LMFDB - Embedded newform 507.2.t.b.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	507.10
Dual form			507.2.t.b.355.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31845 - 0.269162i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(-0.174110 - 0.0741814i) q^{4} +(0.381569 - 1.54808i) q^{5} +(1.34455 + 0.0541834i) q^{6} +(1.87281 - 0.888658i) q^{7} +(2.42447 + 1.67349i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})$	\(q+(-1.31845 - 0.269162i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(-0.174110 - 0.0741814i) q^{4} +(0.381569 - 1.54808i) q^{5} +(1.34455 + 0.0541834i) q^{6} +(1.87281 - 0.888658i) q^{7} +(2.42447 + 1.67349i) q^{8} +(0.948536 - 0.316668i) q^{9} +(-0.919764 + 1.93836i) q^{10} +(0.329322 - 0.986439i) q^{11} +(0.183755 + 0.0452915i) q^{12} +(-2.35927 + 2.72651i) q^{13} +(-2.70839 + 0.667557i) q^{14} +(-0.128297 + 1.58925i) q^{15} +(-2.48388 - 2.58600i) q^{16} +(0.00216254 + 0.00455745i) q^{17} +(-1.33583 + 0.162199i) q^{18} +(6.24636 + 3.60634i) q^{19} +(-0.181274 + 0.241232i) q^{20} +(-1.70600 + 1.17757i) q^{21} +(-0.699705 + 1.21192i) q^{22} +(-3.22724 - 5.58974i) q^{23} +(-2.66152 - 1.26291i) q^{24} +(2.17631 + 1.14221i) q^{25} +(3.84444 - 2.95973i) q^{26} +(-0.885456 + 0.464723i) q^{27} +(-0.391996 + 0.0157969i) q^{28} +(1.80670 - 8.84979i) q^{29} +(0.596918 - 2.06080i) q^{30} +(-2.25864 - 4.30348i) q^{31} +(-0.570205 - 0.901707i) q^{32} +(-0.166821 + 1.02649i) q^{33} +(-0.00162449 - 0.00659083i) q^{34} +(-0.661114 - 3.23835i) q^{35} +(-0.188641 - 0.0152286i) q^{36} +(2.59878 - 4.10964i) q^{37} +(-7.26479 - 6.43604i) q^{38} +(1.89135 - 3.06966i) q^{39} +(3.51580 - 3.11473i) q^{40} +(-0.616945 - 3.79622i) q^{41} +(2.56623 - 1.09337i) q^{42} +(0.178343 - 0.112777i) q^{43} +(-0.130514 + 0.147319i) q^{44} +(-0.128297 - 1.58925i) q^{45} +(2.75039 + 8.23842i) q^{46} +(1.11215 + 0.135039i) q^{47} +(2.86654 + 2.15407i) q^{48} +(-1.70942 + 2.09366i) q^{49} +(-2.56190 - 2.09173i) q^{50} +(-0.00286560 - 0.00415154i) q^{51} +(0.613028 - 0.299699i) q^{52} +(5.40943 - 7.83692i) q^{53} +(1.29251 - 0.374380i) q^{54} +(-1.40143 - 0.886212i) q^{55} +(6.02772 + 0.979600i) q^{56} +(-6.74396 - 2.55765i) q^{57} +(-4.76406 + 11.1817i) q^{58} +(-3.57811 - 3.43682i) q^{59} +(0.140230 - 0.267186i) q^{60} +(-1.23344 + 0.0995738i) q^{61} +(1.81956 + 6.28184i) q^{62} +(1.49502 - 1.43598i) q^{63} +(3.05207 + 8.04766i) q^{64} +(3.32065 + 4.69270i) q^{65} +(0.496238 - 1.30847i) q^{66} +(0.760602 + 1.78520i) q^{67} +(-3.84416e-5 - 0.000953919i) q^{68} +(4.08210 + 4.99967i) q^{69} +4.44753i q^{70} +(-2.24174 + 1.83032i) q^{71} +(2.82964 + 0.819614i) q^{72} +(-6.75398 - 7.62367i) q^{73} +(-4.53250 + 4.71884i) q^{74} +(-2.33135 - 0.778319i) q^{75} +(-0.820031 - 1.09126i) q^{76} +(-0.259851 - 2.14006i) q^{77} +(-3.31988 + 3.53809i) q^{78} +(1.93278 - 15.9179i) q^{79} +(-4.95112 + 2.85853i) q^{80} +(0.799443 - 0.600742i) q^{81} +(-0.208391 + 5.17116i) q^{82} +(-12.4677 + 4.72839i) q^{83} +(0.384386 - 0.0784730i) q^{84} +(0.00788048 - 0.00160881i) q^{85} +(-0.265490 + 0.100687i) q^{86} +(-0.363695 + 9.02500i) q^{87} +(2.44922 - 1.84047i) q^{88} +(6.98752 - 4.03425i) q^{89} +(-0.258613 + 2.12987i) q^{90} +(-1.99552 + 7.20281i) q^{91} +(0.147240 + 1.21263i) q^{92} +(2.91972 + 3.88544i) q^{93} +(-1.42996 - 0.477389i) q^{94} +(7.96633 - 8.29382i) q^{95} +(0.707465 + 0.798563i) q^{96} +(10.6546 + 3.08613i) q^{97} +(2.81732 - 2.30027i) q^{98} -1.03996i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{78}\right)$

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 $

$2$	−1.31845	−	0.269162i	−0.932281	−	0.190327i	−0.290203	−	0.956965i	$-0.593723\pi$
$2$	−1.31845	−	0.269162i	−0.932281	−	0.190327i	−0.642079	+	0.766639i	$0.721928\pi$
$3$	−0.987050	+	0.160411i	−0.569874	+	0.0926135i
$3$	−0.987050	+	0.160411i	−0.569874	+	0.0926135i
$4$	−0.174110	−	0.0741814i	−0.0870550	−	0.0370907i
$5$	0.381569	−	1.54808i	0.170643	−	0.692325i	−0.821817	−	0.569752i	$-0.807039\pi$
$5$	0.381569	−	1.54808i	0.170643	−	0.692325i	0.992460	−	0.122573i	$-0.0391145\pi$
$6$	1.34455	+	0.0541834i	0.548910	+	0.0221203i
$7$	1.87281	−	0.888658i	0.707855	−	0.335881i	−0.0405005	−	0.999180i	$-0.512895\pi$
$7$	1.87281	−	0.888658i	0.707855	−	0.335881i	0.748355	+	0.663298i	$0.230844\pi$
$8$	2.42447	+	1.67349i	0.857179	+	0.591668i
$9$	0.948536	−	0.316668i	0.316179	−	0.105556i
$10$	−0.919764	+	1.93836i	−0.290855	+	0.612964i
$11$	0.329322	−	0.986439i	0.0992942	−	0.297423i	−0.887159	−	0.461463i	$-0.847325\pi$
$11$	0.329322	−	0.986439i	0.0992942	−	0.297423i	0.986454	+	0.164041i	$0.0524528\pi$
$12$	0.183755	+	0.0452915i	0.0530455	+	0.0130745i
$13$	−2.35927	+	2.72651i	−0.654343	+	0.756198i
$13$	−2.35927	+	2.72651i	−0.654343	+	0.756198i
$14$	−2.70839	+	0.667557i	−0.723847	+	0.178412i
$15$	−0.128297	+	1.58925i	−0.0331262	+	0.410341i
$16$	−2.48388	−	2.58600i	−0.620971	−	0.646499i
$17$	0.00216254	+	0.00455745i	0.000524493	+	0.00110534i	0.903713	−	0.428140i	$-0.140831\pi$
$17$	0.00216254	+	0.00455745i	0.000524493	+	0.00110534i	−0.903188	+	0.429245i	$0.858780\pi$
$18$	−1.33583	+	0.162199i	−0.314858	+	0.0382307i
$19$	6.24636	+	3.60634i	1.43301	+	0.827350i	0.997349	−	0.0727600i	$-0.0231807\pi$
$19$	6.24636	+	3.60634i	1.43301	+	0.827350i	0.435663	+	0.900110i	$0.356514\pi$
$20$	−0.181274	+	0.241232i	−0.0405341	+	0.0539411i
$21$	−1.70600	+	1.17757i	−0.372281	+	0.256967i
$22$	−0.699705	+	1.21192i	−0.149178	+	0.258383i
$23$	−3.22724	−	5.58974i	−0.672926	−	1.16554i	−0.977071	−	0.212916i	$-0.931704\pi$
$23$	−3.22724	−	5.58974i	−0.672926	−	1.16554i	0.304145	−	0.952626i	$-0.401629\pi$
$24$	−2.66152	−	1.26291i	−0.543280	−	0.257790i
$25$	2.17631	+	1.14221i	0.435262	+	0.228443i
$26$	3.84444	−	2.95973i	0.753956	−	0.580450i
$27$	−0.885456	+	0.464723i	−0.170406	+	0.0894360i
$28$	−0.391996	+	0.0157969i	−0.0740804	+	0.00298534i
$29$	1.80670	−	8.84979i	0.335495	−	1.64337i	−0.365945	−	0.930637i	$-0.619254\pi$
$29$	1.80670	−	8.84979i	0.335495	−	1.64337i	0.701440	−	0.712729i	$-0.252541\pi$
$30$	0.596918	−	2.06080i	0.108982	−	0.376249i
$31$	−2.25864	−	4.30348i	−0.405664	−	0.772927i	0.593835	−	0.804587i	$-0.297613\pi$
$31$	−2.25864	−	4.30348i	−0.405664	−	0.772927i	−0.999499	+	0.0316594i	$0.989921\pi$
$32$	−0.570205	−	0.901707i	−0.100799	−	0.159401i
$33$	−0.166821	+	1.02649i	−0.0290398	+	0.178689i
$34$	−0.00162449	−	0.00659083i	−0.000278598	−	0.00113032i
$35$	−0.661114	−	3.23835i	−0.111749	−	0.547381i
$36$	−0.188641	−	0.0152286i	−0.0314401	−	0.00253811i
$37$	2.59878	−	4.10964i	0.427236	−	0.675620i	−0.561127	−	0.827729i	$-0.689632\pi$
$37$	2.59878	−	4.10964i	0.427236	−	0.675620i	0.988364	+	0.152109i	$0.0486066\pi$
$38$	−7.26479	−	6.43604i	−1.17850	−	1.04406i
$39$	1.89135	−	3.06966i	0.302859	−	0.491538i
$40$	3.51580	−	3.11473i	0.555897	−	0.492482i
$41$	−0.616945	−	3.79622i	−0.0963507	−	0.592870i	−0.989661	−	0.143429i	$-0.954187\pi$
$41$	−0.616945	−	3.79622i	−0.0963507	−	0.592870i	0.893310	−	0.449441i	$-0.148377\pi$
$42$	2.56623	−	1.09337i	0.395978	−	0.168710i
$43$	0.178343	−	0.112777i	0.0271970	−	0.0171983i	−0.520798	−	0.853680i	$-0.674366\pi$
$43$	0.178343	−	0.112777i	0.0271970	−	0.0171983i	0.547995	+	0.836482i	$0.315391\pi$
$44$	−0.130514	+	0.147319i	−0.0196757	+	0.0222092i
$45$	−0.128297	−	1.58925i	−0.0191254	−	0.236911i
$46$	2.75039	+	8.23842i	0.405523	+	1.21469i
$47$	1.11215	+	0.135039i	0.162223	+	0.0196975i	0.201245	−	0.979541i	$-0.435501\pi$
$47$	1.11215	+	0.135039i	0.162223	+	0.0196975i	−0.0390221	+	0.999238i	$0.512424\pi$
$48$	2.86654	+	2.15407i	0.413750	+	0.310913i
$49$	−1.70942	+	2.09366i	−0.244203	+	0.299095i
$50$	−2.56190	−	2.09173i	−0.362307	−	0.295815i
$51$	−0.00286560	−	0.00415154i	−0.000401264	−	0.000581332i
$52$	0.613028	−	0.299699i	0.0850117	−	0.0415608i
$53$	5.40943	−	7.83692i	0.743043	−	1.07648i	−0.251052	−	0.967974i	$-0.580777\pi$
$53$	5.40943	−	7.83692i	0.743043	−	1.07648i	0.994095	−	0.108510i	$-0.0346080\pi$
$54$	1.29251	−	0.374380i	0.175888	−	0.0509467i
$55$	−1.40143	−	0.886212i	−0.188969	−	0.119497i
$56$	6.02772	+	0.979600i	0.805488	+	0.130904i
$57$	−6.74396	−	2.55765i	−0.893260	−	0.338769i
$58$	−4.76406	+	11.1817i	−0.625552	+	1.46823i
$59$	−3.57811	−	3.43682i	−0.465830	−	0.447436i	0.422690	−	0.906274i	$-0.361086\pi$
$59$	−3.57811	−	3.43682i	−0.465830	−	0.447436i	−0.888519	+	0.458839i	$0.848265\pi$
$60$	0.140230	−	0.267186i	0.0181036	−	0.0344936i
$61$	−1.23344	+	0.0995738i	−0.157926	+	0.0127491i	−0.159177	−	0.987250i	$-0.550884\pi$
$61$	−1.23344	+	0.0995738i	−0.157926	+	0.0127491i	0.00125059	+	0.999999i	$0.499602\pi$
$62$	1.81956	+	6.28184i	0.231084	+	0.797794i
$63$	1.49502	−	1.43598i	0.188354	−	0.180917i
$64$	3.05207	+	8.04766i	0.381509	+	1.00596i
$65$	3.32065	+	4.69270i	0.411876	+	0.582057i
$66$	0.496238	−	1.30847i	0.0610826	−	0.161062i
$67$	0.760602	+	1.78520i	0.0929223	+	0.218097i	0.959955	−	0.280155i	$-0.0903859\pi$
$67$	0.760602	+	1.78520i	0.0929223	+	0.218097i	−0.867033	+	0.498252i	$0.833976\pi$
$68$	−3.84416e−5	0	0.000953919i	−4.66173e−6	0	0.000115680i
$69$	4.08210	+	4.99967i	0.491428	+	0.601890i
$70$			4.44753i			0.531582i
$71$	−2.24174	+	1.83032i	−0.266045	+	0.217219i	−0.756073	−	0.654488i	$-0.772884\pi$
$71$	−2.24174	+	1.83032i	−0.266045	+	0.217219i	0.490027	+	0.871707i	$0.336987\pi$
$72$	2.82964	+	0.819614i	0.333476	+	0.0965924i
$73$	−6.75398	−	7.62367i	−0.790493	−	0.892283i	0.205774	−	0.978599i	$-0.434029\pi$
$73$	−6.75398	−	7.62367i	−0.790493	−	0.892283i	−0.996268	+	0.0863168i	$0.972490\pi$
$74$	−4.53250	+	4.71884i	−0.526893	+	0.548554i
