LMFDB - Embedded newform 432.2.be.c.335.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			335.5
Character	$\chi$	$=$	432.335
Dual form			432.2.be.c.383.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35972 + 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(-4.32834 - 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +O(q^{10})$	\(q+(1.35972 + 1.07292i) q^{3} +(1.16481 - 3.20030i) q^{5} +(-4.32834 - 0.763203i) q^{7} +(0.697681 + 2.91775i) q^{9} +(3.88970 - 1.41573i) q^{11} +(4.63966 - 3.89314i) q^{13} +(5.01749 - 3.10176i) q^{15} +(0.945866 - 0.546096i) q^{17} +(2.45107 + 1.41513i) q^{19} +(-5.06647 - 5.68171i) q^{21} +(0.327067 + 1.85489i) q^{23} +(-5.05492 - 4.24158i) q^{25} +(-2.18186 + 4.71588i) q^{27} +(-3.45728 + 4.12023i) q^{29} +(-1.52041 + 0.268090i) q^{31} +(6.80787 + 2.24833i) q^{33} +(-7.48419 + 12.9630i) q^{35} +(-2.48926 - 4.31152i) q^{37} +(10.4857 - 0.315590i) q^{39} +(-3.29698 - 3.92918i) q^{41} +(-1.43112 - 3.93198i) q^{43} +(10.1503 + 1.16584i) q^{45} +(-1.51654 + 8.60072i) q^{47} +(11.5742 + 4.21266i) q^{49} +(1.87203 + 0.272302i) q^{51} +12.1741i q^{53} -14.0973i q^{55} +(1.81445 + 4.55398i) q^{57} +(-3.09392 - 1.12609i) q^{59} +(-0.463630 + 2.62938i) q^{61} +(-0.792966 - 13.1615i) q^{63} +(-7.05488 - 19.3831i) q^{65} +(-2.32819 - 2.77463i) q^{67} +(-1.54543 + 2.87305i) q^{69} +(0.842160 + 1.45866i) q^{71} +(-5.58205 + 9.66839i) q^{73} +(-2.32240 - 11.1909i) q^{75} +(-17.9164 + 3.15915i) q^{77} +(6.26169 - 7.46239i) q^{79} +(-8.02648 + 4.07131i) q^{81} +(0.240134 + 0.201496i) q^{83} +(-0.645914 - 3.66316i) q^{85} +(-9.12161 + 1.89297i) q^{87} +(6.60573 + 3.81382i) q^{89} +(-23.0533 + 13.3098i) q^{91} +(-2.35498 - 1.26676i) q^{93} +(7.38387 - 6.19580i) q^{95} +(0.903887 - 0.328988i) q^{97} +(6.84452 + 10.3614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.721279	−	0.692645i	$-0.756445\pi$
$7$	−4.32834	−	0.763203i	−1.63596	−	0.288464i	−0.914679	+	0.404181i	$0.867557\pi$
$8$		0			0
$9$	0.697681	+	2.91775i	0.232560	+	0.972582i
$10$		0			0
$11$	3.88970	−	1.41573i	1.17279	−	0.426860i	0.319138	−	0.947708i	$-0.396607\pi$
$11$	3.88970	−	1.41573i	1.17279	−	0.426860i	0.853649	+	0.520849i	$0.174384\pi$
$12$		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	0.754074	−	0.656790i	$-0.228086\pi$
$19$	2.45107	+	1.41513i	0.562314	+	0.324652i	−0.191760	+	0.981442i	$0.561419\pi$
$20$		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	$0.00735942\pi$
$23$	0.327067	+	1.85489i	0.0681982	+	0.386771i	−0.931535	+	0.363653i	$0.881529\pi$
$24$		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	−0.308508	−	0.951222i	$-0.599830\pi$
$31$	−1.52041	+	0.268090i	−0.273074	+	0.0481504i	0.0354340	+	0.999372i	$0.488719\pi$
$32$		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	0.781459	−	0.623956i	$-0.214476\pi$
$43$	−1.43112	−	3.93198i	−0.218244	−	0.599622i	−0.999704	+	0.0243344i	$0.992253\pi$
$44$		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	$0.275359\pi$
$47$	−1.51654	+	8.60072i	−0.221210	+	1.25454i	−0.869799	+	0.493406i	$0.835752\pi$
$48$		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	0.132676	−	0.991159i	$-0.457643\pi$
$59$	−3.09392	−	1.12609i	−0.402793	−	0.146605i	−0.535469	+	0.844555i	$0.679865\pi$
$60$		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	0.604843	−	0.796345i	$-0.293236\pi$
$67$	−2.32819	−	2.77463i	−0.284434	−	0.338975i	−0.889277	+	0.457370i	$0.848792\pi$
$68$		0			0
$69$	−1.54543	+	2.87305i	−0.186048	+	0.345874i
$70$		0			0
$71$	0.842160	+	1.45866i	0.0999460	+	0.173112i	0.911662	−	0.410941i	$-0.134800\pi$
