LMFDB - Embedded newform 432.2.be.c.239.5

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			239.5
Character	$\chi$	$=$	432.239
Dual form			432.2.be.c.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59623 - 0.672336i) q^{3} +(4.18690 + 0.738263i) q^{5} +(-1.26944 - 1.51285i) q^{7} +(2.09593 - 2.14641i) q^{9} +O(q^{10})$	\(q+(1.59623 - 0.672336i) q^{3} +(4.18690 + 0.738263i) q^{5} +(-1.26944 - 1.51285i) q^{7} +(2.09593 - 2.14641i) q^{9} +(0.313474 + 1.77780i) q^{11} +(-3.16732 + 1.15281i) q^{13} +(7.17963 - 1.63656i) q^{15} +(-1.51308 - 0.873578i) q^{17} +(-3.62765 + 2.09442i) q^{19} +(-3.04346 - 1.56138i) q^{21} +(-5.40902 - 4.53870i) q^{23} +(12.2866 + 4.47197i) q^{25} +(1.90249 - 4.83534i) q^{27} +(-3.00752 + 8.26311i) q^{29} +(-3.17218 + 3.78046i) q^{31} +(1.69565 + 2.62702i) q^{33} +(-4.19811 - 7.27134i) q^{35} +(0.864428 - 1.49723i) q^{37} +(-4.28071 + 3.96966i) q^{39} +(-1.58140 - 4.34487i) q^{41} +(9.92458 - 1.74997i) q^{43} +(10.3601 - 7.43946i) q^{45} +(2.63291 - 2.20928i) q^{47} +(0.538276 - 3.05271i) q^{49} +(-3.00257 - 0.377137i) q^{51} +0.511832i q^{53} +7.67488i q^{55} +(-4.38242 + 5.78219i) q^{57} +(1.75988 - 9.98076i) q^{59} +(0.752671 - 0.631566i) q^{61} +(-5.90785 - 0.446106i) q^{63} +(-14.1123 + 2.48838i) q^{65} +(4.10742 + 11.2851i) q^{67} +(-11.6856 - 3.60816i) q^{69} +(-1.03319 + 1.78955i) q^{71} +(1.31302 + 2.27422i) q^{73} +(22.6190 - 1.12243i) q^{75} +(2.29161 - 2.73104i) q^{77} +(-6.02177 + 16.5447i) q^{79} +(-0.214158 - 8.99745i) q^{81} +(-3.45879 - 1.25890i) q^{83} +(-5.69019 - 4.77464i) q^{85} +(0.754866 + 15.2119i) q^{87} +(-6.46750 + 3.73401i) q^{89} +(5.76474 + 3.32827i) q^{91} +(-2.52181 + 8.16728i) q^{93} +(-16.7348 + 6.09098i) q^{95} +(-0.250759 - 1.42213i) q^{97} +(4.47290 + 3.05329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

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
$3$	1.59623	−	0.672336i	0.921586	−	0.388173i
$3$	1.59623	−	0.672336i	0.921586	−	0.388173i
$4$		0			0
$5$	4.18690	+	0.738263i	1.87244	+	0.330161i	0.990090	−	0.140435i	$-0.0448502\pi$
$5$	4.18690	+	0.738263i	1.87244	+	0.330161i	0.882348	+	0.470597i	$0.155961\pi$
$6$		0			0
$7$	−1.26944	−	1.51285i	−0.479801	−	0.571805i	0.470792	−	0.882244i	$-0.343968\pi$
$7$	−1.26944	−	1.51285i	−0.479801	−	0.571805i	−0.950593	+	0.310439i	$0.899524\pi$
$8$		0			0
$9$	2.09593	−	2.14641i	0.698643	−	0.715470i
$10$		0			0
$11$	0.313474	+	1.77780i	0.0945158	+	0.536026i	0.994895	+	0.100919i	$0.0321783\pi$
$11$	0.313474	+	1.77780i	0.0945158	+	0.536026i	−0.900379	+	0.435107i	$0.856711\pi$
$12$		0			0
$13$	−3.16732	+	1.15281i	−0.878456	+	0.319732i	−0.741587	−	0.670857i	$-0.765926\pi$
$13$	−3.16732	+	1.15281i	−0.878456	+	0.319732i	−0.136870	+	0.990589i	$0.543704\pi$
$14$		0			0
$15$	7.17963	−	1.63656i	1.85377	−	0.422558i
$16$		0			0
$17$	−1.51308	−	0.873578i	−0.366976	−	0.211874i	0.305160	−	0.952301i	$-0.401290\pi$
$17$	−1.51308	−	0.873578i	−0.366976	−	0.211874i	−0.672137	+	0.740427i	$0.734623\pi$
$18$		0			0
$19$	−3.62765	+	2.09442i	−0.832240	+	0.480494i	−0.854619	−	0.519256i	$-0.826209\pi$
$19$	−3.62765	+	2.09442i	−0.832240	+	0.480494i	0.0223793	+	0.999750i	$0.492876\pi$
$20$		0			0
$21$	−3.04346	−	1.56138i	−0.664138	−	0.340722i
$22$		0			0
$23$	−5.40902	−	4.53870i	−1.12786	−	0.946385i	−0.128883	−	0.991660i	$-0.541139\pi$
$23$	−5.40902	−	4.53870i	−1.12786	−	0.946385i	−0.998975	+	0.0452747i	$0.985584\pi$
$24$		0			0
$25$	12.2866	+	4.47197i	2.45733	+	0.894393i
$26$		0			0
$27$	1.90249	−	4.83534i	0.366134	−	0.930562i
$28$		0			0
$29$	−3.00752	+	8.26311i	−0.558483	+	1.53442i	0.263355	+	0.964699i	$0.415171\pi$
$29$	−3.00752	+	8.26311i	−0.558483	+	1.53442i	−0.821838	+	0.569721i	$0.807051\pi$
$30$		0			0
$31$	−3.17218	+	3.78046i	−0.569741	+	0.678991i	−0.971578	−	0.236720i	$-0.923928\pi$
$31$	−3.17218	+	3.78046i	−0.569741	+	0.678991i	0.401837	+	0.915711i	$0.368372\pi$
$32$		0			0
$33$	1.69565	+	2.62702i	0.295175	+	0.457306i
$34$		0			0
$35$	−4.19811	−	7.27134i	−0.709611	−	1.22908i
$36$		0			0
$37$	0.864428	−	1.49723i	0.142111	−	0.246144i	−0.786180	−	0.617997i	$-0.787944\pi$
$37$	0.864428	−	1.49723i	0.142111	−	0.246144i	0.928291	+	0.371854i	$0.121278\pi$
$38$		0			0
$39$	−4.28071	+	3.96966i	−0.685462	+	0.635654i
$40$		0			0
$41$	−1.58140	−	4.34487i	−0.246974	−	0.678554i	−0.999793	−	0.0203276i	$-0.993529\pi$
$41$	−1.58140	−	4.34487i	−0.246974	−	0.678554i	0.752820	−	0.658227i	$-0.228693\pi$
$42$		0			0
$43$	9.92458	−	1.74997i	1.51348	−	0.266868i	0.645616	−	0.763662i	$-0.276601\pi$
$43$	9.92458	−	1.74997i	1.51348	−	0.266868i	0.867869	+	0.496794i	$0.165490\pi$
$44$		0			0
$45$	10.3601	−	7.43946i	1.54439	−	1.10901i
$46$		0			0
$47$	2.63291	−	2.20928i	0.384050	−	0.322256i	−0.430240	−	0.902715i	$-0.641571\pi$
$47$	2.63291	−	2.20928i	0.384050	−	0.322256i	0.814290	+	0.580458i	$0.197127\pi$
$48$		0			0
$49$	0.538276	−	3.05271i	0.0768965	−	0.436102i
$50$		0			0
$51$	−3.00257	−	0.377137i	−0.420444	−	0.0528097i
$52$		0			0
$53$			0.511832i			0.0703056i	0.999382	+	0.0351528i	$0.0111918\pi$
$53$			0.511832i			0.0703056i	−0.999382	+	0.0351528i	$0.988808\pi$
$54$		0			0
$55$			7.67488i			1.03488i
$56$		0			0
$57$	−4.38242	+	5.78219i	−0.580466	+	0.765870i
$58$		0			0
$59$	1.75988	−	9.98076i	0.229116	−	1.29938i	−0.625541	−	0.780191i	$-0.715122\pi$
$59$	1.75988	−	9.98076i	0.229116	−	1.29938i	0.854657	−	0.519193i	$-0.173767\pi$
$60$		0			0
$61$	0.752671	−	0.631566i	0.0963697	−	0.0808638i	−0.593330	−	0.804959i	$-0.702187\pi$
$61$	0.752671	−	0.631566i	0.0963697	−	0.0808638i	0.689700	+	0.724096i	$0.257743\pi$
$62$		0			0
$63$	−5.90785	−	0.446106i	−0.744320	−	0.0562041i
$64$		0			0
$65$	−14.1123	+	2.48838i	−1.75042	+	0.308646i
$66$		0			0
$67$	4.10742	+	11.2851i	0.501802	+	1.37869i	0.889514	+	0.456908i	$0.151043\pi$
$67$	4.10742	+	11.2851i	0.501802	+	1.37869i	−0.387712	+	0.921780i	$0.626735\pi$
$68$		0			0
$69$	−11.6856	−	3.60816i	−1.40678	−	0.434372i
$70$		0			0
$71$	−1.03319	+	1.78955i	−0.122618	+	0.212380i	−0.920799	−	0.390037i	$-0.872462\pi$
$71$	−1.03319	+	1.78955i	−0.122618	+	0.212380i	0.798182	+	0.602417i	$0.205796\pi$
$72$		0			0
$73$	1.31302	+	2.27422i	0.153678	+	0.266178i	0.932577	−	0.360972i	$-0.117555\pi$
$73$	1.31302	+	2.27422i	0.153678	+	0.266178i	−0.778899	+	0.627149i	$0.784222\pi$
$74$		0			0
$75$	22.6190	−	1.12243i	2.61182	−	0.129607i
$76$		0			0
$77$	2.29161	−	2.73104i	0.261154	−	0.311231i
$78$		0			0
$79$	−6.02177	+	16.5447i	−0.677502	+	1.86142i	−0.209133	+	0.977887i	$0.567064\pi$
$79$	−6.02177	+	16.5447i	−0.677502	+	1.86142i	−0.468369	+	0.883533i	$0.655158\pi$
$80$		0			0
$81$	−0.214158	−	8.99745i	−0.0237953	−	0.999717i
$82$		0			0
