LMFDB - Embedded newform 225.2.q.a.211.1

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			211.1
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.1

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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	−0.973352	−	0.229314i	$-0.926352\pi$
$2$	−2.53861	−	1.13026i	−1.79507	−	0.799215i	−0.821714	−	0.569901i	$-0.806982\pi$
$3$	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	0.712284	−	0.701891i	$-0.247661\pi$
$7$	−0.665971	−	1.15350i	−0.251713	−	0.435980i	−0.963998	+	0.265911i	$0.914327\pi$
$8$	−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	0.655607	−	0.755102i	$-0.272413\pi$
$11$	1.76824	+	0.787270i	0.533144	+	0.237371i	−0.122463	+	0.992473i	$0.539079\pi$
$12$	−1.30826	+	9.82409i	−0.377663	+	2.83597i
$13$	3.99834	−	1.78018i	1.10894	−	0.493733i	0.231219	−	0.972902i	$-0.425729\pi$
$13$	3.99834	−	1.78018i	1.10894	−	0.493733i	0.877723	+	0.479169i	$0.159062\pi$
$14$	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	0.988576	−	0.150724i	$-0.0481605\pi$
$17$	0.413167	+	1.27160i	0.100208	+	0.308408i	−0.888368	+	0.459132i	$0.848161\pi$
$18$	4.56123	−	6.97806i	1.07509	−	1.64474i
$19$	−0.593455	−	1.82647i	−0.136148	−	0.419020i	0.859619	−	0.510936i	$-0.170701\pi$
$19$	−0.593455	−	1.82647i	−0.136148	−	0.419020i	−0.995767	+	0.0919155i	$0.970701\pi$
$20$	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	0.999436	−	0.0335858i	$-0.0106927\pi$
$23$	0.0712526	+	0.677923i	0.0148572	+	0.141357i	−0.984579	+	0.174943i	$0.944026\pi$
$24$	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	0.115609	−	0.993295i	$-0.463118\pi$
$29$	3.36698	−	0.715675i	0.625233	−	0.132897i	0.509624	+	0.860397i	$0.329785\pi$
$30$	−10.3826	−	2.83409i	−1.89559	−	0.517432i
$31$	8.56171	+	1.81985i	1.53773	+	0.326854i	0.897390	−	0.441238i	$-0.145461\pi$
$31$	8.56171	+	1.81985i	1.53773	+	0.326854i	0.640339	+	0.768093i	$0.278794\pi$
$32$	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	0.676734	−	0.736228i	$-0.263395\pi$
$37$	1.12934	+	0.820511i	0.185662	+	0.134891i	−0.491072	+	0.871119i	$0.663395\pi$
$38$	−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	−0.273168	−	0.961966i	$-0.588071\pi$
$41$	1.65794	−	0.738164i	0.258927	−	0.115282i	0.532095	+	0.846684i	$0.321405\pi$
$42$	−4.41982	+	4.64364i	−0.681992	+	0.716529i
$43$	0.906455	+	1.57003i	0.138233	+	0.239427i	0.926828	−	0.375486i	$-0.122524\pi$
$43$	0.906455	+	1.57003i	0.138233	+	0.239427i	−0.788595	+	0.614913i	$0.789191\pi$
$44$	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	−0.519681	−	0.854360i	$-0.673949\pi$
$47$	−4.43516	+	0.942722i	−0.646934	+	0.137510i	−0.127253	+	0.991870i	$0.540616\pi$
$48$	−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	−0.999744	−	0.0226238i	$-0.992798\pi$
$53$	−1.29321	+	3.98009i	−0.177636	+	0.546708i	0.822108	+	0.569332i	$0.192798\pi$
$54$	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	−0.980362	−	0.197204i	$-0.936814\pi$
$59$	−11.4434	+	5.09492i	−1.48980	+	0.663303i	−0.509439	+	0.860507i	$0.670147\pi$
$60$	17.1572	+	14.0269i	2.21498	+	1.81086i
$61$	−7.41443	−	3.30112i	−0.949320	−	0.422665i	−0.127136	−	0.991885i	$-0.540578\pi$
$61$	−7.41443	−	3.30112i	−0.949320	−	0.422665i	−0.822185	+	0.569221i	$0.807245\pi$
$62$	−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	−0.120001	−	0.992774i	$-0.538290\pi$
$67$	−5.18481	−	1.10207i	−0.633425	−	0.134639i	−0.513424	+	0.858135i	$0.671623\pi$
$68$	−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	−0.992662	−	0.120920i	$-0.961416\pi$
$71$	−0.998557	+	3.07324i	−0.118507	+	0.364727i	0.874155	+	0.485646i	$0.161416\pi$
$72$	30.6611	−	4.76261i	3.61344	−	0.561279i
$73$	0.916492	−	0.665871i	0.107267	−	0.0779343i	−0.532859	−	0.846204i	$-0.678882\pi$
$73$	0.916492	−	0.665871i	0.107267	−	0.0779343i	0.640126	+	0.768270i	$0.278882\pi$
