LMFDB - Embedded newform 432.2.be.b.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	432.191
Dual form			432.2.be.b.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22376 - 1.22573i) q^{3} +(1.15344 + 1.37462i) q^{5} +(-0.0374696 - 0.102947i) q^{7} +(-0.00480931 + 3.00000i) q^{9} +O(q^{10})$	\(q+(-1.22376 - 1.22573i) q^{3} +(1.15344 + 1.37462i) q^{5} +(-0.0374696 - 0.102947i) q^{7} +(-0.00480931 + 3.00000i) q^{9} +(1.39140 + 1.16752i) q^{11} +(0.628601 + 3.56497i) q^{13} +(0.273367 - 3.09601i) q^{15} +(3.51663 - 2.03033i) q^{17} +(-0.846129 - 0.488513i) q^{19} +(-0.0803308 + 0.171910i) q^{21} +(5.93514 + 2.16021i) q^{23} +(0.309093 - 1.75296i) q^{25} +(3.68306 - 3.66539i) q^{27} +(0.912843 + 0.160959i) q^{29} +(0.185026 - 0.508354i) q^{31} +(-0.271680 - 3.13425i) q^{33} +(0.0982937 - 0.170250i) q^{35} +(4.79618 + 8.30722i) q^{37} +(3.60042 - 5.13318i) q^{39} +(0.0246348 - 0.00434378i) q^{41} +(-6.93075 + 8.25975i) q^{43} +(-4.12940 + 3.45371i) q^{45} +(7.54426 - 2.74589i) q^{47} +(5.35312 - 4.49180i) q^{49} +(-6.79215 - 1.82579i) q^{51} -11.7054i q^{53} +3.25932i q^{55} +(0.436678 + 1.63495i) q^{57} +(1.98032 - 1.66168i) q^{59} +(-5.80843 + 2.11410i) q^{61} +(0.309021 - 0.111914i) q^{63} +(-4.17542 + 4.97608i) q^{65} +(-13.5924 + 2.39670i) q^{67} +(-4.61537 - 9.91844i) q^{69} +(0.650941 + 1.12746i) q^{71} +(-3.34757 + 5.79815i) q^{73} +(-2.52690 + 1.76634i) q^{75} +(0.0680578 - 0.186987i) q^{77} +(-8.71473 - 1.53664i) q^{79} +(-8.99995 - 0.0288558i) q^{81} +(-3.02146 + 17.1355i) q^{83} +(6.84715 + 2.49216i) q^{85} +(-0.919812 - 1.31587i) q^{87} +(-4.27071 - 2.46569i) q^{89} +(0.343450 - 0.198291i) q^{91} +(-0.849530 + 0.395314i) q^{93} +(-0.304442 - 1.72657i) q^{95} +(-10.6279 - 8.91789i) q^{97} +(-3.50926 + 4.16859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.22376	−	1.22573i	−0.706540	−	0.707673i
$3$	−1.22376	−	1.22573i	−0.706540	−	0.707673i
$4$		0			0
$5$	1.15344	+	1.37462i	0.515835	+	0.614748i	0.959591	−	0.281400i	$-0.0907987\pi$
$5$	1.15344	+	1.37462i	0.515835	+	0.614748i	−0.443756	+	0.896148i	$0.646354\pi$
$6$		0			0
$7$	−0.0374696	−	0.102947i	−0.0141622	−	0.0389103i	0.932410	−	0.361402i	$-0.117702\pi$
$7$	−0.0374696	−	0.102947i	−0.0141622	−	0.0389103i	−0.946572	+	0.322492i	$0.895480\pi$
$8$		0			0
$9$	−0.00480931	+	3.00000i	−0.00160310	+	0.999999i
$10$		0			0
$11$	1.39140	+	1.16752i	0.419523	+	0.352022i	0.827982	−	0.560755i	$-0.189489\pi$
$11$	1.39140	+	1.16752i	0.419523	+	0.352022i	−0.408458	+	0.912777i	$0.633933\pi$
$12$		0			0
$13$	0.628601	+	3.56497i	0.174343	+	0.988746i	0.938900	+	0.344190i	$0.111847\pi$
$13$	0.628601	+	3.56497i	0.174343	+	0.988746i	−0.764557	+	0.644556i	$0.777042\pi$
$14$		0			0
$15$	0.273367	−	3.09601i	0.0705829	−	0.799386i
$16$		0			0
$17$	3.51663	−	2.03033i	0.852908	−	0.492427i	−0.00872297	−	0.999962i	$-0.502777\pi$
$17$	3.51663	−	2.03033i	0.852908	−	0.492427i	0.861631	+	0.507535i	$0.169443\pi$
$18$		0			0
$19$	−0.846129	−	0.488513i	−0.194115	−	0.112073i	0.399792	−	0.916606i	$-0.369082\pi$
$19$	−0.846129	−	0.488513i	−0.194115	−	0.112073i	−0.593908	+	0.804533i	$0.702416\pi$
$20$		0			0
$21$	−0.0803308	+	0.171910i	−0.0175296	+	0.0375139i
$22$		0			0
$23$	5.93514	+	2.16021i	1.23756	+	0.450436i	0.876181	−	0.481983i	$-0.160083\pi$
$23$	5.93514	+	2.16021i	1.23756	+	0.450436i	0.361381	+	0.932418i	$0.382305\pi$
$24$		0			0
$25$	0.309093	−	1.75296i	0.0618187	−	0.350591i
$26$		0			0
$27$	3.68306	−	3.66539i	0.708805	−	0.705404i
$28$		0			0
$29$	0.912843	+	0.160959i	0.169511	+	0.0298893i	0.257759	−	0.966209i	$-0.417016\pi$
$29$	0.912843	+	0.160959i	0.169511	+	0.0298893i	−0.0882486	+	0.996098i	$0.528127\pi$
$30$		0			0
$31$	0.185026	−	0.508354i	0.0332316	−	0.0913030i	−0.921967	−	0.387268i	$-0.873419\pi$
$31$	0.185026	−	0.508354i	0.0332316	−	0.0913030i	0.955199	+	0.295965i	$0.0956411\pi$
$32$		0			0
$33$	−0.271680	−	3.13425i	−0.0472934	−	0.545603i
$34$		0			0
$35$	0.0982937	−	0.170250i	0.0166147	−	0.0287775i
$36$		0			0
$37$	4.79618	+	8.30722i	0.788486	+	1.36570i	0.926894	+	0.375323i	$0.122468\pi$
$37$	4.79618	+	8.30722i	0.788486	+	1.36570i	−0.138408	+	0.990375i	$0.544198\pi$
$38$		0			0
$39$	3.60042	−	5.13318i	0.576529	−	0.821966i
$40$		0			0
$41$	0.0246348	−	0.00434378i	0.00384731	−	0.000678384i	−0.171724	−	0.985145i	$-0.554934\pi$
$41$	0.0246348	−	0.00434378i	0.00384731	−	0.000678384i	0.175571	+	0.984467i	$0.443823\pi$
$42$		0			0
$43$	−6.93075	+	8.25975i	−1.05693	+	1.25960i	−0.0923729	+	0.995724i	$0.529445\pi$
$43$	−6.93075	+	8.25975i	−1.05693	+	1.25960i	−0.964557	+	0.263875i	$0.914999\pi$
$44$		0			0
$45$	−4.12940	+	3.45371i	−0.615574	+	0.514849i
$46$		0			0
$47$	7.54426	−	2.74589i	1.10044	−	0.400529i	0.272964	−	0.962024i	$-0.411996\pi$
$47$	7.54426	−	2.74589i	1.10044	−	0.400529i	0.827480	+	0.561496i	$0.189774\pi$
$48$		0			0
$49$	5.35312	−	4.49180i	0.764731	−	0.641685i
$50$		0			0
$51$	−6.79215	−	1.82579i	−0.951091	−	0.255661i
$52$		0			0
$53$		−	11.7054i		−	1.60786i	−0.594726	−	0.803928i	$-0.702740\pi$
$53$		−	11.7054i		−	1.60786i	0.594726	−	0.803928i	$-0.297260\pi$
$54$		0			0
$55$			3.25932i			0.439486i
$56$		0			0
$57$	0.436678	+	1.63495i	0.0578394	+	0.216554i
$58$		0			0
$59$	1.98032	−	1.66168i	0.257815	−	0.216333i	−0.504714	−	0.863287i	$-0.668402\pi$
$59$	1.98032	−	1.66168i	0.257815	−	0.216333i	0.762529	+	0.646954i	$0.223957\pi$
$60$		0			0
$61$	−5.80843	+	2.11410i	−0.743694	+	0.270682i	−0.685950	−	0.727649i	$-0.740613\pi$
$61$	−5.80843	+	2.11410i	−0.743694	+	0.270682i	−0.0577441	+	0.998331i	$0.518391\pi$
$62$		0			0
$63$	0.309021	−	0.111914i	0.0389329	−	0.0140998i
$64$		0			0
$65$	−4.17542	+	4.97608i	−0.517897	+	0.617206i
$66$		0			0
$67$	−13.5924	+	2.39670i	−1.66057	+	0.292804i	−0.923669	−	0.383192i	$-0.874825\pi$
$67$	−13.5924	+	2.39670i	−1.66057	+	0.292804i	−0.736905	+	0.675996i	$0.763714\pi$
$68$		0			0
$69$	−4.61537	−	9.91844i	−0.555625	−	1.19404i
$70$		0			0
$71$	0.650941	+	1.12746i	0.0772525	+	0.133805i	0.902064	−	0.431603i	$-0.142052\pi$
$71$	0.650941	+	1.12746i	0.0772525	+	0.133805i	−0.824811	+	0.565408i	$0.808719\pi$
$72$		0			0
$73$	−3.34757	+	5.79815i	−0.391803	+	0.678623i	−0.992687	−	0.120713i	$-0.961482\pi$
$73$	−3.34757	+	5.79815i	−0.391803	+	0.678623i	0.600884	+	0.799336i	$0.294815\pi$
$74$		0			0
$75$	−2.52690	+	1.76634i	−0.291781	+	0.203959i
$76$		0			0
$77$	0.0680578	−	0.186987i	0.00775591	−	0.0213092i
$78$		0			0
$79$	−8.71473	−	1.53664i	−0.980484	−	0.172886i	−0.339639	−	0.940556i	$-0.610305\pi$
$79$	−8.71473	−	1.53664i	−0.980484	−	0.172886i	−0.640845	+	0.767670i	$0.721416\pi$
$80$		0			0
$81$	−8.99995	−	0.0288558i	−0.999995	−	0.00320620i
$82$		0			0
$83$	−3.02146	+	17.1355i	−0.331648	+	1.88087i	0.126460	+	0.991972i	$0.459638\pi$
