LMFDB - Embedded newform 225.2.q.a.121.24

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			121.24
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91440 - 0.406919i) q^{2} +(-0.0970075 - 1.72933i) q^{3} +(1.67227 - 0.744541i) q^{4} +(2.20948 + 0.343819i) q^{5} +(-0.889410 - 3.27117i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 + 0.194964i) q^{8} +(-2.98118 + 0.335516i) q^{9} +O(q^{10})$	\(q+(1.91440 - 0.406919i) q^{2} +(-0.0970075 - 1.72933i) q^{3} +(1.67227 - 0.744541i) q^{4} +(2.20948 + 0.343819i) q^{5} +(-0.889410 - 3.27117i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 + 0.194964i) q^{8} +(-2.98118 + 0.335516i) q^{9} +(4.36974 - 0.240869i) q^{10} +(-2.41607 + 0.513552i) q^{11} +(-1.44978 - 2.81968i) q^{12} +(-3.14597 - 0.668696i) q^{13} +(1.80729 + 2.00720i) q^{14} +(0.380242 - 3.85427i) q^{15} +(-2.88411 + 3.20312i) q^{16} +(3.02773 - 2.19977i) q^{17} +(-5.57065 + 1.85541i) q^{18} +(0.234784 - 0.170581i) q^{19} +(3.95082 - 1.07009i) q^{20} +(1.99986 - 1.30920i) q^{21} +(-4.41636 + 1.96629i) q^{22} +(0.389869 + 0.432993i) q^{23} +(0.363189 + 0.445145i) q^{24} +(4.76358 + 1.51932i) q^{25} -6.29476 q^{26} +(0.869416 + 5.12290i) q^{27} +(2.04372 + 1.48485i) q^{28} +(-0.389966 + 3.71028i) q^{29} +(-0.840441 - 7.53336i) q^{30} +(-0.895263 - 8.51786i) q^{31} +(-3.88624 + 6.73116i) q^{32} +(1.12248 + 4.12837i) q^{33} +(4.90116 - 5.44329i) q^{34} +(1.11366 + 2.87787i) q^{35} +(-4.73552 + 2.78068i) q^{36} +(2.37815 + 7.31918i) q^{37} +(0.380060 - 0.422099i) q^{38} +(-0.851215 + 5.50529i) q^{39} +(-0.659934 + 0.338506i) q^{40} +(-6.21628 - 1.32131i) q^{41} +(3.29579 - 3.32012i) q^{42} +(-3.20269 - 5.54723i) q^{43} +(-3.65796 + 2.65766i) q^{44} +(-6.70220 - 0.283671i) q^{45} +(0.922560 + 0.670279i) q^{46} +(-0.750946 + 7.14477i) q^{47} +(5.81905 + 4.67685i) q^{48} +(2.54776 - 4.41285i) q^{49} +(9.73765 + 0.970205i) q^{50} +(-4.09785 - 5.02255i) q^{51} +(-5.75877 + 1.22407i) q^{52} +(6.69073 + 4.86110i) q^{53} +(3.74902 + 9.45352i) q^{54} +(-5.51482 + 0.303989i) q^{55} +(-0.418171 - 0.186182i) q^{56} +(-0.317767 - 0.389473i) q^{57} +(0.763232 + 7.26166i) q^{58} +(1.90295 + 0.404485i) q^{59} +(-2.23380 - 6.72848i) q^{60} +(12.8255 - 2.72614i) q^{61} +(-5.17998 - 15.9423i) q^{62} +(-2.45804 - 3.33141i) q^{63} +(-2.03692 + 6.26900i) q^{64} +(-6.72104 - 2.55911i) q^{65} +(3.82879 + 7.44661i) q^{66} +(-1.05779 - 10.0642i) q^{67} +(3.42535 - 5.93288i) q^{68} +(0.710969 - 0.716217i) q^{69} +(3.30305 + 5.05624i) q^{70} +(-10.4571 - 7.59752i) q^{71} +(0.734571 - 0.671257i) q^{72} +(1.44065 - 4.43387i) q^{73} +(7.53104 + 13.0442i) q^{74} +(2.16531 - 8.38519i) q^{75} +(0.265618 - 0.460064i) q^{76} +(-2.28089 - 2.53318i) q^{77} +(0.610639 + 10.8857i) q^{78} +(1.66525 - 15.8438i) q^{79} +(-7.47366 + 6.08562i) q^{80} +(8.77486 - 2.00047i) q^{81} -12.4381 q^{82} +(0.184562 + 0.0821725i) q^{83} +(2.36954 - 3.67831i) q^{84} +(7.44602 - 3.81936i) q^{85} +(-8.38852 - 9.31639i) q^{86} +(6.45414 + 0.314456i) q^{87} +(0.548216 - 0.608856i) q^{88} +(-3.30633 + 10.1758i) q^{89} +(-12.9462 + 2.18419i) q^{90} +(-1.37158 - 4.22128i) q^{91} +(0.974347 + 0.433807i) q^{92} +(-14.6434 + 2.37450i) q^{93} +(1.46973 + 13.9836i) q^{94} +(0.577400 - 0.296171i) q^{95} +(12.0174 + 6.06762i) q^{96} +(-1.15412 + 10.9807i) q^{97} +(3.08177 - 9.48471i) q^{98} +(7.03043 - 2.34162i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.91440	−	0.406919i	1.35369	−	0.287735i	0.526746	−	0.850023i	$-0.323412\pi$
$2$	1.91440	−	0.406919i	1.35369	−	0.287735i	0.826942	+	0.562288i	$0.190079\pi$
$3$	−0.0970075	−	1.72933i	−0.0560073	−	0.998430i
$3$	−0.0970075	−	1.72933i	−0.0560073	−	0.998430i
$4$	1.67227	−	0.744541i	0.836134	−	0.372271i
$5$	2.20948	+	0.343819i	0.988108	+	0.153761i
$5$	2.20948	+	0.343819i	0.988108	+	0.153761i
$6$	−0.889410	−	3.27117i	−0.363100	−	1.33545i
$7$	0.690014	+	1.19514i	0.260801	+	0.451720i	0.966455	−	0.256836i	$-0.0826801\pi$
$7$	0.690014	+	1.19514i	0.260801	+	0.451720i	−0.705654	+	0.708556i	$0.749347\pi$
$8$	−0.268345	+	0.194964i	−0.0948743	+	0.0689302i
$9$	−2.98118	+	0.335516i	−0.993726	+	0.111839i
$10$	4.36974	−	0.240869i	1.38183	−	0.0761696i
$11$	−2.41607	+	0.513552i	−0.728473	+	0.154842i	−0.557196	−	0.830381i	$-0.688123\pi$
$11$	−2.41607	+	0.513552i	−0.728473	+	0.154842i	−0.171277	+	0.985223i	$0.554789\pi$
$12$	−1.44978	−	2.81968i	−0.418516	−	0.813971i
$13$	−3.14597	−	0.668696i	−0.872535	−	0.185463i	−0.250181	−	0.968199i	$-0.580490\pi$
$13$	−3.14597	−	0.668696i	−0.872535	−	0.185463i	−0.622354	+	0.782736i	$0.713823\pi$
$14$	1.80729	+	2.00720i	0.483019	+	0.536447i
$15$	0.380242	−	3.85427i	0.0981780	−	0.995169i
$16$	−2.88411	+	3.20312i	−0.721027	+	0.800781i
$17$	3.02773	−	2.19977i	0.734332	−	0.533523i	−0.156599	−	0.987662i	$-0.550053\pi$
$17$	3.02773	−	2.19977i	0.734332	−	0.533523i	0.890931	+	0.454139i	$0.150053\pi$
$18$	−5.57065	+	1.85541i	−1.31302	+	0.437325i
$19$	0.234784	−	0.170581i	0.0538632	−	0.0391339i	−0.560528	−	0.828136i	$-0.689402\pi$
$19$	0.234784	−	0.170581i	0.0538632	−	0.0391339i	0.614391	+	0.789002i	$0.289402\pi$
$20$	3.95082	−	1.07009i	0.883431	−	0.239279i
$21$	1.99986	−	1.30920i	0.436404	−	0.285691i
$22$	−4.41636	+	1.96629i	−0.941571	+	0.419214i
$23$	0.389869	+	0.432993i	0.0812933	+	0.0902854i	0.782419	−	0.622752i	$-0.213986\pi$
$23$	0.389869	+	0.432993i	0.0812933	+	0.0902854i	−0.701126	+	0.713038i	$0.747319\pi$
$24$	0.363189	+	0.445145i	0.0741357	+	0.0908648i
$25$	4.76358	+	1.51932i	0.952715	+	0.303864i
$26$	−6.29476			−1.23450
$27$	0.869416	+	5.12290i	0.167319	+	0.985903i
$28$	2.04372	+	1.48485i	0.386227	+	0.280610i
$29$	−0.389966	+	3.71028i	−0.0724150	+	0.688982i	0.896745	+	0.442548i	$0.145925\pi$
$29$	−0.389966	+	3.71028i	−0.0724150	+	0.688982i	−0.969160	+	0.246434i	$0.920741\pi$
$30$	−0.840441	−	7.53336i	−0.153443	−	1.37540i
$31$	−0.895263	−	8.51786i	−0.160794	−	1.52985i	−0.715976	−	0.698125i	$-0.754018\pi$
$31$	−0.895263	−	8.51786i	−0.160794	−	1.52985i	0.555182	−	0.831729i	$-0.312649\pi$
$32$	−3.88624	+	6.73116i	−0.686996	+	1.18991i
$33$	1.12248	+	4.12837i	0.195398	+	0.718657i
$34$	4.90116	−	5.44329i	0.840543	−	0.933517i
$35$	1.11366	+	2.87787i	0.188243	+	0.486449i
$36$	−4.73552	+	2.78068i	−0.789254	+	0.463447i
$37$	2.37815	+	7.31918i	0.390965	+	1.20327i	0.932060	+	0.362304i	$0.118010\pi$
$37$	2.37815	+	7.31918i	0.390965	+	1.20327i	−0.541095	+	0.840961i	$0.681990\pi$
$38$	0.380060	−	0.422099i	0.0616538	−	0.0684735i
$39$	−0.851215	+	5.50529i	−0.136304	+	0.881553i
$40$	−0.659934	+	0.338506i	−0.104345	+	0.0535226i
$41$	−6.21628	−	1.32131i	−0.970820	−	0.206354i	−0.304906	−	0.952382i	$-0.598625\pi$
$41$	−6.21628	−	1.32131i	−0.970820	−	0.206354i	−0.665914	+	0.746028i	$0.731958\pi$
$42$	3.29579	−	3.32012i	0.508552	−	0.512305i
$43$	−3.20269	−	5.54723i	−0.488406	−	0.845944i	0.511505	−	0.859280i	$-0.329088\pi$
$43$	−3.20269	−	5.54723i	−0.488406	−	0.845944i	−0.999911	+	0.0133363i	$0.995755\pi$
$44$	−3.65796	+	2.65766i	−0.551458	+	0.400657i
$45$	−6.70220	−	0.283671i	−0.999105	−	0.0422872i
$46$	0.922560	+	0.670279i	0.136024	+	0.0988273i
$47$	−0.750946	+	7.14477i	−0.109537	+	1.04217i	0.792311	+	0.610118i	$0.208878\pi$
$47$	−0.750946	+	7.14477i	−0.109537	+	1.04217i	−0.901847	+	0.432055i	$0.857789\pi$
$48$	5.81905	+	4.67685i	0.839907	+	0.675045i
$49$	2.54776	−	4.41285i	0.363966	−	0.630407i
$50$	9.73765	+	0.970205i	1.37711	+	0.137208i
$51$	−4.09785	−	5.02255i	−0.573814	−	0.703298i
$52$	−5.75877	+	1.22407i	−0.798598	+	0.169747i
$53$	6.69073	+	4.86110i	0.919043	+	0.667724i	0.943286	−	0.331982i	$-0.107717\pi$
$53$	6.69073	+	4.86110i	0.919043	+	0.667724i	−0.0242428	+	0.999706i	$0.507717\pi$
$54$	3.74902	+	9.45352i	0.510177	+	1.28646i
$55$	−5.51482	+	0.303989i	−0.743618	+	0.0409899i
$56$	−0.418171	−	0.186182i	−0.0558804	−	0.0248796i
$57$	−0.317767	−	0.389473i	−0.0420892	−	0.0515869i
$58$	0.763232	+	7.26166i	0.100217	+	0.953503i
$59$	1.90295	+	0.404485i	0.247743	+	0.0526595i	0.330109	−	0.943943i	$-0.392914\pi$
$59$	1.90295	+	0.404485i	0.247743	+	0.0526595i	−0.0823661	+	0.996602i	$0.526248\pi$
$60$	−2.23380	−	6.72848i	−0.288382	−	0.868643i
$61$	12.8255	−	2.72614i	1.64214	−	0.349047i	0.708068	−	0.706144i	$-0.249567\pi$
$61$	12.8255	−	2.72614i	1.64214	−	0.349047i	0.934067	+	0.357098i	$0.116234\pi$
$62$	−5.17998	−	15.9423i	−0.657858	−	2.02468i
$63$	−2.45804	−	3.33141i	−0.309684	−	0.419719i
$64$	−2.03692	+	6.26900i	−0.254615	+	0.783625i
$65$	−6.72104	−	2.55911i	−0.833642	−	0.317419i
$66$	3.82879	+	7.44661i	0.471291	+	0.916614i
$67$	−1.05779	−	10.0642i	−0.129229	−	1.22954i	−0.846366	−	0.532602i	$-0.821214\pi$
$67$	−1.05779	−	10.0642i	−0.129229	−	1.22954i	0.717136	−	0.696933i	$-0.245453\pi$
$68$	3.42535	−	5.93288i	0.415385	−	0.719467i
$69$	0.710969	−	0.716217i	0.0855906	−	0.0862224i
$70$	3.30305	+	5.05624i	0.394790	+	0.604336i
$71$	−10.4571	−	7.59752i	−1.24103	−	0.901659i	−0.243361	−	0.969936i	$-0.578250\pi$
$71$	−10.4571	−	7.59752i	−1.24103	−	0.901659i	−0.997666	+	0.0682765i	$0.978250\pi$
$72$	0.734571	−	0.671257i	0.0865700	−	0.0791084i
$73$	1.44065	−	4.43387i	0.168615	−	0.518945i	−0.830669	−	0.556767i	$-0.812042\pi$
$73$	1.44065	−	4.43387i	0.168615	−	0.518945i	0.999285	+	0.0378214i	$0.0120418\pi$
$74$	7.53104	+	13.0442i	0.875466	+	1.51635i
$75$	2.16531	−	8.38519i	0.250028	−	0.968239i
$76$	0.265618	−	0.460064i	0.0304685	−	0.0527729i
