LMFDB - Embedded newform 225.2.e.d.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.2.e.d.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 1.67303i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-2.36603 - 2.36603i) q^{6} +(0.448288 - 0.776457i) q^{7} +0.517638 q^{8} +(-2.59808 - 1.50000i) q^{9} +(-2.36603 + 4.09808i) q^{11} +(-2.89778 + 0.776457i) q^{12} +(1.22474 + 2.12132i) q^{13} +(-0.866025 - 1.50000i) q^{14} +(2.23205 - 3.86603i) q^{16} -0.378937 q^{17} +(-5.01910 + 2.89778i) q^{18} +2.73205 q^{19} +(-1.09808 - 1.09808i) q^{21} +(4.57081 + 7.91688i) q^{22} +(-0.965926 - 1.67303i) q^{23} +(0.232051 - 0.866025i) q^{24} +4.73205 q^{26} +(-3.67423 + 3.67423i) q^{27} -1.55291 q^{28} +(-3.23205 + 5.59808i) q^{29} +(1.36603 + 2.36603i) q^{31} +(-3.79435 - 6.57201i) q^{32} +(5.79555 + 5.79555i) q^{33} +(-0.366025 + 0.633975i) q^{34} +5.19615i q^{36} +4.24264 q^{37} +(2.63896 - 4.57081i) q^{38} +(4.09808 - 1.09808i) q^{39} +(-2.13397 - 3.69615i) q^{41} +(-2.89778 + 0.776457i) q^{42} +(4.57081 - 7.91688i) q^{43} +8.19615 q^{44} -3.73205 q^{46} +(2.19067 - 3.79435i) q^{47} +(-5.46739 - 5.46739i) q^{48} +(3.09808 + 5.36603i) q^{49} +(-0.169873 + 0.633975i) q^{51} +(2.12132 - 3.67423i) q^{52} -3.86370 q^{53} +(2.59808 + 9.69615i) q^{54} +(0.232051 - 0.401924i) q^{56} +(1.22474 - 4.57081i) q^{57} +(6.24384 + 10.8147i) q^{58} +(-1.26795 - 2.19615i) q^{59} +(-5.33013 + 9.23205i) q^{61} +5.27792 q^{62} +(-2.32937 + 1.34486i) q^{63} -5.73205 q^{64} +(15.2942 - 4.09808i) q^{66} +(-2.56961 - 4.45069i) q^{67} +(0.328169 + 0.568406i) q^{68} +(-3.23205 + 0.866025i) q^{69} +3.80385 q^{71} +(-1.34486 - 0.776457i) q^{72} -8.48528 q^{73} +(4.09808 - 7.09808i) q^{74} +(-2.36603 - 4.09808i) q^{76} +(2.12132 + 3.67423i) q^{77} +(2.12132 - 7.91688i) q^{78} +(-0.267949 + 0.464102i) q^{79} +(4.50000 + 7.79423i) q^{81} -8.24504 q^{82} +(-5.20857 + 9.02150i) q^{83} +(-0.696152 + 2.59808i) q^{84} +(-8.83013 - 15.2942i) q^{86} +(7.91688 + 7.91688i) q^{87} +(-1.22474 + 2.12132i) q^{88} -7.39230 q^{89} +2.19615 q^{91} +(-1.67303 + 2.89778i) q^{92} +(4.57081 - 1.22474i) q^{93} +(-4.23205 - 7.33013i) q^{94} +(-12.6962 + 3.40192i) q^{96} +(-5.13922 + 8.90138i) q^{97} +11.9700 q^{98} +(12.2942 - 7.09808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{6} - 12 q^{11} + 4 q^{16} + 8 q^{19} + 12 q^{21} - 12 q^{24} + 24 q^{26} - 12 q^{29} + 4 q^{31} + 4 q^{34} + 12 q^{39} - 24 q^{41} + 24 q^{44} - 16 q^{46} + 4 q^{49} - 36 q^{51} - 12 q^{56}+ \cdots + 36 q^{99}+O(q^{100}) $ 8 * q - 12 * q^6 - 12 * q^11 + 4 * q^16 + 8 * q^19 + 12 * q^21 - 12 * q^24 + 24 * q^26 - 12 * q^29 + 4 * q^31 + 4 * q^34 + 12 * q^39 - 24 * q^41 + 24 * q^44 - 16 * q^46 + 4 * q^49 - 36 * q^51 - 12 * q^56 - 24 * q^59 - 8 * q^61 - 32 * q^64 + 60 * q^66 - 12 * q^69 + 72 * q^71 + 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^81 + 36 * q^84 - 36 * q^86 + 24 * q^89 - 24 * q^91 - 20 * q^94 - 60 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.965926	−	1.67303i	0.683013	−	1.18301i	−0.291044	−	0.956710i	$-0.594003\pi$
$2$	0.965926	−	1.67303i	0.683013	−	1.18301i	0.974057	−	0.226303i	$-0.0726640\pi$
$3$	0.448288	−	1.67303i	0.258819	−	0.965926i
$3$	0.448288	−	1.67303i	0.258819	−	0.965926i
$4$	−0.866025	−	1.50000i	−0.433013	−	0.750000i
$5$		0			0
$5$		0			0
$6$	−2.36603	−	2.36603i	−0.965926	−	0.965926i
$7$	0.448288	−	0.776457i	0.169437	−	0.293473i	−0.768785	−	0.639507i	$-0.779138\pi$
$7$	0.448288	−	0.776457i	0.169437	−	0.293473i	0.938222	+	0.346034i	$0.112472\pi$
$8$	0.517638			0.183013
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$		0			0
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	0.250196	+	0.968195i	$0.419505\pi$
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	−0.963580	+	0.267421i	$0.913828\pi$
$12$	−2.89778	+	0.776457i	−0.836516	+	0.224144i
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	0.984373	−	0.176096i	$-0.0563468\pi$
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	−0.644690	+	0.764444i	$0.723014\pi$
$14$	−0.866025	−	1.50000i	−0.231455	−	0.400892i
$15$		0			0
$16$	2.23205	−	3.86603i	0.558013	−	0.966506i
$17$	−0.378937			−0.0919058			−0.0459529	−	0.998944i	$-0.514632\pi$
$17$	−0.378937			−0.0919058			−0.0459529	+	0.998944i	$0.514632\pi$
$18$	−5.01910	+	2.89778i	−1.18301	+	0.683013i
$19$	2.73205			0.626775			0.313388	−	0.949625i	$-0.398536\pi$
$19$	2.73205			0.626775			0.313388	+	0.949625i	$0.398536\pi$
$20$		0			0
$21$	−1.09808	−	1.09808i	−0.239620	−	0.239620i
$22$	4.57081	+	7.91688i	0.974500	+	1.68788i
$23$	−0.965926	−	1.67303i	−0.201409	−	0.348851i	0.747573	−	0.664179i	$-0.231219\pi$
$23$	−0.965926	−	1.67303i	−0.201409	−	0.348851i	−0.948983	+	0.315328i	$0.897886\pi$
$24$	0.232051	−	0.866025i	0.0473672	−	0.176777i
$25$		0			0
$26$	4.73205			0.928032
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$	−1.55291			−0.293473
$29$	−3.23205	+	5.59808i	−0.600177	+	1.03954i	0.392617	+	0.919702i	$0.371570\pi$
$29$	−3.23205	+	5.59808i	−0.600177	+	1.03954i	−0.992794	+	0.119835i	$0.961764\pi$
$30$		0			0
$31$	1.36603	+	2.36603i	0.245345	+	0.424951i	0.962229	−	0.272243i	$-0.0877653\pi$
$31$	1.36603	+	2.36603i	0.245345	+	0.424951i	−0.716883	+	0.697193i	$0.754432\pi$
$32$	−3.79435	−	6.57201i	−0.670753	−	1.16178i
$33$	5.79555	+	5.79555i	1.00888	+	1.00888i
$34$	−0.366025	+	0.633975i	−0.0627728	+	0.108726i
$35$		0			0
$36$			5.19615i			0.866025i
$37$	4.24264			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$37$	4.24264			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$38$	2.63896	−	4.57081i	0.428096	−	0.741483i
$39$	4.09808	−	1.09808i	0.656217	−	0.175833i
$40$		0			0
$41$	−2.13397	−	3.69615i	−0.333271	−	0.577242i	0.649880	−	0.760037i	$-0.274819\pi$
$41$	−2.13397	−	3.69615i	−0.333271	−	0.577242i	−0.983151	+	0.182795i	$0.941486\pi$
$42$	−2.89778	+	0.776457i	−0.447137	+	0.119810i
$43$	4.57081	−	7.91688i	0.697042	−	1.20731i	−0.272445	−	0.962171i	$-0.587832\pi$
$43$	4.57081	−	7.91688i	0.697042	−	1.20731i	0.969487	−	0.245141i	$-0.0788342\pi$
$44$	8.19615			1.23562
$45$		0			0
$46$	−3.73205			−0.550261
$47$	2.19067	−	3.79435i	0.319542	−	0.553463i	−0.660850	−	0.750518i	$-0.729804\pi$
$47$	2.19067	−	3.79435i	0.319542	−	0.553463i	0.980393	+	0.197054i	$0.0631376\pi$
$48$	−5.46739	−	5.46739i	−0.789149	−	0.789149i
$49$	3.09808	+	5.36603i	0.442582	+	0.766575i
$50$		0			0
$51$	−0.169873	+	0.633975i	−0.0237870	+	0.0887742i
$52$	2.12132	−	3.67423i	0.294174	−	0.509525i
$53$	−3.86370			−0.530720			−0.265360	−	0.964149i	$-0.585491\pi$
$53$	−3.86370			−0.530720			−0.265360	+	0.964149i	$0.585491\pi$
$54$	2.59808	+	9.69615i	0.353553	+	1.31948i
$55$		0			0
$56$	0.232051	−	0.401924i	0.0310091	−	0.0537093i
$57$	1.22474	−	4.57081i	0.162221	−	0.605419i
$58$	6.24384	+	10.8147i	0.819857	+	1.42003i
$59$	−1.26795	−	2.19615i	−0.165073	−	0.285915i	0.771608	−	0.636098i	$-0.219453\pi$
$59$	−1.26795	−	2.19615i	−0.165073	−	0.285915i	−0.936681	+	0.350183i	$0.886119\pi$
$60$		0			0
$61$	−5.33013	+	9.23205i	−0.682453	+	1.18204i	0.291777	+	0.956486i	$0.405753\pi$
$61$	−5.33013	+	9.23205i	−0.682453	+	1.18204i	−0.974230	+	0.225557i	$0.927580\pi$
$62$	5.27792			0.670296
$63$	−2.32937	+	1.34486i	−0.293473	+	0.169437i
$64$	−5.73205			−0.716506
$65$		0			0
$66$	15.2942	−	4.09808i	1.88259	−	0.504438i
$67$	−2.56961	−	4.45069i	−0.313928	−	0.543739i	0.665281	−	0.746593i	$-0.268312\pi$
$67$	−2.56961	−	4.45069i	−0.313928	−	0.543739i	−0.979209	+	0.202854i	$0.934978\pi$
$68$	0.328169	+	0.568406i	0.0397964	+	0.0689294i
$69$	−3.23205	+	0.866025i	−0.389093	+	0.104257i
$70$		0			0
$71$	3.80385			0.451434			0.225717	−	0.974193i	$-0.427528\pi$
$71$	3.80385			0.451434			0.225717	+	0.974193i	$0.427528\pi$
$72$	−1.34486	−	0.776457i	−0.158494	−	0.0915064i
$73$	−8.48528			−0.993127			−0.496564	−	0.868000i	$-0.665405\pi$
$73$	−8.48528			−0.993127			−0.496564	+	0.868000i	$0.665405\pi$
$74$	4.09808	−	7.09808i	0.476392	−	0.825135i
$75$		0			0
