LMFDB - Embedded newform 432.2.u.f.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	432.49
Dual form			432.2.u.f.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997080 + 1.41627i) q^{3} +(1.95510 - 0.711598i) q^{5} +(-0.739573 - 4.19433i) q^{7} +(-1.01166 - 2.82428i) q^{9} +O(q^{10})$	\(q+(-0.997080 + 1.41627i) q^{3} +(1.95510 - 0.711598i) q^{5} +(-0.739573 - 4.19433i) q^{7} +(-1.01166 - 2.82428i) q^{9} +(-2.33115 - 0.848468i) q^{11} +(-4.38271 - 3.67753i) q^{13} +(-0.941573 + 3.47847i) q^{15} +(0.340351 - 0.589505i) q^{17} +(2.58368 + 4.47506i) q^{19} +(6.67773 + 3.13464i) q^{21} +(1.23287 - 6.99197i) q^{23} +(-0.514184 + 0.431451i) q^{25} +(5.00866 + 1.38324i) q^{27} +(4.22836 - 3.54802i) q^{29} +(0.787375 - 4.46543i) q^{31} +(3.52600 - 2.45555i) q^{33} +(-4.43061 - 7.67405i) q^{35} +(-3.69778 + 6.40475i) q^{37} +(9.57830 - 2.54033i) q^{39} +(-0.256172 - 0.214954i) q^{41} +(1.61090 + 0.586320i) q^{43} +(-3.98765 - 4.80184i) q^{45} +(0.889756 + 5.04606i) q^{47} +(-10.4676 + 3.80989i) q^{49} +(0.495544 + 1.06981i) q^{51} +9.45353 q^{53} -5.16139 q^{55} +(-8.91404 - 0.802799i) q^{57} +(9.52366 - 3.46633i) q^{59} +(1.36385 + 7.73479i) q^{61} +(-11.0977 + 6.33201i) q^{63} +(-11.1856 - 4.07121i) q^{65} +(-3.13628 - 2.63165i) q^{67} +(8.67327 + 8.71764i) q^{69} +(-2.77081 + 4.79919i) q^{71} +(-4.43331 - 7.67871i) q^{73} +(-0.0983709 - 1.15842i) q^{75} +(-1.83470 + 10.4051i) q^{77} +(-4.53194 + 3.80275i) q^{79} +(-6.95308 + 5.71443i) q^{81} +(6.90986 - 5.79806i) q^{83} +(0.245929 - 1.39473i) q^{85} +(0.808948 + 9.52617i) q^{87} +(0.983567 + 1.70359i) q^{89} +(-12.1834 + 21.1023i) q^{91} +(5.53919 + 5.56753i) q^{93} +(8.23578 + 6.91064i) q^{95} +(0.443556 + 0.161441i) q^{97} +(-0.0379741 + 7.44216i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q - 3 * q^7 - 6 * q^9	$ 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) $ 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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
$3$	−0.997080	+	1.41627i	−0.575664	+	0.817686i
$3$	−0.997080	+	1.41627i	−0.575664	+	0.817686i
$4$		0			0
$5$	1.95510	−	0.711598i	0.874347	−	0.318236i	0.134421	−	0.990924i	$-0.457083\pi$
$5$	1.95510	−	0.711598i	0.874347	−	0.318236i	0.739926	+	0.672688i	$0.234860\pi$
$6$		0			0
$7$	−0.739573	−	4.19433i	−0.279532	−	1.58531i	−0.724186	−	0.689605i	$-0.757784\pi$
$7$	−0.739573	−	4.19433i	−0.279532	−	1.58531i	0.444653	−	0.895703i	$-0.353327\pi$
$8$		0			0
$9$	−1.01166	−	2.82428i	−0.337221	−	0.941426i
$10$		0			0
$11$	−2.33115	−	0.848468i	−0.702867	−	0.255823i	−0.0342324	−	0.999414i	$-0.510899\pi$
$11$	−2.33115	−	0.848468i	−0.702867	−	0.255823i	−0.668634	+	0.743591i	$0.733121\pi$
$12$		0			0
$13$	−4.38271	−	3.67753i	−1.21555	−	1.01996i	−0.999046	−	0.0436808i	$-0.986092\pi$
$13$	−4.38271	−	3.67753i	−1.21555	−	1.01996i	−0.216500	−	0.976283i	$-0.569464\pi$
$14$		0			0
$15$	−0.941573	+	3.47847i	−0.243113	+	0.898138i
$16$		0			0
$17$	0.340351	−	0.589505i	0.0825473	−	0.142976i	−0.821796	−	0.569782i	$-0.807028\pi$
$17$	0.340351	−	0.589505i	0.0825473	−	0.142976i	0.904343	+	0.426806i	$0.140361\pi$
$18$		0			0
$19$	2.58368	+	4.47506i	0.592736	+	1.02665i	0.993862	+	0.110626i	$0.0352856\pi$
$19$	2.58368	+	4.47506i	0.592736	+	1.02665i	−0.401126	+	0.916023i	$0.631381\pi$
$20$		0			0
$21$	6.67773	+	3.13464i	1.45720	+	0.684035i
$22$		0			0
$23$	1.23287	−	6.99197i	0.257072	−	1.45793i	−0.533627	−	0.845720i	$-0.679171\pi$
$23$	1.23287	−	6.99197i	0.257072	−	1.45793i	0.790698	−	0.612206i	$-0.209718\pi$
$24$		0			0
$25$	−0.514184	+	0.431451i	−0.102837	+	0.0862903i
$26$		0			0
$27$	5.00866	+	1.38324i	0.963917	+	0.266204i
$28$		0			0
$29$	4.22836	−	3.54802i	0.785187	−	0.658850i	−0.159362	−	0.987220i	$-0.550944\pi$
$29$	4.22836	−	3.54802i	0.785187	−	0.658850i	0.944549	+	0.328370i	$0.106499\pi$
$30$		0			0
$31$	0.787375	−	4.46543i	0.141417	−	0.802014i	−0.828758	−	0.559607i	$-0.810952\pi$
$31$	0.787375	−	4.46543i	0.141417	−	0.802014i	0.970175	−	0.242407i	$-0.0779369\pi$
$32$		0			0
$33$	3.52600	−	2.45555i	0.613798	−	0.427456i
$34$		0			0
$35$	−4.43061	−	7.67405i	−0.748910	−	1.29715i
$36$		0			0
$37$	−3.69778	+	6.40475i	−0.607912	+	1.05293i	0.383672	+	0.923469i	$0.374659\pi$
$37$	−3.69778	+	6.40475i	−0.607912	+	1.05293i	−0.991584	+	0.129465i	$0.958674\pi$
$38$		0			0
$39$	9.57830	−	2.54033i	1.53376	−	0.406778i
$40$		0			0
$41$	−0.256172	−	0.214954i	−0.0400074	−	0.0335702i	0.622565	−	0.782568i	$-0.286091\pi$
$41$	−0.256172	−	0.214954i	−0.0400074	−	0.0335702i	−0.662572	+	0.748998i	$0.730535\pi$
$42$		0			0
$43$	1.61090	+	0.586320i	0.245660	+	0.0894130i	0.461916	−	0.886924i	$-0.347162\pi$
$43$	1.61090	+	0.586320i	0.245660	+	0.0894130i	−0.216256	+	0.976337i	$0.569384\pi$
$44$		0			0
$45$	−3.98765	−	4.80184i	−0.594444	−	0.715816i
$46$		0			0
$47$	0.889756	+	5.04606i	0.129784	+	0.736043i	0.978351	+	0.206954i	$0.0663551\pi$
$47$	0.889756	+	5.04606i	0.129784	+	0.736043i	−0.848566	+	0.529089i	$0.822534\pi$
$48$		0			0
$49$	−10.4676	+	3.80989i	−1.49537	+	0.544270i
$50$		0			0
$51$	0.495544	+	1.06981i	0.0693900	+	0.149804i
$52$		0			0
$53$	9.45353			1.29854			0.649271	−	0.760557i	$-0.275074\pi$
$53$	9.45353			1.29854			0.649271	+	0.760557i	$0.275074\pi$
$54$		0			0
$55$	−5.16139			−0.695961
$56$		0			0
$57$	−8.91404	−	0.802799i	−1.18069	−	0.106333i
$58$		0			0
$59$	9.52366	−	3.46633i	1.23987	−	0.451277i	0.362906	−	0.931826i	$-0.381784\pi$
$59$	9.52366	−	3.46633i	1.23987	−	0.451277i	0.876968	+	0.480548i	$0.159562\pi$
$60$		0			0
$61$	1.36385	+	7.73479i	0.174623	+	0.990338i	0.938578	+	0.345068i	$0.112144\pi$
$61$	1.36385	+	7.73479i	0.174623	+	0.990338i	−0.763954	+	0.645270i	$0.776745\pi$
$62$		0			0
$63$	−11.0977	+	6.33201i	−1.39818	+	0.797758i
$64$		0			0
$65$	−11.1856	−	4.07121i	−1.38740	−	0.504971i
$66$		0			0
$67$	−3.13628	−	2.63165i	−0.383157	−	0.321507i	0.430783	−	0.902455i	$-0.358237\pi$
$67$	−3.13628	−	2.63165i	−0.383157	−	0.321507i	−0.813940	+	0.580948i	$0.802682\pi$
$68$		0			0
$69$	8.67327	+	8.71764i	1.04414	+	1.04948i
$70$		0			0
$71$	−2.77081	+	4.79919i	−0.328835	+	0.569559i	−0.982281	−	0.187414i	$-0.939989\pi$
$71$	−2.77081	+	4.79919i	−0.328835	+	0.569559i	0.653446	+	0.756973i	$0.273323\pi$
$72$		0			0
$73$	−4.43331	−	7.67871i	−0.518879	−	0.898725i	−0.999759	−	0.0219389i	$-0.993016\pi$
$73$	−4.43331	−	7.67871i	−0.518879	−	0.898725i	0.480880	−	0.876786i	$-0.340317\pi$
$74$		0			0
$75$	−0.0983709	−	1.15842i	−0.0113589	−	0.133762i
$76$		0			0
$77$	−1.83470	+	10.4051i	−0.209083	+	1.18577i
$78$		0			0
$79$	−4.53194	+	3.80275i	−0.509883	+	0.427842i	−0.861088	−	0.508456i	$-0.830216\pi$
$79$	−4.53194	+	3.80275i	−0.509883	+	0.427842i	0.351205	+	0.936299i	$0.385772\pi$
$80$		0			0
$81$	−6.95308	+	5.71443i	−0.772564	+	0.634937i
$82$		0			0
