LMFDB - Embedded newform 225.2.q.a.31.22

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			31.22
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.956880 - 1.06272i) q^{2} +(0.819476 + 1.52593i) q^{3} +(-0.00470356 - 0.0447514i) q^{4} +(-2.07212 - 0.840433i) q^{5} +(2.40578 + 0.589254i) q^{6} +(1.92019 + 3.32586i) q^{7} +(2.26178 + 1.64328i) q^{8} +(-1.65692 + 2.50092i) q^{9} +O(q^{10})$	\(q+(0.956880 - 1.06272i) q^{2} +(0.819476 + 1.52593i) q^{3} +(-0.00470356 - 0.0447514i) q^{4} +(-2.07212 - 0.840433i) q^{5} +(2.40578 + 0.589254i) q^{6} +(1.92019 + 3.32586i) q^{7} +(2.26178 + 1.64328i) q^{8} +(-1.65692 + 2.50092i) q^{9} +(-2.87591 + 1.39789i) q^{10} +(3.49787 - 3.88478i) q^{11} +(0.0644329 - 0.0438500i) q^{12} +(-2.25011 - 2.49900i) q^{13} +(5.37185 + 1.14182i) q^{14} +(-0.415610 - 3.85062i) q^{15} +(3.99864 - 0.849937i) q^{16} +(-3.90998 - 2.84077i) q^{17} +(1.07232 + 4.15393i) q^{18} +(-1.90903 - 1.38699i) q^{19} +(-0.0278642 + 0.0966831i) q^{20} +(-3.50148 + 5.65553i) q^{21} +(-0.781401 - 7.43453i) q^{22} +(4.56147 + 0.969570i) q^{23} +(-0.654054 + 4.79795i) q^{24} +(3.58734 + 3.48295i) q^{25} -4.80884 q^{26} +(-5.17404 - 0.478889i) q^{27} +(0.139805 - 0.101574i) q^{28} +(-6.71254 - 2.98862i) q^{29} +(-4.48983 - 3.24290i) q^{30} +(0.593962 - 0.264449i) q^{31} +(0.127249 - 0.220402i) q^{32} +(8.79432 + 2.15402i) q^{33} +(-6.76033 + 1.43695i) q^{34} +(-1.18369 - 8.50536i) q^{35} +(0.119713 + 0.0623860i) q^{36} +(0.315262 - 0.970276i) q^{37} +(-3.30069 + 0.701584i) q^{38} +(1.96939 - 5.48139i) q^{39} +(-3.30561 - 5.30596i) q^{40} +(-2.50903 - 2.78656i) q^{41} +(2.65977 + 9.13276i) q^{42} +(-2.34851 - 4.06773i) q^{43} +(-0.190302 - 0.138262i) q^{44} +(5.53519 - 3.78968i) q^{45} +(5.39516 - 3.91981i) q^{46} +(10.9118 + 4.85827i) q^{47} +(4.57373 + 5.40514i) q^{48} +(-3.87423 + 6.71036i) q^{49} +(7.13407 - 0.479583i) q^{50} +(1.13067 - 8.29429i) q^{51} +(-0.101250 + 0.112450i) q^{52} +(2.92011 - 2.12158i) q^{53} +(-5.45986 + 5.04033i) q^{54} +(-10.5129 + 5.10999i) q^{55} +(-1.12228 + 10.6778i) q^{56} +(0.552044 - 4.04964i) q^{57} +(-9.59917 + 4.27383i) q^{58} +(-5.20768 - 5.78372i) q^{59} +(-0.170366 + 0.0367107i) q^{60} +(-4.40843 + 4.89605i) q^{61} +(0.287314 - 0.884263i) q^{62} +(-11.4993 - 0.708433i) q^{63} +(2.41404 + 7.42965i) q^{64} +(2.56225 + 7.06930i) q^{65} +(10.7042 - 7.28479i) q^{66} +(-0.930565 + 0.414314i) q^{67} +(-0.108737 + 0.188339i) q^{68} +(2.25852 + 7.75502i) q^{69} +(-10.1715 - 6.88068i) q^{70} +(-2.82082 + 2.04945i) q^{71} +(-7.85732 + 2.93377i) q^{72} +(-1.38140 - 4.25150i) q^{73} +(-0.729467 - 1.26347i) q^{74} +(-2.37500 + 8.32823i) q^{75} +(-0.0530904 + 0.0919553i) q^{76} +(19.6368 + 4.17393i) q^{77} +(-3.94073 - 7.33794i) q^{78} +(1.49826 + 0.667070i) q^{79} +(-8.99997 - 1.59942i) q^{80} +(-3.50925 - 8.28765i) q^{81} -5.36219 q^{82} +(-1.18152 + 11.2414i) q^{83} +(0.269562 + 0.130095i) q^{84} +(5.71446 + 9.17248i) q^{85} +(-6.57011 - 1.39652i) q^{86} +(-0.940354 - 12.6920i) q^{87} +(14.2952 - 3.03854i) q^{88} +(-0.935178 - 2.87818i) q^{89} +(1.26913 - 9.50864i) q^{90} +(3.99070 - 12.2821i) q^{91} +(0.0219345 - 0.208692i) q^{92} +(0.890268 + 0.689634i) q^{93} +(15.6043 - 6.94749i) q^{94} +(2.79006 + 4.47841i) q^{95} +(0.440596 + 0.0135589i) q^{96} +(14.8057 + 6.59193i) q^{97} +(3.42408 + 10.5382i) q^{98} +(3.91986 + 15.1847i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.956880	−	1.06272i	0.676616	−	0.751458i	−0.302856	−	0.953036i	$-0.597940\pi$
$2$	0.956880	−	1.06272i	0.676616	−	0.751458i	0.979472	+	0.201578i	$0.0646069\pi$
$3$	0.819476	+	1.52593i	0.473125	+	0.880995i
$3$	0.819476	+	1.52593i	0.473125	+	0.880995i
$4$	−0.00470356	−	0.0447514i	−0.00235178	−	0.0223757i
$5$	−2.07212	−	0.840433i	−0.926679	−	0.375853i
$5$	−2.07212	−	0.840433i	−0.926679	−	0.375853i
$6$	2.40578	+	0.589254i	0.982155	+	0.240562i
$7$	1.92019	+	3.32586i	0.725762	+	1.25706i	0.958660	+	0.284556i	$0.0918460\pi$
$7$	1.92019	+	3.32586i	0.725762	+	1.25706i	−0.232897	+	0.972501i	$0.574821\pi$
$8$	2.26178	+	1.64328i	0.799662	+	0.580988i
$9$	−1.65692	+	2.50092i	−0.552306	+	0.833642i
$10$	−2.87591	+	1.39789i	−0.909444	+	0.442052i
$11$	3.49787	−	3.88478i	1.05465	−	1.17131i	0.0698578	−	0.997557i	$-0.477745\pi$
$11$	3.49787	−	3.88478i	1.05465	−	1.17131i	0.984790	−	0.173748i	$-0.0555879\pi$
$12$	0.0644329	−	0.0438500i	0.0186002	−	0.0126584i
$13$	−2.25011	−	2.49900i	−0.624069	−	0.693099i	0.345360	−	0.938470i	$-0.387757\pi$
$13$	−2.25011	−	2.49900i	−0.624069	−	0.693099i	−0.969429	+	0.245371i	$0.921090\pi$
$14$	5.37185	+	1.14182i	1.43569	+	0.305165i
$15$	−0.415610	−	3.85062i	−0.107310	−	0.994226i
$16$	3.99864	−	0.849937i	0.999660	−	0.212484i
$17$	−3.90998	−	2.84077i	−0.948309	−	0.688987i	0.00209712	−	0.999998i	$-0.499332\pi$
$17$	−3.90998	−	2.84077i	−0.948309	−	0.688987i	−0.950406	+	0.311011i	$0.899332\pi$
$18$	1.07232	+	4.15393i	0.252748	+	0.979090i
$19$	−1.90903	−	1.38699i	−0.437961	−	0.318197i	0.346863	−	0.937916i	$-0.387247\pi$
$19$	−1.90903	−	1.38699i	−0.437961	−	0.318197i	−0.784824	+	0.619719i	$0.787247\pi$
$20$	−0.0278642	+	0.0966831i	−0.00623063	+	0.0216190i
$21$	−3.50148	+	5.65553i	−0.764085	+	1.23414i
$22$	−0.781401	−	7.43453i	−0.166595	−	1.58505i
$23$	4.56147	+	0.969570i	0.951132	+	0.202169i	0.657250	−	0.753672i	$-0.271719\pi$
$23$	4.56147	+	0.969570i	0.951132	+	0.202169i	0.293882	+	0.955842i	$0.405053\pi$
$24$	−0.654054	+	4.79795i	−0.133508	+	0.979378i
$25$	3.58734	+	3.48295i	0.717469	+	0.696591i
$26$	−4.80884			−0.943090
$27$	−5.17404	−	0.478889i	−0.995744	−	0.0921622i
$28$	0.139805	−	0.101574i	0.0264207	−	0.0191957i
$29$	−6.71254	−	2.98862i	−1.24649	−	0.554972i	−0.325862	−	0.945417i	$-0.605654\pi$
$29$	−6.71254	−	2.98862i	−1.24649	−	0.554972i	−0.920626	+	0.390445i	$0.872321\pi$
$30$	−4.48983	−	3.24290i	−0.819727	−	0.592070i
$31$	0.593962	−	0.264449i	0.106679	−	0.0474964i	−0.352703	−	0.935735i	$-0.614738\pi$
$31$	0.593962	−	0.264449i	0.106679	−	0.0474964i	0.459382	+	0.888239i	$0.348071\pi$
$32$	0.127249	−	0.220402i	0.0224947	−	0.0389619i
$33$	8.79432	+	2.15402i	1.53089	+	0.374966i
$34$	−6.76033	+	1.43695i	−1.15939	+	0.246435i
$35$	−1.18369	−	8.50536i	−0.200080	−	1.43767i
$36$	0.119713	+	0.0623860i	0.0199522	+	0.0103977i
$37$	0.315262	−	0.970276i	0.0518287	−	0.159512i	−0.921792	−	0.387685i	$-0.873275\pi$
$37$	0.315262	−	0.970276i	0.0518287	−	0.159512i	0.973621	+	0.228172i	$0.0732749\pi$
$38$	−3.30069	+	0.701584i	−0.535443	+	0.113812i
$39$	1.96939	−	5.48139i	0.315354	−	0.877724i
$40$	−3.30561	−	5.30596i	−0.522664	−	0.838945i
$41$	−2.50903	−	2.78656i	−0.391845	−	0.435188i	0.514653	−	0.857399i	$-0.327921\pi$
$41$	−2.50903	−	2.78656i	−0.391845	−	0.435188i	−0.906498	+	0.422211i	$0.861254\pi$
$42$	2.65977	+	9.13276i	0.410411	+	1.40922i
$43$	−2.34851	−	4.06773i	−0.358144	−	0.620324i	0.629507	−	0.776995i	$-0.283257\pi$
$43$	−2.34851	−	4.06773i	−0.358144	−	0.620324i	−0.987651	+	0.156671i	$0.949924\pi$
$44$	−0.190302	−	0.138262i	−0.0286890	−	0.0208438i
$45$	5.53519	−	3.78968i	0.825137	−	0.564932i
$46$	5.39516	−	3.91981i	0.795473	−	0.577945i
$47$	10.9118	+	4.85827i	1.59166	+	0.708651i	0.995548	−	0.0942531i	$-0.0300463\pi$
$47$	10.9118	+	4.85827i	1.59166	+	0.708651i	0.596108	+	0.802904i	$0.296713\pi$
$48$	4.57373	+	5.40514i	0.660161	+	0.780164i
$49$	−3.87423	+	6.71036i	−0.553461	+	0.958623i
$50$	7.13407	−	0.479583i	1.00891	−	0.0678233i
$51$	1.13067	−	8.29429i	0.158326	−	1.16143i
$52$	−0.101250	+	0.112450i	−0.0140409	+	0.0155940i
$53$	2.92011	−	2.12158i	0.401108	−	0.291422i	−0.368884	−	0.929475i	$-0.620260\pi$
$53$	2.92011	−	2.12158i	0.401108	−	0.291422i	0.769992	+	0.638054i	$0.220260\pi$
$54$	−5.45986	+	5.04033i	−0.742993	+	0.685902i
$55$	−10.5129	+	5.10999i	−1.41756	+	0.689031i
$56$	−1.12228	+	10.6778i	−0.149971	+	1.42688i
$57$	0.552044	−	4.04964i	0.0731200	−	0.536388i
$58$	−9.59917	+	4.27383i	−1.26043	+	0.561181i
$59$	−5.20768	−	5.78372i	−0.677982	−	0.752976i	0.301728	−	0.953394i	$-0.402437\pi$
$59$	−5.20768	−	5.78372i	−0.677982	−	0.752976i	−0.979710	+	0.200418i	$0.935770\pi$
$60$	−0.170366	+	0.0367107i	−0.0219941	+	0.00473933i
$61$	−4.40843	+	4.89605i	−0.564441	+	0.626875i	−0.956031	−	0.293264i	$-0.905258\pi$
$61$	−4.40843	+	4.89605i	−0.564441	+	0.626875i	0.391590	+	0.920140i	$0.371925\pi$
$62$	0.287314	−	0.884263i	0.0364890	−	0.112301i
$63$	−11.4993	−	0.708433i	−1.44878	−	0.0892542i
$64$	2.41404	+	7.42965i	0.301755	+	0.928707i
$65$	2.56225	+	7.06930i	0.317808	+	0.876839i
$66$	10.7042	−	7.28479i	1.31760	−	0.896695i
$67$	−0.930565	+	0.414314i	−0.113687	+	0.0506165i	−0.462792	−	0.886467i	$-0.653152\pi$
$67$	−0.930565	+	0.414314i	−0.113687	+	0.0506165i	0.349105	+	0.937084i	$0.386486\pi$
$68$	−0.108737	+	0.188339i	−0.0131863	+	0.0228394i
$69$	2.25852	+	7.75502i	0.271894	+	0.933594i
$70$	−10.1715	−	6.88068i	−1.21573	−	0.822398i
$71$	−2.82082	+	2.04945i	−0.334770	+	0.243225i	−0.742452	−	0.669899i	$-0.766337\pi$
$71$	−2.82082	+	2.04945i	−0.334770	+	0.243225i	0.407682	+	0.913124i	$0.366337\pi$
$72$	−7.85732	+	2.93377i	−0.925994	+	0.345748i
$73$	−1.38140	−	4.25150i	−0.161680	−	0.497601i	0.837096	−	0.547056i	$-0.184252\pi$
$73$	−1.38140	−	4.25150i	−0.161680	−	0.497601i	−0.998776	+	0.0494551i	$0.984252\pi$
$74$	−0.729467	−	1.26347i	−0.0847988	−	0.146876i
$75$	−2.37500	+	8.32823i	−0.274241	+	0.961661i
$76$	−0.0530904	+	0.0919553i	−0.00608989	+	0.0105480i
$77$	19.6368	+	4.17393i	2.23782	+	0.475663i