$77$	−2.28089	−	2.53318i	−0.259931	−	0.288683i
$78$	0.610639	+	10.8857i	0.0691413	+	1.23257i
$79$	1.66525	−	15.8438i	0.187355	−	1.78257i	−0.347558	−	0.937658i	$-0.612989\pi$
$79$	1.66525	−	15.8438i	0.187355	−	1.78257i	0.534913	−	0.844907i	$-0.320344\pi$
$80$	−7.47366	+	6.08562i	−0.835581	+	0.680393i
$81$	8.77486	−	2.00047i	0.974984	−	0.222274i
$82$	−12.4381			−1.37356
$83$	0.184562	+	0.0821725i	0.0202584	+	0.00901960i	0.416841	−	0.908979i	$-0.363137\pi$
$83$	0.184562	+	0.0821725i	0.0202584	+	0.00901960i	−0.396582	+	0.917999i	$0.629804\pi$
$84$	2.36954	−	3.67831i	0.258538	−	0.401336i
$85$	7.44602	−	3.81936i	0.807634	−	0.414267i
$86$	−8.38852	−	9.31639i	−0.904557	−	1.00461i
$87$	6.45414	+	0.314456i	0.691957	+	0.0337132i
$88$	0.548216	−	0.608856i	0.0584401	−	0.0649043i
$89$	−3.30633	+	10.1758i	−0.350471	+	1.07864i	0.608119	+	0.793846i	$0.291924\pi$
$89$	−3.30633	+	10.1758i	−0.350471	+	1.07864i	−0.958589	+	0.284792i	$0.908076\pi$
$90$	−12.9462	+	2.18419i	−1.36464	+	0.230234i
$91$	−1.37158	−	4.22128i	−0.143780	−	0.442510i
$92$	0.974347	+	0.433807i	0.101583	+	0.0452275i
$93$	−14.6434	+	2.37450i	−1.51845	+	0.246225i
$94$	1.46973	+	13.9836i	0.151591	+	1.44229i
$95$	0.577400	−	0.296171i	0.0592400	−	0.0303865i
$96$	12.0174	+	6.06762i	1.22652	+	0.619274i
$97$	−1.15412	+	10.9807i	−0.117183	+	1.11492i	0.765006	+	0.644024i	$0.222736\pi$
$97$	−1.15412	+	10.9807i	−0.117183	+	1.11492i	−0.882188	+	0.470897i	$0.843930\pi$
$98$	3.08177	−	9.48471i	0.311306	−	0.958101i
$99$	7.03043	−	2.34162i	0.706585	−	0.235342i
$100$	9.09717	−	1.00597i	0.909717	−	0.100597i
$101$	7.27293	+	12.5971i	0.723684	+	1.25346i	0.959513	+	0.281663i	$0.0908859\pi$
$101$	7.27293	+	12.5971i	0.723684	+	1.25346i	−0.235830	+	0.971794i	$0.575781\pi$
$102$	−9.88871	−	7.94770i	−0.979128	−	0.786940i
$103$	−5.29819	+	2.35891i	−0.522046	+	0.232430i	−0.650803	−	0.759246i	$-0.725568\pi$
$103$	−5.29819	+	2.35891i	−0.522046	+	0.232430i	0.128757	+	0.991676i	$0.458901\pi$
$104$	0.974577	−	0.433910i	0.0955651	−	0.0425483i
$105$	4.86876	−	2.20506i	0.475143	−	0.215192i
$106$	14.7868	+	6.58352i	1.43622	+	0.639448i
$107$	−12.8622			−1.24344			−0.621718	−	0.783241i	$-0.713565\pi$
$107$	−12.8622			−1.24344			−0.621718	+	0.783241i	$0.713565\pi$
$108$	5.26811	+	7.91954i	0.506924	+	0.762059i
$109$	−4.92848	−	15.1683i	−0.472063	−	1.45286i	−0.849878	−	0.526979i	$-0.823325\pi$
$109$	−4.92848	−	15.1683i	−0.472063	−	1.45286i	0.377816	−	0.925881i	$-0.376675\pi$
$110$	−10.4339	+	2.82604i	−0.994833	+	0.269453i
$111$	12.4266	−	4.82262i	1.17948	−	0.457743i
$112$	−5.81825	−	1.23671i	−0.549773	−	0.116858i
$113$	−7.23421	−	1.53768i	−0.680537	−	0.144653i	−0.145343	−	0.989381i	$-0.546428\pi$
$113$	−7.23421	−	1.53768i	−0.680537	−	0.144653i	−0.535195	+	0.844729i	$0.679762\pi$
$114$	−0.766818	−	0.616302i	−0.0718191	−	0.0577220i
$115$	0.712535	+	1.09073i	0.0664442	+	0.101711i
$116$	2.11033	+	6.49493i	0.195939	+	0.603039i
$117$	9.60306	+	0.937979i	0.887803	+	0.0867162i
$118$	3.80761			0.350519
$119$	4.71821	+	2.10068i	0.432518	+	0.192569i
$120$	0.649409	+	1.10841i	0.0592826	+	0.101183i
$121$	−4.47534	+	1.99255i	−0.406849	+	0.181141i
$122$	23.4438	−	10.4379i	2.12251	−	0.945000i
$123$	−1.68196	+	10.8782i	−0.151657	+	0.980854i
$124$	−7.83902	−	13.5776i	−0.703965	−	1.21930i
$125$	10.0026	+	4.99472i	0.894663	+	0.446741i
$126$	−6.06130	−	5.37744i	−0.539984	−	0.479061i
$127$	−4.27237	+	13.1490i	−0.379112	+	1.16679i	0.561551	+	0.827442i	$0.310205\pi$
$127$	−4.27237	+	13.1490i	−0.379112	+	1.16679i	−0.940663	+	0.339343i	$0.889795\pi$
$128$	0.276375	−	2.62953i	0.0244283	−	0.232420i
$129$	−9.28231	+	6.07664i	−0.817262	+	0.535018i
$130$	−13.9081	−	2.16426i	−1.21982	−	0.189818i
$131$	−0.771502	−	7.34035i	−0.0674065	−	0.641330i	−0.975111	−	0.221719i	$-0.928833\pi$
$131$	−0.771502	−	7.34035i	−0.0674065	−	0.641330i	0.907704	−	0.419611i	$-0.137833\pi$
$132$	4.95083	+	6.06801i	0.430914	+	0.528152i
$133$	0.365872	+	0.162897i	0.0317252	+	0.0141250i
$134$	−6.12034	−	18.8365i	−0.528717	−	1.62722i
$135$	0.159603	+	11.6179i	0.0137364	+	0.999906i
$136$	−0.383599	+	1.18060i	−0.0328933	+	0.101235i
$137$	−2.81986	+	3.13177i	−0.240917	+	0.267565i	−0.851462	−	0.524416i	$-0.824284\pi$
$137$	−2.81986	+	3.13177i	−0.240917	+	0.267565i	0.610545	+	0.791981i	$0.290950\pi$
$138$	1.06964	−	1.66043i	0.0910538	−	0.141346i
$139$	−0.238755	−	0.265165i	−0.0202510	−	0.0224910i	0.732934	−	0.680299i	$-0.238150\pi$
$139$	−0.238755	−	0.265165i	−0.0202510	−	0.0224910i	−0.753185	+	0.657809i	$0.771484\pi$
$140$	4.00503	+	3.98341i	0.338487	+	0.336659i
$141$	12.4285	+	0.605538i	1.04667	+	0.0509955i
$142$	−23.1107	−	10.2895i	−1.93940	−	0.863478i
$143$	7.94429			0.664335
$144$	7.52334	−	10.5168i	0.626945	−	0.876396i
$145$	−2.13729	+	8.06371i	−0.177492	+	0.669654i
$146$	0.953763	−	9.07444i	0.0789339	−	0.751006i
$147$	−7.87844	−	3.97785i	−0.649803	−	0.328087i
$148$	9.42633	+	10.4690i	0.774839	+	0.860546i
$149$	11.6755	−	20.2226i	0.956497	−	1.65670i	0.225591	−	0.974222i	$-0.427569\pi$
$149$	11.6755	−	20.2226i	0.956497	−	1.65670i	0.730905	−	0.682479i	$-0.239098\pi$
$150$	0.733181	−	16.9337i	0.0598639	−	1.38263i
$151$	4.03983	+	6.99720i	0.328757	+	0.569424i	0.982265	−	0.187495i	$-0.0600369\pi$
$151$	4.03983	+	6.99720i	0.328757	+	0.569424i	−0.653508	+	0.756919i	$0.726704\pi$
$152$	−0.0297461	+	0.0915490i	−0.00241273	+	0.00742561i
$153$	−8.28814	+	7.57377i	−0.670056	+	0.612303i
$154$	−5.39734	−	3.92140i	−0.434930	−	0.315995i
$155$	0.950541	−	19.1278i	0.0763493	−	1.53638i
$156$	2.67546	+	9.84009i	0.214208	+	0.787838i
$157$	8.40415	−	14.5564i	0.670724	−	1.16173i	−0.306975	−	0.951718i	$-0.599317\pi$
$157$	8.40415	−	14.5564i	0.670724	−	1.16173i	0.977699	−	0.210011i	$-0.0673500\pi$
$158$	−3.25918	−	31.0090i	−0.259286	−	2.46695i
$159$	7.75741	−	12.0421i	0.615202	−	0.954998i
$160$	−10.9009	+	13.5362i	−0.861788	+	1.07013i
$161$	−0.248472	+	0.764719i	−0.0195824	+	0.0602683i
$162$	15.9846	−	7.40036i	1.25587	−	0.581427i
$163$	1.89571	+	5.83439i	0.148483	+	0.456985i	0.997442	−	0.0714737i	$-0.0227702\pi$
$163$	1.89571	+	5.83439i	0.148483	+	0.456985i	−0.848959	+	0.528459i	$0.822770\pi$
$164$	−11.3791	+	2.41869i	−0.888555	+	0.188868i
$165$	1.06068	+	9.50747i	0.0825736	+	0.740155i
$166$	0.386765	+	0.0822094i	0.0300188	+	0.00638068i
$167$	2.12840	+	20.2504i	0.164701	+	1.56702i	0.694873	+	0.719133i	$0.255461\pi$
$167$	2.12840	+	20.2504i	0.164701	+	1.56702i	−0.530172	+	0.847890i	$0.677873\pi$
$168$	−0.281404	+	0.741218i	−0.0217108	+	0.0571862i
$169$	−2.42612	−	1.08018i	−0.186625	−	0.0830908i
$170$	12.7005	−	10.3417i	0.974085	−	0.793174i
$171$	−0.642702	+	0.587306i	−0.0491486	+	0.0449124i
$172$	−9.48590	−	6.89191i	−0.723293	−	0.525503i
$173$	12.8509	−	2.73155i	0.977037	−	0.207676i	0.308394	−	0.951259i	$-0.400209\pi$
$173$	12.8509	−	2.73155i	0.977037	−	0.207676i	0.668644	+	0.743583i	$0.266875\pi$
$174$	12.4838	−	2.02432i	0.946394	−	0.153463i
$175$	1.47113	+	6.74149i	0.111207	+	0.509609i
$176$	5.32323	−	9.22011i	0.401254	−	0.694992i
$177$	0.514888	−	3.33007i	0.0387014	−	0.250304i
$178$	−2.18891	+	20.8261i	−0.164066	+	1.56098i
$179$	4.14235	+	3.00959i	0.309614	+	0.224947i	0.731731	−	0.681594i	$-0.238713\pi$
$179$	4.14235	+	3.00959i	0.309614	+	0.224947i	−0.422117	+	0.906541i	$0.638713\pi$
$180$	−11.4191	+	4.51569i	−0.851128	+	0.336580i
$181$	−7.20858	+	5.23734i	−0.535810	+	0.389289i	−0.822526	−	0.568727i	$-0.807436\pi$
$181$	−7.20858	+	5.23734i	−0.535810	+	0.389289i	0.286717	+	0.958015i	$0.407436\pi$
$182$	−4.34347	−	7.52312i	−0.321960	−	0.557650i
$183$	−5.95857	−	21.9151i	−0.440470	−	1.62001i
$184$	−0.189038	−	0.0401812i	−0.0139360	−	0.00296220i
$185$	2.73798	+	16.9892i	0.201301	+	1.24907i
$186$	−27.0671	+	10.5044i	−1.98465	+	0.770222i
$187$	−6.18551	+	6.86970i	−0.452329	+	0.502362i
$188$	4.06380	+	12.5071i	0.296383	+	0.912173i
$189$	−5.52267	+	4.57395i	−0.401715	+	0.332706i
$190$	0.984859	−	0.801946i	0.0714492	−	0.0581793i
$191$	−1.26020	+	1.39960i	−0.0911850	+	0.101271i	−0.787010	−	0.616940i	$-0.788372\pi$
$191$	−1.26020	+	1.39960i	−0.0911850	+	0.101271i	0.695825	+	0.718211i	$0.255039\pi$
$192$	11.0388	+	2.91438i	0.796656	+	0.210327i
$193$	−0.740550	+	1.28267i	−0.0533060	+	0.0923286i	−0.891447	−	0.453125i	$-0.850309\pi$
$193$	−0.740550	+	1.28267i	−0.0533060	+	0.0923286i	0.838141	+	0.545453i	$0.183643\pi$
$194$	2.25881	+	21.4911i	0.162173	+	1.54297i
$195$	−3.77357	+	11.8712i	−0.270231	+	0.850111i
$196$	0.974987	−	9.27638i	0.0696419	−	0.662599i
$197$	15.6165	+	11.3460i	1.11263	+	0.808372i	0.983076	−	0.183200i	$-0.0586457\pi$
$197$	15.6165	+	11.3460i	1.11263	+	0.808372i	0.129553	+	0.991572i	$0.458646\pi$
$198$	12.5062	−	7.34362i	0.888780	−	0.521889i
$199$	6.17381			0.437650			0.218825	−	0.975764i	$-0.429778\pi$
$199$	6.17381			0.437650			0.218825	+	0.975764i	$0.429778\pi$
$200$	−1.57449	+	0.521024i	−0.111334	+	0.0368420i
$201$	−17.3017	+	2.80557i	−1.22037	+	0.197889i
$202$	19.0493	+	21.1564i	1.34031	+	1.48856i
$203$	−4.70339	+	2.09408i	−0.330113	+	0.146976i
$204$	−10.5922	−	5.34803i	−0.741602	−	0.374437i
$205$	−13.2804	−	5.05669i	−0.927546	−	0.353174i
$206$	−9.18299	+	6.67183i	−0.639809	+	0.464848i
$207$	−1.30755	−	1.16002i	−0.0908807	−	0.0806272i
$208$	11.2152	−	8.14834i	0.777636	−	0.564986i
$209$	−0.479654	+	0.532709i	−0.0331783	+	0.0368483i
$210$	8.42350	−	6.20257i	0.581277	−	0.428018i
$211$	18.9442	+	21.0397i	1.30417	+	1.44843i	0.818746	+	0.574155i	$0.194669\pi$
