LMFDB - Embedded newform 864.2.y.d.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	864.193
Dual form			864.2.y.d.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28924 + 1.15666i) q^{3} +(-0.110022 + 0.623966i) q^{5} +(3.44796 - 2.89318i) q^{7} +(0.324271 - 2.98242i) q^{9} +O(q^{10})$	\(q+(-1.28924 + 1.15666i) q^{3} +(-0.110022 + 0.623966i) q^{5} +(3.44796 - 2.89318i) q^{7} +(0.324271 - 2.98242i) q^{9} +(-0.462638 - 2.62375i) q^{11} +(-5.71553 + 2.08028i) q^{13} +(-0.579873 - 0.931700i) q^{15} +(-1.09167 + 1.89083i) q^{17} +(-2.62496 - 4.54656i) q^{19} +(-1.09881 + 7.71812i) q^{21} +(-6.59026 - 5.52988i) q^{23} +(4.32123 + 1.57280i) q^{25} +(3.03159 + 4.22013i) q^{27} +(-6.06153 - 2.20622i) q^{29} +(1.26288 + 1.05968i) q^{31} +(3.63124 + 2.84753i) q^{33} +(1.42590 + 2.46972i) q^{35} +(4.93871 - 8.55410i) q^{37} +(4.96250 - 9.29291i) q^{39} +(-10.1895 + 3.70867i) q^{41} +(-0.462029 - 2.62030i) q^{43} +(1.82526 + 0.530467i) q^{45} +(5.34642 - 4.48618i) q^{47} +(2.30239 - 13.0575i) q^{49} +(-0.779626 - 3.70043i) q^{51} +6.33028 q^{53} +1.68803 q^{55} +(8.64302 + 2.82541i) q^{57} +(-0.201352 + 1.14193i) q^{59} +(4.45392 - 3.73728i) q^{61} +(-7.51062 - 11.2214i) q^{63} +(-0.669192 - 3.79517i) q^{65} +(2.55051 - 0.928310i) q^{67} +(14.8926 - 0.493357i) q^{69} +(1.10732 - 1.91793i) q^{71} +(-2.16195 - 3.74461i) q^{73} +(-7.39030 + 2.97049i) q^{75} +(-9.18615 - 7.70810i) q^{77} +(-8.45020 - 3.07562i) q^{79} +(-8.78970 - 1.93422i) q^{81} +(10.9300 + 3.97818i) q^{83} +(-1.05971 - 0.889200i) q^{85} +(10.3666 - 4.16680i) q^{87} +(2.27192 + 3.93508i) q^{89} +(-13.6883 + 23.7088i) q^{91} +(-2.85385 + 0.0945413i) q^{93} +(3.12570 - 1.13766i) q^{95} +(0.872500 + 4.94820i) q^{97} +(-7.97516 + 0.528977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.28924	+	1.15666i	−0.744342	+	0.667799i
$3$	−1.28924	+	1.15666i	−0.744342	+	0.667799i
$4$		0			0
$5$	−0.110022	+	0.623966i	−0.0492034	+	0.279046i	−0.999476	−	0.0323735i	$-0.989693\pi$
$5$	−0.110022	+	0.623966i	−0.0492034	+	0.279046i	0.950272	+	0.311420i	$0.100805\pi$
$6$		0			0
$7$	3.44796	−	2.89318i	1.30321	−	1.09352i	0.313624	−	0.949547i	$-0.398457\pi$
$7$	3.44796	−	2.89318i	1.30321	−	1.09352i	0.989582	−	0.143973i	$-0.0459878\pi$
$8$		0			0
$9$	0.324271	−	2.98242i	0.108090	−	0.994141i
$10$		0			0
$11$	−0.462638	−	2.62375i	−0.139491	−	0.791091i	−0.971627	−	0.236520i	$-0.923993\pi$
$11$	−0.462638	−	2.62375i	−0.139491	−	0.791091i	0.832136	−	0.554572i	$-0.187118\pi$
$12$		0			0
$13$	−5.71553	+	2.08028i	−1.58520	+	0.576966i	−0.976327	−	0.216300i	$-0.930601\pi$
$13$	−5.71553	+	2.08028i	−1.58520	+	0.576966i	−0.608875	+	0.793266i	$0.708379\pi$
$14$		0			0
$15$	−0.579873	−	0.931700i	−0.149723	−	0.240564i
$16$		0			0
$17$	−1.09167	+	1.89083i	−0.264769	+	0.458594i	−0.967503	−	0.252859i	$-0.918629\pi$
$17$	−1.09167	+	1.89083i	−0.264769	+	0.458594i	0.702734	+	0.711453i	$0.251962\pi$
$18$		0			0
$19$	−2.62496	−	4.54656i	−0.602206	−	1.04305i	−0.992486	−	0.122356i	$-0.960955\pi$
$19$	−2.62496	−	4.54656i	−0.602206	−	1.04305i	0.390280	−	0.920696i	$-0.372378\pi$
$20$		0			0
$21$	−1.09881	+	7.71812i	−0.239780	+	1.68423i
$22$		0			0
$23$	−6.59026	−	5.52988i	−1.37416	−	1.15306i	−0.971316	−	0.237794i	$-0.923576\pi$
$23$	−6.59026	−	5.52988i	−1.37416	−	1.15306i	−0.402848	−	0.915267i	$-0.631980\pi$
$24$		0			0
$25$	4.32123	+	1.57280i	0.864247	+	0.314560i
$26$		0			0
$27$	3.03159	+	4.22013i	0.583430	+	0.812164i
$28$		0			0
$29$	−6.06153	−	2.20622i	−1.12560	−	0.409684i	−0.288906	−	0.957357i	$-0.593292\pi$
$29$	−6.06153	−	2.20622i	−1.12560	−	0.409684i	−0.836692	+	0.547673i	$0.815514\pi$
$30$		0			0
$31$	1.26288	+	1.05968i	0.226820	+	0.190325i	0.749114	−	0.662441i	$-0.230479\pi$
$31$	1.26288	+	1.05968i	0.226820	+	0.190325i	−0.522294	+	0.852765i	$0.674924\pi$
$32$		0			0
$33$	3.63124	+	2.84753i	0.632118	+	0.495691i
$34$		0			0
$35$	1.42590	+	2.46972i	0.241020	+	0.417460i
$36$		0			0
$37$	4.93871	−	8.55410i	0.811919	−	1.40628i	−0.0996002	−	0.995028i	$-0.531756\pi$
$37$	4.93871	−	8.55410i	0.811919	−	1.40628i	0.911519	−	0.411257i	$-0.134910\pi$
$38$		0			0
$39$	4.96250	−	9.29291i	0.794635	−	1.48806i
$40$		0			0
$41$	−10.1895	+	3.70867i	−1.59133	+	0.579197i	−0.977628	−	0.210340i	$-0.932543\pi$
$41$	−10.1895	+	3.70867i	−1.59133	+	0.579197i	−0.613703	+	0.789537i	$0.710321\pi$
$42$		0			0
$43$	−0.462029	−	2.62030i	−0.0704588	−	0.399592i	−0.999557	−	0.0297588i	$-0.990526\pi$
$43$	−0.462029	−	2.62030i	−0.0704588	−	0.399592i	0.929098	−	0.369833i	$-0.120585\pi$
$44$		0			0
$45$	1.82526	+	0.530467i	0.272093	+	0.0790773i
$46$		0			0
$47$	5.34642	−	4.48618i	0.779856	−	0.654377i	−0.163357	−	0.986567i	$-0.552232\pi$
$47$	5.34642	−	4.48618i	0.779856	−	0.654377i	0.943212	+	0.332190i	$0.107788\pi$
$48$		0			0
$49$	2.30239	−	13.0575i	0.328913	−	1.86536i
$50$		0			0
$51$	−0.779626	−	3.70043i	−0.109169	−	0.518163i
$52$		0			0
$53$	6.33028			0.869530			0.434765	−	0.900544i	$-0.356831\pi$
$53$	6.33028			0.869530			0.434765	+	0.900544i	$0.356831\pi$
$54$		0			0
$55$	1.68803			0.227614
$56$		0			0
$57$	8.64302	+	2.82541i	1.14480	+	0.374235i
$58$		0			0
$59$	−0.201352	+	1.14193i	−0.0262138	+	0.148666i	−0.995105	−	0.0988198i	$-0.968493\pi$
$59$	−0.201352	+	1.14193i	−0.0262138	+	0.148666i	0.968892	+	0.247486i	$0.0796044\pi$
$60$		0			0
$61$	4.45392	−	3.73728i	0.570265	−	0.478509i	−0.311469	−	0.950256i	$-0.600821\pi$
$61$	4.45392	−	3.73728i	0.570265	−	0.478509i	0.881734	+	0.471747i	$0.156376\pi$
$62$		0			0
$63$	−7.51062	−	11.2214i	−0.946249	−	1.41377i
$64$		0			0
$65$	−0.669192	−	3.79517i	−0.0830030	−	0.470733i
$66$		0			0
$67$	2.55051	−	0.928310i	0.311594	−	0.113411i	−0.181489	−	0.983393i	$-0.558092\pi$
$67$	2.55051	−	0.928310i	0.311594	−	0.113411i	0.493084	+	0.869982i	$0.335870\pi$
$68$		0			0
$69$	14.8926	−	0.493357i	1.79286	−	0.0593933i
$70$		0			0
$71$	1.10732	−	1.91793i	0.131414	−	0.227616i	−0.792808	−	0.609472i	$-0.791382\pi$
$71$	1.10732	−	1.91793i	0.131414	−	0.227616i	0.924222	+	0.381856i	$0.124715\pi$
$72$		0			0
$73$	−2.16195	−	3.74461i	−0.253037	−	0.438274i	0.711323	−	0.702865i	$-0.248096\pi$
$73$	−2.16195	−	3.74461i	−0.253037	−	0.438274i	−0.964361	+	0.264591i	$0.914763\pi$
$74$		0			0
$75$	−7.39030	+	2.97049i	−0.853358	+	0.343002i
$76$		0			0
$77$	−9.18615	−	7.70810i	−1.04686	−	0.878419i
$78$		0			0
$79$	−8.45020	−	3.07562i	−0.950722	−	0.346034i	−0.180331	−	0.983606i	$-0.557717\pi$
$79$	−8.45020	−	3.07562i	−0.950722	−	0.346034i	−0.770391	+	0.637572i	$0.779939\pi$
$80$		0			0
$81$	−8.78970	−	1.93422i	−0.976633	−	0.214914i
$82$		0			0
$83$	10.9300	+	3.97818i	1.19972	+	0.436662i	0.863126	−	0.504988i	$-0.168503\pi$
