−	1.54057i
$280$	20.7368	−	23.4006i	1.23926	−	1.39846i
$281$	7.09336	+	26.4728i	0.423154	+	1.57923i	0.767920	+	0.640545i	$0.221292\pi$
$281$	7.09336	+	26.4728i	0.423154	+	1.57923i	−0.344766	+	0.938689i	$0.612042\pi$
$282$	17.7771	+	6.56380i	1.05861	+	0.390869i
$283$	2.38105	+	18.0859i	0.141539	+	1.07509i	0.903840	+	0.427871i	$0.140736\pi$
$283$	2.38105	+	18.0859i	0.141539	+	1.07509i	−0.762301	+	0.647223i	$0.775930\pi$
$284$	0.148436	+	3.69164i	0.00880805	+	0.219058i
$285$	−6.73959	+	12.2003i	−0.399219	+	0.722682i
$286$	16.2753	+	6.36141i	0.962377	+	0.376158i
$287$	0.176940			0.0104445
$288$	11.9112	−	12.0882i	0.701871	−	0.712304i
$289$	−15.9706			−0.939445
$290$	6.93547	+	2.71083i	0.407265	+	0.159185i
$291$	6.36450	−	0.120332i	0.373093	−	0.00705397i
$292$	−15.3171	+	0.615879i	−0.896364	+	0.0360416i
$293$	−2.55990	−	19.4444i	−0.149551	−	1.13595i	−0.887404	−	0.460992i	$-0.847494\pi$
$293$	−2.55990	−	19.4444i	−0.149551	−	1.13595i	0.737854	−	0.674961i	$-0.235840\pi$
$294$	−6.50168	+	5.40440i	−0.379186	+	0.315191i
$295$	8.62641	+	32.1942i	0.502249	+	1.87442i
$296$	−1.49342	−	24.7445i	−0.0868034	−	1.43825i
$297$	−19.9412	+	17.1821i	−1.15711	+	0.997007i
$298$	6.81553	−	27.6464i	0.394813	−	1.60151i
$299$	12.0443	−	9.24189i	0.696538	−	0.534472i
$300$	−1.36907	−	23.1416i	−0.0790431	−	1.33608i
$301$	22.4793	−	29.2956i	1.29568	−	1.68857i
$302$	−0.544782	+	4.89640i	−0.0313487	+	0.281756i
$303$	20.6725	+	8.10847i	1.18760	+	0.465820i
$304$	−4.28905	−	8.37971i	−0.245994	−	0.480609i
$305$	9.67809			0.554166
$306$	2.81372	+	3.25771i	0.160850	+	0.186231i
$307$	−9.11693	+	3.77636i	−0.520331	+	0.215528i	−0.627362	−	0.778728i	$-0.715865\pi$
$307$	−9.11693	+	3.77636i	−0.520331	+	0.215528i	0.107031	+	0.994256i	$0.465865\pi$
$308$	−5.57651	−	32.2760i	−0.317751	−	1.83909i
$309$	6.20241	+	21.5125i	0.352843	+	1.22380i
$310$	39.8699	−	11.5465i	2.26446	−	0.655799i
$311$	2.93700	+	0.786968i	0.166542	+	0.0446249i	0.341127	−	0.940017i	$-0.389192\pi$
$311$	2.93700	+	0.786968i	0.166542	+	0.0446249i	−0.174584	+	0.984642i	$0.555858\pi$
$312$	11.2614	−	3.99605i	0.637551	−	0.226232i
$313$	31.1097	−	8.33581i	1.75842	−	0.471168i	0.772031	−	0.635584i	$-0.219241\pi$
$313$	31.1097	−	8.33581i	1.75842	−	0.471168i	0.986391	+	0.164416i	$0.0525741\pi$
$314$	−19.5208	+	11.7996i	−1.10162	+	0.665888i
$315$	−3.08274	+	33.0197i	−0.173693	+	1.86045i
$316$	−8.02102	+	2.49866i	−0.451218	+	0.140561i
$317$	−23.4723	−	3.09018i	−1.31833	−	0.173562i	−0.561668	−	0.827363i	$-0.689840\pi$
$317$	−23.4723	−	3.09018i	−1.31833	−	0.173562i	−0.756667	+	0.653801i	$0.773173\pi$
$318$	−3.76455	+	16.6159i	−0.211105	+	0.931775i
$319$	6.75560	−	3.90035i	0.378241	−	0.218378i
$320$	23.5474	+	13.9217i	1.31634	+	0.778245i
$321$	2.62692	+	17.4043i	0.146620	+	0.971415i
$322$	−26.5038	−	10.3594i	−1.47700	−	0.577305i
$323$	2.20601	−	0.913760i	0.122746	−	0.0508430i
$324$	−2.61858	+	17.8085i	−0.145476	+	0.989362i
$325$	6.24656	−	15.0805i	0.346497	−	0.836517i
$326$	−30.6465	+	0.615879i	−1.69735	+	0.0341104i
$327$	−6.83887	+	9.27031i	−0.378191	+	0.512649i
$328$	0.0294154	+	0.151983i	0.00162420	+	0.00839187i
$329$	6.47327	−	24.1586i	0.356883	−	1.33190i
$330$	−34.6430	−	24.4974i	−1.90704	−	1.34854i
$331$	11.4718	+	14.9504i	0.630549	+	0.821747i	0.993944	−	0.109888i	$-0.0350492\pi$
$331$	11.4718	+	14.9504i	0.630549	+	0.821747i	−0.363395	+	0.931635i	$0.618383\pi$
$332$	1.02232	+	1.22692i	0.0561072	+	0.0673358i
$333$	16.7834	+	20.2399i	0.919725	+	1.10914i
$334$	−0.482480	−	0.355049i	−0.0264001	−	0.0194274i
$335$	−16.4130	−	9.47608i	−0.896741	−	0.517733i
$336$	−17.3296	−	14.1901i	−0.945409	−	0.774133i
$337$	8.59333	−	4.96136i	0.468109	−	0.270263i	−0.247339	−	0.968929i	$-0.579556\pi$
$337$	8.59333	−	4.96136i	0.468109	−	0.270263i	0.715448	+	0.698666i	$0.246223\pi$
$338$	−9.90980	−	1.10258i	−0.539022	−	0.0599726i
$339$	5.46511	−	9.89314i	0.296824	−	0.537322i
$340$	−3.99940	+	5.67005i	−0.216898	+	0.307501i
$341$	16.6402	−	40.1731i	0.901119	−	2.17549i
$342$	8.92134	+	4.48354i	0.482411	+	0.242442i
$343$	−8.11173	−	8.11173i	−0.437992	−	0.437992i
$344$	28.9005	+	14.4384i	1.55821	+	0.778465i
$345$	−33.7835	+	14.7478i	−1.81884	+	0.793995i
$346$	−0.419005	−	0.230814i	−0.0225259	−	0.0124086i
$347$	13.7406	−	1.80899i	0.737635	−	0.0971114i	0.247659	−	0.968847i	$-0.420339\pi$
$347$	13.7406	−	1.80899i	0.737635	−	0.0971114i	0.489976	+	0.871736i	$0.337006\pi$
$348$	1.74674	−	5.04021i	0.0936350	−	0.270184i
$349$	1.84749	−	14.0331i	0.0988938	−	0.751173i	−0.868103	−	0.496384i	$-0.834661\pi$
$349$	1.84749	−	14.0331i	0.0988938	−	0.751173i	0.966997	−	0.254789i	$-0.0820059\pi$
$350$	−30.2481	+	4.60228i	−1.61683	+	0.246002i
$351$	−7.13321	+	10.4763i	−0.380743	+	0.559184i
$352$	26.7964	−	10.1557i	1.42826	−	0.541299i
$353$	−16.5111	−	9.53271i	−0.878800	−	0.507375i	−0.00853719	−	0.999964i	$-0.502718\pi$
$353$	−16.5111	−	9.53271i	−0.878800	−	0.507375i	−0.870262	+	0.492588i	$0.836051\pi$
$354$	22.8041	−	7.07405i	1.21202	−	0.375982i
$355$	3.84533	−	5.01133i	0.204089	−	0.265974i
$356$	−6.07182	+	0.244140i	−0.321806	+	0.0129394i
$357$	3.94064	−	4.09252i	0.208561	−	0.216599i
$358$	−26.2582	+	0.527690i	−1.38779	+	0.0278893i
$359$	−5.00750	−	5.00750i	−0.264286	−	0.264286i	0.562507	−	0.826793i	$-0.309837\pi$
$359$	−5.00750	−	5.00750i	−0.264286	−	0.264286i	−0.826793	+	0.562507i	$0.809837\pi$
$360$	−28.8748	+	2.84144i	−1.52184	+	0.149757i
$361$	−9.51874	+	9.51874i	−0.500986	+	0.500986i
$362$	7.67136	−	7.98601i	0.403198	−	0.419736i
$363$	−24.4015	+	7.03537i	−1.28075	+	0.369261i
$364$	−6.61582	−	14.3163i	−0.346763	−	0.750377i
$365$	20.7926	+	15.9547i	1.08834	+	0.835109i
$366$	−0.270303	−	6.92770i	−0.0141290	−	0.362116i
$367$	−9.47147	+	16.4051i	−0.494407	+	0.856337i	−0.999979	−	0.00644662i	$-0.997948\pi$
$367$	−9.47147	+	16.4051i	−0.494407	+	0.856337i	0.505573	+	0.862784i	$0.331281\pi$
$368$	4.49208	−	24.4877i	0.234166	−	1.27651i
$369$	−0.120408	−	0.111631i	−0.00626821	−	0.00581128i
$370$	−25.1199	+	34.1358i	−1.30592	+	1.77463i
$371$	22.2935	+	2.93499i	1.15742	+	0.152377i
$372$	−9.37869	−	28.2169i	−0.486263	−	1.46298i
$373$	4.24995	+	32.2816i	0.220054	+	1.67148i	0.643416	+	0.765517i	$0.277517\pi$
$373$	4.24995	+	32.2816i	0.220054	+	1.67148i	−0.423361	+	0.905961i	$0.639150\pi$
$374$	2.02198	+	6.98185i	0.104554	+	0.361023i
$375$	−5.94928	+	8.06444i	−0.307220	+	0.416446i
$376$	21.8272	+	1.54399i	1.12565	+	0.0796250i