$211$	18.9442	+	21.0397i	1.30417	+	1.44843i	0.485428	+	0.874277i	$0.338664\pi$
$212$	14.8080	+	3.14753i	1.01702	+	0.216174i
$213$	−12.1242	+	18.8208i	−0.830737	+	1.28958i
$214$	−24.6235	+	5.23388i	−1.68323	+	0.357781i
$215$	−5.16903	−	13.3576i	−0.352525	−	0.910982i
$216$	−1.23208	−	1.20520i	−0.0838328	−	0.0820035i
$217$	9.56229	−	6.94741i	0.649130	−	0.471621i
$218$	−15.6074	−	27.0328i	−1.05706	−	1.83089i
$219$	−7.80739	−	2.06125i	−0.527574	−	0.139286i
$220$	−8.99592	+	4.61436i	−0.606505	+	0.311100i
$221$	−10.9961	+	4.89579i	−0.739679	+	0.329326i
$222$	21.8271	−	14.2891i	1.46494	−	0.959019i
$223$	−0.103154	+	0.0219260i	−0.00690767	+	0.00146827i	−0.211364	−	0.977407i	$-0.567791\pi$
$223$	−0.103154	+	0.0219260i	−0.00690767	+	0.00146827i	0.204457	+	0.978876i	$0.434457\pi$
$224$	−10.7262			−0.716677
$225$	−14.7108	−	2.93111i	−0.980722	−	0.195407i
$226$	−14.4749			−0.962857
$227$	9.80643	−	2.08442i	0.650876	−	0.138348i	0.129371	−	0.991596i	$-0.458704\pi$
$227$	9.80643	−	2.08442i	0.650876	−	0.138348i	0.521505	+	0.853248i	$0.325371\pi$
$228$	−0.821370	−	0.414712i	−0.0543965	−	0.0274650i
$229$	−16.0211	+	7.13304i	−1.05870	+	0.471365i	−0.860846	−	0.508866i	$-0.830065\pi$
$229$	−16.0211	+	7.13304i	−1.05870	+	0.471365i	−0.197857	+	0.980231i	$0.563398\pi$
$230$	1.80792	+	1.79816i	0.119211	+	0.118567i
$231$	−4.15945	+	4.19015i	−0.273672	+	0.275692i
$232$	−0.618726	−	1.07167i	−0.0406214	−	0.0703583i
$233$	−7.01516	+	5.09682i	−0.459579	+	0.333903i	−0.793366	−	0.608745i	$-0.791673\pi$
$233$	−7.01516	+	5.09682i	−0.459579	+	0.333903i	0.333787	+	0.942648i	$0.391673\pi$
$234$	18.7658	−	2.11200i	1.22676	−	0.138065i
$235$	−4.11571	+	15.5280i	−0.268479	+	1.01294i
$236$	3.48340	−	0.740420i	0.226750	−	0.0481972i
$237$	−27.5607	−	1.34280i	−1.79026	−	0.0872244i
$238$	9.88737	+	2.10162i	0.640903	+	0.136228i
$239$	−6.77888	−	7.52871i	−0.438490	−	0.486992i	0.482876	−	0.875689i	$-0.339592\pi$
$239$	−6.77888	−	7.52871i	−0.438490	−	0.486992i	−0.921366	+	0.388697i	$0.872925\pi$
$240$	11.2491	+	12.3341i	0.726123	+	0.796162i
$241$	−5.45189	+	6.05494i	−0.351187	+	0.390033i	−0.892694	−	0.450663i	$-0.851187\pi$
$241$	−5.45189	+	6.05494i	−0.351187	+	0.390033i	0.541507	+	0.840697i	$0.317854\pi$
$242$	−7.75680	+	5.63564i	−0.498626	+	0.362273i
$243$	−4.31070	−	14.9806i	−0.276532	−	0.961005i
$244$	19.4179	−	14.1079i	1.24310	−	0.903168i
$245$	7.14644	−	8.87413i	0.456570	−	0.566947i
$246$	1.20659	+	21.5097i	0.0769296	+	1.37141i
$247$	−0.852691	+	0.379643i	−0.0542555	+	0.0241561i
$248$	1.90092	+	2.11118i	0.120708	+	0.134060i
$249$	0.124200	−	0.327141i	0.00787083	−	0.0207317i
$250$	21.1815	+	5.49164i	1.33964	+	0.347322i
$251$	23.5790			1.48829			0.744146	−	0.668017i	$-0.232857\pi$
$251$	23.5790			1.48829			0.744146	+	0.668017i	$0.232857\pi$
$252$	−6.59088	−	3.74090i	−0.415187	−	0.235654i
$253$	−1.16432	−	0.845925i	−0.0731999	−	0.0531828i
$254$	−2.82846	+	26.9110i	−0.177473	+	1.68855i
$255$	−7.32726	−	12.5061i	−0.458851	−	0.783164i
$256$	−1.91894	−	18.2575i	−0.119934	−	1.14109i
$257$	−6.51124	+	11.2778i	−0.406160	+	0.703490i	−0.994456	−	0.105156i	$-0.966466\pi$
$257$	−6.51124	+	11.2778i	−0.406160	+	0.703490i	0.588296	+	0.808646i	$0.299799\pi$
$258$	−15.2974	+	15.4103i	−0.952374	+	0.959403i
$259$	−7.10649	+	7.89255i	−0.441576	+	0.490419i
$260$	−13.1447	+	0.724566i	−0.815202	+	0.0449357i
$261$	−0.0823011	−	11.1919i	−0.00509431	−	0.692759i
$262$	−4.46390	−	13.7385i	−0.275780	−	0.848765i
$263$	−7.53929	+	8.37323i	−0.464892	+	0.516315i	−0.929310	−	0.369301i	$-0.879597\pi$
$263$	−7.53929	+	8.37323i	−0.464892	+	0.516315i	0.464417	+	0.885616i	$0.346264\pi$
$264$	−1.10610	−	0.888984i	−0.0680754	−	0.0547132i
$265$	13.1117	+	13.0409i	0.805444	+	0.801096i
$266$	0.766713	+	0.162970i	0.0470102	+	0.00999233i
$267$	17.9182	+	4.73061i	1.09657	+	0.289509i
$268$	−9.26210	−	16.0424i	−0.565773	−	0.979948i
$269$	−17.7014	+	12.8608i	−1.07927	+	0.784136i	−0.977556	−	0.210677i	$-0.932433\pi$
$269$	−17.7014	+	12.8608i	−1.07927	+	0.784136i	−0.101715	+	0.994814i	$0.532433\pi$
$270$	5.03307	+	22.1763i	0.306303	+	1.34961i
$271$	−9.50877	−	6.90853i	−0.577617	−	0.419663i	0.260247	−	0.965542i	$-0.416196\pi$
$271$	−9.50877	−	6.90853i	−0.577617	−	0.419663i	−0.837864	+	0.545879i	$0.816196\pi$
$272$	−1.68614	+	16.0426i	−0.102237	+	0.972724i
$273$	−7.16694	+	2.78141i	−0.433763	+	0.168339i
$274$	−4.12397	+	7.14292i	−0.249138	+	0.431520i
$275$	−12.2894	−	1.22445i	−0.741078	−	0.0738368i
$276$	0.655678	−	1.72705i	0.0394672	−	0.103956i
$277$	21.5247	−	4.57521i	1.29329	−	0.274898i	0.490649	−	0.871357i	$-0.336760\pi$
$277$	21.5247	−	4.57521i	1.29329	−	0.274898i	0.802643	+	0.596460i	$0.203426\pi$
$278$	−0.564974	−	0.410478i	−0.0338849	−	0.0246188i
$279$	5.52682	+	25.0929i	0.330882	+	1.50227i
$280$	−0.859926	−	0.555139i	−0.0513904	−	0.0331759i
$281$	1.17625	+	0.523699i	0.0701690	+	0.0312413i	0.441521	−	0.897251i	$-0.354439\pi$
$281$	1.17625	+	0.523699i	0.0701690	+	0.0312413i	−0.371352	+	0.928492i	$0.621106\pi$
$282$	24.0396	−	3.89816i	1.43154	−	0.232132i
$283$	−0.803811	−	7.64775i	−0.0477816	−	0.454611i	−0.992088	−	0.125544i	$-0.959932\pi$
$283$	−0.803811	−	7.64775i	−0.0477816	−	0.454611i	0.944306	−	0.329067i	$-0.106734\pi$
$284$	−23.1437	−	4.91935i	−1.37333	−	0.291909i
$285$	−0.568190	−	0.969785i	−0.0336567	−	0.0574451i
$286$	15.2086	−	3.23268i	0.899302	−	0.191153i
$287$	−2.71017	−	8.34105i	−0.159976	−	0.492356i
$288$	9.32716	−	21.3707i	0.549608	−	1.25928i
$289$	−0.925154	+	2.84733i	−0.0544209	+	0.167490i
$290$	−0.810357	+	16.3069i	−0.0475858	+	0.957574i
$291$	19.1012	+	0.930642i	1.11973	+	0.0545552i
$292$	−0.892045	−	8.48724i	−0.0522030	−	0.496678i
$293$	−5.62660	+	9.74556i	−0.328710	+	0.569342i	−0.982256	−	0.187545i	$-0.939947\pi$
$293$	−5.62660	+	9.74556i	−0.328710	+	0.569342i	0.653546	+	0.756886i	$0.273280\pi$
$294$	−16.7012	−	4.40932i	−0.974032	−	0.257157i
$295$	4.06546	+	1.54797i	0.236700	+	0.0901264i
$296$	−2.06514	−	1.50041i	−0.120034	−	0.0872097i
$297$	−4.73144	−	11.9308i	−0.274546	−	0.692295i
$298$	14.1227	−	43.4652i	0.818107	−	2.51787i
$299$	−0.936975	−	1.62289i	−0.0541867	−	0.0938540i
$300$	−2.62215	−	15.6344i	−0.151390	−	0.902655i
$301$	4.41980	−	7.65533i	0.254753	−	0.441246i
$302$	10.5812	+	11.7516i	0.608878	+	0.676227i
$303$	21.0790	−	13.7993i	1.21096	−	0.792751i
$304$	−0.130751	+	1.24402i	−0.00749911	+	0.0713493i
$305$	29.2749	−	1.61370i	1.67628	−	0.0924000i
$306$	−12.7849	+	17.8719i	−0.730866	+	1.02167i
$307$	22.3350			1.27473			0.637363	−	0.770563i	$-0.280025\pi$
$307$	22.3350			1.27473			0.637363	+	0.770563i	$0.280025\pi$
$308$	−5.70031	−	2.53794i	−0.324806	−	0.144613i
$309$	4.59329	+	8.93349i	0.261303	+	0.508209i
$310$	−5.96376	−	37.0052i	−0.338719	−	2.10175i
$311$	−11.1931	−	12.4312i	−0.634705	−	0.704911i	0.336895	−	0.941542i	$-0.390623\pi$
$311$	−11.1931	−	12.4312i	−0.634705	−	0.704911i	−0.971599	+	0.236631i	$0.923957\pi$
$312$	−0.844915	−	1.64327i	−0.0478339	−	0.0930321i
$313$	9.83191	−	10.9194i	0.555732	−	0.617203i	−0.398173	−	0.917310i	$-0.630356\pi$
$313$	9.83191	−	10.9194i	0.555732	−	0.617203i	0.953906	+	0.300107i	$0.0970223\pi$
$314$	10.1657	−	31.2867i	0.573681	−	1.76561i
$315$	−4.28559	−	8.20580i	−0.241466	−	0.462345i
$316$	−9.01161	−	27.7349i	−0.506943	−	1.56021i
$317$	2.69931	+	1.20181i	0.151608	+	0.0675003i	0.481138	−	0.876645i	$-0.340224\pi$
$317$	2.69931	+	1.20181i	0.151608	+	0.0675003i	−0.329530	+	0.944145i	$0.606890\pi$
$318$	9.95067	−	26.2100i	0.558006	−	1.46978i
$319$	−0.963235	−	9.16457i	−0.0539308	−	0.513118i
$320$	−6.65594	+	13.1509i	−0.372078	+	0.735157i
$321$	1.24773	+	22.2430i	0.0696416	+	1.24149i
$322$	−0.164498	+	1.56509i	−0.00916709	+	0.0872190i
$323$	0.335624	−	1.03294i	0.0186746	−	0.0574746i
$324$	13.1845	−	9.87856i	0.732471	−	0.548809i
$325$	−13.9701	−	7.96512i	−0.774922	−	0.441826i
$326$	6.00328	+	10.3980i	0.332491	+	0.575891i
$327$	−25.7529	+	9.99442i	−1.42414	+	0.552692i
$328$	1.92572	−	0.857384i	0.106330	−	0.0473411i
$329$	−9.05716	+	4.03251i	−0.499338	+	0.222319i
$330$	5.89933	+	17.7695i	0.324748	+	0.978180i
$331$	−10.5752	−	4.70838i	−0.581265	−	0.258796i	0.0949721	−	0.995480i	$-0.469724\pi$
$331$	−10.5752	−	4.70838i	−0.581265	−	0.258796i	−0.676237	+	0.736684i	$0.736390\pi$
$332$	0.369819			0.0202964
$333$	−9.54538	−	21.0219i	−0.523084	−	1.15199i
$334$	12.3149	+	37.9013i	0.673841	+	2.07387i
$335$	1.12310	−	22.6003i	0.0613616	−	1.23478i
$336$	−1.57426	+	10.1817i	−0.0858832	+	0.555455i
$337$	19.7551	+	4.19908i	1.07613	+	0.228738i	0.711693	−	0.702490i	$-0.247929\pi$
$337$	19.7551	+	4.19908i	1.07613	+	0.228738i	0.364436	+	0.931229i	$0.381262\pi$
$338$	−5.08413	−	1.08066i	−0.276540	−	0.0587804i
$339$	−1.95738	+	12.6595i	−0.106311	+	0.687571i
$340$	9.60807	−	11.9309i	0.521071	−	0.647041i
$341$	6.53738	+	20.1200i	0.354019	+	1.08956i
$342$	−0.991404	+	1.38587i	−0.0536090	+	0.0749392i
$343$	16.6922			0.901292
$344$	1.94094	+	0.864160i	0.104648	+	0.0465924i
$345$	1.81712	−	1.33802i	0.0978304	−	0.0720365i
$346$	23.4903	−	10.4586i	1.26285	−	0.562256i
$347$	2.29308	−	1.02095i	0.123099	−	0.0548072i	−0.344263	−	0.938873i	$-0.611871\pi$
$347$	2.29308	−	1.02095i	0.123099	−	0.0548072i	0.467362	+	0.884066i	$0.345204\pi$
$348$	11.0272	−	4.27952i	0.591119	−	0.229406i
$349$	−4.09655	−	7.09543i	−0.219283	−	0.379810i	0.735306	−	0.677735i	$-0.237039\pi$
