LMFDB - Embedded newform 784.2.m.g.197.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.4
Root			$1.41216 + 0.0762223i$ of defining polynomial
Character	$\chi$	$=$	784.197
Dual form			784.2.m.g.589.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29150 - 0.576222i) q^{2} +(0.715276 - 0.715276i) q^{3} +(1.33594 - 1.48838i) q^{4} +(-0.867721 - 0.867721i) q^{5} +(0.511620 - 1.33594i) q^{6} +(0.867721 - 2.69204i) q^{8} +1.97676i q^{9} +(-1.62066 - 0.620660i) q^{10} +(-2.97676 - 2.97676i) q^{11} +(-0.109040 - 2.02017i) q^{12} +(2.02017 - 2.02017i) q^{13} -1.24132 q^{15} +(-0.430552 - 3.97676i) q^{16} -0.264559 q^{17} +(1.13905 + 2.55298i) q^{18} +(4.53959 - 4.53959i) q^{19} +(-2.45072 + 0.132279i) q^{20} +(-5.55976 - 2.12921i) q^{22} +1.54621i q^{23} +(-1.30489 - 2.54621i) q^{24} -3.49412i q^{25} +(1.44498 - 3.77310i) q^{26} +(3.55976 + 3.55976i) q^{27} +(-0.328129 + 0.328129i) q^{29} +(-1.60316 + 0.715276i) q^{30} -6.04033 q^{31} +(-2.84756 - 4.88789i) q^{32} -4.25841 q^{33} +(-0.341677 + 0.152445i) q^{34} +(2.94217 + 2.64082i) q^{36} +(6.64863 + 6.64863i) q^{37} +(3.24706 - 8.47869i) q^{38} -2.88995i q^{39} +(-3.08887 + 1.58300i) q^{40} +11.0327i q^{41} +(3.38407 + 3.38407i) q^{43} +(-8.40731 + 0.453791i) q^{44} +(1.71528 - 1.71528i) q^{45} +(0.890960 + 1.99693i) q^{46} -3.12566 q^{47} +(-3.15244 - 2.53652i) q^{48} +(-2.01339 - 4.51265i) q^{50} +(-0.189233 + 0.189233i) q^{51} +(-0.307963 - 5.70559i) q^{52} +(0.430552 + 0.430552i) q^{53} +(6.64863 + 2.54621i) q^{54} +5.16599i q^{55} -6.49412i q^{57} +(-0.234703 + 0.612853i) q^{58} +(4.62640 + 4.62640i) q^{59} +(-1.65832 + 1.84756i) q^{60} +(-4.86772 + 4.86772i) q^{61} +(-7.80108 + 3.48057i) q^{62} +(-6.49412 - 4.67187i) q^{64} -3.50588 q^{65} +(-5.49973 + 2.45379i) q^{66} +(3.34374 - 3.34374i) q^{67} +(-0.353433 + 0.393764i) q^{68} +(1.10597 + 1.10597i) q^{69} +9.03885i q^{71} +(5.32151 + 1.71528i) q^{72} -14.8146i q^{73} +(12.4178 + 4.75561i) q^{74} +(-2.49926 - 2.49926i) q^{75} +(-0.692037 - 12.8212i) q^{76} +(-1.66525 - 3.73237i) q^{78} +12.5904 q^{79} +(-3.07712 + 3.82432i) q^{80} -0.837864 q^{81} +(6.35729 + 14.2487i) q^{82} +(0.715276 - 0.715276i) q^{83} +(0.229563 + 0.229563i) q^{85} +(6.32050 + 2.42055i) q^{86} +0.469405i q^{87} +(-10.5965 + 5.43055i) q^{88} +10.9924i q^{89} +(1.22690 - 3.20366i) q^{90} +(2.30135 + 2.06564i) q^{92} +(-4.32050 + 4.32050i) q^{93} +(-4.03679 + 1.80108i) q^{94} -7.87820 q^{95} +(-5.53298 - 1.45940i) q^{96} +14.2452 q^{97} +(5.88434 - 5.88434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{4} + 4 q^{5} + 16 q^{6} - 4 q^{8} - 12 q^{10} + 12 q^{12} - 8 q^{15} + 8 q^{16} - 24 q^{17} + 6 q^{18} + 12 q^{19} + 8 q^{20} - 4 q^{22} - 8 q^{26} - 12 q^{27} - 16 q^{29} + 20 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^4 + 4 * q^5 + 16 * q^6 - 4 * q^8 - 12 * q^10 + 12 * q^12 - 8 * q^15 + 8 * q^16 - 24 * q^17 + 6 * q^18 + 12 * q^19 + 8 * q^20 - 4 * q^22 - 8 * q^26 - 12 * q^27 - 16 * q^29 + 20 * q^30 - 16 * q^31 - 28 * q^32 + 24 * q^33 + 12 * q^34 + 24 * q^36 + 16 * q^37 + 16 * q^38 - 28 * q^40 - 32 * q^43 - 32 * q^44 + 8 * q^45 + 20 * q^46 - 24 * q^47 - 20 * q^48 - 14 * q^50 + 8 * q^51 - 32 * q^52 - 8 * q^53 + 16 * q^54 + 12 * q^58 + 28 * q^59 - 28 * q^60 - 28 * q^61 - 20 * q^62 - 32 * q^64 - 48 * q^65 + 16 * q^66 - 28 * q^68 - 44 * q^69 + 44 * q^72 - 4 * q^74 - 28 * q^75 + 24 * q^76 + 12 * q^78 - 24 * q^79 + 12 * q^80 + 40 * q^81 - 4 * q^82 - 40 * q^85 - 40 * q^88 + 16 * q^90 + 36 * q^92 + 16 * q^93 - 28 * q^94 + 16 * q^95 - 8 * q^96 + 32 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	1.29150	−	0.576222i	0.913227	−	0.407451i
$2$	1.29150	−	0.576222i	0.913227	−	0.407451i
$3$	0.715276	−	0.715276i	0.412965	−	0.412965i	−0.469805	−	0.882770i	$-0.655676\pi$
$3$	0.715276	−	0.715276i	0.412965	−	0.412965i	0.882770	+	0.469805i	$0.155676\pi$
$4$	1.33594	−	1.48838i	0.667968	−	0.744190i
$5$	−0.867721	−	0.867721i	−0.388056	−	0.388056i	0.485937	−	0.873994i	$-0.338478\pi$
$5$	−0.867721	−	0.867721i	−0.388056	−	0.388056i	−0.873994	+	0.485937i	$0.838478\pi$
$6$	0.511620	−	1.33594i	0.208868	−	0.545393i
$7$		0			0
$7$		0			0
$8$	0.867721	−	2.69204i	0.306786	−	0.951779i
$9$			1.97676i			0.658920i
$10$	−1.62066	−	0.620660i	−0.512498	−	0.196270i
$11$	−2.97676	−	2.97676i	−0.897527	−	0.897527i	0.0976898	−	0.995217i	$-0.468855\pi$
$11$	−2.97676	−	2.97676i	−0.897527	−	0.897527i	−0.995217	+	0.0976898i	$0.968855\pi$
$12$	−0.109040	−	2.02017i	−0.0314771	−	0.583171i
$13$	2.02017	−	2.02017i	0.560293	−	0.560293i	−0.369098	−	0.929391i	$-0.620333\pi$
$13$	2.02017	−	2.02017i	0.560293	−	0.560293i	0.929391	+	0.369098i	$0.120333\pi$
$14$		0			0
$15$	−1.24132			−0.320507
$16$	−0.430552	−	3.97676i	−0.107638	−	0.994190i
$17$	−0.264559			−0.0641649			−0.0320825	−	0.999485i	$-0.510214\pi$
$17$	−0.264559			−0.0641649			−0.0320825	+	0.999485i	$0.510214\pi$
$18$	1.13905	+	2.55298i	0.268478	+	0.601744i
$19$	4.53959	−	4.53959i	1.04145	−	1.04145i	0.0423510	−	0.999103i	$-0.486515\pi$
$19$	4.53959	−	4.53959i	1.04145	−	1.04145i	0.999103	−	0.0423510i	$-0.0134848\pi$
$20$	−2.45072	+	0.132279i	−0.547997	+	0.0295786i
$21$		0			0
$22$	−5.55976	−	2.12921i	−1.18534	−	0.453948i
$23$			1.54621i			0.322407i	0.986921	+	0.161203i	$0.0515375\pi$
$23$			1.54621i			0.322407i	−0.986921	+	0.161203i	$0.948462\pi$
$24$	−1.30489	−	2.54621i	−0.266359	−	0.519743i
$25$		−	3.49412i		−	0.698824i
$26$	1.44498	−	3.77310i	0.283383	−	0.739967i
$27$	3.55976	+	3.55976i	0.685076	+	0.685076i
$28$		0			0
$29$	−0.328129	+	0.328129i	−0.0609320	+	0.0609320i	−0.736916	−	0.675984i	$-0.763719\pi$