$76$	−2.36603	−	4.09808i	−0.271402	−	0.470082i
$77$	2.12132	+	3.67423i	0.241747	+	0.418718i
$78$	2.12132	−	7.91688i	0.240192	−	0.896410i
$79$	−0.267949	+	0.464102i	−0.0301466	+	0.0522155i	−0.880705	−	0.473665i	$-0.842931\pi$
$79$	−0.267949	+	0.464102i	−0.0301466	+	0.0522155i	0.850558	+	0.525880i	$0.176264\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−8.24504			−0.910513
$83$	−5.20857	+	9.02150i	−0.571714	+	0.990238i	0.424676	+	0.905346i	$0.360388\pi$
$83$	−5.20857	+	9.02150i	−0.571714	+	0.990238i	−0.996390	+	0.0848929i	$0.972945\pi$
$84$	−0.696152	+	2.59808i	−0.0759565	+	0.283473i
$85$		0			0
$86$	−8.83013	−	15.2942i	−0.952177	−	1.64922i
$87$	7.91688	+	7.91688i	0.848778	+	0.848778i
$88$	−1.22474	+	2.12132i	−0.130558	+	0.226134i
$89$	−7.39230			−0.783583			−0.391791	−	0.920054i	$-0.628144\pi$
$89$	−7.39230			−0.783583			−0.391791	+	0.920054i	$0.628144\pi$
$90$		0			0
$91$	2.19615			0.230219
$92$	−1.67303	+	2.89778i	−0.174426	+	0.302114i
$93$	4.57081	−	1.22474i	0.473971	−	0.127000i
$94$	−4.23205	−	7.33013i	−0.436503	−	0.756045i
$95$		0			0
$96$	−12.6962	+	3.40192i	−1.29580	+	0.347207i
$97$	−5.13922	+	8.90138i	−0.521808	+	0.903799i	0.477870	+	0.878431i	$0.341409\pi$
$97$	−5.13922	+	8.90138i	−0.521808	+	0.903799i	−0.999678	+	0.0253679i	$0.991924\pi$
$98$	11.9700			1.20916
$99$	12.2942	−	7.09808i	1.23562	−	0.713384i
$100$		0			0
$101$	−1.26795	+	2.19615i	−0.126166	+	0.218525i	−0.922188	−	0.386742i	$-0.873600\pi$
$101$	−1.26795	+	2.19615i	−0.126166	+	0.218525i	0.796022	+	0.605267i	$0.206934\pi$
$102$	0.896575	+	0.896575i	0.0887742	+	0.0887742i
$103$	−4.57081	−	7.91688i	−0.450375	−	0.780073i	0.548034	−	0.836456i	$-0.315376\pi$
$103$	−4.57081	−	7.91688i	−0.450375	−	0.780073i	−0.998409	+	0.0563832i	$0.982043\pi$
$104$	0.633975	+	1.09808i	0.0621663	+	0.107675i
$105$		0			0
$106$	−3.73205	+	6.46410i	−0.362489	+	0.627849i
$107$	−11.7298			−1.13396			−0.566982	−	0.823730i	$-0.691889\pi$
$107$	−11.7298			−1.13396			−0.566982	+	0.823730i	$0.691889\pi$
$108$	8.69333	+	2.32937i	0.836516	+	0.224144i
$109$	−4.66025			−0.446371			−0.223186	−	0.974776i	$-0.571646\pi$
$109$	−4.66025			−0.446371			−0.223186	+	0.974776i	$0.571646\pi$
$110$		0			0
$111$	1.90192	−	7.09808i	0.180523	−	0.673720i
$112$	−2.00120	−	3.46618i	−0.189096	−	0.327524i
$113$	1.27551	+	2.20925i	0.119990	+	0.207829i	0.919764	−	0.392473i	$-0.128380\pi$
$113$	1.27551	+	2.20925i	0.119990	+	0.207829i	−0.799773	+	0.600302i	$0.795047\pi$
$114$	−6.46410	−	6.46410i	−0.605419	−	0.605419i
$115$		0			0
$116$	11.1962			1.03954
$117$		−	7.34847i		−	0.679366i
$118$	−4.89898			−0.450988
$119$	−0.169873	+	0.294229i	−0.0155722	+	0.0269719i
$120$		0			0
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$	10.2970	+	17.8350i	0.932248	+	1.61470i
$123$	−7.14042	+	1.91327i	−0.643830	+	0.172514i
$124$	2.36603	−	4.09808i	0.212475	−	0.368018i
$125$		0			0
$126$			5.19615i			0.462910i
$127$	4.65874			0.413397			0.206698	−	0.978405i	$-0.433728\pi$
$127$	4.65874			0.413397			0.206698	+	0.978405i	$0.433728\pi$
$128$	2.05197	−	3.55412i	0.181370	−	0.314142i
$129$	−11.1962	−	11.1962i	−0.985766	−	0.985766i
$130$		0			0
$131$	0.464102	+	0.803848i	0.0405487	+	0.0702325i	0.885588	−	0.464473i	$-0.153756\pi$
$131$	0.464102	+	0.803848i	0.0405487	+	0.0702325i	−0.845039	+	0.534705i	$0.820423\pi$
$132$	3.67423	−	13.7124i	0.319801	−	1.19351i
$133$	1.22474	−	2.12132i	0.106199	−	0.183942i
$134$	−9.92820			−0.857666
$135$		0			0
$136$	−0.196152			−0.0168199
$137$	−9.28032	+	16.0740i	−0.792871	+	1.37329i	0.131311	+	0.991341i	$0.458081\pi$
$137$	−9.28032	+	16.0740i	−0.792871	+	1.37329i	−0.924182	+	0.381952i	$0.875252\pi$
$138$	−1.67303	+	6.24384i	−0.142418	+	0.531511i
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$	−5.36603	−	5.36603i	−0.451901	−	0.451901i
$142$	3.67423	−	6.36396i	0.308335	−	0.534052i
$143$	−11.5911			−0.969297
$144$	−11.5981	+	6.69615i	−0.966506	+	0.558013i
$145$		0			0
$146$	−8.19615	+	14.1962i	−0.678318	+	1.17488i
$147$	10.3664	−	2.77766i	0.855003	−	0.229097i
$148$	−3.67423	−	6.36396i	−0.302020	−	0.523114i
$149$	−3.86603	−	6.69615i	−0.316717	−	0.548570i	0.663084	−	0.748545i	$-0.269247\pi$
$149$	−3.86603	−	6.69615i	−0.316717	−	0.548570i	−0.979801	+	0.199975i	$0.935914\pi$
$150$		0			0
$151$	11.2942	−	19.5622i	0.919111	−	1.59195i	0.118343	−	0.992973i	$-0.462242\pi$
$151$	11.2942	−	19.5622i	0.919111	−	1.59195i	0.800768	−	0.598975i	$-0.204425\pi$
$152$	1.41421			0.114708
$153$	0.984508	+	0.568406i	0.0795928	+	0.0459529i
$154$	8.19615			0.660465
$155$		0			0
$156$	−5.19615	−	5.19615i	−0.416025	−	0.416025i
$157$	−10.6945	−	18.5235i	−0.853517	−	1.47833i	−0.878014	−	0.478635i	$-0.841132\pi$
$157$	−10.6945	−	18.5235i	−0.853517	−	1.47833i	0.0244975	−	0.999700i	$-0.492201\pi$
$158$	0.517638	+	0.896575i	0.0411811	+	0.0713277i
$159$	−1.73205	+	6.46410i	−0.137361	+	0.512637i
$160$		0			0
$161$	−1.73205			−0.136505
$162$	17.3867			1.36603
$163$	18.9396			1.48346			0.741731	−	0.670697i	$-0.234005\pi$
$163$	18.9396			1.48346			0.741731	+	0.670697i	$0.234005\pi$
$164$	−3.69615	+	6.40192i	−0.288621	+	0.499906i
$165$		0			0
$166$	10.0622	+	17.4282i	0.780976	+	1.35269i
$167$	−8.50386	−	14.7291i	−0.658049	−	1.13977i	−0.981120	−	0.193399i	$-0.938049\pi$
$167$	−8.50386	−	14.7291i	−0.658049	−	1.13977i	0.323071	−	0.946375i	$-0.395285\pi$
$168$	−0.568406	−	0.568406i	−0.0438535	−	0.0438535i
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$		0			0
$171$	−7.09808	−	4.09808i	−0.542803	−	0.313388i
$172$	−15.8338			−1.20731
$173$	0.378937	−	0.656339i	0.0288101	−	0.0499005i	−0.851261	−	0.524743i	$-0.824162\pi$
$173$	0.378937	−	0.656339i	0.0288101	−	0.0499005i	0.880071	+	0.474842i	$0.157495\pi$
$174$	20.8923	−	5.59808i	1.58384	−	0.424389i
$175$		0			0
$176$	10.5622	+	18.2942i	0.796154	+	1.37898i
$177$	−4.24264	+	1.13681i	−0.318896	+	0.0854480i
$178$	−7.14042	+	12.3676i	−0.535197	+	0.926988i
$179$	24.5885			1.83783			0.918914	−	0.394458i	$-0.129068\pi$
$179$	24.5885			1.83783			0.918914	+	0.394458i	$0.129068\pi$
$180$		0			0
$181$	8.46410			0.629132			0.314566	−	0.949236i	$-0.398141\pi$
$181$	8.46410			0.629132			0.314566	+	0.949236i	$0.398141\pi$
$182$	2.12132	−	3.67423i	0.157243	−	0.272352i
$183$	13.0561	+	13.0561i	0.965134	+	0.965134i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$		0			0
$186$	2.36603	−	8.83013i	0.173485	−	0.647456i
$187$	0.896575	−	1.55291i	0.0655641	−	0.113560i
$188$	−7.58871			−0.553463
$189$	1.20577	+	4.50000i	0.0877070	+	0.327327i
$190$		0			0
$191$	−0.169873	+	0.294229i	−0.0122916	+	0.0212896i	−0.872106	−	0.489317i	$-0.837246\pi$
$191$	−0.169873	+	0.294229i	−0.0122916	+	0.0212896i	0.859814	+	0.510607i	$0.170579\pi$
$192$	−2.56961	+	9.58991i	−0.185445	+	0.692092i
$193$	−10.3664	−	17.9551i	−0.746187	−	1.29243i	−0.949638	−	0.313349i	$-0.898549\pi$
$193$	−10.3664	−	17.9551i	−0.746187	−	1.29243i	0.203451	−	0.979085i	$-0.434784\pi$
$194$	9.92820	+	17.1962i	0.712803	+	1.23461i
$195$		0			0
$196$	5.36603	−	9.29423i	0.383288	−	0.663873i
$197$	20.8343			1.48438			0.742190	−	0.670190i	$-0.233787\pi$
$197$	20.8343			1.48438			0.742190	+	0.670190i	$0.233787\pi$
$198$		−	27.4249i		−	1.94900i
$199$	4.58846			0.325267			0.162634	−	0.986687i	$-0.448001\pi$
$199$	4.58846			0.325267			0.162634	+	0.986687i	$0.448001\pi$
$200$		0			0
$201$	−8.59808	+	2.30385i	−0.606462	+	0.162501i
$202$	2.44949	+	4.24264i	0.172345	+	0.298511i
$203$	2.89778	+	5.01910i	0.203384	+	0.352272i
$204$	1.09808	−	0.294229i	0.0768807	−	0.0206001i
$205$		0			0
$206$	−17.6603			−1.23045
$207$			5.79555i			0.402819i
$208$	10.9348			0.758190
$209$	−6.46410	+	11.1962i	−0.447131	+	0.774454i
$210$		0			0
$211$	6.56218	+	11.3660i	0.451759	+	0.782469i	0.998495	−	0.0548353i	$-0.0174634\pi$
$211$	6.56218	+	11.3660i	0.451759	+	0.782469i	−0.546736	+	0.837305i	$0.684130\pi$
$212$	3.34607	+	5.79555i	0.229809	+	0.398040i
$213$	1.70522	−	6.36396i	0.116840	−	0.436051i
$214$	−11.3301	+	19.6244i	−0.774512	+	1.34149i
$215$		0			0
