LMFDB - Embedded newform 576.2.y.a.335.5

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			335.5
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23430 + 1.21512i) q^{3} +(-2.70956 - 0.726024i) q^{5} +(0.00424642 - 0.00735502i) q^{7} +(0.0469689 - 2.99963i) q^{9} +O(q^{10})$	\(q+(-1.23430 + 1.21512i) q^{3} +(-2.70956 - 0.726024i) q^{5} +(0.00424642 - 0.00735502i) q^{7} +(0.0469689 - 2.99963i) q^{9} +(-3.00129 + 0.804193i) q^{11} +(6.42317 + 1.72108i) q^{13} +(4.22660 - 2.39631i) q^{15} -3.37812i q^{17} +(-1.35881 - 1.35881i) q^{19} +(0.00369589 + 0.0142382i) q^{21} +(5.38718 - 3.11029i) q^{23} +(2.48446 + 1.43441i) q^{25} +(3.58694 + 3.75950i) q^{27} +(3.27685 - 0.878030i) q^{29} +(6.70211 - 3.86947i) q^{31} +(2.72729 - 4.63954i) q^{33} +(-0.0168459 + 0.0168459i) q^{35} +(0.769697 + 0.769697i) q^{37} +(-10.0194 + 5.68059i) q^{39} +(2.64756 + 4.58570i) q^{41} +(-1.60713 - 5.99790i) q^{43} +(-2.30507 + 8.09358i) q^{45} +(-0.0955284 + 0.165460i) q^{47} +(3.49996 + 6.06212i) q^{49} +(4.10482 + 4.16959i) q^{51} +(0.750557 - 0.750557i) q^{53} +8.71603 q^{55} +(3.32830 + 0.0260560i) q^{57} +(2.43515 - 9.08809i) q^{59} +(-2.64143 - 9.85796i) q^{61} +(-0.0218629 - 0.0130832i) q^{63} +(-16.1544 - 9.32674i) q^{65} +(-2.08238 + 7.77154i) q^{67} +(-2.87000 + 10.3851i) q^{69} +1.02260i q^{71} -7.30911i q^{73} +(-4.80954 + 1.24844i) q^{75} +(-0.00682989 + 0.0254895i) q^{77} +(4.36074 + 2.51768i) q^{79} +(-8.99559 - 0.281779i) q^{81} +(-3.35017 - 12.5030i) q^{83} +(-2.45259 + 9.15320i) q^{85} +(-2.97769 + 5.06552i) q^{87} -18.1774 q^{89} +(0.0399341 - 0.0399341i) q^{91} +(-3.57052 + 12.9199i) q^{93} +(2.69525 + 4.66831i) q^{95} +(1.64497 - 2.84917i) q^{97} +(2.27132 + 9.04054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	−1.23430	+	1.21512i	−0.712621	+	0.701550i
$3$	−1.23430	+	1.21512i	−0.712621	+	0.701550i
$4$		0			0
$5$	−2.70956	−	0.726024i	−1.21175	−	0.324688i	−0.404302	−	0.914625i	$-0.632486\pi$
$5$	−2.70956	−	0.726024i	−1.21175	−	0.324688i	−0.807449	+	0.589938i	$0.799152\pi$
$6$		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
$11$	−3.00129	+	0.804193i	−0.904923	+	0.242473i	−0.681129	−	0.732163i	$-0.738511\pi$
$11$	−3.00129	+	0.804193i	−0.904923	+	0.242473i	−0.223794	+	0.974637i	$0.571844\pi$
$12$		0			0
$13$	6.42317	+	1.72108i	1.78147	+	0.477342i	0.990850	−	0.134969i	$-0.0430936\pi$
$13$	6.42317	+	1.72108i	1.78147	+	0.477342i	0.790616	+	0.612312i	$0.209760\pi$
$14$		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	0.533848	−	0.845581i	$-0.320746\pi$
$19$	−1.35881	−	1.35881i	−0.311733	−	0.311733i	−0.845581	+	0.533848i	$0.820746\pi$
$20$		0			0
$21$	0.00369589	+	0.0142382i	0.000806510	+	0.00310703i
$22$		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
$27$	3.58694	+	3.75950i	0.690307	+	0.723517i
$28$		0			0
$29$	3.27685	−	0.878030i	0.608496	−	0.163046i	0.0586036	−	0.998281i	$-0.481335\pi$
$29$	3.27685	−	0.878030i	0.608496	−	0.163046i	0.549893	+	0.835235i	$0.314669\pi$
$30$		0			0
$31$	6.70211	−	3.86947i	1.20374	−	0.694977i	0.242352	−	0.970188i	$-0.422081\pi$
$31$	6.70211	−	3.86947i	1.20374	−	0.694977i	0.961384	+	0.275212i	$0.0887479\pi$
$32$		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	0.767539	−	0.641002i	$-0.221481\pi$
$37$	0.769697	+	0.769697i	0.126537	+	0.126537i	−0.641002	+	0.767539i	$0.721481\pi$
$38$		0			0
$39$	−10.0194	+	5.68059i	−1.60439	+	0.909623i
$40$		0			0
$41$	2.64756	+	4.58570i	0.413479	+	0.716166i	0.995267	−	0.0971739i	$-0.0309803\pi$
$41$	2.64756	+	4.58570i	0.413479	+	0.716166i	−0.581789	+	0.813340i	$0.697647\pi$
$42$		0			0
$43$	−1.60713	−	5.99790i	−0.245086	−	0.914672i	−0.973340	−	0.229365i	$-0.926335\pi$
$43$	−1.60713	−	5.99790i	−0.245086	−	0.914672i	0.728255	−	0.685306i	$-0.240332\pi$
$44$		0			0
$45$	−2.30507	+	8.09358i	−0.343619	+	1.20652i
$46$		0			0
$47$	−0.0955284	+	0.165460i	−0.0139343	+	0.0241348i	−0.872908	−	0.487884i	$-0.837769\pi$
$47$	−0.0955284	+	0.165460i	−0.0139343	+	0.0241348i	0.858974	+	0.512019i	$0.171102\pi$
$48$		0			0
$49$	3.49996	+	6.06212i	0.499995	+	0.866016i
$50$		0			0
$51$	4.10482	+	4.16959i	0.574789	+	0.583860i
$52$		0			0
$53$	0.750557	−	0.750557i	0.103097	−	0.103097i	−0.653677	−	0.756774i	$-0.726774\pi$
$53$	0.750557	−	0.750557i	0.103097	−	0.103097i	0.756774	+	0.653677i	$0.226774\pi$
$54$		0			0
$55$	8.71603			1.17527
$56$		0			0
$57$	3.32830	+	0.0260560i	0.440844	+	0.00345120i
$58$		0			0
$59$	2.43515	−	9.08809i	0.317029	−	1.18317i	−0.605057	−	0.796182i	$-0.706850\pi$
$59$	2.43515	−	9.08809i	0.317029	−	1.18317i	0.922086	−	0.386986i	$-0.126484\pi$
$60$		0			0
$61$	−2.64143	−	9.85796i	−0.338201	−	1.26218i	−0.900357	−	0.435152i	$-0.856695\pi$
$61$	−2.64143	−	9.85796i	−0.338201	−	1.26218i	0.562156	−	0.827031i	$-0.309972\pi$
$62$		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
$67$	−2.08238	+	7.77154i	−0.254403	+	0.949445i	0.714019	+	0.700127i	$0.246873\pi$
