LMFDB - Embedded newform 135.2.j.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(19,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("135.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.j (of order $6$, degree $2$, not 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	135.64
Dual form			135.2.j.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67303 + 0.965926i) q^{2} +(0.866025 - 1.50000i) q^{4} +(2.09077 - 0.792893i) q^{5} +(0.776457 - 0.448288i) q^{7} -0.517638i q^{8} +(-2.73205 + 3.34607i) q^{10} +(2.36603 + 4.09808i) q^{11} +(2.12132 + 1.22474i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(2.23205 + 3.86603i) q^{16} -0.378937i q^{17} -2.73205 q^{19} +(0.621320 - 3.82282i) q^{20} +(-7.91688 - 4.57081i) q^{22} +(1.67303 + 0.965926i) q^{23} +(3.74264 - 3.31552i) q^{25} -4.73205 q^{26} -1.55291i q^{28} +(-3.23205 - 5.59808i) q^{29} +(1.36603 - 2.36603i) q^{31} +(-6.57201 - 3.79435i) q^{32} +(0.366025 + 0.633975i) q^{34} +(1.26795 - 1.55291i) q^{35} -4.24264i q^{37} +(4.57081 - 2.63896i) q^{38} +(-0.410432 - 1.08226i) q^{40} +(2.13397 - 3.69615i) q^{41} +(-7.91688 + 4.57081i) q^{43} +8.19615 q^{44} -3.73205 q^{46} +(-3.79435 + 2.19067i) q^{47} +(-3.09808 + 5.36603i) q^{49} +(-3.05902 + 9.16208i) q^{50} +(3.67423 - 2.12132i) q^{52} +3.86370i q^{53} +(8.19615 + 6.69213i) q^{55} +(-0.232051 - 0.401924i) q^{56} +(10.8147 + 6.24384i) q^{58} +(-1.26795 + 2.19615i) q^{59} +(-5.33013 - 9.23205i) q^{61} +5.27792i q^{62} +5.73205 q^{64} +(5.40629 + 0.878680i) q^{65} +(4.45069 + 2.56961i) q^{67} +(-0.568406 - 0.328169i) q^{68} +(-0.621320 + 3.82282i) q^{70} -3.80385 q^{71} -8.48528i q^{73} +(4.09808 + 7.09808i) q^{74} +(-2.36603 + 4.09808i) q^{76} +(3.67423 + 2.12132i) q^{77} +(0.267949 + 0.464102i) q^{79} +(7.73205 + 6.31319i) q^{80} +8.24504i q^{82} +(-9.02150 + 5.20857i) q^{83} +(-0.300457 - 0.792271i) q^{85} +(8.83013 - 15.2942i) q^{86} +(2.12132 - 1.22474i) q^{88} -7.39230 q^{89} +2.19615 q^{91} +(2.89778 - 1.67303i) q^{92} +(4.23205 - 7.33013i) q^{94} +(-5.71209 + 2.16622i) q^{95} +(-8.90138 + 5.13922i) q^{97} -11.9700i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{10} + 12 q^{11} + 4 q^{16} - 8 q^{19} - 12 q^{20} - 4 q^{25} - 24 q^{26} - 12 q^{29} + 4 q^{31} - 4 q^{34} + 24 q^{35} - 4 q^{40} + 24 q^{41} + 24 q^{44} - 16 q^{46} - 4 q^{49} - 24 q^{50} + 24 q^{55}+ \cdots - 12 q^{95}+O(q^{100}) $ 8 * q - 8 * q^10 + 12 * q^11 + 4 * q^16 - 8 * q^19 - 12 * q^20 - 4 * q^25 - 24 * q^26 - 12 * q^29 + 4 * q^31 - 4 * q^34 + 24 * q^35 - 4 * q^40 + 24 * q^41 + 24 * q^44 - 16 * q^46 - 4 * q^49 - 24 * q^50 + 24 * q^55 + 12 * q^56 - 24 * q^59 - 8 * q^61 + 32 * q^64 + 12 * q^70 - 72 * q^71 + 12 * q^74 - 12 * q^76 + 16 * q^79 + 48 * q^80 + 16 * q^85 + 36 * q^86 + 24 * q^89 - 24 * q^91 + 20 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.67303	+	0.965926i	−1.18301	+	0.683013i	−0.956710	−	0.291044i	$-0.905997\pi$
$2$	−1.67303	+	0.965926i	−1.18301	+	0.683013i	−0.226303	+	0.974057i	$0.572664\pi$
$3$		0			0
$3$		0			0
$4$	0.866025	−	1.50000i	0.433013	−	0.750000i
$5$	2.09077	−	0.792893i	0.935021	−	0.354593i
$5$	2.09077	−	0.792893i	0.935021	−	0.354593i
$6$		0			0
$7$	0.776457	−	0.448288i	0.293473	−	0.169437i	−0.346034	−	0.938222i	$-0.612472\pi$
$7$	0.776457	−	0.448288i	0.293473	−	0.169437i	0.639507	+	0.768785i	$0.279138\pi$
$8$		−	0.517638i		−	0.183013i
$9$		0			0
$10$	−2.73205	+	3.34607i	−0.863950	+	1.05812i
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	0.963580	+	0.267421i	$0.0861715\pi$
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	−0.250196	+	0.968195i	$0.580495\pi$
$12$		0			0
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	0.764444	−	0.644690i	$-0.223014\pi$
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	−0.176096	+	0.984373i	$0.556347\pi$
$14$	−0.866025	+	1.50000i	−0.231455	+	0.400892i
$15$		0			0
$16$	2.23205	+	3.86603i	0.558013	+	0.966506i
$17$		−	0.378937i		−	0.0919058i	−0.998944	−	0.0459529i	$-0.985368\pi$
$17$		−	0.378937i		−	0.0919058i	0.998944	−	0.0459529i	$-0.0146324\pi$
$18$		0			0
$19$	−2.73205			−0.626775			−0.313388	−	0.949625i	$-0.601464\pi$
$19$	−2.73205			−0.626775			−0.313388	+	0.949625i	$0.601464\pi$
$20$	0.621320	−	3.82282i	0.138931	−	0.854809i
$21$		0			0
$22$	−7.91688	−	4.57081i	−1.68788	−	0.974500i
$23$	1.67303	+	0.965926i	0.348851	+	0.201409i	0.664179	−	0.747573i	$-0.268781\pi$
$23$	1.67303	+	0.965926i	0.348851	+	0.201409i	−0.315328	+	0.948983i	$0.602114\pi$
$24$		0			0
$25$	3.74264	−	3.31552i	0.748528	−	0.663103i
$26$	−4.73205			−0.928032
$27$		0			0
$28$		−	1.55291i		−	0.293473i
$29$	−3.23205	−	5.59808i	−0.600177	−	1.03954i	−0.992794	−	0.119835i	$-0.961764\pi$
$29$	−3.23205	−	5.59808i	−0.600177	−	1.03954i	0.392617	−	0.919702i	$-0.371570\pi$
$30$		0			0
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	−0.716883	−	0.697193i	$-0.754432\pi$
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	0.962229	+	0.272243i	$0.0877653\pi$
$32$	−6.57201	−	3.79435i	−1.16178	−	0.670753i
$33$		0			0
$34$	0.366025	+	0.633975i	0.0627728	+	0.108726i
$35$	1.26795	−	1.55291i	0.214323	−	0.262490i
$36$		0			0
$37$		−	4.24264i		−	0.697486i	−0.937218	−	0.348743i	$-0.886609\pi$
$37$		−	4.24264i		−	0.697486i	0.937218	−	0.348743i	$-0.113391\pi$
$38$	4.57081	−	2.63896i	0.741483	−	0.428096i
$39$		0			0
$40$	−0.410432	−	1.08226i	−0.0648950	−	0.171121i
$41$	2.13397	−	3.69615i	0.333271	−	0.577242i	−0.649880	−	0.760037i	$-0.725181\pi$
$41$	2.13397	−	3.69615i	0.333271	−	0.577242i	0.983151	+	0.182795i	$0.0585143\pi$
$42$		0			0
$43$	−7.91688	+	4.57081i	−1.20731	+	0.697042i	−0.962171	−	0.272445i	$-0.912168\pi$
$43$	−7.91688	+	4.57081i	−1.20731	+	0.697042i	−0.245141	+	0.969487i	$0.578834\pi$
$44$	8.19615			1.23562
$45$		0			0
$46$	−3.73205			−0.550261
$47$	−3.79435	+	2.19067i	−0.553463	+	0.319542i	−0.750518	−	0.660850i	$-0.770196\pi$
$47$	−3.79435	+	2.19067i	−0.553463	+	0.319542i	0.197054	+	0.980393i	$0.436862\pi$
$48$		0			0
$49$	−3.09808	+	5.36603i	−0.442582	+	0.766575i
$50$	−3.05902	+	9.16208i	−0.432611	+	1.29571i
$51$		0			0
$52$	3.67423	−	2.12132i	0.509525	−	0.294174i
$53$			3.86370i			0.530720i	0.964149	+	0.265360i	$0.0854909\pi$
$53$			3.86370i			0.530720i	−0.964149	+	0.265360i	$0.914509\pi$
$54$		0			0
$55$	8.19615	+	6.69213i	1.10517	+	0.902367i
$56$	−0.232051	−	0.401924i	−0.0310091	−	0.0537093i
$57$		0			0
$58$	10.8147	+	6.24384i	1.42003	+	0.819857i
$59$	−1.26795	+	2.19615i	−0.165073	+	0.285915i	−0.936681	−	0.350183i	$-0.886119\pi$
$59$	−1.26795	+	2.19615i	−0.165073	+	0.285915i	0.771608	+	0.636098i	$0.219453\pi$
$60$		0			0
$61$	−5.33013	−	9.23205i	−0.682453	−	1.18204i	−0.974230	−	0.225557i	$-0.927580\pi$
$61$	−5.33013	−	9.23205i	−0.682453	−	1.18204i	0.291777	−	0.956486i	$-0.405753\pi$
$62$			5.27792i			0.670296i
$63$		0			0
$64$	5.73205			0.716506
$65$	5.40629	+	0.878680i	0.670567	+	0.108987i
$66$		0			0
$67$	4.45069	+	2.56961i	0.543739	+	0.313928i	0.746593	−	0.665281i	$-0.231688\pi$
$67$	4.45069	+	2.56961i	0.543739	+	0.313928i	−0.202854	+	0.979209i	$0.565022\pi$
$68$	−0.568406	−	0.328169i	−0.0689294	−	0.0397964i
$69$		0			0
