LMFDB - Embedded newform 432.2.be.b.335.2

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			335.2
Character	$\chi$	$=$	432.335
Dual form			432.2.be.b.383.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35972 - 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(4.32834 + 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +O(q^{10})$	\(q+(-1.35972 - 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(4.32834 + 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +(-3.88970 + 1.41573i) q^{11} +(4.63966 - 3.89314i) q^{13} +(-5.01749 + 3.10176i) q^{15} +(0.945866 - 0.546096i) q^{17} +(-2.45107 - 1.41513i) q^{19} +(-5.06647 - 5.68171i) q^{21} +(-0.327067 - 1.85489i) q^{23} +(-5.05492 - 4.24158i) q^{25} +(2.18186 - 4.71588i) q^{27} +(-3.45728 + 4.12023i) q^{29} +(1.52041 - 0.268090i) q^{31} +(6.80787 + 2.24833i) q^{33} +(7.48419 - 12.9630i) q^{35} +(-2.48926 - 4.31152i) q^{37} +(-10.4857 + 0.315590i) q^{39} +(-3.29698 - 3.92918i) q^{41} +(1.43112 + 3.93198i) q^{43} +(10.1503 + 1.16584i) q^{45} +(1.51654 - 8.60072i) q^{47} +(11.5742 + 4.21266i) q^{49} +(-1.87203 - 0.272302i) q^{51} +12.1741i q^{53} +14.0973i q^{55} +(1.81445 + 4.55398i) q^{57} +(3.09392 + 1.12609i) q^{59} +(-0.463630 + 2.62938i) q^{61} +(0.792966 + 13.1615i) q^{63} +(-7.05488 - 19.3831i) q^{65} +(2.32819 + 2.77463i) q^{67} +(-1.54543 + 2.87305i) q^{69} +(-0.842160 - 1.45866i) q^{71} +(-5.58205 + 9.66839i) q^{73} +(2.32240 + 11.1909i) q^{75} +(-17.9164 + 3.15915i) q^{77} +(-6.26169 + 7.46239i) q^{79} +(-8.02648 + 4.07131i) q^{81} +(-0.240134 - 0.201496i) q^{83} +(-0.645914 - 3.66316i) q^{85} +(9.12161 - 1.89297i) q^{87} +(6.60573 + 3.81382i) q^{89} +(23.0533 - 13.3098i) q^{91} +(-2.35498 - 1.26676i) q^{93} +(-7.38387 + 6.19580i) q^{95} +(0.903887 - 0.328988i) q^{97} +(-6.84452 - 10.3614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

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
$3$	−1.35972	−	1.07292i	−0.785035	−	0.619451i
$3$	−1.35972	−	1.07292i	−0.785035	−	0.619451i
$4$		0			0
$5$	1.16481	−	3.20030i	0.520921	−	1.43122i	−0.348576	−	0.937281i	$-0.613335\pi$
$5$	1.16481	−	3.20030i	0.520921	−	1.43122i	0.869497	−	0.493938i	$-0.164443\pi$
$6$		0			0
$7$	4.32834	+	0.763203i	1.63596	+	0.288464i	0.914679	−	0.404181i	$-0.132443\pi$
$7$	4.32834	+	0.763203i	1.63596	+	0.288464i	0.721279	+	0.692645i	$0.243555\pi$
$8$		0			0
$9$	0.697681	+	2.91775i	0.232560	+	0.972582i
$10$		0			0
$11$	−3.88970	+	1.41573i	−1.17279	+	0.426860i	−0.853649	−	0.520849i	$-0.825616\pi$
$11$	−3.88970	+	1.41573i	−1.17279	+	0.426860i	−0.319138	+	0.947708i	$0.603393\pi$
$12$		0			0
$13$	4.63966	−	3.89314i	1.28681	−	1.07976i	0.294545	−	0.955638i	$-0.404832\pi$
$13$	4.63966	−	3.89314i	1.28681	−	1.07976i	0.992267	−	0.124125i	$-0.0396124\pi$
$14$		0			0
$15$	−5.01749	+	3.10176i	−1.29551	+	0.800872i
$16$		0			0
$17$	0.945866	−	0.546096i	0.229406	−	0.132448i	−0.380892	−	0.924620i	$-0.624383\pi$
$17$	0.945866	−	0.546096i	0.229406	−	0.132448i	0.610298	+	0.792172i	$0.291050\pi$
$18$		0			0
$19$	−2.45107	−	1.41513i	−0.562314	−	0.324652i	0.191760	−	0.981442i	$-0.438581\pi$
$19$	−2.45107	−	1.41513i	−0.562314	−	0.324652i	−0.754074	+	0.656790i	$0.771914\pi$
$20$		0			0
$21$	−5.06647	−	5.68171i	−1.10560	−	1.23985i
$22$		0			0
$23$	−0.327067	−	1.85489i	−0.0681982	−	0.386771i	−0.999733	−	0.0231182i	$-0.992641\pi$
$23$	−0.327067	−	1.85489i	−0.0681982	−	0.386771i	0.931535	−	0.363653i	$-0.118471\pi$
$24$		0			0
$25$	−5.05492	−	4.24158i	−1.01098	−	0.848316i
$26$		0			0
$27$	2.18186	−	4.71588i	0.419899	−	0.907571i
$28$		0			0
$29$	−3.45728	+	4.12023i	−0.642001	+	0.765107i	−0.984685	−	0.174344i	$-0.944220\pi$
$29$	−3.45728	+	4.12023i	−0.642001	+	0.765107i	0.342684	+	0.939451i	$0.388664\pi$
$30$		0			0
$31$	1.52041	−	0.268090i	0.273074	−	0.0481504i	−0.0354340	−	0.999372i	$-0.511281\pi$
$31$	1.52041	−	0.268090i	0.273074	−	0.0481504i	0.308508	+	0.951222i	$0.400170\pi$
$32$		0			0
$33$	6.80787	+	2.24833i	1.18510	+	0.391385i
$34$		0			0
$35$	7.48419	−	12.9630i	1.26506	−	2.19115i
$36$		0			0
$37$	−2.48926	−	4.31152i	−0.409232	−	0.708810i	0.585572	−	0.810620i	$-0.300870\pi$
$37$	−2.48926	−	4.31152i	−0.409232	−	0.708810i	−0.994804	+	0.101810i	$0.967537\pi$
$38$		0			0
$39$	−10.4857	+	0.315590i	−1.67905	+	0.0505348i
$40$		0			0
$41$	−3.29698	−	3.92918i	−0.514901	−	0.613635i	0.444466	−	0.895796i	$-0.353393\pi$
$41$	−3.29698	−	3.92918i	−0.514901	−	0.613635i	−0.959367	+	0.282160i	$0.908949\pi$
$42$		0			0
$43$	1.43112	+	3.93198i	0.218244	+	0.599622i	0.999704	−	0.0243344i	$-0.00774665\pi$
$43$	1.43112	+	3.93198i	0.218244	+	0.599622i	−0.781459	+	0.623956i	$0.785524\pi$
$44$		0			0
$45$	10.1503	+	1.16584i	1.51312	+	0.173794i
$46$		0			0
$47$	1.51654	−	8.60072i	0.221210	−	1.25454i	−0.648589	−	0.761138i	$-0.724641\pi$
$47$	1.51654	−	8.60072i	0.221210	−	1.25454i	0.869799	−	0.493406i	$-0.164248\pi$
$48$		0			0
$49$	11.5742	+	4.21266i	1.65345	+	0.601808i
$50$		0			0
$51$	−1.87203	−	0.272302i	−0.262137	−	0.0381298i
$52$		0			0
$53$			12.1741i			1.67224i	0.548548	+	0.836119i	$0.315181\pi$
$53$			12.1741i			1.67224i	−0.548548	+	0.836119i	$0.684819\pi$
$54$		0			0
$55$			14.0973i			1.90088i
$56$		0			0
$57$	1.81445	+	4.55398i	0.240330	+	0.603189i
$58$		0			0
$59$	3.09392	+	1.12609i	0.402793	+	0.146605i	0.535469	−	0.844555i	$-0.320135\pi$
$59$	3.09392	+	1.12609i	0.402793	+	0.146605i	−0.132676	+	0.991159i	$0.542357\pi$
$60$		0			0
$61$	−0.463630	+	2.62938i	−0.0593618	+	0.336657i	−0.999996	−	0.00276409i	$-0.999120\pi$
$61$	−0.463630	+	2.62938i	−0.0593618	+	0.336657i	0.940634	+	0.339421i	$0.110231\pi$
$62$		0			0
$63$	0.792966	+	13.1615i	0.0999043	+	1.65819i
$64$		0			0
$65$	−7.05488	−	19.3831i	−0.875050	−	2.40418i
$66$		0			0
$67$	2.32819	+	2.77463i	0.284434	+	0.338975i	0.889277	−	0.457370i	$-0.151208\pi$
$67$	2.32819	+	2.77463i	0.284434	+	0.338975i	−0.604843	+	0.796345i	$0.706764\pi$
$68$		0			0
$69$	−1.54543	+	2.87305i	−0.186048	+	0.345874i
$70$		0			0
$71$	−0.842160	−	1.45866i	−0.0999460	−	0.173112i	0.811716	−	0.584052i	$-0.198534\pi$
$71$	−0.842160	−	1.45866i	−0.0999460	−	0.173112i	−0.911662	+	0.410941i	$0.865200\pi$
$72$		0			0
$73$	−5.58205	+	9.66839i	−0.653329	+	1.13160i	0.328981	+	0.944337i	$0.393295\pi$
$73$	−5.58205	+	9.66839i	−0.653329	+	1.13160i	−0.982310	+	0.187262i	$0.940039\pi$
$74$		0			0
$75$	2.32240	+	11.1909i	0.268167	+	1.29221i
$76$		0			0
$77$	−17.9164	+	3.15915i	−2.04176	+	0.360018i
$78$		0			0
$79$	−6.26169	+	7.46239i	−0.704495	+	0.839584i	−0.993027	−	0.117886i	$-0.962388\pi$
$79$	−6.26169	+	7.46239i	−0.704495	+	0.839584i	0.288532	+	0.957470i	$0.406833\pi$
$80$		0			0
$81$	−8.02648	+	4.07131i	−0.891832	+	0.452368i
$82$		0			0
