LMFDB - Embedded newform 864.2.bi.a.767.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.10
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23024 - 1.21923i) q^{3} +(0.898214 - 2.46782i) q^{5} +(-2.70996 - 0.477839i) q^{7} +(0.0269609 + 2.99988i) q^{9} +O(q^{10})$	\(q+(-1.23024 - 1.21923i) q^{3} +(0.898214 - 2.46782i) q^{5} +(-2.70996 - 0.477839i) q^{7} +(0.0269609 + 2.99988i) q^{9} +(-3.89738 + 1.41853i) q^{11} +(-0.124651 + 0.104595i) q^{13} +(-4.11386 + 1.94088i) q^{15} +(-4.20948 + 2.43034i) q^{17} +(2.41959 + 1.39695i) q^{19} +(2.75130 + 3.89192i) q^{21} +(0.763623 + 4.33072i) q^{23} +(-1.45314 - 1.21933i) q^{25} +(3.62437 - 3.72343i) q^{27} +(4.22414 - 5.03413i) q^{29} +(-1.23059 + 0.216987i) q^{31} +(6.52422 + 3.00668i) q^{33} +(-3.61335 + 6.25850i) q^{35} +(2.72708 + 4.72344i) q^{37} +(0.280876 + 0.0233022i) q^{39} +(-3.17820 - 3.78763i) q^{41} +(-2.20432 - 6.05631i) q^{43} +(7.42739 + 2.62800i) q^{45} +(-1.18624 + 6.72751i) q^{47} +(0.537714 + 0.195712i) q^{49} +(8.14179 + 2.14242i) q^{51} +11.3525i q^{53} +10.8922i q^{55} +(-1.27346 - 4.66861i) q^{57} +(-7.26386 - 2.64383i) q^{59} +(-0.610406 + 3.46178i) q^{61} +(1.36040 - 8.14244i) q^{63} +(0.146158 + 0.401566i) q^{65} +(9.98223 + 11.8964i) q^{67} +(4.34071 - 6.25884i) q^{69} +(-5.22967 - 9.05806i) q^{71} +(-7.26080 + 12.5761i) q^{73} +(0.301063 + 3.27177i) q^{75} +(11.2396 - 1.98184i) q^{77} +(3.58824 - 4.27629i) q^{79} +(-8.99855 + 0.161759i) q^{81} +(-5.75679 - 4.83052i) q^{83} +(2.21664 + 12.5712i) q^{85} +(-11.3345 + 1.04298i) q^{87} +(-7.95110 - 4.59057i) q^{89} +(0.387780 - 0.223885i) q^{91} +(1.77848 + 1.23343i) q^{93} +(5.62074 - 4.71636i) q^{95} +(-16.0795 + 5.85248i) q^{97} +(-4.36050 - 11.6534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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			0
$2$		0			0
$3$	−1.23024	−	1.21923i	−0.710277	−	0.703922i
$3$	−1.23024	−	1.21923i	−0.710277	−	0.703922i
$4$		0			0
$5$	0.898214	−	2.46782i	0.401694	−	1.10364i	−0.559755	−	0.828658i	$-0.689105\pi$
$5$	0.898214	−	2.46782i	0.401694	−	1.10364i	0.961448	−	0.274986i	$-0.0886731\pi$
$6$		0			0
$7$	−2.70996	−	0.477839i	−1.02427	−	0.180606i	−0.363814	−	0.931472i	$-0.618526\pi$
$7$	−2.70996	−	0.477839i	−1.02427	−	0.180606i	−0.660455	+	0.750865i	$0.729637\pi$
$8$		0			0
$9$	0.0269609	+	2.99988i	0.00898697	+	0.999960i
$10$		0			0
$11$	−3.89738	+	1.41853i	−1.17511	+	0.427703i	−0.854471	−	0.519499i	$-0.826118\pi$
$11$	−3.89738	+	1.41853i	−1.17511	+	0.427703i	−0.320635	+	0.947203i	$0.603896\pi$
$12$		0			0
$13$	−0.124651	+	0.104595i	−0.0345721	+	0.0290094i	−0.659910	−	0.751345i	$-0.729406\pi$
$13$	−0.124651	+	0.104595i	−0.0345721	+	0.0290094i	0.625338	+	0.780354i	$0.284961\pi$
$14$		0			0
$15$	−4.11386	+	1.94088i	−1.06219	+	0.501132i
$16$		0			0
$17$	−4.20948	+	2.43034i	−1.02095	+	0.589445i	−0.914378	−	0.404861i	$-0.867320\pi$
$17$	−4.20948	+	2.43034i	−1.02095	+	0.589445i	−0.106570	+	0.994305i	$0.533987\pi$
$18$		0			0
$19$	2.41959	+	1.39695i	0.555092	+	0.320483i	0.751173	−	0.660105i	$-0.229488\pi$
$19$	2.41959	+	1.39695i	0.555092	+	0.320483i	−0.196081	+	0.980588i	$0.562822\pi$
$20$		0			0
$21$	2.75130	+	3.89192i	0.600382	+	0.849286i
$22$		0			0
$23$	0.763623	+	4.33072i	0.159227	+	0.903018i	0.954819	+	0.297187i	$0.0960484\pi$
$23$	0.763623	+	4.33072i	0.159227	+	0.903018i	−0.795593	+	0.605832i	$0.792840\pi$
$24$		0			0
$25$	−1.45314	−	1.21933i	−0.290628	−	0.243866i
$26$		0			0
$27$	3.62437	−	3.72343i	0.697511	−	0.716574i
$28$		0			0
$29$	4.22414	−	5.03413i	0.784403	−	0.934815i	−0.214720	−	0.976676i	$-0.568884\pi$
$29$	4.22414	−	5.03413i	0.784403	−	0.934815i	0.999123	+	0.0418603i	$0.0133284\pi$
$30$		0			0
$31$	−1.23059	+	0.216987i	−0.221021	+	0.0389720i	−0.283062	−	0.959102i	$-0.591350\pi$
$31$	−1.23059	+	0.216987i	−0.221021	+	0.0389720i	0.0620409	+	0.998074i	$0.480239\pi$
$32$		0			0
$33$	6.52422	+	3.00668i	1.13572	+	0.523395i
$34$		0			0
$35$	−3.61335	+	6.25850i	−0.610767	+	1.05788i
$36$		0			0
$37$	2.72708	+	4.72344i	0.448329	+	0.776529i	0.998277	−	0.0586700i	$-0.0186860\pi$
$37$	2.72708	+	4.72344i	0.448329	+	0.776529i	−0.549948	+	0.835199i	$0.685353\pi$
$38$		0			0
$39$	0.280876	+	0.0233022i	0.0449761	+	0.00373133i
$40$		0			0
$41$	−3.17820	−	3.78763i	−0.496351	−	0.591528i	0.458470	−	0.888710i	$-0.348398\pi$
$41$	−3.17820	−	3.78763i	−0.496351	−	0.591528i	−0.954821	+	0.297182i	$0.903953\pi$
$42$		0			0
$43$	−2.20432	−	6.05631i	−0.336155	−	0.923578i	−0.986474	−	0.163917i	$-0.947587\pi$
$43$	−2.20432	−	6.05631i	−0.336155	−	0.923578i	0.650319	−	0.759661i	$-0.274635\pi$
$44$		0			0
$45$	7.42739	+	2.62800i	1.10721	+	0.391759i
$46$		0			0
$47$	−1.18624	+	6.72751i	−0.173031	+	0.981308i	0.767361	+	0.641215i	$0.221569\pi$
$47$	−1.18624	+	6.72751i	−0.173031	+	0.981308i	−0.940392	+	0.340093i	$0.889542\pi$
$48$		0			0
$49$	0.537714	+	0.195712i	0.0768163	+	0.0279589i
$50$		0			0
$51$	8.14179	+	2.14242i	1.14008	+	0.299999i
$52$		0			0
$53$			11.3525i			1.55939i	0.626162	+	0.779693i	$0.284625\pi$
$53$			11.3525i			1.55939i	−0.626162	+	0.779693i	$0.715375\pi$
$54$		0			0
$55$			10.8922i			1.46870i
$56$		0			0
$57$	−1.27346	−	4.66861i	−0.168674	−	0.618373i
$58$		0			0
$59$	−7.26386	−	2.64383i	−0.945674	−	0.344197i	−0.177270	−	0.984162i	$-0.556727\pi$
$59$	−7.26386	−	2.64383i	−0.945674	−	0.344197i	−0.768404	+	0.639965i	$0.778949\pi$
$60$		0			0
$61$	−0.610406	+	3.46178i	−0.0781545	+	0.443236i	0.920470	+	0.390812i	$0.127806\pi$
$61$	−0.610406	+	3.46178i	−0.0781545	+	0.443236i	−0.998625	+	0.0524239i	$0.983305\pi$
$62$		0			0
$63$	1.36040	−	8.14244i	0.171394	−	1.02585i
$64$		0			0
$65$	0.146158	+	0.401566i	0.0181287	+	0.0498082i
$66$		0			0
$67$	9.98223	+	11.8964i	1.21952	+	1.45337i	0.852149	+	0.523299i	$0.175299\pi$
$67$	9.98223	+	11.8964i	1.21952	+	1.45337i	0.367375	+	0.930073i	$0.380257\pi$
$68$		0			0
$69$	4.34071	−	6.25884i	0.522560	−	0.753476i
$70$		0			0
$71$	−5.22967	−	9.05806i	−0.620648	−	1.07499i	−0.989365	−	0.145453i	$-0.953536\pi$
$71$	−5.22967	−	9.05806i	−0.620648	−	1.07499i	0.368717	−	0.929542i	$-0.379797\pi$
$72$		0			0
$73$	−7.26080	+	12.5761i	−0.849813	+	1.47192i	0.0315626	+	0.999502i	$0.489952\pi$
$73$	−7.26080	+	12.5761i	−0.849813	+	1.47192i	−0.881375	+	0.472417i	$0.843382\pi$
$74$		0			0
$75$	0.301063	+	3.27177i	0.0347638	+	0.377792i
$76$		0			0
$77$	11.2396	−	1.98184i	1.28087	−	0.225852i
$78$		0			0
$79$	3.58824	−	4.27629i	0.403708	−	0.481121i	−0.525439	−	0.850831i	$-0.676099\pi$
$79$	3.58824	−	4.27629i	0.403708	−	0.481121i	0.929147	+	0.369711i	$0.120543\pi$
$80$		0			0
$81$	−8.99855	+	0.161759i	−0.999838	+	0.0179732i
$82$		0			0
$83$	−5.75679	−	4.83052i	−0.631890	−	0.530219i	0.269626	−	0.962965i	$-0.413100\pi$
