LMFDB - Embedded newform 512.2.i.b.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	512.97
Dual form			512.2.i.b.417.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.344545 - 1.73215i) q^{3} +(2.21982 - 1.48324i) q^{5} +(2.90595 + 1.20368i) q^{7} +(-0.109979 + 0.0455548i) q^{9} +O(q^{10})$	\(q+(-0.344545 - 1.73215i) q^{3} +(2.21982 - 1.48324i) q^{5} +(2.90595 + 1.20368i) q^{7} +(-0.109979 + 0.0455548i) q^{9} +(-1.75553 - 0.349197i) q^{11} +(5.20730 + 3.47941i) q^{13} +(-3.33401 - 3.33401i) q^{15} +(0.895276 - 0.895276i) q^{17} +(-2.36339 + 3.53706i) q^{19} +(1.08373 - 5.44826i) q^{21} +(-0.709741 - 1.71347i) q^{23} +(0.814201 - 1.96565i) q^{25} +(-2.82675 - 4.23052i) q^{27} +(-7.36008 + 1.46401i) q^{29} -1.14161i q^{31} +3.16115i q^{33} +(8.23605 - 1.63825i) q^{35} +(1.36011 + 2.03555i) q^{37} +(4.23269 - 10.2186i) q^{39} +(-3.08221 - 7.44112i) q^{41} +(1.56753 - 7.88051i) q^{43} +(-0.176565 + 0.264249i) q^{45} +(-6.65222 + 6.65222i) q^{47} +(2.04595 + 2.04595i) q^{49} +(-1.85921 - 1.24228i) q^{51} +(0.674026 + 0.134072i) q^{53} +(-4.41491 + 1.82872i) q^{55} +(6.94100 + 2.87506i) q^{57} +(2.59120 - 1.73138i) q^{59} +(-0.360949 - 1.81461i) q^{61} -0.374427 q^{63} +16.7201 q^{65} +(2.13440 + 10.7304i) q^{67} +(-2.72344 + 1.81974i) q^{69} +(1.97842 + 0.819489i) q^{71} +(-13.1646 + 5.45295i) q^{73} +(-3.68533 - 0.733058i) q^{75} +(-4.68117 - 3.12785i) q^{77} +(0.102033 + 0.102033i) q^{79} +(-6.60646 + 6.60646i) q^{81} +(-5.13230 + 7.68102i) q^{83} +(0.659446 - 3.31526i) q^{85} +(5.07176 + 12.2443i) q^{87} +(-4.64776 + 11.2207i) q^{89} +(10.9441 + 16.3790i) q^{91} +(-1.97743 + 0.393336i) q^{93} +11.3571i q^{95} -12.8041i q^{97} +(0.208979 - 0.0415685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.344545	−	1.73215i	−0.198923	−	1.00005i	−0.943211	−	0.332195i	$-0.892211\pi$
$3$	−0.344545	−	1.73215i	−0.198923	−	1.00005i	0.744287	−	0.667860i	$-0.232789\pi$
$4$		0			0
$5$	2.21982	−	1.48324i	0.992735	−	0.663324i	0.0506563	−	0.998716i	$-0.483869\pi$
$5$	2.21982	−	1.48324i	0.992735	−	0.663324i	0.942079	+	0.335392i	$0.108869\pi$
$6$		0			0
$7$	2.90595	+	1.20368i	1.09835	+	0.454950i	0.856910	−	0.515466i	$-0.172381\pi$
$7$	2.90595	+	1.20368i	1.09835	+	0.454950i	0.241437	+	0.970417i	$0.422381\pi$
$8$		0			0
$9$	−0.109979	+	0.0455548i	−0.0366597	+	0.0151849i
$10$		0			0
$11$	−1.75553	−	0.349197i	−0.529312	−	0.105287i	−0.0768028	−	0.997046i	$-0.524471\pi$
$11$	−1.75553	−	0.349197i	−0.529312	−	0.105287i	−0.452510	+	0.891760i	$0.649471\pi$
$12$		0			0
$13$	5.20730	+	3.47941i	1.44425	+	0.965015i	0.997523	+	0.0703427i	$0.0224093\pi$
$13$	5.20730	+	3.47941i	1.44425	+	0.965015i	0.446724	+	0.894672i	$0.352591\pi$
$14$		0			0
$15$	−3.33401	−	3.33401i	−0.860839	−	0.860839i
$16$		0			0
$17$	0.895276	−	0.895276i	0.217136	−	0.217136i	−0.590154	−	0.807290i	$-0.700933\pi$
$17$	0.895276	−	0.895276i	0.217136	−	0.217136i	0.807290	+	0.590154i	$0.200933\pi$
$18$		0			0
$19$	−2.36339	+	3.53706i	−0.542199	+	0.811458i	−0.996858	−	0.0792076i	$-0.974761\pi$
$19$	−2.36339	+	3.53706i	−0.542199	+	0.811458i	0.454659	+	0.890665i	$0.349761\pi$
$20$		0			0
$21$	1.08373	−	5.44826i	0.236488	−	1.18891i
$22$		0			0
$23$	−0.709741	−	1.71347i	−0.147991	−	0.357282i	0.832448	−	0.554103i	$-0.186938\pi$
$23$	−0.709741	−	1.71347i	−0.147991	−	0.357282i	−0.980440	+	0.196820i	$0.936938\pi$
$24$		0			0
$25$	0.814201	−	1.96565i	0.162840	−	0.393131i
$26$		0			0
$27$	−2.82675	−	4.23052i	−0.544007	−	0.814165i
$28$		0			0
$29$	−7.36008	+	1.46401i	−1.36673	+	0.271860i	−0.823307	−	0.567597i	$-0.807873\pi$
$29$	−7.36008	+	1.46401i	−1.36673	+	0.271860i	−0.543426	+	0.839457i	$0.682873\pi$
$30$		0			0
$31$		−	1.14161i		−	0.205039i	−0.994731	−	0.102520i	$-0.967310\pi$
$31$		−	1.14161i		−	0.205039i	0.994731	−	0.102520i	$-0.0326904\pi$
$32$		0			0
$33$			3.16115i			0.550285i
$34$		0			0
$35$	8.23605	−	1.63825i	1.39215	−	0.276915i
$36$		0			0
$37$	1.36011	+	2.03555i	0.223600	+	0.334642i	0.926260	−	0.376884i	$-0.123005\pi$
$37$	1.36011	+	2.03555i	0.223600	+	0.334642i	−0.702660	+	0.711526i	$0.748005\pi$
$38$		0			0
$39$	4.23269	−	10.2186i	0.677773	−	1.63629i
$40$		0			0
$41$	−3.08221	−	7.44112i	−0.481361	−	1.16211i	−0.958963	−	0.283532i	$-0.908494\pi$
$41$	−3.08221	−	7.44112i	−0.481361	−	1.16211i	0.477602	−	0.878576i	$-0.341506\pi$
$42$		0			0
$43$	1.56753	−	7.88051i	0.239046	−	1.20177i	−0.655641	−	0.755073i	$-0.727601\pi$
$43$	1.56753	−	7.88051i	0.239046	−	1.20177i	0.894687	−	0.446694i	$-0.147399\pi$
$44$		0			0
$45$	−0.176565	+	0.264249i	−0.0263208	+	0.0393919i
$46$		0			0
$47$	−6.65222	+	6.65222i	−0.970325	+	0.970325i	−0.999572	−	0.0292469i	$-0.990689\pi$
$47$	−6.65222	+	6.65222i	−0.970325	+	0.970325i	0.0292469	+	0.999572i	$0.490689\pi$
$48$		0			0
$49$	2.04595	+	2.04595i	0.292279	+	0.292279i
$50$		0			0
$51$	−1.85921	−	1.24228i	−0.260342	−	0.173955i
$52$		0			0
$53$	0.674026	+	0.134072i	0.0925846	+	0.0184162i	0.241165	−	0.970484i	$-0.422470\pi$
$53$	0.674026	+	0.134072i	0.0925846	+	0.0184162i	−0.148581	+	0.988900i	$0.547470\pi$
$54$		0			0
$55$	−4.41491	+	1.82872i	−0.595306	+	0.246584i
$56$		0			0
$57$	6.94100	+	2.87506i	0.919358	+	0.380811i
$58$		0			0
$59$	2.59120	−	1.73138i	0.337345	−	0.225407i	−0.375346	−	0.926885i	$-0.622476\pi$
$59$	2.59120	−	1.73138i	0.337345	−	0.225407i	0.712691	+	0.701478i	$0.247476\pi$
$60$		0			0
$61$	−0.360949	−	1.81461i	−0.0462147	−	0.232337i	0.950774	−	0.309886i	$-0.100291\pi$
$61$	−0.360949	−	1.81461i	−0.0462147	−	0.232337i	−0.996989	+	0.0775484i	$0.975291\pi$
$62$		0			0
$63$	−0.374427			−0.0471734
$64$		0			0
$65$	16.7201			2.07387
$66$		0			0
$67$	2.13440	+	10.7304i	0.260759	+	1.31092i	0.859976	+	0.510335i	$0.170479\pi$
$67$	2.13440	+	10.7304i	0.260759	+	1.31092i	−0.599217	+	0.800587i	$0.704521\pi$
$68$		0			0
$69$	−2.72344	+	1.81974i	−0.327863	+	0.219071i
$70$		0			0
$71$	1.97842	+	0.819489i	0.234795	+	0.0972554i	0.496979	−	0.867763i	$-0.334443\pi$
$71$	1.97842	+	0.819489i	0.234795	+	0.0972554i	−0.262184	+	0.965018i	$0.584443\pi$
$72$		0			0
$73$	−13.1646	+	5.45295i	−1.54080	+	0.638220i	−0.981623	−	0.190829i	$-0.938882\pi$
$73$	−13.1646	+	5.45295i	−1.54080	+	0.638220i	−0.559176	+	0.829049i	$0.688882\pi$
$74$		0			0
$75$	−3.68533	−	0.733058i	−0.425545	−	0.0846462i
$76$		0			0
$77$	−4.68117	−	3.12785i	−0.533468	−	0.356452i
$78$		0			0
$79$	0.102033	+	0.102033i	0.0114796	+	0.0114796i	0.712823	−	0.701344i	$-0.247416\pi$
$79$	0.102033	+	0.102033i	0.0114796	+	0.0114796i	−0.701344	+	0.712823i	$0.747416\pi$
$80$		0			0
$81$	−6.60646	+	6.60646i	−0.734052	+	0.734052i
$82$		0			0
$83$	−5.13230	+	7.68102i	−0.563343	+	0.843102i	−0.998356	−	0.0573223i	$-0.981744\pi$