$71$	0.842160	+	1.45866i	0.0999460	+	0.173112i	−0.811716	+	0.584052i	$0.801466\pi$
$72$		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	−0.288532	−	0.957470i	$-0.593167\pi$
$79$	6.26169	−	7.46239i	0.704495	−	0.839584i	0.993027	+	0.117886i	$0.0376118\pi$
$80$		0			0
$81$	−8.02648	+	4.07131i	−0.891832	+	0.452368i
$82$		0			0
$83$	0.240134	+	0.201496i	0.0263581	+	0.0221171i	0.655872	−	0.754873i	$-0.272301\pi$
$83$	0.240134	+	0.201496i	0.0263581	+	0.0221171i	−0.629513	+	0.776990i	$0.716746\pi$
$84$		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	$0.247742\pi$
$103$	−2.88921	+	7.93804i	−0.284682	+	0.782158i	−0.996788	+	0.0800861i	$0.974480\pi$
$104$		0			0
$105$	−24.0847	+	9.59611i	−2.35042	+	0.936485i
$106$		0			0
$107$	−5.48494			−0.530249			−0.265125	−	0.964214i	$-0.585413\pi$
$107$	−5.48494			−0.530249			−0.265125	+	0.964214i	$0.585413\pi$
$108$		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	0.00614387	−	0.999981i	$-0.498044\pi$
$127$	−9.65557	−	5.57465i	−0.856793	−	0.494670i	−0.862937	+	0.505311i	$0.831378\pi$
$128$		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	$0.104627\pi$
$131$	1.91696	+	10.8716i	0.167486	+	0.949858i	−0.778979	+	0.627050i	$0.784262\pi$
$132$		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	−0.247543	−	0.968877i	$-0.579623\pi$
$139$	−1.75412	+	0.309298i	−0.148782	+	0.0262343i	0.0987610	+	0.995111i	$0.468512\pi$
$140$		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	0.802514	−	0.596633i	$-0.203495\pi$
$151$	−2.40548	−	6.60901i	−0.195755	−	0.537834i	−0.998270	+	0.0587991i	$0.981273\pi$
$152$		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	$-0.891471\pi$
$163$		−	8.53829i		−	0.668770i	0.942437	−	0.334385i	$-0.108529\pi$
$164$		0			0
$165$	15.1253	−	19.1683i	1.17750	−	1.49225i
$166$		0			0
$167$	−21.2266	−	7.72587i	−1.64257	−	0.597846i	−0.655082	−	0.755558i	$-0.727366\pi$
$167$	−21.2266	−	7.72587i	−1.64257	−	0.597846i	−0.987485	+	0.157712i	$0.949588\pi$
$168$		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	0.786542	−	0.617537i	$-0.211869\pi$
$179$	−1.89356	−	3.27975i	−0.141531	−	0.245140i	−0.928074	+	0.372397i	$0.878536\pi$
$180$		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	0.922934	−	0.384959i	$-0.125784\pi$
$191$	9.73071	+	8.16503i	0.704089	+	0.590801i	−0.218844	+	0.975760i	$0.570229\pi$
$192$		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	−0.581328	−	0.813670i	$-0.697467\pi$
$199$	−2.36052	+	1.36285i	−0.167333	+	0.0966097i	0.413995	+	0.910279i	$0.364133\pi$
$200$		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	−0.788626	−	0.614874i	$-0.789207\pi$
$211$	3.06103	−	8.41010i	0.210730	−	0.578975i	0.999355	+	0.0358983i	$0.0114292\pi$
$212$		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	0.798969	−	0.601372i	$-0.205379\pi$
$223$	20.0713	+	3.53911i	1.34407	+	0.236996i	0.545104	+	0.838368i	$0.316490\pi$
$224$		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	$-0.212356\pi$
$227$	26.8955	−	9.78916i	1.78512	−	0.649729i	0.999520	−	0.0309904i	$-0.00986613\pi$
$228$		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	0.949480	−	0.313828i	$-0.101611\pi$
$239$	−0.774137	−	4.39035i	−0.0500748	−	0.283988i	−0.999555	+	0.0298396i	$0.990500\pi$
$240$		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	$0.373482\pi$
$251$	−9.58454	+	16.6009i	−0.604971	+	1.04784i	−0.992056	+	0.125796i	$0.959852\pi$
$252$		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	$-0.868579\pi$
$263$	1.32969	−	7.54107i	0.0819924	−	0.465002i	0.997965	−	0.0637616i	$-0.0203097\pi$