$78$	−3.94073	−	7.33794i	−0.446199	−	0.830858i
$79$	1.49826	+	0.667070i	0.168568	+	0.0750513i	0.489286	−	0.872123i	$-0.337257\pi$
$79$	1.49826	+	0.667070i	0.168568	+	0.0750513i	−0.320718	+	0.947175i	$0.603924\pi$
$80$	−8.99997	−	1.59942i	−1.00623	−	0.178821i
$81$	−3.50925	−	8.28765i	−0.389917	−	0.920850i
$82$	−5.36219			−0.592154
$83$	−1.18152	+	11.2414i	−0.129688	+	1.23390i	0.715185	+	0.698936i	$0.246343\pi$
$83$	−1.18152	+	11.2414i	−0.129688	+	1.23390i	−0.844873	+	0.534967i	$0.820324\pi$
$84$	0.269562	+	0.130095i	0.0294116	+	0.0141945i
$85$	5.71446	+	9.17248i	0.619820	+	0.994895i
$86$	−6.57011	−	1.39652i	−0.708473	−	0.150591i
$87$	−0.940354	−	12.6920i	−0.100817	−	1.36072i
$88$	14.2952	−	3.03854i	1.52388	−	0.323910i
$89$	−0.935178	−	2.87818i	−0.0991286	−	0.305087i	0.889179	−	0.457559i	$-0.151276\pi$
$89$	−0.935178	−	2.87818i	−0.0991286	−	0.305087i	−0.988308	+	0.152473i	$0.951276\pi$
$90$	1.26913	−	9.50864i	0.133778	−	1.00230i
$91$	3.99070	−	12.2821i	0.418339	−	1.28752i
$92$	0.0219345	−	0.208692i	0.00228682	−	0.0217577i
$93$	0.890268	+	0.689634i	0.0923165	+	0.0715117i
$94$	15.6043	−	6.94749i	1.60946	−	0.716579i
$95$	2.79006	+	4.47841i	0.286254	+	0.459475i
$96$	0.440596	+	0.0135589i	0.0449681	+	0.00138385i
$97$	14.8057	+	6.59193i	1.50329	+	0.669309i	0.982820	−	0.184569i	$-0.0590888\pi$
$97$	14.8057	+	6.59193i	1.50329	+	0.669309i	0.520474	+	0.853878i	$0.325755\pi$
$98$	3.42408	+	10.5382i	0.345885	+	1.06452i
$99$	3.91986	+	15.1847i	0.393961	+	1.52612i
$100$	0.138994	−	0.176921i	0.0138994	−	0.0176921i
$101$	−2.79104	−	4.83422i	−0.277719	−	0.481023i	0.693099	−	0.720843i	$-0.256245\pi$
$101$	−2.79104	−	4.83422i	−0.277719	−	0.481023i	−0.970817	+	0.239820i	$0.922912\pi$
$102$	−7.73261	−	9.13823i	−0.765643	−	0.904819i
$103$	−0.0651481	−	0.619843i	−0.00641923	−	0.0610749i	0.990843	−	0.135017i	$-0.0431088\pi$
$103$	−0.0651481	−	0.619843i	−0.00641923	−	0.0610749i	−0.997263	+	0.0739417i	$0.976442\pi$
$104$	−0.982702	−	9.34978i	−0.0963618	−	0.916822i
$105$	12.0086	−	8.77617i	1.17192	−	0.856466i
$106$	0.539538	−	5.13336i	0.0524046	−	0.498596i
$107$	8.51791			0.823458			0.411729	−	0.911306i	$-0.364925\pi$
$107$	8.51791			0.823458			0.411729	+	0.911306i	$0.364925\pi$
$108$	0.00290545	+	0.233798i	0.000279577	+	0.0224972i
$109$	−3.14970	+	9.69377i	−0.301686	+	0.928495i	0.679207	+	0.733947i	$0.262324\pi$
$109$	−3.14970	+	9.69377i	−0.301686	+	0.928495i	−0.980893	+	0.194548i	$0.937676\pi$
$110$	−4.62908	+	16.0619i	−0.441365	+	1.53145i
$111$	1.73892	−	0.314051i	0.165051	−	0.0298084i
$112$	10.5049	+	11.6669i	0.992620	+	1.10242i
$113$	−4.24309	−	4.71243i	−0.399156	−	0.443308i	0.509741	−	0.860328i	$-0.329741\pi$
$113$	−4.24309	−	4.71243i	−0.399156	−	0.443308i	−0.908897	+	0.417020i	$0.863074\pi$
$114$	−3.77541	−	4.46169i	−0.353599	−	0.417876i
$115$	−8.63704	−	5.84268i	−0.805408	−	0.544832i
$116$	−0.102172	+	0.314453i	−0.00948642	+	0.0291962i
$117$	9.97807	−	1.48672i	0.922473	−	0.137447i
$118$	−11.1296			−1.02456
$119$	1.94010	−	18.4588i	0.177849	−	1.69212i
$120$	5.38764	−	9.39224i	0.491822	−	0.857390i
$121$	−1.70660	−	16.2372i	−0.155145	−	1.47611i
$122$	0.984813	+	9.36987i	0.0891607	+	0.848308i
$123$	2.19600	−	6.11213i	0.198007	−	0.551112i
$124$	−0.0146282	−	0.0253368i	−0.00131365	−	0.00227531i
$125$	−4.50621	−	10.2320i	−0.403047	−	0.915179i
$126$	−11.7563	+	11.5427i	−1.04734	+	1.02831i
$127$	4.60449	+	14.1712i	0.408583	+	1.25749i	0.917867	+	0.396889i	$0.129910\pi$
$127$	4.60449	+	14.1712i	0.408583	+	1.25749i	−0.509284	+	0.860599i	$0.670090\pi$
$128$	10.6706	+	4.75086i	0.943157	+	0.419920i
$129$	4.28253	−	6.91707i	0.377055	−	0.609014i
$130$	9.96447	+	4.04151i	0.873942	+	0.354464i
$131$	−12.3027	+	5.47750i	−1.07489	+	0.478571i	−0.866347	−	0.499442i	$-0.833538\pi$
$131$	−12.3027	+	5.47750i	−1.07489	+	0.478571i	−0.208542	+	0.978014i	$0.566872\pi$
$132$	0.0550306	−	0.403689i	0.00478980	−	0.0351366i
$133$	0.947245	−	9.01243i	0.0821365	−	0.781477i
$134$	−0.450138	+	1.38538i	−0.0388860	+	0.119679i
$135$	10.3187	+	5.34075i	0.888096	+	0.459658i
$136$	−4.17535	−	12.8504i	−0.358033	−	1.10191i
$137$	−8.93278	+	1.89872i	−0.763179	+	0.162219i	−0.573028	−	0.819536i	$-0.694231\pi$
$137$	−8.93278	+	1.89872i	−0.763179	+	0.162219i	−0.190151	+	0.981755i	$0.560898\pi$
$138$	10.4026	+	5.02044i	0.885525	+	0.427368i
$139$	−11.4759	−	2.43928i	−0.973376	−	0.206897i	−0.306339	−	0.951922i	$-0.599104\pi$
$139$	−11.4759	−	2.43928i	−0.973376	−	0.206897i	−0.667037	+	0.745025i	$0.732438\pi$
$140$	−0.375059	+	0.0929771i	−0.0316983	+	0.00785800i
$141$	1.52863	+	20.6319i	0.128734	+	1.73752i
$142$	−0.521193	+	4.95882i	−0.0437376	+	0.416135i
$143$	−17.5787			−1.47000
$144$	−4.49979	+	11.4086i	−0.374982	+	0.950714i
$145$	11.3974	+	11.8342i	0.946507	+	0.982778i
$146$	−5.84000	−	2.60014i	−0.483322	−	0.215189i
$147$	−13.4144	−	0.412815i	−1.10640	−	0.0340484i
$148$	−0.0449040	−	0.00954465i	−0.00369109	−	0.000784565i
$149$	−4.73317	+	8.19809i	−0.387756	+	0.671614i	−0.992147	−	0.125074i	$-0.960083\pi$
$149$	−4.73317	+	8.19809i	−0.387756	+	0.671614i	0.604391	+	0.796688i	$0.293416\pi$
$150$	6.57801	+	10.4931i	0.537092	+	0.856756i
$151$	7.67377	+	13.2914i	0.624482	+	1.08164i	0.988641	+	0.150298i	$0.0480234\pi$
$151$	7.67377	+	13.2914i	0.624482	+	1.08164i	−0.364158	+	0.931337i	$0.618643\pi$
$152$	−2.03859	−	6.27414i	−0.165352	−	0.508900i
$153$	13.5831	−	5.07165i	1.09812	−	0.410019i
$154$	23.2258	−	16.8745i	1.87159	−	1.35979i
$155$	−1.45301	+	0.0487838i	−0.116709	+	0.00391841i
$156$	−0.254563	−	0.0623508i	−0.0203813	−	0.00499206i
$157$	10.9037	−	18.8858i	0.870210	−	1.50725i	0.00843010	−	0.999964i	$-0.497317\pi$
$157$	10.9037	−	18.8858i	0.870210	−	1.50725i	0.861780	−	0.507283i	$-0.169350\pi$
$158$	2.14257	−	0.953934i	0.170454	−	0.0758909i
$159$	5.63034	+	2.71729i	0.446515	+	0.215495i
$160$	−0.448909	+	0.349755i	−0.0354893	+	0.0276505i
$161$	5.53422	+	17.0326i	0.436157	+	1.34235i
$162$	−12.1654	−	4.20093i	−0.955804	−	0.330056i
$163$	−3.56614	+	10.9754i	−0.279321	+	0.859663i	0.708722	+	0.705488i	$0.249272\pi$
$163$	−3.56614	+	10.9754i	−0.279321	+	0.859663i	−0.988044	+	0.154175i	$0.950728\pi$
$164$	−0.112901	+	0.125389i	−0.00881609	+	0.00979126i
$165$	−16.4126	−	11.8544i	−1.27772	−	0.922865i
$166$	10.8159	+	12.0123i	0.839477	+	0.932334i
$167$	−3.85690	+	1.71720i	−0.298456	+	0.132881i	−0.550501	−	0.834834i	$-0.685563\pi$
$167$	−3.85690	+	1.71720i	−0.298456	+	0.132881i	0.252045	+	0.967715i	$0.418897\pi$
$168$	−17.2132	+	7.03767i	−1.32803	+	0.542968i
$169$	0.176859	−	1.68270i	0.0136045	−	0.129438i
$170$	15.2159	+	2.70407i	1.16700	+	0.207393i
$171$	6.63185	−	2.47621i	0.507150	−	0.189360i
$172$	−0.170990	+	0.124232i	−0.0130379	+	0.00947258i
$173$	−6.60700	+	7.33782i	−0.502321	+	0.557884i	−0.939968	−	0.341263i	$-0.889145\pi$
$173$	−6.60700	+	7.33782i	−0.502321	+	0.557884i	0.437647	+	0.899147i	$0.355812\pi$
$174$	−14.3878	−	11.1453i	−1.09074	−	0.844927i
$175$	−4.69545	+	18.6189i	−0.354943	+	1.40746i
$176$	10.6849	−	18.5068i	0.805405	−	1.39500i
$177$	4.55797	−	12.6862i	0.342598	−	0.953551i
$178$	−3.95356	−	1.76024i	−0.296332	−	0.131935i
$179$	−2.85965	+	2.07766i	−0.213740	+	0.155292i	−0.689504	−	0.724281i	$-0.742172\pi$
$179$	−2.85965	+	2.07766i	−0.213740	+	0.155292i	0.475764	+	0.879573i	$0.342172\pi$
$180$	−0.195628	−	0.229882i	−0.0145813	−	0.0171344i
$181$	12.3513	+	8.97372i	0.918062	+	0.667011i	0.943041	−	0.332677i	$-0.107952\pi$
$181$	12.3513	+	8.97372i	0.918062	+	0.667011i	−0.0249788	+	0.999688i	$0.507952\pi$
$182$	−9.23386	−	15.9935i	−0.684459	−	1.18552i
$183$	−11.0836	−	2.71474i	−0.819325	−	0.200680i
$184$	8.72379	+	9.68874i	0.643126	+	0.714264i
$185$	−1.46871	+	1.74557i	−0.107982	+	0.128337i
$186$	1.58477	−	0.286211i	0.116201	−	0.0209860i
$187$	−24.7124	+	5.25277i	−1.80715	+	0.384121i
$188$	0.166090	−	0.511171i	0.0121133	−	0.0372810i
$189$	−8.34240	−	18.1277i	−0.606820	−	1.31859i
$190$	7.42906	+	1.32025i	0.538960	+	0.0957808i
$191$	−18.1452	+	3.85689i	−1.31294	+	0.279075i	−0.810603	−	0.585596i	$-0.800861\pi$
$191$	−18.1452	+	3.85689i	−1.31294	+	0.279075i	−0.502340	+	0.864670i	$0.667527\pi$
$192$	−9.35887	+	9.77208i	−0.675419	+	0.705239i
$193$	−5.82208	+	10.0841i	−0.419082	+	0.725872i	−0.995847	−	0.0910384i	$-0.970981\pi$
$193$	−5.82208	+	10.0841i	−0.419082	+	0.725872i	0.576765	+	0.816910i	$0.304315\pi$
$194$	21.1727	−	9.42669i	1.52011	−	0.676797i
$195$	−8.68754	+	9.70294i	−0.622128	+	0.694842i
$196$	0.318520	+	0.141814i	0.0227515	+	0.0101296i
$197$	6.93084	−	5.03555i	0.493802	−	0.358768i	−0.312843	−	0.949805i	$-0.601281\pi$
$197$	6.93084	−	5.03555i	0.493802	−	0.358768i	0.806645	+	0.591037i	$0.201281\pi$
$198$	19.8879	+	10.3642i	1.41337	+	0.736550i
$199$	17.3700			1.23133			0.615663	−	0.788010i	$-0.288888\pi$
$199$	17.3700			1.23133			0.615663	+	0.788010i	$0.288888\pi$
$200$	2.39032	+	13.7727i	0.169021	+	0.973878i
$201$	−1.39479	−	1.08045i	−0.0983809	−	0.0762094i
$202$	−7.80812	−	1.65967i	−0.549378	−	0.116774i
$203$	−2.94961	−	28.0637i	−0.207022	−	1.96968i
$204$	−0.376499	−	0.0115864i	−0.0263602	−	0.000811212i
$205$	2.85709	+	7.88276i	0.199548	+	0.550556i
$206$	−0.721060	−	0.523881i	−0.0502386	−	0.0365005i
$207$	−9.98280	+	9.80140i	−0.693853	+	0.681244i
$208$	−11.1214	−	8.08016i	−0.771129	−	0.560258i
$209$	−12.0657	+	2.56464i	−0.834600	+	0.177400i
$210$	2.16413	−	21.1595i	0.149339	−	1.46015i
$211$	4.59169	+	0.975994i	0.316105	+	0.0671902i	0.363232	−	0.931699i	$-0.381673\pi$