$75$	−2.33135	−	0.778319i	−0.269201	−	0.0898725i
$76$	−0.820031	−	1.09126i	−0.0940640	−	0.125176i
$77$	−0.259851	−	2.14006i	−0.0296128	−	0.243883i
$78$	−3.31988	+	3.53809i	−0.375902	+	0.400610i
$79$	1.93278	−	15.9179i	0.217455	−	1.79090i	−0.319802	−	0.947484i	$-0.603616\pi$
$79$	1.93278	−	15.9179i	0.217455	−	1.79090i	0.537257	−	0.843419i	$-0.319461\pi$
$80$	−4.95112	+	2.85853i	−0.553552	+	0.319593i
$81$	0.799443	−	0.600742i	0.0888270	−	0.0667491i
$82$	−0.208391	+	5.17116i	−0.0230129	+	0.571059i
$83$	−12.4677	+	4.72839i	−1.36851	+	0.519008i	−0.925922	−	0.377715i	$-0.876710\pi$
$83$	−12.4677	+	4.72839i	−1.36851	+	0.519008i	−0.442591	+	0.896724i	$0.645941\pi$
$84$	0.384386	−	0.0784730i	0.0419400	−	0.00856211i
$85$	0.00788048	−	0.00160881i	0.000854758	−	0.000174500i
$86$	−0.265490	+	0.100687i	−0.0286285	+	0.0108574i
$87$	−0.363695	+	9.02500i	−0.0389922	+	0.967582i
$88$	2.44922	−	1.84047i	0.261088	−	0.196195i
$89$	6.98752	−	4.03425i	0.740676	−	0.427629i	−0.0816391	−	0.996662i	$-0.526015\pi$
$89$	6.98752	−	4.03425i	0.740676	−	0.427629i	0.822315	+	0.569032i	$0.192682\pi$
$90$	−0.258613	+	2.12987i	−0.0272602	+	0.224508i
$91$	−1.99552	+	7.20281i	−0.209187	+	0.755060i
$92$	0.147240	+	1.21263i	0.0153508	+	0.126426i
$93$	2.91972	+	3.88544i	0.302761	+	0.402901i
$94$	−1.42996	−	0.477389i	−0.147489	−	0.0492390i
$95$	7.96633	−	8.29382i	0.817328	−	0.850928i
$96$	0.707465	+	0.798563i	0.0722054	+	0.0815030i
$97$	10.6546	+	3.08613i	1.08181	+	0.313349i	0.770813	−	0.637062i	$-0.219850\pi$
$97$	10.6546	+	3.08613i	1.08181	+	0.313349i	0.310995	+	0.950411i	$0.399338\pi$
$98$	2.81732	−	2.30027i	0.284592	−	0.232362i
$99$		−	1.03996i		−	0.104520i
$100$	−0.294186	−	0.360313i	−0.0294186	−	0.0360313i
$101$	0.155040	+	3.84727i	0.0154270	+	0.382817i	0.988398	+	0.151888i	$0.0485355\pi$
$101$	0.155040	+	3.84727i	0.0154270	+	0.382817i	−0.972971	+	0.230929i	$0.925824\pi$
$102$	0.00266070	+	0.00624489i	0.000263448	+	0.000618336i
$103$	−6.35437	+	16.7551i	−0.626115	+	1.65093i	0.126104	+	0.992017i	$0.459753\pi$
$103$	−6.35437	+	16.7551i	−0.626115	+	1.65093i	−0.752219	+	0.658913i	$0.771017\pi$
$104$	−10.2827	+	2.66213i	−1.00831	+	0.261043i
$105$	1.17202	+	3.09036i	0.114377	+	0.301589i
$106$	−9.24145	+	8.87653i	−0.897609	+	0.862165i
$107$	0.383795	+	1.32501i	0.0371028	+	0.128094i	0.976932	−	0.213551i	$-0.0685031\pi$
$107$	0.383795	+	1.32501i	0.0371028	+	0.128094i	−0.939829	+	0.341645i	$0.889016\pi$
$108$	0.188641	−	0.0152286i	0.0181520	−	0.00146538i
$109$	3.56386	−	6.79036i	0.341356	−	0.650399i	−0.652898	−	0.757445i	$-0.726447\pi$
$109$	3.56386	−	6.79036i	0.341356	−	0.650399i	0.994254	+	0.107047i	$0.0341395\pi$
$110$	1.60918	+	1.54564i	0.153429	+	0.147371i
$111$	−1.90589	+	4.47329i	−0.180899	+	0.424586i
$112$	−6.94990	−	2.63575i	−0.656704	−	0.249055i
$113$	−3.12642	−	0.508093i	−0.294109	−	0.0477974i	0.0115664	−	0.999933i	$-0.496318\pi$
$113$	−3.12642	−	0.508093i	−0.294109	−	0.0477974i	−0.305676	+	0.952136i	$0.598882\pi$
$114$	8.20312	+	5.18734i	0.768293	+	0.485839i
$115$	−9.88481	+	2.86317i	−0.921763	+	0.266992i
$116$	−0.971054	+	1.40681i	−0.0901601	+	0.130619i
$117$	−1.37445	+	3.33330i	−0.127068	+	0.308164i
$118$	3.79247	+	5.49435i	0.349125	+	0.505796i
$119$	0.00810003	+	0.00661347i	0.000742529	+	0.000606256i
$120$	−2.97064	+	3.63837i	−0.271181	+	0.332136i
$121$	7.92926	+	5.95845i	0.720842	+	0.541678i
$122$	1.65303	+	0.200714i	0.149658	+	0.0181718i
$123$	1.21791	+	3.64809i	0.109815	+	0.328937i
$124$	0.0740140	+	0.916828i	0.00664665	+	0.0823336i
$125$	7.88512	−	8.90046i	0.705267	−	0.796082i
$126$	−2.35761	+	1.49086i	−0.210033	+	0.132817i
$127$	−3.10988	+	1.32500i	−0.275957	+	0.117574i	−0.525512	−	0.850786i	$-0.676126\pi$
$127$	−3.10988	+	1.32500i	−0.275957	+	0.117574i	0.249554	+	0.968361i	$0.419716\pi$
$128$	−1.51559	−	9.32579i	−0.133960	−	0.824291i
$129$	−0.157942	+	0.139925i	−0.0139061	+	0.0123197i
$130$	−3.11499	−	7.08086i	−0.273203	−	0.621032i
$131$	6.08334	+	5.38937i	0.531504	+	0.470871i	0.885673	−	0.464310i	$-0.153698\pi$
$131$	6.08334	+	5.38937i	0.531504	+	0.470871i	−0.354169	+	0.935181i	$0.615236\pi$
$132$	0.105192	−	0.166348i	0.00915577	−	0.0144787i
$133$	14.9030	+	1.20310i	1.29226	+	0.104322i
$134$	−0.522303	−	2.55841i	−0.0451201	−	0.221013i
$135$	0.381569	+	1.54808i	0.0328402	+	0.133238i
$136$	−0.00238384	+	0.0146684i	−0.000204413	+	0.00125780i
$137$	8.46520	+	13.3866i	0.723231	+	1.14370i	0.983978	+	0.178291i	$0.0570567\pi$
$137$	8.46520	+	13.3866i	0.723231	+	1.14370i	−0.260747	+	0.965407i	$0.583969\pi$
$138$	−4.03631	−	7.69054i	−0.343593	−	0.654662i
$139$	1.44224	−	4.97918i	0.122329	−	0.422329i	−0.875855	−	0.482575i	$-0.839702\pi$
$139$	1.44224	−	4.97918i	0.122329	−	0.422329i	0.998184	+	0.0602466i	$0.0191887\pi$
$140$	−0.125119	+	0.612871i	−0.0105745	+	0.0517971i
$141$	−1.11941	+	0.0451105i	−0.0942710	+	0.00379899i
$142$	3.44826	−	1.80979i	0.289372	−	0.151874i
$143$	1.91258	+	3.22517i	0.159938	+	0.269702i
$144$	−3.17496	−	1.66635i	−0.264580	−	0.138862i
$145$	−13.0109	−	6.17373i	−1.08049	−	0.512700i
$146$	6.85274	+	11.8693i	0.567137	+	0.982310i
$147$	1.35144	−	2.34076i	0.111465	−	0.193063i
$148$	−0.757332	+	0.522748i	−0.0622523	+	0.0429697i
$149$	12.6163	−	16.7892i	1.03357	−	1.37543i	0.109158	−	0.994024i	$-0.465185\pi$
$149$	12.6163	−	16.7892i	1.03357	−	1.37543i	0.924409	−	0.381403i	$-0.124559\pi$
$150$	2.86426	+	1.65368i	0.233866	+	0.135023i
$151$	−10.9090	+	1.32459i	−0.887762	+	0.107794i	−0.551697	−	0.834045i	$-0.686019\pi$
$151$	−10.9090	+	1.32459i	−0.887762	+	0.107794i	−0.336065	+	0.941839i	$0.609096\pi$
$152$	9.10892	+	19.1966i	0.738831	+	1.55705i
$153$	0.00349445	+	0.00363810i	0.000282509	+	0.000294123i
$154$	−0.233426	+	2.89150i	−0.0188100	+	0.233004i
$155$	−7.52397	+	1.85449i	−0.604340	+	0.148956i
$156$	−0.557015	+	0.394155i	−0.0445969	+	0.0315577i
$157$	6.82753	+	1.68283i	0.544896	+	0.134305i	0.502149	−	0.864781i	$-0.332543\pi$
$157$	6.82753	+	1.68283i	0.544896	+	0.134305i	0.0427470	+	0.999086i	$0.486389\pi$
$158$	−6.83277	+	20.4666i	−0.543586	+	1.62824i
$159$	−4.08225	+	8.60317i	−0.323744	+	0.682276i
$160$	−1.61349	+	0.538663i	−0.127558	+	0.0425850i
$161$	−11.0114	−	7.60060i	−0.867817	−	0.599011i
$162$	−1.21572	+	0.576866i	−0.0955159	+	0.0453228i
$163$	13.4773	+	0.543116i	1.05562	+	0.0425401i	0.562001	−	0.827137i	$-0.310032\pi$
$163$	13.4773	+	0.543116i	1.05562	+	0.0425401i	0.493622	+	0.869677i	$0.335673\pi$
$164$	−0.174192	+	0.706726i	−0.0136021	+	0.0551860i
$165$	1.52544	+	0.649930i	0.118756	+	0.0505970i
$166$	17.7107	−	2.87828i	1.37462	−	0.223397i
$167$	−15.0169	−	3.06572i	−1.16204	−	0.237232i	−0.419960	−	0.907543i	$-0.637956\pi$
$167$	−15.0169	−	3.06572i	−1.16204	−	0.237232i	−0.742081	+	0.670310i	$0.766161\pi$
$168$	−6.10680			−0.471150
$169$	−1.86772	−	12.8651i	−0.143671	−	0.989626i
$170$	−0.0108230			−0.000830087
$171$	7.06691	+	1.44272i	0.540420	+	0.110328i
$172$	−0.0394172	+	0.00640592i	−0.00300553	+	0.000488447i
$173$	17.5094	+	7.46006i	1.33122	+	0.567178i	0.936191	−	0.351493i	$-0.114326\pi$
$173$	17.5094	+	7.46006i	1.33122	+	0.567178i	0.395024	+	0.918671i	$0.370736\pi$
$174$	2.90870	−	11.8011i	0.220508	−	0.894637i
$175$	5.09084	+	0.205154i	0.384832	+	0.0155082i
$176$	−3.36892	+	1.59857i	−0.253942	+	0.120497i
$177$	4.08307	+	2.81834i	0.306903	+	0.211840i
$178$	−10.2985	+	3.43816i	−0.771908	+	0.257701i
$179$	−5.08651	+	10.7196i	−0.380183	+	0.801220i	0.619683	+	0.784853i	$0.287261\pi$
$179$	−5.08651	+	10.7196i	−0.380183	+	0.801220i	−0.999866	+	0.0163672i	$0.994790\pi$
$180$	−0.0955546	+	0.286221i	−0.00712222	+	0.0213336i
$181$	10.5390	+	2.59763i	0.783359	+	0.193081i	0.610659	−	0.791894i	$-0.290905\pi$
$181$	10.5390	+	2.59763i	0.783359	+	0.193081i	0.172700	+	0.984974i	$0.444751\pi$
$182$	4.56970	−	8.95939i	0.338729	−	0.664114i
$183$	1.20150	−	0.296143i	0.0888172	−	0.0218915i
$184$	1.53004	−	18.9529i	0.112796	−	1.39723i
$185$	−5.37046	−	5.59124i	−0.394844	−	0.411076i
$186$	−2.80367	−	5.90861i	−0.205575	−	0.433241i
$187$	0.00520782		0.000632344i	0.000380834		4.62416e-5i
$188$	−0.183618	−	0.106012i	−0.0133918	−	0.00773173i
$189$	−1.24531	+	1.65720i	−0.0905829	+	0.120544i
$190$	−12.7356	+	8.79072i	−0.923934	+	0.637746i
$191$	−7.53381	+	13.0489i	−0.545127	+	0.944188i	0.453472	+	0.891271i	$0.350185\pi$
$191$	−7.53381	+	13.0489i	−0.545127	+	0.944188i	−0.998599	+	0.0529175i	$0.983148\pi$
$192$	−4.30348	−	7.45385i	−0.310577	−	0.537936i
$193$	−13.4489	−	6.38160i	−0.968075	−	0.459357i	−0.122064	−	0.992522i	$-0.538951\pi$
$193$	−13.4489	−	6.38160i	−0.968075	−	0.459357i	−0.846011	+	0.533165i	$0.821003\pi$
$194$	−13.2168	−	6.93671i	−0.948911	−	0.498027i
$195$	−4.03041	−	4.09926i	−0.288624	−	0.293554i
$196$	0.452939	−	0.237721i	0.0323528	−	0.0169800i
$197$	−15.5709	+	0.627484i	−1.10938	+	0.0447064i	−0.588180	−	0.808730i	$-0.700155\pi$
$197$	−15.5709	+	0.627484i	−1.10938	+	0.0447064i	−0.521197	+	0.853436i	$0.674514\pi$
$198$	−0.279918	+	1.37113i	−0.0198929	+	0.0974419i
$199$	4.45333	−	15.3747i	0.315689	−	1.08988i	−0.633126	−	0.774049i	$-0.718228\pi$
$199$	4.45333	−	15.3747i	0.315689	−	1.08988i	0.948814	−	0.315834i	$-0.102284\pi$
$200$	3.36490	+	6.41129i	0.237935	+	0.453346i
$201$	−1.03712	−	1.64007i	−0.0731527	−	0.115682i
$202$	0.831129	−	5.11414i	0.0584780	−	0.359830i
$203$	−4.48084	−	18.1795i	−0.314493	−	1.27595i
$204$	0.000190963	0	0.000935399i	1.33701e−5	0	6.54910e-5i
$205$	−6.11227	−	0.493434i	−0.426900	−	0.0344629i
$206$	12.8877	−	20.3803i	0.897931	−	1.41996i
$207$	−4.83125	−	4.28011i	−0.335795	−	0.297488i