$377$	2.65590	−	2.65590i	0.136786	−	0.136786i
$378$	23.7220	+	1.28444i	1.22013	+	0.0660646i
$379$	−12.2740	−	5.08407i	−0.630475	−	0.261151i	0.0444801	−	0.999010i	$-0.485837\pi$
$379$	−12.2740	−	5.08407i	−0.630475	−	0.261151i	−0.674955	+	0.737859i	$0.735837\pi$
$380$	−3.53756	+	15.7007i	−0.181473	+	0.805427i
$381$	0.408671	−	0.246362i	0.0209368	−	0.0126215i
$382$	−11.2052	−	14.0108i	−0.573308	−	0.716854i
$383$	−9.94379	−	17.2232i	−0.508104	−	0.880062i	−0.999956	−	0.00938331i	$-0.997013\pi$
$383$	−9.94379	−	17.2232i	−0.508104	−	0.880062i	0.491852	−	0.870679i	$-0.336320\pi$
$384$	9.30764	−	17.2444i	0.474978	−	0.879997i
$385$	−27.9997	+	48.4968i	−1.42699	+	2.47163i
$386$	18.2506	−	2.77686i	0.928933	−	0.141338i
$387$	−33.7797	+	5.75362i	−1.71712	+	0.292473i
$388$	7.01778	−	2.18614i	0.356274	−	0.110984i
$389$	14.4443	−	11.0835i	0.732354	−	0.561955i	−0.173862	−	0.984770i	$-0.555625\pi$
$389$	14.4443	−	11.0835i	0.732354	−	0.561955i	0.906216	+	0.422815i	$0.138958\pi$
$390$	−19.1650	−	7.07626i	−0.970457	−	0.358320i
$391$	6.09981	+	1.63444i	0.308481	+	0.0826571i
$392$	−5.46563	+	8.08906i	−0.276056	+	0.408559i
$393$	−2.00715	+	17.8468i	−0.101247	+	0.900251i
$394$	−12.0510	+	12.5452i	−0.607118	+	0.632020i
$395$	13.2701	+	5.49664i	0.667689	+	0.276566i
$396$	−16.5680	+	25.4821i	−0.832572	+	1.28052i
$397$	8.97534	+	21.6684i	0.450460	+	1.08751i	0.972148	+	0.234369i	$0.0753025\pi$
$397$	8.97534	+	21.6684i	0.450460	+	1.08751i	−0.521688	+	0.853136i	$0.674698\pi$
$398$	0.939470	+	2.14513i	0.0470914	+	0.107526i
$399$	4.81191	−	12.2679i	0.240897	−	0.614165i
$400$	−8.98173	−	25.2165i	−0.449086	−	1.26083i
$401$	−13.0791	−	22.6536i	−0.653137	−	1.13127i	−0.982357	−	0.187014i	$-0.940119\pi$
$401$	−13.0791	−	22.6536i	−0.653137	−	1.13127i	0.329220	−	0.944253i	$-0.393214\pi$
$402$	−6.32469	+	12.0133i	−0.315447	+	0.599170i
$403$	2.73282	−	20.7578i	0.136131	−	1.03402i
$404$	25.5357	+	2.32278i	1.27045	+	0.115563i
$405$	22.9299	−	20.5251i	1.13939	−	1.01990i
$406$	−6.83567	−	1.68517i	−0.339249	−	0.0836334i
$407$	11.4912	+	42.8858i	0.569598	+	2.12577i
$408$	4.17039	+	2.70446i	0.206465	+	0.133891i
$409$	1.13433	−	4.23336i	0.0560888	−	0.209326i	−0.932194	−	0.361958i	$-0.882108\pi$
$409$	1.13433	−	4.23336i	0.0560888	−	0.209326i	0.988283	+	0.152632i	$0.0487750\pi$
$410$	0.127701	−	0.231820i	0.00630669	−	0.0114488i
$411$	−7.10760	−	6.84382i	−0.350592	−	0.337581i
$412$	13.8152	+	21.8514i	0.680627	+	1.07654i
$413$	−12.0592	−	29.1134i	−0.593393	−	1.43258i
$414$	11.5002	+	23.7707i	0.565205	+	1.16827i
$415$		−	2.73040i		−	0.134030i
$416$	11.1972	−	8.06269i	0.548986	−	0.395306i
$417$	−5.86218	−	7.34786i	−0.287072	−	0.359826i
$418$	10.5304	+	13.1670i	0.515057	+	0.644017i
$419$	−15.2422	−	11.6958i	−0.744631	−	0.571375i	0.165247	−	0.986252i	$-0.447158\pi$
$419$	−15.2422	−	11.6958i	−0.744631	−	0.571375i	−0.909878	+	0.414877i	$0.863825\pi$
$420$	7.23177	+	37.6046i	0.352874	+	1.83492i
$421$	−7.85604	−	10.2382i	−0.382880	−	0.498979i	0.561663	−	0.827366i	$-0.310162\pi$
$421$	−7.85604	−	10.2382i	−0.382880	−	0.498979i	−0.944543	+	0.328387i	$0.893495\pi$
$422$	7.15497	−	4.32489i	0.348299	−	0.210532i
$423$	−19.6466	+	12.3560i	−0.955252	+	0.600770i
$424$	1.18516	+	19.6369i	0.0575565	+	0.953654i
$425$	6.55848	−	1.75734i	0.318133	−	0.0852435i
$426$	−3.69457	−	2.61257i	−0.179002	−	0.126579i
$427$	−9.07199	+	1.19435i	−0.439024	+	0.0577987i
$428$	8.52594	+	18.4497i	0.412117	+	0.891798i
$429$	−18.3287	+	11.0492i	−0.884919	+	0.533462i
$430$	−22.1581	−	50.5945i	−1.06856	−	2.43988i
$431$			22.9373i			1.10485i	0.833562	+	0.552426i	$0.186298\pi$
$431$			22.9373i			1.10485i	−0.833562	+	0.552426i	$0.813702\pi$
$432$	2.84039	+	20.5896i	0.136658	+	0.990618i
$433$		−	5.05969i		−	0.243153i	−0.992582	−	0.121577i	$-0.961205\pi$
$433$		−	5.05969i		−	0.243153i	0.992582	−	0.121577i	$-0.0387950\pi$
$434$	−35.9481	+	15.7437i	−1.72557	+	0.755721i
$435$	−7.81052	+	4.70848i	−0.374486	+	0.225754i
$436$	−4.59263	+	12.4841i	−0.219947	+	0.597880i
$437$	14.5224	−	1.91191i	0.694700	−	0.0914589i
$438$	10.8399	−	15.3292i	0.517949	−	0.732458i
$439$	26.7632	−	7.17118i	1.27734	−	0.342262i	0.444500	−	0.895779i	$-0.353381\pi$
$439$	26.7632	−	7.17118i	1.27734	−	0.342262i	0.832838	+	0.553517i	$0.186715\pi$
$440$	−46.3113	−	15.9880i	−2.20780	−	0.762198i
$441$	−0.391406	−	10.3473i	−0.0186384	−	0.492727i
$442$	1.81048	+	2.99521i	0.0861158	+	0.142467i
$443$	−15.0169	−	19.5704i	−0.713473	−	0.929816i	0.286125	−	0.958192i	$-0.407633\pi$
$443$	−15.0169	−	19.5704i	−0.713473	−	0.929816i	−0.999597	+	0.0283767i	$0.990966\pi$
$444$	25.1364	+	17.0278i	1.19292	+	0.808102i
$445$	8.24237	+	6.32460i	0.390726	+	0.299815i
$446$	14.3246	−	11.4561i	0.678287	−	0.542464i
$447$	21.7488	+	27.2607i	1.02868	+	1.28939i
$448$	−23.7908	−	10.1439i	−1.12401	−	0.479253i
$449$			6.14568i			0.290033i	0.989429	+	0.145016i	$0.0463235\pi$
$449$			6.14568i			0.290033i	−0.989429	+	0.145016i	$0.953677\pi$
$450$	23.4875	+	15.9515i	1.10721	+	0.751963i
$451$	−0.106102	−	0.256152i	−0.00499613	−	0.0120617i
$452$	2.86859	−	12.7316i	0.134927	−	0.598844i
$453$	−4.34646	−	4.18515i	−0.204214	−	0.196636i
$454$	12.9403	+	7.12832i	0.607318	+	0.334549i
$455$	−6.97866	+	26.0447i	−0.327165	+	1.22100i
$456$	11.3375	+	2.09372i	0.530928	+	0.0980475i
$457$	5.21765	+	19.4725i	0.244071	+	0.910886i	0.973848	+	0.227201i	$0.0729573\pi$
$457$	5.21765	+	19.4725i	0.244071	+	0.910886i	−0.729777	+	0.683686i	$0.760376\pi$
$458$	2.36113	−	9.57763i	0.110328	−	0.447533i
$459$	−5.26358	+	0.298836i	−0.245683	+	0.0139485i
$460$	−32.7006	+	27.2476i	−1.52467	+	1.27043i
$461$	0.958414	−	7.27988i	0.0446378	−	0.339058i	−0.954524	−	0.298133i	$-0.903636\pi$
$461$	0.958414	−	7.27988i	0.0446378	−	0.339058i	0.999162	−	0.0409250i	$-0.0130305\pi$
$462$	35.4966	+	18.6880i	1.65145	+	0.869445i
$463$	−5.09551	−	8.82569i	−0.236809	−	0.410165i	0.722988	−	0.690860i	$-0.242768\pi$
$463$	−5.09551	−	8.82569i	−0.236809	−	0.410165i	−0.959797	+	0.280696i	$0.909435\pi$
$464$	0.311082	−	6.15166i	0.0144416	−	0.285584i
$465$	−18.5632	+	47.3266i	−0.860846	+	2.19472i
$466$	−28.3866	+	12.4321i	−1.31498	+	0.575904i
$467$	−12.1045	−	29.2229i	−0.560130	−	1.35227i	−0.909662	−	0.415350i	$-0.863659\pi$
$467$	−12.1045	−	29.2229i	−0.560130	−	1.35227i	0.349532	−	0.936925i	$-0.386341\pi$
$468$	−4.53001	+	13.9162i	−0.209400	+	0.643276i
$469$	16.5546	+	6.85713i	0.764420	+	0.316633i
