LMFDB - Embedded newform 576.2.y.a.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21512 + 1.23430i) q^{3} +(-0.726024 + 2.70956i) q^{5} +(0.00424642 - 0.00735502i) q^{7} +(-0.0469689 + 2.99963i) q^{9} +O(q^{10})$	\(q+(1.21512 + 1.23430i) q^{3} +(-0.726024 + 2.70956i) q^{5} +(0.00424642 - 0.00735502i) q^{7} +(-0.0469689 + 2.99963i) q^{9} +(-0.804193 - 3.00129i) q^{11} +(-1.72108 + 6.42317i) q^{13} +(-4.22660 + 2.39631i) q^{15} -3.37812i q^{17} +(-1.35881 + 1.35881i) q^{19} +(0.0142382 - 0.00369589i) q^{21} +(5.38718 - 3.11029i) q^{23} +(-2.48446 - 1.43441i) q^{25} +(-3.75950 + 3.58694i) q^{27} +(0.878030 + 3.27685i) q^{29} +(-6.70211 + 3.86947i) q^{31} +(2.72729 - 4.63954i) q^{33} +(0.0168459 + 0.0168459i) q^{35} +(0.769697 - 0.769697i) q^{37} +(-10.0194 + 5.68059i) q^{39} +(-2.64756 - 4.58570i) q^{41} +(5.99790 - 1.60713i) q^{43} +(-8.09358 - 2.30507i) q^{45} +(0.0955284 - 0.165460i) q^{47} +(3.49996 + 6.06212i) q^{49} +(4.16959 - 4.10482i) q^{51} +(-0.750557 - 0.750557i) q^{53} +8.71603 q^{55} +(-3.32830 - 0.0260560i) q^{57} +(9.08809 + 2.43515i) q^{59} +(9.85796 - 2.64143i) q^{61} +(0.0218629 + 0.0130832i) q^{63} +(-16.1544 - 9.32674i) q^{65} +(7.77154 + 2.08238i) q^{67} +(10.3851 + 2.87000i) q^{69} +1.02260i q^{71} +7.30911i q^{73} +(-1.24844 - 4.80954i) q^{75} +(-0.0254895 - 0.00682989i) q^{77} +(-4.36074 - 2.51768i) q^{79} +(-8.99559 - 0.281779i) q^{81} +(-12.5030 + 3.35017i) q^{83} +(9.15320 + 2.45259i) q^{85} +(-2.97769 + 5.06552i) q^{87} +18.1774 q^{89} +(0.0399341 + 0.0399341i) q^{91} +(-12.9199 - 3.57052i) q^{93} +(-2.69525 - 4.66831i) q^{95} +(1.64497 - 2.84917i) q^{97} +(9.04054 - 2.27132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.21512	+	1.23430i	0.701550	+	0.712621i
$3$	1.21512	+	1.23430i	0.701550	+	0.712621i
$4$		0			0
$5$	−0.726024	+	2.70956i	−0.324688	+	1.21175i	0.589938	+	0.807449i	$0.299152\pi$
$5$	−0.726024	+	2.70956i	−0.324688	+	1.21175i	−0.914625	+	0.404302i	$0.867514\pi$
$6$		0			0
$7$	0.00424642	−	0.00735502i	0.00160500	−	0.00277994i	−0.865222	−	0.501389i	$-0.832822\pi$
$7$	0.00424642	−	0.00735502i	0.00160500	−	0.00277994i	0.866827	+	0.498609i	$0.166156\pi$
$8$		0			0
$9$	−0.0469689	+	2.99963i	−0.0156563	+	0.999877i
$10$		0			0
$11$	−0.804193	−	3.00129i	−0.242473	−	0.904923i	−0.974637	−	0.223794i	$-0.928156\pi$
$11$	−0.804193	−	3.00129i	−0.242473	−	0.904923i	0.732163	−	0.681129i	$-0.238511\pi$
$12$		0			0
$13$	−1.72108	+	6.42317i	−0.477342	+	1.78147i	0.134969	+	0.990850i	$0.456906\pi$
$13$	−1.72108	+	6.42317i	−0.477342	+	1.78147i	−0.612312	+	0.790616i	$0.709760\pi$
$14$		0			0
$15$	−4.22660	+	2.39631i	−1.09130	+	0.618724i
$16$		0			0
$17$		−	3.37812i		−	0.819314i	−0.912240	−	0.409657i	$-0.865648\pi$
$17$		−	3.37812i		−	0.819314i	0.912240	−	0.409657i	$-0.134352\pi$
$18$		0			0
$19$	−1.35881	+	1.35881i	−0.311733	+	0.311733i	−0.845581	−	0.533848i	$-0.820746\pi$
$19$	−1.35881	+	1.35881i	−0.311733	+	0.311733i	0.533848	+	0.845581i	$0.320746\pi$
$20$		0			0
$21$	0.0142382	−	0.00369589i	0.00310703	−	0.000806510i
$22$		0			0
$23$	5.38718	−	3.11029i	1.12331	−	0.648541i	0.181062	−	0.983472i	$-0.442046\pi$
$23$	5.38718	−	3.11029i	1.12331	−	0.648541i	0.942243	+	0.334931i	$0.108713\pi$
$24$		0			0
$25$	−2.48446	−	1.43441i	−0.496893	−	0.286881i
$26$		0			0
$27$	−3.75950	+	3.58694i	−0.723517	+	0.690307i
$28$		0			0
$29$	0.878030	+	3.27685i	0.163046	+	0.608496i	0.998281	+	0.0586036i	$0.0186648\pi$
$29$	0.878030	+	3.27685i	0.163046	+	0.608496i	−0.835235	+	0.549893i	$0.814669\pi$
$30$		0			0
$31$	−6.70211	+	3.86947i	−1.20374	+	0.694977i	−0.961384	−	0.275212i	$-0.911252\pi$
$31$	−6.70211	+	3.86947i	−1.20374	+	0.694977i	−0.242352	+	0.970188i	$0.577919\pi$
$32$		0			0
$33$	2.72729	−	4.63954i	0.474760	−	0.807640i
$34$		0			0
$35$	0.0168459	+	0.0168459i	0.00284747	+	0.00284747i
$36$		0			0
$37$	0.769697	−	0.769697i	0.126537	−	0.126537i	−0.641002	−	0.767539i	$-0.721481\pi$
$37$	0.769697	−	0.769697i	0.126537	−	0.126537i	0.767539	+	0.641002i	$0.221481\pi$
$38$		0			0
$39$	−10.0194	+	5.68059i	−1.60439	+	0.909623i
$40$		0			0
$41$	−2.64756	−	4.58570i	−0.413479	−	0.716166i	0.581789	−	0.813340i	$-0.302353\pi$
$41$	−2.64756	−	4.58570i	−0.413479	−	0.716166i	−0.995267	+	0.0971739i	$0.969020\pi$
$42$		0			0
$43$	5.99790	−	1.60713i	0.914672	−	0.245086i	0.229365	−	0.973340i	$-0.426335\pi$
$43$	5.99790	−	1.60713i	0.914672	−	0.245086i	0.685306	+	0.728255i	$0.259668\pi$
$44$		0			0
$45$	−8.09358	−	2.30507i	−1.20652	−	0.343619i
$46$		0			0
$47$	0.0955284	−	0.165460i	0.0139343	−	0.0241348i	−0.858974	−	0.512019i	$-0.828898\pi$
$47$	0.0955284	−	0.165460i	0.0139343	−	0.0241348i	0.872908	+	0.487884i	$0.162231\pi$
$48$		0			0
$49$	3.49996	+	6.06212i	0.499995	+	0.866016i
$50$		0			0
$51$	4.16959	−	4.10482i	0.583860	−	0.574789i
$52$		0			0
$53$	−0.750557	−	0.750557i	−0.103097	−	0.103097i	0.653677	−	0.756774i	$-0.273226\pi$
$53$	−0.750557	−	0.750557i	−0.103097	−	0.103097i	−0.756774	+	0.653677i	$0.773226\pi$
$54$		0			0
$55$	8.71603			1.17527
$56$		0			0
$57$	−3.32830	−	0.0260560i	−0.440844	−	0.00345120i
$58$		0			0
$59$	9.08809	+	2.43515i	1.18317	+	0.317029i	0.796182	−	0.605057i	$-0.206850\pi$
$59$	9.08809	+	2.43515i	1.18317	+	0.317029i	0.386986	+	0.922086i	$0.373516\pi$
$60$		0			0
$61$	9.85796	−	2.64143i	1.26218	−	0.338201i	0.435152	−	0.900357i	$-0.356695\pi$
$61$	9.85796	−	2.64143i	1.26218	−	0.338201i	0.827031	+	0.562156i	$0.190028\pi$
$62$		0			0
$63$	0.0218629	+	0.0130832i	0.00275447	+	0.00164832i
$64$		0			0
$65$	−16.1544	−	9.32674i	−2.00371	−	1.15684i
$66$		0			0
$67$	7.77154	+	2.08238i	0.949445	+	0.254403i	0.700127	−	0.714019i	$-0.253127\pi$
$67$	7.77154	+	2.08238i	0.949445	+	0.254403i	0.249318	+	0.968422i	$0.419794\pi$
$68$		0			0
$69$	10.3851	+	2.87000i	1.25022	+	0.345507i
$70$		0			0
$71$			1.02260i			0.121360i	0.998157	+	0.0606801i	$0.0193269\pi$
$71$			1.02260i			0.121360i	−0.998157	+	0.0606801i	$0.980673\pi$
$72$		0			0
$73$			7.30911i			0.855467i	0.903905	+	0.427734i	$0.140688\pi$
$73$			7.30911i			0.855467i	−0.903905	+	0.427734i	$0.859312\pi$
$74$		0			0
$75$	−1.24844	−	4.80954i	−0.144157	−	0.555357i
$76$		0			0
$77$	−0.0254895	−	0.00682989i	−0.00290480	−	0.000778338i
$78$		0			0
$79$	−4.36074	−	2.51768i	−0.490622	−	0.283261i	0.234211	−	0.972186i	$-0.424749\pi$
$79$	−4.36074	−	2.51768i	−0.490622	−	0.283261i	−0.724832	+	0.688925i	$0.758083\pi$
$80$		0			0
$81$	−8.99559	−	0.281779i	−0.999510	−	0.0313088i
$82$		0			0
$83$	−12.5030	+	3.35017i	−1.37238	+	0.367729i	−0.868348	−	0.495955i	$-0.834818\pi$
$83$	−12.5030	+	3.35017i	−1.37238	+	0.367729i	−0.504034	+	0.863684i	$0.668151\pi$
$84$		0			0
$85$	9.15320	+	2.45259i	0.992804	+	0.266021i
$86$		0			0
$87$	−2.97769	+	5.06552i	−0.319242	+	0.543080i
$88$		0			0
$89$	18.1774			1.92680			0.963399	−	0.268070i	$-0.0863859\pi$