$29$	−0.328129	+	0.328129i	−0.0609320	+	0.0609320i	0.675984	+	0.736916i	$0.263719\pi$
$30$	−1.60316	+	0.715276i	−0.292696	+	0.130591i
$31$	−6.04033			−1.08488			−0.542438	−	0.840096i	$-0.682499\pi$
$31$	−6.04033			−1.08488			−0.542438	+	0.840096i	$0.682499\pi$
$32$	−2.84756	−	4.88789i	−0.503381	−	0.864064i
$33$	−4.25841			−0.741294
$34$	−0.341677	+	0.152445i	−0.0585972	+	0.0261440i
$35$		0			0
$36$	2.94217	+	2.64082i	0.490362	+	0.440137i
$37$	6.64863	+	6.64863i	1.09303	+	1.09303i	0.995204	+	0.0978247i	$0.0311884\pi$
$37$	6.64863	+	6.64863i	1.09303	+	1.09303i	0.0978247	+	0.995204i	$0.468812\pi$
$38$	3.24706	−	8.47869i	0.526743	−	1.37543i
$39$		−	2.88995i		−	0.462763i
$40$	−3.08887	+	1.58300i	−0.488394	+	0.250294i
$41$			11.0327i			1.72302i	0.507741	+	0.861510i	$0.330481\pi$
$41$			11.0327i			1.72302i	−0.507741	+	0.861510i	$0.669519\pi$
$42$		0			0
$43$	3.38407	+	3.38407i	0.516066	+	0.516066i	0.916379	−	0.400312i	$-0.131098\pi$
$43$	3.38407	+	3.38407i	0.516066	+	0.516066i	−0.400312	+	0.916379i	$0.631098\pi$
$44$	−8.40731	+	0.453791i	−1.26745	+	0.0684116i
$45$	1.71528	−	1.71528i	0.255698	−	0.255698i
$46$	0.890960	+	1.99693i	0.131365	+	0.294431i
$47$	−3.12566			−0.455925			−0.227962	−	0.973670i	$-0.573206\pi$
$47$	−3.12566			−0.455925			−0.227962	+	0.973670i	$0.573206\pi$
$48$	−3.15244	−	2.53652i	−0.455016	−	0.366115i
$49$		0			0
$50$	−2.01339	−	4.51265i	−0.284736	−	0.638185i
$51$	−0.189233	+	0.189233i	−0.0264979	+	0.0264979i
$52$	−0.307963	−	5.70559i	−0.0427068	−	0.791222i
$53$	0.430552	+	0.430552i	0.0591409	+	0.0591409i	0.736059	−	0.676918i	$-0.236685\pi$
$53$	0.430552	+	0.430552i	0.0591409	+	0.0591409i	−0.676918	+	0.736059i	$0.736685\pi$
$54$	6.64863	+	2.54621i	0.904764	+	0.346495i
$55$			5.16599i			0.696582i
$56$		0			0
$57$		−	6.49412i		−	0.860167i
$58$	−0.234703	+	0.612853i	−0.0308180	+	0.0804715i
$59$	4.62640	+	4.62640i	0.602306	+	0.602306i	0.940924	−	0.338618i	$-0.109959\pi$
$59$	4.62640	+	4.62640i	0.602306	+	0.602306i	−0.338618	+	0.940924i	$0.609959\pi$
$60$	−1.65832	+	1.84756i	−0.214089	+	0.238518i
$61$	−4.86772	+	4.86772i	−0.623248	+	0.623248i	−0.946360	−	0.323113i	$-0.895271\pi$
$61$	−4.86772	+	4.86772i	−0.623248	+	0.623248i	0.323113	+	0.946360i	$0.395271\pi$
$62$	−7.80108	+	3.48057i	−0.990738	+	0.442033i
$63$		0			0
$64$	−6.49412	−	4.67187i	−0.811765	−	0.583984i
$65$	−3.50588			−0.434851
$66$	−5.49973	+	2.45379i	−0.676970	+	0.302041i
$67$	3.34374	−	3.34374i	0.408503	−	0.408503i	−0.472713	−	0.881216i	$-0.656725\pi$
$67$	3.34374	−	3.34374i	0.408503	−	0.408503i	0.881216	+	0.472713i	$0.156725\pi$
$68$	−0.353433	+	0.393764i	−0.0428601	+	0.0477509i
$69$	1.10597	+	1.10597i	0.133143	+	0.133143i
$70$		0			0
$71$			9.03885i			1.07271i	0.843991	+	0.536357i	$0.180200\pi$
$71$			9.03885i			1.07271i	−0.843991	+	0.536357i	$0.819800\pi$
$72$	5.32151	+	1.71528i	0.627146	+	0.202147i
$73$		−	14.8146i		−	1.73392i	−0.498377	−	0.866960i	$-0.666070\pi$
$73$		−	14.8146i		−	1.73392i	0.498377	−	0.866960i	$-0.333930\pi$
$74$	12.4178	+	4.75561i	1.44354	+	0.552828i
$75$	−2.49926	−	2.49926i	−0.288590	−	0.288590i
$76$	−0.692037	−	12.8212i	−0.0793820	−	1.47070i
$77$		0			0
$78$	−1.66525	−	3.73237i	−0.188553	−	0.422607i
$79$	12.5904			1.41653			0.708265	−	0.705947i	$-0.249478\pi$
$79$	12.5904			1.41653			0.708265	+	0.705947i	$0.249478\pi$
$80$	−3.07712	+	3.82432i	−0.344032	+	0.427572i
$81$	−0.837864			−0.0930960
$82$	6.35729	+	14.2487i	0.702045	+	1.57351i
$83$	0.715276	−	0.715276i	0.0785117	−	0.0785117i	−0.666760	−	0.745272i	$-0.732320\pi$
$83$	0.715276	−	0.715276i	0.0785117	−	0.0785117i	0.745272	+	0.666760i	$0.232320\pi$
$84$		0			0
$85$	0.229563	+	0.229563i	0.0248996	+	0.0248996i
$86$	6.32050	+	2.42055i	0.681557	+	0.261014i
$87$			0.469405i			0.0503255i
$88$	−10.5965	+	5.43055i	−1.12960	+	0.578899i
$89$			10.9924i			1.16519i	0.812763	+	0.582595i	$0.197962\pi$
$89$			10.9924i			1.16519i	−0.812763	+	0.582595i	$0.802038\pi$
$90$	1.22690	−	3.20366i	0.129326	−	0.337695i
$91$		0			0
$92$	2.30135	+	2.06564i	0.239932	+	0.215357i
$93$	−4.32050	+	4.32050i	−0.448015	+	0.448015i
$94$	−4.03679	+	1.80108i	−0.416363	+	0.185767i
$95$	−7.87820			−0.808286
$96$	−5.53298	−	1.45940i	−0.564707	−	0.148949i
$97$	14.2452			1.44638			0.723189	−	0.690650i	$-0.242675\pi$
$97$	14.2452			1.44638			0.723189	+	0.690650i	$0.242675\pi$
$98$		0			0
$99$	5.88434	−	5.88434i	0.591399	−	0.591399i
$100$	−5.20058	−	4.66792i	−0.520058	−	0.466792i
$101$	10.5299	+	10.5299i	1.04776	+	1.04776i	0.998801	+	0.0489638i	$0.0155919\pi$
$101$	10.5299	+	10.5299i	1.04776	+	1.04776i	0.0489638	+	0.998801i	$0.484408\pi$
$102$	−0.135353	+	0.353433i	−0.0134020	+	0.0349951i
$103$		−	12.9862i		−	1.27957i	−0.768554	−	0.639785i	$-0.779023\pi$
$103$		−	12.9862i		−	1.27957i	0.768554	−	0.639785i	$-0.220977\pi$
$104$	−3.68542	−	7.19130i	−0.361385	−	0.705165i
$105$		0			0
$106$	0.804151	+	0.307963i	0.0781060	+	0.0299121i
$107$	−1.24132	−	1.24132i	−0.120003	−	0.120003i	0.644555	−	0.764558i	$-0.277043\pi$
$107$	−1.24132	−	1.24132i	−0.120003	−	0.120003i	−0.764558	+	0.644555i	$0.777043\pi$
$108$	10.0539	−	0.542666i	0.967435	−	0.0522181i
$109$	−10.9535	+	10.9535i	−1.04916	+	1.04916i	−0.0504294	+	0.998728i	$0.516059\pi$
$109$	−10.9535	+	10.9535i	−1.04916	+	1.04916i	−0.998728	+	0.0504294i	$0.983941\pi$
$110$	2.97676	+	6.67187i	0.283823	+	0.636138i
$111$	9.51121			0.902764
$112$		0			0
$113$	7.63302			0.718054			0.359027	−	0.933327i	$-0.383109\pi$
$113$	7.63302			0.718054			0.359027	+	0.933327i	$0.383109\pi$
$114$	−3.74206	−	8.38715i	−0.350476	−	0.785528i