$470$	−26.9797	−	25.9166i	−1.24448	−	1.19545i
$471$	3.12220	−	27.7613i	0.143863	−	1.27917i
$472$	23.0023	−	15.1982i	1.05877	−	0.699555i
$473$	−55.8900	−	14.9757i	−2.56983	−	0.688583i
$474$	3.56394	−	9.65239i	0.163697	−	0.443349i
$475$	12.4946	−	9.58746i	0.573293	−	0.439903i
$476$	3.04921	−	5.80851i	0.139760	−	0.266233i
$477$	−13.3191	−	16.0621i	−0.609840	−	0.735435i
$478$	1.39498	+	9.16835i	0.0638048	+	0.419351i
$479$	8.65054	−	14.9832i	0.395253	−	0.684599i	−0.597880	−	0.801585i	$-0.703990\pi$
$479$	8.65054	−	14.9832i	0.395253	−	0.684599i	0.993133	+	0.116987i	$0.0373235\pi$
$480$	−31.0983	+	12.4633i	−1.41944	+	0.568871i
$481$	10.6889	+	18.5137i	0.487372	+	0.844153i
$482$	2.61712	−	2.09306i	0.119207	−	0.0953361i
$483$	29.8478	−	17.9934i	1.35812	−	0.818726i
$484$	−24.7859	+	15.6706i	−1.12663	+	0.712298i
$485$	−11.6103	−	4.80913i	−0.527195	−	0.218371i
$486$	−15.3326	−	15.8402i	−0.695499	−	0.718527i
$487$	−6.88812	+	6.88812i	−0.312131	+	0.312131i	−0.845735	−	0.533604i	$-0.820837\pi$
$487$	−6.88812	+	6.88812i	−0.312131	+	0.312131i	0.533604	+	0.845735i	$0.320837\pi$
$488$	−2.53406	−	7.59385i	−0.114712	−	0.343757i
$489$	22.2869	−	30.2106i	1.00785	−	1.36617i
$490$	16.0320	−	4.64294i	0.724251	−	0.209747i
$491$	4.80297	+	36.4822i	0.216755	+	1.64642i	0.660909	+	0.750466i	$0.270171\pi$
$491$	4.80297	+	36.4822i	0.216755	+	1.64642i	−0.444154	+	0.895950i	$0.646496\pi$
$492$	−0.169506	−	0.0849352i	−0.00764192	−	0.00382917i
$493$	1.54901	+	0.203931i	0.0697638	+	0.00918458i
$494$	6.53844	+	4.81152i	0.294178	+	0.216481i
$495$	49.6504	−	15.3374i	2.23162	−	0.689363i
$496$	−19.4993	−	28.2604i	−0.875543	−	1.26893i
$497$	−2.98607	+	5.17203i	−0.133944	+	0.231997i
$498$	−1.95445	+	0.0762583i	−0.0875811	+	0.00341722i
$499$	22.8932	+	17.5666i	1.02484	+	0.786389i	0.977167	−	0.212474i	$-0.0681520\pi$
$499$	22.8932	+	17.5666i	1.02484	+	0.786389i	0.0476755	+	0.998863i	$0.484819\pi$
$500$	−3.99523	+	10.8602i	−0.178672	+	0.485683i
$501$	0.704954	−	0.203250i	0.0314950	−	0.00908053i
$502$	−20.7309	−	19.9141i	−0.925265	−	0.888809i
$503$	27.2717	−	27.2717i	1.21599	−	1.21599i	0.246961	−	0.969025i	$-0.420568\pi$
$503$	27.2717	−	27.2717i	1.21599	−	1.21599i	0.969025	−	0.246961i	$-0.0794320\pi$
$504$	26.7159	−	6.22687i	1.19002	−	0.277367i
$505$	−30.9983	−	30.9983i	−1.37940	−	1.37940i
$506$	0.895905	+	44.5808i	0.0398279	+	1.98186i
$507$	8.47032	−	8.79679i	0.376180	−	0.390679i
$508$	0.373652	−	0.404959i	0.0165781	−	0.0179672i
$509$	−10.7997	+	14.0745i	−0.478690	+	0.623841i	−0.968807	−	0.247816i	$-0.920287\pi$
$509$	−10.7997	+	14.0745i	−0.478690	+	0.623841i	0.490117	+	0.871656i	$0.336954\pi$
$510$	−2.51782	−	8.11650i	−0.111491	−	0.359405i
$511$	−21.4594	−	12.3896i	−0.949308	−	0.548083i
$512$	4.75801	−	22.1215i	0.210276	−	0.977642i
$513$	−11.0143	+	5.31255i	−0.486294	+	0.234555i
$514$	−0.590463	−	3.88076i	−0.0260442	−	0.171173i
$515$	5.76917	−	43.8212i	0.254220	−	1.93099i
$516$	−35.5973	+	17.2741i	−1.56708	+	0.760451i
$517$	−38.8554	+	5.11541i	−1.70886	+	0.224976i
$518$	19.3342	−	35.0980i	0.849494	−	1.54212i
$519$	0.536952	−	0.234400i	0.0235696	−	0.0102890i
$520$	−23.5313	−	1.66453i	−1.03192	−	0.0729945i
$521$	18.4494	+	18.4494i	0.808283	+	0.808283i	0.984374	−	0.176091i	$-0.0563453\pi$
$521$	18.4494	+	18.4494i	0.808283	+	0.808283i	−0.176091	+	0.984374i	$0.556345\pi$
$522$	3.58853	+	5.45937i	0.157066	+	0.238950i
$523$	13.0762	−	31.5687i	0.571782	−	1.38040i	−0.328254	−	0.944589i	$-0.606460\pi$
$523$	13.0762	−	31.5687i	0.571782	−	1.38040i	0.900036	−	0.435815i	$-0.143540\pi$
$524$	3.53065	+	20.4348i	0.154237	+	0.892700i
$525$	18.1195	−	32.8005i	0.790798	−	1.43153i
$526$	−1.30417	+	11.7216i	−0.0568646	+	0.511088i
$527$	7.54227	−	4.35453i	0.328546	−	0.189686i
$528$	−10.1510	+	33.5967i	−0.441764	+	1.46211i
$529$	13.6304	+	7.86952i	0.592627	+	0.342153i
$530$	19.9349	−	27.0897i	0.865915	−	1.17670i
$531$	−10.1613	+	27.4199i	−0.440961	+	1.18992i
$532$	1.37844	−	15.1540i	0.0597629	−	0.657007i
$533$	−0.0812686	−	0.105911i	−0.00352013	−	0.00458753i
$534$	4.29702	−	6.07664i	0.185950	−	0.262962i
$535$	8.99353	−	33.5643i	0.388824	−	1.45111i
$536$	−3.13783	+	15.3596i	−0.135534	+	0.663432i
$537$	19.0956	−	25.8847i	0.824035	−	1.11701i
$538$	−0.720466	−	35.8508i	−0.0310615	−	1.54564i
$539$	6.69115	−	16.1539i	0.288208	−	0.695796i
$540$	18.8034	−	30.1526i	0.809170	−	1.29756i
$541$	−37.8000	+	15.6573i	−1.62515	+	0.673159i	−0.994676	−	0.103051i	$-0.967139\pi$
$541$	−37.8000	+	15.6573i	−1.62515	+	0.673159i	−0.630474	+	0.776210i	$0.717139\pi$
$542$	3.33419	−	8.53032i	0.143216	−	0.366409i
$543$	2.02412	+	13.4105i	0.0868632	+	0.575501i
$544$	5.49615	+	1.65349i	0.235645	+	0.0708927i
$545$	19.6955	−	11.3712i	0.843661	−	0.487088i
$546$	18.8380	+	4.26800i	0.806194	+	0.182653i
$547$	28.9088	+	3.80592i	1.23605	+	0.162729i	0.720089	−	0.693882i	$-0.244101\pi$
$547$	28.9088	+	3.80592i	1.23605	+	0.162729i	0.515963	+	0.856611i	$0.327434\pi$
$548$	−10.0878	−	5.29565i	−0.430930	−	0.226219i
$549$	6.92703	+	4.91073i	0.295638	+	0.209585i
$550$	24.8008	+	41.0296i	1.05751	+	1.74951i
$551$	3.50046	−	0.937947i	0.149125	−	0.0399579i
$552$	20.4175	+	22.6465i	0.869025	+	0.963899i
$553$	−13.1173	−	3.51478i	−0.557806	−	0.149464i
$554$	−1.15252	−	3.97962i	−0.0489657	−	0.169078i
$555$	−14.3800	−	49.8759i	−0.610399	−	2.11711i
$556$	−8.86953	−	6.25618i	−0.376152	−	0.265321i
$557$	−31.3468	+	12.9843i	−1.32821	+	0.550162i	−0.930144	−	0.367196i	$-0.880318\pi$
$557$	−31.3468	+	12.9843i	−1.32821	+	0.550162i	−0.398064	+	0.917358i	$0.630318\pi$
$558$	34.3955	+	11.9659i	1.45608	+	0.506559i
$559$	−27.8602			−1.17836
$560$	20.1467	+	39.3614i	0.851352	+	1.66332i
$561$	−8.28763	−	3.25070i	−0.349904	−	0.137245i
$562$	−38.5211	−	4.28594i	−1.62492	−	0.180791i
$563$	0.580574	−	0.756619i	0.0244683	−	0.0318877i	−0.780959	−	0.624582i	$-0.785269\pi$
$563$	0.580574	−	0.756619i	0.0244683	−	0.0318877i	0.805427	+	0.592695i	$0.201936\pi$
$564$	−17.7979	+	20.0362i	−0.749428	+	0.843676i
$565$	−17.7018	+	13.5831i	−0.744722	+	0.571445i
$566$	−25.0481	−	6.17499i	−1.05285	−	0.259554i
$567$	−18.9609	+	22.0694i	−0.796283	+	0.926830i
$568$	−4.93895	−	1.70507i	−0.207234	−	0.0715431i
$569$	5.80010	+	21.6463i	0.243153	+	0.907459i	0.974303	+	0.225242i	$0.0723174\pi$
$569$	5.80010	+	21.6463i	0.243153	+	0.907459i	−0.731150	+	0.682217i	$0.761016\pi$
$570$	−12.6001	−	15.1583i	−0.527760	−	0.634913i