$89$	18.1774			1.92680			0.963399	+	0.268070i	$0.0863859\pi$
$90$		0			0
$91$	0.0399341	+	0.0399341i	0.00418623	+	0.00418623i
$92$		0			0
$93$	−12.9199	−	3.57052i	−1.33973	−	0.370246i
$94$		0			0
$95$	−2.69525	−	4.66831i	−0.276527	−	0.478959i
$96$		0			0
$97$	1.64497	−	2.84917i	0.167021	−	0.289289i	−0.770350	−	0.637621i	$-0.779918\pi$
$97$	1.64497	−	2.84917i	0.167021	−	0.289289i	0.937371	+	0.348332i	$0.113252\pi$
$98$		0			0
$99$	9.04054	−	2.27132i	0.908608	−	0.228276i
$100$		0			0
$101$	2.66775	−	0.714822i	0.265451	−	0.0711275i	−0.123638	−	0.992327i	$-0.539456\pi$
$101$	2.66775	−	0.714822i	0.265451	−	0.0711275i	0.389090	+	0.921200i	$0.372790\pi$
$102$		0			0
$103$	−5.52502	−	9.56961i	−0.544396	−	0.942922i	−0.998645	−	0.0520466i	$-0.983426\pi$
$103$	−5.52502	−	9.56961i	−0.544396	−	0.942922i	0.454249	−	0.890875i	$-0.349908\pi$
$104$		0			0
$105$	−0.000323029		0.0412625i	−3.15244e−5		0.00402681i
$106$		0			0
$107$	1.93562	−	1.93562i	0.187124	−	0.187124i	−0.607328	−	0.794451i	$-0.707759\pi$
$107$	1.93562	−	1.93562i	0.187124	−	0.187124i	0.794451	+	0.607328i	$0.207759\pi$
$108$		0			0
$109$	5.98392	+	5.98392i	0.573155	+	0.573155i	0.933009	−	0.359853i	$-0.117173\pi$
$109$	5.98392	+	5.98392i	0.573155	+	0.573155i	−0.359853	+	0.933009i	$0.617173\pi$
$110$		0			0
$111$	1.88531	+	0.0147594i	0.178945	+	0.00140090i
$112$		0			0
$113$	11.7864	−	6.80488i	1.10877	−	0.640149i	0.170260	−	0.985399i	$-0.445539\pi$
$113$	11.7864	−	6.80488i	1.10877	−	0.640149i	0.938511	+	0.345250i	$0.112206\pi$
$114$		0			0
$115$	4.51629	+	16.8550i	0.421146	+	1.57174i
$116$		0			0
$117$	−19.1863	−	5.46430i	−1.77377	−	0.505175i
$118$		0			0
$119$	−0.0248461	−	0.0143449i	−0.00227764	−	0.00131500i
$120$		0			0
$121$	1.16526	−	0.672766i	0.105933	−	0.0611605i
$122$		0			0
$123$	2.44301	−	8.84004i	0.220279	−	0.797079i
$124$		0			0
$125$	−4.22728	+	4.22728i	−0.378100	+	0.378100i
$126$		0			0
$127$		−	7.01184i		−	0.622200i	−0.950377	−	0.311100i	$-0.899303\pi$
$127$		−	7.01184i		−	0.622200i	0.950377	−	0.311100i	$-0.100697\pi$
$128$		0			0
$129$	9.27185	+	5.45032i	0.816340	+	0.479874i
$130$		0			0
$131$	2.15546	−	8.04427i	0.188323	−	0.702831i	−0.805572	−	0.592498i	$-0.798142\pi$
$131$	2.15546	−	8.04427i	0.188323	−	0.702831i	0.993895	−	0.110333i	$-0.0351916\pi$
$132$		0			0
$133$	0.00422400	+	0.0157642i	0.000366268	+	0.00136693i
$134$		0			0
$135$	−6.98953	−	12.7908i	−0.601563	−	1.10086i
$136$		0			0
$137$	2.71852	−	4.70861i	0.232259	−	0.402284i	−0.726214	−	0.687469i	$-0.758722\pi$
$137$	2.71852	−	4.70861i	0.232259	−	0.402284i	0.958472	+	0.285185i	$0.0920550\pi$
$138$		0			0
$139$	−3.64349	+	13.5977i	−0.309037	+	1.15334i	0.620378	+	0.784303i	$0.286979\pi$
$139$	−3.64349	+	13.5977i	−0.309037	+	1.15334i	−0.929414	+	0.369038i	$0.879687\pi$
$140$		0			0
$141$	0.320305	−	0.0831435i	0.0269746	−	0.00700195i
$142$		0			0
$143$	20.6619			1.72783
$144$		0			0
$145$	−9.51629			−0.790285
$146$		0			0
$147$	−3.22956	+	11.6862i	−0.266370	+	0.963860i
$148$		0			0
$149$	2.45769	−	9.17223i	0.201342	−	0.751419i	−0.789191	−	0.614147i	$-0.789500\pi$
$149$	2.45769	−	9.17223i	0.201342	−	0.751419i	0.990533	−	0.137271i	$-0.0438332\pi$
$150$		0			0
$151$	2.26744	−	3.92732i	0.184522	−	0.319601i	−0.758893	−	0.651215i	$-0.774260\pi$
$151$	2.26744	−	3.92732i	0.184522	−	0.319601i	0.943415	+	0.331614i	$0.107593\pi$
$152$		0			0
$153$	10.1331	+	0.158667i	0.819213	+	0.0128274i
$154$		0			0
$155$	−5.61865	−	20.9691i	−0.451301	−	1.68428i
$156$		0			0
$157$	5.12011	−	19.1085i	0.408629	−	1.52502i	−0.388634	−	0.921392i	$-0.627053\pi$
$157$	5.12011	−	19.1085i	0.408629	−	1.52502i	0.797263	−	0.603632i	$-0.206280\pi$
$158$		0			0
$159$	0.0143924	−	1.83843i	0.00114139	−	0.145797i
$160$		0			0
$161$		−	0.0528305i		−	0.00416362i
$162$		0			0
$163$	6.31776	−	6.31776i	0.494845	−	0.494845i	−0.414984	−	0.909829i	$-0.636213\pi$
$163$	6.31776	−	6.31776i	0.494845	−	0.494845i	0.909829	+	0.414984i	$0.136213\pi$
$164$		0			0
$165$	10.5910	+	10.7582i	0.824510	+	0.837521i
$166$		0			0
$167$	−10.2973	+	5.94513i	−0.796827	+	0.460048i	−0.842360	−	0.538915i	$-0.818835\pi$
$167$	−10.2973	+	5.94513i	−0.796827	+	0.460048i	0.0455334	+	0.998963i	$0.485501\pi$
$168$		0			0
$169$	−27.0366	−	15.6096i	−2.07974	−	1.20074i
$170$		0			0
$171$	−4.01212	−	4.13976i	−0.306814	−	0.316575i
$172$		0			0
$173$	−0.125524	−	0.468462i	−0.00954341	−	0.0356165i	0.960990	−	0.276583i	$-0.0892022\pi$
$173$	−0.125524	−	0.468462i	−0.00954341	−	0.0356165i	−0.970533	+	0.240967i	$0.922536\pi$
$174$		0			0
$175$	−0.0211002	+	0.0121822i	−0.00159502	+	0.000920887i
$176$		0			0
$177$	8.03743	+	14.1764i	0.604130	+	1.06556i
$178$		0			0
$179$	−6.91661	−	6.91661i	−0.516971	−	0.516971i	0.399682	−	0.916654i	$-0.369120\pi$
$179$	−6.91661	−	6.91661i	−0.516971	−	0.516971i	−0.916654	+	0.399682i	$0.869120\pi$
$180$		0			0
$181$	−2.19753	+	2.19753i	−0.163341	+	0.163341i	−0.784045	−	0.620704i	$-0.786847\pi$
$181$	−2.19753	+	2.19753i	−0.163341	+	0.163341i	0.620704	+	0.784045i	$0.286847\pi$
$182$		0			0
$183$	15.2389	+	8.95798i	1.12649	+	0.662193i
$184$		0			0
$185$	1.52672	+	2.64436i	0.112247	+	0.194417i
$186$		0			0
$187$	−10.1387	+	2.71666i	−0.741416	+	0.198662i
$188$		0			0
$189$	0.0104176	+	0.0428829i	0.000757766	+	0.00311927i
$190$		0			0
$191$	6.33144	−	10.9664i	0.458127	−	0.793499i	−0.540735	−	0.841193i	$-0.681854\pi$
$191$	6.33144	−	10.9664i	0.458127	−	0.793499i	0.998862	+	0.0476936i	$0.0151871\pi$
$192$		0			0
$193$	4.99499	+	8.65157i	0.359547	+	0.622754i	0.987885	−	0.155187i	$-0.0495979\pi$
$193$	4.99499	+	8.65157i	0.359547	+	0.622754i	−0.628338	+	0.777940i	$0.716265\pi$
$194$		0			0
$195$	−8.11757	−	31.2724i	−0.581311	−	2.23946i
$196$		0			0
$197$	0.273888	+	0.273888i	0.0195137	+	0.0195137i	0.716796	−	0.697283i	$-0.245608\pi$
$197$	0.273888	+	0.273888i	0.0195137	+	0.0195137i	−0.697283	+	0.716796i	$0.745608\pi$
$198$		0			0
$199$	18.0544			1.27984			0.639920	−	0.768441i	$-0.278967\pi$
$199$	18.0544			1.27984			0.639920	+	0.768441i	$0.278967\pi$
$200$		0			0
$201$	6.87308	+	12.1227i	0.484790	+	0.855070i
$202$		0			0
$203$	0.0278298	+	0.00745698i	0.00195327	+	0.000523377i
$204$		0			0
$205$	14.3474	−	3.84438i	1.00207	−	0.268503i
$206$		0			0
$207$	9.07670	+	16.3057i	0.630874	+	1.13332i
$208$		0			0
$209$	5.17094	+	2.98544i	0.357681	+	0.206507i
$210$		0			0
$211$	2.33428	+	0.625467i	0.160698	+	0.0430589i	0.338271	−	0.941049i	$-0.390158\pi$
$211$	2.33428	+	0.625467i	0.160698	+	0.0430589i	−0.177573	+	0.984108i	$0.556825\pi$
$212$		0			0
$213$	−1.26219	+	1.24258i	−0.0864838	+	0.0851402i
$214$		0			0
$215$			17.4185i			1.18793i
$216$		0			0
$217$			0.0657256i			0.00446175i
$218$		0			0
$219$	−9.02160	+	8.88145i	−0.609623	+	0.600153i
$220$		0			0
$221$	21.6982	+	5.81402i	1.45958	+	0.391093i