$74$	−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	−0.747258	−	0.664534i	$-0.768630\pi$
$79$	−10.3069	+	2.19081i	−1.15962	+	0.246485i	−0.412363	+	0.911019i	$0.635297\pi$
$80$	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	−0.991371	−	0.131085i	$-0.958154\pi$
$83$	−6.90004	+	7.66327i	−0.757378	+	0.841153i	0.233993	+	0.972238i	$0.424821\pi$
$84$	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	0.395023	−	0.918671i	$-0.370737\pi$
$89$	13.1208	−	9.53280i	1.39080	−	1.01048i	0.995777	−	0.0918040i	$-0.0292633\pi$
$90$	−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	−0.978826	−	0.204694i	$-0.934380\pi$
$97$	−17.6272	+	3.74678i	−1.78977	+	0.380428i	−0.810946	+	0.585121i	$0.801047\pi$
$98$	−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	0.892940	−	0.450176i	$-0.148639\pi$
$101$	0.568882	+	0.985333i	0.0566059	+	0.0980443i	−0.836334	+	0.548220i	$0.815305\pi$
$102$	5.30893	−	3.63709i	0.525662	−	0.360126i
$103$	8.87792	+	9.85992i	0.874767	+	0.971527i	0.999787	−	0.0206271i	$-0.00656626\pi$
$103$	8.87792	+	9.85992i	0.874767	+	0.971527i	−0.125020	+	0.992154i	$0.539900\pi$
$104$	−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	0.395449	−	0.918488i	$-0.370589\pi$
$109$	−3.71555	−	2.69950i	−0.355885	−	0.258566i	−0.751334	+	0.659923i	$0.770589\pi$
$110$	−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	−0.603725	−	0.797192i	$-0.706318\pi$
$113$	−4.41435	+	1.96539i	−0.415267	+	0.184889i	0.188458	+	0.982081i	$0.439651\pi$
$114$	−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	−0.944647	−	0.328088i	$-0.893596\pi$
$127$	−10.4189	+	7.56979i	−0.924529	+	0.671710i	0.0201180	+	0.999798i	$0.493596\pi$
$128$	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	−0.0130824	−	0.999914i	$-0.504164\pi$
$131$	−4.94144	−	1.05034i	−0.431736	−	0.0917682i	−0.418653	+	0.908146i	$0.637498\pi$
$132$	−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	−0.837679	−	0.546162i	$-0.816088\pi$
$137$	1.11485	−	10.6071i	0.0952482	−	0.906226i	0.932928	−	0.360064i	$-0.117245\pi$
$138$	3.03302	−	1.25103i	0.258188	−	0.106494i
$139$	−1.23871	−	11.7855i	−0.105066	−	0.999635i	−0.912333	−	0.409449i	$-0.865721\pi$
$139$	−1.23871	−	11.7855i	−0.105066	−	0.999635i	0.807267	−	0.590186i	$-0.200946\pi$
$140$	−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	−0.937318	−	0.348475i	$-0.886700\pi$
$149$	−2.03692	+	3.52804i	−0.166871	+	0.289028i	0.770447	+	0.637504i	$0.220033\pi$
$150$	−17.5862	+	16.4279i	−1.43591	+	1.34133i
$151$	−7.69147	−	13.3220i	−0.625923	−	1.08413i	−0.988362	−	0.152123i	$-0.951389\pi$
$151$	−7.69147	−	13.3220i	−0.625923	−	1.08413i	0.362438	−	0.932008i	$-0.381944\pi$
$152$	−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	−0.945641	−	0.325213i	$-0.894564\pi$
$157$	−2.39545	+	4.14905i	−0.191178	+	0.331130i	0.754463	+	0.656343i	$0.227897\pi$
$158$	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	0.279467	−	0.960155i	$-0.409842\pi$
$163$	−6.98791	−	5.07702i	−0.547336	−	0.397663i	−0.826802	+	0.562493i	$0.809842\pi$
$164$	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	0.529933	−	0.848040i	$-0.322217\pi$
$167$	8.64696	+	1.83797i	0.669122	+	0.142226i	0.139189	+	0.990266i	$0.455551\pi$
$168$	−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	0.312657	−	0.949866i	$-0.398781\pi$
$173$	−2.42043	−	1.07765i	−0.184022	−	0.0819319i	−0.496679	+	0.867934i	$0.665448\pi$
$174$	−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	−0.989878	−	0.141924i	$-0.954671\pi$
$179$	−1.41322	+	4.34944i	−0.105629	+	0.325092i	0.884249	+	0.467016i	$0.154671\pi$
$180$	0.768214	+	38.3767i	0.0572593	+	2.86043i
$181$	−0.203772	−	0.627144i	−0.0151462	−	0.0466153i	0.943198	−	0.332232i	$-0.107802\pi$
$181$	−0.203772	−	0.627144i	−0.0151462	−	0.0466153i	−0.958344	+	0.285617i	$0.907802\pi$