$571$	4.55273	+	34.5814i	0.190526	+	1.44719i	0.773035	+	0.634363i	$0.218738\pi$
$571$	4.55273	+	34.5814i	0.190526	+	1.44719i	−0.582509	+	0.812824i	$0.697929\pi$
$572$	−16.7582	+	18.1623i	−0.700694	+	0.759403i
$573$	21.9685	−	0.415353i	0.917748	−	0.0173516i
$574$	−0.0910951	+	0.233061i	−0.00380224	+	0.00972778i
$575$	41.6520			1.73701
$576$	9.78996	+	21.9125i	0.407915	+	0.913020i
$577$	45.3148			1.88648			0.943240	−	0.332111i	$-0.107761\pi$
$577$	45.3148			1.88648			0.943240	+	0.332111i	$0.107761\pi$
$578$	8.22221	−	21.0360i	0.341999	−	0.874983i
$579$	−10.9327	+	19.7907i	−0.454346	+	0.822474i
$580$	−7.14125	+	7.73959i	−0.296524	+	0.321369i
$581$	0.336952	+	2.55940i	0.0139791	+	0.106182i
$582$	−3.11817	+	8.44509i	−0.129252	+	0.350060i
$583$	−9.11929	−	34.0336i	−0.377682	−	1.40953i
$584$	7.07455	−	20.4923i	0.292747	−	0.847978i
$585$	21.1805	−	13.3207i	0.875707	−	0.550743i
$586$	26.9295	+	6.63882i	1.11245	+	0.274247i
$587$	−33.9979	+	26.0875i	−1.40324	+	1.07675i	−0.417464	+	0.908693i	$0.637081\pi$
$587$	−33.9979	+	26.0875i	−1.40324	+	1.07675i	−0.985778	+	0.168052i	$0.946252\pi$
$588$	−3.77124	−	11.3462i	−0.155523	−	0.467910i
$589$	12.2975	−	16.0264i	0.506708	−	0.660355i
$590$	−46.8465	−	5.21223i	−1.92864	−	0.214584i
$591$	−3.17969	−	21.0666i	−0.130795	−	0.866565i
$592$	33.3617	+	10.7723i	1.37116	+	0.442737i
$593$	30.1925			1.23986			0.619929	−	0.784658i	$-0.287161\pi$
$593$	30.1925			1.23986			0.619929	+	0.784658i	$0.287161\pi$
$594$	−12.3654	−	35.1120i	−0.507357	−	1.44066i
$595$	−10.3621	+	4.29214i	−0.424807	+	0.175961i
$596$	32.9062	+	23.2106i	1.34789	+	0.950741i
$597$	−2.78395	−	0.689828i	−0.113940	−	0.0282328i
$598$	5.97236	+	20.6224i	0.244228	+	0.843314i
$599$	21.5351	+	5.77032i	0.879902	+	0.235769i	0.670365	−	0.742032i	$-0.266138\pi$
$599$	21.5351	+	5.77032i	0.879902	+	0.235769i	0.209537	+	0.977801i	$0.432804\pi$
$600$	31.1864	+	10.1108i	1.27318	+	0.412773i
$601$	−10.3822	+	2.78189i	−0.423497	+	0.113476i	−0.464272	−	0.885693i	$-0.653684\pi$
$601$	−10.3822	+	2.78189i	−0.423497	+	0.113476i	0.0407749	+	0.999168i	$0.487017\pi$
$602$	27.0142	+	44.6915i	1.10102	+	1.82149i
$603$	−6.93930	−	15.1105i	−0.282590	−	0.615349i
$604$	−6.16893	−	3.23841i	−0.251010	−	0.131769i
$605$	49.7062	+	6.54395i	2.02085	+	0.266049i
$606$	−21.3232	+	23.0547i	−0.866195	+	0.936533i
$607$	35.3826	−	20.4282i	1.43614	−	0.829153i	0.438557	−	0.898703i	$-0.355490\pi$
$607$	35.3826	−	20.4282i	1.43614	−	0.829153i	0.997578	+	0.0695501i	$0.0221564\pi$
$608$	13.2457	−	1.33526i	0.537183	−	0.0541518i
$609$	6.74032	−	5.37748i	0.273132	−	0.217907i
$610$	−4.98262	+	12.7477i	−0.201740	+	0.516140i
$611$	−17.4338	+	7.22131i	−0.705295	+	0.292143i
$612$	−5.73957	+	2.02898i	−0.232008	+	0.0820165i
$613$	4.23950	−	10.2351i	0.171232	−	0.413390i	−0.814845	−	0.579678i	$-0.803178\pi$
$613$	4.23950	−	10.2351i	0.171232	−	0.413390i	0.986077	+	0.166288i	$0.0531782\pi$
$614$	−0.280398	−	13.9528i	−0.0113159	−	0.563088i
$615$	0.129685	+	0.297075i	0.00522940	+	0.0119792i
$616$	45.3840	+	9.27158i	1.82857	+	0.373563i
$617$	−8.03514	+	29.9876i	−0.323483	+	1.20725i	0.592346	+	0.805684i	$0.298202\pi$
$617$	−8.03514	+	29.9876i	−0.323483	+	1.20725i	−0.915829	+	0.401570i	$0.868465\pi$
$618$	−31.5289	−	2.90574i	−1.26828	−	0.116886i
$619$	−8.54188	−	11.1320i	−0.343327	−	0.447433i	0.589494	−	0.807773i	$-0.299327\pi$
$619$	−8.54188	−	11.1320i	−0.343327	−	0.447433i	−0.932821	+	0.360340i	$0.882661\pi$
$620$	−5.31767	+	58.4602i	−0.213563	+	2.34782i
$621$	−31.6635	−	6.58633i	−1.27061	−	0.264300i
$622$	−2.54865	+	3.46338i	−0.102191	+	0.138869i
$623$	−8.50669	−	4.91134i	−0.340813	−	0.196769i
$624$	−0.534276	+	16.8905i	−0.0213882	+	0.676161i
$625$	−11.8441	+	6.83819i	−0.473764	+	0.273528i
$626$	−5.03665	+	45.2684i	−0.201305	+	1.80929i
$627$	−20.6454	+	0.390337i	−0.824499	+	0.0155886i
$628$	−5.49205	−	31.7872i	−0.219157	−	1.26845i
$629$	−3.40299	+	8.21555i	−0.135686	+	0.327576i
$630$	−41.9056	−	21.0602i	−1.66956	−	0.839059i
$631$	10.2382	+	10.2382i	0.407576	+	0.407576i	0.880893	−	0.473316i	$-0.156943\pi$
$631$	10.2382	+	10.2382i	0.407576	+	0.407576i	−0.473316	+	0.880893i	$0.656943\pi$
$632$	0.838335	−	11.8515i	0.0333472	−	0.471426i
$633$	−1.14438	+	10.1754i	−0.0454850	+	0.404434i
$634$	16.1547	−	29.3261i	0.641583	−	1.16469i
$635$	−0.933988	+	0.122962i	−0.0370642	+	0.00487959i
$636$	−19.9479	−	13.5130i	−0.790987	−	0.535826i
$637$	1.09888	−	8.34685i	0.0435394	−	0.330714i
$638$	1.65941	+	10.9063i	0.0656967	+	0.431786i
$639$	5.29505	−	1.63568i	0.209469	−	0.0647065i
$640$	−30.4603	+	23.8487i	−1.20405	+	0.942701i
$641$	−30.9342	−	17.8598i	−1.22183	−	0.705421i	−0.256519	−	0.966539i	$-0.582576\pi$
$641$	−30.9342	−	17.8598i	−1.22183	−	0.705421i	−0.965307	+	0.261118i	$0.915909\pi$
$642$	−24.2769	−	5.50025i	−0.958134	−	0.217078i
$643$	−3.08269	+	4.01744i	−0.121570	+	0.158432i	−0.850173	−	0.526503i	$-0.823503\pi$
$643$	−3.08269	+	4.01744i	−0.121570	+	0.158432i	0.728604	+	0.684935i	$0.240170\pi$
$644$	27.2902	−	29.5767i	1.07538	−	1.16548i
$645$	65.6617	+	16.2701i	2.58543	+	0.640635i
$646$	0.0678476	+	3.37614i	0.00266943	+	0.132832i
$647$	−16.3305	−	16.3305i	−0.642019	−	0.642019i	0.309033	−	0.951051i	$-0.399995\pi$
$647$	−16.3305	−	16.3305i	−0.642019	−	0.642019i	−0.951051	+	0.309033i	$0.899995\pi$
$648$	−22.1088	−	12.6176i	−0.868514	−	0.495665i
$649$	−34.9155	+	34.9155i	−1.37055	+	1.37055i
$650$	16.6477	+	15.9918i	0.652977	+	0.627249i
$651$	11.5602	−	46.6536i	0.453079	−	1.82850i
$652$	14.9667	−	40.6838i	0.586140	−	1.59330i
$653$	−23.7278	−	18.2070i	−0.928540	−	0.712494i	0.0293678	−	0.999569i	$-0.490651\pi$
$653$	−23.7278	−	18.2070i	−0.928540	−	0.712494i	−0.957908	+	0.287075i	$0.907317\pi$
$654$	−8.68971	−	13.7807i	−0.339795	−	0.538866i
$655$	17.7274	−	30.7047i	0.692666	−	1.19973i
$656$	−0.215332	−	0.0395011i	−0.00840731	−	0.00154226i
$657$	6.78664	+	21.9698i	0.264772	+	0.857125i
$658$	28.4883	+	20.9641i	1.11059	+	0.817265i
$659$	−3.60908	−	0.475144i	−0.140590	−	0.0185090i	0.0599029	−	0.998204i	$-0.480921\pi$
$659$	−3.60908	−	0.475144i	−0.140590	−	0.0185090i	−0.200493	+	0.979695i	$0.564254\pi$
$660$	50.1028	−	33.0187i	1.95025	−	1.28525i
$661$	−5.79535	−	44.0201i	−0.225413	−	1.71218i	−0.612777	−	0.790256i	$-0.709948\pi$
$661$	−5.79535	−	44.0201i	−0.225413	−	1.71218i	0.387364	−	0.921927i	$-0.373386\pi$
$662$	−25.5983	+	7.41340i	−0.994908	+	0.288130i
$663$	−4.25960	−	0.479059i	−0.165429	−	0.0186051i