$83$	−3.02146	+	17.1355i	−0.331648	+	1.88087i	−0.458108	+	0.888897i	$0.651473\pi$
$84$		0			0
$85$	6.84715	+	2.49216i	0.742678	+	0.270313i
$86$		0			0
$87$	−0.919812	−	1.31587i	−0.0986141	−	0.141076i
$88$		0			0
$89$	−4.27071	−	2.46569i	−0.452694	−	0.261363i	0.256273	−	0.966604i	$-0.417505\pi$
$89$	−4.27071	−	2.46569i	−0.452694	−	0.261363i	−0.708967	+	0.705241i	$0.750839\pi$
$90$		0			0
$91$	0.343450	−	0.198291i	0.0360033	−	0.0207865i
$92$		0			0
$93$	−0.849530	+	0.395314i	−0.0880921	+	0.0409921i
$94$		0			0
$95$	−0.304442	−	1.72657i	−0.0312351	−	0.177143i
$96$		0			0
$97$	−10.6279	−	8.91789i	−1.07910	−	0.905475i	−0.0832569	−	0.996528i	$-0.526532\pi$
$97$	−10.6279	−	8.91789i	−1.07910	−	0.905475i	−0.995846	+	0.0910532i	$0.970977\pi$
$98$		0			0
$99$	−3.50926	+	4.16859i	−0.352694	+	0.418959i
$100$		0			0
$101$	−4.68279	−	12.8659i	−0.465955	−	1.28020i	−0.920941	−	0.389703i	$-0.872578\pi$
$101$	−4.68279	−	12.8659i	−0.465955	−	1.28020i	0.454985	−	0.890499i	$-0.349645\pi$
$102$		0			0
$103$	2.07621	+	2.47433i	0.204575	+	0.243803i	0.858571	−	0.512695i	$-0.171353\pi$
$103$	2.07621	+	2.47433i	0.204575	+	0.243803i	−0.653995	+	0.756499i	$0.726908\pi$
$104$		0			0
$105$	−0.328968	+	0.0878641i	−0.0321040	+	0.00857466i
$106$		0			0
$107$	−0.288606			−0.0279006			−0.0139503	−	0.999903i	$-0.504441\pi$
$107$	−0.288606			−0.0279006			−0.0139503	+	0.999903i	$0.504441\pi$
$108$		0			0
$109$	−3.08753			−0.295732			−0.147866	−	0.989007i	$-0.547240\pi$
$109$	−3.08753			−0.295732			−0.147866	+	0.989007i	$0.547240\pi$
$110$		0			0
$111$	4.31300	−	16.0449i	0.409371	−	1.52291i
$112$		0			0
$113$	7.46015	+	8.89065i	0.701791	+	0.836362i	0.992728	−	0.120380i	$-0.0384113\pi$
$113$	7.46015	+	8.89065i	0.701791	+	0.836362i	−0.290936	+	0.956742i	$0.593967\pi$
$114$		0			0
$115$	3.87637	+	10.6502i	0.361473	+	0.993139i
$116$		0			0
$117$	−10.6979	+	1.86866i	−0.989024	+	0.172757i
$118$		0			0
$119$	−0.340783	−	0.285951i	−0.0312395	−	0.0262131i
$120$		0			0
$121$	−1.33724	−	7.58389i	−0.121568	−	0.689445i
$122$		0			0
$123$	−0.0354714	−	0.0248797i	−0.00319835	−	0.00224333i
$124$		0			0
$125$	10.5363	−	6.08314i	0.942396	−	0.544092i
$126$		0			0
$127$	6.76517	+	3.90587i	0.600312	+	0.346590i	0.769164	−	0.639051i	$-0.220673\pi$
$127$	6.76517	+	3.90587i	0.600312	+	0.346590i	−0.168853	+	0.985641i	$0.554006\pi$
$128$		0			0
$129$	18.6058	−	1.61277i	1.63815	−	0.141996i
$130$		0			0
$131$	3.17078	+	1.15407i	0.277032	+	0.100831i	0.476800	−	0.879012i	$-0.341797\pi$
$131$	3.17078	+	1.15407i	0.277032	+	0.100831i	−0.199768	+	0.979843i	$0.564019\pi$
$132$		0			0
$133$	−0.0185868	+	0.105411i	−0.00161168	+	0.00914028i
$134$		0			0
$135$	9.28670	+	0.834988i	0.799272	+	0.0718643i
$136$		0			0
$137$	−17.7688	−	3.13311i	−1.51809	−	0.267680i	−0.648407	−	0.761294i	$-0.724564\pi$
$137$	−17.7688	−	3.13311i	−1.51809	−	0.267680i	−0.869681	+	0.493614i	$0.835675\pi$
$138$		0			0
$139$	5.84789	−	16.0669i	0.496012	−	1.36278i	−0.399087	−	0.916913i	$-0.630673\pi$
$139$	5.84789	−	16.0669i	0.496012	−	1.36278i	0.895099	−	0.445868i	$-0.147105\pi$
$140$		0			0
$141$	−12.5981	−	5.88688i	−1.06095	−	0.495765i
$142$		0			0
$143$	−3.28756	+	5.69422i	−0.274920	+	0.476175i
$144$		0			0
$145$	0.831654	+	1.44047i	0.0690651	+	0.119624i
$146$		0			0
$147$	−12.0567	−	1.06456i	−0.994417	−	0.0878034i
$148$		0			0
$149$	17.4360	−	3.07444i	1.42841	−	0.251868i	0.594648	−	0.803986i	$-0.297291\pi$
$149$	17.4360	−	3.07444i	1.42841	−	0.251868i	0.833766	+	0.552118i	$0.186180\pi$
$150$		0			0
$151$	3.97337	−	4.73527i	0.323348	−	0.385351i	−0.579744	−	0.814799i	$-0.696847\pi$
$151$	3.97337	−	4.73527i	0.323348	−	0.385351i	0.903092	+	0.429448i	$0.141292\pi$
$152$		0			0
$153$	6.07406	+	10.5596i	0.491059	+	0.853696i
$154$		0			0
$155$	0.912208	−	0.332017i	0.0732703	−	0.0266682i
$156$		0			0
$157$	13.5145	−	11.3400i	1.07857	−	0.905032i	0.0827730	−	0.996568i	$-0.473622\pi$
$157$	13.5145	−	11.3400i	1.07857	−	0.905032i	0.995802	+	0.0915368i	$0.0291779\pi$
$158$		0			0
$159$	−14.3476	+	14.3246i	−1.13784	+	1.13601i
$160$		0			0
$161$		−	0.691947i		−	0.0545330i
$162$		0			0
$163$		−	0.563744i		−	0.0441559i	−0.999756	−	0.0220779i	$-0.992972\pi$
$163$		−	0.563744i		−	0.0441559i	0.999756	−	0.0220779i	$-0.00702820\pi$
$164$		0			0
$165$	3.99503	−	3.98863i	0.311013	−	0.310515i
$166$		0			0
$167$	13.0407	−	10.9424i	1.00912	−	0.846750i	0.0208959	−	0.999782i	$-0.493348\pi$
$167$	13.0407	−	10.9424i	1.00912	−	0.846750i	0.988221	+	0.153032i	$0.0489037\pi$
$168$		0			0
$169$	−0.0978970	+	0.0356316i	−0.00753054	+	0.00274089i
$170$		0			0
$171$	1.46961	−	2.53603i	0.112384	−	0.193935i
$172$		0			0
$173$	−11.8795	+	14.1575i	−0.903184	+	1.07637i	0.0935494	+	0.995615i	$0.470179\pi$
$173$	−11.8795	+	14.1575i	−0.903184	+	1.07637i	−0.996734	+	0.0807585i	$0.974266\pi$
$174$		0			0
$175$	−0.192043	+	0.0338624i	−0.0145171	+	0.00255976i
$176$		0			0
$177$	−4.46021	−	0.393820i	−0.335250	−	0.0296013i
$178$		0			0
$179$	−7.48642	−	12.9669i	−0.559561	−	0.969188i	−0.997533	−	0.0701997i	$-0.977636\pi$
$179$	−7.48642	−	12.9669i	−0.559561	−	0.969188i	0.437972	−	0.898989i	$-0.355697\pi$
$180$		0			0
$181$	−9.67055	+	16.7499i	−0.718806	+	1.24501i	0.242667	+	0.970110i	$0.421978\pi$
$181$	−9.67055	+	16.7499i	−0.718806	+	1.24501i	−0.961473	+	0.274899i	$0.911356\pi$
$182$		0			0
$183$	9.69945	+	4.53240i	0.717004	+	0.335044i
$184$		0			0
$185$	−5.88715	+	16.1748i	−0.432832	+	1.18920i
$186$		0			0
$187$	7.26350	+	1.28075i	0.531160	+	0.0936578i
$188$		0			0
$189$	−0.515344	−	0.241819i	−0.0374857	−	0.0175897i
$190$		0			0
$191$	−2.44661	+	13.8754i	−0.177031	+	1.00399i	0.758743	+	0.651390i	$0.225814\pi$
$191$	−2.44661	+	13.8754i	−0.177031	+	1.00399i	−0.935774	+	0.352601i	$0.885297\pi$
$192$		0			0
$193$	2.31451	+	0.842411i	0.166602	+	0.0606381i	0.423975	−	0.905674i	$-0.360635\pi$
$193$	2.31451	+	0.842411i	0.166602	+	0.0606381i	−0.257373	+	0.966312i	$0.582857\pi$
$194$		0			0
$195$	11.2090	−	0.971611i	0.802696	−	0.0695785i
$196$		0			0
$197$	7.93614	+	4.58193i	0.565426	+	0.326449i	0.755321	−	0.655355i	$-0.227481\pi$
$197$	7.93614	+	4.58193i	0.565426	+	0.326449i	−0.189894	+	0.981805i	$0.560814\pi$
$198$		0			0
$199$	7.82997	−	4.52063i	0.555052	−	0.320459i	−0.196105	−	0.980583i	$-0.562829\pi$
$199$	7.82997	−	4.52063i	0.555052	−	0.320459i	0.751157	+	0.660124i	$0.229496\pi$
$200$		0			0
$201$	19.5716	+	13.7275i	1.38047	+	0.968266i
$202$		0			0
$203$	−0.0176337	−	0.100005i	−0.00123764	−	0.00701901i
$204$		0			0
$205$	0.0343858	+	0.0288531i	0.00240161	+	0.00201519i
$206$		0			0
$207$	−6.50918	+	17.7950i	−0.452419	+	1.23684i
$208$		0			0
$209$	−0.606955	−	1.66759i	−0.0419839	−	0.115350i
$210$		0			0
$211$	−10.9596	−	13.0612i	−0.754492	−	0.899169i	0.242994	−	0.970028i	$-0.421870\pi$