$208$	12.9109	−	0.671279i	0.895209	−	0.0465448i
$209$	5.61449	−	4.97400i	0.388362	−	0.344059i
$210$	−0.713434	−	4.38994i	−0.0492316	−	0.302934i
$211$	13.4409	−	5.72664i	0.925311	−	0.394238i	0.123861	−	0.992300i	$-0.460472\pi$
$211$	13.4409	−	5.72664i	0.925311	−	0.394238i	0.801450	+	0.598061i	$0.204062\pi$
$212$	−1.52319	+	0.963207i	−0.104613	+	0.0661534i
$213$	1.91910	−	2.16622i	0.131495	−	0.148427i
$214$	−0.149368	−	1.85026i	−0.0102106	−	0.126481i
$215$	−0.106538	−	0.319122i	−0.00726586	−	0.0217639i
$216$	−2.92447	−	0.355095i	−0.198985	−	0.0241611i
$217$	−8.05431	−	6.05242i	−0.546763	−	0.410865i
$218$	−6.52646	+	7.99346i	−0.442028	+	0.541386i
$219$	7.88944	+	6.44153i	0.533119	+	0.435278i
$220$	0.178263	+	0.258259i	0.0120185	+	0.0174118i
$221$	−0.0175280	−	0.00485606i	−0.00117906	−	0.000326654i
$222$	3.71686	−	5.38479i	0.249459	−	0.361404i
$223$	−16.6351	+	4.81842i	−1.11397	+	0.322665i	−0.783650	−	0.621203i	$-0.786644\pi$
$223$	−16.6351	+	4.81842i	−1.11397	+	0.322665i	−0.330321	+	0.943869i	$0.607157\pi$
$224$	−1.86919	−	1.18201i	−0.124891	−	0.0789761i
$225$	2.42601	+	0.394265i	0.161734	+	0.0262843i
$226$	3.98526	+	1.51141i	0.265096	+	0.100537i
$227$	−3.08121	+	7.23187i	−0.204507	+	0.479996i	−0.990377	−	0.138396i	$-0.955805\pi$
$227$	−3.08121	+	7.23187i	−0.204507	+	0.479996i	0.785870	+	0.618392i	$0.212216\pi$
$228$	0.984462	+	0.945589i	0.0651976	+	0.0626231i
$229$	10.1087	−	19.2605i	0.668000	−	1.27277i	−0.281669	−	0.959511i	$-0.590888\pi$
$229$	10.1087	−	19.2605i	0.668000	−	1.27277i	0.949669	−	0.313255i	$-0.101420\pi$
$230$	13.8032	−	1.11431i	0.910158	−	0.0734756i
$231$	0.599776	+	2.07067i	0.0394624	+	0.136240i
$232$	19.1903	−	18.4325i	1.25991	−	1.21016i
$233$	9.62431	+	25.3772i	0.630510	+	1.66252i	0.743349	+	0.668904i	$0.233236\pi$
$233$	9.62431	+	25.3772i	0.630510	+	1.66252i	−0.112839	+	0.993613i	$0.535994\pi$
$234$	2.70934	−	4.02482i	0.177115	−	0.263111i
$235$	0.633412	−	1.67017i	0.0413192	−	0.108950i
$236$	0.368036	+	0.863813i	0.0239571	+	0.0562295i
$237$	0.645657	+	16.0218i	0.0419399	+	1.04073i
$238$	−0.00889935	−	0.0108997i	−0.000576859	−	0.000706524i
$239$			15.1785i			0.981813i	0.871212	+	0.490907i	$0.163334\pi$
$239$			15.1785i			0.981813i	−0.871212	+	0.490907i	$0.836666\pi$
$240$	4.42846	−	3.61573i	0.285856	−	0.233394i
$241$	−3.77803	−	1.09432i	−0.243365	−	0.0704914i	0.154294	−	0.988025i	$-0.450690\pi$
$241$	−3.77803	−	1.09432i	−0.243365	−	0.0704914i	−0.397658	+	0.917534i	$0.630177\pi$
$242$	−8.85050	−	9.99015i	−0.568932	−	0.642191i
$243$	−0.692724	+	0.721202i	−0.0444383	+	0.0462652i
$244$	0.222141	+	0.0741617i	0.0142211	+	0.00474772i
$245$	2.58891	+	3.44521i	0.165399	+	0.220106i
$246$	−0.623821	−	5.13763i	−0.0397734	−	0.327563i
$247$	−24.5695	+	8.52245i	−1.56332	+	0.542270i
$248$	1.72582	−	14.2134i	0.109590	−	0.902555i
$249$	11.5478	−	6.66713i	0.731812	−	0.422512i
$250$	−12.7918	+	9.61239i	−0.809023	+	0.607941i
$251$	1.08007	−	26.8018i	0.0681737	−	1.69171i	−0.497803	−	0.867290i	$-0.665860\pi$
$251$	1.08007	−	26.8018i	0.0681737	−	1.69171i	0.565976	−	0.824422i	$-0.308499\pi$
$252$	−0.366821	+	0.139117i	−0.0231075	+	0.00876353i
$253$	−6.57674	+	1.34265i	−0.413476	+	0.0844117i
$254$	4.45685	−	0.909872i	0.279647	−	0.0570904i
$255$	−0.00752036	+	0.00285210i	−0.000470943	+	0.000178605i
$256$	0.181203	−	4.49650i	0.0113252	−	0.281031i
$257$	−4.55779	+	3.42496i	−0.284307	+	0.213643i	−0.733322	−	0.679881i	$-0.762031\pi$
$257$	−4.55779	+	3.42496i	−0.284307	+	0.213643i	0.449015	+	0.893524i	$0.351775\pi$
$258$	0.245901	−	0.141971i	0.0153091	−	0.00883872i
$259$	1.21495	−	10.0060i	0.0754931	−	0.621741i
$260$	−0.230048	−	1.06338i	−0.0142669	−	0.0659478i
$261$	−1.08873	−	8.96647i	−0.0673905	−	0.555011i
$262$	−6.56993	−	8.74299i	−0.405892	−	0.540144i
$263$	9.30048	+	3.10496i	0.573492	+	0.191460i	0.588598	−	0.808426i	$-0.299680\pi$
$263$	9.30048	+	3.10496i	0.573492	+	0.191460i	−0.0151057	+	0.999886i	$0.504808\pi$
$264$	−2.12227	+	2.20952i	−0.130617	+	0.135987i
$265$	−10.0681	−	11.3646i	−0.618481	−	0.698121i
$266$	−19.3250	−	5.59755i	−1.18489	−	0.343208i
$267$	−6.24990	+	5.10288i	−0.382488	+	0.312291i
$268$		−	0.367243i		−	0.0224330i
$269$	13.2183	+	16.1895i	0.805936	+	0.987093i	0.999981	+	0.00610012i	$0.00194174\pi$
$269$	13.2183	+	16.1895i	0.805936	+	0.987093i	−0.194045	+	0.980993i	$0.562161\pi$
$270$	−0.0863909	−	2.14377i	−0.00525758	−	0.130466i
$271$	2.64675	+	6.21216i	0.160779	+	0.377362i	0.980812	−	0.194953i	$-0.0624556\pi$
$271$	2.64675	+	6.21216i	0.160779	+	0.377362i	−0.820034	+	0.572315i	$0.806045\pi$
$272$	0.00641407	−	0.0169125i	0.000388910	−	0.00102547i
$273$	0.814262	−	7.42964i	0.0492814	−	0.449662i
$274$	−7.55772	−	19.9281i	−0.456578	−	1.20390i
$275$	1.84343	−	1.77064i	0.111163	−	0.106774i
$276$	−0.339853	−	1.17331i	−0.0204568	−	0.0706249i
$277$	−13.5377	+	1.09287i	−0.813401	+	0.0656645i	−0.480164	−	0.877179i	$-0.659423\pi$
$277$	−13.5377	+	1.09287i	−0.813401	+	0.0656645i	−0.333237	+	0.942843i	$0.608141\pi$
$278$	−3.24172	+	6.17658i	−0.194425	+	0.370447i
$279$	−3.50517	−	3.36677i	−0.209849	−	0.201563i
$280$	3.81649	−	8.95764i	0.228079	−	0.535321i
$281$	−9.04006	−	3.42844i	−0.539285	−	0.204524i	0.0698973	−	0.997554i	$-0.477733\pi$
$281$	−9.04006	−	3.42844i	−0.539285	−	0.204524i	−0.609182	+	0.793030i	$0.708502\pi$
$282$	1.48802	+	0.241826i	0.0886101	+	0.0144005i
$283$	9.80421	+	6.19981i	0.582800	+	0.368540i	0.793095	−	0.609097i	$-0.208468\pi$
$283$	9.80421	+	6.19981i	0.582800	+	0.368540i	−0.210295	+	0.977638i	$0.567443\pi$
$284$	0.526085	−	0.152382i	0.0312174	−	0.00904223i
$285$	−6.53274	+	9.46431i	−0.386966	+	0.560617i
$286$	−1.65353	−	4.76701i	−0.0977755	−	0.281879i
$287$	−4.52896	−	6.56133i	−0.267336	−	0.387303i
$288$	−0.826402	−	0.674737i	−0.0486962	−	0.0397592i
$289$	10.7516	−	13.1683i	0.632444	−	0.774604i
$290$	15.4924	+	11.6418i	0.909742	+	0.683627i
$291$	−11.0116	−	1.33706i	−0.645514	−	0.0783796i
$292$	0.610402	+	1.82838i	0.0357211	+	0.106998i
$293$	−0.562713	−	6.97045i	−0.0328740	−	0.407218i	−0.992177	−	0.124839i	$-0.960159\pi$
$293$	−0.562713	−	6.97045i	−0.0328740	−	0.407218i	0.959303	−	0.282379i	$-0.0911235\pi$
$294$	−2.41185	+	2.72241i	−0.140662	+	0.158774i
$295$	−6.68578	+	4.22783i	−0.389261	+	0.246154i
$296$	13.1781	−	5.61466i	0.765960	−	0.326345i
$297$	0.166821	+	1.02649i	0.00967994	+	0.0595631i
$298$	−21.1529	+	18.7398i	−1.22536	+	1.08557i
$299$	22.8544	+	4.38859i	1.32170	+	0.253799i
$300$	0.348175	+	0.308456i	0.0201019	+	0.0178087i
$301$	0.233781	−	0.369695i	0.0134749	−	0.0213089i
$302$	14.7395	+	1.18989i	0.848160	+	0.0684706i
$303$	−0.770177	−	3.77258i	−0.0442455	−	0.216729i
$304$	−6.18925	−	25.1108i	−0.354978	−	1.44020i
$305$	−0.316494	+	1.94747i	−0.0181224	+	0.111512i
$306$	−0.00362799	−	0.00573721i	−0.000207399	−	0.000327975i
$307$	10.9058	+	20.7792i	0.622425	+	1.18593i	0.968802	+	0.247836i	$0.0797195\pi$
$307$	10.9058	+	20.7792i	0.622425	+	1.18593i	−0.346377	+	0.938095i	$0.612588\pi$
$308$	−0.113510	+	0.391883i	−0.00646785	+	0.0223296i
$309$	3.58438	−	17.5574i	0.203908	−	0.998808i
$310$	10.4191	−	0.419876i	0.591765	−	0.0238473i
$311$	15.0264	−	7.88649i	0.852072	−	0.447202i	0.0186412	−	0.999826i	$-0.494066\pi$
$311$	15.0264	−	7.88649i	0.852072	−	0.447202i	0.833430	+	0.552625i	$0.186374\pi$
$312$	9.72255	−	4.27712i	0.550431	−	0.242144i
$313$	27.0508	+	14.1973i	1.52900	+	0.802481i	0.998965	−	0.0454946i	$-0.0144864\pi$
$313$	27.0508	+	14.1973i	1.52900	+	0.802481i	0.530035	+	0.847976i	$0.322179\pi$
$314$	−8.54876	−	4.05644i	−0.482435	−	0.228918i
$315$	−1.65257	−	2.86234i	−0.0931119	−	0.161274i
$316$	−1.51733	+	2.62809i	−0.0853564	+	0.147842i
$317$	−18.0156	+	12.4353i	−1.01186	+	0.698435i	−0.953974	−	0.299889i	$-0.903050\pi$
$317$	−18.0156	+	12.4353i	−1.01186	+	0.698435i	−0.0578832	+	0.998323i	$0.518435\pi$
$318$	7.69788	−	10.2440i	0.431676	−	0.574456i
$319$	−8.13479	−	4.69663i	−0.455461	−	0.262961i
$320$	13.6230	−	1.65414i	0.761551	−	0.0924690i
$321$	−0.591372	−	1.24629i	−0.0330071	−	0.0695611i
$322$	12.4721	+	12.9848i	0.695042	+	0.723615i
$323$	−0.00292772	+	0.0362663i	−0.000162903	+	0.00201791i
$324$	−0.183755	+	0.0452915i	−0.0102086	+	0.00251620i
$325$	−8.24875	+	3.23894i	−0.457558	+	0.179664i
$326$	−17.6229	−	4.34365i	−0.976041	−	0.240572i
$327$	−2.42846	+	7.27411i	−0.134294	+	0.402259i
$328$	4.85716	−	10.2363i	0.268192	−	0.565203i
$329$	2.20284	−	0.735416i	0.121446	−	0.0405448i
$330$	−1.83628	−	1.26749i	−0.101084	−	0.0697730i
$331$	−21.3584	+	10.1347i	−1.17397	+	0.557054i	−0.912867	−	0.408258i	$-0.866136\pi$
$331$	−21.3584	+	10.1347i	−1.17397	+	0.557054i	−0.261100	+	0.965312i	$0.584085\pi$
$332$	2.52152	+	0.101614i	0.138386	+	0.00557678i
$333$	1.16364	−	4.72109i	0.0637673	−	0.258714i
$334$	18.9738	+	8.08396i	1.03820	+	0.442335i
$335$	3.05386	−	0.496300i	0.166850	−	0.0271158i
$336$	7.28271	+	1.48678i	0.397304	+	0.0811102i
$337$	−9.64180			−0.525222			−0.262611	−	0.964902i	$-0.584584\pi$
$337$	−9.64180			−0.525222			−0.262611	+	0.964902i	$0.584584\pi$
$338$	−1.00032	+	17.4647i	−0.0544104	+	0.949954i
$339$	3.16744			0.172032
$340$	−0.00149142		0.000304475i	−8.08833e−5		1.65125e-5i
$341$	−4.98894	+	0.810781i	−0.270166	+	0.0439063i
$342$	−8.92900	−	3.80429i	−0.482825	−	0.205713i
$343$	−4.81349	+	19.5291i	−0.259904	+	1.05447i
$344$	0.621117	+	0.0250301i	0.0334884	+	0.00134954i
$345$	9.29752	−	4.41173i	0.500562	−	0.237519i
$346$	−21.0772	−	14.5486i	−1.13312	−	0.782135i
$347$	14.7028	−	4.90853i	0.789289	−	0.263503i	0.106686	−	0.994293i	$-0.465976\pi$