$115$	1.34168	−	1.34168i	0.125112	−	0.125112i
$116$	0.0500215	+	0.926739i	0.00464438	+	0.0860456i
$117$	3.99338	+	3.99338i	0.369188	+	0.369188i
$118$	8.64082	+	3.30915i	0.795452	+	0.304632i
$119$		0			0
$120$	−1.07712	+	3.34168i	−0.0983270	+	0.305052i
$121$			6.72221i			0.611110i
$122$	−3.48176	+	9.09154i	−0.315224	+	0.823110i
$123$	7.89143	+	7.89143i	0.711546	+	0.711546i
$124$	−8.06949	+	8.99031i	−0.724662	+	0.807354i
$125$	−7.37052	+	7.37052i	−0.659240	+	0.659240i
$126$		0			0
$127$	−10.7393			−0.952959			−0.476479	−	0.879186i	$-0.658087\pi$
$127$	−10.7393			−0.952959			−0.476479	+	0.879186i	$0.658087\pi$
$128$	−11.0792	−	2.29166i	−0.979271	−	0.202556i
$129$	4.84109			0.426234
$130$	−4.52784	+	2.02017i	−0.397117	+	0.177180i
$131$	12.8869	−	12.8869i	1.12593	−	1.12593i	0.135100	−	0.990832i	$-0.456865\pi$
$131$	12.8869	−	12.8869i	1.12593	−	1.12593i	0.990832	−	0.135100i	$-0.0431355\pi$
$132$	−5.68896	+	6.33813i	−0.495161	+	0.551664i
$133$		0			0
$134$	2.39170	−	6.24518i	0.206611	−	0.539501i
$135$		−	6.17775i		−	0.531696i
$136$	−0.229563	+	0.712202i	−0.0196849	+	0.0610708i
$137$			7.34374i			0.627418i	0.949519	+	0.313709i	$0.101572\pi$
$137$			7.34374i			0.627418i	−0.949519	+	0.313709i	$0.898428\pi$
$138$	2.06564	+	0.791071i	0.175839	+	0.0673404i
$139$	−8.36184	−	8.36184i	−0.709242	−	0.709242i	0.257134	−	0.966376i	$-0.417222\pi$
$139$	−8.36184	−	8.36184i	−0.709242	−	0.709242i	−0.966376	+	0.257134i	$0.917222\pi$
$140$		0			0
$141$	−2.23571	+	2.23571i	−0.188281	+	0.188281i
$142$	5.20839	+	11.6737i	0.437078	+	0.979632i
$143$	−12.0271			−1.00576
$144$	7.86110	−	0.851098i	0.655092	−	0.0709248i
$145$	0.569448			0.0472901
$146$	−8.53652	−	19.1331i	−0.706487	−	1.58346i
$147$		0			0
$148$	18.7778	−	1.01355i	1.54353	−	0.0833132i
$149$	−12.8782	−	12.8782i	−1.05502	−	1.05502i	−0.998395	−	0.0566275i	$-0.981965\pi$
$149$	−12.8782	−	12.8782i	−1.05502	−	1.05502i	−0.0566275	−	0.998395i	$-0.518035\pi$
$150$	−4.66792	−	1.78766i	−0.381134	−	0.145962i
$151$		−	13.0171i		−	1.05932i	−0.848211	−	0.529658i	$-0.822320\pi$
$151$		−	13.0171i		−	1.05932i	0.848211	−	0.529658i	$-0.177680\pi$
$152$	−8.28165	−	16.1598i	−0.671731	−	1.31074i
$153$		−	0.522969i		−	0.0422796i
$154$		0			0
$155$	5.24132	+	5.24132i	0.420993	+	0.420993i
$156$	−4.30135	−	3.86079i	−0.344383	−	0.309111i
$157$	−14.6570	+	14.6570i	−1.16976	+	1.16976i	−0.187493	+	0.982266i	$0.560036\pi$
$157$	−14.6570	+	14.6570i	−1.16976	+	1.16976i	−0.982266	+	0.187493i	$0.939964\pi$
$158$	16.2605	−	7.25487i	1.29361	−	0.577166i
$159$	0.615927			0.0488462
$160$	−1.77044	+	6.71220i	−0.139965	+	0.530646i
$161$		0			0
$162$	−1.08210	+	0.482796i	−0.0850178	+	0.0379321i
$163$	4.44764	−	4.44764i	0.348366	−	0.348366i	−0.511134	−	0.859501i	$-0.670775\pi$
$163$	4.44764	−	4.44764i	0.348366	−	0.348366i	0.859501	+	0.511134i	$0.170775\pi$
$164$	16.4209	+	14.7390i	1.28225	+	1.15092i
$165$	3.69511	+	3.69511i	0.287664	+	0.287664i
$166$	0.511620	−	1.33594i	0.0397094	−	0.103689i
$167$		−	5.45765i		−	0.422326i	−0.977451	−	0.211163i	$-0.932275\pi$
$167$		−	5.45765i		−	0.422326i	0.977451	−	0.211163i	$-0.0677250\pi$
$168$		0			0
$169$			4.83786i			0.372143i
$170$	0.428760	+	0.164201i	0.0328844	+	0.0125936i
$171$	8.97369	+	8.97369i	0.686235	+	0.686235i
$172$	9.55769	−	0.515884i	0.728767	−	0.0393358i
$173$	−11.6223	+	11.6223i	−0.883629	+	0.883629i	−0.993901	−	0.110273i	$-0.964828\pi$
$173$	−11.6223	+	11.6223i	−0.883629	+	0.883629i	0.110273	+	0.993901i	$0.464828\pi$
$174$	0.270482	+	0.606236i	0.0205052	+	0.0459586i
$175$		0			0
$176$	−10.5562	+	13.1195i	−0.795705	+	0.988921i
$177$	6.61831			0.497462
$178$	6.33405	+	14.1966i	0.474757	+	1.06408i
$179$	12.9418	−	12.9418i	0.967313	−	0.967313i	−0.0321695	−	0.999482i	$-0.510242\pi$
$179$	12.9418	−	12.9418i	0.967313	−	0.967313i	0.999482	+	0.0321695i	$0.0102416\pi$
$180$	−0.261485	−	4.84448i	−0.0194899	−	0.361086i
$181$	−1.39069	−	1.39069i	−0.103369	−	0.103369i	0.653531	−	0.756900i	$-0.273287\pi$
$181$	−1.39069	−	1.39069i	−0.103369	−	0.103369i	−0.756900	+	0.653531i	$0.773287\pi$
$182$		0			0
$183$			6.96353i			0.514759i
$184$	4.16245	+	1.34168i	0.306860	+	0.0989098i
$185$		−	11.5383i		−	0.848313i
$186$	−3.09035	+	8.06949i	−0.226596	+	0.591684i
$187$	0.787528	+	0.787528i	0.0575898	+	0.0575898i
$188$	−4.17568	+	4.65217i	−0.304543	+	0.339295i
$189$		0			0
$190$	−10.1747	+	4.53959i	−0.738149	+	0.329337i
$191$	−3.47088			−0.251144			−0.125572	−	0.992084i	$-0.540077\pi$
$191$	−3.47088			−0.251144			−0.125572	+	0.992084i	$0.540077\pi$
$192$	−7.98677	+	1.30341i	−0.576395	+	0.0940657i
$193$	−7.58654			−0.546091			−0.273046	−	0.962001i	$-0.588031\pi$
$193$	−7.58654			−0.546091			−0.273046	+	0.962001i	$0.588031\pi$
$194$	18.3976	−	8.20839i	1.32087	−	0.589328i
$195$	−2.50767	+	2.50767i	−0.179578	+	0.179578i
$196$		0			0
$197$	7.82786	+	7.82786i	0.557712	+	0.557712i	0.928655	−	0.370944i	$-0.120966\pi$
$197$	7.82786	+	7.82786i	0.557712	+	0.557712i	−0.370944	+	0.928655i	$0.620966\pi$
$198$	4.20893	−	10.9903i	0.299116	−	0.781047i
$199$			19.6696i			1.39434i	0.716906	+	0.697170i	$0.245558\pi$
$199$			19.6696i			1.39434i	−0.716906	+	0.697170i	$0.754442\pi$
$200$	−9.40630	−	3.03192i	−0.665126	−	0.214389i
$201$		−	4.78340i		−	0.337395i
$202$	19.6669	+	7.53178i	1.38376	+	0.529935i
$203$		0			0
$204$	0.0288475	+	0.534452i	0.00201973	+	0.0374192i
$205$	9.57331	−	9.57331i	0.668629	−	0.668629i
$206$	−7.48295	−	16.7717i	−0.521362	−	1.16854i
$207$	−3.05648			−0.212440
$208$	−8.90350	−	7.16393i	−0.617347	−	0.496729i
$209$	−27.0266			−1.86947
