LMFDB - Embedded newform 225.2.q.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53861 + 1.13026i) q^{2} +(1.12291 - 1.31874i) q^{3} +(3.82877 - 4.25228i) q^{4} +(1.17441 + 1.90283i) q^{5} +(-1.36012 + 4.61694i) q^{6} +(-0.665971 + 1.15350i) q^{7} +(-3.19614 + 9.83670i) q^{8} +(-0.478132 - 2.96165i) q^{9} +O(q^{10})$	\(q+(-2.53861 + 1.13026i) q^{2} +(1.12291 - 1.31874i) q^{3} +(3.82877 - 4.25228i) q^{4} +(1.17441 + 1.90283i) q^{5} +(-1.36012 + 4.61694i) q^{6} +(-0.665971 + 1.15350i) q^{7} +(-3.19614 + 9.83670i) q^{8} +(-0.478132 - 2.96165i) q^{9} +(-5.13206 - 3.50315i) q^{10} +(1.76824 - 0.787270i) q^{11} +(-1.30826 - 9.82409i) q^{12} +(3.99834 + 1.78018i) q^{13} +(0.386888 - 3.68099i) q^{14} +(3.82809 + 0.587979i) q^{15} +(-1.80807 - 17.2027i) q^{16} +(0.413167 - 1.27160i) q^{17} +(4.56123 + 6.97806i) q^{18} +(-0.593455 + 1.82647i) q^{19} +(12.5879 + 2.29159i) q^{20} +(0.773329 + 2.17351i) q^{21} +(-3.59904 + 3.99714i) q^{22} +(0.0712526 - 0.677923i) q^{23} +(9.38303 + 15.2606i) q^{24} +(-2.24153 + 4.46940i) q^{25} -12.1623 q^{26} +(-4.44254 - 2.69515i) q^{27} +(2.35514 + 7.24837i) q^{28} +(3.36698 + 0.715675i) q^{29} +(-10.3826 + 2.83409i) q^{30} +(8.56171 - 1.81985i) q^{31} +(13.6905 + 23.7127i) q^{32} +(0.947376 - 3.21588i) q^{33} +(0.388368 + 3.69507i) q^{34} +(-2.97703 + 0.0874443i) q^{35} +(-14.4245 - 9.30635i) q^{36} +(1.12934 - 0.820511i) q^{37} +(-0.557835 - 5.30744i) q^{38} +(6.83738 - 3.27378i) q^{39} +(-22.4712 + 5.47059i) q^{40} +(1.65794 + 0.738164i) q^{41} +(-4.41982 - 4.64364i) q^{42} +(0.906455 - 1.57003i) q^{43} +(3.42249 - 10.5333i) q^{44} +(5.07400 - 4.38799i) q^{45} +(0.585348 + 1.80151i) q^{46} +(-4.43516 - 0.942722i) q^{47} +(-24.7161 - 16.9327i) q^{48} +(2.61297 + 4.52579i) q^{49} +(0.638779 - 13.8796i) q^{50} +(-1.21295 - 1.97275i) q^{51} +(22.8786 - 10.1862i) q^{52} +(-1.29321 - 3.98009i) q^{53} +(14.3241 + 1.82070i) q^{54} +(3.57468 + 2.44008i) q^{55} +(-9.21805 - 10.2377i) q^{56} +(1.74223 + 2.83358i) q^{57} +(-9.35635 + 1.98875i) q^{58} +(-11.4434 - 5.09492i) q^{59} +(17.1572 - 14.0269i) q^{60} +(-7.41443 + 3.30112i) q^{61} +(-19.6779 + 14.2968i) q^{62} +(3.73467 + 1.42085i) q^{63} +(-33.5687 - 24.3891i) q^{64} +(1.30831 + 9.69883i) q^{65} +(1.22976 + 9.23463i) q^{66} +(-5.18481 + 1.10207i) q^{67} +(-3.82527 - 6.62556i) q^{68} +(-0.813992 - 0.855212i) q^{69} +(7.45867 - 3.58680i) q^{70} +(-0.998557 - 3.07324i) q^{71} +(30.6611 + 4.76261i) q^{72} +(0.916492 + 0.665871i) q^{73} +(-1.93955 + 3.35940i) q^{74} +(3.37692 + 7.97474i) q^{75} +(5.49445 + 9.51667i) q^{76} +(-0.269482 + 2.56395i) q^{77} +(-13.6572 + 16.0389i) q^{78} +(-10.3069 - 2.19081i) q^{79} +(30.6103 - 23.6434i) q^{80} +(-8.54278 + 2.83212i) q^{81} -5.04319 q^{82} +(-6.90004 - 7.66327i) q^{83} +(12.2033 + 5.03348i) q^{84} +(2.90486 - 0.707187i) q^{85} +(-0.526594 + 5.01021i) q^{86} +(4.72462 - 3.63652i) q^{87} +(2.09261 + 19.9099i) q^{88} +(13.1208 + 9.53280i) q^{89} +(-7.92132 + 16.8743i) q^{90} +(-4.71621 + 3.42652i) q^{91} +(-2.60991 - 2.89860i) q^{92} +(7.21416 - 13.3342i) q^{93} +(12.3246 - 2.61968i) q^{94} +(-4.17242 + 1.01577i) q^{95} +(46.6441 + 8.57310i) q^{96} +(-17.6272 - 3.74678i) q^{97} +(-11.7486 - 8.53587i) q^{98} +(-3.17707 - 4.86049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.53861	+	1.13026i	−1.79507	+	0.799215i	−0.821714	+	0.569901i	$0.806982\pi$
$2$	−2.53861	+	1.13026i	−1.79507	+	0.799215i	−0.973352	+	0.229314i	$0.926352\pi$
$3$	1.12291	−	1.31874i	0.648314	−	0.761373i
$3$	1.12291	−	1.31874i	0.648314	−	0.761373i
$4$	3.82877	−	4.25228i	1.91439	−	2.12614i
$5$	1.17441	+	1.90283i	0.525211	+	0.850972i
$5$	1.17441	+	1.90283i	0.525211	+	0.850972i
$6$	−1.36012	+	4.61694i	−0.555266	+	1.88486i
$7$	−0.665971	+	1.15350i	−0.251713	+	0.435980i	−0.963998	−	0.265911i	$-0.914327\pi$
$7$	−0.665971	+	1.15350i	−0.251713	+	0.435980i	0.712284	+	0.701891i	$0.247661\pi$
$8$	−3.19614	+	9.83670i	−1.13001	+	3.47780i
$9$	−0.478132	−	2.96165i	−0.159377	−	0.987218i
$10$	−5.13206	−	3.50315i	−1.62290	−	1.10779i
$11$	1.76824	−	0.787270i	0.533144	−	0.237371i	−0.122463	−	0.992473i	$-0.539079\pi$
$11$	1.76824	−	0.787270i	0.533144	−	0.237371i	0.655607	+	0.755102i	$0.272413\pi$
$12$	−1.30826	−	9.82409i	−0.377663	−	2.83597i
$13$	3.99834	+	1.78018i	1.10894	+	0.493733i	0.877723	−	0.479169i	$-0.159062\pi$
$13$	3.99834	+	1.78018i	1.10894	+	0.493733i	0.231219	+	0.972902i	$0.425729\pi$
$14$	0.386888	−	3.68099i	0.103400	−	0.983786i
$15$	3.82809	+	0.587979i	0.988409	+	0.151816i
$16$	−1.80807	−	17.2027i	−0.452018	−	4.30066i
$17$	0.413167	−	1.27160i	0.100208	−	0.308408i	−0.888368	−	0.459132i	$-0.848161\pi$
$17$	0.413167	−	1.27160i	0.100208	−	0.308408i	0.988576	+	0.150724i	$0.0481605\pi$
$18$	4.56123	+	6.97806i	1.07509	+	1.64474i
$19$	−0.593455	+	1.82647i	−0.136148	+	0.419020i	−0.995767	−	0.0919155i	$-0.970701\pi$
$19$	−0.593455	+	1.82647i	−0.136148	+	0.419020i	0.859619	+	0.510936i	$0.170701\pi$
$20$	12.5879	+	2.29159i	2.81474	+	0.512416i
$21$	0.773329	+	2.17351i	0.168754	+	0.474300i
$22$	−3.59904	+	3.99714i	−0.767318	+	0.852193i
$23$	0.0712526	−	0.677923i	0.0148572	−	0.141357i	−0.984579	−	0.174943i	$-0.944026\pi$
$23$	0.0712526	−	0.677923i	0.0148572	−	0.141357i	0.999436	+	0.0335858i	$0.0106927\pi$
$24$	9.38303	+	15.2606i	1.91530	+	3.11506i
$25$	−2.24153	+	4.46940i	−0.448306	+	0.893880i
$26$	−12.1623			−2.38522
$27$	−4.44254	−	2.69515i	−0.854967	−	0.518682i
$28$	2.35514	+	7.24837i	0.445079	+	1.36981i
$29$	3.36698	+	0.715675i	0.625233	+	0.132897i	0.509624	−	0.860397i	$-0.329785\pi$
$29$	3.36698	+	0.715675i	0.625233	+	0.132897i	0.115609	+	0.993295i	$0.463118\pi$
$30$	−10.3826	+	2.83409i	−1.89559	+	0.517432i
$31$	8.56171	−	1.81985i	1.53773	−	0.326854i	0.640339	−	0.768093i	$-0.278794\pi$
$31$	8.56171	−	1.81985i	1.53773	−	0.326854i	0.897390	+	0.441238i	$0.145461\pi$
$32$	13.6905	+	23.7127i	2.42017	+	4.19186i
$33$	0.947376	−	3.21588i	0.164917	−	0.559812i
$34$	0.388368	+	3.69507i	0.0666045	+	0.633700i
$35$	−2.97703	+	0.0874443i	−0.503209	+	0.0147808i
$36$	−14.4245	−	9.30635i	−2.40408	−	1.55106i
$37$	1.12934	−	0.820511i	0.185662	−	0.134891i	−0.491072	−	0.871119i	$-0.663395\pi$
$37$	1.12934	−	0.820511i	0.185662	−	0.134891i	0.676734	+	0.736228i	$0.263395\pi$
$38$	−0.557835	−	5.30744i	−0.0904927	−	0.860981i
$39$	6.83738	−	3.27378i	1.09486	−	0.524224i
$40$	−22.4712	+	5.47059i	−3.55300	+	0.864977i
$41$	1.65794	+	0.738164i	0.258927	+	0.115282i	0.532095	−	0.846684i	$-0.321405\pi$
$41$	1.65794	+	0.738164i	0.258927	+	0.115282i	−0.273168	+	0.961966i	$0.588071\pi$
$42$	−4.41982	−	4.64364i	−0.681992	−	0.716529i
$43$	0.906455	−	1.57003i	0.138233	−	0.239427i	−0.788595	−	0.614913i	$-0.789191\pi$
$43$	0.906455	−	1.57003i	0.138233	−	0.239427i	0.926828	+	0.375486i	$0.122524\pi$
$44$	3.42249	−	10.5333i	0.515959	−	1.58796i
$45$	5.07400	−	4.38799i	0.756388	−	0.654124i
$46$	0.585348	+	1.80151i	0.0863048	+	0.265619i
$47$	−4.43516	−	0.942722i	−0.646934	−	0.137510i	−0.127253	−	0.991870i	$-0.540616\pi$
$47$	−4.43516	−	0.942722i	−0.646934	−	0.137510i	−0.519681	+	0.854360i	$0.673949\pi$
$48$	−24.7161	−	16.9327i	−3.56746	−	2.44403i
$49$	2.61297	+	4.52579i	0.373281	+	0.646541i
$50$	0.638779	−	13.8796i	0.0903370	−	1.96287i
$51$	−1.21295	−	1.97275i	−0.169847	−	0.276241i
$52$	22.8786	−	10.1862i	3.17269	−	1.41257i
$53$	−1.29321	−	3.98009i	−0.177636	−	0.546708i	0.822108	−	0.569332i	$-0.192798\pi$
$53$	−1.29321	−	3.98009i	−0.177636	−	0.546708i	−0.999744	+	0.0226238i	$0.992798\pi$
$54$	14.3241	+	1.82070i	1.94926	+	0.247765i
$55$	3.57468	+	2.44008i	0.482009	+	0.329021i
$56$	−9.21805	−	10.2377i	−1.23181	−	1.36807i
$57$	1.74223	+	2.83358i	0.230764	+	0.375316i
$58$	−9.35635	+	1.98875i	−1.22855	+	0.261136i
$59$	−11.4434	−	5.09492i	−1.48980	−	0.663303i	−0.509439	−	0.860507i	$-0.670147\pi$
$59$	−11.4434	−	5.09492i	−1.48980	−	0.663303i	−0.980362	+	0.197204i	$0.936814\pi$
$60$	17.1572	−	14.0269i	2.21498	−	1.81086i
$61$	−7.41443	+	3.30112i	−0.949320	+	0.422665i	−0.822185	−	0.569221i	$-0.807245\pi$
$61$	−7.41443	+	3.30112i	−0.949320	+	0.422665i	−0.127136	+	0.991885i	$0.540578\pi$
$62$	−19.6779	+	14.2968i	−2.49910	+	1.81570i
$63$	3.73467	+	1.42085i	0.470525	+	0.179010i
$64$	−33.5687	−	24.3891i	−4.19608	−	3.04863i
$65$	1.30831	+	9.69883i	0.162276	+	1.20299i
$66$	1.22976	+	9.23463i	0.151373	+	1.13670i
$67$	−5.18481	+	1.10207i	−0.633425	+	0.134639i	−0.513424	−	0.858135i	$-0.671623\pi$
$67$	−5.18481	+	1.10207i	−0.633425	+	0.134639i	−0.120001	+	0.992774i	$0.538290\pi$
$68$	−3.82527	−	6.62556i	−0.463882	−	0.803468i
$69$	−0.813992	−	0.855212i	−0.0979931	−	0.102955i
$70$	7.45867	−	3.58680i	0.891481	−	0.428705i
$71$	−0.998557	−	3.07324i	−0.118507	−	0.364727i	0.874155	−	0.485646i	$-0.161416\pi$
$71$	−0.998557	−	3.07324i	−0.118507	−	0.364727i	−0.992662	+	0.120920i	$0.961416\pi$
$72$	30.6611	+	4.76261i	3.61344	+	0.561279i
$73$	0.916492	+	0.665871i	0.107267	+	0.0779343i	0.640126	−	0.768270i	$-0.278882\pi$
$73$	0.916492	+	0.665871i	0.107267	+	0.0779343i	−0.532859	+	0.846204i	$0.678882\pi$
$74$	−1.93955	+	3.35940i	−0.225468	+	0.390522i
$75$	3.37692	+	7.97474i	0.389933	+	0.920843i
$76$	5.49445	+	9.51667i	0.630257	+	1.09164i
$77$	−0.269482	+	2.56395i	−0.0307104	+	0.292190i
$78$	−13.6572	+	16.0389i	−1.54637	+	1.81604i