$83$	−5.13230	+	7.68102i	−0.563343	+	0.843102i	0.435013	+	0.900424i	$0.356744\pi$
$84$		0			0
$85$	0.659446	−	3.31526i	0.0715270	−	0.359590i
$86$		0			0
$87$	5.07176	+	12.2443i	0.543750	+	1.31273i
$88$		0			0
$89$	−4.64776	+	11.2207i	−0.492662	+	1.18939i	0.460699	+	0.887557i	$0.347599\pi$
$89$	−4.64776	+	11.2207i	−0.492662	+	1.18939i	−0.953360	+	0.301834i	$0.902401\pi$
$90$		0			0
$91$	10.9441	+	16.3790i	1.14725	+	1.71698i
$92$		0			0
$93$	−1.97743	+	0.393336i	−0.205050	+	0.0407870i
$94$		0			0
$95$			11.3571i			1.16522i
$96$		0			0
$97$		−	12.8041i		−	1.30006i	−0.759908	−	0.650031i	$-0.774756\pi$
$97$		−	12.8041i		−	1.30006i	0.759908	−	0.650031i	$-0.225244\pi$
$98$		0			0
$99$	0.208979	−	0.0415685i	0.0210032	−	0.00417779i
$100$		0			0
$101$	0.497823	+	0.745045i	0.0495352	+	0.0741347i	0.855411	−	0.517951i	$-0.173305\pi$
$101$	0.497823	+	0.745045i	0.0495352	+	0.0741347i	−0.805875	+	0.592085i	$0.798305\pi$
$102$		0			0
$103$	−1.27589	+	3.08028i	−0.125718	+	0.303509i	−0.974190	−	0.225731i	$-0.927523\pi$
$103$	−1.27589	+	3.08028i	−0.125718	+	0.303509i	0.848472	+	0.529240i	$0.177523\pi$
$104$		0			0
$105$	−5.67538	−	13.7016i	−0.553861	−	1.33714i
$106$		0			0
$107$	1.20029	−	6.03426i	0.116036	−	0.583354i	−0.878392	−	0.477940i	$-0.841383\pi$
$107$	1.20029	−	6.03426i	0.116036	−	0.583354i	0.994428	−	0.105413i	$-0.0336165\pi$
$108$		0			0
$109$	−1.59700	+	2.39008i	−0.152965	+	0.228928i	−0.900035	−	0.435817i	$-0.856460\pi$
$109$	−1.59700	+	2.39008i	−0.152965	+	0.228928i	0.747071	+	0.664744i	$0.231460\pi$
$110$		0			0
$111$	3.05724	−	3.05724i	0.290181	−	0.290181i
$112$		0			0
$113$	−0.395040	−	0.395040i	−0.0371623	−	0.0371623i	0.688281	−	0.725444i	$-0.258365\pi$
$113$	−0.395040	−	0.395040i	−0.0371623	−	0.0371623i	−0.725444	+	0.688281i	$0.758365\pi$
$114$		0			0
$115$	−4.11698	−	2.75088i	−0.383910	−	0.256521i
$116$		0			0
$117$	−0.731198	−	0.145444i	−0.0675993	−	0.0134463i
$118$		0			0
$119$	3.67926	−	1.52400i	0.337277	−	0.139705i
$120$		0			0
$121$	−7.20273	−	2.98347i	−0.654793	−	0.271224i
$122$		0			0
$123$	−11.8271	+	7.90265i	−1.06642	+	0.712558i
$124$		0			0
$125$	1.49607	+	7.52124i	0.133812	+	0.672720i
$126$		0			0
$127$	20.8005			1.84574			0.922872	−	0.385108i	$-0.125836\pi$
$127$	20.8005			1.84574			0.922872	+	0.385108i	$0.125836\pi$
$128$		0			0
$129$	−14.1903			−1.24938
$130$		0			0
$131$	−0.204695	−	1.02907i	−0.0178843	−	0.0899104i	0.970812	−	0.239840i	$-0.0770951\pi$
$131$	−0.204695	−	1.02907i	−0.0178843	−	0.0899104i	−0.988697	+	0.149930i	$0.952095\pi$
$132$		0			0
$133$	−11.1254	+	7.43376i	−0.964695	+	0.644589i
$134$		0			0
$135$	−12.5497	−	5.19828i	−1.08011	−	0.447396i
$136$		0			0
$137$	11.1139	−	4.60351i	0.949520	−	0.393304i	0.146470	−	0.989215i	$-0.453209\pi$
$137$	11.1139	−	4.60351i	0.949520	−	0.393304i	0.803051	+	0.595911i	$0.203209\pi$
$138$		0			0
$139$	6.58030	+	1.30890i	0.558133	+	0.111020i	0.466093	−	0.884736i	$-0.345661\pi$
$139$	6.58030	+	1.30890i	0.558133	+	0.111020i	0.0920403	+	0.995755i	$0.470661\pi$
$140$		0			0
$141$	13.8146	+	9.23062i	1.16340	+	0.777358i
$142$		0			0
$143$	−7.92658	−	7.92658i	−0.662854	−	0.662854i
$144$		0			0
$145$	−14.1666	+	14.1666i	−1.17647	+	1.17647i
$146$		0			0
$147$	2.83897	−	4.24881i	0.234154	−	0.350436i
$148$		0			0
$149$	1.37106	−	6.89279i	0.112322	−	0.564680i	−0.883107	−	0.469172i	$-0.844552\pi$
$149$	1.37106	−	6.89279i	0.112322	−	0.564680i	0.995429	−	0.0955079i	$-0.0304475\pi$
$150$		0			0
$151$	3.32014	+	8.01552i	0.270189	+	0.652293i	0.999491	−	0.0318981i	$-0.0101552\pi$
$151$	3.32014	+	8.01552i	0.270189	+	0.652293i	−0.729302	+	0.684192i	$0.760155\pi$
$152$		0			0
$153$	−0.0576774	+	0.139246i	−0.00466294	+	0.0112573i
$154$		0			0
$155$	−1.69328	−	2.53417i	−0.136007	−	0.203549i
$156$		0			0
$157$	−5.32031	+	1.05828i	−0.424607	+	0.0844596i	−0.402768	−	0.915302i	$-0.631952\pi$
$157$	−5.32031	+	1.05828i	−0.424607	+	0.0844596i	−0.0218386	+	0.999762i	$0.506952\pi$
$158$		0			0
$159$		−	1.21371i		−	0.0962531i
$160$		0			0
$161$		−	5.83356i		−	0.459749i
$162$		0			0
$163$	−1.98707	+	0.395252i	−0.155639	+	0.0309585i	−0.272295	−	0.962214i	$-0.587783\pi$
$163$	−1.98707	+	0.395252i	−0.155639	+	0.0309585i	0.116656	+	0.993172i	$0.462783\pi$
$164$		0			0
$165$	4.68874	+	7.01719i	0.365018	+	0.546288i
$166$		0			0
$167$	1.22945	−	2.96815i	0.0951375	−	0.229682i	−0.869145	−	0.494557i	$-0.835330\pi$
$167$	1.22945	−	2.96815i	0.0951375	−	0.229682i	0.964283	+	0.264874i	$0.0853305\pi$
$168$		0			0
$169$	10.0348	+	24.2263i	0.771911	+	1.86356i
$170$		0			0
$171$	0.0987931	−	0.496666i	0.00755490	−	0.0379810i
$172$		0			0
$173$	8.03014	−	12.0180i	0.610521	−	0.913709i	−0.389453	−	0.921047i	$-0.627336\pi$
$173$	8.03014	−	12.0180i	0.610521	−	0.913709i	0.999973	+	0.00733795i	$0.00233576\pi$
$174$		0			0
$175$	4.73206	−	4.73206i	0.357710	−	0.357710i
$176$		0			0
$177$	−3.89179	−	3.89179i	−0.292525	−	0.292525i
$178$		0			0
$179$	3.88955	+	2.59891i	0.290719	+	0.194252i	0.692374	−	0.721539i	$-0.256565\pi$
$179$	3.88955	+	2.59891i	0.290719	+	0.194252i	−0.401655	+	0.915791i	$0.631565\pi$
$180$		0			0
$181$	−6.66273	−	1.32530i	−0.495237	−	0.0985088i	−0.0588482	−	0.998267i	$-0.518743\pi$
$181$	−6.66273	−	1.32530i	−0.495237	−	0.0985088i	−0.436389	+	0.899758i	$0.643743\pi$
$182$		0			0
$183$	−3.01881	+	1.25043i	−0.223157	+	0.0924345i
$184$		0			0
$185$	6.03840	+	2.50119i	0.443952	+	0.183891i
$186$		0			0
$187$	−1.88431	+	1.25906i	−0.137794	+	0.0920713i
$188$		0			0
$189$	−3.12217	−	15.6962i	−0.227104	−	1.14173i
$190$		0			0
$191$	−11.5951			−0.838989			−0.419495	−	0.907758i	$-0.637793\pi$
$191$	−11.5951			−0.838989			−0.419495	+	0.907758i	$0.637793\pi$
$192$		0			0
$193$	−12.0011			−0.863855			−0.431927	−	0.901908i	$-0.642166\pi$
$193$	−12.0011			−0.863855			−0.431927	+	0.901908i	$0.642166\pi$
$194$		0			0
$195$	−5.76083	−	28.9616i	−0.412541	−	2.07399i
$196$		0			0
$197$	−3.45531	+	2.30877i	−0.246181	+	0.164493i	−0.672539	−	0.740062i	$-0.734796\pi$
$197$	−3.45531	+	2.30877i	−0.246181	+	0.164493i	0.426358	+	0.904554i	$0.359796\pi$
$198$		0			0
$199$	16.6804	+	6.90923i	1.18244	+	0.489782i	0.885286	−	0.465047i	$-0.153963\pi$
$199$	16.6804	+	6.90923i	1.18244	+	0.489782i	0.297154	+	0.954830i	$0.403963\pi$
$200$		0			0
$201$	17.8511	−	7.39419i	1.25912	−	0.521546i
$202$		0			0
$203$	−23.1503	−	4.60487i	−1.62483	−	0.323199i
$204$		0			0
$205$	−17.8789	−	11.9463i	−1.24872	−	0.834367i
$206$		0			0
$207$	0.156113	+	0.156113i	0.0108506	+	0.0108506i
$208$		0			0
$209$	5.38413	−	5.38413i	0.372428	−	0.372428i
$210$		0			0
$211$	8.80598	−	13.1791i	0.606229	−	0.907286i	−0.393700	−	0.919239i	$-0.628805\pi$
$211$	8.80598	−	13.1791i	0.606229	−	0.907286i	0.999929	+	0.0119535i	$0.00380499\pi$