$83$	−5.75679	−	4.83052i	−0.631890	−	0.530219i	−0.901516	+	0.432747i	$0.857544\pi$
$84$		0			0
$85$	2.21664	+	12.5712i	0.240429	+	1.36354i
$86$		0			0
$87$	−11.3345	+	1.04298i	−1.21518	+	0.111819i
$88$		0			0
$89$	−7.95110	−	4.59057i	−0.842814	−	0.486599i	0.0154055	−	0.999881i	$-0.495096\pi$
$89$	−7.95110	−	4.59057i	−0.842814	−	0.486599i	−0.858220	+	0.513282i	$0.828429\pi$
$90$		0			0
$91$	0.387780	−	0.223885i	0.0406504	−	0.0234695i
$92$		0			0
$93$	1.77848	+	1.23343i	0.184419	+	0.127901i
$94$		0			0
$95$	5.62074	−	4.71636i	0.576676	−	0.483888i
$96$		0			0
$97$	−16.0795	+	5.85248i	−1.63263	+	0.594229i	−0.985728	−	0.168344i	$-0.946158\pi$
$97$	−16.0795	+	5.85248i	−1.63263	+	0.594229i	−0.646902	+	0.762573i	$0.723936\pi$
$98$		0			0
$99$	−4.36050	−	11.6534i	−0.438247	−	1.17121i
$100$		0			0
$101$	−17.7683	−	3.13303i	−1.76801	−	0.311748i	−0.807475	−	0.589902i	$-0.799166\pi$
$101$	−17.7683	−	3.13303i	−1.76801	−	0.311748i	−0.960536	+	0.278154i	$0.910277\pi$
$102$		0			0
$103$	−2.79402	+	7.67649i	−0.275303	+	0.756387i	0.722576	+	0.691291i	$0.242958\pi$
$103$	−2.79402	+	7.67649i	−0.275303	+	0.756387i	−0.997879	+	0.0650964i	$0.979265\pi$
$104$		0			0
$105$	12.0758	−	3.29394i	1.17848	−	0.321455i
$106$		0			0
$107$	−14.6174			−1.41312			−0.706561	−	0.707653i	$-0.749754\pi$
$107$	−14.6174			−1.41312			−0.706561	+	0.707653i	$0.749754\pi$
$108$		0			0
$109$	10.7553			1.03017			0.515086	−	0.857138i	$-0.327760\pi$
$109$	10.7553			1.03017			0.515086	+	0.857138i	$0.327760\pi$
$110$		0			0
$111$	2.40400	−	9.13588i	0.228178	−	0.867139i
$112$		0			0
$113$	1.07598	−	2.95623i	0.101220	−	0.278099i	−0.878738	−	0.477305i	$-0.841614\pi$
$113$	1.07598	−	2.95623i	0.101220	−	0.278099i	0.979958	+	0.199205i	$0.0638361\pi$
$114$		0			0
$115$	11.3734	+	2.00543i	1.06057	+	0.187007i
$116$		0			0
$117$	−0.317133	−	0.371119i	−0.0293189	−	0.0343100i
$118$		0			0
$119$	12.5688	−	4.57468i	1.15218	−	0.419360i
$120$		0			0
$121$	4.75088	−	3.98646i	0.431898	−	0.362406i
$122$		0			0
$123$	−0.708054	+	8.53463i	−0.0638430	+	0.769541i
$124$		0			0
$125$	7.05747	−	4.07463i	0.631239	−	0.364446i
$126$		0			0
$127$	17.5482	+	10.1314i	1.55715	+	0.899020i	0.997528	+	0.0702713i	$0.0223865\pi$
$127$	17.5482	+	10.1314i	1.55715	+	0.899020i	0.559621	+	0.828749i	$0.310947\pi$
$128$		0			0
$129$	−4.67220	+	10.1383i	−0.411364	+	0.892623i
$130$		0			0
$131$	1.73306	+	9.82867i	0.151418	+	0.858735i	0.961988	+	0.273093i	$0.0880465\pi$
$131$	1.73306	+	9.82867i	0.151418	+	0.858735i	−0.810570	+	0.585642i	$0.800842\pi$
$132$		0			0
$133$	−5.88948	−	4.94186i	−0.510683	−	0.428514i
$134$		0			0
$135$	−5.93331	−	12.2887i	−0.510658	−	1.05765i
$136$		0			0
$137$	6.72153	−	8.01041i	0.574259	−	0.684375i	−0.398240	−	0.917281i	$-0.630379\pi$
$137$	6.72153	−	8.01041i	0.574259	−	0.684375i	0.972499	+	0.232906i	$0.0748234\pi$
$138$		0			0
$139$	−12.1861	+	2.14875i	−1.03362	+	0.182254i	−0.664623	−	0.747178i	$-0.731408\pi$
$139$	−12.1861	+	2.14875i	−1.03362	+	0.182254i	−0.368992	+	0.929433i	$0.620297\pi$
$140$		0			0
$141$	9.66173	−	6.83012i	0.813664	−	0.575200i
$142$		0			0
$143$	0.337443	−	0.584469i	0.0282184	−	0.0488757i
$144$		0			0
$145$	−8.62917	−	14.9462i	−0.716614	−	1.24121i
$146$		0			0
$147$	−0.422898	−	0.896369i	−0.0348800	−	0.0739313i
$148$		0			0
$149$	−8.30942	−	9.90278i	−0.680734	−	0.811267i	0.309468	−	0.950910i	$-0.399849\pi$
$149$	−8.30942	−	9.90278i	−0.680734	−	0.811267i	−0.990202	+	0.139642i	$0.955405\pi$
$150$		0			0
$151$	1.97597	+	5.42895i	0.160803	+	0.441801i	0.993761	−	0.111535i	$-0.0355767\pi$
$151$	1.97597	+	5.42895i	0.160803	+	0.441801i	−0.832958	+	0.553336i	$0.813354\pi$
$152$		0			0
$153$	−7.40422	−	12.5624i	−0.598596	−	1.01561i
$154$		0			0
$155$	−0.569851	+	3.23179i	−0.0457715	+	0.259583i
$156$		0			0
$157$	−16.9858	−	6.18231i	−1.35561	−	0.493402i	−0.440916	−	0.897548i	$-0.645346\pi$
$157$	−16.9858	−	6.18231i	−1.35561	−	0.493402i	−0.914694	+	0.404146i	$0.867569\pi$
$158$		0			0
$159$	13.8413	−	13.9663i	1.09769	−	1.10760i
$160$		0			0
$161$		−	12.1010i		−	0.953691i
$162$		0			0
$163$		−	16.5391i		−	1.29544i	−0.761877	−	0.647721i	$-0.775722\pi$
$163$		−	16.5391i		−	1.29544i	0.761877	−	0.647721i	$-0.224278\pi$
$164$		0			0
$165$	13.2801	−	13.4000i	1.03385	−	1.04319i
$166$		0			0
$167$	13.5236	+	4.92218i	1.04649	+	0.380890i	0.807335	−	0.590093i	$-0.200909\pi$
$167$	13.5236	+	4.92218i	1.04649	+	0.380890i	0.239150	+	0.970983i	$0.423131\pi$
$168$		0			0
$169$	−2.25283	+	12.7764i	−0.173294	+	0.982802i
$170$		0			0
$171$	−4.12545	+	7.29614i	−0.315481	+	0.557950i
$172$		0			0
$173$	−4.68925	−	12.8836i	−0.356517	−	0.979523i	−0.980229	−	0.197868i	$-0.936598\pi$
$173$	−4.68925	−	12.8836i	−0.356517	−	0.979523i	0.623711	−	0.781655i	$-0.285624\pi$
$174$		0			0
$175$	3.35531	+	3.99870i	0.253638	+	0.302274i
$176$		0			0
$177$	5.71283	+	12.1088i	0.429403	+	0.910156i
$178$		0			0
$179$	−3.04942	−	5.28174i	−0.227924	−	0.394776i	0.729269	−	0.684227i	$-0.239860\pi$
$179$	−3.04942	−	5.28174i	−0.227924	−	0.394776i	−0.957193	+	0.289451i	$0.906527\pi$
$180$		0			0
$181$	10.8244	−	18.7484i	0.804570	−	1.39356i	−0.112010	−	0.993707i	$-0.535729\pi$
$181$	10.8244	−	18.7484i	0.804570	−	1.39356i	0.916581	−	0.399850i	$-0.130938\pi$
$182$		0			0
$183$	4.97165	−	3.51459i	0.367515	−	0.259806i
$184$		0			0
$185$	14.1061	−	2.48729i	1.03710	−	0.182869i
$186$		0			0
$187$	12.9584	−	15.4433i	0.947614	−	1.12932i
$188$		0			0
$189$	−11.6011	+	8.35849i	−0.843857	+	0.607990i
$190$		0			0
$191$	−7.33528	−	6.15503i	−0.530762	−	0.445362i	0.337602	−	0.941289i	$-0.390384\pi$
$191$	−7.33528	−	6.15503i	−0.530762	−	0.445362i	−0.868364	+	0.495927i	$0.834829\pi$
$192$		0			0
$193$	2.22305	+	12.6076i	0.160019	+	0.907512i	0.954053	+	0.299639i	$0.0968661\pi$
$193$	2.22305	+	12.6076i	0.160019	+	0.907512i	−0.794034	+	0.607874i	$0.792023\pi$
$194$		0			0
$195$	0.309792	−	0.672222i	0.0221847	−	0.0481388i
$196$		0			0
$197$	5.26490	+	3.03969i	0.375108	+	0.216569i	0.675688	−	0.737188i	$-0.263847\pi$
$197$	5.26490	+	3.03969i	0.375108	+	0.216569i	−0.300579	+	0.953757i	$0.597180\pi$
$198$		0			0
$199$	−5.83456	+	3.36858i	−0.413601	+	0.238793i	−0.692336	−	0.721575i	$-0.743418\pi$
$199$	−5.83456	+	3.36858i	−0.413601	+	0.238793i	0.278735	+	0.960368i	$0.410085\pi$
$200$		0			0
$201$	2.22389	−	26.8060i	0.156861	−	1.89075i
$202$		0			0
$203$	−13.8528	+	11.6239i	−0.972274	+	0.815834i
$204$		0			0
$205$	−12.2019	+	4.44113i	−0.852217	+	0.310182i
$206$		0			0
$207$	−12.9711	+	2.40754i	−0.901551	+	0.167335i
$208$		0			0
$209$	−11.4117	−	2.01219i	−0.789363	−	0.139186i
$210$		0			0
$211$	6.57347	−	18.0605i	0.452537	−	1.24333i	−0.478396	−	0.878144i	$-0.658782\pi$
