LMFDB - Embedded newform 225.2.q.a.106.5

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			106.5
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.5

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

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

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	−0.673914	−	0.738810i	$-0.735388\pi$
$2$	−2.24869	−	0.477974i	−1.59007	−	0.337979i	−0.916152	+	0.400831i	$0.868721\pi$
$3$	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	0.378359	+	0.925659i	$0.376489\pi$
$7$	−1.62043	+	2.80667i	−0.612465	+	1.06082i	−0.990824	+	0.135161i	$0.956845\pi$
$8$	−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	−0.0892334	−	0.996011i	$-0.528442\pi$
$11$	−1.90993	−	0.405969i	−0.575866	−	0.122404i	−0.486633	+	0.873607i	$0.661775\pi$
$12$	3.33008	+	4.61365i	0.961312	+	1.33185i
$13$	−3.48590	+	0.740952i	−0.966816	+	0.205503i	−0.664155	−	0.747595i	$-0.731208\pi$
$13$	−3.48590	+	0.740952i	−0.966816	+	0.205503i	−0.302661	+	0.953098i	$0.597875\pi$
$14$	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	0.672406	−	0.740182i	$-0.265261\pi$
$17$	0.726639	+	0.527934i	0.176236	+	0.128043i	−0.496170	+	0.868225i	$0.665261\pi$
$18$	−2.09028	−	6.57240i	−0.492684	−	1.54913i
$19$	0.733140	+	0.532657i	0.168194	+	0.122200i	0.668698	−	0.743534i	$-0.266852\pi$
$19$	0.733140	+	0.532657i	0.168194	+	0.122200i	−0.500504	+	0.865734i	$0.666852\pi$
$20$	−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	−0.248550	+	0.968619i	$0.579954\pi$
$23$	−5.68729	+	6.31638i	−1.18588	+	1.31706i	−0.937332	+	0.348437i	$0.886713\pi$
$24$	−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	0.789115	+	0.614246i	$0.210540\pi$
$29$	0.780596	+	7.42687i	0.144953	+	1.37914i	−0.644162	+	0.764889i	$0.722794\pi$
$30$	3.91899	+	7.99485i	0.715506	+	1.45965i
$31$	0.809799	−	7.70472i	0.145444	−	1.38381i	−0.641660	−	0.766989i	$-0.721754\pi$
$31$	0.809799	−	7.70472i	0.145444	−	1.38381i	0.787104	−	0.616820i	$-0.211579\pi$
$32$	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	0.779780	+	0.626054i	$0.215331\pi$
$37$	−1.33249	+	4.10099i	−0.219061	+	0.674199i	−0.998840	+	0.0481453i	$0.984669\pi$
$38$	−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	−0.540954	−	0.841052i	$-0.681937\pi$
$41$	−4.43771	+	0.943263i	−0.693053	+	0.147313i	−0.152099	+	0.988365i	$0.548603\pi$
$42$	12.2854	−	3.94948i	1.89568	−	0.609417i
$43$	−0.885445	+	1.53364i	−0.135029	+	0.233877i	−0.925609	−	0.378482i	$-0.876446\pi$
$43$	−0.885445	+	1.53364i	−0.135029	+	0.233877i	0.790579	+	0.612359i	$0.209779\pi$
$44$	−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	−0.880102	−	0.474784i	$-0.842526\pi$
$47$	−0.808594	−	7.69326i	−0.117946	−	1.12218i	0.762157	−	0.647393i	$-0.224141\pi$
$48$	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	−0.0995259	−	0.995035i	$-0.531733\pi$
$53$	5.94096	−	4.31636i	0.816053	−	0.592897i	0.915579	+	0.402137i	$0.131733\pi$
$54$	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	0.787786	−	0.615950i	$-0.211228\pi$
$59$	13.5034	−	2.87024i	1.75799	−	0.373673i	0.970207	+	0.242277i	$0.0778942\pi$
$60$	−3.10245	−	12.3390i	−0.400525	−	1.59296i
$61$	6.17017	+	1.31151i	0.790009	+	0.167922i	0.585209	−	0.810882i	$-0.301012\pi$
$61$	6.17017	+	1.31151i	0.790009	+	0.167922i	0.204800	+	0.978804i	$0.434346\pi$
$62$	−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	−0.590949	−	0.806709i	$-0.701246\pi$
$67$	1.26718	−	12.0564i	0.154811	−	1.47292i	0.745759	−	0.666215i	$-0.232087\pi$
$68$	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	−0.951441	−	0.307833i	$-0.900396\pi$
$71$	−8.02747	+	5.83230i	−0.952686	+	0.692167i	−0.00124504	+	0.999999i	$0.500396\pi$
$72$	0.981371	−	8.80840i	0.115656	−	1.03808i
$73$	0.246766	+	0.759468i	0.0288818	+	0.0888891i	0.964458	−	0.264235i	$-0.0851194\pi$
$73$	0.246766	+	0.759468i	0.0288818	+	0.0888891i	−0.935577	+	0.353124i	$0.885119\pi$