$83$	10.9300	+	3.97818i	1.19972	+	0.436662i	0.336593	+	0.941650i	$0.390725\pi$
$84$		0			0
$85$	−1.05971	−	0.889200i	−0.114941	−	0.0964473i
$86$		0			0
$87$	10.3666	−	4.16680i	1.11142	−	0.446728i
$88$		0			0
$89$	2.27192	+	3.93508i	0.240823	+	0.417118i	0.960949	−	0.276725i	$-0.0892492\pi$
$89$	2.27192	+	3.93508i	0.240823	+	0.417118i	−0.720126	+	0.693844i	$0.755916\pi$
$90$		0			0
$91$	−13.6883	+	23.7088i	−1.43492	+	2.48536i
$92$		0			0
$93$	−2.85385	+	0.0945413i	−0.295930	+	0.00980348i
$94$		0			0
$95$	3.12570	−	1.13766i	0.320690	−	0.116722i
$96$		0			0
$97$	0.872500	+	4.94820i	0.0885890	+	0.502413i	0.996524	+	0.0833028i	$0.0265469\pi$
$97$	0.872500	+	4.94820i	0.0885890	+	0.502413i	−0.907935	+	0.419110i	$0.862342\pi$
$98$		0			0
$99$	−7.97516	+	0.528977i	−0.801534	+	0.0531642i
$100$		0			0
$101$	−1.69994	+	1.42642i	−0.169150	+	0.141934i	−0.723433	−	0.690395i	$-0.757437\pi$
$101$	−1.69994	+	1.42642i	−0.169150	+	0.141934i	0.554283	+	0.832328i	$0.312992\pi$
$102$		0			0
$103$	0.617362	−	3.50124i	0.0608305	−	0.344987i	−0.939168	−	0.343457i	$-0.888402\pi$
$103$	0.617362	−	3.50124i	0.0608305	−	0.344987i	0.999999	−	0.00152973i	$-0.000486927\pi$
$104$		0			0
$105$	−4.69495	−	1.53479i	−0.458181	−	0.149780i
$106$		0			0
$107$	−13.0962			−1.26606			−0.633030	−	0.774127i	$-0.718189\pi$
$107$	−13.0962			−1.26606			−0.633030	+	0.774127i	$0.718189\pi$
$108$		0			0
$109$	2.27944			0.218331			0.109166	−	0.994024i	$-0.465182\pi$
$109$	2.27944			0.218331			0.109166	+	0.994024i	$0.465182\pi$
$110$		0			0
$111$	3.52702	+	16.7407i	0.334770	+	1.58896i
$112$		0			0
$113$	−2.96968	+	16.8419i	−0.279364	+	1.58435i	0.445384	+	0.895340i	$0.353067\pi$
$113$	−2.96968	+	16.8419i	−0.279364	+	1.58435i	−0.724748	+	0.689014i	$0.758044\pi$
$114$		0			0
$115$	4.17554	−	3.50369i	0.389371	−	0.326721i
$116$		0			0
$117$	4.35090	+	17.7207i	0.402241	+	1.63828i
$118$		0			0
$119$	1.70648	+	9.67792i	0.156433	+	0.887173i
$120$		0			0
$121$	3.66657	−	1.33452i	0.333325	−	0.121320i
$122$		0			0
$123$	8.84700	−	16.5671i	0.797708	−	1.49381i
$124$		0			0
$125$	−3.04079	+	5.26680i	−0.271976	+	0.471077i
$126$		0			0
$127$	−5.28823	−	9.15947i	−0.469254	−	0.812772i	0.530128	−	0.847918i	$-0.322144\pi$
$127$	−5.28823	−	9.15947i	−0.469254	−	0.812772i	−0.999382	+	0.0351456i	$0.988811\pi$
$128$		0			0
$129$	3.62646	+	2.84378i	0.319292	+	0.250381i
$130$		0			0
$131$	1.07672	+	0.903473i	0.0940733	+	0.0789368i	0.688611	−	0.725131i	$-0.258221\pi$
$131$	1.07672	+	0.903473i	0.0940733	+	0.0789368i	−0.594538	+	0.804067i	$0.702665\pi$
$132$		0			0
$133$	−22.2048	−	8.08187i	−1.92540	−	0.700787i
$134$		0			0
$135$	−2.96676	+	1.42730i	−0.255338	+	0.122843i
$136$		0			0
$137$	−4.22143	−	1.53648i	−0.360661	−	0.131270i	0.155333	−	0.987862i	$-0.450355\pi$
$137$	−4.22143	−	1.53648i	−0.360661	−	0.131270i	−0.515994	+	0.856592i	$0.672577\pi$
$138$		0			0
$139$	5.66621	+	4.75452i	0.480602	+	0.403273i	0.850644	−	0.525742i	$-0.176212\pi$
$139$	5.66621	+	4.75452i	0.480602	+	0.403273i	−0.370042	+	0.929015i	$0.620657\pi$
$140$		0			0
$141$	−1.70382	+	11.9678i	−0.143488	+	1.00787i
$142$		0			0
$143$	8.10237	+	14.0337i	0.677554	+	1.17356i
$144$		0			0
$145$	2.04351	−	3.53946i	0.169704	−	0.293936i
$146$		0			0
$147$	12.1348	+	19.4973i	1.00086	+	1.60811i
$148$		0			0
$149$	10.8130	−	3.93562i	0.885838	−	0.322419i	0.141274	−	0.989970i	$-0.454880\pi$
$149$	10.8130	−	3.93562i	0.885838	−	0.322419i	0.744563	+	0.667552i	$0.232658\pi$
$150$		0			0
$151$	−0.550130	−	3.11994i	−0.0447690	−	0.253897i	0.954207	−	0.299148i	$-0.0967025\pi$
$151$	−0.550130	−	3.11994i	−0.0447690	−	0.253897i	−0.998976	+	0.0452506i	$0.985591\pi$
$152$		0			0
$153$	5.28526	+	3.86897i	0.427288	+	0.312788i
$154$		0			0
$155$	−0.800151	+	0.671407i	−0.0642697	+	0.0539287i
$156$		0			0
$157$	0.773720	−	4.38798i	0.0617496	−	0.350199i	−0.938242	−	0.345981i	$-0.887546\pi$
$157$	0.773720	−	4.38798i	0.0617496	−	0.350199i	0.999991	−	0.00421821i	$-0.00134270\pi$
$158$		0			0
$159$	−8.16124	+	7.32198i	−0.647228	+	0.580671i
$160$		0			0
$161$	−38.7219			−3.05171
$162$		0			0
$163$	14.7936			1.15873			0.579363	−	0.815070i	$-0.303302\pi$
$163$	14.7936			1.15873			0.579363	+	0.815070i	$0.303302\pi$
$164$		0			0
$165$	−2.17628	+	1.95248i	−0.169423	+	0.152001i
$166$		0			0
$167$	2.43795	−	13.8263i	0.188654	−	1.06991i	−0.732516	−	0.680750i	$-0.761654\pi$
$167$	2.43795	−	13.8263i	0.188654	−	1.06991i	0.921170	−	0.389160i	$-0.127235\pi$
$168$		0			0
$169$	18.3811	−	15.4236i	1.41393	−	1.18643i
$170$		0			0
$171$	−14.4110	+	6.35442i	−1.10203	+	0.485934i
$172$		0			0
$173$	0.758809	+	4.30342i	0.0576912	+	0.327183i	0.999971	−	0.00764414i	$-0.00243323\pi$
$173$	0.758809	+	4.30342i	0.0576912	+	0.327183i	−0.942280	+	0.334827i	$0.891322\pi$
$174$		0			0
$175$	19.4498	−	7.07916i	1.47027	−	0.535134i
$176$		0			0
$177$	−1.06123	−	1.70511i	−0.0797669	−	0.128164i
$178$		0			0
$179$	−5.60157	+	9.70220i	−0.418681	+	0.725177i	−0.995807	−	0.0914784i	$-0.970841\pi$
$179$	−5.60157	+	9.70220i	−0.418681	+	0.725177i	0.577126	+	0.816655i	$0.304174\pi$
$180$		0			0
$181$	−6.28190	−	10.8806i	−0.466930	−	0.808746i	0.532357	−	0.846520i	$-0.321307\pi$
$181$	−6.28190	−	10.8806i	−0.466930	−	0.808746i	−0.999286	+	0.0377744i	$0.987973\pi$
$182$		0			0
$183$	−1.41939	+	9.96991i	−0.104925	+	0.736997i
$184$		0			0
$185$	4.79410	+	4.02273i	0.352469	+	0.295757i
$186$		0			0
$187$	5.46612	+	1.98951i	0.399723	+	0.145487i
$188$		0			0
$189$	22.6624	+	5.77988i	1.64845	+	0.420424i
$190$		0			0
$191$	−8.13921	−	2.96243i	−0.588932	−	0.214354i	0.0303275	−	0.999540i	$-0.490345\pi$
$191$	−8.13921	−	2.96243i	−0.588932	−	0.214354i	−0.619260	+	0.785186i	$0.712567\pi$
$192$		0			0
$193$	13.7290	+	11.5200i	0.988234	+	0.829227i	0.985311	−	0.170769i	$-0.0546250\pi$
$193$	13.7290	+	11.5200i	0.988234	+	0.829227i	0.00292332	+	0.999996i	$0.499069\pi$
$194$		0			0
$195$	5.25248	+	4.11886i	0.376138	+	0.294957i
$196$		0			0
$197$	−8.91610	−	15.4431i	−0.635246	−	1.10028i	−0.986463	−	0.163984i	$-0.947565\pi$
$197$	−8.91610	−	15.4431i	−0.635246	−	1.10028i	0.351217	−	0.936294i	$-0.385768\pi$
$198$		0			0
$199$	−10.6608	+	18.4651i	−0.755725	+	1.30895i	0.189288	+	0.981922i	$0.439382\pi$
$199$	−10.6608	+	18.4651i	−0.755725	+	1.30895i	−0.945013	+	0.327032i	$0.893951\pi$
$200$		0			0
$201$	−2.21448	+	4.14689i	−0.156197	+	0.292499i
$202$		0			0
$203$	−27.2829	+	9.93017i	−1.91489	+	0.696961i
$204$		0			0
$205$	−1.19302	−	6.76593i	−0.0833239	−	0.472553i
$206$		0			0
$207$	−18.6295	+	17.8618i	−1.29484	+	1.24148i
$208$		0			0
$209$	−10.7146	+	8.99065i	−0.741147	+	0.621896i
$210$		0			0
$211$	−2.80886	+	15.9298i	−0.193370	+	1.09666i	0.721351	+	0.692570i	$0.243522\pi$