$83$	6.90986	−	5.79806i	0.758456	−	0.636420i	−0.179268	−	0.983800i	$-0.557373\pi$
$83$	6.90986	−	5.79806i	0.758456	−	0.636420i	0.937724	+	0.347380i	$0.112929\pi$
$84$		0			0
$85$	0.245929	−	1.39473i	0.0266748	−	0.151280i
$86$		0			0
$87$	0.808948	+	9.52617i	0.0867283	+	1.02131i
$88$		0			0
$89$	0.983567	+	1.70359i	0.104258	+	0.180580i	0.913435	−	0.406985i	$-0.133420\pi$
$89$	0.983567	+	1.70359i	0.104258	+	0.180580i	−0.809177	+	0.587565i	$0.800087\pi$
$90$		0			0
$91$	−12.1834	+	21.1023i	−1.27717	+	2.21213i
$92$		0			0
$93$	5.53919	+	5.56753i	0.574387	+	0.577326i
$94$		0			0
$95$	8.23578	+	6.91064i	0.844974	+	0.709017i
$96$		0			0
$97$	0.443556	+	0.161441i	0.0450363	+	0.0163919i	0.364440	−	0.931227i	$-0.381260\pi$
$97$	0.443556	+	0.161441i	0.0450363	+	0.0163919i	−0.319404	+	0.947619i	$0.603483\pi$
$98$		0			0
$99$	−0.0379741	+	7.44216i	−0.00381654	+	0.747965i
$100$		0			0
$101$	−2.35090	−	13.3326i	−0.233923	−	1.32665i	−0.844869	−	0.534973i	$-0.820322\pi$
$101$	−2.35090	−	13.3326i	−0.233923	−	1.32665i	0.610946	−	0.791673i	$-0.290789\pi$
$102$		0			0
$103$	2.63679	−	0.959715i	0.259811	−	0.0945635i	−0.208831	−	0.977952i	$-0.566966\pi$
$103$	2.63679	−	0.959715i	0.259811	−	0.0945635i	0.468642	+	0.883388i	$0.344744\pi$
$104$		0			0
$105$	15.2862	+	1.37668i	1.49178	+	0.134350i
$106$		0			0
$107$	−17.3455			−1.67685			−0.838426	−	0.545016i	$-0.816524\pi$
$107$	−17.3455			−1.67685			−0.838426	+	0.545016i	$0.816524\pi$
$108$		0			0
$109$	10.1417			0.971398			0.485699	−	0.874126i	$-0.338565\pi$
$109$	10.1417			0.971398			0.485699	+	0.874126i	$0.338565\pi$
$110$		0			0
$111$	−5.38389	−	11.6231i	−0.511016	−	1.10322i
$112$		0			0
$113$	9.18308	−	3.34237i	0.863871	−	0.314423i	0.128189	−	0.991750i	$-0.459084\pi$
$113$	9.18308	−	3.34237i	0.863871	−	0.314423i	0.735683	+	0.677326i	$0.236862\pi$
$114$		0			0
$115$	−2.56508	−	14.5473i	−0.239195	−	1.35654i
$116$		0			0
$117$	−5.95254	+	16.0984i	−0.550312	+	1.48830i
$118$		0			0
$119$	−2.72429	−	0.991562i	−0.249736	−	0.0908964i
$120$		0			0
$121$	−3.71215	−	3.11486i	−0.337468	−	0.283169i
$122$		0			0
$123$	0.559858	−	0.148484i	0.0504807	−	0.0133883i
$124$		0			0
$125$	−5.89969	+	10.2186i	−0.527684	+	0.913976i
$126$		0			0
$127$	−5.20346	−	9.01266i	−0.461733	−	0.799744i	0.537315	−	0.843382i	$-0.319439\pi$
$127$	−5.20346	−	9.01266i	−0.461733	−	0.799744i	−0.999047	+	0.0436375i	$0.986105\pi$
$128$		0			0
$129$	−2.43659	+	1.69687i	−0.214529	+	0.149401i
$130$		0			0
$131$	−2.62938	+	14.9120i	−0.229730	+	1.30286i	0.623703	+	0.781661i	$0.285627\pi$
$131$	−2.62938	+	14.9120i	−0.229730	+	1.30286i	−0.853433	+	0.521202i	$0.825484\pi$
$132$		0			0
$133$	16.8591	−	14.1464i	1.46187	−	1.22665i
$134$		0			0
$135$	10.7767	−	0.859782i	0.927513	−	0.0739982i
$136$		0			0
$137$	14.5223	−	12.1857i	1.24073	−	1.04109i	0.243260	−	0.969961i	$-0.421783\pi$
$137$	14.5223	−	12.1857i	1.24073	−	1.04109i	0.997467	−	0.0711323i	$-0.0226613\pi$
$138$		0			0
$139$	−1.98835	+	11.2765i	−0.168650	+	0.956460i	0.776571	+	0.630029i	$0.216957\pi$
$139$	−1.98835	+	11.2765i	−0.168650	+	0.956460i	−0.945221	+	0.326431i	$0.894154\pi$
$140$		0			0
$141$	−8.03376	−	3.77118i	−0.676564	−	0.317591i
$142$		0			0
$143$	7.09647	+	12.2914i	0.593437	+	1.02786i
$144$		0			0
$145$	5.74210	−	9.94561i	0.476856	−	0.825938i
$146$		0			0
$147$	5.04117	−	18.6237i	0.415789	−	1.53606i
$148$		0			0
$149$	−7.47668	−	6.27368i	−0.612514	−	0.513960i	0.282927	−	0.959142i	$-0.408695\pi$
$149$	−7.47668	−	6.27368i	−0.612514	−	0.513960i	−0.895440	+	0.445182i	$0.853139\pi$
$150$		0			0
$151$	8.61982	+	3.13736i	0.701471	+	0.255314i	0.668039	−	0.744127i	$-0.267134\pi$
$151$	8.61982	+	3.13736i	0.701471	+	0.255314i	0.0334320	+	0.999441i	$0.489356\pi$
$152$		0			0
$153$	−2.00925	−	0.364865i	−0.162438	−	0.0294976i
$154$		0			0
$155$	−1.63819	−	9.29064i	−0.131583	−	0.746242i
$156$		0			0
$157$	−0.470052	+	0.171085i	−0.0375142	+	0.0136541i	−0.360709	−	0.932678i	$-0.617465\pi$
$157$	−0.470052	+	0.171085i	−0.0375142	+	0.0136541i	0.323195	+	0.946332i	$0.395243\pi$
$158$		0			0
$159$	−9.42592	+	13.3888i	−0.747524	+	1.06180i
$160$		0			0
$161$	−30.2384			−2.38312
$162$		0			0
$163$	7.75047			0.607064			0.303532	−	0.952821i	$-0.401834\pi$
$163$	7.75047			0.607064			0.303532	+	0.952821i	$0.401834\pi$
$164$		0			0
$165$	5.14632	−	7.30994i	0.400640	−	0.569078i
$166$		0			0
$167$	21.9210	−	7.97859i	1.69630	−	0.617402i	0.700902	−	0.713257i	$-0.252781\pi$
$167$	21.9210	−	7.97859i	1.69630	−	0.617402i	0.995395	+	0.0958557i	$0.0305587\pi$
$168$		0			0
$169$	3.42649	+	19.4326i	0.263576	+	1.49482i
$170$		0			0
$171$	10.0250	−	11.8243i	0.766631	−	0.904225i
$172$		0			0
$173$	−5.74869	−	2.09235i	−0.437065	−	0.159079i	0.114110	−	0.993468i	$-0.463598\pi$
$173$	−5.74869	−	2.09235i	−0.437065	−	0.159079i	−0.551175	+	0.834389i	$0.685820\pi$
$174$		0			0
$175$	2.18993	+	1.83757i	0.165543	+	0.138907i
$176$		0			0
$177$	−4.58658	+	16.9443i	−0.344748	+	1.27361i
$178$		0			0
$179$	−2.87922	+	4.98696i	−0.215203	+	0.372743i	−0.953335	−	0.301913i	$-0.902375\pi$
$179$	−2.87922	+	4.98696i	−0.215203	+	0.372743i	0.738132	+	0.674656i	$0.235708\pi$
$180$		0			0
$181$	6.87176	+	11.9022i	0.510774	+	0.884687i	0.999922	+	0.0124858i	$0.00397445\pi$
$181$	6.87176	+	11.9022i	0.510774	+	0.884687i	−0.489148	+	0.872201i	$0.662692\pi$
$182$		0			0
$183$	−12.3145	−	5.78062i	−0.910310	−	0.427316i
$184$		0			0
$185$	−2.67193	+	15.1532i	−0.196444	+	1.11409i
$186$		0			0
$187$	−1.29358	+	1.08545i	−0.0945962	+	0.0793757i
$188$		0			0
$189$	2.09749	−	22.0310i	0.152570	−	1.60252i
$190$		0			0
$191$	5.96488	−	5.00513i	0.431604	−	0.362159i	−0.400953	−	0.916099i	$-0.631321\pi$
$191$	5.96488	−	5.00513i	0.431604	−	0.362159i	0.832556	+	0.553940i	$0.186876\pi$
$192$		0			0
$193$	0.234364	−	1.32915i	0.0168699	−	0.0956741i	−0.975210	−	0.221280i	$-0.928976\pi$
$193$	0.234364	−	1.32915i	0.0168699	−	0.0956741i	0.992080	+	0.125606i	$0.0400876\pi$
$194$		0			0
$195$	16.9188	−	11.7825i	1.21158	−	0.843761i
$196$		0			0
$197$	4.52195	+	7.83225i	0.322176	+	0.558024i	0.980937	−	0.194328i	$-0.0622525\pi$
$197$	4.52195	+	7.83225i	0.322176	+	0.558024i	−0.658761	+	0.752352i	$0.728919\pi$
$198$		0			0
$199$	−2.80907	+	4.86545i	−0.199130	+	0.344903i	−0.948246	−	0.317535i	$-0.897145\pi$
$199$	−2.80907	+	4.86545i	−0.199130	+	0.344903i	0.749117	+	0.662438i	$0.230478\pi$
$200$		0			0
$201$	6.85426	−	1.81786i	0.483462	−	0.128222i
$202$		0			0
$203$	−18.0087	−	15.1111i	−1.26397	−	1.06059i
$204$		0			0
$205$	−0.653803	−	0.237965i	−0.0456636	−	0.0166202i
$206$		0			0
$207$	−20.9945	+	3.59154i	−1.45922	+	0.249629i
$208$		0			0
$209$	−2.22598	−	12.6242i	−0.153975	−	0.873233i
$210$		0			0
$211$	−6.64659	+	2.41916i	−0.457570	+	0.166542i	−0.560513	−	0.828145i	$-0.689396\pi$