$74$	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	0.995861	−	0.0908865i	$-0.0289700\pi$
$79$	0.0254700	+	0.242331i	0.00286560	+	0.0272644i	−0.992996	+	0.118151i	$0.962303\pi$
$80$	−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	−0.161510	−	0.986871i	$-0.551636\pi$
$83$	4.22548	−	1.88131i	0.463807	−	0.206500i	0.625317	+	0.780371i	$0.284970\pi$
$84$	−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	0.998397	+	0.0565946i	$0.0180243\pi$
$89$	2.11267	+	6.50212i	0.223942	+	0.689224i	−0.774455	+	0.632629i	$0.781976\pi$
$90$	−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	0.990449	+	0.137882i	$0.0440293\pi$
$97$	0.495505	+	4.71441i	0.0503109	+	0.478676i	−0.940138	+	0.340794i	$0.889304\pi$
$98$	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	−0.397016	−	0.917812i	$-0.629954\pi$
$101$	5.99315	−	10.3804i	0.596341	−	1.03289i	0.993356	−	0.115080i	$-0.0367126\pi$
$102$	−0.732667	−	3.50056i	−0.0725449	−	0.346607i
$103$	2.01495	+	0.897113i	0.198539	+	0.0883952i	0.503598	−	0.863938i	$-0.332009\pi$
$103$	2.01495	+	0.897113i	0.198539	+	0.0883952i	−0.305059	+	0.952334i	$0.598676\pi$
$104$	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	0.523251	+	0.852178i	$0.324719\pi$
$109$	−4.18621	+	12.8838i	−0.400966	+	1.23405i	−0.924217	+	0.381867i	$0.875281\pi$
$110$	−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	0.652536	−	0.757758i	$-0.273705\pi$
$113$	16.5497	−	3.51775i	1.55687	−	0.330922i	0.904329	+	0.426836i	$0.140372\pi$
$114$	−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	−0.997654	−	0.0684626i	$-0.978191\pi$
$127$	−2.60072	−	8.00418i	−0.230776	−	0.710256i	0.766877	−	0.641794i	$-0.221809\pi$
$128$	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	0.703005	+	0.711185i	$0.251841\pi$
$131$	−1.51655	+	14.4290i	−0.132501	+	1.26067i	−0.835506	+	0.549481i	$0.814825\pi$
$132$	−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	0.545871	−	0.837869i	$-0.316199\pi$
$137$	−4.03189	−	4.47786i	−0.344467	−	0.382570i	−0.890338	+	0.455299i	$0.849532\pi$
$138$	33.6694	−	3.43270i	2.86613	−	0.292210i
$139$	−5.52782	+	6.13927i	−0.468864	+	0.520726i	−0.930475	−	0.366357i	$-0.880605\pi$
$139$	−5.52782	+	6.13927i	−0.468864	+	0.520726i	0.461611	+	0.887083i	$0.347272\pi$
$140$	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	0.998282	−	0.0585987i	$-0.0186632\pi$
$149$	5.47333	+	9.48009i	0.448393	+	0.776639i	−0.549889	+	0.835238i	$0.685330\pi$
$150$	−1.52943	−	19.8505i	−0.124878	−	1.62079i
$151$	−10.5024	+	18.1907i	−0.854675	+	1.48034i	0.0222707	+	0.999752i	$0.492910\pi$
$151$	−10.5024	+	18.1907i	−0.854675	+	1.48034i	−0.876946	+	0.480589i	$0.840423\pi$
$152$	−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	0.966208	−	0.257763i	$-0.0829854\pi$
$157$	3.25622	+	5.63994i	0.259875	+	0.450116i	−0.706333	+	0.707879i	$0.749652\pi$
$158$	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	−0.988262	−	0.152766i	$-0.951182\pi$
$163$	−1.26328	+	3.88796i	−0.0989474	+	0.304529i	0.889315	+	0.457295i	$0.151182\pi$
$164$	−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	0.689135	+	0.724633i	$0.257991\pi$
$167$	−1.75234	+	16.6724i	−0.135600	+	1.29015i	−0.824735	+	0.565519i	$0.808676\pi$
$168$	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	0.446075	−	0.894995i	$-0.352821\pi$
$173$	6.43913	+	1.36868i	0.489558	+	0.104059i	0.0434826	+	0.999054i	$0.486155\pi$
$174$	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	−0.866564	−	0.499066i	$-0.833677\pi$
$179$	−8.82628	+	6.41267i	−0.659707	+	0.479305i	0.206857	+	0.978371i	$0.433677\pi$
$180$	6.09826	−	21.1764i	0.454537	−	1.57839i
$181$	7.04839	+	5.12096i	0.523903	+	0.380638i	0.818072	−	0.575116i	$-0.195043\pi$
$181$	7.04839	+	5.12096i	0.523903	+	0.380638i	−0.294169	+	0.955753i	$0.595043\pi$
$182$	−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	0.450560	−	0.892746i	$-0.351224\pi$