$83$	−3.45879	−	1.25890i	−0.379652	−	0.138182i	0.145143	−	0.989411i	$-0.453636\pi$
$83$	−3.45879	−	1.25890i	−0.379652	−	0.138182i	−0.524795	+	0.851229i	$0.675858\pi$
$84$		0			0
$85$	−5.69019	−	4.77464i	−0.617188	−	0.517882i
$86$		0			0
$87$	0.754866	+	15.2119i	0.0809301	+	1.63089i
$88$		0			0
$89$	−6.46750	+	3.73401i	−0.685554	+	0.395805i	−0.801944	−	0.597399i	$-0.796201\pi$
$89$	−6.46750	+	3.73401i	−0.685554	+	0.395805i	0.116390	+	0.993204i	$0.462868\pi$
$90$		0			0
$91$	5.76474	+	3.32827i	0.604309	+	0.348898i
$92$		0			0
$93$	−2.52181	+	8.16728i	−0.261500	+	0.846907i
$94$		0			0
$95$	−16.7348	+	6.09098i	−1.71696	+	0.624922i
$96$		0			0
$97$	−0.250759	−	1.42213i	−0.0254607	−	0.144395i	0.969427	−	0.245378i	$-0.0789122\pi$
$97$	−0.250759	−	1.42213i	−0.0254607	−	0.144395i	−0.994888	+	0.100983i	$0.967801\pi$
$98$		0			0
$99$	4.47290	+	3.05329i	0.449543	+	0.306868i
$100$		0			0
$101$	−4.74078	−	5.64984i	−0.471725	−	0.562180i	0.476747	−	0.879041i	$-0.341816\pi$
$101$	−4.74078	−	5.64984i	−0.471725	−	0.562180i	−0.948472	+	0.316860i	$0.897371\pi$
$102$		0			0
$103$	−12.8583	−	2.26726i	−1.26696	−	0.223399i	−0.500526	−	0.865721i	$-0.666860\pi$
$103$	−12.8583	−	2.26726i	−1.26696	−	0.223399i	−0.766435	+	0.642322i	$0.777971\pi$
$104$		0			0
$105$	−11.5900	−	8.78423i	−1.13106	−	0.857253i
$106$		0			0
$107$	9.16482			0.885997			0.442998	−	0.896522i	$-0.353915\pi$
$107$	9.16482			0.885997			0.442998	+	0.896522i	$0.353915\pi$
$108$		0			0
$109$	−12.4898			−1.19630			−0.598151	−	0.801383i	$-0.704098\pi$
$109$	−12.4898			−1.19630			−0.598151	+	0.801383i	$0.704098\pi$
$110$		0			0
$111$	0.373187	−	2.97112i	0.0354213	−	0.282006i
$112$		0			0
$113$	−6.38278	−	1.12546i	−0.600441	−	0.105874i	−0.134838	−	0.990868i	$-0.543051\pi$
$113$	−6.38278	−	1.12546i	−0.600441	−	0.105874i	−0.465603	+	0.884994i	$0.654163\pi$
$114$		0			0
$115$	−19.2962	−	22.9964i	−1.79938	−	2.14442i
$116$		0			0
$117$	−4.16407	+	9.21457i	−0.384969	+	0.851888i
$118$		0			0
$119$	0.599163	+	3.39802i	0.0549252	+	0.311496i
$120$		0			0
$121$	7.27432	−	2.64764i	0.661302	−	0.240694i
$122$		0			0
$123$	−5.44550	−	5.87219i	−0.491004	−	0.529478i
$124$		0			0
$125$	29.7319	+	17.1657i	2.65930	+	1.53535i
$126$		0			0
$127$	8.67356	−	5.00768i	0.769654	−	0.444360i	−0.0630972	−	0.998007i	$-0.520098\pi$
$127$	8.67356	−	5.00768i	0.769654	−	0.444360i	0.832751	+	0.553647i	$0.186764\pi$
$128$		0			0
$129$	14.6654	−	9.46602i	1.29122	−	0.833436i
$130$		0			0
$131$	8.79708	+	7.38162i	0.768604	+	0.644936i	0.940351	−	0.340206i	$-0.110497\pi$
$131$	8.79708	+	7.38162i	0.768604	+	0.644936i	−0.171747	+	0.985141i	$0.554941\pi$
$132$		0			0
$133$	7.77362	+	2.82937i	0.674059	+	0.245337i
$134$		0			0
$135$	11.5353	−	18.8406i	0.992799	−	1.62154i
$136$		0			0
$137$	1.13684	−	3.12344i	0.0971268	−	0.266854i	−0.881608	−	0.471982i	$-0.843539\pi$
$137$	1.13684	−	3.12344i	0.0971268	−	0.266854i	0.978735	+	0.205128i	$0.0657611\pi$
$138$		0			0
$139$	−6.27514	+	7.47842i	−0.532251	+	0.634311i	−0.963432	−	0.267954i	$-0.913653\pi$
$139$	−6.27514	+	7.47842i	−0.532251	+	0.634311i	0.431181	+	0.902265i	$0.358097\pi$
$140$		0			0
$141$	2.71737	−	5.29673i	0.228844	−	0.446065i
$142$		0			0
$143$	−3.04233	−	5.26947i	−0.254413	−	0.440656i
$144$		0			0
$145$	−18.6926	+	32.3764i	−1.55233	+	2.68872i
$146$		0			0
$147$	−1.19323	−	5.23475i	−0.0984163	−	0.431755i
$148$		0			0
$149$	−6.99419	−	19.2164i	−0.572986	−	1.57427i	−0.799761	−	0.600319i	$-0.795040\pi$
$149$	−6.99419	−	19.2164i	−0.572986	−	1.57427i	0.226774	−	0.973947i	$-0.427182\pi$
$150$		0			0
$151$	10.4203	−	1.83738i	0.847990	−	0.149524i	0.267265	−	0.963623i	$-0.413880\pi$
$151$	10.4203	−	1.83738i	0.847990	−	0.149524i	0.580725	+	0.814100i	$0.302769\pi$
$152$		0			0
$153$	−5.04637	+	1.41674i	−0.407975	+	0.114536i
$154$		0			0
$155$	−16.0726	+	13.4865i	−1.29098	+	1.08326i
$156$		0			0
$157$	3.76938	−	21.3772i	0.300829	−	1.70609i	−0.341686	−	0.939814i	$-0.610998\pi$
$157$	3.76938	−	21.3772i	0.300829	−	1.70609i	0.642515	−	0.766273i	$-0.277891\pi$
$158$		0			0
$159$	0.344123	+	0.817005i	0.0272907	+	0.0647927i
$160$		0			0
$161$			13.9446i			1.09899i
$162$		0			0
$163$		−	1.10221i		−	0.0863315i	−0.999068	−	0.0431658i	$-0.986256\pi$
$163$		−	1.10221i		−	0.0863315i	0.999068	−	0.0431658i	$-0.0137444\pi$
$164$		0			0
$165$	5.16010	+	12.2509i	0.401713	+	0.953732i
$166$		0			0
$167$	−1.82002	+	10.3218i	−0.140837	+	0.798727i	0.829779	+	0.558092i	$0.188467\pi$
$167$	−1.82002	+	10.3218i	−0.140837	+	0.798727i	−0.970616	+	0.240634i	$0.922645\pi$
$168$		0			0
$169$	−1.25564	+	1.05361i	−0.0965879	+	0.0810468i
$170$		0			0
$171$	−3.10780	+	12.1762i	−0.237660	+	0.931136i
$172$		0			0
$173$	−0.239692	+	0.0422642i	−0.0182235	+	0.00321329i	−0.182752	−	0.983159i	$-0.558501\pi$
$173$	−0.239692	+	0.0422642i	−0.0182235	+	0.00321329i	0.164529	+	0.986372i	$0.447390\pi$
$174$		0			0
$175$	−8.83165	−	24.2648i	−0.667610	−	1.83424i
$176$		0			0
$177$	−3.90124	−	17.1149i	−0.293235	−	1.28643i
$178$		0			0
$179$	0.372275	−	0.644799i	0.0278251	−	0.0481946i	−0.851778	−	0.523904i	$-0.824475\pi$
$179$	0.372275	−	0.644799i	0.0278251	−	0.0481946i	0.879603	+	0.475709i	$0.157809\pi$
$180$		0			0
$181$	8.83351	+	15.3001i	0.656590	+	1.13725i	0.981493	+	0.191500i	$0.0613351\pi$
$181$	8.83351	+	15.3001i	0.656590	+	1.13725i	−0.324903	+	0.945747i	$0.605332\pi$
$182$		0			0
$183$	0.776815	−	1.51418i	0.0574239	−	0.111931i
$184$		0			0
$185$	4.72463	−	5.63059i	0.347361	−	0.413969i
$186$		0			0
$187$	1.07873	−	2.96380i	0.0788848	−	0.216734i
$188$		0			0
$189$	−9.73025	+	3.25997i	−0.707772	+	0.237128i
$190$		0			0
$191$	9.20584	+	3.35065i	0.666111	+	0.242445i	0.652873	−	0.757468i	$-0.273564\pi$
$191$	9.20584	+	3.35065i	0.666111	+	0.242445i	0.0132384	+	0.999912i	$0.495786\pi$
$192$		0			0
$193$	−6.56436	−	5.50815i	−0.472513	−	0.396486i	0.375197	−	0.926945i	$-0.377575\pi$
$193$	−6.56436	−	5.50815i	−0.472513	−	0.396486i	−0.847710	+	0.530459i	$0.822019\pi$
$194$		0			0
$195$	−20.8535	+	13.4603i	−1.49335	+	0.963909i
$196$		0			0
$197$	1.15257	−	0.665435i	0.0821170	−	0.0474103i	−0.458379	−	0.888757i	$-0.651570\pi$
$197$	1.15257	−	0.665435i	0.0821170	−	0.0474103i	0.540496	+	0.841346i	$0.318237\pi$
$198$		0			0
$199$	14.2785	+	8.24368i	1.01217	+	0.584379i	0.911828	−	0.410573i	$-0.134671\pi$
$199$	14.2785	+	8.24368i	1.01217	+	0.584379i	0.100347	+	0.994953i	$0.468005\pi$
$200$		0			0
$201$	14.1438	+	15.2520i	0.997623	+	1.07579i
$202$		0			0
$203$	16.3187	−	5.93953i	1.14535	−	0.416873i
$204$		0			0
$205$	−3.41352	−	19.3590i	−0.238410	−	1.35209i
$206$		0			0
$207$	−21.0788	+	2.09717i	−1.46508	+	0.145763i
$208$		0			0
$209$	−4.86063	−	5.79268i	−0.336217	−	0.400688i
$210$		0			0
$211$	11.8106	+	2.08253i	0.813078	+	0.143368i	0.564701	−	0.825296i	$-0.308992\pi$