$70$	−0.621320	+	3.82282i	−0.0742620	+	0.456915i
$71$	−3.80385			−0.451434			−0.225717	−	0.974193i	$-0.572472\pi$
$71$	−3.80385			−0.451434			−0.225717	+	0.974193i	$0.572472\pi$
$72$		0			0
$73$		−	8.48528i		−	0.993127i	−0.868000	−	0.496564i	$-0.834595\pi$
$73$		−	8.48528i		−	0.993127i	0.868000	−	0.496564i	$-0.165405\pi$
$74$	4.09808	+	7.09808i	0.476392	+	0.825135i
$75$		0			0
$76$	−2.36603	+	4.09808i	−0.271402	+	0.470082i
$77$	3.67423	+	2.12132i	0.418718	+	0.241747i
$78$		0			0
$79$	0.267949	+	0.464102i	0.0301466	+	0.0522155i	0.880705	−	0.473665i	$-0.157069\pi$
$79$	0.267949	+	0.464102i	0.0301466	+	0.0522155i	−0.850558	+	0.525880i	$0.823736\pi$
$80$	7.73205	+	6.31319i	0.864470	+	0.705836i
$81$		0			0
$82$			8.24504i			0.910513i
$83$	−9.02150	+	5.20857i	−0.990238	+	0.571714i	−0.905346	−	0.424676i	$-0.860388\pi$
$83$	−9.02150	+	5.20857i	−0.990238	+	0.571714i	−0.0848929	+	0.996390i	$0.527055\pi$
$84$		0			0
$85$	−0.300457	−	0.792271i	−0.0325891	−	0.0859339i
$86$	8.83013	−	15.2942i	0.952177	−	1.64922i
$87$		0			0
$88$	2.12132	−	1.22474i	0.226134	−	0.130558i
$89$	−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
$92$	2.89778	−	1.67303i	0.302114	−	0.174426i
$93$		0			0
$94$	4.23205	−	7.33013i	0.436503	−	0.756045i
$95$	−5.71209	+	2.16622i	−0.586048	+	0.222250i
$96$		0			0
$97$	−8.90138	+	5.13922i	−0.903799	+	0.521808i	−0.878431	−	0.477870i	$-0.841409\pi$
$97$	−8.90138	+	5.13922i	−0.903799	+	0.521808i	−0.0253679	+	0.999678i	$0.508076\pi$
$98$		−	11.9700i		−	1.20916i
$99$		0			0
$100$	−1.73205	−	8.48528i	−0.173205	−	0.848528i
$101$	1.26795	+	2.19615i	0.126166	+	0.218525i	0.922188	−	0.386742i	$-0.126400\pi$
$101$	1.26795	+	2.19615i	0.126166	+	0.218525i	−0.796022	+	0.605267i	$0.793066\pi$
$102$		0			0
$103$	−7.91688	−	4.57081i	−0.780073	−	0.450375i	0.0563832	−	0.998409i	$-0.482043\pi$
$103$	−7.91688	−	4.57081i	−0.780073	−	0.450375i	−0.836456	+	0.548034i	$0.815376\pi$
$104$	0.633975	−	1.09808i	0.0621663	−	0.107675i
$105$		0			0
$106$	−3.73205	−	6.46410i	−0.362489	−	0.627849i
$107$		−	11.7298i		−	1.13396i	−0.823730	−	0.566982i	$-0.808111\pi$
$107$		−	11.7298i		−	1.13396i	0.823730	−	0.566982i	$-0.191889\pi$
$108$		0			0
$109$	4.66025			0.446371			0.223186	−	0.974776i	$-0.428354\pi$
$109$	4.66025			0.446371			0.223186	+	0.974776i	$0.428354\pi$
$110$	−20.1765	−	3.27928i	−1.92376	−	0.312667i
$111$		0			0
$112$	3.46618	+	2.00120i	0.327524	+	0.189096i
$113$	−2.20925	−	1.27551i	−0.207829	−	0.119990i	0.392473	−	0.919764i	$-0.371620\pi$
$113$	−2.20925	−	1.27551i	−0.207829	−	0.119990i	−0.600302	+	0.799773i	$0.704953\pi$
$114$		0			0
$115$	4.26380	+	0.692993i	0.397602	+	0.0646219i
$116$	−11.1962			−1.03954
$117$		0			0
$118$		−	4.89898i		−	0.450988i
$119$	−0.169873	−	0.294229i	−0.0155722	−	0.0269719i
$120$		0			0
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	17.8350	+	10.2970i	1.61470	+	0.932248i
$123$		0			0
$124$	−2.36603	−	4.09808i	−0.212475	−	0.368018i
$125$	5.19615	−	9.89949i	0.464758	−	0.885438i
$126$		0			0
$127$		−	4.65874i		−	0.413397i	−0.978405	−	0.206698i	$-0.933728\pi$
$127$		−	4.65874i		−	0.413397i	0.978405	−	0.206698i	$-0.0662719\pi$
$128$	3.55412	−	2.05197i	0.314142	−	0.181370i
$129$		0			0
$130$	−9.89363	+	3.75201i	−0.867729	+	0.329073i
$131$	−0.464102	+	0.803848i	−0.0405487	+	0.0702325i	−0.885588	−	0.464473i	$-0.846244\pi$
$131$	−0.464102	+	0.803848i	−0.0405487	+	0.0702325i	0.845039	+	0.534705i	$0.179577\pi$
$132$		0			0
$133$	−2.12132	+	1.22474i	−0.183942	+	0.106199i
$134$	−9.92820			−0.857666
$135$		0			0
$136$	−0.196152			−0.0168199
$137$	16.0740	−	9.28032i	1.37329	−	0.792871i	0.381952	−	0.924182i	$-0.375252\pi$
$137$	16.0740	−	9.28032i	1.37329	−	0.792871i	0.991341	+	0.131311i	$0.0419186\pi$
$138$		0			0
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	−1.23130	−	3.24679i	−0.104063	−	0.274404i
$141$		0			0
$142$	6.36396	−	3.67423i	0.534052	−	0.308335i
$143$			11.5911i			0.969297i
$144$		0			0
$145$	−11.1962	−	9.14162i	−0.929790	−	0.759170i
$146$	8.19615	+	14.1962i	0.678318	+	1.17488i
$147$		0			0
$148$	−6.36396	−	3.67423i	−0.523114	−	0.302020i
$149$	−3.86603	+	6.69615i	−0.316717	+	0.548570i	−0.979801	−	0.199975i	$-0.935914\pi$
$149$	−3.86603	+	6.69615i	−0.316717	+	0.548570i	0.663084	+	0.748545i	$0.269247\pi$
$150$		0			0
$151$	11.2942	+	19.5622i	0.919111	+	1.59195i	0.800768	+	0.598975i	$0.204425\pi$
$151$	11.2942	+	19.5622i	0.919111	+	1.59195i	0.118343	+	0.992973i	$0.462242\pi$
$152$			1.41421i			0.114708i
$153$		0			0
$154$	−8.19615			−0.660465
$155$	0.980040	−	6.02993i	0.0787187	−	0.484335i
$156$		0			0
$157$	18.5235	+	10.6945i	1.47833	+	0.853517i	0.999700	−	0.0244975i	$-0.00779857\pi$
$157$	18.5235	+	10.6945i	1.47833	+	0.853517i	0.478635	+	0.878014i	$0.341132\pi$
$158$	−0.896575	−	0.517638i	−0.0713277	−	0.0411811i
$159$		0			0
$160$	−16.7491	−	2.72222i	−1.32413	−	0.215210i
$161$	1.73205			0.136505
$162$		0			0
$163$			18.9396i			1.48346i	0.670697	+	0.741731i	$0.265995\pi$
$163$			18.9396i			1.48346i	−0.670697	+	0.741731i	$0.734005\pi$
$164$	−3.69615	−	6.40192i	−0.288621	−	0.499906i
$165$		0			0
$166$	10.0622	−	17.4282i	0.780976	−	1.35269i
$167$	−14.7291	−	8.50386i	−1.13977	−	0.658049i	−0.193399	−	0.981120i	$-0.561951\pi$
$167$	−14.7291	−	8.50386i	−1.13977	−	0.658049i	−0.946375	+	0.323071i	$0.895285\pi$
$168$		0			0
$169$	−3.50000	−	6.06218i	−0.269231	−	0.466321i
$170$	1.26795	+	1.03528i	0.0972473	+	0.0794021i
$171$		0			0
$172$			15.8338i			1.20731i
$173$	0.656339	−	0.378937i	0.0499005	−	0.0288101i	−0.474842	−	0.880071i	$-0.657495\pi$
$173$	0.656339	−	0.378937i	0.0499005	−	0.0288101i	0.524743	+	0.851261i	$0.324162\pi$
$174$		0			0
$175$	1.41970	−	4.25214i	0.107319	−	0.321431i
$176$	−10.5622	+	18.2942i	−0.796154	+	1.37898i
$177$		0			0
$178$	12.3676	−	7.14042i	0.926988	−	0.535197i
$179$	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	$0.398141\pi$
$182$	−3.67423	+	2.12132i	−0.272352	+	0.157243i
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−3.36396	−	8.87039i	−0.247323	−	0.652164i
$186$		0			0
$187$	1.55291	−	0.896575i	0.113560	−	0.0655641i
$188$			7.58871i			0.553463i
$189$		0			0
$190$	7.46410	−	9.14162i	0.541503	−	0.663203i
$191$	0.169873	+	0.294229i	0.0122916	+	0.0212896i	0.872106	−	0.489317i	$-0.162754\pi$
$191$	0.169873	+	0.294229i	0.0122916	+	0.0212896i	−0.859814	+	0.510607i	$0.829421\pi$
$192$		0			0
$193$	−17.9551	−	10.3664i	−1.29243	−	0.746187i	−0.313349	−	0.949638i	$-0.601451\pi$
$193$	−17.9551	−	10.3664i	−1.29243	−	0.746187i	−0.979085	+	0.203451i	$0.934784\pi$
$194$	9.92820	−	17.1962i	0.712803	−	1.23461i
$195$		0			0
$196$	5.36603	+	9.29423i	0.383288	+	0.663873i
$197$			20.8343i			1.48438i	0.670190	+	0.742190i	$0.266213\pi$
$197$			20.8343i			1.48438i	−0.670190	+	0.742190i	$0.733787\pi$
$198$		0			0
$199$	−4.58846			−0.325267			−0.162634	−	0.986687i	$-0.551999\pi$
$199$	−4.58846			−0.325267			−0.162634	+	0.986687i	$0.551999\pi$
$200$	−1.71624	−	1.93733i	−0.121356	−	0.136990i
$201$		0			0
$202$	−4.24264	−	2.44949i	−0.298511	−	0.172345i
$203$	−5.01910	−	2.89778i	−0.352272	−	0.203384i
$204$		0			0
$205$	1.53100	−	9.41982i	0.106929	−	0.657909i