$191$	−6.69443	−	7.43491i	−0.484392	−	0.537971i	−0.934952	+	0.354775i	$0.884558\pi$
$192$	4.69735	−	21.7654i	0.339002	−	1.57078i
$193$	5.77682	+	10.0057i	0.415824	+	0.720229i	0.995515	−	0.0946081i	$-0.0301598\pi$
$193$	5.77682	+	10.0057i	0.415824	+	0.720229i	−0.579690	+	0.814837i	$0.696826\pi$
$194$	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	−0.142990	−	0.989724i	$-0.545672\pi$
$197$	10.5844	−	7.69002i	0.754108	−	0.547891i	0.897097	+	0.441833i	$0.145672\pi$
$198$	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	0.321151	−	0.947028i	$-0.395930\pi$
$211$	17.8584	−	19.8337i	1.22942	−	1.36541i	0.908271	−	0.418383i	$-0.137403\pi$
$212$	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	−0.558404	−	0.829569i	$-0.688586\pi$
$223$	−20.9953	−	4.46269i	−1.40595	−	0.298844i	−0.847544	+	0.530725i	$0.821920\pi$
$224$	−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	0.375485	−	0.926828i	$-0.377476\pi$
$227$	5.14571	+	1.09375i	0.341533	+	0.0725950i	−0.0339524	+	0.999423i	$0.510809\pi$
$228$	−0.0160764	+	5.15624i	−0.00106468	+	0.341480i
$229$	15.9866	+	7.11768i	1.05642	+	0.470349i	0.860066	−	0.510183i	$-0.170422\pi$
$229$	15.9866	+	7.11768i	1.05642	+	0.470349i	0.196356	+	0.980533i	$0.437089\pi$
$230$	−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	0.295767	−	0.955260i	$-0.404425\pi$
$233$	−7.95794	−	5.78178i	−0.521342	−	0.378777i	−0.817109	+	0.576483i	$0.804425\pi$
$234$	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	−0.986620	−	0.163036i	$-0.947871\pi$
$239$	−11.1518	+	12.3853i	−0.721347	+	0.801137i	0.265273	+	0.964173i	$0.414538\pi$
$240$	0.147343	−	0.845421i	0.00951095	−	0.0545717i
$241$	14.8435	+	16.4854i	0.956156	+	1.06192i	0.998026	+	0.0627962i	$0.0200018\pi$
$241$	14.8435	+	16.4854i	0.956156	+	1.06192i	−0.0418699	+	0.999123i	$0.513332\pi$
$242$	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	0.716259	−	0.697835i	$-0.245853\pi$
$257$	−3.94709	−	6.83657i	−0.246213	−	0.426453i	−0.962472	+	0.271381i	$0.912520\pi$
$258$	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	0.519962	−	0.854190i	$-0.325946\pi$
$263$	−6.22580	−	6.91445i	−0.383899	−	0.426364i	−0.903861	+	0.427826i	$0.859280\pi$
$264$	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	0.897394	−	0.441229i	$-0.145457\pi$
$269$	12.3841	+	8.99756i	0.755071	+	0.548591i	−0.142324	+	0.989820i	$0.545457\pi$
$270$	−15.0307	+	22.0808i	−0.914741	+	1.34380i
$271$	−6.20201	+	4.50602i	−0.376745	+	0.273721i	−0.760002	−	0.649920i	$-0.774802\pi$
$271$	−6.20201	+	4.50602i	−0.376745	+	0.273721i	0.383257	+	0.923642i	$0.374802\pi$
$272$	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	0.192717	−	0.981254i	$-0.438270\pi$
$277$	−0.504942	−	0.107329i	−0.0303390	−	0.00644876i	−0.223056	+	0.974806i	$0.571603\pi$
$278$	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	−0.333766	−	0.942656i	$-0.608320\pi$
$281$	2.40434	−	1.07048i	0.143431	−	0.0638595i	0.477197	+	0.878796i	$0.341653\pi$
$282$	−18.1827	+	24.8630i	−1.08276	+	1.48057i
$283$	−3.20483	+	30.4919i	−0.190507	+	1.81255i	0.314302	+	0.949323i	$0.398230\pi$
$283$	−3.20483	+	30.4919i	−0.190507	+	1.81255i	−0.504809	+	0.863231i	$0.668437\pi$
$284$	−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	−0.875258	−	0.483656i	$-0.839309\pi$
$293$	−14.6607	−	25.3931i	−0.856488	−	1.48348i	0.0187704	−	0.999824i	$-0.494025\pi$
$294$	−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	−0.211479	−	0.977383i	$-0.567828\pi$
$311$	13.8023	−	15.3290i	0.782655	−	0.869227i	0.994134	+	0.108156i	$0.0344946\pi$
$312$	10.6727	+	14.7865i	0.604224	+	0.837119i
$313$	13.6756	+	15.1883i	0.772990	+	0.858492i	0.993135	−	0.116975i	$-0.0373198\pi$
$313$	13.6756	+	15.1883i	0.772990	+	0.858492i	−0.220145	+	0.975467i	$0.570653\pi$
$314$	−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	−0.408981	−	0.912543i	$-0.634116\pi$