$67$	−2.08238	+	7.77154i	−0.254403	+	0.949445i	−0.968422	+	0.249318i	$0.919794\pi$
$68$		0			0
$69$	−2.87000	+	10.3851i	−0.345507	+	1.25022i
$70$		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	$-0.859312\pi$
$73$		−	7.30911i		−	0.855467i	0.903905	−	0.427734i	$-0.140688\pi$
$74$		0			0
$75$	−4.80954	+	1.24844i	−0.555357	+	0.144157i
$76$		0			0
$77$	−0.00682989	+	0.0254895i	−0.000778338	+	0.00290480i
$78$		0			0
$79$	4.36074	+	2.51768i	0.490622	+	0.283261i	0.724832	−	0.688925i	$-0.241917\pi$
$79$	4.36074	+	2.51768i	0.490622	+	0.283261i	−0.234211	+	0.972186i	$0.575251\pi$
$80$		0			0
$81$	−8.99559	−	0.281779i	−0.999510	−	0.0313088i
$82$		0			0
$83$	−3.35017	−	12.5030i	−0.367729	−	1.37238i	−0.863684	−	0.504034i	$-0.831849\pi$
$83$	−3.35017	−	12.5030i	−0.367729	−	1.37238i	0.495955	−	0.868348i	$-0.334818\pi$
$84$		0			0
$85$	−2.45259	+	9.15320i	−0.266021	+	0.992804i
$86$		0			0
$87$	−2.97769	+	5.06552i	−0.319242	+	0.543080i
$88$		0			0
$89$	−18.1774			−1.92680			−0.963399	−	0.268070i	$-0.913614\pi$
$89$	−18.1774			−1.92680			−0.963399	+	0.268070i	$0.913614\pi$
$90$		0			0
$91$	0.0399341	−	0.0399341i	0.00418623	−	0.00418623i
$92$		0			0
$93$	−3.57052	+	12.9199i	−0.370246	+	1.33973i
$94$		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
$99$	2.27132	+	9.04054i	0.228276	+	0.908608i
$100$		0			0
$101$	0.714822	+	2.66775i	0.0711275	+	0.265451i	0.992327	−	0.123638i	$-0.0394563\pi$
$101$	0.714822	+	2.66775i	0.0711275	+	0.265451i	−0.921200	+	0.389090i	$0.872790\pi$
$102$		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	$-0.292241\pi$
$107$	−1.93562	−	1.93562i	−0.187124	−	0.187124i	−0.794451	+	0.607328i	$0.792241\pi$
$108$		0			0
$109$	5.98392	−	5.98392i	0.573155	−	0.573155i	−0.359853	−	0.933009i	$-0.617173\pi$
$109$	5.98392	−	5.98392i	0.573155	−	0.573155i	0.933009	+	0.359853i	$0.117173\pi$
$110$		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
$115$	−16.8550	+	4.51629i	−1.57174	+	0.421146i
$116$		0			0
$117$	5.46430	−	19.1863i	0.505175	−	1.77377i
$118$		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
$123$	−8.84004	−	2.44301i	−0.797079	−	0.220279i
$124$		0			0
$125$	4.22728	+	4.22728i	0.378100	+	0.378100i
$126$		0			0
$127$			7.01184i			0.622200i	0.950377	+	0.311100i	$0.100697\pi$
$127$			7.01184i			0.622200i	−0.950377	+	0.311100i	$0.899303\pi$
$128$		0			0
$129$	9.27185	+	5.45032i	0.816340	+	0.479874i
$130$		0			0
$131$	8.04427	+	2.15546i	0.702831	+	0.188323i	0.592498	−	0.805572i	$-0.298142\pi$
$131$	8.04427	+	2.15546i	0.702831	+	0.188323i	0.110333	+	0.993895i	$0.464808\pi$
$132$		0			0
$133$	−0.0157642	+	0.00422400i	−0.00136693	+	0.000366268i
$134$		0			0
$135$	−6.98953	−	12.7908i	−0.601563	−	1.10086i
$136$		0			0
$137$	−2.71852	+	4.70861i	−0.232259	+	0.402284i	−0.958472	−	0.285185i	$-0.907945\pi$
$137$	−2.71852	+	4.70861i	−0.232259	+	0.402284i	0.726214	+	0.687469i	$0.241278\pi$
$138$		0			0
$139$	13.5977	+	3.64349i	1.15334	+	0.309037i	0.784303	−	0.620378i	$-0.213021\pi$
$139$	13.5977	+	3.64349i	1.15334	+	0.309037i	0.369038	+	0.929414i	$0.379687\pi$
$140$		0			0
$141$	−0.0831435	−	0.320305i	−0.00700195	−	0.0269746i
$142$		0			0
$143$	−20.6619			−1.72783
$144$		0			0
$145$	−9.51629			−0.790285
$146$		0			0
$147$	−11.6862	−	3.22956i	−0.963860	−	0.266370i
$148$		0			0
$149$	9.17223	+	2.45769i	0.751419	+	0.201342i	0.614147	−	0.789191i	$-0.289500\pi$
$149$	9.17223	+	2.45769i	0.751419	+	0.201342i	0.137271	+	0.990533i	$0.456167\pi$
$150$		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
$155$	−20.9691	+	5.61865i	−1.68428	+	0.451301i
$156$		0			0
$157$	−19.1085	−	5.12011i	−1.52502	−	0.408629i	−0.603632	−	0.797263i	$-0.706280\pi$
$157$	−19.1085	−	5.12011i	−1.52502	−	0.408629i	−0.921392	+	0.388634i	$0.872947\pi$
$158$		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	0.909829	−	0.414984i	$-0.136213\pi$
$163$	6.31776	+	6.31776i	0.494845	+	0.494845i	−0.414984	+	0.909829i	$0.636213\pi$
$164$		0			0
$165$	−10.7582	+	10.5910i	−0.837521	+	0.824510i
$166$		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
$171$	−4.13976	+	4.01212i	−0.316575	+	0.306814i
$172$		0			0
$173$	−0.468462	+	0.125524i	−0.0356165	+	0.00954341i	−0.276583	−	0.960990i	$-0.589202\pi$
$173$	−0.468462	+	0.125524i	−0.0356165	+	0.00954341i	0.240967	+	0.970533i	$0.422536\pi$
$174$		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	$-0.630880\pi$
$179$	6.91661	−	6.91661i	0.516971	−	0.516971i	0.916654	+	0.399682i	$0.130880\pi$
$180$		0			0
$181$	−2.19753	−	2.19753i	−0.163341	−	0.163341i	0.620704	−	0.784045i	$-0.286847\pi$
$181$	−2.19753	−	2.19753i	−0.163341	−	0.163341i	−0.784045	+	0.620704i	$0.786847\pi$
$182$		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
$187$	2.71666	+	10.1387i	0.198662	+	0.741416i
$188$		0			0
$189$	0.0428829	−	0.0104176i	0.00311927	−	0.000757766i
$190$		0			0
$191$	−6.33144	+	10.9664i	−0.458127	+	0.793499i	−0.998862	−	0.0476936i	$-0.984813\pi$
