LMFDB - Embedded newform 225.2.q.a.121.5

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			121.5
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24869 + 0.477974i) q^{2} +(1.49729 - 0.870698i) q^{3} +(3.00107 - 1.33616i) q^{4} +(-2.07749 + 0.827061i) q^{5} +(-2.95078 + 2.67360i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 + 1.73649i) q^{8} +(1.48377 - 2.60738i) q^{9} +O(q^{10})$	\(q+(-2.24869 + 0.477974i) q^{2} +(1.49729 - 0.870698i) q^{3} +(3.00107 - 1.33616i) q^{4} +(-2.07749 + 0.827061i) q^{5} +(-2.95078 + 2.67360i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 + 1.73649i) q^{8} +(1.48377 - 2.60738i) q^{9} +(4.27633 - 2.85279i) q^{10} +(-1.90993 + 0.405969i) q^{11} +(3.33008 - 4.61365i) q^{12} +(-3.48590 - 0.740952i) q^{13} +(4.98536 + 5.53681i) q^{14} +(-2.39049 + 3.04722i) q^{15} +(0.148264 - 0.164664i) q^{16} +(0.726639 - 0.527934i) q^{17} +(-2.09028 + 6.57240i) q^{18} +(0.733140 - 0.532657i) q^{19} +(-5.12960 + 5.25793i) q^{20} +(-4.87002 - 2.79150i) q^{21} +(4.10081 - 1.82580i) q^{22} +(-5.68729 - 6.31638i) q^{23} +(-2.06669 + 4.68108i) q^{24} +(3.63194 - 3.43642i) q^{25} +8.19288 q^{26} +(-0.0486015 - 5.19593i) q^{27} +(-8.61318 - 6.25784i) q^{28} +(0.780596 - 7.42687i) q^{29} +(3.91899 - 7.99485i) q^{30} +(0.809799 + 7.70472i) q^{31} +(2.69961 - 4.67586i) q^{32} +(-2.50625 + 2.27083i) q^{33} +(-1.38165 + 1.53448i) q^{34} +(5.68771 + 4.49063i) q^{35} +(0.969015 - 9.80748i) q^{36} +(-1.33249 - 4.10099i) q^{37} +(-1.39401 + 1.54820i) q^{38} +(-5.86456 + 1.92575i) q^{39} +(3.52918 - 5.58430i) q^{40} +(-4.43771 - 0.943263i) q^{41} +(12.2854 + 3.94948i) q^{42} +(-0.885445 - 1.53364i) q^{43} +(-5.18939 + 3.77032i) q^{44} +(-0.926058 + 6.64398i) q^{45} +(15.8080 + 11.4852i) q^{46} +(-0.808594 + 7.69326i) q^{47} +(0.0786221 - 0.375643i) q^{48} +(-1.75159 + 3.03384i) q^{49} +(-6.52459 + 9.46343i) q^{50} +(0.628320 - 1.42316i) q^{51} +(-11.4515 + 2.43408i) q^{52} +(5.94096 + 4.31636i) q^{53} +(2.59281 + 11.6608i) q^{54} +(3.63211 - 2.42303i) q^{55} +(8.74672 + 3.89429i) q^{56} +(0.633941 - 1.43589i) q^{57} +(1.79453 + 17.0739i) q^{58} +(13.5034 + 2.87024i) q^{59} +(-3.10245 + 12.3390i) q^{60} +(6.17017 - 1.31151i) q^{61} +(-5.50365 - 16.9385i) q^{62} +(-9.72239 + 0.0606264i) q^{63} +(-3.97259 + 12.2264i) q^{64} +(7.85475 - 1.34373i) q^{65} +(4.55039 - 6.30432i) q^{66} +(1.26718 + 12.0564i) q^{67} +(1.47529 - 2.55527i) q^{68} +(-14.0152 - 4.50555i) q^{69} +(-14.9363 - 7.37947i) q^{70} +(-8.02747 - 5.83230i) q^{71} +(0.981371 + 8.80840i) q^{72} +(0.246766 - 0.759468i) q^{73} +(4.95654 + 8.58498i) q^{74} +(2.44599 - 8.30766i) q^{75} +(1.48849 - 2.57813i) q^{76} +(4.23433 + 4.70270i) q^{77} +(12.2671 - 7.13352i) q^{78} +(0.0254700 - 0.242331i) q^{79} +(-0.171830 + 0.464711i) q^{80} +(-4.59685 - 7.73750i) q^{81} +10.4299 q^{82} +(4.22548 + 1.88131i) q^{83} +(-18.3451 - 1.87034i) q^{84} +(-1.07295 + 1.69775i) q^{85} +(2.72413 + 3.02546i) q^{86} +(-5.29778 - 11.7999i) q^{87} +(3.85993 - 4.28688i) q^{88} +(2.11267 - 6.50212i) q^{89} +(-1.09323 - 15.3829i) q^{90} +(3.56906 + 10.9844i) q^{91} +(-25.5076 - 11.3567i) q^{92} +(7.92099 + 10.8311i) q^{93} +(-1.85890 - 17.6863i) q^{94} +(-1.08255 + 1.71294i) q^{95} +(-0.0291570 - 9.35167i) q^{96} +(0.495505 - 4.71441i) q^{97} +(2.48869 - 7.65939i) q^{98} +(-1.77539 + 5.58228i) 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 $

$2$	−2.24869	+	0.477974i	−1.59007	+	0.337979i	−0.916152	−	0.400831i	$-0.868721\pi$
$2$	−2.24869	+	0.477974i	−1.59007	+	0.337979i	−0.673914	+	0.738810i	$0.735388\pi$
$3$	1.49729	−	0.870698i	0.864462	−	0.502698i
$3$	1.49729	−	0.870698i	0.864462	−	0.502698i
$4$	3.00107	−	1.33616i	1.50053	−	0.668081i
$5$	−2.07749	+	0.827061i	−0.929082	+	0.369873i
$5$	−2.07749	+	0.827061i	−0.929082	+	0.369873i
$6$	−2.95078	+	2.67360i	−1.20465	+	1.09149i
$7$	−1.62043	−	2.80667i	−0.612465	−	1.06082i	−0.990824	−	0.135161i	$-0.956845\pi$
$7$	−1.62043	−	2.80667i	−0.612465	−	1.06082i	0.378359	−	0.925659i	$-0.376489\pi$
$8$	−2.39008	+	1.73649i	−0.845021	+	0.613944i
$9$	1.48377	−	2.60738i	0.494590	−	0.869126i
$10$	4.27633	−	2.85279i	1.35229	−	0.902132i
$11$	−1.90993	+	0.405969i	−0.575866	+	0.122404i	−0.486633	−	0.873607i	$-0.661775\pi$
$11$	−1.90993	+	0.405969i	−0.575866	+	0.122404i	−0.0892334	+	0.996011i	$0.528442\pi$
$12$	3.33008	−	4.61365i	0.961312	−	1.33185i
$13$	−3.48590	−	0.740952i	−0.966816	−	0.205503i	−0.302661	−	0.953098i	$-0.597875\pi$
$13$	−3.48590	−	0.740952i	−0.966816	−	0.205503i	−0.664155	+	0.747595i	$0.731208\pi$
$14$	4.98536	+	5.53681i	1.33239	+	1.47977i
$15$	−2.39049	+	3.04722i	−0.617222	+	0.786789i
$16$	0.148264	−	0.164664i	0.0370660	−	0.0411660i
$17$	0.726639	−	0.527934i	0.176236	−	0.128043i	−0.496170	−	0.868225i	$-0.665261\pi$
$17$	0.726639	−	0.527934i	0.176236	−	0.128043i	0.672406	+	0.740182i	$0.265261\pi$
$18$	−2.09028	+	6.57240i	−0.492684	+	1.54913i
$19$	0.733140	−	0.532657i	0.168194	−	0.122200i	−0.500504	−	0.865734i	$-0.666852\pi$
$19$	0.733140	−	0.532657i	0.168194	−	0.122200i	0.668698	+	0.743534i	$0.266852\pi$
$20$	−5.12960	+	5.25793i	−1.14701	+	1.17571i
$21$	−4.87002	−	2.79150i	−1.06272	−	0.609155i
$22$	4.10081	−	1.82580i	0.874295	−	0.389261i
$23$	−5.68729	−	6.31638i	−1.18588	−	1.31706i	−0.937332	−	0.348437i	$-0.886713\pi$
$23$	−5.68729	−	6.31638i	−1.18588	−	1.31706i	−0.248550	−	0.968619i	$-0.579954\pi$
$24$	−2.06669	+	4.68108i	−0.421861	+	0.955521i
$25$	3.63194	−	3.43642i	0.726388	−	0.687285i
$26$	8.19288			1.60676
$27$	−0.0486015	−	5.19593i	−0.00935336	−	0.999956i
$28$	−8.61318	−	6.25784i	−1.62774	−	1.18262i
$29$	0.780596	−	7.42687i	0.144953	−	1.37914i	−0.644162	−	0.764889i	$-0.722794\pi$
$29$	0.780596	−	7.42687i	0.144953	−	1.37914i	0.789115	−	0.614246i	$-0.210540\pi$
$30$	3.91899	−	7.99485i	0.715506	−	1.45965i
$31$	0.809799	+	7.70472i	0.145444	+	1.38381i	0.787104	+	0.616820i	$0.211579\pi$
$31$	0.809799	+	7.70472i	0.145444	+	1.38381i	−0.641660	+	0.766989i	$0.721754\pi$
$32$	2.69961	−	4.67586i	0.477228	−	0.826582i
$33$	−2.50625	+	2.27083i	−0.436282	+	0.395300i
$34$	−1.38165	+	1.53448i	−0.236951	+	0.263161i
$35$	5.68771	+	4.49063i	0.961399	+	0.759055i
$36$	0.969015	−	9.80748i	0.161503	−	1.63458i
$37$	−1.33249	−	4.10099i	−0.219061	−	0.674199i	−0.998840	−	0.0481453i	$-0.984669\pi$
$37$	−1.33249	−	4.10099i	−0.219061	−	0.674199i	0.779780	−	0.626054i	$-0.215331\pi$
$38$	−1.39401	+	1.54820i	−0.226138	+	0.251152i
$39$	−5.86456	+	1.92575i	−0.939082	+	0.308366i
$40$	3.52918	−	5.58430i	0.558013	−	0.882955i
$41$	−4.43771	−	0.943263i	−0.693053	−	0.147313i	−0.152099	−	0.988365i	$-0.548603\pi$
$41$	−4.43771	−	0.943263i	−0.693053	−	0.147313i	−0.540954	+	0.841052i	$0.681937\pi$
$42$	12.2854	+	3.94948i	1.89568	+	0.609417i
$43$	−0.885445	−	1.53364i	−0.135029	−	0.233877i	0.790579	−	0.612359i	$-0.209779\pi$
$43$	−0.885445	−	1.53364i	−0.135029	−	0.233877i	−0.925609	+	0.378482i	$0.876446\pi$
$44$	−5.18939	+	3.77032i	−0.782331	+	0.568397i
$45$	−0.926058	+	6.64398i	−0.138049	+	0.990425i
$46$	15.8080	+	11.4852i	2.33077	+	1.69340i
$47$	−0.808594	+	7.69326i	−0.117946	+	1.12218i	0.762157	+	0.647393i	$0.224141\pi$
$47$	−0.808594	+	7.69326i	−0.117946	+	1.12218i	−0.880102	+	0.474784i	$0.842526\pi$
$48$	0.0786221	−	0.375643i	0.0113481	−	0.0542194i
$49$	−1.75159	+	3.03384i	−0.250227	+	0.433406i
$50$	−6.52459	+	9.46343i	−0.922717	+	1.33833i
$51$	0.628320	−	1.42316i	0.0879824	−	0.199282i
$52$	−11.4515	+	2.43408i	−1.58803	+	0.337547i
$53$	5.94096	+	4.31636i	0.816053	+	0.592897i	0.915579	−	0.402137i	$-0.131733\pi$
$53$	5.94096	+	4.31636i	0.816053	+	0.592897i	−0.0995259	+	0.995035i	$0.531733\pi$
$54$	2.59281	+	11.6608i	0.352837	+	1.58683i
$55$	3.63211	−	2.42303i	0.489753	−	0.326721i
$56$	8.74672	+	3.89429i	1.16883	+	0.520397i
$57$	0.633941	−	1.43589i	0.0839675	−	0.190188i
$58$	1.79453	+	17.0739i	0.235634	+	2.24191i
$59$	13.5034	+	2.87024i	1.75799	+	0.373673i	0.970207	−	0.242277i	$-0.0778942\pi$
$59$	13.5034	+	2.87024i	1.75799	+	0.373673i	0.787786	+	0.615950i	$0.211228\pi$
$60$	−3.10245	+	12.3390i	−0.400525	+	1.59296i
$61$	6.17017	−	1.31151i	0.790009	−	0.167922i	0.204800	−	0.978804i	$-0.434346\pi$
$61$	6.17017	−	1.31151i	0.790009	−	0.167922i	0.585209	+	0.810882i	$0.301012\pi$
$62$	−5.50365	−	16.9385i	−0.698964	−	2.15119i
$63$	−9.72239	+	0.0606264i	−1.22491	+	0.00763821i
$64$	−3.97259	+	12.2264i	−0.496573	+	1.52830i
$65$	7.85475	−	1.34373i	0.974261	−	0.166670i
$66$	4.55039	−	6.30432i	0.560114	−	0.776008i
$67$	1.26718	+	12.0564i	0.154811	+	1.47292i	0.745759	+	0.666215i	$0.232087\pi$
$67$	1.26718	+	12.0564i	0.154811	+	1.47292i	−0.590949	+	0.806709i	$0.701246\pi$
$68$	1.47529	−	2.55527i	0.178905	−	0.309872i
$69$	−14.0152	−	4.50555i	−1.68723	−	0.542405i
$70$	−14.9363	−	7.37947i	−1.78523	−	0.882015i
$71$	−8.02747	−	5.83230i	−0.952686	−	0.692167i	−0.00124504	−	0.999999i	$-0.500396\pi$
$71$	−8.02747	−	5.83230i	−0.952686	−	0.692167i	−0.951441	+	0.307833i	$0.900396\pi$
$72$	0.981371	+	8.80840i	0.115656	+	1.03808i
$73$	0.246766	−	0.759468i	0.0288818	−	0.0888891i	−0.935577	−	0.353124i	$-0.885119\pi$
$73$	0.246766	−	0.759468i	0.0288818	−	0.0888891i	0.964458	+	0.264235i	$0.0851194\pi$
$74$	4.95654	+	8.58498i	0.576186	+	0.997983i
$75$	2.44599	−	8.30766i	0.282439	−	0.959285i
$76$	1.48849	−	2.57813i	0.170741	−	0.295732i
$77$	4.23433	+	4.70270i	0.482547	+	0.535922i