$79$	−10.3069	−	2.19081i	−1.15962	−	0.246485i	−0.412363	−	0.911019i	$-0.635297\pi$
$79$	−10.3069	−	2.19081i	−1.15962	−	0.246485i	−0.747258	+	0.664534i	$0.768630\pi$
$80$	30.6103	−	23.6434i	3.42234	−	2.64341i
$81$	−8.54278	+	2.83212i	−0.949198	+	0.314680i
$82$	−5.04319			−0.556927
$83$	−6.90004	−	7.66327i	−0.757378	−	0.841153i	0.233993	−	0.972238i	$-0.424821\pi$
$83$	−6.90004	−	7.66327i	−0.757378	−	0.841153i	−0.991371	+	0.131085i	$0.958154\pi$
$84$	12.2033	+	5.03348i	1.33149	+	0.549198i
$85$	2.90486	−	0.707187i	0.315076	−	0.0767052i
$86$	−0.526594	+	5.01021i	−0.0567841	+	0.540265i
$87$	4.72462	−	3.63652i	0.506532	−	0.389876i
$88$	2.09261	+	19.9099i	0.223073	+	2.12240i
$89$	13.1208	+	9.53280i	1.39080	+	1.01048i	0.995777	+	0.0918040i	$0.0292633\pi$
$89$	13.1208	+	9.53280i	1.39080	+	1.01048i	0.395023	+	0.918671i	$0.370737\pi$
$90$	−7.92132	+	16.8743i	−0.834981	+	1.77871i
$91$	−4.71621	+	3.42652i	−0.494393	+	0.359197i
$92$	−2.60991	−	2.89860i	−0.272102	−	0.302200i
$93$	7.21416	−	13.3342i	0.748073	−	1.38269i
$94$	12.3246	−	2.61968i	1.27119	−	0.270200i
$95$	−4.17242	+	1.01577i	−0.428081	+	0.104216i
$96$	46.6441	+	8.57310i	4.76059	+	0.874988i
$97$	−17.6272	−	3.74678i	−1.78977	−	0.380428i	−0.810946	−	0.585121i	$-0.801047\pi$
$97$	−17.6272	−	3.74678i	−1.78977	−	0.380428i	−0.978826	+	0.204694i	$0.934380\pi$
$98$	−11.7486	−	8.53587i	−1.18679	−	0.862253i
$99$	−3.17707	−	4.86049i	−0.319308	−	0.488498i
$100$	10.4228	+	26.6440i	1.04228	+	2.66440i
$101$	0.568882	−	0.985333i	0.0566059	−	0.0980443i	−0.836334	−	0.548220i	$-0.815305\pi$
$101$	0.568882	−	0.985333i	0.0566059	−	0.0980443i	0.892940	+	0.450176i	$0.148639\pi$
$102$	5.30893	+	3.63709i	0.525662	+	0.360126i
$103$	8.87792	−	9.85992i	0.874767	−	0.971527i	−0.125020	−	0.992154i	$-0.539900\pi$
$103$	8.87792	−	9.85992i	0.874767	−	0.971527i	0.999787	+	0.0206271i	$0.00656626\pi$
$104$	−30.2903	+	33.6408i	−2.97021	+	3.29876i
$105$	−3.22763	+	4.02411i	−0.314984	+	0.392713i
$106$	7.78150	+	8.64223i	0.755806	+	0.839408i
$107$	3.78058			0.365483			0.182741	−	0.983161i	$-0.441503\pi$
$107$	3.78058			0.365483			0.182741	+	0.983161i	$0.441503\pi$
$108$	−28.4700	+	8.57183i	−2.73953	+	0.824825i
$109$	−3.71555	+	2.69950i	−0.355885	+	0.258566i	−0.751334	−	0.659923i	$-0.770589\pi$
$109$	−3.71555	+	2.69950i	−0.355885	+	0.258566i	0.395449	+	0.918488i	$0.370589\pi$
$110$	−11.8326	−	2.15409i	−1.12820	−	0.205385i
$111$	0.186109	−	2.41066i	0.0176647	−	0.228810i
$112$	21.0473	+	9.37086i	1.98878	+	0.885463i
$113$	−4.41435	−	1.96539i	−0.415267	−	0.184889i	0.188458	−	0.982081i	$-0.439651\pi$
$113$	−4.41435	−	1.96539i	−0.415267	−	0.184889i	−0.603725	+	0.797192i	$0.706318\pi$
$114$	−7.62552	−	5.22416i	−0.714195	−	0.489287i
$115$	1.37365	−	0.660577i	0.128094	−	0.0615991i
$116$	15.9347	−	11.5772i	1.47950	−	1.07492i
$117$	3.36053	−	12.6929i	0.310681	−	1.17346i
$118$	34.8088			3.20441
$119$	1.19162	+	1.32343i	0.109236	+	0.121319i
$120$	−18.0189	+	35.7765i	−1.64489	+	3.26594i
$121$	−4.85356	+	5.39043i	−0.441233	+	0.490039i
$122$	15.0912	−	16.7605i	1.36629	−	1.51742i
$123$	2.83517	−	1.35750i	0.255639	−	0.122401i
$124$	25.0423	−	43.3746i	2.24887	−	3.89516i
$125$	−11.1370	+	0.983645i	−0.996122	+	0.0879799i
$126$	−11.0868	+	0.614172i	−0.987691	+	0.0547148i
$127$	−10.4189	−	7.56979i	−0.924529	−	0.671710i	0.0201180	−	0.999798i	$-0.493596\pi$
$127$	−10.4189	−	7.56979i	−0.924529	−	0.671710i	−0.944647	+	0.328088i	$0.893596\pi$
$128$	59.2181	+	12.5872i	5.23419	+	1.11256i
$129$	−1.05258	−	2.95838i	−0.0926745	−	0.260471i
$130$	−14.2835	−	23.1428i	−1.25275	−	2.02976i
$131$	−4.94144	+	1.05034i	−0.431736	+	0.0917682i	−0.418653	−	0.908146i	$-0.637498\pi$
$131$	−4.94144	+	1.05034i	−0.431736	+	0.0917682i	−0.0130824	+	0.999914i	$0.504164\pi$
$132$	−10.0475	−	16.3414i	−0.874526	−	1.42233i
$133$	−1.71160	−	1.90092i	−0.148414	−	0.164831i
$134$	11.9166	−	8.65789i	1.02943	−	0.747928i
$135$	−0.0889428	−	11.6186i	−0.00765498	−	0.999971i
$136$	11.1878	+	8.12840i	0.959345	+	0.697005i
$137$	1.11485	+	10.6071i	0.0952482	+	0.906226i	0.932928	+	0.360064i	$0.117245\pi$
$137$	1.11485	+	10.6071i	0.0952482	+	0.906226i	−0.837679	+	0.546162i	$0.816088\pi$
$138$	3.03302	+	1.25103i	0.258188	+	0.106494i
$139$	−1.23871	+	11.7855i	−0.105066	+	0.999635i	0.807267	+	0.590186i	$0.200946\pi$
$139$	−1.23871	+	11.7855i	−0.105066	+	0.999635i	−0.912333	+	0.409449i	$0.865721\pi$
$140$	−11.0265	+	12.9940i	−0.931912	+	1.09819i
$141$	−6.22350	+	4.79021i	−0.524113	+	0.403408i
$142$	6.00851	+	6.67312i	0.504223	+	0.559996i
$143$	8.47151			0.708423
$144$	−50.0838	+	13.5800i	−4.17365	+	1.13167i
$145$	2.59241	+	7.24730i	0.215288	+	0.601855i
$146$	−3.07922	−	0.654508i	−0.254838	−	0.0541675i
$147$	8.90246	+	1.63626i	0.734262	+	0.134956i
$148$	0.834928	−	7.94381i	0.0686307	−	0.652977i
$149$	−2.03692	−	3.52804i	−0.166871	−	0.289028i	0.770447	−	0.637504i	$-0.220033\pi$
$149$	−2.03692	−	3.52804i	−0.166871	−	0.289028i	−0.937318	+	0.348475i	$0.886700\pi$
$150$	−17.5862	−	16.4279i	−1.43591	−	1.34133i
$151$	−7.69147	+	13.3220i	−0.625923	+	1.08413i	0.362438	+	0.932008i	$0.381944\pi$
$151$	−7.69147	+	13.3220i	−0.625923	+	1.08413i	−0.988362	+	0.152123i	$0.951389\pi$
$152$	−16.0697	−	11.6753i	−1.30342	−	0.946991i
$153$	−3.96358	−	0.615666i	−0.320436	−	0.0497736i
$154$	−2.21383	−	6.81345i	−0.178395	−	0.549044i
$155$	13.5178	+	14.1542i	1.08578	+	1.13690i
$156$	12.2577	−	41.6090i	0.981405	−	3.33139i
$157$	−2.39545	−	4.14905i	−0.191178	−	0.331130i	0.754463	−	0.656343i	$-0.227897\pi$
$157$	−2.39545	−	4.14905i	−0.191178	−	0.331130i	−0.945641	+	0.325213i	$0.894564\pi$
$158$	28.6414	−	6.08793i	2.27859	−	0.484329i
$159$	−6.70086	−	2.76390i	−0.531413	−	0.219191i
$160$	−29.0430	+	53.8992i	−2.29605	+	4.26111i
$161$	0.734529	+	0.533666i	0.0578890	+	0.0420588i
$162$	18.4857	−	16.8452i	1.45238	−	1.32348i
$163$	−6.98791	+	5.07702i	−0.547336	+	0.397663i	−0.826802	−	0.562493i	$-0.809842\pi$
$163$	−6.98791	+	5.07702i	−0.547336	+	0.397663i	0.279467	+	0.960155i	$0.409842\pi$
$164$	9.48678	−	4.22379i	0.740793	−	0.329822i
$165$	7.23188	−	1.97406i	0.563001	−	0.153680i
$166$	26.1780	+	11.6552i	2.03181	+	0.904618i
$167$	8.64696	−	1.83797i	0.669122	−	0.142226i	0.139189	−	0.990266i	$-0.455551\pi$
$167$	8.64696	−	1.83797i	0.669122	−	0.142226i	0.529933	+	0.848040i	$0.322217\pi$
$168$	−23.8519	+	0.660152i	−1.84021	+	0.0509318i
$169$	4.11903	+	4.57465i	0.316849	+	0.351896i
$170$	−6.57500	+	5.07852i	−0.504279	+	0.389505i
$171$	5.69311	+	0.884316i	0.435363	+	0.0676253i
$172$	−3.20559	−	9.86578i	−0.244424	−	0.752259i
$173$	−2.42043	+	1.07765i	−0.184022	+	0.0819319i	−0.496679	−	0.867934i	$-0.665448\pi$
$173$	−2.42043	+	1.07765i	−0.184022	+	0.0819319i	0.312657	+	0.949866i	$0.398781\pi$
$174$	−7.88372	+	14.5718i	−0.597664	+	1.10468i
$175$	−3.66264	−	5.56208i	−0.276869	−	0.420454i
$176$	−16.7402	−	28.9950i	−1.26184	−	2.18558i
$177$	−19.5688	+	9.36965i	−1.47088	+	0.704266i
$178$	−44.0831	−	9.37014i	−3.30416	−	0.702322i
$179$	−1.41322	−	4.34944i	−0.105629	−	0.325092i	0.884249	−	0.467016i	$-0.154671\pi$
$179$	−1.41322	−	4.34944i	−0.105629	−	0.325092i	−0.989878	+	0.141924i	$0.954671\pi$
$180$	0.768214	−	38.3767i	0.0572593	−	2.86043i
$181$	−0.203772	+	0.627144i	−0.0151462	+	0.0466153i	−0.958344	−	0.285617i	$-0.907802\pi$
$181$	−0.203772	+	0.627144i	−0.0151462	+	0.0466153i	0.943198	+	0.332232i	$0.107802\pi$
$182$	8.09973	−	14.0291i	0.600392	−	1.03991i
$183$	−3.97246	+	13.4845i	−0.293652	+	0.996806i
$184$	6.44080	+	2.86763i	0.474822	+	0.211404i
$185$	2.88760	+	1.18532i	0.212300	+	0.0871466i
$186$	−3.24282	+	42.0041i	−0.237775	+	3.07989i
$187$	−0.270513	−	2.57376i	−0.0197819	−	0.188212i
$188$	−20.9899	+	15.2501i	−1.53085	+	1.11223i
$189$	6.06744	−	3.32956i	0.441342	−	0.242190i
$190$	9.44404	−	7.29457i	0.685143	−	0.529204i
$191$	−1.99133	−	18.9462i	−0.144087	−	1.37090i	−0.792622	−	0.609714i	$-0.791284\pi$
$191$	−1.99133	−	18.9462i	−0.144087	−	1.37090i	0.648535	−	0.761185i	$-0.275382\pi$
$192$	−69.8574	+	16.8814i	−5.04152	+	1.21831i
$193$	−8.65375	−	14.9887i	−0.622910	−	1.07891i	−0.988941	−	0.148309i	$-0.952617\pi$
$193$	−8.65375	−	14.9887i	−0.622910	−	1.07891i	0.366031	−	0.930603i	$-0.380716\pi$
$194$	48.9834	−	10.4117i	3.51680	−	0.747519i
$195$	14.2593	+	9.16563i	1.02113	+	0.656364i
$196$	29.2494	+	6.21715i	2.08924	+	0.444082i
$197$	6.54863	+	20.1546i	0.466571	+	1.43596i	0.856997	+	0.515322i	$0.172328\pi$
$197$	6.54863	+	20.1546i	0.466571	+	1.43596i	−0.390426	+	0.920634i	$0.627672\pi$
$198$	13.5590	+	8.74795i	0.963593	+	0.621690i
$199$	16.4939			1.16922			0.584610	−	0.811315i	$-0.301248\pi$
$199$	16.4939			1.16922			0.584610	+	0.811315i	$0.301248\pi$
$200$	−36.7999	−	36.3341i	−2.60215	−	2.56921i
$201$	−4.36876	+	8.07492i	−0.308148	+	0.569561i
$202$	−0.330485	+	3.14436i	−0.0232529	+	0.221236i
$203$	−3.06784	+	3.40718i	−0.215320	+	0.239137i
$204$	−13.0328	−	2.39541i	−0.912480	−	0.167712i
$205$	0.542501	+	4.02169i	0.0378899	+	0.280887i
$206$	−11.3933	+	35.0648i	−0.793806	+	2.44308i
$207$	−2.04184	+	0.113111i	−0.141918	+	0.00786178i
$208$	23.3945	−	72.0008i	1.62212	−	4.99236i
$209$	0.388554	+	3.69684i	0.0268768	+	0.255716i
$210$	3.64539	−	13.8637i	0.251556	−	0.956685i
$211$	2.27451	−	21.6405i	0.156584	−	1.48980i	−0.580647	−	0.814156i	$-0.697200\pi$
