LMFDB - Embedded newform 256.2.i.a.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

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

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.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:	$2.04417029174$
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			81.2
Character	$\chi$	$=$	256.81
Dual form			256.2.i.a.177.2

$q$-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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

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	0.744287	+	0.667860i	$0.232789\pi$
$3$	−0.344545	+	1.73215i	−0.198923	+	1.00005i	−0.943211	+	0.332195i	$0.892211\pi$
$4$		0			0
$5$	−2.21982	−	1.48324i	−0.992735	−	0.663324i	−0.0506563	−	0.998716i	$-0.516131\pi$
$5$	−2.21982	−	1.48324i	−0.992735	−	0.663324i	−0.942079	+	0.335392i	$0.891131\pi$
$6$		0			0
$7$	−2.90595	+	1.20368i	−1.09835	+	0.454950i	−0.856910	−	0.515466i	$-0.827619\pi$
$7$	−2.90595	+	1.20368i	−1.09835	+	0.454950i	−0.241437	+	0.970417i	$0.577619\pi$
$8$		0			0
$9$	−0.109979	−	0.0455548i	−0.0366597	−	0.0151849i
$10$		0			0
$11$	−1.75553	+	0.349197i	−0.529312	+	0.105287i	−0.452510	−	0.891760i	$-0.649471\pi$
$11$	−1.75553	+	0.349197i	−0.529312	+	0.105287i	−0.0768028	+	0.997046i	$0.524471\pi$
$12$		0			0
$13$	−5.20730	+	3.47941i	−1.44425	+	0.965015i	−0.446724	+	0.894672i	$0.647409\pi$
$13$	−5.20730	+	3.47941i	−1.44425	+	0.965015i	−0.997523	+	0.0703427i	$0.977591\pi$
$14$		0			0
$15$	3.33401	−	3.33401i	0.860839	−	0.860839i
$16$		0			0
$17$	0.895276	+	0.895276i	0.217136	+	0.217136i	0.807290	−	0.590154i	$-0.200933\pi$
$17$	0.895276	+	0.895276i	0.217136	+	0.217136i	−0.590154	+	0.807290i	$0.700933\pi$
$18$		0			0
$19$	−2.36339	−	3.53706i	−0.542199	−	0.811458i	0.454659	−	0.890665i	$-0.349761\pi$
$19$	−2.36339	−	3.53706i	−0.542199	−	0.811458i	−0.996858	+	0.0792076i	$0.974761\pi$
$20$		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	$-0.813062\pi$
$23$	0.709741	−	1.71347i	0.147991	−	0.357282i	0.980440	+	0.196820i	$0.0630615\pi$
$24$		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	$-0.192127\pi$
$29$	7.36008	+	1.46401i	1.36673	+	0.271860i	0.543426	+	0.839457i	$0.317127\pi$
$30$		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	$-0.876995\pi$
$37$	−1.36011	+	2.03555i	−0.223600	+	0.334642i	0.702660	+	0.711526i	$0.251995\pi$
$38$		0			0
$39$	−4.23269	−	10.2186i	−0.677773	−	1.63629i
$40$		0			0
$41$	−3.08221	+	7.44112i	−0.481361	+	1.16211i	0.477602	+	0.878576i	$0.341506\pi$
$41$	−3.08221	+	7.44112i	−0.481361	+	1.16211i	−0.958963	+	0.283532i	$0.908494\pi$
$42$		0			0
$43$	1.56753	+	7.88051i	0.239046	+	1.20177i	0.894687	+	0.446694i	$0.147399\pi$
$43$	1.56753	+	7.88051i	0.239046	+	1.20177i	−0.655641	+	0.755073i	$0.727601\pi$
$44$		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	$-0.00931090\pi$
$47$	6.65222	+	6.65222i	0.970325	+	0.970325i	−0.0292469	+	0.999572i	$0.509311\pi$
$48$		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	$-0.577530\pi$
$53$	−0.674026	+	0.134072i	−0.0925846	+	0.0184162i	0.148581	+	0.988900i	$0.452530\pi$
$54$		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	0.712691	−	0.701478i	$-0.247476\pi$
$59$	2.59120	+	1.73138i	0.337345	+	0.225407i	−0.375346	+	0.926885i	$0.622476\pi$
$60$		0			0
$61$	0.360949	−	1.81461i	0.0462147	−	0.232337i	−0.950774	−	0.309886i	$-0.899709\pi$
$61$	0.360949	−	1.81461i	0.0462147	−	0.232337i	0.996989	+	0.0775484i	$0.0247092\pi$
$62$		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	−0.599217	−	0.800587i	$-0.704521\pi$
$67$	2.13440	−	10.7304i	0.260759	−	1.31092i	0.859976	−	0.510335i	$-0.170479\pi$
$68$		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	$-0.665557\pi$
$71$	−1.97842	+	0.819489i	−0.234795	+	0.0972554i	0.262184	+	0.965018i	$0.415557\pi$