$83$	−0.240134	−	0.201496i	−0.0263581	−	0.0221171i	0.629513	−	0.776990i	$-0.283254\pi$
$83$	−0.240134	−	0.201496i	−0.0263581	−	0.0221171i	−0.655872	+	0.754873i	$0.727699\pi$
$84$		0			0
$85$	−0.645914	−	3.66316i	−0.0700592	−	0.397325i
$86$		0			0
$87$	9.12161	−	1.89297i	0.977940	−	0.202947i
$88$		0			0
$89$	6.60573	+	3.81382i	0.700206	+	0.404264i	0.807424	−	0.589971i	$-0.200861\pi$
$89$	6.60573	+	3.81382i	0.700206	+	0.404264i	−0.107218	+	0.994236i	$0.534194\pi$
$90$		0			0
$91$	23.0533	−	13.3098i	2.41664	−	1.39525i
$92$		0			0
$93$	−2.35498	−	1.26676i	−0.244200	−	0.131357i
$94$		0			0
$95$	−7.38387	+	6.19580i	−0.757569	+	0.635676i
$96$		0			0
$97$	0.903887	−	0.328988i	0.0917758	−	0.0334037i	−0.295724	−	0.955273i	$-0.595561\pi$
$97$	0.903887	−	0.328988i	0.0917758	−	0.0334037i	0.387500	+	0.921870i	$0.373339\pi$
$98$		0			0
$99$	−6.84452	−	10.3614i	−0.687900	−	1.04136i
$100$		0			0
$101$	13.8908	+	2.44933i	1.38219	+	0.243717i	0.814804	−	0.579736i	$-0.196844\pi$
$101$	13.8908	+	2.44933i	1.38219	+	0.243717i	0.567384	+	0.823453i	$0.307955\pi$
$102$		0			0
$103$	2.88921	−	7.93804i	0.284682	−	0.782158i	−0.712106	−	0.702072i	$-0.752258\pi$
$103$	2.88921	−	7.93804i	0.284682	−	0.782158i	0.996788	−	0.0800861i	$-0.0255195\pi$
$104$		0			0
$105$	−24.0847	+	9.59611i	−2.35042	+	0.936485i
$106$		0			0
$107$	5.48494			0.530249			0.265125	−	0.964214i	$-0.414587\pi$
$107$	5.48494			0.530249			0.265125	+	0.964214i	$0.414587\pi$
$108$		0			0
$109$	7.87082			0.753888			0.376944	−	0.926236i	$-0.376975\pi$
$109$	7.87082			0.753888			0.376944	+	0.926236i	$0.376975\pi$
$110$		0			0
$111$	−1.24123	+	8.53325i	−0.117812	+	0.809940i
$112$		0			0
$113$	−3.88780	+	10.6816i	−0.365733	+	1.00484i	0.611233	+	0.791451i	$0.290674\pi$
$113$	−3.88780	+	10.6816i	−0.365733	+	1.00484i	−0.976966	+	0.213393i	$0.931548\pi$
$114$		0			0
$115$	−6.31718	−	1.11389i	−0.589080	−	0.103871i
$116$		0			0
$117$	14.5962	+	10.8212i	1.34942	+	1.00042i
$118$		0			0
$119$	4.51081	−	1.64180i	0.413505	−	0.150504i
$120$		0			0
$121$	4.69894	−	3.94288i	0.427176	−	0.358444i
$122$		0			0
$123$	0.267263	+	8.87999i	0.0240983	+	0.800682i
$124$		0			0
$125$	−4.71532	+	2.72239i	−0.421751	+	0.243498i
$126$		0			0
$127$	9.65557	+	5.57465i	0.856793	+	0.494670i	0.862937	−	0.505311i	$-0.168622\pi$
$127$	9.65557	+	5.57465i	0.856793	+	0.494670i	−0.00614387	+	0.999981i	$0.501956\pi$
$128$		0			0
$129$	2.27278	−	6.88188i	0.200107	−	0.605916i
$130$		0			0
$131$	−1.91696	−	10.8716i	−0.167486	−	0.949858i	−0.946464	−	0.322808i	$-0.895373\pi$
$131$	−1.91696	−	10.8716i	−0.167486	−	0.949858i	0.778979	−	0.627050i	$-0.215738\pi$
$132$		0			0
$133$	−9.52903	−	7.99580i	−0.826272	−	0.693324i
$134$		0			0
$135$	−12.5508	−	12.4757i	−1.08020	−	1.07374i
$136$		0			0
$137$	7.49116	−	8.92762i	0.640013	−	0.762738i	−0.344359	−	0.938838i	$-0.611904\pi$
$137$	7.49116	−	8.92762i	0.640013	−	0.762738i	0.984372	+	0.176100i	$0.0563483\pi$
$138$		0			0
$139$	1.75412	−	0.309298i	0.148782	−	0.0262343i	−0.0987610	−	0.995111i	$-0.531488\pi$
$139$	1.75412	−	0.309298i	0.148782	−	0.0262343i	0.247543	+	0.968877i	$0.420377\pi$
$140$		0			0
$141$	−11.2900	+	10.0675i	−0.950787	+	0.847832i
$142$		0			0
$143$	−12.5352	+	21.7117i	−1.04825	+	1.81562i
$144$		0			0
$145$	9.15888	+	15.8636i	0.760604	+	1.31740i
$146$		0			0
$147$	−11.2178	−	18.1462i	−0.925229	−	1.49668i
$148$		0			0
$149$	4.09859	+	4.88451i	0.335770	+	0.400155i	0.907339	−	0.420399i	$-0.138110\pi$
$149$	4.09859	+	4.88451i	0.335770	+	0.400155i	−0.571570	+	0.820553i	$0.693665\pi$
$150$		0			0
$151$	2.40548	+	6.60901i	0.195755	+	0.537834i	0.998270	−	0.0587991i	$-0.0187271\pi$
$151$	2.40548	+	6.60901i	0.195755	+	0.537834i	−0.802514	+	0.596633i	$0.796505\pi$
$152$		0			0
$153$	2.25328	+	2.37880i	0.182167	+	0.192314i
$154$		0			0
$155$	0.913032	−	5.17806i	0.0733365	−	0.415912i
$156$		0			0
$157$	−18.7388	−	6.82035i	−1.49552	−	0.544323i	−0.540620	−	0.841267i	$-0.681810\pi$
$157$	−18.7388	−	6.82035i	−1.49552	−	0.544323i	−0.954895	+	0.296944i	$0.904033\pi$
$158$		0			0
$159$	13.0618	−	16.5533i	1.03587	−	1.31277i
$160$		0			0
$161$		−	8.27820i		−	0.652414i
$162$		0			0
$163$			8.53829i			0.668770i	0.942437	+	0.334385i	$0.108529\pi$
$163$			8.53829i			0.668770i	−0.942437	+	0.334385i	$0.891471\pi$
$164$		0			0
$165$	15.1253	−	19.1683i	1.17750	−	1.49225i
$166$		0			0
$167$	21.2266	+	7.72587i	1.64257	+	0.597846i	0.987485	−	0.157712i	$-0.0504118\pi$
$167$	21.2266	+	7.72587i	1.64257	+	0.597846i	0.655082	+	0.755558i	$0.272634\pi$
$168$		0			0
$169$	4.11251	−	23.3232i	0.316347	−	1.79409i
$170$		0			0
$171$	2.41891	−	8.13890i	0.184979	−	0.622397i
$172$		0			0
$173$	1.10479	+	3.03538i	0.0839954	+	0.230776i	0.974579	−	0.224044i	$-0.0719260\pi$
$173$	1.10479	+	3.03538i	0.0839954	+	0.230776i	−0.890584	+	0.454820i	$0.849704\pi$
$174$		0			0
$175$	−18.6422	−	22.2169i	−1.40922	−	1.67944i
$176$		0			0
$177$	−2.99865	−	4.85070i	−0.225392	−	0.364601i
$178$		0			0
$179$	1.89356	+	3.27975i	0.141531	+	0.245140i	0.928074	−	0.372397i	$-0.121464\pi$
$179$	1.89356	+	3.27975i	0.141531	+	0.245140i	−0.786542	+	0.617537i	$0.788131\pi$
$180$		0			0
$181$	−11.0399	+	19.1216i	−0.820586	+	1.42130i	0.0846611	+	0.996410i	$0.473019\pi$
$181$	−11.0399	+	19.1216i	−0.820586	+	1.42130i	−0.905247	+	0.424886i	$0.860314\pi$
$182$		0			0
$183$	3.45152	−	3.07778i	0.255144	−	0.227516i
$184$		0			0
$185$	−16.6977	+	2.94426i	−1.22764	+	0.216466i
$186$		0			0
$187$	−2.90600	+	3.46324i	−0.212508	+	0.253257i
$188$		0			0
$189$	13.0430	−	18.7467i	0.948739	−	1.36362i
$190$		0			0
$191$	−9.73071	−	8.16503i	−0.704089	−	0.590801i	0.218844	−	0.975760i	$-0.429771\pi$
$191$	−9.73071	−	8.16503i	−0.704089	−	0.590801i	−0.922934	+	0.384959i	$0.874216\pi$
$192$		0			0
$193$	−1.17091	−	6.64057i	−0.0842841	−	0.477999i	−0.997509	−	0.0705424i	$-0.977527\pi$
$193$	−1.17091	−	6.64057i	−0.0842841	−	0.477999i	0.913225	−	0.407456i	$-0.133584\pi$
$194$		0			0
$195$	−11.2039	+	33.9250i	−0.802327	+	2.42942i
$196$		0			0
$197$	10.9892	+	6.34463i	0.782950	+	0.452036i	0.837475	−	0.546476i	$-0.184031\pi$
$197$	10.9892	+	6.34463i	0.782950	+	0.452036i	−0.0545249	+	0.998512i	$0.517364\pi$
$198$		0			0
$199$	2.36052	−	1.36285i	0.167333	−	0.0966097i	−0.413995	−	0.910279i	$-0.635867\pi$
$199$	2.36052	−	1.36285i	0.167333	−	0.0966097i	0.581328	+	0.813670i	$0.302533\pi$
$200$		0			0
$201$	−0.188731	−	6.27069i	−0.0133120	−	0.442301i
$202$		0			0
$203$	−18.1088	+	15.1951i	−1.27099	+	1.06649i
$204$		0			0
$205$	−16.4149	+	5.97455i	−1.14647	+	0.417281i
$206$		0			0
$207$	5.18391	−	2.24842i	0.360306	−	0.156276i
$208$		0			0
$209$	11.5374	+	2.03435i	0.798055	+	0.140719i
$210$		0			0
