LMFDB - Embedded newform 425.2.k.c.86.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.3
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72275 + 1.25165i) q^{2} +(-0.0844546 + 0.259925i) q^{3} +(0.783211 - 2.41047i) q^{4} +(-2.13220 - 0.673604i) q^{5} +(-0.179841 - 0.553494i) q^{6} +0.609651 q^{7} +(0.351734 + 1.08253i) q^{8} +(2.36662 + 1.71945i) q^{9} +(4.51637 - 1.50832i) q^{10} +(1.38011 - 1.00271i) q^{11} +(0.560396 + 0.407152i) q^{12} +(-1.54945 - 1.12574i) q^{13} +(-1.05028 + 0.763073i) q^{14} +(0.355160 - 0.497321i) q^{15} +(2.14004 + 1.55483i) q^{16} +(-0.309017 - 0.951057i) q^{17} -6.22927 q^{18} +(2.39272 + 7.36405i) q^{19} +(-3.29366 + 4.61203i) q^{20} +(-0.0514879 + 0.158463i) q^{21} +(-1.12254 + 3.45483i) q^{22} +(-1.39658 + 1.01468i) q^{23} -0.311081 q^{24} +(4.09252 + 2.87251i) q^{25} +4.07836 q^{26} +(-1.31012 + 0.951855i) q^{27} +(0.477485 - 1.46955i) q^{28} +(-0.801966 + 2.46820i) q^{29} +(0.0106207 + 1.30130i) q^{30} +(0.0824305 + 0.253695i) q^{31} -7.90936 q^{32} +(0.144072 + 0.443407i) q^{33} +(1.72275 + 1.25165i) q^{34} +(-1.29990 - 0.410663i) q^{35} +(5.99826 - 4.35799i) q^{36} +(8.60996 + 6.25550i) q^{37} +(-13.3393 - 9.69159i) q^{38} +(0.423466 - 0.307666i) q^{39} +(-0.0207721 - 2.54509i) q^{40} +(-0.759890 - 0.552093i) q^{41} +(-0.109640 - 0.337439i) q^{42} -3.06317 q^{43} +(-1.33608 - 4.11204i) q^{44} +(-3.88787 - 5.26037i) q^{45} +(1.13594 - 3.49608i) q^{46} +(-1.51577 + 4.66507i) q^{47} +(-0.584876 + 0.424937i) q^{48} -6.62833 q^{49} +(-10.6458 + 0.173786i) q^{50} +0.273301 q^{51} +(-3.92712 + 2.85322i) q^{52} +(-2.06569 + 6.35754i) q^{53} +(1.06561 - 3.27962i) q^{54} +(-3.61808 + 1.20832i) q^{55} +(0.214435 + 0.659963i) q^{56} -2.11617 q^{57} +(-1.70774 - 5.25588i) q^{58} +(5.50085 + 3.99660i) q^{59} +(-0.920615 - 1.24561i) q^{60} +(2.37055 - 1.72231i) q^{61} +(-0.459546 - 0.333880i) q^{62} +(1.44281 + 1.04827i) q^{63} +(9.34579 - 6.79011i) q^{64} +(2.54543 + 3.44402i) q^{65} +(-0.803192 - 0.583553i) q^{66} +(3.50297 + 10.7810i) q^{67} -2.53452 q^{68} +(-0.145792 - 0.448700i) q^{69} +(2.75341 - 0.919548i) q^{70} +(-0.669700 + 2.06113i) q^{71} +(-1.02893 + 3.16672i) q^{72} +(4.24476 - 3.08400i) q^{73} -22.6626 q^{74} +(-1.09227 + 0.821149i) q^{75} +19.6249 q^{76} +(0.841383 - 0.611300i) q^{77} +(-0.344436 + 1.06007i) q^{78} +(3.72368 - 11.4603i) q^{79} +(-3.51565 - 4.75675i) q^{80} +(2.57514 + 7.92548i) q^{81} +2.00013 q^{82} +(0.582630 + 1.79315i) q^{83} +(0.341646 + 0.248220i) q^{84} +(0.0182494 + 2.23599i) q^{85} +(5.27709 - 3.83403i) q^{86} +(-0.573816 - 0.416901i) q^{87} +(1.57088 + 1.14131i) q^{88} +(10.1908 - 7.40406i) q^{89} +(13.2820 + 4.19606i) q^{90} +(-0.944624 - 0.686309i) q^{91} +(1.35203 + 4.16113i) q^{92} -0.0729032 q^{93} +(-3.22775 - 9.93399i) q^{94} +(-0.141305 - 17.3133i) q^{95} +(0.667982 - 2.05584i) q^{96} +(-2.98220 + 9.17827i) q^{97} +(11.4190 - 8.29637i) q^{98} +4.99029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.72275	+	1.25165i	−1.21817	+	0.885053i	−0.995947	−	0.0899421i	$-0.971332\pi$
$2$	−1.72275	+	1.25165i	−1.21817	+	0.885053i	−0.222224	+	0.974996i	$0.571332\pi$
$3$	−0.0844546	+	0.259925i	−0.0487599	+	0.150068i	−0.972472	−	0.233020i	$-0.925139\pi$
$3$	−0.0844546	+	0.259925i	−0.0487599	+	0.150068i	0.923712	+	0.383088i	$0.125139\pi$
$4$	0.783211	−	2.41047i	0.391605	−	1.20524i
$5$	−2.13220	−	0.673604i	−0.953547	−	0.301245i
$5$	−2.13220	−	0.673604i	−0.953547	−	0.301245i
$6$	−0.179841	−	0.553494i	−0.0734199	−	0.225963i
$7$	0.609651			0.230427			0.115213	−	0.993341i	$-0.463245\pi$
$7$	0.609651			0.230427			0.115213	+	0.993341i	$0.463245\pi$
$8$	0.351734	+	1.08253i	0.124357	+	0.382731i
$9$	2.36662	+	1.71945i	0.788874	+	0.573151i
$10$	4.51637	−	1.50832i	1.42820	−	0.476972i
$11$	1.38011	−	1.00271i	0.416117	−	0.302327i	−0.359956	−	0.932969i	$-0.617208\pi$
$11$	1.38011	−	1.00271i	0.416117	−	0.302327i	0.776074	+	0.630642i	$0.217208\pi$
$12$	0.560396	+	0.407152i	0.161772	+	0.117535i
$13$	−1.54945	−	1.12574i	−0.429740	−	0.312224i	0.351805	−	0.936073i	$-0.385568\pi$
$13$	−1.54945	−	1.12574i	−0.429740	−	0.312224i	−0.781545	+	0.623849i	$0.785568\pi$
$14$	−1.05028	+	0.763073i	−0.280699	+	0.203940i
$15$	0.355160	−	0.497321i	0.0917019	−	0.128408i
$16$	2.14004	+	1.55483i	0.535011	+	0.388708i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−6.22927			−1.46825
$19$	2.39272	+	7.36405i	0.548929	+	1.68943i	0.711461	+	0.702726i	$0.248034\pi$
$19$	2.39272	+	7.36405i	0.548929	+	1.68943i	−0.162532	+	0.986703i	$0.551966\pi$
$20$	−3.29366	+	4.61203i	−0.736485	+	1.03128i
$21$	−0.0514879	+	0.158463i	−0.0112356	+	0.0345796i
$22$	−1.12254	+	3.45483i	−0.239327	+	0.736572i
$23$	−1.39658	+	1.01468i	−0.291207	+	0.211575i	−0.723791	−	0.690019i	$-0.757602\pi$
$23$	−1.39658	+	1.01468i	−0.291207	+	0.211575i	0.432584	+	0.901594i	$0.357602\pi$
$24$	−0.311081			−0.0634991
$25$	4.09252	+	2.87251i	0.818503	+	0.574502i
$26$	4.07836			0.799832
$27$	−1.31012	+	0.951855i	−0.252132	+	0.183185i
$28$	0.477485	−	1.46955i	0.0902362	−	0.277719i
$29$	−0.801966	+	2.46820i	−0.148921	+	0.458333i	−0.997494	−	0.0707455i	$-0.977462\pi$
$29$	−0.801966	+	2.46820i	−0.148921	+	0.458333i	0.848573	+	0.529078i	$0.177462\pi$
$30$	0.0106207	+	1.30130i	0.00193907	+	0.237584i
$31$	0.0824305	+	0.253695i	0.0148050	+	0.0455650i	0.958186	−	0.286146i	$-0.0923742\pi$
$31$	0.0824305	+	0.253695i	0.0148050	+	0.0455650i	−0.943381	+	0.331711i	$0.892374\pi$
$32$	−7.90936			−1.39819
$33$	0.144072	+	0.443407i	0.0250796	+	0.0771872i
$34$	1.72275	+	1.25165i	0.295450	+	0.214657i
$35$	−1.29990	−	0.410663i	−0.219722	−	0.0694148i
$36$	5.99826	−	4.35799i	0.999710	−	0.726332i
$37$	8.60996	+	6.25550i	1.41547	+	1.02840i	0.992499	+	0.122254i	$0.0390122\pi$
$37$	8.60996	+	6.25550i	1.41547	+	1.02840i	0.422969	+	0.906144i	$0.360988\pi$
$38$	−13.3393	−	9.69159i	−2.16392	−	1.57218i
$39$	0.423466	−	0.307666i	0.0678088	−	0.0492660i
$40$	−0.0207721	−	2.54509i	−0.00328435	−	0.402413i
$41$	−0.759890	−	0.552093i	−0.118675	−	0.0862224i	0.526865	−	0.849949i	$-0.323367\pi$
$41$	−0.759890	−	0.552093i	−0.118675	−	0.0862224i	−0.645540	+	0.763727i	$0.723367\pi$
$42$	−0.109640	−	0.337439i	−0.0169179	−	0.0520679i
$43$	−3.06317			−0.467129			−0.233565	−	0.972341i	$-0.575039\pi$
$43$	−3.06317			−0.467129			−0.233565	+	0.972341i	$0.575039\pi$
$44$	−1.33608	−	4.11204i	−0.201422	−	0.619913i
$45$	−3.88787	−	5.26037i	−0.579570	−	0.784170i
$46$	1.13594	−	3.49608i	0.167486	−	0.515468i
$47$	−1.51577	+	4.66507i	−0.221098	+	0.680470i	0.777566	+	0.628801i	$0.216454\pi$
$47$	−1.51577	+	4.66507i	−0.221098	+	0.680470i	−0.998664	+	0.0516690i	$0.983546\pi$
$48$	−0.584876	+	0.424937i	−0.0844196	+	0.0613344i
$49$	−6.62833			−0.946904
$50$	−10.6458	+	0.173786i	−1.50554	+	0.0245770i
$51$	0.273301			0.0382698
$52$	−3.92712	+	2.85322i	−0.544593	+	0.395670i
$53$	−2.06569	+	6.35754i	−0.283744	+	0.873276i	0.703028	+	0.711163i	$0.251831\pi$
$53$	−2.06569	+	6.35754i	−0.283744	+	0.873276i	−0.986772	+	0.162113i	$0.948169\pi$
$54$	1.06561	−	3.27962i	0.145012	−	0.446300i