$206$	17.6603			1.23045
$207$		0			0
$208$			10.9348i			0.758190i
$209$	−6.46410	−	11.1962i	−0.447131	−	0.774454i
$210$		0			0
$211$	6.56218	−	11.3660i	0.451759	−	0.782469i	−0.546736	−	0.837305i	$-0.684130\pi$
$211$	6.56218	−	11.3660i	0.451759	−	0.782469i	0.998495	+	0.0548353i	$0.0174634\pi$
$212$	5.79555	+	3.34607i	0.398040	+	0.229809i
$213$		0			0
$214$	11.3301	+	19.6244i	0.774512	+	1.34149i
$215$	−12.9282	+	15.8338i	−0.881696	+	1.07985i
$216$		0			0
$217$		−	2.44949i		−	0.166282i
$218$	−7.79676	+	4.50146i	−0.528063	+	0.304877i
$219$		0			0
$220$	17.1363	−	6.49867i	1.15533	−	0.438140i
$221$	0.464102	−	0.803848i	0.0312189	−	0.0540726i
$222$		0			0
$223$	14.4889	−	8.36516i	0.970248	−	0.560173i	0.0709359	−	0.997481i	$-0.477401\pi$
$223$	14.4889	−	8.36516i	0.970248	−	0.560173i	0.899312	+	0.437308i	$0.144068\pi$
$224$	−6.80385			−0.454601
$225$		0			0
$226$	4.92820			0.327819
$227$	1.64085	−	0.947343i	0.108907	−	0.0628774i	−0.444557	−	0.895750i	$-0.646639\pi$
$227$	1.64085	−	0.947343i	0.108907	−	0.0628774i	0.553464	+	0.832873i	$0.313306\pi$
$228$		0			0
$229$	9.96410	−	17.2583i	0.658446	−	1.14046i	−0.322571	−	0.946545i	$-0.604547\pi$
$229$	9.96410	−	17.2583i	0.658446	−	1.14046i	0.981018	−	0.193917i	$-0.0621194\pi$
$230$	−7.80286	+	2.95912i	−0.514505	+	0.195118i
$231$		0			0
$232$	−2.89778	+	1.67303i	−0.190248	+	0.109840i
$233$		−	7.07107i		−	0.463241i	−0.972806	−	0.231621i	$-0.925597\pi$
$233$		−	7.07107i		−	0.463241i	0.972806	−	0.231621i	$-0.0744028\pi$
$234$		0			0
$235$	−6.19615	+	7.58871i	−0.404192	+	0.495033i
$236$	2.19615	+	3.80385i	0.142957	+	0.247609i
$237$		0			0
$238$	0.568406	+	0.328169i	0.0368443	+	0.0212721i
$239$	−6.46410	+	11.1962i	−0.418128	+	0.724219i	−0.995751	−	0.0920846i	$-0.970647\pi$
$239$	−6.46410	+	11.1962i	−0.418128	+	0.724219i	0.577623	+	0.816304i	$0.303980\pi$
$240$		0			0
$241$	−3.13397	−	5.42820i	−0.201877	−	0.349661i	0.747256	−	0.664536i	$-0.231371\pi$
$241$	−3.13397	−	5.42820i	−0.201877	−	0.349661i	−0.949133	+	0.314875i	$0.898037\pi$
$242$		−	22.0082i		−	1.41474i
$243$		0			0
$244$	−18.4641			−1.18204
$245$	−2.22268	+	13.6756i	−0.142002	+	0.873700i
$246$		0			0
$247$	−5.79555	−	3.34607i	−0.368762	−	0.212905i
$248$	−1.22474	−	0.707107i	−0.0777714	−	0.0449013i
$249$		0			0
$250$	0.868845	+	21.5813i	0.0549506	+	1.36492i
$251$	−18.5885			−1.17329			−0.586647	−	0.809843i	$-0.699552\pi$
$251$	−18.5885			−1.17329			−0.586647	+	0.809843i	$0.699552\pi$
$252$		0			0
$253$			9.14162i			0.574729i
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	19.4201	+	11.2122i	1.21139	+	0.699396i	0.963062	−	0.269280i	$-0.0867857\pi$
$257$	19.4201	+	11.2122i	1.21139	+	0.699396i	0.248328	+	0.968676i	$0.420119\pi$
$258$		0			0
$259$	−1.90192	−	3.29423i	−0.118180	−	0.204693i
$260$	6.00000	−	7.34847i	0.372104	−	0.455733i
$261$		0			0
$262$		−	1.79315i		−	0.110781i
$263$	6.60420	−	3.81294i	0.407232	−	0.235116i	−0.282368	−	0.959306i	$-0.591120\pi$
$263$	6.60420	−	3.81294i	0.407232	−	0.235116i	0.689600	+	0.724191i	$0.257786\pi$
$264$		0			0
$265$	3.06350	+	8.07812i	0.188190	+	0.496235i
$266$	2.36603	−	4.09808i	0.145070	−	0.251269i
$267$		0			0
$268$	7.70882	−	4.45069i	0.470891	−	0.271869i
$269$	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	$0.753240\pi$
$272$	1.46498	−	0.845807i	0.0888276	−	0.0512846i
$273$		0			0
$274$	−17.9282	+	31.0526i	−1.08308	+	1.87595i
$275$	22.4424	+	7.49303i	1.35333	+	0.451847i
$276$		0			0
$277$	−10.6066	+	6.12372i	−0.637289	+	0.367939i	−0.783569	−	0.621304i	$-0.786603\pi$
$277$	−10.6066	+	6.12372i	−0.637289	+	0.367939i	0.146281	+	0.989243i	$0.453270\pi$
$278$		−	15.4548i		−	0.926918i
$279$		0			0
$280$	−0.803848	−	0.656339i	−0.0480391	−	0.0392237i
$281$	−8.13397	−	14.0885i	−0.485232	−	0.840447i	0.514624	−	0.857416i	$-0.327932\pi$
$281$	−8.13397	−	14.0885i	−0.485232	−	0.840447i	−0.999856	+	0.0169692i	$0.994598\pi$
$282$		0			0
$283$	−3.88229	−	2.24144i	−0.230778	−	0.133240i	0.380153	−	0.924924i	$-0.375871\pi$
$283$	−3.88229	−	2.24144i	−0.230778	−	0.133240i	−0.610931	+	0.791684i	$0.709205\pi$
$284$	−3.29423	+	5.70577i	−0.195477	+	0.338575i
$285$		0			0
$286$	−11.1962	−	19.3923i	−0.662042	−	1.14669i
$287$		−	3.82654i		−	0.225873i
$288$		0			0
$289$	16.8564			0.991553
$290$	27.5617	+	4.47958i	1.61848	+	0.263050i
$291$		0			0
$292$	−12.7279	−	7.34847i	−0.744845	−	0.430037i
$293$	7.67664	+	4.43211i	0.448474	+	0.258927i	0.707186	−	0.707028i	$-0.249965\pi$
$293$	7.67664	+	4.43211i	0.448474	+	0.258927i	−0.258711	+	0.965955i	$0.583298\pi$
$294$		0			0
$295$	−0.909676	+	5.59700i	−0.0529634	+	0.325870i
$296$	−2.19615			−0.127649
$297$		0			0
$298$		−	14.9372i		−	0.865287i
$299$	2.36603	+	4.09808i	0.136831	+	0.236998i
$300$		0			0
$301$	−4.09808	+	7.09808i	−0.236209	+	0.409126i
$302$	−37.7912	−	21.8188i	−2.17464	−	1.25553i
$303$		0			0
$304$	−6.09808	−	10.5622i	−0.349749	−	0.605782i
$305$	−18.4641	−	15.0759i	−1.05725	−	0.863242i
$306$		0			0
$307$		−	25.8719i		−	1.47659i	−0.674478	−	0.738295i	$-0.735631\pi$
$307$		−	25.8719i		−	1.47659i	0.674478	−	0.738295i	$-0.264369\pi$
$308$	6.36396	−	3.67423i	0.362620	−	0.209359i
$309$		0			0
$310$	4.18482	+	11.0349i	0.237682	+	0.626741i
$311$	14.0263	−	24.2942i	0.795357	−	1.37760i	−0.127255	−	0.991870i	$-0.540617\pi$
$311$	14.0263	−	24.2942i	0.795357	−	1.37760i	0.922612	−	0.385729i	$-0.126050\pi$
$312$		0			0
$313$	4.81105	−	2.77766i	0.271936	−	0.157003i	−0.357831	−	0.933786i	$-0.616484\pi$
$313$	4.81105	−	2.77766i	0.271936	−	0.157003i	0.629767	+	0.776784i	$0.283150\pi$
$314$	−41.3205			−2.33185
$315$		0			0
$316$	0.928203			0.0522155
$317$	−30.4428	+	17.5761i	−1.70984	+	0.987174i	−0.775094	+	0.631846i	$0.782297\pi$
$317$	−30.4428	+	17.5761i	−1.70984	+	0.987174i	−0.934742	+	0.355328i	$0.884369\pi$
$318$		0			0
$319$	15.2942	−	26.4904i	0.856312	−	1.48318i
$320$	11.9844	−	4.54490i	0.669948	−	0.254068i
$321$		0			0
$322$	−2.89778	+	1.67303i	−0.161487	+	0.0932345i
$323$			1.03528i			0.0576043i
$324$		0			0
$325$	12.0000	−	2.44949i	0.665640	−	0.135873i
$326$	−18.2942	−	31.6865i	−1.01322	−	1.75495i
$327$		0			0
$328$	−1.91327	−	1.10463i	−0.105643	−	0.0609928i
$329$	−1.96410	+	3.40192i	−0.108284	+	0.187554i
$330$		0			0
$331$	−6.19615	−	10.7321i	−0.340571	−	0.589887i	0.643968	−	0.765053i	$-0.277287\pi$
$331$	−6.19615	−	10.7321i	−0.340571	−	0.589887i	−0.984539	+	0.175166i	$0.943954\pi$
$332$			18.0430i			0.990238i
$333$		0			0
$334$	32.8564			1.79782
$335$	11.3428	+	1.84354i	0.619723	+	0.100723i
$336$		0			0
$337$	−1.55291	−	0.896575i	−0.0845926	−	0.0488396i	0.457107	−	0.889412i	$-0.348886\pi$
$337$	−1.55291	−	0.896575i	−0.0845926	−	0.0488396i	−0.541700	+	0.840572i	$0.682219\pi$
$338$	11.7112	+	6.76148i	0.637007	+	0.367776i
$339$		0			0
$340$	−1.44861	−	0.235442i	−0.0785619	−	0.0127686i
$341$	12.9282			0.700101
$342$		0			0
$343$			11.8313i			0.638833i
$344$	2.36603	+	4.09808i	0.127568	+	0.220953i
$345$		0			0
$346$	−0.732051	+	1.26795i	−0.0393553	+	0.0681654i
$347$	−8.57321	−	4.94975i	−0.460234	−	0.265716i	0.251909	−	0.967751i	$-0.418942\pi$
$347$	−8.57321	−	4.94975i	−0.460234	−	0.265716i	−0.712143	+	0.702035i	$0.752275\pi$