$211$	6.57347	−	18.0605i	0.452537	−	1.24333i	0.930933	−	0.365190i	$-0.118996\pi$
$212$		0			0
$213$	−4.61012	+	17.5197i	−0.315880	+	1.20043i
$214$		0			0
$215$	−16.9258			−1.15433
$216$		0			0
$217$	3.43854			0.233424
$218$		0			0
$219$	24.2656	−	6.61896i	1.63972	−	0.447268i
$220$		0			0
$221$	0.270516	−	0.743236i	0.0181969	−	0.0499954i
$222$		0			0
$223$	2.25189	+	0.397069i	0.150798	+	0.0265897i	0.248537	−	0.968622i	$-0.420050\pi$
$223$	2.25189	+	0.397069i	0.150798	+	0.0265897i	−0.0977396	+	0.995212i	$0.531161\pi$
$224$		0			0
$225$	3.61866	−	4.39212i	0.241244	−	0.292808i
$226$		0			0
$227$	18.6302	−	6.78084i	1.23653	−	0.450060i	0.360701	−	0.932682i	$-0.382538\pi$
$227$	18.6302	−	6.78084i	1.23653	−	0.450060i	0.875829	+	0.482621i	$0.160315\pi$
$228$		0			0
$229$	−13.0955	+	10.9884i	−0.865376	+	0.726136i	−0.963119	−	0.269075i	$-0.913282\pi$
$229$	−13.0955	+	10.9884i	−0.865376	+	0.726136i	0.0977435	+	0.995212i	$0.468838\pi$
$230$		0			0
$231$	−16.2437	−	11.2655i	−1.06876	−	0.741216i
$232$		0			0
$233$	−20.7981	+	12.0078i	−1.36253	+	0.786655i	−0.989960	−	0.141351i	$-0.954856\pi$
$233$	−20.7981	+	12.0078i	−1.36253	+	0.786655i	−0.372567	+	0.928005i	$0.621522\pi$
$234$		0			0
$235$	15.5368	+	8.97018i	1.01351	+	0.585150i
$236$		0			0
$237$	−9.62816	+	0.885968i	−0.625416	+	0.0575498i
$238$		0			0
$239$	1.81930	+	10.3178i	0.117681	+	0.667400i	0.985388	+	0.170325i	$0.0544816\pi$
$239$	1.81930	+	10.3178i	0.117681	+	0.667400i	−0.867707	+	0.497075i	$0.834407\pi$
$240$		0			0
$241$	−12.1712	−	10.2129i	−0.784018	−	0.657870i	0.160239	−	0.987078i	$-0.448774\pi$
$241$	−12.1712	−	10.2129i	−0.784018	−	0.657870i	−0.944257	+	0.329209i	$0.893218\pi$
$242$		0			0
$243$	11.2676	+	10.7723i	0.722814	+	0.691043i
$244$		0			0
$245$	0.965965	−	1.15119i	0.0617133	−	0.0735470i
$246$		0			0
$247$	−0.447719	+	0.0789450i	−0.0284877	+	0.00502315i
$248$		0			0
$249$	1.19270	+	12.9615i	0.0755842	+	0.821403i
$250$		0			0
$251$	0.284052	−	0.491993i	0.0179292	−	0.0310543i	−0.856922	−	0.515447i	$-0.827626\pi$
$251$	0.284052	−	0.491993i	0.0179292	−	0.0310543i	0.874851	+	0.484392i	$0.160959\pi$
$252$		0			0
$253$	−9.11940	−	15.7953i	−0.573332	−	0.993040i
$254$		0			0
$255$	12.6002	−	18.1682i	0.789055	−	1.13773i
$256$		0			0
$257$	3.91810	+	4.66941i	0.244404	+	0.291270i	0.874276	−	0.485430i	$-0.161337\pi$
$257$	3.91810	+	4.66941i	0.244404	+	0.291270i	−0.629871	+	0.776699i	$0.716892\pi$
$258$		0			0
$259$	−5.13323	−	14.1034i	−0.318964	−	0.876345i
$260$		0			0
$261$	15.2157	+	12.5362i	0.941827	+	0.775970i
$262$		0			0
$263$	0.634554	−	3.59874i	0.0391283	−	0.221908i	−0.958973	−	0.283496i	$-0.908506\pi$
$263$	0.634554	−	3.59874i	0.0391283	−	0.221908i	0.998102	+	0.0615888i	$0.0196167\pi$
$264$		0			0
$265$	28.0160	+	10.1970i	1.72101	+	0.626396i
$266$		0			0
$267$	4.18477	+	15.3417i	0.256104	+	0.938896i
$268$		0			0
$269$			4.13751i			0.252268i	0.992013	+	0.126134i	$0.0402570\pi$
$269$			4.13751i			0.252268i	−0.992013	+	0.126134i	$0.959743\pi$
$270$		0			0
$271$		−	6.41761i		−	0.389842i	−0.980819	−	0.194921i	$-0.937555\pi$
$271$		−	6.41761i		−	0.389842i	0.980819	−	0.194921i	$-0.0624451\pi$
$272$		0			0
$273$	−0.750028	−	0.197361i	−0.0453938	−	0.0119449i
$274$		0			0
$275$	7.39310	+	2.69087i	0.445821	+	0.162266i
$276$		0			0
$277$	0.814547	−	4.61952i	0.0489414	−	0.277560i	−0.950510	−	0.310695i	$-0.899438\pi$
$277$	0.814547	−	4.61952i	0.0489414	−	0.277560i	0.999451	+	0.0331352i	$0.0105492\pi$
$278$		0			0
$279$	−0.684112	−	3.68578i	−0.0409567	−	0.220662i
$280$		0			0
$281$	2.83317	+	7.78408i	0.169013	+	0.464359i	0.995064	−	0.0992362i	$-0.0316400\pi$
$281$	2.83317	+	7.78408i	0.169013	+	0.464359i	−0.826051	+	0.563595i	$0.809418\pi$
$282$		0			0
$283$	−15.6587	−	18.6613i	−0.930813	−	1.10930i	−0.993789	−	0.111284i	$-0.964504\pi$
$283$	−15.6587	−	18.6613i	−0.930813	−	1.10930i	0.0629760	−	0.998015i	$-0.479941\pi$
$284$		0			0
$285$	−12.6652	−	1.05073i	−0.750219	−	0.0622400i
$286$		0			0
$287$	6.80291	+	11.7830i	0.401563	+	0.695528i
$288$		0			0
$289$	3.31313	−	5.73851i	0.194890	−	0.337560i
$290$		0			0
$291$	26.9171	+	12.4047i	1.57791	+	0.727178i
$292$		0			0
$293$	−20.2091	+	3.56342i	−1.18063	+	0.208177i	−0.729309	−	0.684185i	$-0.760158\pi$
$293$	−20.2091	+	3.56342i	−1.18063	+	0.208177i	−0.451321	+	0.892361i	$0.649047\pi$
$294$		0			0
$295$	−13.0490	+	15.5512i	−0.759742	+	0.905426i
$296$		0			0
$297$	−8.84376	+	19.6529i	−0.513167	+	1.14038i
$298$		0			0
$299$	−0.548159	−	0.459960i	−0.0317008	−	0.0266002i
$300$		0			0
$301$	3.07967	+	17.4657i	0.177509	+	1.00670i
$302$		0			0
$303$	18.0393	+	25.5180i	1.03633	+	1.46597i
$304$		0			0
$305$	7.99479	+	4.61580i	0.457781	+	0.264300i
$306$		0			0
$307$	6.94860	−	4.01177i	0.396577	−	0.228964i	−0.288429	−	0.957501i	$-0.593133\pi$
$307$	6.94860	−	4.01177i	0.396577	−	0.228964i	0.685006	+	0.728537i	$0.259799\pi$
$308$		0			0
$309$	12.7967	−	6.03735i	0.727979	−	0.343453i
$310$		0			0
$311$	−11.5305	+	9.67523i	−0.653834	+	0.548632i	−0.908232	−	0.418468i	$-0.862567\pi$
$311$	−11.5305	+	9.67523i	−0.653834	+	0.548632i	0.254398	+	0.967100i	$0.418123\pi$
$312$		0			0
$313$	6.55205	−	2.38475i	0.370344	−	0.134794i	−0.150142	−	0.988664i	$-0.547973\pi$
$313$	6.55205	−	2.38475i	0.370344	−	0.134794i	0.520486	+	0.853870i	$0.325751\pi$
$314$		0			0
$315$	−18.8722	−	10.6709i	−1.06333	−	0.601236i
$316$		0			0
$317$	−25.7542	−	4.54115i	−1.44650	−	0.255057i	−0.605392	−	0.795928i	$-0.706984\pi$
$317$	−25.7542	−	4.54115i	−1.44650	−	0.255057i	−0.841106	+	0.540871i	$0.818095\pi$
$318$		0			0
$319$	−9.32202	+	25.6120i	−0.521933	+	1.43400i
$320$		0			0
$321$	17.9829	+	17.8220i	1.00371	+	0.994727i
$322$		0			0
$323$	−13.5803			−0.755627
$324$		0			0
$325$	0.308672			0.0171220
$326$		0			0
$327$	−13.2316	−	13.1132i	−0.731708	−	0.725161i
$328$		0			0
$329$	6.42934	−	17.6645i	0.354461	−	0.973873i
$330$		0			0
$331$	−9.25488	−	1.63188i	−0.508694	−	0.0896965i	−0.0865904	−	0.996244i	$-0.527597\pi$
$331$	−9.25488	−	1.63188i	−0.508694	−	0.0896965i	−0.422104	+	0.906547i	$0.638708\pi$
$332$		0			0
$333$	−14.0962	+	8.30825i	−0.772468	+	0.455290i
$334$		0			0
$335$	38.3243	−	13.9489i	2.09388	−	0.762110i
$336$		0			0
$337$	18.7195	−	15.7076i	1.01972	−	0.855645i	0.0301261	−	0.999546i	$-0.490409\pi$
$337$	18.7195	−	15.7076i	1.01972	−	0.855645i	0.989592	+	0.143901i	$0.0459647\pi$
$338$		0			0
$339$	−4.92804	+	2.32500i	−0.267654	+	0.126277i
$340$		0			0
$341$	4.48829	−	2.59132i	0.243055	−	0.140328i
$342$		0			0
$343$	15.3180	+	8.84387i	0.827096	+	0.477524i
$344$		0			0
$345$	−11.5468	−	16.3339i	−0.621661	−	0.879387i
$346$		0			0
$347$	2.57228	+	14.5881i	0.138087	+	0.783131i	0.972660	+	0.232233i	$0.0746033\pi$