$211$	2.27451	−	21.6405i	0.156584	−	1.48980i	0.737231	−	0.675641i	$-0.236133\pi$
$212$	−21.8759	−	9.73978i	−1.50244	−	0.668931i
$213$	−5.17409	−	2.13415i	−0.354523	−	0.146230i
$214$	−9.59742	+	4.27305i	−0.656066	+	0.292099i
$215$	4.05204	−	0.119021i	0.276347	−	0.00811715i
$216$	40.7104	−	35.0859i	2.76999	−	2.38729i
$217$	−3.60266	+	11.0879i	−0.244565	+	0.752693i
$218$	6.38117	−	11.0525i	0.432188	−	0.748571i
$219$	1.90725	−	0.460897i	0.128880	−	0.0311445i
$220$	24.0626	−	5.85802i	1.62230	−	0.394947i
$221$	3.91565	−	4.34877i	0.263395	−	0.292530i
$222$	2.25222	+	6.33007i	0.151159	+	0.424846i
$223$	20.3865	−	9.07664i	1.36518	−	0.607817i	0.412266	−	0.911063i	$-0.364737\pi$
$223$	20.3865	−	9.07664i	1.36518	−	0.607817i	0.952912	+	0.303247i	$0.0980707\pi$
$224$	−36.4700			−2.43675
$225$	14.3086	+	4.50167i	0.953904	+	0.300112i
$226$	13.4277			0.893198
$227$	11.9191	−	5.30670i	0.791095	−	0.352218i	0.0289139	−	0.999582i	$-0.490795\pi$
$227$	11.9191	−	5.30670i	0.791095	−	0.352218i	0.762181	+	0.647364i	$0.224128\pi$
$228$	18.7198	+	3.44066i	1.23975	+	0.227863i
$229$	−1.49451	+	1.65983i	−0.0987603	+	0.109684i	−0.790499	−	0.612464i	$-0.790179\pi$
$229$	−1.49451	+	1.65983i	−0.0987603	+	0.109684i	0.691738	+	0.722148i	$0.256845\pi$
$230$	−2.74054	+	3.22953i	−0.180706	+	0.212949i
$231$	3.07857	+	3.23447i	0.202555	+	0.212813i
$232$	−17.8012	+	30.8326i	−1.16871	+	2.02426i
$233$	2.96799	−	9.13454i	0.194440	−	0.598424i	−0.805543	−	0.592537i	$-0.798126\pi$
$233$	2.96799	−	9.13454i	0.194440	−	0.598424i	0.999983	−	0.00588639i	$-0.00187371\pi$
$234$	5.81518	+	36.0205i	0.380150	+	2.35473i
$235$	−3.41484	−	9.54649i	−0.222760	−	0.622744i
$236$	−65.4792	+	29.1532i	−4.26233	+	1.89771i
$237$	−14.4629	+	11.1320i	−0.939466	+	0.723104i
$238$	−4.52089	−	2.01283i	−0.293046	−	0.130472i
$239$	−1.66733	+	15.8635i	−0.107850	+	1.02613i	0.798037	+	0.602609i	$0.205872\pi$
$239$	−1.66733	+	15.8635i	−0.107850	+	1.02613i	−0.905887	+	0.423519i	$0.860795\pi$
$240$	3.19334	−	66.9164i	0.206129	−	4.31944i
$241$	−1.23404	−	11.7411i	−0.0794915	−	0.756311i	−0.959568	−	0.281479i	$-0.909175\pi$
$241$	−1.23404	−	11.7411i	−0.0794915	−	0.756311i	0.880076	−	0.474833i	$-0.157491\pi$
$242$	6.22870	−	19.1700i	0.400396	−	1.23229i
$243$	−5.85798	+	14.4459i	−0.375789	+	0.926705i
$244$	−14.3509	+	44.1675i	−0.918721	+	2.82753i
$245$	−5.54312	+	10.2872i	−0.354137	+	0.657222i
$246$	−5.66306	+	6.65063i	−0.361064	+	0.424029i
$247$	−5.62428	+	6.24639i	−0.357864	+	0.397448i
$248$	−9.46311	+	90.0355i	−0.600908	+	5.71726i
$249$	−17.8540	+	0.494147i	−1.13145	+	0.0313153i
$250$	27.1607	−	15.0848i	1.71779	−	0.954045i
$251$	7.61380			0.480579			0.240289	−	0.970701i	$-0.422758\pi$
$251$	7.61380			0.480579			0.240289	+	0.970701i	$0.422758\pi$
$252$	20.3411	−	10.4408i	1.28137	−	0.657707i
$253$	−0.407717	−	1.25482i	−0.0256330	−	0.0788902i
$254$	35.0054	+	7.44062i	2.19643	+	0.466866i
$255$	2.32931	−	4.62486i	0.145867	−	0.289620i
$256$	−83.3855	+	17.7241i	−5.21159	+	1.10776i
$257$	9.46210	+	16.3888i	0.590229	+	1.02231i	0.994201	+	0.107536i	$0.0342961\pi$
$257$	9.46210	+	16.3888i	0.590229	+	1.02231i	−0.403972	+	0.914771i	$0.632371\pi$
$258$	6.01583	+	6.32047i	0.374529	+	0.393495i
$259$	0.194350	+	1.84912i	0.0120763	+	0.114899i
$260$	46.2514	+	31.5713i	2.86839	+	1.95797i
$261$	0.509717	−	10.3140i	0.0315507	−	0.638422i
$262$	11.3572	−	8.25150i	0.701651	−	0.509780i
$263$	0.965647	+	9.18752i	0.0595444	+	0.566527i	0.983101	+	0.183064i	$0.0586017\pi$
$263$	0.965647	+	9.18752i	0.0595444	+	0.566527i	−0.923557	+	0.383462i	$0.874732\pi$
$264$	28.6057	+	19.5974i	1.76056	+	1.20614i
$265$	6.05469	−	7.13502i	0.371937	−	0.438301i
$266$	6.49361	+	2.89114i	0.398149	+	0.177267i
$267$	27.3048	−	6.59834i	1.67102	−	0.403812i
$268$	−15.1652	+	26.2668i	−0.926360	+	1.60450i
$269$	2.61891	−	8.06018i	0.159678	−	0.491438i	−0.838927	−	0.544244i	$-0.816817\pi$
$269$	2.61891	−	8.06018i	0.159678	−	0.491438i	0.998605	+	0.0528061i	$0.0168165\pi$
$270$	13.3578	+	29.3946i	0.812933	+	1.78890i
$271$	−1.02891	−	3.16666i	−0.0625018	−	0.192361i	0.914930	−	0.403613i	$-0.132246\pi$
$271$	−1.02891	−	3.16666i	−0.0625018	−	0.192361i	−0.977432	+	0.211252i	$0.932246\pi$
$272$	−22.6219	−	4.80843i	−1.37165	−	0.291554i
$273$	−0.777207	+	10.0671i	−0.0470387	+	0.609290i
$274$	−14.8190	−	25.6672i	−0.895246	−	1.55061i
$275$	−0.444935	+	9.66766i	−0.0268306	+	0.582982i
$276$	−6.75320	+	0.186909i	−0.406495	+	0.0112506i
$277$	−0.697796	+	0.310679i	−0.0419265	+	0.0186669i	−0.427593	−	0.903971i	$-0.640638\pi$
$277$	−0.697796	+	0.310679i	−0.0419265	+	0.0186669i	0.385666	+	0.922638i	$0.373972\pi$
$278$	−10.1761	−	31.3189i	−0.610323	−	1.87838i
$279$	−9.48339	−	24.4867i	−0.567756	−	1.46598i
$280$	8.65483	−	29.5636i	0.517225	−	1.76676i
$281$	−9.74653	−	10.8246i	−0.581429	−	0.645742i	0.378627	−	0.925549i	$-0.376396\pi$
$281$	−9.74653	−	10.8246i	−0.581429	−	0.645742i	−0.960056	+	0.279807i	$0.909730\pi$
$282$	10.3848	−	19.1946i	0.618407	−	1.14302i
$283$	22.9052	−	4.86864i	1.36157	−	0.289411i	0.531495	−	0.847062i	$-0.321631\pi$
$283$	22.9052	−	4.86864i	1.36157	−	0.289411i	0.830076	+	0.557651i	$0.188297\pi$
$284$	−16.8916	−	7.52060i	−1.00233	−	0.446266i
$285$	−3.34573	+	6.64294i	−0.198184	+	0.393494i
$286$	−21.5058	+	9.57501i	−1.27167	+	0.566182i
$287$	−1.95561	+	1.42083i	−0.115436	+	0.0838692i
$288$	63.6829	−	51.8844i	3.75255	−	3.05732i
$289$	12.3070	+	8.94159i	0.723943	+	0.525976i
$290$	−14.7724	−	15.4679i	−0.867467	−	0.908309i
$291$	−24.7348	+	19.0383i	−1.44998	+	1.11605i
$292$	6.34051	−	1.34772i	0.371050	−	0.0788692i
$293$	2.42396	+	4.19842i	0.141609	+	0.245274i	0.928103	−	0.372324i	$-0.121439\pi$
$293$	2.42396	+	4.19842i	0.141609	+	0.245274i	−0.786494	+	0.617598i	$0.788106\pi$
$294$	−24.4492	+	5.90829i	−1.42591	+	0.344578i
$295$	−3.74443	−	27.7583i	−0.218009	−	1.61615i
$296$	4.46161	+	13.7314i	0.259326	+	0.798122i
$297$	−9.97728	−	1.26819i	−0.578941	−	0.0735876i
$298$	9.15853	+	6.65406i	0.530539	+	0.385459i
$299$	1.49172	−	2.58373i	0.0862682	−	0.149421i
$300$	46.8403	+	16.1739i	2.70433	+	0.933798i
$301$	1.20734	+	2.09118i	0.0695902	+	0.120534i
$302$	4.46827	−	42.5128i	0.257120	−	2.44633i
$303$	−0.660589	−	1.85665i	−0.0379498	−	0.106662i
$304$	32.4931	+	6.90662i	1.86361	+	0.396122i
$305$	−14.9890	−	10.2315i	−0.858269	−	0.585857i
$306$	10.7578	−	2.91694i	0.614984	−	0.166751i
$307$	22.1036			1.26152			0.630759	−	0.775979i	$-0.282744\pi$
$307$	22.1036			1.26152			0.630759	+	0.775979i	$0.282744\pi$
$308$	9.87087	+	10.9627i	0.562445	+	0.624659i
$309$	−3.03351	−	22.7795i	−0.172571	−	1.29588i
$310$	−50.3144	−	20.6534i	−2.85766	−	1.17304i
$311$	2.05925	−	19.5925i	0.116770	−	1.11099i	−0.766539	−	0.642197i	$-0.778023\pi$
$311$	2.05925	−	19.5925i	0.116770	−	1.11099i	0.883309	−	0.468791i	$-0.155310\pi$
$312$	10.3500	+	77.7207i	0.585952	+	4.40007i
$313$	0.418945	+	3.98600i	0.0236802	+	0.225302i	0.999961	+	0.00879521i	$0.00279964\pi$
$313$	0.418945	+	3.98600i	0.0236802	+	0.225302i	−0.976281	+	0.216507i	$0.930534\pi$
$314$	10.7706	+	7.82531i	0.607821	+	0.441608i
$315$	1.68239	+	8.77511i	0.0947920	+	0.494422i
$316$	−48.7789	+	35.4399i	−2.74403	+	1.99365i
$317$	1.00775	+	1.11922i	0.0566008	+	0.0628616i	0.770780	−	0.637101i	$-0.219867\pi$
$317$	1.00775	+	1.11922i	0.0566008	+	0.0628616i	−0.714179	+	0.699963i	$0.753200\pi$
$318$	20.1348	−	0.557273i	1.12910	−	0.0312503i
$319$	6.51706	−	1.38524i	0.364885	−	0.0775588i
$320$	6.98495	−	92.5182i	0.390470	−	5.17192i
$321$	4.24527	−	4.98559i	0.236948	−	0.278269i
$322$	−2.46786	−	0.524560i	−0.137529	−	0.0292326i
$323$	2.07733	+	1.50927i	0.115586	+	0.0839782i
$324$	−20.6654	+	47.1699i	−1.14808	+	2.62055i
$325$	−16.9187	+	13.8799i	−0.938483	+	0.769917i
$326$	12.0012	−	20.7867i	0.664686	−	1.15127i
$327$	−0.612304	+	7.93114i	−0.0338605	+	0.438593i
$328$	−12.5601	+	13.9494i	−0.693517	+	0.770228i
$329$	4.04111	−	4.48811i	0.222794	−	0.247437i
$330$	−16.1277	+	13.1853i	−0.887800	+	0.725824i
$331$	−7.64706	−	8.49292i	−0.420321	−	0.466813i	0.495379	−	0.868677i	$-0.335029\pi$
$331$	−7.64706	−	8.49292i	−0.420321	−	0.466813i	−0.915700	+	0.401864i	$0.868363\pi$
$332$	−59.0051			−3.23833
$333$	−2.97004	−	2.95239i	−0.162757	−	0.161790i
$334$	−19.8738	+	14.4392i	−1.08745	+	0.790077i
$335$	−8.18612	−	8.57154i	−0.447256	−	0.468313i
$336$	35.9920	−	17.2332i	1.96352	−	0.940147i
$337$	−31.5876	−	14.0637i	−1.72069	−	0.766100i	−0.997119	−	0.0758480i	$-0.975834\pi$
$337$	−31.5876	−	14.0637i	−1.72069	−	0.766100i	−0.723569	−	0.690252i	$-0.757500\pi$
$338$	−15.6271	−	6.95765i	−0.850005	−	0.378446i
$339$	−7.54877	+	3.61440i	−0.409993	+	0.196307i
$340$	8.11490	−	15.0600i	0.440092	−	0.816741i
$341$	13.7064	−	9.95831i	0.742245	−	0.539273i
$342$	−15.4521	+	4.18977i	−0.835553	+	0.226557i
$343$	−16.2842			−0.879265
$344$	12.5467	+	13.9345i	0.676474	+	0.751300i
$345$	0.671366	−	2.55326i	0.0361451	−	0.137463i
$346$	4.92651	−	5.47144i	0.264851	−	0.294146i
$347$	−10.0109	+	11.1182i	−0.537412	+	0.596857i	−0.949298	−	0.314379i	$-0.898204\pi$
$347$	−10.0109	+	11.1182i	−0.537412	+	0.596857i	0.411885	+	0.911236i	$0.364870\pi$
$348$	2.62595	−	34.0138i	0.140766	−	1.82333i
$349$	−15.1840	+	26.2994i	−0.812778	+	1.40777i	0.0981339	+	0.995173i	$0.468713\pi$
$349$	−15.1840	+	26.2994i	−0.812778	+	1.40777i	−0.910912	+	0.412600i	$0.864621\pi$