$55$	−3.61808	+	1.20832i	−0.487862	+	0.162930i
$56$	0.214435	+	0.659963i	0.0286551	+	0.0881913i
$57$	−2.11617			−0.280294
$58$	−1.70774	−	5.25588i	−0.224237	−	0.690131i
$59$	5.50085	+	3.99660i	0.716150	+	0.520313i	0.885152	−	0.465302i	$-0.154054\pi$
$59$	5.50085	+	3.99660i	0.716150	+	0.520313i	−0.169002	+	0.985616i	$0.554054\pi$
$60$	−0.920615	−	1.24561i	−0.118851	−	0.160808i
$61$	2.37055	−	1.72231i	0.303518	−	0.220519i	−0.425592	−	0.904915i	$-0.639934\pi$
$61$	2.37055	−	1.72231i	0.303518	−	0.220519i	0.729110	+	0.684396i	$0.239934\pi$
$62$	−0.459546	−	0.333880i	−0.0583624	−	0.0424028i
$63$	1.44281	+	1.04827i	0.181778	+	0.132069i
$64$	9.34579	−	6.79011i	1.16822	−	0.848764i
$65$	2.54543	+	3.44402i	0.315721	+	0.427178i
$66$	−0.803192	−	0.583553i	−0.0988661	−	0.0718304i
$67$	3.50297	+	10.7810i	0.427956	+	1.31711i	0.900136	+	0.435610i	$0.143467\pi$
$67$	3.50297	+	10.7810i	0.427956	+	1.31711i	−0.472180	+	0.881502i	$0.656533\pi$
$68$	−2.53452			−0.307356
$69$	−0.145792	−	0.448700i	−0.0175512	−	0.0540172i
$70$	2.75341	−	0.919548i	0.329095	−	0.109907i
$71$	−0.669700	+	2.06113i	−0.0794788	+	0.244611i	−0.982899	−	0.184146i	$-0.941048\pi$
$71$	−0.669700	+	2.06113i	−0.0794788	+	0.244611i	0.903420	+	0.428756i	$0.141048\pi$
$72$	−1.02893	+	3.16672i	−0.121260	+	0.373201i
$73$	4.24476	−	3.08400i	0.496811	−	0.360954i	−0.310986	−	0.950414i	$-0.600659\pi$
$73$	4.24476	−	3.08400i	0.496811	−	0.360954i	0.807798	+	0.589460i	$0.200659\pi$
$74$	−22.6626			−2.63447
$75$	−1.09227	+	0.821149i	−0.126124	+	0.0948181i
$76$	19.6249			2.25113
$77$	0.841383	−	0.611300i	0.0958845	−	0.0696642i
$78$	−0.344436	+	1.06007i	−0.0389998	+	0.120029i
$79$	3.72368	−	11.4603i	0.418946	−	1.28938i	−0.489727	−	0.871876i	$-0.662903\pi$
$79$	3.72368	−	11.4603i	0.418946	−	1.28938i	0.908673	−	0.417508i	$-0.137097\pi$
$80$	−3.51565	−	4.75675i	−0.393062	−	0.531821i
$81$	2.57514	+	7.92548i	0.286127	+	0.880608i
$82$	2.00013			0.220878
$83$	0.582630	+	1.79315i	0.0639520	+	0.196824i	0.977927	−	0.208946i	$-0.0670034\pi$
$83$	0.582630	+	1.79315i	0.0639520	+	0.196824i	−0.913975	+	0.405770i	$0.867003\pi$
$84$	0.341646	+	0.248220i	0.0372766	+	0.0270831i
$85$	0.0182494	+	2.23599i	0.00197942	+	0.242528i
$86$	5.27709	−	3.83403i	0.569043	−	0.413434i
$87$	−0.573816	−	0.416901i	−0.0615195	−	0.0446965i
$88$	1.57088	+	1.14131i	0.167457	+	0.121664i
$89$	10.1908	−	7.40406i	1.08022	−	0.784829i	0.102502	−	0.994733i	$-0.467315\pi$
$89$	10.1908	−	7.40406i	1.08022	−	0.784829i	0.977722	+	0.209904i	$0.0673152\pi$
$90$	13.2820	+	4.19606i	1.40005	+	0.442304i
$91$	−0.944624	−	0.686309i	−0.0990235	−	0.0719448i
$92$	1.35203	+	4.16113i	0.140959	+	0.433828i
$93$	−0.0729032			−0.00755971
$94$	−3.22775	−	9.93399i	−0.332917	−	1.02461i
$95$	−0.141305	−	17.3133i	−0.0144976	−	1.77631i
$96$	0.667982	−	2.05584i	0.0681756	−	0.209823i
$97$	−2.98220	+	9.17827i	−0.302797	+	0.931912i	0.677694	+	0.735344i	$0.262980\pi$
$97$	−2.98220	+	9.17827i	−0.302797	+	0.931912i	−0.980490	+	0.196568i	$0.937020\pi$
$98$	11.4190	−	8.29637i	1.15349	−	0.838060i
$99$	4.99029			0.501543
$100$	10.1294	−	7.61512i	1.01294	−	0.761512i
$101$	−3.26744			−0.325123			−0.162561	−	0.986698i	$-0.551976\pi$
$101$	−3.26744			−0.325123			−0.162561	+	0.986698i	$0.551976\pi$
$102$	−0.470831	+	0.342078i	−0.0466192	+	0.0338708i
$103$	4.04423	−	12.4469i	0.398490	−	1.22643i	−0.527720	−	0.849419i	$-0.676953\pi$
$103$	4.04423	−	12.4469i	0.398490	−	1.22643i	0.926210	−	0.377008i	$-0.123047\pi$
$104$	0.673649	−	2.07328i	0.0660568	−	0.203302i
$105$	0.216524	−	0.303193i	0.0211306	−	0.0295886i
$106$	−4.39877	−	13.5380i	−0.427246	−	1.31493i
$107$	19.6831			1.90283			0.951416	−	0.307907i	$-0.0996286\pi$
$107$	19.6831			1.90283			0.951416	+	0.307907i	$0.0996286\pi$
$108$	1.26832	+	3.90350i	0.122045	+	0.375615i
$109$	9.71660	+	7.05952i	0.930682	+	0.676180i	0.946160	−	0.323701i	$-0.104927\pi$
$109$	9.71660	+	7.05952i	0.930682	+	0.676180i	−0.0154781	+	0.999880i	$0.504927\pi$
$110$	4.72067	−	6.61022i	0.450098	−	0.630260i
$111$	−2.35311	+	1.70963i	−0.223347	+	0.162271i
$112$	1.30468	+	0.947906i	0.123281	+	0.0895687i
$113$	−8.46827	−	6.15256i	−0.796628	−	0.578784i	0.113295	−	0.993561i	$-0.463859\pi$
$113$	−8.46827	−	6.15256i	−0.796628	−	0.578784i	−0.909923	+	0.414778i	$0.863859\pi$
$114$	3.64565	−	2.64872i	0.341446	−	0.248075i
$115$	3.66128	−	1.22274i	0.341416	−	0.114022i
$116$	5.32142	+	3.86624i	0.494081	+	0.358971i
$117$	−1.73130	−	5.32841i	−0.160059	−	0.492612i
$118$	−14.4790			−1.33290
$119$	−0.188393	−	0.579813i	−0.0172699	−	0.0531514i
$120$	0.663285	+	0.209545i	0.0605493	+	0.0191288i
$121$	−2.49991	+	7.69394i	−0.227265	+	0.699449i
$122$	−1.92815	+	5.93422i	−0.174566	+	0.537259i
$123$	0.207679	−	0.150887i	0.0187258	−	0.0136051i
$124$	0.676086			0.0607143
$125$	−6.79111	−	8.88149i	−0.607415	−	0.794384i
$126$	−3.79768			−0.338324
$127$	4.45825	−	3.23911i	0.395606	−	0.287425i	−0.372143	−	0.928175i	$-0.621377\pi$
$127$	4.45825	−	3.23911i	0.395606	−	0.287425i	0.767749	+	0.640751i	$0.221377\pi$
$128$	−2.71338	+	8.35091i	−0.239831	+	0.738123i
$129$	0.258699	−	0.796194i	0.0227772	−	0.0701009i
$130$	−8.69586	−	2.74720i	−0.762678	−	0.240945i
$131$	3.91777	+	12.0577i	0.342297	+	1.05348i	0.963015	+	0.269448i	$0.0868413\pi$
$131$	3.91777	+	12.0577i	0.342297	+	1.05348i	−0.620718	+	0.784034i	$0.713159\pi$
$132$	1.18166			0.102850
$133$	1.45873	+	4.48950i	0.126488	+	0.389289i
$134$	−19.5289	−	14.1886i	−1.68704	−	1.22570i
$135$	3.43460	−	1.14704i	0.295603	−	0.0987216i
$136$	0.920851	−	0.669038i	0.0789623	−	0.0573695i
$137$	7.40947	+	5.38329i	0.633033	+	0.459926i	0.857450	−	0.514568i	$-0.172048\pi$
$137$	7.40947	+	5.38329i	0.633033	+	0.459926i	−0.224416	+	0.974493i	$0.572048\pi$
$138$	0.812781	+	0.590520i	0.0691885	+	0.0502684i
$139$	10.5378	−	7.65613i	0.893801	−	0.649384i	−0.0430652	−	0.999072i	$-0.513712\pi$
$139$	10.5378	−	7.65613i	0.893801	−	0.649384i	0.936866	+	0.349688i	$0.113712\pi$
$140$	−2.00799	+	2.81173i	−0.169706	+	0.237634i
$141$	−1.08455	−	0.787974i	−0.0913358	−	0.0663593i
$142$	−1.42609	−	4.38905i	−0.119675	−	0.368321i
$143$	−3.26719			−0.273216
$144$	2.39122	+	7.35941i	0.199268	+	0.613284i
$145$	3.37254	−	4.72247i	0.280074	−	0.392180i
$146$	−3.45258	+	10.6259i	−0.285737	+	0.879409i
$147$	0.559793	−	1.72287i	0.0461709	−	0.142100i
$148$	21.8221	−	15.8547i	1.79377	−	1.30325i
$149$	−12.3327			−1.01034			−0.505168	−	0.863021i	$-0.668569\pi$
$149$	−12.3327			−1.01034			−0.505168	+	0.863021i	$0.668569\pi$
$150$	0.853915	−	2.78178i	0.0697219	−	0.227131i
$151$	−6.47708			−0.527097			−0.263549	−	0.964646i	$-0.584893\pi$
$151$	−6.47708			−0.527097			−0.263549	+	0.964646i	$0.584893\pi$
$152$	−7.13017	+	5.18037i	−0.578333	+	0.420184i
$153$	0.903969	−	2.78213i	0.0730816	−	0.224922i
$154$	−0.684359	+	2.10624i	−0.0551472	+	0.169726i
$155$	−0.00486803	−	0.596453i	−0.000391010	−	0.0479082i
$156$	−0.409958	−	1.26172i	−0.0328229	−	0.101019i
$157$	−14.5343			−1.15996			−0.579981	−	0.814630i	$-0.696940\pi$
$157$	−14.5343			−1.15996			−0.579981	+	0.814630i	$0.696940\pi$