$222$		0			0
$223$	−0.0284597	−	0.0164312i	−0.00190581	−	0.00110032i	0.499047	−	0.866575i	$-0.333684\pi$
$223$	−0.0284597	−	0.0164312i	−0.00190581	−	0.00110032i	−0.500953	+	0.865475i	$0.667017\pi$
$224$		0			0
$225$	4.41938	−	7.38511i	0.294626	−	0.492340i
$226$		0			0
$227$	−17.9063	+	4.79797i	−1.18848	+	0.318453i	−0.798285	−	0.602279i	$-0.794259\pi$
$227$	−17.9063	+	4.79797i	−1.18848	+	0.318453i	−0.390196	+	0.920732i	$0.627593\pi$
$228$		0			0
$229$	−26.3567	−	7.06225i	−1.74170	−	0.466687i	−0.758875	−	0.651236i	$-0.774251\pi$
$229$	−26.3567	−	7.06225i	−1.74170	−	0.466687i	−0.982823	+	0.184549i	$0.940918\pi$
$230$		0			0
$231$	−0.0225427	−	0.0397607i	−0.00148320	−	0.00261606i
$232$		0			0
$233$	−7.42838			−0.486649			−0.243325	−	0.969945i	$-0.578238\pi$
$233$	−7.42838			−0.486649			−0.243325	+	0.969945i	$0.578238\pi$
$234$		0			0
$235$	0.378968	+	0.378968i	0.0247211	+	0.0247211i
$236$		0			0
$237$	−2.19127	−	8.44172i	−0.142338	−	0.548349i
$238$		0			0
$239$	−2.67225	−	4.62848i	−0.172854	−	0.299391i	0.766563	−	0.642169i	$-0.221965\pi$
$239$	−2.67225	−	4.62848i	−0.172854	−	0.299391i	−0.939416	+	0.342778i	$0.888632\pi$
$240$		0			0
$241$	−10.9314	+	18.9337i	−0.704151	+	1.21963i	0.262845	+	0.964838i	$0.415339\pi$
$241$	−10.9314	+	18.9337i	−0.704151	+	1.21963i	−0.966997	+	0.254788i	$0.917994\pi$
$242$		0			0
$243$	−10.5829	−	11.4456i	−0.678894	−	0.734236i
$244$		0			0
$245$	−18.9667	+	5.08211i	−1.21174	+	0.324684i
$246$		0			0
$247$	−6.38925	−	11.0665i	−0.406538	−	0.704145i
$248$		0			0
$249$	−19.3277	−	11.3615i	−1.22484	−	0.720008i
$250$		0			0
$251$	−18.4081	+	18.4081i	−1.16191	+	1.16191i	−0.177854	+	0.984057i	$0.556915\pi$
$251$	−18.4081	+	18.4081i	−1.16191	+	1.16191i	−0.984057	+	0.177854i	$0.943085\pi$
$252$		0			0
$253$	−13.6672	−	13.6672i	−0.859251	−	0.859251i
$254$		0			0
$255$	8.09501	+	14.2779i	0.506929	+	0.894120i
$256$		0			0
$257$	−6.96658	+	4.02216i	−0.434563	+	0.250895i	−0.701289	−	0.712877i	$-0.747392\pi$
$257$	−6.96658	+	4.02216i	−0.434563	+	0.250895i	0.266726	+	0.963773i	$0.414058\pi$
$258$		0			0
$259$	−0.00239268	−	0.00892960i	−0.000148674	−	0.000554858i
$260$		0			0
$261$	−9.87060	+	2.47986i	−0.610975	+	0.153499i
$262$		0			0
$263$	3.65553	+	2.11052i	0.225409	+	0.130140i	0.608452	−	0.793590i	$-0.291791\pi$
$263$	3.65553	+	2.11052i	0.225409	+	0.130140i	−0.383043	+	0.923730i	$0.625124\pi$
$264$		0			0
$265$	2.57860	−	1.48876i	0.158402	−	0.0914535i
$266$		0			0
$267$	22.0877	+	22.4363i	1.35174	+	1.37308i
$268$		0			0
$269$	−13.7834	+	13.7834i	−0.840386	+	0.840386i	−0.988909	−	0.148523i	$-0.952548\pi$
$269$	−13.7834	+	13.7834i	−0.840386	+	0.840386i	0.148523	+	0.988909i	$0.452548\pi$
$270$		0			0
$271$			14.3202i			0.869889i	0.900457	+	0.434945i	$0.143232\pi$
$271$			14.3202i			0.869889i	−0.900457	+	0.434945i	$0.856768\pi$
$272$		0			0
$273$	−0.000765759		0.0978152i	−4.63459e−5		0.00592004i
$274$		0			0
$275$	−2.30708	+	8.61014i	−0.139122	+	0.519211i
$276$		0			0
$277$	1.71354	+	6.39501i	0.102956	+	0.384239i	0.998105	−	0.0615286i	$-0.0195975\pi$
$277$	1.71354	+	6.39501i	0.102956	+	0.384239i	−0.895149	+	0.445767i	$0.852931\pi$
$278$		0			0
$279$	−11.2922	−	20.2856i	−0.676046	−	1.21447i
$280$		0			0
$281$	1.84037	−	3.18761i	0.109787	−	0.190157i	−0.805897	−	0.592056i	$-0.798316\pi$
$281$	1.84037	−	3.18761i	0.109787	−	0.190157i	0.915684	+	0.401899i	$0.131650\pi$
$282$		0			0
$283$	1.12390	−	4.19445i	0.0668089	−	0.249334i	−0.924442	−	0.381321i	$-0.875469\pi$
$283$	1.12390	−	4.19445i	0.0668089	−	0.249334i	0.991251	+	0.131987i	$0.0421358\pi$
$284$		0			0
$285$	2.48702	−	8.99929i	0.147318	−	0.533072i
$286$		0			0
$287$	−0.0449706			−0.00265453
$288$		0			0
$289$	5.58832			0.328725
$290$		0			0
$291$	5.51555	−	1.43170i	0.323327	−	0.0839280i
$292$		0			0
$293$	3.93269	−	14.6770i	0.229750	−	0.857439i	−0.750695	−	0.660649i	$-0.770281\pi$
$293$	3.93269	−	14.6770i	0.229750	−	0.857439i	0.980446	−	0.196791i	$-0.0630520\pi$
$294$		0			0
$295$	−13.1963	+	22.8567i	−0.768320	+	1.33077i
$296$		0			0
$297$	13.7888	+	8.39877i	0.800108	+	0.487346i
$298$		0			0
$299$	10.7061	+	39.9558i	0.619152	+	2.31071i
$300$		0			0
$301$	0.0136491	−	0.0509393i	0.000786723	−	0.00293609i
$302$		0			0
$303$	4.12394	+	2.42420i	0.236914	+	0.139267i
$304$		0			0
$305$			28.6285i			1.63926i
$306$		0			0
$307$	−23.4294	+	23.4294i	−1.33718	+	1.33718i	−0.438408	+	0.898776i	$0.644457\pi$
$307$	−23.4294	+	23.4294i	−1.33718	+	1.33718i	−0.898776	+	0.438408i	$0.855543\pi$
$308$		0			0
$309$	5.09817	−	18.4477i	0.290025	−	1.04945i
$310$		0			0
$311$	25.9086	−	14.9583i	1.46914	−	0.848210i	0.469741	−	0.882804i	$-0.344347\pi$
$311$	25.9086	−	14.9583i	1.46914	−	0.848210i	0.999401	+	0.0345940i	$0.0110138\pi$
$312$		0			0
$313$	13.0513	+	7.53519i	0.737705	+	0.425914i	0.821234	−	0.570591i	$-0.193286\pi$
$313$	13.0513	+	7.53519i	0.737705	+	0.425914i	−0.0835293	+	0.996505i	$0.526619\pi$
$314$		0			0
$315$	−0.0513226	+	0.0497401i	−0.00289170	+	0.00280254i
$316$		0			0
$317$	5.40325	+	20.1652i	0.303477	+	1.13259i	0.934248	+	0.356623i	$0.116072\pi$
$317$	5.40325	+	20.1652i	0.303477	+	1.13259i	−0.630772	+	0.775969i	$0.717261\pi$
$318$		0			0
$319$	9.12868	−	5.27045i	0.511108	−	0.295088i
$320$		0			0
$321$	4.74114	+	0.0371167i	0.264625	+	0.00207165i
$322$		0			0
$323$	4.59023	+	4.59023i	0.255407	+	0.255407i
$324$		0			0
$325$	13.4894	−	13.4894i	0.748257	−	0.748257i
$326$		0			0
$327$	−0.114745	+	14.6571i	−0.00634542	+	0.810539i
$328$		0			0
$329$	−0.000811309	−	0.00140523i	−4.47289e−5	−	7.74727e-5i
$330$		0			0
$331$	18.4453	−	4.94242i	1.01385	−	0.271660i	0.286612	−	0.958047i	$-0.407471\pi$
$331$	18.4453	−	4.94242i	1.01385	−	0.271660i	0.727236	+	0.686387i	$0.240804\pi$
$332$		0			0
$333$	2.27266	+	2.34496i	0.124541	+	0.128503i
$334$		0			0
$335$	−11.2846	+	19.5456i	−0.616546	+	1.06789i
$336$		0			0
$337$	−9.91944	−	17.1810i	−0.540346	−	0.935907i	−0.998884	−	0.0472324i	$-0.984960\pi$
$337$	−9.91944	−	17.1810i	−0.540346	−	0.935907i	0.458538	−	0.888675i	$-0.348373\pi$
$338$		0			0
$339$	22.7211	+	6.27915i	1.23404	+	0.341036i
$340$		0			0
$341$	17.0032	+	17.0032i	0.920774	+	0.920774i
$342$		0			0
$343$	0.118899			0.00641996
$344$		0			0
$345$	−15.3162	+	26.0553i	−0.824599	+	1.40277i
$346$		0			0
$347$	−20.9225	−	5.60618i	−1.12318	−	0.300955i	−0.351011	−	0.936372i	$-0.614162\pi$
$347$	−20.9225	−	5.60618i	−1.12318	−	0.300955i	−0.772170	+	0.635416i	$0.780829\pi$
$348$		0			0
$349$	1.59139	−	0.426410i	0.0851849	−	0.0228252i	−0.215975	−	0.976399i	$-0.569293\pi$
$349$	1.59139	−	0.426410i	0.0851849	−	0.0228252i	0.301160	+	0.953574i	$0.402626\pi$
$350$		0			0
$351$	−16.5691	−	30.3213i	−0.884393	−	1.61843i
$352$		0			0
$353$	−3.91868	−	2.26245i	−0.208570	−	0.120418i	0.392076	−	0.919933i	$-0.371757\pi$