$212$		0			0
$213$	0.737818	−	3.70926i	0.0505545	−	0.254155i
$214$		0			0
$215$	−8.20904	−	19.8184i	−0.559852	−	1.35160i
$216$		0			0
$217$	1.37414	−	3.31746i	0.0932825	−	0.225204i
$218$		0			0
$219$	13.9811	+	20.9242i	0.944756	+	1.41393i
$220$		0			0
$221$	7.77700	−	1.54694i	0.523138	−	0.104059i
$222$		0			0
$223$			9.77843i			0.654812i	0.944884	+	0.327406i	$0.106174\pi$
$223$			9.77843i			0.654812i	−0.944884	+	0.327406i	$0.893826\pi$
$224$		0			0
$225$			0.253272i			0.0168848i
$226$		0			0
$227$	8.30819	−	1.65260i	0.551434	−	0.109687i	0.0884942	−	0.996077i	$-0.471795\pi$
$227$	8.30819	−	1.65260i	0.551434	−	0.109687i	0.462940	+	0.886390i	$0.346795\pi$
$228$		0			0
$229$	7.11294	+	10.6453i	0.470037	+	0.703459i	0.988429	−	0.151683i	$-0.0484694\pi$
$229$	7.11294	+	10.6453i	0.470037	+	0.703459i	−0.518393	+	0.855143i	$0.673469\pi$
$230$		0			0
$231$	−3.80503	+	9.18615i	−0.250352	+	0.604404i
$232$		0			0
$233$	−1.63989	−	3.95906i	−0.107433	−	0.259366i	0.861016	−	0.508578i	$-0.169829\pi$
$233$	−1.63989	−	3.95906i	−0.107433	−	0.259366i	−0.968449	+	0.249211i	$0.919829\pi$
$234$		0			0
$235$	−4.89992	+	24.6336i	−0.319636	+	1.60692i
$236$		0			0
$237$	0.141581	−	0.211891i	0.00919669	−	0.0137638i
$238$		0			0
$239$	10.5905	−	10.5905i	0.685040	−	0.685040i	−0.276091	−	0.961131i	$-0.589039\pi$
$239$	10.5905	−	10.5905i	0.685040	−	0.685040i	0.961131	+	0.276091i	$0.0890392\pi$
$240$		0			0
$241$	−2.17798	−	2.17798i	−0.140296	−	0.140296i	0.633471	−	0.773767i	$-0.281630\pi$
$241$	−2.17798	−	2.17798i	−0.140296	−	0.140296i	−0.773767	+	0.633471i	$0.781630\pi$
$242$		0			0
$243$	1.02802	+	0.686898i	0.0659472	+	0.0440645i
$244$		0			0
$245$	7.57629	+	1.50702i	0.484032	+	0.0962799i
$246$		0			0
$247$	−24.6138	+	10.1954i	−1.56614	+	0.648715i
$248$		0			0
$249$	15.0730	+	6.24342i	0.955210	+	0.395661i
$250$		0			0
$251$	20.0734	−	13.4126i	1.26702	−	0.846596i	0.273682	−	0.961820i	$-0.411759\pi$
$251$	20.0734	−	13.4126i	1.26702	−	0.846596i	0.993340	+	0.115224i	$0.0367585\pi$
$252$		0			0
$253$	0.647635	+	3.25588i	0.0407165	+	0.204695i
$254$		0			0
$255$	−5.96972			−0.373839
$256$		0			0
$257$	19.3207			1.20519			0.602595	−	0.798047i	$-0.294134\pi$
$257$	19.3207			1.20519			0.602595	+	0.798047i	$0.294134\pi$
$258$		0			0
$259$	1.50225	+	7.55234i	0.0933455	+	0.469280i
$260$		0			0
$261$	0.742762	−	0.496298i	0.0459758	−	0.0307201i
$262$		0			0
$263$	−25.8007	−	10.6870i	−1.59094	−	0.658990i	−0.600844	−	0.799366i	$-0.705169\pi$
$263$	−25.8007	−	10.6870i	−1.59094	−	0.658990i	−0.990098	+	0.140377i	$0.955169\pi$
$264$		0			0
$265$	1.69508	−	0.702125i	0.104128	−	0.0431312i
$266$		0			0
$267$	21.0372	+	4.18457i	1.28746	+	0.256091i
$268$		0			0
$269$	13.5221	+	9.03520i	0.824459	+	0.550886i	0.894712	−	0.446644i	$-0.147381\pi$
$269$	13.5221	+	9.03520i	0.824459	+	0.550886i	−0.0702534	+	0.997529i	$0.522381\pi$
$270$		0			0
$271$	2.46801	+	2.46801i	0.149921	+	0.149921i	0.778083	−	0.628162i	$-0.216192\pi$
$271$	2.46801	+	2.46801i	0.149921	+	0.149921i	−0.628162	+	0.778083i	$0.716192\pi$
$272$		0			0
$273$	24.6000	−	24.6000i	1.48886	−	1.48886i
$274$		0			0
$275$	−2.11575	+	3.16645i	−0.127585	+	0.190944i
$276$		0			0
$277$	−5.37681	+	27.0311i	−0.323061	+	1.62414i	0.388453	+	0.921468i	$0.373009\pi$
$277$	−5.37681	+	27.0311i	−0.323061	+	1.62414i	−0.711515	+	0.702671i	$0.751991\pi$
$278$		0			0
$279$	0.0520058	+	0.125553i	0.00311350	+	0.00751667i
$280$		0			0
$281$	5.74296	−	13.8647i	0.342596	−	0.827101i	−0.654855	−	0.755754i	$-0.727270\pi$
$281$	5.74296	−	13.8647i	0.342596	−	0.827101i	0.997452	−	0.0713465i	$-0.0227296\pi$
$282$		0			0
$283$	−15.0536	−	22.5293i	−0.894845	−	1.33923i	−0.940329	−	0.340265i	$-0.889483\pi$
$283$	−15.0536	−	22.5293i	−0.894845	−	1.33923i	0.0454844	−	0.998965i	$-0.485517\pi$
$284$		0			0
$285$	19.6722	−	3.91304i	1.16528	−	0.231789i
$286$		0			0
$287$		−	25.3336i		−	1.49539i
$288$		0			0
$289$			15.3970i			0.905704i
$290$		0			0
$291$	−22.1786	+	4.41160i	−1.30013	+	0.258613i
$292$		0			0
$293$	−11.8816	−	17.7821i	−0.694132	−	1.03884i	−0.996330	−	0.0855963i	$-0.972720\pi$
$293$	−11.8816	−	17.7821i	−0.694132	−	1.03884i	0.302198	−	0.953245i	$-0.402280\pi$
$294$		0			0
$295$	3.18395	−	7.68673i	0.185377	−	0.447539i
$296$		0			0
$297$	3.48515	+	8.41390i	0.202229	+	0.488224i
$298$		0			0
$299$	2.26601	−	11.3920i	0.131047	−	0.658818i
$300$		0			0
$301$	14.0408	−	21.0136i	0.809300	−	1.21120i
$302$		0			0
$303$	1.11900	−	1.11900i	0.0642851	−	0.0642851i
$304$		0			0
$305$	−3.49274	−	3.49274i	−0.199994	−	0.199994i
$306$		0			0
$307$	−20.8525	−	13.9332i	−1.19011	−	0.795209i	−0.207025	−	0.978336i	$-0.566378\pi$
$307$	−20.8525	−	13.9332i	−1.19011	−	0.795209i	−0.983089	+	0.183127i	$0.941378\pi$
$308$		0			0
$309$	5.77510	+	1.14874i	0.328534	+	0.0653495i
$310$		0			0
$311$	12.4907	−	5.17383i	0.708284	−	0.293381i	0.000689814	−	1.00000i	$-0.499780\pi$
$311$	12.4907	−	5.17383i	0.708284	−	0.293381i	0.707594	+	0.706619i	$0.249780\pi$
$312$		0			0
$313$	9.36192	+	3.87784i	0.529167	+	0.219188i	0.631238	−	0.775589i	$-0.282547\pi$
$313$	9.36192	+	3.87784i	0.529167	+	0.219188i	−0.102071	+	0.994777i	$0.532547\pi$
$314$		0			0
$315$	−0.831163	+	0.555365i	−0.0468307	+	0.0312913i
$316$		0			0
$317$	1.93405	+	9.72312i	0.108627	+	0.546105i	0.996323	+	0.0856750i	$0.0273047\pi$
$317$	1.93405	+	9.72312i	0.108627	+	0.546105i	−0.887696	+	0.460430i	$0.847695\pi$
$318$		0			0
$319$	13.4321			0.752052
$320$		0			0
$321$	−10.8658			−0.606468
$322$		0			0
$323$	1.05076	+	5.28253i	0.0584659	+	0.293928i
$324$		0			0
$325$	11.0791	−	7.40282i	0.614558	−	0.410635i
$326$		0			0
$327$	4.69020	+	1.94274i	0.259369	+	0.107434i
$328$		0			0
$329$	−27.3382	+	11.3238i	−1.50720	+	0.624304i
$330$		0			0
$331$	17.7915	+	3.53895i	0.977909	+	0.194518i	0.658072	−	0.752955i	$-0.271372\pi$
$331$	17.7915	+	3.53895i	0.977909	+	0.194518i	0.319836	+	0.947473i	$0.396372\pi$
$332$		0			0
$333$	−0.242312	−	0.161908i	−0.0132786	−	0.00887250i
$334$		0			0
$335$	20.6537	+	20.6537i	1.12843	+	1.12843i
$336$		0			0
$337$	6.93868	−	6.93868i	0.377974	−	0.377974i	−0.492397	−	0.870371i	$-0.663879\pi$
$337$	6.93868	−	6.93868i	0.377974	−	0.377974i	0.870371	+	0.492397i	$0.163879\pi$
$338$		0			0
$339$	−0.548158	+	0.820377i	−0.0297719	+	0.0445568i
$340$		0			0
$341$	−0.398646	+	2.00413i	−0.0215879	+	0.108530i
$342$		0			0
$343$	−4.94303	−	11.9335i	−0.266899	−	0.644350i
$344$		0			0
$345$	−3.34643	+	8.07901i	−0.180166	+	0.434959i
$346$		0			0
$347$	−13.9556	−	20.8861i	−0.749178	−	1.12122i	−0.988638	−	0.150318i	$-0.951970\pi$
$347$	−13.9556	−	20.8861i	−0.749178	−	1.12122i	0.239460	−	0.970906i	$-0.423030\pi$
$348$		0			0
