LMFDB - Embedded newform 432.2.be.b.95.1

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			95.1
Character	$\chi$	$=$	432.95
Dual form			432.2.be.b.191.1

$q$-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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{18}\right)$

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	−0.443756	−	0.896148i	$-0.646354\pi$
$5$	1.15344	−	1.37462i	0.515835	−	0.614748i	0.959591	+	0.281400i	$0.0907987\pi$
$6$		0			0
$7$	−0.0374696	+	0.102947i	−0.0141622	+	0.0389103i	−0.946572	−	0.322492i	$-0.895480\pi$
$7$	−0.0374696	+	0.102947i	−0.0141622	+	0.0389103i	0.932410	+	0.361402i	$0.117702\pi$
$8$		0			0
$9$	−0.00480931	−	3.00000i	−0.00160310	−	0.999999i
$10$		0			0
$11$	1.39140	−	1.16752i	0.419523	−	0.352022i	−0.408458	−	0.912777i	$-0.633933\pi$
$11$	1.39140	−	1.16752i	0.419523	−	0.352022i	0.827982	+	0.560755i	$0.189489\pi$
$12$		0			0
$13$	0.628601	−	3.56497i	0.174343	−	0.988746i	−0.764557	−	0.644556i	$-0.777042\pi$
$13$	0.628601	−	3.56497i	0.174343	−	0.988746i	0.938900	−	0.344190i	$-0.111847\pi$
$14$		0			0
$15$	0.273367	+	3.09601i	0.0705829	+	0.799386i
$16$		0			0
$17$	3.51663	+	2.03033i	0.852908	+	0.492427i	0.861631	−	0.507535i	$-0.169443\pi$
$17$	3.51663	+	2.03033i	0.852908	+	0.492427i	−0.00872297	+	0.999962i	$0.502777\pi$
$18$		0			0
$19$	−0.846129	+	0.488513i	−0.194115	+	0.112073i	−0.593908	−	0.804533i	$-0.702416\pi$
$19$	−0.846129	+	0.488513i	−0.194115	+	0.112073i	0.399792	+	0.916606i	$0.369082\pi$
$20$		0			0
$21$	−0.0803308	−	0.171910i	−0.0175296	−	0.0375139i
$22$		0			0
$23$	5.93514	−	2.16021i	1.23756	−	0.450436i	0.361381	−	0.932418i	$-0.382305\pi$
$23$	5.93514	−	2.16021i	1.23756	−	0.450436i	0.876181	+	0.481983i	$0.160083\pi$
$24$		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	−0.0882486	−	0.996098i	$-0.528127\pi$
$29$	0.912843	−	0.160959i	0.169511	−	0.0298893i	0.257759	+	0.966209i	$0.417016\pi$
$30$		0			0
$31$	0.185026	+	0.508354i	0.0332316	+	0.0913030i	0.955199	−	0.295965i	$-0.0956411\pi$
$31$	0.185026	+	0.508354i	0.0332316	+	0.0913030i	−0.921967	+	0.387268i	$0.873419\pi$
$32$		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	−0.138408	−	0.990375i	$-0.544198\pi$
$37$	4.79618	−	8.30722i	0.788486	−	1.36570i	0.926894	−	0.375323i	$-0.122468\pi$
$38$		0			0
$39$	3.60042	+	5.13318i	0.576529	+	0.821966i
$40$		0			0
$41$	0.0246348	+	0.00434378i	0.00384731	+	0.000678384i	0.175571	−	0.984467i	$-0.443823\pi$
$41$	0.0246348	+	0.00434378i	0.00384731	+	0.000678384i	−0.171724	+	0.985145i	$0.554934\pi$
$42$		0			0
$43$	−6.93075	−	8.25975i	−1.05693	−	1.25960i	−0.964557	−	0.263875i	$-0.914999\pi$
$43$	−6.93075	−	8.25975i	−1.05693	−	1.25960i	−0.0923729	−	0.995724i	$-0.529445\pi$
$44$		0			0
$45$	−4.12940	−	3.45371i	−0.615574	−	0.514849i
$46$		0			0
$47$	7.54426	+	2.74589i	1.10044	+	0.400529i	0.827480	−	0.561496i	$-0.189774\pi$
$47$	7.54426	+	2.74589i	1.10044	+	0.400529i	0.272964	+	0.962024i	$0.411996\pi$
$48$		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	$0.297260\pi$
$53$			11.7054i			1.60786i	−0.594726	+	0.803928i	$0.702740\pi$
$54$		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	0.762529	−	0.646954i	$-0.223957\pi$
$59$	1.98032	+	1.66168i	0.257815	+	0.216333i	−0.504714	+	0.863287i	$0.668402\pi$
$60$		0			0
$61$	−5.80843	−	2.11410i	−0.743694	−	0.270682i	−0.0577441	−	0.998331i	$-0.518391\pi$
$61$	−5.80843	−	2.11410i	−0.743694	−	0.270682i	−0.685950	+	0.727649i	$0.740613\pi$
$62$		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	−0.736905	−	0.675996i	$-0.763714\pi$
$67$	−13.5924	−	2.39670i	−1.66057	−	0.292804i	−0.923669	+	0.383192i	$0.874825\pi$
$68$		0			0
$69$	−4.61537	+	9.91844i	−0.555625	+	1.19404i
$70$		0			0
$71$	0.650941	−	1.12746i	0.0772525	−	0.133805i	−0.824811	−	0.565408i	$-0.808719\pi$
$71$	0.650941	−	1.12746i	0.0772525	−	0.133805i	0.902064	+	0.431603i	$0.142052\pi$
$72$		0			0