$347$	2.57228	+	14.5881i	0.138087	+	0.783131i	−0.834573	+	0.550897i	$0.814286\pi$
$348$		0			0
$349$	17.4798	+	14.6673i	0.935670	+	0.785120i	0.976827	−	0.214032i	$-0.0686598\pi$
$349$	17.4798	+	14.6673i	0.935670	+	0.785120i	−0.0411566	+	0.999153i	$0.513104\pi$
$350$		0			0
$351$	−0.0623310	+	0.843222i	−0.00332698	+	0.0450078i
$352$		0			0
$353$	−10.1218	+	12.0627i	−0.538727	+	0.642030i	−0.964902	−	0.262611i	$-0.915416\pi$
$353$	−10.1218	+	12.0627i	−0.538727	+	0.642030i	0.426175	+	0.904641i	$0.359861\pi$
$354$		0			0
$355$	−27.0511	+	4.76983i	−1.43572	+	0.253156i
$356$		0			0
$357$	−21.0402	−	9.69635i	−1.11357	−	0.513185i
$358$		0			0
$359$	−0.192952	+	0.334203i	−0.0101836	+	0.0176386i	−0.871072	−	0.491155i	$-0.836575\pi$
$359$	−0.192952	+	0.334203i	−0.0101836	+	0.0176386i	0.860889	+	0.508793i	$0.169908\pi$
$360$		0			0
$361$	−5.59706	−	9.69438i	−0.294582	−	0.510231i
$362$		0			0
$363$	−10.7051	−	0.888123i	−0.561873	−	0.0466144i
$364$		0			0
$365$	24.5138	+	29.2144i	1.28311	+	1.52915i
$366$		0			0
$367$	0.734846	+	2.01897i	0.0383586	+	0.105389i	0.957393	−	0.288787i	$-0.0932520\pi$
$367$	0.734846	+	2.01897i	0.0383586	+	0.105389i	−0.919035	+	0.394177i	$0.871030\pi$
$368$		0			0
$369$	11.2767	−	9.63632i	0.587043	−	0.501647i
$370$		0			0
$371$	5.42467	−	30.7649i	0.281635	−	1.59723i
$372$		0			0
$373$	20.2712	+	7.37813i	1.04960	+	0.382025i	0.808514	−	0.588478i	$-0.200272\pi$
$373$	20.2712	+	7.37813i	1.04960	+	0.382025i	0.241091	+	0.970502i	$0.422495\pi$
$374$		0			0
$375$	−13.6503	−	3.59191i	−0.704897	−	0.185486i
$376$		0			0
$377$			1.06934i			0.0550736i
$378$		0			0
$379$			18.5756i			0.954167i	0.878858	+	0.477084i	$0.158306\pi$
$379$			18.5756i			0.954167i	−0.878858	+	0.477084i	$0.841694\pi$
$380$		0			0
$381$	−9.23584	−	33.8593i	−0.473167	−	1.73466i
$382$		0			0
$383$	−7.01779	−	2.55427i	−0.358592	−	0.130517i	0.156441	−	0.987687i	$-0.449998\pi$
$383$	−7.01779	−	2.55427i	−0.358592	−	0.130517i	−0.515033	+	0.857170i	$0.672220\pi$
$384$		0			0
$385$	5.20472	−	29.5174i	0.265257	−	1.50435i
$386$		0			0
$387$	18.1088	−	6.77596i	0.920520	−	0.344442i
$388$		0			0
$389$	−5.75885	−	15.8223i	−0.291985	−	0.802223i	−0.995776	−	0.0918159i	$-0.970733\pi$
$389$	−5.75885	−	15.8223i	−0.291985	−	0.802223i	0.703791	−	0.710408i	$-0.251489\pi$
$390$		0			0
$391$	−13.7396	−	16.3742i	−0.694841	−	0.828080i
$392$		0			0
$393$	9.85133	−	14.2046i	0.496934	−	0.716526i
$394$		0			0
$395$	−7.33013	−	12.6962i	−0.368819	−	0.638813i
$396$		0			0
$397$	2.69581	−	4.66928i	0.135299	−	0.234344i	−0.790413	−	0.612575i	$-0.790134\pi$
$397$	2.69581	−	4.66928i	0.135299	−	0.234344i	0.925712	+	0.378230i	$0.123467\pi$
$398$		0			0
$399$	1.22019	+	13.2603i	0.0610859	+	0.663844i
$400$		0			0
$401$	19.3562	−	3.41301i	0.966601	−	0.170438i	0.332001	−	0.943279i	$-0.392276\pi$
$401$	19.3562	−	3.41301i	0.966601	−	0.170438i	0.634600	+	0.772841i	$0.281165\pi$
$402$		0			0
$403$	0.130699	−	0.155762i	0.00651060	−	0.00775903i
$404$		0			0
$405$	−7.68343	+	22.3521i	−0.381793	+	1.11069i
$406$		0			0
$407$	−17.3288	−	14.5406i	−0.858958	−	0.720751i
$408$		0			0
$409$	4.64858	+	26.3634i	0.229857	+	1.30359i	0.853178	+	0.521620i	$0.174672\pi$
$409$	4.64858	+	26.3634i	0.229857	+	1.30359i	−0.623321	+	0.781966i	$0.714217\pi$
$410$		0			0
$411$	−18.0356	+	1.65961i	−0.889630	+	0.0818624i
$412$		0			0
$413$	18.4215	+	10.6356i	0.906461	+	0.523345i
$414$		0			0
$415$	−17.0917	+	9.86790i	−0.838999	+	0.484396i
$416$		0			0
$417$	17.6116	+	12.2142i	0.862446	+	0.598134i
$418$		0			0
$419$	−13.0885	+	10.9825i	−0.639414	+	0.536532i	−0.903838	−	0.427874i	$-0.859263\pi$
$419$	−13.0885	+	10.9825i	−0.639414	+	0.536532i	0.264424	+	0.964407i	$0.414818\pi$
$420$		0			0
$421$	4.75979	−	1.73242i	0.231978	−	0.0844331i	−0.223416	−	0.974723i	$-0.571721\pi$
$421$	4.75979	−	1.73242i	0.231978	−	0.0844331i	0.455394	+	0.890290i	$0.349499\pi$
$422$		0			0
$423$	−20.2137	−	3.37720i	−0.982823	−	0.164205i
$424$		0			0
$425$	9.08035	+	1.60111i	0.440462	+	0.0776653i
$426$		0			0
$427$	3.30835	−	9.08963i	0.160102	−	0.439878i
$428$		0			0
$429$	−1.12774	+	0.307614i	−0.0544476	+	0.0148517i
$430$		0			0
$431$	35.4381			1.70699			0.853496	−	0.521099i	$-0.174478\pi$
$431$	35.4381			1.70699			0.853496	+	0.521099i	$0.174478\pi$
$432$		0			0
$433$	34.2928			1.64801			0.824004	−	0.566583i	$-0.191735\pi$
$433$	34.2928			1.64801			0.824004	+	0.566583i	$0.191735\pi$
$434$		0			0
$435$	−7.60688	+	28.9082i	−0.364722	+	1.38604i
$436$		0			0
$437$	−4.20215	+	11.5453i	−0.201016	+	0.552288i
$438$		0			0
$439$	−13.3303	−	2.35049i	−0.636219	−	0.112183i	−0.153770	−	0.988107i	$-0.549141\pi$
$439$	−13.3303	−	2.35049i	−0.636219	−	0.112183i	−0.482449	+	0.875924i	$0.660253\pi$
$440$		0			0
$441$	−0.572615	+	1.61835i	−0.0272674	+	0.0770645i
$442$		0			0
$443$	−19.6498	+	7.15195i	−0.933591	+	0.339799i	−0.763632	−	0.645652i	$-0.776586\pi$
$443$	−19.6498	+	7.15195i	−0.933591	+	0.339799i	−0.169959	+	0.985451i	$0.554364\pi$
$444$		0			0
$445$	−18.4705	+	15.4986i	−0.875585	+	0.734703i
$446$		0			0
$447$	−1.85121	+	22.3138i	−0.0875593	+	1.05541i
$448$		0			0
$449$	−8.92575	+	5.15328i	−0.421232	+	0.243198i	−0.695604	−	0.718425i	$-0.744863\pi$
$449$	−8.92575	+	5.15328i	−0.421232	+	0.243198i	0.274372	+	0.961624i	$0.411530\pi$
$450$		0			0
$451$	17.7595	+	10.2535i	0.836263	+	0.482817i
$452$		0			0
$453$	4.18821	−	9.08805i	0.196779	−	0.426994i
$454$		0			0
$455$	−0.204199	−	1.15807i	−0.00957299	−	0.0542911i
$456$		0			0
$457$	−20.1854	−	16.9376i	−0.944233	−	0.792305i	0.0340841	−	0.999419i	$-0.489149\pi$
$457$	−20.1854	−	16.9376i	−0.944233	−	0.792305i	−0.978317	+	0.207114i	$0.933593\pi$
$458$		0			0
$459$	−6.20750	+	24.4822i	−0.289741	+	1.14273i
$460$		0			0
$461$	12.5389	−	14.9433i	0.583995	−	0.695979i	−0.390445	−	0.920626i	$-0.627679\pi$
$461$	12.5389	−	14.9433i	0.583995	−	0.695979i	0.974440	+	0.224648i	$0.0721232\pi$
$462$		0			0
$463$	−22.4946	+	3.96641i	−1.04541	+	0.184335i	−0.669877	−	0.742472i	$-0.733653\pi$
$463$	−22.4946	+	3.96641i	−1.04541	+	0.184335i	−0.375538	+	0.926807i	$0.622542\pi$
$464$		0			0
$465$	4.64134	−	3.28108i	0.215237	−	0.152156i
$466$		0			0
$467$	−5.92959	+	10.2704i	−0.274389	+	0.475255i	−0.969981	−	0.243182i	$-0.921809\pi$
$467$	−5.92959	+	10.2704i	−0.274389	+	0.475255i	0.695592	+	0.718437i	$0.255142\pi$
$468$		0			0
$469$	−21.3669	−	37.0086i	−0.986633	−	1.70890i
$470$		0			0
$471$	13.3588	+	28.3152i	0.615542	+	1.30470i
$472$		0			0
$473$	17.1821	+	20.4769i	0.790035	+	0.941527i
$474$		0			0
$475$	−1.81266	−	4.98024i	−0.0831705	−	0.228509i
$476$		0			0
$477$	−34.0561	+	0.306074i	−1.55932	+	0.0140142i
$478$		0			0
$479$	3.81502	−	21.6360i	0.174313	−	0.988576i	−0.764622	−	0.644480i	$-0.777074\pi$