$211$	−6.64659	+	2.41916i	−0.457570	+	0.166542i	0.102943	+	0.994687i	$0.467174\pi$
$212$		0			0
$213$	−4.03424	−	8.70941i	−0.276422	−	0.596759i
$214$		0			0
$215$	3.56669			0.243246
$216$		0			0
$217$	−19.3118			−1.31097
$218$		0			0
$219$	15.2955	+	1.37752i	1.03358	+	0.0930838i
$220$		0			0
$221$	−3.65958	+	1.33198i	−0.246170	+	0.0895987i
$222$		0			0
$223$	−2.77934	−	15.7624i	−0.186118	−	1.05553i	−0.924510	−	0.381157i	$-0.875526\pi$
$223$	−2.77934	−	15.7624i	−0.186118	−	1.05553i	0.738392	−	0.674372i	$-0.235586\pi$
$224$		0			0
$225$	1.73872	+	1.01571i	0.115915	+	0.0677142i
$226$		0			0
$227$	3.95630	+	1.43997i	0.262589	+	0.0955744i	0.469960	−	0.882688i	$-0.344268\pi$
$227$	3.95630	+	1.43997i	0.262589	+	0.0955744i	−0.207371	+	0.978262i	$0.566491\pi$
$228$		0			0
$229$	−10.9610	−	9.19738i	−0.724324	−	0.607780i	0.204253	−	0.978918i	$-0.434523\pi$
$229$	−10.9610	−	9.19738i	−0.724324	−	0.607780i	−0.928578	+	0.371138i	$0.878968\pi$
$230$		0			0
$231$	−12.9071	−	12.9732i	−0.849226	−	0.853571i
$232$		0			0
$233$	3.52385	−	6.10349i	0.230855	−	0.399853i	−0.727205	−	0.686421i	$-0.759181\pi$
$233$	3.52385	−	6.10349i	0.230855	−	0.399853i	0.958060	+	0.286568i	$0.0925143\pi$
$234$		0			0
$235$	5.33032	+	9.23239i	0.347712	+	0.602255i
$236$		0			0
$237$	−0.867026	−	10.2101i	−0.0563194	−	0.663218i
$238$		0			0
$239$	−2.17975	+	12.3620i	−0.140997	+	0.799631i	0.829498	+	0.558509i	$0.188626\pi$
$239$	−2.17975	+	12.3620i	−0.140997	+	0.799631i	−0.970495	+	0.241122i	$0.922485\pi$
$240$		0			0
$241$	22.3747	−	18.7746i	1.44128	−	1.20938i	0.502629	−	0.864502i	$-0.332366\pi$
$241$	22.3747	−	18.7746i	1.44128	−	1.20938i	0.938649	−	0.344874i	$-0.112078\pi$
$242$		0			0
$243$	−1.16042	−	15.5452i	−0.0744412	−	0.997225i
$244$		0			0
$245$	−17.7540	+	14.8974i	−1.13426	+	0.951761i
$246$		0			0
$247$	5.13366	−	29.1144i	0.326647	−	1.85251i
$248$		0			0
$249$	1.32196	+	15.5674i	0.0837757	+	0.986543i
$250$		0			0
$251$	3.31998	+	5.75038i	0.209556	+	0.362961i	0.951575	−	0.307418i	$-0.0994650\pi$
$251$	3.31998	+	5.75038i	0.209556	+	0.362961i	−0.742019	+	0.670379i	$0.766132\pi$
$252$		0			0
$253$	−8.80646	+	15.2532i	−0.553658	+	0.958963i
$254$		0			0
$255$	1.73011	+	1.73896i	0.108344	+	0.108898i
$256$		0			0
$257$	16.0707	+	13.4849i	1.00246	+	0.841165i	0.987324	−	0.158720i	$-0.0507367\pi$
$257$	16.0707	+	13.4849i	1.00246	+	0.841165i	0.0151383	+	0.999885i	$0.495181\pi$
$258$		0			0
$259$	29.5984	+	10.7729i	1.83916	+	0.669398i
$260$		0			0
$261$	−14.2983	−	8.35266i	−0.885040	−	0.517017i
$262$		0			0
$263$	0.306469	+	1.73807i	0.0188977	+	0.107174i	0.992798	−	0.119804i	$-0.0382266\pi$
$263$	0.306469	+	1.73807i	0.0188977	+	0.107174i	−0.973900	+	0.226978i	$0.927115\pi$
$264$		0			0
$265$	18.4826	−	6.72711i	1.13538	−	0.413243i
$266$		0			0
$267$	−3.39344	−	0.305613i	−0.207675	−	0.0187032i
$268$		0			0
$269$	24.8211			1.51337			0.756684	−	0.653781i	$-0.226818\pi$
$269$	24.8211			1.51337			0.756684	+	0.653781i	$0.226818\pi$
$270$		0			0
$271$	13.9629			0.848188			0.424094	−	0.905618i	$-0.360593\pi$
$271$	13.9629			0.848188			0.424094	+	0.905618i	$0.360593\pi$
$272$		0			0
$273$	−17.7388	−	38.2958i	−1.07360	−	2.31777i
$274$		0			0
$275$	1.56471	−	0.569508i	0.0943555	−	0.0343426i
$276$		0			0
$277$	−2.70629	−	15.3481i	−0.162605	−	0.922178i	−0.951500	−	0.307650i	$-0.900457\pi$
$277$	−2.70629	−	15.3481i	−0.162605	−	0.922178i	0.788895	−	0.614528i	$-0.210654\pi$
$278$		0			0
$279$	−13.4082	+	2.29374i	−0.802725	+	0.137323i
$280$		0			0
$281$	18.9646	+	6.90254i	1.13133	+	0.411771i	0.838775	−	0.544478i	$-0.183272\pi$
$281$	18.9646	+	6.90254i	1.13133	+	0.411771i	0.292556	+	0.956248i	$0.405494\pi$
$282$		0			0
$283$	−11.8757	−	9.96486i	−0.705935	−	0.592350i	0.217520	−	0.976056i	$-0.430203\pi$
$283$	−11.8757	−	9.96486i	−0.705935	−	0.592350i	−0.923455	+	0.383706i	$0.874648\pi$
$284$		0			0
$285$	−17.9991	+	4.77366i	−1.06617	+	0.282767i
$286$		0			0
$287$	−0.712130	+	1.23344i	−0.0420357	+	0.0728079i
$288$		0			0
$289$	8.26832	+	14.3212i	0.486372	+	0.842421i
$290$		0			0
$291$	−0.670906	+	0.467227i	−0.0393292	+	0.0273893i
$292$		0			0
$293$	3.79392	−	21.5164i	0.221643	−	1.25700i	−0.647356	−	0.762188i	$-0.724125\pi$
$293$	3.79392	−	21.5164i	0.221643	−	1.25700i	0.868999	−	0.494814i	$-0.164764\pi$
$294$		0			0
$295$	16.1531	−	13.5540i	0.940467	−	0.789146i
$296$		0			0
$297$	−10.5023	−	7.47421i	−0.609404	−	0.433698i
$298$		0			0
$299$	−31.1165	+	26.1098i	−1.79951	+	1.50997i
$300$		0			0
$301$	1.26784	−	7.19028i	0.0730771	−	0.414441i
$302$		0			0
$303$	21.2267	+	9.96417i	1.21944	+	0.572427i
$304$		0			0
$305$	8.17052	+	14.1518i	0.467843	+	0.810328i
$306$		0			0
$307$	12.4443	−	21.5541i	0.710232	−	1.23016i	−0.254539	−	0.967063i	$-0.581924\pi$
$307$	12.4443	−	21.5541i	0.710232	−	1.23016i	0.964770	−	0.263094i	$-0.0847431\pi$
$308$		0			0
$309$	−1.26988	+	4.69134i	−0.0722407	+	0.266881i
$310$		0			0
$311$	−1.69907	−	1.42569i	−0.0963455	−	0.0808435i	0.593343	−	0.804950i	$-0.297808\pi$
$311$	−1.69907	−	1.42569i	−0.0963455	−	0.0808435i	−0.689688	+	0.724107i	$0.742252\pi$
$312$		0			0
$313$	−12.6348	−	4.59869i	−0.714161	−	0.259933i	−0.0407162	−	0.999171i	$-0.512964\pi$
$313$	−12.6348	−	4.59869i	−0.714161	−	0.259933i	−0.673445	+	0.739237i	$0.735186\pi$
$314$		0			0
$315$	−17.1913	+	20.2768i	−0.968623	+	1.14247i
$316$		0			0
$317$	4.76942	+	27.0487i	0.267877	+	1.51921i	0.760715	+	0.649086i	$0.224849\pi$
$317$	4.76942	+	27.0487i	0.267877	+	1.51921i	−0.492838	+	0.870121i	$0.664040\pi$
$318$		0			0
$319$	−12.8673	+	4.68331i	−0.720430	+	0.262215i
$320$		0			0
$321$	17.2948	−	24.5660i	0.965304	−	1.37114i
$322$		0			0
$323$	3.51743			0.195715
$324$		0			0
$325$	3.84019			0.213016
$326$		0			0
$327$	−10.1121	+	14.3634i	−0.559199	+	0.794299i
$328$		0			0
$329$	20.5068	−	7.46386i	1.13058	−	0.411496i
$330$		0			0
$331$	4.12868	+	23.4149i	0.226933	+	1.28700i	0.858956	+	0.512050i	$0.171114\pi$
$331$	4.12868	+	23.4149i	0.226933	+	1.28700i	−0.632023	+	0.774950i	$0.717775\pi$
$332$		0			0
$333$	21.8297	+	3.96412i	1.19626	+	0.217232i
$334$		0			0
$335$	−8.00441	−	2.91337i	−0.437327	−	0.159174i
$336$		0			0
$337$	15.9915	+	13.4184i	0.871110	+	0.730948i	0.964332	−	0.264697i	$-0.0852721\pi$
$337$	15.9915	+	13.4184i	0.871110	+	0.730948i	−0.0932216	+	0.995645i	$0.529717\pi$
$338$		0			0
$339$	−4.42256	+	16.3384i	−0.240200	+	0.887378i
$340$		0			0
$341$	−5.62426	+	9.74150i	−0.304571	+	0.527532i
$342$		0			0
$343$	8.81486	+	15.2678i	0.475958	+	0.824383i
$344$		0			0
$345$	23.1605	+	10.8720i	1.24692	+	0.585327i
$346$		0			0
$347$	−2.31831	+	13.1478i	−0.124454	+	0.705811i	0.857177	+	0.515021i	$0.172216\pi$
$347$	−2.31831	+	13.1478i	−0.124454	+	0.705811i	−0.981631	+	0.190790i	$0.938895\pi$
$348$		0			0