$348$		0			0
$349$	10.7679	+	18.6506i	0.576395	+	0.998346i	0.995889	+	0.0905872i	$0.0288744\pi$
$349$	10.7679	+	18.6506i	0.576395	+	0.998346i	−0.419493	+	0.907758i	$0.637792\pi$
$350$	1.73205	+	8.48528i	0.0925820	+	0.453557i
$351$		0			0
$352$		−	35.9101i		−	1.91402i
$353$	−7.82894	+	4.52004i	−0.416693	+	0.240578i	−0.693661	−	0.720301i	$-0.744004\pi$
$353$	−7.82894	+	4.52004i	−0.416693	+	0.240578i	0.276969	+	0.960879i	$0.410670\pi$
$354$		0			0
$355$	−7.95297	+	3.01604i	−0.422100	+	0.160075i
$356$	−6.40192	+	11.0885i	−0.339301	+	0.587687i
$357$		0			0
$358$	−41.1373	+	23.7506i	−2.17417	+	1.25526i
$359$	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
$362$	−14.1607	+	8.17569i	−0.744271	+	0.429705i
$363$		0			0
$364$	1.90192	−	3.29423i	0.0996879	−	0.172664i
$365$	−6.72792	−	17.7408i	−0.352156	−	0.928595i
$366$		0			0
$367$	21.4770	−	12.3998i	1.12109	−	0.647262i	0.179411	−	0.983774i	$-0.442581\pi$
$367$	21.4770	−	12.3998i	1.12109	−	0.647262i	0.941679	+	0.336512i	$0.109247\pi$
$368$			8.62398i			0.449556i
$369$		0			0
$370$	14.1962	+	11.5911i	0.738023	+	0.602593i
$371$	1.73205	+	3.00000i	0.0899236	+	0.155752i
$372$		0			0
$373$	27.8410	+	16.0740i	1.44155	+	0.832280i	0.997953	−	0.0639468i	$-0.0203688\pi$
$373$	27.8410	+	16.0740i	1.44155	+	0.832280i	0.443597	+	0.896226i	$0.353702\pi$
$374$	−1.73205	+	3.00000i	−0.0895622	+	0.155126i
$375$		0			0
$376$	1.13397	+	1.96410i	0.0584803	+	0.101291i
$377$		−	15.8338i		−	0.815480i
$378$		0			0
$379$	−12.5359			−0.643926			−0.321963	−	0.946752i	$-0.604343\pi$
$379$	−12.5359			−0.643926			−0.321963	+	0.946752i	$0.604343\pi$
$380$	−1.69748	+	10.4441i	−0.0870788	+	0.535773i
$381$		0			0
$382$	−0.568406	−	0.328169i	−0.0290822	−	0.0167906i
$383$	17.7148	+	10.2277i	0.905186	+	0.522609i	0.878879	−	0.477045i	$-0.158292\pi$
$383$	17.7148	+	10.2277i	0.905186	+	0.522609i	0.0263067	+	0.999654i	$0.491625\pi$
$384$		0			0
$385$	9.36396	+	1.52192i	0.477232	+	0.0775641i
$386$	40.0526			2.03862
$387$		0			0
$388$			17.8028i			0.903799i
$389$	12.0622	+	20.8923i	0.611577	+	1.05928i	0.990975	+	0.134048i	$0.0427978\pi$
$389$	12.0622	+	20.8923i	0.611577	+	1.05928i	−0.379398	+	0.925234i	$0.623869\pi$
$390$		0			0
$391$	0.366025	−	0.633975i	0.0185107	−	0.0320615i
$392$	2.77766	+	1.60368i	0.140293	+	0.0809982i
$393$		0			0
$394$	−20.1244	−	34.8564i	−1.01385	−	1.75604i
$395$	0.928203	+	0.757875i	0.0467030	+	0.0381328i
$396$		0			0
$397$			29.3939i			1.47524i	0.675218	+	0.737618i	$0.264050\pi$
$397$			29.3939i			1.47524i	−0.675218	+	0.737618i	$0.735950\pi$
$398$	7.67664	−	4.43211i	0.384795	−	0.222162i
$399$		0			0
$400$	21.1716	+	7.06875i	1.05858	+	0.353437i
$401$	−15.4641	+	26.7846i	−0.772240	+	1.33756i	0.164092	+	0.986445i	$0.447531\pi$
$401$	−15.4641	+	26.7846i	−0.772240	+	1.33756i	−0.936333	+	0.351115i	$0.885803\pi$
$402$		0			0
$403$	5.79555	−	3.34607i	0.288697	−	0.166679i
$404$	4.39230			0.218525
$405$		0			0
$406$	11.1962			0.555656
$407$	17.3867	−	10.0382i	0.861825	−	0.497575i
$408$		0			0
$409$	−11.7321	+	20.3205i	−0.580113	+	1.00478i	0.415353	+	0.909660i	$0.363658\pi$
$409$	−11.7321	+	20.3205i	−0.580113	+	1.00478i	−0.995465	+	0.0951241i	$0.969675\pi$
$410$	6.53744	+	17.2385i	0.322861	+	0.851349i
$411$		0			0
$412$	−13.7124	+	7.91688i	−0.675563	+	0.390036i
$413$			2.27362i			0.111878i
$414$		0			0
$415$	−14.7321	+	18.0430i	−0.723168	+	0.885696i
$416$	−9.29423	−	16.0981i	−0.455687	−	0.789273i
$417$		0			0
$418$	21.6293	+	12.4877i	1.05792	+	0.610793i
$419$	8.02628	−	13.9019i	0.392109	−	0.679153i	−0.600618	−	0.799536i	$-0.705079\pi$
$419$	8.02628	−	13.9019i	0.392109	−	0.679153i	0.992728	+	0.120383i	$0.0384121\pi$
$420$		0			0
$421$	6.26795	+	10.8564i	0.305481	+	0.529109i	0.977368	−	0.211545i	$-0.0678494\pi$
$421$	6.26795	+	10.8564i	0.305481	+	0.529109i	−0.671887	+	0.740653i	$0.734516\pi$
$422$			25.3543i			1.23423i
$423$		0			0
$424$	2.00000			0.0971286
$425$	−1.25637	−	1.41823i	−0.0609430	−	0.0687941i
$426$		0			0
$427$	−8.27723	−	4.77886i	−0.400563	−	0.231265i
$428$	−17.5947	−	10.1583i	−0.850473	−	0.491021i
$429$		0			0
$430$	6.33508	−	38.9781i	0.305505	−	1.87969i
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$		0			0
$433$		−	30.5307i		−	1.46721i	−0.679575	−	0.733606i	$-0.737836\pi$
$433$		−	30.5307i		−	1.46721i	0.679575	−	0.733606i	$-0.262164\pi$
$434$	2.36603	+	4.09808i	0.113573	+	0.196714i
$435$		0			0
$436$	4.03590	−	6.99038i	0.193284	−	0.334779i
$437$	−4.57081	−	2.63896i	−0.218651	−	0.126239i
$438$		0			0
$439$	4.66025	+	8.07180i	0.222422	+	0.385246i	0.955543	−	0.294852i	$-0.0952705\pi$
$439$	4.66025	+	8.07180i	0.222422	+	0.385246i	−0.733121	+	0.680098i	$0.761937\pi$
$440$	3.46410	−	4.24264i	0.165145	−	0.202260i
$441$		0			0
$442$			1.79315i			0.0852915i
$443$	12.0394	−	6.95095i	0.572009	−	0.330250i	−0.185942	−	0.982561i	$-0.559534\pi$
$443$	12.0394	−	6.95095i	0.572009	−	0.330250i	0.757951	+	0.652311i	$0.226200\pi$
$444$		0			0
$445$	−15.4556	+	5.86131i	−0.732666	+	0.277853i
$446$	−16.1603	+	27.9904i	−0.765210	+	1.32538i
$447$		0			0
$448$	4.45069	−	2.56961i	0.210275	−	0.121403i
$449$	−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
$452$	−3.82654	+	2.20925i	−0.179985	+	0.103915i
$453$		0			0
$454$	−1.83013	+	3.16987i	−0.0858921	+	0.148770i
$455$	4.59165	−	1.74131i	0.215260	−	0.0816341i
$456$		0			0
$457$	−29.9623	+	17.2987i	−1.40158	+	0.809201i	−0.994554	−	0.104218i	$-0.966766\pi$
$457$	−29.9623	+	17.2987i	−1.40158	+	0.809201i	−0.407022	+	0.913418i	$0.633433\pi$
$458$			38.4983i			1.79891i
$459$		0			0
$460$	4.73205	−	5.79555i	0.220633	−	0.270219i
$461$	9.35641	+	16.2058i	0.435771	+	0.754778i	0.997358	−	0.0726397i	$-0.0231423\pi$
$461$	9.35641	+	16.2058i	0.435771	+	0.754778i	−0.561587	+	0.827418i	$0.689809\pi$
$462$		0			0
$463$	0.152304	+	0.0879327i	0.00707816	+	0.00408658i	0.503535	−	0.863975i	$-0.332033\pi$
$463$	0.152304	+	0.0879327i	0.00707816	+	0.00408658i	−0.496457	+	0.868061i	$0.665366\pi$
$464$	14.4282	−	24.9904i	0.669813	−	1.16015i
$465$		0			0
$466$	6.83013	+	11.8301i	0.316400	+	0.548020i
$467$		−	5.75839i		−	0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$467$		−	5.75839i		−	0.266467i	0.991085	−	0.133233i	$-0.0425359\pi$
$468$		0			0
$469$	4.60770			0.212764
$470$	3.03624	−	18.6812i	0.140051	−	0.861698i
$471$		0			0
$472$	1.13681	+	0.656339i	0.0523260	+	0.0302104i
$473$	−37.4631	−	21.6293i	−1.72255	−	0.994517i
$474$		0			0
$475$	−10.2251	+	9.05816i	−0.469159	+	0.415617i
$476$	−0.588457			−0.0269719
$477$		0			0
$478$		−	24.9754i		−	1.14235i
$479$	−15.9282	−	27.5885i	−0.727778	−	1.26055i	−0.957820	−	0.287368i	$-0.907220\pi$
$479$	−15.9282	−	27.5885i	−0.727778	−	1.26055i	0.230042	−	0.973181i	$-0.426114\pi$
$480$		0			0
$481$	5.19615	−	9.00000i	0.236924	−	0.410365i
$482$	10.4865	+	6.05437i	0.477646	+	0.275769i
$483$		0			0
$484$	9.86603	+	17.0885i	0.448456	+	0.776748i
$485$	−14.5359	+	17.8028i	−0.660041	+	0.808382i
$486$		0			0
$487$			1.13681i			0.0515139i	0.999668	+	0.0257569i	$0.00819959\pi$
$487$			1.13681i			0.0515139i	−0.999668	+	0.0257569i	$0.991800\pi$
$488$	−4.77886	+	2.75908i	−0.216329	+	0.124898i