$73$	−3.34757	−	5.79815i	−0.391803	−	0.678623i	0.600884	−	0.799336i	$-0.294815\pi$
$73$	−3.34757	−	5.79815i	−0.391803	−	0.678623i	−0.992687	+	0.120713i	$0.961482\pi$
$74$		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	−0.640845	−	0.767670i	$-0.721416\pi$
$79$	−8.71473	+	1.53664i	−0.980484	+	0.172886i	−0.339639	+	0.940556i	$0.610305\pi$
$80$		0			0
$81$	−8.99995	+	0.0288558i	−0.999995	+	0.00320620i
$82$		0			0
$83$	−3.02146	−	17.1355i	−0.331648	−	1.88087i	−0.458108	−	0.888897i	$-0.651473\pi$
$83$	−3.02146	−	17.1355i	−0.331648	−	1.88087i	0.126460	−	0.991972i	$-0.459638\pi$
$84$		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	−0.708967	−	0.705241i	$-0.750839\pi$
$89$	−4.27071	+	2.46569i	−0.452694	+	0.261363i	0.256273	+	0.966604i	$0.417505\pi$
$90$		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	−0.995846	−	0.0910532i	$-0.970977\pi$
$97$	−10.6279	+	8.91789i	−1.07910	+	0.905475i	−0.0832569	+	0.996528i	$0.526532\pi$
$98$		0			0
$99$	−3.50926	−	4.16859i	−0.352694	−	0.418959i
$100$		0			0
$101$	−4.68279	+	12.8659i	−0.465955	+	1.28020i	0.454985	+	0.890499i	$0.349645\pi$
$101$	−4.68279	+	12.8659i	−0.465955	+	1.28020i	−0.920941	+	0.389703i	$0.872578\pi$
$102$		0			0
$103$	2.07621	−	2.47433i	0.204575	−	0.243803i	−0.653995	−	0.756499i	$-0.726908\pi$
$103$	2.07621	−	2.47433i	0.204575	−	0.243803i	0.858571	+	0.512695i	$0.171353\pi$
$104$		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	−0.290936	−	0.956742i	$-0.593967\pi$
$113$	7.46015	−	8.89065i	0.701791	−	0.836362i	0.992728	+	0.120380i	$0.0384113\pi$
$114$		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	−0.168853	−	0.985641i	$-0.554006\pi$
$127$	6.76517	−	3.90587i	0.600312	−	0.346590i	0.769164	+	0.639051i	$0.220673\pi$
$128$		0			0
$129$	18.6058	+	1.61277i	1.63815	+	0.141996i
$130$		0			0
$131$	3.17078	−	1.15407i	0.277032	−	0.100831i	−0.199768	−	0.979843i	$-0.564019\pi$
$131$	3.17078	−	1.15407i	0.277032	−	0.100831i	0.476800	+	0.879012i	$0.341797\pi$
$132$		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	−0.869681	−	0.493614i	$-0.835675\pi$
$137$	−17.7688	+	3.13311i	−1.51809	+	0.267680i	−0.648407	+	0.761294i	$0.724564\pi$
$138$		0			0
$139$	5.84789	+	16.0669i	0.496012	+	1.36278i	0.895099	+	0.445868i	$0.147105\pi$
$139$	5.84789	+	16.0669i	0.496012	+	1.36278i	−0.399087	+	0.916913i	$0.630673\pi$
$140$		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	0.833766	−	0.552118i	$-0.186180\pi$
$149$	17.4360	+	3.07444i	1.42841	+	0.251868i	0.594648	+	0.803986i	$0.297291\pi$
$150$		0			0
$151$	3.97337	+	4.73527i	0.323348	+	0.385351i	0.903092	−	0.429448i	$-0.141292\pi$
$151$	3.97337	+	4.73527i	0.323348	+	0.385351i	−0.579744	+	0.814799i	$0.696847\pi$
$152$		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	0.995802	−	0.0915368i	$-0.0291779\pi$
$157$	13.5145	+	11.3400i	1.07857	+	0.905032i	0.0827730	+	0.996568i	$0.473622\pi$
$158$		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	$0.00702820\pi$
$163$			0.563744i			0.0441559i	−0.999756	+	0.0220779i	$0.992972\pi$
$164$		0			0
$165$	3.99503	+	3.98863i	0.311013	+	0.310515i
$166$		0			0
$167$	13.0407	+	10.9424i	1.00912	+	0.846750i	0.988221	−	0.153032i	$-0.0489037\pi$
$167$	13.0407	+	10.9424i	1.00912	+	0.846750i	0.0208959	+	0.999782i	$0.493348\pi$
$168$		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	−0.996734	−	0.0807585i	$-0.974266\pi$
$173$	−11.8795	−	14.1575i	−0.903184	−	1.07637i	0.0935494	−	0.995615i	$-0.470179\pi$
$174$		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	0.437972	+	0.898989i	$0.355697\pi$
$179$	−7.48642	+	12.9669i	−0.559561	+	0.969188i	−0.997533	+	0.0701997i	$0.977636\pi$
$180$		0			0
$181$	−9.67055	−	16.7499i	−0.718806	−	1.24501i	−0.961473	−	0.274899i	$-0.911356\pi$
$181$	−9.67055	−	16.7499i	−0.718806	−	1.24501i	0.242667	−	0.970110i	$-0.421978\pi$
$182$		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	−0.935774	−	0.352601i	$-0.885297\pi$