$349$	8.77715	−	7.36491i	0.469830	−	0.394234i	−0.376902	−	0.926253i	$-0.623011\pi$
$349$	8.77715	−	7.36491i	0.469830	−	0.394234i	0.846733	+	0.532019i	$0.178566\pi$
$350$		0			0
$351$	−16.8646	−	24.4818i	−0.900165	−	1.30674i
$352$		0			0
$353$	−17.1875	+	14.4220i	−0.914799	+	0.767607i	−0.973026	−	0.230696i	$-0.925900\pi$
$353$	−17.1875	+	14.4220i	−0.914799	+	0.767607i	0.0582273	+	0.998303i	$0.481455\pi$
$354$		0			0
$355$	−2.00212	+	11.3546i	−0.106262	+	0.602639i
$356$		0			0
$357$	4.12066	−	2.86968i	0.218089	−	0.151880i
$358$		0			0
$359$	−4.41502	−	7.64704i	−0.233016	−	0.403595i	0.725678	−	0.688034i	$-0.241526\pi$
$359$	−4.41502	−	7.64704i	−0.233016	−	0.403595i	−0.958694	+	0.284439i	$0.908193\pi$
$360$		0			0
$361$	−3.85077	+	6.66974i	−0.202672	+	0.351039i
$362$		0			0
$363$	8.11280	−	2.15165i	0.425812	−	0.112932i
$364$		0			0
$365$	−14.1317	−	11.8579i	−0.739687	−	0.620671i
$366$		0			0
$367$	20.3876	+	7.42050i	1.06423	+	0.387347i	0.814015	−	0.580844i	$-0.197277\pi$
$367$	20.3876	+	7.42050i	1.06423	+	0.387347i	0.250212	+	0.968191i	$0.419500\pi$
$368$		0			0
$369$	−0.347930	+	0.940962i	−0.0181125	+	0.0489845i
$370$		0			0
$371$	−6.99158	−	39.6512i	−0.362985	−	2.05859i
$372$		0			0
$373$	−30.1587	+	10.9769i	−1.56156	+	0.568361i	−0.971093	−	0.238702i	$-0.923278\pi$
$373$	−30.1587	+	10.9769i	−1.56156	+	0.568361i	−0.590465	+	0.807063i	$0.701056\pi$
$374$		0			0
$375$	−8.58982	−	18.5443i	−0.443576	−	0.957624i
$376$		0			0
$377$	−31.5796			−1.62643
$378$		0			0
$379$	−19.3500			−0.993942			−0.496971	−	0.867767i	$-0.665555\pi$
$379$	−19.3500			−0.993942			−0.496971	+	0.867767i	$0.665555\pi$
$380$		0			0
$381$	17.9527	+	1.61682i	0.919743	+	0.0828320i
$382$		0			0
$383$	−22.2072	+	8.08276i	−1.13474	+	0.413010i	−0.840009	−	0.542572i	$-0.817451\pi$
$383$	−22.2072	+	8.08276i	−1.13474	+	0.413010i	−0.294726	+	0.955582i	$0.595228\pi$
$384$		0			0
$385$	3.81722	+	21.6486i	0.194544	+	1.10331i
$386$		0			0
$387$	0.0262414	−	5.14279i	0.00133392	−	0.261423i
$388$		0			0
$389$	5.25949	+	1.91430i	0.266667	+	0.0970587i	0.471893	−	0.881656i	$-0.343571\pi$
$389$	5.25949	+	1.91430i	0.266667	+	0.0970587i	−0.205226	+	0.978715i	$0.565793\pi$
$390$		0			0
$391$	−3.70219	−	3.10651i	−0.187228	−	0.157103i
$392$		0			0
$393$	−18.4977	−	18.5923i	−0.933086	−	0.937859i
$394$		0			0
$395$	−6.15436	+	10.6597i	−0.309659	+	0.536346i
$396$		0			0
$397$	4.32648	+	7.49368i	0.217140	+	0.376097i	0.953932	−	0.300022i	$-0.0969940\pi$
$397$	4.32648	+	7.49368i	0.217140	+	0.376097i	−0.736793	+	0.676119i	$0.763661\pi$
$398$		0			0
$399$	3.22539	+	37.9822i	0.161471	+	1.90149i
$400$		0			0
$401$	−5.00348	+	28.3761i	−0.249862	+	1.41704i	0.559063	+	0.829125i	$0.311161\pi$
$401$	−5.00348	+	28.3761i	−0.249862	+	1.41704i	−0.808925	+	0.587912i	$0.799950\pi$
$402$		0			0
$403$	−19.8726	+	16.6751i	−0.989924	+	0.830645i
$404$		0			0
$405$	−9.52757	+	16.1201i	−0.473429	+	0.801013i
$406$		0			0
$407$	14.0543	−	11.7930i	0.696645	−	0.584555i
$408$		0			0
$409$	−0.223219	+	1.26594i	−0.0110375	+	0.0625966i	−0.989829	−	0.142262i	$-0.954562\pi$
$409$	−0.223219	+	1.26594i	−0.0110375	+	0.0625966i	0.978792	+	0.204859i	$0.0656735\pi$
$410$		0			0
$411$	2.77834	+	32.7177i	0.137045	+	1.61385i
$412$		0			0
$413$	−21.5824	−	37.3818i	−1.06200	−	1.83944i
$414$		0			0
$415$	9.38357	−	16.2528i	0.460622	−	0.797820i
$416$		0			0
$417$	−13.9881	−	14.0596i	−0.684999	−	0.688503i
$418$		0			0
$419$	−7.32223	−	6.14408i	−0.357714	−	0.300158i	0.446165	−	0.894951i	$-0.352790\pi$
$419$	−7.32223	−	6.14408i	−0.357714	−	0.300158i	−0.803879	+	0.594793i	$0.797234\pi$
$420$		0			0
$421$	−28.9095	−	10.5222i	−1.40896	−	0.512820i	−0.478137	−	0.878285i	$-0.658688\pi$
$421$	−28.9095	−	10.5222i	−1.40896	−	0.512820i	−0.930825	+	0.365465i	$0.880910\pi$
$422$		0			0
$423$	13.3513	−	7.61782i	0.649164	−	0.370391i
$424$		0			0
$425$	0.0793399	+	0.449959i	0.00384855	+	0.0218262i
$426$		0			0
$427$	31.4336	−	11.4409i	1.52118	−	0.553664i
$428$		0			0
$429$	−24.4838	−	2.20501i	−1.18209	−	0.106459i
$430$		0			0
$431$	5.17147			0.249101			0.124551	−	0.992213i	$-0.460251\pi$
$431$	5.17147			0.249101			0.124551	+	0.992213i	$0.460251\pi$
$432$		0			0
$433$	25.7835			1.23907			0.619537	−	0.784968i	$-0.287320\pi$
$433$	25.7835			1.23907			0.619537	+	0.784968i	$0.287320\pi$
$434$		0			0
$435$	8.36037	+	18.0490i	0.400849	+	0.865381i
$436$		0			0
$437$	34.4748	−	12.5478i	1.64915	−	0.600243i
$438$		0			0
$439$	−4.28234	−	24.2864i	−0.204385	−	1.15913i	−0.898404	−	0.439169i	$-0.855273\pi$
$439$	−4.28234	−	24.2864i	−0.204385	−	1.15913i	0.694019	−	0.719956i	$-0.255838\pi$
$440$		0			0
$441$	21.3498	+	25.7090i	1.01666	+	1.22424i
$442$		0			0
$443$	−3.76116	−	1.36895i	−0.178698	−	0.0650409i	0.251121	−	0.967956i	$-0.419201\pi$
$443$	−3.76116	−	1.36895i	−0.178698	−	0.0650409i	−0.429820	+	0.902915i	$0.641423\pi$
$444$		0			0
$445$	3.13524	+	2.63078i	0.148625	+	0.124711i
$446$		0			0
$447$	16.3401	−	4.33367i	0.772860	−	0.204975i
$448$		0			0
$449$	−11.9152	+	20.6377i	−0.562312	+	0.973952i	0.434983	+	0.900439i	$0.356755\pi$
$449$	−11.9152	+	20.6377i	−0.562312	+	0.973952i	−0.997294	+	0.0735135i	$0.976579\pi$
$450$		0			0
$451$	0.414793	+	0.718443i	0.0195318	+	0.0338301i
$452$		0			0
$453$	−13.0380	+	9.07982i	−0.612579	+	0.426607i
$454$		0			0
$455$	−8.80345	+	49.9268i	−0.412712	+	2.34061i
$456$		0			0
$457$	−29.6052	+	24.8417i	−1.38487	+	1.16205i	−0.417502	+	0.908676i	$0.637094\pi$
$457$	−29.6052	+	24.8417i	−1.38487	+	1.16205i	−0.967370	+	0.253369i	$0.918461\pi$
$458$		0			0
$459$	2.52013	−	2.48184i	0.117630	−	0.115843i
$460$		0			0
$461$	−12.4218	+	10.4232i	−0.578542	+	0.485455i	−0.884468	−	0.466601i	$-0.845479\pi$
$461$	−12.4218	+	10.4232i	−0.578542	+	0.485455i	0.305926	+	0.952055i	$0.401034\pi$
$462$		0			0
$463$	−2.21589	+	12.5670i	−0.102981	+	0.584036i	0.889026	+	0.457857i	$0.151383\pi$
$463$	−2.21589	+	12.5670i	−0.102981	+	0.584036i	−0.992007	+	0.126180i	$0.959728\pi$
$464$		0			0
$465$	14.7915	+	6.94339i	0.685939	+	0.321992i
$466$		0			0
$467$	−1.29669	−	2.24593i	−0.0600035	−	0.103929i	0.834463	−	0.551064i	$-0.185778\pi$
$467$	−1.29669	−	2.24593i	−0.0600035	−	0.103929i	−0.894467	+	0.447134i	$0.852445\pi$
$468$		0			0
$469$	−8.71850	+	15.1009i	−0.402583	+	0.697294i
$470$		0			0
$471$	0.226376	−	0.836308i	0.0104309	−	0.0385350i
$472$		0			0
$473$	−3.25777	−	2.73359i	−0.149792	−	0.125691i
$474$		0			0
$475$	−3.25925	−	1.18627i	−0.149545	−	0.0544299i
$476$		0			0
$477$	−9.56378	−	26.6994i	−0.437895	−	1.22248i
$478$		0			0
$479$	0.531048	+	3.01172i	0.0242642	+	0.137609i	0.994533	−	0.104419i	$-0.0332984\pi$
$479$	0.531048	+	3.01172i	0.0242642	+	0.137609i	−0.970269	+	0.242028i	$0.922187\pi$
$480$		0			0
$481$	39.7600	−	14.4714i	1.81290	−	0.659841i
$482$		0			0