$182$	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	0.648535	+	0.761185i	$0.275382\pi$
$191$	−1.99133	+	18.9462i	−0.144087	+	1.37090i	−0.792622	+	0.609714i	$0.791284\pi$
$192$	−69.8574	−	16.8814i	−5.04152	−	1.21831i
$193$	−8.65375	+	14.9887i	−0.622910	+	1.07891i	0.366031	+	0.930603i	$0.380716\pi$
$193$	−8.65375	+	14.9887i	−0.622910	+	1.07891i	−0.988941	+	0.148309i	$0.952617\pi$
$194$	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	−0.390426	−	0.920634i	$-0.627672\pi$
$197$	6.54863	−	20.1546i	0.466571	−	1.43596i	0.856997	−	0.515322i	$-0.172328\pi$
$198$	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	0.737231	+	0.675641i	$0.236133\pi$
$211$	2.27451	+	21.6405i	0.156584	+	1.48980i	−0.580647	+	0.814156i	$0.697200\pi$
$212$	−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	0.952912	−	0.303247i	$-0.0980707\pi$
$223$	20.3865	+	9.07664i	1.36518	+	0.607817i	0.412266	+	0.911063i	$0.364737\pi$
$224$	−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	0.762181	−	0.647364i	$-0.224128\pi$
$227$	11.9191	+	5.30670i	0.791095	+	0.352218i	0.0289139	+	0.999582i	$0.490795\pi$
$228$	18.7198	−	3.44066i	1.23975	−	0.227863i
$229$	−1.49451	−	1.65983i	−0.0987603	−	0.109684i	0.691738	−	0.722148i	$-0.256845\pi$
$229$	−1.49451	−	1.65983i	−0.0987603	−	0.109684i	−0.790499	+	0.612464i	$0.790179\pi$
$230$	−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	0.999983	+	0.00588639i	$0.00187371\pi$
$233$	2.96799	+	9.13454i	0.194440	+	0.598424i	−0.805543	+	0.592537i	$0.798126\pi$
$234$	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	−0.905887	−	0.423519i	$-0.860795\pi$
$239$	−1.66733	−	15.8635i	−0.107850	−	1.02613i	0.798037	−	0.602609i	$-0.205872\pi$
$240$	3.19334	+	66.9164i	0.206129	+	4.31944i
$241$	−1.23404	+	11.7411i	−0.0794915	+	0.756311i	0.880076	+	0.474833i	$0.157491\pi$
$241$	−1.23404	+	11.7411i	−0.0794915	+	0.756311i	−0.959568	+	0.281479i	$0.909175\pi$
$242$	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	−0.403972	−	0.914771i	$-0.632371\pi$
$257$	9.46210	−	16.3888i	0.590229	−	1.02231i	0.994201	−	0.107536i	$-0.0342961\pi$
$258$	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	−0.923557	−	0.383462i	$-0.874732\pi$
$263$	0.965647	−	9.18752i	0.0595444	−	0.566527i	0.983101	−	0.183064i	$-0.0586017\pi$
$264$	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	0.998605	−	0.0528061i	$-0.0168165\pi$
$269$	2.61891	+	8.06018i	0.159678	+	0.491438i	−0.838927	+	0.544244i	$0.816817\pi$
$270$	13.3578	−	29.3946i	0.812933	−	1.78890i
$271$	−1.02891	+	3.16666i	−0.0625018	+	0.192361i	−0.977432	−	0.211252i	$-0.932246\pi$
$271$	−1.02891	+	3.16666i	−0.0625018	+	0.192361i	0.914930	+	0.403613i	$0.132246\pi$
$272$	−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	0.385666	−	0.922638i	$-0.373972\pi$
$277$	−0.697796	−	0.310679i	−0.0419265	−	0.0186669i	−0.427593	+	0.903971i	$0.640638\pi$
$278$	−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	−0.960056	−	0.279807i	$-0.909730\pi$
$281$	−9.74653	+	10.8246i	−0.581429	+	0.645742i	0.378627	+	0.925549i	$0.376396\pi$
$282$	10.3848	+	19.1946i	0.618407	+	1.14302i
$283$	22.9052	+	4.86864i	1.36157	+	0.289411i	0.830076	−	0.557651i	$-0.188297\pi$
$283$	22.9052	+	4.86864i	1.36157	+	0.289411i	0.531495	+	0.847062i	$0.321631\pi$
$284$	−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	−0.786494	−	0.617598i	$-0.788106\pi$
$293$	2.42396	−	4.19842i	0.141609	−	0.245274i	0.928103	+	0.372324i	$0.121439\pi$
$294$	−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	0.883309	+	0.468791i	$0.155310\pi$
$311$	2.05925	+	19.5925i	0.116770	+	1.11099i	−0.766539	+	0.642197i	$0.778023\pi$
$312$	10.3500	−	77.7207i	0.585952	−	4.40007i
$313$	0.418945	−	3.98600i	0.0236802	−	0.225302i	−0.976281	−	0.216507i	$-0.930534\pi$
$313$	0.418945	−	3.98600i	0.0236802	−	0.225302i	0.999961	−	0.00879521i	$-0.00279964\pi$