$191$	−2.44661	−	13.8754i	−0.177031	−	1.00399i	0.758743	−	0.651390i	$-0.225814\pi$
$192$		0			0
$193$	2.31451	−	0.842411i	0.166602	−	0.0606381i	−0.257373	−	0.966312i	$-0.582857\pi$
$193$	2.31451	−	0.842411i	0.166602	−	0.0606381i	0.423975	+	0.905674i	$0.360635\pi$
$194$		0			0
$195$	11.2090	+	0.971611i	0.802696	+	0.0695785i
$196$		0			0
$197$	7.93614	−	4.58193i	0.565426	−	0.326449i	−0.189894	−	0.981805i	$-0.560814\pi$
$197$	7.93614	−	4.58193i	0.565426	−	0.326449i	0.755321	+	0.655355i	$0.227481\pi$
$198$		0			0
$199$	7.82997	+	4.52063i	0.555052	+	0.320459i	0.751157	−	0.660124i	$-0.229496\pi$
$199$	7.82997	+	4.52063i	0.555052	+	0.320459i	−0.196105	+	0.980583i	$0.562829\pi$
$200$		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	−0.997486	−	0.0708592i	$-0.977426\pi$
$211$	−10.9596	+	13.0612i	−0.754492	+	0.899169i	0.242994	+	0.970028i	$0.421870\pi$
$212$		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	−0.994348	−	0.106171i	$-0.966141\pi$
$223$	−2.45483	+	6.74460i	−0.164388	+	0.451651i	0.829960	+	0.557823i	$0.188363\pi$
$224$		0			0
$225$	5.25737	−	0.935710i	0.350492	−	0.0623806i
$226$		0			0
$227$	−20.2092	+	16.9575i	−1.34133	+	1.12551i	−0.360052	+	0.932932i	$0.617241\pi$
$227$	−20.2092	+	16.9575i	−1.34133	+	1.12551i	−0.981281	+	0.192580i	$0.938315\pi$
$228$		0			0
$229$	0.294614	−	1.67084i	0.0194686	−	0.110412i	−0.973525	−	0.228581i	$-0.926591\pi$
$229$	0.294614	−	1.67084i	0.0194686	−	0.110412i	0.992993	+	0.118169i	$0.0377025\pi$
$230$		0			0
$231$	−0.312482	−	0.145408i	−0.0205598	−	0.00956714i
$232$		0			0
$233$	−3.85496	−	2.22566i	−0.252547	−	0.145808i	0.368383	−	0.929674i	$-0.379912\pi$
$233$	−3.85496	−	2.22566i	−0.252547	−	0.145808i	−0.620930	+	0.783866i	$0.713245\pi$
$234$		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	−0.964827	−	0.262884i	$-0.915326\pi$
$239$	−23.7297	+	8.63692i	−1.53495	+	0.558676i	−0.570122	+	0.821560i	$0.693104\pi$
$240$		0			0
$241$	0.665669	+	3.77520i	0.0428795	+	0.243182i	0.998712	−	0.0507286i	$-0.0161543\pi$
$241$	0.665669	+	3.77520i	0.0428795	+	0.243182i	−0.955833	+	0.293911i	$0.905043\pi$
$242$		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	0.994284	+	0.106766i	$0.0340494\pi$
$251$	9.34108	+	16.1792i	0.589604	+	1.02122i	−0.404680	+	0.914458i	$0.632617\pi$
$252$		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	0.131752	−	0.991283i	$-0.457940\pi$
$257$	−1.33829	−	0.235977i	−0.0834802	−	0.0147198i	−0.215232	+	0.976563i	$0.569051\pi$
$258$		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	0.930509	−	0.366268i	$-0.119365\pi$
$263$	22.8321	+	8.31021i	1.40789	+	0.512429i	0.477379	+	0.878698i	$0.341587\pi$
$264$		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	$0.0748061\pi$
$269$			7.63814i			0.465706i	−0.972512	+	0.232853i	$0.925194\pi$
$270$		0			0
$271$			6.51576i			0.395804i	0.980222	+	0.197902i	$0.0634128\pi$
$271$			6.51576i			0.395804i	−0.980222	+	0.197902i	$0.936587\pi$
$272$		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	−0.164304	−	0.986410i	$-0.552538\pi$
$277$	−15.3821	−	5.59863i	−0.924221	−	0.336389i	−0.759916	+	0.650021i	$0.774760\pi$
$278$		0			0
$279$	1.52417	−	0.557521i	0.0912496	−	0.0333779i
$280$		0			0
$281$	−18.6722	−	22.2527i	−1.11389	−	1.32748i	−0.939399	−	0.342825i	$-0.888616\pi$
$281$	−18.6722	−	22.2527i	−1.11389	−	1.32748i	−0.174492	−	0.984659i	$-0.555828\pi$
$282$		0			0
$283$	14.3442	+	2.52928i	0.852677	+	0.150350i	0.582871	−	0.812565i	$-0.301929\pi$
$283$	14.3442	+	2.52928i	0.852677	+	0.150350i	0.269806	+	0.962915i	$0.413040\pi$
$284$		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	0.919011	−	0.394232i	$-0.128989\pi$
$293$	−0.657295	−	1.80590i	−0.0383996	−	0.105502i	−0.957411	+	0.288730i	$0.906767\pi$
$294$		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	0.989225	−	0.146405i	$-0.0467701\pi$