$210$		0			0
$211$	−1.13890	+	1.13890i	−0.0784048	+	0.0784048i	−0.745222	−	0.666817i	$-0.767656\pi$
$211$	−1.13890	+	1.13890i	−0.0784048	+	0.0784048i	0.666817	+	0.745222i	$0.267656\pi$
$212$	1.21601	−	0.0656353i	0.0835162	−	0.00450785i
$213$	6.46527	+	6.46527i	0.442993	+	0.442993i
$214$	−2.31844	−	0.887886i	−0.158485	−	0.0606946i
$215$		−	5.87286i		−	0.400526i
$216$	12.6719	−	6.49412i	0.862212	−	0.441869i
$217$		0			0
$218$	−7.83479	+	20.4581i	−0.530639	+	1.38560i
$219$	−10.5965	−	10.5965i	−0.716048	−	0.716048i
$220$	7.68896	+	6.90143i	0.518390	+	0.465295i
$221$	−0.534452	+	0.534452i	−0.0359512	+	0.0359512i
$222$	12.2837	−	5.48057i	0.824429	−	0.367832i
$223$	8.02710			0.537534			0.268767	−	0.963205i	$-0.413384\pi$
$223$	8.02710			0.537534			0.268767	+	0.963205i	$0.413384\pi$
$224$		0			0
$225$	6.90704			0.460469
$226$	9.85803	−	4.39832i	0.655746	−	0.292572i
$227$	3.57431	−	3.57431i	0.237236	−	0.237236i	−0.578469	−	0.815704i	$-0.696350\pi$
$227$	3.57431	−	3.57431i	0.237236	−	0.237236i	0.815704	+	0.578469i	$0.196350\pi$
$228$	−9.66572	−	8.67573i	−0.640128	−	0.574564i
$229$	−0.636092	−	0.636092i	−0.0420342	−	0.0420342i	0.685777	−	0.727811i	$-0.259462\pi$
$229$	−0.636092	−	0.636092i	−0.0420342	−	0.0420342i	−0.727811	+	0.685777i	$0.759462\pi$
$230$	0.959669	−	2.50588i	0.0632787	−	0.165233i
$231$		0			0
$232$	0.598610	+	1.16806i	0.0393007	+	0.0766868i
$233$			24.5633i			1.60920i	0.593820	+	0.804598i	$0.297619\pi$
$233$			24.5633i			1.60920i	−0.593820	+	0.804598i	$0.702381\pi$
$234$	7.45852	+	2.85637i	0.487579	+	0.186727i
$235$	2.71220	+	2.71220i	0.176925	+	0.176925i
$236$	13.0664	−	0.705270i	0.850551	−	0.0459092i
$237$	9.00561	−	9.00561i	0.584977	−	0.584977i
$238$		0			0
$239$	−29.3026			−1.89543			−0.947714	−	0.319122i	$-0.896612\pi$
$239$	−29.3026			−1.89543			−0.947714	+	0.319122i	$0.896612\pi$
$240$	0.534452	+	4.93643i	0.0344988	+	0.318645i
$241$	−7.94029			−0.511479			−0.255739	−	0.966746i	$-0.582319\pi$
$241$	−7.94029			−0.511479			−0.255739	+	0.966746i	$0.582319\pi$
$242$	3.87349	+	8.68172i	0.248997	+	0.558082i
$243$	−11.2786	+	11.2786i	−0.723521	+	0.723521i
$244$	0.742058	+	13.7480i	0.0475054	+	0.880124i
$245$		0			0
$246$	14.7390	+	5.64455i	0.939723	+	0.359883i
$247$		−	18.3415i		−	1.16704i
$248$	−5.24132	+	16.2608i	−0.332824	+	1.03256i
$249$		−	1.02324i		−	0.0648452i
$250$	−5.27196	+	13.7661i	−0.333428	+	0.870643i
$251$	−6.93336	−	6.93336i	−0.437630	−	0.437630i	0.453584	−	0.891214i	$-0.350145\pi$
$251$	−6.93336	−	6.93336i	−0.437630	−	0.437630i	−0.891214	+	0.453584i	$0.850145\pi$
$252$		0			0
$253$	4.60269	−	4.60269i	0.289369	−	0.289369i
$254$	−13.8698	+	6.18822i	−0.870268	+	0.388284i
$255$	0.328402			0.0205653
$256$	−15.6293	+	3.42440i	−0.976828	+	0.214025i
$257$	8.30489			0.518045			0.259022	−	0.965871i	$-0.416600\pi$
$257$	8.30489			0.518045			0.259022	+	0.965871i	$0.416600\pi$
$258$	6.25226	−	2.78955i	0.389249	−	0.173670i
$259$		0			0
$260$	−4.68363	+	5.21808i	−0.290466	+	0.323612i
$261$	−0.648632	−	0.648632i	−0.0401493	−	0.0401493i
$262$	9.21767	−	24.0691i	0.569470	−	1.48699i
$263$			13.8535i			0.854242i	0.904194	+	0.427121i	$0.140472\pi$
$263$			13.8535i			0.854242i	−0.904194	+	0.427121i	$0.859528\pi$
$264$	−3.69511	+	11.4638i	−0.227418	+	0.705548i
$265$		−	0.747198i		−	0.0459000i
$266$		0			0
$267$	7.86258	+	7.86258i	0.481182	+	0.481182i
$268$	−0.509736	−	9.44379i	−0.0311371	−	0.576871i
$269$	−1.28620	+	1.28620i	−0.0784211	+	0.0784211i	−0.745229	−	0.666808i	$-0.767660\pi$
$269$	−1.28620	+	1.28620i	−0.0784211	+	0.0784211i	0.666808	+	0.745229i	$0.267660\pi$
$270$	−3.55976	−	7.97855i	−0.216640	−	0.485559i
$271$	16.3703			0.994425			0.497212	−	0.867629i	$-0.334357\pi$
$271$	16.3703			0.994425			0.497212	+	0.867629i	$0.334357\pi$
$272$	0.113906	+	1.05209i	0.00690658	+	0.0637921i
$273$		0			0
$274$	4.23163	+	9.48443i	0.255642	+	0.572975i
$275$	−10.4012	+	10.4012i	−0.627214	+	0.627214i
$276$	3.12360	−	0.168599i	0.188018	−	0.0101484i
$277$	8.26842	+	8.26842i	0.496801	+	0.496801i	0.910441	−	0.413640i	$-0.135743\pi$
$277$	8.26842	+	8.26842i	0.496801	+	0.496801i	−0.413640	+	0.910441i	$0.635743\pi$
$278$	−15.6176	−	5.98102i	−0.936681	−	0.358718i
$279$		−	11.9403i		−	0.714846i
$280$		0			0
$281$		−	30.2126i		−	1.80233i	−0.433476	−	0.901165i	$-0.642713\pi$
$281$		−	30.2126i		−	1.80233i	0.433476	−	0.901165i	$-0.357287\pi$
$282$	−1.59915	+	4.17568i	−0.0952280	+	0.248658i
$283$	11.8077	+	11.8077i	0.701895	+	0.701895i	0.964817	−	0.262922i	$-0.0846863\pi$
$283$	11.8077	+	11.8077i	0.701895	+	0.701895i	−0.262922	+	0.964817i	$0.584686\pi$
$284$	13.4533	+	12.0753i	0.798304	+	0.716539i
$285$	−5.63508	+	5.63508i	−0.333794	+	0.333794i
$286$	−15.5330	+	6.93028i	−0.918484	+	0.409796i
$287$		0			0
$288$	9.66218	−	5.62894i	0.569349	−	0.331688i
$289$	−16.9300			−0.995883
$290$	0.735441	−	0.328129i	0.0431866	−	0.0192684i
$291$	10.1892	−	10.1892i	0.597303	−	0.597303i
$292$	−22.0498	−	19.7914i	−1.29037	−	1.15820i
$293$	−15.3849	−	15.3849i	−0.898793	−	0.898793i	0.0965365	−	0.995329i	$-0.469224\pi$
$293$	−15.3849	−	15.3849i	−0.898793	−	0.898793i	−0.995329	+	0.0965365i	$0.969224\pi$
$294$		0			0
$295$		−	8.02885i		−	0.467458i
$296$	23.6675	−	12.1292i	1.37565	−	0.704996i
$297$		−	21.1931i		−	1.22975i
$298$	−24.0529	−	9.21146i	−1.39335	−	0.533606i
$299$	3.12360	+	3.12360i	0.180642	+	0.180642i
$300$	−7.05870	+	0.380999i	−0.407534	+	0.0219970i
$301$		0			0
$302$	−7.50074	−	16.8116i	−0.431619	−	0.967396i
$303$	15.0636			0.865379
$304$	−20.0074	−	16.0983i	−1.14750	−	0.923303i
$305$	8.44764			0.483711