$483$	30.1501	−	42.8259i	1.37188	−	1.94865i
$484$		0			0
$485$	0.982077			0.0445938
$486$		0			0
$487$	4.46808			0.202468			0.101234	−	0.994863i	$-0.467721\pi$
$487$	4.46808			0.202468			0.101234	+	0.994863i	$0.467721\pi$
$488$		0			0
$489$	−7.72784	+	10.9768i	−0.349465	+	0.496387i
$490$		0			0
$491$	28.3262	−	10.3099i	1.27834	−	0.465278i	0.388458	−	0.921466i	$-0.373008\pi$
$491$	28.3262	−	10.3099i	1.27834	−	0.465278i	0.889883	+	0.456188i	$0.150786\pi$
$492$		0			0
$493$	−0.652447	−	3.70021i	−0.0293847	−	0.166649i
$494$		0			0
$495$	5.22158	+	14.5772i	0.234693	+	0.655196i
$496$		0			0
$497$	22.1786	+	8.07235i	0.994847	+	0.362095i
$498$		0			0
$499$	3.92557	+	3.29394i	0.175732	+	0.147457i	0.726411	−	0.687260i	$-0.241187\pi$
$499$	3.92557	+	3.29394i	0.175732	+	0.147457i	−0.550679	+	0.834717i	$0.685631\pi$
$500$		0			0
$501$	−10.5571	+	39.0014i	−0.471657	+	1.74245i
$502$		0			0
$503$	3.32680	−	5.76219i	0.148335	−	0.256923i	−0.782277	−	0.622930i	$-0.785942\pi$
$503$	3.32680	−	5.76219i	0.148335	−	0.256923i	0.930612	+	0.366007i	$0.119275\pi$
$504$		0			0
$505$	−14.0837	−	24.3937i	−0.626717	−	1.08551i
$506$		0			0
$507$	−30.9384	−	14.5230i	−1.37402	−	0.644989i
$508$		0			0
$509$	−1.89801	+	10.7641i	−0.0841278	+	0.477112i	0.913414	+	0.407033i	$0.133436\pi$
$509$	−1.89801	+	10.7641i	−0.0841278	+	0.477112i	−0.997541	+	0.0700798i	$0.977675\pi$
$510$		0			0
$511$	−28.9283	+	24.2737i	−1.27971	+	1.07381i
$512$		0			0
$513$	6.75068	+	25.9879i	0.298050	+	1.14739i
$514$		0			0
$515$	4.47226	−	3.75267i	0.197071	−	0.165363i
$516$		0			0
$517$	2.20726	−	12.5180i	0.0970754	−	0.550542i
$518$		0			0
$519$	8.69525	−	6.05548i	0.381679	−	0.265806i
$520$		0			0
$521$	−11.1465	−	19.3062i	−0.488335	−	0.845822i	0.511575	−	0.859239i	$-0.329062\pi$
$521$	−11.1465	−	19.3062i	−0.488335	−	0.845822i	−0.999910	+	0.0134171i	$0.995729\pi$
$522$		0			0
$523$	11.2501	−	19.4858i	0.491933	−	0.852053i	−0.508024	−	0.861343i	$-0.669624\pi$
$523$	11.2501	−	19.4858i	0.491933	−	0.852053i	0.999957	+	0.00928981i	$0.00295708\pi$
$524$		0			0
$525$	−4.78603	+	1.26933i	−0.208879	+	0.0553983i
$526$		0			0
$527$	−2.36441	−	1.98397i	−0.102995	−	0.0864233i
$528$		0			0
$529$	−25.7547	−	9.37395i	−1.11977	−	0.407563i
$530$		0			0
$531$	−19.4246	−	23.3907i	−0.842956	−	1.01507i
$532$		0			0
$533$	0.332229	+	1.88416i	0.0143904	+	0.0816121i
$534$		0			0
$535$	−33.9121	+	12.3430i	−1.46615	+	0.533635i
$536$		0			0
$537$	−4.19209	−	9.05017i	−0.180902	−	0.390544i
$538$		0			0
$539$	27.6340			1.19028
$540$		0			0
$541$	−31.6333			−1.36002			−0.680012	−	0.733201i	$-0.738025\pi$
$541$	−31.6333			−1.36002			−0.680012	+	0.733201i	$0.738025\pi$
$542$		0			0
$543$	−23.7085	−	2.13519i	−1.01743	−	0.0916298i
$544$		0			0
$545$	19.8280	−	7.21681i	0.849339	−	0.309134i
$546$		0			0
$547$	2.00203	+	11.3541i	0.0856006	+	0.485465i	0.997225	+	0.0744418i	$0.0237175\pi$
$547$	2.00203	+	11.3541i	0.0856006	+	0.485465i	−0.911625	+	0.411024i	$0.865171\pi$
$548$		0			0
$549$	20.4654	−	11.6769i	0.873443	−	0.498358i
$550$		0			0
$551$	26.8023	+	9.75524i	1.14182	+	0.415587i
$552$		0			0
$553$	19.3017	+	16.1960i	0.820790	+	0.688725i
$554$		0			0
$555$	−18.7970	−	18.8932i	−0.797889	−	0.801971i
$556$		0			0
$557$	4.96708	−	8.60324i	0.210462	−	0.364531i	−0.741397	−	0.671067i	$-0.765836\pi$
$557$	4.96708	−	8.60324i	0.210462	−	0.364531i	0.951859	+	0.306535i	$0.0991698\pi$
$558$		0			0
$559$	−4.90390	−	8.49381i	−0.207413	−	0.359250i
$560$		0			0
$561$	−0.247482	−	2.91435i	−0.0104487	−	0.123044i
$562$		0			0
$563$	4.60555	−	26.1193i	0.194101	−	1.10080i	−0.719593	−	0.694396i	$-0.755672\pi$
$563$	4.60555	−	26.1193i	0.194101	−	1.10080i	0.913694	−	0.406403i	$-0.133217\pi$
$564$		0			0
$565$	15.5754	−	13.0693i	0.655262	−	0.549830i
$566$		0			0
$567$	29.1105	+	24.9373i	1.22253	+	1.04727i
$568$		0			0
$569$	27.5862	−	23.1476i	1.15647	−	0.970397i	0.156623	−	0.987658i	$-0.449939\pi$
$569$	27.5862	−	23.1476i	1.15647	−	0.970397i	0.999851	+	0.0172614i	$0.00549475\pi$
$570$		0			0
$571$	−1.24236	+	7.04575i	−0.0519910	+	0.294855i	−0.999706	−	0.0242636i	$-0.992276\pi$
$571$	−1.24236	+	7.04575i	−0.0519910	+	0.294855i	0.947715	+	0.319119i	$0.103387\pi$
$572$		0			0
$573$	1.14117	+	13.4384i	0.0476731	+	0.561398i
$574$		0			0
$575$	2.38277	+	4.12708i	0.0993684	+	0.172111i
$576$		0			0
$577$	7.83173	−	13.5650i	0.326039	−	0.564717i	−0.655683	−	0.755036i	$-0.727619\pi$
$577$	7.83173	−	13.5650i	0.326039	−	0.564717i	0.981722	+	0.190320i	$0.0609525\pi$
$578$		0			0
$579$	1.64876	+	1.65719i	0.0685200	+	0.0688705i
$580$		0			0
$581$	−29.4293	−	24.6941i	−1.22093	−	1.02449i
$582$		0			0
$583$	−22.0375	−	8.02101i	−0.912702	−	0.332196i
$584$		0			0
$585$	−0.182211	+	35.7098i	−0.00753351	+	1.47642i
$586$		0			0
$587$	1.59747	+	9.05971i	0.0659347	+	0.373934i	0.999864	+	0.0164772i	$0.00524508\pi$
$587$	1.59747	+	9.05971i	0.0659347	+	0.373934i	−0.933930	+	0.357457i	$0.883644\pi$
$588$		0			0
$589$	22.0174	−	8.01367i	0.907210	−	0.330197i
$590$		0			0
$591$	−15.6014	−	1.40506i	−0.641754	−	0.0577964i
$592$		0			0
$593$	19.8285			0.814259			0.407129	−	0.913370i	$-0.366530\pi$
$593$	19.8285			0.814259			0.407129	+	0.913370i	$0.366530\pi$
$594$		0			0
$595$	−6.03186			−0.247282
$596$		0			0
$597$	−4.08994	−	8.82965i	−0.167390	−	0.361374i
$598$		0			0
$599$	26.6087	−	9.68479i	1.08720	−	0.395710i	0.264619	−	0.964353i	$-0.414754\pi$
$599$	26.6087	−	9.68479i	1.08720	−	0.395710i	0.822584	+	0.568643i	$0.192531\pi$
$600$		0			0
$601$	−7.14558	−	40.5246i	−0.291474	−	1.65303i	−0.681197	−	0.732100i	$-0.738540\pi$
$601$	−7.14558	−	40.5246i	−0.291474	−	1.65303i	0.389723	−	0.920932i	$-0.372571\pi$
$602$		0			0
$603$	−4.25965	+	11.5201i	−0.173466	+	0.469133i
$604$		0			0
$605$	−9.47414	−	3.44831i	−0.385179	−	0.140194i
$606$		0			0
$607$	−9.62083	−	8.07283i	−0.390497	−	0.327666i	0.426310	−	0.904577i	$-0.359813\pi$
$607$	−9.62083	−	8.07283i	−0.390497	−	0.327666i	−0.816807	+	0.576911i	$0.804258\pi$
$608$		0			0
$609$	39.3576	−	10.4383i	1.59485	−	0.422981i
$610$		0			0
$611$	14.6575	−	25.3875i	0.592978	−	1.02707i
$612$		0			0
$613$	4.01692	+	6.95752i	0.162242	+	0.281011i	0.935672	−	0.352870i	$-0.114794\pi$
$613$	4.01692	+	6.95752i	0.162242	+	0.281011i	−0.773430	+	0.633881i	$0.781461\pi$
$614$		0			0
$615$	0.988917	−	0.688694i	0.0398770	−	0.0277708i
$616$		0			0
$617$	−0.677179	+	3.84047i	−0.0272622	+	0.154612i	−0.995400	−	0.0958065i	$-0.969457\pi$
$617$	−0.677179	+	3.84047i	−0.0272622	+	0.154612i	0.968138	+	0.250418i	$0.0805681\pi$
$618$		0			0
$619$	−21.1733	+	17.7665i	−0.851026	+	0.714095i	−0.960015	−	0.279948i	$-0.909683\pi$
$619$	−21.1733	+	17.7665i	−0.851026	+	0.714095i	0.108990	+	0.994043i	$0.465238\pi$
$620$		0			0
$621$	15.8466	−	33.3150i	0.635902	−	1.33689i
$622$		0			0