$211$	−3.06103	+	8.41010i	−0.210730	+	0.578975i	−0.999355	−	0.0358983i	$-0.988571\pi$
$211$	−3.06103	+	8.41010i	−0.210730	+	0.578975i	0.788626	+	0.614874i	$0.210793\pi$
$212$		0			0
$213$	−0.419929	+	2.88695i	−0.0287731	+	0.197810i
$214$		0			0
$215$	14.2505			0.971878
$216$		0			0
$217$	6.78547			0.460628
$218$		0			0
$219$	17.9634	−	7.15721i	1.21386	−	0.483639i
$220$		0			0
$221$	2.26247	−	6.21609i	0.152190	−	0.418139i
$222$		0			0
$223$	−20.0713	−	3.53911i	−1.34407	−	0.236996i	−0.545104	−	0.838368i	$-0.683510\pi$
$223$	−20.0713	−	3.53911i	−1.34407	−	0.236996i	−0.798969	+	0.601372i	$0.794621\pi$
$224$		0			0
$225$	8.84914	−	17.7082i	0.589943	−	1.18055i
$226$		0			0
$227$	−26.8955	+	9.78916i	−1.78512	+	0.649729i	−0.785597	+	0.618739i	$0.787644\pi$
$227$	−26.8955	+	9.78916i	−1.78512	+	0.649729i	−0.999520	+	0.0309904i	$0.990134\pi$
$228$		0			0
$229$	7.21555	−	6.05457i	0.476817	−	0.400097i	−0.372457	−	0.928050i	$-0.621485\pi$
$229$	7.21555	−	6.05457i	0.476817	−	0.400097i	0.849274	+	0.527953i	$0.177040\pi$
$230$		0			0
$231$	27.7508	+	14.9273i	1.82587	+	0.982147i
$232$		0			0
$233$	5.57469	−	3.21855i	0.365210	−	0.210854i	−0.306154	−	0.951982i	$-0.599042\pi$
$233$	5.57469	−	3.21855i	0.365210	−	0.210854i	0.671364	+	0.741128i	$0.265709\pi$
$234$		0			0
$235$	−25.7584	−	14.8716i	−1.68029	−	0.970118i
$236$		0			0
$237$	16.5207	−	3.42847i	1.07313	−	0.222703i
$238$		0			0
$239$	0.774137	+	4.39035i	0.0500748	+	0.283988i	0.999555	−	0.0298396i	$-0.00949966\pi$
$239$	0.774137	+	4.39035i	0.0500748	+	0.283988i	−0.949480	+	0.313828i	$0.898389\pi$
$240$		0			0
$241$	8.43801	+	7.08033i	0.543540	+	0.456084i	0.872746	−	0.488174i	$-0.162337\pi$
$241$	8.43801	+	7.08033i	0.543540	+	0.456084i	−0.329207	+	0.944258i	$0.606781\pi$
$242$		0			0
$243$	15.2820	+	3.07594i	0.980339	+	0.197322i
$244$		0			0
$245$	26.9636	−	32.1339i	1.72264	−	2.05296i
$246$		0			0
$247$	−16.8814	+	2.97665i	−1.07414	+	0.189400i
$248$		0			0
$249$	0.110325	+	0.531623i	0.00699159	+	0.0336902i
$250$		0			0
$251$	9.58454	−	16.6009i	0.604971	−	1.04784i	−0.387085	−	0.922044i	$-0.626518\pi$
$251$	9.58454	−	16.6009i	0.604971	−	1.04784i	0.992056	−	0.125796i	$-0.0401485\pi$
$252$		0			0
$253$	3.89822	+	6.75191i	0.245079	+	0.424489i
$254$		0			0
$255$	−3.05202	+	5.67389i	−0.191125	+	0.355312i
$256$		0			0
$257$	−1.69182	−	2.01624i	−0.105533	−	0.125769i	0.710692	−	0.703503i	$-0.248382\pi$
$257$	−1.69182	−	2.01624i	−0.105533	−	0.125769i	−0.816226	+	0.577733i	$0.803937\pi$
$258$		0			0
$259$	−7.48379	−	20.5615i	−0.465020	−	1.27763i
$260$		0			0
$261$	−14.4339	−	7.21286i	−0.893433	−	0.446465i
$262$		0			0
$263$	−1.32969	+	7.54107i	−0.0819924	+	0.465002i	0.915973	+	0.401241i	$0.131421\pi$
$263$	−1.32969	+	7.54107i	−0.0819924	+	0.465002i	−0.997965	+	0.0637616i	$0.979690\pi$
$264$		0			0
$265$	38.9607	+	14.1805i	2.39334	+	0.871104i
$266$		0			0
$267$	−4.89002	−	12.2732i	−0.299264	−	0.751105i
$268$		0			0
$269$			7.03704i			0.429056i	0.976718	+	0.214528i	$0.0688213\pi$
$269$			7.03704i			0.429056i	−0.976718	+	0.214528i	$0.931179\pi$
$270$		0			0
$271$		−	24.1189i		−	1.46512i	−0.680704	−	0.732559i	$-0.738326\pi$
$271$		−	24.1189i		−	1.46512i	0.680704	−	0.732559i	$-0.261674\pi$
$272$		0			0
$273$	−45.6264	−	6.63672i	−2.76144	−	0.401673i
$274$		0			0
$275$	25.6670	+	9.34204i	1.54778	+	0.563346i
$276$		0			0
$277$	3.42494	−	19.4238i	0.205785	−	1.16706i	−0.690416	−	0.723413i	$-0.742572\pi$
$277$	3.42494	−	19.4238i	0.205785	−	1.16706i	0.896200	−	0.443650i	$-0.146317\pi$
$278$		0			0
$279$	1.84298	+	4.24914i	0.110336	+	0.254389i
$280$		0			0
$281$	2.28394	+	6.27507i	0.136248	+	0.374339i	0.988988	−	0.147997i	$-0.0472827\pi$
$281$	2.28394	+	6.27507i	0.136248	+	0.374339i	−0.852739	+	0.522337i	$0.825060\pi$
$282$		0			0
$283$	10.6684	+	12.7141i	0.634172	+	0.755777i	0.983438	−	0.181247i	$-0.0580133\pi$
$283$	10.6684	+	12.7141i	0.634172	+	0.755777i	−0.349265	+	0.937024i	$0.613569\pi$
$284$		0			0
$285$	16.6876	−	0.502251i	0.988489	−	0.0297508i
$286$		0			0
$287$	−11.2717	−	19.5231i	−0.665345	−	1.15241i
$288$		0			0
$289$	−7.90356	+	13.6894i	−0.464915	+	0.805257i
$290$		0			0
$291$	−1.58201	−	0.522468i	−0.0927392	−	0.0306276i
$292$		0			0
$293$	−12.2915	+	2.16732i	−0.718075	+	0.126616i	−0.520734	−	0.853719i	$-0.674342\pi$
$293$	−12.2915	+	2.16732i	−0.718075	+	0.126616i	−0.197341	+	0.980335i	$0.563231\pi$
$294$		0			0
$295$	7.20768	−	8.58978i	0.419647	−	0.500116i
$296$		0			0
$297$	−1.81035	+	21.4323i	−0.105047	+	1.24363i
$298$		0			0
$299$	−8.73882	−	7.33274i	−0.505379	−	0.424063i
$300$		0			0
$301$	3.19349	+	18.1112i	0.184070	+	1.04391i
$302$		0			0
$303$	−16.2597	−	18.2342i	−0.934096	−	1.04753i
$304$		0			0
$305$	7.87476	+	4.54650i	0.450908	+	0.260332i
$306$		0			0
$307$	−23.3290	+	13.4690i	−1.33145	+	0.768715i	−0.985523	−	0.169545i	$-0.945770\pi$
$307$	−23.3290	+	13.4690i	−1.33145	+	0.768715i	−0.345931	+	0.938260i	$0.612437\pi$
$308$		0			0
$309$	−12.4454	+	7.69362i	−0.707995	+	0.437675i
$310$		0			0
$311$	−17.6156	+	14.7812i	−0.998888	+	0.838167i	−0.986830	−	0.161761i	$-0.948283\pi$
$311$	−17.6156	+	14.7812i	−0.998888	+	0.838167i	−0.0120581	+	0.999927i	$0.503838\pi$
$312$		0			0
$313$	−9.95877	+	3.62469i	−0.562903	+	0.204880i	−0.607770	−	0.794113i	$-0.707936\pi$
$313$	−9.95877	+	3.62469i	−0.562903	+	0.204880i	0.0448672	+	0.998993i	$0.485714\pi$
$314$		0			0
$315$	43.0443	+	12.7929i	2.42527	+	0.720800i
$316$		0			0
$317$	−34.2177	−	6.03350i	−1.92186	−	0.338875i	−0.922919	−	0.384994i	$-0.874204\pi$
$317$	−34.2177	−	6.03350i	−1.92186	−	0.338875i	−0.998936	+	0.0461189i	$0.985315\pi$
$318$		0			0
$319$	7.61463	−	20.9210i	0.426337	−	1.17135i
$320$		0			0
$321$	−7.45799	−	5.88491i	−0.416264	−	0.328463i
$322$		0			0
$323$	−3.09118			−0.171998
$324$		0			0
$325$	−39.9662			−2.21693
$326$		0			0
$327$	−10.7021	−	8.44477i	−0.591828	−	0.466997i
$328$		0			0
$329$	13.1282	−	36.0694i	0.723780	−	1.98857i
$330$		0			0
$331$	5.68194	+	1.00188i	0.312308	+	0.0550682i	0.327605	−	0.944815i	$-0.393758\pi$
$331$	5.68194	+	1.00188i	0.312308	+	0.0550682i	−0.0152976	+	0.999883i	$0.504870\pi$
$332$		0			0
$333$	10.8432	−	10.2711i	0.594205	−	0.562852i
$334$		0			0
$335$	11.5916	−	4.21899i	0.633316	−	0.230508i
$336$		0			0
$337$	−5.65269	+	4.74317i	−0.307922	+	0.258377i	−0.783632	−	0.621225i	$-0.786635\pi$
$337$	−5.65269	+	4.74317i	−0.307922	+	0.258377i	0.475711	+	0.879602i	$0.342191\pi$
$338$		0			0
$339$	16.7469	−	10.3527i	0.909565	−	0.562284i
$340$		0			0
$341$	−5.53440	+	3.19529i	−0.299705	+	0.173035i
$342$		0			0
$343$	20.2379	+	11.6844i	1.09275	+	0.630897i
$344$		0			0
$345$	7.39448	+	8.29241i	0.398105	+	0.446448i
$346$		0			0
$347$	4.01371	+	22.7629i	0.215467	+	1.22198i	0.880094	+	0.474800i	$0.157480\pi$