$664$	−2.14239	+	0.714914i	−0.0831408	+	0.0277440i
$665$	−18.3957	+	18.3957i	−0.713355	+	0.713355i
$666$	−35.3002	+	11.6864i	−1.36785	+	0.452840i
$667$	8.85476	+	3.66776i	0.342858	+	0.142016i
$668$	0.716059	−	0.452718i	0.0277051	−	0.0175162i
$669$	0.424654	+	22.4605i	0.0164181	+	0.868373i
$670$	20.9316	−	16.7402i	0.808660	−	0.646730i
$671$	7.16902	+	12.4171i	0.276757	+	0.479357i
$672$	27.6127	−	15.5206i	1.06518	−	0.598719i
$673$	−14.6670	+	25.4040i	−0.565371	+	0.979251i	0.431644	+	0.902044i	$0.357934\pi$
$673$	−14.6670	+	25.4040i	−0.565371	+	0.979251i	−0.997015	+	0.0772071i	$0.975400\pi$
$674$	2.11082	+	13.8732i	0.0813059	+	0.534375i
$675$	−33.0241	+	10.8894i	−1.27110	+	0.419132i
$676$	6.55421	−	12.4853i	0.252085	−	0.480203i
$677$	19.1053	−	14.6600i	0.734275	−	0.563429i	−0.172517	−	0.985006i	$-0.555190\pi$
$677$	19.1053	−	14.6600i	0.734275	−	0.563429i	0.906792	+	0.421577i	$0.138523\pi$
$678$	10.2174	+	12.2918i	0.392395	+	0.472065i
$679$	11.4767	+	3.07516i	0.440434	+	0.118014i
$680$	−5.40940	−	8.18704i	−0.207441	−	0.313959i
$681$	−16.5829	+	7.23908i	−0.635458	+	0.277402i
$682$	44.3479	+	42.6006i	1.69817	+	1.63126i
$683$	−12.1200	−	5.02029i	−0.463761	−	0.192096i	0.138554	−	0.990355i	$-0.455755\pi$
$683$	−12.1200	−	5.02029i	−0.463761	−	0.192096i	−0.602314	+	0.798259i	$0.705755\pi$
$684$	−10.4986	+	9.44266i	−0.401425	+	0.361049i
$685$	7.45429	+	17.9962i	0.284814	+	0.687601i
$686$	14.8608	−	6.50835i	0.567386	−	0.248490i
$687$	7.53453	+	9.44403i	0.287460	+	0.360312i
$688$	−33.8969	+	30.6336i	−1.29231	+	1.16790i
$689$	−8.48258	−	14.6923i	−0.323160	−	0.559730i
$690$	−2.03249	−	52.0914i	−0.0773755	−	1.98308i
$691$	0.688925	−	5.23291i	0.0262080	−	0.199069i	−0.973332	−	0.229401i	$-0.926323\pi$
$691$	0.688925	−	5.23291i	0.0262080	−	0.199069i	0.999540	+	0.0303322i	$0.00965651\pi$
$692$	0.519741	−	0.433071i	0.0197576	−	0.0164629i
$693$	−44.6482	+	20.5041i	−1.69605	+	0.778885i
$694$	−4.69140	+	19.0301i	−0.178083	+	0.722372i
$695$	4.80286	+	17.9245i	0.182183	+	0.679916i
$696$	5.73955	+	4.89563i	0.217557	+	0.185569i
$697$	0.0143724	−	0.0536387i	0.000544395	−	0.00203171i
$698$	17.5328	+	9.65818i	0.663627	+	0.365567i
$699$	9.12853	−	36.8402i	0.345273	−	1.39343i
$700$	9.51077	−	42.2113i	0.359473	−	1.59544i
$701$	8.30804	+	20.0574i	0.313790	+	0.757557i	0.999558	+	0.0297363i	$0.00946676\pi$
$701$	8.30804	+	20.0574i	0.313790	+	0.757557i	−0.685767	+	0.727821i	$0.740533\pi$
$702$	−10.1267	−	14.7892i	−0.382207	−	0.558184i
$703$			20.6262i			0.777930i
$704$	−0.418978	+	40.5241i	−0.0157908	+	1.52731i
$705$	45.3056	−	6.83820i	1.70631	−	0.257542i
$706$	21.0568	−	16.8403i	0.792481	−	0.633792i
$707$	32.8824	+	25.2316i	1.23667	+	0.948930i
$708$	−2.42259	+	33.6789i	−0.0910463	+	1.26573i
$709$	−8.32108	−	10.8442i	−0.312505	−	0.407264i	0.610522	−	0.791999i	$-0.290960\pi$
$709$	−8.32108	−	10.8442i	−0.312505	−	0.407264i	−0.923027	+	0.384735i	$0.874293\pi$
$710$	4.62107	+	7.64497i	0.173426	+	0.286910i
$711$	6.70892	+	10.6675i	0.251604	+	0.400063i
$712$	2.80441	−	8.12333i	0.105100	−	0.304435i
$713$	51.6050	−	13.8275i	1.93262	−	0.517844i
$714$	3.36178	+	7.29748i	0.125811	+	0.273101i
$715$	41.8890	−	5.51479i	1.56656	−	0.206242i
$716$	12.8236	−	34.8582i	0.479240	−	1.30271i
$717$	−9.94202	−	5.49211i	−0.371292	−	0.205107i
$718$	9.17378	−	4.01770i	0.342362	−	0.149939i
$719$			4.72503i			0.176214i	0.996111	+	0.0881069i	$0.0280817\pi$
$719$			4.72503i			0.176214i	−0.996111	+	0.0881069i	$0.971918\pi$
$720$	11.1231	−	39.4960i	0.414534	−	1.47193i
$721$			41.7888i			1.55630i
$722$	−7.63725	−	17.4384i	−0.284229	−	0.648991i
$723$	0.0775851	+	4.10357i	0.00288542	+	0.152613i
$724$	6.56948	+	14.2160i	0.244153	+	0.528333i
$725$	10.2169	−	1.34508i	0.379445	−	0.0499548i
$726$	3.29598	−	35.7631i	0.122325	−	1.32729i
$727$	7.62650	−	2.04351i	0.282851	−	0.0757897i	−0.114604	−	0.993411i	$-0.536560\pi$
$727$	7.62650	−	2.04351i	0.282851	−	0.0757897i	0.397455	+	0.917621i	$0.369893\pi$
$728$	22.2631	−	1.34366i	0.825125	−	0.0497993i
$729$	26.8265	−	3.05596i	0.993574	−	0.113184i
$730$	−31.7199	+	19.1734i	−1.17401	+	0.709640i
$731$	−7.05488	−	9.19410i	−0.260934	−	0.340056i
$732$	9.26414	+	3.21059i	0.342412	+	0.118667i
$733$	−21.0718	−	16.1689i	−0.778303	−	0.597213i	0.141343	−	0.989961i	$-0.454858\pi$
$733$	−21.0718	−	16.1689i	−0.778303	−	0.597213i	−0.919646	+	0.392748i	$0.871525\pi$
$734$	−16.7321	−	20.9215i	−0.617592	−	0.772226i
$735$	−7.46438	+	19.0304i	−0.275328	+	0.701946i
$736$	29.9418	+	18.5240i	1.10367	+	0.682802i
$737$		−	28.0775i		−	1.03425i
$738$	0.209028	−	0.101127i	0.00769443	−	0.00372254i
$739$	−6.56055	−	15.8386i	−0.241334	−	0.582631i	0.756082	−	0.654477i	$-0.227111\pi$
$739$	−6.56055	−	15.8386i	−0.241334	−	0.582631i	−0.997416	+	0.0718455i	$0.977111\pi$
$740$	−32.0301	−	50.6616i	−1.17745	−	1.86236i
$741$	−9.55334	+	2.75438i	−0.350951	+	0.101185i
$742$	−15.3433	+	27.8533i	−0.563272	+	1.02253i
$743$	2.72078	−	10.1541i	0.0998157	−	0.372517i	−0.897890	−	0.440220i	$-0.854900\pi$
$743$	2.72078	−	10.1541i	0.0998157	−	0.372517i	0.997706	+	0.0677029i	$0.0215670\pi$
$744$	41.9950	+	2.17370i	1.53961	+	0.0796917i
$745$	−17.8187	−	66.5004i	−0.652828	−	2.43639i
$746$	−44.7085	−	11.0218i	−1.63689	−	0.403536i
$747$	1.38542	−	1.95426i	0.0506900	−	0.0715028i
$748$	−10.2373	−	0.931207i	−0.374312	−	0.0340483i
$749$	−4.28821	+	32.5722i	−0.156688	+	1.19016i
$750$	−7.55937	−	11.9881i	−0.276029	−	0.437743i
$751$	15.7596	+	27.2965i	0.575077	+	0.996062i	0.996033	+	0.0889815i	$0.0283612\pi$
$751$	15.7596	+	27.2965i	0.575077	+	0.996062i	−0.420956	+	0.907081i	$0.638305\pi$
$752$	−13.2711	+	27.9553i	−0.483947	+	1.01942i
$753$	34.8124	−	5.25440i	1.26863	−	0.191481i
$754$	2.13093	+	4.86563i	0.0776038	+	0.177196i
$755$	4.55847	+	11.0051i	0.165900	+	0.400517i
$756$	−13.9048	+	30.5847i	−0.505711	+	1.11236i
$757$	29.0284	+	12.0239i	1.05505	+	0.437018i	0.841693	−	0.539956i	$-0.181559\pi$
$757$	29.0284	+	12.0239i	1.05505	+	0.437018i	0.213361	+	0.976974i	$0.431559\pi$
$758$	13.0157	−	13.5496i	0.472752	−	0.492142i
$759$	−43.9466	−	32.4202i	−1.59516	−	1.17678i
$760$	−18.8592	−	12.7428i	−0.684096	−	0.462231i
$761$	−7.18347	−	1.92481i	−0.260401	−	0.0697741i	0.126257	−	0.991998i	$-0.459704\pi$
$761$	−7.18347	−	1.92481i	−0.260401	−	0.0697741i	−0.386657	+	0.922223i	$0.626370\pi$
$762$	0.114103	+	0.665126i	0.00413353	+	0.0240950i
$763$	−17.0587	+	13.0896i	−0.617567	+	0.473876i