$211$	−10.9596	−	13.0612i	−0.754492	−	0.899169i	−0.997486	+	0.0708592i	$0.977426\pi$
$212$		0			0
$213$	0.585363	−	2.17762i	0.0401084	−	0.149208i
$214$		0			0
$215$	−19.3482			−1.31954
$216$		0			0
$217$	−0.0592663			−0.00402326
$218$		0			0
$219$	11.2036	−	2.99237i	0.757068	−	0.202205i
$220$		0			0
$221$	9.44862	+	11.2604i	0.635583	+	0.757458i
$222$		0			0
$223$	−2.45483	−	6.74460i	−0.164388	−	0.451651i	0.829960	−	0.557823i	$-0.188363\pi$
$223$	−2.45483	−	6.74460i	−0.164388	−	0.451651i	−0.994348	+	0.106171i	$0.966141\pi$
$224$		0			0
$225$	5.25737	+	0.935710i	0.350492	+	0.0623806i
$226$		0			0
$227$	−20.2092	−	16.9575i	−1.34133	−	1.12551i	−0.981281	−	0.192580i	$-0.938315\pi$
$227$	−20.2092	−	16.9575i	−1.34133	−	1.12551i	−0.360052	−	0.932932i	$-0.617241\pi$
$228$		0			0
$229$	0.294614	+	1.67084i	0.0194686	+	0.110412i	0.992993	−	0.118169i	$-0.0377025\pi$
$229$	0.294614	+	1.67084i	0.0194686	+	0.110412i	−0.973525	+	0.228581i	$0.926591\pi$
$230$		0			0
$231$	−0.312482	+	0.145408i	−0.0205598	+	0.00956714i
$232$		0			0
$233$	−3.85496	+	2.22566i	−0.252547	+	0.145808i	−0.620930	−	0.783866i	$-0.713245\pi$
$233$	−3.85496	+	2.22566i	−0.252547	+	0.145808i	0.368383	+	0.929674i	$0.379912\pi$
$234$		0			0
$235$	12.4764	+	7.20326i	0.813871	+	0.469889i
$236$		0			0
$237$	8.78126	+	12.5624i	0.570404	+	0.816013i
$238$		0			0
$239$	−23.7297	−	8.63692i	−1.53495	−	0.558676i	−0.570122	−	0.821560i	$-0.693104\pi$
$239$	−23.7297	−	8.63692i	−1.53495	−	0.558676i	−0.964827	+	0.262884i	$0.915326\pi$
$240$		0			0
$241$	0.665669	−	3.77520i	0.0428795	−	0.243182i	−0.955833	−	0.293911i	$-0.905043\pi$
$241$	0.665669	−	3.77520i	0.0428795	−	0.243182i	0.998712	+	0.0507286i	$0.0161543\pi$
$242$		0			0
$243$	10.9784	+	11.0668i	0.704267	+	0.709935i
$244$		0			0
$245$	12.3490	+	2.17746i	0.788950	+	0.139113i
$246$		0			0
$247$	1.20966	−	3.32351i	0.0769687	−	0.211470i
$248$		0			0
$249$	24.7010	−	17.2663i	1.56536	−	1.09421i
$250$		0			0
$251$	9.34108	−	16.1792i	0.589604	−	1.02122i	−0.404680	−	0.914458i	$-0.632617\pi$
$251$	9.34108	−	16.1792i	0.589604	−	1.02122i	0.994284	−	0.106766i	$-0.0340494\pi$
$252$		0			0
$253$	5.73606	+	9.93515i	0.360623	+	0.624617i
$254$		0			0
$255$	−5.32458	−	11.4425i	−0.333438	−	0.716560i
$256$		0			0
$257$	−1.33829	+	0.235977i	−0.0834802	+	0.0147198i	−0.215232	−	0.976563i	$-0.569051\pi$
$257$	−1.33829	+	0.235977i	−0.0834802	+	0.0147198i	0.131752	+	0.991283i	$0.457940\pi$
$258$		0			0
$259$	0.675492	−	0.805020i	0.0419730	−	0.0500215i
$260$		0			0
$261$	−0.487266	+	2.73775i	−0.0301610	+	0.169463i
$262$		0			0
$263$	22.8321	−	8.31021i	1.40789	−	0.512429i	0.477379	−	0.878698i	$-0.341587\pi$
$263$	22.8321	−	8.31021i	1.40789	−	0.512429i	0.930509	+	0.366268i	$0.119365\pi$
$264$		0			0
$265$	16.0904	−	13.5015i	0.988426	−	0.829388i
$266$		0			0
$267$	2.20407	+	8.25215i	0.134887	+	0.505023i
$268$		0			0
$269$		−	7.63814i		−	0.465706i	−0.972512	−	0.232853i	$-0.925194\pi$
$269$		−	7.63814i		−	0.465706i	0.972512	−	0.232853i	$-0.0748061\pi$
$270$		0			0
$271$		−	6.51576i		−	0.395804i	−0.980222	−	0.197902i	$-0.936587\pi$
$271$		−	6.51576i		−	0.395804i	0.980222	−	0.197902i	$-0.0634128\pi$
$272$		0			0
$273$	−0.663351	−	0.178314i	−0.0401479	−	0.0107921i
$274$		0			0
$275$	2.47669	−	2.07819i	0.149350	−	0.125320i
$276$		0			0
$277$	−15.3821	+	5.59863i	−0.924221	+	0.336389i	−0.759916	−	0.650021i	$-0.774760\pi$
$277$	−15.3821	+	5.59863i	−0.924221	+	0.336389i	−0.164304	+	0.986410i	$0.552538\pi$
$278$		0			0
$279$	1.52417	+	0.557521i	0.0912496	+	0.0333779i
$280$		0			0
$281$	−18.6722	+	22.2527i	−1.11389	+	1.32748i	−0.174492	+	0.984659i	$0.555828\pi$
$281$	−18.6722	+	22.2527i	−1.11389	+	1.32748i	−0.939399	+	0.342825i	$0.888616\pi$
$282$		0			0
$283$	14.3442	−	2.52928i	0.852677	−	0.150350i	0.269806	−	0.962915i	$-0.413040\pi$
$283$	14.3442	−	2.52928i	0.852677	−	0.150350i	0.582871	+	0.812565i	$0.301929\pi$
$284$		0			0
$285$	−1.74374	+	2.48608i	−0.103290	+	0.147263i
$286$		0			0
$287$	−0.00137023	−	0.00237332i	−8.08824e−5	−	0.000140092i
$288$		0			0
$289$	−0.255543	+	0.442614i	−0.0150320	+	0.0260361i
$290$		0			0
$291$	2.07517	+	23.9403i	0.121649	+	1.40341i
$292$		0			0
$293$	−0.657295	+	1.80590i	−0.0383996	+	0.105502i	−0.957411	−	0.288730i	$-0.906767\pi$
$293$	−0.657295	+	1.80590i	−0.0383996	+	0.105502i	0.919011	+	0.394232i	$0.128989\pi$
$294$		0			0
$295$	4.56836	+	0.805525i	0.265980	+	0.0468995i
$296$		0			0
$297$	9.40405	−	0.799966i	0.545678	−	0.0464187i
$298$		0			0
$299$	−3.97027	+	22.5165i	−0.229607	+	1.30216i
$300$		0			0
$301$	1.11001	+	0.404010i	0.0639798	+	0.0232868i
$302$		0			0
$303$	−10.0394	+	21.4846i	−0.576749	+	1.23426i
$304$		0			0
$305$	−9.60576	−	5.54589i	−0.550024	−	0.317557i
$306$		0			0
$307$	23.7774	−	13.7279i	1.35705	−	0.783492i	0.367822	−	0.929896i	$-0.380103\pi$
$307$	23.7774	−	13.7279i	1.35705	−	0.783492i	0.989225	+	0.146405i	$0.0467701\pi$
$308$		0			0
$309$	0.492064	−	5.57287i	0.0279925	−	0.317029i
$310$		0			0
$311$	−3.16971	−	17.9763i	−0.179738	−	1.01934i	−0.932532	−	0.361087i	$-0.882406\pi$
$311$	−3.16971	−	17.9763i	−0.179738	−	1.01934i	0.752794	−	0.658256i	$-0.228705\pi$
$312$		0			0
$313$	−23.3508	−	19.5937i	−1.31987	−	1.10750i	−0.986334	−	0.164761i	$-0.947315\pi$
$313$	−23.3508	−	19.5937i	−1.31987	−	1.10750i	−0.333533	−	0.942738i	$-0.608241\pi$
$314$		0			0
$315$	0.510276	+	0.295700i	0.0287508	+	0.0166608i
$316$		0			0
$317$	−4.40578	−	12.1048i	−0.247453	−	0.679872i	−0.999778	−	0.0210792i	$-0.993290\pi$
$317$	−4.40578	−	12.1048i	−0.247453	−	0.679872i	0.752325	−	0.658792i	$-0.228932\pi$
$318$		0			0
$319$	1.08221	+	1.28972i	0.0605920	+	0.0722107i
$320$		0			0
$321$	0.353186	+	0.353752i	0.0197129	+	0.0197445i
$322$		0			0
$323$	−3.96736			−0.220750
$324$		0			0
$325$	6.44354			0.357423
$326$		0			0
$327$	3.77841	+	3.78447i	0.208946	+	0.209282i
$328$		0			0
$329$	−0.565361	−	0.673771i	−0.0311694	−	0.0371462i
$330$		0			0
$331$	3.04766	+	8.37337i	0.167514	+	0.460242i	0.994837	−	0.101485i	$-0.0323594\pi$
$331$	3.04766	+	8.37337i	0.167514	+	0.460242i	−0.827323	+	0.561727i	$0.810137\pi$
$332$		0			0
$333$	−24.9447	+	14.3486i	−1.36696	+	0.786296i
$334$		0			0
$335$	−18.9726	−	15.9199i	−1.03658	−	0.869796i
$336$		0			0
$337$	−1.58582	−	8.99362i	−0.0863850	−	0.489913i	−0.997049	−	0.0767661i	$-0.975541\pi$
$337$	−1.58582	−	8.99362i	−0.0863850	−	0.489913i	0.910664	−	0.413147i	$-0.135571\pi$
$338$		0			0
$339$	1.76806	−	20.0241i	0.0960279	−	1.08756i
$340$		0			0
$341$	0.850961	−	0.491302i	0.0460821	−	0.0266055i
$342$		0			0
$343$	−1.32713	−	0.766220i	−0.0716584	−	0.0413720i
$344$		0			0
$345$	8.31051	−	17.7847i	0.447423	−	0.957497i
$346$		0			0
$347$	17.6125	+	6.41042i	0.945487	+	0.344129i	0.768330	−	0.640054i	$-0.221088\pi$