$216$	−1.90192	+	1.90192i	−0.129410	+	0.129410i
$217$	2.44949			0.166282
$218$	−4.50146	+	7.79676i	−0.304877	+	0.528063i
$219$	−3.80385	+	14.1962i	−0.257040	+	0.959287i
$220$		0			0
$221$	−0.464102	−	0.803848i	−0.0312189	−	0.0540726i
$222$	−10.0382	−	10.0382i	−0.673720	−	0.673720i
$223$	−8.36516	+	14.4889i	−0.560173	+	0.970248i	0.437308	+	0.899312i	$0.355932\pi$
$223$	−8.36516	+	14.4889i	−0.560173	+	0.970248i	−0.997481	+	0.0709359i	$0.977401\pi$
$224$	−6.80385			−0.454601
$225$		0			0
$226$	4.92820			0.327819
$227$	−0.947343	+	1.64085i	−0.0628774	+	0.108907i	−0.895750	−	0.444557i	$-0.853361\pi$
$227$	−0.947343	+	1.64085i	−0.0628774	+	0.108907i	0.832873	+	0.553464i	$0.186694\pi$
$228$	−7.91688	+	2.12132i	−0.524308	+	0.140488i
$229$	−9.96410	−	17.2583i	−0.658446	−	1.14046i	−0.981018	−	0.193917i	$-0.937881\pi$
$229$	−9.96410	−	17.2583i	−0.658446	−	1.14046i	0.322571	−	0.946545i	$-0.395453\pi$
$230$		0			0
$231$	7.09808	−	1.90192i	0.467019	−	0.125137i
$232$	−1.67303	+	2.89778i	−0.109840	+	0.190248i
$233$	7.07107			0.463241			0.231621	−	0.972806i	$-0.425597\pi$
$233$	7.07107			0.463241			0.231621	+	0.972806i	$0.425597\pi$
$234$	−12.2942	−	7.09808i	−0.803699	−	0.464016i
$235$		0			0
$236$	−2.19615	+	3.80385i	−0.142957	+	0.247609i
$237$	0.656339	+	0.656339i	0.0426338	+	0.0426338i
$238$	0.328169	+	0.568406i	0.0212721	+	0.0368443i
$239$	−6.46410	−	11.1962i	−0.418128	−	0.724219i	0.577623	−	0.816304i	$-0.303980\pi$
$239$	−6.46410	−	11.1962i	−0.418128	−	0.724219i	−0.995751	+	0.0920846i	$0.970647\pi$
$240$		0			0
$241$	−3.13397	+	5.42820i	−0.201877	+	0.349661i	−0.949133	−	0.314875i	$-0.898037\pi$
$241$	−3.13397	+	5.42820i	−0.201877	+	0.349661i	0.747256	+	0.664536i	$0.231371\pi$
$242$	−22.0082			−1.41474
$243$	15.0573	−	4.03459i	0.965926	−	0.258819i
$244$	18.4641			1.18204
$245$		0			0
$246$	−3.69615	+	13.7942i	−0.235658	+	0.879488i
$247$	3.34607	+	5.79555i	0.212905	+	0.368762i
$248$	0.707107	+	1.22474i	0.0449013	+	0.0777714i
$249$	12.7583	+	12.7583i	0.808526	+	0.808526i
$250$		0			0
$251$	18.5885			1.17329			0.586647	−	0.809843i	$-0.300448\pi$
$251$	18.5885			1.17329			0.586647	+	0.809843i	$0.300448\pi$
$252$	4.03459	+	2.32937i	0.254155	+	0.146737i
$253$	9.14162			0.574729
$254$	4.50000	−	7.79423i	0.282355	−	0.489053i
$255$		0			0
$256$	−9.69615	−	16.7942i	−0.606010	−	1.04964i
$257$	11.2122	+	19.4201i	0.699396	+	1.21139i	0.968676	+	0.248328i	$0.0798810\pi$
$257$	11.2122	+	19.4201i	0.699396	+	1.21139i	−0.269280	+	0.963062i	$0.586786\pi$
$258$	−29.5462	+	7.91688i	−1.83946	+	0.492883i
$259$	1.90192	−	3.29423i	0.118180	−	0.204693i
$260$		0			0
$261$	16.7942	−	9.69615i	1.03954	−	0.600177i
$262$	1.79315			0.110781
$263$	3.81294	−	6.60420i	0.235116	−	0.407232i	−0.724191	−	0.689600i	$-0.757786\pi$
$263$	3.81294	−	6.60420i	0.235116	−	0.407232i	0.959306	+	0.282368i	$0.0911198\pi$
$264$	3.00000	+	3.00000i	0.184637	+	0.184637i
$265$		0			0
$266$	−2.36603	−	4.09808i	−0.145070	−	0.251269i
$267$	−3.31388	+	12.3676i	−0.202806	+	0.756883i
$268$	−4.45069	+	7.70882i	−0.271869	+	0.470891i
$269$	17.1962			1.04847			0.524234	−	0.851574i	$-0.324352\pi$
$269$	17.1962			1.04847			0.524234	+	0.851574i	$0.324352\pi$
$270$		0			0
$271$	−23.5167			−1.42854			−0.714268	−	0.699873i	$-0.753240\pi$
$271$	−23.5167			−1.42854			−0.714268	+	0.699873i	$0.753240\pi$
$272$	−0.845807	+	1.46498i	−0.0512846	+	0.0888276i
$273$	0.984508	−	3.67423i	0.0595851	−	0.222375i
$274$	17.9282	+	31.0526i	1.08308	+	1.87595i
$275$		0			0
$276$	4.09808	+	4.09808i	0.246675	+	0.246675i
$277$	−6.12372	+	10.6066i	−0.367939	+	0.637289i	−0.989243	−	0.146281i	$-0.953270\pi$
$277$	−6.12372	+	10.6066i	−0.367939	+	0.637289i	0.621304	+	0.783569i	$0.286603\pi$
$278$	15.4548			0.926918
$279$		−	8.19615i		−	0.490691i
$280$		0			0
$281$	8.13397	−	14.0885i	0.485232	−	0.840447i	−0.514624	−	0.857416i	$-0.672068\pi$
$281$	8.13397	−	14.0885i	0.485232	−	0.840447i	0.999856	+	0.0169692i	$0.00540173\pi$
$282$	−14.1607	+	3.79435i	−0.843258	+	0.225950i
$283$	−2.24144	−	3.88229i	−0.133240	−	0.230778i	0.791684	−	0.610931i	$-0.209205\pi$
$283$	−2.24144	−	3.88229i	−0.133240	−	0.230778i	−0.924924	+	0.380153i	$0.875871\pi$
$284$	−3.29423	−	5.70577i	−0.195477	−	0.338575i
$285$		0			0
$286$	−11.1962	+	19.3923i	−0.662042	+	1.14669i
$287$	−3.82654			−0.225873
$288$			22.7661i			1.34151i
$289$	−16.8564			−0.991553
$290$		0			0
$291$	12.5885	+	12.5885i	0.737948	+	0.737948i
$292$	7.34847	+	12.7279i	0.430037	+	0.744845i
$293$	−4.43211	−	7.67664i	−0.258927	−	0.448474i	0.707028	−	0.707186i	$-0.250035\pi$
$293$	−4.43211	−	7.67664i	−0.258927	−	0.448474i	−0.965955	+	0.258711i	$0.916702\pi$
$294$	5.36603	−	20.0263i	0.312953	−	1.16796i
$295$		0			0
$296$	2.19615			0.127649
$297$	−6.36396	−	23.7506i	−0.369274	−	1.37815i
$298$	−14.9372			−0.865287
$299$	2.36603	−	4.09808i	0.136831	−	0.236998i
$300$		0			0
$301$	−4.09808	−	7.09808i	−0.236209	−	0.409126i
$302$	−21.8188	−	37.7912i	−1.25553	−	2.17464i
$303$	3.10583	+	3.10583i	0.178425	+	0.178425i
$304$	6.09808	−	10.5622i	0.349749	−	0.605782i
$305$		0			0
$306$	1.90192	−	1.09808i	0.108726	−	0.0627728i
$307$	25.8719			1.47659			0.738295	−	0.674478i	$-0.235631\pi$
$307$	25.8719			1.47659			0.738295	+	0.674478i	$0.235631\pi$
$308$	3.67423	−	6.36396i	0.209359	−	0.362620i
$309$	−15.2942	+	4.09808i	−0.870058	+	0.233131i
$310$		0			0
$311$	−14.0263	−	24.2942i	−0.795357	−	1.37760i	−0.922612	−	0.385729i	$-0.873950\pi$
$311$	−14.0263	−	24.2942i	−0.795357	−	1.37760i	0.127255	−	0.991870i	$-0.459383\pi$
$312$	2.12132	−	0.568406i	0.120096	−	0.0321797i
$313$	−2.77766	+	4.81105i	−0.157003	+	0.271936i	−0.933786	−	0.357831i	$-0.883516\pi$
$313$	−2.77766	+	4.81105i	−0.157003	+	0.271936i	0.776784	+	0.629767i	$0.216850\pi$
$314$	−41.3205			−2.33185
$315$		0			0
$316$	0.928203			0.0522155
$317$	17.5761	−	30.4428i	0.987174	−	1.70984i	0.355328	−	0.934742i	$-0.384369\pi$
$317$	17.5761	−	30.4428i	0.987174	−	1.70984i	0.631846	−	0.775094i	$-0.282297\pi$
$318$	9.14162	+	9.14162i	0.512637	+	0.512637i
$319$	−15.2942	−	26.4904i	−0.856312	−	1.48318i
$320$		0			0
$321$	−5.25833	+	19.6244i	−0.293491	+	1.09532i
$322$	−1.67303	+	2.89778i	−0.0932345	+	0.161487i
$323$	−1.03528			−0.0576043
$324$	7.79423	−	13.5000i	0.433013	−	0.750000i
$325$		0			0
$326$	18.2942	−	31.6865i	1.01322	−	1.75495i
$327$	−2.08913	+	7.79676i	−0.115529	+	0.431162i
$328$	−1.10463	−	1.91327i	−0.0609928	−	0.105643i
$329$	−1.96410	−	3.40192i	−0.108284	−	0.187554i
$330$		0			0
$331$	−6.19615	+	10.7321i	−0.340571	+	0.589887i	−0.984539	−	0.175166i	$-0.943954\pi$
$331$	−6.19615	+	10.7321i	−0.340571	+	0.589887i	0.643968	+	0.765053i	$0.277287\pi$
$332$	18.0430			0.990238
$333$	−11.0227	−	6.36396i	−0.604040	−	0.348743i
$334$	−32.8564			−1.79782
$335$		0			0
$336$	−6.69615	+	1.79423i	−0.365305	+	0.0978832i
$337$	0.896575	+	1.55291i	0.0488396	+	0.0845926i	0.889412	−	0.457107i	$-0.151114\pi$
$337$	0.896575	+	1.55291i	0.0488396	+	0.0845926i	−0.840572	+	0.541700i	$0.817781\pi$
$338$	−6.76148	−	11.7112i	−0.367776	−	0.637007i
$339$	4.26795	−	1.14359i	0.231803	−	0.0621115i
$340$		0			0
$341$	−12.9282			−0.700101
$342$	−13.7124	+	7.91688i	−0.741483	+	0.428096i
$343$	11.8313			0.638833
$344$	2.36603	−	4.09808i	0.127568	−	0.220953i
$345$		0			0
$346$	−0.732051	−	1.26795i	−0.0393553	−	0.0681654i
$347$	−4.94975	−	8.57321i	−0.265716	−	0.460234i	0.702035	−	0.712143i	$-0.252275\pi$
$347$	−4.94975	−	8.57321i	−0.265716	−	0.460234i	−0.967751	+	0.251909i	$0.918942\pi$
$348$	5.01910	−	18.7315i	0.269052	−	1.00412i
$349$	−10.7679	+	18.6506i	−0.576395	+	0.998346i	0.419493	+	0.907758i	$0.362208\pi$
$349$	−10.7679	+	18.6506i	−0.576395	+	0.998346i	−0.995889	+	0.0905872i	$0.971126\pi$
$350$		0			0
$351$	−12.2942	−	3.29423i	−0.656217	−	0.175833i
$352$	35.9101			1.91402
$353$	−4.52004	+	7.82894i	−0.240578	+	0.416693i	−0.960879	−	0.276969i	$-0.910670\pi$
$353$	−4.52004	+	7.82894i	−0.240578	+	0.416693i	0.720301	+	0.693661i	$0.244004\pi$