$489$		0			0
$490$	−9.49097	−	25.0266i	−0.428758	−	1.13059i
$491$	−10.8564	+	18.8038i	−0.489943	+	0.848606i	−0.999933	−	0.0115744i	$-0.996316\pi$
$491$	−10.8564	+	18.8038i	−0.489943	+	0.848606i	0.509990	+	0.860180i	$0.329649\pi$
$492$		0			0
$493$	−2.12132	+	1.22474i	−0.0955395	+	0.0551597i
$494$	12.9282			0.581667
$495$		0			0
$496$	12.1962			0.547623
$497$	−2.95352	+	1.70522i	−0.132484	+	0.0764895i
$498$		0			0
$499$	−1.92820	+	3.33975i	−0.0863182	+	0.149508i	−0.905952	−	0.423380i	$-0.860844\pi$
$499$	−1.92820	+	3.33975i	−0.0863182	+	0.149508i	0.819634	+	0.572888i	$0.194177\pi$
$500$	−10.3492	−	16.3674i	−0.462832	−	0.731974i
$501$		0			0
$502$	31.0991	−	17.9551i	1.38802	−	0.801374i
$503$		−	29.3567i		−	1.30895i	−0.756083	−	0.654476i	$-0.772889\pi$
$503$		−	29.3567i		−	1.30895i	0.756083	−	0.654476i	$-0.227111\pi$
$504$		0			0
$505$	4.39230	+	3.58630i	0.195455	+	0.159588i
$506$	−8.83013	−	15.2942i	−0.392547	−	0.679911i
$507$		0			0
$508$	−6.98811	−	4.03459i	−0.310047	−	0.179006i
$509$	5.42820	−	9.40192i	0.240601	−	0.416733i	−0.720285	−	0.693679i	$-0.755989\pi$
$509$	5.42820	−	9.40192i	0.240601	−	0.416733i	0.960886	+	0.276946i	$0.0893222\pi$
$510$		0			0
$511$	−3.80385	−	6.58846i	−0.168272	−	0.291456i
$512$		−	29.2552i		−	1.29291i
$513$		0			0
$514$	−43.3205			−1.91079
$515$	−20.1765	−	3.27928i	−0.889084	−	0.144502i
$516$		0			0
$517$	−17.9551	−	10.3664i	−0.789663	−	0.455912i
$518$	6.36396	+	3.67423i	0.279616	+	0.161437i
$519$		0			0
$520$	0.454838	−	2.79850i	0.0199460	−	0.122722i
$521$	−1.39230			−0.0609980			−0.0304990	−	0.999535i	$-0.509710\pi$
$521$	−1.39230			−0.0609980			−0.0304990	+	0.999535i	$0.509710\pi$
$522$		0			0
$523$		−	30.9468i		−	1.35321i	−0.736347	−	0.676604i	$-0.763451\pi$
$523$		−	30.9468i		−	1.35321i	0.736347	−	0.676604i	$-0.236549\pi$
$524$	0.803848	+	1.39230i	0.0351162	+	0.0608231i
$525$		0			0
$526$	−7.36603	+	12.7583i	−0.321174	+	0.556290i
$527$	−0.896575	−	0.517638i	−0.0390554	−	0.0225487i
$528$		0			0
$529$	−9.63397	−	16.6865i	−0.418868	−	0.725501i
$530$	−12.9282	−	10.5558i	−0.561565	−	0.458516i
$531$		0			0
$532$			4.24264i			0.183942i
$533$	9.05369	−	5.22715i	0.392159	−	0.226413i
$534$		0			0
$535$	−9.30049	−	24.5243i	−0.402095	−	1.06028i
$536$	1.33013	−	2.30385i	0.0574527	−	0.0995111i
$537$		0			0
$538$	−28.7697	+	16.6102i	−1.24035	+	0.716117i
$539$	−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	$0.347898\pi$
$542$	39.3441	−	22.7153i	1.68998	−	0.975708i
$543$		0			0
$544$	−1.43782	+	2.49038i	−0.0616461	+	0.106774i
$545$	9.74352	−	3.69508i	0.417367	−	0.158280i
$546$		0			0
$547$	26.2323	−	15.1452i	1.12161	−	0.647563i	0.179800	−	0.983703i	$-0.442455\pi$
$547$	26.2323	−	15.1452i	1.12161	−	0.647563i	0.941812	+	0.336140i	$0.109122\pi$
$548$		−	32.1480i		−	1.37329i
$549$		0			0
$550$	−44.7846	+	9.14162i	−1.90962	+	0.389800i
$551$	8.83013	+	15.2942i	0.376176	+	0.651556i
$552$		0			0
$553$	0.416102	+	0.240237i	0.0176945	+	0.0102159i
$554$	11.8301	−	20.4904i	0.502614	−	0.870553i
$555$		0			0
$556$	6.92820	+	12.0000i	0.293821	+	0.508913i
$557$			31.1127i			1.31829i	0.752017	+	0.659144i	$0.229081\pi$
$557$			31.1127i			1.31829i	−0.752017	+	0.659144i	$0.770919\pi$
$558$		0			0
$559$	−22.3923			−0.947094
$560$	8.83373	+	1.43574i	0.373293	+	0.0606711i
$561$		0			0
$562$	27.2168	+	15.7136i	1.14807	+	0.662840i
$563$	23.8707	+	13.7818i	1.00603	+	0.580833i	0.910027	−	0.414548i	$-0.136060\pi$
$563$	23.8707	+	13.7818i	1.00603	+	0.580833i	0.0960045	+	0.995381i	$0.469394\pi$
$564$		0			0
$565$	−5.63039	−	0.915103i	−0.236872	−	0.0384987i
$566$	8.66025			0.364018
$567$		0			0
$568$			1.96902i			0.0826181i
$569$	2.66025	+	4.60770i	0.111524	+	0.193165i	0.916385	−	0.400299i	$-0.131094\pi$
$569$	2.66025	+	4.60770i	0.111524	+	0.193165i	−0.804861	+	0.593463i	$0.797760\pi$
$570$		0			0
$571$	−2.73205	+	4.73205i	−0.114333	+	0.198030i	−0.917513	−	0.397706i	$-0.869806\pi$
$571$	−2.73205	+	4.73205i	−0.114333	+	0.198030i	0.803180	+	0.595736i	$0.203140\pi$
$572$	17.3867	+	10.0382i	0.726973	+	0.419718i
$573$		0			0
$574$	3.69615	+	6.40192i	0.154274	+	0.267211i
$575$	9.46410	−	1.93185i	0.394680	−	0.0805638i
$576$		0			0
$577$			28.5617i			1.18904i	0.804082	+	0.594519i	$0.202657\pi$
$577$			28.5617i			1.18904i	−0.804082	+	0.594519i	$0.797343\pi$
$578$	−28.2013	+	16.2820i	−1.17302	+	0.677244i
$579$		0			0
$580$	−23.4086	+	8.87735i	−0.971988	+	0.368612i
$581$	−4.66987	+	8.08846i	−0.193739	+	0.335566i
$582$		0			0
$583$	−15.8338	+	9.14162i	−0.655767	+	0.378607i
$584$	−4.39230			−0.181755
$585$		0			0
$586$	−17.1244			−0.707401
$587$	−19.0597	+	11.0041i	−0.786678	+	0.454189i	−0.838792	−	0.544452i	$-0.816737\pi$
$587$	−19.0597	+	11.0041i	−0.786678	+	0.454189i	0.0521138	+	0.998641i	$0.483404\pi$
$588$		0			0
$589$	−3.73205	+	6.46410i	−0.153776	+	0.266349i
$590$	−3.88437	−	10.2426i	−0.159917	−	0.421683i
$591$		0			0
$592$	16.4022	−	9.46979i	0.674124	−	0.389206i
$593$		−	28.9406i		−	1.18845i	−0.804299	−	0.594224i	$-0.797459\pi$
$593$		−	28.9406i		−	1.18845i	0.804299	−	0.594224i	$-0.202541\pi$
$594$		0			0
$595$	−0.588457	−	0.480473i	−0.0241244	−	0.0196975i
$596$	6.69615	+	11.5981i	0.274285	+	0.475076i
$597$		0			0
$598$	−7.91688	−	4.57081i	−0.323745	−	0.186914i
$599$	−16.8564	+	29.1962i	−0.688734	+	1.19292i	0.283514	+	0.958968i	$0.408500\pi$
$599$	−16.8564	+	29.1962i	−0.688734	+	1.19292i	−0.972248	+	0.233954i	$0.924833\pi$
$600$		0			0
$601$	8.46410	+	14.6603i	0.345258	+	0.598004i	0.985401	−	0.170252i	$-0.0544581\pi$
$601$	8.46410	+	14.6603i	0.345258	+	0.598004i	−0.640143	+	0.768256i	$0.721125\pi$
$602$		−	15.8338i		−	0.645335i
$603$		0			0
$604$	39.1244			1.59195
$605$	−4.08664	+	25.1440i	−0.166146	+	1.02225i
$606$		0			0
$607$	−7.55652	−	4.36276i	−0.306710	−	0.177079i	0.338743	−	0.940879i	$-0.389998\pi$
$607$	−7.55652	−	4.36276i	−0.306710	−	0.177079i	−0.645453	+	0.763800i	$0.723331\pi$
$608$	17.9551	+	10.3664i	0.728174	+	0.420412i
$609$		0			0
$610$	45.4532	+	7.38748i	1.84035	+	0.299110i
$611$	−10.7321			−0.434172
$612$		0			0
$613$			24.3190i			0.982236i	0.871093	+	0.491118i	$0.163412\pi$
$613$			24.3190i			0.982236i	−0.871093	+	0.491118i	$0.836588\pi$
$614$	24.9904	+	43.2846i	1.00853	+	1.74682i
$615$		0			0
$616$	1.09808	−	1.90192i	0.0442428	−	0.0766307i
$617$	11.3509	+	6.55343i	0.456969	+	0.263831i	0.710769	−	0.703426i	$-0.248347\pi$
$617$	11.3509	+	6.55343i	0.456969	+	0.263831i	−0.253800	+	0.967257i	$0.581680\pi$
$618$		0			0
$619$	9.90192	+	17.1506i	0.397992	+	0.689342i	0.993478	−	0.114023i	$-0.0363739\pi$
$619$	9.90192	+	17.1506i	0.397992	+	0.689342i	−0.595486	+	0.803366i	$0.703041\pi$
$620$	−8.19615	−	6.69213i	−0.329165	−	0.268762i
$621$		0			0
$622$			54.1934i			2.17296i
$623$	−5.73981	+	3.31388i	−0.229961	+	0.132768i
$624$		0			0
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	−5.36603	+	9.29423i	−0.214470	+	0.371472i
$627$		0			0
$628$	32.0836	−	18.5235i	1.28028	−	0.739167i
$629$	−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	$0.730817\pi$
$632$	0.240237	−	0.138701i	0.00955610	−	0.00551722i
$633$		0			0
$634$	33.9545	−	58.8109i	1.34850	−	2.33568i