$72$		0			0
$73$	−13.1646	−	5.45295i	−1.54080	−	0.638220i	−0.559176	−	0.829049i	$-0.688882\pi$
$73$	−13.1646	−	5.45295i	−1.54080	−	0.638220i	−0.981623	+	0.190829i	$0.938882\pi$
$74$		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	$-0.752584\pi$
$79$	−0.102033	+	0.102033i	−0.0114796	+	0.0114796i	0.701344	+	0.712823i	$0.252584\pi$
$80$		0			0
$81$	−6.60646	−	6.60646i	−0.734052	−	0.734052i
$82$		0			0
$83$	−5.13230	−	7.68102i	−0.563343	−	0.843102i	0.435013	−	0.900424i	$-0.356744\pi$
$83$	−5.13230	−	7.68102i	−0.563343	−	0.843102i	−0.998356	+	0.0573223i	$0.981744\pi$
$84$		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	−0.953360	−	0.301834i	$-0.902401\pi$
$89$	−4.64776	−	11.2207i	−0.492662	−	1.18939i	0.460699	−	0.887557i	$-0.347599\pi$
$90$		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	$0.225244\pi$
$97$			12.8041i			1.30006i	−0.759908	+	0.650031i	$0.774756\pi$
$98$		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	$-0.826695\pi$
$101$	−0.497823	+	0.745045i	−0.0495352	+	0.0741347i	0.805875	+	0.592085i	$0.201695\pi$
$102$		0			0
$103$	1.27589	+	3.08028i	0.125718	+	0.303509i	0.974190	−	0.225731i	$-0.0724770\pi$
$103$	1.27589	+	3.08028i	0.125718	+	0.303509i	−0.848472	+	0.529240i	$0.822477\pi$
$104$		0			0
$105$	−5.67538	+	13.7016i	−0.553861	+	1.33714i
$106$		0			0
$107$	1.20029	+	6.03426i	0.116036	+	0.583354i	0.994428	+	0.105413i	$0.0336165\pi$
$107$	1.20029	+	6.03426i	0.116036	+	0.583354i	−0.878392	+	0.477940i	$0.841383\pi$
$108$		0			0
$109$	1.59700	+	2.39008i	0.152965	+	0.228928i	0.900035	−	0.435817i	$-0.143540\pi$
$109$	1.59700	+	2.39008i	0.152965	+	0.228928i	−0.747071	+	0.664744i	$0.768540\pi$
$110$		0			0
$111$	−3.05724	−	3.05724i	−0.290181	−	0.290181i
$112$		0			0
$113$	−0.395040	+	0.395040i	−0.0371623	+	0.0371623i	−0.725444	−	0.688281i	$-0.758365\pi$
$113$	−0.395040	+	0.395040i	−0.0371623	+	0.0371623i	0.688281	+	0.725444i	$0.258365\pi$
$114$		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	$-0.874164\pi$
$127$	−20.8005			−1.84574			−0.922872	+	0.385108i	$0.874164\pi$
$128$		0			0
$129$	−14.1903			−1.24938
$130$		0			0
$131$	−0.204695	+	1.02907i	−0.0178843	+	0.0899104i	−0.988697	−	0.149930i	$-0.952095\pi$
$131$	−0.204695	+	1.02907i	−0.0178843	+	0.0899104i	0.970812	+	0.239840i	$0.0770951\pi$
$132$		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	0.803051	−	0.595911i	$-0.203209\pi$
$137$	11.1139	+	4.60351i	0.949520	+	0.393304i	0.146470	+	0.989215i	$0.453209\pi$
$138$		0			0
$139$	6.58030	−	1.30890i	0.558133	−	0.111020i	0.0920403	−	0.995755i	$-0.470661\pi$
$139$	6.58030	−	1.30890i	0.558133	−	0.111020i	0.466093	+	0.884736i	$0.345661\pi$
$140$		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	−0.995429	−	0.0955079i	$-0.969552\pi$
$149$	−1.37106	−	6.89279i	−0.112322	−	0.564680i	0.883107	−	0.469172i	$-0.155448\pi$
$150$		0			0
$151$	−3.32014	+	8.01552i	−0.270189	+	0.652293i	−0.999491	−	0.0318981i	$-0.989845\pi$
$151$	−3.32014	+	8.01552i	−0.270189	+	0.652293i	0.729302	+	0.684192i	$0.239845\pi$
$152$		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	$-0.368048\pi$
$157$	5.32031	+	1.05828i	0.424607	+	0.0844596i	0.0218386	+	0.999762i	$0.493048\pi$
$158$		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	0.116656	−	0.993172i	$-0.462783\pi$
$163$	−1.98707	−	0.395252i	−0.155639	−	0.0309585i	−0.272295	+	0.962214i	$0.587783\pi$
$164$		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	$-0.164670\pi$
$167$	−1.22945	−	2.96815i	−0.0951375	−	0.229682i	−0.964283	+	0.264874i	$0.914670\pi$
$168$		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	$-0.372664\pi$
$173$	−8.03014	−	12.0180i	−0.610521	−	0.913709i	−0.999973	+	0.00733795i	$0.997664\pi$