$307$	23.7774	+	13.7279i	1.35705	+	0.783492i	0.367822	+	0.929896i	$0.380103\pi$
$308$		0			0
$309$	0.492064	+	5.57287i	0.0279925	+	0.317029i
$310$		0			0
$311$	−3.16971	+	17.9763i	−0.179738	+	1.01934i	0.752794	+	0.658256i	$0.228705\pi$
$311$	−3.16971	+	17.9763i	−0.179738	+	1.01934i	−0.932532	+	0.361087i	$0.882406\pi$
$312$		0			0
$313$	−23.3508	+	19.5937i	−1.31987	+	1.10750i	−0.333533	+	0.942738i	$0.608241\pi$
$313$	−23.3508	+	19.5937i	−1.31987	+	1.10750i	−0.986334	+	0.164761i	$0.947315\pi$
$314$		0			0
$315$	0.510276	−	0.295700i	0.0287508	−	0.0166608i
$316$		0			0
$317$	−4.40578	+	12.1048i	−0.247453	+	0.679872i	0.752325	+	0.658792i	$0.228932\pi$
$317$	−4.40578	+	12.1048i	−0.247453	+	0.679872i	−0.999778	+	0.0210792i	$0.993290\pi$
$318$		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	−0.827323	−	0.561727i	$-0.810137\pi$
$331$	3.04766	−	8.37337i	0.167514	−	0.460242i	0.994837	+	0.101485i	$0.0323594\pi$
$332$		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	0.910664	+	0.413147i	$0.135571\pi$
$337$	−1.58582	+	8.99362i	−0.0863850	+	0.489913i	−0.997049	+	0.0767661i	$0.975541\pi$
$338$		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	0.177157	−	0.984183i	$-0.443310\pi$
$347$	17.6125	−	6.41042i	0.945487	−	0.344129i	0.768330	+	0.640054i	$0.221088\pi$
$348$		0			0
$349$	3.31068	+	18.7758i	0.177217	+	1.00505i	0.935554	+	0.353183i	$0.114901\pi$
$349$	3.31068	+	18.7758i	0.177217	+	1.00505i	−0.758338	+	0.651862i	$0.773988\pi$
$350$		0			0
$351$	15.3822	−	10.8259i	0.821041	−	0.577846i
$352$		0			0
$353$	12.6087	−	2.22326i	0.671094	−	0.118332i	0.172290	−	0.985046i	$-0.444884\pi$
$353$	12.6087	−	2.22326i	0.671094	−	0.118332i	0.498805	+	0.866714i	$0.333772\pi$
$354$		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	−0.926000	−	0.377523i	$-0.876776\pi$
$359$	−14.9673	−	25.9241i	−0.789945	−	1.36822i	0.136056	−	0.990701i	$-0.456557\pi$
$360$		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	0.526137	−	0.850400i	$-0.323640\pi$
$367$	−7.71474	−	9.19407i	−0.402706	−	0.479927i	−0.928843	+	0.370473i	$0.879196\pi$
$368$		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	−0.0613456	−	0.998117i	$-0.519539\pi$
$373$	−20.3745	−	17.0962i	−1.05495	−	0.885209i	−0.993605	+	0.112908i	$0.963984\pi$
$374$		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	$0.196236\pi$
$379$			22.5119i			1.15636i	−0.815910	+	0.578179i	$0.803764\pi$
$380$		0			0
$381$	−3.49143	+	13.0721i	−0.178871	+	0.669704i
$382$		0			0
$383$	−22.3710	−	18.7715i	−1.14310	−	0.959177i	−0.143566	−	0.989641i	$-0.545857\pi$
$383$	−22.3710	−	18.7715i	−1.14310	−	0.959177i	−0.999536	+	0.0304640i	$0.990301\pi$
$384$		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	0.719509	−	0.694483i	$-0.244367\pi$
$389$	−1.76256	−	2.10053i	−0.0893651	−	0.106501i	−0.808874	+	0.587982i	$0.799923\pi$
$390$		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	0.947366	−	0.320154i	$-0.103735\pi$
$397$	3.91367	+	6.77868i	0.196422	+	0.340212i	−0.750944	+	0.660366i	$0.770401\pi$
$398$		0			0
$399$	0.151951	+	0.106216i	0.00760704	+	0.00531743i
$400$		0			0
$401$	−2.67952	−	7.36193i	−0.133809	−	0.367637i	0.854634	−	0.519231i	$-0.173782\pi$
$401$	−2.67952	−	7.36193i	−0.133809	−	0.367637i	−0.988443	+	0.151594i	$0.951559\pi$
$402$		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	−0.466398	−	0.884575i	$-0.654448\pi$
$409$	−5.15878	+	1.87764i	−0.255085	+	0.0928434i	0.211313	+	0.977419i	$0.432226\pi$
$410$		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	−0.879353	−	0.476171i	$-0.842024\pi$
$419$	2.24813	−	12.7498i	0.109829	−	0.622868i	0.989181	−	0.146698i	$-0.0468645\pi$
$420$		0			0
$421$	10.1658	−	8.53012i	0.495451	−	0.415733i	−0.360524	−	0.932750i	$-0.617402\pi$
$421$	10.1658	−	8.53012i	0.495451	−	0.415733i	0.855975	+	0.517017i	$0.172958\pi$
$422$		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	0.507333	+	0.861750i	$0.330632\pi$