$314$	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	−0.714179	−	0.699963i	$-0.753200\pi$
$317$	1.00775	−	1.11922i	0.0566008	−	0.0628616i	0.770780	+	0.637101i	$0.219867\pi$
$318$	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	−0.915700	−	0.401864i	$-0.868363\pi$
$331$	−7.64706	+	8.49292i	−0.420321	+	0.466813i	0.495379	+	0.868677i	$0.335029\pi$
$332$	−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	−0.723569	+	0.690252i	$0.757500\pi$
$337$	−31.5876	+	14.0637i	−1.72069	+	0.766100i	−0.997119	+	0.0758480i	$0.975834\pi$
$338$	−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	0.411885	−	0.911236i	$-0.364870\pi$
$347$	−10.0109	−	11.1182i	−0.537412	−	0.596857i	−0.949298	+	0.314379i	$0.898204\pi$
$348$	2.62595	+	34.0138i	0.140766	+	1.82333i
$349$	−15.1840	−	26.2994i	−0.812778	−	1.40777i	−0.910912	−	0.412600i	$-0.864621\pi$
$349$	−15.1840	−	26.2994i	−0.812778	−	1.40777i	0.0981339	−	0.995173i	$-0.468713\pi$
$350$	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	−0.345760	−	0.938323i	$-0.612379\pi$
$353$	−5.26030	+	1.11811i	−0.279978	+	0.0595111i	0.0657827	+	0.997834i	$0.479046\pi$
$354$	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	0.524696	−	0.851290i	$-0.324179\pi$
$359$	−2.32651	−	1.69031i	−0.122788	−	0.0892110i	−0.647485	+	0.762079i	$0.724179\pi$
$360$	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	−0.958481	−	0.285156i	$-0.907955\pi$
$367$	−11.0096	+	12.2274i	−0.574699	+	0.638267i	0.383783	+	0.923423i	$0.374621\pi$
$368$	−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	0.999231	−	0.0392013i	$-0.0124814\pi$
$373$	0.264305	+	2.51469i	0.0136852	+	0.130206i	−0.985546	+	0.169407i	$0.945815\pi$
$374$	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	0.626594	+	0.779346i	$0.284448\pi$
$379$	−6.58832	+	20.2768i	−0.338419	+	1.04155i	−0.965013	+	0.262201i	$0.915552\pi$
$380$	−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	0.00962181	−	0.999954i	$-0.496937\pi$
$383$	−7.59930	−	1.61528i	−0.388306	−	0.0825370i	−0.397928	+	0.917417i	$0.630271\pi$
$384$	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	0.997726	+	0.0674069i	$0.0214726\pi$
$389$	33.8335	+	15.0637i	1.71543	+	0.763757i	0.717702	+	0.696351i	$0.245194\pi$
$390$	−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	−0.562735	−	0.826637i	$-0.690251\pi$
$397$	7.53981	−	23.2052i	0.378412	−	1.16463i	0.941147	−	0.337996i	$-0.109749\pi$
$398$	−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	0.0544484	−	0.998517i	$-0.482660\pi$
$401$	17.8616	−	30.9372i	0.891965	−	1.54493i	0.837517	−	0.546412i	$-0.184007\pi$
$402$	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	−0.797256	−	0.603641i	$-0.793716\pi$
$409$	−17.8400	+	7.94289i	−0.882132	+	0.392750i	−0.0848758	+	0.996392i	$0.527049\pi$
$410$	−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	−0.386122	−	0.922448i	$-0.626185\pi$
$419$	−22.8041	−	4.84717i	−1.11405	−	0.236800i	−0.727933	+	0.685648i	$0.759519\pi$
$420$	4.75379	−	29.1322i	0.231961	−	1.42151i
$421$	23.5935	−	5.01495i	1.14988	−	0.244414i	0.406733	−	0.913547i	$-0.366668\pi$
$421$	23.5935	−	5.01495i	1.14988	−	0.244414i	0.743142	+	0.669133i	$0.233335\pi$
$422$	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	0.999446	−	0.0332902i	$-0.0105986\pi$
$431$	3.55648	+	10.9457i	0.171310	+	0.527237i	−0.828136	+	0.560527i	$0.810599\pi$
$432$	−38.3313	−	81.2965i	−1.84421	−	3.91138i
$433$	−1.01538	−	3.12503i	−0.0487962	−	0.150179i	0.923689	−	0.383142i	$-0.125158\pi$
$433$	−1.01538	−	3.12503i	−0.0487962	−	0.150179i	−0.972486	+	0.232963i	$0.925158\pi$
$434$	−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	−0.268241	−	0.963352i	$-0.586442\pi$
$439$	−24.3810	−	10.8551i	−1.16364	−	0.518086i	−0.895398	+	0.445266i	$0.853109\pi$
$440$	−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	−0.945996	−	0.324180i	$-0.894912\pi$