$174$		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	−0.401655	−	0.915791i	$-0.631565\pi$
$179$	3.88955	−	2.59891i	0.290719	−	0.194252i	0.692374	+	0.721539i	$0.256565\pi$
$180$		0			0
$181$	6.66273	−	1.32530i	0.495237	−	0.0985088i	0.0588482	−	0.998267i	$-0.481257\pi$
$181$	6.66273	−	1.32530i	0.495237	−	0.0985088i	0.436389	+	0.899758i	$0.356257\pi$
$182$		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	$-0.362207\pi$
$191$	11.5951			0.838989			0.419495	+	0.907758i	$0.362207\pi$
$192$		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	$-0.265204\pi$
$197$	3.45531	+	2.30877i	0.246181	+	0.164493i	−0.426358	+	0.904554i	$0.640204\pi$
$198$		0			0
$199$	−16.6804	+	6.90923i	−1.18244	+	0.489782i	−0.885286	−	0.465047i	$-0.846037\pi$
$199$	−16.6804	+	6.90923i	−1.18244	+	0.489782i	−0.297154	+	0.954830i	$0.596037\pi$
$200$		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	0.999929	−	0.0119535i	$-0.00380499\pi$
$211$	8.80598	+	13.1791i	0.606229	+	0.907286i	−0.393700	+	0.919239i	$0.628805\pi$
$212$		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	0.462940	−	0.886390i	$-0.346795\pi$
$227$	8.30819	+	1.65260i	0.551434	+	0.109687i	0.0884942	+	0.996077i	$0.471795\pi$
$228$		0			0
$229$	−7.11294	+	10.6453i	−0.470037	+	0.703459i	−0.988429	−	0.151683i	$-0.951531\pi$
$229$	−7.11294	+	10.6453i	−0.470037	+	0.703459i	0.518393	+	0.855143i	$0.326531\pi$
$230$		0			0
$231$	3.80503	+	9.18615i	0.250352	+	0.604404i
$232$		0			0
$233$	−1.63989	+	3.95906i	−0.107433	+	0.259366i	−0.968449	−	0.249211i	$-0.919829\pi$
$233$	−1.63989	+	3.95906i	−0.107433	+	0.259366i	0.861016	+	0.508578i	$0.169829\pi$
$234$		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	$-0.410961\pi$
$239$	−10.5905	−	10.5905i	−0.685040	−	0.685040i	−0.961131	+	0.276091i	$0.910961\pi$
$240$		0			0
$241$	−2.17798	+	2.17798i	−0.140296	+	0.140296i	−0.773767	−	0.633471i	$-0.781630\pi$
$241$	−2.17798	+	2.17798i	−0.140296	+	0.140296i	0.633471	+	0.773767i	$0.281630\pi$
$242$		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	0.993340	−	0.115224i	$-0.0367585\pi$
$251$	20.0734	+	13.4126i	1.26702	+	0.846596i	0.273682	+	0.961820i	$0.411759\pi$
$252$		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	$-0.294831\pi$
$263$	25.8007	−	10.6870i	1.59094	−	0.658990i	0.990098	+	0.140377i	$0.0448313\pi$
$264$		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	$-0.852619\pi$
$269$	−13.5221	+	9.03520i	−0.824459	+	0.550886i	0.0702534	+	0.997529i	$0.477619\pi$
$270$		0			0
$271$	−2.46801	+	2.46801i	−0.149921	+	0.149921i	−0.778083	−	0.628162i	$-0.783808\pi$
$271$	−2.46801	+	2.46801i	−0.149921	+	0.149921i	0.628162	+	0.778083i	$0.283808\pi$
$272$		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	0.711515	+	0.702671i	$0.248009\pi$
$277$	5.37681	+	27.0311i	0.323061	+	1.62414i	−0.388453	+	0.921468i	$0.626991\pi$
$278$		0			0
$279$	−0.0520058	+	0.125553i	−0.00311350	+	0.00751667i
$280$		0			0
$281$	5.74296	+	13.8647i	0.342596	+	0.827101i	0.997452	+	0.0713465i	$0.0227296\pi$
$281$	5.74296	+	13.8647i	0.342596	+	0.827101i	−0.654855	+	0.755754i	$0.727270\pi$
$282$		0			0
$283$	−15.0536	+	22.5293i	−0.894845	+	1.33923i	0.0454844	+	0.998965i	$0.485517\pi$
$283$	−15.0536	+	22.5293i	−0.894845	+	1.33923i	−0.940329	+	0.340265i	$0.889483\pi$
$284$		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	−0.302198	−	0.953245i	$-0.597720\pi$
$293$	11.8816	−	17.7821i	0.694132	−	1.03884i	0.996330	−	0.0855963i	$-0.0272795\pi$
$294$		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	−0.983089	−	0.183127i	$-0.941378\pi$
$307$	−20.8525	+	13.9332i	−1.19011	+	0.795209i	−0.207025	+	0.978336i	$0.566378\pi$
$308$		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	$-0.500220\pi$
$311$	−12.4907	−	5.17383i	−0.708284	−	0.293381i	−0.707594	+	0.706619i	$0.750220\pi$