$347$	14.7028	−	4.90853i	0.789289	−	0.263503i	0.682603	+	0.730789i	$0.260848\pi$
$348$	0.732810	−	1.54436i	0.0392828	−	0.0827866i
$349$	7.90267	−	23.6714i	0.423020	−	1.26710i	−0.494419	−	0.869224i	$-0.664619\pi$
$349$	7.90267	−	23.6714i	0.423020	−	1.26710i	0.917439	−	0.397877i	$-0.130253\pi$
$350$	−6.65678	−	1.64075i	−0.355820	−	0.0877017i
$351$	0.821954	−	3.51061i	0.0438727	−	0.187383i
$352$	−1.07726	+	0.265521i	−0.0574182	+	0.0141523i
$353$	1.25026	−	15.4873i	0.0665448	−	0.824305i	−0.874282	−	0.485418i	$-0.838667\pi$
$353$	1.25026	−	15.4873i	0.0665448	−	0.824305i	0.940827	−	0.338887i	$-0.110050\pi$
$354$	−4.62472	−	4.81484i	−0.245801	−	0.255906i
$355$	1.97812	+	4.16880i	0.104988	+	0.221257i
$356$	−1.51586	+	0.184059i	−0.0803406	+	0.00975512i
$357$	−0.00905602	−	0.00522849i	−0.000479295	−	0.000276721i
$358$	9.59159	−	12.7641i	0.506931	−	0.674603i
$359$	−2.51711	+	1.73743i	−0.132848	+	0.0916982i	−0.632635	−	0.774450i	$-0.718027\pi$
$359$	−2.51711	+	1.73743i	−0.132848	+	0.0916982i	0.499788	+	0.866148i	$0.333411\pi$
$360$	2.34853	−	4.06778i	0.123779	−	0.214391i
$361$	16.5113	+	28.5984i	0.869016	+	1.50518i
$362$	−13.1959	−	6.26155i	−0.693563	−	0.329100i
$363$	−8.78238	−	4.60935i	−0.460956	−	0.241928i
$364$	0.881754	−	1.10605i	0.0462165	−	0.0579729i
$365$	−14.3792	+	7.54678i	−0.752641	+	0.395017i
$366$	−1.66382	+	0.0670496i	−0.0869692	+	0.00350474i
$367$	−7.46519	+	36.5669i	−0.389680	+	1.90878i	0.0268179	+	0.999640i	$0.491463\pi$
$367$	−7.46519	+	36.5669i	−0.389680	+	1.90878i	−0.416498	+	0.909137i	$0.636743\pi$
$368$	−6.43897	+	22.2299i	−0.335654	+	1.15881i
$369$	−1.78734	−	3.40548i	−0.0930450	−	0.177282i
$370$	5.57570	+	8.81726i	0.289867	+	0.458388i
$371$	3.16649	−	19.4842i	0.164396	−	1.01157i
$372$	−0.220125	−	0.893082i	−0.0114130	−	0.0463042i
$373$	−5.74590	−	28.1453i	−0.297511	−	1.45731i	−0.803777	−	0.594930i	$-0.797180\pi$
$373$	−5.74590	−	28.1453i	−0.297511	−	1.45731i	0.506266	−	0.862377i	$-0.331025\pi$
$374$	−0.00703643		0.000568039i	−0.000363845		2.93726e-5i
$375$	−6.35528	+	10.0501i	−0.328185	+	0.518983i
$376$	2.47038	+	2.18856i	0.127400	+	0.112866i
$377$	19.8666	+	25.8050i	1.02318	+	1.32903i
$378$	2.08793	−	1.84974i	0.107391	−	0.0951405i
$379$	1.90404	+	11.7160i	0.0978040	+	0.601812i	0.988968	+	0.148131i	$0.0473256\pi$
$379$	1.90404	+	11.7160i	0.0978040	+	0.601812i	−0.891164	+	0.453682i	$0.850110\pi$
$380$	−2.00227	+	0.853085i	−0.102714	+	0.0437624i
$381$	2.85706	−	1.80670i	0.146372	−	0.0925600i
$382$	13.4452	−	15.1765i	0.687916	−	0.776497i
$383$	1.55630	+	19.2783i	0.0795234	+	0.985074i	0.906325	+	0.422581i	$0.138876\pi$
$383$	1.55630	+	19.2783i	0.0795234	+	0.985074i	−0.826802	+	0.562493i	$0.809842\pi$
$384$	2.99192	+	8.96191i	0.152681	+	0.457335i
$385$	−3.41215	−	0.414310i	−0.173899	−	0.0211152i
$386$	16.0140	+	12.0337i	0.815091	+	0.612501i
$387$	0.133452	−	0.163448i	0.00678372	−	0.00830855i
$388$	−1.62613	−	1.32770i	−0.0825545	−	0.0674036i
$389$	−5.03663	−	7.29682i	−0.255367	−	0.369963i	0.674242	−	0.738511i	$-0.264471\pi$
$389$	−5.03663	−	7.29682i	−0.255367	−	0.369963i	−0.929609	+	0.368547i	$0.879855\pi$
$390$	4.21050	+	6.48948i	0.213207	+	0.328608i
$391$	0.0184960	−	0.0267960i	0.000935381	−	0.00135513i
$392$	−7.64817	+	2.21532i	−0.386291	+	0.111890i
$393$	−6.86908	−	4.34374i	−0.346499	−	0.219113i
$394$	20.6982	+	3.36379i	1.04276	+	0.169465i
$395$	−23.9048	−	9.06588i	−1.20278	−	0.456154i
$396$	−0.0771456	+	0.181067i	−0.00387671	+	0.00909898i
$397$	13.4084	+	12.8789i	0.672946	+	0.646373i	0.949186	−	0.314715i	$-0.101909\pi$
$397$	13.4084	+	12.8789i	0.672946	+	0.646373i	−0.276240	+	0.961089i	$0.589089\pi$
$398$	−10.0098	+	19.0720i	−0.501744	+	0.955994i
$399$	−14.9030	+	1.20310i	−0.746084	+	0.0602301i
$400$	−2.45193	−	8.46505i	−0.122597	−	0.423253i
$401$	−4.61048	+	4.42843i	−0.230236	+	0.221145i	−0.798961	−	0.601383i	$-0.794617\pi$
$401$	−4.61048	+	4.42843i	−0.230236	+	0.221145i	0.568724	+	0.822528i	$0.307437\pi$
$402$	0.925937	+	2.44150i	0.0461816	+	0.121771i
$403$	17.0622	+	3.99485i	0.849929	+	0.198997i
$404$	0.258402	−	0.681349i	0.0128560	−	0.0338984i
$405$	−0.624958	−	1.46683i	−0.0310544	−	0.0728874i
$406$	1.01451	+	25.1747i	0.0503491	+	1.24940i
$407$	−3.19807	−	3.91693i	−0.158523	−	0.194155i
$408$		−	0.0148608i		−	0.000735720i
$409$	−26.4189	+	21.5704i	−1.30633	+	1.06659i	−0.313185	+	0.949692i	$0.601396\pi$
$409$	−26.4189	+	21.5704i	−1.30633	+	1.06659i	−0.993144	+	0.116893i	$0.962706\pi$
$410$	7.92588	+	2.29576i	0.391431	+	0.113380i
$411$	−10.5029	−	11.8554i	−0.518072	−	0.584782i
$412$	2.34928	−	2.44586i	0.115741	−	0.120499i
$413$	−9.75526	−	3.25678i	−0.480025	−	0.160256i
$414$	5.21769	+	6.94348i	0.256435	+	0.341253i
$415$	2.56265	+	21.1053i	0.125796	+	1.03602i
$416$	3.80378	+	0.572698i	0.186496	+	0.0280788i
$417$	−0.624844	+	5.14605i	−0.0305987	+	0.252003i
$418$	−8.74121	+	5.04674i	−0.427547	+	0.246844i
$419$	−6.99907	+	5.25946i	−0.341927	+	0.256942i	−0.757808	−	0.652477i	$-0.773730\pi$
$419$	−6.99907	+	5.25946i	−0.341927	+	0.256942i	0.415881	+	0.909419i	$0.363473\pi$
$420$	0.0251869	−	0.625005i	0.00122899	−	0.0304971i
$421$	1.32770	−	0.503529i	0.0647080	−	0.0245405i	−0.322039	−	0.946727i	$-0.604368\pi$
$421$	1.32770	−	0.503529i	0.0647080	−	0.0245405i	0.386747	+	0.922186i	$0.373599\pi$
$422$	−19.2625	+	3.93247i	−0.937684	+	0.191430i
$423$	1.09767	−	0.224092i	0.0533707	−	0.0108957i
$424$	26.2300	−	9.94772i	1.27384	−	0.483104i
$425$	−0.000499240		0.0123885i	−2.42167e−5		0.000600931i
$426$	−3.11330	+	2.33949i	−0.150840	+	0.113349i
$427$	−2.22151	+	1.28259i	−0.107507	+	0.0620689i
$428$	0.0314688	−	0.259168i	0.00152110	−	0.0125274i
$429$	−2.40517	−	2.87661i	−0.116122	−	0.138884i
$430$	0.0545695	+	0.449420i	0.00263158	+	0.0216730i
$431$	−2.77829	−	3.69724i	−0.133826	−	0.178090i	0.727555	−	0.686049i	$-0.240656\pi$
$431$	−2.77829	−	3.69724i	−0.133826	−	0.178090i	−0.861381	+	0.507959i	$0.830400\pi$
$432$	3.40114	+	1.13547i	0.163638	+	0.0546302i
$433$	−5.12430	+	5.33496i	−0.246258	+	0.256382i	−0.832847	−	0.553503i	$-0.813291\pi$
$433$	−5.12430	+	5.33496i	−0.246258	+	0.256382i	0.586589	+	0.809885i	$0.300470\pi$
$434$	8.99009	+	10.1477i	0.431538	+	0.487106i
$435$	13.8327	+	4.00669i	0.663227	+	0.192106i
$436$	−1.12422	+	0.917899i	−0.0538405	+	0.0439594i
$437$		−	46.5540i		−	2.22698i
$438$	−8.66797	−	10.6163i	−0.414172	−	0.507268i
$439$	−0.237871	−	5.90271i	−0.0113530	−	0.281721i	−0.994887	−	0.100997i	$-0.967797\pi$
$439$	−0.237871	−	5.90271i	−0.0113530	−	0.281721i	0.983534	−	0.180724i	$-0.0578442\pi$
$440$	−1.91466	−	4.49387i	−0.0912779	−	0.214237i
$441$	−0.958455	+	2.52724i	−0.0456407	+	0.120345i
$442$	0.0218026	+	0.0111203i	0.00103704	+	0.000528940i
$443$	12.5530	+	33.0995i	0.596411	+	1.57261i	0.804152	+	0.594423i	$0.202620\pi$
$443$	12.5530	+	33.0995i	0.596411	+	1.57261i	−0.207741	+	0.978184i	$0.566611\pi$
$444$	0.663670	−	0.637463i	0.0314964	−	0.0302527i
$445$	−3.57914	−	12.3566i	−0.169667	−	0.585760i
$446$	23.2294	−	1.87527i	1.09995	−	0.0887968i
$447$	−9.75973	+	18.5956i	−0.461619	+	0.879542i
$448$	12.8676	+	12.3595i	0.607935	+	0.583930i
$449$	0.596116	−	1.39914i	0.0281325	−	0.0660293i	−0.905321	−	0.424729i	$-0.860369\pi$
$449$	0.596116	−	1.39914i	0.0281325	−	0.0660293i	0.933453	+	0.358699i	$0.116780\pi$
$450$	−3.09244	−	1.17281i	−0.145779	−	0.0552867i
$451$	−3.94791	−	0.641598i	−0.185900	−	0.0302117i
$452$	0.506651	+	0.320387i	0.0238309	+	0.0150697i
$453$	10.5553	−	3.05737i	0.495929	−	0.143648i
$454$	6.00896	−	8.70548i	0.282014	−	0.408568i
$455$	10.3891	+	5.83759i	0.487050	+	0.273671i
$456$	−12.0703	−	17.4869i	−0.565245	−	0.818898i
$457$	9.56095	+	7.80627i	0.447242	+	0.365162i	0.829139	−	0.559043i	$-0.188831\pi$
$457$	9.56095	+	7.80627i	0.447242	+	0.365162i	−0.381896	+	0.924205i	$0.624729\pi$
$458$	−18.5119	+	22.6730i	−0.865005	+	1.05944i
$459$	−0.00403279	−	0.00303044i	−0.000188234	−	0.000141449i
$460$	1.93344	+	0.234762i	0.0901470	+	0.0109458i
$461$	10.7365	+	32.1599i	0.500050	+	1.49783i	0.832129	+	0.554582i	$0.187122\pi$
$461$	10.7365	+	32.1599i	0.500050	+	1.49783i	−0.332079	+	0.943252i	$0.607750\pi$
$462$	−0.233426	−	2.89150i	−0.0108600	−	0.134525i
$463$	−13.0465	+	14.7264i	−0.606320	+	0.684394i	−0.968870	−	0.247570i	$-0.920368\pi$
$463$	−13.0465	+	14.7264i	−0.606320	+	0.684394i	0.362550	+	0.931964i	$0.381906\pi$
$464$	−27.3732	+	17.3097i	−1.27077	+	0.803585i
$465$	7.12906	−	3.03741i	0.330602	−	0.140856i
$466$	−5.85853	−	36.0490i	−0.271391	−	1.66994i
$467$	−5.50552	+	4.87747i	−0.254765	+	0.225702i	−0.780832	−	0.624741i	$-0.785205\pi$
$467$	−5.50552	+	4.87747i	−0.254765	+	0.225702i	0.526067	+	0.850443i	$0.323666\pi$
$468$	0.486575	−	0.478402i	0.0224919	−	0.0221142i
$469$	3.01089	+	2.66742i	0.139030	+	0.123170i
$470$	−1.28467	+	2.03154i	−0.0592572	+	0.0937078i
$471$	−7.00906	−	0.565830i	−0.322960	−	0.0260721i
$472$	−2.92352	−	14.3204i	−0.134566	−	0.659148i
$473$	−0.0525156	−	0.213064i	−0.00241467	−	0.00979669i
$474$	3.46121	−	21.2977i	0.158978	−	0.978234i
$475$	9.47478	+	14.9832i	0.434733	+	0.687475i
$476$	−0.000919701	−	0.00175234i	−4.21544e−5	−	8.03186e-5i
$477$	2.64934	−	9.14660i	0.121305	−	0.418794i
$478$	4.08547	−	20.0120i	0.186865	−	0.915326i
$479$	−0.473340	+	0.0190749i	−0.0216274	+	0.000871556i	−0.0510773	−	0.998695i	$-0.516265\pi$
$479$	−0.473340	+	0.0190749i	−0.0216274	+	0.000871556i	0.0294499	+	0.999566i	$0.490624\pi$
$480$	1.50619	−	0.790510i	0.0687479	−	0.0360817i
$481$	5.07376	+	16.7813i	0.231344	+	0.765162i
$482$	4.68658	+	2.45971i	0.213468	+	0.112037i