$347$	17.6125	+	6.41042i	0.945487	+	0.344129i	0.177157	+	0.984183i	$0.443310\pi$
$348$		0			0
$349$	3.31068	−	18.7758i	0.177217	−	1.00505i	−0.758338	−	0.651862i	$-0.773988\pi$
$349$	3.31068	−	18.7758i	0.177217	−	1.00505i	0.935554	−	0.353183i	$-0.114901\pi$
$350$		0			0
$351$	15.3822	+	10.8259i	0.821041	+	0.577846i
$352$		0			0
$353$	12.6087	+	2.22326i	0.671094	+	0.118332i	0.498805	−	0.866714i	$-0.333772\pi$
$353$	12.6087	+	2.22326i	0.671094	+	0.118332i	0.172290	+	0.985046i	$0.444884\pi$
$354$		0			0
$355$	−0.799008	+	2.19526i	−0.0424070	+	0.116512i
$356$		0			0
$357$	0.0665400	+	0.767642i	0.00352167	+	0.0406279i
$358$		0			0
$359$	−14.9673	+	25.9241i	−0.789945	+	1.36822i	0.136056	+	0.990701i	$0.456557\pi$
$359$	−14.9673	+	25.9241i	−0.789945	+	1.36822i	−0.926000	+	0.377523i	$0.876776\pi$
$360$		0			0
$361$	−9.02271	−	15.6278i	−0.474880	−	0.822515i
$362$		0			0
$363$	−7.65930	+	10.9200i	−0.402009	+	0.573150i
$364$		0			0
$365$	−11.8315	+	2.08621i	−0.619287	+	0.109197i
$366$		0			0
$367$	−7.71474	+	9.19407i	−0.402706	+	0.479927i	−0.928843	−	0.370473i	$-0.879196\pi$
$367$	−7.71474	+	9.19407i	−0.402706	+	0.479927i	0.526137	+	0.850400i	$0.323640\pi$
$368$		0			0
$369$	0.0129128	+	0.0739251i	0.000672215	+	0.00384839i
$370$		0			0
$371$	−1.20503	+	0.438596i	−0.0625622	+	0.0227708i
$372$		0			0
$373$	−20.3745	+	17.0962i	−1.05495	+	0.885209i	−0.993605	−	0.112908i	$-0.963984\pi$
$373$	−20.3745	+	17.0962i	−1.05495	+	0.885209i	−0.0613456	+	0.998117i	$0.519539\pi$
$374$		0			0
$375$	−20.3502	−	5.47031i	−1.05088	−	0.282485i
$376$		0			0
$377$			3.35544i			0.172814i
$378$		0			0
$379$		−	22.5119i		−	1.15636i	−0.815910	−	0.578179i	$-0.803764\pi$
$379$		−	22.5119i		−	1.15636i	0.815910	−	0.578179i	$-0.196236\pi$
$380$		0			0
$381$	−3.49143	−	13.0721i	−0.178871	−	0.669704i
$382$		0			0
$383$	−22.3710	+	18.7715i	−1.14310	+	0.959177i	−0.999536	−	0.0304640i	$-0.990301\pi$
$383$	−22.3710	+	18.7715i	−1.14310	+	0.959177i	−0.143566	+	0.989641i	$0.545857\pi$
$384$		0			0
$385$	0.335537	−	0.122125i	0.0171005	−	0.00622409i
$386$		0			0
$387$	−24.7459	−	20.8320i	−1.25790	−	1.05895i
$388$		0			0
$389$	−1.76256	+	2.10053i	−0.0893651	+	0.106501i	−0.808874	−	0.587982i	$-0.799923\pi$
$389$	−1.76256	+	2.10053i	−0.0893651	+	0.106501i	0.719509	+	0.694483i	$0.244367\pi$
$390$		0			0
$391$	25.2576	−	4.45360i	1.27733	−	0.225228i
$392$		0			0
$393$	−2.46571	−	5.29881i	−0.124378	−	0.267290i
$394$		0			0
$395$	−7.93964	−	13.7519i	−0.399487	−	0.691931i
$396$		0			0
$397$	3.91367	−	6.77868i	0.196422	−	0.340212i	−0.750944	−	0.660366i	$-0.770401\pi$
$397$	3.91367	−	6.77868i	0.196422	−	0.340212i	0.947366	+	0.320154i	$0.103735\pi$
$398$		0			0
$399$	0.151951	−	0.106216i	0.00760704	−	0.00531743i
$400$		0			0
$401$	−2.67952	+	7.36193i	−0.133809	+	0.367637i	−0.988443	−	0.151594i	$-0.951559\pi$
$401$	−2.67952	+	7.36193i	−0.133809	+	0.367637i	0.854634	+	0.519231i	$0.173782\pi$
$402$		0			0
$403$	1.92857	+	0.340060i	0.0960692	+	0.0169396i
$404$		0			0
$405$	−10.3413	−	12.4048i	−0.513861	−	0.616399i
$406$		0			0
$407$	−3.02548	+	17.1583i	−0.149967	+	0.850507i
$408$		0			0
$409$	−5.15878	−	1.87764i	−0.255085	−	0.0928434i	0.211313	−	0.977419i	$-0.432226\pi$
$409$	−5.15878	−	1.87764i	−0.255085	−	0.0928434i	−0.466398	+	0.884575i	$0.654448\pi$
$410$		0			0
$411$	17.9044	+	25.6138i	0.883159	+	1.26344i
$412$		0			0
$413$	−0.245267	−	0.141605i	−0.0120688	−	0.00696792i
$414$		0			0
$415$	−27.0399	+	15.6115i	−1.32734	+	0.766337i
$416$		0			0
$417$	−26.8501	+	12.4942i	−1.31486	+	0.611845i
$418$		0			0
$419$	2.24813	+	12.7498i	0.109829	+	0.622868i	0.989181	+	0.146698i	$0.0468645\pi$
$419$	2.24813	+	12.7498i	0.109829	+	0.622868i	−0.879353	+	0.476171i	$0.842024\pi$
$420$		0			0
$421$	10.1658	+	8.53012i	0.495451	+	0.415733i	0.855975	−	0.517017i	$-0.172958\pi$
$421$	10.1658	+	8.53012i	0.495451	+	0.415733i	−0.360524	+	0.932750i	$0.617402\pi$
$422$		0			0
$423$	8.20137	+	22.6460i	0.398764	+	1.10108i
$424$		0			0
$425$	−2.47211	−	6.79206i	−0.119915	−	0.329463i
$426$		0			0
$427$	0.435280	+	0.518746i	0.0210647	+	0.0251039i
$428$		0			0
$429$	11.0027	−	2.93873i	0.531218	−	0.141883i
$430$		0			0
$431$	−3.50754			−0.168952			−0.0844762	−	0.996425i	$-0.526922\pi$
$431$	−3.50754			−0.168952			−0.0844762	+	0.996425i	$0.526922\pi$
$432$		0			0
$433$	−6.80047			−0.326810			−0.163405	−	0.986559i	$-0.552248\pi$
$433$	−6.80047			−0.326810			−0.163405	+	0.986559i	$0.552248\pi$
$434$		0			0
$435$	0.747871	−	2.78217i	0.0358577	−	0.133395i
$436$		0			0
$437$	−3.96660	−	4.72721i	−0.189748	−	0.226133i
$438$		0			0
$439$	−9.11906	−	25.0544i	−0.435229	−	1.19578i	−0.942562	−	0.334032i	$-0.891591\pi$
$439$	−9.11906	−	25.0544i	−0.435229	−	1.19578i	0.507333	−	0.861750i	$-0.330632\pi$
$440$		0			0
$441$	13.4496	+	16.0809i	0.640459	+	0.765759i
$442$		0			0
$443$	−10.2936	−	8.63732i	−0.489062	−	0.410371i	0.364628	−	0.931153i	$-0.381196\pi$
$443$	−10.2936	−	8.63732i	−0.489062	−	0.410371i	−0.853690	+	0.520782i	$0.825641\pi$
$444$		0			0
$445$	−1.53662	−	8.71463i	−0.0728430	−	0.413113i
$446$		0			0
$447$	−25.1060	−	17.6094i	−1.18747	−	0.832896i
$448$		0			0
$449$	15.8947	−	9.17681i	0.750117	−	0.433081i	−0.0756189	−	0.997137i	$-0.524093\pi$
$449$	15.8947	−	9.17681i	0.750117	−	0.433081i	0.825736	+	0.564056i	$0.190760\pi$
$450$		0			0
$451$	0.0393483	+	0.0227178i	0.00185284	+	0.00106974i
$452$		0			0
$453$	−10.6666	+	0.924592i	−0.501161	+	0.0434411i
$454$		0			0
$455$	0.668723	+	0.243395i	0.0313502	+	0.0114106i
$456$		0			0
$457$	0.210261	−	1.19245i	0.00983562	−	0.0557806i	−0.979495	−	0.201469i	$-0.935429\pi$
$457$	0.210261	−	1.19245i	0.00983562	−	0.0557806i	0.989331	+	0.145688i	$0.0465396\pi$
$458$		0			0
$459$	5.51002	−	20.3676i	0.257186	−	0.950680i
$460$		0			0
$461$	3.12039	+	0.550208i	0.145331	+	0.0256257i	0.245840	−	0.969310i	$-0.420936\pi$
$461$	3.12039	+	0.550208i	0.145331	+	0.0256257i	−0.100509	+	0.994936i	$0.532047\pi$
$462$		0			0
$463$	−6.53132	+	17.9447i	−0.303536	+	0.833959i	0.690342	+	0.723483i	$0.257460\pi$
$463$	−6.53132	+	17.9447i	−0.303536	+	0.833959i	−0.993879	+	0.110476i	$0.964762\pi$
$464$		0			0
$465$	−1.52329	−	0.711808i	−0.0706408	−	0.0330093i
$466$		0			0
$467$	6.32468	−	10.9547i	0.292672	−	0.506922i	−0.681769	−	0.731567i	$-0.738789\pi$
$467$	6.32468	−	10.9547i	0.292672	−	0.506922i	0.974441	+	0.224646i	$0.0721224\pi$
$468$		0			0
$469$	0.756035	+	1.30949i	0.0349104	+	0.0604667i
$470$		0			0
$471$	−30.4383	−	2.68759i	−1.40252	−	0.123838i
$472$		0			0
$473$	−19.2869	+	3.40080i	−0.886814	+	0.156369i
$474$		0			0
$475$	−1.11787	+	1.33223i	−0.0512916	+	0.0611269i
$476$		0			0
$477$	35.1161	+	0.0562948i	1.60785	+	0.00257756i
$478$		0			0
$479$	31.0456	−	11.2997i	1.41851	−	0.516296i	0.484896	−	0.874572i	$-0.338858\pi$