$350$	15.5846	+	9.98021i	0.833032	+	0.533465i
$351$	−12.9650	−	18.6846i	−0.692019	−	0.997313i
$352$	42.8765	+	31.1516i	2.28532	+	1.66038i
$353$	−5.26030	−	1.11811i	−0.279978	−	0.0595111i	0.0657827	−	0.997834i	$-0.479046\pi$
$353$	−5.26030	−	1.11811i	−0.279978	−	0.0595111i	−0.345760	+	0.938323i	$0.612379\pi$
$354$	39.0873	−	45.9037i	2.07747	−	2.43975i
$355$	4.67515	−	5.50933i	0.248131	−	0.292405i
$356$	90.7727	−	19.2943i	4.81094	−	1.02260i
$357$	3.08335	−	0.0853383i	0.163188	−	0.00451658i
$358$	8.50360	+	9.44420i	0.449429	+	0.499142i
$359$	−2.32651	+	1.69031i	−0.122788	+	0.0892110i	−0.647485	−	0.762079i	$-0.724179\pi$
$359$	−2.32651	+	1.69031i	−0.122788	+	0.0892110i	0.524696	+	0.851290i	$0.324179\pi$
$360$	26.9462	+	63.9361i	1.42019	+	3.36973i
$361$	12.3875	+	9.00007i	0.651975	+	0.473688i
$362$	−0.191541	−	1.82239i	−0.0100672	−	0.0957826i
$363$	1.65842	+	12.4536i	0.0870447	+	0.653642i
$364$	−3.48673	+	33.1740i	−0.182754	+	1.73879i
$365$	−0.190703	+	2.52593i	−0.00998186	+	0.132213i
$366$	−5.15654	−	38.7219i	−0.269537	−	2.02402i
$367$	−11.0096	−	12.2274i	−0.574699	−	0.638267i	0.383783	−	0.923423i	$-0.374621\pi$
$367$	−11.0096	−	12.2274i	−0.574699	−	0.638267i	−0.958481	+	0.285156i	$0.907955\pi$
$368$	−11.7909			−0.614643
$369$	1.39347	−	5.26320i	0.0725412	−	0.273991i
$370$	−8.67019	+	0.254670i	−0.450742	+	0.0132397i
$371$	5.45226	+	1.15891i	0.283067	+	0.0601678i
$372$	−29.0793	−	81.7302i	−1.50769	−	4.23751i
$373$	0.264305	−	2.51469i	0.0136852	−	0.130206i	−0.985546	−	0.169407i	$-0.945815\pi$
$373$	0.264305	−	2.51469i	0.0136852	−	0.130206i	0.999231	+	0.0392013i	$0.0124814\pi$
$374$	3.59575	+	6.22802i	0.185932	+	0.322043i
$375$	−11.2087	+	15.7913i	−0.578815	+	0.815459i
$376$	23.4486	−	40.6142i	1.20927	−	2.09452i
$377$	12.1883	+	8.85534i	0.627731	+	0.456073i
$378$	−11.6396	+	15.3102i	−0.598676	+	0.787473i
$379$	−6.58832	−	20.2768i	−0.338419	−	1.04155i	−0.965013	−	0.262201i	$-0.915552\pi$
$379$	−6.58832	−	20.2768i	−0.338419	−	1.04155i	0.626594	−	0.779346i	$-0.284448\pi$
$380$	−11.6559	+	21.6315i	−0.597934	+	1.10967i
$381$	−21.6821	+	5.23959i	−1.11081	+	0.268432i
$382$	26.4693	+	45.8462i	1.35429	+	2.34570i
$383$	−7.59930	+	1.61528i	−0.388306	+	0.0825370i	−0.397928	−	0.917417i	$-0.630271\pi$
$383$	−7.59930	+	1.61528i	−0.388306	+	0.0825370i	0.00962181	+	0.999954i	$0.496937\pi$
$384$	83.0960	−	63.9587i	4.24047	−	3.26388i
$385$	−5.19525	+	2.49835i	−0.264775	+	0.127328i
$386$	38.9096	+	28.2695i	1.98045	+	1.43888i
$387$	−5.08328	−	1.93393i	−0.258398	−	0.0983070i
$388$	−83.4230	+	60.6103i	−4.23516	+	3.07702i
$389$	33.8335	−	15.0637i	1.71543	−	0.763757i	0.717702	−	0.696351i	$-0.245194\pi$
$389$	33.8335	−	15.0637i	1.71543	−	0.763757i	0.997726	−	0.0674069i	$-0.0214726\pi$
$390$	−46.5584	−	7.15117i	−2.35757	−	0.362114i
$391$	−0.832606	−	0.370700i	−0.0421067	−	0.0187471i
$392$	−52.8702	+	11.2379i	−2.67035	+	0.567601i
$393$	−4.16369	+	7.69589i	−0.210030	+	0.388206i
$394$	−39.4044	−	43.7630i	−1.98516	−	2.20475i
$395$	−7.93582	−	22.1853i	−0.399294	−	1.11626i
$396$	−32.8325	−	5.09990i	−1.64989	−	0.256279i
$397$	7.53981	+	23.2052i	0.378412	+	1.16463i	0.941147	+	0.337996i	$0.109749\pi$
$397$	7.53981	+	23.2052i	0.378412	+	1.16463i	−0.562735	+	0.826637i	$0.690251\pi$
$398$	−41.8715	+	18.6424i	−2.09883	+	0.934458i
$399$	−4.42879	+	0.122576i	−0.221717	+	0.00613649i
$400$	80.9384	+	30.4793i	4.04692	+	1.52396i
$401$	17.8616	+	30.9372i	0.891965	+	1.54493i	0.837517	+	0.546412i	$0.184007\pi$
$401$	17.8616	+	30.9372i	0.891965	+	1.54493i	0.0544484	+	0.998517i	$0.482660\pi$
$402$	1.96379	−	25.4369i	0.0979450	−	1.26868i
$403$	37.4723	+	7.96499i	1.86663	+	0.396764i
$404$	−2.01179	−	6.19167i	−0.100090	−	0.308047i
$405$	−15.4218	−	12.9294i	−0.766313	−	0.642467i
$406$	3.93704	−	12.1170i	0.195392	−	0.601354i
$407$	1.35097	−	2.33995i	0.0669652	−	0.115987i
$408$	23.2821	−	5.62625i	1.15264	−	0.278541i
$409$	−17.8400	−	7.94289i	−0.882132	−	0.392750i	−0.0848758	−	0.996392i	$-0.527049\pi$
$409$	−17.8400	−	7.94289i	−0.882132	−	0.392750i	−0.797256	+	0.603641i	$0.793716\pi$
$410$	−5.92276	−	9.59633i	−0.292504	−	0.473929i
$411$	15.2399	+	10.4407i	0.751727	+	0.515000i
$412$	−7.93567	−	75.5028i	−0.390962	−	3.71976i
$413$	13.4979	−	9.80682i	0.664190	−	0.482562i
$414$	5.05559	−	2.59496i	0.248469	−	0.127535i
$415$	6.47845	−	22.1294i	0.318014	−	1.08629i
$416$	12.5267	+	119.183i	0.614170	+	5.84344i
$417$	14.1510	+	14.8676i	0.692979	+	0.728072i
$418$	−5.16478	−	8.94566i	−0.252617	−	0.437546i
$419$	−22.8041	+	4.84717i	−1.11405	+	0.236800i	−0.727933	−	0.685648i	$-0.759519\pi$
$419$	−22.8041	+	4.84717i	−1.11405	+	0.236800i	−0.386122	+	0.922448i	$0.626185\pi$
$420$	4.75379	+	29.1322i	0.231961	+	1.42151i
$421$	23.5935	+	5.01495i	1.14988	+	0.244414i	0.743142	−	0.669133i	$-0.233335\pi$
$421$	23.5935	+	5.01495i	1.14988	+	0.244414i	0.406733	+	0.913547i	$0.366668\pi$
$422$	18.6854	+	57.5076i	0.909589	+	2.79943i
$423$	−0.671424	+	13.5861i	−0.0326458	+	0.660581i
$424$	43.2843			2.10207
$425$	4.75715	+	4.69693i	0.230756	+	0.227835i
$426$	15.5471	−	0.430300i	0.753261	−	0.0208481i
$427$	1.12997	−	10.7510i	0.0546831	−	0.520275i
$428$	14.4750	−	16.0761i	0.699676	−	0.777069i
$429$	9.51277	−	11.1717i	0.459281	−	0.539374i
$430$	−10.1520	+	4.88201i	−0.489574	+	0.235431i
$431$	3.55648	−	10.9457i	0.171310	−	0.527237i	−0.828136	−	0.560527i	$-0.810599\pi$
$431$	3.55648	−	10.9457i	0.171310	−	0.527237i	0.999446	+	0.0332902i	$0.0105986\pi$
$432$	−38.3313	+	81.2965i	−1.84421	+	3.91138i
$433$	−1.01538	+	3.12503i	−0.0487962	+	0.150179i	−0.972486	−	0.232963i	$-0.925158\pi$
$433$	−1.01538	+	3.12503i	−0.0487962	+	0.150179i	0.923689	+	0.383142i	$0.125158\pi$
$434$	−3.38642	−	32.2197i	−0.162553	−	1.54659i
$435$	12.4683	+	4.71938i	0.597810	+	0.226277i
$436$	−2.74694	+	26.1354i	−0.131554	+	1.25166i
$437$	1.19592	+	0.532458i	0.0572086	+	0.0254709i
$438$	−4.32082	+	3.32572i	−0.206457	+	0.158909i
$439$	−24.3810	+	10.8551i	−1.16364	+	0.518086i	−0.895398	−	0.445266i	$-0.853109\pi$
$439$	−24.3810	+	10.8551i	−1.16364	+	0.518086i	−0.268241	+	0.963352i	$0.586442\pi$
$440$	−35.4275	+	27.3642i	−1.68894	+	1.30454i
$441$	12.1545	−	9.90262i	0.578785	−	0.471554i
$442$	−5.02506	+	15.4655i	−0.239018	+	0.735621i
$443$	−15.8645	+	27.4781i	−0.753746	+	1.30553i	0.192250	+	0.981346i	$0.438422\pi$
$443$	−15.8645	+	27.4781i	−0.753746	+	1.30553i	−0.945996	+	0.324180i	$0.894912\pi$
$444$	−9.53824	−	10.0213i	−0.452665	−	0.475588i
$445$	−2.73017	+	36.1620i	−0.129422	+	1.71424i
$446$	−41.4942	+	46.0840i	−1.96481	+	2.18214i
$447$	−6.93983	−	1.27553i	−0.328243	−	0.0603304i
$448$	50.4884	−	22.4789i	2.38535	−	1.06203i
$449$	−5.14754			−0.242927			−0.121464	−	0.992596i	$-0.538759\pi$
$449$	−5.14754			−0.242927			−0.121464	+	0.992596i	$0.538759\pi$
$450$	−41.4119	+	4.74442i	−1.95217	+	0.223654i
$451$	3.51278			0.165410
$452$	−25.2590	+	11.2460i	−1.18808	+	0.528968i
$453$	8.93138	+	25.1025i	0.419633	+	1.17942i
$454$	−24.2598	+	26.9433i	−1.13857	+	1.26451i
$455$	−12.0588	−	4.95001i	−0.565328	−	0.232060i
$456$	−33.4414	+	8.08130i	−1.56604	+	0.378442i
$457$	7.32197	−	12.6820i	0.342508	−	0.593240i	−0.642390	−	0.766378i	$-0.722057\pi$
$457$	7.32197	−	12.6820i	0.342508	−	0.593240i	0.984898	+	0.173137i	$0.0553905\pi$
$458$	1.91795	−	5.90284i	0.0896198	−	0.275822i
$459$	−5.26266	+	4.53558i	−0.245640	+	0.211703i
$460$	2.45045	−	8.37036i	0.114253	−	0.390270i
$461$	32.3602	−	14.4077i	1.50716	−	0.671032i	0.523661	−	0.851927i	$-0.324566\pi$
$461$	32.3602	−	14.4077i	1.50716	−	0.671032i	0.983503	+	0.180894i	$0.0578992\pi$
$462$	−11.4711	−	4.73147i	−0.533683	−	0.220128i
$463$	16.0348	+	7.13914i	0.745199	+	0.331784i	0.743968	−	0.668215i	$-0.232942\pi$
$463$	16.0348	+	7.13914i	0.745199	+	0.331784i	0.00123076	+	0.999999i	$0.499608\pi$
$464$	6.22375	−	59.2150i	0.288930	−	2.74899i
$465$	33.8450	−	1.93244i	1.56953	−	0.0896146i
$466$	2.78985	+	26.5436i	0.129237	+	1.22961i
$467$	0.826963	−	2.54513i	0.0382673	−	0.117775i	−0.930098	−	0.367311i	$-0.880278\pi$
$467$	0.826963	−	2.54513i	0.0382673	−	0.117775i	0.968365	+	0.249537i	$0.0802783\pi$
$468$	−41.1070	−	62.8881i	−1.90017	−	2.90700i
$469$	2.18170	−	6.71459i	0.100742	−	0.310051i
$470$	19.4590	+	20.3751i	0.897575	+	0.939834i
$471$	−8.16138	−	1.50005i	−0.376057	−	0.0691185i
$472$	86.6919	−	96.2811i	3.99032	−	4.43170i
$473$	0.366793	−	3.48981i	0.0168652	−	0.160461i
$474$	24.1335	−	44.6067i	1.10849	−	2.04886i
$475$	−6.83297	−	6.74647i	−0.313518	−	0.309549i
$476$	10.1901			0.467061
$477$	−11.1693	+	5.73305i	−0.511409	+	0.262498i
$478$	−13.6973	−	42.1558i	−0.626498	−	1.92816i
$479$	−31.4711	−	6.68940i	−1.43795	−	0.305646i	−0.578007	−	0.816032i	$-0.696169\pi$
$479$	−31.4711	−	6.68940i	−1.43795	−	0.305646i	−0.859946	+	0.510385i	$0.829503\pi$
$480$	38.4661	+	98.8242i	1.75573	+	4.51069i
$481$	5.97613	−	1.27027i	0.272488	−	0.0579191i
$482$	16.4033	+	28.4113i	0.747148	+	1.29410i
$483$	1.52858	−	0.369389i	0.0695527	−	0.0168078i
$484$	4.33844	+	41.2775i	0.197202	+	1.87625i
$485$	−13.5721	−	37.9418i	−0.616275	−	1.72285i
$486$	−1.45654	−	43.2935i	−0.0660698	−	1.96383i
$487$	4.60192	−	3.34349i	0.208533	−	0.151508i	−0.478617	−	0.878024i	$-0.658862\pi$
$487$	4.60192	−	3.34349i	0.208533	−	0.151508i	0.687150	+	0.726516i	$0.258862\pi$