$211$	4.59169	+	0.975994i	0.316105	+	0.0671902i	−0.0471270	+	0.998889i	$0.515007\pi$
$212$	−0.108679	−	0.120700i	−0.00746407	−	0.00828969i
$213$	−5.43891	−	2.62490i	−0.372668	−	0.179855i
$214$	8.15062	−	9.05218i	0.557165	−	0.618794i
$215$	1.44772	+	10.4026i	0.0987340	+	0.709450i
$216$	−10.9156	−	9.58555i	−0.742713	−	0.652214i
$217$	2.02004	+	1.46764i	0.137129	+	0.0996301i
$218$	7.28791	+	12.6230i	0.493599	+	0.854939i
$219$	5.35547	−	5.59192i	0.361889	−	0.377867i
$220$	0.278127	+	0.446431i	0.0187513	+	0.0300984i
$221$	1.69881	+	16.1631i	0.114274	+	1.08725i
$222$	1.33019	−	2.14850i	0.0892765	−	0.144198i
$223$	10.5491	−	11.7160i	0.706422	−	0.784561i	−0.277963	−	0.960592i	$-0.589659\pi$
$223$	10.5491	−	11.7160i	0.706422	−	0.784561i	0.984385	+	0.176031i	$0.0563259\pi$
$224$	0.977368			0.0653032
$225$	−14.6545	+	3.20071i	−0.976969	+	0.213381i
$226$	−9.06813			−0.603203
$227$	4.82528	−	5.35901i	0.320265	−	0.355690i	−0.561418	−	0.827532i	$-0.689744\pi$
$227$	4.82528	−	5.35901i	0.320265	−	0.355690i	0.881683	+	0.471842i	$0.156411\pi$
$228$	−0.183824	−	0.00565701i	−0.0121740	−	0.000374644i
$229$	−1.07910	−	10.2669i	−0.0713086	−	0.678456i	−0.970533	−	0.240968i	$-0.922535\pi$
$229$	−1.07910	−	10.2669i	−0.0713086	−	0.678456i	0.899224	−	0.437488i	$-0.144132\pi$
$230$	−14.4738	+	3.58804i	−0.954371	+	0.236589i
$231$	9.72277	+	33.3848i	0.639711	+	2.19656i
$232$	−10.2712	−	17.7902i	−0.674337	−	1.16799i
$233$	−10.0148	−	7.27620i	−0.656094	−	0.476680i	0.209248	−	0.977863i	$-0.432898\pi$
$233$	−10.0148	−	7.27620i	−0.656094	−	0.476680i	−0.865341	+	0.501183i	$0.832898\pi$
$234$	7.96784	−	12.0265i	0.520874	−	0.786199i
$235$	−18.5276	−	19.2376i	−1.20861	−	1.25492i
$236$	−0.234334	+	0.260255i	−0.0152539	+	0.0169411i
$237$	0.209890	+	2.83289i	0.0136339	+	0.184016i
$238$	−17.7602	−	19.7247i	−1.15122	−	1.27856i
$239$	−15.6686	−	3.33046i	−1.01352	−	0.215430i	−0.328925	−	0.944356i	$-0.606686\pi$
$239$	−15.6686	−	3.33046i	−1.01352	−	0.215430i	−0.684592	+	0.728927i	$0.740020\pi$
$240$	−4.93466	−	15.0440i	−0.318531	−	0.971086i
$241$	2.86314	−	0.608580i	0.184431	−	0.0392021i	−0.114770	−	0.993392i	$-0.536613\pi$
$241$	2.86314	−	0.608580i	0.184431	−	0.0392021i	0.299201	+	0.954190i	$0.403280\pi$
$242$	−18.8886	−	13.7234i	−1.21421	−	0.882173i
$243$	9.77062	−	12.1464i	0.626785	−	0.779192i
$244$	0.239840	+	0.174254i	0.0153542	+	0.0111555i
$245$	13.6675	−	10.6486i	0.873183	−	0.680316i
$246$	−4.39418	−	8.18231i	−0.280163	−	0.521685i
$247$	0.829435	+	7.89155i	0.0527757	+	0.502127i
$248$	1.77798	+	0.377921i	0.112902	+	0.0239980i
$249$	−18.1218	+	7.40914i	−1.14842	+	0.469535i
$250$	−15.1857	−	5.00196i	−0.960427	−	0.316352i
$251$	−4.72015			−0.297933			−0.148967	−	0.988842i	$-0.547595\pi$
$251$	−4.72015			−0.297933			−0.148967	+	0.988842i	$0.547595\pi$
$252$	0.0223843	+	0.517942i	0.00141008	+	0.0326273i
$253$	19.7220	−	14.3289i	1.23991	−	0.900849i
$254$	19.4660	+	8.66681i	1.22140	+	0.543804i
$255$	−9.31368	+	16.2365i	−0.583245	+	1.01677i
$256$	0.986086	−	0.439034i	0.0616304	−	0.0274396i
$257$	−10.6050	+	18.3684i	−0.661523	+	1.14579i	0.318692	+	0.947858i	$0.396756\pi$
$257$	−10.6050	+	18.3684i	−0.661523	+	1.14579i	−0.980215	+	0.197934i	$0.936577\pi$
$258$	−3.25306	−	11.1699i	−0.202527	−	0.695410i
$259$	3.83236	−	0.814594i	0.238132	−	0.0506164i
$260$	0.304309	−	0.147915i	0.0188725	−	0.00917331i
$261$	18.5964	−	11.8357i	1.15109	−	0.732610i
$262$	−5.95111	+	18.3156i	−0.367661	+	1.13154i
$263$	7.23524	−	1.53790i	0.446144	−	0.0948309i	0.0206393	−	0.999787i	$-0.493430\pi$
$263$	7.23524	−	1.53790i	0.446144	−	0.0948309i	0.425505	+	0.904956i	$0.360096\pi$
$264$	16.3512	+	19.3235i	1.00635	+	1.18928i
$265$	−7.83385	+	1.94201i	−0.481230	+	0.119297i
$266$	−8.67131	−	9.63047i	−0.531672	−	0.590482i
$267$	3.62554	−	3.78562i	0.221880	−	0.231676i
$268$	0.0229181	+	0.0396953i	0.00139994	+	0.00242478i
$269$	22.6424	+	16.4507i	1.38053	+	1.00301i	0.996830	+	0.0795565i	$0.0253504\pi$
$269$	22.6424	+	16.4507i	1.38053	+	1.00301i	0.383700	+	0.923458i	$0.374650\pi$
$270$	15.5495	−	5.85550i	0.946314	−	0.356355i
$271$	−16.6545	+	12.1002i	−1.01169	+	0.735034i	−0.964562	−	0.263855i	$-0.915006\pi$
$271$	−16.6545	+	12.1002i	−1.01169	+	0.735034i	−0.0471255	+	0.998889i	$0.515006\pi$
$272$	−18.0491	−	8.03596i	−1.09439	−	0.487252i
$273$	22.0119	−	3.97538i	1.33222	−	0.240601i
$274$	−6.52978	+	11.3099i	−0.394479	+	0.683257i
$275$	26.0786	−	1.75312i	1.57260	−	0.105717i
$276$	0.336424	−	0.137548i	0.0202504	−	0.00827942i
$277$	−1.82156	+	2.02305i	−0.109447	+	0.121553i	−0.795379	−	0.606112i	$-0.792728\pi$
$277$	−1.82156	+	2.02305i	−0.109447	+	0.121553i	0.685932	+	0.727666i	$0.259395\pi$
$278$	−13.5734	+	9.86163i	−0.814077	+	0.591461i
$279$	−0.322779	+	1.92362i	−0.0193243	+	0.115164i
$280$	11.2995	−	21.1824i	0.675272	−	1.26589i
$281$	2.51223	−	23.9023i	0.149867	−	1.42589i	−0.618452	−	0.785822i	$-0.712240\pi$
$281$	2.51223	−	23.9023i	0.149867	−	1.42589i	0.768319	−	0.640067i	$-0.221093\pi$
$282$	23.3887	+	18.1178i	1.39278	+	1.07890i
$283$	7.03966	−	3.13426i	0.418464	−	0.186312i	−0.186693	−	0.982418i	$-0.559777\pi$
$283$	7.03966	−	3.13426i	0.418464	−	0.186312i	0.605157	+	0.796106i	$0.293110\pi$
$284$	0.104983	+	0.116596i	0.00622962	+	0.00691869i
$285$	−4.54736	+	7.92738i	−0.269362	+	0.469577i
$286$	−16.8207	+	18.6813i	−0.994628	+	1.10465i
$287$	4.44991	−	13.6954i	0.262670	−	0.808415i
$288$	0.340368	+	0.683429i	0.0200564	+	0.0402714i
$289$	1.96470	+	6.04671i	0.115570	+	0.355689i
$290$	23.4825	−	0.788408i	1.37894	−	0.0462969i
$291$	2.07412	+	27.9944i	0.121587	+	1.64106i
$292$	−0.183763	+	0.0818166i	−0.0107539	+	0.00478795i
$293$	−13.7967	+	23.8965i	−0.806010	+	1.39605i	0.109597	+	0.993976i	$0.465044\pi$
$293$	−13.7967	+	23.8965i	−0.806010	+	1.39605i	−0.915607	+	0.402074i	$0.868289\pi$
$294$	−13.2747	+	13.8607i	−0.774193	+	0.808375i
$295$	5.93010	+	16.3612i	0.345264	+	0.952589i
$296$	2.30749	−	1.67649i	0.134120	−	0.0974441i
$297$	−19.9585	+	18.4249i	−1.15811	+	1.06912i
$298$	4.18322	+	12.8746i	0.242327	+	0.745807i
$299$	−7.84086	−	13.5808i	−0.453449	−	0.785397i
$300$	0.383870	+	0.0671120i	0.0221628	+	0.00387471i
$301$	9.01914	−	15.6216i	0.519855	−	0.900415i
$302$	21.4679	+	4.56314i	1.23534	+	0.262579i
$303$	5.08949	−	8.22045i	0.292383	−	0.472253i
$304$	−8.81236	−	3.92352i	−0.505423	−	0.225029i
$305$	13.2496	−	6.44021i	0.758669	−	0.368765i
$306$	7.60759	−	19.2880i	0.434897	−	1.10262i
$307$	−29.8034			−1.70097			−0.850485	−	0.526000i	$-0.823691\pi$
$307$	−29.8034			−1.70097			−0.850485	+	0.526000i	$0.823691\pi$
$308$	0.0944262	−	0.898406i	0.00538043	−	0.0511914i
$309$	0.892449	−	0.607358i	0.0507696	−	0.0345514i
$310$	−1.33851	+	1.59083i	−0.0760224	+	0.0903529i
$311$	5.41338	+	1.15065i	0.306964	+	0.0652473i	0.358818	−	0.933407i	$-0.383180\pi$
$311$	5.41338	+	1.15065i	0.306964	+	0.0652473i	−0.0518541	+	0.998655i	$0.516513\pi$
$312$	13.4618	−	9.16146i	0.762125	−	0.518665i
$313$	−5.60052	+	1.19043i	−0.316560	+	0.0672869i	−0.363452	−	0.931613i	$-0.618402\pi$
$313$	−5.60052	+	1.19043i	−0.316560	+	0.0672869i	0.0468916	+	0.998900i	$0.485068\pi$
$314$	−9.63679	−	29.6590i	−0.543836	−	1.67375i
$315$	23.2325	+	11.1324i	1.30901	+	0.627238i
$316$	0.0228051	−	0.0701870i	0.00128289	−	0.00394833i
$317$	−1.21704	+	11.5794i	−0.0683559	+	0.650363i	0.905679	+	0.423964i	$0.139362\pi$
$317$	−1.21704	+	11.5794i	−0.0683559	+	0.650363i	−0.974035	+	0.226399i	$0.927305\pi$
$318$	8.27528	−	3.38337i	0.464055	−	0.189730i
$319$	−35.0897	+	15.6230i	−1.96465	+	0.874718i
$320$	1.24195	−	17.4240i	0.0694272	−	0.974029i
$321$	6.98023	+	12.9977i	0.389598	+	0.725463i
$322$	23.3965	+	10.4168i	1.30383	+	0.580504i
$323$	3.52414	+	10.8462i	0.196089	+	0.603498i
$324$	−0.354378	+	0.196025i	−0.0196876	+	0.0108903i
$325$	0.631986	−	16.8018i	0.0350563	−	0.931998i
$326$	8.25148	+	14.2920i	0.457007	+	0.791560i
$327$	−17.3731	+	3.13760i	−0.960735	+	0.173510i
$328$	−1.09578	−	10.4257i	−0.0605044	−	0.575661i
$329$	4.79486	+	45.6201i	0.264349	+	2.51511i
$330$	−28.3028	+	6.09874i	−1.55802	+	0.335725i
$331$	2.09180	−	19.9021i	0.114976	−	1.09392i	−0.773120	−	0.634260i	$-0.781305\pi$
$331$	2.09180	−	19.9021i	0.114976	−	1.09392i	0.888095	−	0.459659i	$-0.152028\pi$
$332$	0.508625			0.0279144
$333$	1.90423	+	2.39611i	0.104351	+	0.131306i
$334$	−1.86568	+	5.74198i	−0.102086	+	0.314187i
$335$	2.27644	−	0.0764300i	0.124375	−	0.00417582i
$336$	−9.19430	+	25.5905i	−0.501590	+	1.39607i
$337$	−2.65966	−	2.95385i	−0.144881	−	0.160907i	0.666337	−	0.745651i	$-0.267861\pi$
$337$	−2.65966	−	2.95385i	−0.144881	−	0.160907i	−0.811217	+	0.584745i	$0.801195\pi$
$338$	−1.61901	−	1.79809i	−0.0880625	−	0.0978033i
$339$	3.71372	−	10.3364i	0.201701	−	0.561395i
$340$	0.383603	−	0.298873i	0.0208038	−	0.0162087i
$341$	1.05028	−	3.23242i	0.0568757	−	0.175045i
$342$	3.71437	−	9.41725i	0.200850	−	0.509227i
$343$	−2.87436			−0.155201
$344$	1.37262	−	13.0596i	0.0740067	−	0.704126i
$345$	1.83765	−	17.9674i	0.0989360	−	0.967335i
$346$	1.47596	+	14.0428i	0.0793481	+	0.754946i
$347$	−3.83972	−	36.5325i	−0.206127	−	1.96117i	−0.268989	−	0.963143i	$-0.586689\pi$
$347$	−3.83972	−	36.5325i	−0.206127	−	1.96117i	0.0628621	−	0.998022i	$-0.479977\pi$
$348$	−0.563560	+	0.101779i	−0.0302100	+	0.00545595i
$349$	5.56763	+	9.64341i	0.298028	+	0.516200i	0.975685	−	0.219179i	$-0.0703377\pi$
$349$	5.56763	+	9.64341i	0.298028	+	0.516200i	−0.677657	+	0.735378i	$0.737004\pi$