$349$	−2.23013	+	0.443600i	−0.119376	+	0.0237453i	−0.254417	−	0.967095i	$-0.581883\pi$
$349$	−2.23013	+	0.443600i	−0.119376	+	0.0237453i	0.135041	+	0.990840i	$0.456883\pi$
$350$		0			0
$351$		−	31.8650i		−	1.70083i
$352$		0			0
$353$			13.4949i			0.718259i	0.933288	+	0.359129i	$0.116926\pi$
$353$			13.4949i			0.718259i	−0.933288	+	0.359129i	$0.883074\pi$
$354$		0			0
$355$	5.60724	−	1.11535i	0.297601	−	0.0591966i
$356$		0			0
$357$	−3.90746	−	5.84792i	−0.206805	−	0.309505i
$358$		0			0
$359$	−7.94195	+	19.1736i	−0.419160	+	1.01194i	0.563431	+	0.826163i	$0.309481\pi$
$359$	−7.94195	+	19.1736i	−0.419160	+	1.01194i	−0.982592	+	0.185779i	$0.940519\pi$
$360$		0			0
$361$	0.345785	+	0.834799i	0.0181992	+	0.0439368i
$362$		0			0
$363$	−2.68613	+	13.5041i	−0.140986	+	0.708782i
$364$		0			0
$365$	−21.1350	+	31.6308i	−1.10626	+	1.65563i
$366$		0			0
$367$	−9.25700	+	9.25700i	−0.483212	+	0.483212i	−0.906156	−	0.422944i	$-0.860997\pi$
$367$	−9.25700	+	9.25700i	−0.483212	+	0.483212i	0.422944	+	0.906156i	$0.360997\pi$
$368$		0			0
$369$	0.677958	+	0.677958i	0.0352931	+	0.0352931i
$370$		0			0
$371$	1.79731	+	1.20092i	0.0933115	+	0.0623488i
$372$		0			0
$373$	−12.7838	−	2.54286i	−0.661920	−	0.131664i	−0.147313	−	0.989090i	$-0.547062\pi$
$373$	−12.7838	−	2.54286i	−0.661920	−	0.131664i	−0.514608	+	0.857426i	$0.672062\pi$
$374$		0			0
$375$	12.5124	−	5.18281i	0.646139	−	0.267639i
$376$		0			0
$377$	−43.4201	−	17.9852i	−2.23625	−	0.926284i
$378$		0			0
$379$	−4.61576	+	3.08415i	−0.237096	+	0.158422i	−0.668442	−	0.743764i	$-0.733039\pi$
$379$	−4.61576	+	3.08415i	−0.237096	+	0.158422i	0.431347	+	0.902186i	$0.358039\pi$
$380$		0			0
$381$	−7.16670	−	36.0294i	−0.367161	−	1.84584i
$382$		0			0
$383$	−7.81378			−0.399265			−0.199633	−	0.979871i	$-0.563975\pi$
$383$	−7.81378			−0.399265			−0.199633	+	0.979871i	$0.563975\pi$
$384$		0			0
$385$	−15.0307			−0.766036
$386$		0			0
$387$	0.186600	+	0.938100i	0.00948539	+	0.0476863i
$388$		0			0
$389$	18.4653	−	12.3381i	0.936227	−	0.625567i	0.00895652	−	0.999960i	$-0.497149\pi$
$389$	18.4653	−	12.3381i	0.936227	−	0.625567i	0.927270	+	0.374393i	$0.122149\pi$
$390$		0			0
$391$	−2.16944	−	0.898611i	−0.109713	−	0.0454447i
$392$		0			0
$393$	−1.71197	+	0.709123i	−0.0863577	+	0.0357705i
$394$		0			0
$395$	0.377835	+	0.0751561i	0.0190109	+	0.00378151i
$396$		0			0
$397$	−24.6132	−	16.4460i	−1.23530	−	0.825403i	−0.245717	−	0.969342i	$-0.579023\pi$
$397$	−24.6132	−	16.4460i	−1.23530	−	0.825403i	−0.989587	+	0.143938i	$0.954023\pi$
$398$		0			0
$399$	16.7096	+	16.7096i	0.836524	+	0.836524i
$400$		0			0
$401$	−14.2585	+	14.2585i	−0.712035	+	0.712035i	−0.966961	−	0.254926i	$-0.917949\pi$
$401$	−14.2585	+	14.2585i	−0.712035	+	0.712035i	0.254926	+	0.966961i	$0.417949\pi$
$402$		0			0
$403$	3.97213	−	5.94471i	0.197866	−	0.296127i
$404$		0			0
$405$	−4.86622	+	24.4641i	−0.241804	+	1.21563i
$406$		0			0
$407$	−1.67691	−	4.04841i	−0.0831211	−	0.200672i
$408$		0			0
$409$	5.63715	−	13.6093i	0.278739	−	0.672936i	−0.721062	−	0.692871i	$-0.756346\pi$
$409$	5.63715	−	13.6093i	0.278739	−	0.672936i	0.999801	+	0.0199343i	$0.00634571\pi$
$410$		0			0
$411$	−11.8032	−	17.6647i	−0.582208	−	0.871335i
$412$		0			0
$413$	9.61394	−	1.91233i	0.473071	−	0.0940997i
$414$		0			0
$415$			24.6629i			1.21066i
$416$		0			0
$417$		−	11.8490i		−	0.580248i
$418$		0			0
$419$	−7.40447	+	1.47284i	−0.361732	+	0.0719529i	−0.372610	−	0.927988i	$-0.621537\pi$
$419$	−7.40447	+	1.47284i	−0.361732	+	0.0719529i	0.0108785	+	0.999941i	$0.496537\pi$
$420$		0			0
$421$	−1.83572	−	2.74735i	−0.0894674	−	0.133897i	0.784036	−	0.620715i	$-0.213158\pi$
$421$	−1.83572	−	2.74735i	−0.0894674	−	0.133897i	−0.873504	+	0.486818i	$0.838158\pi$
$422$		0			0
$423$	0.428564	−	1.03464i	0.0208375	−	0.0503061i
$424$		0			0
$425$	−1.03087	−	2.48874i	−0.0500045	−	0.120721i
$426$		0			0
$427$	1.13532	−	5.70764i	0.0549420	−	0.276212i
$428$		0			0
$429$	−10.9989	+	16.4611i	−0.531033	+	0.794748i
$430$		0			0
$431$	−23.3124	+	23.3124i	−1.12292	+	1.12292i	−0.131620	+	0.991300i	$0.542018\pi$
$431$	−23.3124	+	23.3124i	−1.12292	+	1.12292i	−0.991300	+	0.131620i	$0.957982\pi$
$432$		0			0
$433$	4.04942	+	4.04942i	0.194603	+	0.194603i	0.797682	−	0.603079i	$-0.206060\pi$
$433$	4.04942	+	4.04942i	0.194603	+	0.194603i	−0.603079	+	0.797682i	$0.706060\pi$
$434$		0			0
$435$	29.4197	+	19.6576i	1.41056	+	0.942509i
$436$		0			0
$437$	7.73803	+	1.53919i	0.370160	+	0.0736294i
$438$		0			0
$439$	20.7711	−	8.60367i	0.991350	−	0.410631i	0.172732	−	0.984969i	$-0.444740\pi$
$439$	20.7711	−	8.60367i	0.991350	−	0.410631i	0.818618	+	0.574338i	$0.194740\pi$
$440$		0			0
$441$	−0.318215	−	0.131809i	−0.0151531	−	0.00627662i
$442$		0			0
$443$	−29.3173	+	19.5892i	−1.39291	+	0.930711i	−0.392970	+	0.919551i	$0.628553\pi$
$443$	−29.3173	+	19.5892i	−1.39291	+	0.930711i	−0.999938	+	0.0111603i	$0.996447\pi$
$444$		0			0
$445$	6.32575	+	31.8017i	0.299869	+	1.50754i
$446$		0			0
$447$	−12.4117			−0.587054
$448$		0			0
$449$	−4.34734			−0.205163			−0.102582	−	0.994725i	$-0.532710\pi$
$449$	−4.34734			−0.205163			−0.102582	+	0.994725i	$0.532710\pi$
$450$		0			0
$451$	2.81250	+	14.1394i	0.132436	+	0.665799i
$452$		0			0
$453$	12.7401	−	8.51267i	0.598582	−	0.399960i
$454$		0			0
$455$	48.5878	+	20.1257i	2.27783	+	0.943508i
$456$		0			0
$457$	4.60193	−	1.90618i	0.215269	−	0.0891674i	−0.272443	−	0.962172i	$-0.587832\pi$
$457$	4.60193	−	1.90618i	0.215269	−	0.0891674i	0.487712	+	0.873005i	$0.337832\pi$
$458$		0			0
$459$	−6.31820	−	1.25677i	−0.294908	−	0.0586609i
$460$		0			0
$461$	2.25897	+	1.50940i	0.105211	+	0.0702997i	0.607063	−	0.794654i	$-0.292348\pi$
$461$	2.25897	+	1.50940i	0.105211	+	0.0702997i	−0.501852	+	0.864954i	$0.667348\pi$
$462$		0			0
$463$	−15.5966	−	15.5966i	−0.724834	−	0.724834i	0.244752	−	0.969586i	$-0.421293\pi$
$463$	−15.5966	−	15.5966i	−0.724834	−	0.724834i	−0.969586	+	0.244752i	$0.921293\pi$
$464$		0			0
$465$	−3.80614	+	3.80614i	−0.176506	+	0.176506i
$466$		0			0
$467$	−4.30970	+	6.44993i	−0.199429	+	0.298467i	−0.917682	−	0.397315i	$-0.869942\pi$
$467$	−4.30970	+	6.44993i	−0.199429	+	0.298467i	0.718253	+	0.695782i	$0.244942\pi$
$468$		0			0
$469$	−6.71350	+	33.7511i	−0.310001	+	1.55848i
$470$		0			0
$471$	3.66618	+	8.85093i	0.168928	+	0.407829i
$472$		0			0
$473$	−5.50370	+	13.2871i	−0.253060	+	0.610942i
$474$		0			0
$475$	5.02837	+	7.52549i	0.230717	+	0.345293i
$476$		0			0
$477$	−0.0802364	+	0.0159600i	−0.00367377	+	0.000730758i
$478$		0			0
$479$			2.22366i			0.101602i	0.998709	+	0.0508009i	$0.0161774\pi$
$479$			2.22366i			0.101602i	−0.998709	+	0.0508009i	$0.983823\pi$
$480$		0			0
$481$			15.3321i			0.699083i
$482$		0			0
$483$	−10.1046	+	2.00992i	−0.459774	+	0.0914547i