$443$	−15.8645	−	27.4781i	−0.753746	−	1.30553i	0.192250	−	0.981346i	$-0.438422\pi$
$444$	−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	0.984898	−	0.173137i	$-0.0553905\pi$
$457$	7.32197	+	12.6820i	0.342508	+	0.593240i	−0.642390	+	0.766378i	$0.722057\pi$
$458$	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	0.983503	−	0.180894i	$-0.0578992\pi$
$461$	32.3602	+	14.4077i	1.50716	+	0.671032i	0.523661	+	0.851927i	$0.324566\pi$
$462$	−11.4711	+	4.73147i	−0.533683	+	0.220128i
$463$	16.0348	−	7.13914i	0.745199	−	0.331784i	0.00123076	−	0.999999i	$-0.499608\pi$
$463$	16.0348	−	7.13914i	0.745199	−	0.331784i	0.743968	+	0.668215i	$0.232942\pi$
$464$	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	0.968365	−	0.249537i	$-0.0802783\pi$
$467$	0.826963	+	2.54513i	0.0382673	+	0.117775i	−0.930098	+	0.367311i	$0.880278\pi$
$468$	−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	−0.859946	−	0.510385i	$-0.829503\pi$
$479$	−31.4711	+	6.68940i	−1.43795	+	0.305646i	−0.578007	+	0.816032i	$0.696169\pi$
$480$	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	0.687150	−	0.726516i	$-0.258862\pi$
$487$	4.60192	+	3.34349i	0.208533	+	0.151508i	−0.478617	+	0.878024i	$0.658862\pi$
$488$	−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	−0.488827	−	0.872381i	$-0.662575\pi$
$491$	−3.71402	+	1.65359i	−0.167611	+	0.0746254i	0.321216	+	0.947006i	$0.395909\pi$
$492$	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	−0.660124	−	0.751157i	$-0.729496\pi$
$499$	7.15851	−	12.3989i	0.320459	−	0.555051i	0.980583	+	0.196106i	$0.0628296\pi$
$500$	−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	−0.524841	−	0.851200i	$-0.675875\pi$
$503$	8.97302	−	27.6161i	0.400087	−	1.23134i	0.924928	−	0.380142i	$-0.124125\pi$
$504$	−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	−0.863763	−	0.503898i	$-0.831899\pi$
$509$	−24.0786	+	10.7205i	−1.06726	+	0.475177i	−0.203501	+	0.979075i	$0.565232\pi$
$510$	−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	0.206883	+	0.978366i	$0.433668\pi$
$521$	−12.2243	+	37.6226i	−0.535558	+	1.64828i	−0.742441	+	0.669912i	$0.766332\pi$
$522$	10.3636	−	26.7594i	0.453601	−	1.17123i
$523$	−2.79441	+	2.03026i	−0.122191	+	0.0887769i	−0.647202	−	0.762318i	$-0.724061\pi$
$523$	−2.79441	+	2.03026i	−0.122191	+	0.0887769i	0.525011	+	0.851095i	$0.324061\pi$
$524$	−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	0.785248	−	0.619182i	$-0.212536\pi$
$541$	10.2115	+	7.41907i	0.439026	+	0.318971i	−0.346222	+	0.938153i	$0.612536\pi$
$542$	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	0.528876	−	0.848699i	$-0.322614\pi$
$547$	31.7428	−	6.74714i	1.35722	−	0.288487i	0.828349	+	0.560212i	$0.189280\pi$
$548$	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	−0.859475	−	0.511178i	$-0.829209\pi$
$563$	−25.0255	+	11.1421i	−1.05470	+	0.469581i	−0.195222	+	0.980759i	$0.562543\pi$
$564$	−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	0.0974358	−	0.995242i	$-0.468936\pi$
$569$	25.6914	−	28.5332i	1.07704	−	1.19617i	0.979605	−	0.200933i	$-0.0643974\pi$
$570$	0.985223	+	20.6454i	0.0412664	+	0.864739i
$571$	−24.0775	−	26.7408i	−1.00761	−	1.11907i	−0.992873	−	0.119176i	$-0.961975\pi$
$571$	−24.0775	−	26.7408i	−1.00761	−	1.11907i	−0.0147396	−	0.999891i	$-0.504692\pi$
$572$	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	−0.867119	−	0.498101i	$-0.834031\pi$
$577$	−15.8862	+	11.5420i	−0.661351	+	0.480500i	0.205768	+	0.978601i	$0.434031\pi$
$578$	−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	−0.964224	−	0.265089i	$-0.914599\pi$
$587$	0.824834	−	7.84777i	0.0340445	−	0.323912i	0.998268	−	0.0588230i	$-0.0187347\pi$
$588$	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	−0.997225	−	0.0744411i	$-0.976283\pi$
$599$	−10.6255	+	18.4039i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$600$	−89.2382	−	7.72936i	−3.64313	−	0.315550i