$158$	7.92935	+	24.4040i	0.630825	+	1.94148i
$159$	−1.47803	−	1.07385i	−0.117215	−	0.0851617i
$160$	16.8643	+	5.32777i	1.33324	+	0.421197i
$161$	−0.851428	+	0.618599i	−0.0671019	+	0.0487524i
$162$	−14.3563	−	10.4305i	−1.12794	−	0.819494i
$163$	5.73892	+	4.16957i	0.449507	+	0.326586i	0.789401	−	0.613878i	$-0.210391\pi$
$163$	5.73892	+	4.16957i	0.449507	+	0.326586i	−0.339894	+	0.940464i	$0.610391\pi$
$164$	−1.92596	+	1.39929i	−0.150392	+	0.109266i
$165$	−0.00850831	−	1.04248i	−0.000662371	−	0.0811567i
$166$	−3.24813	−	2.35991i	−0.252104	−	0.183164i
$167$	−1.20034	−	3.69427i	−0.0928853	−	0.285871i	0.893812	−	0.448443i	$-0.148021\pi$
$167$	−1.20034	−	3.69427i	−0.0928853	−	0.285871i	−0.986697	+	0.162571i	$0.948021\pi$
$168$	−0.189651			−0.0146319
$169$	−2.88372	−	8.87518i	−0.221825	−	0.682706i
$170$	−2.83013	−	3.82923i	−0.217061	−	0.293688i
$171$	−6.99945	+	21.5421i	−0.535262	+	1.64737i
$172$	−2.39911	+	7.38369i	−0.182930	+	0.563001i
$173$	−7.79637	+	5.66439i	−0.592747	+	0.430656i	−0.843297	−	0.537448i	$-0.819388\pi$
$173$	−7.79637	+	5.66439i	−0.592747	+	0.430656i	0.250550	+	0.968104i	$0.419388\pi$
$174$	1.51036			0.114500
$175$	2.49501	+	1.75123i	0.188605	+	0.132381i
$176$	4.51253			0.340144
$177$	−1.50339	+	1.09228i	−0.113002	+	0.0821004i
$178$	−8.28895	+	25.5108i	−0.621283	+	1.91211i
$179$	−2.28072	+	7.01934i	−0.170469	+	0.524650i	−0.999398	−	0.0347047i	$-0.988951\pi$
$179$	−2.28072	+	7.01934i	−0.170469	+	0.524650i	0.828929	+	0.559354i	$0.188951\pi$
$180$	−15.7250	+	5.25164i	−1.17207	+	0.391434i
$181$	−5.95005	−	18.3124i	−0.442264	−	1.36115i	−0.885457	−	0.464721i	$-0.846154\pi$
$181$	−5.95005	−	18.3124i	−0.442264	−	1.36115i	0.443193	−	0.896426i	$-0.353846\pi$
$182$	2.48638			0.184303
$183$	0.247466	+	0.761622i	0.0182932	+	0.0563007i
$184$	−1.58964	−	1.15494i	−0.117190	−	0.0851433i
$185$	−14.1444	−	19.1377i	−1.03992	−	1.40703i
$186$	0.125594	−	0.0912496i	0.00920902	−	0.00669075i
$187$	−1.38011	−	1.00271i	−0.100923	−	0.0733251i
$188$	10.0579	+	7.30746i	0.733545	+	0.532951i
$189$	−0.798714	+	0.580299i	−0.0580979	+	0.0422106i
$190$	21.9138	+	29.6498i	1.58979	+	2.15102i
$191$	−12.1659	−	8.83903i	−0.880293	−	0.639570i	0.0530363	−	0.998593i	$-0.483110\pi$
$191$	−12.1659	−	8.83903i	−0.880293	−	0.639570i	−0.933329	+	0.359023i	$0.883110\pi$
$192$	0.975623	+	3.00266i	0.0704095	+	0.216698i
$193$	−14.8772			−1.07089			−0.535444	−	0.844571i	$-0.679856\pi$
$193$	−14.8772			−1.07089			−0.535444	+	0.844571i	$0.679856\pi$
$194$	−6.35042	−	19.5446i	−0.455934	−	1.40322i
$195$	−1.11016	+	0.370756i	−0.0795000	+	0.0265504i
$196$	−5.19137	+	15.9774i	−0.370812	+	1.14124i
$197$	0.690434	−	2.12494i	0.0491914	−	0.151396i	−0.923444	−	0.383734i	$-0.874638\pi$
$197$	0.690434	−	2.12494i	0.0491914	−	0.151396i	0.972635	+	0.232339i	$0.0746378\pi$
$198$	−8.59705	+	6.24612i	−0.610966	+	0.443893i
$199$	−23.3729			−1.65686			−0.828432	−	0.560090i	$-0.810766\pi$
$199$	−23.3729			−1.65686			−0.828432	+	0.560090i	$0.810766\pi$
$200$	−1.67009	+	5.44061i	−0.118093	+	0.384709i
$201$	−3.09810			−0.218523
$202$	5.62900	−	4.08971i	0.396055	−	0.287751i
$203$	−0.488920	+	1.50474i	−0.0343154	+	0.105612i
$204$	0.214052	−	0.658785i	0.0149867	−	0.0461242i
$205$	1.24834	+	1.68903i	0.0871881	+	0.117967i
$206$	8.61196	+	26.5049i	0.600024	+	1.84668i
$207$	−5.04987			−0.350990
$208$	−1.56555	−	4.81827i	−0.108551	−	0.334087i
$209$	10.6862	+	7.76397i	0.739179	+	0.537045i
$210$	0.00647495	+	0.793339i	0.000446814	+	0.0547456i
$211$	−14.4681	+	10.5117i	−0.996028	+	0.723656i	−0.961233	−	0.275738i	$-0.911078\pi$
$211$	−14.4681	+	10.5117i	−0.996028	+	0.723656i	−0.0347948	+	0.999394i	$0.511078\pi$
$212$	13.7068	+	9.95859i	0.941389	+	0.683959i
$213$	−0.479178	−	0.348143i	−0.0328328	−	0.0238544i
$214$	−33.9091	+	24.6364i	−2.31798	+	1.68411i
$215$	6.53128	+	2.06336i	0.445429	+	0.140720i
$216$	−1.49122	−	1.08343i	−0.101465	−	0.0737184i
$217$	0.0502538	+	0.154665i	0.00341145	+	0.0104994i
$218$	−25.5754			−1.73218
$219$	0.443117	+	1.36377i	0.0299431	+	0.0921554i
$220$	0.0789039	+	9.66766i	0.00531970	+	0.651793i
$221$	−0.591837	+	1.82149i	−0.0398113	+	0.122526i
$222$	1.91396	−	5.89056i	0.128457	−	0.395349i
$223$	22.9685	−	16.6876i	1.53809	−	1.11749i	0.586566	−	0.809902i	$-0.300480\pi$
$223$	22.9685	−	16.6876i	1.53809	−	1.11749i	0.951521	−	0.307584i	$-0.0995204\pi$
$224$	−4.82195			−0.322180
$225$	4.74630	+	13.8350i	0.316420	+	0.922335i
$226$	22.2896			1.48268
$227$	22.0947	−	16.0528i	1.46648	−	1.06546i	0.484862	−	0.874591i	$-0.338870\pi$
$227$	22.0947	−	16.0528i	1.46648	−	1.06546i	0.981616	−	0.190868i	$-0.0611302\pi$
$228$	−1.65741	+	5.10099i	−0.109765	+	0.337821i
$229$	−2.32767	+	7.16382i	−0.153817	+	0.473399i	−0.998039	−	0.0625942i	$-0.980063\pi$
$229$	−2.32767	+	7.16382i	−0.153817	+	0.473399i	0.844222	+	0.535993i	$0.180063\pi$
$230$	−4.77702	+	6.68914i	−0.314988	+	0.441069i
$231$	0.0878334	+	0.270323i	0.00577901	+	0.0177860i
$232$	−2.95396			−0.193937
$233$	0.265991	+	0.818638i	0.0174257	+	0.0536307i	0.959391	−	0.282079i	$-0.0910240\pi$
$233$	0.265991	+	0.818638i	0.0174257	+	0.0536307i	−0.941966	+	0.335710i	$0.891024\pi$
$234$	9.65194	+	7.01255i	0.630967	+	0.458424i
$235$	6.37433	−	8.92581i	0.415816	−	0.582256i
$236$	13.9420	−	10.1295i	0.907549	−	0.659373i
$237$	2.66433	+	1.93575i	0.173067	+	0.125741i
$238$	1.05028	+	0.763073i	0.0680795	+	0.0494627i
$239$	−2.82468	+	2.05225i	−0.182714	+	0.132749i	−0.675382	−	0.737468i	$-0.736021\pi$
$239$	−2.82468	+	2.05225i	−0.182714	+	0.132749i	0.492669	+	0.870217i	$0.336021\pi$
$240$	1.53331	−	0.512075i	0.0989747	−	0.0330543i
$241$	−15.9258	−	11.5708i	−1.02587	−	0.745340i	−0.0583936	−	0.998294i	$-0.518598\pi$
$241$	−15.9258	−	11.5708i	−1.02587	−	0.745340i	−0.967478	+	0.252954i	$0.918598\pi$
$242$	−5.32342	−	16.3838i	−0.342203	−	1.05319i
$243$	−7.13569			−0.457754
$244$	−2.29493	−	7.06308i	−0.146918	−	0.452167i
$245$	14.1329	+	4.46487i	0.902917	+	0.285250i
$246$	−0.168921	+	0.519884i	−0.0107700	+	0.0331466i
$247$	4.58261	−	14.1038i	0.291584	−	0.897404i
$248$	−0.245638	+	0.178466i	−0.0155980	+	0.0113326i
$249$	−0.515290			−0.0326552
$250$	22.8160	+	6.80050i	1.44301	+	0.430101i
$251$	9.29596			0.586756			0.293378	−	0.955997i	$-0.405221\pi$
$251$	9.29596			0.586756			0.293378	+	0.955997i	$0.405221\pi$
$252$	3.65685	−	2.65685i	0.230360	−	0.167366i
$253$	−0.910009	+	2.80072i	−0.0572118	+	0.176080i
$254$	−3.62623	+	11.1604i	−0.227530	+	0.700265i
$255$	−0.582731	−	0.184097i	−0.0364920	−	0.0115286i
$256$	1.36157	+	4.19049i	0.0850983	+	0.261906i
$257$	−30.7179			−1.91613			−0.958064	−	0.286553i	$-0.907490\pi$
$257$	−30.7179			−1.91613			−0.958064	+	0.286553i	$0.907490\pi$
$258$	0.550884	+	1.69545i	0.0342966	+	0.105554i
$259$	5.24907	+	3.81367i	0.326161	+	0.236970i
$260$	10.2953	−	3.43829i	0.638488	−	0.213234i
$261$	−6.14190	+	4.46235i	−0.380174	+	0.276213i
$262$	−21.8414	−	15.8687i	−1.34937	−	0.980371i
$263$	8.18200	+	5.94457i	0.504524	+	0.366558i	0.810742	−	0.585403i	$-0.199064\pi$
$263$	8.18200	+	5.94457i	0.504524	+	0.366558i	−0.306219	+	0.951961i	$0.599064\pi$