$312$		0			0
$313$	9.36192	−	3.87784i	0.529167	−	0.219188i	−0.102071	−	0.994777i	$-0.532547\pi$
$313$	9.36192	−	3.87784i	0.529167	−	0.219188i	0.631238	+	0.775589i	$0.282547\pi$
$314$		0			0
$315$	−0.831163	−	0.555365i	−0.0468307	−	0.0312913i
$316$		0			0
$317$	−1.93405	+	9.72312i	−0.108627	+	0.546105i	0.887696	+	0.460430i	$0.152305\pi$
$317$	−1.93405	+	9.72312i	−0.108627	+	0.546105i	−0.996323	+	0.0856750i	$0.972695\pi$
$318$		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	0.319836	−	0.947473i	$-0.396372\pi$
$331$	17.7915	−	3.53895i	0.977909	−	0.194518i	0.658072	+	0.752955i	$0.271372\pi$
$332$		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	0.870371	−	0.492397i	$-0.163879\pi$
$337$	6.93868	+	6.93868i	0.377974	+	0.377974i	−0.492397	+	0.870371i	$0.663879\pi$
$338$		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	0.239460	+	0.970906i	$0.423030\pi$
$347$	−13.9556	+	20.8861i	−0.749178	+	1.12122i	−0.988638	+	0.150318i	$0.951970\pi$
$348$		0			0
$349$	2.23013	+	0.443600i	0.119376	+	0.0237453i	0.254417	−	0.967095i	$-0.418117\pi$
$349$	2.23013	+	0.443600i	0.119376	+	0.0237453i	−0.135041	+	0.990840i	$0.543117\pi$
$350$		0			0
$351$		−	31.8650i		−	1.70083i
$352$		0			0
$353$		−	13.4949i		−	0.718259i	−0.933288	−	0.359129i	$-0.883074\pi$
$353$		−	13.4949i		−	0.718259i	0.933288	−	0.359129i	$-0.116926\pi$
$354$		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	0.982592	+	0.185779i	$0.0594809\pi$
$359$	7.94195	+	19.1736i	0.419160	+	1.01194i	−0.563431	+	0.826163i	$0.690519\pi$
$360$		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	$-0.139003\pi$
$367$	9.25700	+	9.25700i	0.483212	+	0.483212i	−0.422944	+	0.906156i	$0.639003\pi$
$368$		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	$-0.452938\pi$
$373$	12.7838	−	2.54286i	0.661920	−	0.131664i	0.514608	+	0.857426i	$0.327938\pi$
$374$		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	0.431347	−	0.902186i	$-0.358039\pi$
$379$	−4.61576	−	3.08415i	−0.237096	−	0.158422i	−0.668442	+	0.743764i	$0.733039\pi$
$380$		0			0
$381$	7.16670	−	36.0294i	0.367161	−	1.84584i
$382$		0			0
$383$	7.81378			0.399265			0.199633	−	0.979871i	$-0.436025\pi$
$383$	7.81378			0.399265			0.199633	+	0.979871i	$0.436025\pi$
$384$		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	$-0.502851\pi$
$389$	−18.4653	−	12.3381i	−0.936227	−	0.625567i	−0.927270	+	0.374393i	$0.877851\pi$
$390$		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	$-0.420977\pi$
$397$	24.6132	−	16.4460i	1.23530	−	0.825403i	0.989587	+	0.143938i	$0.0459767\pi$
$398$		0			0
$399$	−16.7096	+	16.7096i	−0.836524	+	0.836524i
$400$		0			0
$401$	−14.2585	−	14.2585i	−0.712035	−	0.712035i	0.254926	−	0.966961i	$-0.417949\pi$
$401$	−14.2585	−	14.2585i	−0.712035	−	0.712035i	−0.966961	+	0.254926i	$0.917949\pi$
$402$		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	0.999801	−	0.0199343i	$-0.00634571\pi$
$409$	5.63715	+	13.6093i	0.278739	+	0.672936i	−0.721062	+	0.692871i	$0.756346\pi$
$410$		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	0.0108785	−	0.999941i	$-0.496537\pi$
$419$	−7.40447	−	1.47284i	−0.361732	−	0.0719529i	−0.372610	+	0.927988i	$0.621537\pi$
$420$		0			0
$421$	1.83572	−	2.74735i	0.0894674	−	0.133897i	−0.784036	−	0.620715i	$-0.786842\pi$
$421$	1.83572	−	2.74735i	0.0894674	−	0.133897i	0.873504	+	0.486818i	$0.161842\pi$
$422$		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	0.991300	+	0.131620i	$0.0420179\pi$
$431$	23.3124	+	23.3124i	1.12292	+	1.12292i	0.131620	+	0.991300i	$0.457982\pi$
$432$		0			0
$433$	4.04942	−	4.04942i	0.194603	−	0.194603i	−0.603079	−	0.797682i	$-0.706060\pi$
$433$	4.04942	−	4.04942i	0.194603	−	0.194603i	0.797682	+	0.603079i	$0.206060\pi$