$211$	11.8106	+	2.08253i	0.813078	+	0.143368i	0.248377	+	0.968663i	$0.420103\pi$
$212$		0			0
$213$	−0.446046	+	3.55119i	−0.0305626	+	0.243323i
$214$		0			0
$215$	42.8452			2.92202
$216$		0			0
$217$	9.74617			0.661613
$218$		0			0
$219$	3.62493	+	2.74740i	0.244950	+	0.185652i
$220$		0			0
$221$	5.79948	+	1.02260i	0.390115	+	0.0687878i
$222$		0			0
$223$	6.09692	+	7.26603i	0.408280	+	0.486569i	0.930526	−	0.366226i	$-0.119350\pi$
$223$	6.09692	+	7.26603i	0.408280	+	0.486569i	−0.522246	+	0.852795i	$0.674906\pi$
$224$		0			0
$225$	35.3506	−	16.9992i	2.35671	−	1.13328i
$226$		0			0
$227$	−1.39601	−	7.91718i	−0.0926565	−	0.525481i	−0.995440	−	0.0953866i	$-0.969591\pi$
$227$	−1.39601	−	7.91718i	−0.0926565	−	0.525481i	0.902784	−	0.430095i	$-0.141520\pi$
$228$		0			0
$229$	9.27154	−	3.37456i	0.612680	−	0.222997i	−0.0169953	−	0.999856i	$-0.505410\pi$
$229$	9.27154	−	3.37456i	0.612680	−	0.222997i	0.629676	+	0.776858i	$0.283188\pi$
$230$		0			0
$231$	1.82178	−	5.90011i	0.119864	−	0.388199i
$232$		0			0
$233$	17.5103	+	10.1096i	1.14714	+	0.662302i	0.948189	−	0.317707i	$-0.102913\pi$
$233$	17.5103	+	10.1096i	1.14714	+	0.662302i	0.198952	+	0.980009i	$0.436246\pi$
$234$		0			0
$235$	12.6548	−	7.30624i	0.825507	−	0.476606i
$236$		0			0
$237$	1.51142	+	30.4578i	0.0981771	+	1.97845i
$238$		0			0
$239$	−21.0130	−	17.6320i	−1.35922	−	1.14052i	−0.976224	−	0.216766i	$-0.930449\pi$
$239$	−21.0130	−	17.6320i	−1.35922	−	1.14052i	−0.382993	−	0.923751i	$-0.625107\pi$
$240$		0			0
$241$	7.83906	+	2.85318i	0.504958	+	0.183790i	0.581923	−	0.813244i	$-0.302301\pi$
$241$	7.83906	+	2.85318i	0.504958	+	0.183790i	−0.0769646	+	0.997034i	$0.524523\pi$
$242$		0			0
$243$	−6.39115	−	14.2181i	−0.409993	−	0.912089i
$244$		0			0
$245$	4.50741	−	12.3840i	0.287968	−	0.791186i
$246$		0			0
$247$	9.07545	−	10.8157i	0.577457	−	0.688186i
$248$		0			0
$249$	−6.36744	+	0.315973i	−0.403520	+	0.0200240i
$250$		0			0
$251$	−10.0064	−	17.3316i	−0.631600	−	1.09396i	−0.987225	−	0.159335i	$-0.949065\pi$
$251$	−10.0064	−	17.3316i	−0.631600	−	1.09396i	0.355624	−	0.934629i	$-0.384268\pi$
$252$		0			0
$253$	6.37331	−	11.0389i	0.400687	−	0.694009i
$254$		0			0
$255$	−12.2930	−	3.79572i	−0.769820	−	0.237697i
$256$		0			0
$257$	0.768135	+	2.11043i	0.0479150	+	0.131645i	0.961342	−	0.275357i	$-0.0887962\pi$
$257$	0.768135	+	2.11043i	0.0479150	+	0.131645i	−0.913427	+	0.407003i	$0.866574\pi$
$258$		0			0
$259$	−3.36243	+	0.592887i	−0.208931	+	0.0368402i
$260$		0			0
$261$	11.4325	+	23.7743i	0.707651	+	1.47159i
$262$		0			0
$263$	9.74693	−	8.17865i	0.601022	−	0.504317i	−0.290752	−	0.956798i	$-0.593906\pi$
$263$	9.74693	−	8.17865i	0.601022	−	0.504317i	0.891774	+	0.452481i	$0.149461\pi$
$264$		0			0
$265$	−0.377867	+	2.14299i	−0.0232122	+	0.131643i
$266$		0			0
$267$	−7.81314	+	10.3087i	−0.478156	+	0.630882i
$268$		0			0
$269$		−	13.9356i		−	0.849668i	−0.905271	−	0.424834i	$-0.860332\pi$
$269$		−	13.9356i		−	0.849668i	0.905271	−	0.424834i	$-0.139668\pi$
$270$		0			0
$271$		−	1.32883i		−	0.0807208i	−0.999185	−	0.0403604i	$-0.987149\pi$
$271$		−	1.32883i		−	0.0807208i	0.999185	−	0.0403604i	$-0.0128506\pi$
$272$		0			0
$273$	11.4396	+	1.43687i	0.692356	+	0.0869631i
$274$		0			0
$275$	−4.09872	+	23.2450i	−0.247162	+	1.40172i
$276$		0			0
$277$	5.21107	−	4.37261i	0.313103	−	0.262724i	−0.472670	−	0.881239i	$-0.656710\pi$
$277$	5.21107	−	4.37261i	0.313103	−	0.262724i	0.785773	+	0.618515i	$0.212265\pi$
$278$		0			0
$279$	1.46575	+	14.7324i	0.0877521	+	0.882005i
$280$		0			0
$281$	−3.97579	+	0.701039i	−0.237176	+	0.0418205i	−0.290972	−	0.956731i	$-0.593979\pi$
$281$	−3.97579	+	0.701039i	−0.237176	+	0.0418205i	0.0537967	+	0.998552i	$0.482868\pi$
$282$		0			0
$283$	−0.187770	−	0.515894i	−0.0111618	−	0.0306667i	0.933987	−	0.357308i	$-0.116305\pi$
$283$	−0.187770	−	0.515894i	−0.0111618	−	0.0306667i	−0.945148	+	0.326641i	$0.894083\pi$
$284$		0			0
$285$	−22.6175	+	20.9741i	−1.33975	+	1.24240i
$286$		0			0
$287$	−4.56566	+	7.90796i	−0.269502	+	0.466792i
$288$		0			0
$289$	−6.97372	−	12.0788i	−0.410219	−	0.710520i
$290$		0			0
$291$	−1.35642	−	2.10145i	−0.0795146	−	0.123189i
$292$		0			0
$293$	11.7794	−	14.0382i	0.688163	−	0.820121i	−0.302969	−	0.953000i	$-0.597978\pi$
$293$	11.7794	−	14.0382i	0.688163	−	0.820121i	0.991132	+	0.132880i	$0.0424224\pi$
$294$		0			0
$295$	14.7369	−	40.4892i	0.858013	−	2.35737i
$296$		0			0
$297$	9.19264	+	1.86648i	0.533411	+	0.108304i
$298$		0			0
$299$	22.3643	+	8.13995i	1.29336	+	0.470746i
$300$		0			0
$301$	−15.2461	−	12.7930i	−0.878769	−	0.737374i
$302$		0			0
$303$	−11.3660	−	5.83108i	−0.652959	−	0.334987i
$304$		0			0
$305$	3.61762	−	2.08863i	0.207144	−	0.119595i
$306$		0			0
$307$	−11.9994	−	6.92784i	−0.684841	−	0.395393i	0.116836	−	0.993151i	$-0.462725\pi$
$307$	−11.9994	−	6.92784i	−0.684841	−	0.395393i	−0.801676	+	0.597758i	$0.796058\pi$
$308$		0			0
$309$	−22.0491	+	5.02599i	−1.25433	+	0.285918i
$310$		0			0
$311$	−3.49020	+	1.27033i	−0.197911	+	0.0720338i	−0.439074	−	0.898451i	$-0.644693\pi$
$311$	−3.49020	+	1.27033i	−0.197911	+	0.0720338i	0.241163	+	0.970485i	$0.422471\pi$
$312$		0			0
$313$	3.96289	+	22.4747i	0.223996	+	1.27034i	0.864595	+	0.502469i	$0.167575\pi$
$313$	3.96289	+	22.4747i	0.223996	+	1.27034i	−0.640599	+	0.767875i	$0.721314\pi$
$314$		0			0
$315$	−24.4062	−	6.22935i	−1.37514	−	0.350984i
$316$		0			0
$317$	11.1228	+	13.2557i	0.624720	+	0.744512i	0.981874	−	0.189533i	$-0.0606975\pi$
$317$	11.1228	+	13.2557i	0.624720	+	0.744512i	−0.357155	+	0.934045i	$0.616253\pi$
$318$		0			0
$319$	−15.6329	−	2.75650i	−0.875275	−	0.154335i
$320$		0			0
$321$	14.6292	−	6.16184i	0.816523	−	0.343920i
$322$		0			0
$323$	7.31857			0.407216
$324$		0			0
$325$	−44.0710			−2.44462
$326$		0			0
$327$	−19.9366	+	8.39731i	−1.10250	+	0.464372i
$328$		0			0
$329$	−6.68463	−	1.17868i	−0.368536	−	0.0649828i
$330$		0			0
$331$	4.63111	+	5.51914i	0.254549	+	0.303359i	0.878152	−	0.478382i	$-0.158776\pi$
$331$	4.63111	+	5.51914i	0.254549	+	0.303359i	−0.623603	+	0.781741i	$0.714332\pi$
$332$		0			0
$333$	−1.40190	−	4.99351i	−0.0768235	−	0.273643i
$334$		0			0
$335$	8.86603	+	50.2817i	0.484403	+	2.74718i
$336$		0			0
$337$	−23.8554	+	8.68267i	−1.29949	+	0.472975i	−0.896830	−	0.442375i	$-0.854136\pi$
$337$	−23.8554	+	8.68267i	−1.29949	+	0.472975i	−0.402659	+	0.915350i	$0.631914\pi$
$338$		0			0
$339$	−10.9451	+	2.49488i	−0.594456	+	0.135503i
$340$		0			0
$341$	−7.71529	−	4.45443i	−0.417806	−	0.241221i
$342$		0			0
$343$	−17.2738	+	9.97301i	−0.932695	+	0.538492i
$344$		0			0
$345$	−46.2626	−	23.7341i	−2.49070	−	1.27780i
$346$		0			0
$347$	7.38189	+	6.19414i	0.396281	+	0.332519i	0.819054	−	0.573717i	$-0.194499\pi$