$347$	4.01371	+	22.7629i	0.215467	+	1.22198i	−0.664626	+	0.747176i	$0.731409\pi$
$348$		0			0
$349$	−21.3840	−	17.9433i	−1.14466	−	0.960482i	−0.145077	−	0.989420i	$-0.546343\pi$
$349$	−21.3840	−	17.9433i	−1.14466	−	0.960482i	−0.999581	+	0.0289385i	$0.990787\pi$
$350$		0			0
$351$	−8.23647	−	30.3744i	−0.439630	−	1.62126i
$352$		0			0
$353$	−4.12725	+	4.91866i	−0.219671	+	0.261794i	−0.864614	−	0.502437i	$-0.832437\pi$
$353$	−4.12725	+	4.91866i	−0.219671	+	0.261794i	0.644943	+	0.764231i	$0.276881\pi$
$354$		0			0
$355$	−5.64913	+	0.996094i	−0.299825	+	0.0528672i
$356$		0			0
$357$	−7.89496	−	2.60735i	−0.417846	−	0.137996i
$358$		0			0
$359$	−1.88368	+	3.26264i	−0.0994170	+	0.172195i	−0.911443	−	0.411425i	$-0.865031\pi$
$359$	−1.88368	+	3.26264i	−0.0994170	+	0.172195i	0.812026	+	0.583621i	$0.198364\pi$
$360$		0			0
$361$	−5.49484	−	9.51734i	−0.289202	−	0.500913i
$362$		0			0
$363$	−10.6196	+	0.319622i	−0.557387	+	0.0167758i
$364$		0			0
$365$	24.4397	+	29.1261i	1.27923	+	1.52453i
$366$		0			0
$367$	6.60798	+	18.1553i	0.344934	+	0.947697i	0.983941	+	0.178496i	$0.0571233\pi$
$367$	6.60798	+	18.1553i	0.344934	+	0.947697i	−0.639007	+	0.769201i	$0.720654\pi$
$368$		0			0
$369$	9.16412	−	12.3611i	0.477065	−	0.643491i
$370$		0			0
$371$	−9.29129	+	52.6935i	−0.482380	+	2.73571i
$372$		0			0
$373$	−0.646074	−	0.235152i	−0.0334524	−	0.0121757i	0.325240	−	0.945632i	$-0.394555\pi$
$373$	−0.646074	−	0.235152i	−0.0334524	−	0.0121757i	−0.358692	+	0.933456i	$0.616777\pi$
$374$		0			0
$375$	9.33242	+	1.35747i	0.481924	+	0.0700996i
$376$		0			0
$377$			32.5761i			1.67776i
$378$		0			0
$379$		−	17.2965i		−	0.888463i	−0.895912	−	0.444232i	$-0.853477\pi$
$379$		−	17.2965i		−	0.888463i	0.895912	−	0.444232i	$-0.146523\pi$
$380$		0			0
$381$	−7.14772	−	17.9396i	−0.366189	−	0.919075i
$382$		0			0
$383$	−3.32586	−	1.21051i	−0.169944	−	0.0618544i	0.255647	−	0.966770i	$-0.417711\pi$
$383$	−3.32586	−	1.21051i	−0.169944	−	0.0618544i	−0.425591	+	0.904916i	$0.639934\pi$
$384$		0			0
$385$	−10.7591	+	61.0177i	−0.548333	+	3.10975i
$386$		0			0
$387$	−10.4741	+	6.91892i	−0.532426	+	0.351709i
$388$		0			0
$389$	11.5224	+	31.6576i	0.584210	+	1.60510i	0.780913	+	0.624640i	$0.214754\pi$
$389$	11.5224	+	31.6576i	0.584210	+	1.60510i	−0.196703	+	0.980463i	$0.563024\pi$
$390$		0			0
$391$	−1.32231	−	1.57587i	−0.0668720	−	0.0796950i
$392$		0			0
$393$	−9.05786	+	16.8391i	−0.456909	+	0.849421i
$394$		0			0
$395$	16.5882	+	28.7316i	0.834642	+	1.44564i
$396$		0			0
$397$	14.8687	−	25.7534i	0.746239	−	1.29252i	−0.203374	−	0.979101i	$-0.565191\pi$
$397$	14.8687	−	25.7534i	0.746239	−	1.29252i	0.949614	−	0.313423i	$-0.101476\pi$
$398$		0			0
$399$	4.37795	+	21.0960i	0.219172	+	1.05612i
$400$		0			0
$401$	8.62018	−	1.51997i	0.430471	−	0.0759037i	0.0457855	−	0.998951i	$-0.485421\pi$
$401$	8.62018	−	1.51997i	0.430471	−	0.0759037i	0.384686	+	0.923048i	$0.374310\pi$
$402$		0			0
$403$	6.01050	−	7.16303i	0.299404	−	0.356816i
$404$		0			0
$405$	3.68006	+	30.4295i	0.182863	+	1.51205i
$406$		0			0
$407$	15.7864	+	13.2464i	0.782504	+	0.656599i
$408$		0			0
$409$	−3.71415	−	21.0640i	−0.183653	−	1.04155i	−0.927674	−	0.373392i	$-0.878195\pi$
$409$	−3.71415	−	21.0640i	−0.183653	−	1.04155i	0.744021	−	0.668157i	$-0.232916\pi$
$410$		0			0
$411$	−19.7645	+	4.10164i	−0.974911	+	0.202319i
$412$		0			0
$413$	12.5321	+	7.23540i	0.616663	+	0.356031i
$414$		0			0
$415$	−0.924560	+	0.533795i	−0.0453849	+	0.0262030i
$416$		0			0
$417$	−2.71696	−	1.46147i	−0.133050	−	0.0715684i
$418$		0			0
$419$	−28.0877	+	23.5684i	−1.37217	+	1.15139i	−0.400165	+	0.916443i	$0.631047\pi$
$419$	−28.0877	+	23.5684i	−1.37217	+	1.15139i	−0.972008	+	0.234947i	$0.924508\pi$
$420$		0			0
$421$	−10.5196	+	3.82881i	−0.512692	+	0.186605i	−0.585394	−	0.810749i	$-0.699060\pi$
$421$	−10.5196	+	3.82881i	−0.512692	+	0.186605i	0.0727019	+	0.997354i	$0.476838\pi$
$422$		0			0
$423$	26.1528	−	1.57568i	1.27159	−	0.0766122i
$424$		0			0
$425$	−7.09759	−	1.25150i	−0.344284	−	0.0607065i
$426$		0			0
$427$	−4.01350	+	11.0270i	−0.194227	+	0.533634i
$428$		0			0
$429$	40.3393	−	16.0725i	1.94760	−	0.775986i
$430$		0			0
$431$	0.802008			0.0386314			0.0193157	−	0.999813i	$-0.493851\pi$
$431$	0.802008			0.0386314			0.0193157	+	0.999813i	$0.493851\pi$
$432$		0			0
$433$	3.12308			0.150086			0.0750428	−	0.997180i	$-0.476091\pi$
$433$	3.12308			0.150086			0.0750428	+	0.997180i	$0.476091\pi$
$434$		0			0
$435$	4.56692	−	31.3969i	0.218967	−	1.50537i
$436$		0			0
$437$	−1.82324	+	5.00930i	−0.0872172	+	0.239627i
$438$		0			0
$439$	4.04187	+	0.712690i	0.192908	+	0.0340149i	0.269267	−	0.963066i	$-0.413219\pi$
$439$	4.04187	+	0.712690i	0.192908	+	0.0340149i	−0.0763594	+	0.997080i	$0.524330\pi$
$440$		0			0
$441$	−4.21638	+	36.7096i	−0.200780	+	1.74808i
$442$		0			0
$443$	32.3631	−	11.7792i	1.53762	−	0.559646i	0.572143	−	0.820154i	$-0.306112\pi$
$443$	32.3631	−	11.7792i	1.53762	−	0.559646i	0.965472	+	0.260507i	$0.0838899\pi$
$444$		0			0
$445$	19.8998	−	16.6979i	0.943343	−	0.791559i
$446$		0			0
$447$	−0.332244	−	11.0390i	−0.0157146	−	0.522128i
$448$		0			0
$449$	12.4452	−	7.18523i	0.587324	−	0.339092i	−0.176715	−	0.984262i	$-0.556547\pi$
$449$	12.4452	−	7.18523i	0.587324	−	0.339092i	0.764039	+	0.645170i	$0.223214\pi$
$450$		0			0
$451$	18.3869	+	10.6157i	0.865806	+	0.499873i
$452$		0			0
$453$	3.82016	−	11.5673i	0.179487	−	0.543479i
$454$		0			0
$455$	−15.7426	−	89.2810i	−0.738027	−	4.18556i
$456$		0			0
$457$	6.63409	+	5.56666i	0.310330	+	0.260398i	0.784628	−	0.619967i	$-0.212854\pi$
$457$	6.63409	+	5.56666i	0.310330	+	0.260398i	−0.474299	+	0.880364i	$0.657298\pi$
$458$		0			0
$459$	−0.511573	−	5.65209i	−0.0238782	−	0.263817i
$460$		0			0
$461$	−15.0829	+	17.9751i	−0.702481	+	0.837184i	−0.992805	−	0.119745i	$-0.961792\pi$
$461$	−15.0829	+	17.9751i	−0.702481	+	0.837184i	0.290324	+	0.956928i	$0.406237\pi$
$462$		0			0
$463$	30.2719	−	5.33776i	1.40686	−	0.248067i	0.581899	−	0.813261i	$-0.302310\pi$
$463$	30.2719	−	5.33776i	1.40686	−	0.248067i	0.824958	+	0.565194i	$0.191199\pi$
$464$		0			0
$465$	−6.79712	+	6.06110i	−0.315209	+	0.281077i
$466$		0			0
$467$	9.51526	−	16.4809i	0.440314	−	0.762646i	−0.557399	−	0.830245i	$-0.688201\pi$
$467$	9.51526	−	16.4809i	0.440314	−	0.762646i	0.997713	+	0.0675990i	$0.0215338\pi$
$468$		0			0
$469$	7.95960	+	13.7864i	0.367540	+	0.636598i
$470$		0			0
$471$	18.1618	+	29.3790i	0.836850	+	1.35371i
$472$		0			0
$473$	−11.1333	−	13.2681i	−0.511909	−	0.610069i
$474$		0			0
$475$	6.38759	+	17.5498i	0.293083	+	0.805238i
$476$		0			0
$477$	−35.5209	+	8.49362i	−1.62639	+	0.388896i
$478$		0			0
$479$	2.75148	−	15.6044i	0.125718	−	0.712984i	−0.855160	−	0.518363i	$-0.826541\pi$