$211$	−2.80886	+	15.9298i	−0.193370	+	1.09666i	−0.914721	+	0.404086i	$0.867590\pi$
$212$		0			0
$213$	0.790798	+	3.75346i	0.0541846	+	0.257183i
$214$		0			0
$215$	1.68581			0.114971
$216$		0			0
$217$	7.42021			0.503717
$218$		0			0
$219$	7.11852	+	2.32705i	0.481025	+	0.157248i
$220$		0			0
$221$	2.30602	−	13.0781i	0.155120	−	0.879727i
$222$		0			0
$223$	−7.39264	+	6.20316i	−0.495047	+	0.415394i	−0.855831	−	0.517255i	$-0.826954\pi$
$223$	−7.39264	+	6.20316i	−0.495047	+	0.415394i	0.360784	+	0.932650i	$0.382509\pi$
$224$		0			0
$225$	6.09201	−	12.3777i	0.406134	−	0.825182i
$226$		0			0
$227$	−1.54326	−	8.75226i	−0.102430	−	0.580908i	−0.992216	−	0.124530i	$-0.960258\pi$
$227$	−1.54326	−	8.75226i	−0.102430	−	0.580908i	0.889786	−	0.456378i	$-0.150853\pi$
$228$		0			0
$229$	7.99582	−	2.91024i	0.528379	−	0.192314i	−0.0640355	−	0.997948i	$-0.520397\pi$
$229$	7.99582	−	2.91024i	0.528379	−	0.192314i	0.592414	+	0.805633i	$0.298175\pi$
$230$		0			0
$231$	20.7588	−	0.687690i	1.36583	−	0.0452467i
$232$		0			0
$233$	2.59160	−	4.48878i	0.169781	−	0.294070i	−0.768562	−	0.639776i	$-0.779027\pi$
$233$	2.59160	−	4.48878i	0.169781	−	0.294070i	0.938343	+	0.345706i	$0.112361\pi$
$234$		0			0
$235$	2.21100	+	3.82957i	0.144230	+	0.249813i
$236$		0			0
$237$	14.4518	−	5.80881i	0.938744	−	0.377323i
$238$		0			0
$239$	−8.34829	−	7.00505i	−0.540006	−	0.453119i	0.331534	−	0.943443i	$-0.392434\pi$
$239$	−8.34829	−	7.00505i	−0.540006	−	0.453119i	−0.871540	+	0.490324i	$0.836878\pi$
$240$		0			0
$241$	−6.73478	−	2.45126i	−0.433825	−	0.157900i	0.115871	−	0.993264i	$-0.463034\pi$
$241$	−6.73478	−	2.45126i	−0.433825	−	0.157900i	−0.549696	+	0.835365i	$0.685256\pi$
$242$		0			0
$243$	13.5693	−	7.67302i	0.870468	−	0.492225i
$244$		0			0
$245$	7.89412	+	2.87323i	0.504337	+	0.183564i
$246$		0			0
$247$	24.4611	+	20.5253i	1.55642	+	1.30600i
$248$		0			0
$249$	−18.6927	+	7.51344i	−1.18460	+	0.476145i
$250$		0			0
$251$	−0.463159	−	0.802215i	−0.0292343	−	0.0506354i	0.851038	−	0.525104i	$-0.175974\pi$
$251$	−0.463159	−	0.802215i	−0.0292343	−	0.0506354i	−0.880272	+	0.474469i	$0.842640\pi$
$252$		0			0
$253$	−11.4601	+	19.8495i	−0.720493	+	1.24793i
$254$		0			0
$255$	2.39472	−	0.0793314i	0.149963	−	0.00496793i
$256$		0			0
$257$	3.89553	−	1.41786i	0.242996	−	0.0884435i	−0.217651	−	0.976027i	$-0.569839\pi$
$257$	3.89553	−	1.41786i	0.242996	−	0.0884435i	0.460647	+	0.887583i	$0.347617\pi$
$258$		0			0
$259$	−7.72008	−	43.7828i	−0.479703	−	2.72053i
$260$		0			0
$261$	−8.54545	+	17.3626i	−0.528950	+	1.07472i
$262$		0			0
$263$	18.1649	−	15.2421i	1.12009	−	0.939871i	0.121485	−	0.992593i	$-0.461234\pi$
$263$	18.1649	−	15.2421i	1.12009	−	0.939871i	0.998609	+	0.0527227i	$0.0167899\pi$
$264$		0			0
$265$	−0.696471	+	3.94988i	−0.0427838	+	0.242639i
$266$		0			0
$267$	−7.48061	−	2.44542i	−0.457806	−	0.149657i
$268$		0			0
$269$	8.44050			0.514627			0.257313	−	0.966328i	$-0.417163\pi$
$269$	8.44050			0.514627			0.257313	+	0.966328i	$0.417163\pi$
$270$		0			0
$271$	−18.9024			−1.14824			−0.574121	−	0.818771i	$-0.694656\pi$
$271$	−18.9024			−1.14824			−0.574121	+	0.818771i	$0.694656\pi$
$272$		0			0
$273$	−9.77558	−	46.3990i	−0.591645	−	2.80819i
$274$		0			0
$275$	2.12747	−	12.0655i	0.128291	−	0.727576i
$276$		0			0
$277$	0.736157	−	0.617709i	0.0442314	−	0.0371146i	−0.620404	−	0.784282i	$-0.713031\pi$
$277$	0.736157	−	0.617709i	0.0442314	−	0.0371146i	0.664635	+	0.747168i	$0.268587\pi$
$278$		0			0
$279$	3.56994	−	3.42282i	0.213727	−	0.204919i
$280$		0			0
$281$	4.28635	+	24.3091i	0.255702	+	1.45016i	0.794263	+	0.607574i	$0.207857\pi$
$281$	4.28635	+	24.3091i	0.255702	+	1.45016i	−0.538561	+	0.842587i	$0.681032\pi$
$282$		0			0
$283$	−12.2614	+	4.46277i	−0.728862	+	0.265284i	−0.679683	−	0.733506i	$-0.737883\pi$
$283$	−12.2614	+	4.46277i	−0.728862	+	0.265284i	−0.0491789	+	0.998790i	$0.515660\pi$
$284$		0			0
$285$	−2.71389	+	5.08210i	−0.160757	+	0.301037i
$286$		0			0
$287$	−24.4031	+	42.2674i	−1.44047	+	2.49496i
$288$		0			0
$289$	6.11650	+	10.5941i	0.359794	+	0.623182i
$290$		0			0
$291$	−6.84825	−	5.37022i	−0.401451	−	0.314808i
$292$		0			0
$293$	2.15956	+	1.81208i	0.126163	+	0.105863i	0.703686	−	0.710511i	$-0.251536\pi$
$293$	2.15956	+	1.81208i	0.126163	+	0.105863i	−0.577523	+	0.816374i	$0.695981\pi$
$294$		0			0
$295$	−0.690370	−	0.251274i	−0.0401949	−	0.0146297i
$296$		0			0
$297$	9.67004	−	9.90654i	0.561112	−	0.574836i
$298$		0			0
$299$	49.1705	+	17.8966i	2.84360	+	1.03499i
$300$		0			0
$301$	−9.17405	−	7.69795i	−0.528784	−	0.443702i
$302$		0			0
$303$	0.541743	−	3.80524i	0.0311223	−	0.218605i
$304$		0			0
$305$	1.84191	+	3.19028i	0.105467	+	0.182675i
$306$		0			0
$307$	−2.46943	+	4.27718i	−0.140938	+	0.244111i	−0.927850	−	0.372954i	$-0.878345\pi$
$307$	−2.46943	+	4.27718i	−0.140938	+	0.244111i	0.786912	+	0.617065i	$0.211678\pi$
$308$		0			0
$309$	3.25382	+	5.22801i	0.185103	+	0.297411i
$310$		0			0
$311$	−4.63225	+	1.68600i	−0.262671	+	0.0956043i	−0.469998	−	0.882667i	$-0.655746\pi$
$311$	−4.63225	+	1.68600i	−0.262671	+	0.0956043i	0.207328	+	0.978272i	$0.433523\pi$
$312$		0			0
$313$	1.45265	+	8.23839i	0.0821087	+	0.465661i	0.997943	+	0.0641054i	$0.0204194\pi$
$313$	1.45265	+	8.23839i	0.0821087	+	0.465661i	−0.915834	+	0.401556i	$0.868470\pi$
$314$		0			0
$315$	7.82814	−	3.45177i	0.441066	−	0.194485i
$316$		0			0
$317$	−0.620276	+	0.520474i	−0.0348382	+	0.0292327i	−0.660041	−	0.751230i	$-0.729461\pi$
$317$	−0.620276	+	0.520474i	−0.0348382	+	0.0292327i	0.625202	+	0.780463i	$0.285016\pi$
$318$		0			0
$319$	−2.98427	+	16.9247i	−0.167087	+	0.947599i
$320$		0			0
$321$	16.8842	−	15.1479i	0.942381	−	0.845473i
$322$		0			0
$323$	11.4624			0.637783
$324$		0			0
$325$	−27.9700			−1.55150
$326$		0			0
$327$	−2.93875	+	2.63654i	−0.162513	+	0.145801i
$328$		0			0
$329$	5.45491	−	30.9363i	0.300739	−	1.70558i
$330$		0			0
$331$	17.9684	−	15.0773i	0.987633	−	0.828723i	0.00240997	−	0.999997i	$-0.499233\pi$
$331$	17.9684	−	15.0773i	0.987633	−	0.828723i	0.985223	+	0.171274i	$0.0547884\pi$
$332$		0			0
$333$	−23.9105	−	17.5032i	−1.31029	−	0.959168i
$334$		0			0
$335$	0.298622	+	1.69357i	0.0163154	+	0.0925295i
$336$		0			0
$337$	24.3530	−	8.86375i	1.32659	−	0.482839i	0.421026	−	0.907049i	$-0.361670\pi$
$337$	24.3530	−	8.86375i	1.32659	−	0.482839i	0.905564	+	0.424209i	$0.139448\pi$
$338$		0			0
$339$	−15.6517	−	25.1481i	−0.850086	−	1.36586i
$340$		0			0
$341$	2.19609	−	3.80374i	0.118925	−	0.205984i
$342$		0			0
$343$	−14.0857	−	24.3971i	−0.760555	−	1.31732i
$344$		0			0
$345$	−1.33068	+	9.34677i	−0.0716413	+	0.503213i
$346$		0			0
$347$	−16.3207	−	13.6947i	−0.876141	−	0.735170i	0.0892406	−	0.996010i	$-0.471556\pi$