$488$	−8.77456	−	83.4843i	−0.397206	−	3.77916i
$489$	−1.15157	+	14.9163i	−0.0520759	+	0.674537i
$490$	2.44465	−	32.3802i	0.110438	−	1.46279i
$491$	−3.71402	−	1.65359i	−0.167611	−	0.0746254i	0.321216	−	0.947006i	$-0.395909\pi$
$491$	−3.71402	−	1.65359i	−0.167611	−	0.0746254i	−0.488827	+	0.872381i	$0.662575\pi$
$492$	5.08277	−	17.2535i	0.229149	−	0.777848i
$493$	2.30118	−	3.98575i	0.103640	−	0.179509i
$494$	7.21777	−	22.2140i	0.324743	−	0.999456i
$495$	5.51751	−	11.7536i	0.247994	−	0.528287i
$496$	−46.7864	−	143.994i	−2.10077	−	6.46551i
$497$	4.20998	+	0.894859i	0.188843	+	0.0401399i
$498$	44.7657	−	21.4341i	2.00600	−	0.960485i
$499$	7.15851	+	12.3989i	0.320459	+	0.555051i	0.980583	−	0.196106i	$-0.0628296\pi$
$499$	7.15851	+	12.3989i	0.320459	+	0.555051i	−0.660124	+	0.751157i	$0.729496\pi$
$500$	−38.4583	+	51.1238i	−1.71991	+	2.28633i
$501$	7.28599	−	13.4669i	0.325514	−	0.601658i
$502$	−19.3284	+	8.60557i	−0.862670	+	0.384086i
$503$	8.97302	+	27.6161i	0.400087	+	1.23134i	0.924928	+	0.380142i	$0.124125\pi$
$503$	8.97302	+	27.6161i	0.400087	+	1.23134i	−0.524841	+	0.851200i	$0.675875\pi$
$504$	−25.9130	+	32.1956i	−1.15426	+	1.43411i
$505$	2.54302	−	0.0746963i	0.113163	−	0.00332394i
$506$	2.45331	+	2.72468i	0.109063	+	0.121127i
$507$	10.6581	−	0.294985i	0.473341	−	0.0131007i
$508$	−72.0806	+	15.3212i	−3.19806	+	0.679768i
$509$	−24.0786	−	10.7205i	−1.06726	−	0.475177i	−0.203501	−	0.979075i	$-0.565232\pi$
$509$	−24.0786	−	10.7205i	−1.06726	−	0.475177i	−0.863763	+	0.503898i	$0.831899\pi$
$510$	−0.685918	+	14.3734i	−0.0303730	+	0.636466i
$511$	−1.37844	+	0.613719i	−0.0609784	+	0.0271493i
$512$	93.6925	−	68.0716i	4.14066	−	3.00837i
$513$	7.55905	−	6.51471i	0.333740	−	0.287631i
$514$	−42.5442	−	30.9102i	−1.87654	−	1.36339i
$515$	29.1881	+	5.31360i	1.28618	+	0.234145i
$516$	−16.6100	−	6.85109i	−0.731213	−	0.301602i
$517$	−8.58459	+	1.82471i	−0.377550	+	0.0802507i
$518$	−2.58337	−	4.47452i	−0.113507	−	0.196599i
$519$	−1.29680	+	4.40202i	−0.0569234	+	0.193227i
$520$	−99.5860	−	18.1293i	−4.36714	−	0.795024i
$521$	−12.2243	−	37.6226i	−0.535558	−	1.64828i	−0.742441	−	0.669912i	$-0.766332\pi$
$521$	−12.2243	−	37.6226i	−0.535558	−	1.64828i	0.206883	−	0.978366i	$-0.433668\pi$
$522$	10.3636	+	26.7594i	0.453601	+	1.17123i
$523$	−2.79441	−	2.03026i	−0.122191	−	0.0887769i	0.525011	−	0.851095i	$-0.324061\pi$
$523$	−2.79441	−	2.03026i	−0.122191	−	0.0887769i	−0.647202	+	0.762318i	$0.724061\pi$
$524$	−14.4533	+	25.0339i	−0.631397	+	1.09361i
$525$	−11.4477	−	1.41568i	−0.499621	−	0.0617856i
$526$	−12.8357	−	22.2321i	−0.559663	−	0.969364i
$527$	1.22330	−	11.6390i	0.0532879	−	0.507001i
$528$	−57.0345	−	10.4828i	−2.48211	−	0.456207i
$529$	22.0429	+	4.68536i	0.958387	+	0.203711i
$530$	−7.30605	+	24.9564i	−0.317354	+	1.08404i
$531$	−9.61795	+	36.3274i	−0.417383	+	1.57647i
$532$	−14.6366			−0.634576
$533$	5.31497	+	5.90287i	0.230217	+	0.255682i
$534$	−61.8582	+	47.6121i	−2.67687	+	2.06038i
$535$	4.43995	+	7.19381i	0.191956	+	0.311016i
$536$	5.73068	−	54.5238i	0.247528	−	2.35507i
$537$	−7.32268	−	3.02038i	−0.315997	−	0.130339i
$538$	2.46172	+	23.4217i	0.106132	+	1.00978i
$539$	8.18337	+	5.94557i	0.352483	+	0.256094i
$540$	−49.7462	−	44.1068i	−2.14073	−	1.89806i
$541$	10.2115	−	7.41907i	0.439026	−	0.318971i	−0.346222	−	0.938153i	$-0.612536\pi$
$541$	10.2115	−	7.41907i	0.439026	−	0.318971i	0.785248	+	0.619182i	$0.212536\pi$
$542$	6.19115	+	6.87596i	0.265933	+	0.295348i
$543$	0.598220	+	0.972950i	0.0256721	+	0.0417533i
$544$	35.8095	−	7.61155i	1.53532	−	0.326342i
$545$	−9.50027	−	3.89974i	−0.406947	−	0.167047i
$546$	−9.40545	−	26.4349i	−0.402516	−	1.13131i
$547$	31.7428	+	6.74714i	1.35722	+	0.288487i	0.828349	−	0.560212i	$-0.189280\pi$
$547$	31.7428	+	6.74714i	1.35722	+	0.288487i	0.528876	+	0.848699i	$0.322614\pi$
$548$	49.3729	+	35.8715i	2.10911	+	1.53236i
$549$	13.3218	+	20.3806i	0.568562	+	0.869823i
$550$	−9.79746	−	25.0453i	−0.417765	−	1.06793i
$551$	−3.30531	+	5.72497i	−0.140811	+	0.243892i
$552$	11.0141	−	5.27362i	0.468791	−	0.224460i
$553$	9.39120	−	10.4300i	0.399355	−	0.443528i
$554$	1.42028	−	1.57738i	0.0603420	−	0.0670166i
$555$	4.80565	−	2.47696i	0.203988	−	0.105141i
$556$	45.3727	+	50.3914i	1.92423	+	2.13707i
$557$	−31.0263			−1.31462			−0.657312	−	0.753618i	$-0.728307\pi$
$557$	−31.0263			−1.31462			−0.657312	+	0.753618i	$0.728307\pi$
$558$	51.7509	+	51.4434i	2.19079	+	2.17777i
$559$	6.41925	−	4.66385i	0.271505	−	0.197260i
$560$	6.88695	+	51.0547i	0.291027	+	2.15745i
$561$	−3.69788	−	2.53338i	−0.156124	−	0.106959i
$562$	36.9772	+	16.4633i	1.55979	+	0.694464i
$563$	−25.0255	−	11.1421i	−1.05470	−	0.469581i	−0.195222	−	0.980759i	$-0.562543\pi$
$563$	−25.0255	−	11.1421i	−1.05470	−	0.469581i	−0.859475	+	0.511178i	$0.829209\pi$
$564$	−3.45904	+	44.8047i	−0.145652	+	1.88662i
$565$	−1.44443	−	10.7079i	−0.0607678	−	0.450486i
$566$	−52.6444	+	38.2484i	−2.21281	+	1.60770i
$567$	2.42240	−	11.7402i	0.101731	−	0.493041i
$568$	33.4221			1.40236
$569$	25.6914	+	28.5332i	1.07704	+	1.19617i	0.979605	+	0.200933i	$0.0643974\pi$
$569$	25.6914	+	28.5332i	1.07704	+	1.19617i	0.0974358	+	0.995242i	$0.468936\pi$
$570$	0.985223	−	20.6454i	0.0412664	−	0.864739i
$571$	−24.0775	+	26.7408i	−1.00761	+	1.11907i	−0.0147396	+	0.999891i	$0.504692\pi$
$571$	−24.0775	+	26.7408i	−1.00761	+	1.11907i	−0.992873	+	0.119176i	$0.961975\pi$
$572$	32.4355	−	36.0233i	1.35620	−	1.50621i
$573$	−27.2211	−	18.6489i	−1.13718	−	0.779069i
$574$	3.35861	−	5.81729i	0.140186	−	0.242809i
$575$	2.87020	+	1.83804i	0.119695	+	0.0766517i
$576$	−56.1817	+	111.080i	−2.34090	+	4.62833i
$577$	−15.8862	−	11.5420i	−0.661351	−	0.480500i	0.205768	−	0.978601i	$-0.434031\pi$
$577$	−15.8862	−	11.5420i	−0.661351	−	0.480500i	−0.867119	+	0.498101i	$0.834031\pi$
$578$	−41.3490	−	8.78901i	−1.71989	−	0.365575i
$579$	−29.4836	−	5.41903i	−1.22530	−	0.225207i
$580$	40.7433	+	16.7246i	1.69177	+	0.694452i
$581$	13.4348	−	2.85565i	0.557368	−	0.118472i
$582$	41.2737	−	76.2877i	1.71085	−	3.16223i
$583$	−5.42012	−	6.01965i	−0.224478	−	0.249308i
$584$	−9.47921	+	6.88705i	−0.392252	+	0.284988i
$585$	28.0990	−	8.51209i	1.16175	−	0.351931i
$586$	−10.8988	−	7.91843i	−0.450225	−	0.327107i
$587$	0.824834	+	7.84777i	0.0340445	+	0.323912i	0.998268	+	0.0588230i	$0.0187347\pi$
$587$	0.824834	+	7.84777i	0.0340445	+	0.323912i	−0.964224	+	0.265089i	$0.914599\pi$
$588$	41.0433	−	31.5909i	1.69260	−	1.30279i
$589$	−1.75710	+	16.7177i	−0.0724000	+	0.688840i
$590$	40.8798	+	66.2354i	1.68299	+	2.72687i
$591$	33.9322	+	13.9960i	1.39578	+	0.575717i
$592$	−16.1569	−	17.9440i	−0.664044	−	0.737495i
$593$	−33.0220			−1.35605			−0.678025	−	0.735039i	$-0.737164\pi$
$593$	−33.0220			−1.35605			−0.678025	+	0.735039i	$0.737164\pi$
$594$	26.7618	−	8.05751i	1.09805	−	0.330603i
$595$	−1.11882	+	3.82171i	−0.0458670	+	0.156675i
$596$	−22.8011	−	4.84653i	−0.933970	−	0.198522i
$597$	18.5212	−	21.7511i	0.758022	−	0.890212i
$598$	−0.866595	+	8.24510i	−0.0354377	+	0.337167i
$599$	−10.6255	−	18.4039i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$599$	−10.6255	−	18.4039i	−0.434145	−	0.751961i	−0.997225	+	0.0744411i	$0.976283\pi$
$600$	−89.2382	+	7.72936i	−3.64313	+	0.315550i
$601$	16.1753	−	28.0165i	0.659805	−	1.14282i	−0.320861	−	0.947126i	$-0.603972\pi$
$601$	16.1753	−	28.0165i	0.659805	−	1.14282i	0.980666	−	0.195689i	$-0.0626945\pi$
$602$	−5.42855	−	3.94408i	−0.221251	−	0.160749i
$603$	5.74296	+	14.8287i	0.233871	+	0.603870i
$604$	27.2001	+	83.7134i	1.10676	+	3.40625i
$605$	−15.9571	−	2.90495i	−0.648750	−	0.118103i
$606$	3.77547	+	3.96666i	0.153368	+	0.161135i
$607$	−2.58655	−	4.48004i	−0.104985	−	0.181839i	0.808747	−	0.588156i	$-0.200146\pi$
$607$	−2.58655	−	4.48004i	−0.104985	−	0.181839i	−0.913732	+	0.406317i	$0.866813\pi$
$608$	−51.4352	+	10.9329i	−2.08597	+	0.443387i
$609$	1.04826	+	7.87164i	0.0424775	+	0.318975i
$610$	49.6156	+	9.03236i	2.00888	+	0.365710i
$611$	−16.0551	−	11.6647i	−0.649519	−	0.471903i
$612$	−17.7936	+	14.4970i	−0.719265	+	0.586007i
$613$	27.4772	−	19.9633i	1.10979	−	0.806311i	0.127161	−	0.991882i	$-0.459414\pi$
$613$	27.4772	−	19.9633i	1.10979	−	0.806311i	0.982631	+	0.185571i	$0.0594135\pi$
$614$	−56.1123	+	24.9828i	−2.26451	+	1.00822i
$615$	5.91274	+	3.80060i	0.238425	+	0.153255i
$616$	−24.3595	−	10.8456i	−0.981474	−	0.436980i
$617$	37.6552	−	8.00385i	1.51594	−	0.322223i	0.626553	−	0.779379i	$-0.284465\pi$
$617$	37.6552	−	8.00385i	1.51594	−	0.322223i	0.889387	+	0.457156i	$0.151132\pi$
$618$	33.4476	+	54.3995i	1.34546	+	2.18827i
$619$	2.54331	+	2.82463i	0.102224	+	0.113532i	0.792086	−	0.610410i	$-0.208995\pi$
$619$	2.54331	+	2.82463i	0.102224	+	0.113532i	−0.689861	+	0.723941i	$0.742329\pi$
$620$	111.945	−	3.28815i	4.49580	−	0.132055i
$621$	−2.14365	+	2.81967i	−0.0860216	+	0.113149i
$622$	16.9170	+	52.0651i	0.678309	+	2.08762i
$623$	−19.7341	+	8.78619i	−0.790630	+	0.352011i
$624$	−68.6801	−	111.702i	−2.74941	−	4.47165i
$625$	−14.9511	−	20.0366i	−0.598043	−	0.801464i
$626$	−5.56875	−	9.64536i	−0.222572	−	0.385506i
$627$	5.31147	+	3.63883i	0.212120	+	0.145321i
$628$	−26.8146	−	5.69961i	−1.07002	−	0.227439i
$629$	−0.576755	−	1.77507i	−0.0229967	−	0.0707766i
$630$	−14.1891	−	20.3750i	−0.565307	−	0.811760i
$631$	4.65356	−	14.3222i	0.185255	−	0.570157i	−0.814697	−	0.579886i	$-0.803097\pi$