$191$	−6.33144	+	10.9664i	−0.458127	+	0.793499i	0.540735	+	0.841193i	$0.318146\pi$
$192$		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
$195$	31.2724	−	8.11757i	2.23946	−	0.581311i
$196$		0			0
$197$	−0.273888	+	0.273888i	−0.0195137	+	0.0195137i	−0.716796	−	0.697283i	$-0.754392\pi$
$197$	−0.273888	+	0.273888i	−0.0195137	+	0.0195137i	0.697283	+	0.716796i	$0.254392\pi$
$198$		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
$203$	0.00745698	−	0.0278298i	0.000523377	−	0.00195327i
$204$		0			0
$205$	−3.84438	−	14.3474i	−0.268503	−	1.00207i
$206$		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
$211$	−0.625467	+	2.33428i	−0.0430589	+	0.160698i	−0.984108	−	0.177573i	$-0.943175\pi$
$211$	−0.625467	+	2.33428i	−0.0430589	+	0.160698i	0.941049	+	0.338271i	$0.109842\pi$
$212$		0			0
$213$	−1.24258	−	1.26219i	−0.0851402	−	0.0864838i
$214$		0			0
$215$			17.4185i			1.18793i
$216$		0			0
$217$		−	0.0657256i		−	0.00446175i
$218$		0			0
$219$	8.88145	+	9.02160i	0.600153	+	0.609623i
$220$		0			0
$221$	5.81402	−	21.6982i	0.391093	−	1.45958i
$222$		0			0
$223$	0.0284597	+	0.0164312i	0.00190581	+	0.00110032i	0.500953	−	0.865475i	$-0.332983\pi$
$223$	0.0284597	+	0.0164312i	0.00190581	+	0.00110032i	−0.499047	+	0.866575i	$0.666316\pi$
$224$		0			0
$225$	4.41938	−	7.38511i	0.294626	−	0.492340i
$226$		0			0
$227$	−4.79797	−	17.9063i	−0.318453	−	1.18848i	−0.920732	−	0.390196i	$-0.872407\pi$
$227$	−4.79797	−	17.9063i	−0.318453	−	1.18848i	0.602279	−	0.798285i	$-0.294259\pi$
$228$		0			0
$229$	7.06225	−	26.3567i	0.466687	−	1.74170i	−0.184549	−	0.982823i	$-0.559082\pi$
$229$	7.06225	−	26.3567i	0.466687	−	1.74170i	0.651236	−	0.758875i	$-0.274251\pi$
$230$		0			0
$231$	−0.0225427	−	0.0397607i	−0.00148320	−	0.00261606i
$232$		0			0
$233$	7.42838			0.486649			0.243325	−	0.969945i	$-0.421762\pi$
$233$	7.42838			0.486649			0.243325	+	0.969945i	$0.421762\pi$
$234$		0			0
$235$	0.378968	−	0.378968i	0.0247211	−	0.0247211i
$236$		0			0
$237$	−8.44172	+	2.19127i	−0.548349	+	0.142338i
$238$		0			0
$239$	2.67225	+	4.62848i	0.172854	+	0.299391i	0.939416	−	0.342778i	$-0.111368\pi$
$239$	2.67225	+	4.62848i	0.172854	+	0.299391i	−0.766563	+	0.642169i	$0.778035\pi$
$240$		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
$243$	11.4456	−	10.5829i	0.734236	−	0.678894i
$244$		0			0
$245$	−5.08211	−	18.9667i	−0.324684	−	1.21174i
$246$		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	0.984057	+	0.177854i	$0.0569155\pi$
$251$	18.4081	+	18.4081i	1.16191	+	1.16191i	0.177854	+	0.984057i	$0.443085\pi$
$252$		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
$259$	0.00892960	−	0.00239268i	0.000554858	−	0.000148674i
$260$		0			0
$261$	−2.47986	−	9.87060i	−0.153499	−	0.610975i
$262$		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
$267$	22.4363	−	22.0877i	1.37308	−	1.35174i
$268$		0			0
$269$	13.7834	+	13.7834i	0.840386	+	0.840386i	0.988909	−	0.148523i	$-0.0474518\pi$
$269$	13.7834	+	13.7834i	0.840386	+	0.840386i	−0.148523	+	0.988909i	$0.547452\pi$
$270$		0			0
$271$		−	14.3202i		−	0.869889i	−0.900457	−	0.434945i	$-0.856768\pi$
$271$		−	14.3202i		−	0.869889i	0.900457	−	0.434945i	$-0.143232\pi$
$272$		0			0
$273$	−0.000765759		0.0978152i	−4.63459e−5		0.00592004i
$274$		0			0
$275$	−8.61014	−	2.30708i	−0.519211	−	0.139122i
$276$		0			0
$277$	−6.39501	+	1.71354i	−0.384239	+	0.102956i	−0.445767	−	0.895149i	$-0.647069\pi$
$277$	−6.39501	+	1.71354i	−0.384239	+	0.102956i	0.0615286	+	0.998105i	$0.480402\pi$
$278$		0			0
$279$	−11.2922	−	20.2856i	−0.676046	−	1.21447i
$280$		0			0
$281$	−1.84037	+	3.18761i	−0.109787	+	0.190157i	−0.915684	−	0.401899i	$-0.868350\pi$
$281$	−1.84037	+	3.18761i	−0.109787	+	0.190157i	0.805897	+	0.592056i	$0.201684\pi$
$282$		0			0
$283$	−4.19445	−	1.12390i	−0.249334	−	0.0668089i	0.131987	−	0.991251i	$-0.457864\pi$
$283$	−4.19445	−	1.12390i	−0.249334	−	0.0668089i	−0.381321	+	0.924442i	$0.624531\pi$
$284$		0			0
$285$	−8.99929	−	2.48702i	−0.533072	−	0.147318i
$286$		0			0
$287$	0.0449706			0.00265453
$288$		0			0
$289$	5.58832			0.328725
$290$		0			0
$291$	1.43170	+	5.51555i	0.0839280	+	0.323327i
$292$		0			0
$293$	14.6770	+	3.93269i	0.857439	+	0.229750i	0.660649	−	0.750695i	$-0.270281\pi$
$293$	14.6770	+	3.93269i	0.857439	+	0.229750i	0.196791	+	0.980446i	$0.436948\pi$
$294$		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
$299$	39.9558	−	10.7061i	2.31071	−	0.619152i
$300$		0			0
$301$	−0.0509393	−	0.0136491i	−0.00293609	−	0.000786723i
$302$		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	−0.898776	−	0.438408i	$-0.855543\pi$
$307$	−23.4294	−	23.4294i	−1.33718	−	1.33718i	−0.438408	−	0.898776i	$-0.644457\pi$
$308$		0			0
$309$	18.4477	+	5.09817i	1.04945	+	0.290025i
$310$		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	0.0835293	−	0.996505i	$-0.473381\pi$
$313$	−13.0513	−	7.53519i	−0.737705	−	0.425914i	−0.821234	+	0.570591i	$0.806714\pi$