$479$	3.81502	−	21.6360i	0.174313	−	0.988576i	0.938934	−	0.344097i	$-0.111815\pi$
$480$		0			0
$481$	−0.833982	−	0.303545i	−0.0380263	−	0.0138404i
$482$		0			0
$483$	−14.7539	+	14.8871i	−0.671325	+	0.677385i
$484$		0			0
$485$			44.9383i			2.04054i
$486$		0			0
$487$		−	37.8780i		−	1.71642i	−0.513301	−	0.858208i	$-0.671578\pi$
$487$		−	37.8780i		−	1.71642i	0.513301	−	0.858208i	$-0.328422\pi$
$488$		0			0
$489$	−20.1650	+	20.3470i	−0.911891	+	0.920123i
$490$		0			0
$491$	0.849455	+	0.309176i	0.0383354	+	0.0139529i	0.361117	−	0.932521i	$-0.382396\pi$
$491$	0.849455	+	0.309176i	0.0383354	+	0.0139529i	−0.322781	+	0.946474i	$0.604618\pi$
$492$		0			0
$493$	−5.54675	+	31.4572i	−0.249813	+	1.41676i
$494$		0			0
$495$	−32.6753	+	0.293664i	−1.46864	+	0.0131992i
$496$		0			0
$497$	9.84392	+	27.0459i	0.441560	+	1.21318i
$498$		0			0
$499$	15.8353	+	18.8717i	0.708884	+	0.844815i	0.993501	−	0.113826i	$-0.0363107\pi$
$499$	15.8353	+	18.8717i	0.708884	+	0.844815i	−0.284616	+	0.958641i	$0.591866\pi$
$500$		0			0
$501$	−10.6359	−	22.5438i	−0.475178	−	1.00718i
$502$		0			0
$503$	5.28554	+	9.15482i	0.235670	+	0.408193i	0.959467	−	0.281820i	$-0.0909381\pi$
$503$	5.28554	+	9.15482i	0.235670	+	0.408193i	−0.723797	+	0.690013i	$0.757605\pi$
$504$		0			0
$505$	−23.6915	+	41.0349i	−1.05426	+	1.82603i
$506$		0			0
$507$	18.3489	−	12.9713i	0.814903	−	0.576076i
$508$		0			0
$509$	5.16811	−	0.911278i	0.229073	−	0.0403917i	−0.0579334	−	0.998320i	$-0.518451\pi$
$509$	5.16811	−	0.911278i	0.229073	−	0.0403917i	0.287006	+	0.957929i	$0.407340\pi$
$510$		0			0
$511$	25.6858	−	30.6112i	1.13627	−	1.35416i
$512$		0			0
$513$	13.9709	−	3.94611i	0.616832	−	0.174225i
$514$		0			0
$515$	16.4346	+	13.7903i	0.724195	+	0.607672i
$516$		0			0
$517$	−4.91995	−	27.9024i	−0.216379	−	1.22715i
$518$		0			0
$519$	−9.93919	+	21.5672i	−0.436282	+	0.946693i
$520$		0			0
$521$	26.4301	+	15.2594i	1.15792	+	0.668527i	0.950805	−	0.309789i	$-0.100258\pi$
$521$	26.4301	+	15.2594i	1.15792	+	0.668527i	0.207118	+	0.978316i	$0.433592\pi$
$522$		0			0
$523$	−7.96759	+	4.60009i	−0.348399	+	0.201148i	−0.663980	−	0.747751i	$-0.731134\pi$
$523$	−7.96759	+	4.60009i	−0.348399	+	0.201148i	0.315581	+	0.948899i	$0.397801\pi$
$524$		0			0
$525$	0.747512	−	9.01024i	0.0326241	−	0.393239i
$526$		0			0
$527$	4.65280	−	3.90416i	0.202679	−	0.170068i
$528$		0			0
$529$	3.44088	−	1.25238i	0.149603	−	0.0544512i
$530$		0			0
$531$	7.73533	−	21.8620i	0.335685	−	0.948729i
$532$		0			0
$533$	0.792333	+	0.139710i	0.0343198	+	0.00605150i
$534$		0			0
$535$	−13.1296	+	36.0732i	−0.567642	+	1.55958i
$536$		0			0
$537$	−2.68815	+	10.2157i	−0.116002	+	0.440841i
$538$		0			0
$539$	−2.37330			−0.102225
$540$		0			0
$541$	27.8947			1.19929			0.599643	−	0.800268i	$-0.295309\pi$
$541$	27.8947			1.19929			0.599643	+	0.800268i	$0.295309\pi$
$542$		0			0
$543$	−36.1751	+	9.86753i	−1.55242	+	0.423456i
$544$		0			0
$545$	9.66058	−	26.5422i	0.413814	−	1.13694i
$546$		0			0
$547$	−21.7631	−	3.83741i	−0.930521	−	0.164076i	−0.312213	−	0.950012i	$-0.601070\pi$
$547$	−21.7631	−	3.83741i	−0.930521	−	0.164076i	−0.618308	+	0.785936i	$0.712181\pi$
$548$		0			0
$549$	−10.4014	−	1.73781i	−0.443920	−	0.0741680i
$550$		0			0
$551$	17.2531	−	6.27962i	0.735008	−	0.267521i
$552$		0			0
$553$	−11.7674	+	9.87399i	−0.500399	+	0.419885i
$554$		0			0
$555$	−20.3864	−	14.1386i	−0.865355	−	0.600151i
$556$		0			0
$557$	7.98775	−	4.61173i	0.338452	−	0.195405i	−0.321135	−	0.947033i	$-0.604064\pi$
$557$	7.98775	−	4.61173i	0.338452	−	0.195405i	0.659587	+	0.751628i	$0.270731\pi$
$558$		0			0
$559$	0.908230	+	0.524367i	0.0384140	+	0.0221784i
$560$		0			0
$561$	−34.7708	+	3.19955i	−1.46802	+	0.135085i
$562$		0			0
$563$	−2.63338	−	14.9346i	−0.110984	−	0.629419i	−0.988661	−	0.150167i	$-0.952019\pi$
$563$	−2.63338	−	14.9346i	−0.110984	−	0.629419i	0.877677	−	0.479252i	$-0.159092\pi$
$564$		0			0
$565$	−6.32900	−	5.31066i	−0.266263	−	0.223421i
$566$		0			0
$567$	24.4630	+	3.86150i	1.02735	+	0.162168i
$568$		0			0
$569$	2.29665	−	2.73704i	0.0962807	−	0.114743i	−0.715753	−	0.698354i	$-0.753916\pi$
$569$	2.29665	−	2.73704i	0.0962807	−	0.114743i	0.812033	+	0.583611i	$0.198361\pi$
$570$		0			0
$571$	−15.6830	+	2.76533i	−0.656313	+	0.115726i	−0.491881	−	0.870663i	$-0.663690\pi$
$571$	−15.6830	+	2.76533i	−0.656313	+	0.115726i	−0.164432	+	0.986388i	$0.552579\pi$
$572$		0			0
$573$	1.51973	+	16.5155i	0.0634877	+	0.689946i
$574$		0			0
$575$	4.17093	−	7.22426i	0.173940	−	0.301272i
$576$		0			0
$577$	9.41269	+	16.3032i	0.391855	+	0.678713i	0.992694	−	0.120657i	$-0.0385001\pi$
$577$	9.41269	+	16.3032i	0.391855	+	0.678713i	−0.600839	+	0.799370i	$0.705167\pi$
$578$		0			0
$579$	12.6366	−	18.2207i	0.525160	−	0.757226i
$580$		0			0
$581$	13.2925	+	15.8413i	0.551465	+	0.657210i
$582$		0			0
$583$	−16.1039	−	44.2451i	−0.666955	−	1.83244i
$584$		0			0
$585$	−1.20071	+	0.449283i	−0.0496432	+	0.0185756i
$586$		0			0
$587$	−2.20174	+	12.4867i	−0.0908756	+	0.515381i	0.905058	+	0.425289i	$0.139827\pi$
$587$	−2.20174	+	12.4867i	−0.0908756	+	0.515381i	−0.995933	+	0.0900926i	$0.971284\pi$
$588$		0			0
$589$	−3.28065	−	1.19406i	−0.135177	−	0.0492003i
$590$		0			0
$591$	−2.77099	−	10.1587i	−0.113983	−	0.417871i
$592$		0			0
$593$			34.7748i			1.42803i	0.700131	+	0.714014i	$0.253125\pi$
$593$			34.7748i			1.42803i	−0.700131	+	0.714014i	$0.746875\pi$
$594$		0			0
$595$		−	35.1267i		−	1.44005i
$596$		0			0
$597$	11.2850	+	2.96951i	0.461863	+	0.121534i
$598$		0			0
$599$	42.0361	+	15.2999i	1.71755	+	0.625136i	0.997623	−	0.0689154i	$-0.0219539\pi$
$599$	42.0361	+	15.2999i	1.71755	+	0.625136i	0.719925	+	0.694052i	$0.244176\pi$
$600$		0			0
$601$	5.03284	−	28.5427i	0.205294	−	1.16428i	−0.691682	−	0.722202i	$-0.743130\pi$
$601$	5.03284	−	28.5427i	0.205294	−	1.16428i	0.896976	−	0.442078i	$-0.145759\pi$
$602$		0			0
$603$	−35.4185	+	30.2662i	−1.44235	+	1.23254i
$604$		0			0
$605$	−5.57058	−	15.3050i	−0.226476	−	0.622238i
$606$		0			0
$607$	−18.3404	−	21.8573i	−0.744416	−	0.887160i	0.252341	−	0.967638i	$-0.418800\pi$
$607$	−18.3404	−	21.8573i	−0.744416	−	0.887160i	−0.996756	+	0.0804784i	$0.974355\pi$
$608$		0			0
$609$	31.2143	+	2.58962i	1.26487	+	0.104937i
$610$		0			0
$611$	−0.555797	−	0.962668i	−0.0224851	−	0.0389454i
$612$		0			0
$613$	9.57627	−	16.5866i	0.386782	−	0.669926i	−0.605233	−	0.796048i	$-0.706920\pi$
$613$	9.57627	−	16.5866i	0.386782	−	0.669926i	0.992015	+	0.126123i	$0.0402533\pi$
$614$		0			0
$615$	20.4260	+	9.41327i	0.823654	+	0.379580i
$616$		0			0
$617$	28.7867	−	5.07587i	1.15891	−	0.204347i	0.439047	−	0.898464i	$-0.355316\pi$
$617$	28.7867	−	5.07587i	1.15891	−	0.204347i	0.719862	+	0.694117i	$0.244205\pi$
$618$		0			0