$601$	16.1753	+	28.0165i	0.659805	+	1.14282i	0.980666	+	0.195689i	$0.0626945\pi$
$601$	16.1753	+	28.0165i	0.659805	+	1.14282i	−0.320861	+	0.947126i	$0.603972\pi$
$602$	−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	−0.913732	−	0.406317i	$-0.866813\pi$
$607$	−2.58655	+	4.48004i	−0.104985	+	0.181839i	0.808747	+	0.588156i	$0.200146\pi$
$608$	−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	0.982631	−	0.185571i	$-0.0594135\pi$
$613$	27.4772	+	19.9633i	1.10979	+	0.806311i	0.127161	+	0.991882i	$0.459414\pi$
$614$	−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	0.889387	−	0.457156i	$-0.151132\pi$
$617$	37.6552	+	8.00385i	1.51594	+	0.322223i	0.626553	+	0.779379i	$0.284465\pi$
$618$	33.4476	−	54.3995i	1.34546	−	2.18827i
$619$	2.54331	−	2.82463i	0.102224	−	0.113532i	−0.689861	−	0.723941i	$-0.742329\pi$
$619$	2.54331	−	2.82463i	0.102224	−	0.113532i	0.792086	+	0.610410i	$0.208995\pi$
$620$	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	0.999953	−	0.00972902i	$-0.00309689\pi$
$631$	4.65356	+	14.3222i	0.185255	+	0.570157i	−0.814697	+	0.579886i	$0.803097\pi$
$632$	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	0.780576	+	0.625061i	$0.214926\pi$
$641$	−2.85840	+	27.1959i	−0.112900	+	1.07417i	−0.893476	+	0.449111i	$0.851741\pi$
$642$	−5.14204	−	17.4547i	−0.202940	−	0.688883i
$643$	7.99458	−	13.8470i	0.315275	−	0.546073i	−0.664221	−	0.747537i	$-0.731236\pi$
$643$	7.99458	−	13.8470i	0.315275	−	0.546073i	0.979496	+	0.201464i	$0.0645698\pi$
$644$	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	−0.756740	−	0.653716i	$-0.773209\pi$
$647$	6.09758	−	18.7664i	0.239720	−	0.737784i	0.996460	−	0.0840673i	$-0.0267911\pi$
$648$	−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	0.984921	−	0.173005i	$-0.0553478\pi$
$653$	18.1410	+	20.1476i	0.709911	+	0.788436i	−0.275010	+	0.961441i	$0.588681\pi$
$654$	−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	−0.159319	−	0.987227i	$-0.550930\pi$
$659$	5.17975	−	49.2821i	0.201775	−	1.91976i	0.361094	−	0.932529i	$-0.382403\pi$
$660$	19.2950	+	38.3102i	0.751056	+	1.49122i
$661$	−3.25622	−	30.9809i	−0.126652	−	1.20502i	−0.854564	−	0.519346i	$-0.826176\pi$
$661$	−3.25622	−	30.9809i	−0.126652	−	1.20502i	0.727912	−	0.685671i	$-0.240491\pi$
$662$	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	0.325907	−	0.945402i	$-0.394330\pi$
$673$	−4.11415	−	1.83174i	−0.158589	−	0.0706084i	−0.484496	+	0.874793i	$0.660997\pi$
$674$	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	0.909570	−	0.415551i	$-0.136411\pi$
$677$	31.4670	+	14.0100i	1.20938	+	0.538449i	0.299806	+	0.954000i	$0.403078\pi$
$678$	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	−0.973531	−	0.228555i	$-0.926600\pi$
$683$	−8.37000	−	25.7602i	−0.320269	−	0.985687i	0.653262	−	0.757132i	$-0.273400\pi$
$684$	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	−0.722754	−	0.691105i	$-0.757124\pi$
$691$	3.36196	−	31.9869i	0.127895	−	1.21684i	0.850649	−	0.525734i	$-0.176209\pi$
$692$	−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	−0.798289	−	0.602275i	$-0.794261\pi$
$709$	2.86974	−	27.3038i	0.107775	−	1.02541i	0.906064	−	0.423140i	$-0.139072\pi$
$710$	−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	0.966487	+	0.256714i	$0.0826399\pi$
$719$	8.99550	+	27.6853i	0.335475	+	1.03249i	−0.631012	+	0.775773i	$0.717360\pi$
$720$	−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	0.454209	−	0.890895i	$-0.349922\pi$
$727$	2.59030	+	1.15328i	0.0960691	+	0.0427727i	−0.358139	+	0.933668i	$0.616589\pi$
$728$	−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	0.190033	−	0.981778i	$-0.439140\pi$
$733$	−0.966208	−	0.205374i	−0.0356877	−	0.00758565i	−0.225721	+	0.974192i	$0.572474\pi$
$734$	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	−0.186455	−	0.982463i	$-0.559700\pi$