$78$	12.2671	−	7.13352i	1.38898	−	0.807713i
$79$	0.0254700	−	0.242331i	0.00286560	−	0.0272644i	−0.992996	−	0.118151i	$-0.962303\pi$
$79$	0.0254700	−	0.242331i	0.00286560	−	0.0272644i	0.995861	+	0.0908865i	$0.0289700\pi$
$80$	−0.171830	+	0.464711i	−0.0192112	+	0.0519563i
$81$	−4.59685	−	7.73750i	−0.510761	−	0.859723i
$82$	10.4299			1.15179
$83$	4.22548	+	1.88131i	0.463807	+	0.206500i	0.625317	−	0.780371i	$-0.284970\pi$
$83$	4.22548	+	1.88131i	0.463807	+	0.206500i	−0.161510	+	0.986871i	$0.551636\pi$
$84$	−18.3451	−	1.87034i	−2.00162	−	0.204071i
$85$	−1.07295	+	1.69775i	−0.116378	+	0.184147i
$86$	2.72413	+	3.02546i	0.293751	+	0.326243i
$87$	−5.29778	−	11.7999i	−0.567982	−	1.26508i
$88$	3.85993	−	4.28688i	0.411470	−	0.456983i
$89$	2.11267	−	6.50212i	0.223942	−	0.689224i	−0.774455	−	0.632629i	$-0.781976\pi$
$89$	2.11267	−	6.50212i	0.223942	−	0.689224i	0.998397	−	0.0565946i	$-0.0180243\pi$
$90$	−1.09323	−	15.3829i	−0.115237	−	1.62150i
$91$	3.56906	+	10.9844i	0.374139	+	1.15148i
$92$	−25.5076	−	11.3567i	−2.65936	−	1.18402i
$93$	7.92099	+	10.8311i	0.821368	+	1.12314i
$94$	−1.85890	−	17.6863i	−0.191731	−	1.82420i
$95$	−1.08255	+	1.71294i	−0.111067	+	0.175744i
$96$	−0.0291570	−	9.35167i	−0.00297583	−	0.954450i
$97$	0.495505	−	4.71441i	0.0503109	−	0.478676i	−0.940138	−	0.340794i	$-0.889304\pi$
$97$	0.495505	−	4.71441i	0.0503109	−	0.478676i	0.990449	−	0.137882i	$-0.0440293\pi$
$98$	2.48869	−	7.65939i	0.251395	−	0.773715i
$99$	−1.77539	+	5.58228i	−0.178433	+	0.561040i
$100$	6.30808	−	15.1658i	0.630808	−	1.51658i
$101$	5.99315	+	10.3804i	0.596341	+	1.03289i	0.993356	+	0.115080i	$0.0367126\pi$
$101$	5.99315	+	10.3804i	0.596341	+	1.03289i	−0.397016	+	0.917812i	$0.629954\pi$
$102$	−0.732667	+	3.50056i	−0.0725449	+	0.346607i
$103$	2.01495	−	0.897113i	0.198539	−	0.0883952i	−0.305059	−	0.952334i	$-0.598676\pi$
$103$	2.01495	−	0.897113i	0.198539	−	0.0883952i	0.503598	+	0.863938i	$0.332009\pi$
$104$	9.61825	−	4.28232i	0.943147	−	0.419916i
$105$	12.4262	+	1.77151i	1.21267	+	0.172882i
$106$	−15.4225	−	6.86654i	−1.49797	−	0.666937i
$107$	−4.62059			−0.446689			−0.223344	−	0.974740i	$-0.571697\pi$
$107$	−4.62059			−0.446689			−0.223344	+	0.974740i	$0.571697\pi$
$108$	−7.08845	−	15.5284i	−0.682086	−	1.49422i
$109$	−4.18621	−	12.8838i	−0.400966	−	1.23405i	−0.924217	−	0.381867i	$-0.875281\pi$
$109$	−4.18621	−	12.8838i	−0.400966	−	1.23405i	0.523251	−	0.852178i	$-0.324719\pi$
$110$	−7.00935	+	7.18469i	−0.668315	+	0.685034i
$111$	−5.56586	−	4.98019i	−0.528288	−	0.472699i
$112$	−0.702408	−	0.149302i	−0.0663714	−	0.0141077i
$113$	16.5497	+	3.51775i	1.55687	+	0.330922i	0.904329	−	0.426836i	$-0.140372\pi$
$113$	16.5497	+	3.51775i	1.55687	+	0.330922i	0.652536	+	0.757758i	$0.273705\pi$
$114$	−0.739222	+	3.53188i	−0.0692344	+	0.330790i
$115$	17.0393	+	8.41848i	1.58893	+	0.785027i
$116$	−7.58088	−	23.3315i	−0.703867	−	2.16628i
$117$	−7.10422	+	7.98967i	−0.656785	+	0.738645i
$118$	−31.7369			−2.92162
$119$	−2.65920	−	1.18395i	−0.243769	−	0.108533i
$120$	0.421986	−	11.4342i	0.0385219	−	1.04379i
$121$	−6.56597	+	2.92336i	−0.596906	+	0.265760i
$122$	−13.2479	+	5.89836i	−1.19941	+	0.534013i
$123$	−7.46584	+	2.45156i	−0.673172	+	0.221050i
$124$	12.7250	+	22.0404i	1.14274	+	1.97928i
$125$	−4.70319	+	10.1430i	−0.420666	+	0.907215i
$126$	21.8337	−	4.78338i	1.94510	−	0.426138i
$127$	−2.60072	+	8.00418i	−0.230776	+	0.710256i	0.766877	+	0.641794i	$0.221809\pi$
$127$	−2.60072	+	8.00418i	−0.230776	+	0.710256i	−0.997654	+	0.0684626i	$0.978191\pi$
$128$	1.96050	−	18.6529i	0.173285	−	1.64870i
$129$	−2.66110	−	1.52535i	−0.234297	−	0.134299i
$130$	−17.0206	+	6.77601i	−1.49281	+	0.594295i
$131$	−1.51655	−	14.4290i	−0.132501	−	1.26067i	−0.835506	−	0.549481i	$-0.814825\pi$
$131$	−1.51655	−	14.4290i	−0.132501	−	1.26067i	0.703005	−	0.711185i	$-0.251841\pi$
$132$	−4.48724	+	10.1637i	−0.390564	+	0.884633i
$133$	−2.68299	−	1.19455i	−0.232645	−	0.103580i
$134$	−8.61215	−	26.5055i	−0.743976	−	2.28972i
$135$	4.39832	+	10.7543i	0.378547	+	0.925582i
$136$	−0.819971	+	2.52361i	−0.0703119	+	0.216398i
$137$	−4.03189	+	4.47786i	−0.344467	+	0.382570i	−0.890338	−	0.455299i	$-0.849532\pi$
$137$	−4.03189	+	4.47786i	−0.344467	+	0.382570i	0.545871	+	0.837869i	$0.316199\pi$
$138$	33.6694	+	3.43270i	2.86613	+	0.292210i
$139$	−5.52782	−	6.13927i	−0.468864	−	0.520726i	0.461611	−	0.887083i	$-0.347272\pi$
$139$	−5.52782	−	6.13927i	−0.468864	−	0.520726i	−0.930475	+	0.366357i	$0.880605\pi$
$140$	23.0694	+	5.87699i	1.94972	+	0.496696i
$141$	5.48780	+	12.2231i	0.462156	+	1.02937i
$142$	20.8390	+	9.27812i	1.74877	+	0.778603i
$143$	6.95864			0.581911
$144$	−0.209351	−	0.630904i	−0.0174460	−	0.0525753i
$145$	4.52079	+	16.0749i	0.375432	+	1.33494i
$146$	−0.191895	+	1.82576i	−0.0158813	+	0.151101i
$147$	0.0189180	+	6.06765i	0.00156033	+	0.500451i
$148$	−9.47849	−	10.5269i	−0.779127	−	0.865308i
$149$	5.47333	−	9.48009i	0.448393	−	0.776639i	−0.549889	−	0.835238i	$-0.685330\pi$
$149$	5.47333	−	9.48009i	0.448393	−	0.776639i	0.998282	+	0.0585987i	$0.0186632\pi$
$150$	−1.52943	+	19.8505i	−0.124878	+	1.62079i
$151$	−10.5024	−	18.1907i	−0.854675	−	1.48034i	−0.876946	−	0.480589i	$-0.840423\pi$
$151$	−10.5024	−	18.1907i	−0.854675	−	1.48034i	0.0222707	−	0.999752i	$-0.492910\pi$
$152$	−0.827306	+	2.54619i	−0.0671034	+	0.206523i
$153$	−0.298359	−	2.67796i	−0.0241209	−	0.216500i
$154$	−11.7695	−	8.55102i	−0.948411	−	0.689061i
$155$	−8.05462	−	15.3367i	−0.646963	−	1.23188i
$156$	−15.0268	+	13.6153i	−1.20311	+	1.09010i
$157$	3.25622	−	5.63994i	0.259875	−	0.450116i	−0.706333	−	0.707879i	$-0.749652\pi$
$157$	3.25622	−	5.63994i	0.259875	−	0.450116i	0.966208	+	0.257763i	$0.0829854\pi$
$158$	0.0585537	+	0.557102i	0.00465829	+	0.0443206i
$159$	12.6536	+	1.29007i	1.00350	+	0.102309i
$160$	−1.74119	+	11.9468i	−0.137653	+	0.944477i
$161$	−8.51211	+	26.1976i	−0.670848	+	2.06466i
$162$	14.0352	+	15.2021i	1.10271	+	1.19439i
$163$	−1.26328	−	3.88796i	−0.0989474	−	0.304529i	0.889315	−	0.457295i	$-0.151182\pi$
$163$	−1.26328	−	3.88796i	−0.0989474	−	0.304529i	−0.988262	+	0.152766i	$0.951182\pi$
$164$	−14.5782	+	3.09869i	−1.13837	+	0.241967i
$165$	3.32860	−	6.79045i	0.259131	−	0.528636i
$166$	−10.4010	−	2.21081i	−0.807276	−	0.171592i
$167$	−1.75234	−	16.6724i	−0.135600	−	1.29015i	−0.824735	−	0.565519i	$-0.808676\pi$
$167$	−1.75234	−	16.6724i	−0.135600	−	1.29015i	0.689135	−	0.724633i	$-0.257991\pi$
$168$	16.4872	−	1.78486i	1.27201	−	0.137705i
$169$	−0.273579	−	0.121805i	−0.0210445	−	0.00936963i
$170$	1.60126	−	4.33057i	0.122811	−	0.332140i
$171$	−0.301028	−	2.70191i	−0.0230202	−	0.206621i
$172$	−4.70647	−	3.41945i	−0.358865	−	0.260730i
$173$	6.43913	−	1.36868i	0.489558	−	0.104059i	0.0434826	−	0.999054i	$-0.486155\pi$
$173$	6.43913	−	1.36868i	0.489558	−	0.104059i	0.446075	+	0.894995i	$0.352821\pi$
$174$	17.5531	+	24.0021i	1.33070	+	1.81959i
$175$	−15.5302	−	4.62516i	−1.17397	−	0.349630i
$176$	−0.216326	+	0.374687i	−0.0163062	+	0.0282431i
$177$	22.7176	−	7.45980i	1.70756	−	0.560713i
$178$	−1.64289	+	15.6311i	−0.123140	+	1.17160i
$179$	−8.82628	−	6.41267i	−0.659707	−	0.479305i	0.206857	−	0.978371i	$-0.433677\pi$
$179$	−8.82628	−	6.41267i	−0.659707	−	0.479305i	−0.866564	+	0.499066i	$0.833677\pi$
$180$	6.09826	+	21.1764i	0.454537	+	1.57839i
$181$	7.04839	−	5.12096i	0.523903	−	0.380638i	−0.294169	−	0.955753i	$-0.595043\pi$
$181$	7.04839	−	5.12096i	0.523903	−	0.380638i	0.818072	+	0.575116i	$0.195043\pi$
$182$	−13.2760	−	22.9947i	−0.984082	−	1.70448i
$183$	8.09662	−	7.33607i	0.598519	−	0.542298i
$184$	24.5614	+	5.22070i	1.81069	+	0.384875i
$185$	6.16002	+	7.41773i	0.452893	+	0.545362i
$186$	−22.9889	−	20.5699i	−1.68563	−	1.50825i
$187$	−1.17351	+	1.30331i	−0.0858153	+	0.0953076i
$188$	7.85279	+	24.1684i	0.572723	+	1.76266i
$189$	−14.5045	+	8.55604i	−1.05505	+	0.622360i
$190$	1.61558	−	4.36931i	0.117207	−	0.316983i
$191$	−6.69443	+	7.43491i	−0.484392	+	0.537971i	−0.934952	−	0.354775i	$-0.884558\pi$
$191$	−6.69443	+	7.43491i	−0.484392	+	0.537971i	0.450560	+	0.892746i	$0.351224\pi$
$192$	4.69735	+	21.7654i	0.339002	+	1.57078i
$193$	5.77682	−	10.0057i	0.415824	−	0.720229i	−0.579690	−	0.814837i	$-0.696826\pi$
$193$	5.77682	−	10.0057i	0.415824	−	0.720229i	0.995515	+	0.0946081i	$0.0301598\pi$
$194$	1.13913	+	10.8381i	0.0817848	+	0.778130i
$195$	10.5909	−	8.85107i	0.758428	−	0.633839i
$196$	−1.20293	+	11.4452i	−0.0859239	+	0.817511i
$197$	10.5844	+	7.69002i	0.754108	+	0.547891i	0.897097	−	0.441833i	$-0.145672\pi$
$197$	10.5844	+	7.69002i	0.754108	+	0.547891i	−0.142990	+	0.989724i	$0.545672\pi$
$198$	1.32411	−	13.4014i	0.0941004	−	0.952398i
$199$	2.60687			0.184796			0.0923980	−	0.995722i	$-0.470547\pi$
$199$	2.60687			0.184796			0.0923980	+	0.995722i	$0.470547\pi$
$200$	−2.71330	+	14.5202i	−0.191859	+	1.02673i
$201$	12.3948	+	16.9486i	0.874264	+	1.19546i
$202$	−18.4383	−	20.4778i	−1.29732	−	1.44082i
$203$	−22.1097	+	9.84385i	−1.55179	+	0.690903i
$204$	−0.0159338	−	5.11052i	−0.00111559	−	0.357808i
$205$	9.99943	−	1.71063i	0.698391	−	0.119476i
$206$	−4.10221	+	2.98043i	−0.285814	+	0.207656i
$207$	−24.9078	+	5.45687i	−1.73121	+	0.379279i
$208$	−0.638842	+	0.464146i	−0.0442957	+	0.0321827i
$209$	−1.18400	+	1.31497i	−0.0818993	+	0.0909584i
$210$	−28.7893	+	1.95580i	−1.98665	+	0.134963i
$211$	17.8584	+	19.8337i	1.22942	+	1.36541i	0.908271	+	0.418383i	$0.137403\pi$