$347$	7.38189	+	6.19414i	0.396281	+	0.332519i	−0.422773	+	0.906235i	$0.638943\pi$
$348$		0			0
$349$	−1.04043	−	0.378686i	−0.0556930	−	0.0202706i	0.314023	−	0.949415i	$-0.398323\pi$
$349$	−1.04043	−	0.378686i	−0.0556930	−	0.0202706i	−0.369716	+	0.929145i	$0.620545\pi$
$350$		0			0
$351$	−0.451552	+	17.5083i	−0.0241021	+	0.934523i
$352$		0			0
$353$	−10.9418	+	30.0625i	−0.582375	+	1.60006i	0.201734	+	0.979440i	$0.435342\pi$
$353$	−10.9418	+	30.0625i	−0.582375	+	1.60006i	−0.784109	+	0.620623i	$0.786880\pi$
$354$		0			0
$355$	−5.64704	+	6.72988i	−0.299714	+	0.357185i
$356$		0			0
$357$	3.24102	+	5.02120i	0.171533	+	0.265750i
$358$		0			0
$359$	−8.37501	−	14.5059i	−0.442016	−	0.765595i	0.555823	−	0.831301i	$-0.312403\pi$
$359$	−8.37501	−	14.5059i	−0.442016	−	0.765595i	−0.997839	+	0.0657061i	$0.979070\pi$
$360$		0			0
$361$	−0.726778	+	1.25882i	−0.0382515	+	0.0662535i
$362$		0			0
$363$	9.83142	−	9.11704i	0.516016	−	0.478520i
$364$		0			0
$365$	3.81852	+	10.4913i	0.199870	+	0.549140i
$366$		0			0
$367$	4.44634	−	0.784010i	0.232097	−	0.0409250i	−0.0563897	−	0.998409i	$-0.517959\pi$
$367$	4.44634	−	0.784010i	0.232097	−	0.0409250i	0.288487	+	0.957484i	$0.406848\pi$
$368$		0			0
$369$	−12.6404	−	5.71220i	−0.658032	−	0.297365i
$370$		0			0
$371$	0.774328	−	0.649738i	0.0402011	−	0.0337327i
$372$		0			0
$373$	−2.72449	+	15.4513i	−0.141069	+	0.800040i	0.829372	+	0.558698i	$0.188699\pi$
$373$	−2.72449	+	15.4513i	−0.141069	+	0.800040i	−0.970440	+	0.241342i	$0.922412\pi$
$374$		0			0
$375$	59.0002	+	7.41070i	3.04676	+	0.382687i
$376$		0			0
$377$		−	29.6390i		−	1.52649i
$378$		0			0
$379$		−	15.3891i		−	0.790485i	−0.918577	−	0.395242i	$-0.870661\pi$
$379$		−	15.3891i		−	0.790485i	0.918577	−	0.395242i	$-0.129339\pi$
$380$		0			0
$381$	10.4782	−	13.8250i	0.536814	−	0.708275i
$382$		0			0
$383$	3.92194	−	22.2424i	0.200402	−	1.13654i	−0.704111	−	0.710090i	$-0.748654\pi$
$383$	3.92194	−	22.2424i	0.200402	−	1.13654i	0.904513	−	0.426446i	$-0.140235\pi$
$384$		0			0
$385$	11.6110	−	9.74277i	0.591750	−	0.496537i
$386$		0			0
$387$	17.0451	−	24.9700i	0.866450	−	1.26930i
$388$		0			0
$389$	−13.2621	+	2.33846i	−0.672414	+	0.118565i	−0.499423	−	0.866358i	$-0.666455\pi$
$389$	−13.2621	+	2.33846i	−0.672414	+	0.118565i	−0.172992	+	0.984923i	$0.555343\pi$
$390$		0			0
$391$	4.21937	+	11.5926i	0.213383	+	0.586264i
$392$		0			0
$393$	19.0051	+	5.86822i	0.958682	+	0.296012i
$394$		0			0
$395$	−37.4268	+	64.8252i	−1.88315	+	3.26171i
$396$		0			0
$397$	−1.61332	−	2.79436i	−0.0809704	−	0.140245i	0.822697	−	0.568481i	$-0.192469\pi$
$397$	−1.61332	−	2.79436i	−0.0809704	−	0.140245i	−0.903667	+	0.428236i	$0.859135\pi$
$398$		0			0
$399$	14.3108	−	0.710149i	0.716437	−	0.0355519i
$400$		0			0
$401$	18.1787	−	21.6646i	0.907803	−	1.08188i	−0.0885090	−	0.996075i	$-0.528210\pi$
$401$	18.1787	−	21.6646i	0.907803	−	1.08188i	0.996312	−	0.0858023i	$-0.0273453\pi$
$402$		0			0
$403$	5.68917	−	15.6309i	0.283398	−	0.778628i
$404$		0			0
$405$	5.74583	−	37.8295i	0.285513	−	1.87976i
$406$		0			0
$407$	2.93275	+	1.06743i	0.145371	+	0.0529108i
$408$		0			0
$409$	−4.48887	−	3.76661i	−0.221961	−	0.186247i	0.525026	−	0.851086i	$-0.324056\pi$
$409$	−4.48887	−	3.76661i	−0.221961	−	0.186247i	−0.746987	+	0.664839i	$0.768500\pi$
$410$		0			0
$411$	−0.285338	−	5.75009i	−0.0140747	−	0.283631i
$412$		0			0
$413$	−17.3335	+	10.0075i	−0.852925	+	0.492436i
$414$		0			0
$415$	−13.5522	−	7.82437i	−0.665252	−	0.384083i
$416$		0			0
$417$	−4.98859	+	16.1563i	−0.244292	+	0.791178i
$418$		0			0
$419$	−10.0245	+	3.64864i	−0.489731	+	0.178248i	−0.575070	−	0.818105i	$-0.695025\pi$
$419$	−10.0245	+	3.64864i	−0.489731	+	0.178248i	0.0853386	+	0.996352i	$0.472803\pi$
$420$		0			0
$421$	3.69487	+	20.9547i	0.180077	+	1.02127i	0.932119	+	0.362153i	$0.117958\pi$
$421$	3.69487	+	20.9547i	0.180077	+	1.02127i	−0.752042	+	0.659116i	$0.770931\pi$
$422$		0			0
$423$	0.776387	−	10.2818i	0.0377492	−	0.499919i
$424$		0			0
$425$	−14.6841	−	17.4998i	−0.712282	−	0.848864i
$426$		0			0
$427$	−1.91093	−	0.336949i	−0.0924766	−	0.0163061i
$428$		0			0
$429$	−8.39913	−	6.36585i	−0.405514	−	0.307346i
$430$		0			0
$431$	16.3332			0.786744			0.393372	−	0.919379i	$-0.371309\pi$
$431$	16.3332			0.786744			0.393372	+	0.919379i	$0.371309\pi$
$432$		0			0
$433$	36.2969			1.74432			0.872159	−	0.489222i	$-0.162719\pi$
$433$	36.2969			1.74432			0.872159	+	0.489222i	$0.162719\pi$
$434$		0			0
$435$	−8.06986	+	64.2481i	−0.386920	+	3.08046i
$436$		0			0
$437$	29.1280	+	5.13605i	1.39338	+	0.245691i
$438$		0			0
$439$	11.7942	+	14.0558i	0.562906	+	0.670845i	0.970159	−	0.242470i	$-0.0779577\pi$
$439$	11.7942	+	14.0558i	0.562906	+	0.670845i	−0.407253	+	0.913315i	$0.633513\pi$
$440$		0			0
$441$	−5.42419	−	7.55363i	−0.258295	−	0.359697i
$442$		0			0
$443$	−1.71016	−	9.69879i	−0.0812521	−	0.460804i	−0.998103	−	0.0615728i	$-0.980388\pi$
$443$	−1.71016	−	9.69879i	−0.0812521	−	0.460804i	0.916850	−	0.399231i	$-0.130723\pi$
$444$		0			0
$445$	−29.8355	+	10.8592i	−1.41434	+	0.514776i
$446$		0			0
$447$	−24.0842	−	25.9714i	−1.13914	−	1.22840i
$448$		0			0
$449$	−13.3593	−	7.71300i	−0.630465	−	0.363999i	0.150467	−	0.988615i	$-0.451922\pi$
$449$	−13.3593	−	7.71300i	−0.630465	−	0.363999i	−0.780932	+	0.624616i	$0.785255\pi$
$450$		0			0
$451$	7.22856	−	4.17341i	0.340380	−	0.196518i
$452$		0			0
$453$	15.3979	−	9.93881i	0.723455	−	0.466966i
$454$		0			0
$455$	21.6792	+	18.1910i	1.01634	+	0.852809i
$456$		0			0
$457$	−18.6347	−	6.78248i	−0.871695	−	0.317271i	−0.132841	−	0.991137i	$-0.542410\pi$
$457$	−18.6347	−	6.78248i	−0.871695	−	0.317271i	−0.738853	+	0.673866i	$0.764632\pi$
$458$		0			0
$459$	−7.10267	+	5.65430i	−0.331524	+	0.263920i
$460$		0			0
$461$	1.17082	−	3.21680i	0.0545306	−	0.149822i	−0.909437	−	0.415842i	$-0.863487\pi$
$461$	1.17082	−	3.21680i	0.0545306	−	0.149822i	0.963967	+	0.266021i	$0.0857090\pi$
$462$		0			0
$463$	8.06961	−	9.61699i	0.375027	−	0.446939i	−0.545211	−	0.838299i	$-0.683551\pi$
$463$	8.06961	−	9.61699i	0.375027	−	0.446939i	0.920238	+	0.391359i	$0.127995\pi$
$464$		0			0
$465$	−16.5882	+	32.3338i	−0.769258	+	1.49944i
$466$		0			0
$467$	10.1463	+	17.5739i	0.469514	+	0.813221i	0.999392	−	0.0348520i	$-0.0110960\pi$
$467$	10.1463	+	17.5739i	0.469514	+	0.813221i	−0.529879	+	0.848073i	$0.677763\pi$
$468$		0			0
$469$	11.8585	−	20.5396i	0.547576	−	0.948429i
$470$		0			0
$471$	−8.35585	−	36.6573i	−0.385017	−	1.68908i
$472$		0			0
$473$	6.22219	+	17.0953i	0.286097	+	0.786044i
$474$		0			0
$475$	−53.9378	+	9.51068i	−2.47483	+	0.436380i
$476$		0			0
$477$	1.09860	+	1.07276i	0.0503016	+	0.0491185i
$478$		0			0
$479$	−1.80006	+	1.51043i	−0.0822467	+	0.0690131i	−0.682984	−	0.730433i	$-0.739318\pi$