$347$	−16.3207	−	13.6947i	−0.876141	−	0.735170i	−0.965382	+	0.260840i	$0.916000\pi$
$348$		0			0
$349$	−1.94199	−	0.706825i	−0.103952	−	0.0378355i	0.289520	−	0.957172i	$-0.406504\pi$
$349$	−1.94199	−	0.706825i	−0.103952	−	0.0378355i	−0.393473	+	0.919336i	$0.628726\pi$
$350$		0			0
$351$	−26.1062	−	17.8137i	−1.39345	−	0.950824i
$352$		0			0
$353$	6.98928	+	2.54389i	0.372002	+	0.135398i	0.521254	−	0.853402i	$-0.325464\pi$
$353$	6.98928	+	2.54389i	0.372002	+	0.135398i	−0.149252	+	0.988799i	$0.547687\pi$
$354$		0			0
$355$	1.07489	+	0.901943i	0.0570494	+	0.0478702i
$356$		0			0
$357$	−13.3941	−	10.5033i	−0.708892	−	0.555895i
$358$		0			0
$359$	18.7520	+	32.4794i	0.989693	+	1.71420i	0.618865	+	0.785497i	$0.287593\pi$
$359$	18.7520	+	32.4794i	0.989693	+	1.71420i	0.370828	+	0.928702i	$0.379074\pi$
$360$		0			0
$361$	−4.28079	+	7.41455i	−0.225305	+	0.390239i
$362$		0			0
$363$	−3.18350	+	5.96150i	−0.167090	+	0.312898i
$364$		0			0
$365$	2.57437	−	0.936996i	0.134749	−	0.0490446i
$366$		0			0
$367$	1.30427	+	7.39687i	0.0680822	+	0.386113i	0.999741	+	0.0227779i	$0.00725105\pi$
$367$	1.30427	+	7.39687i	0.0680822	+	0.386113i	−0.931658	+	0.363336i	$0.881638\pi$
$368$		0			0
$369$	7.75667	+	31.5920i	0.403796	+	1.64461i
$370$		0			0
$371$	21.8265	−	18.3146i	1.13318	−	0.950849i
$372$		0			0
$373$	−2.78673	+	15.8043i	−0.144291	+	0.818316i	0.823642	+	0.567110i	$0.191938\pi$
$373$	−2.78673	+	15.8043i	−0.144291	+	0.818316i	−0.967934	+	0.251207i	$0.919173\pi$
$374$		0			0
$375$	−2.17160	−	10.3073i	−0.112141	−	0.532267i
$376$		0			0
$377$	39.2344			2.02068
$378$		0			0
$379$	−34.3302			−1.76342			−0.881711	−	0.471790i	$-0.843608\pi$
$379$	−34.3302			−1.76342			−0.881711	+	0.471790i	$0.843608\pi$
$380$		0			0
$381$	17.4122	+	5.69206i	0.892054	+	0.291613i
$382$		0			0
$383$	3.67508	−	20.8424i	0.187788	−	1.06500i	−0.734533	−	0.678573i	$-0.762599\pi$
$383$	3.67508	−	20.8424i	0.187788	−	1.06500i	0.922321	−	0.386425i	$-0.126290\pi$
$384$		0			0
$385$	5.82027	−	4.88379i	0.296629	−	0.248901i
$386$		0			0
$387$	−7.96466	+	0.528281i	−0.404866	+	0.0268540i
$388$		0			0
$389$	−5.43253	−	30.8094i	−0.275440	−	1.56210i	−0.737560	−	0.675282i	$-0.764022\pi$
$389$	−5.43253	−	30.8094i	−0.275440	−	1.56210i	0.462119	−	0.886818i	$-0.347089\pi$
$390$		0			0
$391$	17.6505	−	6.42425i	0.892623	−	0.324888i
$392$		0			0
$393$	−2.43316	+	0.0806048i	−0.122737	+	0.00406598i
$394$		0			0
$395$	2.84879	−	4.93426i	0.143338	−	0.248269i
$396$		0			0
$397$	12.7579	+	22.0974i	0.640301	+	1.10903i	0.985365	+	0.170455i	$0.0545238\pi$
$397$	12.7579	+	22.0974i	0.640301	+	1.10903i	−0.345064	+	0.938579i	$0.612143\pi$
$398$		0			0
$399$	37.9752	−	15.2639i	1.90114	−	0.764152i
$400$		0			0
$401$	−7.78703	−	6.53410i	−0.388866	−	0.326297i	0.427305	−	0.904107i	$-0.359463\pi$
$401$	−7.78703	−	6.53410i	−0.388866	−	0.326297i	−0.816171	+	0.577810i	$0.803907\pi$
$402$		0			0
$403$	−9.42247	−	3.42950i	−0.469367	−	0.170835i
$404$		0			0
$405$	2.17395	−	5.27167i	0.108025	−	0.261951i
$406$		0			0
$407$	−24.7287	−	9.00050i	−1.22576	−	0.446138i
$408$		0			0
$409$	−23.6868	−	19.8756i	−1.17123	−	0.982783i	−0.171238	−	0.985230i	$-0.554777\pi$
$409$	−23.6868	−	19.8756i	−1.17123	−	0.982783i	−0.999997	+	0.00244702i	$0.999221\pi$
$410$		0			0
$411$	7.21961	−	2.90188i	0.356117	−	0.143139i
$412$		0			0
$413$	2.60954	+	4.51986i	0.128407	+	0.222408i
$414$		0			0
$415$	−3.68479	+	6.38224i	−0.180879	+	0.313292i
$416$		0			0
$417$	−12.8045	+	0.424182i	−0.627037	+	0.0207723i
$418$		0			0
$419$	22.8832	−	8.32882i	1.11792	−	0.406889i	0.284027	−	0.958816i	$-0.408329\pi$
$419$	22.8832	−	8.32882i	1.11792	−	0.406889i	0.833893	+	0.551927i	$0.186107\pi$
$420$		0			0
$421$	5.22879	+	29.6540i	0.254836	+	1.44525i	0.796494	+	0.604646i	$0.206686\pi$
$421$	5.22879	+	29.6540i	0.254836	+	1.44525i	−0.541658	+	0.840599i	$0.682203\pi$
$422$		0			0
$423$	−11.6460	−	17.4000i	−0.566248	−	0.846018i
$424$		0			0
$425$	−7.69127	+	6.45374i	−0.373081	+	0.313053i
$426$		0			0
$427$	4.54429	−	25.7720i	0.219914	−	1.24719i
$428$		0			0
$429$	−26.6781	−	8.72111i	−1.28803	−	0.421059i
$430$		0			0
$431$	2.09741			0.101029			0.0505143	−	0.998723i	$-0.483914\pi$
$431$	2.09741			0.101029			0.0505143	+	0.998723i	$0.483914\pi$
$432$		0			0
$433$	15.1676			0.728908			0.364454	−	0.931221i	$-0.381256\pi$
$433$	15.1676			0.728908			0.364454	+	0.931221i	$0.381256\pi$
$434$		0			0
$435$	1.45939	+	6.92686i	0.0699722	+	0.332117i
$436$		0			0
$437$	−7.84279	+	44.4787i	−0.375172	+	2.12770i
$438$		0			0
$439$	−1.45347	+	1.21961i	−0.0693705	+	0.0582087i	−0.676814	−	0.736154i	$-0.736640\pi$
$439$	−1.45347	+	1.21961i	−0.0693705	+	0.0582087i	0.607443	+	0.794363i	$0.292195\pi$
$440$		0			0
$441$	−38.1964	−	11.1009i	−1.81887	−	0.528612i
$442$		0			0
$443$	−6.67722	−	37.8684i	−0.317244	−	1.79918i	−0.559350	−	0.828932i	$-0.688949\pi$
$443$	−6.67722	−	37.8684i	−0.317244	−	1.79918i	0.242106	−	0.970250i	$-0.422162\pi$
$444$		0			0
$445$	−2.70532	+	0.984657i	−0.128245	+	0.0466772i
$446$		0			0
$447$	−9.38839	+	17.5810i	−0.444056	+	0.831551i
$448$		0			0
$449$	−9.45302	+	16.3731i	−0.446116	+	0.772695i	−0.998129	−	0.0611402i	$-0.980526\pi$
$449$	−9.45302	+	16.3731i	−0.446116	+	0.772695i	0.552014	+	0.833835i	$0.313860\pi$
$450$		0			0
$451$	14.4447	+	25.0189i	0.680174	+	1.17810i
$452$		0			0
$453$	4.31797	+	3.38604i	0.202876	+	0.159090i
$454$		0			0
$455$	−13.2875	−	11.1495i	−0.622926	−	0.522697i
$456$		0			0
$457$	−30.0918	−	10.9525i	−1.40763	−	0.512337i	−0.477199	−	0.878795i	$-0.658348\pi$
$457$	−30.0918	−	10.9525i	−1.40763	−	0.512337i	−0.930434	+	0.366458i	$0.880570\pi$
$458$		0			0
$459$	−11.2890	+	1.12523i	−0.526928	+	0.0525214i
$460$		0			0
$461$	15.0538	+	5.47915i	0.701127	+	0.255189i	0.667892	−	0.744258i	$-0.267197\pi$
$461$	15.0538	+	5.47915i	0.701127	+	0.255189i	0.0332348	+	0.999448i	$0.489419\pi$
$462$		0			0
$463$	11.1857	+	9.38595i	0.519846	+	0.436202i	0.864578	−	0.502499i	$-0.167586\pi$
$463$	11.1857	+	9.38595i	0.519846	+	0.436202i	−0.344732	+	0.938701i	$0.612030\pi$
$464$		0			0
$465$	0.254996	−	1.79111i	0.0118251	−	0.0830606i
$466$		0			0
$467$	−14.3380	−	24.8341i	−0.663481	−	1.14918i	−0.979695	−	0.200495i	$-0.935745\pi$
$467$	−14.3380	−	24.8341i	−0.663481	−	1.14918i	0.316213	−	0.948688i	$-0.397588\pi$
$468$		0			0
$469$	6.10829	−	10.5799i	0.282054	−	0.488533i
$470$		0			0
$471$	4.07790	+	6.55209i	0.187900	+	0.301904i
$472$		0			0
$473$	−6.66126	+	2.42450i	−0.306285	+	0.111479i
$474$		0			0
$475$	−4.19222	−	23.7753i	−0.192352	−	1.09088i
$476$		0			0
$477$	2.05272	−	18.8796i	0.0939877	−	0.864436i
$478$		0			0
$479$	−12.2166	+	10.2509i	−0.558191	+	0.468378i	−0.877703	−	0.479204i	$-0.840925\pi$