$764$	24.2235	−	7.54595i	0.876374	−	0.273003i
$765$	9.75938	+	3.61663i	0.352851	+	0.130760i
$766$	27.8053	−	4.23061i	1.00465	−	0.152858i
$767$	−11.8877	+	20.5901i	−0.429239	+	0.743464i
$768$	17.9219	+	21.1378i	0.646701	+	0.762744i
$769$	9.07979	+	15.7267i	0.327426	+	0.567118i	0.982000	−	0.188879i	$-0.0604855\pi$
$769$	9.07979	+	15.7267i	0.327426	+	0.567118i	−0.654575	+	0.755997i	$0.727152\pi$
$770$	−49.4635	−	61.8483i	−1.78254	−	2.22886i
$771$	4.20824	+	2.32469i	0.151556	+	0.0837216i
$772$	−5.73847	+	25.4689i	−0.206532	+	0.916645i
$773$	−18.1390	−	7.51343i	−0.652415	−	0.270239i	0.0318277	−	0.999493i	$-0.489867\pi$
$773$	−18.1390	−	7.51343i	−0.652415	−	0.270239i	−0.684243	+	0.729254i	$0.739867\pi$
$774$	9.81246	−	47.4559i	0.352702	−	1.70577i
$775$	40.6182	−	40.6182i	1.45905	−	1.45905i
$776$	−0.733479	+	10.3691i	−0.0263304	+	0.372230i
$777$	19.6346	+	44.9778i	0.704386	+	1.61357i
$778$	7.16244	+	24.7318i	0.256786	+	0.886677i
$779$	−0.0168124	−	0.127703i	−0.000602365	−	0.00457542i
$780$	19.1875	−	21.6005i	0.687022	−	0.773422i
$781$	9.27801	+	1.22147i	0.331993	+	0.0437077i
$782$	−5.29323	+	7.19304i	−0.189286	+	0.257222i
$783$	−7.97945	−	0.593054i	−0.285162	−	0.0211940i
$784$	−7.84079	−	11.3637i	−0.280028	−	0.405847i
$785$	−27.5756	+	47.7623i	−0.984215	+	1.70471i
$786$	−22.4739	−	11.8319i	−0.801619	−	0.422031i
$787$	−11.3391	−	8.70078i	−0.404194	−	0.310149i	0.386581	−	0.922255i	$-0.373656\pi$
$787$	−11.3391	−	8.70078i	−0.404194	−	0.310149i	−0.790776	+	0.612106i	$0.790323\pi$
$788$	−10.3200	−	22.3319i	−0.367635	−	0.795542i
$789$	−10.4051	−	10.0190i	−0.370432	−	0.356685i
$790$	−14.0719	+	14.6491i	−0.500656	+	0.521191i
$791$	14.9170	−	14.9170i	0.530387	−	0.530387i
$792$	−25.0346	−	34.9420i	−0.889564	−	1.24161i
$793$	4.88166	+	4.88166i	0.173353	+	0.173353i
$794$	−33.1618	+	0.666428i	−1.17687	+	0.0236506i
$795$	11.4118	+	39.5809i	0.404736	+	1.40379i
$796$	−3.30918	+	0.133058i	−0.117291	+	0.00471610i
$797$	3.59016	−	4.67879i	0.127170	−	0.165731i	−0.725429	−	0.688297i	$-0.758359\pi$
$797$	3.59016	−	4.67879i	0.127170	−	0.165731i	0.852599	+	0.522566i	$0.175025\pi$
$798$	13.6817	+	12.6541i	0.484325	+	0.447950i
$799$	−6.79775	−	3.92468i	−0.240487	−	0.138845i
$800$	37.8386	+	1.15187i	1.33780	+	0.0407246i
$801$	2.69028	+	8.70903i	0.0950564	+	0.307718i
$802$	36.5723	−	5.56452i	1.29141	−	0.196490i
$803$	−5.06804	+	38.4956i	−0.178847	+	1.35848i
$804$	−12.5675	−	14.5156i	−0.443220	−	0.511925i
$805$	−68.2150	+	8.98067i	−2.40426	+	0.316527i
$806$	25.9347	+	14.2864i	0.913509	+	0.503218i
$807$	35.3408	+	26.0716i	1.24406	+	0.917762i
$808$	−16.2062	+	32.4390i	−0.570131	+	1.14120i
$809$	−15.3177	−	15.3177i	−0.538542	−	0.538542i	0.384558	−	0.923101i	$-0.374354\pi$
$809$	−15.3177	−	15.3177i	−0.538542	−	0.538542i	−0.923101	+	0.384558i	$0.874354\pi$
$810$	15.2301	+	40.7696i	0.535130	+	1.43250i
$811$	2.56026	−	6.18100i	0.0899027	−	0.217044i	−0.872532	−	0.488556i	$-0.837524\pi$
$811$	2.56026	−	6.18100i	0.0899027	−	0.217044i	0.962435	+	0.271512i	$0.0875237\pi$
$812$	5.73890	−	8.13618i	0.201396	−	0.285524i
$813$	5.79121	+	9.60659i	0.203107	+	0.336918i
$814$	−62.4041	−	6.94320i	−2.18726	−	0.243359i
$815$	−64.1845	+	37.0570i	−2.24829	+	1.29805i
$816$	−5.70931	+	4.10078i	−0.199866	+	0.143556i
$817$	−23.2793	−	13.4403i	−0.814440	−	0.470217i
$818$	4.99208	+	3.67358i	0.174544	+	0.128444i
$819$	−18.2102	+	15.1003i	−0.636316	+	0.527648i
$820$	0.239602	+	0.287553i	0.00836725	+	0.0100418i
$821$	−4.73858	−	6.17544i	−0.165378	−	0.215524i	0.703312	−	0.710882i	$-0.251704\pi$
$821$	−4.73858	−	6.17544i	−0.165378	−	0.215524i	−0.868689	+	0.495357i	$0.835037\pi$
$822$	12.6737	−	5.83850i	0.442048	−	0.203641i
$823$	−9.49944	+	35.4524i	−0.331130	+	1.23579i	0.576875	+	0.816832i	$0.304272\pi$
$823$	−9.49944	+	35.4524i	−0.331130	+	1.23579i	−0.908005	+	0.418960i	$0.862395\pi$
$824$	−35.8946	+	6.94718i	−1.25045	+	0.242017i
$825$	−58.3498	−	6.56236i	−2.03148	−	0.228472i
$826$	44.5559	−	0.895405i	1.55030	−	0.0311551i
$827$	−15.0099	+	36.2371i	−0.521946	+	1.26009i	0.414747	+	0.909937i	$0.363870\pi$
$827$	−15.0099	+	36.2371i	−0.521946	+	1.26009i	−0.936693	+	0.350152i	$0.886130\pi$
$828$	−37.2309	+	2.90976i	−1.29386	+	0.101121i
$829$	28.5351	−	11.8196i	0.991065	−	0.410513i	0.172552	−	0.985000i	$-0.444799\pi$
$829$	28.5351	−	11.8196i	0.991065	−	0.410513i	0.818513	+	0.574488i	$0.194799\pi$
$830$	3.59641	+	1.40570i	0.124833	+	0.0487927i
$831$	4.72391	+	1.85288i	0.163871	+	0.0642758i
$832$	4.85526	+	18.8995i	0.168326	+	0.655224i
$833$	3.03280	−	1.75099i	0.105080	−	0.0606681i
$834$	12.6965	−	3.93857i	0.439643	−	0.136382i
$835$	−1.43600	−	0.189053i	−0.0496948	−	0.00654245i
$836$	−22.7646	+	7.09148i	−0.787329	+	0.245264i
$837$	−37.3004	+	24.4547i	−1.28929	+	0.845277i
$838$	23.2526	−	14.0552i	0.803247	−	0.485530i
$839$	15.4051	−	4.12779i	0.531844	−	0.142507i	0.0171042	−	0.999854i	$-0.494555\pi$
$839$	15.4051	−	4.12779i	0.531844	−	0.142507i	0.514739	+	0.857347i	$0.327889\pi$
$840$	−53.2550	−	9.83469i	−1.83747	−	0.339329i
$841$	−25.7214	−	6.89203i	−0.886945	−	0.237656i
$842$	17.5300	−	5.07678i	0.604125	−	0.174958i
$843$	32.9256	−	34.1947i	1.13402	−	1.17773i
$844$	2.01300	+	11.6509i	0.0692903	+	0.401042i
$845$	−22.2732	+	9.22587i	−0.766222	+	0.317380i
$846$	−6.16023	−	32.2393i	−0.211793	−	1.10841i
$847$	−47.4009			−1.62871
$848$	−26.4754	−	8.54873i	−0.909170	−	0.293565i
$849$	24.6987	−	19.7048i	0.847657	−	0.676267i
$850$	−1.06182	+	9.54340i	−0.0364200	+	0.327336i
$851$	−33.2082	+	43.2778i	−1.13836	+	1.48354i
$852$	5.34330	−	3.52134i	0.183058	−	0.120639i
$853$	−25.3475	+	19.4498i	−0.867882	+	0.665949i	−0.943567	−	0.331182i	$-0.892552\pi$
$853$	−25.3475	+	19.4498i	−0.867882	+	0.665949i	0.0756845	+	0.997132i	$0.475886\pi$
$854$	3.09741	−	12.5643i	0.105991	−	0.429941i
$855$	24.1241	−	0.912542i	0.825028	−	0.0312083i
$856$	−28.6909	+	1.73160i	−0.980633	+	0.0591848i
$857$	−0.378409	−	1.41224i	−0.0129262	−	0.0482413i	0.959162	−	0.282859i	$-0.0912828\pi$
$857$	−0.378409	−	1.41224i	−0.0129262	−	0.0482413i	−0.972088	+	0.234618i	$0.924616\pi$
$858$	−5.11749	−	29.8306i	−0.174708	−	1.01840i
$859$	−5.90430	−	44.8476i	−0.201452	−	1.53018i	−0.731281	−	0.682077i	$-0.761077\pi$
$859$	−5.90430	−	44.8476i	−0.201452	−	1.53018i	0.529828	−	0.848105i	$-0.322256\pi$
$860$	78.0494	−	3.13826i	2.66146	−	0.107014i
$861$	−0.158225	−	0.262466i	−0.00539228	−	0.00894483i