$479$	31.0456	−	11.2997i	1.41851	−	0.516296i	0.933616	+	0.358276i	$0.116635\pi$
$480$		0			0
$481$	−26.6001	+	22.3202i	−1.21286	+	1.01771i
$482$		0			0
$483$	−0.848137	+	0.846779i	−0.0385916	+	0.0385298i
$484$		0			0
$485$		−	24.8956i		−	1.13045i
$486$		0			0
$487$			39.0120i			1.76780i	0.467673	+	0.883901i	$0.345092\pi$
$487$			39.0120i			1.76780i	−0.467673	+	0.883901i	$0.654908\pi$
$488$		0			0
$489$	−0.690996	+	0.689889i	−0.0312479	+	0.0311979i
$490$		0			0
$491$	4.73374	−	3.97208i	0.213631	−	0.179257i	−0.529693	−	0.848190i	$-0.677693\pi$
$491$	4.73374	−	3.97208i	0.213631	−	0.179257i	0.743323	+	0.668932i	$0.233248\pi$
$492$		0			0
$493$	3.53693	−	1.28734i	0.159295	−	0.0579787i
$494$		0			0
$495$	−9.77794	−	0.0156751i	−0.439486	−	0.000704542i
$496$		0			0
$497$	0.0916783	−	0.109258i	0.00411234	−	0.00490089i
$498$		0			0
$499$	−29.7454	+	5.24491i	−1.33159	+	0.234794i	−0.793744	−	0.608252i	$-0.791871\pi$
$499$	−29.7454	+	5.24491i	−1.33159	+	0.234794i	−0.537841	+	0.843046i	$0.680760\pi$
$500$		0			0
$501$	−29.3711	−	2.59336i	−1.31220	−	0.115863i
$502$		0			0
$503$	5.66137	+	9.80578i	0.252428	+	0.437218i	0.964194	−	0.265199i	$-0.0854376\pi$
$503$	5.66137	+	9.80578i	0.252428	+	0.437218i	−0.711766	+	0.702417i	$0.752104\pi$
$504$		0			0
$505$	12.2843	−	21.2771i	0.546646	−	0.946818i
$506$		0			0
$507$	0.163477	+	0.0763903i	0.00726028	+	0.00339261i
$508$		0			0
$509$	6.79275	−	18.6629i	0.301083	−	0.827219i	−0.693229	−	0.720717i	$-0.743813\pi$
$509$	6.79275	−	18.6629i	0.301083	−	0.827219i	0.994312	−	0.106502i	$-0.0339651\pi$
$510$		0			0
$511$	0.722334	+	0.127367i	0.0319542	+	0.00563439i
$512$		0			0
$513$	−4.90693	+	1.30217i	−0.216646	+	0.0574922i
$514$		0			0
$515$	−1.00647	+	5.70800i	−0.0443506	+	0.251524i
$516$		0			0
$517$	13.7030	+	4.98748i	0.602657	+	0.219349i
$518$		0			0
$519$	31.8909	−	2.76434i	1.39986	−	0.121341i
$520$		0			0
$521$	−5.13805	−	2.96646i	−0.225102	−	0.129963i	0.383208	−	0.923662i	$-0.374819\pi$
$521$	−5.13805	−	2.96646i	−0.225102	−	0.129963i	−0.608311	+	0.793699i	$0.708152\pi$
$522$		0			0
$523$	17.2055	−	9.93358i	0.752343	−	0.434365i	−0.0741971	−	0.997244i	$-0.523639\pi$
$523$	17.2055	−	9.93358i	0.752343	−	0.434365i	0.826540	+	0.562878i	$0.190306\pi$
$524$		0			0
$525$	0.276521	+	0.193953i	0.0120684	+	0.00846479i
$526$		0			0
$527$	−0.381458	−	2.16335i	−0.0166166	−	0.0942372i
$528$		0			0
$529$	12.9403	+	10.8582i	0.562622	+	0.472096i
$530$		0			0
$531$	4.97552	+	5.94893i	0.215919	+	0.258162i
$532$		0			0
$533$	0.0309709	+	0.0850918i	0.00134150	+	0.00368574i
$534$		0			0
$535$	−0.332890	−	0.396723i	−0.0143921	−	0.0171518i
$536$		0			0
$537$	−6.73222	+	25.0447i	−0.290517	+	1.08076i
$538$		0			0
$539$	12.6926			0.546710
$540$		0			0
$541$	−1.88488			−0.0810372			−0.0405186	−	0.999179i	$-0.512901\pi$
$541$	−1.88488			−0.0810372			−0.0405186	+	0.999179i	$0.512901\pi$
$542$		0			0
$543$	32.3652	−	8.64444i	1.38892	−	0.370968i
$544$		0			0
$545$	−3.56129	−	4.24418i	−0.152549	−	0.181801i
$546$		0			0
$547$	7.60406	+	20.8920i	0.325126	+	0.893277i	0.989326	+	0.145722i	$0.0465504\pi$
$547$	7.60406	+	20.8920i	0.325126	+	0.893277i	−0.664199	+	0.747556i	$0.731227\pi$
$548$		0			0
$549$	−6.31435	−	17.4354i	−0.269490	−	0.744127i
$550$		0			0
$551$	−0.693752	−	0.582127i	−0.0295548	−	0.0247995i
$552$		0			0
$553$	0.168345	+	0.954733i	0.00715876	+	0.0405994i
$554$		0			0
$555$	27.0303	−	12.5781i	1.14737	−	0.533910i
$556$		0			0
$557$	−29.9947	+	17.3175i	−1.27092	+	0.733764i	−0.975160	−	0.221499i	$-0.928905\pi$
$557$	−29.9947	+	17.3175i	−1.27092	+	0.733764i	−0.295756	+	0.955264i	$0.595572\pi$
$558$		0			0
$559$	−33.8025	−	19.5159i	−1.42969	−	0.825433i
$560$		0			0
$561$	−7.31895	−	10.4704i	−0.309006	−	0.442061i
$562$		0			0
$563$	18.6994	+	6.80604i	0.788087	+	0.286840i	0.704541	−	0.709664i	$-0.251153\pi$
$563$	18.6994	+	6.80604i	0.788087	+	0.286840i	0.0835464	+	0.996504i	$0.473375\pi$
$564$		0			0
$565$	−3.61641	+	20.5097i	−0.152144	+	0.862850i
$566$		0			0
$567$	0.334254	+	0.927599i	0.0140374	+	0.0389555i
$568$		0			0
$569$	38.9668	+	6.87090i	1.63357	+	0.288043i	0.913799	−	0.406166i	$-0.133134\pi$
$569$	38.9668	+	6.87090i	1.63357	+	0.288043i	0.719774	+	0.694209i	$0.244246\pi$
$570$		0			0
$571$	−7.36266	+	20.2288i	−0.308118	+	0.846547i	0.684906	+	0.728632i	$0.259843\pi$
$571$	−7.36266	+	20.2288i	−0.308118	+	0.846547i	−0.993024	+	0.117915i	$0.962379\pi$
$572$		0			0
$573$	20.0016	−	13.9814i	0.835577	−	0.584080i
$574$		0			0
$575$	5.62127	−	9.73633i	0.234423	−	0.406033i
$576$		0			0
$577$	15.4075	+	26.6866i	0.641424	+	1.11098i	0.985115	+	0.171896i	$0.0549892\pi$
$577$	15.4075	+	26.6866i	0.641424	+	1.11098i	−0.343692	+	0.939083i	$0.611677\pi$
$578$		0			0
$579$	−1.79984	−	3.86786i	−0.0747988	−	0.160743i
$580$		0			0
$581$	1.87726	−	0.331012i	0.0778820	−	0.0137327i
$582$		0			0
$583$	13.6663	−	16.2869i	0.566001	−	0.674534i
$584$		0			0
$585$	−14.9081	−	12.5502i	−0.616375	−	0.518886i
$586$		0			0
$587$	35.5365	−	12.9342i	1.46675	−	0.533853i	0.519533	−	0.854451i	$-0.326106\pi$
$587$	35.5365	−	12.9342i	1.46675	−	0.533853i	0.947215	+	0.320598i	$0.103884\pi$
$588$		0			0
$589$	−0.404893	+	0.339745i	−0.0166833	+	0.0139990i
$590$		0			0
$591$	−4.09576	−	15.3347i	−0.168477	−	0.630787i
$592$		0			0
$593$			46.2503i			1.89927i	0.313355	+	0.949636i	$0.398547\pi$
$593$			46.2503i			1.89927i	−0.313355	+	0.949636i	$0.601453\pi$
$594$		0			0
$595$		−	0.798274i		−	0.0327260i
$596$		0			0
$597$	−15.1231	−	4.06521i	−0.618946	−	0.166378i
$598$		0			0
$599$	−1.69945	+	1.42601i	−0.0694377	+	0.0582651i	−0.676846	−	0.736125i	$-0.736654\pi$
$599$	−1.69945	+	1.42601i	−0.0694377	+	0.0582651i	0.607408	+	0.794390i	$0.292209\pi$
$600$		0			0
$601$	31.3863	−	11.4237i	1.28027	−	0.465981i	0.389750	−	0.920921i	$-0.372561\pi$
$601$	31.3863	−	11.4237i	1.28027	−	0.465981i	0.890522	+	0.454940i	$0.150339\pi$
$602$		0			0
$603$	−7.12473	−	40.7886i	−0.290141	−	1.66104i
$604$		0			0
$605$	8.88252	−	10.5858i	0.361126	−	0.430373i
$606$		0			0
$607$	24.0862	−	4.24704i	0.977628	−	0.172382i	0.338067	−	0.941122i	$-0.390227\pi$
$607$	24.0862	−	4.24704i	0.977628	−	0.172382i	0.639561	+	0.768740i	$0.279116\pi$
$608$		0			0
$609$	−0.101000	+	0.143997i	−0.00409272	+	0.00583505i
$610$		0			0
$611$	14.5313	+	25.1690i	0.587875	+	1.01823i
$612$		0			0
$613$	−1.57336	+	2.72514i	−0.0635474	+	0.110067i	−0.896049	−	0.443956i	$-0.853575\pi$
$613$	−1.57336	+	2.72514i	−0.0635474	+	0.110067i	0.832501	+	0.554023i	$0.186908\pi$
$614$		0			0
$615$	−0.00671405	−	0.0774569i	−0.000270737	−	0.00312337i
$616$		0			0
$617$	9.26016	−	25.4421i	0.372800	−	1.02426i	−0.601474	−	0.798893i	$-0.705420\pi$
$617$	9.26016	−	25.4421i	0.372800	−	1.02426i	0.974274	−	0.225367i	$-0.0723582\pi$