$635$	−3.69389	−	9.74036i	−0.146587	−	0.386534i
$636$		0			0
$637$	−13.1440	+	7.58871i	−0.520785	+	0.300675i
$638$			59.0924i			2.33949i
$639$		0			0
$640$	5.80385	−	7.10823i	0.229417	−	0.280978i
$641$	−12.5263	−	21.6962i	−0.494758	−	0.856946i	0.505223	−	0.862989i	$-0.331410\pi$
$641$	−12.5263	−	21.6962i	−0.494758	−	0.856946i	−0.999982	+	0.00604207i	$0.998077\pi$
$642$		0			0
$643$	21.8374	+	12.6078i	0.861181	+	0.497203i	0.864408	−	0.502792i	$-0.167694\pi$
$643$	21.8374	+	12.6078i	0.861181	+	0.497203i	−0.00322641	+	0.999995i	$0.501027\pi$
$644$	1.50000	−	2.59808i	0.0591083	−	0.102379i
$645$		0			0
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$		−	12.3861i		−	0.486950i	−0.969907	−	0.243475i	$-0.921713\pi$
$647$		−	12.3861i		−	0.486950i	0.969907	−	0.243475i	$-0.0782873\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	−17.7104	+	15.6892i	−0.694658	+	0.615381i
$651$		0			0
$652$	28.4094	+	16.4022i	1.11260	+	0.642358i
$653$	−0.392541	−	0.226633i	−0.0153613	−	0.00886885i	0.492300	−	0.870426i	$-0.336156\pi$
$653$	−0.392541	−	0.226633i	−0.0153613	−	0.00886885i	−0.507661	+	0.861557i	$0.669490\pi$
$654$		0			0
$655$	−0.332965	+	2.04864i	−0.0130100	+	0.0800471i
$656$	19.0526			0.743877
$657$		0			0
$658$		−	7.58871i		−	0.295839i
$659$	−18.1244	−	31.3923i	−0.706025	−	1.22287i	−0.966320	−	0.257342i	$-0.917153\pi$
$659$	−18.1244	−	31.3923i	−0.706025	−	1.22287i	0.260296	−	0.965529i	$-0.416180\pi$
$660$		0			0
$661$	15.3923	−	26.6603i	0.598691	−	1.03696i	−0.394323	−	0.918972i	$-0.629021\pi$
$661$	15.3923	−	26.6603i	0.598691	−	1.03696i	0.993015	−	0.117992i	$-0.0376457\pi$
$662$	20.7327	+	11.9700i	0.805800	+	0.465229i
$663$		0			0
$664$	2.69615	+	4.66987i	0.104631	+	0.181226i
$665$	−3.46410	+	4.24264i	−0.134332	+	0.164523i
$666$		0			0
$667$		−	12.4877i		−	0.483525i
$668$	−25.5116	+	14.7291i	−0.987073	+	0.569887i
$669$		0			0
$670$	−20.7576	+	7.87201i	−0.801936	+	0.304122i
$671$	25.2224	−	43.6865i	0.973701	−	1.68650i
$672$		0			0
$673$	1.40061	−	0.808643i	0.0539896	−	0.0311709i	−0.472762	−	0.881190i	$-0.656743\pi$
$673$	1.40061	−	0.808643i	0.0539896	−	0.0311709i	0.526752	+	0.850019i	$0.323410\pi$
$674$	3.46410			0.133432
$675$		0			0
$676$	−12.1244			−0.466321
$677$	28.6496	−	16.5409i	1.10109	−	0.635717i	0.164586	−	0.986363i	$-0.447371\pi$
$677$	28.6496	−	16.5409i	1.10109	−	0.635717i	0.936508	+	0.350646i	$0.114038\pi$
$678$		0			0
$679$	−4.60770	+	7.98076i	−0.176827	+	0.306274i
$680$	−0.410110	+	0.155528i	−0.0157270	+	0.00596422i
$681$		0			0
$682$	−21.6293	+	12.4877i	−0.828229	+	0.478178i
$683$			19.6975i			0.753702i	0.926274	+	0.376851i	$0.122993\pi$
$683$			19.6975i			0.753702i	−0.926274	+	0.376851i	$0.877007\pi$
$684$		0			0
$685$	26.2487	−	32.1480i	1.00291	−	1.22831i
$686$	−11.4282	−	19.7942i	−0.436331	−	0.755747i
$687$		0			0
$688$	−35.3417	−	20.4046i	−1.34739	−	0.777917i
$689$	−4.73205	+	8.19615i	−0.180277	+	0.312249i
$690$		0			0
$691$	−10.1244	−	17.5359i	−0.385149	−	0.667097i	0.606641	−	0.794976i	$-0.292516\pi$
$691$	−10.1244	−	17.5359i	−0.385149	−	0.667097i	−0.991790	+	0.127879i	$0.959183\pi$
$692$		−	1.31268i		−	0.0499005i
$693$		0			0
$694$	19.1244			0.725951
$695$	−2.86976	+	17.6569i	−0.108856	+	0.669763i
$696$		0			0
$697$	−1.40061	−	0.808643i	−0.0530519	−	0.0306295i
$698$	−36.0303	−	20.8021i	−1.36377	−	0.787370i
$699$		0			0
$700$	−5.14871	−	5.81200i	−0.194603	−	0.219673i
$701$	23.1962			0.876107			0.438053	−	0.898949i	$-0.355668\pi$
$701$	23.1962			0.876107			0.438053	+	0.898949i	$0.355668\pi$
$702$		0			0
$703$			11.5911i			0.437167i
$704$	13.5622	+	23.4904i	0.511144	+	0.885327i
$705$		0			0
$706$	8.73205	−	15.1244i	0.328635	−	0.569213i
$707$	1.96902	+	1.13681i	0.0740525	+	0.0427542i
$708$		0			0
$709$	−15.8923	−	27.5263i	−0.596848	−	1.03377i	−0.993283	−	0.115708i	$-0.963086\pi$
$709$	−15.8923	−	27.5263i	−0.596848	−	1.03377i	0.396435	−	0.918063i	$-0.370247\pi$
$710$	10.3923	−	12.7279i	0.390016	−	0.477670i
$711$		0			0
$712$			3.82654i			0.143406i
$713$	4.57081	−	2.63896i	0.171178	−	0.0988298i
$714$		0			0
$715$	9.19051	+	24.2343i	0.343706	+	0.906313i
$716$	21.2942	−	36.8827i	0.795803	−	1.37837i
$717$		0			0
$718$	−16.4022	+	9.46979i	−0.612123	+	0.353409i
$719$	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
$722$	19.2999	−	11.1428i	0.718269	−	0.414693i
$723$		0			0
$724$	7.33013	−	12.6962i	0.272422	−	0.471849i
$725$	−30.6569	−	10.2357i	−1.13857	−	0.380143i
$726$		0			0
$727$	24.5271	−	14.1607i	0.909659	−	0.525192i	0.0293377	−	0.999570i	$-0.490660\pi$
$727$	24.5271	−	14.1607i	0.909659	−	0.525192i	0.880321	+	0.474378i	$0.157327\pi$
$728$		−	1.13681i		−	0.0421331i
$729$		0			0
$730$	28.3923	+	23.1822i	1.05085	+	0.858012i
$731$	1.73205	+	3.00000i	0.0640622	+	0.110959i
$732$		0			0
$733$	35.9101	+	20.7327i	1.32637	+	0.765781i	0.984736	−	0.174052i	$-0.0556861\pi$
$733$	35.9101	+	20.7327i	1.32637	+	0.765781i	0.341635	+	0.939833i	$0.389019\pi$
$734$	−23.9545	+	41.4904i	−0.884176	+	1.53144i
$735$		0			0
$736$	−7.33013	−	12.6962i	−0.270192	−	0.467986i
$737$			24.3190i			0.895803i
$738$		0			0
$739$	45.8564			1.68686			0.843428	−	0.537243i	$-0.180534\pi$
$739$	45.8564			1.68686			0.843428	+	0.537243i	$0.180534\pi$
$740$	−16.2189	−	2.63604i	−0.596217	−	0.0969027i
$741$		0			0
$742$	−5.79555	−	3.34607i	−0.212762	−	0.122838i
$743$	−21.9253	−	12.6586i	−0.804361	−	0.464398i	0.0406329	−	0.999174i	$-0.487063\pi$
$743$	−21.9253	−	12.6586i	−0.804361	−	0.464398i	−0.844994	+	0.534776i	$0.820396\pi$
$744$		0			0
$745$	−2.77364	+	17.0655i	−0.101618	+	0.625230i
$746$	−62.1051			−2.27383
$747$		0			0
$748$		−	3.10583i		−	0.113560i
$749$	−5.25833	−	9.10770i	−0.192135	−	0.332788i
$750$		0			0
$751$	−17.2224	+	29.8301i	−0.628455	+	1.08852i	0.359406	+	0.933181i	$0.382979\pi$
$751$	−17.2224	+	29.8301i	−0.628455	+	1.08852i	−0.987862	+	0.155336i	$0.950354\pi$
$752$	−16.9384	−	9.77938i	−0.617679	−	0.356617i
$753$		0			0
$754$	15.2942	+	26.4904i	0.556983	+	0.964723i
$755$	39.1244	+	31.9449i	1.42388	+	1.16259i
$756$		0			0
$757$			7.34847i			0.267085i	0.991043	+	0.133542i	$0.0426352\pi$
$757$			7.34847i			0.267085i	−0.991043	+	0.133542i	$0.957365\pi$
$758$	20.9730	−	12.1087i	0.761772	−	0.439810i
$759$		0			0
$760$	1.12132	+	2.95680i	0.0406746	+	0.107254i
$761$	1.03590	−	1.79423i	0.0375513	−	0.0650407i	−0.846639	−	0.532168i	$-0.821378\pi$
$761$	1.03590	−	1.79423i	0.0375513	−	0.0650407i	0.884190	+	0.467127i	$0.154711\pi$
$762$		0			0
$763$	3.61849	−	2.08913i	0.130998	−	0.0756318i
$764$	0.588457			0.0212896
$765$		0			0
$766$	−39.5167			−1.42779
$767$	−5.37945	+	3.10583i	−0.194241	+	0.112145i
$768$		0			0
$769$	−13.8205	+	23.9378i	−0.498380	+	0.863220i	−0.999998	−	0.00186930i	$-0.999405\pi$
$769$	−13.8205	+	23.9378i	−0.498380	+	0.863220i	0.501618	+	0.865089i	$0.332738\pi$
$770$	−17.1363	+	6.49867i	−0.617548	+	0.234196i
$771$		0			0
$772$	−31.0991	+	17.9551i	−1.11928	+	0.646217i
$773$		−	7.72741i		−	0.277935i	−0.990297	−	0.138968i	$-0.955622\pi$
$773$		−	7.72741i		−	0.277935i	0.990297	−	0.138968i	$-0.0443784\pi$
$774$		0			0
$775$	−2.73205	−	13.3843i	−0.0981382	−	0.480777i