$314$		0			0
$315$	0.0497401	+	0.0513226i	0.00280254	+	0.00289170i
$316$		0			0
$317$	20.1652	−	5.40325i	1.13259	−	0.303477i	0.356623	−	0.934248i	$-0.383928\pi$
$317$	20.1652	−	5.40325i	1.13259	−	0.303477i	0.775969	+	0.630772i	$0.217261\pi$
$318$		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
$331$	−4.94242	−	18.4453i	−0.271660	−	1.01385i	−0.958047	−	0.286612i	$-0.907471\pi$
$331$	−4.94242	−	18.4453i	−0.271660	−	1.01385i	0.686387	−	0.727236i	$-0.259196\pi$
$332$		0			0
$333$	2.34496	−	2.27266i	0.128503	−	0.124541i
$334$		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
$339$	−6.27915	+	22.7211i	−0.341036	+	1.23404i
$340$		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
$347$	−5.60618	+	20.9225i	−0.300955	+	1.12318i	0.635416	+	0.772170i	$0.280829\pi$
$347$	−5.60618	+	20.9225i	−0.300955	+	1.12318i	−0.936372	+	0.351011i	$0.885838\pi$
$348$		0			0
$349$	−0.426410	−	1.59139i	−0.0228252	−	0.0851849i	0.953574	−	0.301160i	$-0.0973737\pi$
$349$	−0.426410	−	1.59139i	−0.0228252	−	0.0851849i	−0.976399	+	0.215975i	$0.930707\pi$
$350$		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
$355$	0.742431	−	2.77079i	0.0394042	−	0.147058i
$356$		0			0
$357$	0.0480983	−	0.0124852i	0.00254563	−	0.000660784i
$358$		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
$363$	0.620789	−	2.24633i	0.0325830	−	0.117902i
$364$		0			0
$365$	−5.30659	+	19.8045i	−0.277760	+	1.03661i
$366$		0			0
$367$	4.77772	+	2.75842i	0.249395	+	0.143988i	0.619487	−	0.785007i	$-0.287341\pi$
$367$	4.77772	+	2.75842i	0.249395	+	0.143988i	−0.370092	+	0.928995i	$0.620674\pi$
$368$		0			0
$369$	13.8798	−	7.72631i	0.722552	−	0.402215i
$370$		0			0
$371$	−0.00233318	−	0.00870755i	−0.000121133	−	0.000452074i
$372$		0			0
$373$	2.18851	−	8.16763i	0.113317	−	0.422904i	−0.885839	−	0.463993i	$-0.846416\pi$
$373$	2.18851	−	8.16763i	0.113317	−	0.422904i	0.999155	+	0.0410893i	$0.0130828\pi$
$374$		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	−0.0535254	+	0.998566i	$0.517046\pi$
$379$	−20.4820	+	20.4820i	−1.05209	+	1.05209i	−0.998566	+	0.0535254i	$0.982954\pi$
$380$		0			0
$381$	−8.52023	−	8.65468i	−0.436504	−	0.443393i
$382$		0			0
$383$	−2.14427	−	3.71398i	−0.109567	−	0.189776i	0.806028	−	0.591878i	$-0.201613\pi$
$383$	−2.14427	−	3.71398i	−0.109567	−	0.189776i	−0.915595	+	0.402102i	$0.868280\pi$
$384$		0			0
$385$	0.0370120	−	0.0641066i	0.00188630	−	0.00326718i
$386$		0			0
$387$	−18.0670	+	4.53909i	−0.918397	+	0.230735i
$388$		0			0
$389$	−4.19823	−	15.6680i	−0.212859	−	0.794400i	−0.986909	−	0.161276i	$-0.948439\pi$
$389$	−4.19823	−	15.6680i	−0.212859	−	0.794400i	0.774051	−	0.633124i	$-0.218228\pi$
$390$		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	−0.760789	−	0.649000i	$-0.775188\pi$
$397$	−2.22738	+	2.22738i	−0.111789	+	0.111789i	0.649000	+	0.760789i	$0.275188\pi$
$398$		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
$403$	49.7085	−	13.3193i	2.47616	−	0.663484i
$404$		0			0
$405$	24.1695	+	7.29451i	1.20099	+	0.362467i
$406$		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	$0.701988\pi$
$409$	−32.0886	+	18.5263i	−1.58668	+	0.916068i	−0.993850	+	0.110739i	$0.964678\pi$
$410$		0			0
$411$	−2.36607	−	9.11514i	−0.116710	−	0.449617i
$412$		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
$419$	19.9702	+	5.35101i	0.975609	+	0.261414i	0.711195	−	0.702995i	$-0.248155\pi$
$419$	19.9702	+	5.35101i	0.975609	+	0.261414i	0.264415	+	0.964409i	$0.414821\pi$
$420$		0			0
$421$	−9.35966	+	2.50791i	−0.456162	+	0.122228i	−0.479581	−	0.877497i	$-0.659211\pi$
$421$	−9.35966	+	2.50791i	−0.456162	+	0.122228i	0.0234192	+	0.999726i	$0.492545\pi$
$422$		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
$427$	−0.0837222	−	0.0224333i	−0.00405160	−	0.00108562i
$428$		0			0
$429$	25.5028	−	25.1066i	1.23129	−	1.21216i
$430$		0			0
$431$	25.3669			1.22188			0.610941	−	0.791676i	$-0.290791\pi$
$431$	25.3669			1.22188			0.610941	+	0.791676i	$0.290791\pi$
$432$		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
$435$	11.7459	−	11.5634i	0.563174	−	0.554424i
$436$		0			0
$437$	−11.5465	−	3.09387i	−0.552343	−	0.148000i
$438$		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
$443$	5.42439	−	1.45346i	0.257721	−	0.0690560i	−0.127645	−	0.991820i	$-0.540742\pi$
$443$	5.42439	−	1.45346i	0.257721	−	0.0690560i	0.385366	+	0.922764i	$0.374075\pi$
$444$		0			0
$445$	49.2527	+	13.1972i	2.33480	+	0.625608i
$446$		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
$453$	1.97348	+	7.60269i	0.0927220	+	0.357206i
$454$		0			0
$455$	−0.137197	+	0.0792106i	−0.00643189	+	0.00371345i
$456$		0			0
$457$	18.4633	+	10.6598i	0.863675	+	0.498643i	0.865241	−	0.501356i	$-0.167165\pi$
$457$	18.4633	+	10.6598i	0.863675	+	0.498643i	−0.00156649	+	0.999999i	$0.500499\pi$
$458$		0			0
$459$	12.7000	−	12.1171i	0.592787	−	0.565578i
$460$		0			0