$618$		0			0
$619$	−24.1567	−	4.25949i	−0.970942	−	0.171203i	−0.334388	−	0.942436i	$-0.608530\pi$
$619$	−24.1567	−	4.25949i	−0.970942	−	0.171203i	−0.636554	+	0.771232i	$0.719641\pi$
$620$		0			0
$621$	29.7775	−	13.7984i	1.19493	−	0.553710i
$622$		0			0
$623$	−0.0938139	+	0.532045i	−0.00375858	+	0.0213159i
$624$		0			0
$625$	12.1517	+	4.42287i	0.486070	+	0.176915i
$626$		0			0
$627$	−1.30125	+	2.78470i	−0.0519667	+	0.111210i
$628$		0			0
$629$	33.7327	+	19.4756i	1.34501	+	0.776544i
$630$		0			0
$631$	−39.8629	+	23.0148i	−1.58692	+	0.916206i	−0.593105	+	0.805125i	$0.702098\pi$
$631$	−39.8629	+	23.0148i	−1.58692	+	0.916206i	−0.993811	+	0.111081i	$0.964569\pi$
$632$		0			0
$633$	−2.59744	+	29.4173i	−0.103239	+	1.16923i
$634$		0			0
$635$	2.43414	+	13.8047i	0.0965961	+	0.547823i
$636$		0			0
$637$	19.3781	+	16.2602i	0.767789	+	0.644252i
$638$		0			0
$639$	−3.38551	+	1.94740i	−0.133929	+	0.0770379i
$640$		0			0
$641$	−10.3755	−	28.5064i	−0.409807	−	1.12593i	−0.957293	−	0.289120i	$-0.906637\pi$
$641$	−10.3755	−	28.5064i	−0.409807	−	1.12593i	0.547486	−	0.836815i	$-0.315585\pi$
$642$		0			0
$643$	−15.9458	−	19.0034i	−0.628840	−	0.749422i	0.353723	−	0.935350i	$-0.384915\pi$
$643$	−15.9458	−	19.0034i	−0.628840	−	0.749422i	−0.982563	+	0.185928i	$0.940471\pi$
$644$		0			0
$645$	23.6776	+	23.7156i	0.932306	+	0.933801i
$646$		0			0
$647$	39.5989			1.55679			0.778397	−	0.627772i	$-0.216033\pi$
$647$	39.5989			1.55679			0.778397	+	0.627772i	$0.216033\pi$
$648$		0			0
$649$	4.69547			0.184313
$650$		0			0
$651$	0.0725279	+	0.0726443i	0.00284259	+	0.00284715i
$652$		0			0
$653$	−16.5273	−	19.6964i	−0.646762	−	0.770781i	0.338660	−	0.940909i	$-0.390026\pi$
$653$	−16.5273	−	19.6964i	−0.646762	−	0.770781i	−0.985422	+	0.170128i	$0.945582\pi$
$654$		0			0
$655$	2.07090	+	5.68976i	0.0809168	+	0.222317i
$656$		0			0
$657$	−17.3783	−	10.0706i	−0.677994	−	0.392890i
$658$		0			0
$659$	−38.2134	−	32.0648i	−1.48858	−	1.24907i	−0.896385	−	0.443276i	$-0.853816\pi$
$659$	−38.2134	−	32.0648i	−1.48858	−	1.24907i	−0.592198	−	0.805793i	$-0.701739\pi$
$660$		0			0
$661$	4.10673	+	23.2904i	0.159733	+	0.905893i	0.954330	+	0.298755i	$0.0965714\pi$
$661$	4.10673	+	23.2904i	0.159733	+	0.905893i	−0.794596	+	0.607138i	$0.792317\pi$
$662$		0			0
$663$	2.23933	−	25.3615i	0.0869684	−	0.984960i
$664$		0			0
$665$	−0.166338	+	0.0960355i	−0.00645032	+	0.00372410i
$666$		0			0
$667$	5.07014	+	2.92725i	0.196317	+	0.113343i
$668$		0			0
$669$	−5.26289	+	11.2627i	−0.203475	+	0.435443i
$670$		0			0
$671$	−10.5501	−	3.83993i	−0.407283	−	0.148239i
$672$		0			0
$673$	−7.07247	+	40.1100i	−0.272624	+	1.54613i	0.473787	+	0.880640i	$0.342887\pi$
$673$	−7.07247	+	40.1100i	−0.272624	+	1.54613i	−0.746410	+	0.665486i	$0.768224\pi$
$674$		0			0
$675$	−5.28686	−	7.58919i	−0.203491	−	0.292108i
$676$		0			0
$677$	27.5622	+	4.85995i	1.05930	+	0.186783i	0.676046	−	0.736860i	$-0.263692\pi$
$677$	27.5622	+	4.85995i	1.05930	+	0.186783i	0.383254	+	0.923643i	$0.374803\pi$
$678$		0			0
$679$	−0.519845	+	1.42826i	−0.0199498	+	0.0548117i
$680$		0			0
$681$	3.94598	+	45.5230i	0.151210	+	1.74444i
$682$		0			0
$683$	−0.0671037	+	0.116227i	−0.00256765	+	0.00444730i	−0.867306	−	0.497775i	$-0.834151\pi$
$683$	−0.0671037	+	0.116227i	−0.00256765	+	0.00444730i	0.864739	+	0.502222i	$0.167484\pi$
$684$		0			0
$685$	−16.1884	−	28.0391i	−0.618527	−	1.07132i
$686$		0			0
$687$	1.68745	−	2.40583i	0.0643803	−	0.0917880i
$688$		0			0
$689$	41.7294	−	7.35801i	1.58976	−	0.280318i
$690$		0			0
$691$	−4.64904	+	5.54051i	−0.176858	+	0.210771i	−0.847190	−	0.531291i	$-0.821707\pi$
$691$	−4.64904	+	5.54051i	−0.176858	+	0.210771i	0.670332	+	0.742061i	$0.266152\pi$
$692$		0			0
$693$	0.560634	+	0.205072i	0.0212967	+	0.00779006i
$694$		0			0
$695$	28.8311	−	10.4937i	1.09363	−	0.398047i
$696$		0			0
$697$	0.0778121	−	0.0652921i	0.00294734	−	0.00247311i
$698$		0			0
$699$	7.44562	+	2.00144i	0.281619	+	0.0757016i
$700$		0			0
$701$			15.7113i			0.593407i	0.954970	+	0.296703i	$0.0958872\pi$
$701$			15.7113i			0.593407i	−0.954970	+	0.296703i	$0.904113\pi$
$702$		0			0
$703$		−	9.37197i		−	0.353471i
$704$		0			0
$705$	−6.43894	−	24.1077i	−0.242505	−	0.907950i
$706$		0			0
$707$	−1.14904	+	0.964159i	−0.0432141	+	0.0362609i
$708$		0			0
$709$	3.37957	−	1.23006i	0.126922	−	0.0461960i	−0.277778	−	0.960645i	$-0.589598\pi$
$709$	3.37957	−	1.23006i	0.126922	−	0.0461960i	0.404701	+	0.914449i	$0.367376\pi$
$710$		0			0
$711$	4.65183	−	26.1368i	0.174457	−	0.980206i
$712$		0			0
$713$	2.19630	−	2.61745i	0.0822523	−	0.0980244i
$714$		0			0
$715$	−11.6194	+	2.04881i	−0.434540	+	0.0766212i
$716$		0			0
$717$	18.4531	+	39.6557i	0.689143	+	1.48097i
$718$		0			0
$719$	21.2087	+	36.7345i	0.790950	+	1.36997i	0.925379	+	0.379042i	$0.123747\pi$
$719$	21.2087	+	36.7345i	0.790950	+	1.36997i	−0.134429	+	0.990923i	$0.542920\pi$
$720$		0			0
$721$	0.176930	−	0.306452i	0.00658923	−	0.0114129i
$722$		0			0
$723$	−5.44198	+	3.80402i	−0.202389	+	0.141473i
$724$		0			0
$725$	0.564307	−	1.55042i	0.0209579	−	0.0575812i
$726$		0			0
$727$	−7.03446	−	1.24037i	−0.260894	−	0.0460026i	0.0416711	−	0.999131i	$-0.486732\pi$
$727$	−7.03446	−	1.24037i	−0.260894	−	0.0460026i	−0.302565	+	0.953129i	$0.597843\pi$
$728$		0			0
$729$	0.129851	−	26.9997i	0.00480930	−	0.999988i
$730$		0			0
$731$	−7.60290	+	43.1182i	−0.281203	+	1.59478i
$732$		0			0
$733$	−25.3224	−	9.21661i	−0.935305	−	0.340423i	−0.170995	−	0.985272i	$-0.554698\pi$
$733$	−25.3224	−	9.21661i	−0.935305	−	0.340423i	−0.764310	+	0.644849i	$0.776920\pi$
$734$		0			0
$735$	−12.4433	−	17.8012i	−0.458978	−	0.656608i
$736$		0			0
$737$	−21.7107	−	12.5347i	−0.799723	−	0.461720i
$738$		0			0
$739$	−8.02620	+	4.63393i	−0.295249	+	0.170462i	−0.640306	−	0.768120i	$-0.721193\pi$
$739$	−8.02620	+	4.63393i	−0.295249	+	0.170462i	0.345058	+	0.938581i	$0.387859\pi$
$740$		0			0
$741$	−5.55404	+	2.58448i	−0.204033	+	0.0949431i
$742$		0			0
$743$	−2.56527	−	14.5484i	−0.0941106	−	0.533728i	−0.995016	−	0.0997127i	$-0.968208\pi$
$743$	−2.56527	−	14.5484i	−0.0941106	−	0.533728i	0.900906	−	0.434015i	$-0.142903\pi$
$744$		0			0
$745$	24.3376	+	20.4217i	0.891661	+	0.748192i
$746$		0			0
$747$	−51.3920	−	9.14676i	−1.88033	−	0.334663i
$748$		0			0
$749$	0.0108140	+	0.0297111i	0.000395134	+	0.00108562i
$750$		0			0
$751$	22.7883	+	27.1580i	0.831556	+	0.991010i	0.999986	+	0.00529624i	$0.00168585\pi$
$751$	22.7883	+	27.1580i	0.831556	+	0.991010i	−0.168430	+	0.985714i	$0.553870\pi$
$752$		0			0
$753$	−31.2626	+	8.34993i	−1.13927	+	0.304288i
$754$		0			0
$755$	11.0922			0.403688
$756$		0			0
$757$	12.9971			0.472387			0.236194	−	0.971706i	$-0.424100\pi$
$757$	12.9971			0.472387			0.236194	+	0.971706i	$0.424100\pi$
$758$		0			0