$349$	−4.09655	−	7.09543i	−0.219283	−	0.379810i	−0.954589	+	0.297926i	$0.903705\pi$
$350$	5.55958	+	12.3073i	0.297172	+	0.657853i
$351$	0.690509	−	16.6979i	0.0368566	−	0.891266i
$352$	5.93263	−	18.2587i	0.316210	−	0.973194i
$353$	2.01664	−	19.1871i	0.107335	−	1.02122i	−0.799766	−	0.600312i	$-0.795043\pi$
$353$	2.01664	−	19.1871i	0.107335	−	1.02122i	0.907101	−	0.420913i	$-0.138290\pi$
$354$	−0.369367	−	6.58462i	−0.0196316	−	0.349969i
$355$	−20.4925	−	20.3819i	−1.08763	−	1.08176i
$356$	2.04727	+	19.4784i	0.108505	+	1.03236i
$357$	3.17508	−	8.36313i	0.168043	−	0.442624i
$358$	9.15479	+	4.07597i	0.483845	+	0.215422i
$359$	−8.64746	−	26.6141i	−0.456395	−	1.40464i	−0.869489	−	0.493952i	$-0.835552\pi$
$359$	−8.64746	−	26.6141i	−0.456395	−	1.40464i	0.413094	−	0.910688i	$-0.364448\pi$
$360$	1.85381	−	1.23057i	0.0977043	−	0.0648566i
$361$	−5.84530	+	17.9900i	−0.307647	+	0.946841i
$362$	−11.6690	+	12.9597i	−0.613307	+	0.681147i
$363$	3.87992	+	7.54606i	0.203643	+	0.396065i
$364$	−5.43656	−	6.03791i	−0.284953	−	0.316473i
$365$	4.70754	−	9.30121i	0.246404	−	0.486847i
$366$	−20.3248	−	39.5296i	−1.06239	−	2.06625i
$367$	2.92910	+	1.30412i	0.152898	+	0.0680744i	0.481759	−	0.876304i	$-0.339998\pi$
$367$	2.92910	+	1.30412i	0.152898	+	0.0680744i	−0.328861	+	0.944378i	$0.606665\pi$
$368$	−2.51136			−0.130913
$369$	18.9752	+	1.85340i	0.987808	+	0.0964842i
$370$	12.1548	+	31.4101i	0.631900	+	1.63293i
$371$	−1.19299	+	11.3506i	−0.0619372	+	0.589293i
$372$	−22.7197	+	14.8734i	−1.17796	+	0.771150i
$373$	10.2416	+	11.3744i	0.530288	+	0.588945i	0.947457	−	0.319884i	$-0.103644\pi$
$373$	10.2416	+	11.3744i	0.530288	+	0.588945i	−0.417168	+	0.908829i	$0.636977\pi$
$374$	−9.04614	+	15.6684i	−0.467765	+	0.810193i
$375$	7.66719	−	17.7824i	0.395932	−	0.918280i
$376$	−1.19146	−	2.06367i	−0.0614449	−	0.106426i
$377$	3.70788	−	11.4117i	0.190965	−	0.587731i
$378$	−8.71140	+	11.0037i	−0.448066	+	0.565967i
$379$	5.89428	+	4.28245i	0.302769	+	0.219975i	0.728788	−	0.684740i	$-0.240084\pi$
$379$	5.89428	+	4.28245i	0.302769	+	0.219975i	−0.426019	+	0.904714i	$0.640084\pi$
$380$	0.745055	−	0.925175i	0.0382205	−	0.0474605i
$381$	23.1535	+	6.11280i	1.18619	+	0.313168i
$382$	−1.84301	+	3.19219i	−0.0942968	+	0.163327i
$383$	3.10910	+	29.5811i	0.158867	+	1.51152i	0.725884	+	0.687817i	$0.241431\pi$
$383$	3.10910	+	29.5811i	0.158867	+	1.51152i	−0.567017	+	0.823706i	$0.691903\pi$
$384$	−4.57414	−	0.222860i	−0.233423	−	0.0113728i
$385$	−4.16861	−	6.38122i	−0.212452	−	0.325217i
$386$	−0.895769	+	2.75689i	−0.0455934	+	0.140322i
$387$	11.4090	+	15.4627i	0.579951	+	0.786014i
$388$	6.24559	+	19.2219i	0.317072	+	0.975846i
$389$	4.40694	−	0.936723i	0.223441	−	0.0474938i	−0.0948308	−	0.995493i	$-0.530231\pi$
$389$	4.40694	−	0.936723i	0.223441	−	0.0474938i	0.318271	+	0.948000i	$0.396898\pi$
$390$	−2.39353	+	24.2617i	−0.121201	+	1.22854i
$391$	2.13290	+	0.453363i	0.107866	+	0.0229275i
$392$	0.176669	+	1.68089i	0.00892311	+	0.0848977i
$393$	−12.6191	+	2.04625i	−0.636548	+	0.103220i
$394$	34.5132	+	15.3663i	1.73875	+	0.774141i
$395$	9.12673	−	34.4339i	0.459216	−	1.73256i
$396$	10.0133	−	9.15026i	0.503189	−	0.459818i
$397$	−20.0082	−	14.5368i	−1.00418	−	0.729582i	−0.0412026	−	0.999151i	$-0.513119\pi$
$397$	−20.0082	−	14.5368i	−1.00418	−	0.729582i	−0.962981	+	0.269569i	$0.913119\pi$
$398$	11.8192	−	2.51224i	0.592441	−	0.125927i
$399$	0.246210	−	0.648517i	0.0123259	−	0.0324665i
$400$	−18.6052	+	10.8764i	−0.930262	+	0.543822i
$401$	7.15907	−	12.3999i	0.357507	−	0.619220i	−0.630037	−	0.776565i	$-0.716960\pi$
$401$	7.15907	−	12.3999i	0.357507	−	0.619220i	0.987544	+	0.157345i	$0.0502935\pi$
$402$	−31.9808	+	12.4114i	−1.59506	+	0.619023i
$403$	−2.87939	+	27.3956i	−0.143433	+	1.36467i
$404$	21.5413	+	15.6507i	1.07172	+	0.778651i
$405$	20.0756	−	1.40303i	0.997567	−	0.0697169i
$406$	−8.15206	+	5.92282i	−0.404580	+	0.293945i
$407$	−9.50454	−	16.4624i	−0.471123	−	0.816009i
$408$	2.07885	+	0.548843i	0.102919	+	0.0271718i
$409$	−21.4203	−	4.55302i	−1.05916	−	0.225132i	−0.354779	−	0.934950i	$-0.615444\pi$
$409$	−21.4203	−	4.55302i	−1.05916	−	0.225132i	−0.704385	+	0.709818i	$0.748777\pi$
$410$	−27.4818	−	4.27647i	−1.35723	−	0.211200i
$411$	5.68942	+	4.57267i	0.280638	+	0.225553i
$412$	−7.10368	+	7.88944i	−0.349973	+	0.388685i
$413$	0.829648	+	2.55339i	0.0408243	+	0.125644i
$414$	−2.97521	−	1.68869i	−0.146223	−	0.0829945i
$415$	0.379534	+	0.245014i	0.0186306	+	0.0120273i
$416$	16.7271	−	18.5773i	0.820113	−	0.910828i
$417$	−0.435397	+	0.438610i	−0.0213215	+	0.0214788i
$418$	−0.701481	+	1.21500i	−0.0343106	+	0.0594276i
$419$	0.123849	+	1.17835i	0.00605044	+	0.0575661i	0.997131	−	0.0757016i	$-0.0241196\pi$
$419$	0.123849	+	1.17835i	0.00605044	+	0.0575661i	−0.991080	+	0.133268i	$0.957453\pi$
$420$	6.50012	−	7.31245i	0.317173	−	0.356811i
$421$	1.24110	−	11.8083i	0.0604877	−	0.575502i	−0.921740	−	0.387808i	$-0.873232\pi$
$421$	1.24110	−	11.8083i	0.0604877	−	0.575502i	0.982228	−	0.187693i	$-0.0601011\pi$
$422$	44.8283	+	32.5697i	2.18221	+	1.58547i
$423$	−0.158485	−	21.5518i	−0.00770578	−	1.04788i
$424$	−2.74316			−0.133220
$425$	17.7650	−	5.87870i	0.861728	−	0.285159i
$426$	−15.5521	+	40.9642i	−0.753502	+	1.98472i
$427$	12.1079	+	13.4472i	0.585942	+	0.650754i
$428$	−21.5091	+	9.57645i	−1.03968	+	0.462895i
$429$	−0.770656	−	13.7383i	−0.0372076	−	0.663292i
$430$	−15.3311	−	23.4685i	−0.739330	−	1.13175i
$431$	−16.7241	+	12.1508i	−0.805573	+	0.585283i	−0.912544	−	0.408979i	$-0.865885\pi$
$431$	−16.7241	+	12.1508i	−0.805573	+	0.585283i	0.106971	+	0.994262i	$0.465885\pi$
$432$	−18.9168	−	11.9901i	−0.910134	−	0.576876i
$433$	−10.6992	+	7.77342i	−0.514170	+	0.373566i	−0.814403	−	0.580299i	$-0.802936\pi$
$433$	−10.6992	+	7.77342i	−0.514170	+	0.373566i	0.300233	+	0.953866i	$0.402936\pi$
$434$	15.4790	−	17.1912i	0.743018	−	0.825205i
$435$	14.1522	+	2.91384i	0.678544	+	0.139708i
$436$	−19.5352	−	21.6960i	−0.935565	−	1.03905i
$437$	0.165396	+	0.0351559i	0.00791194	+	0.00168174i
$438$	−15.7852	−	0.769083i	−0.754248	−	0.0367482i
$439$	13.6794	−	2.90764i	0.652881	−	0.138774i	0.130449	−	0.991455i	$-0.458358\pi$
$439$	13.6794	−	2.90764i	0.652881	−	0.138774i	0.522432	+	0.852681i	$0.325025\pi$
$440$	1.42061	−	1.15677i	0.0677248	−	0.0551466i
$441$	−6.11475	+	14.0103i	−0.291178	+	0.667158i
$442$	−19.0588	+	13.8470i	−0.906536	+	0.658637i
$443$	0.0129892	+	0.0224980i	0.000617136	+	0.00106891i	0.866334	−	0.499465i	$-0.166470\pi$
$443$	0.0129892	+	0.0224980i	0.000617136	+	0.00106891i	−0.865717	+	0.500534i	$0.833137\pi$
$444$	17.1899	−	17.3168i	0.815799	−	0.821820i
$445$	−10.8039	+	21.3465i	−0.512155	+	1.01192i
$446$	−0.188555	+	0.0839503i	−0.00892836	+	0.00397516i
$447$	−36.1042	−	18.2291i	−1.70767	−	0.862208i
$448$	−8.89784	+	1.89129i	−0.420383	+	0.0893552i
$449$	−32.1952			−1.51939			−0.759693	−	0.650282i	$-0.774651\pi$
$449$	−32.1952			−1.51939			−0.759693	+	0.650282i	$0.774651\pi$
$450$	−29.3552	+	0.374788i	−1.38382	+	0.0176677i
$451$	15.6975			0.739168
$452$	−13.2424	+	2.81476i	−0.622870	+	0.132395i
$453$	11.7086	−	7.66500i	0.550117	−	0.360133i
$454$	17.9253	−	7.98085i	0.841275	−	0.374560i
$455$	−1.57911	−	9.79840i	−0.0740299	−	0.459356i
$456$	0.161204	+	0.0425599i	0.00754908	+	0.00199305i
$457$	5.72265	+	9.91192i	0.267694	+	0.463660i	0.968266	−	0.249922i	$-0.0804050\pi$
$457$	5.72265	+	9.91192i	0.267694	+	0.463660i	−0.700572	+	0.713582i	$0.747072\pi$
$458$	−27.7682	+	20.1748i	−1.29752	+	0.942707i
$459$	13.9016	+	13.5982i	0.648870	+	0.634711i
$460$	2.00365	+	1.29349i	0.0934205	+	0.0603091i
$461$	−2.53271	+	0.538343i	−0.117960	+	0.0250732i	−0.266513	−	0.963831i	$-0.585872\pi$
$461$	−2.53271	+	0.538343i	−0.117960	+	0.0250732i	0.148553	+	0.988904i	$0.452538\pi$
$462$	−6.25782	+	9.71420i	−0.291140	+	0.451945i
$463$	−27.8889	−	5.92797i	−1.29611	−	0.275496i	−0.492321	−	0.870414i	$-0.663851\pi$
$463$	−27.8889	−	5.92797i	−1.29611	−	0.275496i	−0.803787	+	0.594918i	$0.797185\pi$
$464$	−10.7598	−	11.9500i	−0.499511	−	0.554763i
$465$	−33.1706	+	0.211742i	−1.53825	+	0.00981928i
$466$	−11.3559	+	12.6120i	−0.526050	+	0.584238i
$467$	−19.1318	+	13.9001i	−0.885316	+	0.643220i	−0.934653	−	0.355562i	$-0.884289\pi$
$467$	−19.1318	+	13.9001i	−0.885316	+	0.643220i	0.0493364	+	0.998782i	$0.484289\pi$
$468$	16.7572	−	5.58132i	0.774604	−	0.257997i
$469$	11.2982	−	8.20863i	0.521703	−	0.379039i
$470$	−1.56048	+	31.4017i	−0.0719795	+	1.44845i
$471$	−25.9882	−	13.1215i	−1.19747	−	0.604606i
$472$	−0.589508	+	0.262466i	−0.0271343	+	0.0120810i
$473$	10.5867	+	11.7577i	0.486778	+	0.540621i
$474$	−53.3087	+	8.64431i	−2.44855	+	0.397046i
$475$	1.37758	−	0.455862i	0.0632077	−	0.0209164i
$476$	9.45415			0.433330
$477$	−21.5773	−	12.2470i	−0.987954	−	0.560750i
$478$	−16.0411	−	11.6545i	−0.733703	−	0.533066i
$479$	2.83024	−	26.9279i	0.129317	−	1.23037i	−0.716765	−	0.697315i	$-0.754378\pi$
$479$	2.83024	−	26.9279i	0.129317	−	1.23037i	0.846082	−	0.533053i	$-0.178955\pi$
$480$	24.4660	+	17.5381i	1.11672	+	0.800501i
$481$	−2.58726	−	24.6162i	−0.117969	−	1.12240i
$482$	−7.97326	+	13.8101i	−0.363172	+	0.629032i
$483$	1.34656	+	0.355508i	0.0612705	+	0.0161762i
$484$	−6.00043	+	6.66415i	−0.272747	+	0.302916i
$485$	−6.32537	+	23.8648i	−0.287220	+	1.08364i
$486$	−14.3483	−	26.9248i	−0.650853	−	1.22133i
$487$	1.88824	+	5.81140i	0.0855643	+	0.263340i	0.984680	−	0.174371i	$-0.0557893\pi$