$461$	−37.4962	+	10.0471i	−1.74637	+	0.467938i	−0.983845	−	0.179021i	$-0.942707\pi$
$461$	−37.4962	+	10.0471i	−1.74637	+	0.467938i	−0.762525	+	0.646959i	$0.776040\pi$
$462$		0			0
$463$	−7.29597	+	4.21233i	−0.339073	+	0.195764i	−0.659862	−	0.751387i	$-0.729385\pi$
$463$	−7.29597	+	4.21233i	−0.339073	+	0.195764i	0.320789	+	0.947151i	$0.396052\pi$
$464$		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	$-0.969639\pi$
$467$	−19.4539	+	19.4539i	−0.900219	+	0.900219i	0.0952358	+	0.995455i	$0.469639\pi$
$468$		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
$475$	−1.42683	−	5.32501i	−0.0654676	−	0.244328i
$476$		0			0
$477$	−2.21614	−	2.28665i	−0.101470	−	0.104698i
$478$		0			0
$479$	−10.4276	+	18.0611i	−0.476450	+	0.825235i	−0.999636	−	0.0269835i	$-0.991410\pi$
$479$	−10.4276	+	18.0611i	−0.476450	+	0.825235i	0.523186	+	0.852218i	$0.324743\pi$
$480$		0			0
$481$	3.61918	+	6.26860i	0.165020	+	0.285824i
$482$		0			0
$483$	0.0641953	+	0.0652084i	0.00292099	+	0.00296708i
$484$		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
$491$	−0.378725	+	1.41342i	−0.0170916	+	0.0637868i	−0.973945	−	0.226785i	$-0.927179\pi$
$491$	−0.378725	+	1.41342i	−0.0170916	+	0.0637868i	0.956853	+	0.290571i	$0.0938453\pi$
$492$		0			0
$493$	−2.96609	−	11.0696i	−0.133586	−	0.498550i
$494$		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
$499$	−9.43390	+	35.2078i	−0.422319	+	1.57612i	0.347389	+	0.937721i	$0.387068\pi$
$499$	−9.43390	+	35.2078i	−0.422319	+	1.57612i	−0.769708	+	0.638396i	$0.779598\pi$
$500$		0			0
$501$	5.48583	−	19.8505i	0.245089	−	0.886854i
$502$		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
$507$	−52.3387	+	13.5859i	−2.32444	+	0.603370i
$508$		0			0
$509$	1.05732	−	3.94598i	0.0468650	−	0.174903i	−0.938526	−	0.345207i	$-0.887809\pi$
$509$	1.05732	−	3.94598i	0.0468650	−	0.174903i	0.985391	+	0.170305i	$0.0544752\pi$
$510$		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
$515$	8.02259	+	29.9407i	0.353517	+	1.31934i
$516$		0			0
$517$	0.153647	−	0.573417i	0.00675737	−	0.0252189i
$518$		0			0
$519$	0.425694	−	0.724171i	0.0186859	−	0.0317876i
$520$		0			0
$521$	−13.4286			−0.588318			−0.294159	−	0.955757i	$-0.595039\pi$
$521$	−13.4286			−0.588318			−0.294159	+	0.955757i	$0.595039\pi$
$522$		0			0
$523$	−23.5806	+	23.5806i	−1.03111	+	1.03111i	−0.0316083	+	0.999500i	$0.510063\pi$
$523$	−23.5806	+	23.5806i	−1.03111	+	1.03111i	−0.999500	+	0.0316083i	$0.989937\pi$
$524$		0			0
$525$	−0.0112410	+	0.0406757i	−0.000490599	+	0.00177523i
$526$		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
$531$	−27.1465	−	7.73140i	−1.17806	−	0.335514i
$532$		0			0
$533$	9.11332	+	34.0114i	0.394742	+	1.47320i
$534$		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	−0.519148	+	0.854684i	$0.673751\pi$
$541$	−31.9545	+	31.9545i	−1.37383	+	1.37383i	−0.854684	+	0.519148i	$0.826249\pi$
$542$		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
$547$	10.3053	−	2.76131i	0.440625	−	0.118065i	−0.0316846	−	0.999498i	$-0.510087\pi$
$547$	10.3053	−	2.76131i	0.440625	−	0.118065i	0.472309	+	0.881433i	$0.343421\pi$
$548$		0			0
$549$	−29.6943	+	7.46031i	−1.26732	+	0.318398i
$550$		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
$555$	5.09763	+	1.40877i	0.216382	+	0.0597989i
$556$		0			0
$557$	−11.6850	−	11.6850i	−0.495109	−	0.495109i	0.414802	−	0.909912i	$-0.363851\pi$
$557$	−11.6850	−	11.6850i	−0.495109	−	0.495109i	−0.909912	+	0.414802i	$0.863851\pi$
$558$		0			0
$559$		−	41.2915i		−	1.74645i
$560$		0			0
$561$	−15.6729	−	9.21309i	−0.661711	−	0.388977i
$562$		0			0
$563$	−8.64631	−	2.31677i	−0.364398	−	0.0976403i	0.0719737	−	0.997407i	$-0.477070\pi$
$563$	−8.64631	−	2.31677i	−0.364398	−	0.0976403i	−0.436372	+	0.899766i	$0.643737\pi$
$564$		0			0
$565$	−36.8764	+	9.88100i	−1.55140	+	0.415697i
$566$		0			0
$567$	−0.0402716	+	0.0649662i	−0.00169125	+	0.00272832i
$568$		0			0
$569$	−6.28570	+	10.8872i	−0.263510	+	0.456413i	−0.967172	−	0.254122i	$-0.918214\pi$
$569$	−6.28570	+	10.8872i	−0.263510	+	0.456413i	0.703662	+	0.710535i	$0.251547\pi$
$570$		0			0
$571$	−13.9023	−	3.72510i	−0.581791	−	0.155890i	−0.0440924	−	0.999027i	$-0.514040\pi$
$571$	−13.9023	−	3.72510i	−0.581791	−	0.155890i	−0.537699	+	0.843137i	$0.680706\pi$
$572$		0			0
$573$	−5.51059	−	21.2292i	−0.230208	−	0.886863i
$574$		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
$579$	−16.6780	−	4.60908i	−0.693113	−	0.191547i
$580$		0			0
$581$	−0.106186	−	0.0284525i	−0.00440534	−	0.00118041i
$582$		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
$587$	−17.2954	+	4.63428i	−0.713856	+	0.191277i	−0.597428	−	0.801922i	$-0.703811\pi$
$587$	−17.2954	+	4.63428i	−0.713856	+	0.191277i	−0.116427	+	0.993199i	$0.537144\pi$
$588$		0			0
$589$	−14.3648	−	3.84904i	−0.591891	−	0.158597i
$590$		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
$597$	−22.2844	+	21.9382i	−0.912041	+	0.897872i