$439$	−9.11906	+	25.0544i	−0.435229	+	1.19578i	−0.942562	+	0.334032i	$0.891591\pi$
$440$		0			0
$441$	13.4496	−	16.0809i	0.640459	−	0.765759i
$442$		0			0
$443$	−10.2936	+	8.63732i	−0.489062	+	0.410371i	−0.853690	−	0.520782i	$-0.825641\pi$
$443$	−10.2936	+	8.63732i	−0.489062	+	0.410371i	0.364628	+	0.931153i	$0.381196\pi$
$444$		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	0.825736	−	0.564056i	$-0.190760\pi$
$449$	15.8947	+	9.17681i	0.750117	+	0.433081i	−0.0756189	+	0.997137i	$0.524093\pi$
$450$		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	0.989331	−	0.145688i	$-0.0465396\pi$
$457$	0.210261	+	1.19245i	0.00983562	+	0.0557806i	−0.979495	+	0.201469i	$0.935429\pi$
$458$		0			0
$459$	5.51002	+	20.3676i	0.257186	+	0.950680i
$460$		0			0
$461$	3.12039	−	0.550208i	0.145331	−	0.0256257i	−0.100509	−	0.994936i	$-0.532047\pi$
$461$	3.12039	−	0.550208i	0.145331	−	0.0256257i	0.245840	+	0.969310i	$0.420936\pi$
$462$		0			0
$463$	−6.53132	−	17.9447i	−0.303536	−	0.833959i	−0.993879	−	0.110476i	$-0.964762\pi$
$463$	−6.53132	−	17.9447i	−0.303536	−	0.833959i	0.690342	−	0.723483i	$-0.257460\pi$
$464$		0			0
$465$	−1.52329	+	0.711808i	−0.0706408	+	0.0330093i
$466$		0			0
$467$	6.32468	+	10.9547i	0.292672	+	0.506922i	0.974441	−	0.224646i	$-0.0721224\pi$
$467$	6.32468	+	10.9547i	0.292672	+	0.506922i	−0.681769	+	0.731567i	$0.738789\pi$
$468$		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	0.933616	−	0.358276i	$-0.116635\pi$
$479$	31.0456	+	11.2997i	1.41851	+	0.516296i	0.484896	+	0.874572i	$0.338858\pi$
$480$		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	$-0.654908\pi$
$487$		−	39.0120i		−	1.76780i	0.467673	−	0.883901i	$-0.345092\pi$
$488$		0			0
$489$	−0.690996	−	0.689889i	−0.0312479	−	0.0311979i
$490$		0			0
$491$	4.73374	+	3.97208i	0.213631	+	0.179257i	0.743323	−	0.668932i	$-0.233248\pi$
$491$	4.73374	+	3.97208i	0.213631	+	0.179257i	−0.529693	+	0.848190i	$0.677693\pi$
$492$		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	−0.537841	−	0.843046i	$-0.680760\pi$
$499$	−29.7454	−	5.24491i	−1.33159	−	0.234794i	−0.793744	+	0.608252i	$0.791871\pi$
$500$		0			0
$501$	−29.3711	+	2.59336i	−1.31220	+	0.115863i
$502$		0			0
$503$	5.66137	−	9.80578i	0.252428	−	0.437218i	−0.711766	−	0.702417i	$-0.752104\pi$
$503$	5.66137	−	9.80578i	0.252428	−	0.437218i	0.964194	+	0.265199i	$0.0854376\pi$
$504$		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	0.994312	+	0.106502i	$0.0339651\pi$
$509$	6.79275	+	18.6629i	0.301083	+	0.827219i	−0.693229	+	0.720717i	$0.743813\pi$
$510$		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	−0.608311	−	0.793699i	$-0.708152\pi$
$521$	−5.13805	+	2.96646i	−0.225102	+	0.129963i	0.383208	+	0.923662i	$0.374819\pi$
$522$		0			0
$523$	17.2055	+	9.93358i	0.752343	+	0.434365i	0.826540	−	0.562878i	$-0.190306\pi$
$523$	17.2055	+	9.93358i	0.752343	+	0.434365i	−0.0741971	+	0.997244i	$0.523639\pi$
$524$		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	−0.664199	−	0.747556i	$-0.731227\pi$
$547$	7.60406	−	20.8920i	0.325126	−	0.893277i	0.989326	−	0.145722i	$-0.0465504\pi$
$548$		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	−0.295756	−	0.955264i	$-0.595572\pi$
$557$	−29.9947	−	17.3175i	−1.27092	−	0.733764i	−0.975160	+	0.221499i	$0.928905\pi$
$558$		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	0.0835464	−	0.996504i	$-0.473375\pi$
$563$	18.6994	−	6.80604i	0.788087	−	0.286840i	0.704541	+	0.709664i	$0.251153\pi$
$564$		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	0.719774	−	0.694209i	$-0.244246\pi$
$569$	38.9668	−	6.87090i	1.63357	−	0.288043i	0.913799	+	0.406166i	$0.133134\pi$
$570$		0			0
$571$	−7.36266	−	20.2288i	−0.308118	−	0.846547i	−0.993024	−	0.117915i	$-0.962379\pi$
$571$	−7.36266	−	20.2288i	−0.308118	−	0.846547i	0.684906	−	0.728632i	$-0.259843\pi$
$572$		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	−0.343692	−	0.939083i	$-0.611677\pi$