$350$	15.2938	+	22.8060i	0.817486	+	1.21903i
$351$	10.4454	+	14.0075i	0.557536	+	0.747665i
$352$	−0.411112	−	1.26527i	−0.0219124	−	0.0674393i
$353$	−2.71907	−	1.21061i	−0.144722	−	0.0644343i	0.333098	−	0.942892i	$-0.391906\pi$
$353$	−2.71907	−	1.21061i	−0.144722	−	0.0644343i	−0.477820	+	0.878458i	$0.658573\pi$
$354$	−9.12045	−	16.9830i	−0.484746	−	0.902636i
$355$	7.56750	−	1.87598i	0.401641	−	0.0995668i
$356$	−0.124404	+	0.0553882i	−0.00659339	+	0.00293557i
$357$	29.7567	−	12.1661i	1.57489	−	0.643900i
$358$	−0.528368	+	5.02709i	−0.0279251	+	0.265690i
$359$	0.714480	−	2.19894i	0.0377088	−	0.116056i	−0.930430	−	0.366469i	$-0.880567\pi$
$359$	0.714480	−	2.19894i	0.0377088	−	0.116056i	0.968139	+	0.250413i	$0.0805665\pi$
$360$	18.7469	+	0.524434i	0.988050	+	0.0276401i
$361$	−4.15068	−	12.7745i	−0.218457	−	0.672341i
$362$	21.3552	−	4.53920i	1.12241	−	0.238575i
$363$	23.3783	−	15.9101i	1.22704	−	0.835065i
$364$	−0.568412	−	0.120820i	−0.0297929	−	0.00633267i
$365$	−0.710688	+	9.97059i	−0.0371991	+	0.521885i
$366$	−13.4907	+	9.18114i	−0.705171	+	0.479906i
$367$	1.77075	−	16.8476i	0.0924324	−	0.879435i	−0.845816	−	0.533474i	$-0.820886\pi$
$367$	1.77075	−	16.8476i	0.0924324	−	0.879435i	0.938249	−	0.345961i	$-0.112447\pi$
$368$	19.0637			0.993766
$369$	11.1262	−	1.65780i	0.579209	−	0.0863015i
$370$	0.449676	+	3.23113i	0.0233775	+	0.167979i
$371$	12.6632	+	5.63803i	0.657442	+	0.292712i
$372$	0.0266746	−	0.0430844i	0.00138302	−	0.00223382i
$373$	24.6592	+	5.24148i	1.27681	+	0.271394i	0.795927	−	0.605393i	$-0.206984\pi$
$373$	24.6592	+	5.24148i	1.27681	+	0.271394i	0.480880	+	0.876787i	$0.340317\pi$
$374$	−18.0645	+	31.2886i	−0.934094	+	1.61790i
$375$	11.9206	−	15.2610i	0.615577	−	0.788077i
$376$	16.6967	+	28.9196i	0.861069	+	1.49141i
$377$	7.63542	+	23.4994i	0.393244	+	1.21028i
$378$	−27.2474	−	8.48036i	−1.40145	−	0.436182i
$379$	19.7932	−	14.3806i	1.01671	−	0.738681i	0.0511021	−	0.998693i	$-0.483727\pi$
$379$	19.7932	−	14.3806i	1.01671	−	0.738681i	0.965605	+	0.260012i	$0.0837266\pi$
$380$	0.187292	−	0.145923i	0.00960787	−	0.00748570i
$381$	−17.8509	+	18.6391i	−0.914530	+	0.954908i
$382$	−13.2640	+	22.9739i	−0.678645	+	1.17545i
$383$	−0.00459473	+	0.00204571i	−0.000234780	+	0.000104531i	−0.406854	−	0.913493i	$-0.633374\pi$
$383$	−0.00459473	+	0.00204571i	−0.000234780	+	0.000104531i	0.406619	+	0.913598i	$0.366708\pi$
$384$	1.49483	+	20.1758i	0.0762829	+	1.02959i
$385$	−37.1818	−	25.1523i	−1.89496	−	1.28188i
$386$	5.14561	+	15.8365i	0.261904	+	0.806059i
$387$	14.0644	+	0.866458i	0.714932	+	0.0440445i
$388$	0.225358	−	0.693582i	0.0114408	−	0.0352113i
$389$	6.97691	−	7.74865i	0.353744	−	0.392872i	−0.539841	−	0.841767i	$-0.681516\pi$
$389$	6.97691	−	7.74865i	0.353744	−	0.392872i	0.893584	+	0.448895i	$0.148182\pi$
$390$	1.99860	+	18.5170i	0.101203	+	0.937645i
$391$	−15.0809	−	16.7491i	−0.762675	−	0.847037i
$392$	−19.7897	+	8.81094i	−0.999531	+	0.445020i
$393$	−18.4400	−	14.2843i	−0.930176	−	0.720548i
$394$	1.28059	−	12.1840i	0.0645151	−	0.613820i
$395$	−2.54395	−	2.64144i	−0.128000	−	0.132905i
$396$	0.661097	−	0.246841i	0.0332214	−	0.0124042i
$397$	−4.80180	+	3.48871i	−0.240996	+	0.175094i	−0.701727	−	0.712446i	$-0.747587\pi$
$397$	−4.80180	+	3.48871i	−0.240996	+	0.175094i	0.460731	+	0.887540i	$0.347587\pi$
$398$	16.6210	−	18.4595i	0.833135	−	0.925290i
$399$	14.5286	−	5.94004i	0.727338	−	0.297374i
$400$	17.3048	+	10.8781i	0.865239	+	0.543903i
$401$	9.95507	−	17.2427i	0.497133	−	0.861059i	−0.502862	−	0.864367i	$-0.667720\pi$
$401$	9.95507	−	17.2427i	0.497133	−	0.861059i	0.999995	+	0.00330780i	$0.00105291\pi$
$402$	−2.48287	+	0.448409i	−0.123834	+	0.0223646i
$403$	−1.99734	−	0.889274i	−0.0994946	−	0.0442979i
$404$	−0.203210	+	0.147641i	−0.0101101	+	0.00734540i
$405$	0.306362	+	20.1223i	0.0152232	+	0.999884i
$406$	−32.6463	−	23.7190i	−1.62021	−	1.17715i
$407$	−2.66656	−	4.61862i	−0.132177	−	0.228937i
$408$	16.1872	−	16.9019i	0.801386	−	0.836768i
$409$	−3.27138	−	3.63324i	−0.161759	−	0.179652i	0.656816	−	0.754051i	$-0.271903\pi$
$409$	−3.27138	−	3.63324i	−0.161759	−	0.179652i	−0.818576	+	0.574399i	$0.805236\pi$
$410$	11.1111	+	4.50656i	0.548737	+	0.222563i
$411$	−10.2175	−	12.0748i	−0.503993	−	0.595607i
$412$	−0.0274324	+	0.00583093i	−0.00135150	+	0.000287269i
$413$	9.23611	−	28.4258i	0.454479	−	1.39874i
$414$	0.863825	+	19.9877i	0.0424547	+	0.982342i
$415$	11.8959	−	22.3005i	0.583946	−	1.09469i
$416$	−0.837111	+	0.177933i	−0.0410427	+	0.00872390i
$417$	−5.68208	−	19.5104i	−0.278253	−	0.955428i
$418$	−8.81990	+	15.2765i	−0.431395	+	0.747199i
$419$	11.6448	−	5.18460i	0.568886	−	0.253284i	−0.102075	−	0.994777i	$-0.532548\pi$
$419$	11.6448	−	5.18460i	0.568886	−	0.253284i	0.670961	+	0.741492i	$0.265882\pi$
$420$	−0.449228	−	0.496121i	−0.0219201	−	0.0242082i
$421$	−16.0386	−	7.14085i	−0.781674	−	0.348024i	−0.0232033	−	0.999731i	$-0.507387\pi$
$421$	−16.0386	−	7.14085i	−0.781674	−	0.348024i	−0.758471	+	0.651707i	$0.774053\pi$
$422$	5.43091	−	3.94579i	0.264372	−	0.192078i
$423$	−30.2302	+	19.2400i	−1.46984	+	0.935479i
$424$	10.0910			0.490063
$425$	−4.13218	−	23.8091i	−0.200440	−	1.15491i
$426$	−7.99392	+	3.26833i	−0.387307	+	0.158351i
$427$	−24.7486	−	5.26047i	−1.19767	−	0.254572i
$428$	−0.0400645	−	0.381188i	−0.00193659	−	0.0184254i
$429$	−14.4053	−	26.8238i	−0.695495	−	1.29507i
$430$	12.4404	+	8.41549i	0.599927	+	0.405831i
$431$	23.8727	+	17.3445i	1.14991	+	0.835456i	0.988469	−	0.151427i	$-0.0483867\pi$
$431$	23.8727	+	17.3445i	1.14991	+	0.835456i	0.161438	+	0.986883i	$0.448387\pi$
$432$	−21.0961	+	2.48270i	−1.01499	+	0.119449i
$433$	15.9668	+	11.6006i	0.767316	+	0.557488i	0.901146	−	0.433517i	$-0.142727\pi$
$433$	15.9668	+	11.6006i	0.767316	+	0.557488i	−0.133830	+	0.991004i	$0.542727\pi$
$434$	3.49263	−	0.742382i	0.167652	−	0.0356355i
$435$	−8.71823	+	27.0896i	−0.418007	+	1.29884i
$436$	0.448624	+	0.0953580i	0.0214852	+	0.00456682i
$437$	−7.36318	−	8.17764i	−0.352229	−	0.391190i
$438$	−0.818120	−	11.0422i	−0.0390913	−	0.527616i
$439$	8.21559	−	9.12433i	0.392109	−	0.435481i	−0.514476	−	0.857505i	$-0.672014\pi$
$439$	8.21559	−	9.12433i	0.392109	−	0.435481i	0.906585	+	0.422024i	$0.138680\pi$
$440$	−32.1751	−	5.71796i	−1.53389	−	0.272593i
$441$	−10.3628	−	20.8077i	−0.493468	−	0.990842i
$442$	18.8024	+	13.6608i	0.894341	+	0.649777i
$443$	−11.4062	−	19.7562i	−0.541926	−	0.938643i	−0.998793	−	0.0491085i	$-0.984362\pi$
$443$	−11.4062	−	19.7562i	−0.541926	−	0.938643i	0.456868	−	0.889535i	$-0.348971\pi$
$444$	−0.0222333	−	0.0763420i	−0.00105515	−	0.00362303i
$445$	−0.481121	+	6.74988i	−0.0228073	+	0.319975i
$446$	−2.35660	−	22.4216i	−0.111588	−	1.06169i
$447$	−16.3884	−	0.504339i	−0.775146	−	0.0238544i
$448$	−20.0746	+	22.2951i	−0.948435	+	1.05334i
$449$	−4.10374			−0.193668			−0.0968338	−	0.995301i	$-0.530872\pi$
$449$	−4.10374			−0.193668			−0.0968338	+	0.995301i	$0.530872\pi$
$450$	−10.6212	+	18.6364i	−0.500686	+	0.878528i
$451$	−19.6015			−0.922997
$452$	−0.190930	+	0.212049i	−0.00898058	+	0.00997395i
$453$	−13.9932	+	22.6016i	−0.657457	+	1.06191i
$454$	−1.07793	−	10.2559i	−0.0505900	−	0.481331i
$455$	−18.5915	+	22.0961i	−0.871583	+	1.03588i
$456$	7.90331	−	8.25225i	0.370107	−	0.386447i
$457$	9.06472	+	15.7006i	0.424030	+	0.734441i	0.996329	−	0.0856035i	$-0.0272818\pi$
$457$	9.06472	+	15.7006i	0.424030	+	0.734441i	−0.572299	+	0.820045i	$0.693948\pi$
$458$	−11.9434	−	8.67742i	−0.558080	−	0.405469i
$459$	18.8700	+	16.5707i	0.880775	+	0.773453i
$460$	−0.220843	+	0.414001i	−0.0102968	+	0.0193029i
$461$	15.7461	−	17.4878i	0.733370	−	0.814490i	−0.254939	−	0.966957i	$-0.582055\pi$
$461$	15.7461	−	17.4878i	0.733370	−	0.814490i	0.988308	+	0.152468i	$0.0487220\pi$
$462$	44.7823	+	21.6126i	2.08346	+	1.00551i
$463$	−2.39487	−	2.65977i	−0.111299	−	0.123610i	0.684921	−	0.728617i	$-0.259837\pi$
$463$	−2.39487	−	2.65977i	−0.111299	−	0.123610i	−0.796220	+	0.605008i	$0.793170\pi$
$464$	−29.3812	−	6.24516i	−1.36399	−	0.289924i
$465$	−1.26515	−	2.17721i	−0.0586699	−	0.100966i
$466$	−17.3156	+	3.68054i	−0.802129	+	0.170498i
$467$	12.8399	+	9.32877i	0.594162	+	0.431684i	0.843802	−	0.536655i	$-0.180312\pi$
$467$	12.8399	+	9.32877i	0.594162	+	0.431684i	−0.249640	+	0.968339i	$0.580312\pi$
$468$	−0.113465	−	0.439539i	−0.00524493	−	0.0203177i
$469$	−3.16481	−	2.29937i	−0.146137	−	0.106175i
$470$	−38.1729	+	1.28163i	−1.76078	+	0.0591171i
$471$	37.7536	+	1.16183i	1.73960	+	0.0535345i
$472$	−2.27437	−	21.6392i	−0.104686	−	0.996026i
$473$	−24.0170	−	5.10498i	−1.10430	−	0.234727i
$474$	3.21142	+	2.48768i	0.147505	+	0.114263i
$475$	−2.01752	−	11.6247i	−0.0925700	−	0.533376i
$476$	−0.835184			−0.0382806
$477$	0.467541	+	10.8183i	0.0214072	+	0.495334i
$478$	−18.5323	+	13.4645i	−0.847648	+	0.615852i
$479$	−15.3830	−	6.84896i	−0.702868	−	0.312937i	0.0240023	−	0.999712i	$-0.492359\pi$
$479$	−15.3830	−	6.84896i	−0.702868	−	0.312937i	−0.726870	+	0.686775i	$0.759026\pi$
$480$	−0.901570	−	0.398387i	−0.0411509	−	0.0181838i
$481$	−3.13410	+	1.39539i	−0.142903	+	0.0636244i
$482$	2.09293	−	3.62506i	0.0953304	−	0.165117i
$483$	−21.4553	+	22.4026i	−0.976251	+	1.01935i
$484$	−0.718609	+	0.152745i	−0.0326640	+	0.00694295i
$485$	−25.1391	−	26.1025i	−1.14151	−	1.18525i
$486$	−3.55895	−	22.0061i	−0.161437	−	0.998217i
$487$	−3.07445	+	9.46219i	−0.139317	+	0.428773i	−0.996236	−	0.0866771i	$-0.972375\pi$