$434$		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	$-0.555260\pi$
$439$	−20.7711	−	8.60367i	−0.991350	−	0.410631i	−0.818618	+	0.574338i	$0.805260\pi$
$440$		0			0
$441$	−0.318215	+	0.131809i	−0.0151531	+	0.00627662i
$442$		0			0
$443$	−29.3173	−	19.5892i	−1.39291	−	0.930711i	−0.999938	−	0.0111603i	$-0.996447\pi$
$443$	−29.3173	−	19.5892i	−1.39291	−	0.930711i	−0.392970	−	0.919551i	$-0.628553\pi$
$444$		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	0.487712	−	0.873005i	$-0.337832\pi$
$457$	4.60193	+	1.90618i	0.215269	+	0.0891674i	−0.272443	+	0.962172i	$0.587832\pi$
$458$		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	$-0.707652\pi$
$461$	−2.25897	+	1.50940i	−0.105211	+	0.0702997i	0.501852	+	0.864954i	$0.332652\pi$
$462$		0			0
$463$	15.5966	−	15.5966i	0.724834	−	0.724834i	−0.244752	−	0.969586i	$-0.578707\pi$
$463$	15.5966	−	15.5966i	0.724834	−	0.724834i	0.969586	+	0.244752i	$0.0787066\pi$
$464$		0			0
$465$	−3.80614	−	3.80614i	−0.176506	−	0.176506i
$466$		0			0
$467$	−4.30970	−	6.44993i	−0.199429	−	0.298467i	0.718253	−	0.695782i	$-0.244942\pi$
$467$	−4.30970	−	6.44993i	−0.199429	−	0.298467i	−0.917682	+	0.397315i	$0.869942\pi$
$468$		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	0.818196	+	0.574939i	$0.194974\pi$
$487$	14.2601	+	34.4270i	0.646187	+	1.56003i	−0.172009	+	0.985095i	$0.555026\pi$
$488$		0			0
$489$	1.36927	−	3.30571i	0.0619204	−	0.149489i
$490$		0			0
$491$	−7.46638	−	37.5360i	−0.336953	−	1.69398i	−0.662997	−	0.748622i	$-0.730716\pi$
$491$	−7.46638	−	37.5360i	−0.336953	−	1.69398i	0.326044	−	0.945355i	$-0.394284\pi$
$492$		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	−0.0769897	−	0.997032i	$-0.524531\pi$
$499$	18.1987	−	12.1600i	0.814685	−	0.544355i	0.891675	+	0.452677i	$0.149531\pi$
$500$		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	$-0.703185\pi$
$503$	−35.5491	−	14.7249i	−1.58505	−	0.656551i	−0.989204	+	0.146545i	$0.953185\pi$
$504$		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	0.823430	+	0.567417i	$0.192057\pi$
$509$	−3.48480	+	17.5193i	−0.154461	+	0.776529i	−0.977892	+	0.209112i	$0.932943\pi$
$510$		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	0.658785	−	0.752331i	$-0.271071\pi$
$521$	13.5272	+	5.60316i	0.592639	+	0.245479i	−0.0661468	+	0.997810i	$0.521071\pi$
$522$		0			0
$523$	23.5557	−	4.68553i	1.03002	−	0.204884i	0.348980	−	0.937130i	$-0.386528\pi$
$523$	23.5557	−	4.68553i	1.03002	−	0.204884i	0.681040	+	0.732246i	$0.261528\pi$
$524$		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	$-0.346924\pi$
$541$	12.8082	+	2.54771i	0.550668	+	0.109535i	0.0880890	+	0.996113i	$0.471924\pi$
$542$		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	0.733266	−	0.679942i	$-0.237995\pi$
$547$	26.9082	+	5.35238i	1.15051	+	0.228851i	0.417247	+	0.908793i	$0.362995\pi$
$548$		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	$-0.106085\pi$
$557$	6.63444	+	9.92914i	0.281110	+	0.420711i	−0.663865	+	0.747852i	$0.731085\pi$
$558$		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	0.185705	−	0.982606i	$-0.440543\pi$
$563$	27.6327	−	18.4636i	1.16458	−	0.778148i	0.978875	+	0.204458i	$0.0655432\pi$
$564$		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	−0.933168	−	0.359440i	$-0.882968\pi$
$569$	−31.9367	+	13.2286i	−1.33886	+	0.554572i	−0.405687	+	0.914012i	$0.632968\pi$
$570$		0			0
$571$	−18.6137	−	12.4373i	−0.778959	−	0.520484i	0.101369	−	0.994849i	$-0.467678\pi$
$571$	−18.6137	−	12.4373i	−0.778959	−	0.520484i	−0.880328	+	0.474365i	$0.842678\pi$
$572$		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	−0.836726	−	0.547623i	$-0.815533\pi$
$587$	−33.9240	+	6.74790i	−1.40019	+	0.278516i	−0.563468	+	0.826138i	$0.690533\pi$
$588$		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	0.999199	−	0.0400057i	$-0.0127376\pi$