$317$	−0.0799592	+	0.0356001i	−0.00449095	+	0.00199950i	0.404490	+	0.914542i	$0.367449\pi$
$318$	−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	0.247846	−	0.968799i	$-0.420277\pi$
$331$	20.6249	−	9.18279i	1.13365	−	0.504732i	0.885800	+	0.464067i	$0.153610\pi$
$332$	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	−0.295653	−	0.955295i	$-0.595537\pi$
$337$	−3.25281	+	0.691407i	−0.177192	+	0.0376633i	0.118461	+	0.992959i	$0.462204\pi$
$338$	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	0.0396331	−	0.999214i	$-0.487381\pi$
$347$	−12.6001	−	5.60992i	−0.676408	−	0.301156i	−0.716041	+	0.698058i	$0.754048\pi$
$348$	−31.6655	+	28.3335i	−1.69745	+	1.51883i
$349$	−7.45084	+	12.9052i	−0.398834	+	0.690801i	−0.993582	−	0.113111i	$-0.963918\pi$
$349$	−7.45084	+	12.9052i	−0.398834	+	0.690801i	0.594748	+	0.803912i	$0.297252\pi$
$350$	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	0.988845	+	0.148950i	$0.0475895\pi$
$353$	0.987835	+	9.39862i	0.0525771	+	0.500238i	−0.936268	+	0.351288i	$0.885744\pi$
$354$	−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	−0.933876	−	0.357596i	$-0.883596\pi$
$359$	0.603190	−	1.85643i	0.0318351	−	0.0979785i	0.965712	+	0.259618i	$0.0835965\pi$
$360$	−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	−0.572698	−	0.819767i	$-0.694103\pi$
$367$	−6.64186	+	2.95715i	−0.346702	+	0.154362i	0.225996	+	0.974128i	$0.427436\pi$
$368$	−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	−0.925136	−	0.379637i	$-0.876049\pi$
$373$	−8.70785	+	9.67105i	−0.450875	+	0.500748i	0.474260	+	0.880385i	$0.342716\pi$
$374$	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	−0.569174	−	0.822217i	$-0.692737\pi$
$379$	0.718684	−	0.522154i	0.0369163	−	0.0268213i	0.606090	+	0.795396i	$0.292737\pi$
$380$	−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	0.821656	+	0.569984i	$0.193051\pi$
$383$	−1.96783	+	18.7226i	−0.100551	+	0.956681i	−0.922207	+	0.386697i	$0.873616\pi$
$384$	−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	0.923581	−	0.383403i	$-0.125248\pi$
$389$	31.7812	+	6.75530i	1.61137	+	0.342507i	0.687790	+	0.725910i	$0.258581\pi$
$390$	−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	−0.911451	−	0.411409i	$-0.865037\pi$
$397$	−15.9764	+	11.6075i	−0.801832	+	0.582565i	0.109619	+	0.993974i	$0.465037\pi$
$398$	−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	0.966509	−	0.256631i	$-0.0826125\pi$
$401$	5.22664	+	9.05280i	0.261006	+	0.452075i	−0.705504	+	0.708706i	$0.749279\pi$
$402$	−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	−0.382676	−	0.923883i	$-0.624997\pi$
$409$	−7.20958	+	1.53244i	−0.356491	+	0.0757744i	0.0261852	+	0.999657i	$0.491664\pi$
$410$	−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	−0.987623	−	0.156847i	$-0.949867\pi$
$419$	0.225746	−	2.14783i	0.0110284	−	0.104928i	0.998651	+	0.0519187i	$0.0165337\pi$
$420$	39.6588	+	11.2869i	1.93515	+	0.550746i
$421$	−3.30546	−	31.4493i	−0.161098	−	1.53275i	−0.714383	−	0.699755i	$-0.753292\pi$
$421$	−3.30546	−	31.4493i	−0.161098	−	1.53275i	0.553285	−	0.832992i	$-0.313374\pi$
$422$	−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	0.878980	−	0.476858i	$-0.158225\pi$
$431$	14.4718	+	10.5144i	0.697081	+	0.506459i	−0.181899	+	0.983317i	$0.558225\pi$
$432$	−0.862787	+	0.762366i	−0.0415109	+	0.0366794i
$433$	26.2239	+	19.0528i	1.26024	+	0.915620i	0.998770	−	0.0495910i	$-0.0157918\pi$
$433$	26.2239	+	19.0528i	1.26024	+	0.915620i	0.261473	+	0.965211i	$0.415792\pi$
$434$	−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	−0.0834213	−	0.996514i	$-0.526585\pi$
$439$	−11.8370	−	2.51603i	−0.564949	−	0.120084i	−0.481528	+	0.876431i	$0.659918\pi$
$440$	−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	−0.965101	−	0.261878i	$-0.915658\pi$
$443$	−5.38308	+	9.32377i	−0.255758	+	0.442986i	0.709343	+	0.704863i	$0.248992\pi$