$479$	2.75148	−	15.6044i	0.125718	−	0.712984i	0.980879	−	0.194620i	$-0.0623474\pi$
$480$		0			0
$481$	−28.3347	−	10.3130i	−1.29195	−	0.470232i
$482$		0			0
$483$	−8.88186	+	11.2560i	−0.404139	+	0.512168i
$484$		0			0
$485$		−	3.27592i		−	0.148752i
$486$		0			0
$487$			4.49577i			0.203723i	0.994799	+	0.101861i	$0.0324798\pi$
$487$			4.49577i			0.203723i	−0.994799	+	0.101861i	$0.967520\pi$
$488$		0			0
$489$	9.16091	−	11.6097i	0.414271	−	0.525008i
$490$		0			0
$491$	34.4443	+	12.5367i	1.55445	+	0.565773i	0.969456	−	0.245266i	$-0.0788753\pi$
$491$	34.4443	+	12.5367i	1.55445	+	0.565773i	0.584992	+	0.811039i	$0.301097\pi$
$492$		0			0
$493$	−1.02008	+	5.78519i	−0.0459423	+	0.260552i
$494$		0			0
$495$	−41.1322	+	9.83539i	−1.84876	+	0.442068i
$496$		0			0
$497$	−2.53190	−	6.95633i	−0.113571	−	0.312034i
$498$		0			0
$499$	−23.9018	−	28.4851i	−1.06999	−	1.27517i	−0.959627	−	0.281275i	$-0.909243\pi$
$499$	−23.9018	−	28.4851i	−1.06999	−	1.27517i	−0.110364	−	0.993891i	$-0.535202\pi$
$500$		0			0
$501$	−20.5731	−	33.2795i	−0.919137	−	1.48682i
$502$		0			0
$503$	19.5952	+	33.9399i	0.873706	+	1.51330i	0.858135	+	0.513425i	$0.171623\pi$
$503$	19.5952	+	33.9399i	0.873706	+	1.51330i	0.0155717	+	0.999879i	$0.495043\pi$
$504$		0			0
$505$	24.0188	−	41.6018i	1.06882	−	1.85126i
$506$		0			0
$507$	−30.6159	+	27.3007i	−1.35970	+	1.21247i
$508$		0			0
$509$	−13.0715	+	2.30486i	−0.579385	+	0.102161i	−0.455658	−	0.890155i	$-0.650596\pi$
$509$	−13.0715	+	2.30486i	−0.579385	+	0.102161i	−0.123727	+	0.992316i	$0.539485\pi$
$510$		0			0
$511$	−31.5399	+	37.5878i	−1.39524	+	1.66279i
$512$		0			0
$513$	−12.0214	+	8.47133i	−0.530760	+	0.374018i
$514$		0			0
$515$	−22.0387	−	18.4927i	−0.971143	−	0.814886i
$516$		0			0
$517$	6.27745	+	35.6012i	0.276082	+	1.56574i
$518$		0			0
$519$	1.75452	−	5.31262i	0.0770149	−	0.233198i
$520$		0			0
$521$	−38.3054	−	22.1156i	−1.67819	−	0.968903i	−0.962815	−	0.270162i	$-0.912923\pi$
$521$	−38.3054	−	22.1156i	−1.67819	−	0.968903i	−0.715375	−	0.698741i	$-0.753744\pi$
$522$		0			0
$523$	−38.8478	+	22.4288i	−1.69870	+	0.980742i	−0.751694	+	0.659512i	$0.770763\pi$
$523$	−38.8478	+	22.4288i	−1.69870	+	0.980742i	−0.947001	+	0.321230i	$0.895904\pi$
$524$		0			0
$525$	1.51120	+	50.2104i	0.0659540	+	2.19136i
$526$		0			0
$527$	1.29170	−	1.08387i	0.0562675	−	0.0472141i
$528$		0			0
$529$	18.2793	−	6.65312i	0.794752	−	0.289266i
$530$		0			0
$531$	−1.12709	+	9.81291i	−0.0489115	+	0.425844i
$532$		0			0
$533$	−30.5937	−	5.39450i	−1.32516	−	0.233662i
$534$		0			0
$535$	6.38894	−	17.5535i	0.276218	−	0.758902i
$536$		0			0
$537$	0.944193	−	6.49118i	0.0407449	−	0.280115i
$538$		0			0
$539$	−50.9840			−2.19604
$540$		0			0
$541$	10.2100			0.438964			0.219482	−	0.975617i	$-0.429563\pi$
$541$	10.2100			0.438964			0.219482	+	0.975617i	$0.429563\pi$
$542$		0			0
$543$	35.5271	−	14.1551i	1.52461	−	0.607454i
$544$		0			0
$545$	9.16805	−	25.1890i	0.392716	−	1.07898i
$546$		0			0
$547$	41.0351	+	7.23559i	1.75453	+	0.309372i	0.956172	−	0.292807i	$-0.0945893\pi$
$547$	41.0351	+	7.23559i	1.75453	+	0.309372i	0.798361	+	0.602178i	$0.205700\pi$
$548$		0			0
$549$	−7.99532	+	0.481711i	−0.341232	+	0.0205589i
$550$		0			0
$551$	14.3047	−	5.20647i	0.609399	−	0.221803i
$552$		0			0
$553$	−32.7980	+	27.5208i	−1.39471	+	1.17030i
$554$		0			0
$555$	25.8632	+	13.9120i	1.09783	+	0.590530i
$556$		0			0
$557$	21.7735	−	12.5709i	0.922571	−	0.532647i	0.0381165	−	0.999273i	$-0.487864\pi$
$557$	21.7735	−	12.5709i	0.922571	−	0.532647i	0.884454	+	0.466627i	$0.154531\pi$
$558$		0			0
$559$	21.9477	+	12.6715i	0.928289	+	0.535948i
$560$		0			0
$561$	7.66714	−	1.59113i	0.323707	−	0.0671774i
$562$		0			0
$563$	−7.04571	−	39.9582i	−0.296941	−	1.68404i	−0.659206	−	0.751962i	$-0.729108\pi$
$563$	−7.04571	−	39.9582i	−0.296941	−	1.68404i	0.362265	−	0.932075i	$-0.382003\pi$
$564$		0			0
$565$	29.6559	+	24.8843i	1.24763	+	1.04689i
$566$		0			0
$567$	−37.8486	+	11.4962i	−1.58949	+	0.482794i
$568$		0			0
$569$	2.01852	−	2.40558i	0.0846208	−	0.100847i	−0.722073	−	0.691817i	$-0.756810\pi$
$569$	2.01852	−	2.40558i	0.0846208	−	0.100847i	0.806694	+	0.590970i	$0.201255\pi$
$570$		0			0
$571$	−8.87330	+	1.56460i	−0.371336	+	0.0654765i	−0.356202	−	0.934409i	$-0.615929\pi$
$571$	−8.87330	+	1.56460i	−0.371336	+	0.0654765i	−0.0151338	+	0.999885i	$0.504817\pi$
$572$		0			0
$573$	4.47061	+	21.5424i	0.186762	+	0.899949i
$574$		0			0
$575$	−6.21436	+	10.7636i	−0.259157	+	0.448873i
$576$		0			0
$577$	0.994209	+	1.72202i	0.0413895	+	0.0716886i	0.885978	−	0.463727i	$-0.153488\pi$
$577$	0.994209	+	1.72202i	0.0413895	+	0.0716886i	−0.844589	+	0.535416i	$0.820155\pi$
$578$		0			0
$579$	−5.53269	+	10.2856i	−0.229931	+	0.427456i
$580$		0			0
$581$	−0.885598	−	1.05541i	−0.0367408	−	0.0437860i
$582$		0			0
$583$	−17.2352	−	47.3534i	−0.713811	−	1.96118i
$584$		0			0
$585$	51.6330	−	34.1076i	2.13476	−	1.41017i
$586$		0			0
$587$	7.64588	−	43.3619i	0.315579	−	1.78974i	−0.253374	−	0.967369i	$-0.581540\pi$
$587$	7.64588	−	43.3619i	0.315579	−	1.78974i	0.568953	−	0.822370i	$-0.307349\pi$
$588$		0			0
$589$	−4.10602	−	1.49447i	−0.169186	−	0.0615785i
$590$		0			0
$591$	−8.13499	−	20.4175i	−0.334629	−	0.839863i
$592$		0			0
$593$		−	37.9415i		−	1.55807i	−0.626979	−	0.779036i	$-0.715709\pi$
$593$		−	37.9415i		−	1.55807i	0.626979	−	0.779036i	$-0.284291\pi$
$594$		0			0
$595$		−	16.3483i		−	0.670217i
$596$		0			0
$597$	−4.67188	−	0.679561i	−0.191207	−	0.0278126i
$598$		0			0
$599$	−33.3395	−	12.1346i	−1.36221	−	0.495805i	−0.445476	−	0.895294i	$-0.646965\pi$
$599$	−33.3395	−	12.1346i	−1.36221	−	0.495805i	−0.916738	+	0.399489i	$0.869188\pi$
$600$		0			0
$601$	4.82497	−	27.3638i	0.196815	−	1.11619i	−0.712996	−	0.701168i	$-0.752662\pi$
$601$	4.82497	−	27.3638i	0.196815	−	1.11619i	0.909811	−	0.415024i	$-0.136227\pi$
$602$		0			0
$603$	−6.47134	+	8.72888i	−0.263533	+	0.355468i
$604$		0			0
$605$	−7.14501	−	19.6308i	−0.290486	−	0.798104i
$606$		0			0
$607$	18.0150	+	21.4694i	0.731207	+	0.871418i	0.995668	−	0.0929782i	$-0.0296387\pi$
$607$	18.0150	+	21.4694i	0.731207	+	0.871418i	−0.264462	+	0.964396i	$0.585194\pi$
$608$		0			0
$609$	40.9261	−	1.23176i	1.65841	−	0.0499136i
$610$		0			0
$611$	−26.4476	−	45.8086i	−1.06995	−	1.85322i
$612$		0			0
$613$	−2.08983	+	3.61970i	−0.0844076	+	0.146198i	−0.905139	−	0.425117i	$-0.860233\pi$
$613$	−2.08983	+	3.61970i	−0.0844076	+	0.146198i	0.820731	+	0.571315i	$0.193566\pi$
$614$		0			0
$615$	28.7300	+	9.48822i	1.15850	+	0.382602i
$616$		0			0
$617$	−26.3586	+	4.64774i	−1.06116	+	0.187111i	−0.676870	−	0.736102i	$-0.736664\pi$
$617$	−26.3586	+	4.64774i	−1.06116	+	0.187111i	−0.384288	+	0.923213i	$0.625553\pi$
$618$		0			0