$479$	−1.80006	+	1.51043i	−0.0822467	+	0.0690131i	0.600737	+	0.799446i	$0.294874\pi$
$480$		0			0
$481$	−1.01189	+	5.73874i	−0.0461384	+	0.261664i
$482$		0			0
$483$	9.37548	+	22.2589i	0.426599	+	1.01282i
$484$		0			0
$485$		−	6.13943i		−	0.278777i
$486$		0			0
$487$			6.67682i			0.302555i	0.988491	+	0.151278i	$0.0483388\pi$
$487$			6.67682i			0.302555i	−0.988491	+	0.151278i	$0.951661\pi$
$488$		0			0
$489$	−0.741053	−	1.75938i	−0.0335116	−	0.0795620i
$490$		0			0
$491$	4.97852	−	28.2346i	0.224677	−	1.27421i	−0.638623	−	0.769520i	$-0.720496\pi$
$491$	4.97852	−	28.2346i	0.224677	−	1.27421i	0.863301	−	0.504690i	$-0.168393\pi$
$492$		0			0
$493$	11.7691	−	9.87545i	0.530053	−	0.444768i
$494$		0			0
$495$	16.4735	+	16.0860i	0.740427	+	0.723013i
$496$		0			0
$497$	4.01890	−	0.708640i	0.180272	−	0.0317868i
$498$		0			0
$499$	10.7802	+	29.6183i	0.482587	+	1.32590i	0.907267	+	0.420554i	$0.138164\pi$
$499$	10.7802	+	29.6183i	0.482587	+	1.32590i	−0.424680	+	0.905344i	$0.639613\pi$
$500$		0			0
$501$	4.03456	+	17.6997i	0.180251	+	0.790765i
$502$		0			0
$503$	8.82536	−	15.2860i	0.393504	−	0.681568i	−0.599405	−	0.800446i	$-0.704596\pi$
$503$	8.82536	−	15.2860i	0.393504	−	0.681568i	0.992909	+	0.118878i	$0.0379296\pi$
$504$		0			0
$505$	−15.6781	−	27.1553i	−0.697666	−	1.20839i
$506$		0			0
$507$	−1.29592	+	2.52602i	−0.0575539	+	0.112184i
$508$		0			0
$509$	−9.38432	+	11.1838i	−0.415953	+	0.495713i	−0.932815	−	0.360356i	$-0.882655\pi$
$509$	−9.38432	+	11.1838i	−0.415953	+	0.495713i	0.516863	+	0.856068i	$0.327100\pi$
$510$		0			0
$511$	1.77377	−	4.87339i	0.0784669	−	0.215586i
$512$		0			0
$513$	3.22570	+	21.5255i	0.142418	+	0.950376i
$514$		0			0
$515$	−52.1624	−	18.9856i	−2.29855	−	0.836603i
$516$		0			0
$517$	4.75300	+	3.98824i	0.209037	+	0.175402i
$518$		0			0
$519$	−0.354189	+	0.228617i	−0.0155472	+	0.0100352i
$520$		0			0
$521$	−30.1782	+	17.4234i	−1.32213	+	0.763334i	−0.984069	−	0.177790i	$-0.943105\pi$
$521$	−30.1782	+	17.4234i	−1.32213	+	0.763334i	−0.338064	+	0.941123i	$0.609772\pi$
$522$		0			0
$523$	24.2393	+	13.9946i	1.05991	+	0.611940i	0.925408	−	0.378973i	$-0.123723\pi$
$523$	24.2393	+	13.9946i	1.05991	+	0.611940i	0.134504	+	0.990913i	$0.457056\pi$
$524$		0			0
$525$	−30.4114	−	32.7944i	−1.32726	−	1.43127i
$526$		0			0
$527$	8.10230	−	2.94900i	0.352942	−	0.128460i
$528$		0			0
$529$	4.66372	+	26.4493i	0.202770	+	1.14997i
$530$		0			0
$531$	−17.7342	−	24.6964i	−0.769600	−	1.07173i
$532$		0			0
$533$	10.0176	+	11.9385i	0.433911	+	0.517115i
$534$		0			0
$535$	38.3722	+	6.76605i	1.65897	+	0.292522i
$536$		0			0
$537$	0.160717	−	1.27954i	0.00693544	−	0.0552164i
$538$		0			0
$539$	5.59584			0.241030
$540$		0			0
$541$	8.19075			0.352148			0.176074	−	0.984377i	$-0.443660\pi$
$541$	8.19075			0.352148			0.176074	+	0.984377i	$0.443660\pi$
$542$		0			0
$543$	24.3872	+	18.4835i	1.04655	+	0.793201i
$544$		0			0
$545$	−52.2934	−	9.22073i	−2.24000	−	0.394973i
$546$		0			0
$547$	12.5634	+	14.9725i	0.537174	+	0.640179i	0.964552	−	0.263894i	$-0.0850071\pi$
$547$	12.5634	+	14.9725i	0.537174	+	0.640179i	−0.427378	+	0.904073i	$0.640563\pi$
$548$		0			0
$549$	0.221946	−	2.93926i	0.00947241	−	0.125445i
$550$		0			0
$551$	−6.39620	−	36.2747i	−0.272487	−	1.54535i
$552$		0			0
$553$	32.6739	−	11.8923i	1.38944	−	0.505713i
$554$		0			0
$555$	3.75596	−	12.1643i	0.159432	−	0.516345i
$556$		0			0
$557$	19.6096	+	11.3216i	0.830885	+	0.479712i	0.854156	−	0.520018i	$-0.174075\pi$
$557$	19.6096	+	11.3216i	0.830885	+	0.479712i	−0.0232707	+	0.999729i	$0.507408\pi$
$558$		0			0
$559$	−29.4169	+	16.9839i	−1.24420	+	0.718341i
$560$		0			0
$561$	−0.270754	−	5.45618i	−0.0114312	−	0.230360i
$562$		0			0
$563$	−27.9805	−	23.4784i	−1.17924	−	0.989498i	−0.999984	−	0.00569511i	$-0.998187\pi$
$563$	−27.9805	−	23.4784i	−1.17924	−	0.989498i	−0.179254	−	0.983803i	$-0.557368\pi$
$564$		0			0
$565$	−25.8932	−	9.42434i	−1.08933	−	0.396485i
$566$		0			0
$567$	−13.3400	+	11.7457i	−0.560226	+	0.493272i
$568$		0			0
$569$	−3.87353	+	10.6424i	−0.162387	+	0.446155i	−0.994024	−	0.109166i	$-0.965182\pi$
$569$	−3.87353	+	10.6424i	−0.162387	+	0.446155i	0.831637	+	0.555320i	$0.187404\pi$
$570$		0			0
$571$	−12.9162	+	15.3929i	−0.540525	+	0.644172i	−0.965305	−	0.261124i	$-0.915907\pi$
$571$	−12.9162	+	15.3929i	−0.540525	+	0.644172i	0.424781	+	0.905296i	$0.360351\pi$
$572$		0			0
$573$	16.9474	−	0.840987i	0.707989	−	0.0351328i
$574$		0			0
$575$	−46.1616	−	79.9543i	−1.92507	−	3.33433i
$576$		0			0
$577$	0.972478	−	1.68438i	0.0404848	−	0.0701217i	−0.845073	−	0.534651i	$-0.820443\pi$
$577$	0.972478	−	1.68438i	0.0404848	−	0.0701217i	0.885558	+	0.464529i	$0.153776\pi$
$578$		0			0
$579$	−14.1816	−	4.37885i	−0.589367	−	0.181979i
$580$		0			0
$581$	2.48618	+	6.83073i	0.103144	+	0.283387i
$582$		0			0
$583$	−0.909934	+	0.160446i	−0.0376856	+	0.00664499i
$584$		0			0
$585$	−24.2373	+	35.5063i	−1.00209	+	1.46801i
$586$		0			0
$587$	31.3602	−	26.3143i	1.29437	−	1.08611i	0.303284	−	0.952900i	$-0.401917\pi$
$587$	31.3602	−	26.3143i	1.29437	−	1.08611i	0.991088	−	0.133207i	$-0.0425276\pi$
$588$		0			0
$589$	3.58968	−	20.3581i	0.147910	−	0.838840i
$590$		0			0
$591$	1.39237	−	1.83710i	0.0572745	−	0.0755683i
$592$		0			0
$593$		−	33.8316i		−	1.38930i	−0.719349	−	0.694649i	$-0.755560\pi$
$593$		−	33.8316i		−	1.38930i	0.719349	−	0.694649i	$-0.244440\pi$
$594$		0			0
$595$			14.6695i			0.601392i
$596$		0			0
$597$	28.3343	+	3.55892i	1.15965	+	0.145657i
$598$		0			0
$599$	−5.18292	+	29.3938i	−0.211768	+	1.20100i	0.674659	+	0.738130i	$0.264291\pi$
$599$	−5.18292	+	29.3938i	−0.211768	+	1.20100i	−0.886427	+	0.462868i	$0.846820\pi$
$600$		0			0
$601$	10.6280	−	8.91796i	0.433525	−	0.363771i	−0.399755	−	0.916622i	$-0.630905\pi$
$601$	10.6280	−	8.91796i	0.433525	−	0.363771i	0.833280	+	0.552851i	$0.186460\pi$
$602$		0			0
$603$	32.8312	+	14.8365i	1.33699	+	0.604187i
$604$		0			0
$605$	32.4115	−	5.71502i	1.31772	−	0.232349i
$606$		0			0
$607$	−6.30592	−	17.3254i	−0.255949	−	0.703215i	−0.999407	−	0.0344323i	$-0.989038\pi$
$607$	−6.30592	−	17.3254i	−0.255949	−	0.703215i	0.743458	−	0.668783i	$-0.233185\pi$
$608$		0			0
$609$	22.0552	−	20.4526i	0.893720	−	0.828779i
$610$		0			0
$611$	−5.79240	+	10.0327i	−0.234336	+	0.405881i
$612$		0			0
$613$	13.0815	+	22.6579i	0.528358	+	0.915143i	0.999453	+	0.0330609i	$0.0105255\pi$
$613$	13.0815	+	22.6579i	0.528358	+	0.915143i	−0.471095	+	0.882082i	$0.656141\pi$
$614$		0			0
$615$	−18.4645	−	28.6065i	−0.744562	−	1.15353i
$616$		0			0
$617$	−12.3160	+	14.6776i	−0.495823	+	0.590898i	−0.954688	−	0.297607i	$-0.903811\pi$
$617$	−12.3160	+	14.6776i	−0.495823	+	0.590898i	0.458866	+	0.888506i	$0.348256\pi$