$444$	−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	−0.623597	−	0.781746i	$-0.714329\pi$
$457$	7.80737	−	13.5228i	0.365213	−	0.632568i	0.988810	+	0.149178i	$0.0476627\pi$
$458$	−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	0.0338016	−	0.999429i	$-0.489239\pi$
$461$	−7.33926	−	1.56001i	−0.341823	−	0.0726568i	−0.375625	+	0.926772i	$0.622572\pi$
$462$	−25.0677	+	2.55573i	−1.16626	+	0.118903i
$463$	32.3798	−	6.88254i	1.50482	−	0.319859i	0.619556	−	0.784952i	$-0.287313\pi$
$463$	32.3798	−	6.88254i	1.50482	−	0.319859i	0.885262	+	0.465093i	$0.153979\pi$
$464$	−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	0.524608	−	0.851344i	$-0.324212\pi$
$467$	−2.65707	−	1.93048i	−0.122955	−	0.0893318i	−0.647563	+	0.762012i	$0.724212\pi$
$468$	−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	−0.996419	−	0.0845471i	$-0.973056\pi$
$479$	−0.861271	−	8.19445i	−0.0393525	−	0.374414i	0.957067	−	0.289867i	$-0.0936110\pi$
$480$	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	−0.786343	−	0.617790i	$-0.788028\pi$
$487$	4.69938	−	14.4632i	0.212949	−	0.655391i	0.999293	−	0.0376012i	$-0.0119716\pi$
$488$	−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	−0.242692	−	0.970103i	$-0.578030\pi$
$491$	−1.54722	+	0.328872i	−0.0698252	+	0.0148418i	0.172867	+	0.984945i	$0.444697\pi$
$492$	−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	−0.970739	−	0.240135i	$-0.922808\pi$
$499$	−15.4879	−	26.8258i	−0.693333	−	1.20089i	0.277407	−	0.960753i	$-0.410525\pi$
$500$	−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	0.105375	−	0.994433i	$-0.466396\pi$
$503$	24.3048	−	17.6585i	1.08370	−	0.787354i	0.978324	+	0.207079i	$0.0663957\pi$
$504$	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	−0.626285	−	0.779594i	$-0.715425\pi$
$509$	−19.8838	+	4.22644i	−0.881335	+	0.187334i	−0.255050	+	0.966928i	$0.582092\pi$
$510$	−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	−0.862555	−	0.505964i	$-0.831137\pi$
$521$	−14.7886	+	10.7445i	−0.647898	+	0.470726i	0.214656	+	0.976690i	$0.431137\pi$
$522$	47.1807	−	20.6546i	2.06504	−	0.904029i
$523$	0.681075	+	2.09613i	0.0297813	+	0.0916575i	0.964842	−	0.262829i	$-0.0846556\pi$
$523$	0.681075	+	2.09613i	0.0297813	+	0.0916575i	−0.935061	+	0.354487i	$0.884656\pi$
$524$	−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	−0.928658	−	0.370938i	$-0.879036\pi$
$541$	0.946056	−	2.91166i	0.0406741	−	0.125182i	0.969332	+	0.245756i	$0.0790362\pi$
$542$	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	−0.999989	−	0.00473219i	$-0.998494\pi$
$547$	−0.534090	−	5.08153i	−0.0228360	−	0.217270i	0.977153	−	0.212538i	$-0.0681730\pi$
$548$	−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	−0.590480	−	0.807052i	$-0.701062\pi$
$563$	−19.0213	+	4.04311i	−0.801653	+	0.170397i	−0.211173	+	0.977449i	$0.567728\pi$
$564$	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	−0.419375	−	0.907813i	$-0.637751\pi$
$569$	−0.604819	+	0.269283i	−0.0253553	+	0.0112889i	0.394020	+	0.919102i	$0.371084\pi$
$570$	−1.38535	+	7.94882i	−0.0580259	+	0.332939i
$571$	16.8064	+	7.48268i	0.703325	+	0.313141i	0.727056	−	0.686578i	$-0.240888\pi$
$571$	16.8064	+	7.48268i	0.703325	+	0.313141i	−0.0237311	+	0.999718i	$0.507555\pi$
$572$	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	0.888312	−	0.459241i	$-0.151878\pi$
$577$	−2.40887	−	7.41374i	−0.100283	−	0.308638i	−0.988594	+	0.150603i	$0.951878\pi$
$578$	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	0.910297	−	0.413955i	$-0.135853\pi$
$587$	9.77501	+	10.8563i	0.403458	+	0.448086i	−0.506839	+	0.862041i	$0.669186\pi$
$588$	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	0.976409	−	0.215931i	$-0.0692785\pi$
$599$	7.37178	+	12.7683i	0.301203	+	0.521699i	−0.675206	+	0.737629i	$0.735945\pi$
$600$	8.58009	−	24.1034i	0.350281	−	0.984018i
$601$	6.78135	−	11.7456i	0.276617	−	0.479115i	−0.693925	−	0.720048i	$-0.744120\pi$