$483$	12.0880	+	5.73582i	0.550023	+	0.260989i
$484$	−0.938558	−	1.62563i	−0.0426617	−	0.0738923i
$485$	8.84305	−	15.3166i	0.401542	−	0.695491i
$486$	1.10744	−	0.764410i	0.0502345	−	0.0346744i
$487$	5.50173	−	7.32148i	0.249307	−	0.331768i	−0.657389	−	0.753551i	$-0.728339\pi$
$487$	5.50173	−	7.32148i	0.249307	−	0.331768i	0.906697	+	0.421783i	$0.138596\pi$
$488$	−3.15708	−	1.82274i	−0.142914	−	0.0825115i
$489$	−13.3899	+	1.62583i	−0.605511	+	0.0735224i
$490$	−2.48601	−	5.23916i	−0.112307	−	0.236681i
$491$	−15.8519	−	16.5036i	−0.715387	−	0.744797i	0.259925	−	0.965629i	$-0.416302\pi$
$491$	−15.8519	−	16.5036i	−0.715387	−	0.744797i	−0.975312	+	0.220832i	$0.929123\pi$
$492$	0.0585697	−	0.725516i	0.00264053	−	0.0327088i
$493$	0.0442396	−	0.0109041i	0.00199245	−	0.000491095i
$494$	34.6875	−	4.62318i	1.56066	−	0.208007i
$495$	−1.60994	−	0.396816i	−0.0723616	−	0.0178355i
$496$	−5.51858	+	16.5302i	−0.247792	+	0.742227i
$497$	−2.57181	+	5.41998i	−0.115362	+	0.243119i
$498$	−17.0197	+	5.68200i	−0.762670	+	0.254617i
$499$	−6.49730	−	4.48476i	−0.290859	−	0.200766i	0.413695	−	0.910415i	$-0.364238\pi$
$499$	−6.49730	−	4.48476i	−0.290859	−	0.200766i	−0.704555	+	0.709650i	$0.748853\pi$
$500$	−2.03313	+	0.964731i	−0.0909242	+	0.0431441i
$501$	15.3142	+	0.617141i	0.684188	+	0.0275718i
$502$	−8.63805	+	35.0459i	−0.385535	+	1.56418i
$503$	−13.9558	−	5.94603i	−0.622260	−	0.265120i	0.0577405	−	0.998332i	$-0.481610\pi$
$503$	−13.9558	−	5.94603i	−0.622260	−	0.265120i	−0.680001	+	0.733211i	$0.738021\pi$
$504$	6.02772	−	0.979600i	0.268496	−	0.0436348i
$505$	6.01506	+	1.22798i	0.267666	+	0.0546445i
$506$	9.03246			0.401542
$507$	3.90725	+	12.3989i	0.173527	+	0.550656i
$508$	0.639752			0.0283844
$509$	3.98516	+	0.813577i	0.176639	+	0.0360612i	0.287531	−	0.957771i	$-0.407166\pi$
$509$	3.98516	+	0.813577i	0.176639	+	0.0360612i	−0.110892	+	0.993832i	$0.535371\pi$
$510$	0.0106829	−	0.00173613i	0.000473045	−	7.68773e-5i
$511$	−19.4237	−	8.27568i	−0.859255	−	0.366094i
$512$	−5.97137	+	24.2268i	−0.263900	+	1.07068i
$513$	−7.20682	−	0.290425i	−0.318189	−	0.0128226i
$514$	6.93107	−	3.28883i	0.305716	−	0.145064i
$515$	23.5137	+	16.2303i	1.03614	+	0.715194i
$516$	0.0378792	−	0.0126459i	0.00166754	−	0.000556706i
$517$	0.499462	−	1.05259i	0.0219663	−	0.0462930i
$518$	−4.29507	+	12.8653i	−0.188715	+	0.565270i
$519$	−18.4793	−	4.55475i	−0.811153	−	0.199931i
$520$	0.197627	+	16.9344i	0.00866651	+	0.742621i
$521$	−20.8994	+	5.15123i	−0.915618	+	0.225680i	−0.668852	−	0.743396i	$-0.733214\pi$
$521$	−20.8994	+	5.15123i	−0.915618	+	0.225680i	−0.246766	+	0.969075i	$0.579368\pi$
$522$	−0.978012	+	12.1148i	−0.0428064	+	0.530252i
$523$	7.23154	+	7.52883i	0.316213	+	0.329213i	0.860273	−	0.509834i	$-0.170293\pi$
$523$	7.23154	+	7.52883i	0.316213	+	0.329213i	−0.544060	+	0.839046i	$0.683114\pi$
$524$	−0.659380	−	1.38961i	−0.0288051	−	0.0607055i
$525$	−5.05783	+	0.614131i	−0.220742	+	0.0268029i
$526$	−11.4264	−	6.59705i	−0.498216	−	0.287645i
$527$	0.0147285	−	0.0196001i	0.000641584	−	0.000853793i
$528$	3.06887	−	2.11829i	0.133555	−	0.0921866i
$529$	−9.33014	+	16.1603i	−0.405658	+	0.702621i
$530$	10.2154	+	17.6936i	0.443728	+	0.768559i
$531$	−4.48229	−	2.12687i	−0.194515	−	0.0922985i
$532$	−2.50552	−	1.31500i	−0.108628	−	0.0570124i
$533$	11.8060	+	7.27418i	0.511373	+	0.315080i
$534$	9.61365	−	5.04563i	0.416023	−	0.218346i
$535$	2.19768	−	0.0885633i	0.0950138	−	0.00382893i
$536$	−1.14345	+	5.60101i	−0.0493897	+	0.241927i
$537$	3.30110	−	11.3967i	0.142453	−	0.491804i
$538$	−13.0700	−	24.9029i	−0.563489	−	1.07364i
$539$	1.50232	+	2.37573i	0.0647096	+	0.102330i
$540$	0.0484041	−	0.297842i	0.00208298	−	0.0128171i
$541$	6.65188	+	26.9878i	0.285987	+	1.16029i	0.921555	+	0.388249i	$0.126920\pi$
$541$	6.65188	+	26.9878i	0.285987	+	1.16029i	−0.635568	+	0.772045i	$0.719234\pi$
$542$	−1.81752	−	8.90280i	−0.0780691	−	0.382408i
$543$	−10.8192	−	0.873418i	−0.464298	−	0.0374820i
$544$	0.00287640	−	0.00454866i	0.000123325	−	0.000195022i
$545$	−9.15220	−	8.10814i	−0.392037	−	0.347315i
$546$	−3.07334	+	9.57640i	−0.131527	+	0.409832i
$547$	23.9608	−	21.2275i	1.02449	−	0.907620i	0.0287295	−	0.999587i	$-0.490854\pi$
$547$	23.9608	−	21.2275i	1.02449	−	0.907620i	0.995762	+	0.0919669i	$0.0293154\pi$
$548$	−0.480837	−	2.95871i	−0.0205403	−	0.126390i
$549$	−1.13843	+	0.485041i	−0.0485872	+	0.0207011i
$550$	−2.90705	+	1.83831i	−0.123957	+	0.0783857i
$551$	43.2006	−	48.7634i	1.84041	−	2.07739i
$552$	1.53004	+	18.9529i	0.0651226	+	0.806689i
$553$	−10.5258	−	31.5287i	−0.447604	−	1.34074i
$554$	18.1429	+	2.20294i	0.770816	+	0.0935940i
$555$	6.19781	+	4.65735i	0.263082	+	0.197693i
$556$	−0.620470	+	0.759938i	−0.0263138	+	0.0322286i
$557$	−15.8215	−	12.9179i	−0.670380	−	0.547349i	0.234976	−	0.972001i	$-0.424499\pi$
$557$	−15.8215	−	12.9179i	−0.670380	−	0.547349i	−0.905356	+	0.424653i	$0.860396\pi$
$558$	3.71517	+	5.38236i	0.157276	+	0.227853i
$559$	−0.113270	+	0.752324i	−0.00479081	+	0.0318199i
$560$	−6.73223	+	9.75332i	−0.284489	+	0.412153i
$561$	−0.00503895	+	0.00145955i	−0.000212744	+	6.16222e-5i
$562$	10.9960	+	6.95346i	0.463839	+	0.293314i
$563$	−28.5645	−	4.64219i	−1.20385	−	0.195645i	−0.474794	−	0.880097i	$-0.657477\pi$
$563$	−28.5645	−	4.64219i	−1.20385	−	0.195645i	−0.729058	+	0.684452i	$0.760042\pi$
$564$	0.198246	+	0.0751849i	0.00834767	+	0.00316585i
$565$	−1.97952	+	4.64610i	−0.0832789	+	0.195463i
$566$	−11.2576	−	10.8130i	−0.473191	−	0.454506i
$567$	0.963348	−	1.83551i	0.0404568	−	0.0770840i
$568$	−8.49805	+	0.686033i	−0.356570	+	0.0287853i
$569$	−1.62523	−	5.61096i	−0.0681334	−	0.235224i	0.919224	−	0.393736i	$-0.128817\pi$
$569$	−1.62523	−	5.61096i	−0.0681334	−	0.235224i	−0.987357	+	0.158512i	$0.949330\pi$
$570$	11.1605	−	10.7198i	0.467462	−	0.449003i
$571$	9.61939	+	25.3643i	0.402559	+	1.06146i	0.971072	+	0.238787i	$0.0767497\pi$
$571$	9.61939	+	25.3643i	0.402559	+	1.06146i	−0.568513	+	0.822674i	$0.692481\pi$
$572$	−0.0937515	−	0.703413i	−0.00391995	−	0.0294112i
$573$	5.34305	−	14.0885i	0.223209	−	0.588554i
$574$	4.20512	+	9.86978i	0.175518	+	0.411957i
$575$	−0.638781	−	15.8512i	−0.0266390	−	0.661041i
$576$	5.44344	+	6.66700i	0.226810	+	0.277792i
$577$		−	14.7889i		−	0.615672i	−0.951439	−	0.307836i	$-0.900395\pi$
$577$		−	14.7889i		−	0.615672i	0.951439	−	0.307836i	$-0.0996047\pi$
$578$	−17.7197	+	14.4677i	−0.737044	+	0.601778i
$579$	14.2984	+	4.14160i	0.594223	+	0.172119i
$580$	1.80734	+	2.04007i	0.0750459	+	0.0847093i
$581$	−19.1478	+	19.9349i	−0.794383	+	0.827040i
$582$	14.1584	+	4.72676i	0.586883	+	0.195930i
$583$	−5.94920	−	7.91694i	−0.246391	−	0.327886i
$584$	−3.61668	−	29.7860i	−0.149659	−	1.23255i
$585$	4.63578	+	3.39965i	0.191666	+	0.140558i
$586$	−1.13428	+	9.34162i	−0.0468566	+	0.385899i
$587$	18.9023	−	10.9133i	0.780183	−	0.450439i	−0.0563124	−	0.998413i	$-0.517934\pi$
$587$	18.9023	−	10.9133i	0.780183	−	0.450439i	0.836495	+	0.547975i	$0.184601\pi$
$588$	−0.408940	+	0.307299i	−0.0168644	+	0.0126728i
$589$	1.41152	−	35.0265i	0.0581606	−	1.44324i
$590$	9.95280	−	3.77460i	0.409750	−	0.155398i
$591$	15.2686	−	3.11710i	0.628065	−	0.128220i
$592$	−17.0826	+	3.48743i	−0.702089	+	0.143333i
$593$	3.89178	−	1.47596i	0.159816	−	0.0606104i	−0.273399	−	0.961901i	$-0.588148\pi$
$593$	3.89178	−	1.47596i	0.159816	−	0.0606104i	0.433216	+	0.901290i	$0.357379\pi$
$594$	0.0563486	−	1.39827i	0.00231201	−	0.0573719i
$595$	0.0133289	−	0.0100160i	0.000546433	−	0.000410618i
$596$	−3.44207	+	1.98728i	−0.140993	+	0.0814022i
$597$	−1.92939	+	15.8900i	−0.0789647	+	0.650333i
$598$	−28.9510	−	11.9377i	−1.18390	−	0.488167i
$599$	2.17324	+	17.8982i	0.0887960	+	0.731301i	0.967312	+	0.253588i	$0.0816108\pi$
$599$	2.17324	+	17.8982i	0.0887960	+	0.731301i	−0.878516	+	0.477712i	$0.841466\pi$
$600$	−4.34977	−	5.78849i	−0.177579	−	0.236314i
$601$	19.8580	+	6.62957i	0.810025	+	0.270426i	0.691362	−	0.722509i	$-0.257011\pi$
$601$	19.8580	+	6.62957i	0.810025	+	0.270426i	0.118663	+	0.992935i	$0.462139\pi$
$602$	−0.407735	+	0.424498i	−0.0166181	+	0.0173012i
$603$	1.28677	+	1.45247i	0.0524015	+	0.0591490i
$604$	1.99763	+	0.578620i	0.0812823	+	0.0235437i
$605$	12.2498	−	10.0016i	0.498023	−	0.406623i
$606$			5.18124i			0.210473i
$607$	−16.1506	−	19.7809i	−0.655534	−	0.802883i	0.334696	−	0.942326i	$-0.391366\pi$
$607$	−16.1506	−	19.7809i	−0.655534	−	0.802883i	−0.990230	+	0.139443i	$0.955469\pi$
$608$	−0.309845	−	7.68874i	−0.0125659	−	0.311819i
$609$	7.33901	+	17.2253i	0.297392	+	0.698004i
$610$	0.941466	−	2.48244i	0.0381188	−	0.100511i
$611$	−2.99203	+	2.71369i	−0.121045	+	0.109784i
$612$	−0.000338539	0	0.000892653i	−1.36846e−5	0	3.60834e-5i
$613$	−2.51746	+	2.41805i	−0.101679	+	0.0976643i	−0.741841	−	0.670576i	$-0.766047\pi$
$613$	−2.51746	+	2.41805i	−0.101679	+	0.0976643i	0.640161	+	0.768240i	$0.278867\pi$
$614$	−8.78567	−	30.3317i	−0.354561	−	1.22409i
$615$	6.11227	−	0.493434i	0.246471	−	0.0198972i
$616$	2.95137	−	5.62337i	0.118914	−	0.226572i
$617$	−8.74639	−	8.40102i	−0.352116	−	0.338212i	0.495708	−	0.868489i	$-0.334909\pi$
$617$	−8.74639	−	8.40102i	−0.352116	−	0.338212i	−0.847825	+	0.530277i	$0.822088\pi$
$618$	−9.45161	+	22.1837i	−0.380200	+	0.892361i
$619$	−7.62133	−	2.89039i	−0.306327	−	0.116174i	0.196651	−	0.980473i	$-0.436993\pi$
$619$	−7.62133	−	2.89039i	−0.306327	−	0.116174i	−0.502978	+	0.864299i	$0.667762\pi$
$620$	1.44757	+	0.235253i	0.0581358	+	0.00944798i
$621$	5.45526	+	3.44970i	0.218912	+	0.138432i
$622$	−21.9343	+	6.35334i	−0.879485	+	0.254746i
$623$	9.50122	−	13.7649i	0.380658	−	0.551479i