$211$	17.8584	+	19.8337i	1.22942	+	1.36541i	0.321151	+	0.947028i	$0.395930\pi$
$212$	23.5966	+	5.01560i	1.62062	+	0.344473i
$213$	−17.0976	−	1.74316i	−1.17151	−	0.119439i
$214$	10.3903	−	2.20852i	0.710265	−	0.150971i
$215$	3.10791	+	2.45380i	0.211958	+	0.167348i
$216$	9.13886	+	12.3343i	0.621821	+	0.839242i
$217$	20.3124	−	14.7578i	1.37889	−	1.00182i
$218$	15.5716	+	26.9708i	1.05464	+	1.82670i
$219$	−0.291786	−	1.35201i	−0.0197171	−	0.0913601i
$220$	7.66264	−	12.1247i	0.516615	−	0.817450i
$221$	−2.92417	+	1.30192i	−0.196701	+	0.0875769i
$222$	14.8963	+	8.53857i	0.999775	+	0.573072i
$223$	−20.9953	+	4.46269i	−1.40595	+	0.298844i	−0.847544	−	0.530725i	$-0.821920\pi$
$223$	−20.9953	+	4.46269i	−1.40595	+	0.298844i	−0.558404	+	0.829569i	$0.688586\pi$
$224$	−17.4981			−1.16914
$225$	−3.57110	−	14.5687i	−0.238073	−	0.971247i
$226$	−38.8966			−2.58736
$227$	5.14571	−	1.09375i	0.341533	−	0.0725950i	−0.0339524	−	0.999423i	$-0.510809\pi$
$227$	5.14571	−	1.09375i	0.341533	−	0.0725950i	0.375485	+	0.926828i	$0.377476\pi$
$228$	−0.0160764	−	5.15624i	−0.00106468	−	0.341480i
$229$	15.9866	−	7.11768i	1.05642	−	0.470349i	0.196356	−	0.980533i	$-0.437089\pi$
$229$	15.9866	−	7.11768i	1.05642	−	0.470349i	0.860066	+	0.510183i	$0.170422\pi$
$230$	−42.3400	−	10.7862i	−2.79182	−	0.711222i
$231$	10.4347	+	3.35450i	0.686550	+	0.220710i
$232$	11.0310	+	19.1063i	0.724223	+	1.25439i
$233$	−7.95794	+	5.78178i	−0.521342	+	0.378777i	−0.817109	−	0.576483i	$-0.804425\pi$
$233$	−7.95794	+	5.78178i	−0.521342	+	0.378777i	0.295767	+	0.955260i	$0.404425\pi$
$234$	12.1564	−	21.3619i	0.794686	−	1.39647i
$235$	−4.68294	−	16.6514i	−0.305482	−	1.08622i
$236$	44.3597	−	9.42895i	2.88757	−	0.613772i
$237$	−0.172861	−	0.385017i	−0.0112285	−	0.0250095i
$238$	6.54563	+	1.39132i	0.424290	+	0.0901857i
$239$	−11.1518	−	12.3853i	−0.721347	−	0.801137i	0.265273	−	0.964173i	$-0.414538\pi$
$239$	−11.1518	−	12.3853i	−0.721347	−	0.801137i	−0.986620	+	0.163036i	$0.947871\pi$
$240$	0.147343	+	0.845421i	0.00951095	+	0.0545717i
$241$	14.8435	−	16.4854i	0.956156	−	1.06192i	−0.0418699	−	0.999123i	$-0.513332\pi$
$241$	14.8435	−	16.4854i	0.956156	−	1.06192i	0.998026	−	0.0627962i	$-0.0200018\pi$
$242$	13.3676	−	9.71210i	0.859299	−	0.624317i
$243$	−13.6199	−	7.58284i	−0.873714	−	0.486439i
$244$	16.7647	−	12.1803i	1.07325	−	0.779762i
$245$	1.12974	−	7.75145i	0.0721764	−	0.495222i
$246$	15.6166	−	9.08128i	0.995678	−	0.579002i
$247$	−2.95033	+	1.31357i	−0.187725	+	0.0835805i
$248$	−15.3147	−	17.0087i	−0.972484	−	1.08005i
$249$	7.96483	−	0.862253i	0.504751	−	0.0546431i
$250$	5.72795	−	25.0564i	0.362267	−	1.58471i
$251$	−7.63595			−0.481977			−0.240989	−	0.970528i	$-0.577472\pi$
$251$	−7.63595			−0.481977			−0.240989	+	0.970528i	$0.577472\pi$
$252$	−29.0965	+	13.1726i	−1.83291	+	0.829798i
$253$	13.4266	+	9.75499i	0.844122	+	0.613291i
$254$	2.02242	−	19.2420i	0.126898	−	1.20735i
$255$	−0.128294	+	3.47625i	−0.00803406	+	0.217691i
$256$	1.81950	+	17.3113i	0.113718	+	1.08196i
$257$	−3.94709	+	6.83657i	−0.246213	+	0.426453i	−0.962472	−	0.271381i	$-0.912520\pi$
$257$	−3.94709	+	6.83657i	−0.246213	+	0.426453i	0.716259	+	0.697835i	$0.245853\pi$
$258$	6.71308	+	2.15810i	0.417938	+	0.134357i
$259$	−9.35091	+	10.3852i	−0.581037	+	0.645307i
$260$	21.7772	−	14.5278i	1.35056	−	0.900979i
$261$	−18.2064	−	13.0551i	−1.12695	−	0.808089i
$262$	10.3069	+	31.7215i	0.636764	+	1.95976i
$263$	−6.22580	+	6.91445i	−0.383899	+	0.426364i	−0.903861	−	0.427826i	$-0.859280\pi$
$263$	−6.22580	+	6.91445i	−0.383899	+	0.426364i	0.519962	+	0.854190i	$0.325946\pi$
$264$	2.04686	−	9.77955i	0.125976	−	0.601890i
$265$	−15.9122	−	4.05366i	−0.977477	−	0.249015i
$266$	6.60419	+	1.40376i	0.404929	+	0.0860703i
$267$	−2.49810	−	11.5751i	−0.152881	−	0.708383i
$268$	19.9122	+	34.4889i	1.21633	+	2.10675i
$269$	12.3841	−	8.99756i	0.755071	−	0.548591i	−0.142324	−	0.989820i	$-0.545457\pi$
$269$	12.3841	−	8.99756i	0.755071	−	0.548591i	0.897394	+	0.441229i	$0.145457\pi$
$270$	−15.0307	−	22.0808i	−0.914741	−	1.34380i
$271$	−6.20201	−	4.50602i	−0.376745	−	0.273721i	0.383257	−	0.923642i	$-0.374802\pi$
$271$	−6.20201	−	4.50602i	−0.376745	−	0.273721i	−0.760002	+	0.649920i	$0.774802\pi$
$272$	0.0208028	−	0.197925i	0.00126135	−	0.0120010i
$273$	14.9080	+	13.3393i	0.902276	+	0.807333i
$274$	6.92617	−	11.9965i	0.418425	−	0.724734i
$275$	−5.54168	+	8.03779i	−0.334176	+	0.484697i
$276$	−48.0807	+	5.20510i	−2.89412	+	0.313310i
$277$	−0.504942	+	0.107329i	−0.0303390	+	0.00644876i	−0.223056	−	0.974806i	$-0.571603\pi$
$277$	−0.504942	+	0.107329i	−0.0303390	+	0.00644876i	0.192717	+	0.981254i	$0.438270\pi$
$278$	15.3648	+	11.1632i	0.921519	+	0.669523i
$279$	21.2907	+	9.32058i	1.27464	+	0.558009i
$280$	−21.3921	−	0.856285i	−1.27842	−	0.0511728i
$281$	2.40434	+	1.07048i	0.143431	+	0.0638595i	0.477197	−	0.878796i	$-0.341653\pi$
$281$	2.40434	+	1.07048i	0.143431	+	0.0638595i	−0.333766	+	0.942656i	$0.608320\pi$
$282$	−18.1827	−	24.8630i	−1.08276	−	1.48057i
$283$	−3.20483	−	30.4919i	−0.190507	−	1.81255i	−0.504809	−	0.863231i	$-0.668437\pi$
$283$	−3.20483	−	30.4919i	−0.190507	−	1.81255i	0.314302	−	0.949323i	$-0.398230\pi$
$284$	−31.8839	−	6.77713i	−1.89196	−	0.402148i
$285$	−0.129441	+	3.50735i	−0.00766744	+	0.207757i
$286$	−15.6478	+	3.32605i	−0.925276	+	0.196674i
$287$	4.54357	+	13.9837i	0.268198	+	0.825429i
$288$	−8.18613	−	13.9768i	−0.482372	−	0.823590i
$289$	−5.00400	+	15.4007i	−0.294353	+	0.905925i
$290$	−17.8492	−	33.9866i	−1.04814	−	1.99576i
$291$	−3.36291	−	7.49029i	−0.197137	−	0.439088i
$292$	−0.274210	−	2.60894i	−0.0160469	−	0.152676i
$293$	−14.6607	+	25.3931i	−0.856488	+	1.48348i	0.0187704	+	0.999824i	$0.494025\pi$
$293$	−14.6607	+	25.3931i	−0.856488	+	1.48348i	−0.875258	+	0.483656i	$0.839309\pi$
$294$	−2.94272	−	13.6352i	−0.171623	−	0.795223i
$295$	−30.4271	+	5.20524i	−1.77153	+	0.303061i
$296$	10.3061	+	7.48784i	0.599031	+	0.435222i
$297$	2.20221	+	9.90413i	0.127785	+	0.574696i
$298$	−7.77660	+	23.9339i	−0.450486	+	1.38645i
$299$	15.1452	+	26.2323i	0.875871	+	1.51705i
$300$	−3.75979	−	28.2001i	−0.217071	−	1.62813i
$301$	−2.86960	+	4.97030i	−0.165401	+	0.286483i
$302$	32.3114	+	35.8855i	1.85931	+	2.06498i
$303$	18.0117	+	10.3243i	1.03475	+	0.593117i
$304$	0.0209889	−	0.199696i	0.00120379	−	0.0114533i
$305$	−11.7338	+	7.82776i	−0.671874	+	0.448216i
$306$	1.95091	+	5.87929i	0.111526	+	0.336097i
$307$	9.35518			0.533929			0.266964	−	0.963706i	$-0.413979\pi$
$307$	9.35518			0.533929			0.266964	+	0.963706i	$0.413979\pi$
$308$	18.9911	+	8.45537i	1.08212	+	0.481789i
$309$	2.23585	−	3.09765i	0.127193	−	0.176219i
$310$	25.4429	+	30.6377i	1.44506	+	1.74010i
$311$	13.8023	+	15.3290i	0.782655	+	0.869227i	0.994134	−	0.108156i	$-0.0344946\pi$
$311$	13.8023	+	15.3290i	0.782655	+	0.869227i	−0.211479	+	0.977383i	$0.567828\pi$
$312$	10.6727	−	14.7865i	0.604224	−	0.837119i
$313$	13.6756	−	15.1883i	0.772990	−	0.858492i	−0.220145	−	0.975467i	$-0.570653\pi$
$313$	13.6756	−	15.1883i	0.772990	−	0.858492i	0.993135	+	0.116975i	$0.0373198\pi$
$314$	−4.62649	+	14.2389i	−0.261088	+	0.803547i
$315$	20.1480	−	8.16696i	1.13521	−	0.460156i
$316$	−0.247356	−	0.761283i	−0.0139149	−	0.0428255i
$317$	−0.0799592	−	0.0356001i	−0.00449095	−	0.00199950i	0.404490	−	0.914542i	$-0.367449\pi$
$317$	−0.0799592	−	0.0356001i	−0.00449095	−	0.00199950i	−0.408981	+	0.912543i	$0.634116\pi$
$318$	−29.0707	+	3.14712i	−1.63020	+	0.176482i
$319$	1.52419	+	14.5017i	0.0853384	+	0.811940i
$320$	−1.85893	−	28.6857i	−0.103918	−	1.60358i
$321$	−6.91837	+	4.02314i	−0.386146	+	0.224550i
$322$	6.61935	−	62.9789i	0.368882	−	3.50968i
$323$	0.251520	−	0.774099i	0.0139950	−	0.0430720i
$324$	−24.1340	−	17.0786i	−1.34078	−	0.948813i
$325$	−15.2068	+	9.28795i	−0.843522	+	0.515203i
$326$	4.69907	+	8.13902i	0.260257	+	0.450779i
$327$	−17.4859	−	15.6459i	−0.966972	−	0.865222i
$328$	12.2444	−	5.45158i	0.676086	−	0.301013i
$329$	22.9027	−	10.1969i	1.26267	−	0.562175i
$330$	−4.23934	+	16.8606i	−0.233368	+	0.928146i
$331$	20.6249	+	9.18279i	1.13365	+	0.504732i	0.885800	−	0.464067i	$-0.153610\pi$
$331$	20.6249	+	9.18279i	1.13365	+	0.504732i	0.247846	+	0.968799i	$0.420277\pi$
$332$	15.1947			0.833917
$333$	−12.6700	−	2.61062i	−0.694310	−	0.143061i
$334$	11.9095	+	36.6536i	0.651658	+	2.00560i
$335$	−12.6039	−	23.9990i	−0.688627	−	1.31121i
$336$	−1.18171	+	0.388038i	−0.0644674	+	0.0211692i
$337$	−3.25281	−	0.691407i	−0.177192	−	0.0376633i	0.118461	−	0.992959i	$-0.462204\pi$
$337$	−3.25281	−	0.691407i	−0.177192	−	0.0376633i	−0.295653	+	0.955295i	$0.595537\pi$
$338$	0.673414	+	0.143139i	0.0366289	+	0.00778572i
$339$	27.8426	−	9.14270i	1.51221	−	0.496563i
$340$	−0.951531	+	6.52871i	−0.0516040	+	0.354069i
$341$	−4.67454	−	14.3867i	−0.253140	−	0.779086i
$342$	1.96837	+	5.93189i	0.106437	+	0.320760i
$343$	−11.3327			−0.611909
$344$	4.77944	+	2.12794i	0.257690	+	0.114731i
$345$	32.8428	−	2.23118i	1.76820	−	0.120123i
$346$	−13.8254	+	6.15548i	−0.743259	+	0.330920i
$347$	−12.6001	+	5.60992i	−0.676408	+	0.301156i	−0.716041	−	0.698058i	$-0.754048\pi$
$347$	−12.6001	+	5.60992i	−0.676408	+	0.301156i	0.0396331	+	0.999214i	$0.487381\pi$
$348$	−31.6655	−	28.3335i	−1.69745	−	1.51883i
$349$	−7.45084	−	12.9052i	−0.398834	−	0.690801i	0.594748	−	0.803912i	$-0.297252\pi$