$759$	5.15819	−	19.1891i	0.187231	−	0.696520i
$760$		0			0
$761$	−9.68871	−	11.5466i	−0.351215	−	0.418562i	0.561295	−	0.827616i	$-0.310303\pi$
$761$	−9.68871	−	11.5466i	−0.351215	−	0.418562i	−0.912510	+	0.409054i	$0.865859\pi$
$762$		0			0
$763$	0.115689	+	0.317852i	0.00418821	+	0.0115070i
$764$		0			0
$765$	−7.50940	+	20.5294i	−0.271503	+	0.742243i
$766$		0			0
$767$	7.16869	+	6.01524i	0.258846	+	0.217198i
$768$		0			0
$769$	3.04896	+	17.2915i	0.109948	+	0.623547i	0.989128	+	0.147057i	$0.0469801\pi$
$769$	3.04896	+	17.2915i	0.109948	+	0.623547i	−0.879180	+	0.476490i	$0.841909\pi$
$770$		0			0
$771$	1.92699	+	1.35160i	0.0693989	+	0.0486766i
$772$		0			0
$773$	−28.6124	+	16.5194i	−1.02912	+	0.594161i	−0.916732	−	0.399503i	$-0.869183\pi$
$773$	−28.6124	+	16.5194i	−1.02912	+	0.594161i	−0.112386	+	0.993665i	$0.535849\pi$
$774$		0			0
$775$	−0.833931	−	0.481471i	−0.0299557	−	0.0172949i
$776$		0			0
$777$	−1.81338	+	0.157185i	−0.0650545	+	0.00563899i
$778$		0			0
$779$	−0.0229662	−	0.00835901i	−0.000822849	−	0.000299493i
$780$		0			0
$781$	−0.410620	+	2.32874i	−0.0146931	+	0.0833290i
$782$		0			0
$783$	3.95203	−	2.75310i	0.141234	−	0.0983879i
$784$		0			0
$785$	31.1764	+	5.49724i	1.11273	+	0.196205i
$786$		0			0
$787$	−17.2840	+	47.4873i	−0.616107	+	1.69274i	0.100211	+	0.994966i	$0.468048\pi$
$787$	−17.2840	+	47.4873i	−0.616107	+	1.69274i	−0.716318	+	0.697774i	$0.754174\pi$
$788$		0			0
$789$	−38.1271	−	17.8162i	−1.35736	−	0.634273i
$790$		0			0
$791$	0.635737	−	1.10113i	0.0226042	−	0.0391516i
$792$		0			0
$793$	−11.1879	−	19.3780i	−0.397294	−	0.688133i
$794$		0			0
$795$	−36.2400	−	3.19986i	−1.28530	−	0.113487i
$796$		0			0
$797$	−18.6605	+	3.29034i	−0.660987	+	0.116550i	−0.494071	−	0.869421i	$-0.664492\pi$
$797$	−18.6605	+	3.29034i	−0.660987	+	0.116550i	−0.166916	+	0.985971i	$0.553381\pi$
$798$		0			0
$799$	20.9553	−	24.9736i	0.741346	−	0.883502i
$800$		0			0
$801$	7.41761	−	12.8003i	0.262089	−	0.452275i
$802$		0			0
$803$	−11.4273	+	4.15920i	−0.403261	+	0.146775i
$804$		0			0
$805$	0.951162	−	0.798120i	0.0335241	−	0.0281300i
$806$		0			0
$807$	−9.36227	+	9.34728i	−0.329568	+	0.329040i
$808$		0			0
$809$			23.9122i			0.840709i	0.907360	+	0.420355i	$0.138094\pi$
$809$			23.9122i			0.840709i	−0.907360	+	0.420355i	$0.861906\pi$
$810$		0			0
$811$			8.39157i			0.294668i	0.989087	+	0.147334i	$0.0470692\pi$
$811$			8.39157i			0.294668i	−0.989087	+	0.147334i	$0.952931\pi$
$812$		0			0
$813$	−7.98653	+	7.97374i	−0.280100	+	0.279651i
$814$		0			0
$815$	0.774933	−	0.650246i	0.0271447	−	0.0227771i
$816$		0			0
$817$	9.89930	−	3.60305i	0.346333	−	0.126055i
$818$		0			0
$819$	0.593220	+	1.03130i	0.0207288	+	0.0360366i
$820$		0			0
$821$	7.64673	−	9.11302i	0.266873	−	0.318047i	−0.615920	−	0.787808i	$-0.711216\pi$
$821$	7.64673	−	9.11302i	0.266873	−	0.318047i	0.882793	+	0.469762i	$0.155660\pi$
$822$		0			0
$823$	0.106247	−	0.0187342i	0.00370353	−	0.000653032i	−0.171796	−	0.985133i	$-0.554957\pi$
$823$	0.106247	−	0.0187342i	0.00370353	−	0.000653032i	0.175500	+	0.984479i	$0.443846\pi$
$824$		0			0
$825$	−5.57818	−	0.492533i	−0.194207	−	0.0171478i
$826$		0			0
$827$	−14.5115	−	25.1347i	−0.504615	−	0.874019i	−0.999986	−	0.00533723i	$-0.998301\pi$
$827$	−14.5115	−	25.1347i	−0.504615	−	0.874019i	0.495371	−	0.868682i	$-0.335032\pi$
$828$		0			0
$829$	16.6372	−	28.8164i	0.577833	−	1.00084i	−0.417895	−	0.908496i	$-0.637232\pi$
$829$	16.6372	−	28.8164i	0.577833	−	1.00084i	0.995727	−	0.0923405i	$-0.0294348\pi$
$830$		0			0
$831$	25.6864	+	12.0028i	0.891052	+	0.416374i
$832$		0			0
$833$	9.70511	−	26.6646i	0.336262	−	0.923873i
$834$		0			0
$835$	30.0833	+	5.30450i	1.04108	+	0.183570i
$836$		0			0
$837$	−1.18185	−	2.55049i	−0.0408508	−	0.0881577i
$838$		0			0
$839$	−2.06560	+	11.7146i	−0.0713126	+	0.404434i	0.928167	+	0.372165i	$0.121384\pi$
$839$	−2.06560	+	11.7146i	−0.0713126	+	0.404434i	−0.999479	+	0.0322689i	$0.989727\pi$
$840$		0			0
$841$	−26.4437	−	9.62472i	−0.911852	−	0.331887i
$842$		0			0
$843$	50.1261	−	4.34498i	1.72643	−	0.149649i
$844$		0			0
$845$	−0.161898	−	0.0934720i	−0.00556947	−	0.00321554i
$846$		0			0
$847$	−0.730633	+	0.421831i	−0.0251048	+	0.0144943i
$848$		0			0
$849$	−20.6541	−	14.4869i	−0.708849	−	0.497188i
$850$		0			0
$851$	10.5206	+	59.6653i	0.360641	+	2.04530i
$852$		0			0
$853$	17.6854	+	14.8398i	0.605535	+	0.508105i	0.893220	−	0.449621i	$-0.148441\pi$
$853$	17.6854	+	14.8398i	0.605535	+	0.508105i	−0.287684	+	0.957725i	$0.592885\pi$
$854$		0			0
$855$	5.18118	−	0.905020i	0.177193	−	0.0309510i
$856$		0			0
$857$	−5.83078	−	16.0199i	−0.199176	−	0.547231i	0.799388	−	0.600816i	$-0.205157\pi$
$857$	−5.83078	−	16.0199i	−0.199176	−	0.547231i	−0.998563	+	0.0535848i	$0.982935\pi$
$858$		0			0
$859$	−10.9442	−	13.0428i	−0.373413	−	0.445016i	0.546311	−	0.837582i	$-0.316032\pi$
$859$	−10.9442	−	13.0428i	−0.373413	−	0.445016i	−0.919724	+	0.392567i	$0.871587\pi$
$860$		0			0
$861$	−0.00123219	+	0.00458391i	−4.19930e−5	+	0.000156219i
$862$		0			0
$863$	37.2672			1.26859			0.634295	−	0.773091i	$-0.281291\pi$
$863$	37.2672			1.26859			0.634295	+	0.773091i	$0.281291\pi$
$864$		0			0
$865$	−33.1635			−1.12759
$866$		0			0
$867$	0.855248	−	0.228428i	0.0290457	−	0.00775783i
$868$		0			0
$869$	−10.3316	−	12.3128i	−0.350477	−	0.417682i
$870$		0			0
$871$	−17.0884	−	46.9499i	−0.579017	−	1.59084i
$872$		0			0
$873$	26.8048	−	31.8409i	0.907204	−	1.07765i
$874$		0			0
$875$	−1.02103	−	0.856748i	−0.0345172	−	0.0289634i
$876$		0			0
$877$	−2.30800	−	13.0893i	−0.0779355	−	0.441994i	−0.998659	−	0.0517778i	$-0.983511\pi$
$877$	−2.30800	−	13.0893i	−0.0779355	−	0.441994i	0.920723	−	0.390217i	$-0.127600\pi$
$878$		0			0
$879$	3.01792	−	1.40433i	0.101792	−	0.0473670i
$880$		0			0
$881$	42.4341	−	24.4993i	1.42964	−	0.825404i	0.432549	−	0.901610i	$-0.357614\pi$
$881$	42.4341	−	24.4993i	1.42964	−	0.825404i	0.997092	+	0.0762067i	$0.0242809\pi$
$882$		0			0
$883$	−15.0988	−	8.71730i	−0.508115	−	0.293360i	0.223943	−	0.974602i	$-0.428107\pi$
$883$	−15.0988	−	8.71730i	−0.508115	−	0.293360i	−0.732059	+	0.681242i	$0.761440\pi$
$884$		0			0
$885$	−4.60323	−	6.58533i	−0.154736	−	0.221363i
$886$		0			0
$887$	−43.1388	−	15.7012i	−1.44846	−	0.527195i	−0.506298	−	0.862359i	$-0.668986\pi$
$887$	−43.1388	−	15.7012i	−1.44846	−	0.527195i	−0.942160	+	0.335163i	$0.891208\pi$
$888$		0			0
$889$	0.148609	−	0.842805i	0.00498420	−	0.0282668i
$890$		0			0
$891$	−12.4889	−	10.5478i	−0.418393	−	0.353365i
$892$		0			0
$893$	−7.72482	−	1.36209i	−0.258501	−	0.0455807i
$894$		0			0
$895$	9.18933	−	25.2475i	0.307165	−	0.843930i
$896$		0			0
$897$	32.4578	−	22.6884i	1.08373	−	0.757544i
$898$		0			0
$899$	0.250723	−	0.434265i	0.00836209	−	0.0144836i
$900$		0			0
$901$	−23.7657	−	41.1635i	−0.791752	−	1.37135i