$631$	4.65356	−	14.3222i	0.185255	−	0.570157i	0.999953	+	0.00972902i	$0.00309689\pi$
$632$	54.4927	−	94.3842i	2.16760	−	3.75440i
$633$	−25.9841	−	27.2999i	−1.03278	−	1.08508i
$634$	−3.82329	−	1.70224i	−0.151842	−	0.0676044i
$635$	2.16796	−	28.7155i	0.0860330	−	1.13954i
$636$	−37.4090	+	17.9116i	−1.48336	+	0.710242i
$637$	2.39083	+	22.7472i	0.0947281	+	0.901277i
$638$	−14.9786	+	10.8826i	−0.593007	+	0.430845i
$639$	−8.62444	+	4.42680i	−0.341177	+	0.175121i
$640$	45.5949	+	127.465i	1.80230	+	5.03848i
$641$	−2.85840	−	27.1959i	−0.112900	−	1.07417i	−0.893476	−	0.449111i	$-0.851741\pi$
$641$	−2.85840	−	27.1959i	−0.112900	−	1.07417i	0.780576	−	0.625061i	$-0.214926\pi$
$642$	−5.14204	+	17.4547i	−0.202940	+	0.688883i
$643$	7.99458	+	13.8470i	0.315275	+	0.546073i	0.979496	−	0.201464i	$-0.0645698\pi$
$643$	7.99458	+	13.8470i	0.315275	+	0.546073i	−0.664221	+	0.747537i	$0.731236\pi$
$644$	5.08165	−	1.08014i	0.200245	−	0.0425634i
$645$	4.39313	−	5.47723i	0.172980	−	0.215666i
$646$	−6.97941	−	1.48352i	−0.274601	−	0.0583683i
$647$	6.09758	+	18.7664i	0.239720	+	0.737784i	0.996460	+	0.0840673i	$0.0267911\pi$
$647$	6.09758	+	18.7664i	0.239720	+	0.737784i	−0.756740	+	0.653716i	$0.773209\pi$
$648$	−0.554840	−	93.0846i	−0.0217962	−	3.65671i
$649$	−24.2457			−0.951728
$650$	27.2622	−	54.3581i	1.06931	−	2.13210i
$651$	10.5765	+	17.2017i	0.414525	+	0.674186i
$652$	−5.16622	+	49.1533i	−0.202325	+	1.92499i
$653$	18.1410	−	20.1476i	0.709911	−	0.788436i	−0.275010	−	0.961441i	$-0.588681\pi$
$653$	18.1410	−	20.1476i	0.709911	−	0.788436i	0.984921	+	0.173005i	$0.0553478\pi$
$654$	−7.40985	−	20.8261i	−0.289748	−	0.814365i
$655$	−7.80188	−	8.16920i	−0.304845	−	0.319197i
$656$	9.70070	−	29.8557i	0.378749	−	1.16567i
$657$	1.53387	−	3.03271i	0.0598421	−	0.118317i
$658$	−5.18606	+	15.9610i	−0.202174	+	0.622226i
$659$	5.17975	+	49.2821i	0.201775	+	1.91976i	0.361094	+	0.932529i	$0.382403\pi$
$659$	5.17975	+	49.2821i	0.201775	+	1.91976i	−0.159319	+	0.987227i	$0.550930\pi$
$660$	19.2950	−	38.3102i	0.751056	−	1.49122i
$661$	−3.25622	+	30.9809i	−0.126652	+	1.20502i	0.727912	+	0.685671i	$0.240491\pi$
$661$	−3.25622	+	30.9809i	−0.126652	+	1.20502i	−0.854564	+	0.519346i	$0.826176\pi$
$662$	29.0121	+	12.9170i	1.12759	+	0.502034i
$663$	−1.33795	−	10.0470i	−0.0519616	−	0.390194i
$664$	97.4348	−	43.3808i	3.78120	−	1.68350i
$665$	1.60702	−	5.48934i	0.0623175	−	0.212867i
$666$	10.8767	+	4.13804i	0.421465	+	0.160346i
$667$	0.725079	−	2.23156i	0.0280752	−	0.0864065i
$668$	25.2917	−	43.8065i	0.978565	−	1.69492i
$669$	10.9225	−	37.0766i	0.422289	−	1.43347i
$670$	30.4694	+	12.5073i	1.17714	+	0.483200i
$671$	−10.5116	+	11.6743i	−0.405796	+	0.450682i
$672$	−40.9526	+	48.0943i	−1.57978	+	1.85528i
$673$	−4.11415	+	1.83174i	−0.158589	+	0.0706084i	−0.484496	−	0.874793i	$-0.660997\pi$
$673$	−4.11415	+	1.83174i	−0.158589	+	0.0706084i	0.325907	+	0.945402i	$0.394330\pi$
$674$	96.0843			3.70103
$675$	22.0038	−	13.8142i	0.846926	−	0.531710i
$676$	35.2235			1.35475
$677$	31.4670	−	14.0100i	1.20938	−	0.538449i	0.299806	−	0.954000i	$-0.403078\pi$
$677$	31.4670	−	14.0100i	1.20938	−	0.538449i	0.909570	+	0.415551i	$0.136411\pi$
$678$	15.0781	−	17.7076i	0.579073	−	0.680056i
$679$	16.0611	−	17.8377i	0.616368	−	0.684546i
$680$	−2.32795	+	30.8345i	−0.0892727	+	1.18245i
$681$	6.38592	−	21.6771i	0.244709	−	0.830667i
$682$	−23.5398	+	40.7721i	−0.901384	+	1.56124i
$683$	−8.37000	+	25.7602i	−0.320269	+	0.985687i	0.653262	+	0.757132i	$0.273400\pi$
$683$	−8.37000	+	25.7602i	−0.320269	+	0.985687i	−0.973531	+	0.228555i	$0.926600\pi$
$684$	25.5580	−	20.8229i	0.977235	−	0.796183i
$685$	−18.8742	+	14.5784i	−0.721148	+	0.557014i
$686$	41.3392	−	18.4054i	1.57834	−	0.702722i
$687$	0.510664	+	3.83471i	0.0194830	+	0.146303i
$688$	−28.6475	−	12.7547i	−1.09218	−	0.486269i
$689$	1.91457	−	18.2159i	0.0729394	−	0.693972i
$690$	1.18151	+	7.24053i	0.0449793	+	0.275642i
$691$	3.36196	+	31.9869i	0.127895	+	1.21684i	0.850649	+	0.525734i	$0.176209\pi$
$691$	3.36196	+	31.9869i	0.127895	+	1.21684i	−0.722754	+	0.691105i	$0.757124\pi$
$692$	−4.68483	+	14.4184i	−0.178091	+	0.548107i
$693$	7.72239	−	0.427795i	0.293349	−	0.0162506i
$694$	12.8472	−	39.5397i	0.487674	−	1.50090i
$695$	−23.8806	+	11.4840i	−0.905843	+	0.435611i
$696$	20.6709	+	58.0975i	0.783528	+	2.20218i
$697$	1.62366	−	1.80325i	0.0615003	−	0.0683030i
$698$	8.82094	−	83.9256i	0.333877	−	3.17663i
$699$	−8.71325	−	14.1713i	−0.329566	−	0.536008i
$700$	−37.6750	−	5.72139i	−1.42398	−	0.216248i
$701$	−33.8606			−1.27890			−0.639449	−	0.768834i	$-0.720837\pi$
$701$	−33.8606			−1.27890			−0.639449	+	0.768834i	$0.720837\pi$
$702$	54.0315	+	32.7792i	2.03929	+	1.23717i
$703$	0.828426	+	2.54963i	0.0312447	+	0.0961612i
$704$	−78.5582	−	16.6981i	−2.96077	−	0.629332i
$705$	−16.4239	−	6.21660i	−0.618559	−	0.234131i
$706$	14.6176	−	3.10706i	0.550140	−	0.116936i
$707$	0.757718	+	1.31241i	0.0284969	+	0.0493581i
$708$	−35.0820	+	119.086i	−1.31846	+	4.47554i
$709$	2.86974	+	27.3038i	0.107775	+	1.02541i	0.906064	+	0.423140i	$0.139072\pi$
$709$	2.86974	+	27.3038i	0.107775	+	1.02541i	−0.798289	+	0.602275i	$0.794261\pi$
$710$	−5.64139	+	19.2701i	−0.211717	+	0.723196i
$711$	−1.56033	+	31.5731i	−0.0585171	+	1.18408i
$712$	−135.707	+	98.5970i	−5.08584	+	3.69508i
$713$	−0.623673	−	5.93385i	−0.0233567	−	0.222225i
$714$	−7.73096	+	3.70163i	−0.289324	+	0.138530i
$715$	9.94901	+	16.1198i	0.372072	+	0.602848i
$716$	−23.9059	−	10.6436i	−0.893407	−	0.397770i
$717$	19.0476	+	20.0122i	0.711345	+	0.747367i
$718$	3.99560	−	6.92059i	0.149115	−	0.258274i
$719$	8.99550	−	27.6853i	0.335475	−	1.03249i	−0.631012	−	0.775773i	$-0.717360\pi$
$719$	8.99550	−	27.6853i	0.335475	−	1.03249i	0.966487	−	0.256714i	$-0.0826399\pi$
$720$	−84.6593	−	79.3525i	−3.15507	−	2.95729i
$721$	5.46094	+	16.8071i	0.203376	+	0.625927i
$722$	−41.6195	−	8.84649i	−1.54892	−	0.329232i
$723$	−16.8692	−	11.5569i	−0.627371	−	0.429805i
$724$	1.88660	+	3.26769i	0.0701150	+	0.121443i
$725$	−10.7458	+	13.4442i	−0.399090	+	0.499305i
$726$	−18.2859	−	29.7402i	−0.678652	−	1.10376i
$727$	2.59030	−	1.15328i	0.0960691	−	0.0427727i	−0.358139	−	0.933668i	$-0.616589\pi$
$727$	2.59030	−	1.15328i	0.0960691	−	0.0427727i	0.454209	+	0.890895i	$0.349922\pi$
$728$	−18.6321	−	57.3436i	−0.690550	−	2.12529i
$729$	12.4723	+	23.9466i	0.461939	+	0.886912i
$730$	−2.37084	−	6.62790i	−0.0877488	−	0.245309i
$731$	−1.62192	−	1.80133i	−0.0599890	−	0.0666245i
$732$	42.1305	+	68.5213i	1.55719	+	2.53262i
$733$	−0.966208	+	0.205374i	−0.0356877	+	0.00758565i	−0.225721	−	0.974192i	$-0.572474\pi$
$733$	−0.966208	+	0.205374i	−0.0356877	+	0.00758565i	0.190033	+	0.981778i	$0.439140\pi$
$734$	41.7693	+	18.5969i	1.54173	+	0.686424i
$735$	7.34160	+	18.8615i	0.270799	+	0.695717i
$736$	17.0509	−	7.59154i	0.628504	−	0.279828i
$737$	−8.30035	+	6.03056i	−0.305747	+	0.222139i
$738$	2.41131	+	14.9362i	0.0887615	+	0.549808i
$739$	18.7656	+	13.6340i	0.690305	+	0.501536i	0.876760	−	0.480927i	$-0.159700\pi$
$739$	18.7656	+	13.6340i	0.690305	+	0.501536i	−0.186455	+	0.982463i	$0.559700\pi$
$740$	16.0963	−	7.74055i	0.591711	−	0.284548i
$741$	1.92177	+	14.4311i	0.0705980	+	0.530139i
$742$	−15.1510	+	3.22045i	−0.556211	+	0.118226i
$743$	1.11329	+	1.92828i	0.0408427	+	0.0707416i	0.885724	−	0.464212i	$-0.153662\pi$
$743$	1.11329	+	1.92828i	0.0408427	+	0.0707416i	−0.844881	+	0.534954i	$0.820329\pi$
$744$	108.107	+	113.581i	3.96339	+	4.16410i
$745$	4.32109	−	8.01926i	0.158313	−	0.293803i
$746$	2.17129	+	6.68255i	0.0794967	+	0.244666i
$747$	−19.3968	+	24.0996i	−0.709693	+	0.881758i
$748$	−11.9801	−	8.70405i	−0.438036	−	0.318252i
$749$	−2.51776	+	4.36089i	−0.0919969	+	0.159343i
$750$	10.6062	−	52.7566i	0.387284	−	1.92640i
$751$	13.5281	+	23.4314i	0.493648	+	0.855023i	0.999973	−	0.00731948i	$-0.00232988\pi$
$751$	13.5281	+	23.4314i	0.493648	+	0.855023i	−0.506325	+	0.862342i	$0.668997\pi$
$752$	−8.19823	+	78.0010i	−0.298959	+	2.84440i
$753$	8.54963	−	10.0406i	0.311566	−	0.365899i
$754$	−40.9502	−	8.70424i	−1.49132	−	0.316990i
$755$	−34.3825	+	1.00992i	−1.25131	+	0.0367547i
$756$	9.07264	−	38.5486i	0.329969	−	1.40200i
$757$	34.3552			1.24866			0.624330	−	0.781161i	$-0.285372\pi$
$757$	34.3552			1.24866			0.624330	+	0.781161i	$0.285372\pi$
$758$	39.6432	+	44.0282i	1.43990	+	1.59918i
$759$	−2.11261	−	0.871388i	−0.0766831	−	0.0316294i
$760$	3.34376	−	44.2894i	0.121291	−	1.60654i
$761$	−3.74226	+	35.6052i	−0.135657	+	1.29069i	0.688878	+	0.724877i	$0.258104\pi$
$761$	−3.74226	+	35.6052i	−0.135657	+	1.29069i	−0.824535	+	0.565811i	$0.808563\pi$
$762$	49.1202	−	37.8077i	1.77944	−	1.36963i
$763$	−0.639418	−	6.08366i	−0.0231485	−	0.220243i
$764$	−88.1890	−	64.0730i	−3.19056	−	2.31808i
$765$	−3.48335	−	8.26506i	−0.125941	−	0.298824i
$766$	17.4659	−	12.6898i	0.631070	−	0.458499i
$767$	−36.6847	−	40.7425i	−1.32461	−	1.47113i
$768$	−70.2612	+	129.866i	−2.53533	+	4.68614i
$769$	15.9962	−	3.40010i	0.576839	−	0.122611i	0.0897516	−	0.995964i	$-0.471393\pi$
$769$	15.9962	−	3.40010i	0.576839	−	0.122611i	0.487087	+	0.873353i	$0.338059\pi$
$770$	10.3649	−	12.2143i	0.373526	−	0.440173i
$771$	32.2377	+	5.92522i	1.16101	+	0.213392i
$772$	−96.8696	−	20.5903i	−3.48641	−	0.741060i