$487$	−3.07445	+	9.46219i	−0.139317	+	0.428773i	0.856920	+	0.515450i	$0.172375\pi$
$488$	−18.0165	+	3.82953i	−0.815569	+	0.173355i
$489$	−19.6701	+	3.55244i	−0.889513	+	0.160647i
$490$	1.76159	−	24.7142i	0.0795804	−	1.11647i
$491$	7.86619	+	8.73629i	0.354996	+	0.394263i	0.894020	−	0.448027i	$-0.147873\pi$
$491$	7.86619	+	8.73629i	0.354996	+	0.394263i	−0.539024	+	0.842291i	$0.681207\pi$
$492$	−0.283855	−	0.0695254i	−0.0127972	−	0.00313445i
$493$	17.7559	+	30.7542i	0.799688	+	1.38510i
$494$	9.18019	+	6.66980i	0.413036	+	0.300089i
$495$	4.63930	−	34.7588i	0.208521	−	1.56229i
$496$	2.15027	−	1.56227i	0.0965502	−	0.0701478i
$497$	−12.2327	−	5.44634i	−0.548710	−	0.244302i
$498$	−9.46650	+	26.3481i	−0.424204	+	1.18069i
$499$	12.7440	−	22.0733i	0.570501	−	0.988137i	−0.426013	−	0.904717i	$-0.640082\pi$
$499$	12.7440	−	22.0733i	0.570501	−	0.988137i	0.996514	−	0.0834204i	$-0.0265844\pi$
$500$	−0.436701	+	0.249786i	−0.0195299	+	0.0111708i
$501$	−5.78097	−	4.47815i	−0.258275	−	0.200069i
$502$	−4.51661	+	5.01621i	−0.201586	+	0.223884i
$503$	−3.86329	+	2.80684i	−0.172256	+	0.125151i	−0.670573	−	0.741844i	$-0.733952\pi$
$503$	−3.86329	+	2.80684i	−0.172256	+	0.125151i	0.498317	+	0.866995i	$0.333952\pi$
$504$	−24.8448	−	20.4990i	−1.10668	−	0.913096i
$505$	1.72052	+	12.3628i	0.0765621	+	0.550135i
$506$	3.64397	−	34.6700i	0.161994	−	1.54127i
$507$	2.71261	−	1.10906i	0.120471	−	0.0492550i
$508$	0.612521	−	0.272712i	0.0271762	−	0.0120996i
$509$	−0.140363	−	0.155889i	−0.00622150	−	0.00690968i	0.740026	−	0.672578i	$-0.234813\pi$
$509$	−0.140363	−	0.155889i	−0.00622150	−	0.00690968i	−0.746248	+	0.665669i	$0.768146\pi$
$510$	8.34281	+	25.4342i	0.369426	+	1.12625i
$511$	11.4874	−	12.7580i	0.508171	−	0.564381i
$512$	−6.74190	+	20.7494i	−0.297953	+	0.917005i
$513$	9.21316	+	8.09054i	0.406771	+	0.357206i
$514$	9.37282	+	28.8466i	0.413417	+	1.27237i
$515$	−0.385942	+	1.33914i	−0.0170066	+	0.0590095i
$516$	−0.329691	−	0.159114i	−0.0145138	−	0.00700460i
$517$	57.0415	−	25.3965i	2.50868	−	1.11694i
$518$	2.80142	−	4.85221i	0.123088	−	0.213194i
$519$	−16.6113	−	4.06864i	−0.729154	−	0.178594i
$520$	−5.82160	+	20.1997i	−0.255294	+	0.885818i
$521$	−10.5015	+	7.62978i	−0.460079	+	0.334267i	−0.793562	−	0.608489i	$-0.791776\pi$
$521$	−10.5015	+	7.62978i	−0.460079	+	0.334267i	0.333484	+	0.942756i	$0.391776\pi$
$522$	5.21651	−	31.0882i	0.228321	−	1.36069i
$523$	11.1175	+	34.2162i	0.486136	+	1.49617i	0.830329	+	0.557273i	$0.188152\pi$
$523$	11.1175	+	34.2162i	0.486136	+	1.49617i	−0.344194	+	0.938899i	$0.611848\pi$
$524$	0.302992	+	0.524797i	0.0132363	+	0.0229259i
$525$	−32.2590	+	8.09284i	−1.40790	+	0.353201i
$526$	5.28890	−	9.16064i	0.230607	−	0.399423i
$527$	−3.07362	−	0.653317i	−0.133889	−	0.0284590i
$528$	36.9961	+	1.13852i	1.61005	+	0.0495478i
$529$	−1.14461	−	0.509612i	−0.0497655	−	0.0221570i
$530$	−5.43223	+	10.1835i	−0.235961	+	0.442342i
$531$	23.0933	−	3.44088i	1.00217	−	0.149321i
$532$	−0.407774			−0.0176792
$533$	−1.31802	+	12.5402i	−0.0570900	+	0.543175i
$534$	−0.553850	−	7.47533i	−0.0239675	−	0.323489i
$535$	−17.6501	−	7.15874i	−0.763081	−	0.309499i
$536$	−2.78557	−	0.592092i	−0.120318	−	0.0255745i
$537$	−5.51378	−	2.66103i	−0.237937	−	0.114832i
$538$	39.1485	−	8.32127i	1.68781	−	0.358756i
$539$	12.5167	+	38.5225i	0.539133	+	1.65928i
$540$	0.190471	−	0.486898i	0.00819656	−	0.0209528i
$541$	5.95413	−	18.3249i	0.255988	−	0.787850i	−0.737646	−	0.675188i	$-0.764062\pi$
$541$	5.95413	−	18.3249i	0.255988	−	0.787850i	0.993633	−	0.112661i	$-0.0359376\pi$
$542$	−3.07719	+	29.2775i	−0.132177	+	1.25758i
$543$	−3.57169	+	26.2009i	−0.153276	+	1.12439i
$544$	−1.12365	+	0.500282i	−0.0481762	+	0.0214494i
$545$	14.6735	−	17.4395i	0.628544	−	0.747027i
$546$	16.8380	−	27.1965i	0.720601	−	1.16390i
$547$	39.9472	+	17.7856i	1.70802	+	0.760459i	0.998440	+	0.0558322i	$0.0177812\pi$
$547$	39.9472	+	17.7856i	1.70802	+	0.760459i	0.709578	+	0.704627i	$0.248885\pi$
$548$	0.126986	+	0.390823i	0.00542458	+	0.0166951i
$549$	−4.94026	−	19.1375i	−0.210845	−	0.816768i
$550$	23.0910	−	29.3918i	0.984603	−	1.25327i
$551$	8.66924	+	15.0156i	0.369322	+	0.639685i
$552$	−7.63540	+	21.2516i	−0.324984	+	0.904527i
$553$	0.658364	+	6.26392i	0.0279965	+	0.266369i
$554$	0.406925	+	3.87163i	0.0172886	+	0.164490i
$555$	−3.86719	−	0.810697i	−0.164153	−	0.0344122i
$556$	−0.0551836	+	0.525037i	−0.00234031	+	0.0222665i
$557$	42.9035			1.81788			0.908939	−	0.416929i	$-0.136894\pi$
$557$	42.9035			1.81788			0.908939	+	0.416929i	$0.136894\pi$
$558$	1.73542	+	2.18370i	0.0734661	+	0.0924435i
$559$	−4.88088	+	15.0218i	−0.206439	+	0.635354i
$560$	−11.9622	−	33.0038i	−0.505494	−	1.39467i
$561$	−28.2665	−	33.4048i	−1.19341	−	1.41035i
$562$	−22.9976	−	25.5414i	−0.970094	−	1.07740i
$563$	10.6413	+	11.8183i	0.448476	+	0.498083i	0.924411	−	0.381397i	$-0.124557\pi$
$563$	10.6413	+	11.8183i	0.448476	+	0.498083i	−0.475935	+	0.879480i	$0.657890\pi$
$564$	0.916117	−	0.165452i	0.0385755	−	0.00696678i
$565$	4.83170	+	13.3307i	0.203271	+	0.560828i
$566$	3.40526	−	10.4803i	0.143134	−	0.440520i
$567$	20.8252	−	27.5851i	0.874574	−	1.15847i
$568$	−9.74791			−0.409013
$569$	−2.46904	+	23.4914i	−0.103508	+	0.984810i	0.812313	+	0.583222i	$0.198208\pi$
$569$	−2.46904	+	23.4914i	−0.103508	+	0.984810i	−0.915820	+	0.401588i	$0.868458\pi$
$570$	4.07333	+	12.4181i	0.170613	+	0.520138i
$571$	0.122040	+	1.16113i	0.00510720	+	0.0485917i	0.996779	−	0.0802014i	$-0.0255563\pi$
$571$	0.122040	+	1.16113i	0.00510720	+	0.0485917i	−0.991671	+	0.128793i	$0.958890\pi$
$572$	0.0826824	+	0.786670i	0.00345712	+	0.0328923i
$573$	−20.7549	−	24.5277i	−0.867050	−	1.02466i
$574$	−10.2964	−	17.8339i	−0.429763	−	0.744372i
$575$	12.9866	+	19.3656i	0.541578	+	0.807600i
$576$	−22.5809	−	6.27299i	−0.940870	−	0.261374i
$577$	−10.2147	−	31.4377i	−0.425244	−	1.30877i	−0.902760	−	0.430144i	$-0.858463\pi$
$577$	−10.2147	−	31.4377i	−0.425244	−	1.30877i	0.477516	−	0.878623i	$-0.341537\pi$
$578$	8.30596	+	3.69805i	0.345482	+	0.153819i
$579$	−20.1587	−	0.620367i	−0.837768	−	0.0257816i
$580$	0.475989	−	0.565714i	0.0197643	−	0.0234900i
$581$	−39.6560	+	17.6560i	−1.64521	+	0.732494i
$582$	31.7350	+	24.5831i	1.31546	+	1.01900i
$583$	1.97228	−	18.7650i	0.0816835	−	0.777167i
$584$	3.86200	−	11.8860i	0.159811	−	0.491847i
$585$	−21.9252	−	5.30524i	−0.906497	−	0.219345i
$586$	12.1936	+	37.5281i	0.503714	+	1.55027i
$587$	−3.60347	+	0.765941i	−0.148731	+	0.0316138i	−0.281675	−	0.959510i	$-0.590890\pi$
$587$	−3.60347	+	0.765941i	−0.148731	+	0.0316138i	0.132944	+	0.991123i	$0.457557\pi$
$588$	0.0446212	+	0.602253i	0.00184015	+	0.0248365i
$589$	−1.50068	−	0.318979i	−0.0618343	−	0.0131433i
$590$	23.0619	+	9.35369i	0.949442	+	0.385085i
$591$	13.3635	+	6.44945i	0.549703	+	0.265295i
$592$	0.435945	−	4.14774i	0.0179172	−	0.170471i
$593$	18.3600			0.753956			0.376978	−	0.926222i	$-0.376963\pi$
$593$	18.3600			0.753956			0.376978	+	0.926222i	$0.376963\pi$
$594$	0.482681	+	38.8408i	0.0198047	+	1.59366i
$595$	−19.5335	+	36.6184i	−0.800797	+	1.50121i
$596$	0.389138	+	0.173256i	0.0159397	+	0.00709682i
$597$	14.2343	+	26.5054i	0.582571	+	1.08479i
$598$	−21.9354	−	4.66250i	−0.897004	−	0.190664i
$599$	21.7553	−	37.6813i	0.888897	−	1.53961i	0.0477161	−	0.998861i	$-0.484806\pi$
$599$	21.7553	−	37.6813i	0.888897	−	1.53961i	0.841181	−	0.540754i	$-0.181861\pi$
$600$	−19.0574	+	14.9339i	−0.778014	+	0.609673i
$601$	4.47712	+	7.75460i	0.182626	+	0.316317i	0.942774	−	0.333433i	$-0.108207\pi$
$601$	4.47712	+	7.75460i	0.182626	+	0.316317i	−0.760148	+	0.649750i	$0.774874\pi$
$602$	−7.97120	−	24.5328i	−0.324882	−	0.999884i
$603$	0.505700	−	3.01376i	0.0205937	−	0.122730i
$604$	0.558712	−	0.405928i	0.0227337	−	0.0165170i
$605$	−10.1100	+	35.0796i	−0.411030	+	1.42619i
$606$	−3.86604	−	13.2747i	−0.157047	−	0.539248i
$607$	2.21210	−	3.83147i	0.0897864	−	0.155515i	−0.817634	−	0.575738i	$-0.804715\pi$
$607$	2.21210	−	3.83147i	0.0897864	−	0.155515i	0.907421	+	0.420223i	$0.138048\pi$
$608$	−0.548617	+	0.244260i	−0.0222494	+	0.00990605i
$609$	40.4060	−	27.4984i	1.63734	−	1.11429i
$610$	5.83410	−	20.2431i	0.236216	−	0.819621i
$611$	−12.4121	−	38.2004i	−0.502138	−	1.54542i
$612$	−0.290852	−	0.584005i	−0.0117570	−	0.0236070i
$613$	−6.60377	+	20.3243i	−0.266724	+	0.820891i	0.724568	+	0.689204i	$0.242040\pi$
$613$	−6.60377	+	20.3243i	−0.266724	+	0.820891i	−0.991291	+	0.131687i	$0.957960\pi$
$614$	−28.5183	+	31.6727i	−1.15090	+	1.27821i
$615$	−9.68721	+	10.8195i	−0.390626	+	0.436282i
$616$	37.5553	+	41.7093i	1.51314	+	1.68052i
$617$	−29.4288	+	13.1026i	−1.18476	+	0.527489i	−0.902014	−	0.431706i	$-0.857912\pi$
$617$	−29.4288	+	13.1026i	−1.18476	+	0.527489i	−0.282745	+	0.959195i	$0.591245\pi$
$618$	0.208513	−	1.52959i	0.00838763	−	0.0615293i
$619$	4.20729	−	40.0297i	0.169105	−	1.60893i	−0.500178	−	0.865922i	$-0.666732\pi$
$619$	4.20729	−	40.0297i	0.169105	−	1.60893i	0.669284	−	0.743007i	$-0.266601\pi$
$620$	0.00901746	+	0.0647948i	0.000362150	+	0.00260222i
$621$	−23.1369	−	7.20103i	−0.928452	−	0.288967i
$622$	6.40277	−	4.65188i	0.256728	−	0.186524i
$623$	7.77671	−	8.63691i	0.311567	−	0.346031i
$624$	3.21604	−	23.5919i	0.128745	−	0.944434i
$625$	0.738068	+	24.9891i	0.0295227	+	0.999564i
$626$	−4.09393	+	7.09089i	−0.163626	+	0.283409i
$627$	−13.8010	−	16.3097i	−0.551158	−	0.651347i
$628$	−0.896449	−	0.399125i	−0.0357722	−	0.0159268i
$629$	−3.98900	+	2.89817i	−0.159052	+	0.115558i
$630$	34.0614	−	14.0374i	1.35704	−	0.559264i