$598$		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	0.333133	−	0.942880i	$-0.391894\pi$
$601$	−7.76786	−	4.48478i	−0.316858	−	0.182938i	−0.649991	+	0.759942i	$0.725227\pi$
$602$		0			0
$603$	23.2140	+	6.61139i	0.945345	+	0.269237i
$604$		0			0
$605$	3.64579	−	0.976888i	0.148223	−	0.0397161i
$606$		0			0
$607$	20.1239	−	11.6185i	0.816802	−	0.471581i	−0.0325103	−	0.999471i	$-0.510350\pi$
$607$	20.1239	−	11.6185i	0.816802	−	0.471581i	0.849312	+	0.527890i	$0.177017\pi$
$608$		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	0.974831	−	0.222945i	$-0.0715670\pi$
$613$	18.6158	+	18.6158i	0.751886	+	0.751886i	−0.222945	+	0.974831i	$0.571567\pi$
$614$		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	$-0.902917\pi$
$617$	−18.3062	−	31.7073i	−0.736981	−	1.27649i	0.216868	−	0.976201i	$-0.430416\pi$
$618$		0			0
$619$	−6.87138	−	25.6443i	−0.276184	−	1.03073i	−0.955044	−	0.296465i	$-0.904192\pi$
$619$	−6.87138	−	25.6443i	−0.276184	−	1.03073i	0.678860	−	0.734268i	$-0.262474\pi$
$620$		0			0
$621$	31.0166	+	9.09671i	1.24465	+	0.365039i
$622$		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
$627$	−10.0101	+	2.59839i	−0.399766	+	0.103770i
$628$		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
$635$	5.09076	−	18.9990i	0.202021	−	0.753952i
$636$		0			0
$637$	12.0475	+	44.9617i	0.477338	+	1.78145i
$638$		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
$643$	1.52303	−	5.68404i	0.0600626	−	0.224157i	−0.929370	−	0.369149i	$-0.879649\pi$
$643$	1.52303	−	5.68404i	0.0600626	−	0.224157i	0.989433	+	0.144993i	$0.0463158\pi$
$644$		0			0
$645$	−21.1655	−	21.4995i	−0.833392	−	0.846544i
$646$		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
$651$	0.0798645	+	0.0811248i	0.00313014	+	0.00317953i
$652$		0			0
$653$	−5.70340	+	21.2854i	−0.223191	+	0.832962i	0.759930	+	0.650005i	$0.225233\pi$
$653$	−5.70340	+	21.2854i	−0.223191	+	0.832962i	−0.983121	+	0.182956i	$0.941433\pi$
$654$		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
$659$	6.39350	+	23.8609i	0.249055	+	0.929487i	0.971302	+	0.237851i	$0.0764430\pi$
$659$	6.39350	+	23.8609i	0.249055	+	0.929487i	−0.722246	+	0.691636i	$0.756890\pi$
$660$		0			0
$661$	−0.958674	+	3.57782i	−0.0372881	+	0.139161i	−0.982060	−	0.188566i	$-0.939616\pi$
$661$	−0.958674	+	3.57782i	−0.0372881	+	0.139161i	0.944772	+	0.327727i	$0.106283\pi$
$662$		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
$669$	−0.0550936	+	0.0143010i	−0.00213004	+	0.000552908i
$670$		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
$675$	3.51896	+	14.4855i	0.135445	+	0.557546i
$676$		0			0
$677$	−6.56283	−	24.4928i	−0.252230	−	0.941335i	−0.969611	−	0.244654i	$-0.921326\pi$
$677$	−6.56283	−	24.4928i	−0.252230	−	0.941335i	0.717381	−	0.696681i	$-0.245341\pi$
$678$		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	$-0.266278\pi$
$683$	−1.88928	−	1.88928i	−0.0722912	−	0.0722912i	−0.742328	+	0.670037i	$0.766278\pi$
$684$		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
$691$	−19.4017	+	5.19868i	−0.738077	+	0.197767i	−0.608223	−	0.793766i	$-0.708117\pi$
$691$	−19.4017	+	5.19868i	−0.738077	+	0.197767i	−0.129854	+	0.991533i	$0.541451\pi$
$692$		0			0
$693$	0.0761384	+	0.0216844i	0.00289226	+	0.000823722i
$694$		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
$699$	−9.16881	+	9.02637i	−0.346796	+	0.341409i
$700$		0			0
$701$	10.9010	+	10.9010i	0.411725	+	0.411725i	0.882339	−	0.470614i	$-0.155968\pi$
$701$	10.9010	+	10.9010i	0.411725	+	0.411725i	−0.470614	+	0.882339i	$0.655968\pi$
$702$		0			0
$703$		−	2.09175i		−	0.0788918i
$704$		0			0
$705$	−0.00726692	+	0.928249i	−0.000273688	+	0.0349599i
$706$		0			0
$707$	0.0226568	+	0.00607088i	0.000852098	+	0.000228319i
$708$		0			0
$709$	15.4807	−	4.14803i	0.581389	−	0.155783i	0.0438741	−	0.999037i	$-0.486030\pi$
$709$	15.4807	−	4.14803i	0.581389	−	0.155783i	0.537515	+	0.843254i	$0.319363\pi$
$710$		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
$715$	55.9845	+	15.0010i	2.09370	+	0.561006i
$716$		0			0
$717$	−8.92251	−	2.46580i	−0.333217	−	0.0920871i
$718$		0			0
$719$	21.7763			0.812119			0.406060	−	0.913847i	$-0.366903\pi$
$719$	21.7763			0.812119			0.406060	+	0.913847i	$0.366903\pi$
$720$		0			0
$721$	−0.0938463			−0.00349502
$722$		0			0
$723$	−9.51416	−	36.6527i	−0.353835	−	1.36313i
$724$		0			0
$725$	9.40068	+	2.51890i	0.349132	+	0.0935497i
$726$		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
$731$	−20.2616	+	5.42908i	−0.749403	+	0.200802i
$732$		0			0
$733$	12.7415	+	3.41408i	0.470618	+	0.126102i	0.486331	−	0.873775i	$-0.338335\pi$
$733$	12.7415	+	3.41408i	0.470618	+	0.126102i	−0.0157124	+	0.999877i	$0.505002\pi$
$734$		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	0.990742	−	0.135758i	$-0.0433470\pi$
$739$	23.2424	+	23.2424i	0.854984	+	0.854984i	−0.135758	+	0.990742i	$0.543347\pi$
$740$		0			0
$741$	21.3334	+	5.89563i	0.783701	+	0.216582i