$484$		0			0
$485$	−18.9916	−	28.4229i	−0.862363	−	1.29062i
$486$		0			0
$487$	−14.2601	+	34.4270i	−0.646187	+	1.56003i	0.172009	+	0.985095i	$0.444974\pi$
$487$	−14.2601	+	34.4270i	−0.646187	+	1.56003i	−0.818196	+	0.574939i	$0.805026\pi$
$488$		0			0
$489$	1.36927	+	3.30571i	0.0619204	+	0.149489i
$490$		0			0
$491$	−7.46638	+	37.5360i	−0.336953	+	1.69398i	0.326044	+	0.945355i	$0.394284\pi$
$491$	−7.46638	+	37.5360i	−0.336953	+	1.69398i	−0.662997	+	0.748622i	$0.730716\pi$
$492$		0			0
$493$	−5.27861	+	7.89999i	−0.237737	+	0.355798i
$494$		0			0
$495$	0.402241	−	0.402241i	0.0180794	−	0.0180794i
$496$		0			0
$497$	4.76279	+	4.76279i	0.213640	+	0.213640i
$498$		0			0
$499$	18.1987	+	12.1600i	0.814685	+	0.544355i	0.891675	−	0.452677i	$-0.149531\pi$
$499$	18.1987	+	12.1600i	0.814685	+	0.544355i	−0.0769897	+	0.997032i	$0.524531\pi$
$500$		0			0
$501$	−5.56487	−	1.10692i	−0.248620	−	0.0494536i
$502$		0			0
$503$	35.5491	−	14.7249i	1.58505	−	0.656551i	0.595850	−	0.803096i	$-0.296815\pi$
$503$	35.5491	−	14.7249i	1.58505	−	0.656551i	0.989204	+	0.146545i	$0.0468153\pi$
$504$		0			0
$505$	2.21016	+	0.915477i	0.0983507	+	0.0407382i
$506$		0			0
$507$	38.5060	−	25.7289i	1.71011	−	1.14266i
$508$		0			0
$509$	3.48480	+	17.5193i	0.154461	+	0.776529i	0.977892	+	0.209112i	$0.0670573\pi$
$509$	3.48480	+	17.5193i	0.154461	+	0.776529i	−0.823430	+	0.567417i	$0.807943\pi$
$510$		0			0
$511$	−44.8193			−1.98269
$512$		0			0
$513$	21.6443			0.955620
$514$		0			0
$515$	1.73653	+	8.73014i	0.0765207	+	0.384696i
$516$		0			0
$517$	14.0011	−	9.35524i	0.615768	−	0.411443i
$518$		0			0
$519$	−23.5836	−	9.76865i	−1.03521	−	0.428796i
$520$		0			0
$521$	13.5272	−	5.60316i	0.592639	−	0.245479i	−0.0661468	−	0.997810i	$-0.521071\pi$
$521$	13.5272	−	5.60316i	0.592639	−	0.245479i	0.658785	+	0.752331i	$0.271071\pi$
$522$		0			0
$523$	23.5557	+	4.68553i	1.03002	+	0.204884i	0.681040	−	0.732246i	$-0.261528\pi$
$523$	23.5557	+	4.68553i	1.03002	+	0.204884i	0.348980	+	0.937130i	$0.386528\pi$
$524$		0			0
$525$	−9.82702	−	6.56621i	−0.428886	−	0.286573i
$526$		0			0
$527$	−1.02205	−	1.02205i	−0.0445214	−	0.0445214i
$528$		0			0
$529$	13.8312	−	13.8312i	0.601357	−	0.601357i
$530$		0			0
$531$	−0.206105	+	0.308457i	−0.00894418	+	0.0133859i
$532$		0			0
$533$	9.84069	−	49.4725i	0.426247	−	2.14289i
$534$		0			0
$535$	−6.28581	−	15.1753i	−0.271759	−	0.656085i
$536$		0			0
$537$	3.16157	−	7.63271i	0.136432	−	0.329376i
$538$		0			0
$539$	−2.87729	−	4.30618i	−0.123934	−	0.185480i
$540$		0			0
$541$	−12.8082	+	2.54771i	−0.550668	+	0.109535i	−0.462579	−	0.886578i	$-0.653076\pi$
$541$	−12.8082	+	2.54771i	−0.550668	+	0.109535i	−0.0880890	+	0.996113i	$0.528076\pi$
$542$		0			0
$543$			11.9975i			0.514860i
$544$		0			0
$545$			7.67427i			0.328730i
$546$		0			0
$547$	26.9082	−	5.35238i	1.15051	−	0.228851i	0.417247	−	0.908793i	$-0.362995\pi$
$547$	26.9082	−	5.35238i	1.15051	−	0.228851i	0.733266	+	0.679942i	$0.237995\pi$
$548$		0			0
$549$	0.122361	+	0.183126i	0.00522224	+	0.00781564i
$550$		0			0
$551$	12.2164	−	29.4931i	0.520438	−	1.25645i
$552$		0			0
$553$	0.173688	+	0.419319i	0.00738595	+	0.0178313i
$554$		0			0
$555$	2.25192	−	11.3212i	0.0955886	−	0.480556i
$556$		0			0
$557$	−6.63444	+	9.92914i	−0.281110	+	0.420711i	−0.944976	−	0.327141i	$-0.893915\pi$
$557$	−6.63444	+	9.92914i	−0.281110	+	0.420711i	0.663865	+	0.747852i	$0.268915\pi$
$558$		0			0
$559$	35.5821	−	35.5821i	1.50496	−	1.50496i
$560$		0			0
$561$	2.83010	+	2.83010i	0.119487	+	0.119487i
$562$		0			0
$563$	27.6327	+	18.4636i	1.16458	+	0.778148i	0.978875	−	0.204458i	$-0.0655432\pi$
$563$	27.6327	+	18.4636i	1.16458	+	0.778148i	0.185705	+	0.982606i	$0.440543\pi$
$564$		0			0
$565$	−1.46286	−	0.290981i	−0.0615429	−	0.0122417i
$566$		0			0
$567$	−27.1502	+	11.2460i	−1.14020	+	0.472286i
$568$		0			0
$569$	−31.9367	−	13.2286i	−1.33886	−	0.554572i	−0.405687	−	0.914012i	$-0.632968\pi$
$569$	−31.9367	−	13.2286i	−1.33886	−	0.554572i	−0.933168	+	0.359440i	$0.882968\pi$
$570$		0			0
$571$	−18.6137	+	12.4373i	−0.778959	+	0.520484i	−0.880328	−	0.474365i	$-0.842678\pi$
$571$	−18.6137	+	12.4373i	−0.778959	+	0.520484i	0.101369	+	0.994849i	$0.467678\pi$
$572$		0			0
$573$	3.99502	+	20.0843i	0.166895	+	0.839035i
$574$		0			0
$575$	−3.94595			−0.164558
$576$		0			0
$577$	−46.1161			−1.91984			−0.959920	−	0.280274i	$-0.909575\pi$
$577$	−46.1161			−1.91984			−0.959920	+	0.280274i	$0.909575\pi$
$578$		0			0
$579$	4.13491	+	20.7876i	0.171841	+	0.863902i
$580$		0			0
$581$	−24.1597	+	16.1430i	−1.00231	+	0.669725i
$582$		0			0
$583$	−1.13646	−	0.470735i	−0.0470672	−	0.0194959i
$584$		0			0
$585$	−1.83886	+	0.761680i	−0.0760275	+	0.0314916i
$586$		0			0
$587$	−33.9240	−	6.74790i	−1.40019	−	0.278516i	−0.563468	−	0.826138i	$-0.690533\pi$
$587$	−33.9240	−	6.74790i	−1.40019	−	0.278516i	−0.836726	+	0.547623i	$0.815533\pi$
$588$		0			0
$589$	4.03794	+	2.69807i	0.166381	+	0.111172i
$590$		0			0
$591$	5.18963	+	5.18963i	0.213473	+	0.213473i
$592$		0			0
$593$	23.3579	−	23.3579i	0.959194	−	0.959194i	−0.0400057	−	0.999199i	$-0.512738\pi$
$593$	23.3579	−	23.3579i	0.959194	−	0.959194i	0.999199	+	0.0400057i	$0.0127376\pi$
$594$		0			0
$595$	5.90685	−	8.84022i	0.242157	−	0.362414i
$596$		0			0
$597$	6.22066	−	31.2734i	0.254595	−	1.27993i
$598$		0			0
$599$	16.4727	+	39.7685i	0.673055	+	1.62490i	0.776391	+	0.630252i	$0.217048\pi$
$599$	16.4727	+	39.7685i	0.673055	+	1.62490i	−0.103336	+	0.994647i	$0.532952\pi$
$600$		0			0
$601$	14.2850	−	34.4871i	0.582698	−	1.40676i	−0.307661	−	0.951496i	$-0.599546\pi$
$601$	14.2850	−	34.4871i	0.582698	−	1.40676i	0.890358	−	0.455260i	$-0.150454\pi$
$602$		0			0
$603$	−0.723559	−	1.08288i	−0.0294656	−	0.0440984i
$604$		0			0
$605$	−20.4140	+	4.06059i	−0.829946	+	0.165086i
$606$		0			0
$607$			4.05117i			0.164432i	0.996615	+	0.0822160i	$0.0261997\pi$
$607$			4.05117i			0.164432i	−0.996615	+	0.0822160i	$0.973800\pi$
$608$		0			0
$609$			41.6862i			1.68921i
$610$		0			0
$611$	−57.7859	+	11.4943i	−2.33777	+	0.465011i
$612$		0			0
$613$	−7.80817	−	11.6857i	−0.315369	−	0.471983i	0.639592	−	0.768715i	$-0.279103\pi$
$613$	−7.80817	−	11.6857i	−0.315369	−	0.471983i	−0.954961	+	0.296732i	$0.904103\pi$
$614$		0			0
$615$	−14.5327	+	35.0849i	−0.586013	+	1.41476i
$616$		0			0
$617$	15.0351	+	36.2979i	0.605289	+	1.46130i	0.868070	+	0.496441i	$0.165360\pi$
$617$	15.0351	+	36.2979i	0.605289	+	1.46130i	−0.262781	+	0.964855i	$0.584640\pi$
$618$		0			0
$619$	3.87037	−	19.4577i	0.155563	−	0.782070i	−0.821680	−	0.569949i	$-0.806963\pi$
$619$	3.87037	−	19.4577i	0.155563	−	0.782070i	0.977243	−	0.212121i	$-0.0680370\pi$
$620$		0			0
$621$	−5.24260	+	7.84611i	−0.210378	+	0.314853i