$354$	−2.19615	+	8.19615i	−0.116724	+	0.435621i
$355$		0			0
$356$	6.40192	+	11.0885i	0.339301	+	0.587687i
$357$	0.416102	+	0.416102i	0.0220225	+	0.0220225i
$358$	23.7506	−	41.1373i	1.25526	−	2.17417i
$359$	9.80385			0.517427			0.258714	−	0.965954i	$-0.416701\pi$
$359$	9.80385			0.517427			0.258714	+	0.965954i	$0.416701\pi$
$360$		0			0
$361$	−11.5359			−0.607153
$362$	8.17569	−	14.1607i	0.429705	−	0.744271i
$363$	−19.0597	+	5.10703i	−1.00037	+	0.268050i
$364$	−1.90192	−	3.29423i	−0.0996879	−	0.172664i
$365$		0			0
$366$	34.4545	−	9.23205i	1.80096	−	0.482567i
$367$	12.3998	−	21.4770i	0.647262	−	1.12109i	−0.336512	−	0.941679i	$-0.609247\pi$
$367$	12.3998	−	21.4770i	0.647262	−	1.12109i	0.983774	−	0.179411i	$-0.0574193\pi$
$368$	−8.62398			−0.449556
$369$			12.8038i			0.666542i
$370$		0			0
$371$	−1.73205	+	3.00000i	−0.0899236	+	0.155752i
$372$	−5.79555	−	5.79555i	−0.300486	−	0.300486i
$373$	16.0740	+	27.8410i	0.832280	+	1.44155i	0.896226	+	0.443597i	$0.146298\pi$
$373$	16.0740	+	27.8410i	0.832280	+	1.44155i	−0.0639468	+	0.997953i	$0.520369\pi$
$374$	−1.73205	−	3.00000i	−0.0895622	−	0.155126i
$375$		0			0
$376$	1.13397	−	1.96410i	0.0584803	−	0.101291i
$377$	−15.8338			−0.815480
$378$	8.69333	+	2.32937i	0.447137	+	0.119810i
$379$	12.5359			0.643926			0.321963	−	0.946752i	$-0.395657\pi$
$379$	12.5359			0.643926			0.321963	+	0.946752i	$0.395657\pi$
$380$		0			0
$381$	2.08846	−	7.79423i	0.106995	−	0.399310i
$382$	0.328169	+	0.568406i	0.0167906	+	0.0290822i
$383$	−10.2277	−	17.7148i	−0.522609	−	0.905186i	−0.999654	−	0.0263067i	$-0.991625\pi$
$383$	−10.2277	−	17.7148i	−0.522609	−	0.905186i	0.477045	−	0.878879i	$-0.341708\pi$
$384$	−5.02628	−	5.02628i	−0.256496	−	0.256496i
$385$		0			0
$386$	−40.0526			−2.03862
$387$	−23.7506	+	13.7124i	−1.20731	+	0.697042i
$388$	17.8028			0.903799
$389$	12.0622	−	20.8923i	0.611577	−	1.05928i	−0.379398	−	0.925234i	$-0.623869\pi$
$389$	12.0622	−	20.8923i	0.611577	−	1.05928i	0.990975	−	0.134048i	$-0.0427978\pi$
$390$		0			0
$391$	0.366025	+	0.633975i	0.0185107	+	0.0320615i
$392$	1.60368	+	2.77766i	0.0809982	+	0.140293i
$393$	1.55291	−	0.416102i	0.0783342	−	0.0209896i
$394$	20.1244	−	34.8564i	1.01385	−	1.75604i
$395$		0			0
$396$	−21.2942	−	12.2942i	−1.07008	−	0.617808i
$397$	−29.3939			−1.47524			−0.737618	−	0.675218i	$-0.764050\pi$
$397$	−29.3939			−1.47524			−0.737618	+	0.675218i	$0.764050\pi$
$398$	4.43211	−	7.67664i	0.222162	−	0.384795i
$399$	−3.00000	−	3.00000i	−0.150188	−	0.150188i
$400$		0			0
$401$	15.4641	+	26.7846i	0.772240	+	1.33756i	0.936333	+	0.351115i	$0.114197\pi$
$401$	15.4641	+	26.7846i	0.772240	+	1.33756i	−0.164092	+	0.986445i	$0.552469\pi$
$402$	−4.45069	+	16.6102i	−0.221980	+	0.828442i
$403$	−3.34607	+	5.79555i	−0.166679	+	0.288697i
$404$	4.39230			0.218525
$405$		0			0
$406$	11.1962			0.555656
$407$	−10.0382	+	17.3867i	−0.497575	+	0.861825i
$408$	−0.0879327	+	0.328169i	−0.00435332	+	0.0162468i
$409$	11.7321	+	20.3205i	0.580113	+	1.00478i	0.995465	+	0.0951241i	$0.0303248\pi$
$409$	11.7321	+	20.3205i	0.580113	+	1.00478i	−0.415353	+	0.909660i	$0.636342\pi$
$410$		0			0
$411$	22.7321	+	22.7321i	1.12129	+	1.12129i
$412$	−7.91688	+	13.7124i	−0.390036	+	0.675563i
$413$	−2.27362			−0.111878
$414$	9.69615	+	5.59808i	0.476540	+	0.275130i
$415$		0			0
$416$	9.29423	−	16.0981i	0.455687	−	0.789273i
$417$	13.3843	−	3.58630i	0.655430	−	0.175622i
$418$	12.4877	+	21.6293i	0.610793	+	1.05792i
$419$	8.02628	+	13.9019i	0.392109	+	0.679153i	0.992728	−	0.120383i	$-0.0384121\pi$
$419$	8.02628	+	13.9019i	0.392109	+	0.679153i	−0.600618	+	0.799536i	$0.705079\pi$
$420$		0			0
$421$	6.26795	−	10.8564i	0.305481	−	0.529109i	−0.671887	−	0.740653i	$-0.734516\pi$
$421$	6.26795	−	10.8564i	0.305481	−	0.529109i	0.977368	+	0.211545i	$0.0678494\pi$
$422$	25.3543			1.23423
$423$	−11.3831	+	6.57201i	−0.553463	+	0.319542i
$424$	−2.00000			−0.0971286
$425$		0			0
$426$	−9.00000	−	9.00000i	−0.436051	−	0.436051i
$427$	4.77886	+	8.27723i	0.231265	+	0.400563i
$428$	10.1583	+	17.5947i	0.491021	+	0.850473i
$429$	−5.19615	+	19.3923i	−0.250873	+	0.936269i
$430$		0			0
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$	6.00361	+	22.4058i	0.288849	+	1.07800i
$433$	−30.5307			−1.46721			−0.733606	−	0.679575i	$-0.762164\pi$
$433$	−30.5307			−1.46721			−0.733606	+	0.679575i	$0.762164\pi$
$434$	2.36603	−	4.09808i	0.113573	−	0.196714i
$435$		0			0
$436$	4.03590	+	6.99038i	0.193284	+	0.334779i
$437$	−2.63896	−	4.57081i	−0.126239	−	0.218651i
$438$	20.0764	+	20.0764i	0.959287	+	0.959287i
$439$	−4.66025	+	8.07180i	−0.222422	+	0.385246i	−0.955543	−	0.294852i	$-0.904730\pi$
$439$	−4.66025	+	8.07180i	−0.222422	+	0.385246i	0.733121	+	0.680098i	$0.238063\pi$
$440$		0			0
$441$		−	18.5885i		−	0.885165i
$442$	−1.79315			−0.0852915
$443$	6.95095	−	12.0394i	0.330250	−	0.572009i	−0.652311	−	0.757951i	$-0.726200\pi$
$443$	6.95095	−	12.0394i	0.330250	−	0.572009i	0.982561	+	0.185942i	$0.0595338\pi$
$444$	−12.2942	+	3.29423i	−0.583458	+	0.156337i
$445$		0			0
$446$	16.1603	+	27.9904i	0.765210	+	1.32538i
$447$	−12.9360	+	3.46618i	−0.611851	+	0.163945i
$448$	−2.56961	+	4.45069i	−0.121403	+	0.210275i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$	20.1962			0.951000
$452$	2.20925	−	3.82654i	0.103915	−	0.179985i
$453$	−27.6651	−	27.6651i	−1.29982	−	1.29982i
$454$	1.83013	+	3.16987i	0.0858921	+	0.148770i
$455$		0			0
$456$	0.633975	−	2.36603i	0.0296886	−	0.110799i
$457$	−17.2987	+	29.9623i	−0.809201	+	1.40158i	0.104218	+	0.994554i	$0.466766\pi$
$457$	−17.2987	+	29.9623i	−0.809201	+	1.40158i	−0.913418	+	0.407022i	$0.866567\pi$
$458$	−38.4983			−1.79891
$459$	1.39230	−	1.39230i	0.0649872	−	0.0649872i
$460$		0			0
$461$	−9.35641	+	16.2058i	−0.435771	+	0.754778i	−0.997358	−	0.0726397i	$-0.976858\pi$
$461$	−9.35641	+	16.2058i	−0.435771	+	0.754778i	0.561587	+	0.827418i	$0.310191\pi$
$462$	3.67423	−	13.7124i	0.170941	−	0.637960i
$463$	0.0879327	+	0.152304i	0.00408658	+	0.00707816i	0.868061	−	0.496457i	$-0.165366\pi$
$463$	0.0879327	+	0.152304i	0.00408658	+	0.00707816i	−0.863975	+	0.503535i	$0.832033\pi$
$464$	14.4282	+	24.9904i	0.669813	+	1.16015i
$465$		0			0
$466$	6.83013	−	11.8301i	0.316400	−	0.548020i
$467$	−5.75839			−0.266467			−0.133233	−	0.991085i	$-0.542536\pi$
$467$	−5.75839			−0.266467			−0.133233	+	0.991085i	$0.542536\pi$
$468$	−11.0227	+	6.36396i	−0.509525	+	0.294174i
$469$	−4.60770			−0.212764
$470$		0			0
$471$	−35.7846	+	9.58846i	−1.64887	+	0.441813i
$472$	−0.656339	−	1.13681i	−0.0302104	−	0.0523260i
$473$	21.6293	+	37.4631i	0.994517	+	1.72255i
$474$	1.73205	−	0.464102i	0.0795557	−	0.0213169i
$475$		0			0
$476$	0.588457			0.0269719
$477$	10.0382	+	5.79555i	0.459617	+	0.265360i
$478$	−24.9754			−1.14235
$479$	−15.9282	+	27.5885i	−0.727778	+	1.26055i	0.230042	+	0.973181i	$0.426114\pi$
$479$	−15.9282	+	27.5885i	−0.727778	+	1.26055i	−0.957820	+	0.287368i	$0.907220\pi$
$480$		0			0
$481$	5.19615	+	9.00000i	0.236924	+	0.410365i
$482$	6.05437	+	10.4865i	0.275769	+	0.477646i
$483$	−0.776457	+	2.89778i	−0.0353300	+	0.131853i
$484$	−9.86603	+	17.0885i	−0.448456	+	0.776748i
$485$		0			0
$486$	7.79423	−	29.0885i	0.353553	−	1.31948i
$487$	−1.13681			−0.0515139			−0.0257569	−	0.999668i	$-0.508200\pi$
$487$	−1.13681			−0.0515139			−0.0257569	+	0.999668i	$0.508200\pi$
$488$	−2.75908	+	4.77886i	−0.124898	+	0.216329i
$489$	8.49038	−	31.6865i	0.383948	−	1.43291i
$490$		0			0
$491$	10.8564	+	18.8038i	0.489943	+	0.848606i	0.999933	−	0.0115744i	$-0.00368433\pi$
$491$	10.8564	+	18.8038i	0.489943	+	0.848606i	−0.509990	+	0.860180i	$0.670351\pi$
$492$	9.05369	+	9.05369i	0.408172	+	0.408172i
$493$	1.22474	−	2.12132i	0.0551597	−	0.0955395i
$494$	12.9282			0.581667
$495$		0			0
$496$	12.1962			0.547623
$497$	1.70522	−	2.95352i	0.0764895	−	0.132484i
$498$	33.6687	−	9.02150i	1.50873	−	0.404263i
$499$	1.92820	+	3.33975i	0.0863182	+	0.149508i	0.905952	−	0.423380i	$-0.139156\pi$
$499$	1.92820	+	3.33975i	0.0863182	+	0.149508i	−0.819634	+	0.572888i	$0.805823\pi$