$619$	−6.86358	+	8.17970i	−0.275871	+	0.328770i	−0.886134	−	0.463429i	$-0.846619\pi$
$619$	−6.86358	+	8.17970i	−0.275871	+	0.328770i	0.610264	+	0.792198i	$0.291064\pi$
$620$		0			0
$621$	18.8928	+	12.8529i	0.758142	+	0.515767i
$622$		0			0
$623$	19.3536	+	16.2396i	0.775386	+	0.650626i
$624$		0			0
$625$	−5.36335	−	30.4171i	−0.214534	−	1.21668i
$626$		0			0
$627$	11.5858	+	16.3889i	0.462690	+	0.654511i
$628$		0			0
$629$	−22.9592	−	13.2555i	−0.915441	−	0.528530i
$630$		0			0
$631$	−0.521761	+	0.301239i	−0.0207710	+	0.0119921i	−0.510350	−	0.859967i	$-0.670484\pi$
$631$	−0.521761	+	0.301239i	−0.0207710	+	0.0119921i	0.489579	+	0.871959i	$0.337151\pi$
$632$		0			0
$633$	−30.1068	+	14.2041i	−1.19664	+	0.564561i
$634$		0			0
$635$	40.7646	−	34.2056i	1.61769	−	1.35741i
$636$		0			0
$637$	−0.0874973	+	0.0318464i	−0.00346677	+	0.00126180i
$638$		0			0
$639$	27.0321	−	15.9326i	1.06937	−	0.630284i
$640$		0			0
$641$	−29.6795	−	5.23329i	−1.17227	−	0.206703i	−0.446591	−	0.894738i	$-0.647362\pi$
$641$	−29.6795	−	5.23329i	−1.17227	−	0.206703i	−0.725677	+	0.688035i	$0.758473\pi$
$642$		0			0
$643$	−3.70260	+	10.1728i	−0.146016	+	0.401176i	−0.991042	−	0.133549i	$-0.957363\pi$
$643$	−3.70260	+	10.1728i	−0.146016	+	0.401176i	0.845026	+	0.534725i	$0.179585\pi$
$644$		0			0
$645$	20.8228	+	20.6365i	0.819896	+	0.812561i
$646$		0			0
$647$	−32.2861			−1.26930			−0.634649	−	0.772800i	$-0.718855\pi$
$647$	−32.2861			−1.26930			−0.634649	+	0.772800i	$0.718855\pi$
$648$		0			0
$649$	32.0604			1.25848
$650$		0			0
$651$	−4.23022	−	4.19237i	−0.165795	−	0.164312i
$652$		0			0
$653$	−10.3261	+	28.3706i	−0.404090	+	1.11023i	0.556157	+	0.831077i	$0.312275\pi$
$653$	−10.3261	+	28.3706i	−0.404090	+	1.11023i	−0.960247	+	0.279151i	$0.909947\pi$
$654$		0			0
$655$	25.8121	+	4.55137i	1.00856	+	0.177837i
$656$		0			0
$657$	−37.9225	−	21.4425i	−1.47950	−	0.836550i
$658$		0			0
$659$	−24.2662	+	8.83218i	−0.945278	+	0.344053i	−0.768248	−	0.640152i	$-0.778871\pi$
$659$	−24.2662	+	8.83218i	−0.945278	+	0.344053i	−0.177030	+	0.984205i	$0.556649\pi$
$660$		0			0
$661$	16.6530	−	13.9735i	0.647727	−	0.543508i	−0.258653	−	0.965970i	$-0.583279\pi$
$661$	16.6530	−	13.9735i	0.647727	−	0.543508i	0.906380	+	0.422463i	$0.138834\pi$
$662$		0			0
$663$	−1.23897	+	0.584535i	−0.0481177	+	0.0227014i
$664$		0			0
$665$	−17.4856	+	10.0953i	−0.678064	+	0.391481i
$666$		0			0
$667$	25.0271	+	14.4494i	0.969053	+	0.559483i
$668$		0			0
$669$	−2.28624	−	3.23406i	−0.0883911	−	0.125036i
$670$		0			0
$671$	−2.53166	−	14.3578i	−0.0977338	−	0.554276i
$672$		0			0
$673$	−1.26099	−	1.05810i	−0.0486076	−	0.0407866i	0.618160	−	0.786052i	$-0.287878\pi$
$673$	−1.26099	−	1.05810i	−0.0486076	−	0.0407866i	−0.666768	+	0.745265i	$0.732323\pi$
$674$		0			0
$675$	−9.80681	+	0.991364i	−0.377464	+	0.0381576i
$676$		0			0
$677$	−3.09735	+	3.69128i	−0.119041	+	0.141867i	−0.822274	−	0.569092i	$-0.807295\pi$
$677$	−3.09735	+	3.69128i	−0.119041	+	0.141867i	0.703233	+	0.710960i	$0.251739\pi$
$678$		0			0
$679$	46.3715	−	8.17655i	1.77957	−	0.313787i
$680$		0			0
$681$	−31.1869	−	14.3725i	−1.19509	−	0.550754i
$682$		0			0
$683$	12.7847	−	22.1437i	0.489193	−	0.847307i	−0.510730	−	0.859741i	$-0.670625\pi$
$683$	12.7847	−	22.1437i	0.489193	−	0.847307i	0.999923	+	0.0124345i	$0.00395813\pi$
$684$		0			0
$685$	−13.7309	−	23.7826i	−0.524631	−	0.908687i
$686$		0			0
$687$	29.5080	+	2.44806i	1.12580	+	0.0933991i
$688$		0			0
$689$	−1.18741	−	1.41511i	−0.0452369	−	0.0539112i
$690$		0			0
$691$	1.82346	+	5.00991i	0.0693676	+	0.190586i	0.969532	−	0.244964i	$-0.0787762\pi$
$691$	1.82346	+	5.00991i	0.0693676	+	0.190586i	−0.900165	+	0.435550i	$0.856554\pi$
$692$		0			0
$693$	6.24832	+	33.6640i	0.237354	+	1.27879i
$694$		0			0
$695$	−5.64304	+	32.0033i	−0.214053	+	1.21395i
$696$		0			0
$697$	22.5838	+	8.21982i	0.855422	+	0.311348i
$698$		0			0
$699$	40.2267	+	10.5852i	1.52151	+	0.400370i
$700$		0			0
$701$		−	8.85544i		−	0.334465i	−0.985917	−	0.167233i	$-0.946517\pi$
$701$		−	8.85544i		−	0.334465i	0.985917	−	0.167233i	$-0.0534831\pi$
$702$		0			0
$703$			15.2384i			0.574726i
$704$		0			0
$705$	−8.17723	−	29.9784i	−0.307972	−	1.12905i
$706$		0			0
$707$	46.6543	+	16.9808i	1.75462	+	0.638628i
$708$		0			0
$709$	−1.80405	+	10.2313i	−0.0677526	+	0.384244i	0.932009	+	0.362434i	$0.118054\pi$
$709$	−1.80405	+	10.2313i	−0.0677526	+	0.384244i	−0.999762	+	0.0218104i	$0.993057\pi$
$710$		0			0
$711$	12.9251	+	10.6490i	0.484729	+	0.399368i
$712$		0			0
$713$	−1.87942	−	5.16366i	−0.0703848	−	0.193381i
$714$		0			0
$715$	−1.13927	−	1.35773i	−0.0426062	−	0.0507762i
$716$		0			0
$717$	10.3415	−	14.9114i	0.386212	−	0.556877i
$718$		0			0
$719$	−14.0383	−	24.3150i	−0.523539	−	0.906796i	−0.999625	−	0.0273972i	$-0.991278\pi$
$719$	−14.0383	−	24.3150i	−0.523539	−	0.906796i	0.476086	−	0.879399i	$-0.342055\pi$
$720$		0			0
$721$	11.2398	−	19.4679i	0.418592	−	0.725023i
$722$		0			0
$723$	2.52165	+	27.4038i	0.0937813	+	1.01916i
$724$		0			0
$725$	−12.2765	+	2.16468i	−0.455939	+	0.0803944i
$726$		0			0
$727$	−13.2829	+	15.8300i	−0.492637	+	0.587102i	−0.953886	−	0.300169i	$-0.902957\pi$
$727$	−13.2829	+	15.8300i	−0.492637	+	0.587102i	0.461249	+	0.887271i	$0.347401\pi$
$728$		0			0
$729$	−0.727866	−	26.9902i	−0.0269580	−	0.999637i
$730$		0			0
$731$	23.9979	+	20.1366i	0.887595	+	0.744781i
$732$		0			0
$733$	−4.16136	−	23.6002i	−0.153703	−	0.871694i	−0.959962	−	0.280131i	$-0.909622\pi$
$733$	−4.16136	−	23.6002i	−0.153703	−	0.871694i	0.806259	−	0.591563i	$-0.201489\pi$
$734$		0			0
$735$	−2.59193	+	0.238506i	−0.0956049	+	0.00879741i
$736$		0			0
$737$	−55.7800	−	32.2046i	−2.05468	−	1.18627i
$738$		0			0
$739$	−33.3120	+	19.2327i	−1.22540	+	0.707485i	−0.966064	−	0.258302i	$-0.916837\pi$
$739$	−33.3120	+	19.2327i	−1.22540	+	0.707485i	−0.259336	+	0.965787i	$0.583504\pi$
$740$		0			0
$741$	0.647052	+	0.448751i	0.0237701	+	0.0164853i
$742$		0			0
$743$	7.00921	−	5.88142i	0.257143	−	0.215768i	−0.505098	−	0.863062i	$-0.668544\pi$
$743$	7.00921	−	5.88142i	0.257143	−	0.215768i	0.762241	+	0.647294i	$0.224099\pi$
$744$		0			0
$745$	−31.9020	+	11.6114i	−1.16880	+	0.425407i
$746$		0			0
$747$	14.3358	−	17.3999i	0.524518	−	0.636629i
$748$		0			0
$749$	39.6127	+	6.98479i	1.44742	+	0.255219i
$750$		0			0
$751$	2.80369	−	7.70309i	0.102308	−	0.281090i	−0.877969	−	0.478718i	$-0.841102\pi$
$751$	2.80369	−	7.70309i	0.102308	−	0.281090i	0.980277	+	0.197628i	$0.0633239\pi$
$752$		0			0
$753$	−0.949303	+	0.258942i	−0.0345945	+	0.00943639i
$754$		0			0
$755$	15.1725			0.552185
$756$		0			0
$757$	52.5864			1.91128			0.955642	−	0.294529i	$-0.0951629\pi$
$757$	52.5864			1.91128			0.955642	+	0.294529i	$0.0951629\pi$
$758$		0			0
$759$	−8.03904	+	30.5506i	−0.291798	+	1.10891i