$622$		0			0
$623$	−27.0123	+	27.0123i	−1.08223	+	1.08223i
$624$		0			0
$625$	21.9990	+	21.9990i	0.879961	+	0.879961i
$626$		0			0
$627$	−11.1812	−	7.47103i	−0.446533	−	0.298364i
$628$		0			0
$629$	3.04005	+	0.604703i	0.121215	+	0.0241111i
$630$		0			0
$631$	−1.83341	+	0.759422i	−0.0729868	+	0.0302321i	−0.418878	−	0.908042i	$-0.637577\pi$
$631$	−1.83341	+	0.759422i	−0.0729868	+	0.0302321i	0.345891	+	0.938275i	$0.387577\pi$
$632$		0			0
$633$	−25.8622	−	10.7125i	−1.02793	−	0.425782i
$634$		0			0
$635$	46.1734	−	30.8521i	1.83233	−	1.22433i
$636$		0			0
$637$	3.53519	+	17.7726i	0.140069	+	0.704177i
$638$		0			0
$639$	−0.254916			−0.0100843
$640$		0			0
$641$	9.28564			0.366761			0.183380	−	0.983042i	$-0.441296\pi$
$641$	9.28564			0.366761			0.183380	+	0.983042i	$0.441296\pi$
$642$		0			0
$643$	−2.48018	−	12.4687i	−0.0978086	−	0.491717i	−0.998374	−	0.0569971i	$-0.981847\pi$
$643$	−2.48018	−	12.4687i	−0.0978086	−	0.491717i	0.900566	−	0.434720i	$-0.143153\pi$
$644$		0			0
$645$	−31.4999	+	21.0476i	−1.24031	+	0.828747i
$646$		0			0
$647$	−3.35949	−	1.39155i	−0.132075	−	0.0547073i	0.315667	−	0.948870i	$-0.397772\pi$
$647$	−3.35949	−	1.39155i	−0.132075	−	0.0547073i	−0.447742	+	0.894163i	$0.647772\pi$
$648$		0			0
$649$	−5.15352	+	2.13466i	−0.202293	+	0.0837927i
$650$		0			0
$651$	−6.21978	−	1.23719i	−0.243772	−	0.0484893i
$652$		0			0
$653$	−3.60748	−	2.41044i	−0.141172	−	0.0943279i	0.482979	−	0.875632i	$-0.339555\pi$
$653$	−3.60748	−	2.41044i	−0.141172	−	0.0943279i	−0.624151	+	0.781304i	$0.714555\pi$
$654$		0			0
$655$	−1.98074	−	1.98074i	−0.0773941	−	0.0773941i
$656$		0			0
$657$	1.19942	−	1.19942i	0.0467939	−	0.0467939i
$658$		0			0
$659$	17.8435	−	26.7046i	0.695083	−	1.04026i	−0.301153	−	0.953576i	$-0.597371\pi$
$659$	17.8435	−	26.7046i	0.695083	−	1.04026i	0.996235	−	0.0866888i	$-0.0276286\pi$
$660$		0			0
$661$	4.81079	−	24.1855i	0.187118	−	0.940706i	−0.767085	−	0.641546i	$-0.778293\pi$
$661$	4.81079	−	24.1855i	0.187118	−	0.940706i	0.954203	−	0.299160i	$-0.0967065\pi$
$662$		0			0
$663$	−5.35906	−	12.9379i	−0.208129	−	0.502467i
$664$		0			0
$665$	−13.6704	+	33.0033i	−0.530115	+	1.27981i
$666$		0			0
$667$	7.73228	+	11.5722i	0.299395	+	0.448077i
$668$		0			0
$669$	16.9377	−	3.36911i	0.654848	−	0.130257i
$670$		0			0
$671$			3.31165i			0.127845i
$672$		0			0
$673$		−	44.2289i		−	1.70490i	−0.522811	−	0.852449i	$-0.675117\pi$
$673$		−	44.2289i		−	1.70490i	0.522811	−	0.852449i	$-0.324883\pi$
$674$		0			0
$675$	−10.6173	+	2.11191i	−0.408659	+	0.0812874i
$676$		0			0
$677$	18.1929	+	27.2277i	0.699212	+	1.04644i	0.995810	+	0.0914418i	$0.0291476\pi$
$677$	18.1929	+	27.2277i	0.699212	+	1.04644i	−0.296599	+	0.955002i	$0.595852\pi$
$678$		0			0
$679$	15.4121	−	37.2082i	0.591463	−	1.42792i
$680$		0			0
$681$	−5.72510	−	13.8216i	−0.219386	−	0.529645i
$682$		0			0
$683$	2.97371	−	14.9498i	0.113786	−	0.572040i	−0.881261	−	0.472630i	$-0.843305\pi$
$683$	2.97371	−	14.9498i	0.113786	−	0.572040i	0.995047	−	0.0994097i	$-0.0316954\pi$
$684$		0			0
$685$	17.8427	−	26.7035i	0.681734	−	1.02029i
$686$		0			0
$687$	15.9884	−	15.9884i	0.609997	−	0.609997i
$688$		0			0
$689$	3.04337	+	3.04337i	0.115943	+	0.115943i
$690$		0			0
$691$	−36.9458	−	24.6864i	−1.40549	−	0.939115i	−0.999684	−	0.0251542i	$-0.991992\pi$
$691$	−36.9458	−	24.6864i	−1.40549	−	0.939115i	−0.405802	−	0.913961i	$-0.633008\pi$
$692$		0			0
$693$	0.657319	+	0.130749i	0.0249695	+	0.00496674i
$694$		0			0
$695$	16.5485	−	6.85462i	0.627721	−	0.260010i
$696$		0			0
$697$	−9.42128	−	3.90242i	−0.356857	−	0.147815i
$698$		0			0
$699$	−6.29265	+	4.20461i	−0.238010	+	0.159033i
$700$		0			0
$701$	−6.76034	−	33.9865i	−0.255335	−	1.28365i	−0.869286	−	0.494310i	$-0.835421\pi$
$701$	−6.76034	−	33.9865i	−0.255335	−	1.28365i	0.613951	−	0.789344i	$-0.289579\pi$
$702$		0			0
$703$	−10.4143			−0.392783
$704$		0			0
$705$	44.3572			1.67059
$706$		0			0
$707$	0.549851	+	2.76429i	0.0206793	+	0.103962i
$708$		0			0
$709$	16.8515	−	11.2598i	0.632870	−	0.422870i	−0.197329	−	0.980337i	$-0.563227\pi$
$709$	16.8515	−	11.2598i	0.632870	−	0.422870i	0.830199	+	0.557467i	$0.188227\pi$
$710$		0			0
$711$	−0.0158696	−	0.00657341i	−0.000595157	−	0.000246522i
$712$		0			0
$713$	−1.95611	+	0.810247i	−0.0732568	+	0.0303440i
$714$		0			0
$715$	−29.3526	−	5.83860i	−1.09773	−	0.218351i
$716$		0			0
$717$	−21.9931	−	14.6953i	−0.821348	−	0.548807i
$718$		0			0
$719$	−22.8834	−	22.8834i	−0.853406	−	0.853406i	0.137145	−	0.990551i	$-0.456207\pi$
$719$	−22.8834	−	22.8834i	−0.853406	−	0.853406i	−0.990551	+	0.137145i	$0.956207\pi$
$720$		0			0
$721$	−7.41538	+	7.41538i	−0.276163	+	0.276163i
$722$		0			0
$723$	−3.02217	+	4.52300i	−0.112396	+	0.168212i
$724$		0			0
$725$	−3.11484	+	15.6594i	−0.115682	+	0.581575i
$726$		0			0
$727$	−13.3809	−	32.3043i	−0.496269	−	1.19810i	−0.951479	−	0.307715i	$-0.900436\pi$
$727$	−13.3809	−	32.3043i	−0.496269	−	1.19810i	0.455210	−	0.890384i	$-0.349564\pi$
$728$		0			0
$729$	−9.89057	+	23.8779i	−0.366317	+	0.884368i
$730$		0			0
$731$	−5.65186	−	8.45860i	−0.209042	−	0.312853i
$732$		0			0
$733$	41.3984	−	8.23465i	1.52908	−	0.304154i	0.642342	−	0.766418i	$-0.277963\pi$
$733$	41.3984	−	8.23465i	1.52908	−	0.304154i	0.886742	+	0.462264i	$0.152963\pi$
$734$		0			0
$735$		−	13.6425i		−	0.503210i
$736$		0			0
$737$		−	19.5828i		−	0.721341i
$738$		0			0
$739$	9.79618	−	1.94858i	0.360358	−	0.0716797i	−0.0115908	−	0.999933i	$-0.503690\pi$
$739$	9.79618	−	1.94858i	0.360358	−	0.0716797i	0.371949	+	0.928253i	$0.378690\pi$
$740$		0			0
$741$	26.1404	+	39.1219i	0.960292	+	1.43718i
$742$		0			0
$743$	10.3765	−	25.0512i	0.380678	−	0.919039i	−0.611157	−	0.791510i	$-0.709295\pi$
$743$	10.3765	−	25.0512i	0.380678	−	0.919039i	0.991835	−	0.127529i	$-0.0407046\pi$
$744$		0			0
$745$	−7.18014	−	17.3344i	−0.263060	−	0.635083i
$746$		0			0
$747$	0.214537	−	1.07855i	0.00784951	−	0.0394622i
$748$		0			0
$749$	10.7513	−	16.0905i	0.392845	−	0.587934i
$750$		0			0
$751$	23.4465	−	23.4465i	0.855575	−	0.855575i	−0.135238	−	0.990813i	$-0.543180\pi$
$751$	23.4465	−	23.4465i	0.855575	−	0.855575i	0.990813	+	0.135238i	$0.0431800\pi$
$752$		0			0
$753$	−30.1488	−	30.1488i	−1.09868	−	1.09868i
$754$		0			0
$755$	19.2590	+	12.8685i	0.700908	+	0.468332i
$756$		0			0
$757$	34.9718	+	6.95632i	1.27107	+	0.252832i	0.784127	−	0.620601i	$-0.213111\pi$
$757$	34.9718	+	6.95632i	1.27107	+	0.252832i	0.486945	+	0.873433i	$0.338111\pi$
$758$		0			0
$759$	5.41652	−	2.24360i	0.196607	−	0.0814374i
$760$		0			0
$761$	41.9043	+	17.3573i	1.51903	+	0.629202i	0.977397	−	0.211413i	$-0.0678065\pi$
$761$	41.9043	+	17.3573i	1.51903	+	0.629202i	0.541632	+	0.840616i	$0.317807\pi$
$762$		0			0