$349$	−7.45084	−	12.9052i	−0.398834	−	0.690801i	−0.993582	+	0.113111i	$0.963918\pi$
$350$	37.1334	+	2.97753i	1.98486	+	0.159156i
$351$	−3.68051	+	18.1485i	−0.196451	+	0.968695i
$352$	−3.25781	+	10.0265i	−0.173642	+	0.534415i
$353$	0.987835	−	9.39862i	0.0525771	−	0.500238i	−0.936268	−	0.351288i	$-0.885744\pi$
$353$	0.987835	−	9.39862i	0.0525771	−	0.500238i	0.988845	−	0.148950i	$-0.0475895\pi$
$354$	−47.5194	+	27.6332i	−2.52563	+	1.46869i
$355$	21.5007	+	5.47734i	1.14114	+	0.290707i
$356$	−2.34763	−	22.3362i	−0.124424	−	1.18382i
$357$	−5.01247	+	0.542638i	−0.265288	+	0.0287195i
$358$	22.9127	+	10.2014i	1.21097	+	0.539160i
$359$	0.603190	+	1.85643i	0.0318351	+	0.0979785i	0.965712	−	0.259618i	$-0.0835965\pi$
$359$	0.603190	+	1.85643i	0.0318351	+	0.0979785i	−0.933876	+	0.357596i	$0.883596\pi$
$360$	−9.32388	−	17.4877i	−0.491411	−	0.921684i
$361$	−5.61755	+	17.2890i	−0.295661	+	0.909950i
$362$	−13.4020	+	14.8844i	−0.704393	+	0.782307i
$363$	−7.28582	+	10.0941i	−0.382406	+	0.529803i
$364$	25.3880	+	28.1962i	1.33069	+	1.47788i
$365$	0.115472	+	1.78188i	0.00604408	+	0.0932679i
$366$	−14.7004	+	20.3665i	−0.768400	+	1.06458i
$367$	−6.64186	−	2.95715i	−0.346702	−	0.154362i	0.225996	−	0.974128i	$-0.427436\pi$
$367$	−6.64186	−	2.95715i	−0.346702	−	0.154362i	−0.572698	+	0.819767i	$0.694103\pi$
$368$	−1.88330			−0.0981738
$369$	−9.04398	+	10.1712i	−0.470811	+	0.529491i
$370$	−17.3975	−	13.7359i	−0.904451	−	0.714093i
$371$	2.48768	−	23.6687i	0.129154	−	1.22882i
$372$	38.2436	+	21.9212i	1.98284	+	1.13656i
$373$	−8.70785	−	9.67105i	−0.450875	−	0.500748i	0.474260	−	0.880385i	$-0.342716\pi$
$373$	−8.70785	−	9.67105i	−0.450875	−	0.500748i	−0.925136	+	0.379637i	$0.876049\pi$
$374$	2.01591	−	3.49165i	0.104240	−	0.180549i
$375$	1.78941	+	19.2821i	0.0924049	+	0.995722i
$376$	−11.4267	−	19.7916i	−0.589287	−	1.02067i
$377$	−8.22403	+	25.3110i	−0.423559	+	1.30358i
$378$	28.5265	−	26.1727i	1.46725	−	1.34618i
$379$	0.718684	+	0.522154i	0.0369163	+	0.0268213i	0.606090	−	0.795396i	$-0.292737\pi$
$379$	0.718684	+	0.522154i	0.0369163	+	0.0268213i	−0.569174	+	0.822217i	$0.692737\pi$
$380$	−0.960043	+	6.58712i	−0.0492492	+	0.337912i
$381$	3.07519	+	14.2490i	0.157547	+	0.730000i
$382$	11.5000	−	19.9186i	0.588391	−	1.01912i
$383$	−1.96783	−	18.7226i	−0.100551	−	0.956681i	−0.922207	−	0.386697i	$-0.873616\pi$
$383$	−1.96783	−	18.7226i	−0.100551	−	0.956681i	0.821656	−	0.569984i	$-0.193051\pi$
$384$	−13.3056	−	29.6358i	−0.678997	−	1.51235i
$385$	−12.6862	−	6.26777i	−0.646549	−	0.319435i
$386$	−8.20780	+	25.2610i	−0.417766	+	1.28575i
$387$	−5.31257	+	0.0331278i	−0.270053	+	0.00168398i
$388$	−4.81217	−	14.8103i	−0.244301	−	0.751881i
$389$	31.7812	−	6.75530i	1.61137	−	0.342507i	0.687790	−	0.725910i	$-0.258581\pi$
$389$	31.7812	−	6.75530i	1.61137	−	0.342507i	0.923581	+	0.383403i	$0.125248\pi$
$390$	−19.5850	+	24.9655i	−0.991726	+	1.26418i
$391$	−7.46724	−	1.58721i	−0.377635	−	0.0802687i
$392$	−1.08181	−	10.2927i	−0.0546397	−	0.519862i
$393$	−14.8340	−	20.2840i	−0.748276	−	1.02319i
$394$	−27.4767	−	12.2334i	−1.38426	−	0.616311i
$395$	0.147509	+	0.524506i	0.00742197	+	0.0263907i
$396$	2.13077	+	19.1250i	0.107075	+	0.961068i
$397$	−15.9764	−	11.6075i	−0.801832	−	0.582565i	0.109619	−	0.993974i	$-0.465037\pi$
$397$	−15.9764	−	11.6075i	−0.801832	−	0.582565i	−0.911451	+	0.411409i	$0.865037\pi$
$398$	−5.86204	+	1.24602i	−0.293838	+	0.0624571i
$399$	−5.05731	+	0.547492i	−0.253182	+	0.0274089i
$400$	−0.0273688	−	1.10755i	−0.00136844	−	0.0553774i
$401$	5.22664	−	9.05280i	0.261006	−	0.452075i	−0.705504	−	0.708706i	$-0.749279\pi$
$401$	5.22664	−	9.05280i	0.261006	−	0.452075i	0.966509	+	0.256631i	$0.0826125\pi$
$402$	−35.9732	−	32.1879i	−1.79418	−	1.60538i
$403$	2.88595	−	27.4579i	0.143759	−	1.36778i
$404$	31.8558	+	23.1446i	1.58488	+	1.15149i
$405$	15.9493	+	12.2727i	0.792527	+	0.609836i
$406$	45.0127	−	32.7036i	2.23394	−	1.62305i
$407$	4.20985	+	7.29167i	0.208674	+	0.361435i
$408$	0.969567	+	4.49253i	0.0480007	+	0.222413i
$409$	−7.20958	−	1.53244i	−0.356491	−	0.0757744i	0.0261852	−	0.999657i	$-0.491664\pi$
$409$	−7.20958	−	1.53244i	−0.356491	−	0.0757744i	−0.382676	+	0.923883i	$0.624997\pi$
$410$	−21.6680	+	8.62616i	−1.07011	+	0.426015i
$411$	−2.13805	+	10.2152i	−0.105462	+	0.503880i
$412$	4.84831	−	5.38460i	0.238859	−	0.265280i
$413$	−13.8255	−	42.5506i	−0.680309	−	2.09378i
$414$	53.4018	−	24.1761i	2.62455	−	1.18819i
$415$	−10.3344	−	0.413665i	−0.507294	−	0.0203060i
$416$	−12.8751	+	14.2993i	−0.631256	+	0.701081i
$417$	−13.6222	−	4.37922i	−0.667083	−	0.214451i
$418$	2.03394	−	3.52289i	0.0994833	−	0.172310i
$419$	0.225746	+	2.14783i	0.0110284	+	0.104928i	0.998651	−	0.0519187i	$-0.0165337\pi$
$419$	0.225746	+	2.14783i	0.0110284	+	0.104928i	−0.987623	+	0.156847i	$0.949867\pi$
$420$	39.6588	−	11.2869i	1.93515	−	0.550746i
$421$	−3.30546	+	31.4493i	−0.161098	+	1.53275i	0.553285	+	0.832992i	$0.313374\pi$
$421$	−3.30546	+	31.4493i	−0.161098	+	1.53275i	−0.714383	+	0.699755i	$0.753292\pi$
$422$	−49.6380	−	36.0641i	−2.41634	−	1.75557i
$423$	18.8595	+	13.5233i	0.916979	+	0.657527i
$424$	−21.6947			−1.05359
$425$	0.824904	−	4.41447i	0.0400137	−	0.214133i
$426$	39.2805	−	4.25241i	1.90315	−	0.206030i
$427$	−13.6793	−	15.1924i	−0.661988	−	0.735212i
$428$	−13.8667	+	6.17385i	−0.670272	+	0.298424i
$429$	10.4191	−	6.05887i	0.503040	−	0.292525i
$430$	−8.16160	−	4.03233i	−0.393587	−	0.194456i
$431$	14.4718	−	10.5144i	0.697081	−	0.506459i	−0.181899	−	0.983317i	$-0.558225\pi$
$431$	14.4718	−	10.5144i	0.697081	−	0.506459i	0.878980	+	0.476858i	$0.158225\pi$
$432$	−0.862787	−	0.762366i	−0.0415109	−	0.0366794i
$433$	26.2239	−	19.0528i	1.26024	−	0.915620i	0.261473	−	0.965211i	$-0.415792\pi$
$433$	26.2239	−	19.0528i	1.26024	−	0.915620i	0.998770	+	0.0495910i	$0.0157918\pi$
$434$	−38.6224	+	42.8945i	−1.85394	+	2.05900i
$435$	20.7653	+	20.1325i	0.995620	+	0.965281i
$436$	−29.7779	−	33.0718i	−1.42610	−	1.58385i
$437$	−7.53404	−	1.60141i	−0.360402	−	0.0766058i
$438$	1.30236	+	2.90078i	0.0622292	+	0.138605i
$439$	−11.8370	+	2.51603i	−0.564949	+	0.120084i	−0.481528	−	0.876431i	$-0.659918\pi$
$439$	−11.8370	+	2.51603i	−0.564949	+	0.120084i	−0.0834213	+	0.996514i	$0.526585\pi$
$440$	−4.47345	+	12.0984i	−0.213263	+	0.576767i
$441$	5.31142	+	9.06858i	0.252925	+	0.431837i
$442$	5.95327	−	4.32530i	0.283168	−	0.205734i
$443$	−5.38308	−	9.32377i	−0.255758	−	0.442986i	0.709343	−	0.704863i	$-0.248992\pi$
$443$	−5.38308	−	9.32377i	−0.255758	−	0.442986i	−0.965101	+	0.261878i	$0.915658\pi$
$444$	−23.3579	−	7.50899i	−1.10851	−	0.356361i
$445$	0.988603	+	15.2554i	0.0468643	+	0.723176i
$446$	45.0789	−	20.0704i	2.13455	−	0.950362i
$447$	−0.0591146	−	18.9601i	−0.00279602	−	0.896781i
$448$	40.7527	−	8.66224i	1.92538	−	0.409253i
$449$	−27.1471			−1.28115			−0.640575	−	0.767896i	$-0.721304\pi$
$449$	−27.1471			−1.28115			−0.640575	+	0.767896i	$0.721304\pi$
$450$	14.9938	+	31.0537i	0.706813	+	1.46388i
$451$	8.85865			0.417138
$452$	54.3671	−	11.5561i	2.55721	−	0.543552i
$453$	−31.5638	−	18.0924i	−1.48300	−	0.850056i
$454$	−11.0483	+	4.91903i	−0.518524	+	0.230862i
$455$	−16.4995	−	19.8682i	−0.773508	−	0.931437i
$456$	0.978240	+	4.53272i	0.0458103	+	0.212264i
$457$	7.80737	+	13.5228i	0.365213	+	0.632568i	0.988810	−	0.149178i	$-0.0476627\pi$
$457$	7.80737	+	13.5228i	0.365213	+	0.632568i	−0.623597	+	0.781746i	$0.714329\pi$
$458$	−32.5468	+	23.6466i	−1.52081	+	1.10493i
$459$	−2.77842	−	3.74991i	−0.129686	−	0.175031i
$460$	62.3846	+	2.49714i	2.90870	+	0.116430i
$461$	−7.33926	+	1.56001i	−0.341823	+	0.0726568i	−0.375625	−	0.926772i	$-0.622572\pi$
$461$	−7.33926	+	1.56001i	−0.341823	+	0.0726568i	0.0338016	+	0.999429i	$0.489239\pi$
$462$	−25.0677	−	2.55573i	−1.16626	−	0.118903i
$463$	32.3798	+	6.88254i	1.50482	+	0.319859i	0.885262	−	0.465093i	$-0.153979\pi$
$463$	32.3798	+	6.88254i	1.50482	+	0.319859i	0.619556	+	0.784952i	$0.287313\pi$
$464$	−1.10720	−	1.22967i	−0.0514006	−	0.0570862i
$465$	−25.4138	−	15.9504i	−1.17854	−	0.739684i
$466$	15.1314	−	16.8051i	0.700949	−	0.778483i
$467$	−2.65707	+	1.93048i	−0.122955	+	0.0893318i	−0.647563	−	0.762012i	$-0.724212\pi$
$467$	−2.65707	+	1.93048i	−0.122955	+	0.0893318i	0.524608	+	0.851344i	$0.324212\pi$
$468$	−10.6448	+	33.4699i	−0.492054	+	1.54715i
$469$	31.7849	−	23.0931i	1.46769	−	1.06634i
$470$	18.4895	+	35.2056i	0.852855	+	1.62391i
$471$	−0.0351687	−	11.2798i	−0.00162049	−	0.519747i
$472$	−37.2584	+	16.5885i	−1.71495	+	0.763547i
$473$	2.31375	+	2.56968i	0.106386	+	0.118154i
$474$	0.572739	+	0.783161i	0.0263068	+	0.0359718i
$475$	0.832284	−	4.45396i	0.0381878	−	0.204362i
$476$	−9.56241			−0.438292
$477$	20.0694	−	9.08585i	0.918915	−	0.416012i
$478$	30.9967	+	22.5204i	1.41776	+	1.03006i
$479$	−0.861271	+	8.19445i	−0.0393525	+	0.374414i	0.957067	+	0.289867i	$0.0936110\pi$
$479$	−0.861271	+	8.19445i	−0.0393525	+	0.374414i	−0.996419	+	0.0845471i	$0.973056\pi$
$480$	7.79497	+	19.4039i	0.355790	+	0.885662i
$481$	1.60631	+	15.2830i	0.0732413	+	0.696844i
$482$	−25.4989	+	44.1655i	−1.16145	+	2.01168i
$483$	10.0651	+	46.6369i	0.457976	+	2.12205i
$484$	−15.7988	+	17.5464i	−0.718129	+	0.797563i
$485$	2.86970	+	10.2040i	0.130306	+	0.463338i
$486$	34.2513	+	10.5415i	1.55367	+	0.478173i
$487$	4.69938	+	14.4632i	0.212949	+	0.655391i	0.999293	+	0.0376012i	$0.0119716\pi$
$487$	4.69938	+	14.4632i	0.212949	+	0.655391i	−0.786343	+	0.617790i	$0.788028\pi$