$479$	−12.2166	+	10.2509i	−0.558191	+	0.468378i	0.319513	+	0.947582i	$0.396481\pi$
$480$		0			0
$481$	−10.4324	+	59.1651i	−0.475677	+	2.69770i
$482$		0			0
$483$	49.9218	−	44.7881i	2.27152	−	2.03793i
$484$		0			0
$485$	−3.18350			−0.144555
$486$		0			0
$487$	2.28598			0.103588			0.0517938	−	0.998658i	$-0.483506\pi$
$487$	2.28598			0.103588			0.0517938	+	0.998658i	$0.483506\pi$
$488$		0			0
$489$	−19.0725	+	17.1112i	−0.862488	+	0.773795i
$490$		0			0
$491$	−6.49458	+	36.8326i	−0.293096	+	1.66223i	0.381745	+	0.924268i	$0.375323\pi$
$491$	−6.49458	+	36.8326i	−0.293096	+	1.66223i	−0.674841	+	0.737963i	$0.735788\pi$
$492$		0			0
$493$	10.7888	−	9.05287i	0.485903	−	0.407721i
$494$		0			0
$495$	0.547380	−	5.03443i	0.0246029	−	0.226281i
$496$		0			0
$497$	−1.73093	−	9.81661i	−0.0776429	−	0.440335i
$498$		0			0
$499$	19.7292	−	7.18085i	0.883201	−	0.321459i	0.139700	−	0.990194i	$-0.455386\pi$
$499$	19.7292	−	7.18085i	0.883201	−	0.321459i	0.743501	+	0.668735i	$0.233164\pi$
$500$		0			0
$501$	12.8492	+	20.6453i	0.574061	+	0.922362i
$502$		0			0
$503$	5.71418	−	9.89725i	0.254783	−	0.441297i	−0.710054	−	0.704147i	$-0.751329\pi$
$503$	5.71418	−	9.89725i	0.254783	−	0.441297i	0.964836	+	0.262851i	$0.0846627\pi$
$504$		0			0
$505$	−0.703005	−	1.21764i	−0.0312833	−	0.0541843i
$506$		0			0
$507$	−5.85777	+	41.1454i	−0.260153	+	1.82733i
$508$		0			0
$509$	−0.524575	−	0.440171i	−0.0232514	−	0.0195102i	0.631088	−	0.775711i	$-0.282609\pi$
$509$	−0.524575	−	0.440171i	−0.0232514	−	0.0195102i	−0.654339	+	0.756201i	$0.727053\pi$
$510$		0			0
$511$	−18.2882	−	6.65635i	−0.809021	−	0.294460i
$512$		0			0
$513$	11.2293	−	24.8609i	0.495784	−	1.09764i
$514$		0			0
$515$	2.11673	+	0.770427i	0.0932743	+	0.0339491i
$516$		0			0
$517$	−14.2441	−	11.9522i	−0.626454	−	0.525658i
$518$		0			0
$519$	−5.95588	−	4.67045i	−0.261434	−	0.205010i
$520$		0			0
$521$	4.94365	+	8.56266i	0.216585	+	0.375137i	0.953762	−	0.300563i	$-0.0971747\pi$
$521$	4.94365	+	8.56266i	0.216585	+	0.375137i	−0.737176	+	0.675700i	$0.763841\pi$
$522$		0			0
$523$	8.70164	−	15.0717i	0.380496	−	0.659039i	−0.610637	−	0.791911i	$-0.709087\pi$
$523$	8.70164	−	15.0717i	0.380496	−	0.659039i	0.991133	+	0.132872i	$0.0424199\pi$
$524$		0			0
$525$	−16.8873	+	31.6236i	−0.737021	+	1.38017i
$526$		0			0
$527$	−3.38233	+	1.23107i	−0.147337	+	0.0536262i
$528$		0			0
$529$	8.85799	+	50.2361i	0.385130	+	2.18418i
$530$		0			0
$531$	3.34041	+	0.970811i	0.144962	+	0.0421296i
$532$		0			0
$533$	50.5232	−	42.3940i	2.18840	−	1.83629i
$534$		0			0
$535$	1.44087	−	8.17160i	0.0622944	−	0.353289i
$536$		0			0
$537$	−4.00040	−	18.9876i	−0.172630	−	0.819374i
$538$		0			0
$539$	−35.3248			−1.52155
$540$		0			0
$541$	2.20067			0.0946143			0.0473072	−	0.998880i	$-0.484936\pi$
$541$	2.20067			0.0946143			0.0473072	+	0.998880i	$0.484936\pi$
$542$		0			0
$543$	20.6840	+	6.76161i	0.887635	+	0.290169i
$544$		0			0
$545$	−0.250789	+	1.42230i	−0.0107426	+	0.0609245i
$546$		0			0
$547$	16.9099	−	14.1891i	0.723014	−	0.606681i	−0.205203	−	0.978719i	$-0.565785\pi$
$547$	16.9099	−	14.1891i	0.723014	−	0.606681i	0.928217	+	0.372038i	$0.121341\pi$
$548$		0			0
$549$	−9.70187	−	14.4954i	−0.414066	−	0.618646i
$550$		0			0
$551$	5.88057	+	33.3503i	0.250521	+	1.42077i
$552$		0			0
$553$	−38.0343	+	13.8433i	−1.61738	+	0.588679i
$554$		0			0
$555$	−10.8337	+	0.358894i	−0.459864	+	0.0152342i
$556$		0			0
$557$	16.9433	−	29.3467i	0.717912	−	1.24346i	−0.243914	−	0.969797i	$-0.578431\pi$
$557$	16.9433	−	29.3467i	0.717912	−	1.24346i	0.961826	−	0.273663i	$-0.0882352\pi$
$558$		0			0
$559$	8.09170	+	14.0152i	0.342242	+	0.592781i
$560$		0			0
$561$	−9.34832	+	3.75750i	−0.394686	+	0.158642i
$562$		0			0
$563$	−20.3543	−	17.0793i	−0.857833	−	0.719807i	0.103667	−	0.994612i	$-0.466942\pi$
$563$	−20.3543	−	17.0793i	−0.857833	−	0.719807i	−0.961500	+	0.274805i	$0.911387\pi$
$564$		0			0
$565$	−10.1821	−	3.70596i	−0.428362	−	0.155911i
$566$		0			0
$567$	−35.9026	+	18.7611i	−1.50777	+	0.787890i
$568$		0			0
$569$	−18.7991	−	6.84231i	−0.788099	−	0.286844i	−0.0835532	−	0.996503i	$-0.526627\pi$
$569$	−18.7991	−	6.84231i	−0.788099	−	0.286844i	−0.704545	+	0.709659i	$0.748849\pi$
$570$		0			0
$571$	−8.99142	−	7.54469i	−0.376279	−	0.315736i	0.434961	−	0.900450i	$-0.356762\pi$
$571$	−8.99142	−	7.54469i	−0.376279	−	0.315736i	−0.811240	+	0.584714i	$0.801207\pi$
$572$		0			0
$573$	13.9199	−	5.59503i	0.581512	−	0.233736i
$574$		0			0
$575$	−19.7806	−	34.2611i	−0.824910	−	1.42879i
$576$		0			0
$577$	9.63954	−	16.6962i	0.401299	−	0.695071i	−0.592584	−	0.805509i	$-0.701892\pi$
$577$	9.63954	−	16.6962i	0.401299	−	0.695071i	0.993883	+	0.110438i	$0.0352253\pi$
$578$		0			0
$579$	−31.0247	+	1.02777i	−1.28934	+	0.0427129i
$580$		0			0
$581$	49.1957	−	17.9058i	2.04098	−	0.742856i
$582$		0			0
$583$	−2.92863	−	16.6091i	−0.121291	−	0.687878i
$584$		0			0
$585$	−11.5358	+	0.765149i	−0.476947	+	0.0316350i
$586$		0			0
$587$	12.3723	−	10.3816i	0.510661	−	0.428496i	−0.350701	−	0.936488i	$-0.614056\pi$
$587$	12.3723	−	10.3816i	0.510661	−	0.428496i	0.861362	+	0.507992i	$0.169612\pi$
$588$		0			0
$589$	1.50290	−	8.52338i	0.0619260	−	0.351200i
$590$		0			0
$591$	29.3575	+	9.59698i	1.20760	+	0.394767i
$592$		0			0
$593$	46.9935			1.92979			0.964897	−	0.262630i	$-0.0845897\pi$
$593$	46.9935			1.92979			0.964897	+	0.262630i	$0.0845897\pi$
$594$		0			0
$595$	−6.22644			−0.255259
$596$		0			0
$597$	−7.61350	−	36.1368i	−0.311600	−	1.47898i
$598$		0			0
$599$	5.28443	−	29.9695i	0.215916	−	1.22452i	−0.663394	−	0.748270i	$-0.730885\pi$
$599$	5.28443	−	29.9695i	0.215916	−	1.22452i	0.879310	−	0.476250i	$-0.158004\pi$
$600$		0			0
$601$	12.1151	−	10.1658i	0.494185	−	0.414670i	−0.361338	−	0.932435i	$-0.617680\pi$
$601$	12.1151	−	10.1658i	0.494185	−	0.414670i	0.855523	+	0.517764i	$0.173236\pi$
$602$		0			0
$603$	−1.94156	−	7.90772i	−0.0790663	−	0.322027i
$604$		0			0
$605$	0.429294	+	2.43465i	0.0174533	+	0.0989824i
$606$		0			0
$607$	10.4661	−	3.80934i	0.424805	−	0.154616i	−0.120766	−	0.992681i	$-0.538535\pi$
$607$	10.4661	−	3.80934i	0.424805	−	0.154616i	0.545571	+	0.838065i	$0.316313\pi$
$608$		0			0
$609$	23.6883	−	44.3594i	0.959900	−	1.79754i
$610$		0			0
$611$	−21.2251	+	36.7630i	−0.858676	+	1.48727i
$612$		0			0
$613$	−7.81559	−	13.5370i	−0.315669	−	0.546754i	0.663911	−	0.747812i	$-0.268896\pi$
$613$	−7.81559	−	13.5370i	−0.315669	−	0.546754i	−0.979579	+	0.201057i	$0.935562\pi$
$614$		0			0
$615$	9.36398	+	7.34299i	0.377592	+	0.296098i
$616$		0			0
$617$	32.3344	+	27.1318i	1.30174	+	1.09229i	0.989842	+	0.142169i	$0.0454076\pi$
$617$	32.3344	+	27.1318i	1.30174	+	1.09229i	0.311893	+	0.950117i	$0.399037\pi$
$618$		0			0