$623$	6.41799	−	5.38533i	0.257131	−	0.215759i
$624$		0			0
$625$	−3.68019	+	20.8714i	−0.147208	+	0.834856i
$626$		0			0
$627$	20.0988	+	9.43472i	0.802668	+	0.376786i
$628$		0			0
$629$	2.51709	+	4.35973i	0.100363	+	0.173834i
$630$		0			0
$631$	6.29226	−	10.8985i	0.250491	−	0.433863i	−0.713170	−	0.700991i	$-0.752741\pi$
$631$	6.29226	−	10.8985i	0.250491	−	0.433863i	0.963661	+	0.267128i	$0.0860747\pi$
$632$		0			0
$633$	3.20099	−	11.8255i	0.127228	−	0.470021i
$634$		0			0
$635$	−16.5867	−	13.9179i	−0.658222	−	0.552314i
$636$		0			0
$637$	59.8874	+	21.7972i	2.37282	+	0.863637i
$638$		0			0
$639$	16.3574	+	2.97038i	0.647088	+	0.117507i
$640$		0			0
$641$	−7.12752	−	40.4222i	−0.281520	−	1.59658i	−0.717457	−	0.696603i	$-0.754694\pi$
$641$	−7.12752	−	40.4222i	−0.281520	−	1.59658i	0.435936	−	0.899977i	$-0.356417\pi$
$642$		0			0
$643$	−17.0607	+	6.20958i	−0.672808	+	0.244882i	−0.655756	−	0.754973i	$-0.727650\pi$
$643$	−17.0607	+	6.20958i	−0.672808	+	0.244882i	−0.0170514	+	0.999855i	$0.505428\pi$
$644$		0			0
$645$	−3.55628	+	5.05141i	−0.140028	+	0.198899i
$646$		0			0
$647$	−0.286590			−0.0112670			−0.00563350	−	0.999984i	$-0.501793\pi$
$647$	−0.286590			−0.0112670			−0.00563350	+	0.999984i	$0.501793\pi$
$648$		0			0
$649$	−25.1421			−0.986914
$650$		0			0
$651$	19.2554	−	27.3508i	0.754679	−	1.07196i
$652$		0			0
$653$	−6.82970	+	2.48581i	−0.267267	+	0.0972771i	−0.472177	−	0.881504i	$-0.656532\pi$
$653$	−6.82970	+	2.48581i	−0.267267	+	0.0972771i	0.204911	+	0.978781i	$0.434310\pi$
$654$		0			0
$655$	5.47061	+	31.0254i	0.213755	+	1.21226i
$656$		0			0
$657$	−17.2018	+	20.2892i	−0.671106	+	0.791555i
$658$		0			0
$659$	10.3014	+	3.74940i	0.401285	+	0.146056i	0.534775	−	0.844994i	$-0.320396\pi$
$659$	10.3014	+	3.74940i	0.401285	+	0.146056i	−0.133490	+	0.991050i	$0.542619\pi$
$660$		0			0
$661$	−12.9108	−	10.8334i	−0.502171	−	0.421372i	0.356193	−	0.934412i	$-0.384075\pi$
$661$	−12.9108	−	10.8334i	−0.502171	−	0.421372i	−0.858364	+	0.513041i	$0.828519\pi$
$662$		0			0
$663$	1.76245	−	6.51106i	0.0684479	−	0.252869i
$664$		0			0
$665$	22.8946	−	39.6545i	0.887813	−	1.53774i
$666$		0			0
$667$	−19.5946	−	33.9388i	−0.758705	−	1.31412i
$668$		0			0
$669$	25.0951	+	11.7801i	0.970233	+	0.455444i
$670$		0			0
$671$	3.38338	−	19.1881i	0.130614	−	0.740749i
$672$		0			0
$673$	−29.7906	+	24.9973i	−1.14834	+	0.963574i	−0.999680	−	0.0253140i	$-0.991941\pi$
$673$	−29.7906	+	24.9973i	−1.14834	+	0.963574i	−0.148663	+	0.988888i	$0.547497\pi$
$674$		0			0
$675$	−3.17217	+	1.44975i	−0.122097	+	0.0558010i
$676$		0			0
$677$	10.3174	−	8.65735i	0.396531	−	0.332729i	−0.422620	−	0.906307i	$-0.638889\pi$
$677$	10.3174	−	8.65735i	0.396531	−	0.332729i	0.819151	+	0.573578i	$0.194445\pi$
$678$		0			0
$679$	0.349095	−	1.97982i	0.0133971	−	0.0759785i
$680$		0			0
$681$	−5.98414	+	4.16743i	−0.229313	+	0.159696i
$682$		0			0
$683$	13.8061	+	23.9128i	0.528275	+	0.914998i	0.999457	+	0.0329623i	$0.0104941\pi$
$683$	13.8061	+	23.9128i	0.528275	+	0.914998i	−0.471182	+	0.882036i	$0.656173\pi$
$684$		0			0
$685$	19.7213	−	34.1583i	0.753512	−	1.30512i
$686$		0			0
$687$	23.9550	−	6.35327i	0.913941	−	0.242392i
$688$		0			0
$689$	−41.4321	−	34.7656i	−1.57844	−	1.32446i
$690$		0			0
$691$	−19.5307	−	7.10858i	−0.742982	−	0.270423i	−0.0573322	−	0.998355i	$-0.518259\pi$
$691$	−19.5307	−	7.10858i	−0.742982	−	0.270423i	−0.685649	+	0.727932i	$0.740482\pi$
$692$		0			0
$693$	31.2430	−	5.34475i	1.18682	−	0.203030i
$694$		0			0
$695$	4.13691	+	23.4616i	0.156922	+	0.889948i
$696$		0			0
$697$	−0.213905	+	0.0778551i	−0.00810223	+	0.00294897i
$698$		0			0
$699$	5.13065	+	11.0764i	0.194059	+	0.418948i
$700$		0			0
$701$	0.227676			0.00859920			0.00429960	−	0.999991i	$-0.498631\pi$
$701$	0.227676			0.00859920			0.00429960	+	0.999991i	$0.498631\pi$
$702$		0			0
$703$	−38.2155			−1.44133
$704$		0			0
$705$	−18.3903	−	1.65624i	−0.692621	−	0.0623774i
$706$		0			0
$707$	−54.1828	+	19.7209i	−2.03775	+	0.741681i
$708$		0			0
$709$	3.26873	+	18.5379i	0.122760	+	0.696205i	0.982613	+	0.185664i	$0.0594436\pi$
$709$	3.26873	+	18.5379i	0.122760	+	0.696205i	−0.859854	+	0.510541i	$0.829445\pi$
$710$		0			0
$711$	15.3248	+	8.95234i	0.574725	+	0.335739i
$712$		0			0
$713$	−30.2514	−	11.0106i	−1.13292	−	0.412350i
$714$		0			0
$715$	22.6209	+	18.9812i	0.845972	+	0.709855i
$716$		0			0
$717$	−15.3346	−	15.4130i	−0.572680	−	0.575610i
$718$		0			0
$719$	4.87179	−	8.43819i	0.181687	−	0.314692i	−0.760768	−	0.649024i	$-0.775177\pi$
$719$	4.87179	−	8.43819i	0.181687	−	0.314692i	0.942455	+	0.334332i	$0.108511\pi$
$720$		0			0
$721$	−5.97546	−	10.3498i	−0.222538	−	0.385447i
$722$		0			0
$723$	4.28060	+	50.4084i	0.159197	+	1.87471i
$724$		0			0
$725$	−0.643358	+	3.64866i	−0.0238937	+	0.135508i
$726$		0			0
$727$	18.6693	−	15.6654i	0.692405	−	0.580997i	−0.227197	−	0.973849i	$-0.572956\pi$
$727$	18.6693	−	15.6654i	0.692405	−	0.580997i	0.919602	+	0.392852i	$0.128512\pi$
$728$		0			0
$729$	23.1733	+	13.8563i	0.858270	+	0.513198i
$730$		0			0
$731$	0.893911	−	0.750080i	0.0330625	−	0.0277427i
$732$		0			0
$733$	−2.27026	+	12.8753i	−0.0838541	+	0.475560i	0.913744	+	0.406291i	$0.133178\pi$
$733$	−2.27026	+	12.8753i	−0.0838541	+	0.475560i	−0.997598	+	0.0692695i	$0.977933\pi$
$734$		0			0
$735$	−3.39661	−	39.9985i	−0.125286	−	1.47537i
$736$		0			0
$737$	5.07825	+	8.79579i	0.187060	+	0.323997i
$738$		0			0
$739$	−17.9397	+	31.0725i	−0.659922	+	1.14302i	0.320713	+	0.947176i	$0.396077\pi$
$739$	−17.9397	+	31.0725i	−0.659922	+	1.14302i	−0.980635	+	0.195842i	$0.937256\pi$
$740$		0			0
$741$	36.1153	+	36.3001i	1.32673	+	1.33352i
$742$		0			0
$743$	−39.7781	−	33.3778i	−1.45932	−	1.22451i	−0.925408	−	0.378972i	$-0.876278\pi$
$743$	−39.7781	−	33.3778i	−1.45932	−	1.22451i	−0.533910	−	0.845541i	$-0.679278\pi$
$744$		0			0
$745$	−19.0820	−	6.94527i	−0.699110	−	0.254455i
$746$		0			0
$747$	−23.3658	−	13.6497i	−0.854909	−	0.499416i
$748$		0			0
$749$	12.8283	+	72.7527i	0.468734	+	2.65832i
$750$		0			0
$751$	3.08467	−	1.12273i	0.112561	−	0.0409690i	−0.285125	−	0.958490i	$-0.592035\pi$
$751$	3.08467	−	1.12273i	0.112561	−	0.0409690i	0.397687	+	0.917521i	$0.369813\pi$
$752$		0			0
$753$	−11.4544	−	1.03158i	−0.417422	−	0.0375930i
$754$		0			0
$755$	19.0851			0.694579
$756$		0			0
$757$	−3.70968			−0.134831			−0.0674153	−	0.997725i	$-0.521475\pi$
$757$	−3.70968			−0.134831			−0.0674153	+	0.997725i	$0.521475\pi$
$758$		0			0
$759$	−12.8220	−	27.6811i	−0.465410	−	1.00476i
$760$		0			0
$761$	−20.5395	+	7.47578i	−0.744557	+	0.270997i	−0.686314	−	0.727306i	$-0.740772\pi$
$761$	−20.5395	+	7.47578i	−0.744557	+	0.270997i	−0.0582436	+	0.998302i	$0.518550\pi$
$762$		0			0
$763$	−7.50053	−	42.5376i	−0.271537	−	1.53996i
$764$		0			0
$765$	−4.18791	+	0.716428i	−0.151414	+	0.0259025i