$618$		0			0
$619$	−6.02766	+	16.5608i	−0.242272	+	0.665637i	0.757644	+	0.652668i	$0.226350\pi$
$619$	−6.02766	+	16.5608i	−0.242272	+	0.665637i	−0.999916	+	0.0129686i	$0.995872\pi$
$620$		0			0
$621$	−32.2368	+	17.5196i	−1.29362	+	0.703038i
$622$		0			0
$623$	13.8591	+	5.04430i	0.555253	+	0.202096i
$624$		0			0
$625$	61.7309	+	51.7984i	2.46924	+	2.07194i
$626$		0			0
$627$	−11.6533	−	5.97849i	−0.465389	−	0.238758i
$628$		0			0
$629$	−2.61590	+	1.51029i	−0.104303	+	0.0602192i
$630$		0			0
$631$	−18.9375	−	10.9336i	−0.753892	−	0.435260i	0.0732067	−	0.997317i	$-0.476677\pi$
$631$	−18.9375	−	10.9336i	−0.753892	−	0.435260i	−0.827098	+	0.562057i	$0.810010\pi$
$632$		0			0
$633$	20.2527	−	4.61650i	0.804973	−	0.183489i
$634$		0			0
$635$	40.0123	−	14.5633i	1.58784	−	0.577926i
$636$		0			0
$637$	1.81431	+	10.2894i	0.0718855	+	0.407683i
$638$		0			0
$639$	1.67560	+	5.96842i	0.0662856	+	0.236107i
$640$		0			0
$641$	8.37132	+	9.97655i	0.330647	+	0.394050i	0.905597	−	0.424138i	$-0.139423\pi$
$641$	8.37132	+	9.97655i	0.330647	+	0.394050i	−0.574950	+	0.818188i	$0.694979\pi$
$642$		0			0
$643$	−20.5512	−	3.62373i	−0.810461	−	0.142906i	−0.246964	−	0.969025i	$-0.579433\pi$
$643$	−20.5512	−	3.62373i	−0.810461	−	0.142906i	−0.563497	+	0.826118i	$0.690544\pi$
$644$		0			0
$645$	68.3909	−	28.8063i	2.69289	−	1.13425i
$646$		0			0
$647$	−20.0883			−0.789751			−0.394875	−	0.918735i	$-0.629212\pi$
$647$	−20.0883			−0.789751			−0.394875	+	0.918735i	$0.629212\pi$
$648$		0			0
$649$	18.2954			0.718159
$650$		0			0
$651$	15.5572	−	6.55270i	0.609734	−	0.256820i
$652$		0			0
$653$	7.40965	+	1.30652i	0.289962	+	0.0511281i	0.316737	−	0.948513i	$-0.397413\pi$
$653$	7.40965	+	1.30652i	0.289962	+	0.0511281i	−0.0267752	+	0.999641i	$0.508524\pi$
$654$		0			0
$655$	31.3829	+	37.4007i	1.22623	+	1.46137i
$656$		0			0
$657$	7.63342	+	1.94832i	0.297808	+	0.0760113i
$658$		0			0
$659$	−8.07319	−	45.7853i	−0.314487	−	1.78354i	−0.575083	−	0.818095i	$-0.695030\pi$
$659$	−8.07319	−	45.7853i	−0.314487	−	1.78354i	0.260597	−	0.965448i	$-0.416081\pi$
$660$		0			0
$661$	37.5470	−	13.6660i	1.46041	−	0.531546i	0.514932	−	0.857231i	$-0.327817\pi$
$661$	37.5470	−	13.6660i	1.46041	−	0.531546i	0.945478	+	0.325685i	$0.105595\pi$
$662$		0			0
$663$	9.94486	−	2.26688i	0.386227	−	0.0880383i
$664$		0			0
$665$	30.4586	+	17.5853i	1.18113	+	0.681927i
$666$		0			0
$667$	53.7715	−	31.0450i	2.08204	−	1.20207i
$668$		0			0
$669$	14.6173	+	7.49911i	0.565138	+	0.289932i
$670$		0			0
$671$	1.35874	+	1.14012i	0.0524535	+	0.0440137i
$672$		0			0
$673$	−23.8306	−	8.67365i	−0.918604	−	0.334345i	−0.160921	−	0.986967i	$-0.551446\pi$
$673$	−23.8306	−	8.67365i	−0.918604	−	0.334345i	−0.757683	+	0.652623i	$0.773669\pi$
$674$		0			0
$675$	44.9987	−	50.9022i	1.73200	−	1.95923i
$676$		0			0
$677$	5.71041	−	15.6892i	0.219469	−	0.602986i	−0.780279	−	0.625431i	$-0.784923\pi$
$677$	5.71041	−	15.6892i	0.219469	−	0.602986i	0.999748	+	0.0224457i	$0.00714528\pi$
$678$		0			0
$679$	−1.83315	+	2.18466i	−0.0703497	+	0.0838395i
$680$		0			0
$681$	−7.55136	−	11.6991i	−0.289369	−	0.448310i
$682$		0			0
$683$	2.39233	+	4.14363i	0.0915398	+	0.158552i	0.908159	−	0.418625i	$-0.137488\pi$
$683$	2.39233	+	4.14363i	0.0915398	+	0.158552i	−0.816619	+	0.577176i	$0.804154\pi$
$684$		0			0
$685$	7.06576	−	12.2383i	0.269969	−	0.467600i
$686$		0			0
$687$	12.5307	−	11.6202i	0.478076	−	0.443337i
$688$		0			0
$689$	−0.590045	−	1.62114i	−0.0224789	−	0.0617604i
$690$		0			0
$691$	−46.6062	+	8.21794i	−1.77298	+	0.312625i	−0.962123	−	0.272614i	$-0.912112\pi$
$691$	−46.6062	+	8.21794i	−1.77298	+	0.312625i	−0.810861	+	0.585239i	$0.801001\pi$
$692$		0			0
$693$	−1.05887	−	10.6428i	−0.0402231	−	0.404287i
$694$		0			0
$695$	−31.7944	+	26.6787i	−1.20603	+	1.01198i
$696$		0			0
$697$	−1.40279	+	7.95562i	−0.0531345	+	0.301340i
$698$		0			0
$699$	34.7477	+	4.36447i	1.31428	+	0.165079i
$700$		0			0
$701$		−	1.98736i		−	0.0750617i	−0.999295	−	0.0375308i	$-0.988051\pi$
$701$		−	1.98736i		−	0.0750617i	0.999295	−	0.0375308i	$-0.0119492\pi$
$702$		0			0
$703$			7.24191i			0.273134i
$704$		0			0
$705$	15.2877	−	20.1707i	0.575770	−	0.759674i
$706$		0			0
$707$	−2.52927	+	14.3442i	−0.0951231	+	0.539470i
$708$		0			0
$709$	−32.0486	+	26.8920i	−1.20361	+	1.00995i	−0.204092	+	0.978952i	$0.565424\pi$
$709$	−32.0486	+	26.8920i	−1.20361	+	1.00995i	−0.999519	+	0.0309977i	$0.990132\pi$
$710$		0			0
$711$	22.8904	+	47.6016i	0.858459	+	1.78520i
$712$		0			0
$713$	34.3168	−	6.05098i	1.28517	−	0.226611i
$714$		0			0
$715$	−8.84768	−	24.3088i	−0.330884	−	0.909097i
$716$		0			0
$717$	−45.3962	−	14.0170i	−1.69535	−	0.523475i
$718$		0			0
$719$	−10.7447	+	18.6104i	−0.400710	+	0.694049i	−0.993812	−	0.111078i	$-0.964570\pi$
$719$	−10.7447	+	18.6104i	−0.400710	+	0.694049i	0.593102	+	0.805127i	$0.297903\pi$
$720$		0			0
$721$	12.8927	+	22.3308i	0.480149	+	0.831642i
$722$		0			0
$723$	14.4313	−	0.716127i	0.536705	−	0.0266330i
$724$		0			0
$725$	−73.9047	+	88.0762i	−2.74475	+	3.27107i
$726$		0			0
$727$	−2.78558	+	7.65333i	−0.103312	+	0.283846i	−0.980569	−	0.196174i	$-0.937148\pi$
$727$	−2.78558	+	7.65333i	−0.103312	+	0.283846i	0.877258	+	0.480020i	$0.159371\pi$
$728$		0			0
$729$	−19.7611	−	18.3984i	−0.731892	−	0.681421i
$730$		0			0
$731$	−16.5454	−	6.02205i	−0.611955	−	0.222733i
$732$		0			0
$733$	31.7728	+	26.6606i	1.17356	+	0.984731i	1.00000		9.33087e-5i	$-2.97011e-5\pi$
$733$	31.7728	+	26.6606i	1.17356	+	0.984731i	0.173556	+	0.984824i	$0.444474\pi$
$734$		0			0
$735$	−1.13133	−	22.7983i	−0.0417296	−	0.840928i
$736$		0			0
$737$	−18.7750	+	10.8397i	−0.691585	+	0.399287i
$738$		0			0
$739$	−15.6244	−	9.02075i	−0.574753	−	0.331834i	0.184293	−	0.982871i	$-0.441001\pi$
$739$	−15.6244	−	9.02075i	−0.574753	−	0.331834i	−0.759045	+	0.651038i	$0.774334\pi$
$740$		0			0
$741$	7.21476	−	23.3661i	0.265041	−	0.858376i
$742$		0			0
$743$	−28.4353	+	10.3496i	−1.04319	+	0.379690i	−0.806088	−	0.591795i	$-0.798419\pi$
$743$	−28.4353	+	10.3496i	−1.04319	+	0.379690i	−0.237101	+	0.971485i	$0.576197\pi$
$744$		0			0
$745$	−15.0972	−	85.6206i	−0.553119	−	3.13689i
$746$		0			0
$747$	−9.95149	+	4.78543i	−0.364106	+	0.175090i
$748$		0			0
$749$	−11.6341	−	13.8650i	−0.425102	−	0.506617i
$750$		0			0
$751$	8.07225	+	1.42336i	0.294561	+	0.0519390i	0.318976	−	0.947763i	$-0.396661\pi$
$751$	8.07225	+	1.42336i	0.294561	+	0.0519390i	−0.0244149	+	0.999702i	$0.507772\pi$
$752$		0			0
$753$	−27.6253	−	20.9377i	−1.00672	−	0.763012i
$754$		0			0
$755$	44.9851			1.63718
$756$		0			0
$757$	12.4321			0.451852			0.225926	−	0.974144i	$-0.427459\pi$
$757$	12.4321			0.451852			0.225926	+	0.974144i	$0.427459\pi$
$758$		0			0