$624$	−12.6360	+	2.73364i	−0.505846	+	0.109433i
$625$	−3.78890	−	5.48917i	−0.151556	−	0.219567i
$626$	−31.8436	−	25.9995i	−1.27272	−	1.03915i
$627$	−4.74390	+	5.81022i	−0.189453	+	0.232038i
$628$	−1.06391	−	0.799474i	−0.0424545	−	0.0319025i
$629$	0.0243494	+	0.00295656i	0.000970876	+	0.000117886i
$630$	1.40839	+	4.21865i	0.0561116	+	0.168075i
$631$	−0.749424	−	9.28329i	−0.0298341	−	0.369562i	−0.994397	−	0.105709i	$-0.966289\pi$
$631$	−0.749424	−	9.28329i	−0.0298341	−	0.369562i	0.964563	−	0.263853i	$-0.0849933\pi$
$632$	31.3244	−	35.3579i	1.24602	−	1.40646i
$633$	−12.3482	+	7.80856i	−0.490799	+	0.310362i
$634$	27.0997	−	11.5461i	1.07627	−	0.458554i
$635$	0.864574	+	5.31994i	0.0343096	+	0.211115i
$636$	1.34896	−	1.19507i	0.0534896	−	0.0473876i
$637$	−1.67541	−	9.60028i	−0.0663822	−	0.380377i
$638$	9.46112	+	8.38182i	0.374569	+	0.331840i
$639$	−1.54677	+	2.44602i	−0.0611891	+	0.0967629i
$640$	−15.0154	−	1.21217i	−0.593536	−	0.0479152i
$641$	3.99002	+	19.5444i	0.157596	+	0.771958i	0.979359	+	0.202128i	$0.0647858\pi$
$641$	3.99002	+	19.5444i	0.157596	+	0.771958i	−0.821763	+	0.569830i	$0.807009\pi$
$642$	0.444237	+	1.80234i	0.0175326	+	0.0711326i
$643$	6.44952	−	39.6855i	0.254344	−	1.56504i	−0.474433	−	0.880292i	$-0.657347\pi$
$643$	6.44952	−	39.6855i	0.254344	−	1.56504i	0.728777	−	0.684751i	$-0.240089\pi$
$644$	1.35337	+	2.14018i	0.0533301	+	0.0843349i
$645$	0.156350	+	0.297899i	0.00615626	+	0.0117298i
$646$	0.0136216	−	0.0470271i	0.000535933	−	0.00185026i
$647$	−4.88446	+	23.9257i	−0.192028	+	0.940615i	0.763521	+	0.645783i	$0.223469\pi$
$647$	−4.88446	+	23.9257i	−0.192028	+	0.940615i	−0.955549	+	0.294832i	$0.904736\pi$
$648$	2.94356	−	0.118621i	0.115634	−	0.00465989i
$649$	−4.56856	+	2.39776i	−0.179332	+	0.0941205i
$650$	11.7473	−	2.05011i	0.460768	−	0.0804118i
$651$	8.92089	+	4.68204i	0.349637	+	0.183504i
$652$	−2.30624	−	1.09433i	−0.0903194	−	0.0428571i
$653$	−15.2836	−	26.4720i	−0.598094	−	1.03593i	−0.993102	−	0.117251i	$-0.962592\pi$
$653$	−15.2836	−	26.4720i	−0.598094	−	1.03593i	0.395008	−	0.918678i	$-0.370742\pi$
$654$	5.15970	−	8.93687i	0.201760	−	0.349459i
$655$	10.6644	−	7.36111i	0.416693	−	0.287622i
$656$	−8.28459	+	11.0248i	−0.323459	+	0.430445i
$657$	−8.82057	−	5.09256i	−0.344123	−	0.198680i
$658$	−3.10227	+	0.376684i	−0.120939	+	0.0146847i
$659$	−7.12482	−	15.0152i	−0.277544	−	0.584911i	0.716034	−	0.698066i	$-0.245956\pi$
$659$	−7.12482	−	15.0152i	−0.277544	−	0.584911i	−0.993577	+	0.113155i	$0.963904\pi$
$660$	−0.217382	−	0.226319i	−0.00846159	−	0.00880945i
$661$	−3.94723	+	48.8952i	−0.153529	+	1.90180i	0.222085	+	0.975027i	$0.428714\pi$
$661$	−3.94723	+	48.8952i	−0.153529	+	1.90180i	−0.375615	+	0.926776i	$0.622568\pi$
$662$	30.8878	−	7.61316i	1.20049	−	0.295894i
$663$	0.0180799	+	0.00198150i	0.000702167	+	7.69550e-5i
$664$	−38.1405	−	9.40080i	−1.48014	−	0.364822i
$665$	7.54902	−	22.6121i	0.292738	−	0.876859i
$666$	−2.80494	+	5.91129i	−0.108689	+	0.229058i
$667$	−55.2987	+	18.4614i	−2.14117	+	0.714829i
$668$	2.38717	+	1.64775i	0.0923624	+	0.0637532i
$669$	15.6468	−	7.42449i	0.604939	−	0.287047i
$670$	−4.15993	−	0.167639i	−0.160712	−	0.00647648i
$671$	−0.307976	+	1.24951i	−0.0118893	+	0.0482367i
$672$	2.03460	+	0.866860i	0.0784862	+	0.0334399i
$673$	20.0864	−	3.26435i	0.774272	−	0.125831i	0.239578	−	0.970877i	$-0.422991\pi$
$673$	20.0864	−	3.26435i	0.774272	−	0.125831i	0.534694	+	0.845046i	$0.320427\pi$
$674$	12.7122	+	2.59521i	0.489655	+	0.0999638i
$675$	−2.45784			−0.0946022
$676$	−0.629164	+	2.37850i	−0.0241986	+	0.0914807i
$677$	−43.0078			−1.65292			−0.826462	−	0.562992i	$-0.809650\pi$
$677$	−43.0078			−1.65292			−0.826462	+	0.562992i	$0.809650\pi$
$678$	−4.17610	−	0.852557i	−0.160382	−	0.0327422i
$679$	22.6965	−	3.68854i	0.871011	−	0.141553i
$680$	0.0217983	+	0.00928739i	0.000835927	+	0.000356155i
$681$	1.88124	−	7.63248i	0.0720892	−	0.292477i
$682$	6.79587	+	0.273864i	0.260227	+	0.0104868i
$683$	29.4015	−	13.9512i	1.12502	−	0.533827i	0.227047	−	0.973884i	$-0.427093\pi$
$683$	29.4015	−	13.9512i	1.12502	−	0.533827i	0.897970	+	0.440057i	$0.145042\pi$
$684$	−1.12340	−	0.775425i	−0.0429541	−	0.0296491i
$685$	23.9537	−	7.99692i	0.915224	−	0.305547i
$686$	11.6028	−	24.4525i	0.442998	−	0.933599i
$687$	−6.88817	+	20.6326i	−0.262800	+	0.787182i
$688$	−0.734623	−	0.181068i	−0.0280072	−	0.00690317i
$689$	8.60514	+	33.2383i	0.327830	+	1.26628i
$690$	−13.4457	+	3.31408i	−0.511871	+	0.126165i
$691$	−1.78208	+	22.0750i	−0.0677936	+	0.839774i	0.870105	+	0.492866i	$0.164051\pi$
$691$	−1.78208	+	22.0750i	−0.0677936	+	0.839774i	−0.937899	+	0.346908i	$0.887232\pi$
$692$	−2.49517	−	2.59774i	−0.0948520	−	0.0987514i
$693$	−0.924168	−	1.94764i	−0.0351062	−	0.0739848i
$694$	−20.7061	+	2.51417i	−0.785991	+	0.0954366i
$695$	−7.15788	−	4.13260i	−0.271514	−	0.156759i
$696$	−15.9850	+	21.2722i	−0.605910	+	0.806320i
$697$	0.0159669	−	0.0110212i	0.000604790	−	0.000417456i
$698$	−16.7907	+	29.0823i	−0.635537	+	1.10078i
$699$	−13.5705	−	23.5047i	−0.513282	−	0.889031i
$700$	−0.871148	−	0.413365i	−0.0329263	−	0.0156237i
$701$	4.84654	+	2.54366i	0.183051	+	0.0960728i	0.553760	−	0.832677i	$-0.313193\pi$
$701$	4.84654	+	2.54366i	0.183051	+	0.0960728i	−0.370708	+	0.928749i	$0.620885\pi$
$702$	−2.02863	+	4.40731i	−0.0765656	+	0.166343i
$703$	31.0536	−	16.2982i	1.17121	−	0.614698i
$704$	8.94364	−	0.360416i	0.337076	−	0.0135837i
$705$	−0.357295	+	1.75015i	−0.0134565	+	0.0659144i
$706$	−5.81700	+	20.0826i	−0.218926	+	0.755819i
$707$	3.70926	+	7.06741i	0.139501	+	0.265797i
$708$	−0.501836	−	0.793590i	−0.0188601	−	0.0298249i
$709$	2.55955	−	15.7496i	0.0961260	−	0.591487i	−0.893640	−	0.448785i	$-0.851857\pi$
$709$	2.55955	−	15.7496i	0.0961260	−	0.591487i	0.989766	−	0.142702i	$-0.0455790\pi$
$710$	−1.48596	−	6.02876i	−0.0557670	−	0.226255i
$711$	−3.20737	−	15.7108i	−0.120286	−	0.589199i
$712$	23.6923	+	1.91264i	0.887906	+	0.0716792i
$713$	−16.7662	+	26.5136i	−0.627898	+	0.992941i
$714$	0.0105325	+	0.00933102i	0.000394171	+	0.000349205i
$715$	5.72262	−	1.73021i	0.214014	−	0.0647062i
$716$	1.68081	−	1.48906i	0.0628147	−	0.0556489i
$717$	−2.43480	−	14.9819i	−0.0909292	−	0.559510i
$718$	3.78632	−	1.61320i	0.141304	−	0.0602041i
$719$	25.5025	−	16.1268i	0.951081	−	0.601427i	0.0336977	−	0.999432i	$-0.489272\pi$
$719$	25.5025	−	16.1268i	0.951081	−	0.601427i	0.917383	+	0.398005i	$0.130297\pi$
$720$	−3.79111	+	4.27928i	−0.141286	+	0.159479i
$721$	2.98904	+	37.0260i	0.111318	+	1.37892i
$722$	−14.0716	−	42.1497i	−0.523692	−	1.56865i
$723$	3.90465	+	0.474110i	0.145215	+	0.0176324i
$724$	−1.64225	−	1.23407i	−0.0610338	−	0.0458640i
$725$	14.0403	−	17.1962i	0.521443	−	0.638652i
$726$	10.3384	+	8.44106i	0.383695	+	0.313277i
$727$	−21.7474	−	31.5065i	−0.806566	−	1.16851i	−0.982892	−	0.184180i	$-0.941037\pi$
$727$	−21.7474	−	31.5065i	−0.806566	−	1.16851i	0.176327	−	0.984332i	$-0.443578\pi$
$728$	−16.8919	+	14.1235i	−0.626055	+	0.523452i
$729$	0.568065	−	0.822984i	0.0210394	−	0.0304809i
$730$	20.9895	−	6.07968i	0.776856	−	0.225019i
$731$	0.000899649	0	0.000568903i	3.32747e−5	0	2.10416e-5i
$732$	−0.231161	−	0.0375673i	−0.00854396	−	0.00138853i
$733$	43.3203	+	16.4292i	1.60007	+	0.606827i	0.983570	−	0.180526i	$-0.0577799\pi$
$733$	43.3203	+	16.4292i	1.60007	+	0.606827i	0.616502	+	0.787353i	$0.288549\pi$
$734$	19.6849	−	46.2021i	0.726582	−	1.70535i
$735$	−3.10803	−	2.98531i	−0.114642	−	0.110115i
$736$	−3.20012	+	6.09733i	−0.117958	+	0.224750i
$737$	2.01147	−	0.162383i	0.0740935	−	0.00598144i
$738$	1.43988	+	4.97103i	0.0530025	+	0.182986i
$739$	−18.2755	+	17.5539i	−0.672276	+	0.645730i	−0.949021	−	0.315213i	$-0.897924\pi$
$739$	−18.2755	+	17.5539i	−0.672276	+	0.645730i	0.276744	+	0.960944i	$0.410744\pi$
$740$	0.520285	+	1.37188i	0.0191261	+	0.0504313i
$741$	22.8843	−	12.3533i	0.840674	−	0.453810i
$742$	−9.41925	+	24.8365i	−0.345791	+	0.911777i
$743$	−6.88974	−	16.1708i	−0.252760	−	0.593249i	0.744468	−	0.667658i	$-0.232703\pi$
$743$	−6.88974	−	16.1708i	−0.252760	−	0.593249i	−0.997228	+	0.0744090i	$0.976293\pi$
$744$	0.576521	+	14.3062i	0.0211363	+	0.524492i
$745$	−21.1772	−	25.9373i	−0.775872	−	0.950270i
$746$			38.6546i			1.41524i
$747$	−10.3288	+	8.43319i	−0.377910	+	0.308554i
$748$	−0.000953642	0	0.000276226i	−3.48686e−5	0	1.00998e-5i
$749$	1.89626	+	2.14043i	0.0692877	+	0.0782097i
$750$	11.0842	−	11.5399i	0.404737	−	0.421376i
$751$	−14.9024	−	4.97516i	−0.543798	−	0.181546i	0.0314803	−	0.999504i	$-0.489978\pi$
$751$	−14.9024	−	4.97516i	−0.543798	−	0.181546i	−0.575278	+	0.817958i	$0.695106\pi$
$752$	−2.41323	−	3.21143i	−0.0880015	−	0.117109i
$753$	3.23322	+	26.6279i	0.117825	+	0.970376i
$754$	−19.2472	−	39.3698i	−0.700943	−	1.43376i
$755$	−2.11195	+	17.3935i	−0.0768618	+	0.633014i
$756$	0.339754	−	0.196157i	0.0123567	−	0.00713417i
$757$	20.5393	−	15.4343i	0.746512	−	0.560968i	−0.157988	−	0.987441i	$-0.550501\pi$
$757$	20.5393	−	15.4343i	0.746512	−	0.560968i	0.904500	+	0.426473i	$0.140244\pi$
$758$	0.643144	−	15.9594i	0.0233600	−	0.579673i
$759$	6.27620	−	2.38025i	0.227811	−	0.0863975i
$760$	33.1937	−	6.77655i	1.20406	−	0.245811i
$761$	−19.7022	+	4.02222i	−0.714203	+	0.145806i	−0.543369	−	0.839494i	$-0.682851\pi$
$761$	−19.7022	+	4.02222i	−0.714203	+	0.145806i	−0.170834	+	0.985300i	$0.554646\pi$
$762$	−4.25318	+	1.61302i	−0.154076	+	0.0584335i
$763$	0.640107	−	15.8841i	0.0231734	−	0.575043i
$764$	2.27970	−	1.71308i	0.0824767	−	0.0619772i
$765$	0.00696547	−	0.00402151i	0.000251837	−	0.000145398i
$766$	3.13709	−	25.8362i	0.113348	−	0.933501i