$306$	−0.301347	−	0.675414i	−0.0172268	−	0.0386108i
$307$	8.15291	−	8.15291i	0.465311	−	0.465311i	−0.435080	−	0.900392i	$-0.643280\pi$
$307$	8.15291	−	8.15291i	0.465311	−	0.465311i	0.900392	+	0.435080i	$0.143280\pi$
$308$		0			0
$309$	−9.28874	−	9.28874i	−0.528418	−	0.528418i
$310$	9.78932	+	3.74899i	0.555996	+	0.212928i
$311$		−	31.1072i		−	1.76393i	−0.471316	−	0.881964i	$-0.656221\pi$
$311$		−	31.1072i		−	1.76393i	0.471316	−	0.881964i	$-0.343779\pi$
$312$	−7.77985	−	2.50767i	−0.440448	−	0.141969i
$313$		−	3.17986i		−	0.179736i	−0.995954	−	0.0898681i	$-0.971355\pi$
$313$		−	3.17986i		−	0.179736i	0.995954	−	0.0898681i	$-0.0286445\pi$
$314$	−10.4838	+	27.3753i	−0.591637	+	1.54488i
$315$		0			0
$316$	16.8200	−	18.7393i	0.946197	−	1.05417i
$317$	1.56945	−	1.56945i	0.0881490	−	0.0881490i	−0.661657	−	0.749806i	$-0.730147\pi$
$317$	1.56945	−	1.56945i	0.0881490	−	0.0881490i	0.749806	+	0.661657i	$0.230147\pi$
$318$	0.795468	−	0.354911i	0.0446077	−	0.0199024i
$319$	1.95352			0.109376
$320$	1.58120	+	9.68896i	0.0883920	+	0.541629i
$321$	−1.77577			−0.0991139
$322$		0			0
$323$	−1.20099	+	1.20099i	−0.0668248	+	0.0668248i
$324$	−1.11933	+	1.24706i	−0.0621852	+	0.0692812i
$325$	−7.05870	−	7.05870i	−0.391546	−	0.391546i
$326$	3.18129	−	8.30695i	0.176195	−	0.460080i
$327$			15.6696i			0.866530i
$328$	29.7004	+	9.57331i	1.63993	+	0.528597i
$329$		0			0
$330$	6.90143	+	2.64302i	0.379911	+	0.145494i
$331$	1.95967	+	1.95967i	0.107713	+	0.107713i	0.758909	−	0.651196i	$-0.225733\pi$
$331$	1.95967	+	1.95967i	0.107713	+	0.107713i	−0.651196	+	0.758909i	$0.725733\pi$
$332$	−0.109040	−	2.02017i	−0.00598435	−	0.110871i
$333$	−13.1428	+	13.1428i	−0.720218	+	0.720218i
$334$	−3.14482	−	7.04854i	−0.172077	−	0.385679i
$335$	−5.80287			−0.317045
$336$		0			0
$337$	−28.7067			−1.56375			−0.781876	−	0.623434i	$-0.785737\pi$
$337$	−28.7067			−1.56375			−0.781876	+	0.623434i	$0.785737\pi$
$338$	2.78769	+	6.24809i	0.151630	+	0.339851i
$339$	5.45971	−	5.45971i	0.296531	−	0.296531i
$340$	0.648359	−	0.0349957i	0.0351622	−	0.00189791i
$341$	17.9806	+	17.9806i	0.973705	+	0.973705i
$342$	16.7603	+	6.41866i	0.906295	+	0.347082i
$343$		0			0
$344$	12.0465	−	6.17362i	0.649503	−	0.332859i
$345$		−	1.91934i		−	0.103334i
$346$	−8.31316	+	21.7072i	−0.446919	+	1.16699i
$347$	4.41880	+	4.41880i	0.237213	+	0.237213i	0.815695	−	0.578482i	$-0.196355\pi$
$347$	4.41880	+	4.41880i	0.237213	+	0.237213i	−0.578482	+	0.815695i	$0.696355\pi$
$348$	0.698653	+	0.627095i	0.0374518	+	0.0336158i
$349$	7.46427	−	7.46427i	0.399553	−	0.399553i	−0.478522	−	0.878075i	$-0.658827\pi$
$349$	7.46427	−	7.46427i	0.399553	−	0.399553i	0.878075	+	0.478522i	$0.158827\pi$
$350$		0			0
$351$	14.3826			0.767686
$352$	−6.07358	+	23.0266i	−0.323723	+	1.22732i
$353$	6.70687			0.356971			0.178485	−	0.983943i	$-0.442880\pi$
$353$	6.70687			0.356971			0.178485	+	0.983943i	$0.442880\pi$
$354$	8.54753	−	3.81362i	0.454296	−	0.202691i
$355$	7.84320	−	7.84320i	0.416274	−	0.416274i
$356$	16.3608	+	14.6851i	0.867122	+	0.778309i
$357$		0			0
$358$	9.25693	−	24.1716i	0.489244	−	1.27751i
$359$			11.7540i			0.620353i	0.950679	+	0.310176i	$0.100388\pi$
$359$			11.7540i			0.620353i	−0.950679	+	0.310176i	$0.899612\pi$
$360$	−3.12921	−	6.10597i	−0.164924	−	0.321813i
$361$		−	22.2158i		−	1.16925i
$362$	−2.59742	−	0.994727i	−0.136517	−	0.0522817i
$363$	4.80823	+	4.80823i	0.252367	+	0.252367i
$364$		0			0
$365$	−12.8550	+	12.8550i	−0.672859	+	0.672859i
$366$	4.01254	+	8.99338i	0.209739	+	0.470092i
$367$	−34.4703			−1.79934			−0.899669	−	0.436573i	$-0.856192\pi$
$367$	−34.4703			−1.79934			−0.899669	+	0.436573i	$0.856192\pi$
$368$	6.14890	−	0.665723i	0.320534	−	0.0347032i
$369$	−21.8090			−1.13533
$370$	−6.64863	−	14.9017i	−0.345646	−	0.774703i
$371$		0			0
$372$	0.658638	+	12.2025i	0.0341488	+	0.632668i
$373$	−8.79753	−	8.79753i	−0.455519	−	0.455519i	0.441662	−	0.897181i	$-0.354389\pi$
$373$	−8.79753	−	8.79753i	−0.455519	−	0.455519i	−0.897181	+	0.441662i	$0.854389\pi$
$374$	1.47088	+	0.563300i	0.0760575	+	0.0291275i
$375$			10.5439i			0.544486i
$376$	−2.71220	+	8.41440i	−0.139871	+	0.433939i
$377$			1.32575i			0.0682795i
$378$		0			0
$379$	−0.171601	−	0.171601i	−0.00881456	−	0.00881456i	0.702686	−	0.711500i	$-0.251984\pi$
$379$	−0.171601	−	0.171601i	−0.00881456	−	0.00881456i	−0.711500	+	0.702686i	$0.751984\pi$
$380$	−10.5248	+	11.7258i	−0.539909	+	0.601518i
$381$	−7.68156	+	7.68156i	−0.393538	+	0.393538i
$382$	−4.48264	+	2.00000i	−0.229352	+	0.102329i
$383$	−21.7161			−1.10964			−0.554819	−	0.831971i	$-0.687213\pi$
$383$	−21.7161			−1.10964			−0.554819	+	0.831971i	$0.687213\pi$
$384$	−9.56384	+	6.28551i	−0.488053	+	0.320756i
$385$		0			0
$386$	−9.79800	+	4.37153i	−0.498705	+	0.222505i
$387$	−6.68950	+	6.68950i	−0.340047	+	0.340047i
$388$	19.0306	−	21.2022i	0.966134	−	1.07638i
$389$	11.3320	+	11.3320i	0.574555	+	0.574555i	0.933398	−	0.358843i	$-0.116829\pi$
$389$	11.3320	+	11.3320i	0.574555	+	0.574555i	−0.358843	+	0.933398i	$0.616829\pi$
$390$	−1.79368	+	4.68363i	−0.0908263	+	0.237165i
$391$		−	0.409063i		−	0.0206872i
$392$		0			0
$393$		−	18.4353i		−	0.929940i
$394$	14.6203	+	5.59908i	0.736558	+	0.282078i
$395$	−10.9249	−	10.9249i	−0.549694	−	0.549694i
$396$	−0.897037	−	16.6192i	−0.0450778	−	0.835148i
$397$	14.7477	−	14.7477i	0.740164	−	0.740164i	−0.232445	−	0.972609i	$-0.574673\pi$
$397$	14.7477	−	14.7477i	0.740164	−	0.740164i	0.972609	+	0.232445i	$0.0746727\pi$
$398$	11.3341	+	25.4032i	0.568125	+	1.27335i
$399$		0			0
$400$	−13.8953	+	1.50440i	−0.694764	+	0.0752200i