$759$	2.75145	−	21.9057i	0.0998715	−	0.795126i
$760$		0			0
$761$	32.3875	+	5.71079i	1.17405	+	0.207016i	0.726449	−	0.687220i	$-0.241169\pi$
$761$	32.3875	+	5.71079i	1.17405	+	0.207016i	0.447596	+	0.894236i	$0.352280\pi$
$762$		0			0
$763$	15.8549	+	18.8952i	0.573987	+	0.684051i
$764$		0			0
$765$	−22.1746	+	2.20618i	−0.801723	+	0.0797647i
$766$		0			0
$767$	5.93182	+	33.6410i	0.214186	+	1.21471i
$768$		0			0
$769$	−15.0019	+	5.46024i	−0.540981	+	0.196901i	−0.598035	−	0.801470i	$-0.704052\pi$
$769$	−15.0019	+	5.46024i	−0.540981	+	0.196901i	0.0570536	+	0.998371i	$0.481829\pi$
$770$		0			0
$771$	2.64504	+	2.85230i	0.0952590	+	0.102723i
$772$		0			0
$773$	−31.6586	−	18.2781i	−1.13868	−	0.657417i	−0.192576	−	0.981282i	$-0.561684\pi$
$773$	−31.6586	−	18.2781i	−1.13868	−	0.657417i	−0.946103	+	0.323865i	$0.895018\pi$
$774$		0			0
$775$	−55.8816	+	32.2632i	−2.00733	+	1.15893i
$776$		0			0
$777$	−4.96861	+	3.20707i	−0.178248	+	0.115053i
$778$		0			0
$779$	14.8368	+	12.4495i	0.531582	+	0.446050i
$780$		0			0
$781$	−3.50533	−	1.27584i	−0.125431	−	0.0456530i
$782$		0			0
$783$	34.2332	+	30.2629i	1.22339	+	1.08151i
$784$		0			0
$785$	31.5640	−	86.7215i	1.12657	−	3.09522i
$786$		0			0
$787$	30.2330	−	36.0303i	1.07769	−	1.28434i	0.121184	−	0.992630i	$-0.461331\pi$
$787$	30.2330	−	36.0303i	1.07769	−	1.28434i	0.956506	−	0.291712i	$-0.0942248\pi$
$788$		0			0
$789$	10.0596	−	19.6082i	0.358131	−	0.698072i
$790$		0			0
$791$	6.39987	+	11.0849i	0.227553	+	0.394134i
$792$		0			0
$793$	−1.65587	+	2.86806i	−0.0588018	+	0.101848i
$794$		0			0
$795$	0.837644	+	3.67477i	0.0297082	+	0.130331i
$796$		0			0
$797$	−10.2658	−	28.2049i	−0.363632	−	0.999070i	−0.977735	−	0.209844i	$-0.932704\pi$
$797$	−10.2658	−	28.2049i	−0.363632	−	0.999070i	0.614103	−	0.789226i	$-0.289518\pi$
$798$		0			0
$799$	−5.91379	+	1.04276i	−0.209215	+	0.0368902i
$800$		0			0
$801$	−5.54070	+	21.7081i	−0.195771	+	0.767020i
$802$		0			0
$803$	−3.63151	+	3.04720i	−0.128153	+	0.107533i
$804$		0			0
$805$	−10.2948	+	58.3848i	−0.362845	+	2.05779i
$806$		0			0
$807$	−9.36939	−	22.2445i	−0.329818	−	0.783043i
$808$		0			0
$809$			29.1407i			1.02453i	0.858827	+	0.512266i	$0.171194\pi$
$809$			29.1407i			1.02453i	−0.858827	+	0.512266i	$0.828806\pi$
$810$		0			0
$811$		−	28.3787i		−	0.996509i	−0.867031	−	0.498255i	$-0.833974\pi$
$811$		−	28.3787i		−	0.996509i	0.867031	−	0.498255i	$-0.166026\pi$
$812$		0			0
$813$	−0.893422	−	2.12113i	−0.0313337	−	0.0743912i
$814$		0			0
$815$	0.813719	−	4.61483i	0.0285033	−	0.161650i
$816$		0			0
$817$	−32.3377	+	27.1346i	−1.13135	+	0.949318i
$818$		0			0
$819$	19.2263	−	5.39767i	0.671822	−	0.188610i
$820$		0			0
$821$	1.65056	−	0.291038i	0.0576049	−	0.0101573i	−0.144771	−	0.989465i	$-0.546245\pi$
$821$	1.65056	−	0.291038i	0.0576049	−	0.0101573i	0.202376	+	0.979308i	$0.435134\pi$
$822$		0			0
$823$	3.27702	+	9.00355i	0.114230	+	0.313844i	0.983612	−	0.180296i	$-0.0577054\pi$
$823$	3.27702	+	9.00355i	0.114230	+	0.313844i	−0.869383	+	0.494140i	$0.835483\pi$
$824$		0			0
$825$	9.08591	+	39.8601i	0.316331	+	1.38775i
$826$		0			0
$827$	−18.3642	+	31.8078i	−0.638587	+	1.10607i	0.347156	+	0.937808i	$0.387148\pi$
$827$	−18.3642	+	31.8078i	−0.638587	+	1.10607i	−0.985743	+	0.168258i	$0.946186\pi$
$828$		0			0
$829$	11.1409	+	19.2966i	0.386940	+	0.670199i	0.992036	−	0.125953i	$-0.0401988\pi$
$829$	11.1409	+	19.2966i	0.386940	+	0.670199i	−0.605097	+	0.796152i	$0.706865\pi$
$830$		0			0
$831$	5.37823	−	10.4833i	0.186569	−	0.363661i
$832$		0			0
$833$	−3.48124	+	4.14878i	−0.120618	+	0.143747i
$834$		0			0
$835$	−15.2405	+	41.8728i	−0.527418	+	1.44907i
$836$		0			0
$837$	12.2448	+	22.5309i	0.423242	+	0.778781i
$838$		0			0
$839$	−40.0188	−	14.5656i	−1.38160	−	0.502862i	−0.458938	−	0.888468i	$-0.651770\pi$
$839$	−40.0188	−	14.5656i	−1.38160	−	0.502862i	−0.922663	+	0.385607i	$0.873992\pi$
$840$		0			0
$841$	−37.0184	−	31.0621i	−1.27650	−	1.07111i
$842$		0			0
$843$	−5.87496	+	3.79209i	−0.202344	+	0.130606i
$844$		0			0
$845$	−6.03509	+	3.48436i	−0.207613	+	0.119866i
$846$		0			0
$847$	−13.2398	−	7.64398i	−0.454924	−	0.262650i
$848$		0			0
$849$	−0.646579	−	0.697243i	−0.0221905	−	0.0239293i
$850$		0			0
$851$	−11.4712	+	4.17518i	−0.393228	+	0.143123i
$852$		0			0
$853$	0.115822	+	0.656862i	0.00396568	+	0.0224905i	0.986726	−	0.162392i	$-0.0519208\pi$
$853$	0.115822	+	0.656862i	0.00396568	+	0.0224905i	−0.982761	+	0.184882i	$0.940810\pi$
$854$		0			0
$855$	−22.0013	+	48.6861i	−0.752428	+	1.66503i
$856$		0			0
$857$	36.4655	+	43.4579i	1.24564	+	1.48449i	0.812275	+	0.583275i	$0.198229\pi$
$857$	36.4655	+	43.4579i	1.24564	+	1.48449i	0.433363	+	0.901219i	$0.357327\pi$
$858$		0			0
$859$	−19.0689	−	3.36237i	−0.650623	−	0.114722i	−0.161411	−	0.986887i	$-0.551605\pi$
$859$	−19.0689	−	3.36237i	−0.650623	−	0.114722i	−0.489212	+	0.872165i	$0.662716\pi$
$860$		0			0
$861$	−1.97107	+	15.6926i	−0.0671737	+	0.534803i
$862$		0			0
$863$	18.1335			0.617273			0.308636	−	0.951180i	$-0.400127\pi$
$863$	18.1335			0.617273			0.308636	+	0.951180i	$0.400127\pi$
$864$		0			0
$865$	−1.03477			−0.0351832
$866$		0			0
$867$	−19.2527	−	14.5920i	−0.653857	−	0.495570i
$868$		0			0
$869$	−31.3007	−	5.51916i	−1.06180	−	0.187225i
$870$		0			0
$871$	−26.0190	−	31.0083i	−0.881621	−	1.05068i
$872$		0			0
$873$	−3.57804	−	2.44244i	−0.121098	−	0.0826642i
$874$		0			0
$875$	−11.7735	−	66.7708i	−0.398017	−	2.25727i
$876$		0			0
$877$	16.6730	−	6.06847i	0.563007	−	0.204918i	−0.0448094	−	0.998996i	$-0.514268\pi$
$877$	16.6730	−	6.06847i	0.563007	−	0.204918i	0.607816	+	0.794078i	$0.292046\pi$
$878$		0			0
$879$	9.36438	−	30.3280i	0.315853	−	1.02294i
$880$		0			0
$881$	−0.421306	−	0.243241i	−0.0141942	−	0.00819500i	0.492886	−	0.870094i	$-0.335942\pi$
$881$	−0.421306	−	0.243241i	−0.0141942	−	0.00819500i	−0.507080	+	0.861899i	$0.669275\pi$
$882$		0			0
$883$	−9.45185	+	5.45703i	−0.318080	+	0.183644i	−0.650536	−	0.759475i	$-0.725456\pi$
$883$	−9.45185	+	5.45703i	−0.318080	+	0.183644i	0.332456	+	0.943119i	$0.392123\pi$
$884$		0			0
$885$	−3.69884	−	74.5383i	−0.124335	−	2.50558i
$886$		0			0
$887$	−2.28856	−	1.92033i	−0.0768422	−	0.0644783i	0.603558	−	0.797319i	$-0.293749\pi$
$887$	−2.28856	−	1.92033i	−0.0768422	−	0.0644783i	−0.680400	+	0.732841i	$0.738194\pi$
$888$		0			0
$889$	−18.5864	−	6.76490i	−0.623368	−	0.226888i
$890$		0			0
$891$	15.9285	−	3.20119i	0.533625	−	0.107244i
$892$		0			0
$893$	−4.92412	+	13.5289i	−0.164780	+	0.452728i
$894$		0			0
$895$	2.03471	−	2.42487i	0.0680128	−	0.0810545i
$896$		0			0
$897$	41.1715	−	2.04307i	1.37468	−	0.0682160i
$898$		0			0
$899$	−21.6979	−	37.5819i	−0.723667	−	1.25343i
$900$		0			0
$901$	0.447126	−	0.774444i	0.0148959	−	0.0258005i