$264$		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	$0.261674\pi$
$271$			24.1189i			1.46512i	−0.680704	+	0.732559i	$0.738326\pi$
$272$		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	0.349265	−	0.937024i	$-0.386431\pi$
$283$	−10.6684	−	12.7141i	−0.634172	−	0.755777i	−0.983438	+	0.181247i	$0.941987\pi$
$284$		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	0.345931	−	0.938260i	$-0.387563\pi$
$307$	23.3290	−	13.4690i	1.33145	−	0.768715i	0.985523	+	0.169545i	$0.0542297\pi$
$308$		0			0
$309$	−12.4454	+	7.69362i	−0.707995	+	0.437675i
$310$		0			0
$311$	17.6156	−	14.7812i	0.998888	−	0.838167i	0.0120581	−	0.999927i	$-0.496162\pi$
$311$	17.6156	−	14.7812i	0.998888	−	0.838167i	0.986830	+	0.161761i	$0.0517173\pi$
$312$		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	0.0152976	−	0.999883i	$-0.495130\pi$
$331$	−5.68194	−	1.00188i	−0.312308	−	0.0550682i	−0.327605	+	0.944815i	$0.606242\pi$
$332$		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	$-0.842520\pi$
$347$	−4.01371	−	22.7629i	−0.215467	−	1.22198i	0.664626	−	0.747176i	$-0.268591\pi$
$348$		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	−0.812026	−	0.583621i	$-0.801636\pi$
$359$	1.88368	−	3.26264i	0.0994170	−	0.172195i	0.911443	+	0.411425i	$0.134969\pi$
$360$		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	$-0.942877\pi$
$367$	−6.60798	−	18.1553i	−0.344934	−	0.947697i	0.639007	−	0.769201i	$-0.279346\pi$
$368$		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	$0.146523\pi$
$379$			17.2965i			0.888463i	−0.895912	+	0.444232i	$0.853477\pi$
$380$		0			0
$381$	−7.14772	−	17.9396i	−0.366189	−	0.919075i
$382$		0			0
$383$	3.32586	+	1.21051i	0.169944	+	0.0618544i	0.425591	−	0.904916i	$-0.360066\pi$
$383$	3.32586	+	1.21051i	0.169944	+	0.0618544i	−0.255647	+	0.966770i	$0.582289\pi$
$384$		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	$-0.368953\pi$
$419$	28.0877	−	23.5684i	1.37217	−	1.15139i	0.972008	−	0.234947i	$-0.0754917\pi$
$420$		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	$-0.506149\pi$
$431$	−0.802008			−0.0386314			−0.0193157	+	0.999813i	$0.506149\pi$
$432$		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	0.0763594	−	0.997080i	$-0.475670\pi$
$439$	−4.04187	−	0.712690i	−0.192908	−	0.0340149i	−0.269267	+	0.963066i	$0.586781\pi$
$440$		0			0
$441$	−4.21638	+	36.7096i	−0.200780	+	1.74808i
$442$		0			0
$443$	−32.3631	+	11.7792i	−1.53762	+	0.559646i	−0.965472	−	0.260507i	$-0.916110\pi$
$443$	−32.3631	+	11.7792i	−1.53762	+	0.559646i	−0.572143	+	0.820154i	$0.693888\pi$
$444$		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	−0.824958	−	0.565194i	$-0.808801\pi$
$463$	−30.2719	+	5.33776i	−1.40686	+	0.248067i	−0.581899	+	0.813261i	$0.697690\pi$
$464$		0			0
$465$	−6.79712	+	6.06110i	−0.315209	+	0.281077i
$466$		0			0
$467$	−9.51526	+	16.4809i	−0.440314	+	0.762646i	−0.997713	−	0.0675990i	$-0.978466\pi$
$467$	−9.51526	+	16.4809i	−0.440314	+	0.762646i	0.557399	+	0.830245i	$0.311799\pi$
$468$		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	$0.173459\pi$
$479$	−2.75148	+	15.6044i	−0.125718	+	0.712984i	−0.980879	+	0.194620i	$0.937653\pi$
$480$		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	$-0.967520\pi$
$487$		−	4.49577i		−	0.203723i	0.994799	−	0.101861i	$-0.0324798\pi$
$488$		0			0
$489$	9.16091	−	11.6097i	0.414271	−	0.525008i
$490$		0			0
$491$	−34.4443	−	12.5367i	−1.55445	−	0.565773i	−0.584992	−	0.811039i	$-0.698903\pi$
$491$	−34.4443	−	12.5367i	−1.55445	−	0.565773i	−0.969456	+	0.245266i	$0.921125\pi$