$401$	−0.146885			−0.00733506			−0.00366753	−	0.999993i	$-0.501167\pi$
$401$	−0.146885			−0.00733506			−0.00366753	+	0.999993i	$0.501167\pi$
$402$	−2.75630	−	6.17775i	−0.137472	−	0.308118i
$403$	−12.2025	+	12.2025i	−0.607848	+	0.607848i
$404$	29.7398	−	1.60523i	1.47961	−	0.0798630i
$405$	0.727032	+	0.727032i	0.0361265	+	0.0361265i
$406$		0			0
$407$		−	39.5828i		−	1.96205i
$408$	0.345220	+	0.673622i	0.0170909	+	0.0333492i
$409$		−	2.27164i		−	0.112326i	−0.998422	−	0.0561628i	$-0.982113\pi$
$409$		−	2.27164i		−	0.112326i	0.998422	−	0.0561628i	$-0.0178866\pi$
$410$	6.84756	−	17.8803i	0.338177	−	0.883043i
$411$	5.25280	+	5.25280i	0.259102	+	0.259102i
$412$	−19.3284	−	17.3488i	−0.952244	−	0.854712i
$413$		0			0
$414$	−3.94744	+	1.76121i	−0.194006	+	0.0865590i
$415$	−1.24132			−0.0609340
$416$	−15.6269	−	4.12180i	−0.766170	−	0.202088i
$417$	−11.9620			−0.585784
$418$	−34.9048	+	15.5733i	−1.70725	+	0.761715i
$419$	−19.3654	+	19.3654i	−0.946061	+	0.946061i	−0.998618	−	0.0525570i	$-0.983263\pi$
$419$	−19.3654	+	19.3654i	−0.946061	+	0.946061i	0.0525570	+	0.998618i	$0.483263\pi$
$420$		0			0
$421$	8.11005	+	8.11005i	0.395260	+	0.395260i	0.876557	−	0.481298i	$-0.159834\pi$
$421$	8.11005	+	8.11005i	0.395260	+	0.395260i	−0.481298	+	0.876557i	$0.659834\pi$
$422$	−0.814625	+	2.12714i	−0.0396553	+	0.103548i
$423$		−	6.17869i		−	0.300418i
$424$	1.53266	−	0.785463i	0.0744326	−	0.0381454i
$425$			0.924401i			0.0448400i
$426$	12.0753	+	4.62446i	0.585051	+	0.224056i
$427$		0			0
$428$	−3.50588	+	0.189233i	−0.169463	+	0.00914690i
$429$	−8.60269	+	8.60269i	−0.415342	+	0.415342i
$430$	−3.38407	−	7.58479i	−0.163194	−	0.365771i
$431$	−10.7658			−0.518569			−0.259284	−	0.965801i	$-0.583487\pi$
$431$	−10.7658			−0.518569			−0.259284	+	0.965801i	$0.583487\pi$
$432$	12.6236	−	15.6890i	0.607355	−	0.754836i
$433$	−4.99439			−0.240015			−0.120008	−	0.992773i	$-0.538292\pi$
$433$	−4.99439			−0.240015			−0.120008	+	0.992773i	$0.538292\pi$
$434$		0			0
$435$	0.407313	−	0.407313i	0.0195291	−	0.0195291i
$436$	1.66981	+	30.9362i	0.0799692	+	1.48158i
$437$	7.01916	+	7.01916i	0.335772	+	0.335772i
$438$	−19.7914	−	7.57945i	−0.945669	−	0.362160i
$439$			1.69924i			0.0811004i	0.999178	+	0.0405502i	$0.0129111\pi$
$439$			1.69924i			0.0811004i	−0.999178	+	0.0405502i	$0.987089\pi$
$440$	13.9070	+	4.48264i	0.662992	+	0.213701i
$441$		0			0
$442$	−0.382281	+	0.998208i	−0.0181833	+	0.0474799i
$443$	−7.90291	−	7.90291i	−0.375479	−	0.375479i	0.493989	−	0.869468i	$-0.335538\pi$
$443$	−7.90291	−	7.90291i	−0.375479	−	0.375479i	−0.869468	+	0.493989i	$0.835538\pi$
$444$	12.7064	−	14.1563i	0.603018	−	0.671828i
$445$	9.53831	−	9.53831i	0.452159	−	0.452159i
$446$	10.3670	−	4.62539i	0.490891	−	0.219019i
$447$	−18.4229			−0.871375
$448$		0			0
$449$	4.05419			0.191329			0.0956646	−	0.995414i	$-0.469502\pi$
$449$	4.05419			0.191329			0.0956646	+	0.995414i	$0.469502\pi$
$450$	8.92043	−	3.97999i	0.420513	−	0.187619i
$451$	32.8417	−	32.8417i	1.54646	−	1.54646i
$452$	10.1972	−	11.3608i	0.479637	−	0.534369i
$453$	−9.31081	−	9.31081i	−0.437460	−	0.437460i
$454$	2.55662	−	6.67582i	0.119988	−	0.313312i
$455$		0			0
$456$	−17.4824	−	5.63508i	−0.818689	−	0.263887i
$457$		−	10.1498i		−	0.474789i	−0.971413	−	0.237395i	$-0.923707\pi$
$457$		−	10.1498i		−	0.474789i	0.971413	−	0.237395i	$-0.0762935\pi$
$458$	−1.18804	−	0.454981i	−0.0555136	−	0.0212599i
$459$	−0.941765	−	0.941765i	−0.0439578	−	0.0439578i
$460$	−0.204532	−	3.78932i	−0.00953633	−	0.176678i
$461$	−1.02609	+	1.02609i	−0.0477897	+	0.0477897i	−0.730598	−	0.682808i	$-0.760759\pi$
$461$	−1.02609	+	1.02609i	−0.0477897	+	0.0477897i	0.682808	+	0.730598i	$0.260759\pi$
$462$		0			0
$463$	10.5945			0.492369			0.246185	−	0.969223i	$-0.420823\pi$
$463$	10.5945			0.492369			0.246185	+	0.969223i	$0.420823\pi$
$464$	1.44617	+	1.16361i	0.0671366	+	0.0540194i
$465$	7.49798			0.347710
$466$	14.1539	+	31.7235i	0.655668	+	1.46956i
$467$	−9.26741	+	9.26741i	−0.428844	+	0.428844i	−0.888235	−	0.459390i	$-0.848068\pi$
$467$	−9.26741	+	9.26741i	−0.428844	+	0.428844i	0.459390	+	0.888235i	$0.348068\pi$
$468$	11.2786	−	0.608770i	0.521352	−	0.0281404i
$469$		0			0
$470$	5.06564	+	1.93997i	0.233660	+	0.0894843i
$471$			20.9677i			0.966139i
$472$	16.4689	−	8.44002i	0.758041	−	0.388483i
$473$		−	20.1472i		−	0.926367i
$474$	6.44149	−	16.8200i	0.295868	−	0.772566i
$475$	−15.8619	−	15.8619i	−0.727793	−	0.727793i
$476$		0			0
$477$	−0.851098	+	0.851098i	−0.0389691	+	0.0389691i
$478$	−37.8443	+	16.8848i	−1.73096	+	0.772293i
$479$	−33.4766			−1.52958			−0.764792	−	0.644277i	$-0.777158\pi$
$479$	−33.4766			−1.52958			−0.764792	+	0.644277i	$0.777158\pi$
$480$	3.53473	+	6.06743i	0.161337	+	0.276939i
$481$	26.8627			1.22483
$482$	−10.2549	+	4.57537i	−0.467096	+	0.208402i
$483$		0			0
$484$	10.0052	+	8.98044i	0.454782	+	0.408202i
$485$	−12.3608	−	12.3608i	−0.561277	−	0.561277i
$486$	−8.06729	+	21.0652i	−0.365940	+	0.955538i
$487$		−	23.0248i		−	1.04335i	−0.853143	−	0.521677i	$-0.825307\pi$
$487$		−	23.0248i		−	1.04335i	0.853143	−	0.521677i	$-0.174693\pi$
$488$	8.88026	+	17.3279i	0.401991	+	0.784397i
$489$		−	6.36258i		−	0.287726i
$490$		0			0
$491$	−21.9341	−	21.9341i	−0.989874	−	0.989874i	0.0100754	−	0.999949i	$-0.496793\pi$
$491$	−21.9341	−	21.9341i	−0.989874	−	0.989874i	−0.999949	+	0.0100754i	$0.996793\pi$
$492$	22.2879	−	1.20301i	1.00482	−	0.0542357i
$493$	0.0868093	−	0.0868093i	0.00390970	−	0.00390970i
$494$	−10.5688	−	23.6880i	−0.475511	−	1.06577i
$495$	−10.2119			−0.458992
$496$	2.60068	+	24.0209i	0.116774	+	1.07857i
$497$		0			0