$776$	2.66025	+	4.60770i	0.0954976	+	0.165407i
$777$		0			0
$778$	−40.3608	−	23.3023i	−1.44701	−	0.835429i
$779$	−5.83013	+	10.0981i	−0.208886	+	0.361801i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$			1.41421i			0.0505722i
$783$		0			0
$784$	−27.6603			−0.987866
$785$	47.2080	+	7.67268i	1.68492	+	0.273850i
$786$		0			0
$787$	14.1285	+	8.15711i	0.503628	+	0.290770i	0.730210	−	0.683222i	$-0.239422\pi$
$787$	14.1285	+	8.15711i	0.503628	+	0.290770i	−0.226583	+	0.973992i	$0.572755\pi$
$788$	31.2514	+	18.0430i	1.11328	+	0.642755i
$789$		0			0
$790$	−2.28497	−	0.371374i	−0.0812954	−	0.0132129i
$791$	−2.28719			−0.0813230
$792$		0			0
$793$		−	26.1122i		−	0.927271i
$794$	−28.3923	−	49.1769i	−1.00761	−	1.74522i
$795$		0			0
$796$	−3.97372	+	6.88269i	−0.140845	+	0.243950i
$797$	13.7768	+	7.95404i	0.487999	+	0.281747i	0.723744	−	0.690068i	$-0.242420\pi$
$797$	13.7768	+	7.95404i	0.487999	+	0.281747i	−0.235745	+	0.971815i	$0.575753\pi$
$798$		0			0
$799$	0.830127	+	1.43782i	0.0293678	+	0.0508665i
$800$	−37.1769	+	7.58871i	−1.31440	+	0.268301i
$801$		0			0
$802$		−	59.7487i		−	2.10980i
$803$	34.7733	−	20.0764i	1.22712	−	0.708480i
$804$		0			0
$805$	3.62132	−	1.37333i	0.127635	−	0.0484036i
$806$	−6.46410	+	11.1962i	−0.227688	+	0.394368i
$807$		0			0
$808$	1.13681	−	0.656339i	0.0399929	−	0.0230899i
$809$	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	$0.222758\pi$
$812$	−8.69333	+	5.01910i	−0.305076	+	0.176136i
$813$		0			0
$814$	−19.3923	+	33.5885i	−0.679700	+	1.17727i
$815$	15.0171	+	39.5983i	0.526025	+	1.38707i
$816$		0			0
$817$	21.6293	−	12.4877i	0.756714	−	0.436889i
$818$		−	45.3292i		−	1.58490i
$819$		0			0
$820$	−12.8038	−	10.4543i	−0.447130	−	0.365080i
$821$	−14.7224	−	25.5000i	−0.513816	−	0.889956i	−0.999872	−	0.0160280i	$-0.994898\pi$
$821$	−14.7224	−	25.5000i	−0.513816	−	0.889956i	0.486055	−	0.873928i	$-0.338435\pi$
$822$		0			0
$823$	1.76097	+	1.01669i	0.0613834	+	0.0354397i	0.530378	−	0.847762i	$-0.322050\pi$
$823$	1.76097	+	1.01669i	0.0613834	+	0.0354397i	−0.468994	+	0.883201i	$0.655383\pi$
$824$	−2.36603	+	4.09808i	−0.0824244	+	0.142763i
$825$		0			0
$826$	−2.19615	−	3.80385i	−0.0764139	−	0.132353i
$827$		−	11.5539i		−	0.401770i	−0.979615	−	0.200885i	$-0.935618\pi$
$827$		−	11.5539i		−	0.401770i	0.979615	−	0.200885i	$-0.0643818\pi$
$828$		0			0
$829$	−31.5885			−1.09711			−0.548556	−	0.836114i	$-0.684822\pi$
$829$	−31.5885			−1.09711			−0.548556	+	0.836114i	$0.684822\pi$
$830$	7.21900	−	44.4166i	0.250575	−	1.54172i
$831$		0			0
$832$	12.1595	+	7.02030i	0.421555	+	0.243385i
$833$	2.03339	+	1.17398i	0.0704527	+	0.0406759i
$834$		0			0
$835$	−37.5379	−	6.10100i	−1.29905	−	0.211134i
$836$	−22.3923			−0.774454
$837$		0			0
$838$			31.0112i			1.07126i
$839$	−0.633975	−	1.09808i	−0.0218872	−	0.0379098i	0.854874	−	0.518835i	$-0.173634\pi$
$839$	−0.633975	−	1.09808i	−0.0218872	−	0.0379098i	−0.876762	+	0.480925i	$0.840301\pi$
$840$		0			0
$841$	−6.39230	+	11.0718i	−0.220424	+	0.381786i
$842$	−20.9730	−	12.1087i	−0.722776	−	0.417295i
$843$		0			0
$844$	−11.3660	−	19.6865i	−0.391235	−	0.677638i
$845$	−12.1244	−	9.89949i	−0.417091	−	0.340553i
$846$		0			0
$847$			10.2141i			0.350959i
$848$	−14.9372	+	8.62398i	−0.512945	+	0.296149i
$849$		0			0
$850$	3.47185	+	1.15918i	0.119084	+	0.0397594i
$851$	4.09808	−	7.09808i	0.140480	−	0.243319i
$852$		0			0
$853$	30.2669	−	17.4746i	1.03632	−	0.598319i	0.117530	−	0.993069i	$-0.462502\pi$
$853$	30.2669	−	17.4746i	1.03632	−	0.598319i	0.918788	+	0.394750i	$0.129169\pi$
$854$	18.4641			0.631829
$855$		0			0
$856$	−6.07180			−0.207530
$857$	−7.67664	+	4.43211i	−0.262229	+	0.151398i	−0.625351	−	0.780344i	$-0.715044\pi$
$857$	−7.67664	+	4.43211i	−0.262229	+	0.151398i	0.363122	+	0.931742i	$0.381711\pi$
$858$		0			0
$859$	−11.2224	+	19.4378i	−0.382904	+	0.663210i	−0.991476	−	0.130289i	$-0.958409\pi$
$859$	−11.2224	+	19.4378i	−0.382904	+	0.663210i	0.608572	+	0.793499i	$0.291743\pi$
$860$	12.5545	+	33.1047i	0.428104	+	1.12886i
$861$		0			0
$862$	−10.0382	+	5.79555i	−0.341902	+	0.197397i
$863$			13.0697i			0.444898i	0.974944	+	0.222449i	$0.0714050\pi$
$863$			13.0697i			0.444898i	−0.974944	+	0.222449i	$0.928595\pi$
$864$		0			0
$865$	1.07180	−	1.31268i	0.0364422	−	0.0446324i
$866$	29.4904	+	51.0788i	1.00212	+	1.73573i
$867$		0			0
$868$	−3.67423	−	2.12132i	−0.124712	−	0.0720023i
$869$	−1.26795	+	2.19615i	−0.0430122	+	0.0744994i
$870$		0			0
$871$	6.29423	+	10.9019i	0.213272	+	0.369398i
$872$		−	2.41233i		−	0.0816916i
$873$		0			0
$874$	10.1962			0.344890
$875$	−0.403233	−	10.0159i	−0.0136317	−	0.338599i
$876$		0			0
$877$	4.09034	+	2.36156i	0.138121	+	0.0797441i	0.567468	−	0.823395i	$-0.307923\pi$
$877$	4.09034	+	2.36156i	0.138121	+	0.0797441i	−0.429347	+	0.903139i	$0.641256\pi$
$878$	−15.5935	−	9.00292i	−0.526256	−	0.303834i
$879$		0			0
$880$	−7.57772	+	46.6237i	−0.255445	+	1.57168i
$881$	8.41154			0.283392			0.141696	−	0.989910i	$-0.454744\pi$
$881$	8.41154			0.283392			0.141696	+	0.989910i	$0.454744\pi$
$882$		0			0
$883$		−	17.6913i		−	0.595359i	−0.954666	−	0.297679i	$-0.903787\pi$
$883$		−	17.6913i		−	0.595359i	0.954666	−	0.297679i	$-0.0962126\pi$
$884$	−0.803848	−	1.39230i	−0.0270363	−	0.0468283i
$885$		0			0
$886$	−13.4282	+	23.2583i	−0.451129	+	0.781379i
$887$	−24.4070	−	14.0914i	−0.819506	−	0.473142i	0.0307403	−	0.999527i	$-0.490214\pi$
$887$	−24.4070	−	14.0914i	−0.819506	−	0.473142i	−0.850246	+	0.526386i	$0.823547\pi$
$888$		0			0
$889$	−2.08846	−	3.61731i	−0.0700446	−	0.121321i
$890$	20.1962	−	24.7351i	0.676977	−	0.829124i
$891$		0			0
$892$		−	28.9778i		−	0.970248i
$893$	10.3664	−	5.98502i	0.346897	−	0.200281i
$894$		0			0
$895$	51.4088	−	19.4960i	1.71841	−	0.651680i
$896$	1.83975	−	3.18653i	0.0614616	−	0.106455i
$897$		0			0
$898$	20.0764	−	11.5911i	0.669958	−	0.386800i
$899$	−17.6603			−0.589002
$900$		0			0
$901$	1.46410			0.0487763
$902$	−33.7888	+	19.5080i	−1.12504	+	0.649545i
$903$		0			0
$904$	−0.660254	+	1.14359i	−0.0219597	+	0.0380354i
$905$	17.6965	−	6.71113i	0.588251	−	0.223085i
$906$		0			0
$907$	−43.0506	+	24.8553i	−1.42947	+	0.825305i	−0.997079	−	0.0763808i	$-0.975664\pi$
$907$	−43.0506	+	24.8553i	−1.42947	+	0.825305i	−0.432392	+	0.901686i	$0.642330\pi$
$908$		−	3.28169i		−	0.108907i
$909$		0			0
$910$	−6.00000	+	7.34847i	−0.198898	+	0.243599i
$911$	11.0718	+	19.1769i	0.366825	+	0.635360i	0.989067	−	0.147465i	$-0.0471114\pi$
$911$	11.0718	+	19.1769i	0.366825	+	0.635360i	−0.622242	+	0.782825i	$0.713778\pi$
$912$		0			0
$913$	−42.6902	−	24.6472i	−1.41284	−	0.815703i
$914$	33.4186	−	57.8827i	1.10539	−	1.91459i
$915$		0			0
$916$	−17.2583	−	29.8923i	−0.570231	−	0.987670i
$917$			0.832204i			0.0274818i
$918$		0			0
$919$	15.1769			0.500640			0.250320	−	0.968163i	$-0.419464\pi$
$919$	15.1769			0.500640			0.250320	+	0.968163i	$0.419464\pi$
$920$	0.358719	−	2.20711i	0.0118266	−	0.0727662i
$921$		0			0
$922$	−31.3071	−	18.0752i	−1.03105	−	0.595275i
$923$	−8.06918	−	4.65874i	−0.265600	−	0.153344i
$924$		0			0
$925$	−14.0665	−	15.8787i	−0.462505	−	0.522088i
$926$	−0.339746			−0.0111647
$927$		0			0
$928$			49.0542i			1.61028i