$487$	1.88824	+	5.81140i	0.0855643	+	0.263340i	−0.899116	+	0.437711i	$0.855789\pi$
$488$	−2.91016	+	3.23205i	−0.131737	+	0.146308i
$489$	9.90570	−	3.84429i	0.447951	−	0.173845i
$490$	10.0701	−	19.8967i	0.454922	−	0.898841i
$491$	23.5777	+	5.01160i	1.06405	+	0.226170i	0.706492	−	0.707721i	$-0.250277\pi$
$491$	23.5777	+	5.01160i	1.06405	+	0.226170i	0.357556	+	0.933892i	$0.383610\pi$
$492$	5.28658	+	19.4435i	0.238337	+	0.876582i
$493$	6.98107	+	12.0916i	0.314411	+	0.544577i
$494$	−1.47791	+	1.07377i	−0.0664944	+	0.0483110i
$495$	16.3387	−	2.75656i	0.734369	−	0.123898i
$496$	29.8658	+	21.6988i	1.34101	+	0.974304i
$497$	1.86456	−	17.7401i	0.0836368	−	0.795751i
$498$	0.104648	−	0.676819i	0.00468940	−	0.0303290i
$499$	−4.18052	+	7.24087i	−0.187146	+	0.324146i	−0.944298	−	0.329093i	$-0.893257\pi$
$499$	−4.18052	+	7.24087i	−0.187146	+	0.324146i	0.757152	+	0.653239i	$0.226590\pi$
$500$	20.4459	+	0.905119i	0.914367	+	0.0404782i
$501$	34.8132	−	5.64516i	1.55534	−	0.252207i
$502$	45.1397	−	9.59474i	2.01468	−	0.428234i
$503$	21.1533	+	15.3688i	0.943178	+	0.685259i	0.949183	−	0.314723i	$-0.101912\pi$
$503$	21.1533	+	15.3688i	0.943178	+	0.685259i	−0.00600579	+	0.999982i	$0.501912\pi$
$504$	1.30911	+	0.414738i	0.0583124	+	0.0184739i
$505$	11.7383	+	30.3335i	0.522345	+	1.34983i
$506$	−2.57319	−	1.14566i	−0.114392	−	0.0509308i
$507$	−1.63264	+	4.30036i	−0.0725080	+	0.190986i
$508$	2.64543	+	25.1696i	0.117372	+	1.11672i
$509$	31.8433	+	6.76850i	1.41143	+	0.300009i	0.849680	−	0.527299i	$-0.176795\pi$
$509$	31.8433	+	6.76850i	1.41143	+	0.300009i	0.561750	+	0.827307i	$0.310128\pi$
$510$	−19.1163	−	20.9602i	−0.846484	−	0.928133i
$511$	6.29316	−	1.33765i	0.278393	−	0.0591743i
$512$	−9.46884	−	29.1421i	−0.418468	−	1.28791i
$513$	1.07799	+	1.05447i	0.0475946	+	0.0465561i
$514$	−7.87599	+	24.2398i	−0.347395	+	1.06917i
$515$	−12.5173	+	3.39033i	−0.551576	+	0.149396i
$516$	−10.9982	+	17.0728i	−0.484168	+	0.751590i
$517$	−1.85487	−	17.6479i	−0.0815772	−	0.776155i
$518$	−10.3931	+	18.0013i	−0.456645	+	0.790931i
$519$	−5.97039	−	21.9585i	−0.262071	−	0.963872i
$520$	2.30249	−	0.623635i	0.100971	−	0.0273482i
$521$	12.7402	+	9.25627i	0.558157	+	0.405525i	0.830784	−	0.556595i	$-0.187893\pi$
$521$	12.7402	+	9.25627i	0.558157	+	0.405525i	−0.272627	+	0.962120i	$0.587893\pi$
$522$	−4.71174	−	21.3922i	−0.206227	−	0.936313i
$523$	−4.06035	+	12.4965i	−0.177547	+	0.546432i	−0.999741	−	0.0227752i	$-0.992750\pi$
$523$	−4.06035	+	12.4965i	−0.177547	+	0.546432i	0.822194	+	0.569207i	$0.192750\pi$
$524$	−6.75536	−	11.7006i	−0.295109	−	0.511144i
$525$	11.5156	−	3.19805i	0.502580	−	0.139575i
$526$	−11.0260	+	19.0976i	−0.480757	+	0.832696i
$527$	−21.4480	−	23.8204i	−0.934289	−	1.03763i
$528$	−16.4610	−	8.31122i	−0.716374	−	0.361699i
$529$	2.36867	−	22.5364i	0.102986	−	0.979843i
$530$	30.4076	+	19.6301i	1.32082	+	0.852679i
$531$	−5.80875	−	0.567370i	−0.252078	−	0.0246218i
$532$	0.733120			0.0317848
$533$	18.6727	+	8.31361i	0.808803	+	0.360102i
$534$	36.2276	+	1.76507i	1.56772	+	0.0763819i
$535$	−28.4188	−	4.42228i	−1.22865	−	0.191192i
$536$	2.24601	+	2.49444i	0.0970127	+	0.107743i
$537$	4.80274	−	7.45545i	0.207254	−	0.321726i
$538$	−28.6542	+	31.8238i	−1.23537	+	1.37202i
$539$	−3.88934	+	11.9702i	−0.167526	+	0.515592i
$540$	8.91687	+	19.3093i	0.383721	+	0.830941i
$541$	−10.0048	−	30.7916i	−0.430139	−	1.32383i	−0.897987	−	0.440023i	$-0.854970\pi$
$541$	−10.0048	−	30.7916i	−0.430139	−	1.32383i	0.467847	−	0.883809i	$-0.345030\pi$
$542$	−21.0148	−	9.35641i	−0.902665	−	0.401892i
$543$	9.75639	+	11.9580i	0.418687	+	0.513166i
$544$	3.04056	+	28.9290i	0.130363	+	1.24032i
$545$	−5.67421	−	35.2085i	−0.243056	−	1.50817i
$546$	−12.5886	+	8.24111i	−0.538743	+	0.352687i
$547$	−1.46528	+	13.9413i	−0.0626511	+	0.596085i	0.917487	+	0.397767i	$0.130215\pi$
$547$	−1.46528	+	13.9413i	−0.0626511	+	0.596085i	−0.980138	+	0.198318i	$0.936452\pi$
$548$	−2.38382	+	7.33666i	−0.101832	+	0.313406i
$549$	−37.3204	+	12.4303i	−1.59280	+	0.530511i
$550$	−24.0251	+	2.65670i	−1.02443	+	0.113282i
$551$	0.541345	+	0.937637i	0.0230621	+	0.0399447i
$552$	−0.0511485	+	0.330807i	−0.00217703	+	0.0140801i
$553$	20.0846	−	8.94223i	0.854083	−	0.380262i
$554$	39.3452	−	17.5176i	1.67162	−	0.744251i
$555$	29.1144	−	6.38296i	1.23584	−	0.270942i
$556$	−0.596689	−	0.265663i	−0.0253052	−	0.0112666i
$557$	−4.26938			−0.180900			−0.0904498	−	0.995901i	$-0.528830\pi$
$557$	−4.26938			−0.180900			−0.0904498	+	0.995901i	$0.528830\pi$
$558$	20.7913	+	45.7890i	0.880168	+	1.93840i
$559$	6.36616	+	19.5930i	0.269260	+	0.828697i
$560$	−12.4301	−	4.73291i	−0.525267	−	0.200002i
$561$	12.4800	+	10.0304i	0.526907	+	0.423483i
$562$	2.46491	+	0.523934i	0.103976	+	0.0221008i
$563$	11.9299	+	2.53577i	0.502784	+	0.106870i	0.452320	−	0.891856i	$-0.350597\pi$
$563$	11.9299	+	2.53577i	0.502784	+	0.106870i	0.0504643	+	0.998726i	$0.483930\pi$
$564$	21.2347	−	8.24094i	0.894141	−	0.347006i
$565$	−15.4551	−	5.88473i	−0.650203	−	0.247572i
$566$	−4.65083	−	14.3138i	−0.195489	−	0.601654i
$567$	8.44561	+	9.10683i	0.354682	+	0.382451i
$568$	4.28735			0.179893
$569$	−15.1783	−	6.75783i	−0.636309	−	0.283303i	0.0631194	−	0.998006i	$-0.479895\pi$
$569$	−15.1783	−	6.75783i	−0.636309	−	0.283303i	−0.699428	+	0.714703i	$0.746562\pi$
$570$	−1.48237	−	1.62535i	−0.0620896	−	0.0680785i
$571$	−15.2502	+	6.78981i	−0.638199	+	0.284145i	−0.700217	−	0.713930i	$-0.746913\pi$
$571$	−15.2502	+	6.78981i	−0.638199	+	0.284145i	0.0620173	+	0.998075i	$0.480247\pi$
$572$	13.2850	−	5.91485i	0.555473	−	0.247313i
$573$	2.54262	+	2.04354i	0.106219	+	0.0853700i
$574$	−8.58249	−	14.8653i	−0.358226	−	0.620466i
$575$	1.19931	+	2.65493i	0.0500149	+	0.110718i
$576$	3.96908	−	19.3724i	0.165378	−	0.807185i
$577$	9.92545	−	30.5474i	0.413202	−	1.27171i	−0.500647	−	0.865651i	$-0.666905\pi$
$577$	9.92545	−	30.5474i	0.413202	−	1.27171i	0.913849	−	0.406054i	$-0.133095\pi$
$578$	−0.612485	+	5.82741i	−0.0254760	+	0.242388i
$579$	2.29000	+	1.15623i	0.0951692	+	0.0480512i
$580$	2.42965	+	15.0760i	0.100886	+	0.625996i
$581$	0.0291431	+	0.277278i	0.00120906	+	0.0115034i
$582$	36.9461	−	5.99103i	1.53147	−	0.248336i
$583$	−18.6617	−	8.30873i	−0.772889	−	0.344112i
$584$	0.477853	+	1.47068i	0.0197737	+	0.0608572i
$585$	20.8952	+	5.37416i	0.863912	+	0.222194i
$586$	−6.80594	+	20.9465i	−0.281151	+	0.865293i
$587$	7.24525	−	8.04666i	0.299043	−	0.332121i	−0.574832	−	0.818272i	$-0.694933\pi$
$587$	7.24525	−	8.04666i	0.299043	−	0.332121i	0.873875	+	0.486150i	$0.161599\pi$
$588$	−16.1365	−	0.786198i	−0.665459	−	0.0324222i
$589$	−1.66318	−	1.84715i	−0.0685301	−	0.0761104i
$590$	8.41283	+	1.30913i	0.346351	+	0.0538960i
$591$	18.1062	−	28.1067i	0.744788	−	1.15616i
$592$	−30.3031	−	13.4918i	−1.24545	−	0.554509i
$593$	8.57810			0.352260			0.176130	−	0.984367i	$-0.443642\pi$
$593$	8.57810			0.352260			0.176130	+	0.984367i	$0.443642\pi$
$594$	−13.9128	−	20.9151i	−0.570848	−	0.858155i
$595$	9.70252	+	6.26362i	0.397765	+	0.256783i
$596$	4.46804	−	42.5105i	0.183018	−	1.74130i
$597$	−0.598906	−	10.6766i	−0.0245116	−	0.436963i
$598$	−2.45413	−	2.72559i	−0.100357	−	0.111458i
$599$	6.67217	−	11.5565i	0.272617	−	0.472187i	−0.696914	−	0.717155i	$-0.745444\pi$
$599$	6.67217	−	11.5565i	0.272617	−	0.472187i	0.969531	+	0.244968i	$0.0787774\pi$
$600$	1.05376	+	2.67228i	0.0430196	+	0.109095i
$601$	−3.48996	−	6.04478i	−0.142358	−	0.246572i	0.786026	−	0.618194i	$-0.212135\pi$
$601$	−3.48996	−	6.04478i	−0.142358	−	0.246572i	−0.928384	+	0.371622i	$0.878802\pi$
$602$	5.34619	−	16.4539i	0.217895	−	0.670610i
$603$	6.53015	+	29.6482i	0.265928	+	1.20737i
$604$	11.9654	+	8.69336i	0.486865	+	0.353728i
$605$	−10.5732	+	2.86378i	−0.429863	+	0.116429i
$606$	34.7385	−	34.9949i	1.41116	−	1.42157i
$607$	2.00295	−	3.46922i	0.0812974	−	0.140811i	−0.822510	−	0.568751i	$-0.807427\pi$
$607$	2.00295	−	3.46922i	0.0812974	−	0.140811i	0.903807	+	0.427939i	$0.140760\pi$
$608$	0.235779	+	2.24329i	0.00956211	+	0.0909774i
$609$	4.07763	+	7.93058i	0.165234	+	0.321363i
$610$	55.3874	−	15.0018i	2.24257	−	0.607405i
$611$	7.14014	−	21.9751i	0.288859	−	0.889017i
$612$	−8.22100	+	18.8362i	−0.332314	+	0.761410i
$613$	−11.1550	−	34.3317i	−0.450548	−	1.38664i	−0.876283	−	0.481796i	$-0.839985\pi$
$613$	−11.1550	−	34.3317i	−0.450548	−	1.38664i	0.425735	−	0.904848i	$-0.360015\pi$
$614$	42.7582	−	9.08855i	1.72558	−	0.366784i
$615$	−7.45639	+	23.4568i	−0.300671	+	0.945871i
$616$	1.10594	+	0.235076i	0.0445598	+	0.00947147i
$617$	−4.71827	−	44.8913i	−0.189950	−	1.80726i	−0.510343	−	0.859971i	$-0.670482\pi$
$617$	−4.71827	−	44.8913i	−0.189950	−	1.80726i	0.320393	−	0.947285i	$-0.396185\pi$
$618$	12.4286	+	15.2332i	0.499953	+	0.612770i
$619$	10.7418	+	4.78255i	0.431749	+	0.192227i	0.611092	−	0.791560i	$-0.290731\pi$
$619$	10.7418	+	4.78255i	0.431749	+	0.192227i	−0.179343	+	0.983787i	$0.557397\pi$
$620$	−12.6519	−	32.6946i	−0.508113	−	1.31305i
$621$	−1.87922	+	2.37371i	−0.0754107	+	0.0952538i
$622$	−26.4867	−	19.2437i	−1.06202	−	0.771602i
$623$	−14.4430	+	3.06995i	−0.578645	+	0.122995i
$624$	−15.1791	−	18.6044i	−0.607652	−	0.744772i
$625$	20.3833	+	14.4748i	0.815333	+	0.578992i
$626$	14.3789	−	24.9050i	0.574697	−	0.995405i
$627$	0.967761	+	0.777804i	0.0386487	+	0.0310625i
$628$	3.21613	−	30.5995i	0.128338	−	1.22105i
$629$	23.3009	+	16.9291i	0.929068	+	0.675008i
$630$	−11.5434	−	13.9653i	−0.459902	−	0.556392i