$862$	−30.2124	−	11.8089i	−1.02904	−	0.402214i
$863$	−2.40611			−0.0819051			−0.0409525	−	0.999161i	$-0.513039\pi$
$863$	−2.40611			−0.0819051			−0.0409525	+	0.999161i	$0.513039\pi$
$864$	−28.5824	−	6.85897i	−0.972394	−	0.233347i
$865$	−1.15664			−0.0393269
$866$	6.66449	+	2.60491i	0.226469	+	0.0885184i
$867$	14.2813	+	23.6901i	0.485018	+	0.804559i
$868$	−2.22978	−	55.4553i	−0.0756838	−	1.88228i
$869$	2.77751	+	21.0973i	0.0942205	+	0.715675i
$870$	−2.18075	−	12.7119i	−0.0739342	−	0.430974i
$871$	−3.49903	−	13.0586i	−0.118560	−	0.442473i
$872$	−14.0793	−	12.4765i	−0.476785	−	0.422509i
$873$	−5.86979	−	9.33324i	−0.198662	−	0.315882i
$874$	−4.95832	+	20.1128i	−0.167718	+	0.680326i
$875$	−14.8398	+	11.3869i	−0.501675	+	0.384949i
$876$	14.6105	+	22.1700i	0.493643	+	0.749055i
$877$	32.9486	−	42.9395i	1.11260	−	1.44996i	0.234099	−	0.972213i	$-0.424786\pi$
$877$	32.9486	−	42.9395i	1.11260	−	1.44996i	0.878496	−	0.477750i	$-0.158547\pi$
$878$	−4.33296	+	38.9437i	−0.146230	+	1.31429i
$879$	−26.5539	+	21.1849i	−0.895641	+	0.714549i
$880$	44.9016	−	52.7687i	1.51363	−	1.77883i
$881$	−0.533574			−0.0179766			−0.00898828	−	0.999960i	$-0.502861\pi$
$881$	−0.533574			−0.0179766			−0.00898828	+	0.999960i	$0.502861\pi$
$882$	13.8307	+	4.81159i	0.465702	+	0.162015i
$883$	29.2475	−	12.1147i	0.984256	−	0.407692i	0.168255	−	0.985743i	$-0.446187\pi$
$883$	29.2475	−	12.1147i	0.984256	−	0.407692i	0.816000	+	0.578051i	$0.196187\pi$
$884$	−4.87730	+	0.842680i	−0.164042	+	0.0283424i
$885$	40.0417	−	41.5849i	1.34599	−	1.39786i
$886$	33.5088	−	9.70430i	1.12575	−	0.326022i
$887$	12.6223	+	3.38214i	0.423816	+	0.113561i	0.464422	−	0.885614i	$-0.346262\pi$
$887$	12.6223	+	3.38214i	0.423816	+	0.113561i	−0.0406061	+	0.999175i	$0.512929\pi$
$888$	−35.3696	+	24.3425i	−1.18693	+	0.816880i
$889$	0.860322	−	0.230523i	0.0288543	−	0.00773148i
$890$	−12.5741	+	7.60051i	−0.421483	+	0.254770i
$891$	43.3192	+	14.2153i	1.45125	+	0.476232i
$892$	7.71494	+	24.7659i	0.258315	+	0.829225i
$893$	−18.0510	−	2.37645i	−0.604052	−	0.0795250i
$894$	−47.1042	+	14.6122i	−1.57540	+	0.488705i
$895$	−54.9938	+	31.7507i	−1.83824	+	1.06131i
$896$	25.6096	−	26.1142i	0.855556	−	0.872413i
$897$	−24.4794	−	9.60166i	−0.817342	−	0.320590i
$898$	−8.09492	−	3.16401i	−0.270131	−	0.105584i
$899$	12.2117	−	5.05825i	0.407283	−	0.168702i
$900$	−33.1031	+	22.7246i	−1.10344	+	0.757488i
$901$	2.70057	−	6.51976i	0.0899692	−	0.217205i
$902$	0.392021	−	0.00787814i	0.0130529	−	0.000262314i
$903$	−63.5574	−	7.14804i	−2.11506	−	0.237872i
$904$	15.2929	+	10.3331i	0.508633	+	0.343674i
$905$	6.92977	−	25.8623i	0.230353	−	0.859690i
$906$	7.75028	−	3.57037i	0.257486	−	0.118618i
$907$	12.5825	+	16.3979i	0.417796	+	0.544483i	0.954079	−	0.299556i	$-0.0968385\pi$
$907$	12.5825	+	16.3979i	0.417796	+	0.544483i	−0.536283	+	0.844039i	$0.680172\pi$
$908$	−16.0514	+	13.3747i	−0.532683	+	0.443855i
$909$	−6.45807	−	37.9156i	−0.214201	−	1.25758i
$910$	−30.7125	−	22.6008i	−1.01811	−	0.749211i
$911$	−14.2097	−	8.20400i	−0.470790	−	0.271811i	0.245781	−	0.969326i	$-0.420956\pi$
$911$	−14.2097	−	8.20400i	−0.470790	−	0.271811i	−0.716570	+	0.697515i	$0.754289\pi$
$912$	−8.59475	+	13.8556i	−0.284601	+	0.458804i
$913$	3.50313	−	2.02253i	0.115937	−	0.0669361i
$914$	−28.3349	−	3.15260i	−0.937236	−	0.104279i
$915$	−8.65440	−	14.3561i	−0.286105	−	0.474598i
$916$	11.3998	+	8.04092i	0.376660	+	0.265679i
$917$	−12.8280	+	30.9695i	−0.423618	+	1.02270i
$918$	2.31626	−	7.08689i	0.0764478	−	0.233902i
$919$	18.3088	+	18.3088i	0.603951	+	0.603951i	0.941359	−	0.337408i	$-0.109550\pi$
$919$	18.3088	+	18.3088i	0.603951	+	0.603951i	−0.337408	+	0.941359i	$0.609550\pi$
$920$	−19.0544	−	57.1004i	−0.628204	−	1.88254i
$921$	13.7543	+	10.1468i	0.453219	+	0.334348i
$922$	9.09543	+	5.01034i	0.299542	+	0.165007i
$923$	4.46733	−	0.588135i	0.147044	−	0.0193587i
$924$	−42.8903	+	37.1340i	−1.41099	+	1.22162i
$925$	−7.65567	+	58.1506i	−0.251717	+	1.91198i
$926$	14.2483	−	2.16790i	0.468228	−	0.0712415i
$927$	26.3644	−	28.4374i	0.865922	−	0.934008i
$928$	7.94265	+	3.57684i	0.260730	+	0.117416i
$929$	−8.79944	−	5.08036i	−0.288700	−	0.166681i	0.348655	−	0.937251i	$-0.386638\pi$
$929$	−8.79944	−	5.08036i	−0.288700	−	0.166681i	−0.637356	+	0.770570i	$0.719972\pi$
$930$	−52.7804	−	48.8163i	−1.73074	−	1.60075i
$931$	4.94489	−	6.44431i	0.162062	−	0.211204i
$932$	−1.76076	−	43.7905i	−0.0576755	−	1.43441i
$933$	−1.45899	−	5.06037i	−0.0477651	−	0.165669i
$934$	44.7234	−	0.898772i	1.46340	−	0.0294087i
$935$	12.4273	+	12.4273i	0.406415	+	0.406415i
$936$	−15.9978	−	13.1313i	−0.522905	−	0.429211i
$937$	33.3527	−	33.3527i	1.08959	−	1.08959i	0.0940154	−	0.995571i	$-0.470030\pi$
$937$	33.3527	−	33.3527i	1.08959	−	1.08959i	0.995571	−	0.0940154i	$-0.0299703\pi$
$938$	−17.5549	+	18.2750i	−0.573188	+	0.596699i
$939$	−40.1841	−	38.6928i	−1.31136	−	1.26269i
$940$	48.0268	−	22.1941i	1.56646	−	0.723891i
$941$	13.1814	+	10.1144i	0.429701	+	0.329721i	0.800864	−	0.598847i	$-0.204374\pi$
$941$	13.1814	+	10.1144i	0.429701	+	0.329721i	−0.371163	+	0.928568i	$0.621041\pi$
$942$	34.9591	+	18.4050i	1.13903	+	0.599667i
$943$	0.170326	−	0.295013i	0.00554657	−	0.00960695i
$944$	8.17631	+	38.1225i	0.266116	+	1.24078i
$945$	51.7368	−	24.9543i	1.68300	−	0.811762i
$946$	48.4997	−	65.9068i	1.57686	−	2.14282i
$947$	1.96007	+	0.258048i	0.0636937	+	0.00838544i	0.162306	−	0.986741i	$-0.448107\pi$
$947$	1.96007	+	0.258048i	0.0636937	+	0.00838544i	−0.0986120	+	0.995126i	$0.531440\pi$
$948$	10.8790	+	9.66371i	0.353334	+	0.313863i
$949$	2.44024	+	18.5355i	0.0792137	+	0.601688i
$950$	6.19567	+	21.3935i	0.201014	+	0.694098i
$951$	16.4057	+	37.5812i	0.531990	+	1.21865i
$952$	6.08098	+	7.00676i	0.197086	+	0.227090i
$953$	26.9641	−	26.9641i	0.873451	−	0.873451i	−0.119395	−	0.992847i	$-0.538096\pi$
$953$	26.9641	−	26.9641i	0.873451	−	0.873451i	0.992847	+	0.119395i	$0.0380956\pi$
$954$	28.0138	−	9.27420i	0.906979	−	0.300263i
$955$	−40.0755	−	16.5998i	−1.29681	−	0.537158i
$956$	−12.7945	−	2.88277i	−0.413803	−	0.0932353i
$957$	−11.8267	−	6.53320i	−0.382301	−	0.211189i
$958$	15.2818	+	19.1081i	0.493733	+	0.617355i
$959$	−9.20833	−	15.9493i	−0.297353	−	0.515030i
$960$	−0.405846	−	47.3784i	−0.0130986	−	1.52913i
$961$	21.3398	−	36.9616i	0.688379	−	1.19231i
$962$	−29.8888	+	4.54762i	−0.963653	+	0.146621i
$963$	23.4678	−	19.4601i	0.756241	−	0.627092i
$964$	1.40953	+	4.52478i	0.0453980	+	0.145733i