$353$	−3.91868	−	2.26245i	−0.208570	−	0.120418i	−0.600647	+	0.799514i	$0.705090\pi$
$354$		0			0
$355$	−2.77079	−	0.742431i	−0.147058	−	0.0394042i
$356$		0			0
$357$	−0.0124852	−	0.0480983i	−0.000660784	−	0.00254563i
$358$		0			0
$359$			11.0661i			0.584046i	0.956411	+	0.292023i	$0.0943284\pi$
$359$			11.0661i			0.584046i	−0.956411	+	0.292023i	$0.905672\pi$
$360$		0			0
$361$			15.3073i			0.805645i
$362$		0			0
$363$	2.24633	+	0.620789i	0.117902	+	0.0325830i
$364$		0			0
$365$	−19.8045	−	5.30659i	−1.03661	−	0.277760i
$366$		0			0
$367$	−4.77772	−	2.75842i	−0.249395	−	0.143988i	0.370092	−	0.928995i	$-0.379326\pi$
$367$	−4.77772	−	2.75842i	−0.249395	−	0.143988i	−0.619487	+	0.785007i	$0.712659\pi$
$368$		0			0
$369$	13.8798	−	7.72631i	0.722552	−	0.402215i
$370$		0			0
$371$	−0.00870755	+	0.00233318i	−0.000452074	+	0.000121133i
$372$		0			0
$373$	−8.16763	−	2.18851i	−0.422904	−	0.113317i	0.0410893	−	0.999155i	$-0.486917\pi$
$373$	−8.16763	−	2.18851i	−0.422904	−	0.113317i	−0.463993	+	0.885839i	$0.653584\pi$
$374$		0			0
$375$	−10.3544	−	0.0810606i	−0.534697	−	0.00418595i
$376$		0			0
$377$	−22.5589			−1.16184
$378$		0			0
$379$	−20.4820	−	20.4820i	−1.05209	−	1.05209i	−0.998566	−	0.0535254i	$-0.982954\pi$
$379$	−20.4820	−	20.4820i	−1.05209	−	1.05209i	−0.0535254	−	0.998566i	$-0.517046\pi$
$380$		0			0
$381$	8.65468	−	8.52023i	0.443393	−	0.436504i
$382$		0			0
$383$	2.14427	+	3.71398i	0.109567	+	0.189776i	0.915595	−	0.402102i	$-0.131720\pi$
$383$	2.14427	+	3.71398i	0.109567	+	0.189776i	−0.806028	+	0.591878i	$0.798387\pi$
$384$		0			0
$385$	0.0370120	−	0.0641066i	0.00188630	−	0.00326718i
$386$		0			0
$387$	4.53909	+	18.0670i	0.230735	+	0.918397i
$388$		0			0
$389$	−15.6680	+	4.19823i	−0.794400	+	0.212859i	−0.633124	−	0.774051i	$-0.718228\pi$
$389$	−15.6680	+	4.19823i	−0.794400	+	0.212859i	−0.161276	+	0.986909i	$0.551561\pi$
$390$		0			0
$391$	−10.5069	−	18.1985i	−0.531358	−	0.920339i
$392$		0			0
$393$	12.5481	−	7.11428i	0.632970	−	0.358868i
$394$		0			0
$395$	9.98779	−	9.98779i	0.502540	−	0.502540i
$396$		0			0
$397$	−2.22738	−	2.22738i	−0.111789	−	0.111789i	0.649000	−	0.760789i	$-0.275188\pi$
$397$	−2.22738	−	2.22738i	−0.111789	−	0.111789i	−0.760789	+	0.649000i	$0.775188\pi$
$398$		0			0
$399$	−0.0143250	+	0.0243691i	−0.000717147	+	0.00121998i
$400$		0			0
$401$	7.43343	−	4.29169i	0.371208	−	0.214317i	−0.302778	−	0.953061i	$-0.597914\pi$
$401$	7.43343	−	4.29169i	0.371208	−	0.214317i	0.673986	+	0.738744i	$0.264581\pi$
$402$		0			0
$403$	−13.3193	−	49.7085i	−0.663484	−	2.47616i
$404$		0			0
$405$	7.29451	−	24.1695i	0.362467	−	1.20099i
$406$		0			0
$407$	−2.92907	−	1.69110i	−0.145189	−	0.0838246i
$408$		0			0
$409$	32.0886	−	18.5263i	1.58668	−	0.916068i	0.592828	−	0.805329i	$-0.298012\pi$
$409$	32.0886	−	18.5263i	1.58668	−	0.916068i	0.993850	−	0.110739i	$-0.0353218\pi$
$410$		0			0
$411$	9.11514	−	2.36607i	0.449617	−	0.116710i
$412$		0			0
$413$	0.0565024	−	0.0565024i	0.00278030	−	0.00278030i
$414$		0			0
$415$		−	36.3099i		−	1.78238i
$416$		0			0
$417$	−21.2108	+	12.0257i	−1.03870	+	0.588900i
$418$		0			0
$419$	5.35101	−	19.9702i	0.261414	−	0.975609i	−0.702995	−	0.711195i	$-0.748155\pi$
$419$	5.35101	−	19.9702i	0.261414	−	0.975609i	0.964409	−	0.264415i	$-0.0851788\pi$
$420$		0			0
$421$	2.50791	+	9.35966i	0.122228	+	0.456162i	0.999726	−	0.0234192i	$-0.00745525\pi$
$421$	2.50791	+	9.35966i	0.122228	+	0.456162i	−0.877497	+	0.479581i	$0.840789\pi$
$422$		0			0
$423$	0.491833	+	0.294322i	0.0239137	+	0.0143104i
$424$		0			0
$425$	−4.84559	+	8.39281i	−0.235046	+	0.407111i
$426$		0			0
$427$	0.0224333	−	0.0837222i	0.00108562	−	0.00405160i
$428$		0			0
$429$	25.1066	+	25.5028i	1.21216	+	1.23129i
$430$		0			0
$431$	−25.3669			−1.22188			−0.610941	−	0.791676i	$-0.709209\pi$
$431$	−25.3669			−1.22188			−0.610941	+	0.791676i	$0.709209\pi$
$432$		0			0
$433$	−10.5243			−0.505764			−0.252882	−	0.967497i	$-0.581378\pi$
$433$	−10.5243			−0.505764			−0.252882	+	0.967497i	$0.581378\pi$
$434$		0			0
$435$	−11.5634	−	11.7459i	−0.554424	−	0.563174i
$436$		0			0
$437$	−3.09387	+	11.5465i	−0.148000	+	0.552343i
$438$		0			0
$439$	−1.65348	+	2.86391i	−0.0789163	+	0.136687i	−0.902783	−	0.430097i	$-0.858479\pi$
$439$	−1.65348	+	2.86391i	−0.0789163	+	0.136687i	0.823866	+	0.566784i	$0.191813\pi$
$440$		0			0
$441$	−18.3485	+	10.2139i	−0.873738	+	0.486375i
$442$		0			0
$443$	1.45346	+	5.42439i	0.0690560	+	0.257721i	0.991820	−	0.127645i	$-0.0407419\pi$
$443$	1.45346	+	5.42439i	0.0690560	+	0.257721i	−0.922764	+	0.385366i	$0.874075\pi$
$444$		0			0
$445$	−13.1972	+	49.2527i	−0.625608	+	2.33480i
$446$		0			0
$447$	14.3076	−	8.11184i	0.676728	−	0.383677i
$448$		0			0
$449$			3.76456i			0.177661i	0.996047	+	0.0888303i	$0.0283129\pi$
$449$			3.76456i			0.177661i	−0.996047	+	0.0888303i	$0.971687\pi$
$450$		0			0
$451$	−11.6339	+	11.6339i	−0.547818	+	0.547818i
$452$		0			0
$453$	7.60269	−	1.97348i	0.357206	−	0.0927220i
$454$		0			0
$455$	−0.137197	+	0.0792106i	−0.00643189	+	0.00371345i
$456$		0			0
$457$	−18.4633	−	10.6598i	−0.863675	−	0.498643i	0.00156649	−	0.999999i	$-0.499501\pi$
$457$	−18.4633	−	10.6598i	−0.863675	−	0.498643i	−0.865241	+	0.501356i	$0.832835\pi$
$458$		0			0
$459$	12.1171	+	12.7000i	0.565578	+	0.592787i
$460$		0			0
$461$	−10.0471	−	37.4962i	−0.467938	−	1.74637i	−0.646959	−	0.762525i	$-0.723960\pi$
$461$	−10.0471	−	37.4962i	−0.467938	−	1.74637i	0.179021	−	0.983845i	$-0.442707\pi$
$462$		0			0
$463$	7.29597	−	4.21233i	0.339073	−	0.195764i	−0.320789	−	0.947151i	$-0.603948\pi$
$463$	7.29597	−	4.21233i	0.339073	−	0.195764i	0.659862	+	0.751387i	$0.270615\pi$
$464$		0			0
$465$	19.0547	−	32.4150i	0.883641	−	1.50321i
$466$		0			0
$467$	19.4539	+	19.4539i	0.900219	+	0.900219i	0.995455	−	0.0952358i	$-0.0303605\pi$
$467$	19.4539	+	19.4539i	0.900219	+	0.900219i	−0.0952358	+	0.995455i	$0.530361\pi$
$468$		0			0
$469$	0.0483172	−	0.0483172i	0.00223108	−	0.00223108i
$470$		0			0
$471$	29.8071	−	16.8994i	1.37344	−	0.778683i
$472$		0			0
$473$	−9.64695	−	16.7090i	−0.443567	−	0.768281i
$474$		0			0
$475$	5.32501	−	1.42683i	0.244328	−	0.0654676i
$476$		0			0
$477$	2.28665	−	2.21614i	0.104698	−	0.101470i
$478$		0			0
$479$	10.4276	−	18.0611i	0.476450	−	0.825235i	−0.523186	−	0.852218i	$-0.675257\pi$
$479$	10.4276	−	18.0611i	0.476450	−	0.825235i	0.999636	+	0.0269835i	$0.00859016\pi$
$480$		0			0
$481$	3.61918	+	6.26860i	0.165020	+	0.285824i
$482$		0			0
$483$	0.0652084	−	0.0641953i	0.00296708	−	0.00292099i
$484$		0			0
$485$	6.52570	+	6.52570i	0.296317	+	0.296317i
$486$		0			0
$487$	−34.0126			−1.54126			−0.770629	−	0.637284i	$-0.780058\pi$
$487$	−34.0126			−1.54126			−0.770629	+	0.637284i	$0.780058\pi$
$488$		0			0
$489$	15.4748	+	0.121147i	0.699795	+	0.00547844i
$490$		0			0