$498$	−0.589613	−	1.32151i	−0.0264212	−	0.0592184i
$499$	6.12180	−	6.12180i	0.274050	−	0.274050i	−0.556678	−	0.830728i	$-0.687924\pi$
$499$	6.12180	−	6.12180i	0.274050	−	0.274050i	0.830728	+	0.556678i	$0.187924\pi$
$500$	1.12360	+	20.8167i	0.0502488	+	0.930951i
$501$	−3.90372	−	3.90372i	−0.174406	−	0.174406i
$502$	−12.9496	−	4.95926i	−0.577968	−	0.221343i
$503$			11.5286i			0.514034i	0.966407	+	0.257017i	$0.0827396\pi$
$503$			11.5286i			0.514034i	−0.966407	+	0.257017i	$0.917260\pi$
$504$		0			0
$505$		−	18.2740i		−	0.813183i
$506$	3.29220	−	8.59655i	0.146356	−	0.382163i
$507$	3.46041	+	3.46041i	0.153682	+	0.153682i
$508$	−14.3470	+	15.9842i	−0.636546	+	0.709182i
$509$	17.9337	−	17.9337i	0.794896	−	0.794896i	−0.187390	−	0.982286i	$-0.560003\pi$
$509$	17.9337	−	17.9337i	0.794896	−	0.794896i	0.982286	+	0.187390i	$0.0600027\pi$
$510$	0.424131	−	0.189233i	0.0187808	−	0.00837936i
$511$		0			0
$512$	−18.2119	+	13.4285i	−0.804861	+	0.593463i
$513$	32.3197			1.42695
$514$	10.7258	−	4.78546i	0.473093	−	0.211078i
$515$	−11.2684	+	11.2684i	−0.496546	+	0.496546i
$516$	6.46739	−	7.20539i	0.284711	−	0.317199i
$517$	9.30435	+	9.30435i	0.409205	+	0.409205i
$518$		0			0
$519$			16.6263i			0.729815i
$520$	−3.04212	+	9.43795i	−0.133406	+	0.413882i
$521$		−	0.287525i		−	0.0125967i	−0.999980	−	0.00629835i	$-0.997995\pi$
$521$		−	0.287525i		−	0.0125967i	0.999980	−	0.00629835i	$-0.00200484\pi$
$522$	−1.21146	−	0.463951i	−0.0530243	−	0.0203066i
$523$	3.84300	+	3.84300i	0.168043	+	0.168043i	0.786119	−	0.618076i	$-0.212087\pi$
$523$	3.84300	+	3.84300i	0.168043	+	0.168043i	−0.618076	+	0.786119i	$0.712087\pi$
$524$	−1.96454	−	36.3966i	−0.0858211	−	1.58999i
$525$		0			0
$526$	7.98268	+	17.8917i	0.348062	+	0.780117i
$527$	1.59802			0.0696109
$528$	1.83347	+	16.9347i	0.0797914	+	0.736987i
$529$	20.6092			0.896054
$530$	−0.430552	−	0.965004i	−0.0187020	−	0.0419171i
$531$	−9.14529	+	9.14529i	−0.396872	+	0.396872i
$532$		0			0
$533$	22.2879	+	22.2879i	0.965396	+	0.965396i
$534$	14.6851	+	5.62392i	0.635487	+	0.243371i
$535$			2.15424i			0.0931358i
$536$	−6.10004	−	11.9029i	−0.263482	−	0.514127i
$537$		−	18.5139i		−	0.798932i
$538$	−0.919989	+	2.40226i	−0.0396635	+	0.103569i
$539$		0			0
$540$	−9.19484	−	8.25308i	−0.395683	−	0.355156i
$541$	26.3532	−	26.3532i	1.13301	−	1.13301i	0.143339	−	0.989674i	$-0.454216\pi$
$541$	26.3532	−	26.3532i	1.13301	−	1.13301i	0.989674	−	0.143339i	$-0.0457840\pi$
$542$	21.1422	−	9.43293i	0.908136	−	0.405179i
$543$	−1.98945			−0.0853757
$544$	0.753346	+	1.29313i	0.0322994	+	0.0554426i
$545$	19.0092			0.814264
$546$		0			0
$547$	10.4205	−	10.4205i	0.445550	−	0.445550i	−0.448322	−	0.893872i	$-0.647978\pi$
$547$	10.4205	−	10.4205i	0.445550	−	0.445550i	0.893872	+	0.448322i	$0.147978\pi$
$548$	10.9303	+	9.81077i	0.466919	+	0.419095i
$549$	−9.62232	−	9.62232i	−0.410671	−	0.410671i
$550$	−7.43970	+	19.4265i	−0.317230	+	0.828347i
$551$			2.97914i			0.126916i
$552$	3.93697	−	2.01763i	0.167569	−	0.0858761i
$553$		0			0
$554$	15.4431	+	5.91420i	0.656114	+	0.251270i
$555$	−8.25308	−	8.25308i	−0.350324	−	0.350324i
$556$	−23.6165	+	1.27472i	−1.00156	+	0.0540601i
$557$	7.74720	−	7.74720i	0.328259	−	0.328259i	−0.523665	−	0.851924i	$-0.675436\pi$
$557$	7.74720	−	7.74720i	0.328259	−	0.328259i	0.851924	+	0.523665i	$0.175436\pi$
$558$	−6.88026	−	15.4209i	−0.291265	−	0.652817i
$559$	13.6728			0.578297
$560$		0			0
$561$	1.12660			0.0475651
$562$	−17.4092	−	39.0195i	−0.734361	−	1.64594i
$563$	−14.0570	+	14.0570i	−0.592430	+	0.592430i	−0.938287	−	0.345857i	$-0.887588\pi$
$563$	−14.0570	+	14.0570i	−0.592430	+	0.592430i	0.345857	+	0.938287i	$0.387588\pi$
$564$	0.340822	+	6.31436i	0.0143512	+	0.265882i
$565$	−6.62333	−	6.62333i	−0.278645	−	0.278645i
$566$	22.0535	+	8.44576i	0.926977	+	0.355002i
$567$		0			0
$568$	24.3329	+	7.84320i	1.02099	+	0.329093i
$569$		−	26.9645i		−	1.13041i	−0.824951	−	0.565205i	$-0.808797\pi$
$569$		−	26.9645i		−	1.13041i	0.824951	−	0.565205i	$-0.191203\pi$
$570$	−4.03064	+	10.5248i	−0.168825	+	0.440834i
$571$	21.8131	+	21.8131i	0.912852	+	0.912852i	0.996496	−	0.0836439i	$-0.0266558\pi$
$571$	21.8131	+	21.8131i	0.912852	+	0.912852i	−0.0836439	+	0.996496i	$0.526656\pi$
$572$	−16.0674	+	17.9009i	−0.671813	+	0.748474i
$573$	−2.48264	+	2.48264i	−0.103714	+	0.103714i
$574$		0			0
$575$	5.40264			0.225306
$576$	9.23517	−	12.8373i	0.384799	−	0.534889i
$577$	−8.16250			−0.339809			−0.169905	−	0.985461i	$-0.554346\pi$
$577$	−8.16250			−0.339809			−0.169905	+	0.985461i	$0.554346\pi$
$578$	−21.8651	+	9.75545i	−0.909467	+	0.405773i
$579$	−5.42647	+	5.42647i	−0.225516	+	0.225516i
$580$	0.760746	−	0.847555i	0.0315883	−	0.0351928i
$581$		0			0
$582$	7.28811	−	19.0306i	0.302102	−	0.788845i
$583$		−	2.56330i		−	0.106161i
$584$	−39.8815	−	12.8550i	−1.65031	−	0.531942i
$585$		−	6.93028i		−	0.286532i
$586$	−28.7346	−	11.0044i	−1.18702	−	0.454588i
$587$	0.0166226	+	0.0166226i	0.000686087	+	0.000686087i	0.707450	−	0.706764i	$-0.249846\pi$
$587$	0.0166226	+	0.0166226i	0.000686087	+	0.000686087i	−0.706764	+	0.707450i	$0.749846\pi$
$588$		0			0
$589$	−27.4206	+	27.4206i	−1.12985	+	1.12985i
$590$	−4.62640	−	10.3692i	−0.190466	−	0.426895i
$591$	11.1982			0.460631
$592$	23.5774	−	29.3026i	0.969027	−	1.20433i
$593$	−16.7146			−0.686386			−0.343193	−	0.939265i	$-0.611508\pi$
$593$	−16.7146			−0.686386			−0.343193	+	0.939265i	$0.611508\pi$
$594$	−12.2119	−	27.3708i	−0.501062	−	1.12304i
$595$		0			0
$596$	−36.3721	+	1.96321i	−1.48986	+	0.0804163i
$597$	14.0692	+	14.0692i	0.575813	+	0.575813i