$619$	−4.89647	−	1.78217i	−0.196806	−	0.0716315i	0.241737	−	0.970342i	$-0.422283\pi$
$619$	−4.89647	−	1.78217i	−0.196806	−	0.0716315i	−0.438543	+	0.898710i	$0.644505\pi$
$620$		0			0
$621$	3.35784	−	44.5761i	0.134745	−	1.78878i
$622$		0			0
$623$	19.2184	+	6.99493i	0.769969	+	0.280246i
$624$		0			0
$625$	14.6618	+	12.3027i	0.586470	+	0.492107i
$626$		0			0
$627$	3.41459	−	23.9843i	0.136366	−	0.957840i
$628$		0			0
$629$	10.7829	+	18.6765i	0.429943	+	0.744682i
$630$		0			0
$631$	18.2625	−	31.6315i	0.727017	−	1.25923i	−0.231121	−	0.972925i	$-0.574239\pi$
$631$	18.2625	−	31.6315i	0.727017	−	1.25923i	0.958138	−	0.286306i	$-0.0924274\pi$
$632$		0			0
$633$	−14.8041	−	23.7863i	−0.588412	−	0.945419i
$634$		0			0
$635$	6.29703	−	2.29193i	0.249890	−	0.0909525i
$636$		0			0
$637$	14.0039	+	79.4201i	0.554855	+	3.14674i
$638$		0			0
$639$	−5.36100	−	3.92441i	−0.212078	−	0.155247i
$640$		0			0
$641$	24.1848	−	20.2934i	0.955241	−	0.801542i	−0.0249313	−	0.999689i	$-0.507937\pi$
$641$	24.1848	−	20.2934i	0.955241	−	0.801542i	0.980172	+	0.198147i	$0.0634922\pi$
$642$		0			0
$643$	−2.75410	+	15.6193i	−0.108611	+	0.615964i	0.881105	+	0.472920i	$0.156800\pi$
$643$	−2.75410	+	15.6193i	−0.108611	+	0.615964i	−0.989716	+	0.143044i	$0.954311\pi$
$644$		0			0
$645$	−2.17341	+	1.94991i	−0.0855780	+	0.0767777i
$646$		0			0
$647$	32.4062			1.27402			0.637009	−	0.770856i	$-0.280171\pi$
$647$	32.4062			1.27402			0.637009	+	0.770856i	$0.280171\pi$
$648$		0			0
$649$	3.08928			0.121265
$650$		0			0
$651$	−9.56642	+	8.58267i	−0.374938	+	0.336381i
$652$		0			0
$653$	−0.255616	+	1.44967i	−0.0100030	+	0.0567299i	−0.989401	−	0.145211i	$-0.953614\pi$
$653$	−0.255616	+	1.44967i	−0.0100030	+	0.0567299i	0.979398	+	0.201941i	$0.0647250\pi$
$654$		0			0
$655$	−0.682200	+	0.572434i	−0.0266558	+	0.0223668i
$656$		0			0
$657$	−11.8691	+	5.23359i	−0.463057	+	0.204182i
$658$		0			0
$659$	2.80071	+	15.8836i	0.109100	+	0.618738i	0.989503	+	0.144512i	$0.0461611\pi$
$659$	2.80071	+	15.8836i	0.109100	+	0.618738i	−0.880403	+	0.474226i	$0.842728\pi$
$660$		0			0
$661$	−17.0254	+	6.19674i	−0.662212	+	0.241025i	−0.651191	−	0.758914i	$-0.725730\pi$
$661$	−17.0254	+	6.19674i	−0.662212	+	0.241025i	−0.0110207	+	0.999939i	$0.503508\pi$
$662$		0			0
$663$	12.1539	+	19.5281i	0.472018	+	0.758407i
$664$		0			0
$665$	7.48583	−	12.9658i	0.290288	−	0.502794i
$666$		0			0
$667$	27.7469	+	48.0591i	1.07437	+	1.86086i
$668$		0			0
$669$	2.35592	−	16.5481i	0.0910851	−	0.639787i
$670$		0			0
$671$	−11.8662	−	9.95696i	−0.458091	−	0.384384i
$672$		0			0
$673$	−14.2056	−	5.17042i	−0.547586	−	0.199305i	0.0533876	−	0.998574i	$-0.482998\pi$
$673$	−14.2056	−	5.17042i	−0.547586	−	0.199305i	−0.600974	+	0.799269i	$0.705220\pi$
$674$		0			0
$675$	6.46280	+	23.0042i	0.248753	+	0.885433i
$676$		0			0
$677$	11.4765	+	4.17709i	0.441076	+	0.160539i	0.553005	−	0.833178i	$-0.313481\pi$
$677$	11.4765	+	4.17709i	0.441076	+	0.160539i	−0.111930	+	0.993716i	$0.535703\pi$
$678$		0			0
$679$	17.3244	+	14.5369i	0.664848	+	0.557874i
$680$		0			0
$681$	12.1130	+	9.49872i	0.464172	+	0.363992i
$682$		0			0
$683$	7.81793	+	13.5410i	0.299145	+	0.518134i	0.975941	−	0.218037i	$-0.0699653\pi$
$683$	7.81793	+	13.5410i	0.299145	+	0.518134i	−0.676796	+	0.736171i	$0.736632\pi$
$684$		0			0
$685$	1.42316	−	2.46499i	0.0543762	−	0.0941823i
$686$		0			0
$687$	−6.94236	+	13.0005i	−0.264867	+	0.495998i
$688$		0			0
$689$	−36.1809	+	13.1688i	−1.37838	+	0.501690i
$690$		0			0
$691$	7.74859	+	43.9445i	0.294770	+	1.67173i	0.668134	+	0.744041i	$0.267093\pi$
$691$	7.74859	+	43.9445i	0.294770	+	1.67173i	−0.373364	+	0.927685i	$0.621796\pi$
$692$		0			0
$693$	−25.9676	+	24.8975i	−0.986428	+	0.945777i
$694$		0			0
$695$	−3.59007	+	3.01243i	−0.136179	+	0.114268i
$696$		0			0
$697$	4.11111	−	23.3153i	0.155719	−	0.883128i
$698$		0			0
$699$	1.85081	+	8.78471i	0.0700041	+	0.332268i
$700$		0			0
$701$	−31.3282			−1.18325			−0.591624	−	0.806214i	$-0.701513\pi$
$701$	−31.3282			−1.18325			−0.591624	+	0.806214i	$0.701513\pi$
$702$		0			0
$703$	−51.8556			−1.95577
$704$		0			0
$705$	−7.28002	−	2.37985i	−0.274181	−	0.0896302i
$706$		0			0
$707$	−1.73443	+	9.83644i	−0.0652300	+	0.369937i
$708$		0			0
$709$	12.9667	−	10.8804i	0.486976	−	0.408622i	−0.365965	−	0.930629i	$-0.619261\pi$
$709$	12.9667	−	10.8804i	0.486976	−	0.408622i	0.852941	+	0.522007i	$0.174817\pi$
$710$		0			0
$711$	−11.9130	+	24.2047i	−0.446771	+	0.907749i
$712$		0			0
$713$	−2.46279	−	13.9672i	−0.0922321	−	0.523074i
$714$		0			0
$715$	−9.64801	+	3.51159i	−0.360815	+	0.131326i
$716$		0			0
$717$	18.8654	−	0.624967i	0.704542	−	0.0233398i
$718$		0			0
$719$	2.15840	−	3.73847i	0.0804949	−	0.139421i	−0.822968	−	0.568088i	$-0.807683\pi$
$719$	2.15840	−	3.73847i	0.0804949	−	0.139421i	0.903463	+	0.428667i	$0.141017\pi$
$720$		0			0
$721$	−8.00107	−	13.8583i	−0.297975	−	0.516108i
$722$		0			0
$723$	11.5180	−	4.62960i	0.428360	−	0.172177i
$724$		0			0
$725$	−22.7234	−	19.0672i	−0.843925	−	0.708137i
$726$		0			0
$727$	−27.3206	−	9.94387i	−1.01326	−	0.368798i	−0.218578	−	0.975819i	$-0.570142\pi$
$727$	−27.3206	−	9.94387i	−1.01326	−	0.368798i	−0.794685	+	0.607022i	$0.792364\pi$
$728$		0			0
$729$	−8.61892	+	25.5874i	−0.319219	+	0.947681i
$730$		0			0
$731$	5.45893	+	1.98689i	0.201906	+	0.0734877i
$732$		0			0
$733$	33.1021	+	27.7760i	1.22265	+	1.02593i	0.998682	+	0.0513328i	$0.0163469\pi$
$733$	33.1021	+	27.7760i	1.22265	+	1.02593i	0.223972	+	0.974596i	$0.428098\pi$
$734$		0			0
$735$	−13.5008	+	5.42655i	−0.497983	+	0.200161i
$736$		0			0
$737$	−3.61562	−	6.26244i	−0.133183	−	0.230680i
$738$		0			0
$739$	−12.6164	+	21.8523i	−0.464103	+	0.803851i	−0.999161	−	0.0409652i	$-0.986957\pi$
$739$	−12.6164	+	21.8523i	−0.464103	+	0.803851i	0.535057	+	0.844816i	$0.320290\pi$
$740$		0			0
$741$	−55.2771	+	1.83120i	−2.03065	+	0.0672708i
$742$		0			0
$743$	23.7129	−	8.63079i	0.869942	−	0.316633i	0.131798	−	0.991277i	$-0.457925\pi$
$743$	23.7129	−	8.63079i	0.869942	−	0.316633i	0.738144	+	0.674644i	$0.235703\pi$
$744$		0			0
$745$	1.26602	+	7.17997i	0.0463835	+	0.263054i
$746$		0			0
$747$	15.4089	−	31.3078i	0.563781	−	1.14549i
$748$		0			0
$749$	−45.1552	+	37.8897i	−1.64994	+	1.38446i
$750$		0			0
$751$	0.788828	−	4.47366i	0.0287847	−	0.163246i	−0.967027	−	0.254674i	$-0.918032\pi$
$751$	0.788828	−	4.47366i	0.0287847	−	0.163246i	0.995812	+	0.0914275i	$0.0291430\pi$
$752$		0			0
$753$	1.52501	+	0.498528i	0.0555746	+	0.0181674i
$754$		0			0
$755$	2.00727			0.0730519
$756$		0			0
$757$	−9.51249			−0.345737			−0.172869	−	0.984945i	$-0.555304\pi$
$757$	−9.51249			−0.345737			−0.172869	+	0.984945i	$0.555304\pi$
$758$		0			0
$759$	−8.18434	−	38.8463i	−0.297073	−	1.41003i
$760$		0			0