$491$	−1.41342	−	0.378725i	−0.0637868	−	0.0170916i	0.226785	−	0.973945i	$-0.427179\pi$
$491$	−1.41342	−	0.378725i	−0.0637868	−	0.0170916i	−0.290571	+	0.956853i	$0.593845\pi$
$492$		0			0
$493$	11.0696	−	2.96609i	0.498550	−	0.133586i
$494$		0			0
$495$	−0.409383	+	26.1449i	−0.0184004	+	1.17513i
$496$		0			0
$497$	0.00752124	+	0.00434239i	0.000337374	+	0.000194783i
$498$		0			0
$499$	35.2078	+	9.43390i	1.57612	+	0.422319i	0.937721	−	0.347389i	$-0.112932\pi$
$499$	35.2078	+	9.43390i	1.57612	+	0.422319i	0.638396	+	0.769708i	$0.279598\pi$
$500$		0			0
$501$	−19.8505	−	5.48583i	−0.886854	−	0.245089i
$502$		0			0
$503$			10.8529i			0.483908i	0.970288	+	0.241954i	$0.0777882\pi$
$503$			10.8529i			0.483908i	−0.970288	+	0.241954i	$0.922212\pi$
$504$		0			0
$505$			7.74741i			0.344755i
$506$		0			0
$507$	−13.5859	−	52.3387i	−0.603370	−	2.32444i
$508$		0			0
$509$	3.94598	+	1.05732i	0.174903	+	0.0468650i	0.345207	−	0.938526i	$-0.387809\pi$
$509$	3.94598	+	1.05732i	0.174903	+	0.0468650i	−0.170305	+	0.985391i	$0.554475\pi$
$510$		0			0
$511$	0.0537587	+	0.0310376i	0.00237814	+	0.00137302i
$512$		0			0
$513$	0.234485	−	9.98244i	0.0103528	−	0.440736i
$514$		0			0
$515$	29.9407	−	8.02259i	1.31934	−	0.353517i
$516$		0			0
$517$	−0.573417	−	0.153647i	−0.0252189	−	0.00675737i
$518$		0			0
$519$	0.425694	−	0.724171i	0.0186859	−	0.0317876i
$520$		0			0
$521$	13.4286			0.588318			0.294159	−	0.955757i	$-0.404961\pi$
$521$	13.4286			0.588318			0.294159	+	0.955757i	$0.404961\pi$
$522$		0			0
$523$	−23.5806	−	23.5806i	−1.03111	−	1.03111i	−0.999500	−	0.0316083i	$-0.989937\pi$
$523$	−23.5806	−	23.5806i	−1.03111	−	1.03111i	−0.0316083	−	0.999500i	$-0.510063\pi$
$524$		0			0
$525$	−0.0406757	−	0.0112410i	−0.00177523	−	0.000490599i
$526$		0			0
$527$	13.0715	+	22.6405i	0.569404	+	0.986237i
$528$		0			0
$529$	7.84782	−	13.5928i	0.341210	−	0.590992i
$530$		0			0
$531$	−7.73140	+	27.1465i	−0.335514	+	1.17806i
$532$		0			0
$533$	34.0114	−	9.11332i	1.47320	−	0.394742i
$534$		0			0
$535$	3.83937	+	6.64999i	0.165991	+	0.287504i
$536$		0			0
$537$	0.132630	−	16.9416i	0.00572340	−	0.731086i
$538$		0			0
$539$	15.3795	−	15.3795i	0.662443	−	0.662443i
$540$		0			0
$541$	−31.9545	−	31.9545i	−1.37383	−	1.37383i	−0.854684	−	0.519148i	$-0.826249\pi$
$541$	−31.9545	−	31.9545i	−1.37383	−	1.37383i	−0.519148	−	0.854684i	$-0.673751\pi$
$542$		0			0
$543$	−5.38266	−	0.0421388i	−0.230992	−	0.00180835i
$544$		0			0
$545$	−20.5582	+	11.8693i	−0.880618	+	0.508425i
$546$		0			0
$547$	−2.76131	−	10.3053i	−0.118065	−	0.440625i	0.881433	−	0.472309i	$-0.156579\pi$
$547$	−2.76131	−	10.3053i	−0.118065	−	0.440625i	−0.999498	+	0.0316846i	$0.989913\pi$
$548$		0			0
$549$	7.46031	+	29.6943i	0.318398	+	1.26732i
$550$		0			0
$551$	−5.64571	−	3.25955i	−0.240515	−	0.138862i
$552$		0			0
$553$	−0.0370351	+	0.0213822i	−0.00157489	+	0.000909265i
$554$		0			0
$555$	−1.40877	+	5.09763i	−0.0597989	+	0.216382i
$556$		0			0
$557$	11.6850	−	11.6850i	0.495109	−	0.495109i	−0.414802	−	0.909912i	$-0.636149\pi$
$557$	11.6850	−	11.6850i	0.495109	−	0.495109i	0.909912	+	0.414802i	$0.136149\pi$
$558$		0			0
$559$			41.2915i			1.74645i
$560$		0			0
$561$	−15.6729	−	9.21309i	−0.661711	−	0.388977i
$562$		0			0
$563$	−2.31677	+	8.64631i	−0.0976403	+	0.364398i	−0.997407	−	0.0719737i	$-0.977070\pi$
$563$	−2.31677	+	8.64631i	−0.0976403	+	0.364398i	0.899766	+	0.436372i	$0.143737\pi$
$564$		0			0
$565$	9.88100	+	36.8764i	0.415697	+	1.55140i
$566$		0			0
$567$	−0.0402716	+	0.0649662i	−0.00169125	+	0.00272832i
$568$		0			0
$569$	6.28570	−	10.8872i	0.263510	−	0.456413i	−0.703662	−	0.710535i	$-0.748453\pi$
$569$	6.28570	−	10.8872i	0.263510	−	0.456413i	0.967172	+	0.254122i	$0.0817864\pi$
$570$		0			0
$571$	3.72510	−	13.9023i	0.155890	−	0.581791i	−0.843137	−	0.537699i	$-0.819294\pi$
$571$	3.72510	−	13.9023i	0.155890	−	0.581791i	0.999027	−	0.0440924i	$-0.0140396\pi$
$572$		0			0
$573$	21.2292	−	5.51059i	0.886863	−	0.230208i
$574$		0			0
$575$	−17.8457			−0.744216
$576$		0			0
$577$	17.0561			0.710056			0.355028	−	0.934856i	$-0.384471\pi$
$577$	17.0561			0.710056			0.355028	+	0.934856i	$0.384471\pi$
$578$		0			0
$579$	−4.60908	+	16.6780i	−0.191547	+	0.693113i
$580$		0			0
$581$	−0.0284525	+	0.106186i	−0.00118041	+	0.00440534i
$582$		0			0
$583$	−1.64905	+	2.85623i	−0.0682965	+	0.118293i
$584$		0			0
$585$	28.7356	−	48.0192i	1.18807	−	1.98535i
$586$		0			0
$587$	−4.63428	−	17.2954i	−0.191277	−	0.713856i	−0.993199	−	0.116427i	$-0.962856\pi$
$587$	−4.63428	−	17.2954i	−0.191277	−	0.713856i	0.801922	−	0.597428i	$-0.203811\pi$
$588$		0			0
$589$	3.84904	−	14.3648i	0.158597	−	0.591891i
$590$		0			0
$591$	−0.00525195	+	0.670864i	−0.000216037	+	0.0275957i
$592$		0			0
$593$		−	25.5455i		−	1.04903i	−0.851402	−	0.524514i	$-0.824247\pi$
$593$		−	25.5455i		−	1.04903i	0.851402	−	0.524514i	$-0.175753\pi$
$594$		0			0
$595$	0.0569073	−	0.0569073i	0.00233297	−	0.00233297i
$596$		0			0
$597$	21.9382	+	22.2844i	0.897872	+	0.912041i
$598$		0			0
$599$	−1.66118	+	0.959083i	−0.0678740	+	0.0391871i	−0.533553	−	0.845767i	$-0.679143\pi$
$599$	−1.66118	+	0.959083i	−0.0678740	+	0.0391871i	0.465679	+	0.884954i	$0.345810\pi$
$600$		0			0
$601$	7.76786	+	4.48478i	0.316858	+	0.182938i	0.649991	−	0.759942i	$-0.274773\pi$
$601$	7.76786	+	4.48478i	0.316858	+	0.182938i	−0.333133	+	0.942880i	$0.608106\pi$
$602$		0			0
$603$	−6.61139	+	23.2140i	−0.269237	+	0.945345i
$604$		0			0
$605$	0.976888	+	3.64579i	0.0397161	+	0.148223i
$606$		0			0
$607$	−20.1239	+	11.6185i	−0.816802	+	0.471581i	−0.849312	−	0.527890i	$-0.822983\pi$
$607$	−20.1239	+	11.6185i	−0.816802	+	0.471581i	0.0325103	+	0.999471i	$0.489650\pi$
$608$		0			0
$609$	0.0246125	+	0.0434113i	0.000997347	+	0.00175912i
$610$		0			0
$611$	0.898366	+	0.898366i	0.0363440	+	0.0363440i
$612$		0			0
$613$	18.6158	−	18.6158i	0.751886	−	0.751886i	−0.222945	−	0.974831i	$-0.571567\pi$
$613$	18.6158	−	18.6158i	0.751886	−	0.751886i	0.974831	+	0.222945i	$0.0715670\pi$
$614$		0			0
$615$	22.1789	+	13.0376i	0.894340	+	0.525725i
$616$		0			0
$617$	18.3062	+	31.7073i	0.736981	+	1.27649i	0.953849	+	0.300288i	$0.0970827\pi$
$617$	18.3062	+	31.7073i	0.736981	+	1.27649i	−0.216868	+	0.976201i	$0.569584\pi$
$618$		0			0
$619$	25.6443	−	6.87138i	1.03073	−	0.276184i	0.296465	−	0.955044i	$-0.404192\pi$
$619$	25.6443	−	6.87138i	1.03073	−	0.276184i	0.734268	+	0.678860i	$0.237526\pi$
$620$		0			0
$621$	−9.09671	+	31.0166i	−0.365039	+	1.24465i
$622$		0			0
$623$	0.0771889	−	0.133695i	0.00309251	−	0.00535638i
$624$		0			0
$625$	−15.5570	−	26.9455i	−0.622280	−	1.07782i
$626$		0			0
$627$	2.59839	+	10.0101i	0.103770	+	0.399766i
$628$		0			0
$629$	−2.60013	−	2.60013i	−0.103674	−	0.103674i
$630$		0			0
$631$	28.2467			1.12449			0.562243	−	0.826972i	$-0.309939\pi$
$631$	28.2467			1.12449			0.562243	+	0.826972i	$0.309939\pi$