$760$		0			0
$761$	13.7230	−	37.7037i	0.497459	−	1.36676i	−0.396264	−	0.918137i	$-0.629693\pi$
$761$	13.7230	−	37.7037i	0.497459	−	1.36676i	0.893723	−	0.448620i	$-0.148084\pi$
$762$		0			0
$763$	−29.1465	−	5.13931i	−1.05517	−	0.186056i
$764$		0			0
$765$	−37.6524	+	6.98859i	−1.36132	+	0.252673i
$766$		0			0
$767$	1.18198	−	0.430206i	0.0426789	−	0.0155338i
$768$		0			0
$769$	2.51649	−	2.11159i	0.0907471	−	0.0761458i	−0.596286	−	0.802772i	$-0.703357\pi$
$769$	2.51649	−	2.11159i	0.0907471	−	0.0761458i	0.687033	+	0.726627i	$0.258913\pi$
$770$		0			0
$771$	0.872892	−	10.5215i	0.0314364	−	0.378924i
$772$		0			0
$773$	8.01544	−	4.62772i	0.288295	−	0.166447i	−0.348877	−	0.937168i	$-0.613437\pi$
$773$	8.01544	−	4.62772i	0.288295	−	0.166447i	0.637173	+	0.770721i	$0.280104\pi$
$774$		0			0
$775$	2.05280	+	1.18519i	0.0737388	+	0.0425731i
$776$		0			0
$777$	−10.8802	+	23.6092i	−0.390326	+	0.846974i
$778$		0			0
$779$	−2.39880	−	13.6043i	−0.0859461	−	0.487424i
$780$		0			0
$781$	33.2312	+	27.8843i	1.18911	+	0.997778i
$782$		0			0
$783$	−3.43440	−	33.9739i	−0.122735	−	1.21413i
$784$		0			0
$785$	−30.5137	+	36.3648i	−1.08908	+	1.29792i
$786$		0			0
$787$	24.7152	−	4.35795i	0.881001	−	0.155344i	0.285192	−	0.958470i	$-0.407943\pi$
$787$	24.7152	−	4.35795i	0.881001	−	0.155344i	0.595809	+	0.803126i	$0.296832\pi$
$788$		0			0
$789$	−5.16834	+	3.65363i	−0.183998	+	0.130073i
$790$		0			0
$791$	−4.32847	+	7.49714i	−0.153903	+	0.266567i
$792$		0			0
$793$	−0.285997	−	0.495362i	−0.0101561	−	0.0175908i
$794$		0			0
$795$	−22.0338	−	46.7026i	−0.781458	−	1.65637i
$796$		0			0
$797$	−27.5305	−	32.8095i	−0.975179	−	1.16217i	−0.986751	−	0.162240i	$-0.948128\pi$
$797$	−27.5305	−	32.8095i	−0.975179	−	1.16217i	0.0115719	−	0.999933i	$-0.496316\pi$
$798$		0			0
$799$	−11.3567	−	31.2023i	−0.401771	−	1.10386i
$800$		0			0
$801$	13.5568	−	23.9761i	0.479005	−	0.847153i
$802$		0			0
$803$	10.4586	−	59.3135i	0.369075	−	2.09313i
$804$		0			0
$805$	−29.8631	−	10.8693i	−1.05254	−	0.383092i
$806$		0			0
$807$	5.04457	−	5.09011i	0.177577	−	0.179180i
$808$		0			0
$809$			4.97939i			0.175066i	0.996162	+	0.0875331i	$0.0278983\pi$
$809$			4.97939i			0.175066i	−0.996162	+	0.0875331i	$0.972102\pi$
$810$		0			0
$811$		−	24.5760i		−	0.862978i	−0.902118	−	0.431489i	$-0.857988\pi$
$811$		−	24.5760i		−	0.862978i	0.902118	−	0.431489i	$-0.142012\pi$
$812$		0			0
$813$	−7.82454	+	7.89518i	−0.274419	+	0.276896i
$814$		0			0
$815$	−40.8156	−	14.8557i	−1.42971	−	0.520371i
$816$		0			0
$817$	3.12682	−	17.7331i	0.109394	−	0.620403i
$818$		0			0
$819$	0.682083	+	1.15726i	0.0238339	+	0.0404378i
$820$		0			0
$821$	−5.96288	−	16.3829i	−0.208106	−	0.571767i	0.791097	−	0.611691i	$-0.209510\pi$
$821$	−5.96288	−	16.3829i	−0.208106	−	0.571767i	−0.999203	+	0.0399245i	$0.987288\pi$
$822$		0			0
$823$	−20.9758	−	24.9980i	−0.731169	−	0.871374i	0.264495	−	0.964387i	$-0.414795\pi$
$823$	−20.9758	−	24.9980i	−0.731169	−	0.871374i	−0.995665	+	0.0930131i	$0.970350\pi$
$824$		0			0
$825$	−5.81447	−	12.3243i	−0.202434	−	0.429077i
$826$		0			0
$827$	−2.46607	−	4.27136i	−0.0857537	−	0.148530i	0.819958	−	0.572423i	$-0.193996\pi$
$827$	−2.46607	−	4.27136i	−0.0857537	−	0.148530i	−0.905712	+	0.423893i	$0.860663\pi$
$828$		0			0
$829$	−22.3193	+	38.6582i	−0.775182	+	1.34265i	0.159510	+	0.987196i	$0.449008\pi$
$829$	−22.3193	+	38.6582i	−0.775182	+	1.34265i	−0.934692	+	0.355458i	$0.884325\pi$
$830$		0			0
$831$	−6.63434	+	4.68998i	−0.230143	+	0.162694i
$832$		0			0
$833$	−2.73914	+	0.482985i	−0.0949057	+	0.0167344i
$834$		0			0
$835$	24.2941	−	28.9526i	0.840733	−	1.00195i
$836$		0			0
$837$	−3.65219	+	5.36847i	−0.126238	+	0.185561i
$838$		0			0
$839$	−14.4800	−	12.1502i	−0.499905	−	0.419470i	0.357655	−	0.933854i	$-0.383576\pi$
$839$	−14.4800	−	12.1502i	−0.499905	−	0.419470i	−0.857560	+	0.514384i	$0.828021\pi$
$840$		0			0
$841$	−2.46335	−	13.9704i	−0.0849431	−	0.481736i
$842$		0			0
$843$	6.00510	−	13.0305i	0.206827	−	0.448796i
$844$		0			0
$845$	29.5064	+	17.0355i	1.01505	+	0.586041i
$846$		0			0
$847$	−14.7796	+	8.53300i	−0.507833	+	0.293197i
$848$		0			0
$849$	−3.48852	+	42.0493i	−0.119726	+	1.44313i
$850$		0			0
$851$	−18.3734	+	15.4172i	−0.629834	+	0.528493i
$852$		0			0
$853$	38.8802	−	14.1512i	1.33123	−	0.484530i	0.424193	−	0.905572i	$-0.360558\pi$
$853$	38.8802	−	14.1512i	1.33123	−	0.484530i	0.907041	+	0.421042i	$0.138336\pi$
$854$		0			0
$855$	14.3000	+	16.7344i	0.489051	+	0.572304i
$856$		0			0
$857$	38.5413	+	6.79587i	1.31655	+	0.232143i	0.787429	−	0.616406i	$-0.211412\pi$
$857$	38.5413	+	6.79587i	1.31655	+	0.232143i	0.529118	+	0.848548i	$0.322523\pi$
$858$		0			0
$859$	−7.73509	+	21.2520i	−0.263918	+	0.725109i	0.734976	+	0.678093i	$0.237193\pi$
$859$	−7.73509	+	21.2520i	−0.263918	+	0.725109i	−0.998894	+	0.0470158i	$0.985029\pi$
$860$		0			0
$861$	5.99698	−	22.7902i	0.204376	−	0.776687i
$862$		0			0
$863$	−5.06741			−0.172497			−0.0862484	−	0.996274i	$-0.527488\pi$
$863$	−5.06741			−0.172497			−0.0862484	+	0.996274i	$0.527488\pi$
$864$		0			0
$865$	−36.0064			−1.22426
$866$		0			0
$867$	−11.0725	+	3.02026i	−0.376042	+	0.102573i
$868$		0			0
$869$	−7.91868	+	21.7564i	−0.268623	+	0.738035i
$870$		0			0
$871$	−2.48860	−	0.438807i	−0.0843230	−	0.0148684i
$872$		0			0
$873$	−17.9902	−	48.0789i	−0.608877	−	1.62722i
$874$		0			0
$875$	−21.0725	+	7.66976i	−0.712380	+	0.259285i
$876$		0			0
$877$	−3.89014	+	3.26422i	−0.131361	+	0.110225i	−0.706101	−	0.708111i	$-0.749548\pi$
$877$	−3.89014	+	3.26422i	−0.131361	+	0.110225i	0.574740	+	0.818336i	$0.305103\pi$
$878$		0			0
$879$	29.2066	+	20.2557i	0.985115	+	0.683209i
$880$		0			0
$881$	−25.8545	+	14.9271i	−0.871059	+	0.502906i	−0.867700	−	0.497088i	$-0.834403\pi$
$881$	−25.8545	+	14.9271i	−0.871059	+	0.502906i	−0.00335923	+	0.999994i	$0.501069\pi$
$882$		0			0
$883$	−28.4281	−	16.4130i	−0.956682	−	0.552341i	−0.0615317	−	0.998105i	$-0.519599\pi$
$883$	−28.4281	−	16.4130i	−0.956682	−	0.552341i	−0.895150	+	0.445765i	$0.852932\pi$
$884$		0			0
$885$	35.0138	−	3.22192i	1.17698	−	0.108304i
$886$		0			0
$887$	3.44683	+	19.5480i	0.115733	+	0.656356i	0.986385	+	0.164456i	$0.0525867\pi$
$887$	3.44683	+	19.5480i	0.115733	+	0.656356i	−0.870651	+	0.491901i	$0.836302\pi$
$888$		0			0
$889$	−42.7137	−	35.8410i	−1.43257	−	1.20207i
$890$		0			0
$891$	34.8413	−	13.3952i	1.16723	−	0.448755i
$892$		0			0
$893$	−12.2682	+	14.6207i	−0.410540	+	0.489263i
$894$		0			0
$895$	−15.7734	+	2.78128i	−0.527248	+	0.0929680i
$896$		0			0
$897$	0.113568	+	1.23419i	0.00379193	+	0.0412084i
$898$		0			0
$899$	−4.10586	+	7.11155i	−0.136938	+	0.237184i
$900$		0			0
$901$	−27.5905	−	47.7881i	−0.919172	−	1.59205i
$902$		0			0