$500$		0			0
$501$	−28.4545	+	7.62436i	−1.27125	+	0.340631i
$502$	17.9551	−	31.0991i	0.801374	−	1.38802i
$503$	29.3567			1.30895			0.654476	−	0.756083i	$-0.272889\pi$
$503$	29.3567			1.30895			0.654476	+	0.756083i	$0.272889\pi$
$504$	−1.20577	+	0.696152i	−0.0537093	+	0.0310091i
$505$		0			0
$506$	8.83013	−	15.2942i	0.392547	−	0.679911i
$507$	−8.57321	−	8.57321i	−0.380750	−	0.380750i
$508$	−4.03459	−	6.98811i	−0.179006	−	0.310047i
$509$	5.42820	+	9.40192i	0.240601	+	0.416733i	0.960886	−	0.276946i	$-0.0893222\pi$
$509$	5.42820	+	9.40192i	0.240601	+	0.416733i	−0.720285	+	0.693679i	$0.755989\pi$
$510$		0			0
$511$	−3.80385	+	6.58846i	−0.168272	+	0.291456i
$512$	−29.2552			−1.29291
$513$	−10.0382	+	10.0382i	−0.443197	+	0.443197i
$514$	43.3205			1.91079
$515$		0			0
$516$	−7.09808	+	26.4904i	−0.312475	+	1.16617i
$517$	10.3664	+	17.9551i	0.455912	+	0.789663i
$518$	−3.67423	−	6.36396i	−0.161437	−	0.279616i
$519$	−0.928203	−	0.928203i	−0.0407436	−	0.0407436i
$520$		0			0
$521$	1.39230			0.0609980			0.0304990	−	0.999535i	$-0.490290\pi$
$521$	1.39230			0.0609980			0.0304990	+	0.999535i	$0.490290\pi$
$522$		−	37.4631i		−	1.63971i
$523$	−30.9468			−1.35321			−0.676604	−	0.736347i	$-0.736549\pi$
$523$	−30.9468			−1.35321			−0.676604	+	0.736347i	$0.736549\pi$
$524$	0.803848	−	1.39230i	0.0351162	−	0.0608231i
$525$		0			0
$526$	−7.36603	−	12.7583i	−0.321174	−	0.556290i
$527$	−0.517638	−	0.896575i	−0.0225487	−	0.0390554i
$528$	35.3417	−	9.46979i	1.53805	−	0.412120i
$529$	9.63397	−	16.6865i	0.418868	−	0.725501i
$530$		0			0
$531$			7.60770i			0.330146i
$532$	−4.24264			−0.183942
$533$	5.22715	−	9.05369i	0.226413	−	0.392159i
$534$	17.4904	+	17.4904i	0.756883	+	0.756883i
$535$		0			0
$536$	−1.33013	−	2.30385i	−0.0574527	−	0.0995111i
$537$	11.0227	−	41.1373i	0.475665	−	1.77521i
$538$	16.6102	−	28.7697i	0.716117	−	1.24035i
$539$	−29.3205			−1.26292
$540$		0			0
$541$	21.3923			0.919727			0.459864	−	0.887990i	$-0.347898\pi$
$541$	21.3923			0.919727			0.459864	+	0.887990i	$0.347898\pi$
$542$	−22.7153	+	39.3441i	−0.975708	+	1.68998i
$543$	3.79435	−	14.1607i	0.162831	−	0.607695i
$544$	1.43782	+	2.49038i	0.0616461	+	0.106774i
$545$		0			0
$546$	−5.19615	−	5.19615i	−0.222375	−	0.222375i
$547$	15.1452	−	26.2323i	0.647563	−	1.12161i	−0.336140	−	0.941812i	$-0.609122\pi$
$547$	15.1452	−	26.2323i	0.647563	−	1.12161i	0.983703	−	0.179800i	$-0.0575451\pi$
$548$	32.1480			1.37329
$549$	27.6962	−	15.9904i	1.18204	−	0.682453i
$550$		0			0
$551$	−8.83013	+	15.2942i	−0.376176	+	0.651556i
$552$	−1.67303	+	0.448288i	−0.0712090	+	0.0190804i
$553$	0.240237	+	0.416102i	0.0102159	+	0.0176945i
$554$	11.8301	+	20.4904i	0.502614	+	0.870553i
$555$		0			0
$556$	6.92820	−	12.0000i	0.293821	−	0.508913i
$557$	31.1127			1.31829			0.659144	−	0.752017i	$-0.270919\pi$
$557$	31.1127			1.31829			0.659144	+	0.752017i	$0.270919\pi$
$558$	−13.7124	−	7.91688i	−0.580493	−	0.335148i
$559$	22.3923			0.947094
$560$		0			0
$561$	−2.19615	−	2.19615i	−0.0927216	−	0.0927216i
$562$	−15.7136	−	27.2168i	−0.662840	−	1.14807i
$563$	−13.7818	−	23.8707i	−0.580833	−	1.00603i	−0.995381	−	0.0960045i	$-0.969394\pi$
$563$	−13.7818	−	23.8707i	−0.580833	−	1.00603i	0.414548	−	0.910027i	$-0.363940\pi$
$564$	−3.40192	+	12.6962i	−0.143247	+	0.534604i
$565$		0			0
$566$	−8.66025			−0.364018
$567$	8.06918			0.338874
$568$	1.96902			0.0826181
$569$	2.66025	−	4.60770i	0.111524	−	0.193165i	−0.804861	−	0.593463i	$-0.797760\pi$
$569$	2.66025	−	4.60770i	0.111524	−	0.193165i	0.916385	+	0.400299i	$0.131094\pi$
$570$		0			0
$571$	−2.73205	−	4.73205i	−0.114333	−	0.198030i	0.803180	−	0.595736i	$-0.203140\pi$
$571$	−2.73205	−	4.73205i	−0.114333	−	0.198030i	−0.917513	+	0.397706i	$0.869806\pi$
$572$	10.0382	+	17.3867i	0.419718	+	0.726973i
$573$	0.416102	+	0.416102i	0.0173829	+	0.0173829i
$574$	−3.69615	+	6.40192i	−0.154274	+	0.267211i
$575$		0			0
$576$	14.8923	+	8.59808i	0.620513	+	0.358253i
$577$	−28.5617			−1.18904			−0.594519	−	0.804082i	$-0.702657\pi$
$577$	−28.5617			−1.18904			−0.594519	+	0.804082i	$0.702657\pi$
$578$	−16.2820	+	28.2013i	−0.677244	+	1.17302i
$579$	−34.6865	+	9.29423i	−1.44152	+	0.386255i
$580$		0			0
$581$	4.66987	+	8.08846i	0.193739	+	0.335566i
$582$	33.2204	−	8.90138i	1.37703	−	0.368974i
$583$	9.14162	−	15.8338i	0.378607	−	0.655767i
$584$	−4.39230			−0.181755
$585$		0			0
$586$	−17.1244			−0.707401
$587$	11.0041	−	19.0597i	0.454189	−	0.786678i	−0.544452	−	0.838792i	$-0.683263\pi$
$587$	11.0041	−	19.0597i	0.454189	−	0.786678i	0.998641	+	0.0521138i	$0.0165959\pi$
$588$	−13.1440	−	13.1440i	−0.542050	−	0.542050i
$589$	3.73205	+	6.46410i	0.153776	+	0.266349i
$590$		0			0
$591$	9.33975	−	34.8564i	0.384186	−	1.43380i
$592$	9.46979	−	16.4022i	0.389206	−	0.674124i
$593$	28.9406			1.18845			0.594224	−	0.804299i	$-0.297459\pi$
$593$	28.9406			1.18845			0.594224	+	0.804299i	$0.297459\pi$
$594$	−45.8827	−	12.2942i	−1.88259	−	0.504438i
$595$		0			0
$596$	−6.69615	+	11.5981i	−0.274285	+	0.475076i
$597$	2.05695	−	7.67664i	0.0841853	−	0.314184i
$598$	−4.57081	−	7.91688i	−0.186914	−	0.323745i
$599$	−16.8564	−	29.1962i	−0.688734	−	1.19292i	−0.972248	−	0.233954i	$-0.924833\pi$
$599$	−16.8564	−	29.1962i	−0.688734	−	1.19292i	0.283514	−	0.958968i	$-0.408500\pi$
$600$		0			0
$601$	8.46410	−	14.6603i	0.345258	−	0.598004i	−0.640143	−	0.768256i	$-0.721125\pi$
$601$	8.46410	−	14.6603i	0.345258	−	0.598004i	0.985401	+	0.170252i	$0.0544581\pi$
$602$	−15.8338			−0.645335
$603$			15.4176i			0.627855i
$604$	−39.1244			−1.59195
$605$		0			0
$606$	8.19615	−	2.19615i	0.332946	−	0.0892126i
$607$	4.36276	+	7.55652i	0.177079	+	0.306710i	0.940879	−	0.338743i	$-0.110002\pi$
$607$	4.36276	+	7.55652i	0.177079	+	0.306710i	−0.763800	+	0.645453i	$0.776669\pi$
$608$	−10.3664	−	17.9551i	−0.420412	−	0.728174i
$609$	9.69615	−	2.59808i	0.392908	−	0.105279i
$610$		0			0
$611$	10.7321			0.434172
$612$		−	1.96902i		−	0.0795928i
$613$	24.3190			0.982236			0.491118	−	0.871093i	$-0.336588\pi$
$613$	24.3190			0.982236			0.491118	+	0.871093i	$0.336588\pi$
$614$	24.9904	−	43.2846i	1.00853	−	1.74682i
$615$		0			0
$616$	1.09808	+	1.90192i	0.0442428	+	0.0766307i
$617$	6.55343	+	11.3509i	0.263831	+	0.456969i	0.967257	−	0.253800i	$-0.0816805\pi$
$617$	6.55343	+	11.3509i	0.263831	+	0.456969i	−0.703426	+	0.710769i	$0.748347\pi$
$618$	−7.91688	+	29.5462i	−0.318463	+	1.18852i
$619$	−9.90192	+	17.1506i	−0.397992	+	0.689342i	−0.993478	−	0.114023i	$-0.963626\pi$
$619$	−9.90192	+	17.1506i	−0.397992	+	0.689342i	0.595486	+	0.803366i	$0.296959\pi$
$620$		0			0
$621$	9.69615	+	2.59808i	0.389093	+	0.104257i
$622$	−54.1934			−2.17296
$623$	−3.31388	+	5.73981i	−0.132768	+	0.229961i
$624$	4.90192	−	18.2942i	0.196234	−	0.732355i
$625$		0			0
$626$	5.36603	+	9.29423i	0.214470	+	0.371472i
$627$	15.8338	+	15.8338i	0.632339	+	0.632339i
$628$	−18.5235	+	32.0836i	−0.739167	+	1.28028i
$629$	−1.60770			−0.0641030
$630$		0			0
$631$	−33.3205			−1.32647			−0.663234	−	0.748412i	$-0.730817\pi$
$631$	−33.3205			−1.32647			−0.663234	+	0.748412i	$0.730817\pi$
$632$	−0.138701	+	0.240237i	−0.00551722	+	0.00955610i
$633$	21.9575	−	5.88349i	0.872731	−	0.233848i
$634$	−33.9545	−	58.8109i	−1.34850	−	2.33568i
$635$		0			0
$636$	11.1962	−	3.00000i	0.443956	−	0.118958i
$637$	−7.58871	+	13.1440i	−0.300675	+	0.520785i
$638$	−59.0924			−2.33949
$639$	−9.88269	−	5.70577i	−0.390953	−	0.225717i
$640$		0			0
$641$	12.5263	−	21.6962i	0.494758	−	0.856946i	−0.505223	−	0.862989i	$-0.668590\pi$
$641$	12.5263	−	21.6962i	0.494758	−	0.856946i	0.999982	+	0.00604207i	$0.00192326\pi$
$642$	27.7530	+	27.7530i	1.09532	+	1.09532i
$643$	12.6078	+	21.8374i	0.497203	+	0.861181i	0.999995	−	0.00322641i	$-0.00102700\pi$
$643$	12.6078	+	21.8374i	0.497203	+	0.861181i	−0.502792	+	0.864408i	$0.667694\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$		0			0
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	−12.3861			−0.486950			−0.243475	−	0.969907i	$-0.578287\pi$