$264$	−0.429324	+	0.311922i	−0.0264231	+	0.0191975i
$265$	8.68692	−	12.1641i	0.533633	−	0.747233i
$266$	−8.13234	−	5.90849i	−0.498625	−	0.362273i
$267$	1.06384	+	3.27415i	0.0651057	+	0.200375i
$268$	28.7310			1.75502
$269$	−5.21215	−	16.0414i	−0.317791	−	0.978059i	−0.974591	−	0.223994i	$-0.928090\pi$
$269$	−5.21215	−	16.0414i	−0.317791	−	0.978059i	0.656800	−	0.754065i	$-0.271910\pi$
$270$	−4.48127	+	6.27500i	−0.272721	+	0.381884i
$271$	6.29022	−	19.3593i	0.382104	−	1.17599i	−0.556456	−	0.830877i	$-0.687839\pi$
$271$	6.29022	−	19.3593i	0.382104	−	1.17599i	0.938560	−	0.345117i	$-0.112161\pi$
$272$	0.817424	−	2.51577i	0.0495636	−	0.152541i
$273$	0.258167	−	0.187569i	0.0156250	−	0.0113522i
$274$	−19.5027			−1.17820
$275$	8.52838	−	0.139220i	0.514281	−	0.00839531i
$276$	−1.19577			−0.0719766
$277$	6.22505	−	4.52276i	0.374027	−	0.271746i	−0.384852	−	0.922978i	$-0.625747\pi$
$277$	6.22505	−	4.52276i	0.374027	−	0.271746i	0.758879	+	0.651232i	$0.225747\pi$
$278$	−8.57114	+	26.3793i	−0.514063	+	1.58212i
$279$	−0.241134	+	0.742135i	−0.0144363	+	0.0444305i
$280$	−0.0126637	−	1.55161i	−0.000756802	−	0.0927267i
$281$	6.71255	+	20.6591i	0.400437	+	1.23242i	0.924646	+	0.380828i	$0.124361\pi$
$281$	6.71255	+	20.6591i	0.400437	+	1.23242i	−0.524209	+	0.851590i	$0.675639\pi$
$282$	2.85469			0.169994
$283$	0.647887	+	1.99399i	0.0385129	+	0.118530i	0.968465	−	0.249151i	$-0.0801516\pi$
$283$	0.647887	+	1.99399i	0.0385129	+	0.118530i	−0.929952	+	0.367682i	$0.880152\pi$
$284$	4.44377	+	3.22859i	0.263690	+	0.191582i
$285$	4.51210	+	1.42546i	0.267274	+	0.0844372i
$286$	5.62857	−	4.08939i	0.332824	−	0.241811i
$287$	−0.463268	−	0.336584i	−0.0273459	−	0.0198679i
$288$	−18.7185	−	13.5998i	−1.10300	−	0.801373i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	0.100853	+	12.3569i	0.00592227	+	0.725623i
$291$	−2.13380	−	1.55029i	−0.125085	−	0.0908799i
$292$	−4.10935	−	12.6473i	−0.240482	−	0.740127i
$293$	−1.51774			−0.0886676			−0.0443338	−	0.999017i	$-0.514117\pi$
$293$	−1.51774			−0.0886676			−0.0443338	+	0.999017i	$0.514117\pi$
$294$	1.19205	+	3.66874i	0.0695216	+	0.213965i
$295$	−9.03676	−	12.2269i	−0.526141	−	0.711879i
$296$	−3.74333	+	11.5208i	−0.217576	+	0.669631i
$297$	−0.853668	+	2.62732i	−0.0495348	+	0.152453i
$298$	21.2463	−	15.4363i	1.23076	−	0.894201i
$299$	3.30620			0.191202
$300$	1.12388	+	3.27602i	0.0648874	+	0.189141i
$301$	−1.86747			−0.107639
$302$	11.1584	−	8.10706i	0.642095	−	0.466509i
$303$	0.275951	−	0.849289i	0.0158530	−	0.0487904i
$304$	−6.32933	+	19.4797i	−0.363012	+	1.11724i
$305$	−6.21463	+	2.07548i	−0.355849	+	0.118842i
$306$	1.92495	+	5.92439i	0.110042	+	0.338675i
$307$	−9.41647			−0.537427			−0.268713	−	0.963220i	$-0.586598\pi$
$307$	−9.41647			−0.537427			−0.268713	+	0.963220i	$0.586598\pi$
$308$	−0.814544	−	2.50691i	−0.0464130	−	0.142844i
$309$	2.89369	+	2.10239i	0.164617	+	0.119601i
$310$	0.754939	+	1.02145i	0.0428777	+	0.0580144i
$311$	12.9124	−	9.38142i	0.732196	−	0.531972i	−0.158061	−	0.987429i	$-0.550524\pi$
$311$	12.9124	−	9.38142i	0.732196	−	0.531972i	0.890257	+	0.455458i	$0.150524\pi$
$312$	0.482004	+	0.350196i	0.0272881	+	0.0198260i
$313$	−12.6666	−	9.20279i	−0.715956	−	0.520172i	0.169134	−	0.985593i	$-0.445903\pi$
$313$	−12.6666	−	9.20279i	−0.715956	−	0.520172i	−0.885090	+	0.465421i	$0.845903\pi$
$314$	25.0390	−	18.1919i	1.41303	−	1.02663i
$315$	−2.37025	−	3.20699i	−0.133548	−	0.180694i
$316$	−24.7083	−	17.9517i	−1.38995	−	1.00986i
$317$	5.95022	+	18.3129i	0.334197	+	1.02855i	0.967116	+	0.254336i	$0.0818568\pi$
$317$	5.95022	+	18.3129i	0.334197	+	1.02855i	−0.632919	+	0.774218i	$0.718143\pi$
$318$	3.89036			0.218161
$319$	1.36808	+	4.21051i	0.0765976	+	0.235743i
$320$	−24.5009	+	8.18249i	−1.36964	+	0.457415i
$321$	−1.66233	+	5.11611i	−0.0927820	+	0.285554i
$322$	0.692530	−	2.13139i	0.0385932	−	0.118778i
$323$	6.26423	−	4.55123i	0.348551	−	0.253237i
$324$	21.1210			1.17339
$325$	−3.10744	−	9.05792i	−0.172370	−	0.502443i
$326$	−15.1056			−0.836622
$327$	−2.65556	+	1.92937i	−0.146853	+	0.106695i
$328$	0.330375	−	1.01679i	0.0182419	−	0.0561429i
$329$	−0.924093	+	2.84407i	−0.0509469	+	0.156798i
$330$	1.31948	+	1.78528i	0.0726349	+	0.0982765i
$331$	−2.94172	−	9.05368i	−0.161692	−	0.497635i	0.837086	−	0.547072i	$-0.184258\pi$
$331$	−2.94172	−	9.05368i	−0.161692	−	0.497635i	−0.998777	+	0.0494363i	$0.984258\pi$
$332$	4.77867			0.262263
$333$	9.62049	+	29.6088i	0.527200	+	1.62255i
$334$	6.69185	+	4.86191i	0.366162	+	0.266032i
$335$	−0.206872	−	25.3469i	−0.0113026	−	1.38485i
$336$	−0.356571	+	0.259064i	−0.0194525	+	0.0141331i
$337$	2.24991	+	1.63465i	0.122560	+	0.0890453i	0.647377	−	0.762170i	$-0.275866\pi$
$337$	2.24991	+	1.63465i	0.122560	+	0.0890453i	−0.524816	+	0.851215i	$0.675866\pi$
$338$	16.0766	+	11.6803i	0.874452	+	0.635326i
$339$	2.31439	−	1.68150i	0.125700	−	0.0913265i
$340$	5.40410	+	1.70726i	0.293078	+	0.0925894i
$341$	0.368144	+	0.267472i	0.0199361	+	0.0144844i
$342$	−14.9049	−	45.8727i	−0.805966	−	2.48051i
$343$	−8.30853			−0.448618
$344$	−1.07742	−	3.31596i	−0.0580906	−	0.178785i
$345$	0.00860989	+	1.05492i	0.000463541	+	0.0567951i
$346$	6.34136	−	19.5167i	0.340914	−	1.04923i
$347$	7.38903	−	22.7411i	0.396664	−	1.22081i	−0.530995	−	0.847375i	$-0.678182\pi$
$347$	7.38903	−	22.7411i	0.396664	−	1.22081i	0.927658	−	0.373430i	$-0.121818\pi$
$348$	−1.45435	+	1.05665i	−0.0779613	+	0.0566422i
$349$	22.3598			1.19689			0.598445	−	0.801164i	$-0.295785\pi$
$349$	22.3598			1.19689			0.598445	+	0.801164i	$0.295785\pi$
$350$	−6.49022	+	0.105949i	−0.346917	+	0.00566320i
$351$	3.10150			0.165546
$352$	−10.9157	+	7.93075i	−0.581811	+	0.422710i
$353$	−3.47452	+	10.6935i	−0.184930	+	0.569156i	−0.999947	−	0.0102806i	$-0.996728\pi$
$353$	−3.47452	+	10.6935i	−0.184930	+	0.569156i	0.815017	+	0.579437i	$0.196728\pi$
$354$	1.22282	−	3.76344i	0.0649920	−	0.200025i
$355$	2.81631	−	3.94361i	0.149474	−	0.209305i
$356$	−9.86574	−	30.3636i	−0.522883	−	1.60927i
$357$	0.166618			0.00881838
$358$	−4.85666	−	14.9473i	−0.256683	−	0.789988i
$359$	12.4016	+	9.01031i	0.654533	+	0.475546i	0.864812	−	0.502095i	$-0.167437\pi$
$359$	12.4016	+	9.01031i	0.654533	+	0.475546i	−0.210279	+	0.977641i	$0.567437\pi$
$360$	4.32699	−	6.05897i	0.228053	−	0.319336i
$361$	−33.1328	+	24.0724i	−1.74383	+	1.26697i
$362$	33.1712	+	24.1003i	1.74344	+	1.26668i
$363$	−1.78872	−	1.29958i	−0.0938833	−	0.0682102i
$364$	−2.39417	+	1.73947i	−0.125489	+	0.0911728i
$365$	−11.1280	+	3.71640i	−0.582468	+	0.194525i
$366$	−1.37961	−	1.00235i	−0.0721134	−	0.0523934i
$367$	0.301641	+	0.928356i	0.0157455	+	0.0484598i	0.958621	−	0.284687i	$-0.0918896\pi$
$367$	0.301641	+	0.928356i	0.0157455	+	0.0484598i	−0.942875	+	0.333147i	$0.891890\pi$
$368$	−4.56640			−0.238040
$369$	−0.849077	−	2.61319i	−0.0442012	−	0.136037i
$370$	48.3210	+	15.2656i	2.51209	+	0.793620i
$371$	−1.25935	+	3.87588i	−0.0653823	+	0.201226i
$372$	−0.0570986	+	0.175731i	−0.00296042	+	0.00911124i
$373$	10.8652	−	7.89403i	0.562578	−	0.408737i	−0.269823	−	0.962910i	$-0.586965\pi$