$488$	−12.4698	+	13.8491i	−0.564480	+	0.626918i
$489$	−5.27674	−	4.72149i	−0.238622	−	0.213513i
$490$	1.16456	+	17.9706i	0.0526093	+	0.811829i
$491$	−1.54722	−	0.328872i	−0.0698252	−	0.0148418i	0.172867	−	0.984945i	$-0.444697\pi$
$491$	−1.54722	−	0.328872i	−0.0698252	−	0.0148418i	−0.242692	+	0.970103i	$0.578030\pi$
$492$	−19.1298	+	17.3329i	−0.862439	+	0.781426i
$493$	−3.35369	−	5.80876i	−0.151043	−	0.261613i
$494$	6.00653	−	4.36400i	0.270246	−	0.196345i
$495$	−0.928537	−	13.0655i	−0.0417346	−	0.587250i
$496$	1.38875	+	1.00899i	0.0623569	+	0.0453049i
$497$	−3.36137	+	31.9813i	−0.150778	+	1.43456i
$498$	−17.4983	+	5.74593i	−0.784119	+	0.257481i
$499$	−15.4879	+	26.8258i	−0.693333	+	1.20089i	0.277407	+	0.960753i	$0.410525\pi$
$499$	−15.4879	+	26.8258i	−0.693333	+	1.20089i	−0.970739	+	0.240135i	$0.922808\pi$
$500$	−0.561945	+	36.7240i	−0.0251309	+	1.64235i
$501$	−17.1404	−	23.4378i	−0.765778	−	1.04712i
$502$	17.1709	−	3.64979i	0.766375	−	0.162898i
$503$	24.3048	+	17.6585i	1.08370	+	0.787354i	0.978324	−	0.207079i	$-0.0663957\pi$
$503$	24.3048	+	17.6585i	1.08370	+	0.787354i	0.105375	+	0.994433i	$0.466396\pi$
$504$	23.1320	−	17.0278i	1.03038	−	0.758478i
$505$	−21.0360	−	16.6086i	−0.936088	−	0.739072i
$506$	−34.8549	−	15.5184i	−1.54949	−	0.689877i
$507$	−0.515683	+	0.0558266i	−0.0229023	+	0.00247935i
$508$	2.88995	+	27.4961i	0.128221	+	1.21994i
$509$	−19.8838	−	4.22644i	−0.881335	−	0.187334i	−0.255050	−	0.966928i	$-0.582092\pi$
$509$	−19.8838	−	4.22644i	−0.881335	−	0.187334i	−0.626285	+	0.779594i	$0.715425\pi$
$510$	−1.37307	−	7.87834i	−0.0608004	−	0.348859i
$511$	−2.53144	+	0.538075i	−0.111984	+	0.0238030i
$512$	−0.774259	−	2.38292i	−0.0342177	−	0.105311i
$513$	−2.80328	−	3.78345i	−0.123768	−	0.167043i
$514$	5.60810	−	17.2599i	0.247363	−	0.761304i
$515$	−3.44407	+	3.53023i	−0.151764	+	0.155561i
$516$	−10.0243	−	1.02200i	−0.441293	−	0.0449912i
$517$	−1.57886	−	15.0219i	−0.0694382	−	0.660661i
$518$	16.0634	−	27.8227i	0.705787	−	1.22246i
$519$	8.44955	−	7.65585i	0.370894	−	0.336054i
$520$	−16.4401	+	16.8514i	−0.720945	+	0.738981i
$521$	−14.7886	−	10.7445i	−0.647898	−	0.470726i	0.214656	−	0.976690i	$-0.431137\pi$
$521$	−14.7886	−	10.7445i	−0.647898	−	0.470726i	−0.862555	+	0.505964i	$0.831137\pi$
$522$	47.1807	+	20.6546i	2.06504	+	0.904029i
$523$	0.681075	−	2.09613i	0.0297813	−	0.0916575i	−0.935061	−	0.354487i	$-0.884656\pi$
$523$	0.681075	−	2.09613i	0.0297813	−	0.0916575i	0.964842	+	0.262829i	$0.0846556\pi$
$524$	−23.8307	−	41.2760i	−1.04105	−	1.80315i
$525$	−27.2804	+	6.59689i	−1.19061	+	0.287912i
$526$	10.6950	−	18.5243i	0.466323	−	0.807696i
$527$	4.65602	+	5.17103i	0.202819	+	0.225254i
$528$	0.00233642	+	0.749371i	0.000101680	+	0.0326122i
$529$	−5.14718	+	48.9722i	−0.223790	+	2.12922i
$530$	37.7191	+	1.50983i	1.63842	+	0.0655827i
$531$	27.5197	−	30.9497i	1.19425	−	1.34310i
$532$	−9.64795			−0.418292
$533$	14.7705	+	6.57625i	0.639781	+	0.284849i
$534$	11.1501	+	24.8348i	0.482510	+	1.07471i
$535$	9.59923	−	3.82151i	0.415011	−	0.165218i
$536$	−23.9645	−	26.6153i	−1.03511	−	1.14961i
$537$	−18.7990	−	1.91662i	−0.811237	−	0.0827081i
$538$	−23.5474	+	26.1520i	−1.01520	+	1.12749i
$539$	2.11377	−	6.50552i	0.0910465	−	0.280212i
$540$	27.5691	+	26.3975i	1.18639	+	1.13597i
$541$	0.946056	+	2.91166i	0.0406741	+	0.125182i	0.969332	−	0.245756i	$-0.0790362\pi$
$541$	0.946056	+	2.91166i	0.0406741	+	0.125182i	−0.928658	+	0.370938i	$0.879036\pi$
$542$	16.1002	+	7.16826i	0.691562	+	0.307903i
$543$	6.09470	−	13.8046i	0.261549	−	0.592412i
$544$	−0.506905	−	4.82288i	−0.0217334	−	0.206779i
$545$	19.3525	+	23.3038i	0.828970	+	0.998224i
$546$	−39.8995	−	22.8704i	−1.70754	−	0.978763i
$547$	−0.534090	+	5.08153i	−0.0228360	+	0.217270i	0.977153	+	0.212538i	$0.0681730\pi$
$547$	−0.534090	+	5.08153i	−0.0228360	+	0.217270i	−0.999989	+	0.00473219i	$0.998494\pi$
$548$	−6.11682	+	18.8256i	−0.261297	+	0.804191i
$549$	5.73551	−	18.0339i	0.244786	−	0.769670i
$550$	8.61967	−	20.7233i	0.367544	−	0.883644i
$551$	−3.38369	−	5.86072i	−0.144150	−	0.249675i
$552$	41.3213	−	13.5687i	1.75875	−	0.577522i
$553$	−0.721415	+	0.321194i	−0.0306777	+	0.0136586i
$554$	1.08416	−	0.482699i	0.0460615	−	0.0205079i
$555$	15.6819	+	5.74299i	0.665661	+	0.243776i
$556$	−24.7924	−	11.0383i	−1.05143	−	0.468128i
$557$	23.7393			1.00587			0.502934	−	0.864325i	$-0.332254\pi$
$557$	23.7393			1.00587			0.502934	+	0.864325i	$0.332254\pi$
$558$	−52.3312	−	10.7827i	−2.21536	−	0.456469i
$559$	1.95023	+	6.00218i	0.0824858	+	0.253865i
$560$	1.58273	−	0.270762i	0.0668825	−	0.0114418i
$561$	−0.622293	+	2.97321i	−0.0262732	+	0.125529i
$562$	−5.91828	−	1.25797i	−0.249648	−	0.0530642i
$563$	−19.0213	−	4.04311i	−0.801653	−	0.170397i	−0.211173	−	0.977449i	$-0.567728\pi$
$563$	−19.0213	−	4.04311i	−0.801653	−	0.170397i	−0.590480	+	0.807052i	$0.701062\pi$
$564$	32.8013	+	29.3497i	1.38118	+	1.23585i
$565$	−37.2913	+	6.37952i	−1.56886	+	0.268389i
$566$	21.7810	+	67.0350i	0.915524	+	2.81769i
$567$	−14.2677	+	25.4399i	−0.599188	+	1.06838i
$568$	29.3141			1.22999
$569$	−0.604819	−	0.269283i	−0.0253553	−	0.0112889i	0.394020	−	0.919102i	$-0.371084\pi$
$569$	−0.604819	−	0.269283i	−0.0253553	−	0.0112889i	−0.419375	+	0.907813i	$0.637751\pi$
$570$	−1.38535	−	7.94882i	−0.0580259	−	0.332939i
$571$	16.8064	−	7.48268i	0.703325	−	0.313141i	−0.0237311	−	0.999718i	$-0.507555\pi$
$571$	16.8064	−	7.48268i	0.703325	−	0.313141i	0.727056	+	0.686578i	$0.240888\pi$
$572$	20.8833	−	9.29787i	0.873177	−	0.388763i
$573$	−3.54995	+	16.9611i	−0.148301	+	0.708559i
$574$	−16.9009	−	29.2732i	−0.705430	−	1.22184i
$575$	−42.3617	−	3.39676i	−1.76660	−	0.141655i
$576$	25.9844	+	28.4992i	1.08268	+	1.18747i
$577$	−2.40887	+	7.41374i	−0.100283	+	0.308638i	−0.988594	−	0.150603i	$-0.951878\pi$
$577$	−2.40887	+	7.41374i	−0.100283	+	0.308638i	0.888312	+	0.459241i	$0.151878\pi$
$578$	3.89130	−	37.0233i	0.161857	−	1.53997i
$579$	−0.0623923	−	20.0114i	−0.00259294	−	0.831645i
$580$	35.0458	+	42.2012i	1.45520	+	1.75231i
$581$	−1.56690	−	14.9081i	−0.0650059	−	0.618490i
$582$	11.1423	+	15.2360i	0.461864	+	0.631551i
$583$	−13.0991	−	5.83211i	−0.542511	−	0.241541i
$584$	0.729022	+	2.24370i	0.0301671	+	0.0928449i
$585$	8.15101	−	22.4741i	0.337003	−	0.929189i
$586$	20.8302	−	64.1087i	0.860487	−	2.64831i
$587$	9.77501	−	10.8563i	0.403458	−	0.448086i	−0.506839	−	0.862041i	$-0.669186\pi$
$587$	9.77501	−	10.8563i	0.403458	−	0.448086i	0.910297	+	0.413955i	$0.135853\pi$
$588$	8.16413	+	18.1841i	0.336683	+	0.749902i
$589$	4.69767	+	5.21729i	0.193564	+	0.214975i
$590$	65.9331	−	26.2483i	2.71442	−	1.08063i
$591$	22.5436	+	2.29839i	0.927321	+	0.0945432i
$592$	−0.872847	−	0.388616i	−0.0358738	−	0.0159720i
$593$	−17.7208			−0.727707			−0.363853	−	0.931456i	$-0.618539\pi$
$593$	−17.7208			−0.727707			−0.363853	+	0.931456i	$0.618539\pi$
$594$	−9.68601	−	21.2187i	−0.397422	−	0.870616i
$595$	6.50368	+	0.260330i	0.266625	+	0.0106725i
$596$	3.75891	−	35.7636i	0.153971	−	1.46494i
$597$	3.90324	−	2.26979i	0.159749	−	0.0928965i
$598$	−46.5953	−	51.7493i	−1.90542	−	2.11619i
$599$	7.37178	−	12.7683i	0.301203	−	0.521699i	−0.675206	−	0.737629i	$-0.735945\pi$
$599$	7.37178	−	12.7683i	0.301203	−	0.521699i	0.976409	+	0.215931i	$0.0692785\pi$
$600$	8.58009	+	24.1034i	0.350281	+	0.984018i
$601$	6.78135	+	11.7456i	0.276617	+	0.479115i	0.970542	−	0.240933i	$-0.0774533\pi$
$601$	6.78135	+	11.7456i	0.276617	+	0.479115i	−0.693925	+	0.720048i	$0.744120\pi$
$602$	4.07718	−	12.5483i	0.166173	−	0.511429i
$603$	33.3158	+	14.5849i	1.35673	+	0.593944i
$604$	−55.8242	−	40.5587i	−2.27146	−	1.65031i
$605$	11.2230	−	11.5037i	0.456278	−	0.467692i
$606$	−45.4376	−	14.6071i	−1.84578	−	0.593373i
$607$	−16.6848	+	28.8989i	−0.677216	+	1.17297i	0.298600	+	0.954378i	$0.403480\pi$
$607$	−16.6848	+	28.8989i	−0.677216	+	1.17297i	−0.975816	+	0.218594i	$0.929853\pi$
$608$	−0.511439	−	4.86602i	−0.0207416	−	0.197343i
$609$	−24.5336	+	33.9900i	−0.994152	+	1.37734i
$610$	22.6442	−	23.2107i	0.916836	−	0.939772i
$611$	8.51901	−	26.2188i	0.344642	−	1.06070i
$612$	−4.47358	−	7.63807i	−0.180834	−	0.308751i
$613$	5.32757	+	16.3966i	0.215178	+	0.662251i	0.999141	+	0.0414429i	$0.0131955\pi$
$613$	5.32757	+	16.3966i	0.215178	+	0.662251i	−0.783962	+	0.620808i	$0.786805\pi$
$614$	−21.0369	+	4.47154i	−0.848981	+	0.180457i
$615$	13.4826	−	11.2678i	0.543672	−	0.454362i
$616$	−18.2866	−	3.88694i	−0.736788	−	0.156609i
$617$	−2.61997	−	24.9273i	−0.105476	−	1.00354i	−0.911401	−	0.411519i	$-0.864998\pi$
$617$	−2.61997	−	24.9273i	−0.105476	−	1.00354i	0.805925	−	0.592018i	$-0.201668\pi$
$618$	−3.54715	+	8.03435i	−0.142687	+	0.323189i
$619$	14.2589	+	6.34849i	0.573116	+	0.255167i	0.672766	−	0.739855i	$-0.265106\pi$
$619$	14.2589	+	6.34849i	0.573116	+	0.255167i	−0.0996508	+	0.995022i	$0.531773\pi$
$620$	−44.6648	−	35.2643i	−1.79378	−	1.41625i
$621$	−32.5430	+	29.8577i	−1.30591	+	1.19815i
$622$	−38.3639	−	27.8730i	−1.53825	−	1.11761i
$623$	−21.6727	+	4.60668i	−0.868300	+	0.184563i
$624$	−0.552403	+	1.25120i	−0.0221138	+	0.0500881i
$625$	1.38198	−	24.9618i	0.0552793	−	0.998471i
$626$	−23.4926	+	40.6903i	−0.938952	+	1.62631i
$627$	−0.627859	+	2.99981i	−0.0250743	+	0.119801i
$628$	2.23627	−	21.2767i	0.0892368	−	0.849032i
$629$	−3.13330	−	2.27647i	−0.124933	−	0.0907690i
$630$	−41.4032	+	27.9952i	−1.64954	+	1.11536i