$619$	19.8689	−	23.6788i	0.798597	−	0.951731i	−0.201015	−	0.979588i	$-0.564424\pi$
$619$	19.8689	−	23.6788i	0.798597	−	0.951731i	0.999612	+	0.0278575i	$0.00886846\pi$
$620$		0			0
$621$	−9.46104	−	2.50470i	−0.379658	−	0.100510i
$622$		0			0
$623$	25.6811	+	21.5490i	1.02889	+	0.863343i
$624$		0			0
$625$	−2.50929	−	14.2309i	−0.100372	−	0.569235i
$626$		0			0
$627$	−13.5049	−	15.1448i	−0.539333	−	0.604826i
$628$		0			0
$629$	−4.70901	−	2.71875i	−0.187761	−	0.108404i
$630$		0			0
$631$	4.48915	−	2.59181i	0.178710	−	0.103178i	−0.407976	−	0.912993i	$-0.633765\pi$
$631$	4.48915	−	2.59181i	0.178710	−	0.103178i	0.586687	+	0.809814i	$0.300432\pi$
$632$		0			0
$633$	13.1855	−	8.15115i	0.524077	−	0.323979i
$634$		0			0
$635$	29.0875	−	24.4073i	1.15430	−	0.968575i
$636$		0			0
$637$	70.1008	−	25.5146i	2.77749	−	1.01093i
$638$		0			0
$639$	3.66845	−	3.47489i	0.145122	−	0.137465i
$640$		0			0
$641$	32.6707	+	5.76073i	1.29042	+	0.227535i	0.776397	−	0.630244i	$-0.217045\pi$
$641$	32.6707	+	5.76073i	1.29042	+	0.227535i	0.514019	+	0.857779i	$0.328156\pi$
$642$		0			0
$643$	−7.68834	+	21.1236i	−0.303199	+	0.833032i	0.690741	+	0.723102i	$0.257285\pi$
$643$	−7.68834	+	21.1236i	−0.303199	+	0.833032i	−0.993939	+	0.109929i	$0.964938\pi$
$644$		0			0
$645$	−19.3767	−	15.2897i	−0.762958	−	0.602031i
$646$		0			0
$647$	20.0311			0.787505			0.393752	−	0.919217i	$-0.371177\pi$
$647$	20.0311			0.787505			0.393752	+	0.919217i	$0.371177\pi$
$648$		0			0
$649$	−13.6286			−0.534971
$650$		0			0
$651$	−9.22635	−	7.28028i	−0.361609	−	0.285337i
$652$		0			0
$653$	−4.59529	+	12.6255i	−0.179828	+	0.494072i	−0.996553	−	0.0829537i	$-0.973565\pi$
$653$	−4.59529	+	12.6255i	−0.179828	+	0.494072i	0.816726	+	0.577026i	$0.195787\pi$
$654$		0			0
$655$	−37.0254	−	6.52858i	−1.44670	−	0.255093i
$656$		0			0
$657$	−32.1044	−	9.54155i	−1.25251	−	0.372251i
$658$		0			0
$659$	−36.5498	+	13.3030i	−1.42378	+	0.518213i	−0.935141	−	0.354275i	$-0.884728\pi$
$659$	−36.5498	+	13.3030i	−1.42378	+	0.518213i	−0.488636	+	0.872488i	$0.662505\pi$
$660$		0			0
$661$	3.65798	−	3.06941i	0.142279	−	0.119386i	−0.568871	−	0.822427i	$-0.692619\pi$
$661$	3.65798	−	3.06941i	0.142279	−	0.119386i	0.711149	+	0.703041i	$0.248175\pi$
$662$		0			0
$663$	−9.74570	+	6.02469i	−0.378492	+	0.233980i
$664$		0			0
$665$	−36.6885	+	21.1821i	−1.42272	+	0.821408i
$666$		0			0
$667$	8.77332	+	5.06528i	0.339704	+	0.196128i
$668$		0			0
$669$	23.4942	+	26.3471i	0.908337	+	1.01864i
$670$		0			0
$671$	−1.91912	−	10.8839i	−0.0740867	−	0.420167i
$672$		0			0
$673$	−15.6817	−	13.1585i	−0.604487	−	0.507225i	0.288397	−	0.957511i	$-0.406878\pi$
$673$	−15.6817	−	13.1585i	−0.604487	−	0.507225i	−0.892884	+	0.450286i	$0.851322\pi$
$674$		0			0
$675$	−31.0319	+	14.5838i	−1.19442	+	0.561332i
$676$		0			0
$677$	2.71884	−	3.24019i	0.104494	−	0.124531i	−0.711263	−	0.702926i	$-0.751876\pi$
$677$	2.71884	−	3.24019i	0.104494	−	0.124531i	0.815757	+	0.578395i	$0.196321\pi$
$678$		0			0
$679$	4.16341	−	0.734122i	0.159777	−	0.0281730i
$680$		0			0
$681$	47.0733	+	15.5462i	1.80385	+	0.595732i
$682$		0			0
$683$	4.10080	−	7.10280i	0.156913	−	0.271781i	−0.776841	−	0.629697i	$-0.783179\pi$
$683$	4.10080	−	7.10280i	0.156913	−	0.271781i	0.933754	+	0.357916i	$0.116512\pi$
$684$		0			0
$685$	−19.8453	−	34.3730i	−0.758248	−	1.31332i
$686$		0			0
$687$	−16.3072	+	0.490802i	−0.622159	+	0.0187253i
$688$		0			0
$689$	47.3954	+	56.4836i	1.80562	+	2.15185i
$690$		0			0
$691$	7.36741	+	20.2418i	0.280269	+	0.770034i	0.997330	+	0.0730233i	$0.0232647\pi$
$691$	7.36741	+	20.2418i	0.280269	+	0.770034i	−0.717061	+	0.697011i	$0.754513\pi$
$692$		0			0
$693$	−21.7175	−	50.0715i	−0.824980	−	1.90206i
$694$		0			0
$695$	1.05337	−	5.97398i	0.0399567	−	0.226606i
$696$		0			0
$697$	−5.26421	−	1.91602i	−0.199396	−	0.0725743i
$698$		0			0
$699$	−11.0333	−	1.60487i	−0.417316	−	0.0607019i
$700$		0			0
$701$		−	27.8257i		−	1.05096i	−0.850806	−	0.525481i	$-0.823886\pi$
$701$		−	27.8257i		−	1.05096i	0.850806	−	0.525481i	$-0.176114\pi$
$702$		0			0
$703$			14.0905i			0.531432i
$704$		0			0
$705$	19.0682	+	47.8580i	0.718149	+	1.80244i
$706$		0			0
$707$	58.2548	+	21.2030i	2.19090	+	0.797422i
$708$		0			0
$709$	0.557300	−	3.16061i	0.0209298	−	0.118699i	−0.972553	−	0.232682i	$-0.925250\pi$
$709$	0.557300	−	3.16061i	0.0209298	−	0.118699i	0.993483	+	0.113983i	$0.0363610\pi$
$710$		0			0
$711$	−26.1420	−	13.0636i	−0.980402	−	0.489925i
$712$		0			0
$713$	−0.994554	−	2.73251i	−0.0372463	−	0.102333i
$714$		0			0
$715$	54.8826	+	65.4066i	2.05249	+	2.44607i
$716$		0			0
$717$	3.65789	−	6.80024i	0.136606	−	0.253960i
$718$		0			0
$719$	−6.67788	−	11.5664i	−0.249043	−	0.431355i	0.714218	−	0.699924i	$-0.246783\pi$
$719$	−6.67788	−	11.5664i	−0.249043	−	0.431355i	−0.963260	+	0.268569i	$0.913449\pi$
$720$		0			0
$721$	18.5638	−	32.1535i	0.691353	−	1.19746i
$722$		0			0
$723$	−3.87670	−	18.6806i	−0.144176	−	0.694738i
$724$		0			0
$725$	34.9526	−	6.16308i	1.29811	−	0.228891i
$726$		0			0
$727$	−2.08083	+	2.47984i	−0.0771737	+	0.0919720i	−0.803250	−	0.595642i	$-0.796898\pi$
$727$	−2.08083	+	2.47984i	−0.0771737	+	0.0919720i	0.726076	+	0.687614i	$0.241342\pi$
$728$		0			0
$729$	−17.4790	−	20.5788i	−0.647369	−	0.762177i
$730$		0			0
$731$	3.50089	+	2.93760i	0.129485	+	0.108651i
$732$		0			0
$733$	−8.17205	−	46.3460i	−0.301842	−	1.71183i	−0.638011	−	0.770027i	$-0.720243\pi$
$733$	−8.17205	−	46.3460i	−0.301842	−	1.71183i	0.336170	−	0.941801i	$-0.390868\pi$
$734$		0			0
$735$	−71.1401	+	14.7634i	−2.62404	+	0.544556i
$736$		0			0
$737$	−12.9841	−	7.49637i	−0.478276	−	0.276132i
$738$		0			0
$739$	3.41970	−	1.97436i	0.125796	−	0.0726281i	−0.435782	−	0.900052i	$-0.643528\pi$
$739$	3.41970	−	1.97436i	0.125796	−	0.0726281i	0.561577	+	0.827424i	$0.310195\pi$
$740$		0			0
$741$	26.1477	+	14.0650i	0.960561	+	0.516691i
$742$		0			0
$743$	−37.8736	+	31.7797i	−1.38945	+	1.16589i	−0.423885	+	0.905716i	$0.639334\pi$
$743$	−37.8736	+	31.7797i	−1.38945	+	1.16589i	−0.965563	+	0.260170i	$0.916222\pi$
$744$		0			0
$745$	20.4060	−	7.42718i	0.747618	−	0.272111i
$746$		0			0
$747$	0.420378	−	0.841229i	0.0153808	−	0.0307790i
$748$		0			0
$749$	23.7407	+	4.18612i	0.867465	+	0.152958i
$750$		0			0
$751$	−16.7877	+	46.1239i	−0.612592	+	1.68308i	0.111830	+	0.993727i	$0.464329\pi$
$751$	−16.7877	+	46.1239i	−0.612592	+	1.68308i	−0.724423	+	0.689356i	$0.757894\pi$
$752$		0			0
$753$	−30.8438	+	12.2891i	−1.12401	+	0.447841i
$754$		0			0
$755$	23.9528			0.871731
$756$		0			0
$757$	23.1774			0.842397			0.421199	−	0.906968i	$-0.361610\pi$
$757$	23.1774			0.842397			0.421199	+	0.906968i	$0.361610\pi$
$758$		0			0
$759$	1.94378	−	13.3632i	0.0705548	−	0.485053i