$903$	17.5059	−	25.2417i	0.582561	−	0.839992i
$904$		0			0
$905$	−36.5451	−	43.5527i	−1.21480	−	1.44774i
$906$		0			0
$907$	1.69570	+	4.65889i	0.0563048	+	0.154696i	0.964656	−	0.263512i	$-0.0848807\pi$
$907$	1.69570	+	4.65889i	0.0563048	+	0.154696i	−0.908351	+	0.418208i	$0.862658\pi$
$908$		0			0
$909$	8.91966	−	53.3872i	0.295846	−	1.77074i
$910$		0			0
$911$	−7.13353	+	40.4562i	−0.236344	+	1.34037i	0.603420	+	0.797424i	$0.293804\pi$
$911$	−7.13353	+	40.4562i	−0.236344	+	1.34037i	−0.839764	+	0.542951i	$0.817307\pi$
$912$		0			0
$913$	29.2887	+	10.6602i	0.969314	+	0.352801i
$914$		0			0
$915$	−4.20777	−	15.4260i	−0.139105	−	0.509968i
$916$		0			0
$917$		−	27.4634i		−	0.906923i
$918$		0			0
$919$		−	5.92178i		−	0.195341i	−0.995219	−	0.0976707i	$-0.968861\pi$
$919$		−	5.92178i		−	0.195341i	0.995219	−	0.0976707i	$-0.0311392\pi$
$920$		0			0
$921$	−13.4397	−	3.53650i	−0.442853	−	0.116532i
$922$		0			0
$923$	1.59931	+	0.582103i	0.0526421	+	0.0191601i
$924$		0			0
$925$	1.79660	−	10.1890i	0.0590718	−	0.335013i
$926$		0			0
$927$	−23.1039	−	8.17474i	−0.758831	−	0.268494i
$928$		0			0
$929$	−8.91690	−	24.4990i	−0.292554	−	0.803786i	−0.995691	−	0.0927315i	$-0.970440\pi$
$929$	−8.91690	−	24.4990i	−0.292554	−	0.803786i	0.703137	−	0.711054i	$-0.251782\pi$
$930$		0			0
$931$	1.02765	+	1.22470i	0.0336798	+	0.0401380i
$932$		0			0
$933$	25.9815	+	2.15549i	0.850598	+	0.0705677i
$934$		0			0
$935$	−26.4718	−	45.8505i	−0.865720	−	1.49947i
$936$		0			0
$937$	−17.3505	+	30.0519i	−0.566816	+	0.981753i	0.430063	+	0.902799i	$0.358491\pi$
$937$	−17.3505	+	30.0519i	−0.566816	+	0.981753i	−0.996878	+	0.0789544i	$0.974842\pi$
$938$		0			0
$939$	−10.9681	−	5.05464i	−0.357931	−	0.164952i
$940$		0			0
$941$	−30.5493	+	5.38667i	−0.995879	+	0.175600i	−0.647755	−	0.761848i	$-0.724292\pi$
$941$	−30.5493	+	5.38667i	−0.995879	+	0.175600i	−0.348123	+	0.937449i	$0.613181\pi$
$942$		0			0
$943$	13.9762	−	16.6562i	0.455128	−	0.542401i
$944$		0			0
$945$	10.2070	+	36.1372i	0.332033	+	1.17554i
$946$		0			0
$947$	33.2257	+	27.8797i	1.07969	+	0.905967i	0.995895	−	0.0905162i	$-0.0288517\pi$
$947$	33.2257	+	27.8797i	1.07969	+	0.905967i	0.0837943	+	0.996483i	$0.473296\pi$
$948$		0			0
$949$	−0.410325	−	2.32707i	−0.0133197	−	0.0755399i
$950$		0			0
$951$	26.1470	+	36.9869i	0.847874	+	1.19938i
$952$		0			0
$953$	−3.18660	−	1.83978i	−0.103224	−	0.0595965i	0.447499	−	0.894284i	$-0.352315\pi$
$953$	−3.18660	−	1.83978i	−0.103224	−	0.0595965i	−0.550723	+	0.834688i	$0.685648\pi$
$954$		0			0
$955$	−21.7782	+	12.5736i	−0.704725	+	0.406873i
$956$		0			0
$957$	42.6952	−	20.1432i	1.38014	−	0.651136i
$958$		0			0
$959$	−22.0428	+	18.4961i	−0.711799	+	0.597270i
$960$		0			0
$961$	−27.6632	+	10.0686i	−0.892361	+	0.324793i
$962$		0			0
$963$	−0.394099	−	43.8505i	−0.0126997	−	1.41306i
$964$		0			0
$965$	33.1100	+	5.83819i	1.06585	+	0.187938i
$966$		0			0
$967$	14.2442	−	39.1355i	0.458061	−	1.25851i	−0.468865	−	0.883270i	$-0.655337\pi$
$967$	14.2442	−	39.1355i	0.458061	−	1.25851i	0.926926	−	0.375244i	$-0.122441\pi$
$968$		0			0
$969$	16.7069	+	16.5575i	0.536704	+	0.531903i
$970$		0			0
$971$	46.0203			1.47686			0.738431	−	0.674329i	$-0.235567\pi$
$971$	46.0203			1.47686			0.738431	+	0.674329i	$0.235567\pi$
$972$		0			0
$973$	34.0507			1.09162
$974$		0			0
$975$	−0.379739	−	0.376341i	−0.0121614	−	0.0120526i
$976$		0			0
$977$	−10.8463	+	29.8001i	−0.347005	+	0.953388i	0.636303	+	0.771439i	$0.280463\pi$
$977$	−10.8463	+	29.8001i	−0.347005	+	0.953388i	−0.983308	+	0.181949i	$0.941759\pi$
$978$		0			0
$979$	37.5003	+	6.61232i	1.19852	+	0.211331i
$980$		0			0
$981$	0.289973	+	32.2646i	0.00925813	+	1.03013i
$982$		0			0
$983$	−12.9923	+	4.72882i	−0.414391	+	0.150826i	−0.540798	−	0.841153i	$-0.681878\pi$
$983$	−12.9923	+	4.72882i	−0.414391	+	0.150826i	0.126407	+	0.991978i	$0.459655\pi$
$984$		0			0
$985$	12.2304	−	10.2625i	0.389694	−	0.326992i
$986$		0			0
$987$	−29.4466	+	13.8926i	−0.937296	+	0.442207i
$988$		0			0
$989$	24.5449	−	14.1710i	0.780483	−	0.450612i
$990$		0			0
$991$	16.0288	+	9.25425i	0.509173	+	0.293971i	0.732494	−	0.680774i	$-0.238356\pi$
$991$	16.0288	+	9.25425i	0.509173	+	0.293971i	−0.223321	+	0.974745i	$0.571690\pi$
$992$		0			0
$993$	9.39604	+	13.2914i	0.298174	+	0.421791i
$994$		0			0
$995$	3.07239	+	17.4244i	0.0974012	+	0.552390i
$996$		0			0
$997$	−15.8196	−	13.2743i	−0.501013	−	0.420400i	0.356940	−	0.934127i	$-0.383820\pi$
$997$	−15.8196	−	13.2743i	−0.501013	−	0.420400i	−0.857954	+	0.513727i	$0.828264\pi$
$998$		0			0
$999$	27.4713	+	6.96541i	0.869155	+	0.220376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.10	yes	216
4.3	odd	2	inner	864.2.bi.a.767.27	yes	216
27.5	odd	18	inner	864.2.bi.a.383.27	yes	216
108.59	even	18	inner	864.2.bi.a.383.10	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.10	✓	216	108.59	even	18	inner
864.2.bi.a.383.27	yes	216	27.5	odd	18	inner
864.2.bi.a.767.10	yes	216	1.1	even	1	trivial
864.2.bi.a.767.27	yes	216	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23024 - 1.21923i) q^{3} +(0.898214 - 2.46782i) q^{5} +(-2.70996 - 0.477839i) q^{7} +(0.0269609 + 2.99988i) q^{9} +O(q^{10})\)	\(q+(-1.23024 - 1.21923i) q^{3} +(0.898214 - 2.46782i) q^{5} +(-2.70996 - 0.477839i) q^{7} +(0.0269609 + 2.99988i) q^{9} +(-3.89738 + 1.41853i) q^{11} +(-0.124651 + 0.104595i) q^{13} +(-4.11386 + 1.94088i) q^{15} +(-4.20948 + 2.43034i) q^{17} +(2.41959 + 1.39695i) q^{19} +(2.75130 + 3.89192i) q^{21} +(0.763623 + 4.33072i) q^{23} +(-1.45314 - 1.21933i) q^{25} +(3.62437 - 3.72343i) q^{27} +(4.22414 - 5.03413i) q^{29} +(-1.23059 + 0.216987i) q^{31} +(6.52422 + 3.00668i) q^{33} +(-3.61335 + 6.25850i) q^{35} +(2.72708 + 4.72344i) q^{37} +(0.280876 + 0.0233022i) q^{39} +(-3.17820 - 3.78763i) q^{41} +(-2.20432 - 6.05631i) q^{43} +(7.42739 + 2.62800i) q^{45} +(-1.18624 + 6.72751i) q^{47} +(0.537714 + 0.195712i) q^{49} +(8.14179 + 2.14242i) q^{51} +11.3525i q^{53} +10.8922i q^{55} +(-1.27346 - 4.66861i) q^{57} +(-7.26386 - 2.64383i) q^{59} +(-0.610406 + 3.46178i) q^{61} +(1.36040 - 8.14244i) q^{63} +(0.146158 + 0.401566i) q^{65} +(9.98223 + 11.8964i) q^{67} +(4.34071 - 6.25884i) q^{69} +(-5.22967 - 9.05806i) q^{71} +(-7.26080 + 12.5761i) q^{73} +(0.301063 + 3.27177i) q^{75} +(11.2396 - 1.98184i) q^{77} +(3.58824 - 4.27629i) q^{79} +(-8.99855 + 0.161759i) q^{81} +(-5.75679 - 4.83052i) q^{83} +(2.21664 + 12.5712i) q^{85} +(-11.3345 + 1.04298i) q^{87} +(-7.95110 - 4.59057i) q^{89} +(0.387780 - 0.223885i) q^{91} +(1.77848 + 1.23343i) q^{93} +(5.62074 - 4.71636i) q^{95} +(-16.0795 + 5.85248i) q^{97} +(-4.36050 - 11.6534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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