$761$	7.46513	−	42.3369i	0.270611	−	1.53471i	−0.481956	−	0.876195i	$-0.660074\pi$
$761$	7.46513	−	42.3369i	0.270611	−	1.53471i	0.752567	−	0.658515i	$-0.228815\pi$
$762$		0			0
$763$	7.85943	−	6.59484i	0.284530	−	0.238749i
$764$		0			0
$765$	−2.99560	+	2.87215i	−0.108306	+	0.103843i
$766$		0			0
$767$	−1.22469	−	6.94558i	−0.0442211	−	0.250790i
$768$		0			0
$769$	−9.99054	+	3.63626i	−0.360268	+	0.131127i	−0.515811	−	0.856702i	$-0.672509\pi$
$769$	−9.99054	+	3.63626i	−0.360268	+	0.131127i	0.155543	+	0.987829i	$0.450287\pi$
$770$		0			0
$771$	−3.38229	+	6.33376i	−0.121810	+	0.228105i
$772$		0			0
$773$	−2.02035	+	3.49935i	−0.0726669	+	0.125863i	−0.900069	−	0.435747i	$-0.856484\pi$
$773$	−2.02035	+	3.49935i	−0.0726669	+	0.125863i	0.827402	+	0.561610i	$0.189818\pi$
$774$		0			0
$775$	3.79053	+	6.56540i	0.136160	+	0.235836i
$776$		0			0
$777$	60.5948	+	47.5169i	2.17383	+	1.70466i
$778$		0			0
$779$	43.6086	+	36.5920i	1.56244	+	1.31104i
$780$		0			0
$781$	−5.54446	−	2.01802i	−0.198396	−	0.0722104i
$782$		0			0
$783$	−9.06557	−	32.2688i	−0.323977	−	1.15319i
$784$		0			0
$785$	2.65283	+	0.965550i	0.0946835	+	0.0344620i
$786$		0			0
$787$	−9.49661	−	7.96860i	−0.338518	−	0.284050i	0.457642	−	0.889136i	$-0.348694\pi$
$787$	−9.49661	−	7.96860i	−0.338518	−	0.284050i	−0.796160	+	0.605086i	$0.793139\pi$
$788$		0			0
$789$	−5.78886	+	40.6614i	−0.206089	+	1.44758i
$790$		0			0
$791$	38.4873	+	66.6620i	1.36845	+	2.37023i
$792$		0			0
$793$	−17.6819	+	30.6259i	−0.627902	+	1.08756i
$794$		0			0
$795$	−3.67076	−	5.89792i	−0.130188	−	0.209178i
$796$		0			0
$797$	−34.2876	+	12.4797i	−1.21453	+	0.442053i	−0.868273	−	0.496087i	$-0.834770\pi$
$797$	−34.2876	+	12.4797i	−1.21453	+	0.442053i	−0.346257	+	0.938140i	$0.612547\pi$
$798$		0			0
$799$	2.64607	+	15.0066i	0.0936113	+	0.530896i
$800$		0			0
$801$	12.4728	−	5.49980i	0.440705	−	0.194326i
$802$		0			0
$803$	−8.82473	+	7.40483i	−0.311418	+	0.261311i
$804$		0			0
$805$	4.26027	−	24.1612i	0.150155	−	0.851569i
$806$		0			0
$807$	−10.8818	+	9.76280i	−0.383058	+	0.343667i
$808$		0			0
$809$	−6.02328			−0.211767			−0.105884	−	0.994379i	$-0.533767\pi$
$809$	−6.02328			−0.211767			−0.105884	+	0.994379i	$0.533767\pi$
$810$		0			0
$811$	−26.0322			−0.914113			−0.457056	−	0.889438i	$-0.651096\pi$
$811$	−26.0322			−0.914113			−0.457056	+	0.889438i	$0.651096\pi$
$812$		0			0
$813$	24.3698	−	21.8637i	0.854685	−	0.766794i
$814$		0			0
$815$	−1.62762	+	9.23072i	−0.0570132	+	0.323338i
$816$		0			0
$817$	−10.7005	+	8.97881i	−0.374364	+	0.314129i
$818$		0			0
$819$	66.2709	+	48.5123i	2.31569	+	1.69516i
$820$		0			0
$821$	7.15846	+	40.5977i	0.249832	+	1.41687i	0.808998	+	0.587812i	$0.200011\pi$
$821$	7.15846	+	40.5977i	0.249832	+	1.41687i	−0.559166	+	0.829056i	$0.688878\pi$
$822$		0			0
$823$	−5.13508	+	1.86902i	−0.178998	+	0.0651499i	−0.429964	−	0.902846i	$-0.641474\pi$
$823$	−5.13508	+	1.86902i	−0.178998	+	0.0651499i	0.250966	+	0.967996i	$0.419252\pi$
$824$		0			0
$825$	11.2129	+	18.0161i	0.390382	+	0.627238i
$826$		0			0
$827$	6.36965	−	11.0326i	0.221495	−	0.383640i	−0.733767	−	0.679401i	$-0.762240\pi$
$827$	6.36965	−	11.0326i	0.221495	−	0.383640i	0.955262	+	0.295761i	$0.0955732\pi$
$828$		0			0
$829$	12.4276	+	21.5252i	0.431628	+	0.747602i	0.997014	−	0.0772248i	$-0.0246059\pi$
$829$	12.4276	+	21.5252i	0.431628	+	0.747602i	−0.565385	+	0.824827i	$0.691273\pi$
$830$		0			0
$831$	−0.234602	+	1.64786i	−0.00813825	+	0.0571636i
$832$		0			0
$833$	22.1761	+	18.6079i	0.768355	+	0.644726i
$834$		0			0
$835$	8.35891	+	3.04240i	0.289272	+	0.105286i
$836$		0			0
$837$	−0.643457	+	8.54204i	−0.0222411	+	0.295256i
$838$		0			0
$839$	−15.5444	−	5.65769i	−0.536651	−	0.195325i	0.0594546	−	0.998231i	$-0.481064\pi$
$839$	−15.5444	−	5.65769i	−0.536651	−	0.195325i	−0.596106	+	0.802906i	$0.703286\pi$
$840$		0			0
$841$	9.65951	+	8.10529i	0.333087	+	0.279493i
$842$		0			0
$843$	−33.6435	−	26.3824i	−1.15875	−	0.908658i
$844$		0			0
$845$	7.60147	+	13.1661i	0.261498	+	0.452929i
$846$		0			0
$847$	8.78118	−	15.2094i	0.301725	−	0.522603i
$848$		0			0
$849$	10.6459	−	19.9358i	0.365366	−	0.684195i
$850$		0			0
$851$	−79.8505	+	29.0632i	−2.73724	+	0.996274i
$852$		0			0
$853$	−0.295246	−	1.67442i	−0.0101090	−	0.0573311i	0.979336	−	0.202240i	$-0.0648222\pi$
$853$	−0.295246	−	1.67442i	−0.0101090	−	0.0573311i	−0.989445	+	0.144909i	$0.953711\pi$
$854$		0			0
$855$	−2.37942	−	9.69108i	−0.0813744	−	0.331428i
$856$		0			0
$857$	31.5593	−	26.4814i	1.07805	−	0.904587i	0.0822880	−	0.996609i	$-0.473777\pi$
$857$	31.5593	−	26.4814i	1.07805	−	0.904587i	0.995757	+	0.0920214i	$0.0293328\pi$
$858$		0			0
$859$	−4.44434	+	25.2051i	−0.151639	+	0.859986i	0.810156	+	0.586215i	$0.199382\pi$
$859$	−4.44434	+	25.2051i	−0.151639	+	0.859986i	−0.961795	+	0.273772i	$0.911729\pi$
$860$		0			0
$861$	−17.4276	−	82.7188i	−0.593932	−	2.81905i
$862$		0			0
$863$	26.3601			0.897307			0.448653	−	0.893706i	$-0.351904\pi$
$863$	26.3601			0.897307			0.448653	+	0.893706i	$0.351904\pi$
$864$		0			0
$865$	−2.76867			−0.0941378
$866$		0			0
$867$	−20.1394	−	6.58359i	−0.683970	−	0.223591i
$868$		0			0
$869$	−4.16028	+	23.5941i	−0.141128	+	0.800376i
$870$		0			0
$871$	−12.6464	+	10.6116i	−0.428506	+	0.359559i
$872$		0			0
$873$	15.0405	−	0.997611i	0.509045	−	0.0337640i
$874$		0			0
$875$	4.75329	+	26.9572i	0.160691	+	0.911321i
$876$		0			0
$877$	1.59646	−	0.581066i	0.0539088	−	0.0196212i	−0.314925	−	0.949117i	$-0.601979\pi$
$877$	1.59646	−	0.581066i	0.0539088	−	0.0196212i	0.368834	+	0.929495i	$0.379757\pi$
$878$		0			0
$879$	−4.88015	+	0.161668i	−0.164603	+	0.00545293i
$880$		0			0
$881$	2.29591	−	3.97663i	0.0773512	−	0.133976i	−0.824755	−	0.565490i	$-0.808687\pi$
$881$	2.29591	−	3.97663i	0.0773512	−	0.133976i	0.902106	+	0.431514i	$0.142020\pi$
$882$		0			0
$883$	2.40692	+	4.16891i	0.0809993	+	0.140295i	0.903679	−	0.428210i	$-0.140856\pi$
$883$	2.40692	+	4.16891i	0.0809993	+	0.140295i	−0.822680	+	0.568505i	$0.807522\pi$
$884$		0			0
$885$	1.18069	−	0.474572i	0.0396885	−	0.0159526i
$886$		0			0
$887$	8.49950	+	7.13193i	0.285385	+	0.239467i	0.774230	−	0.632904i	$-0.218137\pi$
$887$	8.49950	+	7.13193i	0.285385	+	0.239467i	−0.488845	+	0.872371i	$0.662582\pi$
$888$		0			0
$889$	−44.7336	−	16.2817i	−1.50032	−	0.546071i
$890$		0			0
$891$	−1.00848	+	23.9568i	−0.0337852	+	0.802584i
$892$		0			0
$893$	−34.4308	−	12.5318i	−1.15218	−	0.419360i
$894$		0			0
$895$	−5.43755	−	4.56265i	−0.181757	−	0.152513i
$896$		0			0
$897$	−84.0928	+	33.8006i	−2.80778	+	1.12857i
$898$		0			0
$899$	−5.31710	−	9.20949i	−0.177335	−	0.307154i
$900$		0			0
$901$	−6.91059	+	11.9695i	−0.230225	+	0.398761i
$902$		0			0
$903$	20.7315	−	0.686785i	0.689900	−	0.0228548i