$577$	15.4075	−	26.6866i	0.641424	−	1.11098i	0.985115	−	0.171896i	$-0.0549892\pi$
$578$		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	0.947215	−	0.320598i	$-0.103884\pi$
$587$	35.5365	+	12.9342i	1.46675	+	0.533853i	0.519533	+	0.854451i	$0.326106\pi$
$588$		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	$-0.601453\pi$
$593$		−	46.2503i		−	1.89927i	0.313355	−	0.949636i	$-0.398547\pi$
$594$		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	0.607408	−	0.794390i	$-0.292209\pi$
$599$	−1.69945	−	1.42601i	−0.0694377	−	0.0582651i	−0.676846	+	0.736125i	$0.736654\pi$
$600$		0			0
$601$	31.3863	+	11.4237i	1.28027	+	0.465981i	0.890522	−	0.454940i	$-0.150339\pi$
$601$	31.3863	+	11.4237i	1.28027	+	0.465981i	0.389750	+	0.920921i	$0.372561\pi$
$602$		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	0.639561	−	0.768740i	$-0.279116\pi$
$607$	24.0862	+	4.24704i	0.977628	+	0.172382i	0.338067	+	0.941122i	$0.390227\pi$
$608$		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	0.832501	−	0.554023i	$-0.186908\pi$
$613$	−1.57336	−	2.72514i	−0.0635474	−	0.110067i	−0.896049	+	0.443956i	$0.853575\pi$
$614$		0			0
$615$	−0.00671405	+	0.0774569i	−0.000270737	+	0.00312337i
$616$		0			0
$617$	9.26016	+	25.4421i	0.372800	+	1.02426i	0.974274	+	0.225367i	$0.0723582\pi$
$617$	9.26016	+	25.4421i	0.372800	+	1.02426i	−0.601474	+	0.798893i	$0.705420\pi$
$618$		0			0
$619$	−24.1567	+	4.25949i	−0.970942	+	0.171203i	−0.636554	−	0.771232i	$-0.719641\pi$
$619$	−24.1567	+	4.25949i	−0.970942	+	0.171203i	−0.334388	+	0.942436i	$0.608530\pi$
$620$		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	−0.993811	−	0.111081i	$-0.964569\pi$
$631$	−39.8629	−	23.0148i	−1.58692	−	0.916206i	−0.593105	−	0.805125i	$-0.702098\pi$
$632$		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	0.547486	+	0.836815i	$0.315585\pi$
$641$	−10.3755	+	28.5064i	−0.409807	+	1.12593i	−0.957293	+	0.289120i	$0.906637\pi$
$642$		0			0
$643$	−15.9458	+	19.0034i	−0.628840	+	0.749422i	−0.982563	−	0.185928i	$-0.940471\pi$
$643$	−15.9458	+	19.0034i	−0.628840	+	0.749422i	0.353723	+	0.935350i	$0.384915\pi$
$644$		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	−0.985422	−	0.170128i	$-0.945582\pi$
$653$	−16.5273	+	19.6964i	−0.646762	+	0.770781i	0.338660	+	0.940909i	$0.390026\pi$
$654$		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	−0.592198	+	0.805793i	$0.701739\pi$
$659$	−38.2134	+	32.0648i	−1.48858	+	1.24907i	−0.896385	+	0.443276i	$0.853816\pi$
$660$		0			0
$661$	4.10673	−	23.2904i	0.159733	−	0.905893i	−0.794596	−	0.607138i	$-0.792317\pi$
$661$	4.10673	−	23.2904i	0.159733	−	0.905893i	0.954330	−	0.298755i	$-0.0965714\pi$
$662$		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	−0.746410	−	0.665486i	$-0.768224\pi$
$673$	−7.07247	−	40.1100i	−0.272624	−	1.54613i	0.473787	−	0.880640i	$-0.342887\pi$
$674$		0			0
$675$	−5.28686	+	7.58919i	−0.203491	+	0.292108i
$676$		0			0
$677$	27.5622	−	4.85995i	1.05930	−	0.186783i	0.383254	−	0.923643i	$-0.374803\pi$
$677$	27.5622	−	4.85995i	1.05930	−	0.186783i	0.676046	+	0.736860i	$0.263692\pi$
$678$		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	0.864739	−	0.502222i	$-0.167484\pi$
$683$	−0.0671037	−	0.116227i	−0.00256765	−	0.00444730i	−0.867306	+	0.497775i	$0.834151\pi$
$684$		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	0.670332	−	0.742061i	$-0.266152\pi$
$691$	−4.64904	−	5.54051i	−0.176858	−	0.210771i	−0.847190	+	0.531291i	$0.821707\pi$
$692$		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	$-0.904113\pi$
$701$		−	15.7113i		−	0.593407i	0.954970	−	0.296703i	$-0.0958872\pi$
$702$		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	0.404701	−	0.914449i	$-0.367376\pi$
$709$	3.37957	+	1.23006i	0.126922	+	0.0461960i	−0.277778	+	0.960645i	$0.589598\pi$
$710$		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	−0.134429	−	0.990923i	$-0.542920\pi$