$373$	10.8652	−	7.89403i	0.562578	−	0.408737i	0.832402	+	0.554173i	$0.186965\pi$
$374$	3.63262			0.187838
$375$	2.88206	−	1.01509i	0.148829	−	0.0524192i
$376$	−5.58320			−0.287932
$377$	4.02116	−	2.92154i	0.207100	−	0.150467i
$378$	0.649653	−	1.99943i	0.0334146	−	0.102839i
$379$	7.01439	−	21.5881i	0.360305	−	1.10891i	−0.592564	−	0.805523i	$-0.701884\pi$
$379$	7.01439	−	21.5881i	0.360305	−	1.10891i	0.952869	−	0.303382i	$-0.0981157\pi$
$380$	−41.8440	−	13.2194i	−2.14655	−	0.678140i
$381$	0.465405	+	1.43237i	0.0238434	+	0.0733824i
$382$	32.0223			1.63840
$383$	4.59650	+	14.1466i	0.234870	+	0.722856i	0.997139	+	0.0755952i	$0.0240857\pi$
$383$	4.59650	+	14.1466i	0.234870	+	0.722856i	−0.762268	+	0.647261i	$0.775914\pi$
$384$	−1.94145	−	1.41055i	−0.0990742	−	0.0719816i
$385$	−2.20577	+	0.736653i	−0.112416	+	0.0375433i
$386$	25.6298	−	18.6212i	1.30452	−	0.947792i
$387$	−7.24937	−	5.26697i	−0.368506	−	0.267735i
$388$	19.7883	+	14.3770i	1.00460	+	0.729883i
$389$	−10.4242	+	7.57363i	−0.528528	+	0.383998i	−0.819807	−	0.572640i	$-0.805919\pi$
$389$	−10.4242	+	7.57363i	−0.528528	+	0.383998i	0.291279	+	0.956638i	$0.405919\pi$
$390$	1.44847	−	2.02826i	0.0733462	−	0.102705i
$391$	1.39658	+	1.01468i	0.0706282	+	0.0513144i
$392$	−2.33141	−	7.17533i	−0.117754	−	0.362409i
$393$	−3.46496			−0.174784
$394$	1.47024	+	4.52493i	0.0740696	+	0.227963i
$395$	−15.6593	+	21.9273i	−0.787905	+	1.10328i
$396$	3.90845	−	12.0290i	0.196407	−	0.604478i
$397$	−10.1209	+	31.1491i	−0.507956	+	1.56333i	0.287788	+	0.957694i	$0.407080\pi$
$397$	−10.1209	+	31.1491i	−0.507956	+	1.56333i	−0.795744	+	0.605633i	$0.792920\pi$
$398$	40.2658	−	29.2548i	2.01834	−	1.46641i
$399$	−1.29013			−0.0645872
$400$	4.29189	+	12.5105i	0.214595	+	0.625524i
$401$	19.0704			0.952332			0.476166	−	0.879355i	$-0.342026\pi$
$401$	19.0704			0.952332			0.476166	+	0.879355i	$0.342026\pi$
$402$	5.33726	−	3.87775i	0.266198	−	0.193404i
$403$	0.157873	−	0.485883i	0.00786421	−	0.0242036i
$404$	−2.55910	+	7.87609i	−0.127320	+	0.391850i
$405$	−0.152078	−	18.6333i	−0.00755682	−	0.925896i
$406$	−1.04113	−	3.20426i	−0.0516702	−	0.159025i
$407$	18.1551			0.899913
$408$	0.0961292	+	0.295855i	0.00475911	+	0.0146470i
$409$	−10.7633	−	7.82003i	−0.532213	−	0.386675i	0.288972	−	0.957338i	$-0.406687\pi$
$409$	−10.7633	−	7.82003i	−0.532213	−	0.386675i	−0.821185	+	0.570662i	$0.806687\pi$
$410$	−4.26468	−	1.34730i	−0.210617	−	0.0665383i
$411$	−2.02501	+	1.47126i	−0.0998866	+	0.0725719i
$412$	−26.8354	−	19.4970i	−1.32208	−	0.960550i
$413$	3.35360	+	2.43653i	0.165020	+	0.119894i
$414$	8.69969	−	6.32069i	0.427566	−	0.310645i
$415$	−0.0344079	−	4.21581i	−0.00168902	−	0.206946i
$416$	12.2551	+	8.90389i	0.600858	+	0.436549i
$417$	1.10005	+	3.38562i	0.0538699	+	0.165794i
$418$	−28.1275			−1.37576
$419$	1.05673	+	3.25228i	0.0516246	+	0.158884i	0.973545	−	0.228495i	$-0.0733804\pi$
$419$	1.05673	+	3.25228i	0.0516246	+	0.158884i	−0.921920	+	0.387379i	$0.873380\pi$
$420$	−0.561254	−	0.759389i	−0.0273864	−	0.0370544i
$421$	−3.48563	+	10.7277i	−0.169879	+	0.522835i	−0.999363	−	0.0356968i	$-0.988635\pi$
$421$	−3.48563	+	10.7277i	−0.169879	+	0.522835i	0.829483	+	0.558531i	$0.188635\pi$
$422$	11.7680	−	36.2182i	0.572858	−	1.76308i
$423$	−11.6086	+	8.43416i	−0.564431	+	0.410083i
$424$	−7.60878			−0.369515
$425$	1.46726	−	4.77987i	0.0711727	−	0.231858i
$426$	1.26126			0.0611083
$427$	1.44521	−	1.05001i	0.0699386	−	0.0508134i
$428$	15.4160	−	47.4455i	0.745159	−	2.29336i
$429$	0.275929	−	0.849223i	0.0133220	−	0.0410009i
$430$	−13.8344	+	4.62023i	−0.667154	+	0.222808i
$431$	−6.79245	−	20.9050i	−0.327181	−	1.00696i	−0.970447	−	0.241316i	$-0.922421\pi$
$431$	−6.79245	−	20.9050i	−0.327181	−	1.00696i	0.643266	−	0.765643i	$-0.277579\pi$
$432$	−4.28368			−0.206099
$433$	−0.658362	−	2.02623i	−0.0316388	−	0.0973743i	0.933990	−	0.357299i	$-0.116302\pi$
$433$	−0.658362	−	2.02623i	−0.0316388	−	0.0973743i	−0.965629	+	0.259925i	$0.916302\pi$
$434$	−0.280163	−	0.203550i	−0.0134482	−	0.00977072i
$435$	0.942661	+	1.27544i	0.0451971	+	0.0611527i
$436$	24.6269	−	17.8925i	1.17942	−	0.856896i
$437$	−10.8138	−	7.85666i	−0.517292	−	0.375835i
$438$	−2.47036	−	1.79482i	−0.118038	−	0.0857598i
$439$	6.93163	−	5.03612i	0.330829	−	0.240361i	−0.409954	−	0.912106i	$-0.634455\pi$
$439$	6.93163	−	5.03612i	0.330829	−	0.240361i	0.740782	+	0.671745i	$0.234455\pi$
$440$	−2.58064	−	3.49166i	−0.123027	−	0.166458i
$441$	−15.6867	−	11.3971i	−0.746988	−	0.542718i
$442$	−1.26028	−	3.87875i	−0.0599455	−	0.184493i
$443$	24.2529			1.15229			0.576145	−	0.817347i	$-0.304556\pi$
$443$	24.2529			1.15229			0.576145	+	0.817347i	$0.304556\pi$
$444$	2.27805	+	7.01111i	0.108111	+	0.332733i
$445$	−26.7162	+	8.92233i	−1.26647	+	0.422959i
$446$	−18.6820	+	57.4973i	−0.884619	+	2.72258i
$447$	1.04156	−	3.20558i	0.0492639	−	0.151619i
$448$	5.69767	−	4.13960i	0.269190	−	0.195578i
$449$	40.0462			1.88990			0.944948	−	0.327220i	$-0.106112\pi$
$449$	40.0462			1.88990			0.944948	+	0.327220i	$0.106112\pi$
$450$	−25.4934	−	17.8936i	−1.20177	−	0.843514i
$451$	−1.60231			−0.0754501
$452$	−21.4630	+	15.5938i	−1.00954	+	0.733470i
$453$	0.547019	−	1.68355i	0.0257012	−	0.0791002i
$454$	−17.9713	+	55.3099i	−0.843434	+	2.59582i
$455$	1.55182	+	2.09965i	0.0727506	+	0.0984330i
$456$	−0.744330	−	2.29081i	−0.0348565	−	0.107277i
$457$	−1.43925			−0.0673254			−0.0336627	−	0.999433i	$-0.510717\pi$
$457$	−1.43925			−0.0673254			−0.0336627	+	0.999433i	$0.510717\pi$
$458$	−4.95663	−	15.2549i	−0.231608	−	0.712817i
$459$	1.31012	+	0.951855i	0.0611510	+	0.0444288i
$460$	−0.0798459	−	9.78308i	−0.00372283	−	0.456138i
$461$	−20.9604	+	15.2287i	−0.976225	+	0.709269i	−0.956862	−	0.290543i	$-0.906164\pi$
$461$	−20.9604	+	15.2287i	−0.976225	+	0.709269i	−0.0193634	+	0.999813i	$0.506164\pi$
$462$	−0.489667	−	0.355764i	−0.0227814	−	0.0165516i
$463$	−10.0449	−	7.29805i	−0.466826	−	0.339169i	0.329377	−	0.944199i	$-0.393161\pi$
$463$	−10.0449	−	7.29805i	−0.466826	−	0.339169i	−0.796203	+	0.605029i	$0.793161\pi$
$464$	−5.55388	+	4.03513i	−0.257832	+	0.187326i
$465$	0.155444	+	0.0491079i	0.00720854	+	0.00227732i
$466$	−1.48289	−	1.07738i	−0.0686935	−	0.0499088i
$467$	7.00568	+	21.5613i	0.324184	+	0.997737i	0.971807	+	0.235776i	$0.0757632\pi$
$467$	7.00568	+	21.5613i	0.324184	+	0.997737i	−0.647623	+	0.761961i	$0.724237\pi$
$468$	−14.2000			−0.656394
$469$	2.13559	+	6.57267i	0.0986123	+	0.303498i
$470$	0.190619	+	23.3554i	0.00879258	+	1.07731i
$471$	1.22749	−	3.77782i	0.0565596	−	0.174073i
$472$	−2.39159	+	7.36055i	−0.110082	+	0.338797i
$473$	−4.22750	+	3.07146i	−0.194381	+	0.141226i
$474$	−7.01288			−0.322112
$475$	−11.3610	+	37.0106i	−0.521280	+	1.69816i
$476$	−1.54517			−0.0708230
$477$	−15.8202	+	11.4941i	−0.724357	+	0.526276i
$478$	2.29752	−	7.07105i	0.105086	−	0.323423i
$479$	3.57389	−	10.9993i	0.163295	−	0.502571i	−0.835611	−	0.549321i	$-0.814886\pi$
$479$	3.57389	−	10.9993i	0.163295	−	0.502571i	0.998907	+	0.0467498i	$0.0148864\pi$
$480$	−2.80909	+	3.93349i	−0.128217	+	0.179538i
$481$	−6.29862	−	19.3852i	−0.287192	−	0.883887i
$482$	41.9189			1.90935