$631$	−0.646758	−	0.469897i	−0.0257470	−	0.0187063i	0.574837	−	0.818268i	$-0.305065\pi$
$631$	−0.646758	−	0.469897i	−0.0257470	−	0.0187063i	−0.600584	+	0.799561i	$0.705065\pi$
$632$	2.29257	+	3.97084i	0.0911934	+	0.157952i
$633$	2.27348	+	7.80640i	0.0903629	+	0.310276i
$634$	11.1411	+	12.3735i	0.442470	+	0.491413i
$635$	2.36887	−	33.2341i	0.0940059	−	1.31885i
$636$	0.0951197	−	0.264746i	0.00377174	−	0.0104979i
$637$	25.4867	−	5.41736i	1.00982	−	0.214644i
$638$	−16.9738	+	52.2399i	−0.671999	+	2.06820i
$639$	−0.451645	−	10.4504i	−0.0178668	−	0.413412i
$640$	−18.1180	−	18.8123i	−0.716175	−	0.743620i
$641$	28.1541	−	5.98433i	1.11202	−	0.236367i	0.384954	−	0.922936i	$-0.374217\pi$
$641$	28.1541	−	5.98433i	1.11202	−	0.236367i	0.727065	+	0.686569i	$0.240884\pi$
$642$	20.4922	+	5.01922i	0.808763	+	0.198093i
$643$	24.5329	−	42.4923i	0.967484	−	1.67573i	0.264695	−	0.964332i	$-0.414729\pi$
$643$	24.5329	−	42.4923i	0.967484	−	1.67573i	0.702789	−	0.711399i	$-0.251938\pi$
$644$	0.736200	−	0.327777i	0.0290103	−	0.0129162i
$645$	−14.6872	+	10.7338i	−0.578309	+	0.422643i
$646$	14.8987	+	6.63332i	0.586180	+	0.260984i
$647$	−11.9156	+	8.65721i	−0.468452	+	0.340350i	−0.796838	−	0.604194i	$-0.793495\pi$
$647$	−11.9156	+	8.65721i	−0.468452	+	0.340350i	0.328386	+	0.944544i	$0.393495\pi$
$648$	5.68179	−	24.5116i	0.223202	−	0.962906i
$649$	−40.6843			−1.59700
$650$	−17.2509	−	16.7490i	−0.676638	−	0.656948i
$651$	−0.584146	+	4.28513i	−0.0228945	+	0.167948i
$652$	0.507939	+	0.107966i	0.0198924	+	0.00422827i
$653$	2.79240	+	26.5679i	0.109275	+	1.03968i	0.902481	+	0.430730i	$0.141744\pi$
$653$	2.79240	+	26.5679i	0.109275	+	1.03968i	−0.793206	+	0.608954i	$0.791590\pi$
$654$	−13.2896	+	21.4651i	−0.519663	+	0.839352i
$655$	30.0960	−	1.01045i	1.17595	−	0.0394817i
$656$	−12.4011	−	9.00994i	−0.484182	−	0.351779i
$657$	12.9216	+	3.58962i	0.504118	+	0.140044i
$658$	53.0696	+	38.5573i	2.06887	+	1.50312i
$659$	5.26842	−	1.11984i	0.205228	−	0.0436226i	−0.104150	−	0.994562i	$-0.533212\pi$
$659$	5.26842	−	1.11984i	0.205228	−	0.0436226i	0.309379	+	0.950939i	$0.399879\pi$
$660$	−0.453304	+	0.790242i	−0.0176448	+	0.0307601i
$661$	23.7568	+	5.04966i	0.924032	+	0.196409i	0.645273	−	0.763952i	$-0.276744\pi$
$661$	23.7568	+	5.04966i	0.924032	+	0.196409i	0.278759	+	0.960361i	$0.410077\pi$
$662$	−19.1488	−	21.2669i	−0.744240	−	0.826563i
$663$	−23.2716	+	15.8375i	−0.903794	+	0.615079i
$664$	−21.1451	+	23.4840i	−0.820590	+	0.911357i
$665$	−9.53715	+	17.8787i	−0.369835	+	0.693307i
$666$	4.36852	+	0.269129i	0.169277	+	0.0104286i
$667$	−27.7214	−	20.1408i	−1.07338	−	0.779854i
$668$	0.0949884	+	0.164525i	0.00367521	+	0.00636565i
$669$	26.5225	+	6.49624i	1.02542	+	0.251159i
$670$	2.09706	−	2.49236i	0.0810164	−	0.0962883i
$671$	3.59998	+	34.2515i	0.138976	+	1.32227i
$672$	0.800930	+	1.49139i	0.0308966	+	0.0575318i
$673$	22.8188	−	25.3428i	0.879599	−	0.976893i	−0.120276	−	0.992741i	$-0.538378\pi$
$673$	22.8188	−	25.3428i	0.879599	−	0.976893i	0.999874	+	0.0158471i	$0.00504451\pi$
$674$	−5.68410			−0.218943
$675$	−16.8931	−	19.7389i	−0.650216	−	0.759750i
$676$	−0.0761349			−0.00292826
$677$	3.34059	−	3.71010i	0.128389	−	0.142591i	−0.675522	−	0.737339i	$-0.736082\pi$
$677$	3.34059	−	3.71010i	0.128389	−	0.142591i	0.803912	+	0.594749i	$0.202748\pi$
$678$	−7.43111	−	13.8373i	−0.285390	−	0.531419i
$679$	6.50590	+	61.8995i	0.249673	+	2.37548i
$680$	−2.14809	+	30.1367i	−0.0823756	+	1.15569i
$681$	12.1317	+	2.97144i	0.464887	+	0.113866i
$682$	−2.43018	−	4.20919i	−0.0930563	−	0.161178i
$683$	6.26357	+	4.55075i	0.239669	+	0.174130i	0.701136	−	0.713028i	$-0.252677\pi$
$683$	6.26357	+	4.55075i	0.239669	+	0.174130i	−0.461467	+	0.887157i	$0.652677\pi$
$684$	−0.142007	−	0.285137i	−0.00542977	−	0.0109025i
$685$	20.1055	+	3.57303i	0.768192	+	0.136519i
$686$	−2.75042	+	3.05465i	−0.105012	+	0.116627i
$687$	14.7823	−	10.0601i	0.563979	−	0.383817i
$688$	−12.8481	−	14.2693i	−0.489831	−	0.544013i
$689$	−11.8724	−	2.52356i	−0.452303	−	0.0961400i
$690$	−17.3360	−	19.1456i	−0.659970	−	0.728861i
$691$	−31.3939	+	6.67298i	−1.19428	+	0.253852i	−0.761813	−	0.647797i	$-0.775690\pi$
$691$	−31.3939	+	6.67298i	−1.19428	+	0.253852i	−0.432468	+	0.901649i	$0.642357\pi$
$692$	0.359454	+	0.261158i	0.0136644	+	0.00992775i
$693$	−42.9752	+	42.1943i	−1.63249	+	1.60283i
$694$	−42.4980	−	30.8766i	−1.61320	−	1.17206i
$695$	21.7294	+	14.6992i	0.824244	+	0.557574i
$696$	18.7296	−	30.2518i	0.709944	−	1.14669i
$697$	1.89429	+	18.0230i	0.0717514	+	0.682669i
$698$	15.5758	+	3.31074i	0.589553	+	0.125313i
$699$	2.89605	−	21.2446i	0.109539	−	0.803545i
$700$	0.855307	+	0.122553i	0.0323276	+	0.00463205i
$701$	−2.23365			−0.0843639			−0.0421819	−	0.999110i	$-0.513431\pi$
$701$	−2.23365			−0.0843639			−0.0421819	+	0.999110i	$0.513431\pi$
$702$	24.8811	+	2.30290i	0.939077	+	0.0869173i
$703$	−1.94761	+	1.41502i	−0.0734553	+	0.0533684i
$704$	37.3066	+	16.6100i	1.40604	+	0.626011i
$705$	14.1723	−	44.0365i	0.533758	−	1.65851i
$706$	−3.88837	+	1.73121i	−0.146341	+	0.0651551i
$707$	10.7186	−	18.5652i	0.403115	−	0.698216i
$708$	−0.589162	−	0.144305i	−0.0221421	−	0.00542332i
$709$	−40.0642	+	8.51592i	−1.50464	+	0.319822i	−0.885197	−	0.465216i	$-0.845976\pi$
$709$	−40.0642	+	8.51592i	−1.50464	+	0.319822i	−0.619447	+	0.785038i	$0.712643\pi$
$710$	5.24754	−	9.83724i	0.196936	−	0.369185i
$711$	−4.15079	+	2.64177i	−0.155667	+	0.0990740i
$712$	2.61449	−	8.04659i	0.0979823	−	0.301559i
$713$	2.96574	−	0.630388i	0.111068	−	0.0236082i
$714$	15.5444	−	43.2647i	0.581735	−	1.61914i
$715$	36.4251	+	14.7737i	1.36222	+	0.552506i
$716$	0.106429	+	0.118201i	0.00397742	+	0.00441738i
$717$	−7.75799	−	26.6384i	−0.289727	−	0.994829i
$718$	−1.65319	−	2.86342i	−0.0616967	−	0.106862i
$719$	11.5919	+	8.42199i	0.432304	+	0.314087i	0.782570	−	0.622563i	$-0.213909\pi$
$719$	11.5919	+	8.42199i	0.432304	+	0.314087i	−0.350265	+	0.936650i	$0.613909\pi$
$720$	18.9122	−	19.8581i	0.704817	−	0.740069i
$721$	1.93641	−	1.40689i	0.0721158	−	0.0523952i
$722$	−17.5474	−	7.81262i	−0.653048	−	0.290756i
$723$	3.27493	+	3.87024i	0.121796	+	0.143936i
$724$	0.343491	−	0.594944i	0.0127657	−	0.0221109i
$725$	−13.6710	−	34.1007i	−0.507728	−	1.26647i
$726$	5.46213	−	40.0687i	0.202719	−	1.48709i
$727$	−22.8565	+	25.3847i	−0.847700	+	0.941466i	−0.998893	−	0.0470382i	$-0.985022\pi$
$727$	−22.8565	+	25.3847i	−0.847700	+	0.941466i	0.151193	+	0.988504i	$0.451688\pi$
$728$	29.2091	−	21.2217i	1.08256	−	0.786527i
$729$	26.5413	+	4.95558i	0.983012	+	0.183540i
$730$	9.91593	+	10.2959i	0.367005	+	0.381069i
$731$	−2.37287	+	22.5763i	−0.0877636	+	0.835015i
$732$	−0.0693560	+	0.508776i	−0.00256347	+	0.0188049i
$733$	−40.6252	+	18.0875i	−1.50053	+	0.668078i	−0.982326	−	0.187180i	$-0.940065\pi$
$733$	−40.6252	+	18.0875i	−1.50053	+	0.668078i	−0.518202	+	0.855258i	$0.673398\pi$
$734$	−16.2099	−	18.0029i	−0.598318	−	0.664499i
$735$	27.4492	+	12.1293i	1.01248	+	0.447396i
$736$	0.794139	−	0.881980i	0.0292723	−	0.0325102i
$737$	−1.64548	+	5.06426i	−0.0606119	+	0.186544i
$738$	8.88470	−	13.4104i	0.327050	−	0.493644i
$739$	−6.83528	−	21.0368i	−0.251440	−	0.773852i	−0.994510	−	0.104639i	$-0.966631\pi$
$739$	−6.83528	−	21.0368i	−0.251440	−	0.773852i	0.743071	−	0.669213i	$-0.233369\pi$
$740$	0.0850248	+	0.0575165i	0.00312557	+	0.00211435i
$741$	−11.3622	+	7.73259i	−0.417402	+	0.284064i
$742$	18.1089	−	8.06258i	0.664797	−	0.295987i
$743$	5.42519	−	9.39670i	0.199031	−	0.344732i	−0.749184	−	0.662362i	$-0.769554\pi$
$743$	5.42519	−	9.39670i	0.199031	−	0.344732i	0.948214	+	0.317631i	$0.102887\pi$
$744$	0.880331	+	3.02277i	0.0322745	+	0.110820i
$745$	16.6976	−	13.0095i	0.611754	−	0.476631i
$746$	29.1662	−	21.1905i	1.06785	−	0.775838i
$747$	−26.1562	−	21.5809i	−0.957005	−	0.789605i
$748$	0.351305	+	1.08120i	0.0128450	+	0.0395328i
$749$	16.3560	+	28.3294i	0.597635	+	1.03513i
$750$	−4.81168	−	27.2713i	−0.175698	−	0.995806i
$751$	7.68498	−	13.3108i	0.280429	−	0.485717i	−0.691062	−	0.722796i	$-0.742857\pi$
$751$	7.68498	−	13.3108i	0.280429	−	0.485717i	0.971490	+	0.237079i	$0.0761900\pi$
$752$	47.7618	+	10.1521i	1.74169	+	0.370208i
$753$	−3.86805	−	7.20261i	−0.140960	−	0.262478i
$754$	32.2795	+	14.3718i	1.17555	+	0.523389i
$755$	−4.73045	−	33.9905i	−0.172159	−	1.23704i
$756$	−0.771999	+	0.458598i	−0.0280773	+	0.0166791i
$757$	−32.9738			−1.19845			−0.599226	−	0.800580i	$-0.704525\pi$
$757$	−32.9738			−1.19845			−0.599226	+	0.800580i	$0.704525\pi$
$758$	3.65712	−	34.7952i	0.132833	−	1.26382i
$759$	38.0266	+	18.3522i	1.38028	+	0.666143i
$760$	−1.04879	+	14.7141i	−0.0380438	+	0.533735i
$761$	31.3838	+	6.67084i	1.13766	+	0.241818i	0.737971	−	0.674832i	$-0.235784\pi$
$761$	31.3838	+	6.67084i	1.13766	+	0.241818i	0.399691	+	0.916650i	$0.369117\pi$
$762$	2.72697	+	36.8059i	0.0987876	+	1.33334i
$763$	−38.2881	+	8.13839i	−1.38612	+	0.294630i
$764$	0.257948	+	0.793883i	0.00933224	+	0.0287217i
$765$	−32.4081	−	0.906597i	−1.17172	−	0.0327781i
$766$	−0.00222259	+	0.00684042i	−8.03054e−5	+	0.000247155i
$767$	−2.73566	+	26.0280i	−0.0987788	+	0.939818i
$768$	1.47801	+	1.14492i	0.0533331	+	0.0413137i
$769$	−38.7820	+	17.2669i	−1.39852	+	0.622659i	−0.960999	−	0.276552i	$-0.910808\pi$
$769$	−38.7820	+	17.2669i	−1.39852	+	0.622659i	−0.437516	+	0.899211i	$0.644142\pi$
$770$	−62.3085	+	15.4463i	−2.24544	+	0.556645i
$771$	−36.7195	−	1.13001i	−1.32242	−	0.0406963i
$772$	0.478663	+	0.213114i	0.0172275	+	0.00767016i