$631$	−4.14912	+	3.01451i	−0.165174	+	0.120006i	−0.667301	−	0.744788i	$-0.732551\pi$
$631$	−4.14912	+	3.01451i	−0.165174	+	0.120006i	0.502128	+	0.864793i	$0.332551\pi$
$632$	0.359931	+	0.623419i	0.0143173	+	0.0247983i
$633$	44.0084	+	14.1477i	1.74918	+	0.562319i
$634$	0.196820	+	0.0418353i	0.00781670	+	0.00166149i
$635$	−1.21698	−	18.7796i	−0.0482944	−	0.745244i
$636$	39.6980	−	13.0357i	1.57413	−	0.516897i
$637$	8.35380	−	9.27783i	0.330989	−	0.367601i
$638$	−10.3589	−	31.8814i	−0.410112	−	1.26220i
$639$	−27.1179	+	12.2769i	−1.07277	+	0.485665i
$640$	11.3541	+	40.3726i	0.448812	+	1.59587i
$641$	1.99934	−	2.22049i	0.0789692	−	0.0877042i	−0.702365	−	0.711817i	$-0.747873\pi$
$641$	1.99934	−	2.22049i	0.0789692	−	0.0877042i	0.781334	+	0.624113i	$0.214539\pi$
$642$	13.6343	−	12.3536i	0.538104	−	0.487558i
$643$	−14.7308	+	25.5144i	−0.580925	+	1.00619i	0.414445	+	0.910074i	$0.363976\pi$
$643$	−14.7308	+	25.5144i	−0.580925	+	1.00619i	−0.995370	+	0.0961173i	$0.969358\pi$
$644$	9.45878	+	89.9943i	0.372728	+	3.54627i
$645$	6.78998	+	0.967999i	0.267355	+	0.0381149i
$646$	−0.195592	+	1.86093i	−0.00769545	+	0.0732174i
$647$	18.7975	+	13.6572i	0.739005	+	0.536919i	0.892399	−	0.451246i	$-0.149020\pi$
$647$	18.7975	+	13.6572i	0.739005	+	0.536919i	−0.153394	+	0.988165i	$0.549020\pi$
$648$	24.4230	+	10.5108i	0.959425	+	0.412905i
$649$	−26.9558			−1.05811
$650$	29.7561	−	28.1542i	1.16713	−	1.10430i
$651$	17.5640	−	39.7827i	0.688386	−	1.55921i
$652$	−8.98612	−	9.98010i	−0.351924	−	0.390851i
$653$	1.19250	−	0.530934i	0.0466661	−	0.0207771i	−0.383271	−	0.923636i	$-0.625202\pi$
$653$	1.19250	−	0.530934i	0.0466661	−	0.0207771i	0.429937	+	0.902859i	$0.358536\pi$
$654$	46.7987	+	26.8251i	1.82998	+	1.04894i
$655$	15.0843	+	28.7218i	0.589391	+	1.12225i
$656$	−0.813274	+	0.590878i	−0.0317530	+	0.0230699i
$657$	−1.61408	−	1.77029i	−0.0629712	−	0.0690656i
$658$	−46.6272	+	33.8767i	−1.81772	+	1.32065i
$659$	−14.5132	+	16.1186i	−0.565355	+	0.627891i	−0.956252	−	0.292544i	$-0.905498\pi$
$659$	−14.5132	+	16.1186i	−0.565355	+	0.627891i	0.390897	+	0.920435i	$0.372165\pi$
$660$	0.916226	−	24.8261i	0.0356641	−	0.966356i
$661$	−3.82004	−	4.24259i	−0.148582	−	0.165017i	0.664259	−	0.747502i	$-0.268747\pi$
$661$	−3.82004	−	4.24259i	−0.148582	−	0.165017i	−0.812841	+	0.582485i	$0.802080\pi$
$662$	−50.7682	−	10.7911i	−1.97316	−	0.419408i
$663$	−3.24475	+	4.49543i	−0.126016	+	0.174588i
$664$	−13.3661	+	2.84106i	−0.518706	+	0.110254i
$665$	6.56186	+	0.262659i	0.254458	+	0.0101855i
$666$	29.7387	−	0.185443i	1.15235	−	0.00718576i
$667$	−51.3504	+	37.3082i	−1.98830	+	1.44458i
$668$	−27.5360	−	47.6937i	−1.06540	−	1.84533i
$669$	−27.5504	+	24.9625i	−1.06516	+	0.965106i
$670$	39.8133	+	47.9421i	1.53812	+	1.85217i
$671$	−11.2522	+	5.00979i	−0.434385	+	0.193401i
$672$	−26.1998	+	15.2356i	−1.01068	+	0.587724i
$673$	3.33214	−	0.708269i	0.128445	−	0.0273018i	−0.143241	−	0.989688i	$-0.545752\pi$
$673$	3.33214	−	0.708269i	0.128445	−	0.0273018i	0.271685	+	0.962386i	$0.412419\pi$
$674$	7.64505			0.294476
$675$	−18.0319	−	18.7043i	−0.694049	−	0.719928i
$676$	−0.983780			−0.0378377
$677$	36.9300	−	7.84972i	1.41934	−	0.301689i	0.566584	−	0.824004i	$-0.308265\pi$
$677$	36.9300	−	7.84972i	1.41934	−	0.301689i	0.852753	+	0.522315i	$0.174931\pi$
$678$	−58.2396	+	33.8672i	−2.23668	+	1.30066i
$679$	−14.0347	+	6.24866i	−0.538603	+	0.239801i
$680$	−0.383698	−	5.92095i	−0.0147141	−	0.227058i
$681$	6.75230	−	6.11803i	0.258749	−	0.234443i
$682$	17.3881	+	30.1170i	0.665824	+	1.15324i
$683$	10.4985	−	7.62763i	0.401715	−	0.291863i	−0.368524	−	0.929618i	$-0.620137\pi$
$683$	10.4985	−	7.62763i	0.401715	−	0.291863i	0.770239	+	0.637755i	$0.220137\pi$
$684$	−4.51360	−	7.70640i	−0.172582	−	0.294662i
$685$	4.67274	−	12.6373i	0.178536	−	0.482848i
$686$	25.4838	−	5.41675i	0.972976	−	0.206812i
$687$	17.7392	−	24.5767i	0.676794	−	0.937660i
$688$	−0.383814	−	0.0815822i	−0.0146328	−	0.00311029i
$689$	−17.5114	−	19.4484i	−0.667131	−	0.740924i
$690$	−72.7869	+	20.7153i	−2.77095	+	0.788616i
$691$	32.5060	−	36.1016i	1.23659	−	1.37337i	0.334167	−	0.942514i	$-0.391545\pi$
$691$	32.5060	−	36.1016i	1.23659	−	1.37337i	0.902421	−	0.430856i	$-0.141788\pi$
$692$	17.4955	−	12.7112i	0.665078	−	0.483208i
$693$	18.5445	−	4.06278i	0.704447	−	0.154332i
$694$	25.6523	−	18.6375i	0.973749	−	0.707470i
$695$	16.5616	+	8.18243i	0.628216	+	0.310377i
$696$	33.1525	+	19.0030i	1.25664	+	0.720309i
$697$	−3.72259	+	1.65741i	−0.141003	+	0.0627787i
$698$	22.9230	+	25.4586i	0.867649	+	0.963622i
$699$	−6.88118	+	15.5860i	−0.260270	+	0.589516i
$700$	−52.7872	+	6.87043i	−1.99517	+	0.259678i
$701$	32.6872			1.23458			0.617290	−	0.786736i	$-0.288231\pi$
$701$	32.6872			1.23458			0.617290	+	0.786736i	$0.288231\pi$
$702$	−0.398186	−	42.5696i	−0.0150286	−	1.60669i
$703$	−3.16133	−	2.29684i	−0.119232	−	0.0866269i
$704$	2.62385	−	24.9643i	0.0988901	−	0.940877i
$705$	−21.5101	−	20.8546i	−0.810117	−	0.785431i
$706$	2.27096	+	21.6068i	0.0854688	+	0.813181i
$707$	19.4230	−	33.6416i	0.730476	−	1.26522i
$708$	58.2097	−	52.7418i	2.18765	−	1.98216i
$709$	6.72933	−	7.47367i	0.252725	−	0.280680i	−0.603411	−	0.797431i	$-0.706192\pi$
$709$	6.72933	−	7.47367i	0.252725	−	0.280680i	0.856136	+	0.516751i	$0.172859\pi$
$710$	−50.9664	−	2.04009i	−1.91274	−	0.0765633i
$711$	−0.594057	−	0.425973i	−0.0222789	−	0.0159752i
$712$	6.24146	+	19.2092i	0.233909	+	0.719897i
$713$	44.0604	−	48.9340i	1.65007	−	1.83259i
$714$	11.0121	−	3.61606i	0.412119	−	0.135328i
$715$	−14.4565	+	5.75522i	−0.540643	+	0.215233i
$716$	−35.0566	−	7.45151i	−1.31013	−	0.278476i
$717$	−27.4813	−	8.83458i	−1.02631	−	0.329933i
$718$	−2.24371	−	3.88622i	−0.0837346	−	0.145033i
$719$	−1.59555	+	1.15923i	−0.0595039	+	0.0432321i	−0.617140	−	0.786854i	$-0.711709\pi$
$719$	−1.59555	+	1.15923i	−0.0595039	+	0.0432321i	0.557636	+	0.830086i	$0.311709\pi$
$720$	0.956722	+	1.13755i	0.0356549	+	0.0423940i
$721$	−5.78298	−	4.20158i	−0.215370	−	0.156475i
$722$	4.36843	−	41.5628i	0.162576	−	1.54681i
$723$	7.87130	−	37.6077i	0.292737	−	1.39865i
$724$	14.3103	−	24.7861i	0.531837	−	0.921169i
$725$	−22.6868	−	29.6564i	−0.842567	−	1.10141i
$726$	11.5588	−	26.1810i	0.428989	−	0.971667i
$727$	−6.46761	+	1.37473i	−0.239870	+	0.0509860i	−0.326278	−	0.945274i	$-0.605795\pi$
$727$	−6.46761	+	1.37473i	−0.239870	+	0.0509860i	0.0864078	+	0.996260i	$0.472461\pi$
$728$	−27.6047	−	20.0560i	−1.02310	−	0.743326i
$729$	−26.9953	+	0.505060i	−0.999825	+	0.0187059i
$730$	−1.11135	−	3.95171i	−0.0411330	−	0.146259i
$731$	−1.45306	−	0.646943i	−0.0537433	−	0.0239281i
$732$	14.4963	−	32.8344i	0.535800	−	1.21359i
$733$	−1.45324	−	13.8266i	−0.0536765	−	0.510698i	−0.988020	−	0.154325i	$-0.950680\pi$
$733$	−1.45324	−	13.8266i	−0.0536765	−	0.510698i	0.934344	−	0.356373i	$-0.115987\pi$
$734$	16.3489	+	3.47507i	0.603450	+	0.128267i
$735$	−5.05762	−	12.5898i	−0.186553	−	0.464383i
$736$	−44.8879	+	9.54122i	−1.65459	+	0.351694i
$737$	−7.31475	−	22.5125i	−0.269442	−	0.829258i
$738$	15.4756	−	27.1947i	0.569663	−	1.00105i
$739$	−0.707775	+	2.17831i	−0.0260359	+	0.0801304i	−0.963230	−	0.268677i	$-0.913413\pi$
$739$	−0.707775	+	2.17831i	−0.0260359	+	0.0801304i	0.937194	+	0.348808i	$0.113413\pi$
$740$	28.3979	+	14.0303i	1.04393	+	0.515765i
$741$	−3.27378	+	4.53564i	−0.120265	+	0.166621i
$742$	5.71899	+	54.4126i	0.209951	+	1.99755i
$743$	−12.7978	+	22.1664i	−0.469506	+	0.813207i	−0.999392	−	0.0348611i	$-0.988901\pi$
$743$	−12.7978	+	22.1664i	−0.469506	+	0.813207i	0.529887	+	0.848068i	$0.322234\pi$
$744$	−37.7400	−	12.1325i	−1.38362	−	0.444800i
$745$	−3.53019	+	24.2216i	−0.129336	+	0.887410i
$746$	24.2038	+	17.5851i	0.886164	+	0.643836i
$747$	11.1749	−	8.22601i	0.408869	−	0.300974i
$748$	−1.78034	+	5.47932i	−0.0650956	+	0.200344i
$749$	7.48734	+	12.9684i	0.273581	+	0.473857i
$750$	−13.2402	−	42.5041i	−0.483463	−	1.55203i
$751$	18.1894	−	31.5050i	0.663742	−	1.14963i	−0.315883	−	0.948798i	$-0.602301\pi$
$751$	18.1894	−	31.5050i	0.663742	−	1.14963i	0.979625	−	0.200836i	$-0.0643660\pi$
$752$	1.14692	+	1.27378i	0.0418237	+	0.0464500i
$753$	−11.4333	+	6.64861i	−0.416651	+	0.242289i
$754$	6.39533	−	60.8475i	0.232904	−	2.21593i
$755$	36.8635	+	29.1049i	1.34160	+	1.05924i
$756$	−32.0967	+	45.0576i	−1.16734	+	1.63873i
$757$	35.2024			1.27945			0.639727	−	0.768602i	$-0.279048\pi$
$757$	35.2024			1.27945			0.639727	+	0.768602i	$0.279048\pi$
$758$	−1.86567	−	0.830652i	−0.0677644	−	0.0301706i
$759$	28.5972	+	2.91557i	1.03801	+	0.105828i
$760$	−0.387130	−	5.97391i	−0.0140427	−	0.216697i
$761$	−14.9853	−	16.6429i	−0.543218	−	0.603305i	0.407559	−	0.913179i	$-0.366380\pi$
$761$	−14.9853	−	16.6429i	−0.543218	−	0.603305i	−0.950778	+	0.309874i	$0.899713\pi$
$762$	−13.7258	−	30.5718i	−0.497234	−	1.10750i
$763$	−29.3771	+	32.6266i	−1.06352	+	1.18116i
$764$	−10.1562	+	31.2575i	−0.367438	+	1.13086i
$765$	2.83467	+	5.31667i	0.102488	+	0.192225i
$766$	13.3740	+	41.1608i	0.483221	+	1.48720i
$767$	−44.9448	−	20.0107i	−1.62286	−	0.722546i
$768$	17.7973	+	24.3359i	0.642204	+	0.878147i
$769$	−0.781310	−	7.43367i	−0.0281747	−	0.268065i	−0.999536	−	0.0304576i	$-0.990304\pi$
$769$	−0.781310	−	7.43367i	−0.0281747	−	0.268065i	0.971361	−	0.237607i	$-0.0763631\pi$
$770$	31.5232	+	8.03061i	1.13602	+	0.289403i
$771$	0.0426305	+	13.6731i	0.00153530	+	0.492424i