$483$	−0.0888820	−	0.273551i	−0.00404427	−	0.0124470i
$484$	16.5881	+	12.0520i	0.754004	+	0.547816i
$485$	12.5411	−	17.5610i	0.569464	−	0.797406i
$486$	12.2930	−	8.93141i	0.557623	−	0.405137i
$487$	28.4263	+	20.6529i	1.28812	+	0.935873i	0.999766	−	0.0216518i	$-0.00689252\pi$
$487$	28.4263	+	20.6529i	1.28812	+	0.935873i	0.288352	+	0.957524i	$0.406893\pi$
$488$	2.69824	+	1.96039i	0.122144	+	0.0887426i
$489$	−1.56845	+	1.13955i	−0.0709279	+	0.0515321i
$490$	−29.9360	+	9.99762i	−1.35237	+	0.451647i
$491$	−14.9296	−	10.8470i	−0.673762	−	0.489517i	0.197520	−	0.980299i	$-0.436711\pi$
$491$	−14.9296	−	10.8470i	−0.673762	−	0.489517i	−0.871283	+	0.490782i	$0.836711\pi$
$492$	−0.201054	−	0.618781i	−0.00906422	−	0.0278968i
$493$	2.59522			0.116883
$494$	9.75839	+	30.0332i	0.439051	+	1.35126i
$495$	−10.6403	−	3.36148i	−0.478245	−	0.151087i
$496$	−0.218048	+	0.671084i	−0.00979066	+	0.0301326i
$497$	−0.408284	+	1.25657i	−0.0183140	+	0.0563648i
$498$	0.887718	−	0.644965i	0.0397796	−	0.0289016i
$499$	−17.5459			−0.785461			−0.392731	−	0.919654i	$-0.628470\pi$
$499$	−17.5459			−0.785461			−0.392731	+	0.919654i	$0.628470\pi$
$500$	−26.7275	+	9.41372i	−1.19529	+	0.420994i
$501$	1.06161			0.0474291
$502$	−16.0147	+	11.6353i	−0.714769	+	0.519310i
$503$	9.44423	−	29.0664i	0.421097	−	1.29600i	−0.485584	−	0.874190i	$-0.661393\pi$
$503$	9.44423	−	29.0664i	0.421097	−	1.29600i	0.906682	−	0.421815i	$-0.138607\pi$
$504$	−0.627288	+	1.93059i	−0.0279416	+	0.0859955i
$505$	6.96683	+	2.20096i	0.310020	+	0.0979415i
$506$	−1.93781	−	5.96397i	−0.0861462	−	0.265131i
$507$	2.55042			0.113268
$508$	−4.31604	−	13.2834i	−0.191493	−	0.589356i
$509$	−26.6649	−	19.3732i	−1.18190	−	0.858702i	−0.189517	−	0.981877i	$-0.560692\pi$
$509$	−26.6649	−	19.3732i	−1.18190	−	0.858702i	−0.992385	+	0.123175i	$0.960692\pi$
$510$	1.23433	−	0.412225i	0.0546570	−	0.0182536i
$511$	2.58782	−	1.88016i	0.114478	−	0.0831735i
$512$	−21.7981	−	15.8373i	−0.963350	−	0.699915i
$513$	−10.1443	−	7.37023i	−0.447880	−	0.325404i
$514$	52.9194	−	38.4482i	2.33417	−	1.69588i
$515$	−17.0074	+	23.8150i	−0.749434	+	1.04941i
$516$	−1.71659	−	1.24717i	−0.0755686	−	0.0549038i
$517$	2.58576	+	7.95816i	0.113722	+	0.349999i
$518$	−13.8163			−0.607052
$519$	−0.813876	−	2.50485i	−0.0357252	−	0.109951i
$520$	−2.83292	+	3.96687i	−0.124232	+	0.173959i
$521$	−3.91399	+	12.0460i	−0.171475	+	0.527745i	−0.999455	−	0.0330121i	$-0.989490\pi$
$521$	−3.91399	+	12.0460i	−0.171475	+	0.527745i	0.827980	+	0.560758i	$0.189490\pi$
$522$	4.99566	−	15.3751i	0.218654	−	0.672948i
$523$	12.7811	−	9.28599i	0.558877	−	0.406048i	−0.272171	−	0.962249i	$-0.587742\pi$
$523$	12.7811	−	9.28599i	0.558877	−	0.406048i	0.831048	+	0.556201i	$0.187742\pi$
$524$	32.1331			1.40374
$525$	−0.665903	+	0.500615i	−0.0290624	+	0.0218486i
$526$	−21.5361			−0.939019
$527$	0.215806	−	0.156792i	0.00940065	−	0.00682997i
$528$	−0.381104	+	1.17292i	−0.0165854	+	0.0510447i
$529$	−6.18652	+	19.0401i	−0.268979	+	0.827832i
$530$	0.259775	+	31.8287i	0.0112839	+	1.38255i
$531$	6.14647	+	18.9169i	0.266734	+	0.820924i
$532$	11.9643			0.518719
$533$	0.555899	+	1.71088i	0.0240786	+	0.0741064i
$534$	−5.93083	−	4.30900i	−0.256652	−	0.186469i
$535$	−41.9681	−	13.2586i	−1.81444	−	0.573218i
$536$	−10.4386	+	7.58410i	−0.450880	+	0.327583i
$537$	−1.63188	−	1.18563i	−0.0704209	−	0.0511638i
$538$	29.0575	+	21.1115i	1.25276	+	0.910182i
$539$	−9.14779	+	6.64626i	−0.394023	+	0.286275i
$540$	−0.0749024	−	9.17738i	−0.00322329	−	0.394932i
$541$	−2.03024	−	1.47506i	−0.0872870	−	0.0634177i	0.543286	−	0.839548i	$-0.317180\pi$
$541$	−2.03024	−	1.47506i	−0.0872870	−	0.0634177i	−0.630573	+	0.776130i	$0.717180\pi$
$542$	13.3947	+	41.2245i	0.575350	+	1.77075i
$543$	5.26235			0.225829
$544$	2.44413	+	7.52224i	0.104791	+	0.322514i
$545$	−15.9624	−	21.5974i	−0.683753	−	0.925132i
$546$	−0.209986	+	0.646271i	−0.00898658	+	0.0276578i
$547$	−3.65241	+	11.2410i	−0.156166	+	0.480629i	−0.998277	−	0.0586749i	$-0.981312\pi$
$547$	−3.65241	+	11.2410i	−0.156166	+	0.480629i	0.842111	+	0.539304i	$0.181312\pi$
$548$	18.7795	−	13.6441i	0.802219	−	0.582846i
$549$	8.57162			0.365828
$550$	−14.5181	+	10.9144i	−0.619052	+	0.465393i
$551$	−20.0948			−0.856068
$552$	0.434450	−	0.315646i	0.0184914	−	0.0134348i
$553$	2.27014	−	6.98678i	0.0965363	−	0.297108i
$554$	−5.06329	+	15.5832i	−0.215119	+	0.662067i
$555$	6.16891	−	2.06021i	0.261856	−	0.0874511i
$556$	−10.2016	−	31.3974i	−0.432645	−	1.33154i
$557$	−35.2654			−1.49424			−0.747122	−	0.664687i	$-0.768565\pi$
$557$	−35.2654			−1.49424			−0.747122	+	0.664687i	$0.768565\pi$
$558$	−0.513482	−	1.58033i	−0.0217374	−	0.0669009i
$559$	4.74623	+	3.44834i	0.200744	+	0.145849i
$560$	−2.14332	−	2.89996i	−0.0905719	−	0.122546i
$561$	0.377184	−	0.274040i	0.0159247	−	0.0115700i
$562$	−37.4221	−	27.1888i	−1.57856	−	1.14689i
$563$	19.4254	+	14.1134i	0.818681	+	0.594807i	0.916335	−	0.400414i	$-0.131134\pi$
$563$	19.4254	+	14.1134i	0.818681	+	0.594807i	−0.0976530	+	0.995221i	$0.531134\pi$
$564$	−2.74882	+	1.99714i	−0.115746	+	0.0840946i
$565$	13.9116	+	18.8227i	0.585266	+	0.791877i
$566$	−3.61194	−	2.62423i	−0.151821	−	0.110304i
$567$	1.56994	+	4.83178i	0.0659313	+	0.202916i
$568$	−2.46678			−0.103504
$569$	−13.5996	−	41.8553i	−0.570126	−	1.75467i	−0.652208	−	0.758040i	$-0.726157\pi$
$569$	−13.5996	−	41.8553i	−0.570126	−	1.75467i	0.0820821	−	0.996626i	$-0.473843\pi$
$570$	−9.55743	+	3.19187i	−0.400317	+	0.133693i
$571$	9.86449	−	30.3598i	0.412816	−	1.27052i	−0.501374	−	0.865231i	$-0.667172\pi$
$571$	9.86449	−	30.3598i	0.412816	−	1.27052i	0.914190	−	0.405286i	$-0.132828\pi$
$572$	−2.55890	+	7.87548i	−0.106993	+	0.329290i
$573$	3.32495	−	2.41572i	0.138902	−	0.100918i
$574$	1.21938			0.0508961
$575$	−8.63020	+	0.140883i	−0.359904	+	0.00587521i
$576$	33.7932			1.40805
$577$	−6.19320	+	4.49962i	−0.257826	+	0.187322i	−0.709188	−	0.705019i	$-0.750938\pi$
$577$	−6.19320	+	4.49962i	−0.257826	+	0.187322i	0.451362	+	0.892341i	$0.350938\pi$
$578$	0.658034	−	2.02522i	0.0273706	−	0.0842380i
$579$	1.25645	−	3.86696i	0.0522164	−	0.160705i
$580$	−8.74199	−	11.8281i	−0.362991	−	0.491135i
$581$	0.355201	+	1.09320i	0.0147362	+	0.0453534i
$582$	5.61644			0.232809
$583$	3.52387	+	10.8454i	0.145944	+	0.449169i
$584$	4.83153	+	3.51031i	0.199930	+	0.145258i
$585$	0.102244	+	12.5274i	0.00422728	+	0.517945i
$586$	2.61470	−	1.89969i	0.108012	−	0.0784756i
$587$	−7.40325	−	5.37878i	−0.305565	−	0.222006i	0.424426	−	0.905462i	$-0.360476\pi$
$587$	−7.40325	−	5.37878i	−0.305565	−	0.222006i	−0.729991	+	0.683457i	$0.760476\pi$
$588$	−3.71449	−	2.69873i	−0.153183	−	0.111294i
$589$	−1.67099	+	1.21404i	−0.0688519	+	0.0500238i
$590$	30.8720	+	9.75310i	1.27098	+	0.401529i
$591$	0.494014	+	0.358922i	0.0203210	+	0.0147641i
$592$	8.69943	+	26.7741i	0.357544	+	1.10041i
$593$	24.2602			0.996247			0.498123	−	0.867106i	$-0.334023\pi$
$593$	24.2602			0.996247			0.498123	+	0.867106i	$0.334023\pi$
$594$	−1.81784	−	5.59472i	−0.0745867	−	0.229554i
$595$	0.0111257	+	1.36318i	0.000456111	+	0.0558848i
$596$	−9.65912	+	29.7277i	−0.395653	+	1.21769i