$773$	0.355723	+	1.09480i	0.0127945	+	0.0393773i	0.957250	−	0.289262i	$-0.0934099\pi$
$773$	0.355723	+	1.09480i	0.0127945	+	0.0393773i	−0.944455	+	0.328639i	$0.893410\pi$
$774$	14.3787	−	14.1174i	0.516832	−	0.507441i
$775$	3.05181	+	1.12007i	0.109624	+	0.0402342i
$776$	22.6549	+	39.2395i	0.813265	+	1.40862i
$777$	4.38354	+	5.18037i	0.157259	+	0.185845i
$778$	−1.55860	−	14.8290i	−0.0558783	−	0.531647i
$779$	0.924877	+	8.79962i	0.0331372	+	0.315279i
$780$	0.475082	+	0.343141i	0.0170107	+	0.0122864i
$781$	−1.90522	+	18.1270i	−0.0681742	+	0.648634i
$782$	−32.2302			−1.15255
$783$	33.2997	+	18.6778i	1.19004	+	0.667490i
$784$	−9.78826	+	30.1252i	−0.349581	+	1.07590i
$785$	−38.4660	+	29.9697i	−1.37291	+	1.06966i
$786$	−32.8251	+	5.92825i	−1.17083	+	0.211454i
$787$	6.85895	+	7.61763i	0.244495	+	0.271539i	0.852885	−	0.522099i	$-0.174851\pi$
$787$	6.85895	+	7.61763i	0.244495	+	0.271539i	−0.608390	+	0.793638i	$0.708184\pi$
$788$	−0.257947	−	0.286479i	−0.00918899	−	0.0102054i
$789$	8.27584	+	9.78020i	0.294628	+	0.348184i
$790$	−5.24137	+	0.175975i	−0.186480	+	0.00626093i
$791$	7.52535	−	23.1607i	0.267571	−	0.823498i
$792$	−16.0868	+	40.7859i	−0.571621	+	1.44926i
$793$	22.1547			0.786737
$794$	−0.887213	+	8.44126i	−0.0314860	+	0.299569i
$795$	−9.38303	−	10.3625i	−0.332782	−	0.367519i
$796$	−0.0817007	−	0.777330i	−0.00289580	−	0.0275517i
$797$	5.05457	+	48.0910i	0.179042	+	1.70347i	0.602961	+	0.797770i	$0.293987\pi$
$797$	5.05457	+	48.0910i	0.179042	+	1.70347i	−0.423919	+	0.905700i	$0.639346\pi$
$798$	7.58947	−	21.1237i	0.268664	−	0.747773i
$799$	−28.8639	−	49.9937i	−1.02113	−	1.76865i
$800$	1.22414	−	0.347455i	0.0432798	−	0.0122844i
$801$	8.74763	+	2.43010i	0.309082	+	0.0858633i
$802$	−8.79839	−	27.0787i	−0.310682	−	0.956181i
$803$	−21.3481	−	9.50479i	−0.753358	−	0.335417i
$804$	−0.0417913	+	0.0675007i	−0.00147387	+	0.00238057i
$805$	2.84719	−	39.9446i	0.100350	−	1.40786i
$806$	−2.85627	+	1.27169i	−0.100608	+	0.0447934i
$807$	−6.54763	+	48.0316i	−0.230488	+	1.69079i
$808$	1.63126	−	15.5204i	0.0573876	−	0.546007i
$809$	−4.53484	+	13.9568i	−0.159436	+	0.490695i	−0.998583	−	0.0532099i	$-0.983055\pi$
$809$	−4.53484	+	13.9568i	−0.159436	+	0.490695i	0.839147	+	0.543905i	$0.183055\pi$
$810$	21.6776	+	18.9290i	0.761672	+	0.665098i
$811$	8.81534	+	27.1308i	0.309549	+	0.952692i	0.977941	+	0.208883i	$0.0669829\pi$
$811$	8.81534	+	27.1308i	0.309549	+	0.952692i	−0.668392	+	0.743809i	$0.733017\pi$
$812$	−1.24201	+	0.263998i	−0.0435862	+	0.00926452i
$813$	−32.1120	−	15.4977i	−1.12622	−	0.543529i
$814$	−7.45990	−	1.58565i	−0.261469	−	0.0555770i
$815$	16.6136	−	19.7453i	0.581948	−	0.691648i
$816$	−2.52848	−	34.1269i	−0.0885144	−	1.19468i
$817$	−1.15854	+	11.0228i	−0.0405321	+	0.385638i
$818$	−6.99144			−0.244450
$819$	24.1044	+	30.3309i	0.842275	+	1.05985i
$820$	0.339326	−	0.164936i	0.0118498	−	0.00575980i
$821$	−48.9692	−	21.8025i	−1.70904	−	0.760912i	−0.998351	−	0.0574003i	$-0.981719\pi$
$821$	−48.9692	−	21.8025i	−1.70904	−	0.760912i	−0.710684	−	0.703511i	$-0.751614\pi$
$822$	−22.6091	−	0.695776i	−0.788584	−	0.0242680i
$823$	1.99694	+	0.424463i	0.0696090	+	0.0147958i	0.242585	−	0.970130i	$-0.422005\pi$
$823$	1.99694	+	0.424463i	0.0696090	+	0.0147958i	−0.172976	+	0.984926i	$0.555338\pi$
$824$	0.871226	−	1.50901i	0.0303506	−	0.0525688i
$825$	24.0459	+	38.3574i	0.837171	+	1.33543i
$826$	−21.3709	−	37.0155i	−0.743589	−	1.28793i
$827$	13.2520	+	40.7853i	0.460816	+	1.41824i	0.864170	+	0.503201i	$0.167844\pi$
$827$	13.2520	+	40.7853i	0.460816	+	1.41824i	−0.403354	+	0.915044i	$0.632156\pi$
$828$	0.485580	+	0.400642i	0.0168751	+	0.0139233i
$829$	30.3646	−	22.0611i	1.05460	−	0.766215i	0.0815222	−	0.996672i	$-0.474022\pi$
$829$	30.3646	−	22.0611i	1.05460	−	0.766215i	0.973083	+	0.230456i	$0.0740219\pi$
$830$	−12.3163	−	33.9809i	−0.427505	−	1.17949i
$831$	−4.57976	−	1.12173i	−0.158870	−	0.0389125i
$832$	13.1349	−	22.7503i	0.455370	−	0.788723i
$833$	34.2107	−	15.2316i	1.18533	−	0.527744i
$834$	−26.1712	−	12.6306i	−0.906235	−	0.437363i
$835$	9.43515	−	0.316779i	0.326517	−	0.0109626i
$836$	0.171523	+	0.527892i	0.00593223	+	0.0182575i
$837$	−3.19982	+	1.08383i	−0.110602	+	0.0374625i
$838$	5.63288	−	17.3362i	0.194585	−	0.598870i
$839$	−0.521107	+	0.578748i	−0.0179906	+	0.0199806i	−0.752073	−	0.659080i	$-0.770946\pi$
$839$	−0.521107	+	0.578748i	−0.0179906	+	0.0199806i	0.734082	+	0.679060i	$0.237613\pi$
$840$	41.5825	−	0.116319i	1.43473	−	0.00401337i
$841$	16.7216	+	18.5713i	0.576608	+	0.640388i
$842$	−22.9358	+	10.2117i	−0.790419	+	0.351917i
$843$	38.5318	−	15.7538i	1.32711	−	0.542591i
$844$	0.0220798	−	0.210075i	0.000760017	−	0.00723108i
$845$	−1.78067	+	3.33811i	−0.0612568	+	0.114834i
$846$	−8.47991	+	50.5366i	−0.291545	+	1.73749i
$847$	50.7256	−	36.8543i	1.74295	−	1.26633i
$848$	9.87324	−	10.9653i	0.339049	−	0.376552i
$849$	10.5515	+	8.17356i	0.362126	+	0.280516i
$850$	−29.2564	−	18.3911i	−1.00349	−	0.630808i
$851$	2.37881	−	4.12022i	0.0815445	−	0.141239i
$852$	−0.0918856	+	0.255745i	−0.00314795	+	0.00876167i
$853$	−1.93565	−	0.861806i	−0.0662753	−	0.0295077i	0.373331	−	0.927698i	$-0.378215\pi$
$853$	−1.93565	−	0.861806i	−0.0662753	−	0.0295077i	−0.439607	+	0.898190i	$0.644882\pi$
$854$	−29.2718	+	21.2672i	−1.00166	+	0.727750i
$855$	−15.8231	−	0.442641i	−0.541137	−	0.0151380i
$856$	19.2657	+	13.9973i	0.658488	+	0.478419i
$857$	2.95942	+	5.12586i	0.101092	+	0.175096i	0.912135	−	0.409890i	$-0.134433\pi$
$857$	2.95942	+	5.12586i	0.101092	+	0.175096i	−0.811043	+	0.584987i	$0.801100\pi$
$858$	−42.2904	−	10.3583i	−1.44377	−	0.353627i
$859$	20.6752	+	22.9621i	0.705428	+	0.783457i	0.984230	−	0.176891i	$-0.0566041\pi$
$859$	20.6752	+	22.9621i	0.705428	+	0.783457i	−0.278802	+	0.960349i	$0.589937\pi$
$860$	0.458720	−	0.113717i	0.0156422	−	0.00387771i
$861$	24.5448	−	4.43282i	0.836485	−	0.151070i
$862$	41.2757	−	8.77342i	1.40586	−	0.298824i
$863$	9.30552	−	28.6394i	0.316764	−	0.974898i	−0.658259	−	0.752792i	$-0.728707\pi$
$863$	9.30552	−	28.6394i	0.316764	−	0.974898i	0.975022	−	0.222106i	$-0.0712933\pi$
$864$	−0.763940	+	1.07943i	−0.0259898	+	0.0367230i
$865$	19.8574	−	9.65208i	0.675173	−	0.328180i
$866$	27.6065	−	5.86794i	0.938107	−	0.199401i
$867$	−7.61683	+	7.95312i	−0.258681	+	0.270102i
$868$	0.0561777	−	0.0973026i	0.00190679	−	0.00330266i
$869$	7.83216	−	3.48710i	0.265688	−	0.118292i
$870$	20.4464	+	35.1865i	0.693197	+	1.19293i
$871$	3.12925	+	1.39323i	0.106031	+	0.0472078i
$872$	−23.0535	+	16.7494i	−0.780692	+	0.567206i
$873$	−41.0178	+	26.1057i	−1.38824	+	0.883544i
$874$	−15.7362			−0.532286
$875$	25.3775	−	34.6344i	0.857916	−	1.17086i
$876$	−0.275436	−	0.213363i	−0.00930611	−	0.00720886i
$877$	−41.4649	−	8.81364i	−1.40017	−	0.297615i	−0.554883	−	0.831928i	$-0.687237\pi$
$877$	−41.4649	−	8.81364i	−1.40017	−	0.297615i	−0.845287	+	0.534313i	$0.820570\pi$
$878$	−1.83531	−	17.4618i	−0.0619386	−	0.589306i
$879$	−47.7704	−	1.47009i	−1.61126	−	0.0495850i
$880$	−37.6941	+	29.3683i	−1.27067	+	0.990006i
$881$	0.943118	+	0.685215i	0.0317744	+	0.0230855i	0.603559	−	0.797318i	$-0.293749\pi$
$881$	0.943118	+	0.685215i	0.0317744	+	0.0230855i	−0.571785	+	0.820404i	$0.693749\pi$
$882$	−32.0288	−	8.89762i	−1.07846	−	0.299598i
$883$	−13.1391	−	9.54614i	−0.442167	−	0.321253i	0.344328	−	0.938849i	$-0.388107\pi$
$883$	−13.1391	−	9.54614i	−0.442167	−	0.321253i	−0.786495	+	0.617596i	$0.788107\pi$
$884$	0.715330	−	0.152048i	0.0240592	−	0.00511393i
$885$	−20.1065	+	22.4566i	−0.675873	+	0.754869i
$886$	−31.9097	−	6.78261i	−1.07203	−	0.227866i
$887$	−19.4632	−	21.6161i	−0.653511	−	0.725798i	0.321757	−	0.946822i	$-0.395727\pi$
$887$	−19.4632	−	21.6161i	−0.653511	−	0.725798i	−0.975268	+	0.221025i	$0.929060\pi$
$888$	4.44914	+	2.14722i	0.149303	+	0.0720561i
$889$	−38.2898	+	42.5252i	−1.28420	+	1.42625i
$890$	6.71288	+	6.97013i	0.225016	+	0.233639i
$891$	−44.4706	−	15.3565i	−1.48982	−	0.514461i
$892$	−0.573925	−	0.416981i	−0.0192164	−	0.0139615i
$893$	−14.0926	−	24.4092i	−0.471592	−	0.816822i
$894$	−16.2177	+	16.9338i	−0.542402	+	0.566349i
$895$	7.67167	−	1.90181i	0.256436	−	0.0635704i
$896$	4.68885	+	44.6114i	0.156644	+	1.49036i
$897$	14.2979	−	23.0937i	0.477393	−	0.771077i
$898$	−3.92679	+	4.36114i	−0.131039	+	0.145533i
$899$	−4.77733			−0.159333
$900$	0.212165	+	0.640756i	0.00707215	+	0.0213585i
$901$	−17.4445			−0.581160
$902$	−18.7562	+	20.8309i	−0.624514	+	0.693593i
$903$	31.2284	+	0.961027i	1.03922	+	0.0319810i
$904$	−1.85310	−	17.6311i	−0.0616333	−	0.586401i
$905$	−18.0515	−	28.9750i	−0.600051	−	0.963162i
$906$	10.6294	+	36.4979i	0.353138	+	1.21256i
$907$	−2.44109	−	4.22810i	−0.0810552	−	0.140392i	0.822648	−	0.568551i	$-0.192496\pi$
$907$	−2.44109	−	4.22810i	−0.0810552	−	0.140392i	−0.903703	+	0.428159i	$0.859162\pi$
$908$	−0.262519	−	0.190731i	−0.00871200	−	0.00632964i
$909$	16.7145	+	1.02973i	0.554386	+	0.0341538i
$910$	5.69216	+	40.9009i	0.188693	+	1.35585i
$911$	−34.1968	+	37.9794i	−1.13299	+	1.25831i	−0.170989	+	0.985273i	$0.554696\pi$
$911$	−34.1968	+	37.9794i	−1.13299	+	1.25831i	−0.962002	+	0.273042i	$0.911970\pi$
$912$	−1.23451	−	16.6623i	−0.0408789	−	0.551743i
$913$	39.5375	+	43.9109i	1.30850	+	1.45324i
$914$	25.3592	+	5.39026i	0.838807	+	0.178294i
$915$	20.6850	+	14.9403i	0.683826	+	0.493912i
$916$	−0.454382	+	0.0965820i	−0.0150132	+	0.00319116i
$917$	−41.8408	−	30.3991i	−1.38170	−	1.00387i
$918$	35.6663	−	4.19740i	1.17716	−	0.138535i