$632$		0			0
$633$	2.06441	+	3.64120i	0.0820530	+	0.144725i
$634$		0			0
$635$	18.9990	+	5.09076i	0.753952	+	0.202021i
$636$		0			0
$637$	−44.9617	+	12.0475i	−1.78145	+	0.477338i
$638$		0			0
$639$	−3.06742	−	0.0480304i	−0.121345	−	0.00190005i
$640$		0			0
$641$	14.4080	+	8.31845i	0.569081	+	0.328559i	0.756782	−	0.653667i	$-0.226770\pi$
$641$	14.4080	+	8.31845i	0.569081	+	0.328559i	−0.187701	+	0.982226i	$0.560104\pi$
$642$		0			0
$643$	−5.68404	−	1.52303i	−0.224157	−	0.0600626i	0.144993	−	0.989433i	$-0.453684\pi$
$643$	−5.68404	−	1.52303i	−0.224157	−	0.0600626i	−0.369149	+	0.929370i	$0.620351\pi$
$644$		0			0
$645$	−21.4995	+	21.1655i	−0.846544	+	0.833392i
$646$		0			0
$647$		−	37.4518i		−	1.47238i	−0.676773	−	0.736192i	$-0.736622\pi$
$647$		−	37.4518i		−	1.47238i	0.676773	−	0.736192i	$-0.263378\pi$
$648$		0			0
$649$		−	29.2343i		−	1.14755i
$650$		0			0
$651$	−0.0811248	+	0.0798645i	−0.00317953	+	0.00313014i
$652$		0			0
$653$	−21.2854	−	5.70340i	−0.832962	−	0.223191i	−0.182956	−	0.983121i	$-0.558567\pi$
$653$	−21.2854	−	5.70340i	−0.832962	−	0.223191i	−0.650005	+	0.759930i	$0.725233\pi$
$654$		0			0
$655$	20.2315	+	11.6807i	0.790510	+	0.456401i
$656$		0			0
$657$	−21.9247	−	0.343301i	−0.855362	−	0.0133935i
$658$		0			0
$659$	23.8609	−	6.39350i	0.929487	−	0.249055i	0.237851	−	0.971302i	$-0.423557\pi$
$659$	23.8609	−	6.39350i	0.929487	−	0.249055i	0.691636	+	0.722246i	$0.256890\pi$
$660$		0			0
$661$	3.57782	+	0.958674i	0.139161	+	0.0372881i	0.327727	−	0.944772i	$-0.393717\pi$
$661$	3.57782	+	0.958674i	0.139161	+	0.0372881i	−0.188566	+	0.982060i	$0.560384\pi$
$662$		0			0
$663$	19.1897	+	33.8467i	0.745267	+	1.31450i
$664$		0			0
$665$	−0.0457807			−0.00177530
$666$		0			0
$667$	14.9221	+	14.9221i	0.577785	+	0.577785i
$668$		0			0
$669$	−0.0143010	−	0.0550936i	−0.000552908	−	0.00213004i
$670$		0			0
$671$	−15.8554	−	27.4624i	−0.612091	−	1.06017i
$672$		0			0
$673$	17.3782	−	30.0999i	0.669880	−	1.16027i	−0.308058	−	0.951368i	$-0.599679\pi$
$673$	17.3782	−	30.0999i	0.669880	−	1.16027i	0.977937	−	0.208898i	$-0.0669877\pi$
$674$		0			0
$675$	14.4855	−	3.51896i	0.557546	−	0.135445i
$676$		0			0
$677$	−24.4928	+	6.56283i	−0.941335	+	0.252230i	−0.696681	−	0.717381i	$-0.745341\pi$
$677$	−24.4928	+	6.56283i	−0.941335	+	0.252230i	−0.244654	+	0.969611i	$0.578674\pi$
$678$		0			0
$679$	−0.0139705	−	0.0241976i	−0.000536137	−	0.000928617i
$680$		0			0
$681$	−27.6804	−	16.2715i	−1.06071	−	0.623526i
$682$		0			0
$683$	1.88928	−	1.88928i	0.0722912	−	0.0722912i	−0.670037	−	0.742328i	$-0.733722\pi$
$683$	1.88928	−	1.88928i	0.0722912	−	0.0722912i	0.742328	+	0.670037i	$0.233722\pi$
$684$		0			0
$685$	10.7845	+	10.7845i	0.412056	+	0.412056i
$686$		0			0
$687$	−23.3096	−	41.1134i	−0.889317	−	1.56857i
$688$		0			0
$689$	6.11273	−	3.52918i	0.232876	−	0.134451i
$690$		0			0
$691$	5.19868	+	19.4017i	0.197767	+	0.738077i	0.991533	+	0.129854i	$0.0414508\pi$
$691$	5.19868	+	19.4017i	0.197767	+	0.738077i	−0.793766	+	0.608223i	$0.791883\pi$
$692$		0			0
$693$	0.0216844	−	0.0761384i	0.000823722	−	0.00289226i
$694$		0			0
$695$	−34.1985	−	19.7445i	−1.29722	−	0.748951i
$696$		0			0
$697$	−15.4910	+	8.94375i	−0.586765	+	0.338769i
$698$		0			0
$699$	−9.02637	−	9.16881i	−0.341409	−	0.346796i
$700$		0			0
$701$	−10.9010	+	10.9010i	−0.411725	+	0.411725i	−0.882339	−	0.470614i	$-0.844032\pi$
$701$	−10.9010	+	10.9010i	−0.411725	+	0.411725i	0.470614	+	0.882339i	$0.344032\pi$
$702$		0			0
$703$			2.09175i			0.0788918i
$704$		0			0
$705$	−0.00726692	+	0.928249i	−0.000273688	+	0.0349599i
$706$		0			0
$707$	0.00607088	−	0.0226568i	0.000228319	−	0.000852098i
$708$		0			0
$709$	−4.14803	−	15.4807i	−0.155783	−	0.581389i	−0.999037	−	0.0438741i	$-0.986030\pi$
$709$	−4.14803	−	15.4807i	−0.155783	−	0.581389i	0.843254	−	0.537515i	$-0.180637\pi$
$710$		0			0
$711$	7.75692	−	12.9624i	0.290907	−	0.486127i
$712$		0			0
$713$	−24.0703	+	41.6911i	−0.901441	+	1.56134i
$714$		0			0
$715$	−15.0010	+	55.9845i	−0.561006	+	2.09370i
$716$		0			0
$717$	2.46580	−	8.92251i	0.0920871	−	0.333217i
$718$		0			0
$719$	−21.7763			−0.812119			−0.406060	−	0.913847i	$-0.633097\pi$
$719$	−21.7763			−0.812119			−0.406060	+	0.913847i	$0.633097\pi$
$720$		0			0
$721$	−0.0938463			−0.00349502
$722$		0			0
$723$	−36.6527	+	9.51416i	−1.36313	+	0.353835i
$724$		0			0
$725$	2.51890	−	9.40068i	0.0935497	−	0.349132i
$726$		0			0
$727$	2.62325	−	4.54360i	0.0972908	−	0.168513i	−0.813272	−	0.581884i	$-0.802316\pi$
$727$	2.62325	−	4.54360i	0.0972908	−	0.168513i	0.910562	+	0.413372i	$0.135649\pi$
$728$		0			0
$729$	1.26775	−	26.9702i	0.0469536	−	0.998897i
$730$		0			0
$731$	−5.42908	−	20.2616i	−0.200802	−	0.749403i
$732$		0			0
$733$	−3.41408	+	12.7415i	−0.126102	+	0.470618i	−0.999877	−	0.0157124i	$-0.994998\pi$
$733$	−3.41408	+	12.7415i	−0.126102	+	0.470618i	0.873775	+	0.486331i	$0.161665\pi$
$734$		0			0
$735$	−29.3196	−	17.2351i	−1.08147	−	0.635728i
$736$		0			0
$737$		−	24.9993i		−	0.920860i
$738$		0			0
$739$	23.2424	−	23.2424i	0.854984	−	0.854984i	−0.135758	−	0.990742i	$-0.543347\pi$
$739$	23.2424	−	23.2424i	0.854984	−	0.854984i	0.990742	+	0.135758i	$0.0433470\pi$
$740$		0			0
$741$	5.89563	−	21.3334i	0.216582	−	0.783701i
$742$		0			0
$743$	−24.5336	+	14.1645i	−0.900049	+	0.519643i	−0.877216	−	0.480096i	$-0.840602\pi$
$743$	−24.5336	+	14.1645i	−0.900049	+	0.519643i	−0.0228329	+	0.999739i	$0.507269\pi$
$744$		0			0
$745$	23.0683	+	13.3185i	0.845159	+	0.487953i
$746$		0			0
$747$	−9.46202	−	37.6617i	−0.346197	−	1.37797i
$748$		0			0
$749$	−0.00601707	−	0.0224560i	−0.000219859	−	0.000820525i
$750$		0			0
$751$	22.5527	−	13.0208i	0.822960	−	0.475136i	−0.0284763	−	0.999594i	$-0.509066\pi$
$751$	22.5527	−	13.0208i	0.822960	−	0.475136i	0.851436	+	0.524458i	$0.175732\pi$
$752$		0			0
$753$	−45.0891	−	0.352986i	−1.64314	−	0.0128635i
$754$		0			0
$755$	8.99509	+	8.99509i	0.327365	+	0.327365i
$756$		0			0
$757$	4.87465	−	4.87465i	0.177172	−	0.177172i	−0.612950	−	0.790122i	$-0.710017\pi$
$757$	4.87465	−	4.87465i	0.177172	−	0.177172i	0.790122	+	0.612950i	$0.210017\pi$
$758$		0			0
$759$	0.262077	−	33.4767i	0.00951279	−	1.21513i
$760$		0			0
$761$	3.18964	+	5.52462i	0.115624	+	0.200267i	0.918029	−	0.396513i	$-0.129780\pi$
$761$	3.18964	+	5.52462i	0.115624	+	0.200267i	−0.802405	+	0.596780i	$0.796446\pi$
$762$		0			0
$763$	0.0694221	−	0.0186016i	0.00251325	−	0.000673423i
$764$		0			0
$765$	−7.78679	+	27.3410i	−0.281532	+	0.988518i
$766$		0			0
$767$	−31.2827	+	54.1832i	−1.12955	+	1.95644i
$768$		0			0
$769$	−9.57641	−	16.5868i	−0.345334	−	0.598136i	0.640080	−	0.768308i	$-0.278901\pi$
$769$	−9.57641	−	16.5868i	−0.345334	−	0.598136i	−0.985414	+	0.170172i	$0.945568\pi$
$770$		0			0
$771$	−13.4298	−	3.71141i	−0.483661	−	0.133663i