$601$	6.78135	−	11.7456i	0.276617	−	0.479115i	0.970542	+	0.240933i	$0.0774533\pi$
$602$	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	−0.975816	−	0.218594i	$-0.929853\pi$
$607$	−16.6848	−	28.8989i	−0.677216	−	1.17297i	0.298600	−	0.954378i	$-0.403480\pi$
$608$	−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	−0.783962	−	0.620808i	$-0.786805\pi$
$613$	5.32757	−	16.3966i	0.215178	−	0.662251i	0.999141	−	0.0414429i	$-0.0131955\pi$
$614$	−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	0.805925	+	0.592018i	$0.201668\pi$
$617$	−2.61997	+	24.9273i	−0.105476	+	1.00354i	−0.911401	+	0.411519i	$0.864998\pi$
$618$	−3.54715	−	8.03435i	−0.142687	−	0.323189i
$619$	14.2589	−	6.34849i	0.573116	−	0.255167i	−0.0996508	−	0.995022i	$-0.531773\pi$
$619$	14.2589	−	6.34849i	0.573116	−	0.255167i	0.672766	+	0.739855i	$0.265106\pi$
$620$	−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	0.502128	−	0.864793i	$-0.332551\pi$
$631$	−4.14912	−	3.01451i	−0.165174	−	0.120006i	−0.667301	+	0.744788i	$0.732551\pi$
$632$	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	0.781334	−	0.624113i	$-0.214539\pi$
$641$	1.99934	+	2.22049i	0.0789692	+	0.0877042i	−0.702365	+	0.711817i	$0.747873\pi$
$642$	13.6343	+	12.3536i	0.538104	+	0.487558i
$643$	−14.7308	−	25.5144i	−0.580925	−	1.00619i	−0.995370	−	0.0961173i	$-0.969358\pi$
$643$	−14.7308	−	25.5144i	−0.580925	−	1.00619i	0.414445	−	0.910074i	$-0.363976\pi$
$644$	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	−0.153394	−	0.988165i	$-0.549020\pi$
$647$	18.7975	−	13.6572i	0.739005	−	0.536919i	0.892399	+	0.451246i	$0.149020\pi$
$648$	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	0.429937	−	0.902859i	$-0.358536\pi$
$653$	1.19250	+	0.530934i	0.0466661	+	0.0207771i	−0.383271	+	0.923636i	$0.625202\pi$
$654$	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	0.390897	−	0.920435i	$-0.372165\pi$
$659$	−14.5132	−	16.1186i	−0.565355	−	0.627891i	−0.956252	+	0.292544i	$0.905498\pi$
$660$	0.916226	+	24.8261i	0.0356641	+	0.966356i
$661$	−3.82004	+	4.24259i	−0.148582	+	0.165017i	−0.812841	−	0.582485i	$-0.802080\pi$
$661$	−3.82004	+	4.24259i	−0.148582	+	0.165017i	0.664259	+	0.747502i	$0.268747\pi$
$662$	−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	0.271685	−	0.962386i	$-0.412419\pi$
$673$	3.33214	+	0.708269i	0.128445	+	0.0273018i	−0.143241	+	0.989688i	$0.545752\pi$
$674$	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	0.852753	−	0.522315i	$-0.174931\pi$
$677$	36.9300	+	7.84972i	1.41934	+	0.301689i	0.566584	+	0.824004i	$0.308265\pi$
$678$	−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	0.770239	−	0.637755i	$-0.220137\pi$
$683$	10.4985	+	7.62763i	0.401715	+	0.291863i	−0.368524	+	0.929618i	$0.620137\pi$
$684$	−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	0.902421	+	0.430856i	$0.141788\pi$
$691$	32.5060	+	36.1016i	1.23659	+	1.37337i	0.334167	+	0.942514i	$0.391545\pi$
$692$	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	0.856136	−	0.516751i	$-0.172859\pi$
$709$	6.72933	+	7.47367i	0.252725	+	0.280680i	−0.603411	+	0.797431i	$0.706192\pi$
$710$	−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	0.557636	−	0.830086i	$-0.311709\pi$
$719$	−1.59555	−	1.15923i	−0.0595039	−	0.0432321i	−0.617140	+	0.786854i	$0.711709\pi$
$720$	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	0.0864078	−	0.996260i	$-0.472461\pi$
$727$	−6.46761	−	1.37473i	−0.239870	−	0.0509860i	−0.326278	+	0.945274i	$0.605795\pi$
$728$	−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	0.934344	+	0.356373i	$0.115987\pi$
$733$	−1.45324	+	13.8266i	−0.0536765	+	0.510698i	−0.988020	+	0.154325i	$0.950680\pi$
$734$	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	0.937194	−	0.348808i	$-0.113413\pi$
$739$	−0.707775	−	2.17831i	−0.0260359	−	0.0801304i	−0.963230	+	0.268677i	$0.913413\pi$
$740$	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	0.529887	−	0.848068i	$-0.322234\pi$