$719$	21.2087	−	36.7345i	0.790950	−	1.36997i	0.925379	−	0.379042i	$-0.123747\pi$
$720$		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	−0.302565	−	0.953129i	$-0.597843\pi$
$727$	−7.03446	+	1.24037i	−0.260894	+	0.0460026i	0.0416711	+	0.999131i	$0.486732\pi$
$728$		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	−0.764310	−	0.644849i	$-0.776920\pi$
$733$	−25.3224	+	9.21661i	−0.935305	+	0.340423i	−0.170995	+	0.985272i	$0.554698\pi$
$734$		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	0.345058	−	0.938581i	$-0.387859\pi$
$739$	−8.02620	−	4.63393i	−0.295249	−	0.170462i	−0.640306	+	0.768120i	$0.721193\pi$
$740$		0			0
$741$	−5.55404	−	2.58448i	−0.204033	−	0.0949431i
$742$		0			0
$743$	−2.56527	+	14.5484i	−0.0941106	+	0.533728i	0.900906	+	0.434015i	$0.142903\pi$
$743$	−2.56527	+	14.5484i	−0.0941106	+	0.533728i	−0.995016	+	0.0997127i	$0.968208\pi$
$744$		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	−0.168430	−	0.985714i	$-0.553870\pi$
$751$	22.7883	−	27.1580i	0.831556	−	0.991010i	0.999986	−	0.00529624i	$-0.00168585\pi$
$752$		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	−0.912510	−	0.409054i	$-0.865859\pi$
$761$	−9.68871	+	11.5466i	−0.351215	+	0.418562i	0.561295	+	0.827616i	$0.310303\pi$
$762$		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	−0.879180	−	0.476490i	$-0.841909\pi$
$769$	3.04896	−	17.2915i	0.109948	−	0.623547i	0.989128	−	0.147057i	$-0.0469801\pi$
$770$		0			0
$771$	1.92699	−	1.35160i	0.0693989	−	0.0486766i
$772$		0			0
$773$	−28.6124	−	16.5194i	−1.02912	−	0.594161i	−0.112386	−	0.993665i	$-0.535849\pi$
$773$	−28.6124	−	16.5194i	−1.02912	−	0.594161i	−0.916732	+	0.399503i	$0.869183\pi$
$774$		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	−0.716318	−	0.697774i	$-0.754174\pi$
$787$	−17.2840	−	47.4873i	−0.616107	−	1.69274i	0.100211	−	0.994966i	$-0.468048\pi$
$788$		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	−0.166916	−	0.985971i	$-0.553381\pi$
$797$	−18.6605	−	3.29034i	−0.660987	−	0.116550i	−0.494071	+	0.869421i	$0.664492\pi$
$798$		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	$-0.861906\pi$
$809$		−	23.9122i		−	0.840709i	0.907360	−	0.420355i	$-0.138094\pi$
$810$		0			0
$811$		−	8.39157i		−	0.294668i	−0.989087	−	0.147334i	$-0.952931\pi$
$811$		−	8.39157i		−	0.294668i	0.989087	−	0.147334i	$-0.0470692\pi$
$812$		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	0.882793	−	0.469762i	$-0.155660\pi$
$821$	7.64673	+	9.11302i	0.266873	+	0.318047i	−0.615920	+	0.787808i	$0.711216\pi$
$822$		0			0
$823$	0.106247	+	0.0187342i	0.00370353	+	0.000653032i	0.175500	−	0.984479i	$-0.443846\pi$
$823$	0.106247	+	0.0187342i	0.00370353	+	0.000653032i	−0.171796	+	0.985133i	$0.554957\pi$
$824$		0			0
$825$	−5.57818	+	0.492533i	−0.194207	+	0.0171478i
$826$		0			0
$827$	−14.5115	+	25.1347i	−0.504615	+	0.874019i	0.495371	+	0.868682i	$0.335032\pi$
$827$	−14.5115	+	25.1347i	−0.504615	+	0.874019i	−0.999986	+	0.00533723i	$0.998301\pi$
$828$		0			0
$829$	16.6372	+	28.8164i	0.577833	+	1.00084i	0.995727	+	0.0923405i	$0.0294348\pi$
$829$	16.6372	+	28.8164i	0.577833	+	1.00084i	−0.417895	+	0.908496i	$0.637232\pi$
$830$		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	−0.999479	−	0.0322689i	$-0.989727\pi$
$839$	−2.06560	−	11.7146i	−0.0713126	−	0.404434i	0.928167	−	0.372165i	$-0.121384\pi$
$840$		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	−0.287684	−	0.957725i	$-0.592885\pi$
$853$	17.6854	−	14.8398i	0.605535	−	0.508105i	0.893220	+	0.449621i	$0.148441\pi$
$854$		0			0
$855$	5.18118	+	0.905020i	0.177193	+	0.0309510i
$856$		0			0
$857$	−5.83078	+	16.0199i	−0.199176	+	0.547231i	−0.998563	−	0.0535848i	$-0.982935\pi$
$857$	−5.83078	+	16.0199i	−0.199176	+	0.547231i	0.799388	+	0.600816i	$0.205157\pi$
$858$		0			0
$859$	−10.9442	+	13.0428i	−0.373413	+	0.445016i	−0.919724	−	0.392567i	$-0.871587\pi$