$772$		0			0
$773$	−26.0627	−	26.0627i	−0.937411	−	0.937411i	0.0607427	−	0.998153i	$-0.480653\pi$
$773$	−26.0627	−	26.0627i	−0.937411	−	0.937411i	−0.998153	+	0.0607427i	$0.980653\pi$
$774$		0			0
$775$	22.2015			0.797503
$776$		0			0
$777$	0.00811437	−	0.0138038i	0.000291101	−	0.000495209i
$778$		0			0
$779$	9.82864	+	2.63358i	0.352148	+	0.0943577i
$780$		0			0
$781$	3.06912	−	0.822367i	0.109822	−	0.0294266i
$782$		0			0
$783$	−15.0548	−	9.16991i	−0.538016	−	0.327706i
$784$		0			0
$785$	48.0583	+	27.7464i	1.71527	+	0.990313i
$786$		0			0
$787$	−11.0575	−	2.96285i	−0.394158	−	0.105614i	0.0562956	−	0.998414i	$-0.482071\pi$
$787$	−11.0575	−	2.96285i	−0.394158	−	0.105614i	−0.450454	+	0.892800i	$0.648738\pi$
$788$		0			0
$789$	1.83690	+	7.07653i	0.0653953	+	0.251931i
$790$		0			0
$791$		−	0.115586i		−	0.00410975i
$792$		0			0
$793$			67.8655i			2.40997i
$794$		0			0
$795$	4.97087	+	1.37374i	0.176299	+	0.0487215i
$796$		0			0
$797$	−4.17990	−	1.12000i	−0.148060	−	0.0396725i	0.184028	−	0.982921i	$-0.441086\pi$
$797$	−4.17990	−	1.12000i	−0.148060	−	0.0396725i	−0.332088	+	0.943249i	$0.607753\pi$
$798$		0			0
$799$	−0.558944	−	0.322706i	−0.0197740	−	0.0114165i
$800$		0			0
$801$	−0.853772	+	54.5255i	−0.0301666	+	1.92656i
$802$		0			0
$803$	21.9368	−	5.87794i	0.774132	−	0.207428i
$804$		0			0
$805$	0.143147	+	0.0383562i	0.00504528	+	0.00135188i
$806$		0			0
$807$	−33.7612	−	0.264304i	−1.18845	−	0.00930394i
$808$		0			0
$809$	−22.7884			−0.801198			−0.400599	−	0.916253i	$-0.631198\pi$
$809$	−22.7884			−0.801198			−0.400599	+	0.916253i	$0.631198\pi$
$810$		0			0
$811$	14.9053	+	14.9053i	0.523396	+	0.523396i	0.918595	−	0.395200i	$-0.129325\pi$
$811$	14.9053	+	14.9053i	0.523396	+	0.523396i	−0.395200	+	0.918595i	$0.629325\pi$
$812$		0			0
$813$	−17.6753	+	17.4007i	−0.619901	+	0.610270i
$814$		0			0
$815$	12.5315	+	21.7052i	0.438959	+	0.760299i
$816$		0			0
$817$	−5.96623	+	10.3338i	−0.208732	+	0.361535i
$818$		0			0
$819$	−0.121663	+	0.117912i	−0.00425126	+	0.00412018i
$820$		0			0
$821$	43.8854	−	11.7591i	1.53161	−	0.410394i	0.608067	−	0.793886i	$-0.291945\pi$
$821$	43.8854	−	11.7591i	1.53161	−	0.410394i	0.923544	+	0.383492i	$0.125279\pi$
$822$		0			0
$823$	22.8842	+	39.6366i	0.797694	+	1.38165i	0.921115	+	0.389292i	$0.127280\pi$
$823$	22.8842	+	39.6366i	0.797694	+	1.38165i	−0.123421	+	0.992354i	$0.539386\pi$
$824$		0			0
$825$	−13.4308	+	7.61473i	−0.467601	+	0.265111i
$826$		0			0
$827$	−22.0262	+	22.0262i	−0.765925	+	0.765925i	−0.977386	−	0.211461i	$-0.932178\pi$
$827$	−22.0262	+	22.0262i	−0.765925	+	0.765925i	0.211461	+	0.977386i	$0.432178\pi$
$828$		0			0
$829$	28.3392	+	28.3392i	0.984261	+	0.984261i	0.999878	−	0.0156173i	$-0.00497134\pi$
$829$	28.3392	+	28.3392i	0.984261	+	0.984261i	−0.0156173	+	0.999878i	$0.504971\pi$
$830$		0			0
$831$	−5.81117	+	9.88571i	−0.201587	+	0.342931i
$832$		0			0
$833$	20.4785	−	11.8233i	0.709539	−	0.409653i
$834$		0			0
$835$	−8.63262	−	32.2174i	−0.298744	−	1.11493i
$836$		0			0
$837$	11.3171	−	38.5874i	0.391176	−	1.33377i
$838$		0			0
$839$	−15.8724	−	9.16393i	−0.547976	−	0.316374i	0.200329	−	0.979729i	$-0.435799\pi$
$839$	−15.8724	−	9.16393i	−0.547976	−	0.316374i	−0.748305	+	0.663355i	$0.769132\pi$
$840$		0			0
$841$	15.1479	−	8.74565i	0.522342	−	0.301574i
$842$		0			0
$843$	6.17072	−	1.60177i	0.212531	−	0.0551679i
$844$		0			0
$845$	61.9244	−	61.9244i	2.13026	−	2.13026i
$846$		0			0
$847$		−	0.0114274i		−	0.000392650i
$848$		0			0
$849$	6.54287	−	3.70954i	0.224551	−	0.127311i
$850$		0			0
$851$	1.75252	−	6.54048i	0.0600755	−	0.224205i
$852$		0			0
$853$	6.36992	+	23.7728i	0.218102	+	0.813967i	0.985052	+	0.172260i	$0.0551068\pi$
$853$	6.36992	+	23.7728i	0.218102	+	0.813967i	−0.766950	+	0.641707i	$0.778227\pi$
$854$		0			0
$855$	14.1298	−	7.86550i	0.483229	−	0.268994i
$856$		0			0
$857$	0.838395	−	1.45214i	0.0286390	−	0.0496043i	−0.851351	−	0.524597i	$-0.824216\pi$
$857$	0.838395	−	1.45214i	0.0286390	−	0.0496043i	0.879990	+	0.474993i	$0.157549\pi$
$858$		0			0
$859$	−3.61213	+	13.4806i	−0.123244	+	0.459954i	−0.999771	−	0.0213994i	$-0.993188\pi$
$859$	−3.61213	+	13.4806i	−0.123244	+	0.459954i	0.876527	+	0.481353i	$0.159855\pi$
$860$		0			0
$861$	−0.0546446	−	0.0555070i	−0.00186228	−	0.00189167i
$862$		0			0
$863$	31.6409			1.07707			0.538535	−	0.842603i	$-0.318978\pi$
$863$	31.6409			1.07707			0.538535	+	0.842603i	$0.318978\pi$
$864$		0			0
$865$	1.36046			0.0462570
$866$		0			0
$867$	6.79048	+	6.89764i	0.230617	+	0.234256i
$868$		0			0
$869$	−4.04940	+	15.1126i	−0.137366	+	0.512658i
$870$		0			0
$871$	−26.7509	+	46.3340i	−0.906421	+	1.56997i
$872$		0			0
$873$	8.46919	+	5.06812i	0.286639	+	0.171530i
$874$		0			0
$875$	0.0131409	+	0.0490426i	0.000444244	+	0.00165794i
$876$		0			0
$877$	−7.88760	+	29.4369i	−0.266345	+	0.994014i	0.695077	+	0.718936i	$0.255370\pi$
$877$	−7.88760	+	29.4369i	−0.266345	+	0.994014i	−0.961422	+	0.275078i	$0.911296\pi$
$878$		0			0
$879$	22.8944	−	12.9802i	0.772210	−	0.437812i
$880$		0			0
$881$			10.2116i			0.344037i	0.985094	+	0.172019i	$0.0550290\pi$
$881$			10.2116i			0.344037i	−0.985094	+	0.172019i	$0.944971\pi$
$882$		0			0
$883$	−7.98299	+	7.98299i	−0.268649	+	0.268649i	−0.828556	−	0.559907i	$-0.810837\pi$
$883$	−7.98299	+	7.98299i	−0.268649	+	0.268649i	0.559907	+	0.828556i	$0.310837\pi$
$884$		0			0
$885$	−44.2471	+	11.4855i	−1.48735	+	0.386080i
$886$		0			0
$887$	−9.34850	+	5.39736i	−0.313892	+	0.181226i	−0.648667	−	0.761073i	$-0.724673\pi$
$887$	−9.34850	+	5.39736i	−0.313892	+	0.181226i	0.334775	+	0.942298i	$0.391340\pi$
$888$		0			0
$889$	−0.0515723	−	0.0297753i	−0.00172968	−	0.000998630i
$890$		0			0
$891$	6.38849	+	27.2250i	0.214022	+	0.912071i
$892$		0			0
$893$	0.0950241	+	0.354635i	0.00317986	+	0.0118674i
$894$		0			0
$895$	23.7626	−	13.7193i	0.794295	−	0.458586i
$896$		0			0
$897$	−36.3081	+	61.7657i	−1.21229	+	2.06230i
$898$		0			0
$899$	−18.5643	−	18.5643i	−0.619155	−	0.619155i
$900$		0			0
$901$	−2.53547	+	2.53547i	−0.0844688	+	0.0844688i
$902$		0			0
$903$	0.0794594	−	0.0450503i	0.00264424	−	0.00149918i
$904$		0			0
$905$	−4.35887	−	7.54978i	−0.144894	−	0.250963i
$906$		0			0
$907$	−7.67746	+	2.05717i	−0.254926	+	0.0683072i	−0.384019	−	0.923325i	$-0.625460\pi$
$907$	−7.67746	+	2.05717i	−0.254926	+	0.0683072i	0.129093	+	0.991633i	$0.458794\pi$
$908$		0			0
$909$	2.01890	+	8.03585i	0.0669628	+	0.266532i
$910$		0			0
$911$	17.5142	−	30.3354i	0.580270	−	1.00506i	−0.415176	−	0.909741i	$-0.636280\pi$
$911$	17.5142	−	30.3354i	0.580270	−	1.00506i	0.995447	−	0.0953171i	$-0.0303865\pi$
$912$		0			0
$913$	20.1096	+	34.8309i	0.665532	+	1.15274i
$914$		0			0
$915$	−35.3360	+	34.7870i	−1.16817	+	1.15002i
$916$		0			0
$917$	−0.0500128	−	0.0500128i	−0.00165157	−	0.00165157i
$918$		0			0