$492$		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	$0.0907573\pi$
$499$	23.9018	+	28.4851i	1.06999	+	1.27517i	0.110364	+	0.993891i	$0.464798\pi$
$500$		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	$-0.828377\pi$
$503$	−19.5952	−	33.9399i	−0.873706	−	1.51330i	−0.0155717	−	0.999879i	$-0.504957\pi$
$504$		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	$-0.229237\pi$
$523$	38.8478	−	22.4288i	1.69870	−	0.980742i	0.947001	−	0.321230i	$-0.104096\pi$
$524$		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	−0.798361	−	0.602178i	$-0.794300\pi$
$547$	−41.0351	−	7.23559i	−1.75453	−	0.309372i	−0.956172	+	0.292807i	$0.905411\pi$
$548$		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	$0.270892\pi$
$563$	7.04571	+	39.9582i	0.296941	+	1.68404i	−0.362265	+	0.932075i	$0.617997\pi$
$564$		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	0.0151338	−	0.999885i	$-0.495183\pi$
$571$	8.87330	−	1.56460i	0.371336	−	0.0654765i	0.356202	+	0.934409i	$0.384071\pi$
$572$		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	$0.418460\pi$
$587$	−7.64588	+	43.3619i	−0.315579	+	1.78974i	−0.568953	+	0.822370i	$0.692651\pi$
$588$		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	0.916738	−	0.399489i	$-0.130812\pi$
$599$	33.3395	+	12.1346i	1.36221	+	0.495805i	0.445476	+	0.895294i	$0.353035\pi$
$600$		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	0.264462	−	0.964396i	$-0.414806\pi$
$607$	−18.0150	−	21.4694i	−0.731207	−	0.871418i	−0.995668	+	0.0929782i	$0.970361\pi$
$608$		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	−0.999612	−	0.0278575i	$-0.991132\pi$
$619$	−19.8689	+	23.6788i	−0.798597	+	0.951731i	0.201015	+	0.979588i	$0.435576\pi$
$620$		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	−0.586687	−	0.809814i	$-0.699568\pi$
$631$	−4.48915	+	2.59181i	−0.178710	+	0.103178i	0.407976	+	0.912993i	$0.366235\pi$
$632$		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	$-0.742715\pi$
$643$	7.68834	−	21.1236i	0.303199	−	0.833032i	0.993939	−	0.109929i	$-0.0350624\pi$
$644$		0			0
$645$	−19.3767	−	15.2897i	−0.762958	−	0.602031i
$646$		0			0
$647$	−20.0311			−0.787505			−0.393752	−	0.919217i	$-0.628823\pi$
$647$	−20.0311			−0.787505			−0.393752	+	0.919217i	$0.628823\pi$
$648$		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	0.488636	−	0.872488i	$-0.337495\pi$
$659$	36.5498	−	13.3030i	1.42378	−	0.518213i	0.935141	+	0.354275i	$0.115272\pi$
$660$		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	−0.933754	−	0.357916i	$-0.883488\pi$
$683$	−4.10080	+	7.10280i	−0.156913	+	0.271781i	0.776841	+	0.629697i	$0.216821\pi$
$684$		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	$-0.976735\pi$
$691$	−7.36741	−	20.2418i	−0.280269	−	0.770034i	0.717061	−	0.697011i	$-0.245487\pi$
$692$		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	0.963260	−	0.268569i	$-0.0865507\pi$
$719$	6.67788	+	11.5664i	0.249043	+	0.431355i	−0.714218	+	0.699924i	$0.753217\pi$
$720$		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	−0.726076	−	0.687614i	$-0.758658\pi$
$727$	2.08083	−	2.47984i	0.0771737	−	0.0919720i	0.803250	+	0.595642i	$0.203102\pi$
$728$		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	−0.561577	−	0.827424i	$-0.689805\pi$
$739$	−3.41970	+	1.97436i	−0.125796	+	0.0726281i	0.435782	+	0.900052i	$0.356472\pi$
$740$		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	$-0.360666\pi$
$743$	37.8736	−	31.7797i	1.38945	−	1.16589i	0.965563	−	0.260170i	$-0.0837785\pi$
$744$		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	$-0.535671\pi$