$766$		0			0
$767$	−54.4870	−	19.8316i	−1.96741	−	0.716079i
$768$		0			0
$769$	−2.44362	−	2.05044i	−0.0881193	−	0.0739409i	0.597664	−	0.801747i	$-0.296096\pi$
$769$	−2.44362	−	2.05044i	−0.0881193	−	0.0739409i	−0.685783	+	0.727806i	$0.740540\pi$
$770$		0			0
$771$	−35.1221	+	9.31496i	−1.26489	+	0.335470i
$772$		0			0
$773$	22.7097	−	39.3344i	0.816812	−	1.41476i	−0.0912081	−	0.995832i	$-0.529073\pi$
$773$	22.7097	−	39.3344i	0.816812	−	1.41476i	0.908020	−	0.418927i	$-0.137594\pi$
$774$		0			0
$775$	1.52176	+	2.63576i	0.0546632	+	0.0946794i
$776$		0			0
$777$	−44.7694	+	31.1780i	−1.60609	+	1.11850i
$778$		0			0
$779$	0.300066	−	1.70176i	0.0107510	−	0.0609718i
$780$		0			0
$781$	10.5311	−	8.83667i	0.376833	−	0.316201i
$782$		0			0
$783$	26.0862	−	11.9220i	0.932243	−	0.426056i
$784$		0			0
$785$	−0.797255	+	0.668976i	−0.0284552	+	0.0238768i
$786$		0			0
$787$	−0.633058	+	3.59025i	−0.0225661	+	0.127979i	−0.994010	−	0.109292i	$-0.965142\pi$
$787$	−0.633058	+	3.59025i	−0.0225661	+	0.127979i	0.971444	+	0.237271i	$0.0762528\pi$
$788$		0			0
$789$	−2.76716	−	1.29895i	−0.0985135	−	0.0462439i
$790$		0			0
$791$	−20.8105	−	36.0449i	−0.739938	−	1.28161i
$792$		0			0
$793$	22.4676	−	38.9150i	0.797846	−	1.38191i
$794$		0			0
$795$	−8.90118	+	32.8838i	−0.315692	+	1.16627i
$796$		0			0
$797$	−22.2489	−	18.6691i	−0.788097	−	0.661292i	0.157177	−	0.987571i	$-0.449761\pi$
$797$	−22.2489	−	18.6691i	−0.788097	−	0.661292i	−0.945274	+	0.326279i	$0.894205\pi$
$798$		0			0
$799$	3.27751	+	1.19292i	0.115950	+	0.0422023i
$800$		0			0
$801$	3.81636	−	4.50132i	0.134845	−	0.159046i
$802$		0			0
$803$	3.81954	+	21.6617i	0.134789	+	0.764425i
$804$		0			0
$805$	−59.1191	+	21.5176i	−2.08367	+	0.758395i
$806$		0			0
$807$	−24.7486	+	35.1534i	−0.871192	+	1.23746i
$808$		0			0
$809$	2.22527			0.0782362			0.0391181	−	0.999235i	$-0.487545\pi$
$809$	2.22527			0.0782362			0.0391181	+	0.999235i	$0.487545\pi$
$810$		0			0
$811$	15.6813			0.550647			0.275323	−	0.961352i	$-0.411215\pi$
$811$	15.6813			0.550647			0.275323	+	0.961352i	$0.411215\pi$
$812$		0			0
$813$	−13.9222	+	19.7753i	−0.488272	+	0.693552i
$814$		0			0
$815$	15.1529	−	5.51522i	0.530784	−	0.193190i
$816$		0			0
$817$	1.53823	+	8.72374i	0.0538159	+	0.305205i
$818$		0			0
$819$	71.9244	+	13.0610i	2.51324	+	0.456387i
$820$		0			0
$821$	2.22581	+	0.810127i	0.0776812	+	0.0282736i	0.380568	−	0.924753i	$-0.375728\pi$
$821$	2.22581	+	0.810127i	0.0776812	+	0.0282736i	−0.302887	+	0.953026i	$0.597951\pi$
$822$		0			0
$823$	41.5031	+	34.8252i	1.44671	+	1.21393i	0.934940	+	0.354807i	$0.115453\pi$
$823$	41.5031	+	34.8252i	1.44671	+	1.21393i	0.511767	+	0.859124i	$0.328991\pi$
$824$		0			0
$825$	−0.753562	+	2.78390i	−0.0262356	+	0.0969230i
$826$		0			0
$827$	16.1687	−	28.0050i	0.562241	−	0.973829i	−0.435060	−	0.900401i	$-0.643273\pi$
$827$	16.1687	−	28.0050i	0.562241	−	0.973829i	0.997301	−	0.0734277i	$-0.0233938\pi$
$828$		0			0
$829$	13.0283	+	22.5658i	0.452493	+	0.783741i	0.998540	−	0.0540134i	$-0.0172014\pi$
$829$	13.0283	+	22.5658i	0.452493	+	0.783741i	−0.546047	+	0.837754i	$0.683868\pi$
$830$		0			0
$831$	24.4355	+	11.4705i	0.847658	+	0.397906i
$832$		0			0
$833$	−1.31670	+	7.46740i	−0.0456211	+	0.258730i
$834$		0			0
$835$	37.1802	−	31.1979i	1.28667	−	1.07965i
$836$		0			0
$837$	10.1204	−	21.2767i	0.349814	−	0.735429i
$838$		0			0
$839$	26.6070	−	22.3259i	0.918576	−	0.770777i	−0.0551551	−	0.998478i	$-0.517565\pi$
$839$	26.6070	−	22.3259i	0.918576	−	0.770777i	0.973731	+	0.227701i	$0.0731209\pi$
$840$		0			0
$841$	0.254819	−	1.44515i	0.00878686	−	0.0498328i
$842$		0			0
$843$	−28.6851	+	19.9766i	−0.987966	+	0.688032i
$844$		0			0
$845$	20.5273	+	35.5544i	0.706161	+	1.22311i
$846$		0			0
$847$	−10.3193	+	17.8736i	−0.354577	+	0.614145i
$848$		0			0
$849$	25.9540	−	6.88342i	0.890738	−	0.236238i
$850$		0			0
$851$	40.2229	+	33.7510i	1.37882	+	1.15697i
$852$		0			0
$853$	−16.4815	−	5.99877i	−0.564315	−	0.205394i	0.0440801	−	0.999028i	$-0.485964\pi$
$853$	−16.4815	−	5.99877i	−0.564315	−	0.205394i	−0.608396	+	0.793634i	$0.708187\pi$
$854$		0			0
$855$	11.1857	−	30.2514i	0.382544	−	1.03458i
$856$		0			0
$857$	0.0600734	+	0.340693i	0.00205207	+	0.0116379i	0.985817	−	0.167826i	$-0.0536747\pi$
$857$	0.0600734	+	0.340693i	0.00205207	+	0.0116379i	−0.983765	+	0.179464i	$0.942564\pi$
$858$		0			0
$859$	39.3253	−	14.3132i	1.34176	−	0.488361i	0.431394	−	0.902163i	$-0.358022\pi$
$859$	39.3253	−	14.3132i	1.34176	−	0.488361i	0.910367	+	0.413802i	$0.135800\pi$
$860$		0			0
$861$	−1.03685	−	2.23841i	−0.0353356	−	0.0762849i
$862$		0			0
$863$	−1.65260			−0.0562552			−0.0281276	−	0.999604i	$-0.508954\pi$
$863$	−1.65260			−0.0562552			−0.0281276	+	0.999604i	$0.508954\pi$
$864$		0			0
$865$	−12.7282			−0.432771
$866$		0			0
$867$	−28.5269	−	2.56913i	−0.968823	−	0.0872522i
$868$		0			0
$869$	13.7911	−	5.01955i	0.467831	−	0.170277i
$870$		0			0
$871$	4.06743	+	23.0675i	0.137819	+	0.781613i
$872$		0			0
$873$	0.00722548	−	1.41605i	0.000244545	−	0.0479260i
$874$		0			0
$875$	47.2233	+	17.1879i	1.59644	+	0.581056i
$876$		0			0
$877$	4.57937	+	3.84255i	0.154634	+	0.129754i	0.716822	−	0.697256i	$-0.245596\pi$
$877$	4.57937	+	3.84255i	0.154634	+	0.129754i	−0.562188	+	0.827009i	$0.690040\pi$
$878$		0			0
$879$	26.6903	+	26.8268i	0.900241	+	0.904846i
$880$		0			0
$881$	−12.0661	+	20.8992i	−0.406519	+	0.704111i	−0.994497	−	0.104765i	$-0.966591\pi$
$881$	−12.0661	+	20.8992i	−0.406519	+	0.704111i	0.587978	+	0.808877i	$0.299924\pi$
$882$		0			0
$883$	1.53478	+	2.65832i	0.0516495	+	0.0894595i	0.890694	−	0.454603i	$-0.150219\pi$
$883$	1.53478	+	2.65832i	0.0516495	+	0.0894595i	−0.839045	+	0.544062i	$0.816885\pi$
$884$		0			0
$885$	3.09032	+	36.3916i	0.103880	+	1.22329i
$886$		0			0
$887$	−3.67707	+	20.8537i	−0.123464	+	0.700198i	0.858745	+	0.512404i	$0.171245\pi$
$887$	−3.67707	+	20.8537i	−0.123464	+	0.700198i	−0.982208	+	0.187794i	$0.939866\pi$
$888$		0			0
$889$	−33.9537	+	28.4906i	−1.13877	+	0.955543i
$890$		0			0
$891$	21.0571	−	7.42171i	0.705441	−	0.248637i
$892$		0			0
$893$	−20.2826	+	17.0191i	−0.678730	+	0.569522i
$894$		0			0
$895$	−2.08046	+	11.7989i	−0.0695420	+	0.394392i
$896$		0			0
$897$	−5.95305	−	70.1031i	−0.198766	−	2.34067i
$898$		0			0
$899$	−12.5141	−	21.6751i	−0.417368	−	0.722903i
$900$		0			0
$901$	3.21752	−	5.57290i	0.107191	−	0.185660i
$902$		0			0
$903$	8.91926	+	8.96489i	0.296814	+	0.298333i
$904$		0			0
$905$	21.9046	+	18.3801i	0.728133	+	0.610976i
$906$		0			0
$907$	−43.6493	−	15.8870i	−1.44935	−	0.527521i	−0.506941	−	0.861981i	$-0.669224\pi$
$907$	−43.6493	−	15.8870i	−1.44935	−	0.527521i	−0.942410	+	0.334460i	$0.891446\pi$
$908$		0			0
$909$	−35.2767	+	20.1277i	−1.17005	+	0.667594i
$910$		0			0