$902$		0			0
$903$	−0.863182	−	1.85498i	−0.0287249	−	0.0617298i
$904$		0			0
$905$	−34.1791	+	6.02670i	−1.13615	+	0.200334i
$906$		0			0
$907$	−12.4264	+	14.8092i	−0.412611	+	0.491731i	−0.931822	−	0.362915i	$-0.881781\pi$
$907$	−12.4264	+	14.8092i	−0.412611	+	0.491731i	0.519211	+	0.854646i	$0.326226\pi$
$908$		0			0
$909$	38.6201	−	13.9865i	1.28095	−	0.463903i
$910$		0			0
$911$	17.6273	−	6.41580i	0.584018	−	0.212565i	−0.0330786	−	0.999453i	$-0.510531\pi$
$911$	17.6273	−	6.41580i	0.584018	−	0.212565i	0.617096	+	0.786888i	$0.288309\pi$
$912$		0			0
$913$	−24.2102	+	20.3148i	−0.801241	+	0.672321i
$914$		0			0
$915$	4.95743	+	18.5609i	0.163888	+	0.613604i
$916$		0			0
$917$		−	0.369664i		−	0.0122074i
$918$		0			0
$919$			25.3399i			0.835885i	0.908473	+	0.417943i	$0.137249\pi$
$919$			25.3399i			0.835885i	−0.908473	+	0.417943i	$0.862751\pi$
$920$		0			0
$921$	−45.9245	−	12.3449i	−1.51326	−	0.406778i
$922$		0			0
$923$	−3.61019	+	3.02931i	−0.118831	+	0.0997110i
$924$		0			0
$925$	16.0447	−	5.83978i	0.527545	−	0.192011i
$926$		0			0
$927$	−7.43298	+	6.21673i	−0.244131	+	0.204184i
$928$		0			0
$929$	13.3320	−	15.8884i	0.437407	−	0.521282i	−0.501637	−	0.865078i	$-0.667269\pi$
$929$	13.3320	−	15.8884i	0.437407	−	0.521282i	0.939044	+	0.343797i	$0.111713\pi$
$930$		0			0
$931$	−6.72373	+	1.18557i	−0.220361	+	0.0388556i
$932$		0			0
$933$	−18.1551	+	25.8839i	−0.594370	+	0.847402i
$934$		0			0
$935$	6.61748	+	11.4618i	0.216415	+	0.374841i
$936$		0			0
$937$	4.18164	−	7.24281i	0.136608	−	0.236612i	−0.789602	−	0.613619i	$-0.789713\pi$
$937$	4.18164	−	7.24281i	0.136608	−	0.236612i	0.926211	+	0.377006i	$0.123047\pi$
$938$		0			0
$939$	4.55940	+	52.5997i	0.148790	+	1.71653i
$940$		0			0
$941$	−12.9967	+	35.7082i	−0.423681	+	1.16405i	0.525904	+	0.850544i	$0.323727\pi$
$941$	−12.9967	+	35.7082i	−0.423681	+	1.16405i	−0.949585	+	0.313510i	$0.898495\pi$
$942$		0			0
$943$	0.155594	+	0.0274355i	0.00506685	+	0.000893422i
$944$		0			0
$945$	−0.262010	−	0.987325i	−0.00852318	−	0.0321177i
$946$		0			0
$947$	8.26393	−	46.8671i	0.268542	−	1.52298i	−0.490215	−	0.871602i	$-0.663082\pi$
$947$	8.26393	−	46.8671i	0.268542	−	1.52298i	0.758756	−	0.651374i	$-0.225807\pi$
$948$		0			0
$949$	−22.7746	−	8.28926i	−0.739293	−	0.269081i
$950$		0			0
$951$	−9.44551	+	20.2136i	−0.306292	+	0.655472i
$952$		0			0
$953$	−5.44770	−	3.14523i	−0.176468	−	0.101884i	0.409164	−	0.912461i	$-0.365820\pi$
$953$	−5.44770	−	3.14523i	−0.176468	−	0.101884i	−0.585632	+	0.810577i	$0.699154\pi$
$954$		0			0
$955$	−21.8955	+	12.6413i	−0.708520	+	0.409064i
$956$		0			0
$957$	0.256484	−	2.90481i	0.00829095	−	0.0938991i
$958$		0			0
$959$	0.343244	+	1.94664i	0.0110839	+	0.0628602i
$960$		0			0
$961$	23.5232	+	19.7383i	0.758813	+	0.636719i
$962$		0			0
$963$	0.00138800	−	0.865818i	4.47276e−5	−	0.0279006i
$964$		0			0
$965$	1.51165	+	4.15323i	0.0486618	+	0.133697i
$966$		0			0
$967$	36.6410	+	43.6671i	1.17830	+	1.40424i	0.895502	+	0.445058i	$0.146817\pi$
$967$	36.6410	+	43.6671i	1.17830	+	1.40424i	0.282795	+	0.959181i	$0.408739\pi$
$968$		0			0
$969$	4.85511	+	4.86290i	0.155969	+	0.156219i
$970$		0			0
$971$	−28.1754			−0.904190			−0.452095	−	0.891970i	$-0.649323\pi$
$971$	−28.1754			−0.904190			−0.452095	+	0.891970i	$0.649323\pi$
$972$		0			0
$973$	−1.87316			−0.0600508
$974$		0			0
$975$	−7.88536	−	7.89801i	−0.252534	−	0.252939i
$976$		0			0
$977$	−37.0940	−	44.2069i	−1.18674	−	1.41431i	−0.887921	−	0.459996i	$-0.847851\pi$
$977$	−37.0940	−	44.2069i	−1.18674	−	1.41431i	−0.298822	−	0.954309i	$-0.596594\pi$
$978$		0			0
$979$	−3.06351	−	8.41693i	−0.0979103	−	0.269006i
$980$		0			0
$981$	0.0148489	−	9.26259i	0.000474089	−	0.295732i
$982$		0			0
$983$	−19.4777	−	16.3437i	−0.621243	−	0.521285i	0.276951	−	0.960884i	$-0.410676\pi$
$983$	−19.4777	−	16.3437i	−0.621243	−	0.521285i	−0.898194	+	0.439599i	$0.855120\pi$
$984$		0			0
$985$	2.85547	+	16.1941i	0.0909827	+	0.515989i
$986$		0			0
$987$	−0.133991	+	1.51751i	−0.00426498	+	0.0483030i
$988$		0			0
$989$	−58.9778	+	34.0508i	−1.87538	+	1.08275i
$990$		0			0
$991$	−2.80307	−	1.61835i	−0.0890423	−	0.0514086i	0.454818	−	0.890585i	$-0.349704\pi$
$991$	−2.80307	−	1.61835i	−0.0890423	−	0.0514086i	−0.543860	+	0.839176i	$0.683038\pi$
$992$		0			0
$993$	6.53385	−	13.9826i	0.207345	−	0.443725i
$994$		0			0
$995$	15.2455	+	5.54893i	0.483316	+	0.175913i
$996$		0			0
$997$	6.59640	−	37.4101i	0.208910	−	1.18479i	−0.682257	−	0.731113i	$-0.739001\pi$
$997$	6.59640	−	37.4101i	0.208910	−	1.18479i	0.891167	−	0.453676i	$-0.149888\pi$
$998$		0			0
$999$	48.1138	+	13.0161i	1.52225	+	0.411812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.191.1	yes	36
4.3	odd	2		432.2.be.c.191.6	yes	36
27.14	odd	18		432.2.be.c.95.6	yes	36
108.95	even	18	inner	432.2.be.b.95.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.95.1	✓	36	108.95	even	18	inner
432.2.be.b.191.1	yes	36	1.1	even	1	trivial
432.2.be.c.95.6	yes	36	27.14	odd	18
432.2.be.c.191.6	yes	36	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22376 - 1.22573i) q^{3} +(1.15344 + 1.37462i) q^{5} +(-0.0374696 - 0.102947i) q^{7} +(-0.00480931 + 3.00000i) q^{9} +O(q^{10})\)	\(q+(-1.22376 - 1.22573i) q^{3} +(1.15344 + 1.37462i) q^{5} +(-0.0374696 - 0.102947i) q^{7} +(-0.00480931 + 3.00000i) q^{9} +(1.39140 + 1.16752i) q^{11} +(0.628601 + 3.56497i) q^{13} +(0.273367 - 3.09601i) q^{15} +(3.51663 - 2.03033i) q^{17} +(-0.846129 - 0.488513i) q^{19} +(-0.0803308 + 0.171910i) q^{21} +(5.93514 + 2.16021i) q^{23} +(0.309093 - 1.75296i) q^{25} +(3.68306 - 3.66539i) q^{27} +(0.912843 + 0.160959i) q^{29} +(0.185026 - 0.508354i) q^{31} +(-0.271680 - 3.13425i) q^{33} +(0.0982937 - 0.170250i) q^{35} +(4.79618 + 8.30722i) q^{37} +(3.60042 - 5.13318i) q^{39} +(0.0246348 - 0.00434378i) q^{41} +(-6.93075 + 8.25975i) q^{43} +(-4.12940 + 3.45371i) q^{45} +(7.54426 - 2.74589i) q^{47} +(5.35312 - 4.49180i) q^{49} +(-6.79215 - 1.82579i) q^{51} -11.7054i q^{53} +3.25932i q^{55} +(0.436678 + 1.63495i) q^{57} +(1.98032 - 1.66168i) q^{59} +(-5.80843 + 2.11410i) q^{61} +(0.309021 - 0.111914i) q^{63} +(-4.17542 + 4.97608i) q^{65} +(-13.5924 + 2.39670i) q^{67} +(-4.61537 - 9.91844i) q^{69} +(0.650941 + 1.12746i) q^{71} +(-3.34757 + 5.79815i) q^{73} +(-2.52690 + 1.76634i) q^{75} +(0.0680578 - 0.186987i) q^{77} +(-8.71473 - 1.53664i) q^{79} +(-8.99995 - 0.0288558i) q^{81} +(-3.02146 + 17.1355i) q^{83} +(6.84715 + 2.49216i) q^{85} +(-0.919812 - 1.31587i) q^{87} +(-4.27071 - 2.46569i) q^{89} +(0.343450 - 0.198291i) q^{91} +(-0.849530 + 0.395314i) q^{93} +(-0.304442 - 1.72657i) q^{95} +(-10.6279 - 8.91789i) q^{97} +(-3.50926 + 4.16859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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