$859$	−10.9442	+	13.0428i	−0.373413	+	0.445016i	0.546311	+	0.837582i	$0.316032\pi$
$860$		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	0.920723	+	0.390217i	$0.127600\pi$
$877$	−2.30800	+	13.0893i	−0.0779355	+	0.441994i	−0.998659	+	0.0517778i	$0.983511\pi$
$878$		0			0
$879$	3.01792	+	1.40433i	0.101792	+	0.0473670i
$880$		0			0
$881$	42.4341	+	24.4993i	1.42964	+	0.825404i	0.997092	−	0.0762067i	$-0.0242809\pi$
$881$	42.4341	+	24.4993i	1.42964	+	0.825404i	0.432549	+	0.901610i	$0.357614\pi$
$882$		0			0
$883$	−15.0988	+	8.71730i	−0.508115	+	0.293360i	−0.732059	−	0.681242i	$-0.761440\pi$
$883$	−15.0988	+	8.71730i	−0.508115	+	0.293360i	0.223943	+	0.974602i	$0.428107\pi$
$884$		0			0
$885$	−4.60323	+	6.58533i	−0.154736	+	0.221363i
$886$		0			0
$887$	−43.1388	+	15.7012i	−1.44846	+	0.527195i	−0.942160	−	0.335163i	$-0.891208\pi$
$887$	−43.1388	+	15.7012i	−1.44846	+	0.527195i	−0.506298	+	0.862359i	$0.668986\pi$
$888$		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	0.519211	−	0.854646i	$-0.326226\pi$
$907$	−12.4264	−	14.8092i	−0.412611	−	0.491731i	−0.931822	+	0.362915i	$0.881781\pi$
$908$		0			0
$909$	38.6201	+	13.9865i	1.28095	+	0.463903i
$910$		0			0
$911$	17.6273	+	6.41580i	0.584018	+	0.212565i	0.617096	−	0.786888i	$-0.288309\pi$
$911$	17.6273	+	6.41580i	0.584018	+	0.212565i	−0.0330786	+	0.999453i	$0.510531\pi$
$912$		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	$-0.862751\pi$
$919$		−	25.3399i		−	0.835885i	0.908473	−	0.417943i	$-0.137249\pi$
$920$		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	0.939044	−	0.343797i	$-0.111713\pi$
$929$	13.3320	+	15.8884i	0.437407	+	0.521282i	−0.501637	+	0.865078i	$0.667269\pi$
$930$		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	0.926211	−	0.377006i	$-0.123047\pi$
$937$	4.18164	+	7.24281i	0.136608	+	0.236612i	−0.789602	+	0.613619i	$0.789713\pi$
$938$		0			0
$939$	4.55940	−	52.5997i	0.148790	−	1.71653i
$940$		0			0
$941$	−12.9967	−	35.7082i	−0.423681	−	1.16405i	−0.949585	−	0.313510i	$-0.898495\pi$
$941$	−12.9967	−	35.7082i	−0.423681	−	1.16405i	0.525904	−	0.850544i	$-0.323727\pi$
$942$		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	0.758756	+	0.651374i	$0.225807\pi$
$947$	8.26393	+	46.8671i	0.268542	+	1.52298i	−0.490215	+	0.871602i	$0.663082\pi$
$948$		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	−0.585632	−	0.810577i	$-0.699154\pi$
$953$	−5.44770	+	3.14523i	−0.176468	+	0.101884i	0.409164	+	0.912461i	$0.365820\pi$
$954$		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	0.282795	−	0.959181i	$-0.408739\pi$
$967$	36.6410	−	43.6671i	1.17830	−	1.40424i	0.895502	−	0.445058i	$-0.146817\pi$
$968$		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	−0.298822	+	0.954309i	$0.596594\pi$
$977$	−37.0940	+	44.2069i	−1.18674	+	1.41431i	−0.887921	+	0.459996i	$0.847851\pi$
$978$		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	−0.898194	−	0.439599i	$-0.855120\pi$
$983$	−19.4777	+	16.3437i	−0.621243	+	0.521285i	0.276951	+	0.960884i	$0.410676\pi$
$984$		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	−0.543860	−	0.839176i	$-0.683038\pi$
$991$	−2.80307	+	1.61835i	−0.0890423	+	0.0514086i	0.454818	+	0.890585i	$0.349704\pi$
$992$		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	0.891167	+	0.453676i	$0.149888\pi$
$997$	6.59640	+	37.4101i	0.208910	+	1.18479i	−0.682257	+	0.731113i	$0.739001\pi$
$998$		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.95.1	✓	36
4.3	odd	2		432.2.be.c.95.6	yes	36
27.2	odd	18		432.2.be.c.191.6	yes	36
108.83	even	18	inner	432.2.be.b.191.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.95.1	✓	36	1.1	even	1	trivial
432.2.be.b.191.1	yes	36	108.83	even	18	inner
432.2.be.c.95.6	yes	36	4.3	odd	2
432.2.be.c.191.6	yes	36	27.2	odd	18

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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