$919$	−14.6917	−	10.6741i	−0.484634	−	0.352107i	0.318483	−	0.947928i	$-0.396827\pi$
$919$	−14.6917	−	10.6741i	−0.484634	−	0.352107i	−0.803117	+	0.595822i	$0.796827\pi$
$920$	−9.93397	−	27.4080i	−0.327513	−	0.903614i
$921$	−24.4232	−	45.4778i	−0.804771	−	1.49855i
$922$	−3.51758	−	33.4675i	−0.115845	−	1.10219i
$923$	11.4687	+	2.43776i	0.377498	+	0.0802397i
$924$	1.44828	−	0.592134i	0.0476450	−	0.0194798i
$925$	4.51038	−	2.38267i	0.148300	−	0.0783418i
$926$	−5.11819			−0.168194
$927$	1.65813	+	0.864098i	0.0544600	+	0.0283807i
$928$	−1.51286	+	1.09916i	−0.0496622	+	0.0360817i
$929$	22.5716	+	10.0495i	0.740551	+	0.329715i	0.742104	−	0.670284i	$-0.233828\pi$
$929$	22.5716	+	10.0495i	0.740551	+	0.329715i	−0.00155345	+	0.999999i	$0.500494\pi$
$930$	−3.52437	−	0.738830i	−0.115569	−	0.0242272i
$931$	16.7032	−	7.43675i	0.547425	−	0.243729i
$932$	−0.278515	+	0.482401i	−0.00912305	+	0.0158016i
$933$	2.68033	+	9.20335i	0.0877499	+	0.301304i
$934$	22.2002	−	4.71879i	0.726412	−	0.154404i
$935$	55.6215	+	9.88472i	1.81902	+	0.323265i
$936$	25.0114	+	13.0342i	0.817522	+	0.426035i
$937$	−0.780220	+	2.40127i	−0.0254887	+	0.0784461i	−0.962992	−	0.269531i	$-0.913131\pi$
$937$	−0.780220	+	2.40127i	−0.0254887	+	0.0784461i	0.937503	+	0.347977i	$0.113131\pi$
$938$	−5.47193	+	1.16309i	−0.178665	+	0.0379764i
$939$	−6.40600	−	7.57047i	−0.209052	−	0.247053i
$940$	−0.773762	+	0.919619i	−0.0252373	+	0.0299947i
$941$	2.79133	+	3.10008i	0.0909947	+	0.101060i	0.786922	−	0.617052i	$-0.211673\pi$
$941$	2.79133	+	3.10008i	0.0909947	+	0.101060i	−0.695928	+	0.718112i	$0.745007\pi$
$942$	37.3604	−	39.0099i	1.21727	−	1.27101i
$943$	−8.74311	−	15.1435i	−0.284715	−	0.493140i
$944$	−25.7394	−	18.7008i	−0.837747	−	0.608659i
$945$	2.05132	+	44.5739i	0.0667295	+	1.44999i
$946$	−28.4066	+	20.6386i	−0.923577	+	0.671018i
$947$	50.0397	+	22.2791i	1.62607	+	0.723974i	0.998509	−	0.0545912i	$-0.0173856\pi$
$947$	50.0397	+	22.2791i	1.62607	+	0.723974i	0.627564	+	0.778565i	$0.284052\pi$
$948$	0.125789	−	0.0227176i	0.00408542	−	0.000737832i
$949$	−7.51623	+	13.0185i	−0.243987	+	0.422598i
$950$	−14.2843	−	8.97934i	−0.463444	−	0.291328i
$951$	−18.6667	+	7.63191i	−0.605308	+	0.247482i
$952$	34.7212	−	38.5618i	1.12532	−	1.24980i
$953$	−6.88510	+	5.00232i	−0.223030	+	0.162041i	−0.693690	−	0.720274i	$-0.744016\pi$
$953$	−6.88510	+	5.00232i	−0.223030	+	0.162041i	0.470659	+	0.882315i	$0.344016\pi$
$954$	11.9442	+	9.85490i	0.386707	+	0.319064i
$955$	40.8405	+	7.25793i	1.32157	+	0.234861i
$956$	−0.0753446	+	0.716856i	−0.00243682	+	0.0231848i
$957$	−52.5947	−	40.7418i	−1.70015	−	1.31700i
$958$	−21.9982	+	9.79425i	−0.710731	+	0.316438i
$959$	−23.4675	−	26.0633i	−0.757805	−	0.841627i
$960$	27.6055	−	12.3834i	0.890963	−	0.399672i
$961$	−20.4602	+	22.7233i	−0.660006	+	0.733011i
$962$	−1.51604	+	4.66590i	−0.0488792	+	0.150435i
$963$	−14.1135	+	21.3027i	−0.454801	+	0.686469i
$964$	−0.0407017	−	0.125267i	−0.00131091	−	0.00403458i
$965$	20.5391	−	16.0024i	0.661176	−	0.515137i
$966$	3.27759	+	44.2376i	0.105455	+	1.42332i
$967$	−43.5021	+	19.3684i	−1.39893	+	0.622845i	−0.961097	−	0.276211i	$-0.910921\pi$
$967$	−43.5021	+	19.3684i	−1.39893	+	0.622845i	−0.437835	+	0.899056i	$0.644254\pi$
$968$	22.8223	−	39.5294i	0.733537	−	1.27052i
$969$	−13.6626	+	14.2658i	−0.438905	+	0.458283i
$970$	−51.7948	+	1.73897i	−1.66303	+	0.0558351i
$971$	4.89465	−	3.55617i	0.157077	−	0.114123i	−0.506471	−	0.862257i	$-0.669050\pi$
$971$	4.89465	−	3.55617i	0.157077	−	0.114123i	0.663547	+	0.748134i	$0.269050\pi$
$972$	−0.589525	−	0.380117i	−0.0189090	−	0.0121923i
$973$	−13.9232	−	42.8512i	−0.446358	−	1.37375i
$974$	7.11380	+	12.3215i	0.227941	+	0.394805i
$975$	26.1563	−	12.8043i	0.837672	−	0.410067i
$976$	−13.4664	+	23.3244i	−0.431048	+	0.746597i
$977$	7.13278	+	1.51612i	0.228198	+	0.0485049i	0.320591	−	0.947218i	$-0.396118\pi$
$977$	7.13278	+	1.51612i	0.228198	+	0.0485049i	−0.0923934	+	0.995723i	$0.529452\pi$
$978$	−15.0467	+	24.3031i	−0.481139	+	0.777128i
$979$	−14.4522	−	6.43455i	−0.461895	−	0.205649i
$980$	−0.540826	−	0.561552i	−0.0172761	−	0.0179381i
$981$	−19.0246	−	23.9389i	−0.607409	−	0.764311i
$982$	16.8113			0.536469
$983$	2.52668	−	24.0397i	0.0805885	−	0.766748i	−0.877365	−	0.479824i	$-0.840701\pi$
$983$	2.52668	−	24.0397i	0.0805885	−	0.766748i	0.957953	−	0.286924i	$-0.0926328\pi$
$984$	15.0108	−	10.2157i	0.478528	−	0.325663i
$985$	−18.5936	+	4.60934i	−0.592440	+	0.146866i
$986$	49.6735	+	10.5584i	1.58193	+	0.336249i
$987$	−65.6837	+	44.7012i	−2.09073	+	1.42285i
$988$	0.349256	−	0.0742367i	0.0111113	−	0.00236178i
$989$	−6.76869	−	20.8319i	−0.215232	−	0.662415i
$990$	−32.4997	−	38.1903i	−1.03291	−	1.21377i
$991$	15.5428	−	47.8359i	0.493734	−	1.51956i	−0.325186	−	0.945650i	$-0.605427\pi$
$991$	15.5428	−	47.8359i	0.493734	−	1.51956i	0.818920	−	0.573907i	$-0.194573\pi$
$992$	0.0172961	−	0.164561i	0.000549152	−	0.00522483i
$993$	32.0834	−	13.1174i	1.01814	−	0.416267i
$994$	−17.4931	+	7.78845i	−0.554849	+	0.247035i
$995$	−35.9926	−	14.5983i	−1.14104	−	0.462798i
$996$	0.416806	+	0.776125i	0.0132070	+	0.0245925i
$997$	−35.4434	−	15.7804i	−1.12250	−	0.499771i	−0.240328	−	0.970692i	$-0.577255\pi$
$997$	−35.4434	−	15.7804i	−1.12250	−	0.499771i	−0.882176	+	0.470921i	$0.843922\pi$
$998$	−11.2633	−	34.6649i	−0.356534	−	1.09730i
$999$	−2.09583	+	4.86927i	−0.0663092	+	0.154057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.22	✓	224
3.2	odd	2		675.2.r.a.631.7		224
9.2	odd	6		675.2.r.a.181.22		224
9.7	even	3	inner	225.2.q.a.106.7	yes	224
25.21	even	5	inner	225.2.q.a.121.7	yes	224
75.71	odd	10		675.2.r.a.496.22		224
225.146	odd	30		675.2.r.a.46.7		224
225.196	even	15	inner	225.2.q.a.196.22	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.22	✓	224	1.1	even	1	trivial
225.2.q.a.106.7	yes	224	9.7	even	3	inner
225.2.q.a.121.7	yes	224	25.21	even	5	inner
225.2.q.a.196.22	yes	224	225.196	even	15	inner
675.2.r.a.46.7		224	225.146	odd	30
675.2.r.a.181.22		224	9.2	odd	6
675.2.r.a.496.22		224	75.71	odd	10
675.2.r.a.631.7		224	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.956880 - 1.06272i) q^{2} +(0.819476 + 1.52593i) q^{3} +(-0.00470356 - 0.0447514i) q^{4} +(-2.07212 - 0.840433i) q^{5} +(2.40578 + 0.589254i) q^{6} +(1.92019 + 3.32586i) q^{7} +(2.26178 + 1.64328i) q^{8} +(-1.65692 + 2.50092i) q^{9} +O(q^{10})\)	\(q+(0.956880 - 1.06272i) q^{2} +(0.819476 + 1.52593i) q^{3} +(-0.00470356 - 0.0447514i) q^{4} +(-2.07212 - 0.840433i) q^{5} +(2.40578 + 0.589254i) q^{6} +(1.92019 + 3.32586i) q^{7} +(2.26178 + 1.64328i) q^{8} +(-1.65692 + 2.50092i) q^{9} +(-2.87591 + 1.39789i) q^{10} +(3.49787 - 3.88478i) q^{11} +(0.0644329 - 0.0438500i) q^{12} +(-2.25011 - 2.49900i) q^{13} +(5.37185 + 1.14182i) q^{14} +(-0.415610 - 3.85062i) q^{15} +(3.99864 - 0.849937i) q^{16} +(-3.90998 - 2.84077i) q^{17} +(1.07232 + 4.15393i) q^{18} +(-1.90903 - 1.38699i) q^{19} +(-0.0278642 + 0.0966831i) q^{20} +(-3.50148 + 5.65553i) q^{21} +(-0.781401 - 7.43453i) q^{22} +(4.56147 + 0.969570i) q^{23} +(-0.654054 + 4.79795i) q^{24} +(3.58734 + 3.48295i) q^{25} -4.80884 q^{26} +(-5.17404 - 0.478889i) q^{27} +(0.139805 - 0.101574i) q^{28} +(-6.71254 - 2.98862i) q^{29} +(-4.48983 - 3.24290i) q^{30} +(0.593962 - 0.264449i) q^{31} +(0.127249 - 0.220402i) q^{32} +(8.79432 + 2.15402i) q^{33} +(-6.76033 + 1.43695i) q^{34} +(-1.18369 - 8.50536i) q^{35} +(0.119713 + 0.0623860i) q^{36} +(0.315262 - 0.970276i) q^{37} +(-3.30069 + 0.701584i) q^{38} +(1.96939 - 5.48139i) q^{39} +(-3.30561 - 5.30596i) q^{40} +(-2.50903 - 2.78656i) q^{41} +(2.65977 + 9.13276i) q^{42} +(-2.34851 - 4.06773i) q^{43} +(-0.190302 - 0.138262i) q^{44} +(5.53519 - 3.78968i) q^{45} +(5.39516 - 3.91981i) q^{46} +(10.9118 + 4.85827i) q^{47} +(4.57373 + 5.40514i) q^{48} +(-3.87423 + 6.71036i) q^{49} +(7.13407 - 0.479583i) q^{50} +(1.13067 - 8.29429i) q^{51} +(-0.101250 + 0.112450i) q^{52} +(2.92011 - 2.12158i) q^{53} +(-5.45986 + 5.04033i) q^{54} +(-10.5129 + 5.10999i) q^{55} +(-1.12228 + 10.6778i) q^{56} +(0.552044 - 4.04964i) q^{57} +(-9.59917 + 4.27383i) q^{58} +(-5.20768 - 5.78372i) q^{59} +(-0.170366 + 0.0367107i) q^{60} +(-4.40843 + 4.89605i) q^{61} +(0.287314 - 0.884263i) q^{62} +(-11.4993 - 0.708433i) q^{63} +(2.41404 + 7.42965i) q^{64} +(2.56225 + 7.06930i) q^{65} +(10.7042 - 7.28479i) q^{66} +(-0.930565 + 0.414314i) q^{67} +(-0.108737 + 0.188339i) q^{68} +(2.25852 + 7.75502i) q^{69} +(-10.1715 - 6.88068i) q^{70} +(-2.82082 + 2.04945i) q^{71} +(-7.85732 + 2.93377i) q^{72} +(-1.38140 - 4.25150i) q^{73} +(-0.729467 - 1.26347i) q^{74} +(-2.37500 + 8.32823i) q^{75} +(-0.0530904 + 0.0919553i) q^{76} +(19.6368 + 4.17393i) q^{77} +(-3.94073 - 7.33794i) q^{78} +(1.49826 + 0.667070i) q^{79} +(-8.99997 - 1.59942i) q^{80} +(-3.50925 - 8.28765i) q^{81} -5.36219 q^{82} +(-1.18152 + 11.2414i) q^{83} +(0.269562 + 0.130095i) q^{84} +(5.71446 + 9.17248i) q^{85} +(-6.57011 - 1.39652i) q^{86} +(-0.940354 - 12.6920i) q^{87} +(14.2952 - 3.03854i) q^{88} +(-0.935178 - 2.87818i) q^{89} +(1.26913 - 9.50864i) q^{90} +(3.99070 - 12.2821i) q^{91} +(0.0219345 - 0.208692i) q^{92} +(0.890268 + 0.689634i) q^{93} +(15.6043 - 6.94749i) q^{94} +(2.79006 + 4.47841i) q^{95} +(0.440596 + 0.0135589i) q^{96} +(14.8057 + 6.59193i) q^{97} +(3.42408 + 10.5382i) q^{98} +(3.91986 + 15.1847i) 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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