$773$	12.3397	+	8.96534i	0.443829	+	0.322461i	0.787155	−	0.616756i	$-0.211553\pi$
$773$	12.3397	+	8.96534i	0.443829	+	0.322461i	−0.343325	+	0.939217i	$0.611553\pi$
$774$	15.0903	−	0.835952i	0.542409	−	0.0300477i
$775$	−11.0577	+	42.3450i	−0.397205	+	1.52108i
$776$	93.1949	−	161.418i	3.34550	−	5.79458i
$777$	2.65674	+	1.82010i	0.0953100	+	0.0652959i
$778$	−68.8641	+	76.4814i	−2.46890	+	2.74199i
$779$	−2.33215	+	2.59011i	−0.0835579	+	0.0928004i
$780$	93.5706	−	25.5416i	3.35036	−	0.914535i
$781$	−4.18516	−	4.64809i	−0.149757	−	0.166322i
$782$	2.53265			0.0905673
$783$	−13.0291	−	12.2539i	−0.465623	−	0.437920i
$784$	73.1312	−	53.1329i	2.61183	−	1.89760i
$785$	5.08169	−	9.43081i	0.181373	−	0.336600i
$786$	1.87161	−	24.2429i	0.0667582	−	0.864716i
$787$	30.3230	+	13.5007i	1.08090	+	0.481246i	0.868374	−	0.495910i	$-0.165165\pi$
$787$	30.3230	+	13.5007i	1.08090	+	0.481246i	0.212523	+	0.977156i	$0.431832\pi$
$788$	110.776	+	49.3208i	3.94624	+	1.75698i
$789$	13.2003	+	9.04335i	0.469942	+	0.321952i
$790$	45.2210	+	47.3501i	1.60889	+	1.68464i
$791$	5.20690	−	3.78303i	0.185136	−	0.134509i
$792$	57.9656	−	15.7171i	2.05972	−	0.558484i
$793$	−35.5220			−1.26142
$794$	−45.3685	−	50.3868i	−1.61007	−	1.78816i
$795$	−2.61032	−	15.9965i	−0.0925784	−	0.567339i
$796$	63.1513	−	70.1366i	2.23834	−	2.48593i
$797$	28.2627	−	31.3890i	1.00112	−	1.11185i	0.00739598	−	0.999973i	$-0.497646\pi$
$797$	28.2627	−	31.3890i	1.00112	−	1.11185i	0.993722	−	0.111881i	$-0.0356876\pi$
$798$	11.1044	−	5.31686i	0.393092	−	0.188215i
$799$	−3.03122	+	5.25023i	−0.107237	+	0.185740i
$800$	−136.669	+	8.03572i	−4.83199	+	0.284106i
$801$	21.9594	−	43.4171i	0.775897	−	1.53407i
$802$	−80.3106	−	58.3491i	−2.83587	−	2.06038i
$803$	2.14480	+	0.455891i	0.0756882	+	0.0160880i
$804$	17.6099	+	49.4942i	0.621052	+	1.74553i
$805$	−0.152840	+	2.02443i	−0.00538692	+	0.0713517i
$806$	−104.130	+	22.1335i	−3.66782	+	0.779620i
$807$	−7.68845	−	12.5045i	−0.270646	−	0.440181i
$808$	7.87420	+	8.74518i	0.277013	+	0.307654i
$809$	−30.2321	+	21.9649i	−1.06291	+	0.772246i	−0.974624	−	0.223850i	$-0.928138\pi$
$809$	−30.2321	+	21.9649i	−1.06291	+	0.772246i	−0.0882817	+	0.996096i	$0.528138\pi$
$810$	53.7634	+	15.3920i	1.88905	+	0.540821i
$811$	−30.3450	−	22.0469i	−1.06556	−	0.774172i	−0.0904481	−	0.995901i	$-0.528830\pi$
$811$	−30.3450	−	22.0469i	−1.06556	−	0.774172i	−0.975108	+	0.221729i	$0.928830\pi$
$812$	2.74224	+	26.0907i	0.0962337	+	0.915602i
$813$	−5.33136	−	2.19902i	−0.186979	−	0.0771231i
$814$	−0.784831	+	7.46717i	−0.0275083	+	0.261724i
$815$	−17.8674	−	7.33433i	−0.625867	−	0.256910i
$816$	−31.7435	+	24.4329i	−1.11124	+	0.855321i
$817$	2.32966	+	2.58735i	0.0815045	+	0.0905199i
$818$	54.2663			1.89738
$819$	12.4031	+	12.3294i	0.433401	+	0.430825i
$820$	19.1785	+	13.0913i	0.669742	+	0.457168i
$821$	−2.65732	−	0.564831i	−0.0927411	−	0.0197127i	0.161307	−	0.986904i	$-0.448429\pi$
$821$	−2.65732	−	0.564831i	−0.0927411	−	0.0197127i	−0.254048	+	0.967191i	$0.581762\pi$
$822$	−50.4887	−	9.27973i	−1.76099	−	0.323668i
$823$	−0.534527	+	5.08568i	−0.0186324	+	0.177276i	−0.999880	−	0.0154746i	$-0.995074\pi$
$823$	−0.534527	+	5.08568i	−0.0186324	+	0.177276i	0.981248	+	0.192750i	$0.0617408\pi$
$824$	68.6141	+	118.843i	2.39028	+	4.14009i
$825$	12.2495	+	11.4427i	0.426472	+	0.398383i
$826$	−23.1817	+	40.1518i	−0.806594	+	1.39706i
$827$	21.7468	+	15.8000i	0.756210	+	0.549419i	0.897745	−	0.440515i	$-0.145204\pi$
$827$	21.7468	+	15.8000i	0.756210	+	0.549419i	−0.141536	+	0.989933i	$0.545204\pi$
$828$	−7.33677	+	9.11557i	−0.254970	+	0.316788i
$829$	2.27728	+	7.00875i	0.0790932	+	0.243424i	0.982783	−	0.184764i	$-0.0591521\pi$
$829$	2.27728	+	7.00875i	0.0790932	+	0.243424i	−0.903690	+	0.428188i	$0.859152\pi$
$830$	8.56578	+	63.5002i	0.297323	+	2.20412i
$831$	−0.373861	+	1.26907i	−0.0129691	+	0.0440237i
$832$	−90.8022	−	157.274i	−3.14800	−	5.45250i
$833$	6.83457	−	1.45273i	0.236804	−	0.0503342i
$834$	−52.7282	−	21.7488i	−1.82583	−	0.753098i
$835$	13.6524	+	14.2952i	0.472461	+	0.494705i
$836$	17.2077	+	12.5021i	0.595141	+	0.432395i
$837$	−42.9405	−	14.9903i	−1.48424	−	0.518142i
$838$	52.4122	−	38.0797i	1.81055	−	1.31544i
$839$	−16.3700	+	7.28840i	−0.565155	+	0.251623i	−0.669367	−	0.742932i	$-0.733435\pi$
$839$	−16.3700	+	7.28840i	−0.565155	+	0.251623i	0.104212	+	0.994555i	$0.466768\pi$
$840$	−29.2680	−	44.6108i	−1.00984	−	1.53922i
$841$	−15.6684	−	6.97603i	−0.540291	−	0.240553i
$842$	−65.5627	+	13.9358i	−2.25944	+	0.480259i
$843$	−25.2193	+	0.697999i	−0.868600	+	0.0240403i
$844$	−83.3132	−	92.5287i	−2.86776	−	3.18497i
$845$	−3.86736	+	13.2103i	−0.133041	+	0.454449i
$846$	−13.6514	−	35.2488i	−0.469345	−	1.21188i
$847$	−2.98550	−	9.18843i	−0.102583	−	0.315718i
$848$	−66.1300	+	29.4430i	−2.27091	+	1.01108i
$849$	19.3000	−	35.6729i	0.662376	−	1.22429i
$850$	−17.3853	−	6.54685i	−0.596311	−	0.224555i
$851$	−0.475775	−	0.824067i	−0.0163094	−	0.0282486i
$852$	−28.8854	+	13.8305i	−0.989599	+	0.473826i
$853$	7.25604	+	1.54232i	0.248442	+	0.0528080i	0.330449	−	0.943824i	$-0.392800\pi$
$853$	7.25604	+	1.54232i	0.248442	+	0.0528080i	−0.0820073	+	0.996632i	$0.526133\pi$
$854$	9.28283	+	28.5696i	0.317652	+	0.977632i
$855$	5.00333	+	11.8716i	0.171110	+	0.405999i
$856$	−12.0833	+	37.1885i	−0.412998	+	1.27108i
$857$	−21.8655	+	37.8721i	−0.746911	+	1.29369i	0.202386	+	0.979306i	$0.435130\pi$
$857$	−21.8655	+	37.8721i	−0.746911	+	1.29369i	−0.949297	+	0.314382i	$0.898203\pi$
$858$	−11.5223	+	39.1124i	−0.393364	+	1.33528i
$859$	−29.5873	−	13.1731i	−1.00951	−	0.449461i	−0.165738	−	0.986170i	$-0.553001\pi$
$859$	−29.5873	−	13.1731i	−1.00951	−	0.449461i	−0.843767	+	0.536709i	$0.819667\pi$
$860$	15.0082	−	17.6861i	0.511777	−	0.603092i
$861$	−0.322275	+	4.17441i	−0.0109831	+	0.142263i
$862$	3.34301	+	31.8066i	0.113863	+	1.08334i
$863$	22.8636	−	16.6114i	0.778285	−	0.565457i	−0.126179	−	0.992008i	$-0.540271\pi$
$863$	22.8636	−	16.6114i	0.778285	−	0.565457i	0.904464	+	0.426550i	$0.140271\pi$
$864$	3.08851	−	142.243i	0.105073	−	4.83920i
$865$	−4.89315	−	3.34008i	−0.166372	−	0.113566i
$866$	−0.954438	−	9.08087i	−0.0324331	−	0.308581i
$867$	25.6113	−	6.18911i	0.869806	−	0.210193i
$868$	33.3549	+	57.7725i	1.13214	+	1.96092i
$869$	−19.9499	+	4.24048i	−0.676753	+	0.143848i
$870$	−36.9863	+	2.11179i	−1.25395	+	0.0715964i
$871$	−22.6925	−	4.82344i	−0.768907	−	0.163436i
$872$	−14.6788	−	45.1767i	−0.497087	−	1.52988i
$873$	−2.66853	+	53.9971i	−0.0903160	+	1.82753i
$874$	−3.63778			−0.123050
$875$	6.28228	−	13.5015i	0.212380	−	0.456435i
$876$	5.34256	−	9.87484i	0.180508	−	0.333640i
$877$	3.33372	−	31.7182i	0.112572	−	1.07105i	−0.781740	−	0.623605i	$-0.785668\pi$
$877$	3.33372	−	31.7182i	0.112572	−	1.07105i	0.894312	−	0.447445i	$-0.147666\pi$
$878$	49.6246	−	55.1137i	1.67475	−	1.86000i
$879$	8.25850	+	1.51790i	0.278552	+	0.0511974i
$880$	35.5126	−	65.9058i	1.19713	−	2.22168i
$881$	−10.7884	+	33.2031i	−0.363469	+	1.11864i	0.587466	+	0.809249i	$0.300126\pi$
$881$	−10.7884	+	33.2031i	−0.363469	+	1.11864i	−0.950934	+	0.309393i	$0.899874\pi$
$882$	−19.6629	+	38.8766i	−0.662084	+	1.30904i
$883$	−7.77330	+	23.9238i	−0.261592	+	0.805099i	0.730866	+	0.682521i	$0.239116\pi$
$883$	−7.77330	+	23.9238i	−0.261592	+	0.805099i	−0.992459	+	0.122578i	$0.960884\pi$
$884$	−3.50007	−	33.3009i	−0.117720	−	1.12003i
$885$	−40.8106	−	26.2323i	−1.37183	−	0.881789i
$886$	9.21630	−	87.6872i	0.309628	−	2.94591i
$887$	−10.2280	−	4.55381i	−0.343424	−	0.152902i	0.227775	−	0.973714i	$-0.426855\pi$
$887$	−10.2280	−	4.55381i	−0.343424	−	0.152902i	−0.571199	+	0.820812i	$0.693522\pi$
$888$	23.1181	+	9.53550i	0.775793	+	0.319990i
$889$	15.6704	−	6.97691i	0.525568	−	0.233998i
$890$	−33.9417	−	94.8870i	−1.13773	−	3.18062i
$891$	−12.8760	+	11.7333i	−0.431363	+	0.393082i
$892$	39.4587	−	121.441i	1.32118	−	4.06616i
$893$	4.35392	−	7.54121i	0.145698	−	0.252357i
$894$	19.0592	−	4.60576i	0.637435	−	0.154040i
$895$	6.61655	−	7.79713i	0.221167	−	0.260629i
$896$	−53.9568	+	59.9251i	−1.80257	+	2.00196i
$897$	−1.73219	−	4.86848i	−0.0578361	−	0.162554i
$898$	13.0676	−	5.81806i	0.436071	−	0.194151i
$899$	30.1296			1.00488
$900$	73.9267	−	43.6082i	2.46422	−	1.45361i
$901$	−5.59539			−0.186409
$902$	−8.91756	+	3.97035i	−0.296922	+	0.132198i
$903$	4.11346	+	0.756047i	0.136887	+	0.0251597i
$904$	33.4419	−	37.1410i	1.11226	−	1.23529i
$905$	−1.43266	+	0.348781i	−0.0476233	+	0.0115939i
$906$	−51.0456	−	53.6306i	−1.69588	−	1.78176i
$907$	5.12058	−	8.86910i	0.170026	−	0.294494i	−0.768403	−	0.639967i	$-0.778948\pi$
$907$	5.12058	−	8.86910i	0.170026	−	0.294494i	0.938429	+	0.345473i	$0.112281\pi$
$908$	23.0697	−	71.0014i	0.765596	−	2.35626i
$909$	−3.19021	−	1.21371i	−0.105813	−	0.0402563i
$910$	36.2075	−	1.06352i	1.20027	−	0.0352555i
$911$	−14.4576	+	6.43693i	−0.479001	+	0.213265i	−0.632011	−	0.774960i	$-0.717770\pi$
$911$	−14.4576	+	6.43693i	−0.479001	+	0.213265i	0.153010	+	0.988225i	$0.451103\pi$
$912$	45.5949	−	35.0943i	1.50980	−	1.16209i
$913$	−18.2340	−	8.11829i	−0.603457	−	0.268676i
$914$	−4.25361	+	40.4704i	−0.140697	+	1.33864i
$915$	−30.3241	+	8.27744i	−1.00248	+	0.273644i
$916$	1.33590	+	12.7102i	0.0441393	+	0.419957i
$917$	2.07930	−	6.39942i	0.0686644	−	0.211327i
$918$	8.23343	−	17.4622i	0.271744	−	0.576339i