$597$	1.97395	−	6.07520i	0.0807885	−	0.248641i
$598$	−5.69576	+	4.13821i	−0.232917	+	0.169224i
$599$	31.4876			1.28655			0.643274	−	0.765636i	$-0.277576\pi$
$599$	31.4876			1.28655			0.643274	+	0.765636i	$0.277576\pi$
$600$	−1.27310	−	0.893582i	−0.0519742	−	0.0364803i
$601$	35.0320			1.42899			0.714493	−	0.699642i	$-0.246657\pi$
$601$	35.0320			1.42899			0.714493	+	0.699642i	$0.246657\pi$
$602$	3.21718	−	2.33742i	0.131123	−	0.0952662i
$603$	−10.2473	+	31.5378i	−0.417301	+	1.28432i
$604$	−5.07292	+	15.6128i	−0.206414	+	0.635277i
$605$	10.5130	−	14.7210i	0.427413	−	0.598495i
$606$	0.587621	+	1.80851i	0.0238705	+	0.0734658i
$607$	−4.91243			−0.199390			−0.0996948	−	0.995018i	$-0.531787\pi$
$607$	−4.91243			−0.199390			−0.0996948	+	0.995018i	$0.531787\pi$
$608$	−18.9249	−	58.2449i	−0.767506	−	2.36214i
$609$	−0.349827	−	0.254164i	−0.0141757	−	0.0102993i
$610$	8.10850	−	11.3541i	0.328304	−	0.459715i
$611$	7.60027	−	5.52192i	0.307474	−	0.223393i
$612$	−5.99826	−	4.35799i	−0.242465	−	0.176161i
$613$	1.37021	+	0.995515i	0.0553422	+	0.0402085i	0.615112	−	0.788439i	$-0.289111\pi$
$613$	1.37021	+	0.995515i	0.0553422	+	0.0402085i	−0.559770	+	0.828648i	$0.689111\pi$
$614$	16.2223	−	11.7862i	0.654678	−	0.475651i
$615$	−0.544450	+	0.181828i	−0.0219544	+	0.00733203i
$616$	0.957691	+	0.695803i	0.0385865	+	0.0280347i
$617$	8.48639	+	26.1184i	0.341649	+	1.05149i	0.963353	+	0.268236i	$0.0864408\pi$
$617$	8.48639	+	26.1184i	0.341649	+	1.05149i	−0.621704	+	0.783252i	$0.713559\pi$
$618$	−7.61660			−0.306384
$619$	9.08175	+	27.9508i	0.365026	+	1.12344i	0.949965	+	0.312358i	$0.101119\pi$
$619$	9.08175	+	27.9508i	0.365026	+	1.12344i	−0.584938	+	0.811078i	$0.698881\pi$
$620$	−1.44155	−	0.455414i	−0.0578939	−	0.0182899i
$621$	0.863860	−	2.65869i	0.0346655	−	0.106689i
$622$	−10.5026	+	32.3238i	−0.421117	+	1.29607i
$623$	6.21284	−	4.51389i	0.248912	−	0.180845i
$624$	1.38461			0.0554286
$625$	8.49737	+	23.5116i	0.339895	+	0.940463i
$626$	33.3401			1.33254
$627$	−2.92054	+	2.12190i	−0.116635	+	0.0847405i
$628$	−11.3834	+	35.0345i	−0.454247	+	1.39803i
$629$	3.28871	−	10.1216i	0.131130	−	0.403575i
$630$	8.09740	+	2.55813i	0.322608	+	0.101918i
$631$	1.19845	+	3.68846i	0.0477097	+	0.146835i	0.972073	−	0.234677i	$-0.0754033\pi$
$631$	1.19845	+	3.68846i	0.0477097	+	0.146835i	−0.924364	+	0.381513i	$0.875403\pi$
$632$	13.7158			0.545586
$633$	−1.51035	−	4.64839i	−0.0600312	−	0.184757i
$634$	−33.1722	−	24.1010i	−1.31744	−	0.957173i
$635$	−11.6877	+	3.90332i	−0.463814	+	0.154899i
$636$	−3.74609	+	2.72169i	−0.148542	+	0.107922i
$637$	10.2703	+	7.46178i	0.406922	+	0.295646i
$638$	−7.62696	−	5.54131i	−0.301954	−	0.219383i
$639$	−5.12894	+	3.72639i	−0.202898	+	0.147414i
$640$	11.4107	−	15.9780i	0.451046	−	0.631587i
$641$	7.55433	+	5.48854i	0.298378	+	0.216784i	0.726894	−	0.686750i	$-0.240963\pi$
$641$	7.55433	+	5.48854i	0.298378	+	0.216784i	−0.428516	+	0.903534i	$0.640963\pi$
$642$	−3.53983	−	10.8945i	−0.139706	−	0.429970i
$643$	4.62477			0.182383			0.0911916	−	0.995833i	$-0.470932\pi$
$643$	4.62477			0.182383			0.0911916	+	0.995833i	$0.470932\pi$
$644$	0.824269	+	2.53684i	0.0324807	+	0.0999654i
$645$	−1.08792	+	1.52338i	−0.0428366	+	0.0599830i
$646$	−5.09517	+	15.6813i	−0.200467	+	0.616973i
$647$	8.26495	−	25.4369i	0.324929	−	1.00003i	−0.646544	−	0.762877i	$-0.723786\pi$
$647$	8.26495	−	25.4369i	0.324929	−	1.00003i	0.971473	−	0.237151i	$-0.0762137\pi$
$648$	−7.67376	+	5.57532i	−0.301454	+	0.219019i
$649$	11.5992			0.455307
$650$	16.6908	+	11.7151i	0.654665	+	0.459505i
$651$	−0.0444455			−0.00174196
$652$	14.5454	−	10.5679i	0.569643	−	0.413870i
$653$	5.52768	−	17.0124i	0.216315	−	0.665749i	−0.782743	−	0.622345i	$-0.786180\pi$
$653$	5.52768	−	17.0124i	0.216315	−	0.665749i	0.999058	−	0.0434033i	$-0.0138200\pi$
$654$	2.15996	−	6.64768i	0.0844612	−	0.259945i
$655$	−0.231369	−	28.3483i	−0.00904032	−	1.10766i
$656$	−0.767787	−	2.36301i	−0.0299771	−	0.0922599i
$657$	15.3485			0.598803
$658$	−1.96780	−	6.05627i	−0.0767129	−	0.236098i
$659$	28.4403	+	20.6631i	1.10788	+	0.804920i	0.982328	−	0.187167i	$-0.0599306\pi$
$659$	28.4403	+	20.6631i	1.10788	+	0.804920i	0.125550	+	0.992087i	$0.459931\pi$
$660$	−2.51953	−	0.795970i	−0.0980724	−	0.0309831i
$661$	32.4759	−	23.5951i	1.26316	−	0.917743i	0.264256	−	0.964453i	$-0.414874\pi$
$661$	32.4759	−	23.5951i	1.26316	−	0.917743i	0.998909	+	0.0467098i	$0.0148736\pi$
$662$	16.3999	+	11.9153i	0.637402	+	0.463100i
$663$	−0.423466	−	0.307666i	−0.0164461	−	0.0119488i
$664$	−1.73620	+	1.26142i	−0.0673777	+	0.0489527i
$665$	−0.0861469	−	10.5551i	−0.00334063	−	0.409309i
$666$	−53.6338	−	38.9672i	−2.07827	−	1.50995i
$667$	−1.38441	−	4.26077i	−0.0536046	−	0.164978i
$668$	−9.84507			−0.380917
$669$	2.39772	+	7.37943i	0.0927014	+	0.285305i
$670$	32.0819	+	43.4075i	1.23943	+	1.67698i
$671$	1.54464	−	4.75393i	0.0596303	−	0.183523i
$672$	0.407236	−	1.25334i	0.0157095	−	0.0483488i
$673$	31.5645	−	22.9330i	1.21672	−	0.884001i	0.220899	−	0.975297i	$-0.429101\pi$
$673$	31.5645	−	22.9330i	1.21672	−	0.884001i	0.995824	+	0.0912961i	$0.0291010\pi$
$674$	−5.92206			−0.228109
$675$	−8.09588	+	0.132160i	−0.311611	+	0.00508684i
$676$	−23.6519			−0.909690
$677$	7.69182	−	5.58843i	0.295620	−	0.214781i	−0.430081	−	0.902790i	$-0.641515\pi$
$677$	7.69182	−	5.58843i	0.295620	−	0.214781i	0.725702	+	0.688009i	$0.241515\pi$
$678$	−1.88246	+	5.79362i	−0.0722955	+	0.222503i
$679$	−1.81810	+	5.59554i	−0.0697724	+	0.214737i
$680$	−2.41410	+	0.806230i	−0.0925765	+	0.0309175i
$681$	2.30650	+	7.09869i	0.0883854	+	0.272022i
$682$	−0.969005			−0.0371051
$683$	−12.6811	−	39.0284i	−0.485228	−	1.49338i	−0.831650	−	0.555300i	$-0.812603\pi$
$683$	−12.6811	−	39.0284i	−0.485228	−	1.49338i	0.346422	−	0.938079i	$-0.387397\pi$
$684$	46.4446	+	33.7440i	1.77586	+	1.29023i
$685$	−12.1722	−	16.4693i	−0.465077	−	0.629259i
$686$	14.3136	−	10.3994i	0.546494	−	0.397051i
$687$	−1.66547	−	1.21004i	−0.0635417	−	0.0461658i
$688$	−6.55532	−	4.76272i	−0.249919	−	0.181577i
$689$	10.3576	−	7.52526i	0.394594	−	0.286690i
$690$	−1.33523	−	1.80660i	−0.0508314	−	0.0687759i
$691$	−2.71580	−	1.97315i	−0.103314	−	0.0750620i	0.534929	−	0.844897i	$-0.320338\pi$
$691$	−2.71580	−	1.97315i	−0.103314	−	0.0750620i	−0.638243	+	0.769835i	$0.720338\pi$
$692$	7.54767	+	23.2294i	0.286919	+	0.883047i
$693$	3.04234			0.115569
$694$	15.7345	+	48.4258i	0.597273	+	1.83822i
$695$	−27.6258	+	9.22609i	−1.04790	+	0.349966i
$696$	0.249476	−	0.767808i	0.00945637	−	0.0291037i
$697$	−0.290252	+	0.893305i	−0.0109941	+	0.0338363i
$698$	−38.5204	+	27.9867i	−1.45802	+	1.05931i
$699$	−0.235248			−0.00889791
$700$	6.17541	−	4.64257i	0.233409	−	0.175473i
$701$	−5.79510			−0.218878			−0.109439	−	0.993994i	$-0.534905\pi$
$701$	−5.79510			−0.218878			−0.109439	+	0.993994i	$0.534905\pi$
$702$	−5.34312	+	3.88201i	−0.201663	+	0.146517i
$703$	−25.4646	+	78.3718i	−0.960414	+	2.95585i
$704$	6.08969	−	18.7421i	0.229514	−	0.706371i
$705$	1.78170	+	2.41067i	0.0671026	+	0.0907912i
$706$	−7.39879	−	22.7711i	−0.278457	−	0.857003i