$763$	−7.51770	+	5.02316i	−0.272159	+	0.181851i
$764$		0			0
$765$	0.0785008	+	0.394650i	0.00283820	+	0.0142686i
$766$		0			0
$767$	19.5174			0.704731
$768$		0			0
$769$	−0.661601			−0.0238579			−0.0119290	−	0.999929i	$-0.503797\pi$
$769$	−0.661601			−0.0238579			−0.0119290	+	0.999929i	$0.503797\pi$
$770$		0			0
$771$	−6.65684	−	33.4662i	−0.239740	−	1.20526i
$772$		0			0
$773$	20.9389	−	13.9909i	0.753119	−	0.503218i	−0.118770	−	0.992922i	$-0.537895\pi$
$773$	20.9389	−	13.9909i	0.753119	−	0.503218i	0.871889	+	0.489704i	$0.162895\pi$
$774$		0			0
$775$	−2.24401	−	0.929499i	−0.0806072	−	0.0333886i
$776$		0			0
$777$	12.5642	−	5.20425i	0.450737	−	0.186701i
$778$		0			0
$779$	33.6042	+	6.68429i	1.20399	+	0.239489i
$780$		0			0
$781$	−3.18701	−	2.12950i	−0.114040	−	0.0761993i
$782$		0			0
$783$	26.9986	+	26.9986i	0.964852	+	0.964852i
$784$		0			0
$785$	−10.2405	+	10.2405i	−0.365498	+	0.365498i
$786$		0			0
$787$	−24.2752	+	36.3304i	−0.865318	+	1.29504i	0.0889350	+	0.996037i	$0.471654\pi$
$787$	−24.2752	+	36.3304i	−0.865318	+	1.29504i	−0.954253	+	0.299002i	$0.903346\pi$
$788$		0			0
$789$	−9.62195	+	48.3728i	−0.342551	+	1.72212i
$790$		0			0
$791$	−0.672464	−	1.62347i	−0.0239101	−	0.0577240i
$792$		0			0
$793$	4.43421	−	10.7051i	0.157463	−	0.380150i
$794$		0			0
$795$	−1.80021	−	2.69421i	−0.0638470	−	0.0955538i
$796$		0			0
$797$	15.2693	−	3.03726i	0.540867	−	0.107585i	0.0829060	−	0.996557i	$-0.473580\pi$
$797$	15.2693	−	3.03726i	0.540867	−	0.107585i	0.457961	+	0.888972i	$0.348580\pi$
$798$		0			0
$799$			11.9111i			0.421386i
$800$		0			0
$801$		−	1.44577i		−	0.0510837i
$802$		0			0
$803$	25.0150	−	4.97579i	0.882760	−	0.175592i
$804$		0			0
$805$	−8.65255	−	12.9495i	−0.304962	−	0.456408i
$806$		0			0
$807$	10.9913	−	26.5353i	0.386912	−	0.934088i
$808$		0			0
$809$	−11.9884	−	28.9426i	−0.421490	−	1.01757i	−0.981908	−	0.189357i	$-0.939360\pi$
$809$	−11.9884	−	28.9426i	−0.421490	−	1.01757i	0.560419	−	0.828209i	$-0.310640\pi$
$810$		0			0
$811$	4.91692	−	24.7190i	0.172656	−	0.868002i	−0.793208	−	0.608951i	$-0.791590\pi$
$811$	4.91692	−	24.7190i	0.172656	−	0.868002i	0.965864	−	0.259050i	$-0.0834096\pi$
$812$		0			0
$813$	3.42461	−	5.12529i	0.120106	−	0.179752i
$814$		0			0
$815$	−3.82468	+	3.82468i	−0.133973	+	0.133973i
$816$		0			0
$817$	24.1692	+	24.1692i	0.845572	+	0.845572i
$818$		0			0
$819$	−1.94976	−	1.30279i	−0.0681300	−	0.0455230i
$820$		0			0
$821$	26.8954	+	5.34982i	0.938655	+	0.186710i	0.640632	−	0.767848i	$-0.278673\pi$
$821$	26.8954	+	5.34982i	0.938655	+	0.186710i	0.298024	+	0.954559i	$0.403673\pi$
$822$		0			0
$823$	−28.5108	+	11.8096i	−0.993824	+	0.411655i	−0.819529	−	0.573038i	$-0.805765\pi$
$823$	−28.5108	+	11.8096i	−0.993824	+	0.411655i	−0.174295	+	0.984693i	$0.555765\pi$
$824$		0			0
$825$	6.21373	+	2.57381i	0.216334	+	0.0896086i
$826$		0			0
$827$	−44.8557	+	29.9716i	−1.55978	+	1.04221i	−0.587265	+	0.809395i	$0.699795\pi$
$827$	−44.8557	+	29.9716i	−1.55978	+	1.04221i	−0.972520	+	0.232820i	$0.925205\pi$
$828$		0			0
$829$	−0.547508	−	2.75251i	−0.0190157	−	0.0955985i	0.970112	−	0.242658i	$-0.0780192\pi$
$829$	−0.547508	−	2.75251i	−0.0190157	−	0.0955985i	−0.989128	+	0.147059i	$0.953019\pi$
$830$		0			0
$831$	48.6743			1.68849
$832$		0			0
$833$	3.66339			0.126929
$834$		0			0
$835$	−1.67332	−	8.41233i	−0.0579075	−	0.291121i
$836$		0			0
$837$	−4.82960	+	3.22704i	−0.166936	+	0.111543i
$838$		0			0
$839$	−25.0080	−	10.3586i	−0.863371	−	0.357620i	−0.0933462	−	0.995634i	$-0.529756\pi$
$839$	−25.0080	−	10.3586i	−0.863371	−	0.357620i	−0.770025	+	0.638014i	$0.779756\pi$
$840$		0			0
$841$	25.2350	−	10.4527i	0.870171	−	0.360437i
$842$		0			0
$843$	−25.9945	−	5.17062i	−0.895297	−	0.178086i
$844$		0			0
$845$	58.2089	+	38.8939i	2.00245	+	1.33799i
$846$		0			0
$847$	−17.3396	−	17.3396i	−0.595797	−	0.595797i
$848$		0			0
$849$	−33.8374	+	33.8374i	−1.16130	+	1.16130i
$850$		0			0
$851$	2.52251	−	3.77521i	0.0864707	−	0.129413i
$852$		0			0
$853$	1.05082	−	5.28282i	0.0359793	−	0.180880i	−0.958617	−	0.284699i	$-0.908106\pi$
$853$	1.05082	−	5.28282i	0.0359793	−	0.180880i	0.994596	+	0.103819i	$0.0331063\pi$
$854$		0			0
$855$	−0.517371	−	1.24905i	−0.0176937	−	0.0427164i
$856$		0			0
$857$	16.2865	−	39.3192i	0.556337	−	1.34312i	−0.356310	−	0.934368i	$-0.615965\pi$
$857$	16.2865	−	39.3192i	0.556337	−	1.34312i	0.912647	−	0.408749i	$-0.134035\pi$
$858$		0			0
$859$	6.15821	+	9.21642i	0.210116	+	0.314460i	0.921526	−	0.388317i	$-0.126943\pi$
$859$	6.15821	+	9.21642i	0.210116	+	0.314460i	−0.711411	+	0.702777i	$0.751943\pi$
$860$		0			0
$861$	−43.8814	+	8.72856i	−1.49547	+	0.297468i
$862$		0			0
$863$			8.38657i			0.285482i	0.989760	+	0.142741i	$0.0455916\pi$
$863$			8.38657i			0.285482i	−0.989760	+	0.142741i	$0.954408\pi$
$864$		0			0
$865$		−	38.5884i		−	1.31204i
$866$		0			0
$867$	26.6698	−	5.30495i	0.905753	−	0.180166i
$868$		0			0
$869$	−0.143493	−	0.214752i	−0.00486766	−	0.00728496i
$870$		0			0
$871$	−26.2208	+	63.3027i	−0.888459	+	2.14493i
$872$		0			0
$873$	0.583289	+	1.40818i	0.0197414	+	0.0476598i
$874$		0			0
$875$	−4.70570	+	23.6572i	−0.159082	+	0.799758i
$876$		0			0
$877$	21.5743	−	32.2883i	0.728514	−	1.09030i	−0.263560	−	0.964643i	$-0.584897\pi$
$877$	21.5743	−	32.2883i	0.728514	−	1.09030i	0.992074	−	0.125655i	$-0.0401032\pi$
$878$		0			0
$879$	−26.7074	+	26.7074i	−0.900819	+	0.900819i
$880$		0			0
$881$	−2.03075	−	2.03075i	−0.0684177	−	0.0684177i	0.672070	−	0.740488i	$-0.265405\pi$
$881$	−2.03075	−	2.03075i	−0.0684177	−	0.0684177i	−0.740488	+	0.672070i	$0.765405\pi$
$882$		0			0
$883$	−34.7885	−	23.2450i	−1.17073	−	0.782255i	−0.190804	−	0.981628i	$-0.561110\pi$
$883$	−34.7885	−	23.2450i	−1.17073	−	0.782255i	−0.979924	+	0.199373i	$0.936110\pi$
$884$		0			0
$885$	−14.4115	−	2.86664i	−0.484439	−	0.0963609i
$886$		0			0
$887$	−14.6194	+	6.05554i	−0.490870	+	0.203325i	−0.614368	−	0.789020i	$-0.710589\pi$
$887$	−14.6194	+	6.05554i	−0.490870	+	0.203325i	0.123498	+	0.992345i	$0.460589\pi$
$888$		0			0
$889$	60.4452	+	25.0372i	2.02727	+	0.839721i
$890$		0			0
$891$	13.9048	−	9.29089i	0.465828	−	0.311257i
$892$		0			0
$893$	−7.80752	−	39.2511i	−0.261269	−	1.31349i
$894$		0			0
$895$	12.4889			0.417459
$896$		0			0
$897$	−20.5134			−0.684922
$898$		0			0
$899$	1.67133	+	8.40234i	0.0557419	+	0.280234i
$900$		0			0
$901$	0.723471	−	0.483408i	0.0241023	−	0.0161046i
$902$		0			0
$903$	−41.2363	−	17.0806i	−1.37226	−	0.568408i
$904$		0			0
$905$	−16.7558	+	6.94049i	−0.556983	+	0.230710i
$906$		0			0
$907$	33.2090	+	6.60568i	1.10269	+	0.219338i	0.712690	−	0.701479i	$-0.247476\pi$
$907$	33.2090	+	6.60568i	1.10269	+	0.219338i	0.389996	+	0.920817i	$0.372476\pi$