$751$	16.7877	−	46.1239i	0.612592	−	1.68308i	0.724423	−	0.689356i	$-0.242106\pi$
$752$		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	−0.241133	−	0.970492i	$-0.577519\pi$
$787$	−3.80955	+	0.671726i	−0.135796	+	0.0239444i	0.105337	+	0.994437i	$0.466408\pi$
$788$		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	$0.169892\pi$
$811$			28.9764i			1.01750i	−0.860914	+	0.508750i	$0.830108\pi$
$812$		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	0.517983	−	0.855391i	$-0.326683\pi$
$823$	−11.8871	−	14.1665i	−0.414359	−	0.493814i	−0.932342	+	0.361577i	$0.882238\pi$
$824$		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	$0.126481\pi$
$827$	22.8962	+	39.6573i	0.796178	+	1.37902i	−0.125911	+	0.992042i	$0.540185\pi$
$828$		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	0.457303	−	0.889311i	$-0.348815\pi$
$839$	−9.82182	−	8.24148i	−0.339087	−	0.284528i	−0.796390	+	0.604783i	$0.793260\pi$
$840$		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	−0.851910	−	0.523688i	$-0.824556\pi$
$859$	4.02440	−	11.0570i	0.137311	−	0.377258i	0.989221	+	0.146429i	$0.0467781\pi$
$860$		0			0
$861$	−5.62043	+	38.6396i	−0.191544	+	1.31683i
$862$		0			0
$863$	42.2871			1.43947			0.719735	−	0.694249i	$-0.244263\pi$
$863$	42.2871			1.43947			0.719735	+	0.694249i	$0.244263\pi$
$864$		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	0.894705	−	0.446657i	$-0.147386\pi$
$883$	28.3853	+	16.3883i	0.955241	+	0.551509i	0.0605358	+	0.998166i	$0.480719\pi$
$884$		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	$0.187687\pi$
$887$	7.15697	+	40.5892i	0.240308	+	1.36285i	−0.590835	+	0.806793i	$0.701201\pi$
$888$		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	0.999732	−	0.0231338i	$-0.00736436\pi$
$907$	6.59619	+	18.1229i	0.219023	+	0.601760i	−0.780710	+	0.624894i	$0.785142\pi$
$908$		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	$-0.709885\pi$
$911$	7.04402	−	39.9486i	0.233379	−	1.32356i	0.846001	−	0.533181i	$-0.179003\pi$
$912$		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	$0.0676188\pi$
$919$			12.7830i			0.421673i	−0.977521	+	0.210837i	$0.932381\pi$
$920$		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	0.435176	−	0.900345i	$-0.356686\pi$
$947$	−11.5684	−	9.70706i	−0.375923	−	0.315437i	−0.811100	+	0.584908i	$0.801131\pi$
$948$		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	−0.798956	−	0.601389i	$-0.794614\pi$
$967$	6.20829	−	17.0571i	0.199645	−	0.548520i	0.998601	+	0.0528686i	$0.0168364\pi$
$968$		0			0
$969$	4.20314	+	3.31659i	0.135024	+	0.106544i
$970$		0			0
$971$	−37.5876			−1.20624			−0.603122	−	0.797649i	$-0.706077\pi$
$971$	−37.5876			−1.20624			−0.603122	+	0.797649i	$0.706077\pi$
$972$		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	−0.327339	−	0.944907i	$-0.606152\pi$
$983$	0.917961	−	0.334111i	0.0292784	−	0.0106565i	0.356618	+	0.934250i	$0.383930\pi$
$984$		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	0.907268	−	0.420553i	$-0.138164\pi$
$991$	31.3760	+	18.1150i	0.996693	+	0.575441i	0.0894245	+	0.995994i	$0.471497\pi$
$992$		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.c.335.5	yes	36
4.3	odd	2		432.2.be.b.335.2	✓	36
27.5	odd	18		432.2.be.b.383.2	yes	36
108.59	even	18	inner	432.2.be.c.383.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.2	✓	36	4.3	odd	2
432.2.be.b.383.2	yes	36	27.5	odd	18
432.2.be.c.335.5	yes	36	1.1	even	1	trivial
432.2.be.c.383.5	yes	36	108.59	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
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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