$742$		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
$747$	−37.6617	+	9.46202i	−1.37797	+	0.346197i
$748$		0			0
$749$	−0.0224560	+	0.00601707i	−0.000820525	+	0.000219859i
$750$		0			0
$751$	−22.5527	+	13.0208i	−0.822960	+	0.475136i	−0.851436	−	0.524458i	$-0.824268\pi$
$751$	−22.5527	+	13.0208i	−0.822960	+	0.475136i	0.0284763	+	0.999594i	$0.490934\pi$
$752$		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	0.790122	−	0.612950i	$-0.210017\pi$
$757$	4.87465	+	4.87465i	0.177172	+	0.177172i	−0.612950	+	0.790122i	$0.710017\pi$
$758$		0			0
$759$	0.262077	−	33.4767i	0.00951279	−	1.21513i
$760$		0			0
$761$	−3.18964	−	5.52462i	−0.115624	−	0.200267i	0.802405	−	0.596780i	$-0.203554\pi$
$761$	−3.18964	−	5.52462i	−0.115624	−	0.200267i	−0.918029	+	0.396513i	$0.870220\pi$
$762$		0			0
$763$	−0.0186016	−	0.0694221i	−0.000673423	−	0.00251325i
$764$		0			0
$765$	27.3410	+	7.78679i	0.988518	+	0.281532i
$766$		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
$771$	3.71141	−	13.4298i	0.133663	−	0.483661i
$772$		0			0
$773$	26.0627	−	26.0627i	0.937411	−	0.937411i	−0.0607427	−	0.998153i	$-0.519347\pi$
$773$	26.0627	−	26.0627i	0.937411	−	0.937411i	0.998153	+	0.0607427i	$0.0193469\pi$
$774$		0			0
$775$	22.2015			0.797503
$776$		0			0
$777$	−0.00811437	+	0.0138038i	−0.000291101	+	0.000495209i
$778$		0			0
$779$	2.63358	−	9.82864i	0.0943577	−	0.352148i
$780$		0			0
$781$	−0.822367	−	3.06912i	−0.0294266	−	0.109822i
$782$		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
$787$	2.96285	−	11.0575i	0.105614	−	0.394158i	−0.892800	−	0.450454i	$-0.851262\pi$
$787$	2.96285	−	11.0575i	0.105614	−	0.394158i	0.998414	+	0.0562956i	$0.0179289\pi$
$788$		0			0
$789$	−7.07653	+	1.83690i	−0.251931	+	0.0653953i
$790$		0			0
$791$		−	0.115586i		−	0.00410975i
$792$		0			0
$793$		−	67.8655i		−	2.40997i
$794$		0			0
$795$	1.37374	−	4.97087i	0.0487215	−	0.176299i
$796$		0			0
$797$	−1.12000	+	4.17990i	−0.0396725	+	0.148060i	−0.982921	−	0.184028i	$-0.941086\pi$
$797$	−1.12000	+	4.17990i	−0.0396725	+	0.148060i	0.943249	+	0.332088i	$0.107753\pi$
$798$		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
$803$	5.87794	+	21.9368i	0.207428	+	0.774132i
$804$		0			0
$805$	−0.0383562	+	0.143147i	−0.00135188	+	0.00504528i
$806$		0			0
$807$	−33.7612	−	0.264304i	−1.18845	−	0.00930394i
$808$		0			0
$809$	22.7884			0.801198			0.400599	−	0.916253i	$-0.368802\pi$
$809$	22.7884			0.801198			0.400599	+	0.916253i	$0.368802\pi$
$810$		0			0
$811$	14.9053	−	14.9053i	0.523396	−	0.523396i	−0.395200	−	0.918595i	$-0.629325\pi$
$811$	14.9053	−	14.9053i	0.523396	−	0.523396i	0.918595	+	0.395200i	$0.129325\pi$
$812$		0			0
$813$	17.4007	+	17.6753i	0.610270	+	0.619901i
$814$		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
$819$	−0.117912	−	0.121663i	−0.00412018	−	0.00425126i
$820$		0			0
$821$	11.7591	+	43.8854i	0.410394	+	1.53161i	0.793886	+	0.608067i	$0.208055\pi$
$821$	11.7591	+	43.8854i	0.410394	+	1.53161i	−0.383492	+	0.923544i	$0.625279\pi$
$822$		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	$-0.0678222\pi$
$827$	22.0262	+	22.0262i	0.765925	+	0.765925i	−0.211461	+	0.977386i	$0.567822\pi$
$828$		0			0
$829$	28.3392	−	28.3392i	0.984261	−	0.984261i	−0.0156173	−	0.999878i	$-0.504971\pi$
$829$	28.3392	−	28.3392i	0.984261	−	0.984261i	0.999878	+	0.0156173i	$0.00497134\pi$
$830$		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
$835$	32.2174	−	8.63262i	1.11493	−	0.298744i
$836$		0			0
$837$	38.5874	+	11.3171i	1.33377	+	0.391176i
$838$		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
$843$	−1.60177	−	6.17072i	−0.0551679	−	0.212531i
$844$		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
$851$	6.54048	+	1.75252i	0.224205	+	0.0600755i
$852$		0			0
$853$	−23.7728	+	6.36992i	−0.813967	+	0.218102i	−0.641707	−	0.766950i	$-0.721773\pi$
$853$	−23.7728	+	6.36992i	−0.813967	+	0.218102i	−0.172260	+	0.985052i	$0.555107\pi$
$854$		0			0
$855$	14.1298	−	7.86550i	0.483229	−	0.268994i
$856$		0			0
$857$	−0.838395	+	1.45214i	−0.0286390	+	0.0496043i	−0.879990	−	0.474993i	$-0.842451\pi$
$857$	−0.838395	+	1.45214i	−0.0286390	+	0.0496043i	0.851351	+	0.524597i	$0.175784\pi$
$858$		0			0
$859$	13.4806	+	3.61213i	0.459954	+	0.123244i	0.481353	−	0.876527i	$-0.340145\pi$
$859$	13.4806	+	3.61213i	0.459954	+	0.123244i	−0.0213994	+	0.999771i	$0.506812\pi$
$860$		0			0
$861$	−0.0555070	+	0.0546446i	−0.00189167	+	0.00186228i
$862$		0			0
$863$	−31.6409			−1.07707			−0.538535	−	0.842603i	$-0.681022\pi$
$863$	−31.6409			−1.07707			−0.538535	+	0.842603i	$0.681022\pi$
$864$		0			0
$865$	1.36046			0.0462570
$866$		0			0
$867$	−6.89764	+	6.79048i	−0.234256	+	0.230617i
$868$		0			0
$869$	−15.1126	−	4.04940i	−0.512658	−	0.137366i
$870$		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
$875$	0.0490426	−	0.0131409i	0.00165794	−	0.000444244i
$876$		0			0
$877$	29.4369	+	7.88760i	0.994014	+	0.266345i	0.718936	−	0.695077i	$-0.244630\pi$