$965$	35.4116	−	27.1723i	1.13994	−	0.874706i
$966$	8.33368	+	48.5783i	0.268132	+	1.56298i
$967$	27.1215	+	7.26719i	0.872169	+	0.233697i	0.667026	−	0.745035i	$-0.267567\pi$
$967$	27.1215	+	7.26719i	0.872169	+	0.233697i	0.205144	+	0.978732i	$0.434234\pi$
$968$	−7.88017	−	40.7151i	−0.253278	−	1.30863i
$969$	−3.32811	−	2.45521i	−0.106914	−	0.0788726i
$970$	12.3118	−	12.8168i	0.395309	−	0.411524i
$971$	−20.4051	−	8.45209i	−0.654832	−	0.271240i	0.0304300	−	0.999537i	$-0.490312\pi$
$971$	−20.4051	−	8.45209i	−0.654832	−	0.271240i	−0.685262	+	0.728297i	$0.740312\pi$
$972$	28.7581	−	12.0405i	0.922415	−	0.386200i
$973$	−6.71411	−	16.2093i	−0.215244	−	0.519646i
$974$	−5.52660	−	12.6191i	−0.177084	−	0.404342i
$975$	−27.9557	+	4.21949i	−0.895299	+	0.135132i
$976$	11.3070	+	0.571782i	0.361930	+	0.0183023i
$977$	−21.1381	−	36.6123i	−0.676269	−	1.17133i	−0.976096	−	0.217339i	$-0.930262\pi$
$977$	−21.1381	−	36.6123i	−0.676269	−	1.17133i	0.299827	−	0.953994i	$-0.403071\pi$
$978$	28.3185	+	44.9091i	0.905525	+	1.43603i
$979$	−2.00902	+	15.2600i	−0.0642084	+	0.487711i
$980$	−2.13827	+	23.5072i	−0.0683046	+	0.750911i
$981$	19.8667	+	1.85477i	0.634295	+	0.0592182i
$982$	−50.5260	−	12.4560i	−1.61235	−	0.397486i
$983$	10.5728	+	39.4582i	0.337220	+	1.25852i	0.901442	+	0.432899i	$0.142509\pi$
$983$	10.5728	+	39.4582i	0.337220	+	1.25852i	−0.564222	+	0.825623i	$0.690824\pi$
$984$	0.199142	−	0.179541i	0.00634841	−	0.00572356i
$985$	−10.8860	+	40.6271i	−0.346857	+	1.29449i
$986$	−1.06610	+	1.93532i	−0.0339514	+	0.0616332i
$987$	−41.6244	+	12.0010i	−1.32492	+	0.381996i
$988$	−9.70383	+	6.13511i	−0.308720	+	0.195184i
$989$	−27.2056	−	65.6802i	−0.865088	−	2.08851i
$990$	−5.35981	+	73.2943i	−0.170346	+	2.32945i
$991$		−	8.36275i		−	0.265651i	−0.991139	−	0.132826i	$-0.957595\pi$
$991$		−	8.36275i		−	0.265651i	0.991139	−	0.132826i	$-0.0424051\pi$
$992$	47.2628	−	11.1344i	1.50059	−	0.353519i
$993$	11.9184	−	30.3859i	0.378219	−	0.964267i
$994$	−5.27512	−	6.59592i	−0.167317	−	0.209210i
$995$	4.49214	+	3.44694i	0.142410	+	0.109275i
$996$	0.905775	−	2.61361i	0.0287006	−	0.0828155i
$997$	16.3843	+	21.3525i	0.518897	+	0.676240i	0.977142	−	0.212586i	$-0.0681885\pi$
$997$	16.3843	+	21.3525i	0.518897	+	0.676240i	−0.458245	+	0.888826i	$0.651522\pi$
$998$	−34.9245	+	21.1105i	−1.10552	+	0.668240i
$999$	15.0150	−	42.9949i	0.475052	−	1.36030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.18	✓	368
3.2	odd	2		864.2.bn.a.683.29		368
9.4	even	3		864.2.bn.a.395.14		368
9.5	odd	6	inner	288.2.bf.a.203.33	yes	368
32.3	odd	8	inner	288.2.bf.a.227.33	yes	368
96.35	even	8		864.2.bn.a.35.14		368
288.67	odd	24		864.2.bn.a.611.29		368
288.131	even	24	inner	288.2.bf.a.131.18	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.18	✓	368	1.1	even	1	trivial
288.2.bf.a.131.18	yes	368	288.131	even	24	inner
288.2.bf.a.203.33	yes	368	9.5	odd	6	inner
288.2.bf.a.227.33	yes	368	32.3	odd	8	inner
864.2.bn.a.35.14		368	96.35	even	8
864.2.bn.a.395.14		368	9.4	even	3
864.2.bn.a.611.29		368	288.67	odd	24
864.2.bn.a.683.29		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.514835 + 1.31717i) q^{2} +(-0.894226 - 1.48336i) q^{3} +(-1.46989 - 1.35625i) q^{4} +(0.446317 + 3.39012i) q^{5} +(2.41422 - 0.414163i) q^{6} +(-0.836733 - 3.12273i) q^{7} +(2.54317 - 1.23785i) q^{8} +(-1.40072 + 2.65292i) q^{9} +O(q^{10})\)	\(q+(-0.514835 + 1.31717i) q^{2} +(-0.894226 - 1.48336i) q^{3} +(-1.46989 - 1.35625i) q^{4} +(0.446317 + 3.39012i) q^{5} +(2.41422 - 0.414163i) q^{6} +(-0.836733 - 3.12273i) q^{7} +(2.54317 - 1.23785i) q^{8} +(-1.40072 + 2.65292i) q^{9} +(-4.69515 - 1.15747i) q^{10} +(-4.01895 + 3.08385i) q^{11} +(-0.697402 + 3.39317i) q^{12} +(-1.48486 + 1.93511i) q^{13} +(4.54395 + 0.505569i) q^{14} +(4.62966 - 3.69358i) q^{15} +(0.321150 + 3.98709i) q^{16} -1.01461 q^{17} +(-2.77321 - 3.21081i) q^{18} +(-2.17425 + 0.900605i) q^{19} +(3.94182 - 5.58842i) q^{20} +(-3.88391 + 4.03360i) q^{21} +(-1.99287 - 6.88133i) q^{22} +(-6.01199 - 1.61091i) q^{23} +(-4.11035 - 2.66552i) q^{24} +(-6.46406 + 1.73204i) q^{25} +(-1.78442 - 2.95208i) q^{26} +(5.18780 - 0.294534i) q^{27} +(-3.00531 + 5.72489i) q^{28} +(-1.52671 - 0.200995i) q^{29} +(2.48157 + 7.99965i) q^{30} +(-7.43368 + 4.29184i) q^{31} +(-5.41702 - 1.62968i) q^{32} +(8.16831 + 3.20390i) q^{33} +(0.522355 - 1.33641i) q^{34} +(10.2130 - 4.23035i) q^{35} +(5.65694 - 1.99976i) q^{36} +(3.35400 - 8.09728i) q^{37} +(-0.0668708 - 3.32753i) q^{38} +(4.19827 + 0.472162i) q^{39} +(5.33152 + 8.06918i) q^{40} +(-0.0141655 + 0.0528664i) q^{41} +(-3.31338 - 7.19242i) q^{42} +(6.95331 + 9.06173i) q^{43} +(10.0899 + 0.917801i) q^{44} +(-9.61887 - 3.56456i) q^{45} +(5.21703 - 7.08948i) q^{46} +(6.69989 + 3.86818i) q^{47} +(5.62711 - 4.04174i) q^{48} +(-2.98914 + 1.72578i) q^{49} +(1.04653 - 9.40600i) q^{50} +(0.907288 + 1.50503i) q^{51} +(4.80709 - 0.830548i) q^{52} +(-2.66169 + 6.42590i) q^{53} +(-2.28291 + 6.98486i) q^{54} +(-12.2483 - 12.2483i) q^{55} +(-5.99343 - 6.90589i) q^{56} +(3.28020 + 2.41986i) q^{57} +(1.05075 - 1.90746i) q^{58} +(9.66398 - 1.27229i) q^{59} +(-11.8145 - 0.849841i) q^{60} +(0.369438 - 2.80616i) q^{61} +(-1.82597 - 12.0010i) q^{62} +(9.45638 + 2.15429i) q^{63} +(4.93545 - 6.29614i) q^{64} +(-7.22297 - 4.17019i) q^{65} +(-8.42542 + 9.10960i) q^{66} +(-3.37411 + 4.39723i) q^{67} +(1.49136 + 1.37606i) q^{68} +(2.98652 + 10.3585i) q^{69} +(0.314107 + 15.6302i) q^{70} +(-1.30625 - 1.30625i) q^{71} +(-0.278354 + 8.48071i) q^{72} +(5.41978 - 5.41978i) q^{73} +(8.93876 + 8.58656i) q^{74} +(8.34957 + 8.03970i) q^{75} +(4.41736 + 1.62505i) q^{76} +(12.9928 + 9.96974i) q^{77} +(-2.78334 + 5.28676i) q^{78} +(2.10030 - 3.63783i) q^{79} +(-13.3734 + 2.86824i) q^{80} +(-5.07596 - 7.43200i) q^{81} +(-0.0623413 - 0.0458759i) q^{82} +(-0.791678 - 0.104226i) q^{83} +(11.1795 - 0.661383i) q^{84} +(-0.452837 - 3.43964i) q^{85} +(-15.5157 + 4.49342i) q^{86} +(1.06707 + 2.44439i) q^{87} +(-6.40354 + 12.8176i) q^{88} +(2.14845 - 2.14845i) q^{89} +(9.64728 - 10.8346i) q^{90} +(7.28526 + 3.01765i) q^{91} +(6.65216 + 10.5216i) q^{92} +(13.0137 + 7.18896i) q^{93} +(-8.54440 + 6.83343i) q^{94} +(-4.02356 - 6.96902i) q^{95} +(2.42663 + 9.49271i) q^{96} +(-1.83760 + 3.18282i) q^{97} +(-0.734236 - 4.82570i) q^{98} +(-2.55178 - 14.9816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

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