$647$	−12.3861			−0.486950			−0.243475	+	0.969907i	$0.578287\pi$
$648$	2.32937	+	4.03459i	0.0915064	+	0.158494i
$649$	12.0000			0.471041
$650$		0			0
$651$	1.09808	−	4.09808i	0.0430370	−	0.160616i
$652$	−16.4022	−	28.4094i	−0.642358	−	1.11260i
$653$	0.226633	+	0.392541i	0.00886885	+	0.0153613i	0.870426	−	0.492300i	$-0.163844\pi$
$653$	0.226633	+	0.392541i	0.00886885	+	0.0153613i	−0.861557	+	0.507661i	$0.830510\pi$
$654$	11.0263	+	11.0263i	0.431162	+	0.431162i
$655$		0			0
$656$	−19.0526			−0.743877
$657$	22.0454	+	12.7279i	0.860073	+	0.496564i
$658$	−7.58871			−0.295839
$659$	−18.1244	+	31.3923i	−0.706025	+	1.22287i	0.260296	+	0.965529i	$0.416180\pi$
$659$	−18.1244	+	31.3923i	−0.706025	+	1.22287i	−0.966320	+	0.257342i	$0.917153\pi$
$660$		0			0
$661$	15.3923	+	26.6603i	0.598691	+	1.03696i	0.993015	+	0.117992i	$0.0376457\pi$
$661$	15.3923	+	26.6603i	0.598691	+	1.03696i	−0.394323	+	0.918972i	$0.629021\pi$
$662$	11.9700	+	20.7327i	0.465229	+	0.805800i
$663$	−1.55291	+	0.416102i	−0.0603102	+	0.0161601i
$664$	−2.69615	+	4.66987i	−0.104631	+	0.181226i
$665$		0			0
$666$	−21.2942	+	12.2942i	−0.825135	+	0.476392i
$667$	12.4877			0.483525
$668$	−14.7291	+	25.5116i	−0.569887	+	0.987073i
$669$	20.4904	+	20.4904i	0.792204	+	0.792204i
$670$		0			0
$671$	−25.2224	−	43.6865i	−0.973701	−	1.68650i
$672$	−3.05008	+	11.3831i	−0.117659	+	0.439111i
$673$	−0.808643	+	1.40061i	−0.0311709	+	0.0539896i	−0.881190	−	0.472762i	$-0.843257\pi$
$673$	−0.808643	+	1.40061i	−0.0311709	+	0.0539896i	0.850019	+	0.526752i	$0.176590\pi$
$674$	3.46410			0.133432
$675$		0			0
$676$	−12.1244			−0.466321
$677$	−16.5409	+	28.6496i	−0.635717	+	1.10109i	0.350646	+	0.936508i	$0.385962\pi$
$677$	−16.5409	+	28.6496i	−0.635717	+	1.10109i	−0.986363	+	0.164586i	$0.947371\pi$
$678$	2.20925	−	8.24504i	0.0848459	−	0.316649i
$679$	4.60770	+	7.98076i	0.176827	+	0.306274i
$680$		0			0
$681$	2.32051	+	2.32051i	0.0889221	+	0.0889221i
$682$	−12.4877	+	21.6293i	−0.478178	+	0.828229i
$683$	−19.6975			−0.753702			−0.376851	−	0.926274i	$-0.622993\pi$
$683$	−19.6975			−0.753702			−0.376851	+	0.926274i	$0.622993\pi$
$684$			14.1962i			0.542803i
$685$		0			0
$686$	11.4282	−	19.7942i	0.436331	−	0.755747i
$687$	−33.3405	+	8.93357i	−1.27202	+	0.340837i
$688$	−20.4046	−	35.3417i	−0.777917	−	1.34739i
$689$	−4.73205	−	8.19615i	−0.180277	−	0.312249i
$690$		0			0
$691$	−10.1244	+	17.5359i	−0.385149	+	0.667097i	−0.991790	−	0.127879i	$-0.959183\pi$
$691$	−10.1244	+	17.5359i	−0.385149	+	0.667097i	0.606641	+	0.794976i	$0.292516\pi$
$692$	−1.31268			−0.0499005
$693$		−	12.7279i		−	0.483494i
$694$	−19.1244			−0.725951
$695$		0			0
$696$	4.09808	+	4.09808i	0.155337	+	0.155337i
$697$	0.808643	+	1.40061i	0.0306295	+	0.0530519i
$698$	20.8021	+	36.0303i	0.787370	+	1.36377i
$699$	3.16987	−	11.8301i	0.119896	−	0.447456i
$700$		0			0
$701$	−23.1962			−0.876107			−0.438053	−	0.898949i	$-0.644332\pi$
$701$	−23.1962			−0.876107			−0.438053	+	0.898949i	$0.644332\pi$
$702$	−17.3867	+	17.3867i	−0.656217	+	0.656217i
$703$	11.5911			0.437167
$704$	13.5622	−	23.4904i	0.511144	−	0.885327i
$705$		0			0
$706$	8.73205	+	15.1244i	0.328635	+	0.569213i
$707$	1.13681	+	1.96902i	0.0427542	+	0.0740525i
$708$	5.37945	+	5.37945i	0.202172	+	0.202172i
$709$	15.8923	−	27.5263i	0.596848	−	1.03377i	−0.396435	−	0.918063i	$-0.629753\pi$
$709$	15.8923	−	27.5263i	0.596848	−	1.03377i	0.993283	−	0.115708i	$-0.0369138\pi$
$710$		0			0
$711$	1.39230	−	0.803848i	0.0522155	−	0.0301466i
$712$	−3.82654			−0.143406
$713$	2.63896	−	4.57081i	0.0988298	−	0.171178i
$714$	1.09808	−	0.294229i	0.0410945	−	0.0110112i
$715$		0			0
$716$	−21.2942	−	36.8827i	−0.795803	−	1.37837i
$717$	−21.6293	+	5.79555i	−0.807761	+	0.216439i
$718$	9.46979	−	16.4022i	0.353409	−	0.612123i
$719$	19.6077			0.731244			0.365622	−	0.930763i	$-0.380856\pi$
$719$	19.6077			0.731244			0.365622	+	0.930763i	$0.380856\pi$
$720$		0			0
$721$	−8.19615			−0.305241
$722$	−11.1428	+	19.2999i	−0.414693	+	0.718269i
$723$	7.67664	+	7.67664i	0.285497	+	0.285497i
$724$	−7.33013	−	12.6962i	−0.272422	−	0.471849i
$725$		0			0
$726$	−9.86603	+	36.8205i	−0.366163	+	1.36654i
$727$	14.1607	−	24.5271i	0.525192	−	0.909659i	−0.474378	−	0.880321i	$-0.657327\pi$
$727$	14.1607	−	24.5271i	0.525192	−	0.909659i	0.999570	−	0.0293377i	$-0.00933982\pi$
$728$	1.13681			0.0421331
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	−1.73205	+	3.00000i	−0.0640622	+	0.110959i
$732$	8.27723	−	30.8910i	0.305935	−	1.14177i
$733$	20.7327	+	35.9101i	0.765781	+	1.32637i	0.939833	+	0.341635i	$0.110981\pi$
$733$	20.7327	+	35.9101i	0.765781	+	1.32637i	−0.174052	+	0.984736i	$0.555686\pi$
$734$	−23.9545	−	41.4904i	−0.884176	−	1.53144i
$735$		0			0
$736$	−7.33013	+	12.6962i	−0.270192	+	0.467986i
$737$	24.3190			0.895803
$738$	21.4213	+	12.3676i	0.788527	+	0.455256i
$739$	−45.8564			−1.68686			−0.843428	−	0.537243i	$-0.819466\pi$
$739$	−45.8564			−1.68686			−0.843428	+	0.537243i	$0.819466\pi$
$740$		0			0
$741$	11.1962	−	3.00000i	0.411301	−	0.110208i
$742$	3.34607	+	5.79555i	0.122838	+	0.212762i
$743$	12.6586	+	21.9253i	0.464398	+	0.804361i	0.999174	−	0.0406329i	$-0.0129374\pi$
$743$	12.6586	+	21.9253i	0.464398	+	0.804361i	−0.534776	+	0.844994i	$0.679604\pi$
$744$	2.36603	−	0.633975i	0.0867427	−	0.0232426i
$745$		0			0
$746$	62.1051			2.27383
$747$	27.0645	−	15.6257i	0.990238	−	0.571714i
$748$	−3.10583			−0.113560
$749$	−5.25833	+	9.10770i	−0.192135	+	0.332788i
$750$		0			0
$751$	−17.2224	−	29.8301i	−0.628455	−	1.08852i	−0.987862	−	0.155336i	$-0.950354\pi$
$751$	−17.2224	−	29.8301i	−0.628455	−	1.08852i	0.359406	−	0.933181i	$-0.382979\pi$
$752$	−9.77938	−	16.9384i	−0.356617	−	0.617679i
$753$	8.33298	−	31.0991i	0.303671	−	1.13331i
$754$	−15.2942	+	26.4904i	−0.556983	+	0.964723i
$755$		0			0
$756$	5.70577	−	5.70577i	0.207517	−	0.207517i
$757$	−7.34847			−0.267085			−0.133542	−	0.991043i	$-0.542635\pi$
$757$	−7.34847			−0.267085			−0.133542	+	0.991043i	$0.542635\pi$
$758$	12.1087	−	20.9730i	0.439810	−	0.761772i
$759$	4.09808	−	15.2942i	0.148751	−	0.555145i
$760$		0			0
$761$	−1.03590	−	1.79423i	−0.0375513	−	0.0650407i	0.846639	−	0.532168i	$-0.178622\pi$
$761$	−1.03590	−	1.79423i	−0.0375513	−	0.0650407i	−0.884190	+	0.467127i	$0.845289\pi$
$762$	−11.0227	−	11.0227i	−0.399310	−	0.399310i
$763$	−2.08913	+	3.61849i	−0.0756318	+	0.130998i
$764$	0.588457			0.0212896
$765$		0			0
$766$	−39.5167			−1.42779
$767$	3.10583	−	5.37945i	0.112145	−	0.194241i
$768$	−32.4440	+	8.69333i	−1.17072	+	0.313694i
$769$	13.8205	+	23.9378i	0.498380	+	0.863220i	0.999998	−	0.00186930i	$-0.000595016\pi$
$769$	13.8205	+	23.9378i	0.498380	+	0.863220i	−0.501618	+	0.865089i	$0.667262\pi$
$770$		0			0
$771$	37.5167	−	10.0526i	1.35113	−	0.362034i
$772$	−17.9551	+	31.0991i	−0.646217	+	1.11928i
$773$	7.72741			0.277935			0.138968	−	0.990297i	$-0.455622\pi$
$773$	7.72741			0.277935			0.138968	+	0.990297i	$0.455622\pi$
$774$			52.9808i			1.90435i
$775$		0			0
$776$	−2.66025	+	4.60770i	−0.0954976	+	0.165407i
$777$	−4.65874	−	4.65874i	−0.167131	−	0.167131i
$778$	−23.3023	−	40.3608i	−0.835429	−	1.44701i
$779$	−5.83013	−	10.0981i	−0.208886	−	0.361801i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	1.41421			0.0505722
$783$	−8.69333	−	32.4440i	−0.310674	−	1.15945i
$784$	27.6603			0.987866
$785$		0			0
$786$	0.803848	−	3.00000i	0.0286723	−	0.107006i
$787$	−8.15711	−	14.1285i	−0.290770	−	0.503628i	0.683222	−	0.730210i	$-0.260578\pi$
$787$	−8.15711	−	14.1285i	−0.290770	−	0.503628i	−0.973992	+	0.226583i	$0.927245\pi$
$788$	−18.0430	−	31.2514i	−0.642755	−	1.11328i
$789$	−9.33975	−	9.33975i	−0.332504	−	0.332504i
$790$		0			0
$791$	2.28719			0.0813230
$792$	6.36396	−	3.67423i	0.226134	−	0.130558i
$793$	−26.1122			−0.927271
$794$	−28.3923	+	49.1769i	−1.00761	+	1.74522i
$795$		0			0
$796$	−3.97372	−	6.88269i	−0.140845	−	0.243950i
$797$	7.95404	+	13.7768i	0.281747	+	0.487999i	0.971815	−	0.235745i	$-0.0757529\pi$
$797$	7.95404	+	13.7768i	0.281747	+	0.487999i	−0.690068	+	0.723744i	$0.742420\pi$