$877$	29.4369	+	7.88760i	0.994014	+	0.266345i	0.275078	+	0.961422i	$0.411296\pi$
$878$		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	0.559907	−	0.828556i	$-0.310837\pi$
$883$	−7.98299	−	7.98299i	−0.268649	−	0.268649i	−0.828556	+	0.559907i	$0.810837\pi$
$884$		0			0
$885$	−11.4855	−	44.2471i	−0.386080	−	1.48735i
$886$		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
$891$	27.2250	−	6.38849i	0.912071	−	0.214022i
$892$		0			0
$893$	0.354635	−	0.0950241i	0.0118674	−	0.00317986i
$894$		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
$907$	2.05717	+	7.67746i	0.0683072	+	0.254926i	0.991633	−	0.129093i	$-0.0412065\pi$
$907$	2.05717	+	7.67746i	0.0683072	+	0.254926i	−0.923325	+	0.384019i	$0.874540\pi$
$908$		0			0
$909$	8.03585	−	2.01890i	0.266532	−	0.0669628i
$910$		0			0
$911$	−17.5142	+	30.3354i	−0.580270	+	1.00506i	0.415176	+	0.909741i	$0.363720\pi$
$911$	−17.5142	+	30.3354i	−0.580270	+	1.00506i	−0.995447	+	0.0953171i	$0.969614\pi$
$912$		0			0
$913$	20.1096	+	34.8309i	0.665532	+	1.15274i
$914$		0			0
$915$	−34.7870	−	35.3360i	−1.15002	−	1.16817i
$916$		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
$923$	−1.75998	+	6.56833i	−0.0579304	+	0.216199i
$924$		0			0
$925$	0.808226	+	3.01634i	0.0265743	+	0.0991767i
$926$		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
$931$	3.48148	−	12.9931i	0.114101	−	0.425831i
$932$		0			0
$933$	−13.8027	+	49.9451i	−0.451880	+	1.63513i
$934$		0			0
$935$		−	29.4438i		−	0.962914i
$936$		0			0
$937$			5.72005i			0.186866i	0.995626	+	0.0934330i	$0.0297841\pi$
$937$			5.72005i			0.186866i	−0.995626	+	0.0934330i	$0.970216\pi$
$938$		0			0
$939$	25.2654	−	6.55828i	0.824504	−	0.214021i
$940$		0			0
$941$	6.14201	−	22.9223i	0.200224	−	0.747245i	−0.790629	−	0.612296i	$-0.790246\pi$
$941$	6.14201	−	22.9223i	0.200224	−	0.747245i	0.990853	−	0.134949i	$-0.0430871\pi$
$942$		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
$947$	−14.0030	−	52.2601i	−0.455038	−	1.69822i	−0.687977	−	0.725732i	$-0.741501\pi$
$947$	−14.0030	−	52.2601i	−0.455038	−	1.69822i	0.232940	−	0.972491i	$-0.425166\pi$
$948$		0			0
$949$	12.5796	−	46.9477i	0.408351	−	1.52399i
$950$		0			0
$951$	−18.3242	+	31.1724i	−0.594204	+	1.01083i
$952$		0			0
$953$	2.80246			0.0907805			0.0453902	−	0.998969i	$-0.485547\pi$
$953$	2.80246			0.0907805			0.0453902	+	0.998969i	$0.485547\pi$
$954$		0			0
$955$	25.1173	−	25.1173i	0.812775	−	0.812775i
$956$		0			0
$957$	4.86326	−	17.5977i	0.157207	−	0.568854i
$958$		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
$963$	−5.89707	+	5.71524i	−0.190030	+	0.184171i
$964$		0			0
$965$	−7.25296	−	27.0684i	−0.233481	−	0.871363i
$966$		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	$-0.423040\pi$
$971$	−22.7938	−	22.7938i	−0.731487	−	0.731487i	−0.970914	+	0.239428i	$0.923040\pi$
$972$		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
$979$	54.5556	−	14.6181i	1.74360	−	0.467197i
$980$		0			0
$981$	−17.6685	−	18.2306i	−0.564112	−	0.582059i
$982$		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
$987$	−0.00270891		0.000748629i	−8.62257e−5		2.38291e-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	$-0.619766\pi$
$991$		−	58.5560i		−	1.86009i	0.367440	−	0.930047i	$-0.380234\pi$
$992$		0			0
$993$	28.5137	+	16.7614i	0.904855	+	0.531906i
$994$		0			0
$995$	−48.9194	−	13.1079i	−1.55085	−	0.415549i
$996$		0			0
$997$	43.9362	−	11.7727i	1.39147	−	0.372844i	0.516199	−	0.856469i	$-0.327347\pi$
$997$	43.9362	−	11.7727i	1.39147	−	0.372844i	0.875276	+	0.483624i	$0.160680\pi$
$998$		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.335.5		88
3.2	odd	2		1728.2.z.a.143.18		88
4.3	odd	2		144.2.u.a.11.14	✓	88
9.4	even	3		1728.2.z.a.719.18		88
9.5	odd	6	inner	576.2.y.a.527.16		88
12.11	even	2		432.2.v.a.251.9		88
16.3	odd	4	inner	576.2.y.a.47.16		88
16.13	even	4		144.2.u.a.83.6	yes	88
36.23	even	6		144.2.u.a.59.6	yes	88
36.31	odd	6		432.2.v.a.395.17		88
48.29	odd	4		432.2.v.a.35.17		88
48.35	even	4		1728.2.z.a.1007.18		88
144.13	even	12		432.2.v.a.179.9		88
144.67	odd	12		1728.2.z.a.1583.18		88
144.77	odd	12		144.2.u.a.131.14	yes	88
144.131	even	12	inner	576.2.y.a.239.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.14	✓	88	4.3	odd	2
144.2.u.a.59.6	yes	88	36.23	even	6
144.2.u.a.83.6	yes	88	16.13	even	4
144.2.u.a.131.14	yes	88	144.77	odd	12
432.2.v.a.35.17		88	48.29	odd	4
432.2.v.a.179.9		88	144.13	even	12
432.2.v.a.251.9		88	12.11	even	2
432.2.v.a.395.17		88	36.31	odd	6
576.2.y.a.47.16		88	16.3	odd	4	inner
576.2.y.a.239.5		88	144.131	even	12	inner
576.2.y.a.335.5		88	1.1	even	1	trivial
576.2.y.a.527.16		88	9.5	odd	6	inner
1728.2.z.a.143.18		88	3.2	odd	2
1728.2.z.a.719.18		88	9.4	even	3
1728.2.z.a.1007.18		88	48.35	even	4
1728.2.z.a.1583.18		88	144.67	odd	12

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)

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