$904$		0			0
$905$	7.48025	−	2.72259i	0.248652	−	0.0905019i
$906$		0			0
$907$	2.31198	+	13.1119i	0.0767681	+	0.435374i	0.998831	+	0.0483340i	$0.0153912\pi$
$907$	2.31198	+	13.1119i	0.0767681	+	0.435374i	−0.922063	+	0.387040i	$0.873498\pi$
$908$		0			0
$909$	3.70293	+	5.53247i	0.122819	+	0.183500i
$910$		0			0
$911$	0.306097	−	0.256846i	0.0101414	−	0.00850968i	−0.637703	−	0.770282i	$-0.720115\pi$
$911$	0.306097	−	0.256846i	0.0101414	−	0.00850968i	0.647844	+	0.761773i	$0.275671\pi$
$912$		0			0
$913$	5.38114	−	30.5180i	0.178090	−	1.01000i
$914$		0			0
$915$	−6.06473	−	1.98256i	−0.200494	−	0.0655416i
$916$		0			0
$917$	6.32639			0.208916
$918$		0			0
$919$	−27.9099			−0.920664			−0.460332	−	0.887747i	$-0.652270\pi$
$919$	−27.9099			−0.920664			−0.460332	+	0.887747i	$0.652270\pi$
$920$		0			0
$921$	−1.76356	−	8.37059i	−0.0581113	−	0.275820i
$922$		0			0
$923$	−2.33907	+	13.2655i	−0.0769913	+	0.436639i
$924$		0			0
$925$	34.7952	−	29.1966i	1.14406	−	0.959980i
$926$		0			0
$927$	−10.2420	−	2.97658i	−0.336391	−	0.0977638i
$928$		0			0
$929$	−2.74104	−	15.5452i	−0.0899306	−	0.510022i	−0.996183	−	0.0872853i	$-0.972181\pi$
$929$	−2.74104	−	15.5452i	−0.0899306	−	0.510022i	0.906253	−	0.422736i	$-0.138930\pi$
$930$		0			0
$931$	−65.4103	+	23.8074i	−2.14374	+	0.780256i
$932$		0			0
$933$	4.02194	−	7.53159i	0.131672	−	0.246573i
$934$		0			0
$935$	−1.84278	+	3.19179i	−0.0602653	+	0.104383i
$936$		0			0
$937$	6.40102	+	11.0869i	0.209112	+	0.362193i	0.951435	−	0.307849i	$-0.0996093\pi$
$937$	6.40102	+	11.0869i	0.209112	+	0.362193i	−0.742323	+	0.670042i	$0.766276\pi$
$938$		0			0
$939$	−11.4018	−	8.94102i	−0.372085	−	0.291779i
$940$		0			0
$941$	0.0976652	+	0.0819508i	0.00318379	+	0.00267152i	0.644378	−	0.764707i	$-0.277116\pi$
$941$	0.0976652	+	0.0819508i	0.00318379	+	0.00267152i	−0.641194	+	0.767379i	$0.721561\pi$
$942$		0			0
$943$	87.6599	+	31.9056i	2.85460	+	1.03899i
$944$		0			0
$945$	−6.09982	+	13.5047i	−0.198427	+	0.439306i
$946$		0			0
$947$	28.0903	+	10.2240i	0.912812	+	0.332236i	0.755375	−	0.655293i	$-0.227455\pi$
$947$	28.0903	+	10.2240i	0.912812	+	0.332236i	0.157437	+	0.987529i	$0.449677\pi$
$948$		0			0
$949$	20.1465	+	16.9050i	0.653985	+	0.548758i
$950$		0			0
$951$	0.197672	−	1.38846i	0.00640997	−	0.0450240i
$952$		0			0
$953$	−13.3176	−	23.0668i	−0.431401	−	0.747208i	0.565593	−	0.824684i	$-0.308647\pi$
$953$	−13.3176	−	23.0668i	−0.431401	−	0.747208i	−0.996994	+	0.0774762i	$0.975314\pi$
$954$		0			0
$955$	2.74395	−	4.75266i	0.0887921	−	0.153792i
$956$		0			0
$957$	−15.7286	−	25.2717i	−0.508435	−	0.816918i
$958$		0			0
$959$	−19.0006	+	6.91566i	−0.613562	+	0.223318i
$960$		0			0
$961$	−4.91115	−	27.8525i	−0.158424	−	0.898469i
$962$		0			0
$963$	−4.24672	+	39.0585i	−0.136849	+	1.25864i
$964$		0			0
$965$	−8.69858	+	7.29898i	−0.280017	+	0.234962i
$966$		0			0
$967$	−5.57449	+	31.6145i	−0.179264	+	1.01665i	0.753843	+	0.657055i	$0.228198\pi$
$967$	−5.57449	+	31.6145i	−0.179264	+	1.01665i	−0.933107	+	0.359600i	$0.882913\pi$
$968$		0			0
$969$	−14.7777	+	13.2581i	−0.474729	+	0.425911i
$970$		0			0
$971$	−31.5051			−1.01105			−0.505523	−	0.862813i	$-0.668701\pi$
$971$	−31.5051			−1.01105			−0.505523	+	0.862813i	$0.668701\pi$
$972$		0			0
$973$	33.2926			1.06731
$974$		0			0
$975$	36.0600	−	32.3518i	1.15484	−	1.03609i
$976$		0			0
$977$	7.20870	−	40.8826i	0.230627	−	1.30795i	−0.621004	−	0.783807i	$-0.713275\pi$
$977$	7.20870	−	40.8826i	0.230627	−	1.30795i	0.851631	−	0.524142i	$-0.175614\pi$
$978$		0			0
$979$	9.27361	−	7.78148i	0.296386	−	0.248697i
$980$		0			0
$981$	0.739157	−	6.79826i	0.0235995	−	0.217052i
$982$		0			0
$983$	−10.5268	−	59.7005i	−0.335753	−	1.90415i	−0.419667	−	0.907678i	$-0.637853\pi$
$983$	−10.5268	−	59.7005i	−0.335753	−	1.90415i	0.0839133	−	0.996473i	$-0.473258\pi$
$984$		0			0
$985$	10.6170	−	3.86426i	0.338285	−	0.123126i
$986$		0			0
$987$	28.7502	+	46.1938i	0.915128	+	1.47036i
$988$		0			0
$989$	−11.4450	+	19.8234i	−0.363931	+	0.630348i
$990$		0			0
$991$	−5.29369	−	9.16895i	−0.168160	−	0.291261i	0.769613	−	0.638510i	$-0.220449\pi$
$991$	−5.29369	−	9.16895i	−0.168160	−	0.291261i	−0.937773	+	0.347249i	$0.887116\pi$
$992$		0			0
$993$	−5.72625	+	40.2216i	−0.181717	+	1.27639i
$994$		0			0
$995$	−10.3487	−	8.68355i	−0.328074	−	0.275287i
$996$		0			0
$997$	−50.6554	−	18.4371i	−1.60427	−	0.583907i	−0.623977	−	0.781443i	$-0.714484\pi$
$997$	−50.6554	−	18.4371i	−1.60427	−	0.583907i	−0.980296	+	0.197536i	$0.936706\pi$
$998$		0			0
$999$	51.0715	−	5.09054i	1.61583	−	0.161058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.193.3	✓	60
4.3	odd	2	inner	864.2.y.d.193.8	yes	60
27.7	even	9	inner	864.2.y.d.385.3	yes	60
108.7	odd	18	inner	864.2.y.d.385.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.193.3	✓	60	1.1	even	1	trivial
864.2.y.d.193.8	yes	60	4.3	odd	2	inner
864.2.y.d.385.3	yes	60	27.7	even	9	inner
864.2.y.d.385.8	yes	60	108.7	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28924 + 1.15666i) q^{3} +(-0.110022 + 0.623966i) q^{5} +(3.44796 - 2.89318i) q^{7} +(0.324271 - 2.98242i) q^{9} +O(q^{10})\)	\(q+(-1.28924 + 1.15666i) q^{3} +(-0.110022 + 0.623966i) q^{5} +(3.44796 - 2.89318i) q^{7} +(0.324271 - 2.98242i) q^{9} +(-0.462638 - 2.62375i) q^{11} +(-5.71553 + 2.08028i) q^{13} +(-0.579873 - 0.931700i) q^{15} +(-1.09167 + 1.89083i) q^{17} +(-2.62496 - 4.54656i) q^{19} +(-1.09881 + 7.71812i) q^{21} +(-6.59026 - 5.52988i) q^{23} +(4.32123 + 1.57280i) q^{25} +(3.03159 + 4.22013i) q^{27} +(-6.06153 - 2.20622i) q^{29} +(1.26288 + 1.05968i) q^{31} +(3.63124 + 2.84753i) q^{33} +(1.42590 + 2.46972i) q^{35} +(4.93871 - 8.55410i) q^{37} +(4.96250 - 9.29291i) q^{39} +(-10.1895 + 3.70867i) q^{41} +(-0.462029 - 2.62030i) q^{43} +(1.82526 + 0.530467i) q^{45} +(5.34642 - 4.48618i) q^{47} +(2.30239 - 13.0575i) q^{49} +(-0.779626 - 3.70043i) q^{51} +6.33028 q^{53} +1.68803 q^{55} +(8.64302 + 2.82541i) q^{57} +(-0.201352 + 1.14193i) q^{59} +(4.45392 - 3.73728i) q^{61} +(-7.51062 - 11.2214i) q^{63} +(-0.669192 - 3.79517i) q^{65} +(2.55051 - 0.928310i) q^{67} +(14.8926 - 0.493357i) q^{69} +(1.10732 - 1.91793i) q^{71} +(-2.16195 - 3.74461i) q^{73} +(-7.39030 + 2.97049i) q^{75} +(-9.18615 - 7.70810i) q^{77} +(-8.45020 - 3.07562i) q^{79} +(-8.78970 - 1.93422i) q^{81} +(10.9300 + 3.97818i) q^{83} +(-1.05971 - 0.889200i) q^{85} +(10.3666 - 4.16680i) q^{87} +(2.27192 + 3.93508i) q^{89} +(-13.6883 + 23.7088i) q^{91} +(-2.85385 + 0.0945413i) q^{93} +(3.12570 - 1.13766i) q^{95} +(0.872500 + 4.94820i) q^{97} +(-7.97516 + 0.528977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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