$919$	−25.9311			−0.855387			−0.427694	−	0.903924i	$-0.640674\pi$
$919$	−25.9311			−0.855387			−0.427694	+	0.903924i	$0.640674\pi$
$920$		0			0
$921$	−57.3882	−	0.449271i	−1.89101	−	0.0148040i
$922$		0			0
$923$	−6.56833	−	1.75998i	−0.216199	−	0.0579304i
$924$		0			0
$925$	−3.01634	+	0.808226i	−0.0991767	+	0.0265743i
$926$		0			0
$927$	28.9648	−	16.1235i	0.951329	−	0.529567i
$928$		0			0
$929$	−23.3443	−	13.4779i	−0.765903	−	0.442194i	0.0655082	−	0.997852i	$-0.479133\pi$
$929$	−23.3443	−	13.4779i	−0.765903	−	0.442194i	−0.831411	+	0.555658i	$0.812466\pi$
$930$		0			0
$931$	−12.9931	−	3.48148i	−0.425831	−	0.114101i
$932$		0			0
$933$	49.9451	+	13.8027i	1.63513	+	0.451880i
$934$		0			0
$935$		−	29.4438i		−	0.962914i
$936$		0			0
$937$		−	5.72005i		−	0.186866i	−0.995626	−	0.0934330i	$-0.970216\pi$
$937$		−	5.72005i		−	0.186866i	0.995626	−	0.0934330i	$-0.0297841\pi$
$938$		0			0
$939$	6.55828	+	25.2654i	0.214021	+	0.824504i
$940$		0			0
$941$	22.9223	+	6.14201i	0.747245	+	0.200224i	0.612296	−	0.790629i	$-0.290246\pi$
$941$	22.9223	+	6.14201i	0.747245	+	0.200224i	0.134949	+	0.990853i	$0.456913\pi$
$942$		0			0
$943$	−28.5257	−	16.4693i	−0.928925	−	0.536315i
$944$		0			0
$945$	−0.123757	−	0.00290702i	−0.00402582	−	9.45655e-5i
$946$		0			0
$947$	−52.2601	+	14.0030i	−1.69822	+	0.455038i	−0.972491	−	0.232940i	$-0.925166\pi$
$947$	−52.2601	+	14.0030i	−1.69822	+	0.455038i	−0.725732	+	0.687977i	$0.758499\pi$
$948$		0			0
$949$	−46.9477	−	12.5796i	−1.52399	−	0.408351i
$950$		0			0
$951$	−18.3242	+	31.1724i	−0.594204	+	1.01083i
$952$		0			0
$953$	−2.80246			−0.0907805			−0.0453902	−	0.998969i	$-0.514453\pi$
$953$	−2.80246			−0.0907805			−0.0453902	+	0.998969i	$0.514453\pi$
$954$		0			0
$955$	25.1173	+	25.1173i	0.812775	+	0.812775i
$956$		0			0
$957$	17.5977	+	4.86326i	0.568854	+	0.157207i
$958$		0			0
$959$	−0.0230880	−	0.0399895i	−0.000745550	−	0.00129133i
$960$		0			0
$961$	14.4456	−	25.0204i	0.465986	−	0.807111i
$962$		0			0
$963$	5.71524	+	5.89707i	0.184171	+	0.190030i
$964$		0			0
$965$	−27.0684	+	7.25296i	−0.871363	+	0.233481i
$966$		0			0
$967$	7.66141	+	13.2699i	0.246374	+	0.426733i	0.962517	−	0.271221i	$-0.0874275\pi$
$967$	7.66141	+	13.2699i	0.246374	+	0.426733i	−0.716143	+	0.697954i	$0.754094\pi$
$968$		0			0
$969$	−0.0880203	+	11.2434i	−0.00282762	+	0.361189i
$970$		0			0
$971$	22.7938	−	22.7938i	0.731487	−	0.731487i	−0.239428	−	0.970914i	$-0.576960\pi$
$971$	22.7938	−	22.7938i	0.731487	−	0.731487i	0.970914	+	0.239428i	$0.0769598\pi$
$972$		0			0
$973$	0.0845395	+	0.0845395i	0.00271021	+	0.00271021i
$974$		0			0
$975$	33.0411	+	0.258667i	1.05816	+	0.00828397i
$976$		0			0
$977$	−20.2451	+	11.6885i	−0.647699	+	0.373949i	−0.787574	−	0.616220i	$-0.788663\pi$
$977$	−20.2451	+	11.6885i	−0.647699	+	0.373949i	0.139875	+	0.990169i	$0.455330\pi$
$978$		0			0
$979$	−14.6181	−	54.5556i	−0.467197	−	1.74360i
$980$		0			0
$981$	−18.2306	+	17.6685i	−0.582059	+	0.564112i
$982$		0			0
$983$	30.2556	+	17.4681i	0.965005	+	0.557146i	0.897710	−	0.440587i	$-0.145230\pi$
$983$	30.2556	+	17.4681i	0.965005	+	0.557146i	0.0672949	+	0.997733i	$0.478563\pi$
$984$		0			0
$985$	−0.940963	+	0.543265i	−0.0299816	+	0.0173099i
$986$		0			0
$987$	0.000748629	−	0.00270891i	2.38291e−5	−	8.62257e-5i
$988$		0			0
$989$	27.3131	−	27.3131i	0.868507	−	0.868507i
$990$		0			0
$991$			58.5560i			1.86009i	0.367440	+	0.930047i	$0.380234\pi$
$991$			58.5560i			1.86009i	−0.367440	+	0.930047i	$0.619766\pi$
$992$		0			0
$993$	28.5137	+	16.7614i	0.904855	+	0.531906i
$994$		0			0
$995$	−13.1079	+	48.9194i	−0.415549	+	1.55085i
$996$		0			0
$997$	−11.7727	−	43.9362i	−0.372844	−	1.39147i	−0.856469	−	0.516199i	$-0.827347\pi$
$997$	−11.7727	−	43.9362i	−0.372844	−	1.39147i	0.483624	−	0.875276i	$-0.339320\pi$
$998$		0			0
$999$	−0.132824	+	5.65453i	−0.00420235	+	0.178902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.16		88
3.2	odd	2		1728.2.z.a.1007.18		88
4.3	odd	2		144.2.u.a.83.6	yes	88
9.4	even	3		1728.2.z.a.1583.18		88
9.5	odd	6	inner	576.2.y.a.239.5		88
12.11	even	2		432.2.v.a.35.17		88
16.5	even	4		144.2.u.a.11.14	✓	88
16.11	odd	4	inner	576.2.y.a.335.5		88
36.23	even	6		144.2.u.a.131.14	yes	88
36.31	odd	6		432.2.v.a.179.9		88
48.5	odd	4		432.2.v.a.251.9		88
48.11	even	4		1728.2.z.a.143.18		88
144.5	odd	12		144.2.u.a.59.6	yes	88
144.59	even	12	inner	576.2.y.a.527.16		88
144.85	even	12		432.2.v.a.395.17		88
144.139	odd	12		1728.2.z.a.719.18		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.14	✓	88	16.5	even	4
144.2.u.a.59.6	yes	88	144.5	odd	12
144.2.u.a.83.6	yes	88	4.3	odd	2
144.2.u.a.131.14	yes	88	36.23	even	6
432.2.v.a.35.17		88	12.11	even	2
432.2.v.a.179.9		88	36.31	odd	6
432.2.v.a.251.9		88	48.5	odd	4
432.2.v.a.395.17		88	144.85	even	12
576.2.y.a.47.16		88	1.1	even	1	trivial
576.2.y.a.239.5		88	9.5	odd	6	inner
576.2.y.a.335.5		88	16.11	odd	4	inner
576.2.y.a.527.16		88	144.59	even	12	inner
1728.2.z.a.143.18		88	48.11	even	4
1728.2.z.a.719.18		88	144.139	odd	12
1728.2.z.a.1007.18		88	3.2	odd	2
1728.2.z.a.1583.18		88	9.4	even	3

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.21512 + 1.23430i) q^{3} +(-0.726024 + 2.70956i) q^{5} +(0.00424642 - 0.00735502i) q^{7} +(-0.0469689 + 2.99963i) q^{9} +O(q^{10})\)	\(q+(1.21512 + 1.23430i) q^{3} +(-0.726024 + 2.70956i) q^{5} +(0.00424642 - 0.00735502i) q^{7} +(-0.0469689 + 2.99963i) q^{9} +(-0.804193 - 3.00129i) q^{11} +(-1.72108 + 6.42317i) q^{13} +(-4.22660 + 2.39631i) q^{15} -3.37812i q^{17} +(-1.35881 + 1.35881i) q^{19} +(0.0142382 - 0.00369589i) q^{21} +(5.38718 - 3.11029i) q^{23} +(-2.48446 - 1.43441i) q^{25} +(-3.75950 + 3.58694i) q^{27} +(0.878030 + 3.27685i) q^{29} +(-6.70211 + 3.86947i) q^{31} +(2.72729 - 4.63954i) q^{33} +(0.0168459 + 0.0168459i) q^{35} +(0.769697 - 0.769697i) q^{37} +(-10.0194 + 5.68059i) q^{39} +(-2.64756 - 4.58570i) q^{41} +(5.99790 - 1.60713i) q^{43} +(-8.09358 - 2.30507i) q^{45} +(0.0955284 - 0.165460i) q^{47} +(3.49996 + 6.06212i) q^{49} +(4.16959 - 4.10482i) q^{51} +(-0.750557 - 0.750557i) q^{53} +8.71603 q^{55} +(-3.32830 - 0.0260560i) q^{57} +(9.08809 + 2.43515i) q^{59} +(9.85796 - 2.64143i) q^{61} +(0.0218629 + 0.0130832i) q^{63} +(-16.1544 - 9.32674i) q^{65} +(7.77154 + 2.08238i) q^{67} +(10.3851 + 2.87000i) q^{69} +1.02260i q^{71} +7.30911i q^{73} +(-1.24844 - 4.80954i) q^{75} +(-0.0254895 - 0.00682989i) q^{77} +(-4.36074 - 2.51768i) q^{79} +(-8.99559 - 0.281779i) q^{81} +(-12.5030 + 3.35017i) q^{83} +(9.15320 + 2.45259i) q^{85} +(-2.97769 + 5.06552i) q^{87} +18.1774 q^{89} +(0.0399341 + 0.0399341i) q^{91} +(-12.9199 - 3.57052i) q^{93} +(-2.69525 - 4.66831i) q^{95} +(1.64497 - 2.84917i) q^{97} +(9.04054 - 2.27132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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