$631$	−28.9418	+	21.0275i	−1.15216	+	0.837090i	−0.988766	−	0.149472i	$-0.952243\pi$
$631$	−28.9418	+	21.0275i	−1.15216	+	0.837090i	−0.163390	+	0.986562i	$0.552243\pi$
$632$	2.64211	+	4.57626i	0.105097	+	0.182034i
$633$	34.5469	−	34.8019i	1.37312	−	1.38325i
$634$	5.65660	+	1.20235i	0.224652	+	0.0477513i
$635$	−13.9606	+	27.5835i	−0.554009	+	1.09462i
$636$	4.00665	−	25.9133i	0.158874	−	1.02753i
$637$	−10.9660	+	12.1790i	−0.434490	+	0.482550i
$638$	−5.57326	−	17.1527i	−0.220648	−	0.679083i
$639$	33.7235	+	19.1410i	1.33408	+	0.757208i
$640$	1.51473	−	5.71486i	0.0598748	−	0.225900i
$641$	−26.5621	+	29.5003i	−1.04914	+	1.16519i	−0.0632170	+	0.998000i	$0.520136\pi$
$641$	−26.5621	+	29.5003i	−1.04914	+	1.16519i	−0.985925	+	0.167190i	$0.946531\pi$
$642$	11.4398	+	42.0744i	0.451492	+	1.66054i
$643$	−16.4497	+	28.4917i	−0.648712	+	1.12360i	0.334718	+	0.942318i	$0.391359\pi$
$643$	−16.4497	+	28.4917i	−0.648712	+	1.12360i	−0.983431	+	0.181284i	$0.941975\pi$
$644$	0.153853	+	1.46381i	0.00606266	+	0.0576823i
$645$	−22.5983	+	10.2348i	−0.889808	+	0.402993i
$646$	0.222195	−	2.11405i	0.00874215	−	0.0831760i
$647$	−25.9334	−	18.8417i	−1.01955	−	0.740745i	−0.0533576	−	0.998575i	$-0.516992\pi$
$647$	−25.9334	−	18.8417i	−1.01955	−	0.740745i	−0.966190	+	0.257831i	$0.916992\pi$
$648$	−1.96467	+	2.24760i	−0.0771795	+	0.0882940i
$649$	−4.80539			−0.188628
$650$	−29.9856	−	9.56376i	−1.17613	−	0.375122i
$651$	−12.9420	−	15.8624i	−0.507237	−	0.621697i
$652$	7.51408	+	8.34523i	0.294274	+	0.326824i
$653$	−25.7218	+	11.4521i	−1.00657	+	0.448154i	−0.842732	−	0.538333i	$-0.819054\pi$
$653$	−25.7218	+	11.4521i	−1.00657	+	0.448154i	−0.163838	+	0.986487i	$0.552387\pi$
$654$	−45.2346	+	29.6127i	−1.76881	+	1.15795i
$655$	0.819139	−	16.4836i	0.0320064	−	0.644068i
$656$	22.1607	−	16.1007i	0.865232	−	0.628628i
$657$	−2.80720	+	13.7015i	−0.109519	+	0.534547i
$658$	−15.6982	+	11.4054i	−0.611978	+	0.444628i
$659$	−18.0833	+	20.0836i	−0.704427	+	0.782345i	−0.984074	−	0.177758i	$-0.943116\pi$
$659$	−18.0833	+	20.0836i	−0.704427	+	0.782345i	0.279648	+	0.960103i	$0.409782\pi$
$660$	8.85244	+	15.1093i	0.344581	+	0.588129i
$661$	−6.55085	−	7.27545i	−0.254798	−	0.282982i	0.602152	−	0.798382i	$-0.294310\pi$
$661$	−6.55085	−	7.27545i	−0.254798	−	0.282982i	−0.856950	+	0.515399i	$0.827644\pi$
$662$	−22.1611	−	4.71049i	−0.861316	−	0.183078i
$663$	9.53315	+	18.5410i	0.370237	+	0.720073i
$664$	−0.0655471	+	0.0139325i	−0.00254372	+	0.000540684i
$665$	0.752380	+	0.485711i	0.0291760	+	0.0188351i
$666$	−26.8279	−	36.3602i	−1.03956	−	1.40893i
$667$	−1.75856	+	1.27767i	−0.0680919	+	0.0494716i
$668$	18.6365	+	32.2794i	0.721068	+	1.24893i
$669$	0.0479240	+	0.176260i	0.00185285	+	0.00681460i
$670$	−7.04641	−	43.7230i	−0.272227	−	1.68917i
$671$	−29.5873	+	13.1731i	−1.14220	+	0.508542i
$672$	1.04053	+	18.5492i	0.0401391	+	0.715552i
$673$	4.29453	−	0.912830i	0.165542	−	0.0351870i	−0.124395	−	0.992233i	$-0.539699\pi$
$673$	4.29453	−	0.912830i	0.165542	−	0.0351870i	0.289937	+	0.957046i	$0.406366\pi$
$674$	39.5279			1.52256
$675$	−3.64180	+	25.7243i	−0.140173	+	0.990127i
$676$	−4.86137			−0.186976
$677$	6.59213	−	1.40120i	0.253356	−	0.0538525i	−0.0794826	−	0.996836i	$-0.525327\pi$
$677$	6.59213	−	1.40120i	0.253356	−	0.0538525i	0.332839	+	0.942984i	$0.391993\pi$
$678$	1.40418	+	25.0319i	0.0539270	+	0.961345i
$679$	−13.9198	+	6.19750i	−0.534193	+	0.237838i
$680$	−1.25346	+	2.47661i	−0.0480682	+	0.0949737i
$681$	−4.55595	−	16.7564i	−0.174585	−	0.642106i
$682$	20.7024	+	35.8576i	0.792736	+	1.37306i
$683$	14.2153	−	10.3280i	0.543933	−	0.395191i	−0.281611	−	0.959529i	$-0.590869\pi$
$683$	14.2153	−	10.3280i	0.543933	−	0.395191i	0.825544	+	0.564338i	$0.190869\pi$
$684$	−0.637495	+	1.46065i	−0.0243752	+	0.0558494i
$685$	−7.30717	+	5.95005i	−0.279193	+	0.227340i
$686$	31.9555	−	6.79236i	1.22007	−	0.259333i
$687$	13.8896	+	27.0138i	0.529920	+	1.03064i
$688$	27.0054	+	5.74017i	1.02957	+	0.218842i
$689$	−17.7982	−	19.7669i	−0.678059	−	0.753061i
$690$	2.93423	−	3.30093i	0.111704	−	0.125664i
$691$	−27.4569	+	30.4940i	−1.04451	+	1.16005i	−0.0576719	+	0.998336i	$0.518368\pi$
$691$	−27.4569	+	30.4940i	−1.04451	+	1.16005i	−0.986838	+	0.161710i	$0.948299\pi$
$692$	19.4564	−	14.1359i	0.739622	−	0.537367i
$693$	7.64966	+	6.78660i	0.290587	+	0.257801i
$694$	3.97444	−	2.88760i	0.150868	−	0.109612i
$695$	−0.436356	−	0.667964i	−0.0165519	−	0.0253373i
$696$	−1.79324	+	1.17394i	−0.0679727	+	0.0444982i
$697$	−21.7278	+	9.67384i	−0.822999	+	0.366423i
$698$	−10.7297	−	11.9166i	−0.406126	−	0.451048i
$699$	9.49461	+	11.6371i	0.359119	+	0.440156i
$700$	7.47945	+	10.1783i	0.282697	+	0.384702i
$701$	−30.2765			−1.14353			−0.571763	−	0.820419i	$-0.693740\pi$
$701$	−30.2765			−1.14353			−0.571763	+	0.820419i	$0.693740\pi$
$702$	−5.47277	−	32.2474i	−0.206556	−	1.21710i
$703$	1.80686	+	1.31276i	0.0681472	+	0.0495118i
$704$	1.70189	−	16.1924i	0.0641425	−	0.610275i
$705$	27.2524	+	5.61109i	1.02638	+	0.211326i
$706$	−3.94692	−	37.5524i	−0.148544	−	1.41330i
$707$	−10.0368	+	17.3843i	−0.377475	+	0.653805i
$708$	−1.61835	−	5.95213i	−0.0608212	−	0.223695i
$709$	−7.40315	+	8.22203i	−0.278031	+	0.308785i	−0.865946	−	0.500138i	$-0.833283\pi$
$709$	−7.40315	+	8.22203i	−0.278031	+	0.308785i	0.587914	+	0.808923i	$0.299949\pi$
$710$	−47.5247	−	30.6804i	−1.78357	−	1.15141i
$711$	0.351445	+	47.7919i	0.0131802	+	1.79234i
$712$	−1.09669	−	3.37525i	−0.0411001	−	0.126493i
$713$	3.33914	−	3.70849i	0.125052	−	0.138884i
$714$	2.67526	−	17.3024i	0.100119	−	0.647527i
$715$	17.5527	+	2.73140i	0.656435	+	0.102149i
$716$	9.16788	+	1.94869i	0.342620	+	0.0728261i
$717$	−12.3620	+	12.4533i	−0.461669	+	0.465076i
$718$	−27.3845	−	47.4314i	−1.02198	−	1.77012i
$719$	1.95143	−	1.41780i	0.0727761	−	0.0528749i	−0.550802	−	0.834636i	$-0.685678\pi$
$719$	1.95143	−	1.41780i	0.0727761	−	0.0528749i	0.623578	+	0.781761i	$0.285678\pi$
$720$	20.2385	−	20.6499i	0.754244	−	0.769575i
$721$	−6.47504	−	4.70439i	−0.241143	−	0.175201i
$722$	−3.86979	+	36.8186i	−0.144019	+	1.37025i
$723$	10.9999	+	8.84076i	0.409090	+	0.328791i
$724$	−8.15526	+	14.1253i	−0.303088	+	0.524964i
$725$	−7.49475	+	17.0817i	−0.278348	+	0.634400i
$726$	10.4984	+	12.8674i	0.389631	+	0.477553i
$727$	−21.2556	+	4.51802i	−0.788328	+	0.167564i	−0.584447	−	0.811432i	$-0.698689\pi$
$727$	−21.2556	+	4.51802i	−0.788328	+	0.167564i	−0.203880	+	0.978996i	$0.565355\pi$
$728$	1.19105	+	0.865351i	0.0441434	+	0.0320721i
$729$	−25.4882	+	8.90787i	−0.944009	+	0.329921i
$730$	5.22729	−	19.7219i	0.193470	−	0.729939i
$731$	−21.8995	−	9.75029i	−0.809983	−	0.360628i
$732$	−26.2810	−	32.2115i	−0.971374	−	1.19057i
$733$	−3.18371	−	30.2909i	−0.117593	−	1.11882i	−0.881070	−	0.472986i	$-0.843176\pi$
$733$	−3.18371	−	30.2909i	−0.117593	−	1.11882i	0.763477	−	0.645835i	$-0.223491\pi$
$734$	6.13815	+	1.30470i	0.226563	+	0.0481575i
$735$	−16.0396	−	11.4977i	−0.591628	−	0.424100i
$736$	−4.42967	+	0.941556i	−0.163280	+	0.0347062i
$737$	7.72417	+	23.7725i	0.284523	+	0.875673i
$738$	37.0803	−	4.17320i	1.36495	−	0.153618i
$739$	13.7160	−	42.2135i	0.504551	−	1.55285i	−0.296973	−	0.954886i	$-0.595977\pi$
$739$	13.7160	−	42.2135i	0.504551	−	1.55285i	0.801524	−	0.597962i	$-0.204023\pi$
$740$	17.2278	+	26.3720i	0.633307	+	0.969453i
$741$	0.739246	+	1.43776i	0.0271569	+	0.0528174i
$742$	2.33490	+	22.2151i	0.0857167	+	0.815540i
$743$	12.5838	−	21.7958i	0.461655	−	0.799609i	−0.537389	−	0.843335i	$-0.680589\pi$
$743$	12.5838	−	21.7958i	0.461655	−	0.799609i	0.999044	+	0.0437252i	$0.0139226\pi$
$744$	3.46653	−	3.49212i	0.127089	−	0.128027i
$745$	32.7497	−	40.6671i	1.19986	−	1.48993i
$746$	24.2350	+	17.6077i	0.887305	+	0.644665i
$747$	−0.577784	−	0.183047i	−0.0211400	−	0.00669735i
$748$	−5.22904	+	16.0933i	−0.191193	+	0.588431i
$749$	−8.87511	−	15.3721i	−0.324289	−	0.561686i
$750$	7.44209	−	37.1626i	0.271747	−	1.35699i
$751$	−25.2077	+	43.6611i	−0.919844	+	1.59322i	−0.120193	+	0.992751i	$0.538351\pi$
$751$	−25.2077	+	43.6611i	−0.919844	+	1.59322i	−0.799651	+	0.600465i	$0.794982\pi$
$752$	−20.7198	−	23.0117i	−0.755573	−	0.839149i
$753$	−2.28734	−	40.7759i	−0.0833552	−	1.48596i
$754$	2.45475	−	23.3553i	0.0893965	−	0.850551i
$755$	6.52015	+	16.8491i	0.237293	+	0.613202i
$756$	−5.82989	+	11.7607i	−0.212031	+	0.427733i
$757$	8.34393			0.303265			0.151633	−	0.988437i	$-0.451547\pi$
$757$	8.34393			0.303265			0.151633	+	0.988437i	$0.451547\pi$
$758$	13.0266	+	5.79984i	0.473149	+	0.210660i
$759$	−1.34994	+	2.09555i	−0.0489996	+	0.0760636i
$760$	−0.0971996	+	0.192048i	−0.00352580	+	0.00696632i
$761$	4.93074	+	5.47614i	0.178739	+	0.198510i	0.825856	−	0.563881i	$-0.190692\pi$
$761$	4.93074	+	5.47614i	0.178739	+	0.198510i	−0.647117	+	0.762391i	$0.724026\pi$
$762$	46.8125	+	2.28078i	1.69584	+	0.0826239i
$763$	14.7275	−	16.3566i	0.533172	−	0.592147i
$764$	−1.06534	+	3.27877i	−0.0385426	+	0.118622i
$765$	−20.9165	+	13.8844i	−0.756236	+	0.501993i
$766$	17.9892	+	55.3650i	0.649975	+	2.00042i
$767$	−5.71615	−	2.54499i	−0.206398	−	0.0918944i
$768$	−31.3871	+	5.08959i	−1.13258	+	0.183655i
$769$	1.45499	+	13.8433i	0.0524682	+	0.499201i	0.988925	+	0.148418i	$0.0474180\pi$
$769$	1.45499	+	13.8433i	0.0524682	+	0.499201i	−0.936457	+	0.350784i	$0.885915\pi$
$770$	−10.5770	−	10.5199i	−0.381170	−	0.379113i
$771$	20.1347	+	10.1661i	0.725134	+	0.366122i
$772$	−0.283397	+	2.69634i	−0.0101997	+	0.0970433i