$911$	4.44322	+	25.1988i	0.147210	+	0.834872i	0.965566	+	0.260159i	$0.0837751\pi$
$911$	4.44322	+	25.1988i	0.147210	+	0.834872i	−0.818355	+	0.574713i	$0.805114\pi$
$912$		0			0
$913$	−21.0274	+	7.65333i	−0.695904	+	0.253288i
$914$		0			0
$915$	−28.1894	−	2.53874i	−0.931914	−	0.0839282i
$916$		0			0
$917$	64.4903			2.12966
$918$		0			0
$919$	23.2063			0.765505			0.382752	−	0.923851i	$-0.374976\pi$
$919$	23.2063			0.765505			0.382752	+	0.923851i	$0.374976\pi$
$920$		0			0
$921$	18.1186	+	39.1156i	0.597027	+	1.28890i
$922$		0			0
$923$	29.7928	−	10.8437i	0.980644	−	0.356925i
$924$		0			0
$925$	−0.861997	−	4.88863i	−0.0283423	−	0.160737i
$926$		0			0
$927$	−5.37805	−	6.47613i	−0.176638	−	0.212704i
$928$		0			0
$929$	5.37628	+	1.95680i	0.176390	+	0.0642007i	0.428705	−	0.903444i	$-0.358970\pi$
$929$	5.37628	+	1.95680i	0.176390	+	0.0642007i	−0.252315	+	0.967645i	$0.581192\pi$
$930$		0			0
$931$	−44.0943	−	36.9995i	−1.44513	−	1.21261i
$932$		0			0
$933$	3.71328	−	0.984823i	0.121567	−	0.0322417i
$934$		0			0
$935$	−1.75668	+	3.04267i	−0.0574497	+	0.0995058i
$936$		0			0
$937$	−12.6584	−	21.9249i	−0.413531	−	0.716256i	0.581742	−	0.813373i	$-0.302371\pi$
$937$	−12.6584	−	21.9249i	−0.413531	−	0.716256i	−0.995273	+	0.0971171i	$0.969038\pi$
$938$		0			0
$939$	19.1109	−	13.3091i	0.623661	−	0.434325i
$940$		0			0
$941$	1.64780	−	9.34516i	0.0537169	−	0.304644i	−0.946098	−	0.323880i	$-0.895012\pi$
$941$	1.64780	−	9.34516i	0.0537169	−	0.304644i	0.999815	+	0.0192367i	$0.00612361\pi$
$942$		0			0
$943$	−1.81878	+	1.52614i	−0.0592276	+	0.0496979i
$944$		0			0
$945$	−11.5764	−	44.5653i	−0.376580	−	1.44971i
$946$		0			0
$947$	−36.8676	+	30.9356i	−1.19804	+	1.00527i	−0.198351	+	0.980131i	$0.563559\pi$
$947$	−36.8676	+	30.9356i	−1.19804	+	1.00527i	−0.999684	+	0.0251400i	$0.991997\pi$
$948$		0			0
$949$	−8.80880	+	49.9572i	−0.285946	+	1.62168i
$950$		0			0
$951$	−43.0639	−	20.2149i	−1.39644	−	0.655514i
$952$		0			0
$953$	11.0133	+	19.0757i	0.356757	+	0.617922i	0.987417	−	0.158138i	$-0.0505490\pi$
$953$	11.0133	+	19.0757i	0.356757	+	0.617922i	−0.630660	+	0.776059i	$0.717216\pi$
$954$		0			0
$955$	8.10029	−	14.0301i	0.262119	−	0.454004i
$956$		0			0
$957$	6.19687	−	22.8933i	0.200316	−	0.740034i
$958$		0			0
$959$	−61.8511	−	51.8992i	−1.99728	−	1.67591i
$960$		0			0
$961$	9.81040	+	3.57069i	0.316464	+	0.115184i
$962$		0			0
$963$	17.5478	+	48.9884i	0.565469	+	1.57863i
$964$		0			0
$965$	−0.487612	−	2.76539i	−0.0156968	−	0.0890209i
$966$		0			0
$967$	31.8898	−	11.6069i	1.02551	−	0.373254i	0.226138	−	0.974095i	$-0.427390\pi$
$967$	31.8898	−	11.6069i	1.02551	−	0.373254i	0.799368	+	0.600841i	$0.205168\pi$
$968$		0			0
$969$	−3.50716	+	4.98164i	−0.112666	+	0.160033i
$970$		0			0
$971$	−36.1756			−1.16093			−0.580465	−	0.814286i	$-0.697129\pi$
$971$	−36.1756			−1.16093			−0.580465	+	0.814286i	$0.697129\pi$
$972$		0			0
$973$	48.7679			1.56343
$974$		0			0
$975$	−3.82898	+	5.43876i	−0.122625	+	0.174180i
$976$		0			0
$977$	−53.2406	+	19.3780i	−1.70332	+	0.619956i	−0.996196	−	0.0871372i	$-0.972228\pi$
$977$	−53.2406	+	19.3780i	−1.70332	+	0.619956i	−0.707120	+	0.707094i	$0.750006\pi$
$978$		0			0
$979$	−0.847398	−	4.80584i	−0.0270830	−	0.153595i
$980$		0			0
$981$	−10.2600	−	28.6430i	−0.327576	−	0.914499i
$982$		0			0
$983$	−37.5948	−	13.6834i	−1.19909	−	0.436432i	−0.336181	−	0.941797i	$-0.609135\pi$
$983$	−37.5948	−	13.6834i	−1.19909	−	0.436432i	−0.862905	+	0.505366i	$0.831358\pi$
$984$		0			0
$985$	14.4143	+	12.0950i	0.459277	+	0.385379i
$986$		0			0
$987$	−9.87604	+	36.4853i	−0.314358	+	1.16134i
$988$		0			0
$989$	6.08557	−	10.5405i	0.193510	−	0.335169i
$990$		0			0
$991$	−2.34039	−	4.05368i	−0.0743450	−	0.128769i	0.826456	−	0.563001i	$-0.190353\pi$
$991$	−2.34039	−	4.05368i	−0.0743450	−	0.128769i	−0.900801	+	0.434232i	$0.857020\pi$
$992$		0			0
$993$	−37.2785	−	17.4992i	−1.18300	−	0.555320i
$994$		0			0
$995$	−2.02976	+	11.5114i	−0.0643478	+	0.364935i
$996$		0			0
$997$	−18.0879	+	15.1775i	−0.572849	+	0.480677i	−0.882590	−	0.470144i	$-0.844202\pi$
$997$	−18.0879	+	15.1775i	−0.572849	+	0.480677i	0.309741	+	0.950821i	$0.399758\pi$
$998$		0			0
$999$	−27.3802	+	26.9643i	−0.866272	+	0.853112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.f.49.3		30
4.3	odd	2		216.2.q.b.49.3	✓	30
12.11	even	2		648.2.q.b.361.2		30
27.16	even	9	inner	432.2.u.f.97.3		30
108.11	even	18		648.2.q.b.289.2		30
108.23	even	18		5832.2.a.l.1.12		15
108.31	odd	18		5832.2.a.k.1.4		15
108.43	odd	18		216.2.q.b.97.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.49.3	✓	30	4.3	odd	2
216.2.q.b.97.3	yes	30	108.43	odd	18
432.2.u.f.49.3		30	1.1	even	1	trivial
432.2.u.f.97.3		30	27.16	even	9	inner
648.2.q.b.289.2		30	108.11	even	18
648.2.q.b.361.2		30	12.11	even	2
5832.2.a.k.1.4		15	108.31	odd	18
5832.2.a.l.1.12		15	108.23	even	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.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.997080 + 1.41627i) q^{3} +(1.95510 - 0.711598i) q^{5} +(-0.739573 - 4.19433i) q^{7} +(-1.01166 - 2.82428i) q^{9} +O(q^{10})\)	\(q+(-0.997080 + 1.41627i) q^{3} +(1.95510 - 0.711598i) q^{5} +(-0.739573 - 4.19433i) q^{7} +(-1.01166 - 2.82428i) q^{9} +(-2.33115 - 0.848468i) q^{11} +(-4.38271 - 3.67753i) q^{13} +(-0.941573 + 3.47847i) q^{15} +(0.340351 - 0.589505i) q^{17} +(2.58368 + 4.47506i) q^{19} +(6.67773 + 3.13464i) q^{21} +(1.23287 - 6.99197i) q^{23} +(-0.514184 + 0.431451i) q^{25} +(5.00866 + 1.38324i) q^{27} +(4.22836 - 3.54802i) q^{29} +(0.787375 - 4.46543i) q^{31} +(3.52600 - 2.45555i) q^{33} +(-4.43061 - 7.67405i) q^{35} +(-3.69778 + 6.40475i) q^{37} +(9.57830 - 2.54033i) q^{39} +(-0.256172 - 0.214954i) q^{41} +(1.61090 + 0.586320i) q^{43} +(-3.98765 - 4.80184i) q^{45} +(0.889756 + 5.04606i) q^{47} +(-10.4676 + 3.80989i) q^{49} +(0.495544 + 1.06981i) q^{51} +9.45353 q^{53} -5.16139 q^{55} +(-8.91404 - 0.802799i) q^{57} +(9.52366 - 3.46633i) q^{59} +(1.36385 + 7.73479i) q^{61} +(-11.0977 + 6.33201i) q^{63} +(-11.1856 - 4.07121i) q^{65} +(-3.13628 - 2.63165i) q^{67} +(8.67327 + 8.71764i) q^{69} +(-2.77081 + 4.79919i) q^{71} +(-4.43331 - 7.67871i) q^{73} +(-0.0983709 - 1.15842i) q^{75} +(-1.83470 + 10.4051i) q^{77} +(-4.53194 + 3.80275i) q^{79} +(-6.95308 + 5.71443i) q^{81} +(6.90986 - 5.79806i) q^{83} +(0.245929 - 1.39473i) q^{85} +(0.808948 + 9.52617i) q^{87} +(0.983567 + 1.70359i) q^{89} +(-12.1834 + 21.1023i) q^{91} +(5.53919 + 5.56753i) q^{93} +(8.23578 + 6.91064i) q^{95} +(0.443556 + 0.161441i) q^{97} +(-0.0379741 + 7.44216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q - 3 * q^7 - 6 * q^9	\( 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) \) 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Introduction

L-functions

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