$798$	−7.91688	+	2.12132i	−0.280254	+	0.0750939i
$799$	−0.830127	+	1.43782i	−0.0293678	+	0.0508665i
$800$		0			0
$801$	19.2058	+	11.0885i	0.678603	+	0.391791i
$802$	59.7487			2.10980
$803$	20.0764	−	34.7733i	0.708480	−	1.22712i
$804$	10.9019	+	10.9019i	0.384481	+	0.384481i
$805$		0			0
$806$	6.46410	+	11.1962i	0.227688	+	0.394368i
$807$	7.70882	−	28.7697i	0.271363	−	1.01274i
$808$	−0.656339	+	1.13681i	−0.0230899	+	0.0399929i
$809$	37.1769			1.30707			0.653535	−	0.756896i	$-0.273285\pi$
$809$	37.1769			1.30707			0.653535	+	0.756896i	$0.273285\pi$
$810$		0			0
$811$	43.5692			1.52992			0.764961	−	0.644076i	$-0.222758\pi$
$811$	43.5692			1.52992			0.764961	+	0.644076i	$0.222758\pi$
$812$	5.01910	−	8.69333i	0.176136	−	0.305076i
$813$	−10.5422	+	39.3441i	−0.369732	+	1.37986i
$814$	19.3923	+	33.5885i	0.679700	+	1.17727i
$815$		0			0
$816$	2.07180	+	2.07180i	0.0725274	+	0.0725274i
$817$	12.4877	−	21.6293i	0.436889	−	0.756714i
$818$	45.3292			1.58490
$819$	−5.70577	−	3.29423i	−0.199376	−	0.115110i
$820$		0			0
$821$	14.7224	−	25.5000i	0.513816	−	0.889956i	−0.486055	−	0.873928i	$-0.661565\pi$
$821$	14.7224	−	25.5000i	0.513816	−	0.889956i	0.999872	−	0.0160280i	$-0.00510208\pi$
$822$	59.9889	−	16.0740i	2.09235	−	0.560645i
$823$	1.01669	+	1.76097i	0.0354397	+	0.0613834i	0.883201	−	0.468994i	$-0.155383\pi$
$823$	1.01669	+	1.76097i	0.0354397	+	0.0613834i	−0.847762	+	0.530378i	$0.822050\pi$
$824$	−2.36603	−	4.09808i	−0.0824244	−	0.142763i
$825$		0			0
$826$	−2.19615	+	3.80385i	−0.0764139	+	0.132353i
$827$	−11.5539			−0.401770			−0.200885	−	0.979615i	$-0.564382\pi$
$827$	−11.5539			−0.401770			−0.200885	+	0.979615i	$0.564382\pi$
$828$	8.69333	−	5.01910i	0.302114	−	0.174426i
$829$	31.5885			1.09711			0.548556	−	0.836114i	$-0.315178\pi$
$829$	31.5885			1.09711			0.548556	+	0.836114i	$0.315178\pi$
$830$		0			0
$831$	15.0000	+	15.0000i	0.520344	+	0.520344i
$832$	−7.02030	−	12.1595i	−0.243385	−	0.421555i
$833$	−1.17398	−	2.03339i	−0.0406759	−	0.0704527i
$834$	6.92820	−	25.8564i	0.239904	−	0.895334i
$835$		0			0
$836$	22.3923			0.774454
$837$	−13.7124	−	3.67423i	−0.473971	−	0.127000i
$838$	31.0112			1.07126
$839$	−0.633975	+	1.09808i	−0.0218872	+	0.0379098i	−0.876762	−	0.480925i	$-0.840301\pi$
$839$	−0.633975	+	1.09808i	−0.0218872	+	0.0379098i	0.854874	+	0.518835i	$0.173634\pi$
$840$		0			0
$841$	−6.39230	−	11.0718i	−0.220424	−	0.381786i
$842$	−12.1087	−	20.9730i	−0.417295	−	0.722776i
$843$	−19.9241	−	19.9241i	−0.686222	−	0.686222i
$844$	11.3660	−	19.6865i	0.391235	−	0.677638i
$845$		0			0
$846$			25.3923i			0.873005i
$847$	−10.2141			−0.350959
$848$	−8.62398	+	14.9372i	−0.296149	+	0.512945i
$849$	−7.50000	+	2.00962i	−0.257399	+	0.0689699i
$850$		0			0
$851$	−4.09808	−	7.09808i	−0.140480	−	0.243319i
$852$	−11.0227	+	2.95352i	−0.377632	+	0.101186i
$853$	−17.4746	+	30.2669i	−0.598319	+	1.03632i	0.394750	+	0.918788i	$0.370831\pi$
$853$	−17.4746	+	30.2669i	−0.598319	+	1.03632i	−0.993069	+	0.117530i	$0.962502\pi$
$854$	18.4641			0.631829
$855$		0			0
$856$	−6.07180			−0.207530
$857$	4.43211	−	7.67664i	0.151398	−	0.262229i	−0.780344	−	0.625351i	$-0.784956\pi$
$857$	4.43211	−	7.67664i	0.151398	−	0.262229i	0.931742	+	0.363122i	$0.118289\pi$
$858$	27.4249	+	27.4249i	0.936269	+	0.936269i
$859$	11.2224	+	19.4378i	0.382904	+	0.663210i	0.991476	−	0.130289i	$-0.0415905\pi$
$859$	11.2224	+	19.4378i	0.382904	+	0.663210i	−0.608572	+	0.793499i	$0.708257\pi$
$860$		0			0
$861$	−1.71539	+	6.40192i	−0.0584603	+	0.218177i
$862$	−5.79555	+	10.0382i	−0.197397	+	0.341902i
$863$	−13.0697			−0.444898			−0.222449	−	0.974944i	$-0.571405\pi$
$863$	−13.0697			−0.444898			−0.222449	+	0.974944i	$0.571405\pi$
$864$	38.0885	+	10.2058i	1.29580	+	0.347207i
$865$		0			0
$866$	−29.4904	+	51.0788i	−1.00212	+	1.73573i
$867$	−7.55652	+	28.2013i	−0.256633	+	0.957767i
$868$	−2.12132	−	3.67423i	−0.0720023	−	0.124712i
$869$	−1.26795	−	2.19615i	−0.0430122	−	0.0744994i
$870$		0			0
$871$	6.29423	−	10.9019i	0.213272	−	0.369398i
$872$	−2.41233			−0.0816916
$873$	26.7042	−	15.4176i	0.903799	−	0.521808i
$874$	−10.1962			−0.344890
$875$		0			0
$876$	24.5885	−	6.58846i	0.830767	−	0.222603i
$877$	−2.36156	−	4.09034i	−0.0797441	−	0.138121i	0.823395	−	0.567468i	$-0.192077\pi$
$877$	−2.36156	−	4.09034i	−0.0797441	−	0.138121i	−0.903139	+	0.429347i	$0.858744\pi$
$878$	9.00292	+	15.5935i	0.303834	+	0.526256i
$879$	−14.8301	+	3.97372i	−0.500208	+	0.134030i
$880$		0			0
$881$	−8.41154			−0.283392			−0.141696	−	0.989910i	$-0.545256\pi$
$881$	−8.41154			−0.283392			−0.141696	+	0.989910i	$0.545256\pi$
$882$	−31.0991	−	17.9551i	−1.04716	−	0.604579i
$883$	−17.6913			−0.595359			−0.297679	−	0.954666i	$-0.596213\pi$
$883$	−17.6913			−0.595359			−0.297679	+	0.954666i	$0.596213\pi$
$884$	−0.803848	+	1.39230i	−0.0270363	+	0.0468283i
$885$		0			0
$886$	−13.4282	−	23.2583i	−0.451129	−	0.781379i
$887$	−14.0914	−	24.4070i	−0.473142	−	0.819506i	0.526386	−	0.850246i	$-0.323547\pi$
$887$	−14.0914	−	24.4070i	−0.473142	−	0.819506i	−0.999527	+	0.0307403i	$0.990214\pi$
$888$	0.984508	−	3.67423i	0.0330379	−	0.123299i
$889$	2.08846	−	3.61731i	0.0700446	−	0.121321i
$890$		0			0
$891$	−42.5885			−1.42677
$892$	28.9778			0.970248
$893$	5.98502	−	10.3664i	0.200281	−	0.346897i
$894$	−6.69615	+	24.9904i	−0.223953	+	0.835803i
$895$		0			0
$896$	−1.83975	−	3.18653i	−0.0614616	−	0.106455i
$897$	−5.79555	−	5.79555i	−0.193508	−	0.193508i
$898$	−11.5911	+	20.0764i	−0.386800	+	0.669958i
$899$	−17.6603			−0.589002
$900$		0			0
$901$	1.46410			0.0487763
$902$	19.5080	−	33.7888i	0.649545	−	1.12504i
$903$	−13.7124	+	3.67423i	−0.456321	+	0.122271i
$904$	0.660254	+	1.14359i	0.0219597	+	0.0380354i
$905$		0			0
$906$	−73.0070	+	19.5622i	−2.42550	+	0.649910i
$907$	−24.8553	+	43.0506i	−0.825305	+	1.42947i	0.0763808	+	0.997079i	$0.475664\pi$
$907$	−24.8553	+	43.0506i	−0.825305	+	1.42947i	−0.901686	+	0.432392i	$0.857670\pi$
$908$	3.28169			0.108907
$909$	6.58846	−	3.80385i	0.218525	−	0.126166i
$910$		0			0
$911$	−11.0718	+	19.1769i	−0.366825	+	0.635360i	−0.989067	−	0.147465i	$-0.952889\pi$
$911$	−11.0718	+	19.1769i	−0.366825	+	0.635360i	0.622242	+	0.782825i	$0.286222\pi$
$912$	−14.9372	−	14.9372i	−0.494619	−	0.494619i
$913$	−24.6472	−	42.6902i	−0.815703	−	1.41284i
$914$	33.4186	+	57.8827i	1.10539	+	1.91459i
$915$		0			0
$916$	−17.2583	+	29.8923i	−0.570231	+	0.987670i
$917$	0.832204			0.0274818
$918$	−0.984508	−	3.67423i	−0.0324936	−	0.121268i
$919$	−15.1769			−0.500640			−0.250320	−	0.968163i	$-0.580536\pi$
$919$	−15.1769			−0.500640			−0.250320	+	0.968163i	$0.580536\pi$
$920$		0			0
$921$	11.5981	−	43.2846i	0.382170	−	1.42628i
$922$	18.0752	+	31.3071i	0.595275	+	1.03105i
$923$	4.65874	+	8.06918i	0.153344	+	0.265600i
$924$	−9.00000	−	9.00000i	−0.296078	−	0.296078i
$925$		0			0
$926$	0.339746			0.0111647
$927$			27.4249i			0.900751i
$928$	49.0542			1.61028
$929$	−1.73205	+	3.00000i	−0.0568267	+	0.0984268i	−0.893039	−	0.449979i	$-0.851432\pi$
$929$	−1.73205	+	3.00000i	−0.0568267	+	0.0984268i	0.836213	+	0.548405i	$0.184765\pi$
$930$		0			0
$931$	8.46410	+	14.6603i	0.277400	+	0.480470i
$932$	−6.12372	−	10.6066i	−0.200589	−	0.347431i
$933$	−46.9328	+	12.5756i	−1.53651	+	0.411707i
$934$	−5.56218	+	9.63397i	−0.182000	+	0.315233i
$935$		0			0
$936$		−	3.80385i		−	0.124333i
$937$	13.8647			0.452941			0.226471	−	0.974018i	$-0.427281\pi$
$937$	13.8647			0.452941			0.226471	+	0.974018i	$0.427281\pi$
$938$	−4.45069	+	7.70882i	−0.145320	+	0.251702i
$939$	6.80385	+	6.80385i	0.222035	+	0.222035i
$940$		0			0
$941$	4.16025	+	7.20577i	0.135620	+	0.234901i	0.925834	−	0.377930i	$-0.123364\pi$
$941$	4.16025	+	7.20577i	0.135620	+	0.234901i	−0.790214	+	0.612831i	$0.790031\pi$
$942$	−18.5235	+	69.1306i	−0.603527	+	2.25240i
$943$	−4.12252	+	7.14042i	−0.134248	+	0.232524i
$944$	−11.3205			−0.368451
$945$		0			0
$946$	83.5692			2.71707
$947$	−1.15539	+	2.00120i	−0.0375453	+	0.0650303i	−0.884187	−	0.467132i	$-0.845287\pi$