$773$	7.27997	−	22.4054i	0.261842	−	0.805867i	−0.730562	−	0.682847i	$-0.760742\pi$
$773$	7.27997	−	22.4054i	0.261842	−	0.805867i	0.992404	−	0.123021i	$-0.0392582\pi$
$774$	28.1335	+	24.9593i	1.01124	+	0.897145i
$775$	8.67672	−	41.9357i	0.311677	−	1.50637i
$776$	−1.83114	−	3.17162i	−0.0657340	−	0.113855i
$777$	14.3382	+	11.5238i	0.514381	+	0.413415i
$778$	8.05548	−	3.58653i	0.288803	−	0.128583i
$779$	−1.68488	+	0.750156i	−0.0603670	+	0.0268771i
$780$	2.52815	+	22.6613i	0.0905224	+	0.811406i
$781$	29.1668	+	12.9859i	1.04367	+	0.464671i
$782$	4.26772			0.152613
$783$	−19.3465	+	1.22802i	−0.691386	+	0.0438859i
$784$	6.78690	+	20.8879i	0.242389	+	0.745998i
$785$	23.5736	−	29.2726i	0.841376	−	1.04478i
$786$	−23.3253	+	9.05230i	−0.831987	+	0.322885i
$787$	27.9180	+	5.93416i	0.995170	+	0.211530i	0.676585	−	0.736364i	$-0.263459\pi$
$787$	27.9180	+	5.93416i	0.995170	+	0.211530i	0.318585	+	0.947894i	$0.396792\pi$
$788$	34.5625	+	7.34650i	1.23124	+	0.261708i
$789$	15.2115	+	12.2257i	0.541542	+	0.435245i
$790$	3.46042	−	69.6343i	0.123116	−	2.47748i
$791$	−3.15397	−	9.70691i	−0.112142	−	0.345138i
$792$	−1.43005	+	1.99904i	−0.0508146	+	0.0710329i
$793$	−42.1715			−1.49756
$794$	−44.2191	−	19.6876i	−1.56928	−	0.698688i
$795$	21.2801	−	23.9395i	0.754728	−	0.849047i
$796$	10.3243	−	4.59666i	0.365934	−	0.162924i
$797$	−7.64384	+	3.40326i	−0.270759	+	0.120550i	−0.537625	−	0.843184i	$-0.680678\pi$
$797$	−7.64384	+	3.40326i	−0.270759	+	0.120550i	0.266866	+	0.963734i	$0.414012\pi$
$798$	0.207452	−	1.34171i	0.00734373	−	0.0474961i
$799$	13.4432	+	23.2843i	0.475587	+	0.823741i
$800$	−28.7392	+	26.1600i	−1.01608	+	0.924894i
$801$	6.44261	−	31.4454i	0.227638	−	1.11107i
$802$	8.65961	−	26.6515i	0.305781	−	0.941098i
$803$	−1.20369	+	11.4524i	−0.0424775	+	0.404146i
$804$	−26.8442	+	17.5735i	−0.946722	+	0.619769i
$805$	−0.811919	+	1.60420i	−0.0286164	+	0.0565406i
$806$	5.63547	+	53.6179i	0.198501	+	1.88861i
$807$	23.9577	+	29.3639i	0.843352	+	1.03366i
$808$	−4.40763	−	1.96241i	−0.155060	−	0.0690372i
$809$	12.4306	+	38.2574i	0.437036	+	1.34506i	0.890986	+	0.454030i	$0.150014\pi$
$809$	12.4306	+	38.2574i	0.437036	+	1.34506i	−0.453951	+	0.891027i	$0.649986\pi$
$810$	37.8620	−	10.8551i	1.33033	−	0.381410i
$811$	3.05198	−	9.39304i	0.107170	−	0.329834i	−0.883064	−	0.469253i	$-0.844523\pi$
$811$	3.05198	−	9.39304i	0.107170	−	0.329834i	0.990234	+	0.139418i	$0.0445233\pi$
$812$	−6.30619	+	7.00373i	−0.221304	+	0.245783i
$813$	−11.0247	+	17.1140i	−0.386654	+	0.600214i
$814$	−24.8944	−	27.6480i	−0.872548	−	0.969062i
$815$	2.18255	+	13.5427i	0.0764513	+	0.474381i
$816$	27.9065	+	1.35965i	0.976923	+	0.0475973i
$817$	−1.69819	−	0.756084i	−0.0594122	−	0.0264520i
$818$	−42.8598			−1.49856
$819$	5.50523	+	12.1242i	0.192368	+	0.423654i
$820$	−25.9734	+	1.43171i	−0.907029	+	0.0499974i
$821$	1.75713	−	16.7179i	0.0613241	−	0.583460i	−0.920110	−	0.391660i	$-0.871901\pi$
$821$	1.75713	−	16.7179i	0.0613241	−	0.583460i	0.981434	−	0.191800i	$-0.0614324\pi$
$822$	12.7525	+	6.43880i	0.444796	+	0.224579i
$823$	20.7562	+	23.0521i	0.723514	+	0.803544i	0.986932	−	0.161138i	$-0.0515163\pi$
$823$	20.7562	+	23.0521i	0.723514	+	0.803544i	−0.263417	+	0.964682i	$0.584850\pi$
$824$	0.961840	−	1.66596i	0.0335073	−	0.0580363i
$825$	−0.925309	+	21.3712i	−0.0322151	+	0.744050i
$826$	2.62730	+	4.55063i	0.0914156	+	0.158337i
$827$	−12.1795	+	37.4846i	−0.423522	+	1.30347i	0.480880	+	0.876787i	$0.340317\pi$
$827$	−12.1795	+	37.4846i	−0.423522	+	1.30347i	−0.904402	+	0.426681i	$0.859683\pi$
$828$	−3.05025	−	0.966347i	−0.106004	−	0.0335829i
$829$	−19.1615	−	13.9216i	−0.665505	−	0.483518i	0.203012	−	0.979176i	$-0.434927\pi$
$829$	−19.1615	−	13.9216i	−0.665505	−	0.483518i	−0.868518	+	0.495658i	$0.834927\pi$
$830$	0.826282	+	0.314617i	0.0286807	+	0.0109205i
$831$	−10.0001	−	36.7795i	−0.346900	−	1.27587i
$832$	10.6002	−	18.3600i	0.367494	−	0.636519i
$833$	−1.99335	−	18.9654i	−0.0690653	−	0.657113i
$834$	−0.655046	+	1.01685i	−0.0226824	+	0.0352106i
$835$	−2.25982	+	45.4746i	−0.0782043	+	1.57371i
$836$	−0.405485	+	1.24795i	−0.0140240	+	0.0431614i
$837$	42.8578	−	11.9919i	1.48138	−	0.414501i
$838$	0.716591	+	2.20544i	0.0247542	+	0.0761856i
$839$	2.03863	−	0.433325i	0.0703814	−	0.0149600i	−0.172586	−	0.984994i	$-0.555212\pi$
$839$	2.03863	−	0.433325i	0.0703814	−	0.0149600i	0.242968	+	0.970034i	$0.421879\pi$
$840$	−0.876601	+	1.54095i	−0.0302456	+	0.0531679i
$841$	14.7522	+	3.13567i	0.508695	+	0.108126i
$842$	−2.42905	−	23.1109i	−0.0837107	−	0.796454i
$843$	0.791544	−	2.08492i	0.0272622	−	0.0718086i
$844$	47.3447	+	21.0792i	1.62967	+	0.725577i
$845$	−4.98908	−	3.22078i	−0.171630	−	0.110798i
$846$	−9.07324	−	41.1944i	−0.311945	−	1.41629i
$847$	−5.46942	−	3.97377i	−0.187932	−	0.136540i
$848$	−34.8675	+	7.41131i	−1.19735	+	0.254506i
$849$	−13.1475	+	2.13194i	−0.451222	+	0.0731682i
$850$	31.6172	−	18.4831i	1.08446	−	0.633965i
$851$	−2.24199	+	3.88324i	−0.0768545	+	0.133116i
$852$	−6.26207	+	40.5004i	−0.214535	+	1.38752i
$853$	4.52638	−	43.0656i	0.154980	−	1.47454i	−0.589973	−	0.807423i	$-0.700862\pi$
$853$	4.52638	−	43.0656i	0.154980	−	1.47454i	0.744953	−	0.667116i	$-0.232472\pi$
$854$	28.6513	+	20.8164i	0.980427	+	0.712322i
$855$	−1.62196	+	1.07667i	−0.0554699	+	0.0368212i
$856$	3.45151	−	2.50767i	0.117970	−	0.0857103i
$857$	−7.87916	−	13.6471i	−0.269147	−	0.466176i	0.699495	−	0.714638i	$-0.253408\pi$
$857$	−7.87916	−	13.6471i	−0.269147	−	0.466176i	−0.968642	+	0.248462i	$0.920075\pi$
$858$	−7.06573	−	25.9871i	−0.241220	−	0.887185i
$859$	−0.498797	−	0.106022i	−0.0170187	−	0.00361744i	0.199394	−	0.979919i	$-0.436102\pi$
$859$	−0.498797	−	0.106022i	−0.0170187	−	0.00361744i	−0.216413	+	0.976302i	$0.569436\pi$
$860$	−18.5893	−	18.4889i	−0.633890	−	0.630468i
$861$	−14.1615	+	5.49593i	−0.482624	+	0.187301i
$862$	−27.0724	+	30.0669i	−0.922088	+	1.02408i
$863$	−17.2401	−	53.0596i	−0.586860	−	1.80617i	−0.591668	−	0.806182i	$-0.701530\pi$
$863$	−17.2401	−	53.0596i	−0.586860	−	1.80617i	0.00480758	−	0.999988i	$-0.498470\pi$
$864$	−37.8618	−	14.0566i	−1.28809	−	0.478216i
$865$	29.3330	−	1.61690i	0.997351	−	0.0549761i
$866$	−17.3194	+	19.2352i	−0.588538	+	0.653637i
$867$	5.01373	+	1.32369i	0.170275	+	0.0449548i
$868$	10.8181	−	18.7374i	0.367189	−	0.635990i
$869$	4.11324	+	39.1349i	0.139532	+	1.32756i
$870$	28.2786	−	0.180514i	0.958736	−	0.00612001i
$871$	−3.40211	+	32.3689i	−0.115276	+	1.09678i
$872$	4.27981	+	3.10946i	0.144933	+	0.105300i
$873$	−0.243572	−	33.1226i	−0.00824368	−	1.12103i
$874$	0.330940			0.0111942
$875$	0.932582	+	15.4010i	0.0315270	+	0.520648i
$876$	−14.5907	+	2.36597i	−0.492975	+	0.0799386i
$877$	0.416955	+	0.463075i	0.0140796	+	0.0156369i	0.750143	−	0.661275i	$-0.229984\pi$
$877$	0.416955	+	0.463075i	0.0140796	+	0.0156369i	−0.736064	+	0.676912i	$0.763318\pi$
$878$	25.0047	−	11.1328i	0.843867	−	0.375714i
$879$	17.3991	+	8.78487i	0.586858	+	0.296306i
$880$	14.9316	−	18.5414i	0.503345	−	0.625030i
$881$	0.224011	−	0.162753i	0.00754711	−	0.00548330i	−0.584005	−	0.811750i	$-0.698515\pi$
$881$	0.224011	−	0.162753i	0.00754711	−	0.00548330i	0.591552	+	0.806267i	$0.298515\pi$
$882$	−6.00503	+	29.3096i	−0.202200	+	0.986906i
$883$	−11.9127	+	8.65510i	−0.400895	+	0.291267i	−0.769906	−	0.638158i	$-0.779697\pi$
$883$	−11.9127	+	8.65510i	−0.400895	+	0.291267i	0.369010	+	0.929425i	$0.379697\pi$
$884$	−14.7433	+	16.3741i	−0.495872	+	0.550722i
$885$	2.28258	−	7.18069i	0.0767280	−	0.241376i
$886$	0.0340214	+	0.0377846i	0.00114297	+	0.00126940i
$887$	−13.2379	−	2.81379i	−0.444484	−	0.0944779i	−0.0197678	−	0.999805i	$-0.506293\pi$
$887$	−13.2379	−	2.81379i	−0.444484	−	0.0944779i	−0.424716	+	0.905327i	$0.639626\pi$
$888$	−2.39438	+	3.71686i	−0.0803500	+	0.124730i
$889$	−18.6629	+	3.96692i	−0.625933	+	0.133046i
$890$	−11.9968	+	45.2622i	−0.402132	+	1.51719i
$891$	−20.1733	+	9.33962i	−0.675832	+	0.312889i
$892$	−0.156176	+	0.113468i	−0.00522915	+	0.00379920i
$893$	1.04245	+	1.80558i	0.0348843	+	0.0604214i
$894$	−76.5358	−	20.2064i	−2.55974	−	0.675803i
$895$	8.11767	+	8.07384i	0.271344	+	0.269879i
$896$	3.33336	−	1.48411i	0.111360	−	0.0495805i
$897$	−2.71562	+	1.77777i	−0.0906719	+	0.0593581i
$898$	−61.6347	+	13.1009i	−2.05678	+	0.437181i
$899$	31.9528			1.06569
$900$	−26.7828	+	6.05122i	−0.892759	+	0.201707i
$901$	30.9510			1.03113
$902$	30.0514	−	6.38763i	1.00060	−	0.212685i
$903$	−13.6674	−	6.90069i	−0.454821	−	0.229640i
$904$	2.24106	−	0.997782i	0.0745364	−	0.0331858i
$905$	−17.7279	+	9.09334i	−0.589295	+	0.302273i
$906$	19.2959	−	19.4383i	0.641064	−	0.645796i
$907$	3.57179	+	6.18652i	0.118599	+	0.205420i	0.919213	−	0.393761i	$-0.128826\pi$
$907$	3.57179	+	6.18652i	0.118599	+	0.205420i	−0.800614	+	0.599181i	$0.795493\pi$
$908$	14.8470	−	10.7870i	0.492716	−	0.357979i
$909$	−25.9084	−	35.1140i	−0.859329	−	1.16466i
$910$	−7.01021	−	18.1155i	−0.232386	−	0.600524i
$911$	12.3295	−	2.62071i	0.408493	−	0.0868280i	0.000918202	−	1.00000i	$-0.499708\pi$
$911$	12.3295	−	2.62071i	0.408493	−	0.0868280i	0.407575	+	0.913172i	$0.366374\pi$
$912$	2.16400	+	0.105434i	0.0716573	+	0.00349126i
$913$	−0.488116	−	0.103752i	−0.0161543	−	0.00343370i
$914$	14.9888	+	16.6468i	0.495786	+	0.550626i
$915$	−5.63050	−	50.4695i	−0.186139	−	1.66847i
$916$	−21.4807	+	23.8567i	−0.709741	+	0.788248i
$917$	8.24040	−	5.98700i	0.272122	−	0.197708i
$918$	32.1466	+	20.3757i	1.06100	+	0.672498i