$743$	−12.7978	−	22.1664i	−0.469506	−	0.813207i	−0.999392	+	0.0348611i	$0.988901\pi$
$744$	−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	0.979625	+	0.200836i	$0.0643660\pi$
$751$	18.1894	+	31.5050i	0.663742	+	1.14963i	−0.315883	+	0.948798i	$0.602301\pi$
$752$	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	−0.950778	−	0.309874i	$-0.899713\pi$
$761$	−14.9853	+	16.6429i	−0.543218	+	0.603305i	0.407559	+	0.913179i	$0.366380\pi$
$762$	−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	0.971361	+	0.237607i	$0.0763631\pi$
$769$	−0.781310	+	7.43367i	−0.0281747	+	0.268065i	−0.999536	+	0.0304576i	$0.990304\pi$
$770$	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	−1.00000		0.000832682i	$-0.999735\pi$
$773$	−5.32348	−	16.3840i	−0.191472	−	0.589291i	0.808527	−	0.588459i	$-0.200265\pi$
$774$	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	−0.198929	−	0.980014i	$-0.563746\pi$
$787$	0.503503	−	0.107023i	0.0179479	−	0.00381495i	0.216877	+	0.976199i	$0.430413\pi$
$788$	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	0.532032	−	0.846724i	$-0.321429\pi$
$797$	7.30599	+	3.25284i	0.258792	+	0.115221i	−0.273240	+	0.961946i	$0.588095\pi$
$798$	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	−0.974070	−	0.226247i	$-0.927354\pi$
$809$	−1.50879	+	4.64358i	−0.0530463	+	0.163260i	0.921024	+	0.389506i	$0.127354\pi$
$810$	−41.7311	+	19.9742i	−1.46628	+	0.701822i
$811$	−13.8925	−	42.7567i	−0.487832	−	1.50139i	−0.827838	−	0.560968i	$-0.810429\pi$
$811$	−13.8925	−	42.7567i	−0.487832	−	1.50139i	0.340006	−	0.940423i	$-0.389571\pi$
$812$	−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	−0.467003	−	0.884256i	$-0.654666\pi$
$821$	−5.56020	−	52.9017i	−0.194052	−	1.84628i	0.272951	−	0.962028i	$-0.412000\pi$
$822$	−0.0748059	+	23.9928i	−0.00260916	+	0.836846i
$823$	33.1996	−	36.8719i	1.15727	−	1.28527i	0.205429	−	0.978672i	$-0.434141\pi$
$823$	33.1996	−	36.8719i	1.15727	−	1.28527i	0.951838	−	0.306603i	$-0.0991923\pi$
$824$	−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	0.859008	−	0.511962i	$-0.171081\pi$
$827$	−3.93599	−	12.1137i	−0.136868	−	0.421236i	−0.995876	+	0.0907261i	$0.971081\pi$
$828$	−67.4588	−	49.6573i	−2.34436	−	1.72571i
$829$	−42.5264	+	30.8972i	−1.47700	+	1.07310i	−0.498494	+	0.866893i	$0.666113\pi$
$829$	−42.5264	+	30.8972i	−1.47700	+	1.07310i	−0.978507	+	0.206211i	$0.933887\pi$
$830$	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	0.793824	−	0.608147i	$-0.208087\pi$
$839$	36.8344	+	7.82938i	1.27166	+	0.270300i	0.477839	+	0.878447i	$0.341420\pi$
$840$	−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	0.924228	+	0.381841i	$0.124710\pi$
$853$	2.90852	+	27.6727i	0.0995859	+	0.947497i	−0.824642	+	0.565655i	$0.808623\pi$
$854$	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	−0.392399	−	0.919795i	$-0.628355\pi$
$857$	17.5755	−	30.4416i	0.600366	−	1.03986i	0.992765	−	0.120070i	$-0.0383118\pi$
$858$	−20.5334	−	18.6046i	−0.700999	−	0.635151i
$859$	23.7541	−	5.04908i	0.810478	−	0.172272i	0.216009	−	0.976391i	$-0.430696\pi$
$859$	23.7541	−	5.04908i	0.810478	−	0.172272i	0.594468	+	0.804119i	$0.297363\pi$
$860$	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	−0.984926	−	0.172975i	$-0.944662\pi$
$863$	−2.53910	+	7.81456i	−0.0864321	+	0.266011i	0.898494	+	0.438985i	$0.144662\pi$
$864$	−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	−0.284984	−	0.958532i	$-0.591988\pi$
$877$	20.6733	−	22.9600i	0.698087	−	0.775304i	0.983070	+	0.183228i	$0.0586548\pi$
$878$	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	0.313723	−	0.949514i	$-0.398424\pi$
$881$	−14.6144	−	10.6180i	−0.492373	−	0.357730i	−0.806096	+	0.591785i	$0.798424\pi$
$882$	−16.2783	+	17.8537i	−0.548118	+	0.601166i
$883$	22.5517	+	16.3848i	0.758925	+	0.551391i	0.898580	−	0.438809i	$-0.144599\pi$