$760$		0			0
$761$	−2.42482	+	6.66214i	−0.0878997	+	0.241502i	−0.975852	−	0.218433i	$-0.929905\pi$
$761$	−2.42482	+	6.66214i	−0.0878997	+	0.241502i	0.887952	+	0.459936i	$0.152128\pi$
$762$		0			0
$763$	34.0676	+	6.00703i	1.23333	+	0.217469i
$764$		0			0
$765$	10.2375	−	4.44033i	0.370138	−	0.160540i
$766$		0			0
$767$	18.7388	−	6.82035i	0.676618	−	0.246269i
$768$		0			0
$769$	−34.5271	+	28.9717i	−1.24508	+	1.04475i	−0.247970	+	0.968768i	$0.579763\pi$
$769$	−34.5271	+	28.9717i	−1.24508	+	1.04475i	−0.997109	+	0.0759780i	$0.975792\pi$
$770$		0			0
$771$	0.137144	+	4.55671i	0.00493914	+	0.164106i
$772$		0			0
$773$	−13.9113	+	8.03167i	−0.500353	+	0.288879i	−0.728859	−	0.684663i	$-0.759949\pi$
$773$	−13.9113	+	8.03167i	−0.500353	+	0.288879i	0.228506	+	0.973542i	$0.426616\pi$
$774$		0			0
$775$	−8.82270	−	5.09379i	−0.316921	−	0.182974i
$776$		0			0
$777$	−11.8851	+	35.9875i	−0.426374	+	1.29104i
$778$		0			0
$779$	2.52083	+	14.2963i	0.0903181	+	0.512219i
$780$		0			0
$781$	5.34083	+	4.48149i	0.191110	+	0.160360i
$782$		0			0
$783$	11.8872	+	25.2939i	0.424813	+	0.903929i
$784$		0			0
$785$	−43.6543	+	52.0252i	−1.55809	+	1.85686i
$786$		0			0
$787$	3.80955	−	0.671726i	0.135796	−	0.0239444i	−0.105337	−	0.994437i	$-0.533592\pi$
$787$	3.80955	−	0.671726i	0.135796	−	0.0239444i	0.241133	+	0.970492i	$0.422481\pi$
$788$		0			0
$789$	9.89898	−	8.82709i	0.352413	−	0.314253i
$790$		0			0
$791$	−24.9800	+	43.2666i	−0.888185	+	1.53838i
$792$		0			0
$793$	8.08545	+	14.0044i	0.287123	+	0.497311i
$794$		0			0
$795$	−37.7611	−	61.0834i	−1.33925	−	2.16640i
$796$		0			0
$797$	−18.7183	−	22.3076i	−0.663036	−	0.790175i	0.324782	−	0.945789i	$-0.394709\pi$
$797$	−18.7183	−	22.3076i	−0.663036	−	0.790175i	−0.987818	+	0.155614i	$0.950264\pi$
$798$		0			0
$799$	−3.26238	−	8.96330i	−0.115415	−	0.317099i
$800$		0			0
$801$	−6.51907	+	21.9347i	−0.230340	+	0.775024i
$802$		0			0
$803$	8.02460	−	45.5098i	0.283182	−	1.60600i
$804$		0			0
$805$	−26.4928	−	9.64257i	−0.933747	−	0.339856i
$806$		0			0
$807$	7.55019	−	9.56841i	0.265779	−	0.336824i
$808$		0			0
$809$		−	26.6021i		−	0.935280i	−0.883919	−	0.467640i	$-0.845104\pi$
$809$		−	26.6021i		−	0.935280i	0.883919	−	0.467640i	$-0.154896\pi$
$810$		0			0
$811$		−	28.9764i		−	1.01750i	−0.860914	−	0.508750i	$-0.830108\pi$
$811$		−	28.9764i		−	1.01750i	0.860914	−	0.508750i	$-0.169892\pi$
$812$		0			0
$813$	−25.8777	+	32.7949i	−0.907569	+	1.15017i
$814$		0			0
$815$	27.3251	+	9.94552i	0.957156	+	0.348376i
$816$		0			0
$817$	2.05646	−	11.6628i	0.0719465	−	0.408029i
$818$		0			0
$819$	54.9185	+	57.9776i	1.91901	+	2.02590i
$820$		0			0
$821$	12.9587	+	35.6037i	0.452261	+	1.24258i	0.931129	+	0.364690i	$0.118825\pi$
$821$	12.9587	+	35.6037i	0.452261	+	1.24258i	−0.478868	+	0.877887i	$0.658953\pi$
$822$		0			0
$823$	11.8871	+	14.1665i	0.414359	+	0.493814i	0.932342	−	0.361577i	$-0.117762\pi$
$823$	11.8871	+	14.1665i	0.414359	+	0.493814i	−0.517983	+	0.855391i	$0.673317\pi$
$824$		0			0
$825$	−24.8767	−	40.2413i	−0.866097	−	1.40102i
$826$		0			0
$827$	−22.8962	−	39.6573i	−0.796178	−	1.37902i	−0.922089	−	0.386979i	$-0.873519\pi$
$827$	−22.8962	−	39.6573i	−0.796178	−	1.37902i	0.125911	−	0.992042i	$-0.459815\pi$
$828$		0			0
$829$	−1.33848	+	2.31832i	−0.0464874	+	0.0805186i	−0.888333	−	0.459200i	$-0.848136\pi$
$829$	−1.33848	+	2.31832i	−0.0464874	+	0.0805186i	0.841845	+	0.539719i	$0.181469\pi$
$830$		0			0
$831$	−25.4972	+	22.7362i	−0.884487	+	0.788712i
$832$		0			0
$833$	13.2481	−	2.33600i	0.459021	−	0.0809378i
$834$		0			0
$835$	49.4502	−	58.9325i	1.71130	−	2.03944i
$836$		0			0
$837$	2.05305	−	7.75502i	0.0709638	−	0.268053i
$838$		0			0
$839$	9.82182	+	8.24148i	0.339087	+	0.284528i	0.796390	−	0.604783i	$-0.206740\pi$
$839$	9.82182	+	8.24148i	0.339087	+	0.284528i	−0.457303	+	0.889311i	$0.651185\pi$
$840$		0			0
$841$	0.0123193	+	0.0698665i	0.000424805	+	0.00240919i
$842$		0			0
$843$	3.62714	−	10.9828i	0.124925	−	0.378269i
$844$		0			0
$845$	−69.8511	−	40.3285i	−2.40295	−	1.38734i
$846$		0			0
$847$	23.3478	−	13.4799i	0.802240	−	0.463174i
$848$		0			0
$849$	−0.864816	−	28.7341i	−0.0296804	−	0.986150i
$850$		0			0
$851$	−7.18324	+	6.02746i	−0.246238	+	0.206619i
$852$		0			0
$853$	−42.1984	+	15.3590i	−1.44485	+	0.525881i	−0.941147	−	0.337998i	$-0.890250\pi$
$853$	−42.1984	+	15.3590i	−1.44485	+	0.525881i	−0.503700	+	0.863879i	$0.668028\pi$
$854$		0			0
$855$	−23.2294	−	17.2216i	−0.794428	−	0.588965i
$856$		0			0
$857$	24.5634	+	4.33119i	0.839071	+	0.147951i	0.576638	−	0.817000i	$-0.304364\pi$
$857$	24.5634	+	4.33119i	0.839071	+	0.147951i	0.262432	+	0.964950i	$0.415475\pi$
$858$		0			0
$859$	−4.02440	+	11.0570i	−0.137311	+	0.377258i	−0.989221	−	0.146429i	$-0.953222\pi$
$859$	−4.02440	+	11.0570i	−0.137311	+	0.377258i	0.851910	+	0.523688i	$0.175444\pi$
$860$		0			0
$861$	−5.62043	+	38.6396i	−0.191544	+	1.31683i
$862$		0			0
$863$	−42.2871			−1.43947			−0.719735	−	0.694249i	$-0.755737\pi$
$863$	−42.2871			−1.43947			−0.719735	+	0.694249i	$0.755737\pi$
$864$		0			0
$865$	11.0010			0.374045
$866$		0			0
$867$	25.4342	−	10.1338i	0.863792	−	0.344162i
$868$		0			0
$869$	13.7913	−	37.8913i	0.467838	−	1.28537i
$870$		0			0
$871$	21.6041	+	3.80938i	0.732026	+	0.129076i
$872$		0			0
$873$	1.59053	+	2.40778i	0.0538312	+	0.0814911i
$874$		0			0
$875$	−22.4872	+	8.18468i	−0.760207	+	0.276693i
$876$		0			0
$877$	−8.97200	+	7.52840i	−0.302963	+	0.254216i	−0.781576	−	0.623810i	$-0.785584\pi$
$877$	−8.97200	+	7.52840i	−0.302963	+	0.254216i	0.478613	+	0.878026i	$0.341140\pi$
$878$		0			0
$879$	19.0383	+	10.2408i	0.642147	+	0.345415i
$880$		0			0
$881$	−15.0481	+	8.68805i	−0.506985	+	0.292708i	−0.731593	−	0.681741i	$-0.761223\pi$
$881$	−15.0481	+	8.68805i	−0.506985	+	0.292708i	0.224609	+	0.974449i	$0.427890\pi$
$882$		0			0
$883$	−28.3853	−	16.3883i	−0.955241	−	0.551509i	−0.0605358	−	0.998166i	$-0.519281\pi$
$883$	−28.3853	−	16.3883i	−0.955241	−	0.551509i	−0.894705	+	0.446657i	$0.852614\pi$
$884$		0			0
$885$	−19.0166	+	3.94643i	−0.639235	+	0.132658i
$886$		0			0
$887$	−7.15697	−	40.5892i	−0.240308	−	1.36285i	−0.831142	−	0.556060i	$-0.812313\pi$
$887$	−7.15697	−	40.5892i	−0.240308	−	1.36285i	0.590835	−	0.806793i	$-0.298799\pi$
$888$		0			0
$889$	37.5380	+	31.4981i	1.25898	+	1.05641i
$890$		0			0
$891$	25.4567	−	27.1995i	0.852831	−	0.911218i
$892$		0			0
$893$	−15.8882	+	18.9349i	−0.531680	+	0.633631i
$894$		0			0
$895$	12.7018	−	2.23967i	0.424575	−	0.0748641i
$896$		0			0
$897$	4.01490	+	19.3465i	0.134054	+	0.645962i
$898$		0			0
$899$	−4.15191	+	7.19131i	−0.138474	+	0.239844i
$900$		0			0
$901$	6.64821	+	11.5150i	0.221484	+	0.383622i
$902$		0			0
$903$	15.0896	−	28.0525i	0.502151	−	0.933529i