$739$	18.7656	−	13.6340i	0.690305	−	0.501536i	0.876760	+	0.480927i	$0.159700\pi$
$740$	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	−0.844881	−	0.534954i	$-0.820329\pi$
$743$	1.11329	−	1.92828i	0.0408427	−	0.0707416i	0.885724	+	0.464212i	$0.153662\pi$
$744$	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	−0.506325	−	0.862342i	$-0.668997\pi$
$751$	13.5281	−	23.4314i	0.493648	−	0.855023i	0.999973	+	0.00731948i	$0.00232988\pi$
$752$	−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	−0.824535	−	0.565811i	$-0.808563\pi$
$761$	−3.74226	−	35.6052i	−0.135657	−	1.29069i	0.688878	−	0.724877i	$-0.258104\pi$
$762$	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	0.487087	−	0.873353i	$-0.338059\pi$
$769$	15.9962	+	3.40010i	0.576839	+	0.122611i	0.0897516	+	0.995964i	$0.471393\pi$
$770$	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	−0.343325	−	0.939217i	$-0.611553\pi$
$773$	12.3397	−	8.96534i	0.443829	−	0.322461i	0.787155	+	0.616756i	$0.211553\pi$
$774$	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	0.212523	−	0.977156i	$-0.431832\pi$
$787$	30.3230	−	13.5007i	1.08090	−	0.481246i	0.868374	+	0.495910i	$0.165165\pi$
$788$	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	0.993722	+	0.111881i	$0.0356876\pi$
$797$	28.2627	+	31.3890i	1.00112	+	1.11185i	0.00739598	+	0.999973i	$0.497646\pi$
$798$	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	−0.0882817	−	0.996096i	$-0.528138\pi$
$809$	−30.2321	−	21.9649i	−1.06291	−	0.772246i	−0.974624	+	0.223850i	$0.928138\pi$
$810$	53.7634	−	15.3920i	1.88905	−	0.540821i
$811$	−30.3450	+	22.0469i	−1.06556	+	0.774172i	−0.975108	−	0.221729i	$-0.928830\pi$
$811$	−30.3450	+	22.0469i	−1.06556	+	0.774172i	−0.0904481	+	0.995901i	$0.528830\pi$
$812$	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	−0.254048	−	0.967191i	$-0.581762\pi$
$821$	−2.65732	+	0.564831i	−0.0927411	+	0.0197127i	0.161307	+	0.986904i	$0.448429\pi$
$822$	−50.4887	+	9.27973i	−1.76099	+	0.323668i
$823$	−0.534527	−	5.08568i	−0.0186324	−	0.177276i	0.981248	−	0.192750i	$-0.0617408\pi$
$823$	−0.534527	−	5.08568i	−0.0186324	−	0.177276i	−0.999880	+	0.0154746i	$0.995074\pi$
$824$	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	−0.141536	−	0.989933i	$-0.545204\pi$
$827$	21.7468	−	15.8000i	0.756210	−	0.549419i	0.897745	+	0.440515i	$0.145204\pi$
$828$	−7.33677	−	9.11557i	−0.254970	−	0.316788i
$829$	2.27728	−	7.00875i	0.0790932	−	0.243424i	−0.903690	−	0.428188i	$-0.859152\pi$
$829$	2.27728	−	7.00875i	0.0790932	−	0.243424i	0.982783	+	0.184764i	$0.0591521\pi$
$830$	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	0.104212	−	0.994555i	$-0.466768\pi$
$839$	−16.3700	−	7.28840i	−0.565155	−	0.251623i	−0.669367	+	0.742932i	$0.733435\pi$
$840$	−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	−0.0820073	−	0.996632i	$-0.526133\pi$
$853$	7.25604	−	1.54232i	0.248442	−	0.0528080i	0.330449	+	0.943824i	$0.392800\pi$
$854$	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	−0.949297	−	0.314382i	$-0.898203\pi$
$857$	−21.8655	−	37.8721i	−0.746911	−	1.29369i	0.202386	−	0.979306i	$-0.435130\pi$
$858$	−11.5223	−	39.1124i	−0.393364	−	1.33528i
$859$	−29.5873	+	13.1731i	−1.00951	+	0.449461i	−0.843767	−	0.536709i	$-0.819667\pi$
$859$	−29.5873	+	13.1731i	−1.00951	+	0.449461i	−0.165738	+	0.986170i	$0.553001\pi$
$860$	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	0.904464	−	0.426550i	$-0.140271\pi$
$863$	22.8636	+	16.6114i	0.778285	+	0.565457i	−0.126179	+	0.992008i	$0.540271\pi$
$864$	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	0.894312	+	0.447445i	$0.147666\pi$
$877$	3.33372	+	31.7182i	0.112572	+	1.07105i	−0.781740	+	0.623605i	$0.785668\pi$
$878$	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	−0.950934	−	0.309393i	$-0.899874\pi$