$593$	23.3579	+	23.3579i	0.959194	+	0.959194i	−0.0400057	+	0.999199i	$0.512738\pi$
$594$		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	0.103336	+	0.994647i	$0.467048\pi$
$599$	−16.4727	+	39.7685i	−0.673055	+	1.62490i	−0.776391	+	0.630252i	$0.782952\pi$
$600$		0			0
$601$	14.2850	+	34.4871i	0.582698	+	1.40676i	0.890358	+	0.455260i	$0.150454\pi$
$601$	14.2850	+	34.4871i	0.582698	+	1.40676i	−0.307661	+	0.951496i	$0.599546\pi$
$602$		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	$-0.720897\pi$
$613$	7.80817	−	11.6857i	0.315369	−	0.471983i	0.954961	+	0.296732i	$0.0958967\pi$
$614$		0			0
$615$	14.5327	+	35.0849i	0.586013	+	1.41476i
$616$		0			0
$617$	15.0351	−	36.2979i	0.605289	−	1.46130i	−0.262781	−	0.964855i	$-0.584640\pi$
$617$	15.0351	−	36.2979i	0.605289	−	1.46130i	0.868070	−	0.496441i	$-0.165360\pi$
$618$		0			0
$619$	3.87037	+	19.4577i	0.155563	+	0.782070i	0.977243	+	0.212121i	$0.0680370\pi$
$619$	3.87037	+	19.4577i	0.155563	+	0.782070i	−0.821680	+	0.569949i	$0.806963\pi$
$620$		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	$-0.362423\pi$
$631$	1.83341	+	0.759422i	0.0729868	+	0.0302321i	−0.345891	+	0.938275i	$0.612423\pi$
$632$		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	0.900566	+	0.434720i	$0.143153\pi$
$643$	−2.48018	+	12.4687i	−0.0978086	+	0.491717i	−0.998374	+	0.0569971i	$0.981847\pi$
$644$		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	$-0.602228\pi$
$647$	3.35949	−	1.39155i	0.132075	−	0.0547073i	0.447742	+	0.894163i	$0.352228\pi$
$648$		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	$-0.660445\pi$
$653$	3.60748	−	2.41044i	0.141172	−	0.0943279i	0.624151	+	0.781304i	$0.285445\pi$
$654$		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	0.996235	+	0.0866888i	$0.0276286\pi$
$659$	17.8435	+	26.7046i	0.695083	+	1.04026i	−0.301153	+	0.953576i	$0.597371\pi$
$660$		0			0
$661$	−4.81079	−	24.1855i	−0.187118	−	0.940706i	−0.954203	−	0.299160i	$-0.903293\pi$
$661$	−4.81079	−	24.1855i	−0.187118	−	0.940706i	0.767085	−	0.641546i	$-0.221707\pi$
$662$		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	$0.324883\pi$
$673$			44.2289i			1.70490i	−0.522811	+	0.852449i	$0.675117\pi$
$674$		0			0
$675$	−10.6173	−	2.11191i	−0.408659	−	0.0812874i
$676$		0			0
$677$	−18.1929	+	27.2277i	−0.699212	+	1.04644i	0.296599	+	0.955002i	$0.404148\pi$
$677$	−18.1929	+	27.2277i	−0.699212	+	1.04644i	−0.995810	+	0.0914418i	$0.970852\pi$
$678$		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	0.995047	+	0.0994097i	$0.0316954\pi$
$683$	2.97371	+	14.9498i	0.113786	+	0.572040i	−0.881261	+	0.472630i	$0.843305\pi$
$684$		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	−0.405802	+	0.913961i	$0.633008\pi$
$691$	−36.9458	+	24.6864i	−1.40549	+	0.939115i	−0.999684	+	0.0251542i	$0.991992\pi$
$692$		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	−0.613951	−	0.789344i	$-0.710421\pi$
$701$	6.76034	−	33.9865i	0.255335	−	1.28365i	0.869286	−	0.494310i	$-0.164579\pi$
$702$		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	$-0.436773\pi$
$709$	−16.8515	−	11.2598i	−0.632870	−	0.422870i	−0.830199	+	0.557467i	$0.811773\pi$
$710$		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	$-0.543793\pi$
$719$	22.8834	−	22.8834i	0.853406	−	0.853406i	0.990551	+	0.137145i	$0.0437925\pi$
$720$		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	−0.455210	−	0.890384i	$-0.650436\pi$
$727$	13.3809	−	32.3043i	0.496269	−	1.19810i	0.951479	−	0.307715i	$-0.0995642\pi$
$728$		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	$-0.722037\pi$
$733$	−41.3984	−	8.23465i	−1.52908	−	0.304154i	−0.886742	+	0.462264i	$0.847037\pi$
$734$		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	0.371949	−	0.928253i	$-0.378690\pi$