$767$	17.8122	−	1.64738i	0.643162	−	0.0594833i
$768$	0.542433	+	4.46734i	0.0195734	+	0.161201i
$769$	7.75758	+	10.3235i	0.279746	+	0.372274i	0.917344	−	0.398095i	$-0.130329\pi$
$769$	7.75758	+	10.3235i	0.279746	+	0.372274i	−0.637599	+	0.770369i	$0.720072\pi$
$770$	4.38722	+	1.46467i	0.158104	+	0.0527830i
$771$	3.94937	−	4.11173i	0.142233	−	0.148080i
$772$	1.86820	+	2.10876i	0.0672379	+	0.0758959i
$773$	−49.6458	−	14.3801i	−1.78564	−	0.517216i	−0.790218	−	0.612826i	$-0.790033\pi$
$773$	−49.6458	−	14.3801i	−1.78564	−	0.517216i	−0.995419	+	0.0956097i	$0.969520\pi$
$774$	−0.219943	+	0.179578i	−0.00790568	+	0.00645479i
$775$		−	11.9455i		−	0.429096i
$776$	20.6670	+	25.3125i	0.741904	+	0.908667i
$777$	0.405859	+	10.0713i	0.0145601	+	0.361306i
$778$	4.67649	+	10.9761i	0.167660	+	0.393513i
$779$	9.83677	−	25.9374i	0.352439	−	0.929305i
$780$	0.397646	+	1.01270i	0.0142380	+	0.0362606i
$781$	1.06725	+	2.81410i	0.0381892	+	0.100697i
$782$	−0.0315984	+	0.0303507i	−0.00112996	+	0.00108534i
$783$	2.51295	+	8.67572i	0.0898056	+	0.310045i
$784$	9.66022	−	0.779854i	0.345008	−	0.0278519i
$785$	5.21034	−	9.92747i	0.185965	−	0.354327i
$786$	7.88733	+	7.57588i	0.281332	+	0.270223i
$787$	−12.4849	+	29.3032i	−0.445040	+	1.04455i	0.534839	+	0.844954i	$0.320372\pi$
$787$	−12.4849	+	29.3032i	−0.445040	+	1.04455i	−0.979879	+	0.199593i	$0.936038\pi$
$788$	2.75759	+	1.04582i	0.0982351	+	0.0372557i
$789$	−9.67811	−	1.57285i	−0.344550	−	0.0559948i
$790$	29.0769	+	18.3871i	1.03451	+	0.654185i
$791$	−6.30671	+	1.82676i	−0.224241	+	0.0649522i
$792$	1.74036	−	2.52135i	0.0618410	−	0.0895921i
$793$	2.63853	−	3.59792i	0.0936970	−	0.127766i
$794$	−14.2117	−	20.5891i	−0.504353	−	0.730681i
$795$	11.7608	+	9.60238i	0.417112	+	0.340561i
$796$	−1.91589	+	2.34653i	−0.0679068	+	0.0831707i
$797$	38.9498	+	29.2689i	1.37967	+	1.03676i	0.993440	+	0.114357i	$0.0364809\pi$
$797$	38.9498	+	29.2689i	1.37967	+	1.03676i	0.386235	+	0.922401i	$0.373776\pi$
$798$	19.9726	+	2.42512i	0.707024	+	0.0858482i
$799$	0.00178962	+	0.00536058i	6.33124e−5	+	0.000189644i
$800$	−0.210999	−	2.61369i	−0.00745993	−	0.0924079i
$801$	5.35040	−	6.03936i	0.189047	−	0.213390i
$802$	7.27063	−	4.59767i	0.256735	−	0.162349i
$803$	−9.74451	+	4.15175i	−0.343876	+	0.146512i
$804$	0.0589100	+	0.362488i	0.00207759	+	0.0127840i
$805$	−15.9680	+	14.1464i	−0.562797	+	0.498594i
$806$	−21.4203	−	9.85949i	−0.754499	−	0.347286i
$807$	−15.6441	−	13.8595i	−0.550700	−	0.487878i
$808$	−6.06247	+	9.58703i	−0.213277	+	0.337271i
$809$	29.6209	+	2.39125i	1.04142	+	0.0840717i	0.589321	−	0.807899i	$-0.299395\pi$
$809$	29.6209	+	2.39125i	1.04142	+	0.0840717i	0.452094	+	0.891970i	$0.350677\pi$
$810$	0.429157	+	2.10215i	0.0150790	+	0.0738620i
$811$	−6.74780	−	27.3769i	−0.236947	−	0.961333i	−0.962090	−	0.272734i	$-0.912072\pi$
$811$	−6.74780	−	27.3769i	−0.236947	−	0.961333i	0.725142	−	0.688599i	$-0.241774\pi$
$812$	−0.568420	+	3.49763i	−0.0199476	+	0.122743i
$813$	−3.60898	−	5.70714i	−0.126572	−	0.200158i
$814$	3.16219	+	6.02505i	0.110835	+	0.211178i
$815$	5.98330	−	20.6567i	0.209586	−	0.723574i
$816$	−0.00361805	+	0.0177224i	−0.000126657	+	0.000620407i
$817$	1.52070	−	0.0612822i	0.0532027	−	0.00214399i
$818$	40.6378	−	21.3284i	1.42087	−	0.745728i
$819$	0.388080	+	7.46404i	0.0135606	+	0.260815i
$820$	1.02760	+	0.539329i	0.0358855	+	0.0188342i
$821$	22.3466	+	10.6036i	0.779902	+	0.370068i	0.776655	−	0.629927i	$-0.216915\pi$
$821$	22.3466	+	10.6036i	0.779902	+	0.370068i	0.00324721	+	0.999995i	$0.498966\pi$
$822$	10.6565	+	18.4577i	0.371689	+	0.643785i
$823$	−12.7264	+	22.0428i	−0.443614	+	0.768362i	−0.997955	−	0.0639279i	$-0.979637\pi$
$823$	−12.7264	+	22.0428i	−0.443614	+	0.768362i	0.554340	+	0.832290i	$0.312971\pi$
$824$	−43.4455	+	29.9882i	−1.51349	+	1.04469i
$825$	−1.53553	+	2.04342i	−0.0534602	+	0.0711426i
$826$	11.9852	+	6.91964i	0.417017	+	0.240765i
$827$	−14.6764	+	1.78203i	−0.510347	+	0.0619673i	−0.371660	−	0.928369i	$-0.621211\pi$
$827$	−14.6764	+	1.78203i	−0.510347	+	0.0619673i	−0.138687	+	0.990336i	$0.544288\pi$
$828$	0.523664	+	1.10360i	0.0181986	+	0.0383527i
$829$	9.77132	+	10.1730i	0.339372	+	0.353324i	0.868917	−	0.494958i	$-0.164817\pi$
$829$	9.77132	+	10.1730i	0.339372	+	0.353324i	−0.529545	+	0.848282i	$0.677637\pi$
$830$	2.30205	−	28.5160i	0.0799053	−	0.989804i
$831$	13.1871	−	3.25032i	0.457454	−	0.112752i
$832$	−29.1427	−	10.6651i	−1.01034	−	0.369744i
$833$	−0.0132385	−	0.00326299i	−0.000458686	−	0.000113056i
$834$	2.20895	−	6.61660i	0.0764896	−	0.229114i
$835$	−10.4760	+	22.0776i	−0.362536	+	0.764028i
$836$	−1.34652	+	0.449534i	−0.0465703	+	0.0155474i
$837$	3.99985	+	2.76090i	0.138255	+	0.0954306i
$838$	10.6435	−	5.05042i	0.367675	−	0.174464i
$839$	−42.2446	−	1.70240i	−1.45845	−	0.0587734i	−0.701696	−	0.712477i	$-0.747573\pi$
$839$	−42.2446	−	1.70240i	−1.45845	−	0.0587734i	−0.756751	+	0.653703i	$0.773214\pi$
$840$	−2.33016	+	9.45384i	−0.0803983	+	0.326189i
$841$	−48.3753	−	20.6108i	−1.66811	−	0.710716i
$842$	−1.88603	+	0.306509i	−0.0649968	+	0.0105630i
$843$	9.47295	+	1.93392i	0.326266	+	0.0666076i
$844$	−2.76501			−0.0951756
$845$	−20.6290	−	2.01754i	−0.709659	−	0.0694055i
$846$	−1.50754			−0.0518303
$847$	20.1450	+	4.11263i	0.692191	+	0.141312i
$848$	−33.7027	+	5.47721i	−1.15735	+	0.188088i
$849$	−10.6718	−	4.54682i	−0.366254	−	0.156046i
$850$	0.00399274	−	0.0161992i	0.000136950	−	0.000555627i
$851$	−31.3587	−	1.26371i	−1.07496	−	0.0433195i
$852$	−0.494829	+	0.234799i	−0.0169526	+	0.00804409i
$853$	23.4042	+	16.1548i	0.801345	+	0.553129i	0.896868	−	0.442299i	$-0.145837\pi$
$853$	23.4042	+	16.1548i	0.801345	+	0.553129i	−0.0955226	+	0.995427i	$0.530452\pi$
$854$	3.27417	−	1.09308i	0.112040	−	0.0374044i
$855$	4.92996	−	10.3897i	0.168601	−	0.355319i
$856$	−1.28690	+	3.85473i	−0.0439852	+	0.131752i
$857$	−6.63277	−	1.63483i	−0.226571	−	0.0558447i	0.124396	−	0.992233i	$-0.460301\pi$
$857$	−6.63277	−	1.63483i	−0.226571	−	0.0558447i	−0.350967	+	0.936388i	$0.614147\pi$
$858$	2.39680	+	4.44003i	0.0818255	+	0.151580i
$859$	35.8670	−	8.84042i	1.22377	−	0.301631i	0.426070	−	0.904690i	$-0.359898\pi$
$859$	35.8670	−	8.84042i	1.22377	−	0.301631i	0.797697	+	0.603059i	$0.206052\pi$
$860$	−0.00512346	+	0.0634655i	−0.000174709	+	0.00216415i
$861$	5.52282	+	5.74987i	0.188217	+	0.195955i
$862$	2.66787	+	5.62241i	0.0908680	+	0.191500i
$863$	28.9625	−	3.51668i	0.985894	−	0.119709i	0.388321	−	0.921524i	$-0.373055\pi$
$863$	28.9625	−	3.51668i	0.985894	−	0.119709i	0.597572	+	0.801815i	$0.296132\pi$
$864$	0.923936	+	0.533435i	0.0314329	+	0.0181478i
$865$	18.2298	−	24.2595i	0.619833	−	0.824848i
$866$	8.19207	−	5.65458i	0.278378	−	0.192150i
$867$	−8.49999	+	14.7224i	−0.288675	+	0.499999i
$868$	0.953360	+	1.65127i	0.0323592	+	0.0560477i
$869$	−15.0655	−	7.14868i	−0.511063	−	0.242502i
$870$	−17.1592	−	9.00584i	−0.581751	−	0.305327i
$871$	−6.66182	−	2.13797i	−0.225727	−	0.0724423i
$872$	20.0040	−	10.4989i	0.677422	−	0.355539i
$873$	11.0835	−	0.446651i	0.375121	−	0.0151168i
$874$	−12.5306	+	61.3789i	−0.423854	+	2.07617i
$875$	6.85784	−	23.6760i	0.231837	−	0.800396i
$876$	−0.895789	−	1.70678i	−0.0302659	−	0.0576669i
$877$	−16.6682	−	26.3587i	−0.562847	−	0.890071i	0.437110	−	0.899408i	$-0.356002\pi$
$877$	−16.6682	−	26.3587i	−0.562847	−	0.890071i	−0.999956	+	0.00933735i	$0.997028\pi$
$878$	−1.27517	+	7.84643i	−0.0430348	+	0.264804i
$879$	1.67357	+	6.78992i	0.0564479	+	0.229018i
$880$	1.18925	+	5.82535i	0.0400897	+	0.196372i
$881$	−47.9065	−	3.86741i	−1.61401	−	0.130296i	−0.759776	−	0.650184i	$-0.774692\pi$
$881$	−47.9065	−	3.86741i	−1.61401	−	0.130296i	−0.854234	+	0.519888i	$0.825974\pi$
$882$	1.94391	−	3.07404i	0.0654548	−	0.103508i
$883$	−8.00449	−	7.09136i	−0.269372	−	0.238643i	0.517613	−	0.855615i	$-0.326821\pi$
$883$	−8.00449	−	7.09136i	−0.269372	−	0.238643i	−0.786985	+	0.616972i	$0.788359\pi$
$884$	0.00269156	+	0.00214574i	9.05271e−5	+	7.21689e-5i
$885$	5.92101	−	5.24556i	0.199032	−	0.176327i
$886$	−7.64129	−	47.0187i	−0.256714	−	1.57963i
$887$	24.8371	−	10.5821i	0.833947	−	0.355312i	0.0675797	−	0.997714i	$-0.478472\pi$
$887$	24.8371	−	10.5821i	0.833947	−	0.355312i	0.766368	+	0.642402i	$0.222062\pi$
$888$	−12.1068	+	7.65586i	−0.406277	+	0.256914i
$889$	−4.64674	+	5.24508i	−0.155847	+	0.175914i
$890$	1.39296	+	17.2549i	0.0466921	+	0.578385i
$891$	−0.329322	−	0.986439i	−0.0110327	−	0.0330469i
$892$	3.25378	+	0.395080i	0.108945	+	0.0132283i
$893$	6.45986	+	4.85427i	0.216171	+	0.162442i
$894$	17.8729	−	21.8903i	0.597759	−	0.732122i
$895$	14.6540	+	11.9646i	0.489829	+	0.399933i
$896$	−11.1258	−	16.1186i	−0.371688	−	0.538483i
$897$	−23.2624	−	0.665654i	−0.776710	−	0.0222256i
$898$	−1.16254	+	1.68423i	−0.0387945	+	0.0562036i
$899$	−42.1656	+	12.2134i	−1.40630	+	0.407340i
$900$	−0.393146	−	0.248610i	−0.0131049	−	0.00828701i
$901$	0.0474145	+	0.00770561i	0.00157961	+	0.000256711i
$902$	5.03241	+	1.90854i	0.167561	+	0.0635475i
$903$	−0.171450	+	0.402409i	−0.00570551	+	0.0133913i
$904$	−6.72962	−	6.46389i	−0.223824	−	0.214986i
$905$	8.04272	−	15.3241i	0.267349	−	0.509391i
$906$	−14.7395	+	1.18989i	−0.489685	+	0.0395315i
$907$	−9.75241	−	33.6692i	−0.323823	−	1.11797i	−0.943021	−	0.332733i	$-0.892029\pi$
$907$	−9.75241	−	33.6692i	−0.323823	−	1.11797i	0.619198	−	0.785235i	$-0.287458\pi$
$908$	1.07294	−	1.03057i	0.0356068	−	0.0342008i
$909$	1.36537	+	3.60018i	0.0452864	+	0.119410i
$910$	−12.1262	−	10.4929i	−0.401981	−	0.347837i
$911$	−16.5648	+	43.6778i	−0.548816	+	1.44711i	0.317811	+	0.948154i	$0.397052\pi$