$947$	−1.15539	+	2.00120i	−0.0375453	+	0.0650303i	0.846642	+	0.532163i	$0.178621\pi$
$948$	0.416102	−	1.55291i	0.0135144	−	0.0504363i
$949$	−10.3923	−	18.0000i	−0.337348	−	0.584305i
$950$		0			0
$951$	−43.0526	−	43.0526i	−1.39607	−	1.39607i
$952$	−0.0879327	+	0.152304i	−0.00284992	+	0.00493620i
$953$	−37.0197			−1.19919			−0.599594	−	0.800305i	$-0.704671\pi$
$953$	−37.0197			−1.19919			−0.599594	+	0.800305i	$0.704671\pi$
$954$	19.3923	−	11.1962i	0.627849	−	0.362489i
$955$		0			0
$956$	−11.1962	+	19.3923i	−0.362109	+	0.627192i
$957$	−51.1755	+	13.7124i	−1.65427	+	0.443260i
$958$	30.7709	+	53.2968i	0.994163	+	1.72194i
$959$	8.32051	+	14.4115i	0.268683	+	0.465373i
$960$		0			0
$961$	11.7679	−	20.3827i	0.379611	−	0.657506i
$962$	20.0764			0.647289
$963$	30.4749	+	17.5947i	0.982041	+	0.566982i
$964$	10.8564			0.349661
$965$		0			0
$966$	4.09808	+	4.09808i	0.131853	+	0.131853i
$967$	17.3545	+	30.0588i	0.558082	+	0.966627i	0.997657	+	0.0684208i	$0.0217960\pi$
$967$	17.3545	+	30.0588i	0.558082	+	0.966627i	−0.439574	+	0.898206i	$0.644871\pi$
$968$	−2.94855	−	5.10703i	−0.0947698	−	0.164146i
$969$	−0.464102	+	1.73205i	−0.0149091	+	0.0556415i
$970$		0			0
$971$	27.8038			0.892268			0.446134	−	0.894966i	$-0.352800\pi$
$971$	27.8038			0.892268			0.446134	+	0.894966i	$0.352800\pi$
$972$	−19.0919	−	19.0919i	−0.612372	−	0.612372i
$973$	7.17260			0.229943
$974$	−1.09808	+	1.90192i	−0.0351846	+	0.0609416i
$975$		0			0
$976$	23.7942	+	41.2128i	0.761635	+	1.31919i
$977$	7.77817	+	13.4722i	0.248846	+	0.431014i	0.963206	−	0.268765i	$-0.0866154\pi$
$977$	7.77817	+	13.4722i	0.248846	+	0.431014i	−0.714360	+	0.699778i	$0.753282\pi$
$978$	−44.8115	−	44.8115i	−1.43291	−	1.43291i
$979$	17.4904	−	30.2942i	0.558995	−	0.968208i
$980$		0			0
$981$	12.1077	+	6.99038i	0.386569	+	0.223186i
$982$	41.9459			1.33855
$983$	−17.9365	+	31.0669i	−0.572085	+	0.990881i	0.424266	+	0.905537i	$0.360532\pi$
$983$	−17.9365	+	31.0669i	−0.572085	+	0.990881i	−0.996352	+	0.0853431i	$0.972801\pi$
$984$	−3.69615	+	0.990381i	−0.117829	+	0.0315722i
$985$		0			0
$986$	−2.36603	−	4.09808i	−0.0753496	−	0.130509i
$987$	−6.57201	+	1.76097i	−0.209189	+	0.0560521i
$988$	5.79555	−	10.0382i	0.184381	−	0.319358i
$989$	−17.6603			−0.561563
$990$		0			0
$991$	25.0718			0.796432			0.398216	−	0.917292i	$-0.369629\pi$
$991$	25.0718			0.796432			0.398216	+	0.917292i	$0.369629\pi$
$992$	10.3664	−	17.9551i	0.329132	−	0.570074i
$993$	15.1774	+	15.1774i	0.481641	+	0.481641i
$994$	−3.29423	−	5.70577i	−0.104487	−	0.180976i
$995$		0			0
$996$	8.08846	−	30.1865i	0.256293	−	0.956497i
$997$	7.58871	−	13.1440i	0.240337	−	0.416275i	−0.720473	−	0.693483i	$-0.756075\pi$
$997$	7.58871	−	13.1440i	0.240337	−	0.416275i	0.960810	+	0.277207i	$0.0894088\pi$
$998$	7.45001			0.235826
$999$	−15.5885	+	15.5885i	−0.493197	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.e.d.151.4		8
3.2	odd	2		675.2.e.d.451.1		8
5.2	odd	4		45.2.j.a.34.4	yes	8
5.3	odd	4		45.2.j.a.34.1	yes	8
5.4	even	2	inner	225.2.e.d.151.1		8
9.2	odd	6		2025.2.a.r.1.4		4
9.4	even	3	inner	225.2.e.d.76.4		8
9.5	odd	6		675.2.e.d.226.1		8
9.7	even	3		2025.2.a.t.1.1		4
15.2	even	4		135.2.j.a.19.1		8
15.8	even	4		135.2.j.a.19.4		8
15.14	odd	2		675.2.e.d.451.4		8
20.3	even	4		720.2.by.d.529.1		8
20.7	even	4		720.2.by.d.529.4		8
45.2	even	12		405.2.b.c.244.4		4
45.4	even	6	inner	225.2.e.d.76.1		8
45.7	odd	12		405.2.b.d.244.1		4
45.13	odd	12		45.2.j.a.4.4	yes	8
45.14	odd	6		675.2.e.d.226.4		8
45.22	odd	12		45.2.j.a.4.1	✓	8
45.23	even	12		135.2.j.a.64.1		8
45.29	odd	6		2025.2.a.r.1.1		4
45.32	even	12		135.2.j.a.64.4		8
45.34	even	6		2025.2.a.t.1.4		4
45.38	even	12		405.2.b.c.244.1		4
45.43	odd	12		405.2.b.d.244.4		4
60.23	odd	4		2160.2.by.c.289.2		8
60.47	odd	4		2160.2.by.c.289.4		8
180.23	odd	12		2160.2.by.c.1009.4		8
180.67	even	12		720.2.by.d.49.1		8
180.103	even	12		720.2.by.d.49.4		8
180.167	odd	12		2160.2.by.c.1009.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.1	✓	8	45.22	odd	12
45.2.j.a.4.4	yes	8	45.13	odd	12
45.2.j.a.34.1	yes	8	5.3	odd	4
45.2.j.a.34.4	yes	8	5.2	odd	4
135.2.j.a.19.1		8	15.2	even	4
135.2.j.a.19.4		8	15.8	even	4
135.2.j.a.64.1		8	45.23	even	12
135.2.j.a.64.4		8	45.32	even	12
225.2.e.d.76.1		8	45.4	even	6	inner
225.2.e.d.76.4		8	9.4	even	3	inner
225.2.e.d.151.1		8	5.4	even	2	inner
225.2.e.d.151.4		8	1.1	even	1	trivial
405.2.b.c.244.1		4	45.38	even	12
405.2.b.c.244.4		4	45.2	even	12
405.2.b.d.244.1		4	45.7	odd	12
405.2.b.d.244.4		4	45.43	odd	12
675.2.e.d.226.1		8	9.5	odd	6
675.2.e.d.226.4		8	45.14	odd	6
675.2.e.d.451.1		8	3.2	odd	2
675.2.e.d.451.4		8	15.14	odd	2
720.2.by.d.49.1		8	180.67	even	12
720.2.by.d.49.4		8	180.103	even	12
720.2.by.d.529.1		8	20.3	even	4
720.2.by.d.529.4		8	20.7	even	4
2025.2.a.r.1.1		4	45.29	odd	6
2025.2.a.r.1.4		4	9.2	odd	6
2025.2.a.t.1.1		4	9.7	even	3
2025.2.a.t.1.4		4	45.34	even	6
2160.2.by.c.289.2		8	60.23	odd	4
2160.2.by.c.289.4		8	60.47	odd	4
2160.2.by.c.1009.2		8	180.167	odd	12
2160.2.by.c.1009.4		8	180.23	odd	12

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 1.67303i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-0.866025 - 1.50000i) q^{4} +(-2.36603 - 2.36603i) q^{6} +(0.448288 - 0.776457i) q^{7} +0.517638 q^{8} +(-2.59808 - 1.50000i) q^{9} +(-2.36603 + 4.09808i) q^{11} +(-2.89778 + 0.776457i) q^{12} +(1.22474 + 2.12132i) q^{13} +(-0.866025 - 1.50000i) q^{14} +(2.23205 - 3.86603i) q^{16} -0.378937 q^{17} +(-5.01910 + 2.89778i) q^{18} +2.73205 q^{19} +(-1.09808 - 1.09808i) q^{21} +(4.57081 + 7.91688i) q^{22} +(-0.965926 - 1.67303i) q^{23} +(0.232051 - 0.866025i) q^{24} +4.73205 q^{26} +(-3.67423 + 3.67423i) q^{27} -1.55291 q^{28} +(-3.23205 + 5.59808i) q^{29} +(1.36603 + 2.36603i) q^{31} +(-3.79435 - 6.57201i) q^{32} +(5.79555 + 5.79555i) q^{33} +(-0.366025 + 0.633975i) q^{34} +5.19615i q^{36} +4.24264 q^{37} +(2.63896 - 4.57081i) q^{38} +(4.09808 - 1.09808i) q^{39} +(-2.13397 - 3.69615i) q^{41} +(-2.89778 + 0.776457i) q^{42} +(4.57081 - 7.91688i) q^{43} +8.19615 q^{44} -3.73205 q^{46} +(2.19067 - 3.79435i) q^{47} +(-5.46739 - 5.46739i) q^{48} +(3.09808 + 5.36603i) q^{49} +(-0.169873 + 0.633975i) q^{51} +(2.12132 - 3.67423i) q^{52} -3.86370 q^{53} +(2.59808 + 9.69615i) q^{54} +(0.232051 - 0.401924i) q^{56} +(1.22474 - 4.57081i) q^{57} +(6.24384 + 10.8147i) q^{58} +(-1.26795 - 2.19615i) q^{59} +(-5.33013 + 9.23205i) q^{61} +5.27792 q^{62} +(-2.32937 + 1.34486i) q^{63} -5.73205 q^{64} +(15.2942 - 4.09808i) q^{66} +(-2.56961 - 4.45069i) q^{67} +(0.328169 + 0.568406i) q^{68} +(-3.23205 + 0.866025i) q^{69} +3.80385 q^{71} +(-1.34486 - 0.776457i) q^{72} -8.48528 q^{73} +(4.09808 - 7.09808i) q^{74} +(-2.36603 - 4.09808i) q^{76} +(2.12132 + 3.67423i) q^{77} +(2.12132 - 7.91688i) q^{78} +(-0.267949 + 0.464102i) q^{79} +(4.50000 + 7.79423i) q^{81} -8.24504 q^{82} +(-5.20857 + 9.02150i) q^{83} +(-0.696152 + 2.59808i) q^{84} +(-8.83013 - 15.2942i) q^{86} +(7.91688 + 7.91688i) q^{87} +(-1.22474 + 2.12132i) q^{88} -7.39230 q^{89} +2.19615 q^{91} +(-1.67303 + 2.89778i) q^{92} +(4.57081 - 1.22474i) q^{93} +(-4.23205 - 7.33013i) q^{94} +(-12.6962 + 3.40192i) q^{96} +(-5.13922 + 8.90138i) q^{97} +11.9700 q^{98} +(12.2942 - 7.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{6} - 12 q^{11} + 4 q^{16} + 8 q^{19} + 12 q^{21} - 12 q^{24} + 24 q^{26} - 12 q^{29} + 4 q^{31} + 4 q^{34} + 12 q^{39} - 24 q^{41} + 24 q^{44} - 16 q^{46} + 4 q^{49} - 36 q^{51} - 12 q^{56}+ \cdots + 36 q^{99}+O(q^{100}) \) 8 * q - 12 * q^6 - 12 * q^11 + 4 * q^16 + 8 * q^19 + 12 * q^21 - 12 * q^24 + 24 * q^26 - 12 * q^29 + 4 * q^31 + 4 * q^34 + 12 * q^39 - 24 * q^41 + 24 * q^44 - 16 * q^46 + 4 * q^49 - 36 * q^51 - 12 * q^56 - 24 * q^59 - 8 * q^61 - 32 * q^64 + 60 * q^66 - 12 * q^69 + 72 * q^71 + 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^81 + 36 * q^84 - 36 * q^86 + 24 * q^89 - 24 * q^91 - 20 * q^94 - 60 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more