$739$	9.79618	+	1.94858i	0.360358	+	0.0716797i	−0.0115908	+	0.999933i	$0.503690\pi$
$740$		0			0
$741$	−26.1404	+	39.1219i	−0.960292	+	1.43718i
$742$		0			0
$743$	−10.3765	−	25.0512i	−0.380678	−	0.919039i	−0.991835	−	0.127529i	$-0.959295\pi$
$743$	−10.3765	−	25.0512i	−0.380678	−	0.919039i	0.611157	−	0.791510i	$-0.290705\pi$
$744$		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	$-0.456820\pi$
$751$	−23.4465	−	23.4465i	−0.855575	−	0.855575i	−0.990813	+	0.135238i	$0.956820\pi$
$752$		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	$-0.786889\pi$
$757$	−34.9718	+	6.95632i	−1.27107	+	0.252832i	−0.486945	+	0.873433i	$0.661889\pi$
$758$		0			0
$759$	−5.41652	−	2.24360i	−0.196607	−	0.0814374i
$760$		0			0
$761$	41.9043	−	17.3573i	1.51903	−	0.629202i	0.541632	−	0.840616i	$-0.317807\pi$
$761$	41.9043	−	17.3573i	1.51903	−	0.629202i	0.977397	+	0.211413i	$0.0678065\pi$
$762$		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	$-0.462105\pi$
$773$	−20.9389	−	13.9909i	−0.753119	−	0.503218i	−0.871889	+	0.489704i	$0.837105\pi$
$774$		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	−0.954253	−	0.299002i	$-0.903346\pi$
$787$	−24.2752	−	36.3304i	−0.865318	−	1.29504i	0.0889350	−	0.996037i	$-0.471654\pi$
$788$		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	$-0.526420\pi$
$797$	−15.2693	−	3.03726i	−0.540867	−	0.107585i	−0.457961	+	0.888972i	$0.651420\pi$
$798$		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	0.560419	+	0.828209i	$0.310640\pi$
$809$	−11.9884	+	28.9426i	−0.421490	+	1.01757i	−0.981908	+	0.189357i	$0.939360\pi$
$810$		0			0
$811$	4.91692	+	24.7190i	0.172656	+	0.868002i	0.965864	+	0.259050i	$0.0834096\pi$
$811$	4.91692	+	24.7190i	0.172656	+	0.868002i	−0.793208	+	0.608951i	$0.791590\pi$
$812$		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	$-0.721327\pi$
$821$	−26.8954	+	5.34982i	−0.938655	+	0.186710i	−0.298024	+	0.954559i	$0.596327\pi$
$822$		0			0
$823$	28.5108	+	11.8096i	0.993824	+	0.411655i	0.819529	−	0.573038i	$-0.194235\pi$
$823$	28.5108	+	11.8096i	0.993824	+	0.411655i	0.174295	+	0.984693i	$0.444235\pi$
$824$		0			0
$825$	6.21373	−	2.57381i	0.216334	−	0.0896086i
$826$		0			0
$827$	−44.8557	−	29.9716i	−1.55978	−	1.04221i	−0.972520	−	0.232820i	$-0.925205\pi$
$827$	−44.8557	−	29.9716i	−1.55978	−	1.04221i	−0.587265	−	0.809395i	$-0.699795\pi$
$828$		0			0
$829$	0.547508	−	2.75251i	0.0190157	−	0.0955985i	−0.970112	−	0.242658i	$-0.921981\pi$
$829$	0.547508	−	2.75251i	0.0190157	−	0.0955985i	0.989128	+	0.147059i	$0.0469808\pi$
$830$		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	$-0.470244\pi$
$839$	25.0080	−	10.3586i	0.863371	−	0.357620i	0.770025	+	0.638014i	$0.220244\pi$
$840$		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	$-0.0918937\pi$
$853$	−1.05082	−	5.28282i	−0.0359793	−	0.180880i	−0.994596	+	0.103819i	$0.966894\pi$
$854$		0			0
$855$	0.517371	−	1.24905i	0.0176937	−	0.0427164i
$856$		0			0
$857$	16.2865	+	39.3192i	0.556337	+	1.34312i	0.912647	+	0.408749i	$0.134035\pi$
$857$	16.2865	+	39.3192i	0.556337	+	1.34312i	−0.356310	+	0.934368i	$0.615965\pi$
$858$		0			0
$859$	6.15821	−	9.21642i	0.210116	−	0.314460i	−0.711411	−	0.702777i	$-0.751943\pi$
$859$	6.15821	−	9.21642i	0.210116	−	0.314460i	0.921526	+	0.388317i	$0.126943\pi$
$860$		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	−0.992074	−	0.125655i	$-0.959897\pi$
$877$	−21.5743	−	32.2883i	−0.728514	−	1.09030i	0.263560	−	0.964643i	$-0.415103\pi$
$878$		0			0
$879$	26.7074	+	26.7074i	0.900819	+	0.900819i
$880$		0			0
$881$	−2.03075	+	2.03075i	−0.0684177	+	0.0684177i	−0.740488	−	0.672070i	$-0.765405\pi$
$881$	−2.03075	+	2.03075i	−0.0684177	+	0.0684177i	0.672070	+	0.740488i	$0.265405\pi$
$882$		0			0