$911$	−16.5648	+	43.6778i	−0.548816	+	1.44711i	−0.866627	+	0.498956i	$0.833717\pi$
$912$	10.1372	+	23.7928i	0.335675	+	0.787857i
$913$	0.558371	+	13.8558i	0.0184794	+	0.458561i
$914$	−10.5044	−	12.8656i	−0.347456	−	0.425556i
$915$		−	1.97302i		−	0.0652260i
$916$	−3.18879	+	2.60356i	−0.105361	+	0.0860242i
$917$	16.1822	+	4.68724i	0.534384	+	0.154786i
$918$	0.00450133	+	0.00508095i	0.000148566	+	0.000167696i
$919$	−17.5169	+	18.2371i	−0.577831	+	0.601586i	−0.944397	−	0.328806i	$-0.893354\pi$
$919$	−17.5169	+	18.2371i	−0.577831	+	0.601586i	0.366567	+	0.930392i	$0.380533\pi$
$920$	−28.7569	−	9.60046i	−0.948086	−	0.316518i
$921$	−14.0978	−	18.7607i	−0.464537	−	0.618186i
$922$	−5.49931	−	45.2909i	−0.181110	−	1.49158i
$923$	0.298464	−	10.4303i	0.00982407	−	0.343319i
$924$	0.0491779	−	0.405016i	0.00161783	−	0.0133241i
$925$	10.3498	−	5.97547i	0.340300	−	0.196472i
$926$	21.1648	−	15.9043i	0.695519	−	0.522649i
$927$	−0.721549	+	17.9051i	−0.0236988	+	0.588079i
$928$	−9.01011	+	3.41708i	−0.295771	+	0.112171i
$929$	−21.6567	+	4.42125i	−0.710534	+	0.145057i	−0.541680	−	0.840585i	$-0.682212\pi$
$929$	−21.6567	+	4.42125i	−0.710534	+	0.145057i	−0.168854	+	0.985641i	$0.554006\pi$
$930$	−10.2168	+	2.08578i	−0.335023	+	0.0683954i
$931$	−18.2281	+	6.91302i	−0.597403	+	0.226565i
$932$	0.206828	−	5.13238i	0.00677486	−	0.168117i
$933$	−13.5668	+	10.1948i	−0.444156	+	0.333762i
$934$	8.57156	−	4.94879i	0.280470	−	0.161930i
$935$	0.00100822	−	0.00830343i	3.29723e−5	−	0.000271551i
$936$	−8.91055	+	5.78134i	−0.291250	+	0.188969i
$937$	−2.03971	−	16.7985i	−0.0666345	−	0.548784i	−0.987351	−	0.158552i	$-0.949318\pi$
$937$	−2.03971	−	16.7985i	−0.0666345	−	0.548784i	0.920716	−	0.390233i	$-0.127605\pi$
$938$	−3.25172	−	4.32726i	−0.106173	−	0.141290i
$939$	−28.9779	−	9.67424i	−0.945657	−	0.315707i
$940$	−0.234179	+	0.243806i	−0.00763807	+	0.00795208i
$941$	22.9232	+	25.8750i	0.747276	+	0.843501i	0.992019	−	0.126087i	$-0.0402419\pi$
$941$	22.9232	+	25.8750i	0.747276	+	0.843501i	−0.244743	+	0.969588i	$0.578703\pi$
$942$	9.08876	+	2.63259i	0.296128	+	0.0857744i
$943$	−19.2288	+	15.6999i	−0.626177	+	0.511258i
$944$			17.7896i			0.579003i
$945$	2.09032	+	2.56018i	0.0679982	+	0.0832827i
$946$	0.0118900	+	0.295048i	0.000386579	+	0.00959285i
$947$	−0.444980	−	1.04441i	−0.0144599	−	0.0339387i	0.912593	−	0.408869i	$-0.134077\pi$
$947$	−0.444980	−	1.04441i	−0.0144599	−	0.0339387i	−0.927053	+	0.374931i	$0.877667\pi$
$948$	1.07610	−	2.83745i	0.0349502	−	0.0921562i
$949$	36.7204	−	0.428534i	1.19200	−	0.0139108i
$950$	−8.45907	−	22.3047i	−0.274449	−	0.723661i
$951$	15.7876	−	15.1641i	0.511946	−	0.491731i
$952$	0.00857069	+	0.0295895i	0.000277778	+	0.000959000i
$953$	41.3213	−	3.33580i	1.33853	−	0.108057i	0.609633	−	0.792683i	$-0.291317\pi$
$953$	41.3213	−	3.33580i	1.33853	−	0.108057i	0.728894	+	0.684626i	$0.240035\pi$
$954$	−5.95494	+	11.3462i	−0.192798	+	0.367346i
$955$	17.3262	+	16.6420i	0.560663	+	0.538524i
$956$	1.12596	−	2.64272i	0.0364161	−	0.0854718i
$957$	8.78284	+	3.33089i	0.283909	+	0.107672i
$958$	0.629206	+	0.102256i	0.0203287	+	0.00330374i
$959$	27.7498	+	17.5479i	0.896089	+	0.566652i
$960$	−13.1813	+	3.81800i	−0.425424	+	0.123226i
$961$	4.19154	−	6.07250i	0.135211	−	0.195887i
$962$	−2.17257	−	23.4909i	−0.0700466	−	0.757378i
$963$	0.783632	+	1.13529i	0.0252522	+	0.0365841i
$964$	0.576615	+	0.470792i	0.0185715	+	0.0151632i
$965$	−15.0109	+	18.3851i	−0.483219	+	0.591836i
$966$	−14.3935	−	10.8160i	−0.463103	−	0.347999i
$967$	24.1459	+	2.93184i	0.776478	+	0.0942815i	0.499175	−	0.866501i	$-0.333636\pi$
$967$	24.1459	+	2.93184i	0.776478	+	0.0942815i	0.277303	+	0.960783i	$0.410559\pi$
$968$	9.25283	+	27.7156i	0.297397	+	0.890813i
$969$	−0.00292772	−	0.0362663i	−9.40519e−5	−	0.00116504i
$970$	−15.7817	+	17.8139i	−0.506721	+	0.571970i
$971$	26.9704	−	17.0551i	0.865522	−	0.547323i	−0.0263283	−	0.999653i	$-0.508382\pi$
$971$	26.9704	−	17.0551i	0.865522	−	0.547323i	0.891851	+	0.452330i	$0.149407\pi$
$972$	0.174110	−	0.0741814i	0.00558458	−	0.00237937i
$973$	−1.72376	−	10.6067i	−0.0552611	−	0.340035i
$974$	−9.22440	+	8.17211i	−0.295569	+	0.261851i
$975$	7.62237	−	4.52019i	0.244111	−	0.144762i
$976$	3.32123	+	2.94235i	0.106310	+	0.0941823i
$977$	1.09447	−	1.73077i	0.0350153	−	0.0553723i	−0.827229	−	0.561865i	$-0.810084\pi$
$977$	1.09447	−	1.73077i	0.0350153	−	0.0553723i	0.862244	+	0.506493i	$0.169058\pi$
$978$	18.0914	+	1.46049i	0.578500	+	0.0467014i
$979$	−1.67840	−	8.22133i	−0.0536418	−	0.262755i
$980$	−0.195185	−	0.791895i	−0.00623494	−	0.0252961i
$981$	1.23016	−	7.56947i	0.0392759	−	0.241674i
$982$	16.4577	+	26.0258i	0.525187	+	0.830517i
$983$	4.37691	+	8.33951i	0.139602	+	0.265989i	0.945212	−	0.326457i	$-0.105855\pi$
$983$	4.37691	+	8.33951i	0.139602	+	0.265989i	−0.805610	+	0.592446i	$0.798162\pi$
$984$	−3.15225	+	10.8828i	−0.100490	+	0.346932i
$985$	−4.96995	+	24.3444i	−0.158356	+	0.775678i
$986$	−0.0612624	+	0.00246879i	−0.00195099	+	7.86223e-5i
$987$	−2.05634	+	1.07925i	−0.0654541	+	0.0343530i
$988$	4.91001	+	0.338757i	0.156208	+	0.0107773i
$989$	−1.20595	−	0.632931i	−0.0383469	−	0.0201260i
$990$	2.01582	+	0.956516i	0.0640668	+	0.0304001i
$991$	−13.5860	−	23.5317i	−0.431574	−	0.747508i	0.565435	−	0.824793i	$-0.308708\pi$
$991$	−13.5860	−	23.5317i	−0.431574	−	0.747508i	−0.997009	+	0.0772849i	$0.975375\pi$
$992$	−2.59259	+	4.49050i	−0.0823148	+	0.142573i
$993$	19.4561	−	13.4296i	0.617422	−	0.426176i
$994$	4.84965	−	6.45371i	0.153822	−	0.204699i
$995$	−22.1021	−	12.7606i	−0.700683	−	0.404540i
$996$	−2.50517	+	0.304182i	−0.0793792	+	0.00963838i
$997$	−4.85977	−	10.2417i	−0.153910	−	0.324359i	0.811819	−	0.583909i	$-0.198477\pi$
$997$	−4.85977	−	10.2417i	−0.153910	−	0.324359i	−0.965730	+	0.259549i	$0.916426\pi$
$998$	7.35920	+	7.66174i	0.232952	+	0.242528i
$999$	−0.391259	+	4.84661i	−0.0123789	+	0.153340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.10.5	✓	360
169.17	even	78	inner	507.2.t.b.355.5	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.10.5	✓	360	1.1	even	1	trivial
507.2.t.b.355.5	yes	360	169.17	even	78	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31845 - 0.269162i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(-0.174110 - 0.0741814i) q^{4} +(0.381569 - 1.54808i) q^{5} +(1.34455 + 0.0541834i) q^{6} +(1.87281 - 0.888658i) q^{7} +(2.42447 + 1.67349i) q^{8} +(0.948536 - 0.316668i) q^{9} +O(q^{10})\)	\(q+(-1.31845 - 0.269162i) q^{2} +(-0.987050 + 0.160411i) q^{3} +(-0.174110 - 0.0741814i) q^{4} +(0.381569 - 1.54808i) q^{5} +(1.34455 + 0.0541834i) q^{6} +(1.87281 - 0.888658i) q^{7} +(2.42447 + 1.67349i) q^{8} +(0.948536 - 0.316668i) q^{9} +(-0.919764 + 1.93836i) q^{10} +(0.329322 - 0.986439i) q^{11} +(0.183755 + 0.0452915i) q^{12} +(-2.35927 + 2.72651i) q^{13} +(-2.70839 + 0.667557i) q^{14} +(-0.128297 + 1.58925i) q^{15} +(-2.48388 - 2.58600i) q^{16} +(0.00216254 + 0.00455745i) q^{17} +(-1.33583 + 0.162199i) q^{18} +(6.24636 + 3.60634i) q^{19} +(-0.181274 + 0.241232i) q^{20} +(-1.70600 + 1.17757i) q^{21} +(-0.699705 + 1.21192i) q^{22} +(-3.22724 - 5.58974i) q^{23} +(-2.66152 - 1.26291i) q^{24} +(2.17631 + 1.14221i) q^{25} +(3.84444 - 2.95973i) q^{26} +(-0.885456 + 0.464723i) q^{27} +(-0.391996 + 0.0157969i) q^{28} +(1.80670 - 8.84979i) q^{29} +(0.596918 - 2.06080i) q^{30} +(-2.25864 - 4.30348i) q^{31} +(-0.570205 - 0.901707i) q^{32} +(-0.166821 + 1.02649i) q^{33} +(-0.00162449 - 0.00659083i) q^{34} +(-0.661114 - 3.23835i) q^{35} +(-0.188641 - 0.0152286i) q^{36} +(2.59878 - 4.10964i) q^{37} +(-7.26479 - 6.43604i) q^{38} +(1.89135 - 3.06966i) q^{39} +(3.51580 - 3.11473i) q^{40} +(-0.616945 - 3.79622i) q^{41} +(2.56623 - 1.09337i) q^{42} +(0.178343 - 0.112777i) q^{43} +(-0.130514 + 0.147319i) q^{44} +(-0.128297 - 1.58925i) q^{45} +(2.75039 + 8.23842i) q^{46} +(1.11215 + 0.135039i) q^{47} +(2.86654 + 2.15407i) q^{48} +(-1.70942 + 2.09366i) q^{49} +(-2.56190 - 2.09173i) q^{50} +(-0.00286560 - 0.00415154i) q^{51} +(0.613028 - 0.299699i) q^{52} +(5.40943 - 7.83692i) q^{53} +(1.29251 - 0.374380i) q^{54} +(-1.40143 - 0.886212i) q^{55} +(6.02772 + 0.979600i) q^{56} +(-6.74396 - 2.55765i) q^{57} +(-4.76406 + 11.1817i) q^{58} +(-3.57811 - 3.43682i) q^{59} +(0.140230 - 0.267186i) q^{60} +(-1.23344 + 0.0995738i) q^{61} +(1.81956 + 6.28184i) q^{62} +(1.49502 - 1.43598i) q^{63} +(3.05207 + 8.04766i) q^{64} +(3.32065 + 4.69270i) q^{65} +(0.496238 - 1.30847i) q^{66} +(0.760602 + 1.78520i) q^{67} +(-3.84416e-5 - 0.000953919i) q^{68} +(4.08210 + 4.99967i) q^{69} +4.44753i q^{70} +(-2.24174 + 1.83032i) q^{71} +(2.82964 + 0.819614i) q^{72} +(-6.75398 - 7.62367i) q^{73} +(-4.53250 + 4.71884i) q^{74} +(-2.33135 - 0.778319i) q^{75} +(-0.820031 - 1.09126i) q^{76} +(-0.259851 - 2.14006i) q^{77} +(-3.31988 + 3.53809i) q^{78} +(1.93278 - 15.9179i) q^{79} +(-4.95112 + 2.85853i) q^{80} +(0.799443 - 0.600742i) q^{81} +(-0.208391 + 5.17116i) q^{82} +(-12.4677 + 4.72839i) q^{83} +(0.384386 - 0.0784730i) q^{84} +(0.00788048 - 0.00160881i) q^{85} +(-0.265490 + 0.100687i) q^{86} +(-0.363695 + 9.02500i) q^{87} +(2.44922 - 1.84047i) q^{88} +(6.98752 - 4.03425i) q^{89} +(-0.258613 + 2.12987i) q^{90} +(-1.99552 + 7.20281i) q^{91} +(0.147240 + 1.21263i) q^{92} +(2.91972 + 3.88544i) q^{93} +(-1.42996 - 0.477389i) q^{94} +(7.96633 - 8.29382i) q^{95} +(0.707465 + 0.798563i) q^{96} +(10.6546 + 3.08613i) q^{97} +(2.81732 - 2.30027i) q^{98} -1.03996i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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