$908$		0			0
$909$	−0.0886904	−	0.0592611i	−0.00294168	−	0.00196556i
$910$		0			0
$911$	−0.835916	−	0.835916i	−0.0276951	−	0.0276951i	0.693124	−	0.720819i	$-0.256234\pi$
$911$	−0.835916	−	0.835916i	−0.0276951	−	0.0276951i	−0.720819	+	0.693124i	$0.756234\pi$
$912$		0			0
$913$	11.6921	−	11.6921i	0.386952	−	0.386952i
$914$		0			0
$915$	−4.84653	+	7.25335i	−0.160221	+	0.239788i
$916$		0			0
$917$	0.643843	−	3.23682i	0.0212616	−	0.106889i
$918$		0			0
$919$	16.7837	+	40.5195i	0.553645	+	1.33662i	0.914723	+	0.404081i	$0.132409\pi$
$919$	16.7837	+	40.5195i	0.553645	+	1.33662i	−0.361079	+	0.932535i	$0.617591\pi$
$920$		0			0
$921$	−16.9497	+	40.9202i	−0.558511	+	1.34837i
$922$		0			0
$923$	7.45090	+	11.1511i	0.245249	+	0.367042i
$924$		0			0
$925$	5.10858	−	1.01616i	0.167969	−	0.0334111i
$926$		0			0
$927$		−	0.396889i		−	0.0130356i
$928$		0			0
$929$			24.2586i			0.795898i	0.917407	+	0.397949i	$0.130278\pi$
$929$			24.2586i			0.795898i	−0.917407	+	0.397949i	$0.869722\pi$
$930$		0			0
$931$	−12.0721	+	2.40128i	−0.395646	+	0.0786988i
$932$		0			0
$933$	−13.2654	−	19.8531i	−0.434291	−	0.649963i
$934$		0			0
$935$	−2.31536	+	5.58976i	−0.0757202	+	0.182805i
$936$		0			0
$937$	15.6361	+	37.7490i	0.510810	+	1.23320i	0.943413	+	0.331620i	$0.107595\pi$
$937$	15.6361	+	37.7490i	0.510810	+	1.23320i	−0.432603	+	0.901585i	$0.642405\pi$
$938$		0			0
$939$	3.49137	−	17.5523i	0.113937	−	0.572798i
$940$		0			0
$941$	−32.3350	+	48.3927i	−1.05409	+	1.57756i	−0.264041	+	0.964511i	$0.585055\pi$
$941$	−32.3350	+	48.3927i	−1.05409	+	1.57756i	−0.790048	+	0.613045i	$0.789945\pi$
$942$		0			0
$943$	−10.5625	+	10.5625i	−0.343964	+	0.343964i
$944$		0			0
$945$	−30.2119	−	30.2119i	−0.982793	−	0.982793i
$946$		0			0
$947$	−22.2642	−	14.8765i	−0.723489	−	0.483420i	0.138490	−	0.990364i	$-0.455775\pi$
$947$	−22.2642	−	14.8765i	−0.723489	−	0.483420i	−0.861979	+	0.506944i	$0.830775\pi$
$948$		0			0
$949$	−87.5251	−	17.4098i	−2.84119	−	0.565147i
$950$		0			0
$951$	16.1755	−	6.70011i	0.524526	−	0.217266i
$952$		0			0
$953$	26.8881	+	11.1374i	0.870992	+	0.360777i	0.772996	−	0.634410i	$-0.218757\pi$
$953$	26.8881	+	11.1374i	0.870992	+	0.360777i	0.0979952	+	0.995187i	$0.468757\pi$
$954$		0			0
$955$	−25.7390	+	17.1982i	−0.832894	+	0.556522i
$956$		0			0
$957$	−4.62796	−	23.2663i	−0.149601	−	0.752093i
$958$		0			0
$959$	37.8375			1.22184
$960$		0			0
$961$	29.6967			0.957959
$962$		0			0
$963$	0.142883	+	0.718321i	0.00460434	+	0.0231476i
$964$		0			0
$965$	−26.6402	+	17.8004i	−0.857579	+	0.573016i
$966$		0			0
$967$	55.2681	+	22.8928i	1.77730	+	0.736183i	0.993319	+	0.115402i	$0.0368157\pi$
$967$	55.2681	+	22.8928i	1.77730	+	0.736183i	0.783984	+	0.620781i	$0.213184\pi$
$968$		0			0
$969$	8.78808	−	3.64014i	0.282314	−	0.116938i
$970$		0			0
$971$	38.4459	+	7.64736i	1.23379	+	0.245415i	0.768561	−	0.639777i	$-0.220973\pi$
$971$	38.4459	+	7.64736i	1.23379	+	0.245415i	0.465226	+	0.885192i	$0.345973\pi$
$972$		0			0
$973$	17.5465	+	11.7242i	0.562516	+	0.375861i
$974$		0			0
$975$	−16.6400	−	16.6400i	−0.532907	−	0.532907i
$976$		0			0
$977$	−13.4608	+	13.4608i	−0.430651	+	0.430651i	−0.888850	−	0.458199i	$-0.848495\pi$
$977$	−13.4608	+	13.4608i	−0.430651	+	0.430651i	0.458199	+	0.888850i	$0.348495\pi$
$978$		0			0
$979$	12.0775	−	18.0753i	0.385999	−	0.577688i
$980$		0			0
$981$	0.0667568	−	0.335609i	0.00213138	−	0.0107152i
$982$		0			0
$983$	5.14323	+	12.4169i	0.164044	+	0.396036i	0.984431	−	0.175772i	$-0.0562421\pi$
$983$	5.14323	+	12.4169i	0.164044	+	0.396036i	−0.820387	+	0.571808i	$0.806242\pi$
$984$		0			0
$985$	−4.24573	+	10.2501i	−0.135280	+	0.326595i
$986$		0			0
$987$	29.0338	+	43.4522i	0.924156	+	1.38310i
$988$		0			0
$989$	−14.6155	+	2.90721i	−0.464747	+	0.0924439i
$990$		0			0
$991$		−	48.2518i		−	1.53277i	−0.642382	−	0.766385i	$-0.722054\pi$
$991$		−	48.2518i		−	1.53277i	0.642382	−	0.766385i	$-0.277946\pi$
$992$		0			0
$993$		−	32.0368i		−	1.01666i
$994$		0			0
$995$	47.2755	−	9.40368i	1.49873	−	0.298117i
$996$		0			0
$997$	9.52673	+	14.2578i	0.301715	+	0.451548i	0.951087	−	0.308923i	$-0.0999684\pi$
$997$	9.52673	+	14.2578i	0.301715	+	0.451548i	−0.649373	+	0.760470i	$0.724968\pi$
$998$		0			0
$999$	4.76674	−	11.5079i	0.150813	−	0.364095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.97.2		56
4.3	odd	2		512.2.i.a.97.6		56
8.3	odd	2		256.2.i.a.177.2		56
8.5	even	2		64.2.i.a.21.1	✓	56
24.5	odd	2		576.2.bd.a.469.7		56
64.3	odd	16		512.2.i.a.417.6		56
64.29	even	16		64.2.i.a.61.1	yes	56
64.35	odd	16		256.2.i.a.81.2		56
64.61	even	16	inner	512.2.i.b.417.2		56
192.29	odd	16		576.2.bd.a.253.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.1	✓	56	8.5	even	2
64.2.i.a.61.1	yes	56	64.29	even	16
256.2.i.a.81.2		56	64.35	odd	16
256.2.i.a.177.2		56	8.3	odd	2
512.2.i.a.97.6		56	4.3	odd	2
512.2.i.a.417.6		56	64.3	odd	16
512.2.i.b.97.2		56	1.1	even	1	trivial
512.2.i.b.417.2		56	64.61	even	16	inner
576.2.bd.a.253.7		56	192.29	odd	16
576.2.bd.a.469.7		56	24.5	odd	2

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.344545 - 1.73215i) q^{3} +(2.21982 - 1.48324i) q^{5} +(2.90595 + 1.20368i) q^{7} +(-0.109979 + 0.0455548i) q^{9} +O(q^{10})\)	\(q+(-0.344545 - 1.73215i) q^{3} +(2.21982 - 1.48324i) q^{5} +(2.90595 + 1.20368i) q^{7} +(-0.109979 + 0.0455548i) q^{9} +(-1.75553 - 0.349197i) q^{11} +(5.20730 + 3.47941i) q^{13} +(-3.33401 - 3.33401i) q^{15} +(0.895276 - 0.895276i) q^{17} +(-2.36339 + 3.53706i) q^{19} +(1.08373 - 5.44826i) q^{21} +(-0.709741 - 1.71347i) q^{23} +(0.814201 - 1.96565i) q^{25} +(-2.82675 - 4.23052i) q^{27} +(-7.36008 + 1.46401i) q^{29} -1.14161i q^{31} +3.16115i q^{33} +(8.23605 - 1.63825i) q^{35} +(1.36011 + 2.03555i) q^{37} +(4.23269 - 10.2186i) q^{39} +(-3.08221 - 7.44112i) q^{41} +(1.56753 - 7.88051i) q^{43} +(-0.176565 + 0.264249i) q^{45} +(-6.65222 + 6.65222i) q^{47} +(2.04595 + 2.04595i) q^{49} +(-1.85921 - 1.24228i) q^{51} +(0.674026 + 0.134072i) q^{53} +(-4.41491 + 1.82872i) q^{55} +(6.94100 + 2.87506i) q^{57} +(2.59120 - 1.73138i) q^{59} +(-0.360949 - 1.81461i) q^{61} -0.374427 q^{63} +16.7201 q^{65} +(2.13440 + 10.7304i) q^{67} +(-2.72344 + 1.81974i) q^{69} +(1.97842 + 0.819489i) q^{71} +(-13.1646 + 5.45295i) q^{73} +(-3.68533 - 0.733058i) q^{75} +(-4.68117 - 3.12785i) q^{77} +(0.102033 + 0.102033i) q^{79} +(-6.60646 + 6.60646i) q^{81} +(-5.13230 + 7.68102i) q^{83} +(0.659446 - 3.31526i) q^{85} +(5.07176 + 12.2443i) q^{87} +(-4.64776 + 11.2207i) q^{89} +(10.9441 + 16.3790i) q^{91} +(-1.97743 + 0.393336i) q^{93} +11.3571i q^{95} -12.8041i q^{97} +(0.208979 - 0.0415685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

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