$919$	32.7101	−	23.7653i	1.07901	−	0.783945i	0.101498	−	0.994836i	$-0.467637\pi$
$919$	32.7101	−	23.7653i	1.07901	−	0.783945i	0.977510	+	0.210891i	$0.0676365\pi$
$920$	−0.403859	−	0.153774i	−0.0133148	−	0.00506978i
$921$	−2.16666	−	38.6247i	−0.0713940	−	1.27273i
$922$	−4.62956	+	2.06121i	−0.152466	+	0.0678825i
$923$	27.8172	+	30.8942i	0.915615	+	1.01689i
$924$	−3.83597	+	10.1039i	−0.126194	+	0.332395i
$925$	0.208292	+	38.4786i	0.00684860	+	1.26517i
$926$	−55.8028			−1.83380
$927$	15.0034	−	8.80995i	0.492776	−	0.289357i
$928$	−23.4590	−	17.0440i	−0.770080	−	0.559496i
$929$	−4.51113	+	42.9205i	−0.148005	+	1.40818i	0.628375	+	0.777911i	$0.283721\pi$
$929$	−4.51113	+	42.9205i	−0.148005	+	1.40818i	−0.776380	+	0.630265i	$0.782946\pi$
$930$	−63.4157	+	13.9031i	−2.07948	+	0.455901i
$931$	−0.154573	−	1.47067i	−0.00506594	−	0.0481992i
$932$	−7.93644	+	13.7463i	−0.259967	+	0.450276i
$933$	−20.4119	+	20.5626i	−0.668256	+	0.673188i
$934$	−30.9699	+	34.3955i	−1.01336	+	1.12546i
$935$	−16.0287	+	13.0517i	−0.524194	+	0.426838i
$936$	−2.75980	+	1.62055i	−0.0902070	+	0.0529693i
$937$	4.03157	+	12.4079i	0.131706	+	0.405348i	0.995063	−	0.0992446i	$-0.0316426\pi$
$937$	4.03157	+	12.4079i	0.131706	+	0.405348i	−0.863357	+	0.504593i	$0.831643\pi$
$938$	18.2891	−	20.3121i	0.597160	−	0.663213i
$939$	−19.8371	−	15.9434i	−0.647360	−	0.520292i
$940$	4.67869	+	29.0313i	0.152602	+	0.946897i
$941$	54.3653	+	11.5557i	1.77226	+	0.376705i	0.974166	−	0.225833i	$-0.0725103\pi$
$941$	54.3653	+	11.5557i	1.77226	+	0.376705i	0.798091	+	0.602538i	$0.205844\pi$
$942$	−55.0912	−	14.5448i	−1.79497	−	0.473894i
$943$	−1.85142	−	3.20675i	−0.0602904	−	0.104426i
$944$	−6.78393	+	4.92881i	−0.220798	+	0.160419i
$945$	−13.7748	+	8.20723i	−0.448095	+	0.266981i
$946$	25.0517	+	18.2011i	0.814501	+	0.591770i
$947$	1.96736	−	18.7182i	0.0639305	−	0.608258i	−0.914913	−	0.403650i	$-0.867741\pi$
$947$	1.96736	−	18.7182i	0.0639305	−	0.608258i	0.978844	−	0.204608i	$-0.0655920\pi$
$948$	−47.0886	+	18.2746i	−1.52937	+	0.593530i
$949$	−7.49716	+	12.9855i	−0.243368	+	0.421526i
$950$	2.45175	−	1.43327i	0.0795452	−	0.0465013i
$951$	1.81647	−	4.78458i	0.0589032	−	0.155151i
$952$	−1.67567	+	0.356174i	−0.0543086	+	0.0115437i
$953$	−24.1648	−	17.5568i	−0.782775	−	0.568720i	0.123035	−	0.992402i	$-0.460737\pi$
$953$	−24.1648	−	17.5568i	−0.782775	−	0.568720i	−0.905811	+	0.423683i	$0.860737\pi$
$954$	−46.2911	−	14.6654i	−1.49873	−	0.474811i
$955$	−3.26560	+	2.65909i	−0.105672	+	0.0860463i
$956$	−16.9415	−	7.54286i	−0.547929	−	0.243954i
$957$	−15.7551	+	2.55479i	−0.509292	+	0.0825845i
$958$	−5.53926	−	52.7026i	−0.178965	−	1.70274i
$959$	−5.68864	−	1.20916i	−0.183696	−	0.0390458i
$960$	23.3879	+	10.2346i	0.754842	+	0.330320i
$961$	−41.4299	+	8.80620i	−1.33645	+	0.284071i
$962$	−14.9699	−	46.0725i	−0.482648	−	1.48544i
$963$	38.3446	−	4.31548i	1.23564	−	0.139065i
$964$	−4.60887	+	14.1846i	−0.148442	+	0.456857i
$965$	−2.07723	+	2.57942i	−0.0668686	+	0.0830343i
$966$	2.72252	+	0.132645i	0.0875956	+	0.00426780i
$967$	−4.02864	−	38.3299i	−0.129552	−	1.23261i	−0.845317	−	0.534266i	$-0.820588\pi$
$967$	−4.02864	−	38.3299i	−0.129552	−	1.23261i	0.715764	−	0.698342i	$-0.246078\pi$
$968$	0.812459	−	1.40722i	0.0261134	−	0.0452298i
$969$	−1.81886	−	0.480202i	−0.0584303	−	0.0154263i
$970$	−2.39828	+	48.2607i	−0.0770040	+	1.54956i
$971$	−22.5194	−	16.3613i	−0.722682	−	0.525059i	0.164558	−	0.986367i	$-0.447380\pi$
$971$	−22.5194	−	16.3613i	−0.722682	−	0.525059i	−0.887240	+	0.461308i	$0.847380\pi$
$972$	−18.3623	−	21.8420i	−0.588971	−	0.700584i
$973$	0.152164	−	0.468313i	0.00487816	−	0.0150134i
$974$	5.97962	+	10.3570i	0.191599	+	0.331860i
$975$	−12.4191	+	24.9316i	−0.397731	+	0.798451i
$976$	−28.2579	+	48.9441i	−0.904513	+	1.56666i
$977$	−0.846392	−	0.940013i	−0.0270785	−	0.0300737i	0.729453	−	0.684030i	$-0.239774\pi$
$977$	−0.846392	−	0.940013i	−0.0270785	−	0.0300737i	−0.756532	+	0.653957i	$0.773108\pi$
$978$	17.3992	−	11.3903i	0.556365	−	0.364223i
$979$	2.76251	−	26.2835i	0.0882902	−	0.840025i
$980$	5.34361	−	20.1607i	0.170695	−	0.644011i
$981$	19.7819	+	43.5658i	0.631587	+	1.39095i
$982$	47.1766			1.50547
$983$	44.7740	+	19.9347i	1.42807	+	0.635817i	0.967744	−	0.251934i	$-0.0810666\pi$
$983$	44.7740	+	19.9347i	1.42807	+	0.635817i	0.460324	+	0.887751i	$0.347733\pi$
$984$	−1.66951	−	3.24703i	−0.0532221	−	0.103512i
$985$	30.6033	+	30.4381i	0.975102	+	0.969838i
$986$	18.2849	+	20.3074i	0.582309	+	0.646720i
$987$	7.85216	+	15.2717i	0.249937	+	0.486102i
$988$	−1.14327	+	1.26973i	−0.0363722	+	0.0403954i
$989$	1.15328	−	3.54944i	0.0366722	−	0.112866i
$990$	30.1571	−	11.9257i	0.958456	−	0.379023i
$991$	−16.1594	−	49.7336i	−0.513321	−	1.57984i	−0.786316	−	0.617824i	$-0.788014\pi$
$991$	−16.1594	−	49.7336i	−0.513321	−	1.57984i	0.272995	−	0.962015i	$-0.411986\pi$
$992$	60.8143	+	27.0763i	1.93086	+	0.859673i
$993$	−7.11647	+	18.7448i	−0.225834	+	0.594847i
$994$	−3.64926	−	34.7204i	−0.115747	−	1.10126i
$995$	13.6409	+	2.12268i	0.432445	+	0.0672933i
$996$	−0.0358752	−	0.639539i	−0.00113675	−	0.0202646i
$997$	1.90356	−	18.1112i	0.0602864	−	0.573587i	−0.922129	−	0.386881i	$-0.873552\pi$
$997$	1.90356	−	18.1112i	0.0602864	−	0.573587i	0.982416	−	0.186706i	$-0.0597810\pi$
$998$	−5.05675	+	15.5631i	−0.160069	+	0.492641i
$999$	−35.4278	+	18.5464i	−1.12089	+	0.586783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.24	yes	224
3.2	odd	2		675.2.r.a.496.5		224
9.2	odd	6		675.2.r.a.46.24		224
9.7	even	3	inner	225.2.q.a.196.5	yes	224
25.6	even	5	inner	225.2.q.a.31.5	✓	224
75.56	odd	10		675.2.r.a.631.24		224
225.56	odd	30		675.2.r.a.181.5		224
225.106	even	15	inner	225.2.q.a.106.24	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.5	✓	224	25.6	even	5	inner
225.2.q.a.106.24	yes	224	225.106	even	15	inner
225.2.q.a.121.24	yes	224	1.1	even	1	trivial
225.2.q.a.196.5	yes	224	9.7	even	3	inner
675.2.r.a.46.24		224	9.2	odd	6
675.2.r.a.181.5		224	225.56	odd	30
675.2.r.a.496.5		224	3.2	odd	2
675.2.r.a.631.24		224	75.56	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)

\(f(q)\)	\(=\)	\(q+(1.91440 - 0.406919i) q^{2} +(-0.0970075 - 1.72933i) q^{3} +(1.67227 - 0.744541i) q^{4} +(2.20948 + 0.343819i) q^{5} +(-0.889410 - 3.27117i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 + 0.194964i) q^{8} +(-2.98118 + 0.335516i) q^{9} +O(q^{10})\)	\(q+(1.91440 - 0.406919i) q^{2} +(-0.0970075 - 1.72933i) q^{3} +(1.67227 - 0.744541i) q^{4} +(2.20948 + 0.343819i) q^{5} +(-0.889410 - 3.27117i) q^{6} +(0.690014 + 1.19514i) q^{7} +(-0.268345 + 0.194964i) q^{8} +(-2.98118 + 0.335516i) q^{9} +(4.36974 - 0.240869i) q^{10} +(-2.41607 + 0.513552i) q^{11} +(-1.44978 - 2.81968i) q^{12} +(-3.14597 - 0.668696i) q^{13} +(1.80729 + 2.00720i) q^{14} +(0.380242 - 3.85427i) q^{15} +(-2.88411 + 3.20312i) q^{16} +(3.02773 - 2.19977i) q^{17} +(-5.57065 + 1.85541i) q^{18} +(0.234784 - 0.170581i) q^{19} +(3.95082 - 1.07009i) q^{20} +(1.99986 - 1.30920i) q^{21} +(-4.41636 + 1.96629i) q^{22} +(0.389869 + 0.432993i) q^{23} +(0.363189 + 0.445145i) q^{24} +(4.76358 + 1.51932i) q^{25} -6.29476 q^{26} +(0.869416 + 5.12290i) q^{27} +(2.04372 + 1.48485i) q^{28} +(-0.389966 + 3.71028i) q^{29} +(-0.840441 - 7.53336i) q^{30} +(-0.895263 - 8.51786i) q^{31} +(-3.88624 + 6.73116i) q^{32} +(1.12248 + 4.12837i) q^{33} +(4.90116 - 5.44329i) q^{34} +(1.11366 + 2.87787i) q^{35} +(-4.73552 + 2.78068i) q^{36} +(2.37815 + 7.31918i) q^{37} +(0.380060 - 0.422099i) q^{38} +(-0.851215 + 5.50529i) q^{39} +(-0.659934 + 0.338506i) q^{40} +(-6.21628 - 1.32131i) q^{41} +(3.29579 - 3.32012i) q^{42} +(-3.20269 - 5.54723i) q^{43} +(-3.65796 + 2.65766i) q^{44} +(-6.70220 - 0.283671i) q^{45} +(0.922560 + 0.670279i) q^{46} +(-0.750946 + 7.14477i) q^{47} +(5.81905 + 4.67685i) q^{48} +(2.54776 - 4.41285i) q^{49} +(9.73765 + 0.970205i) q^{50} +(-4.09785 - 5.02255i) q^{51} +(-5.75877 + 1.22407i) q^{52} +(6.69073 + 4.86110i) q^{53} +(3.74902 + 9.45352i) q^{54} +(-5.51482 + 0.303989i) q^{55} +(-0.418171 - 0.186182i) q^{56} +(-0.317767 - 0.389473i) q^{57} +(0.763232 + 7.26166i) q^{58} +(1.90295 + 0.404485i) q^{59} +(-2.23380 - 6.72848i) q^{60} +(12.8255 - 2.72614i) q^{61} +(-5.17998 - 15.9423i) q^{62} +(-2.45804 - 3.33141i) q^{63} +(-2.03692 + 6.26900i) q^{64} +(-6.72104 - 2.55911i) q^{65} +(3.82879 + 7.44661i) q^{66} +(-1.05779 - 10.0642i) q^{67} +(3.42535 - 5.93288i) q^{68} +(0.710969 - 0.716217i) q^{69} +(3.30305 + 5.05624i) q^{70} +(-10.4571 - 7.59752i) q^{71} +(0.734571 - 0.671257i) q^{72} +(1.44065 - 4.43387i) q^{73} +(7.53104 + 13.0442i) q^{74} +(2.16531 - 8.38519i) q^{75} +(0.265618 - 0.460064i) q^{76} +(-2.28089 - 2.53318i) q^{77} +(0.610639 + 10.8857i) q^{78} +(1.66525 - 15.8438i) q^{79} +(-7.47366 + 6.08562i) q^{80} +(8.77486 - 2.00047i) q^{81} -12.4381 q^{82} +(0.184562 + 0.0821725i) q^{83} +(2.36954 - 3.67831i) q^{84} +(7.44602 - 3.81936i) q^{85} +(-8.38852 - 9.31639i) q^{86} +(6.45414 + 0.314456i) q^{87} +(0.548216 - 0.608856i) q^{88} +(-3.30633 + 10.1758i) q^{89} +(-12.9462 + 2.18419i) q^{90} +(-1.37158 - 4.22128i) q^{91} +(0.974347 + 0.433807i) q^{92} +(-14.6434 + 2.37450i) q^{93} +(1.46973 + 13.9836i) q^{94} +(0.577400 - 0.296171i) q^{95} +(12.0174 + 6.06762i) q^{96} +(-1.15412 + 10.9807i) q^{97} +(3.08177 - 9.48471i) q^{98} +(7.03043 - 2.34162i) 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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