$904$		0			0
$905$	48.3355	+	57.6040i	1.60673	+	1.91482i
$906$		0			0
$907$	−6.59619	−	18.1229i	−0.219023	−	0.601760i	0.780710	−	0.624894i	$-0.214858\pi$
$907$	−6.59619	−	18.1229i	−0.219023	−	0.601760i	−0.999732	+	0.0231338i	$0.992636\pi$
$908$		0			0
$909$	2.54484	+	42.2387i	0.0844072	+	1.40097i
$910$		0			0
$911$	−7.04402	+	39.9486i	−0.233379	+	1.32356i	0.612623	+	0.790376i	$0.290115\pi$
$911$	−7.04402	+	39.9486i	−0.233379	+	1.32356i	−0.846001	+	0.533181i	$0.820997\pi$
$912$		0			0
$913$	1.21931	+	0.443793i	0.0403533	+	0.0146874i
$914$		0			0
$915$	−5.82944	−	14.6310i	−0.192716	−	0.483685i
$916$		0			0
$917$		−	48.5191i		−	1.60224i
$918$		0			0
$919$		−	12.7830i		−	0.421673i	−0.977521	−	0.210837i	$-0.932381\pi$
$919$		−	12.7830i		−	0.421673i	0.977521	−	0.210837i	$-0.0676188\pi$
$920$		0			0
$921$	46.1720	+	6.71608i	1.52142	+	0.221302i
$922$		0			0
$923$	−9.58613	−	3.48906i	−0.315531	−	0.114844i
$924$		0			0
$925$	−5.70467	+	32.3528i	−0.187568	+	1.06375i
$926$		0			0
$927$	25.1769	+	2.89177i	0.826919	+	0.0949780i
$928$		0			0
$929$	−8.39195	−	23.0567i	−0.275331	−	0.756465i	−0.997876	−	0.0651416i	$-0.979250\pi$
$929$	−8.39195	−	23.0567i	−0.275331	−	0.756465i	0.722545	−	0.691324i	$-0.242972\pi$
$930$		0			0
$931$	−22.4077	−	26.7044i	−0.734382	−	0.875203i
$932$		0			0
$933$	39.8114	−	1.19821i	1.30337	−	0.0392277i
$934$		0			0
$935$	7.69846	+	13.3341i	0.251767	+	0.436073i
$936$		0			0
$937$	−21.9431	+	38.0066i	−0.716850	+	1.24162i	0.245392	+	0.969424i	$0.421083\pi$
$937$	−21.9431	+	38.0066i	−0.716850	+	1.24162i	−0.962242	+	0.272196i	$0.912250\pi$
$938$		0			0
$939$	17.4302	+	5.75640i	0.568812	+	0.187853i
$940$		0			0
$941$	16.3254	−	2.87860i	0.532191	−	0.0938397i	0.0989065	−	0.995097i	$-0.468466\pi$
$941$	16.3254	−	2.87860i	0.532191	−	0.0938397i	0.433285	+	0.901257i	$0.357354\pi$
$942$		0			0
$943$	−6.20987	+	7.40063i	−0.202221	+	0.240998i
$944$		0			0
$945$	−44.8024	−	63.5780i	−1.45742	−	2.06819i
$946$		0			0
$947$	11.5684	+	9.70706i	0.375923	+	0.315437i	0.811100	−	0.584908i	$-0.198869\pi$
$947$	11.5684	+	9.70706i	0.375923	+	0.315437i	−0.435176	+	0.900345i	$0.643314\pi$
$948$		0			0
$949$	11.7416	+	66.5898i	0.381147	+	2.16159i
$950$		0			0
$951$	40.0530	+	44.9167i	1.29881	+	1.45652i
$952$		0			0
$953$	14.3938	+	8.31026i	0.466261	+	0.269196i	0.714673	−	0.699459i	$-0.246575\pi$
$953$	14.3938	+	8.31026i	0.466261	+	0.269196i	−0.248412	+	0.968654i	$0.579909\pi$
$954$		0			0
$955$	−37.4651	+	21.6305i	−1.21234	+	0.699945i
$956$		0			0
$957$	−32.8004	+	20.2768i	−1.06029	+	0.655457i
$958$		0			0
$959$	39.2379	−	32.9245i	1.26706	−	1.06319i
$960$		0			0
$961$	−26.8907	+	9.78741i	−0.867441	+	0.315723i
$962$		0			0
$963$	3.82674	+	16.0037i	0.123315	+	0.515711i
$964$		0			0
$965$	−22.6157	−	3.98776i	−0.728026	−	0.128371i
$966$		0			0
$967$	−6.20829	+	17.0571i	−0.199645	+	0.548520i	−0.998601	−	0.0528686i	$-0.983164\pi$
$967$	−6.20829	+	17.0571i	−0.199645	+	0.548520i	0.798956	+	0.601389i	$0.205386\pi$
$968$		0			0
$969$	4.20314	+	3.31659i	0.135024	+	0.106544i
$970$		0			0
$971$	37.5876			1.20624			0.603122	−	0.797649i	$-0.293923\pi$
$971$	37.5876			1.20624			0.603122	+	0.797649i	$0.293923\pi$
$972$		0			0
$973$	7.82846			0.250969
$974$		0			0
$975$	54.3429	+	42.8806i	1.74036	+	1.37328i
$976$		0			0
$977$	11.1414	−	30.6108i	0.356445	−	0.979326i	−0.623808	−	0.781578i	$-0.714415\pi$
$977$	11.1414	−	30.6108i	0.356445	−	0.979326i	0.980253	−	0.197748i	$-0.0633627\pi$
$978$		0			0
$979$	−31.0936	−	5.48265i	−0.993757	−	0.175226i
$980$		0			0
$981$	5.49132	+	22.9650i	0.175324	+	0.733218i
$982$		0			0
$983$	−0.917961	+	0.334111i	−0.0292784	+	0.0106565i	−0.356618	−	0.934250i	$-0.616070\pi$
$983$	−0.917961	+	0.334111i	−0.0292784	+	0.0106565i	0.327339	+	0.944907i	$0.393848\pi$
$984$		0			0
$985$	33.1051	−	27.7785i	1.05482	−	0.885097i
$986$		0			0
$987$	−56.5503	+	34.9588i	−1.80002	+	1.11275i
$988$		0			0
$989$	6.82531	−	3.94060i	0.217032	−	0.125304i
$990$		0			0
$991$	−31.3760	−	18.1150i	−0.996693	−	0.575441i	−0.0894245	−	0.995994i	$-0.528503\pi$
$991$	−31.3760	−	18.1150i	−0.996693	−	0.575441i	−0.907268	+	0.420553i	$0.861836\pi$
$992$		0			0
$993$	−6.65091	−	7.45855i	−0.211060	−	0.236690i
$994$		0			0
$995$	−1.61195	−	9.14185i	−0.0511024	−	0.289816i
$996$		0			0
$997$	41.3798	+	34.7218i	1.31051	+	1.09965i	0.988225	+	0.153008i	$0.0488960\pi$
$997$	41.3798	+	34.7218i	1.31051	+	1.09965i	0.322287	+	0.946642i	$0.395548\pi$
$998$		0			0
$999$	−25.7638	+	2.33189i	−0.815132	+	0.0737779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.335.2	✓	36
4.3	odd	2		432.2.be.c.335.5	yes	36
27.5	odd	18		432.2.be.c.383.5	yes	36
108.59	even	18	inner	432.2.be.b.383.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.2	✓	36	1.1	even	1	trivial
432.2.be.b.383.2	yes	36	108.59	even	18	inner
432.2.be.c.335.5	yes	36	4.3	odd	2
432.2.be.c.383.5	yes	36	27.5	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35972 - 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(4.32834 + 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +O(q^{10})\)	\(q+(-1.35972 - 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(4.32834 + 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +(-3.88970 + 1.41573i) q^{11} +(4.63966 - 3.89314i) q^{13} +(-5.01749 + 3.10176i) q^{15} +(0.945866 - 0.546096i) q^{17} +(-2.45107 - 1.41513i) q^{19} +(-5.06647 - 5.68171i) q^{21} +(-0.327067 - 1.85489i) q^{23} +(-5.05492 - 4.24158i) q^{25} +(2.18186 - 4.71588i) q^{27} +(-3.45728 + 4.12023i) q^{29} +(1.52041 - 0.268090i) q^{31} +(6.80787 + 2.24833i) q^{33} +(7.48419 - 12.9630i) q^{35} +(-2.48926 - 4.31152i) q^{37} +(-10.4857 + 0.315590i) q^{39} +(-3.29698 - 3.92918i) q^{41} +(1.43112 + 3.93198i) q^{43} +(10.1503 + 1.16584i) q^{45} +(1.51654 - 8.60072i) q^{47} +(11.5742 + 4.21266i) q^{49} +(-1.87203 - 0.272302i) q^{51} +12.1741i q^{53} +14.0973i q^{55} +(1.81445 + 4.55398i) q^{57} +(3.09392 + 1.12609i) q^{59} +(-0.463630 + 2.62938i) q^{61} +(0.792966 + 13.1615i) q^{63} +(-7.05488 - 19.3831i) q^{65} +(2.32819 + 2.77463i) q^{67} +(-1.54543 + 2.87305i) q^{69} +(-0.842160 - 1.45866i) q^{71} +(-5.58205 + 9.66839i) q^{73} +(2.32240 + 11.1909i) q^{75} +(-17.9164 + 3.15915i) q^{77} +(-6.26169 + 7.46239i) q^{79} +(-8.02648 + 4.07131i) q^{81} +(-0.240134 - 0.201496i) q^{83} +(-0.645914 - 3.66316i) q^{85} +(9.12161 - 1.89297i) q^{87} +(6.60573 + 3.81382i) q^{89} +(23.0533 - 13.3098i) q^{91} +(-2.35498 - 1.26676i) q^{93} +(-7.38387 + 6.19580i) q^{95} +(0.903887 - 0.328988i) q^{97} +(-6.84452 - 10.3614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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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