$772$	3.96733	−	37.7466i	0.142787	−	1.35853i
$773$	−5.32348	+	16.3840i	−0.191472	+	0.589291i	0.808527	+	0.588459i	$0.200265\pi$
$773$	−5.32348	+	16.3840i	−0.191472	+	0.589291i	−1.00000		0.000832682i	$0.999735\pi$
$774$	11.9305	−	2.61377i	0.428833	−	0.0939498i
$775$	29.4178	+	25.2003i	1.05672	+	0.905221i
$776$	7.00225	+	12.1283i	0.251366	+	0.435379i
$777$	−4.95864	+	23.6916i	−0.177890	+	0.849930i
$778$	−68.2373	+	30.3812i	−2.44643	+	1.08922i
$779$	−3.75589	+	1.67223i	−0.134569	+	0.0599139i
$780$	19.9574	−	40.7138i	0.714591	−	1.45779i
$781$	17.6997	+	7.88039i	0.633343	+	0.281983i
$782$	17.5502			0.627593
$783$	−38.6274	−	3.69496i	−1.38043	−	0.132047i
$784$	0.239866	+	0.738233i	0.00856666	+	0.0263655i
$785$	−2.10020	+	14.4100i	−0.0749592	+	0.514316i
$786$	43.0523	+	38.5221i	1.53563	+	1.37404i
$787$	0.503503	+	0.107023i	0.0179479	+	0.00381495i	0.216877	−	0.976199i	$-0.430413\pi$
$787$	0.503503	+	0.107023i	0.0179479	+	0.00381495i	−0.198929	+	0.980014i	$0.563746\pi$
$788$	42.0396	+	8.93580i	1.49760	+	0.318325i
$789$	−3.30145	+	15.7738i	−0.117535	+	0.561561i
$790$	−0.582402	−	1.10895i	−0.0207209	−	0.0394545i
$791$	−16.9445	−	52.1498i	−0.602477	−	1.85423i
$792$	−5.45029	−	16.4250i	−0.193668	−	0.583639i
$793$	−22.4804			−0.798302
$794$	41.4741	+	18.4654i	1.47186	+	0.655314i
$795$	−27.3547	+	7.78518i	−0.970171	+	0.276112i
$796$	7.82339	−	3.48320i	0.277293	−	0.123459i
$797$	7.30599	−	3.25284i	0.258792	−	0.115221i	−0.273240	−	0.961946i	$-0.588095\pi$
$797$	7.30599	−	3.25284i	0.258792	−	0.115221i	0.532032	+	0.846724i	$0.321429\pi$
$798$	11.1107	−	3.64841i	0.393313	−	0.129152i
$799$	3.47398	+	6.01711i	0.122901	+	0.212870i
$800$	−6.26341	−	26.2594i	−0.221445	−	0.928411i
$801$	−13.8188	−	15.1562i	−0.488263	−	0.535517i
$802$	−7.42609	+	22.8552i	−0.262224	+	0.807044i
$803$	−0.162986	+	1.55071i	−0.00575167	+	0.0547234i
$804$	59.8438	+	34.3025i	2.11053	+	1.20976i
$805$	−3.98316	−	61.4653i	−0.140388	−	2.16637i
$806$	6.63458	+	63.1239i	0.233693	+	2.22344i
$807$	10.7084	−	24.2548i	0.376955	−	0.853808i
$808$	−32.3497	−	14.4030i	−1.13806	−	0.506696i
$809$	−1.50879	−	4.64358i	−0.0530463	−	0.163260i	0.921024	−	0.389506i	$-0.127354\pi$
$809$	−1.50879	−	4.64358i	−0.0530463	−	0.163260i	−0.974070	+	0.226247i	$0.927354\pi$
$810$	−41.7311	−	19.9742i	−1.46628	−	0.701822i
$811$	−13.8925	+	42.7567i	−0.487832	+	1.50139i	0.340006	+	0.940423i	$0.389571\pi$
$811$	−13.8925	+	42.7567i	−0.487832	+	1.50139i	−0.827838	+	0.560968i	$0.810429\pi$
$812$	−53.1996	+	59.0841i	−1.86694	+	2.07345i
$813$	−13.2096	−	1.34676i	−0.463281	−	0.0472329i
$814$	−12.9519	−	14.3845i	−0.453963	−	0.504177i
$815$	5.84003	+	7.03241i	0.204567	+	0.246334i
$816$	−0.141185	−	0.314465i	−0.00494247	−	0.0110085i
$817$	−1.46606	−	0.652731i	−0.0512908	−	0.0228362i
$818$	16.9446			0.592454
$819$	33.9362	+	6.99248i	1.18583	+	0.244337i
$820$	27.7233	−	18.4946i	0.968139	−	0.645858i
$821$	−5.56020	+	52.9017i	−0.194052	+	1.84628i	0.272951	+	0.962028i	$0.412000\pi$
$821$	−5.56020	+	52.9017i	−0.194052	+	1.84628i	−0.467003	+	0.884256i	$0.654666\pi$
$822$	−0.0748059	−	23.9928i	−0.00260916	−	0.836846i
$823$	33.1996	+	36.8719i	1.15727	+	1.28527i	0.951838	+	0.306603i	$0.0991923\pi$
$823$	33.1996	+	36.8719i	1.15727	+	1.28527i	0.205429	+	0.978672i	$0.434141\pi$
$824$	−3.25806	+	5.64312i	−0.113500	+	0.196588i
$825$	−1.29903	+	16.8601i	−0.0452264	+	0.586992i
$826$	51.4274	+	89.0749i	1.78939	+	3.09931i
$827$	−3.93599	+	12.1137i	−0.136868	+	0.421236i	−0.995876	−	0.0907261i	$-0.971081\pi$
$827$	−3.93599	+	12.1137i	−0.136868	+	0.421236i	0.859008	+	0.511962i	$0.171081\pi$
$828$	−67.4588	+	49.6573i	−2.34436	+	1.72571i
$829$	−42.5264	−	30.8972i	−1.47700	−	1.07310i	−0.978507	−	0.206211i	$-0.933887\pi$
$829$	−42.5264	−	30.8972i	−1.47700	−	1.07310i	−0.498494	−	0.866893i	$-0.666113\pi$
$830$	23.4365	−	4.00935i	0.813493	−	0.139167i
$831$	−0.662595	+	0.600354i	−0.0229852	+	0.0208261i
$832$	22.9072	−	39.6764i	0.794164	−	1.37553i
$833$	0.328895	+	3.12923i	0.0113956	+	0.108421i
$834$	32.7253	+	3.33645i	1.13319	+	0.115532i
$835$	17.4296	+	33.1876i	0.603176	+	1.14850i
$836$	−1.79627	+	5.52834i	−0.0621251	+	0.191202i
$837$	39.9938	−	4.58212i	1.38239	−	0.158381i
$838$	−1.53424	−	4.72191i	−0.0529995	−	0.163116i
$839$	36.8344	−	7.82938i	1.27166	−	0.270300i	0.477839	−	0.878447i	$-0.341420\pi$
$839$	36.8344	−	7.82938i	1.27166	−	0.270300i	0.793824	+	0.608147i	$0.208087\pi$
$840$	−32.7757	+	17.3439i	−1.13087	+	0.598422i
$841$	−26.1828	−	5.56533i	−0.902855	−	0.191908i
$842$	−7.59902	−	72.2998i	−0.261879	−	2.49162i
$843$	4.53207	−	0.490630i	0.156093	−	0.0168982i
$844$	80.0953	+	35.6607i	2.75699	+	1.22749i
$845$	0.669098	+	0.0267828i	0.0230177	+	0.000921355i
$846$	−48.8729	−	21.3955i	−1.68029	−	0.735592i
$847$	18.8446	+	13.6914i	0.647508	+	0.470442i
$848$	1.59158	−	0.338301i	0.0546551	−	0.0116173i
$849$	−31.3478	−	42.8648i	−1.07585	−	1.47112i
$850$	0.255046	+	10.3211i	0.00874799	+	0.354009i
$851$	−18.3251	+	31.7401i	−0.628178	+	1.08804i
$852$	−53.6403	+	17.6139i	−1.83769	+	0.603442i
$853$	2.90852	−	27.6727i	0.0995859	−	0.947497i	−0.824642	−	0.565655i	$-0.808623\pi$
$853$	2.90852	−	27.6727i	0.0995859	−	0.947497i	0.924228	−	0.381841i	$-0.124710\pi$
$854$	38.0221	+	27.6247i	1.30109	+	0.945297i
$855$	2.86003	+	5.36423i	0.0978110	+	0.183453i
$856$	11.0436	−	8.02363i	0.377462	−	0.274242i
$857$	17.5755	+	30.4416i	0.600366	+	1.03986i	0.992765	+	0.120070i	$0.0383118\pi$
$857$	17.5755	+	30.4416i	0.600366	+	1.03986i	−0.392399	+	0.919795i	$0.628355\pi$
$858$	−20.5334	+	18.6046i	−0.700999	+	0.635151i
$859$	23.7541	+	5.04908i	0.810478	+	0.172272i	0.594468	−	0.804119i	$-0.297363\pi$
$859$	23.7541	+	5.04908i	0.810478	+	0.172272i	0.216009	+	0.976391i	$0.430696\pi$
$860$	12.6057	+	3.21134i	0.429852	+	0.109506i
$861$	18.9786	+	16.9816i	0.646789	+	0.578730i
$862$	−27.5170	+	30.5607i	−0.937232	+	1.04090i
$863$	−2.53910	−	7.81456i	−0.0864321	−	0.266011i	0.898494	−	0.438985i	$-0.144662\pi$
$863$	−2.53910	−	7.81456i	−0.0864321	−	0.266011i	−0.984926	+	0.172975i	$0.944662\pi$
$864$	−24.4266	−	13.7997i	−0.831010	−	0.469475i
$865$	−12.2453	+	8.16897i	−0.416351	+	0.277753i
$866$	−49.8628	+	55.3783i	−1.69441	+	1.88183i
$867$	5.91693	+	27.4164i	0.200949	+	0.931108i
$868$	41.2400	−	71.4297i	1.39978	−	2.42448i
$869$	0.0497327	+	0.473175i	0.00168707	+	0.0160514i
$870$	−56.3176	−	35.3466i	−1.90935	−	1.19836i
$871$	4.51595	−	42.9664i	0.153017	−	1.45586i
$872$	32.3781	+	23.5240i	1.09646	+	0.796624i
$873$	−11.5570	−	8.28707i	−0.391147	−	0.280475i
$874$	17.7072			0.598954
$875$	36.0892	−	3.23569i	1.22004	−	0.109386i
$876$	−2.68217	−	3.66759i	−0.0906220	−	0.123916i
$877$	20.6733	+	22.9600i	0.698087	+	0.775304i	0.983070	−	0.183228i	$-0.0586548\pi$
$877$	20.6733	+	22.9600i	0.698087	+	0.775304i	−0.284984	+	0.958532i	$0.591988\pi$
$878$	25.4152	−	11.3156i	0.857721	−	0.381882i
$879$	0.158343	+	50.7859i	0.00534076	+	1.71297i
$880$	0.139526	−	0.957325i	0.00470341	−	0.0322714i
$881$	−14.6144	+	10.6180i	−0.492373	+	0.357730i	−0.806096	−	0.591785i	$-0.798424\pi$
$881$	−14.6144	+	10.6180i	−0.492373	+	0.357730i	0.313723	+	0.949514i	$0.398424\pi$
$882$	−16.2783	−	17.8537i	−0.548118	−	0.601166i
$883$	22.5517	−	16.3848i	0.758925	−	0.551391i	−0.139655	−	0.990200i	$-0.544599\pi$
$883$	22.5517	−	16.3848i	0.758925	−	0.551391i	0.898580	+	0.438809i	$0.144599\pi$
$884$	−7.03605	+	7.81432i	−0.236648	+	0.262824i
$885$	−41.0260	+	34.2865i	−1.37907	+	1.15253i
$886$	16.5614	+	18.3933i	0.556392	+	0.617936i
$887$	22.2848	+	4.73679i	0.748251	+	0.159046i	0.566228	−	0.824249i	$-0.308402\pi$
$887$	22.2848	+	4.73679i	0.748251	+	0.159046i	0.182023	+	0.983294i	$0.441735\pi$
$888$	21.9509	+	2.23796i	0.736625	+	0.0751011i
$889$	26.6793	−	5.67087i	0.894797	−	0.190195i
$890$	−9.51476	−	33.8322i	−0.318935	−	1.13406i
$891$	11.9209	+	12.9119i	0.399364	+	0.432566i
$892$	−57.0454	+	41.4459i	−1.91002	+	1.38771i
$893$	3.50506	+	6.07093i	0.117292	+	0.203156i
$894$	9.19537	+	42.6072i	0.307539	+	1.42500i
$895$	23.6402	+	6.02239i	0.790204	+	0.201306i
$896$	−55.5292	+	24.7232i	−1.85510	+	0.825944i
$897$	45.5172	+	26.0905i	1.51978	+	0.871136i
$898$	61.0454	−	12.9756i	2.03711	−	0.433002i
$899$	57.8541			1.92954
$900$	−30.1832	−	38.9501i	−1.00611	−	1.29834i
$901$	6.59569			0.219734
$902$	−19.9204	+	4.23421i	−0.663276	+	0.140984i
$903$	0.0309931	+	9.94055i	0.00103139	+	0.330801i
$904$	−45.6637	+	20.3308i	−1.51875	+	0.676192i
$905$	−10.4076	+	16.4682i	−0.345961	+	0.547421i
$906$	79.6251	+	25.5976i	2.64537	+	0.850422i
$907$	−0.183281	−	0.317451i	−0.00608574	−	0.0105408i	0.862966	−	0.505261i	$-0.168604\pi$
$907$	−0.183281	−	0.317451i	−0.00608574	−	0.0105408i	−0.869052	+	0.494720i	$0.835270\pi$
$908$	13.9812	−	10.1579i	0.463982	−	0.337103i
$909$	35.9582	−	0.224226i	1.19266	−	0.00743711i
$910$	46.5988	+	36.7912i	1.54473	+	1.21962i
$911$	−52.9968	+	11.2648i	−1.75586	+	0.373220i	−0.969604	−	0.244680i	$-0.921317\pi$
$911$	−52.9968	+	11.2648i	−1.75586	+	0.373220i	−0.786257	+	0.617900i	$0.787984\pi$
$912$	−0.142448	−	0.317278i	−0.00471693	−	0.0105061i
$913$	−8.83414	−	1.87775i	−0.292367	−	0.0621446i
$914$	−24.0199	−	26.6768i	−0.794508	−	0.882390i
$915$	−10.7533	+	21.9370i	−0.355492	+	0.725215i
$916$	38.4664	−	42.7213i	1.27097	−	1.41155i
$917$	−38.0399	+	27.6376i	−1.25619	+	0.912674i
$918$	8.04018	+	7.10437i	0.265365	+	0.234479i