$883$	−34.7885	+	23.2450i	−1.17073	+	0.782255i	−0.979924	−	0.199373i	$-0.936110\pi$
$883$	−34.7885	+	23.2450i	−1.17073	+	0.782255i	−0.190804	+	0.981628i	$0.561110\pi$
$884$		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	$-0.289411\pi$
$887$	14.6194	+	6.05554i	0.490870	+	0.203325i	−0.123498	+	0.992345i	$0.539411\pi$
$888$		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	0.389996	−	0.920817i	$-0.372476\pi$
$907$	33.2090	−	6.60568i	1.10269	−	0.219338i	0.712690	+	0.701479i	$0.247476\pi$
$908$		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	$-0.743766\pi$
$911$	0.835916	−	0.835916i	0.0276951	−	0.0276951i	0.720819	+	0.693124i	$0.243766\pi$
$912$		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	0.361079	+	0.932535i	$0.382409\pi$
$919$	−16.7837	+	40.5195i	−0.553645	+	1.33662i	−0.914723	+	0.404081i	$0.867591\pi$
$920$		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	$-0.869722\pi$
$929$		−	24.2586i		−	0.795898i	0.917407	−	0.397949i	$-0.130278\pi$
$930$		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	−0.432603	−	0.901585i	$-0.642405\pi$
$937$	15.6361	−	37.7490i	0.510810	−	1.23320i	0.943413	−	0.331620i	$-0.107595\pi$
$938$		0			0
$939$	3.49137	+	17.5523i	0.113937	+	0.572798i
$940$		0			0
$941$	32.3350	+	48.3927i	1.05409	+	1.57756i	0.790048	+	0.613045i	$0.210055\pi$
$941$	32.3350	+	48.3927i	1.05409	+	1.57756i	0.264041	+	0.964511i	$0.414945\pi$
$942$		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	−0.861979	−	0.506944i	$-0.830775\pi$
$947$	−22.2642	+	14.8765i	−0.723489	+	0.483420i	0.138490	+	0.990364i	$0.455775\pi$
$948$		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	0.0979952	−	0.995187i	$-0.468757\pi$
$953$	26.8881	−	11.1374i	0.870992	−	0.360777i	0.772996	+	0.634410i	$0.218757\pi$
$954$		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	−0.783984	+	0.620781i	$0.786816\pi$
$967$	−55.2681	+	22.8928i	−1.77730	+	0.736183i	−0.993319	+	0.115402i	$0.963184\pi$
$968$		0			0
$969$	8.78808	+	3.64014i	0.282314	+	0.116938i
$970$		0			0
$971$	38.4459	−	7.64736i	1.23379	−	0.245415i	0.465226	−	0.885192i	$-0.345973\pi$
$971$	38.4459	−	7.64736i	1.23379	−	0.245415i	0.768561	+	0.639777i	$0.220973\pi$
$972$		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	0.458199	−	0.888850i	$-0.348495\pi$
$977$	−13.4608	−	13.4608i	−0.430651	−	0.430651i	−0.888850	+	0.458199i	$0.848495\pi$
$978$		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	$-0.943758\pi$
$983$	−5.14323	+	12.4169i	−0.164044	+	0.396036i	0.820387	+	0.571808i	$0.193758\pi$
$984$		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	$-0.900032\pi$
$997$	−9.52673	+	14.2578i	−0.301715	+	0.451548i	0.649373	+	0.760470i	$0.275032\pi$
$998$		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	256.2.i.a.81.2		56
4.3	odd	2		64.2.i.a.61.1	yes	56
8.3	odd	2		512.2.i.b.417.2		56
8.5	even	2		512.2.i.a.417.6		56
12.11	even	2		576.2.bd.a.253.7		56
64.11	odd	16		512.2.i.b.97.2		56
64.21	even	16	inner	256.2.i.a.177.2		56
64.43	odd	16		64.2.i.a.21.1	✓	56
64.53	even	16		512.2.i.a.97.6		56
192.107	even	16		576.2.bd.a.469.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.1	✓	56	64.43	odd	16
64.2.i.a.61.1	yes	56	4.3	odd	2
256.2.i.a.81.2		56	1.1	even	1	trivial
256.2.i.a.177.2		56	64.21	even	16	inner
512.2.i.a.97.6		56	64.53	even	16
512.2.i.a.417.6		56	8.5	even	2
512.2.i.b.97.2		56	64.11	odd	16
512.2.i.b.417.2		56	8.3	odd	2
576.2.bd.a.253.7		56	12.11	even	2
576.2.bd.a.469.7		56	192.107	even	16

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.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

L-functions

Modular forms

Varieties

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Groups

Database

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