$707$	−1.99200			−0.0749169
$708$	1.45543	+	4.47936i	0.0546985	+	0.168345i
$709$	7.76838	+	5.64406i	0.291748	+	0.211967i	0.724025	−	0.689774i	$-0.242290\pi$
$709$	7.76838	+	5.64406i	0.291748	+	0.211967i	−0.432278	+	0.901741i	$0.642290\pi$
$710$	0.0842193	+	10.3189i	0.00316070	+	0.387262i
$711$	28.5180	−	20.7195i	1.06951	−	0.777043i
$712$	11.5995	+	8.42756i	0.434711	+	0.315836i
$713$	−0.372539	−	0.270665i	−0.0139517	−	0.0101365i
$714$	−0.287042	+	0.208549i	−0.0107423	+	0.00780473i
$715$	6.96629	+	2.20079i	0.260524	+	0.0823049i
$716$	15.1336	+	10.9952i	0.565571	+	0.410911i
$717$	−0.294873	−	0.907527i	−0.0110123	−	0.0338922i
$718$	−32.6428			−1.21822
$719$	5.24924	+	16.1555i	0.195764	+	0.602498i	0.999967	+	0.00814401i	$0.00259235\pi$
$719$	5.24924	+	16.1555i	0.195764	+	0.602498i	−0.804203	+	0.594354i	$0.797408\pi$
$720$	−0.141216	−	17.3024i	−0.00526281	−	0.644823i
$721$	2.46557	−	7.58825i	0.0918227	−	0.282601i
$722$	26.9493	−	82.9416i	1.00295	−	3.08677i
$723$	4.35254	−	3.16231i	0.161873	−	0.117607i
$724$	−48.8016			−1.81370
$725$	−10.3720	+	7.79748i	−0.385206	+	0.289591i
$726$	4.70814			0.174736
$727$	−31.5645	+	22.9329i	−1.17066	+	0.850536i	−0.991088	−	0.133209i	$-0.957472\pi$
$727$	−31.5645	+	22.9329i	−1.17066	+	0.850536i	−0.179574	+	0.983745i	$0.557472\pi$
$728$	0.410691	−	1.26398i	0.0152212	−	0.0468461i
$729$	−7.12279	+	21.9217i	−0.263807	+	0.811914i
$730$	14.5192	−	20.3309i	0.537381	−	0.752481i
$731$	0.946572	+	2.91325i	0.0350102	+	0.107750i
$732$	2.02969			0.0750194
$733$	−16.0248	−	49.3192i	−0.591889	−	1.82165i	−0.569639	−	0.821895i	$-0.692917\pi$
$733$	−16.0248	−	49.3192i	−0.591889	−	1.82165i	−0.0222495	−	0.999752i	$-0.507083\pi$
$734$	−1.68164	−	1.22178i	−0.0620703	−	0.0450967i
$735$	−2.35412	+	3.29641i	−0.0868329	+	0.121590i
$736$	11.0461	−	8.02543i	0.407163	−	0.295821i
$737$	15.6447	+	11.3665i	0.576278	+	0.418691i
$738$	4.73356	+	3.43913i	0.174245	+	0.126596i
$739$	−34.9163	+	25.3682i	−1.28442	+	0.933184i	−0.999677	−	0.0254205i	$-0.991908\pi$
$739$	−34.9163	+	25.3682i	−1.28442	+	0.933184i	−0.284741	+	0.958605i	$0.591908\pi$
$740$	−57.2088	+	19.1059i	−2.10304	+	0.702346i
$741$	3.27891	+	2.38227i	0.120454	+	0.0875147i
$742$	−2.68172	−	8.25347i	−0.0984489	−	0.302994i
$743$	43.6298			1.60062			0.800311	−	0.599585i	$-0.204668\pi$
$743$	43.6298			1.60062			0.800311	+	0.599585i	$0.204668\pi$
$744$	−0.0256425	−	0.0789196i	−0.000940101	−	0.00289333i
$745$	26.2958	+	8.30737i	0.963403	+	0.304358i
$746$	−8.83747	+	27.1989i	−0.323563	+	0.995824i
$747$	−1.70437	+	5.24552i	−0.0623597	+	0.191923i
$748$	−3.49791	+	2.54138i	−0.127896	+	0.0929220i
$749$	11.9998			0.438463
$750$	−3.69453	+	5.35610i	−0.134905	+	0.195577i
$751$	−4.78198			−0.174497			−0.0872484	−	0.996187i	$-0.527807\pi$
$751$	−4.78198			−0.174497			−0.0872484	+	0.996187i	$0.527807\pi$
$752$	−10.4972	+	7.62668i	−0.382794	+	0.278116i
$753$	−0.785087	+	2.41625i	−0.0286102	+	0.0880530i
$754$	−3.27071	+	10.0662i	−0.119112	+	0.366589i
$755$	13.8104	+	4.36298i	0.502612	+	0.158785i
$756$	0.773236	+	2.37978i	0.0281223	+	0.0865516i
$757$	−33.5265			−1.21854			−0.609271	−	0.792962i	$-0.708538\pi$
$757$	−33.5265			−1.21854			−0.609271	+	0.792962i	$0.708538\pi$
$758$	14.9367	+	45.9706i	0.542527	+	1.66973i
$759$	−0.651122	−	0.473068i	−0.0236342	−	0.0171713i
$760$	18.6924	−	6.24266i	0.678046	−	0.226445i
$761$	−34.8707	+	25.3350i	−1.26406	+	0.918394i	−0.998950	−	0.0458237i	$-0.985409\pi$
$761$	−34.8707	+	25.3350i	−1.26406	+	0.918394i	−0.265112	+	0.964218i	$0.585409\pi$
$762$	−2.59461	−	1.88509i	−0.0939927	−	0.0682897i
$763$	5.92374	+	4.30385i	0.214454	+	0.155810i
$764$	−30.8347	+	22.4027i	−1.11556	+	0.810502i
$765$	−3.80149	+	5.32313i	−0.137443	+	0.192458i
$766$	−25.6253	−	18.6178i	−0.925879	−	0.672690i
$767$	−4.02415	−	12.3851i	−0.145304	−	0.447199i
$768$	−1.20420			−0.0434529
$769$	−10.0756	−	31.0094i	−0.363334	−	1.11823i	−0.951018	−	0.309136i	$-0.899960\pi$
$769$	−10.0756	−	31.0094i	−0.363334	−	1.11823i	0.587684	−	0.809091i	$-0.300040\pi$
$770$	2.87796	−	4.02993i	0.103714	−	0.145229i
$771$	2.59427	−	7.98433i	0.0934303	−	0.287549i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72275 + 1.25165i) q^{2} +(-0.0844546 + 0.259925i) q^{3} +(0.783211 - 2.41047i) q^{4} +(-2.13220 - 0.673604i) q^{5} +(-0.179841 - 0.553494i) q^{6} +0.609651 q^{7} +(0.351734 + 1.08253i) q^{8} +(2.36662 + 1.71945i) q^{9} +(4.51637 - 1.50832i) q^{10} +(1.38011 - 1.00271i) q^{11} +(0.560396 + 0.407152i) q^{12} +(-1.54945 - 1.12574i) q^{13} +(-1.05028 + 0.763073i) q^{14} +(0.355160 - 0.497321i) q^{15} +(2.14004 + 1.55483i) q^{16} +(-0.309017 - 0.951057i) q^{17} -6.22927 q^{18} +(2.39272 + 7.36405i) q^{19} +(-3.29366 + 4.61203i) q^{20} +(-0.0514879 + 0.158463i) q^{21} +(-1.12254 + 3.45483i) q^{22} +(-1.39658 + 1.01468i) q^{23} -0.311081 q^{24} +(4.09252 + 2.87251i) q^{25} +4.07836 q^{26} +(-1.31012 + 0.951855i) q^{27} +(0.477485 - 1.46955i) q^{28} +(-0.801966 + 2.46820i) q^{29} +(0.0106207 + 1.30130i) q^{30} +(0.0824305 + 0.253695i) q^{31} -7.90936 q^{32} +(0.144072 + 0.443407i) q^{33} +(1.72275 + 1.25165i) q^{34} +(-1.29990 - 0.410663i) q^{35} +(5.99826 - 4.35799i) q^{36} +(8.60996 + 6.25550i) q^{37} +(-13.3393 - 9.69159i) q^{38} +(0.423466 - 0.307666i) q^{39} +(-0.0207721 - 2.54509i) q^{40} +(-0.759890 - 0.552093i) q^{41} +(-0.109640 - 0.337439i) q^{42} -3.06317 q^{43} +(-1.33608 - 4.11204i) q^{44} +(-3.88787 - 5.26037i) q^{45} +(1.13594 - 3.49608i) q^{46} +(-1.51577 + 4.66507i) q^{47} +(-0.584876 + 0.424937i) q^{48} -6.62833 q^{49} +(-10.6458 + 0.173786i) q^{50} +0.273301 q^{51} +(-3.92712 + 2.85322i) q^{52} +(-2.06569 + 6.35754i) q^{53} +(1.06561 - 3.27962i) q^{54} +(-3.61808 + 1.20832i) q^{55} +(0.214435 + 0.659963i) q^{56} -2.11617 q^{57} +(-1.70774 - 5.25588i) q^{58} +(5.50085 + 3.99660i) q^{59} +(-0.920615 - 1.24561i) q^{60} +(2.37055 - 1.72231i) q^{61} +(-0.459546 - 0.333880i) q^{62} +(1.44281 + 1.04827i) q^{63} +(9.34579 - 6.79011i) q^{64} +(2.54543 + 3.44402i) q^{65} +(-0.803192 - 0.583553i) q^{66} +(3.50297 + 10.7810i) q^{67} -2.53452 q^{68} +(-0.145792 - 0.448700i) q^{69} +(2.75341 - 0.919548i) q^{70} +(-0.669700 + 2.06113i) q^{71} +(-1.02893 + 3.16672i) q^{72} +(4.24476 - 3.08400i) q^{73} -22.6626 q^{74} +(-1.09227 + 0.821149i) q^{75} +19.6249 q^{76} +(0.841383 - 0.611300i) q^{77} +(-0.344436 + 1.06007i) q^{78} +(3.72368 - 11.4603i) q^{79} +(-3.51565 - 4.75675i) q^{80} +(2.57514 + 7.92548i) q^{81} +2.00013 q^{82} +(0.582630 + 1.79315i) q^{83} +(0.341646 + 0.248220i) q^{84} +(0.0182494 + 2.23599i) q^{85} +(5.27709 - 3.83403i) q^{86} +(-0.573816 - 0.416901i) q^{87} +(1.57088 + 1.14131i) q^{88} +(10.1908 - 7.40406i) q^{89} +(13.2820 + 4.19606i) q^{90} +(-0.944624 - 0.686309i) q^{91} +(1.35203 + 4.16113i) q^{92} -0.0729032 q^{93} +(-3.22775 - 9.93399i) q^{94} +(-0.141305 - 17.3133i) q^{95} +(0.667982 - 2.05584i) q^{96} +(-2.98220 + 9.17827i) q^{97} +(11.4190 - 8.29637i) q^{98} +4.99029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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