$919$	−29.1500	+	21.1787i	−0.961568	+	0.698620i	−0.953514	−	0.301347i	$-0.902564\pi$
$919$	−29.1500	+	21.1787i	−0.961568	+	0.698620i	−0.00805385	+	0.999968i	$0.502564\pi$
$920$	−55.3440	+	9.46786i	−1.82464	+	0.312146i
$921$	14.0074	−	8.14554i	0.461561	−	0.268405i
$922$	15.7581	−	7.01595i	0.518965	−	0.231058i
$923$	23.6615	+	26.2788i	0.778829	+	0.864977i
$924$	35.7973	−	3.87532i	1.17764	−	0.127489i
$925$	−18.9323	−	10.3156i	−0.622490	−	0.339173i
$926$	−76.1019			−2.50086
$927$	0.650608	−	6.58485i	0.0213688	−	0.216275i
$928$	−32.6197	−	23.6996i	−1.07079	−	0.777977i
$929$	1.05099	−	9.99955i	0.0344820	−	0.328074i	−0.963659	−	0.267134i	$-0.913923\pi$
$929$	1.05099	−	9.99955i	0.0344820	−	0.328074i	0.998141	−	0.0609405i	$-0.0194100\pi$
$930$	64.7717	+	23.7205i	2.12395	+	0.777826i
$931$	0.331838	+	3.15722i	0.0108755	+	0.103474i
$932$	−16.1569	+	27.9846i	−0.529237	+	0.916666i
$933$	34.0129	+	10.9344i	1.11353	+	0.357975i
$934$	5.05222	−	5.61106i	0.165314	−	0.183599i
$935$	1.36003	−	3.67818i	0.0444778	−	0.120289i
$936$	3.10564	−	31.4324i	0.101511	−	1.02740i
$937$	−5.85784	−	18.0286i	−0.191367	−	0.588968i	−1.00000		0.000653814i	$-0.999792\pi$
$937$	−5.85784	−	18.0286i	−0.191367	−	0.588968i	0.808633	−	0.588314i	$-0.200208\pi$
$938$	−60.4367	+	67.1217i	−1.97333	+	2.19160i
$939$	7.25195	−	34.6486i	0.236658	−	1.13071i
$940$	−36.3028	−	43.7149i	−1.18407	−	1.42582i
$941$	46.9128	+	9.97162i	1.52931	+	0.325066i	0.894311	−	0.447445i	$-0.147666\pi$
$941$	46.9128	+	9.97162i	1.52931	+	0.325066i	0.635002	+	0.772511i	$0.280999\pi$
$942$	5.47055	+	25.3481i	0.178240	+	0.825884i
$943$	19.2805	+	33.3948i	0.627860	+	1.08749i
$944$	2.47469	−	1.79797i	0.0805444	−	0.0585189i
$945$	23.0566	−	29.7712i	0.750030	−	0.968457i
$946$	−6.43115	−	4.67250i	−0.209095	−	0.151916i
$947$	4.02015	−	38.2492i	0.130637	−	1.24293i	−0.711118	−	0.703072i	$-0.751811\pi$
$947$	4.02015	−	38.2492i	0.130637	−	1.24293i	0.841756	−	0.539859i	$-0.181522\pi$
$948$	−1.03321	−	0.924491i	−0.0335572	−	0.0300261i
$949$	−1.42293	+	2.46459i	−0.0461903	+	0.0800040i
$950$	0.257327	+	10.4134i	0.00834879	+	0.337855i
$951$	−0.150719	+	0.0163165i	−0.00488741	+	0.000529099i
$952$	8.41164	−	1.78795i	0.272623	−	0.0579478i
$953$	26.9203	+	19.5587i	0.872034	+	0.633569i	0.931132	−	0.364683i	$-0.118823\pi$
$953$	26.9203	+	19.5587i	0.872034	+	0.633569i	−0.0590983	+	0.998252i	$0.518823\pi$
$954$	−40.7871	+	30.0239i	−1.32053	+	0.972061i
$955$	7.75848	−	20.9827i	0.251059	−	0.678983i
$956$	−50.0159	−	22.2685i	−1.61763	−	0.720215i
$957$	14.9088	+	20.3862i	0.481932	+	0.658992i
$958$	−1.98000	−	18.8385i	−0.0639709	−	0.608643i
$959$	19.1013	+	4.06010i	0.616812	+	0.131107i
$960$	−27.7600	−	41.3324i	−0.895950	−	1.33400i
$961$	−28.3844	+	6.03329i	−0.915625	+	0.194622i
$962$	−10.9170	−	33.5990i	−0.351977	−	1.08327i
$963$	−6.85589	+	12.0476i	−0.220928	+	0.388229i
$964$	22.5193	−	69.3072i	0.725297	−	2.23224i
$965$	−3.72593	+	25.5646i	−0.119942	+	0.822954i
$966$	−44.9245	−	100.061i	−1.44542	−	3.21942i
$967$	−4.59861	−	43.7528i	−0.147881	−	1.40700i	−0.776909	−	0.629613i	$-0.783213\pi$
$967$	−4.59861	−	43.7528i	−0.147881	−	1.40700i	0.629027	−	0.777383i	$-0.283453\pi$
$968$	10.6168	−	18.3888i	0.341237	−	0.591040i
$969$	−0.297407	−	1.37805i	−0.00955410	−	0.0442694i
$970$	−11.3303	−	21.5739i	−0.363794	−	0.692697i
$971$	15.7738	+	11.4603i	0.506204	+	0.367779i	0.811382	−	0.584517i	$-0.198716\pi$
$971$	15.7738	+	11.4603i	0.506204	+	0.367779i	−0.305178	+	0.952295i	$0.598716\pi$
$972$	−51.0060	−	4.55827i	−1.63602	−	0.146207i
$973$	−8.27344	+	25.4630i	−0.265234	+	0.816307i
$974$	−17.4805	−	30.2771i	−0.560112	−	0.970142i
$975$	−14.6821	+	27.1473i	−0.470202	+	0.869410i
$976$	0.698856	−	1.21045i	0.0223698	−	0.0387457i
$977$	−30.0457	−	33.3691i	−0.961248	−	1.06757i	−0.997669	−	0.0682370i	$-0.978263\pi$
$977$	−30.0457	−	33.3691i	−0.961248	−	1.06757i	0.0364216	−	0.999337i	$-0.488404\pi$
$978$	14.1225	+	8.09503i	0.451588	+	0.258851i
$979$	−1.39539	+	13.2763i	−0.0445970	+	0.424312i
$980$	−6.96676	−	24.7721i	−0.222545	−	0.791316i
$981$	−39.8044	−	8.20160i	−1.27086	−	0.261857i
$982$	3.63642			0.116043
$983$	−46.8586	−	20.8628i	−1.49456	−	0.665419i	−0.513314	−	0.858201i	$-0.671582\pi$
$983$	−46.8586	−	20.8628i	−1.49456	−	0.665419i	−0.981242	+	0.192782i	$0.938249\pi$
$984$	13.5868	−	18.8238i	0.433133	−	0.600081i
$985$	−28.3491	−	7.22200i	−0.903278	−	0.230112i
$986$	10.3179	+	11.4591i	0.328587	+	0.364933i
$987$	25.4136	−	35.2091i	0.808923	−	1.12072i
$988$	−7.09899	+	7.88423i	−0.225849	+	0.250831i
$989$	−4.65124	+	14.3150i	−0.147901	+	0.455192i
$990$	8.33296	+	28.9365i	0.264839	+	0.919661i
$991$	2.34318	+	7.21156i	0.0744335	+	0.229083i	0.981351	−	0.192226i	$-0.0615708\pi$
$991$	2.34318	+	7.21156i	0.0744335	+	0.229083i	−0.906917	+	0.421309i	$0.861571\pi$
$992$	38.2123	+	17.0132i	1.21324	+	0.540170i
$993$	38.8769	−	4.20872i	1.23372	−	0.133560i
$994$	−7.72755	−	73.5227i	−0.245103	−	2.33200i
$995$	−5.41575	+	2.15604i	−0.171691	+	0.0683510i
$996$	22.7509	−	13.2300i	0.720890	−	0.419208i
$997$	−2.44900	+	23.3007i	−0.0775606	+	0.737940i	0.884764	+	0.466039i	$0.154319\pi$
$997$	−2.44900	+	23.3007i	−0.0775606	+	0.737940i	−0.962325	+	0.271902i	$0.912347\pi$
$998$	22.0054	−	67.7258i	0.696570	−	2.14382i
$999$	−21.2437	+	7.12285i	−0.672121	+	0.225357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.5	yes	224
3.2	odd	2		675.2.r.a.496.24		224
9.2	odd	6		675.2.r.a.46.5		224
9.7	even	3	inner	225.2.q.a.196.24	yes	224
25.6	even	5	inner	225.2.q.a.31.24	✓	224
75.56	odd	10		675.2.r.a.631.5		224
225.56	odd	30		675.2.r.a.181.24		224
225.106	even	15	inner	225.2.q.a.106.5	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.24	✓	224	25.6	even	5	inner
225.2.q.a.106.5	yes	224	225.106	even	15	inner
225.2.q.a.121.5	yes	224	1.1	even	1	trivial
225.2.q.a.196.24	yes	224	9.7	even	3	inner
675.2.r.a.46.5		224	9.2	odd	6
675.2.r.a.181.24		224	225.56	odd	30
675.2.r.a.496.24		224	3.2	odd	2
675.2.r.a.631.5		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)

\(f(q)\)	\(=\)	\(q+(-2.24869 + 0.477974i) q^{2} +(1.49729 - 0.870698i) q^{3} +(3.00107 - 1.33616i) q^{4} +(-2.07749 + 0.827061i) q^{5} +(-2.95078 + 2.67360i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 + 1.73649i) q^{8} +(1.48377 - 2.60738i) q^{9} +O(q^{10})\)	\(q+(-2.24869 + 0.477974i) q^{2} +(1.49729 - 0.870698i) q^{3} +(3.00107 - 1.33616i) q^{4} +(-2.07749 + 0.827061i) q^{5} +(-2.95078 + 2.67360i) q^{6} +(-1.62043 - 2.80667i) q^{7} +(-2.39008 + 1.73649i) q^{8} +(1.48377 - 2.60738i) q^{9} +(4.27633 - 2.85279i) q^{10} +(-1.90993 + 0.405969i) q^{11} +(3.33008 - 4.61365i) q^{12} +(-3.48590 - 0.740952i) q^{13} +(4.98536 + 5.53681i) q^{14} +(-2.39049 + 3.04722i) q^{15} +(0.148264 - 0.164664i) q^{16} +(0.726639 - 0.527934i) q^{17} +(-2.09028 + 6.57240i) q^{18} +(0.733140 - 0.532657i) q^{19} +(-5.12960 + 5.25793i) q^{20} +(-4.87002 - 2.79150i) q^{21} +(4.10081 - 1.82580i) q^{22} +(-5.68729 - 6.31638i) q^{23} +(-2.06669 + 4.68108i) q^{24} +(3.63194 - 3.43642i) q^{25} +8.19288 q^{26} +(-0.0486015 - 5.19593i) q^{27} +(-8.61318 - 6.25784i) q^{28} +(0.780596 - 7.42687i) q^{29} +(3.91899 - 7.99485i) q^{30} +(0.809799 + 7.70472i) q^{31} +(2.69961 - 4.67586i) q^{32} +(-2.50625 + 2.27083i) q^{33} +(-1.38165 + 1.53448i) q^{34} +(5.68771 + 4.49063i) q^{35} +(0.969015 - 9.80748i) q^{36} +(-1.33249 - 4.10099i) q^{37} +(-1.39401 + 1.54820i) q^{38} +(-5.86456 + 1.92575i) q^{39} +(3.52918 - 5.58430i) q^{40} +(-4.43771 - 0.943263i) q^{41} +(12.2854 + 3.94948i) q^{42} +(-0.885445 - 1.53364i) q^{43} +(-5.18939 + 3.77032i) q^{44} +(-0.926058 + 6.64398i) q^{45} +(15.8080 + 11.4852i) q^{46} +(-0.808594 + 7.69326i) q^{47} +(0.0786221 - 0.375643i) q^{48} +(-1.75159 + 3.03384i) q^{49} +(-6.52459 + 9.46343i) q^{50} +(0.628320 - 1.42316i) q^{51} +(-11.4515 + 2.43408i) q^{52} +(5.94096 + 4.31636i) q^{53} +(2.59281 + 11.6608i) q^{54} +(3.63211 - 2.42303i) q^{55} +(8.74672 + 3.89429i) q^{56} +(0.633941 - 1.43589i) q^{57} +(1.79453 + 17.0739i) q^{58} +(13.5034 + 2.87024i) q^{59} +(-3.10245 + 12.3390i) q^{60} +(6.17017 - 1.31151i) q^{61} +(-5.50365 - 16.9385i) q^{62} +(-9.72239 + 0.0606264i) q^{63} +(-3.97259 + 12.2264i) q^{64} +(7.85475 - 1.34373i) q^{65} +(4.55039 - 6.30432i) q^{66} +(1.26718 + 12.0564i) q^{67} +(1.47529 - 2.55527i) q^{68} +(-14.0152 - 4.50555i) q^{69} +(-14.9363 - 7.37947i) q^{70} +(-8.02747 - 5.83230i) q^{71} +(0.981371 + 8.80840i) q^{72} +(0.246766 - 0.759468i) q^{73} +(4.95654 + 8.58498i) q^{74} +(2.44599 - 8.30766i) q^{75} +(1.48849 - 2.57813i) q^{76} +(4.23433 + 4.70270i) q^{77} +(12.2671 - 7.13352i) q^{78} +(0.0254700 - 0.242331i) q^{79} +(-0.171830 + 0.464711i) q^{80} +(-4.59685 - 7.73750i) q^{81} +10.4299 q^{82} +(4.22548 + 1.88131i) q^{83} +(-18.3451 - 1.87034i) q^{84} +(-1.07295 + 1.69775i) q^{85} +(2.72413 + 3.02546i) q^{86} +(-5.29778 - 11.7999i) q^{87} +(3.85993 - 4.28688i) q^{88} +(2.11267 - 6.50212i) q^{89} +(-1.09323 - 15.3829i) q^{90} +(3.56906 + 10.9844i) q^{91} +(-25.5076 - 11.3567i) q^{92} +(7.92099 + 10.8311i) q^{93} +(-1.85890 - 17.6863i) q^{94} +(-1.08255 + 1.71294i) q^{95} +(-0.0291570 - 9.35167i) q^{96} +(0.495505 - 4.71441i) q^{97} +(2.48869 - 7.65939i) q^{98} +(-1.77539 + 5.58228i) 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

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