$929$	−1.73205	−	3.00000i	−0.0568267	−	0.0984268i	0.836213	−	0.548405i	$-0.184765\pi$
$929$	−1.73205	−	3.00000i	−0.0568267	−	0.0984268i	−0.893039	+	0.449979i	$0.851432\pi$
$930$		0			0
$931$	8.46410	−	14.6603i	0.277400	−	0.480470i
$932$	−10.6066	−	6.12372i	−0.347431	−	0.200589i
$933$		0			0
$934$	5.56218	+	9.63397i	0.182000	+	0.315233i
$935$	2.53590	−	3.10583i	0.0829327	−	0.101571i
$936$		0			0
$937$		−	13.8647i		−	0.452941i	−0.974018	−	0.226471i	$-0.927281\pi$
$937$		−	13.8647i		−	0.452941i	0.974018	−	0.226471i	$-0.0727187\pi$
$938$	−7.70882	+	4.45069i	−0.251702	+	0.145320i
$939$		0			0
$940$	6.01703	+	15.8662i	0.196254	+	0.517500i
$941$	−4.16025	+	7.20577i	−0.135620	+	0.234901i	−0.925834	−	0.377930i	$-0.876636\pi$
$941$	−4.16025	+	7.20577i	−0.135620	+	0.234901i	0.790214	+	0.612831i	$0.209969\pi$
$942$		0			0
$943$	7.14042	−	4.12252i	0.232524	−	0.134248i
$944$	−11.3205			−0.368451
$945$		0			0
$946$	83.5692			2.71707
$947$	2.00120	−	1.15539i	0.0650303	−	0.0375453i	−0.467132	−	0.884187i	$-0.654713\pi$
$947$	2.00120	−	1.15539i	0.0650303	−	0.0375453i	0.532163	+	0.846642i	$0.321379\pi$
$948$		0			0
$949$	10.3923	−	18.0000i	0.337348	−	0.584305i
$950$	8.35739	−	25.0313i	0.271150	−	0.812121i
$951$		0			0
$952$	−0.152304	+	0.0879327i	−0.00493620	+	0.00284992i
$953$			37.0197i			1.19919i	0.800305	+	0.599594i	$0.204671\pi$
$953$			37.0197i			1.19919i	−0.800305	+	0.599594i	$0.795329\pi$
$954$		0			0
$955$	0.588457	+	0.480473i	0.0190420	+	0.0155478i
$956$	11.1962	+	19.3923i	0.362109	+	0.627192i
$957$		0			0
$958$	53.2968	+	30.7709i	1.72194	+	0.994163i
$959$	8.32051	−	14.4115i	0.268683	−	0.465373i
$960$		0			0
$961$	11.7679	+	20.3827i	0.379611	+	0.657506i
$962$			20.0764i			0.647289i
$963$		0			0
$964$	−10.8564			−0.349661
$965$	−45.7593	−	7.43723i	−1.47305	−	0.239413i
$966$		0			0
$967$	−30.0588	−	17.3545i	−0.966627	−	0.558082i	−0.0684208	−	0.997657i	$-0.521796\pi$
$967$	−30.0588	−	17.3545i	−0.966627	−	0.558082i	−0.898206	+	0.439574i	$0.855129\pi$
$968$	5.10703	+	2.94855i	0.164146	+	0.0947698i
$969$		0			0
$970$	7.12288	−	43.8252i	0.228702	−	1.40714i
$971$	−27.8038			−0.892268			−0.446134	−	0.894966i	$-0.647200\pi$
$971$	−27.8038			−0.892268			−0.446134	+	0.894966i	$0.647200\pi$
$972$		0			0
$973$			7.17260i			0.229943i
$974$	−1.09808	−	1.90192i	−0.0351846	−	0.0609416i
$975$		0			0
$976$	23.7942	−	41.2128i	0.761635	−	1.31919i
$977$	13.4722	+	7.77817i	0.431014	+	0.248846i	0.699778	−	0.714360i	$-0.253282\pi$
$977$	13.4722	+	7.77817i	0.431014	+	0.248846i	−0.268765	+	0.963206i	$0.586615\pi$
$978$		0			0
$979$	−17.4904	−	30.2942i	−0.558995	−	0.968208i
$980$	18.5885	+	15.1774i	0.593786	+	0.484825i
$981$		0			0
$982$		−	41.9459i		−	1.33855i
$983$	−31.0669	+	17.9365i	−0.990881	+	0.572085i	−0.905537	−	0.424266i	$-0.860532\pi$
$983$	−31.0669	+	17.9365i	−0.990881	+	0.572085i	−0.0853431	+	0.996352i	$0.527199\pi$
$984$		0			0
$985$	16.5193	+	43.5597i	0.526350	+	1.38793i
$986$	2.36603	−	4.09808i	0.0753496	−	0.130509i
$987$		0			0
$988$	−10.0382	+	5.79555i	−0.319358	+	0.184381i
$989$	−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	$0.369629\pi$
$992$	−17.9551	+	10.3664i	−0.570074	+	0.329132i
$993$		0			0
$994$	3.29423	−	5.70577i	0.104487	−	0.180976i
$995$	−9.59341	+	3.63816i	−0.304132	+	0.115337i
$996$		0			0
$997$	13.1440	−	7.58871i	0.416275	−	0.240337i	−0.277207	−	0.960810i	$-0.589409\pi$
$997$	13.1440	−	7.58871i	0.416275	−	0.240337i	0.693483	+	0.720473i	$0.256075\pi$
$998$		−	7.45001i		−	0.235826i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.1	✓	8	15.14	odd	2
45.2.j.a.4.4	yes	8	3.2	odd	2
45.2.j.a.34.1	yes	8	9.2	odd	6
45.2.j.a.34.4	yes	8	45.29	odd	6
135.2.j.a.19.1		8	45.34	even	6	inner
135.2.j.a.19.4		8	9.7	even	3	inner
135.2.j.a.64.1		8	1.1	even	1	trivial
135.2.j.a.64.4		8	5.4	even	2	inner
225.2.e.d.76.1		8	15.8	even	4
225.2.e.d.76.4		8	15.2	even	4
225.2.e.d.151.1		8	45.38	even	12
225.2.e.d.151.4		8	45.2	even	12
405.2.b.c.244.1		4	9.4	even	3
405.2.b.c.244.4		4	45.4	even	6
405.2.b.d.244.1		4	45.14	odd	6
405.2.b.d.244.4		4	9.5	odd	6
675.2.e.d.226.1		8	5.2	odd	4
675.2.e.d.226.4		8	5.3	odd	4
675.2.e.d.451.1		8	45.7	odd	12
675.2.e.d.451.4		8	45.43	odd	12
720.2.by.d.49.1		8	60.59	even	2
720.2.by.d.49.4		8	12.11	even	2
720.2.by.d.529.1		8	36.11	even	6
720.2.by.d.529.4		8	180.119	even	6
2025.2.a.r.1.1		4	45.13	odd	12
2025.2.a.r.1.4		4	45.22	odd	12
2025.2.a.t.1.1		4	45.32	even	12
2025.2.a.t.1.4		4	45.23	even	12
2160.2.by.c.289.2		8	36.7	odd	6
2160.2.by.c.289.4		8	180.79	odd	6
2160.2.by.c.1009.2		8	20.19	odd	2
2160.2.by.c.1009.4		8	4.3	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67303 + 0.965926i) q^{2} +(0.866025 - 1.50000i) q^{4} +(2.09077 - 0.792893i) q^{5} +(0.776457 - 0.448288i) q^{7} -0.517638i q^{8} +(-2.73205 + 3.34607i) q^{10} +(2.36603 + 4.09808i) q^{11} +(2.12132 + 1.22474i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(2.23205 + 3.86603i) q^{16} -0.378937i q^{17} -2.73205 q^{19} +(0.621320 - 3.82282i) q^{20} +(-7.91688 - 4.57081i) q^{22} +(1.67303 + 0.965926i) q^{23} +(3.74264 - 3.31552i) q^{25} -4.73205 q^{26} -1.55291i q^{28} +(-3.23205 - 5.59808i) q^{29} +(1.36603 - 2.36603i) q^{31} +(-6.57201 - 3.79435i) q^{32} +(0.366025 + 0.633975i) q^{34} +(1.26795 - 1.55291i) q^{35} -4.24264i q^{37} +(4.57081 - 2.63896i) q^{38} +(-0.410432 - 1.08226i) q^{40} +(2.13397 - 3.69615i) q^{41} +(-7.91688 + 4.57081i) q^{43} +8.19615 q^{44} -3.73205 q^{46} +(-3.79435 + 2.19067i) q^{47} +(-3.09808 + 5.36603i) q^{49} +(-3.05902 + 9.16208i) q^{50} +(3.67423 - 2.12132i) q^{52} +3.86370i q^{53} +(8.19615 + 6.69213i) q^{55} +(-0.232051 - 0.401924i) q^{56} +(10.8147 + 6.24384i) q^{58} +(-1.26795 + 2.19615i) q^{59} +(-5.33013 - 9.23205i) q^{61} +5.27792i q^{62} +5.73205 q^{64} +(5.40629 + 0.878680i) q^{65} +(4.45069 + 2.56961i) q^{67} +(-0.568406 - 0.328169i) q^{68} +(-0.621320 + 3.82282i) q^{70} -3.80385 q^{71} -8.48528i q^{73} +(4.09808 + 7.09808i) q^{74} +(-2.36603 + 4.09808i) q^{76} +(3.67423 + 2.12132i) q^{77} +(0.267949 + 0.464102i) q^{79} +(7.73205 + 6.31319i) q^{80} +8.24504i q^{82} +(-9.02150 + 5.20857i) q^{83} +(-0.300457 - 0.792271i) q^{85} +(8.83013 - 15.2942i) q^{86} +(2.12132 - 1.22474i) q^{88} -7.39230 q^{89} +2.19615 q^{91} +(2.89778 - 1.67303i) q^{92} +(4.23205 - 7.33013i) q^{94} +(-5.71209 + 2.16622i) q^{95} +(-8.90138 + 5.13922i) q^{97} -11.9700i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{10} + 12 q^{11} + 4 q^{16} - 8 q^{19} - 12 q^{20} - 4 q^{25} - 24 q^{26} - 12 q^{29} + 4 q^{31} - 4 q^{34} + 24 q^{35} - 4 q^{40} + 24 q^{41} + 24 q^{44} - 16 q^{46} - 4 q^{49} - 24 q^{50} + 24 q^{55}+ \cdots - 12 q^{95}+O(q^{100}) \) 8 * q - 8 * q^10 + 12 * q^11 + 4 * q^16 - 8 * q^19 - 12 * q^20 - 4 * q^25 - 24 * q^26 - 12 * q^29 + 4 * q^31 - 4 * q^34 + 24 * q^35 - 4 * q^40 + 24 * q^41 + 24 * q^44 - 16 * q^46 - 4 * q^49 - 24 * q^50 + 24 * q^55 + 12 * q^56 - 24 * q^59 - 8 * q^61 + 32 * q^64 + 12 * q^70 - 72 * q^71 + 12 * q^74 - 12 * q^76 + 16 * q^79 + 48 * q^80 + 16 * q^85 + 36 * q^86 + 24 * q^89 - 24 * q^91 + 20 * q^94 - 12 * q^95

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