$902$		0			0
$903$	−32.9375	−	10.1701i	−1.09609	−	0.338440i
$904$		0			0
$905$	25.6895	+	70.5814i	0.853949	+	2.34621i
$906$		0			0
$907$	38.1122	−	6.72021i	1.26549	−	0.223141i	0.499684	−	0.866208i	$-0.333449\pi$
$907$	38.1122	−	6.72021i	1.26549	−	0.223141i	0.765810	+	0.643067i	$0.222338\pi$
$908$		0			0
$909$	−22.0632	−	1.66601i	−0.731791	−	0.0552581i
$910$		0			0
$911$	8.14166	−	6.83166i	0.269745	−	0.226343i	−0.497874	−	0.867249i	$-0.665886\pi$
$911$	8.14166	−	6.83166i	0.269745	−	0.226343i	0.767619	+	0.640906i	$0.221441\pi$
$912$		0			0
$913$	1.15382	−	6.54366i	0.0381860	−	0.216563i
$914$		0			0
$915$	4.37031	−	5.76621i	0.144478	−	0.190625i
$916$		0			0
$917$		−	22.6792i		−	0.748933i
$918$		0			0
$919$			48.9343i			1.61420i	0.590418	+	0.807098i	$0.298963\pi$
$919$			48.9343i			1.61420i	−0.590418	+	0.807098i	$0.701037\pi$
$920$		0			0
$921$	−23.8117	−	2.99086i	−0.784621	−	0.0985520i
$922$		0			0
$923$	1.20945	−	6.85914i	0.0398096	−	0.225771i
$924$		0			0
$925$	17.3165	−	14.5303i	0.569363	−	0.477752i
$926$		0			0
$927$	−31.8165	+	22.8471i	−1.04499	+	0.750397i
$928$		0			0
$929$	−5.15541	+	0.909037i	−0.169143	+	0.0298245i	−0.257578	−	0.966257i	$-0.582925\pi$
$929$	−5.15541	+	0.909037i	−0.169143	+	0.0298245i	0.0884350	+	0.996082i	$0.471813\pi$
$930$		0			0
$931$	4.44100	+	12.2015i	0.145548	+	0.399890i
$932$		0			0
$933$	−4.71709	+	4.37433i	−0.154431	+	0.143209i
$934$		0			0
$935$	6.70461	−	11.6127i	0.219264	−	0.379777i
$936$		0			0
$937$	−28.7145	−	49.7349i	−0.938061	−	1.62477i	−0.769082	−	0.639150i	$-0.779286\pi$
$937$	−28.7145	−	49.7349i	−0.938061	−	1.62477i	−0.168979	−	0.985620i	$-0.554047\pi$
$938$		0			0
$939$	21.4362	+	33.2105i	0.699545	+	1.08378i
$940$		0			0
$941$	5.74647	−	6.84838i	0.187330	−	0.223251i	−0.664203	−	0.747552i	$-0.731229\pi$
$941$	5.74647	−	6.84838i	0.187330	−	0.223251i	0.851533	+	0.524301i	$0.175673\pi$
$942$		0			0
$943$	−11.1662	+	30.6790i	−0.363623	+	0.999045i
$944$		0			0
$945$	−43.1463	+	6.46568i	−1.40355	+	0.210328i
$946$		0			0
$947$	50.5054	+	18.3825i	1.64121	+	0.597350i	0.987249	−	0.159182i	$-0.0508856\pi$
$947$	50.5054	+	18.3825i	1.64121	+	0.597350i	0.653957	+	0.756532i	$0.273108\pi$
$948$		0			0
$949$	−6.78051	−	5.68952i	−0.220105	−	0.184690i
$950$		0			0
$951$	26.6669	+	13.6809i	0.864733	+	0.443633i
$952$		0			0
$953$	11.0235	−	6.36443i	0.357087	−	0.206164i	−0.310715	−	0.950503i	$-0.600569\pi$
$953$	11.0235	−	6.36443i	0.357087	−	0.206164i	0.667802	+	0.744339i	$0.267235\pi$
$954$		0			0
$955$	36.0702	+	20.8252i	1.16721	+	0.673887i
$956$		0			0
$957$	−26.8071	+	6.11053i	−0.866550	+	0.197525i
$958$		0			0
$959$	−6.16846	+	2.24514i	−0.199190	+	0.0724992i
$960$		0			0
$961$	1.15395	+	6.54439i	0.0372242	+	0.211109i
$962$		0			0
$963$	19.2088	−	19.6715i	0.618996	−	0.633904i
$964$		0			0
$965$	−23.4179	−	27.9083i	−0.753847	−	0.898400i
$966$		0			0
$967$	−21.8749	−	3.85714i	−0.703450	−	0.124037i	−0.189530	−	0.981875i	$-0.560696\pi$
$967$	−21.8749	−	3.85714i	−0.703450	−	0.124037i	−0.513921	+	0.857838i	$0.671807\pi$
$968$		0			0
$969$	11.6822	−	4.92054i	0.375285	−	0.158070i
$970$		0			0
$971$	−33.9474			−1.08942			−0.544712	−	0.838623i	$-0.683361\pi$
$971$	−33.9474			−1.08942			−0.544712	+	0.838623i	$0.683361\pi$
$972$		0			0
$973$	19.2796			0.618077
$974$		0			0
$975$	−70.3476	+	29.6305i	−2.25293	+	0.948935i
$976$		0			0
$977$	−18.7009	−	3.29747i	−0.598295	−	0.105496i	−0.133705	−	0.991021i	$-0.542687\pi$
$977$	−18.7009	−	3.29747i	−0.598295	−	0.105496i	−0.464590	+	0.885526i	$0.653798\pi$
$978$		0			0
$979$	−8.66571	−	10.3274i	−0.276957	−	0.330065i
$980$		0			0
$981$	−26.1777	+	26.8081i	−0.835788	+	0.855918i
$982$		0			0
$983$	3.33476	+	18.9124i	0.106362	+	0.603210i	0.990667	+	0.136301i	$0.0435215\pi$
$983$	3.33476	+	18.9124i	0.106362	+	0.603210i	−0.884305	+	0.466909i	$0.845367\pi$
$984$		0			0
$985$	5.31695	−	1.93521i	0.169412	−	0.0616610i
$986$		0			0
$987$	−11.4627	+	2.61286i	−0.364862	+	0.0831684i
$988$		0			0
$989$	−61.6248	−	35.5791i	−1.95956	−	1.13135i
$990$		0			0
$991$	34.3164	−	19.8126i	1.09009	−	0.629367i	0.156493	−	0.987679i	$-0.449981\pi$
$991$	34.3164	−	19.8126i	1.09009	−	0.629367i	0.933602	+	0.358312i	$0.116648\pi$
$992$		0			0
$993$	11.1030	+	5.69618i	0.352345	+	0.180763i
$994$		0			0
$995$	53.6965	+	45.0568i	1.70230	+	1.42840i
$996$		0			0
$997$	−13.8784	−	5.05134i	−0.439534	−	0.159977i	0.112768	−	0.993621i	$-0.464028\pi$
$997$	−13.8784	−	5.05134i	−0.439534	−	0.159977i	−0.552302	+	0.833644i	$0.686251\pi$
$998$		0			0
$999$	−5.59507	−	7.02827i	−0.177020	−	0.222365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.c.239.5	yes	36
4.3	odd	2		432.2.be.b.239.2	yes	36
27.20	odd	18		432.2.be.b.47.2	✓	36
108.47	even	18	inner	432.2.be.c.47.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.2	✓	36	27.20	odd	18
432.2.be.b.239.2	yes	36	4.3	odd	2
432.2.be.c.47.5	yes	36	108.47	even	18	inner
432.2.be.c.239.5	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.59623 - 0.672336i) q^{3} +(4.18690 + 0.738263i) q^{5} +(-1.26944 - 1.51285i) q^{7} +(2.09593 - 2.14641i) q^{9} +O(q^{10})\)	\(q+(1.59623 - 0.672336i) q^{3} +(4.18690 + 0.738263i) q^{5} +(-1.26944 - 1.51285i) q^{7} +(2.09593 - 2.14641i) q^{9} +(0.313474 + 1.77780i) q^{11} +(-3.16732 + 1.15281i) q^{13} +(7.17963 - 1.63656i) q^{15} +(-1.51308 - 0.873578i) q^{17} +(-3.62765 + 2.09442i) q^{19} +(-3.04346 - 1.56138i) q^{21} +(-5.40902 - 4.53870i) q^{23} +(12.2866 + 4.47197i) q^{25} +(1.90249 - 4.83534i) q^{27} +(-3.00752 + 8.26311i) q^{29} +(-3.17218 + 3.78046i) q^{31} +(1.69565 + 2.62702i) q^{33} +(-4.19811 - 7.27134i) q^{35} +(0.864428 - 1.49723i) q^{37} +(-4.28071 + 3.96966i) q^{39} +(-1.58140 - 4.34487i) q^{41} +(9.92458 - 1.74997i) q^{43} +(10.3601 - 7.43946i) q^{45} +(2.63291 - 2.20928i) q^{47} +(0.538276 - 3.05271i) q^{49} +(-3.00257 - 0.377137i) q^{51} +0.511832i q^{53} +7.67488i q^{55} +(-4.38242 + 5.78219i) q^{57} +(1.75988 - 9.98076i) q^{59} +(0.752671 - 0.631566i) q^{61} +(-5.90785 - 0.446106i) q^{63} +(-14.1123 + 2.48838i) q^{65} +(4.10742 + 11.2851i) q^{67} +(-11.6856 - 3.60816i) q^{69} +(-1.03319 + 1.78955i) q^{71} +(1.31302 + 2.27422i) q^{73} +(22.6190 - 1.12243i) q^{75} +(2.29161 - 2.73104i) q^{77} +(-6.02177 + 16.5447i) q^{79} +(-0.214158 - 8.99745i) q^{81} +(-3.45879 - 1.25890i) q^{83} +(-5.69019 - 4.77464i) q^{85} +(0.754866 + 15.2119i) q^{87} +(-6.46750 + 3.73401i) q^{89} +(5.76474 + 3.32827i) q^{91} +(-2.52181 + 8.16728i) q^{93} +(-16.7348 + 6.09098i) q^{95} +(-0.250759 - 1.42213i) q^{97} +(4.47290 + 3.05329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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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