$919$	9.57341	−	29.4639i	0.315798	−	0.971925i	−0.659627	−	0.751593i	$-0.729286\pi$
$919$	9.57341	−	29.4639i	0.315798	−	0.971925i	0.975425	−	0.220332i	$-0.0707142\pi$
$920$	2.10751	+	15.6235i	0.0694827	+	0.515092i
$921$	24.8204	−	29.1488i	0.817860	−	0.960485i
$922$	−65.8653	+	73.1509i	−2.16916	+	2.40910i
$923$	1.47834	−	14.0655i	0.0486602	−	0.462971i
$924$	25.5411	−	0.706903i	0.840239	−	0.0232554i
$925$	1.13575	+	6.88666i	0.0373432	+	0.226432i
$926$	−48.7750			−1.60285
$927$	−33.4465	−	21.5790i	−1.09853	−	0.708746i
$928$	29.1252	+	89.6383i	0.956083	+	2.94252i
$929$	12.2762	+	2.60938i	0.402769	+	0.0856111i	0.404842	−	0.914387i	$-0.367327\pi$
$929$	12.2762	+	2.60938i	0.402769	+	0.0856111i	−0.00207325	+	0.999998i	$0.500660\pi$
$930$	−83.7351	+	43.1594i	−2.74578	+	1.41525i
$931$	−9.81689	+	2.08664i	−0.321735	+	0.0683870i
$932$	−27.4789	−	47.5948i	−0.900101	−	1.55902i
$933$	−23.5250	−	24.7163i	−0.770173	−	0.809175i
$934$	0.777327	+	7.39577i	0.0254349	+	0.241997i
$935$	4.57974	−	3.53739i	0.149774	−	0.115685i
$936$	114.115	+	73.6247i	3.72997	+	2.40650i
$937$	27.5507	−	20.0167i	0.900042	−	0.653919i	−0.0384349	−	0.999261i	$-0.512237\pi$
$937$	27.5507	−	20.0167i	0.900042	−	0.653919i	0.938477	+	0.345342i	$0.112237\pi$
$938$	2.05075	+	19.5116i	0.0669594	+	0.637077i
$939$	5.72692	+	3.92345i	0.186891	+	0.128037i
$940$	−53.6691	−	22.0305i	−1.75049	−	0.718555i
$941$	−0.509092	−	0.226662i	−0.0165959	−	0.00738898i	0.398422	−	0.917202i	$-0.369558\pi$
$941$	−0.509092	−	0.226662i	−0.0165959	−	0.00738898i	−0.415018	+	0.909813i	$0.636225\pi$
$942$	22.4140	−	5.41646i	0.730287	−	0.176478i
$943$	0.618551	−	1.07136i	0.0201428	−	0.0348884i
$944$	−66.9557	+	206.069i	−2.17922	+	6.70696i
$945$	13.4612	+	7.63506i	0.437894	+	0.248368i
$946$	3.01325	+	9.27382i	0.0979691	+	0.301518i
$947$	−43.4768	−	9.24128i	−1.41281	−	0.300301i	−0.562590	−	0.826736i	$-0.690195\pi$
$947$	−43.4768	−	9.24128i	−1.41281	−	0.300301i	−0.850216	+	0.526435i	$0.823528\pi$
$948$	−8.03851	+	104.122i	−0.261079	+	3.38174i
$949$	2.47908	+	4.29390i	0.0804745	+	0.139386i
$950$	24.9715	+	9.40361i	0.810182	+	0.305093i
$951$	2.60757	−	0.0721700i	0.0845562	−	0.00234027i
$952$	−16.8268	+	7.49178i	−0.545360	+	0.242810i
$953$	16.1754	+	49.7828i	0.523973	+	1.61262i	0.766338	+	0.642438i	$0.222077\pi$
$953$	16.1754	+	49.7828i	0.523973	+	1.61262i	−0.242365	+	0.970185i	$0.577923\pi$
$954$	21.8747	−	27.1782i	0.708220	−	0.879928i
$955$	33.7128	−	26.0397i	1.09092	−	0.842626i
$956$	61.0725	+	67.8279i	1.97523	+	2.19371i
$957$	5.49132	−	10.1498i	0.177509	−	0.328096i
$958$	87.4536	−	18.5888i	2.82550	−	0.600578i
$959$	−12.9777	−	5.77804i	−0.419072	−	0.186583i
$960$	−114.164	−	113.101i	−3.68461	−	3.65032i
$961$	41.6712	−	18.5532i	1.34423	−	0.598490i
$962$	−13.7353	+	9.97929i	−0.442844	+	0.321745i
$963$	−1.80762	−	11.1968i	−0.0582497	−	0.360811i
$964$	−54.6514	−	39.7066i	−1.76020	−	1.27886i
$965$	18.3580	−	34.0695i	0.590964	−	1.09674i
$966$	−3.46295	+	2.66542i	−0.111419	+	0.0857586i
$967$	−40.8449	+	8.68186i	−1.31348	+	0.279190i	−0.810822	−	0.585293i	$-0.800979\pi$
$967$	−40.8449	+	8.68186i	−1.31348	+	0.279190i	−0.502662	+	0.864483i	$0.667646\pi$
$968$	−37.5114	−	64.9716i	−1.20566	−	2.08827i
$969$	4.32300	−	1.04468i	0.138875	−	0.0335598i
$970$	77.3383	+	80.9795i	2.48318	+	2.60009i
$971$	−7.39178	−	22.7495i	−0.237213	−	0.730068i	−0.996820	−	0.0796851i	$-0.974609\pi$
$971$	−7.39178	−	22.7495i	−0.237213	−	0.730068i	0.759607	−	0.650383i	$-0.225391\pi$
$972$	38.9992	+	80.2199i	1.25090	+	2.57305i
$973$	−12.7696	−	9.27766i	−0.409375	−	0.297428i
$974$	−7.90346	+	13.6892i	−0.253243	+	0.438630i
$975$	−0.694374	+	37.8973i	−0.0222378	+	1.21368i
$976$	70.1938	+	121.579i	2.24685	+	3.89165i
$977$	2.11843	−	20.1555i	0.0677746	−	0.644832i	−0.906922	−	0.421299i	$-0.861574\pi$
$977$	2.11843	−	20.1555i	0.0677746	−	0.644832i	0.974696	−	0.223533i	$-0.0717590\pi$
$978$	−13.9359	−	39.1681i	−0.445620	−	1.25246i
$979$	30.7056	+	6.52667i	0.981354	+	0.208593i
$980$	22.5205	+	62.9581i	0.719393	+	2.01112i
$981$	9.77152	+	9.71345i	0.311980	+	0.310126i
$982$	11.2974			0.360515
$983$	−16.1645	−	17.9525i	−0.515566	−	0.572594i	0.428000	−	0.903779i	$-0.359218\pi$
$983$	−16.1645	−	17.9525i	−0.515566	−	0.572594i	−0.943566	+	0.331185i	$0.892552\pi$
$984$	4.29169	+	32.2275i	0.136814	+	1.02737i
$985$	−30.6601	+	36.1307i	−0.976910	+	1.15122i
$986$	−1.33684	+	12.7192i	−0.0425737	+	0.405062i
$987$	−1.38081	−	10.3689i	−0.0439518	−	0.330046i
$988$	5.02735	+	47.8320i	0.159941	+	1.52174i
$989$	−0.999770	−	0.726375i	−0.0317908	−	0.0230974i
$990$	−0.722120	+	36.0741i	−0.0229505	+	1.14651i
$991$	−8.15033	+	5.92156i	−0.258904	+	0.188105i	−0.709664	−	0.704541i	$-0.751153\pi$
$991$	−8.15033	+	5.92156i	−0.258904	+	0.188105i	0.450760	+	0.892645i	$0.351153\pi$
$992$	160.368	+	178.107i	5.09169	+	5.65489i
$993$	−19.7869	+	0.547645i	−0.627919	+	0.0173790i
$994$	−11.6989	+	2.48668i	−0.371067	+	0.0788727i
$995$	19.3705	+	31.3851i	0.614087	+	0.994973i
$996$	−66.2576	+	77.8122i	−2.09945	+	2.46557i
$997$	−16.7636	−	3.56321i	−0.530909	−	0.112848i	−0.0653454	−	0.997863i	$-0.520815\pi$
$997$	−16.7636	−	3.56321i	−0.530909	−	0.112848i	−0.465563	+	0.885015i	$0.654148\pi$
$998$	−32.1866	−	23.3849i	−1.01885	−	0.740237i
$999$	−7.22852	+	0.601423i	−0.228700	+	0.0190282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.1	✓	224
3.2	odd	2		675.2.r.a.316.28		224
9.4	even	3	inner	225.2.q.a.166.28	yes	224
9.5	odd	6		675.2.r.a.91.1		224
25.11	even	5	inner	225.2.q.a.61.28	yes	224
75.11	odd	10		675.2.r.a.586.1		224
225.86	odd	30		675.2.r.a.361.28		224
225.211	even	15	inner	225.2.q.a.211.1	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.1	✓	224	1.1	even	1	trivial
225.2.q.a.61.28	yes	224	25.11	even	5	inner
225.2.q.a.166.28	yes	224	9.4	even	3	inner
225.2.q.a.211.1	yes	224	225.211	even	15	inner
675.2.r.a.91.1		224	9.5	odd	6
675.2.r.a.316.28		224	3.2	odd	2
675.2.r.a.361.28		224	225.86	odd	30
675.2.r.a.586.1		224	75.11	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.53861 + 1.13026i) q^{2} +(1.12291 - 1.31874i) q^{3} +(3.82877 - 4.25228i) q^{4} +(1.17441 + 1.90283i) q^{5} +(-1.36012 + 4.61694i) q^{6} +(-0.665971 + 1.15350i) q^{7} +(-3.19614 + 9.83670i) q^{8} +(-0.478132 - 2.96165i) q^{9} +O(q^{10})\)	\(q+(-2.53861 + 1.13026i) q^{2} +(1.12291 - 1.31874i) q^{3} +(3.82877 - 4.25228i) q^{4} +(1.17441 + 1.90283i) q^{5} +(-1.36012 + 4.61694i) q^{6} +(-0.665971 + 1.15350i) q^{7} +(-3.19614 + 9.83670i) q^{8} +(-0.478132 - 2.96165i) q^{9} +(-5.13206 - 3.50315i) q^{10} +(1.76824 - 0.787270i) q^{11} +(-1.30826 - 9.82409i) q^{12} +(3.99834 + 1.78018i) q^{13} +(0.386888 - 3.68099i) q^{14} +(3.82809 + 0.587979i) q^{15} +(-1.80807 - 17.2027i) q^{16} +(0.413167 - 1.27160i) q^{17} +(4.56123 + 6.97806i) q^{18} +(-0.593455 + 1.82647i) q^{19} +(12.5879 + 2.29159i) q^{20} +(0.773329 + 2.17351i) q^{21} +(-3.59904 + 3.99714i) q^{22} +(0.0712526 - 0.677923i) q^{23} +(9.38303 + 15.2606i) q^{24} +(-2.24153 + 4.46940i) q^{25} -12.1623 q^{26} +(-4.44254 - 2.69515i) q^{27} +(2.35514 + 7.24837i) q^{28} +(3.36698 + 0.715675i) q^{29} +(-10.3826 + 2.83409i) q^{30} +(8.56171 - 1.81985i) q^{31} +(13.6905 + 23.7127i) q^{32} +(0.947376 - 3.21588i) q^{33} +(0.388368 + 3.69507i) q^{34} +(-2.97703 + 0.0874443i) q^{35} +(-14.4245 - 9.30635i) q^{36} +(1.12934 - 0.820511i) q^{37} +(-0.557835 - 5.30744i) q^{38} +(6.83738 - 3.27378i) q^{39} +(-22.4712 + 5.47059i) q^{40} +(1.65794 + 0.738164i) q^{41} +(-4.41982 - 4.64364i) q^{42} +(0.906455 - 1.57003i) q^{43} +(3.42249 - 10.5333i) q^{44} +(5.07400 - 4.38799i) q^{45} +(0.585348 + 1.80151i) q^{46} +(-4.43516 - 0.942722i) q^{47} +(-24.7161 - 16.9327i) q^{48} +(2.61297 + 4.52579i) q^{49} +(0.638779 - 13.8796i) q^{50} +(-1.21295 - 1.97275i) q^{51} +(22.8786 - 10.1862i) q^{52} +(-1.29321 - 3.98009i) q^{53} +(14.3241 + 1.82070i) q^{54} +(3.57468 + 2.44008i) q^{55} +(-9.21805 - 10.2377i) q^{56} +(1.74223 + 2.83358i) q^{57} +(-9.35635 + 1.98875i) q^{58} +(-11.4434 - 5.09492i) q^{59} +(17.1572 - 14.0269i) q^{60} +(-7.41443 + 3.30112i) q^{61} +(-19.6779 + 14.2968i) q^{62} +(3.73467 + 1.42085i) q^{63} +(-33.5687 - 24.3891i) q^{64} +(1.30831 + 9.69883i) q^{65} +(1.22976 + 9.23463i) q^{66} +(-5.18481 + 1.10207i) q^{67} +(-3.82527 - 6.62556i) q^{68} +(-0.813992 - 0.855212i) q^{69} +(7.45867 - 3.58680i) q^{70} +(-0.998557 - 3.07324i) q^{71} +(30.6611 + 4.76261i) q^{72} +(0.916492 + 0.665871i) q^{73} +(-1.93955 + 3.35940i) q^{74} +(3.37692 + 7.97474i) q^{75} +(5.49445 + 9.51667i) q^{76} +(-0.269482 + 2.56395i) q^{77} +(-13.6572 + 16.0389i) q^{78} +(-10.3069 - 2.19081i) q^{79} +(30.6103 - 23.6434i) q^{80} +(-8.54278 + 2.83212i) q^{81} -5.04319 q^{82} +(-6.90004 - 7.66327i) q^{83} +(12.2033 + 5.03348i) q^{84} +(2.90486 - 0.707187i) q^{85} +(-0.526594 + 5.01021i) q^{86} +(4.72462 - 3.63652i) q^{87} +(2.09261 + 19.9099i) q^{88} +(13.1208 + 9.53280i) q^{89} +(-7.92132 + 16.8743i) q^{90} +(-4.71621 + 3.42652i) q^{91} +(-2.60991 - 2.89860i) q^{92} +(7.21416 - 13.3342i) q^{93} +(12.3246 - 2.61968i) q^{94} +(-4.17242 + 1.01577i) q^{95} +(46.6441 + 8.57310i) q^{96} +(-17.6272 - 3.74678i) q^{97} +(-11.7486 - 8.53587i) q^{98} +(-3.17707 - 4.86049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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