$881$	−10.7884	−	33.2031i	−0.363469	−	1.11864i	0.587466	−	0.809249i	$-0.300126\pi$
$882$	−19.6629	−	38.8766i	−0.662084	−	1.30904i
$883$	−7.77330	−	23.9238i	−0.261592	−	0.805099i	−0.992459	−	0.122578i	$-0.960884\pi$
$883$	−7.77330	−	23.9238i	−0.261592	−	0.805099i	0.730866	−	0.682521i	$-0.239116\pi$
$884$	−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	−0.571199	−	0.820812i	$-0.693522\pi$
$887$	−10.2280	+	4.55381i	−0.343424	+	0.152902i	0.227775	+	0.973714i	$0.426855\pi$
$888$	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	0.938429	−	0.345473i	$-0.112281\pi$
$907$	5.12058	+	8.86910i	0.170026	+	0.294494i	−0.768403	+	0.639967i	$0.778948\pi$
$908$	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	0.153010	−	0.988225i	$-0.451103\pi$
$911$	−14.4576	−	6.43693i	−0.479001	−	0.213265i	−0.632011	+	0.774960i	$0.717770\pi$
$912$	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	0.975425	+	0.220332i	$0.0707142\pi$
$919$	9.57341	+	29.4639i	0.315798	+	0.971925i	−0.659627	+	0.751593i	$0.729286\pi$
$920$	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	−0.00207325	−	0.999998i	$-0.500660\pi$
$929$	12.2762	−	2.60938i	0.402769	−	0.0856111i	0.404842	+	0.914387i	$0.367327\pi$
$930$	−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	0.938477	−	0.345342i	$-0.112237\pi$
$937$	27.5507	+	20.0167i	0.900042	+	0.653919i	−0.0384349	+	0.999261i	$0.512237\pi$
$938$	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	−0.415018	−	0.909813i	$-0.636225\pi$
$941$	−0.509092	+	0.226662i	−0.0165959	+	0.00738898i	0.398422	+	0.917202i	$0.369558\pi$
$942$	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	−0.850216	−	0.526435i	$-0.823528\pi$
$947$	−43.4768	+	9.24128i	−1.41281	+	0.300301i	−0.562590	+	0.826736i	$0.690195\pi$
$948$	−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	−0.242365	−	0.970185i	$-0.577923\pi$
$953$	16.1754	−	49.7828i	0.523973	−	1.61262i	0.766338	−	0.642438i	$-0.222077\pi$
$954$	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	−0.502662	−	0.864483i	$-0.667646\pi$
$967$	−40.8449	−	8.68186i	−1.31348	−	0.279190i	−0.810822	+	0.585293i	$0.800979\pi$
$968$	−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	0.759607	+	0.650383i	$0.225391\pi$
$971$	−7.39178	+	22.7495i	−0.237213	+	0.730068i	−0.996820	+	0.0796851i	$0.974609\pi$
$972$	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	0.974696	+	0.223533i	$0.0717590\pi$
$977$	2.11843	+	20.1555i	0.0677746	+	0.644832i	−0.906922	+	0.421299i	$0.861574\pi$
$978$	−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	−0.943566	−	0.331185i	$-0.892552\pi$
$983$	−16.1645	+	17.9525i	−0.515566	+	0.572594i	0.428000	+	0.903779i	$0.359218\pi$
$984$	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	0.450760	−	0.892645i	$-0.351153\pi$
$991$	−8.15033	−	5.92156i	−0.258904	−	0.188105i	−0.709664	+	0.704541i	$0.751153\pi$
$992$	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	−0.465563	−	0.885015i	$-0.654148\pi$
$997$	−16.7636	+	3.56321i	−0.530909	+	0.112848i	−0.0653454	+	0.997863i	$0.520815\pi$
$998$	−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.211.1	yes	224
3.2	odd	2		675.2.r.a.361.28		224
9.2	odd	6		675.2.r.a.586.1		224
9.7	even	3	inner	225.2.q.a.61.28	yes	224
25.16	even	5	inner	225.2.q.a.166.28	yes	224
75.41	odd	10		675.2.r.a.91.1		224
225.16	even	15	inner	225.2.q.a.16.1	✓	224
225.191	odd	30		675.2.r.a.316.28		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.1	✓	224	225.16	even	15	inner
225.2.q.a.61.28	yes	224	9.7	even	3	inner
225.2.q.a.166.28	yes	224	25.16	even	5	inner
225.2.q.a.211.1	yes	224	1.1	even	1	trivial
675.2.r.a.91.1		224	75.41	odd	10
675.2.r.a.316.28		224	225.191	odd	30
675.2.r.a.361.28		224	3.2	odd	2
675.2.r.a.586.1		224	9.2	odd	6

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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more