$883$	22.5517	+	16.3848i	0.758925	+	0.551391i	−0.139655	+	0.990200i	$0.544599\pi$
$884$	−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	0.182023	−	0.983294i	$-0.441735\pi$
$887$	22.2848	−	4.73679i	0.748251	−	0.159046i	0.566228	+	0.824249i	$0.308402\pi$
$888$	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	−0.869052	−	0.494720i	$-0.835270\pi$
$907$	−0.183281	+	0.317451i	−0.00608574	+	0.0105408i	0.862966	+	0.505261i	$0.168604\pi$
$908$	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	−0.786257	−	0.617900i	$-0.787984\pi$
$911$	−52.9968	−	11.2648i	−1.75586	−	0.373220i	−0.969604	+	0.244680i	$0.921317\pi$
$912$	−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	−0.00805385	−	0.999968i	$-0.502564\pi$
$919$	−29.1500	−	21.1787i	−0.961568	−	0.698620i	−0.953514	+	0.301347i	$0.902564\pi$
$920$	−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	0.998141	+	0.0609405i	$0.0194100\pi$
$929$	1.05099	+	9.99955i	0.0344820	+	0.328074i	−0.963659	+	0.267134i	$0.913923\pi$
$930$	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	0.808633	+	0.588314i	$0.200208\pi$
$937$	−5.85784	+	18.0286i	−0.191367	+	0.588968i	−1.00000		0.000653814i	$0.999792\pi$
$938$	−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	0.635002	−	0.772511i	$-0.280999\pi$
$941$	46.9128	−	9.97162i	1.52931	−	0.325066i	0.894311	+	0.447445i	$0.147666\pi$
$942$	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	0.841756	+	0.539859i	$0.181522\pi$
$947$	4.02015	+	38.2492i	0.130637	+	1.24293i	−0.711118	+	0.703072i	$0.751811\pi$
$948$	−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	−0.0590983	−	0.998252i	$-0.518823\pi$
$953$	26.9203	−	19.5587i	0.872034	−	0.633569i	0.931132	+	0.364683i	$0.118823\pi$
$954$	−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	0.629027	+	0.777383i	$0.283453\pi$
$967$	−4.59861	+	43.7528i	−0.147881	+	1.40700i	−0.776909	+	0.629613i	$0.783213\pi$
$968$	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	−0.305178	−	0.952295i	$-0.598716\pi$
$971$	15.7738	−	11.4603i	0.506204	−	0.367779i	0.811382	+	0.584517i	$0.198716\pi$
$972$	−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	0.0364216	+	0.999337i	$0.488404\pi$
$977$	−30.0457	+	33.3691i	−0.961248	+	1.06757i	−0.997669	+	0.0682370i	$0.978263\pi$
$978$	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	−0.981242	−	0.192782i	$-0.938249\pi$
$983$	−46.8586	+	20.8628i	−1.49456	+	0.665419i	−0.513314	+	0.858201i	$0.671582\pi$
$984$	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	−0.906917	−	0.421309i	$-0.861571\pi$
$991$	2.34318	−	7.21156i	0.0744335	−	0.229083i	0.981351	+	0.192226i	$0.0615708\pi$
$992$	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	−0.962325	−	0.271902i	$-0.912347\pi$
$997$	−2.44900	−	23.3007i	−0.0775606	−	0.737940i	0.884764	−	0.466039i	$-0.154319\pi$
$998$	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.106.5	yes	224
3.2	odd	2		675.2.r.a.181.24		224
9.4	even	3	inner	225.2.q.a.31.24	✓	224
9.5	odd	6		675.2.r.a.631.5		224
25.21	even	5	inner	225.2.q.a.196.24	yes	224
75.71	odd	10		675.2.r.a.46.5		224
225.121	even	15	inner	225.2.q.a.121.5	yes	224
225.221	odd	30		675.2.r.a.496.24		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.24	✓	224	9.4	even	3	inner
225.2.q.a.106.5	yes	224	1.1	even	1	trivial
225.2.q.a.121.5	yes	224	225.121	even	15	inner
225.2.q.a.196.24	yes	224	25.21	even	5	inner
675.2.r.a.46.5		224	75.71	odd	10
675.2.r.a.181.24		224	3.2	odd	2
675.2.r.a.496.24		224	225.221	odd	30
675.2.r.a.631.5		224	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.24869 - 0.477974i) q^{2} +(1.49729 + 0.870698i) q^{3} +(3.00107 + 1.33616i) q^{4} +(-2.07749 - 0.827061i) q^{5} +(-2.95078 - 2.67360i) q^{6} +(-1.62043 + 2.80667i) q^{7} +(-2.39008 - 1.73649i) q^{8} +(1.48377 + 2.60738i) q^{9} +O(q^{10})\)	\(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

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