$598$	5.83401	+	2.23423i	0.238570	+	0.0913646i
$599$			17.5716i			0.717954i	0.933346	+	0.358977i	$0.116874\pi$
$599$			17.5716i			0.717954i	−0.933346	+	0.358977i	$0.883126\pi$
$600$	−8.89676	+	4.55944i	−0.363209	+	0.186138i
$601$			6.99237i			0.285225i	0.989779	+	0.142612i	$0.0455503\pi$
$601$			6.99237i			0.285225i	−0.989779	+	0.142612i	$0.954450\pi$
$602$		0			0
$603$	6.60978	+	6.60978i	0.269171	+	0.269171i
$604$	−19.3744	−	17.3900i	−0.788332	−	0.707589i
$605$	5.83300	−	5.83300i	0.237145	−	0.237145i
$606$	19.4546	−	8.67997i	0.790288	−	0.352599i
$607$	6.25546			0.253901			0.126951	−	0.991909i	$-0.459481\pi$
$607$	6.25546			0.253901			0.126951	+	0.991909i	$0.459481\pi$
$608$	−35.1157	−	9.26227i	−1.42413	−	0.375635i
$609$		0			0
$610$	10.9101	−	4.86772i	0.441738	−	0.197088i
$611$	−6.31436	+	6.31436i	−0.255451	+	0.255451i
$612$	−0.778377	−	0.698653i	−0.0314640	−	0.0282414i
$613$	−5.69897	−	5.69897i	−0.230179	−	0.230179i	0.582588	−	0.812767i	$-0.302040\pi$
$613$	−5.69897	−	5.69897i	−0.230179	−	0.230179i	−0.812767	+	0.582588i	$0.802040\pi$
$614$	5.83158	−	15.2274i	0.235344	−	0.614526i
$615$		−	13.6951i		−	0.552240i
$616$		0			0
$617$			44.4895i			1.79108i	0.444980	+	0.895541i	$0.353211\pi$
$617$			44.4895i			1.79108i	−0.444980	+	0.895541i	$0.646789\pi$
$618$	−17.3488	−	6.64401i	−0.697870	−	0.267261i
$619$	13.8751	+	13.8751i	0.557688	+	0.557688i	0.928649	−	0.370960i	$-0.120971\pi$
$619$	13.8751	+	13.8751i	0.557688	+	0.557688i	−0.370960	+	0.928649i	$0.620971\pi$
$620$	14.8031	−	0.799011i	0.594508	−	0.0320891i
$621$	−5.50413	+	5.50413i	−0.220873	+	0.220873i
$622$	−17.9247	−	40.1749i	−0.718714	−	1.61087i
$623$		0			0
$624$	−11.4926	+	1.24427i	−0.460074	+	0.0498108i
$625$	−4.67950			−0.187180
$626$	−1.83230	−	4.10678i	−0.0732336	−	0.164140i
$627$	−19.3314	+	19.3314i	−0.772024	+	0.772024i
$628$	2.23439	+	41.3961i	0.0891618	+	1.65188i
$629$	−1.75895	−	1.75895i	−0.0701341	−	0.0701341i
$630$		0			0
$631$			8.64101i			0.343993i	0.985098	+	0.171997i	$0.0550218\pi$
$631$			8.64101i			0.343993i	−0.985098	+	0.171997i	$0.944978\pi$
$632$	10.9249	−	33.8938i	0.434571	−	1.34822i
$633$			1.62925i			0.0647569i
$634$	1.12259	−	2.93129i	0.0445837	−	0.116416i
$635$	9.31871	+	9.31871i	0.369802	+	0.369802i
$636$	0.822839	−	0.916733i	0.0326277	−	0.0363508i
$637$		0			0
$638$	2.52297	−	1.12566i	0.0998853	−	0.0445654i
$639$	−17.8676			−0.706833
$640$	7.62512	+	11.6022i	0.301409	+	0.458615i
$641$	15.0886			0.595966			0.297983	−	0.954571i	$-0.403686\pi$
$641$	15.0886			0.595966			0.297983	+	0.954571i	$0.403686\pi$
$642$	−2.29341	+	1.02324i	−0.0905135	+	0.0403840i
$643$	12.3557	−	12.3557i	0.487261	−	0.487261i	−0.420180	−	0.907441i	$-0.638033\pi$
$643$	12.3557	−	12.3557i	0.487261	−	0.487261i	0.907441	+	0.420180i	$0.138033\pi$
$644$		0			0
$645$	−4.20072	−	4.20072i	−0.165403	−	0.165403i
$646$	−0.859038	+	2.24311i	−0.0337984	+	0.0882540i
$647$			40.8085i			1.60435i	0.597091	+	0.802173i	$0.296323\pi$
$647$			40.8085i			1.60435i	−0.597091	+	0.802173i	$0.703677\pi$
$648$	−0.727032	+	2.25556i	−0.0285605	+	0.0886068i
$649$		−	27.5434i		−	1.08117i
$650$	−13.1837	−	5.04892i	−0.517107	−	0.198035i
$651$		0			0
$652$	−0.678019	−	12.5615i	−0.0265533	−	0.491948i
$653$	−9.88380	+	9.88380i	−0.386783	+	0.386783i	−0.873538	−	0.486755i	$-0.838180\pi$
$653$	−9.88380	+	9.88380i	−0.386783	+	0.386783i	0.486755	+	0.873538i	$0.338180\pi$
$654$	9.02916	+	20.2372i	0.353068	+	0.791339i
$655$	−22.3644			−0.873850
$656$	43.8744	−	4.75015i	1.71301	−	0.185462i
$657$	29.2850			1.14252
$658$		0			0
$659$	−2.71835	+	2.71835i	−0.105892	+	0.105892i	−0.758068	−	0.652176i	$-0.773856\pi$
$659$	−2.71835	+	2.71835i	−0.105892	+	0.105892i	0.652176	+	0.758068i	$0.273856\pi$
$660$	10.4362	−	0.563300i	0.406227	−	0.0219264i
$661$	9.77297	+	9.77297i	0.380125	+	0.380125i	0.871147	−	0.491022i	$-0.163377\pi$
$661$	9.77297	+	9.77297i	0.380125	+	0.380125i	−0.491022	+	0.871147i	$0.663377\pi$
$662$	3.66011	+	1.40170i	0.142254	+	0.0544788i
$663$			0.764562i			0.0296931i
$664$	−1.30489	−	2.54621i	−0.0506395	−	0.0988121i
$665$		0			0
$666$	−9.40070	+	24.5470i	−0.364270	+	0.951177i
$667$	−0.507355	−	0.507355i	−0.0196449	−	0.0196449i
$668$	−8.12306	−	7.29107i	−0.314291	−	0.282100i
$669$	5.74159	−	5.74159i	0.221983	−	0.221983i
$670$	−7.49440	+	3.34374i	−0.289534	+	0.129180i
$671$	28.9801			1.11876
$672$		0			0
$673$	−19.1036			−0.736391			−0.368195	−	0.929748i	$-0.620024\pi$
$673$	−19.1036			−0.736391			−0.368195	+	0.929748i	$0.620024\pi$
$674$	−37.0746	+	16.5414i	−1.42806	+	0.637152i
$675$	12.4382	−	12.4382i	0.478748	−	0.478748i
$676$	7.20058	+	6.46308i	0.276945	+	0.248580i
$677$	−10.4225	−	10.4225i	−0.400568	−	0.400568i	0.477865	−	0.878433i	$-0.341411\pi$
$677$	−10.4225	−	10.4225i	−0.400568	−	0.400568i	−0.878433	+	0.477865i	$0.841411\pi$
$678$	3.90520	−	10.1972i	0.149978	−	0.391622i
$679$		0			0
$680$	0.817189	−	0.418796i	0.0313378	−	0.0160601i
$681$		−	5.11324i		−	0.195940i
$682$	33.5828	+	12.8611i	1.28595	+	0.492477i
$683$	−35.0483	−	35.0483i	−1.34109	−	1.34109i	−0.894980	−	0.446107i	$-0.852810\pi$
$683$	−35.0483	−	35.0483i	−1.34109	−	1.34109i	−0.446107	−	0.894980i	$-0.647190\pi$
$684$	25.3445	−	1.36799i	0.969072	−	0.0523064i
$685$	6.37232	−	6.37232i	0.243474	−	0.243474i
$686$		0			0
$687$	−0.909963			−0.0347172
$688$	12.0006	−	14.9147i	0.457520	−	0.568616i
$689$	1.73957			0.0662724
$690$	−1.10597	−	2.47882i	−0.0421034	−	0.0943672i
$691$	−4.01456	+	4.01456i	−0.152721	+	0.152721i	−0.779332	−	0.626611i	$-0.784441\pi$
$691$	−4.01456	+	4.01456i	−0.152721	+	0.152721i	0.626611	+	0.779332i	$0.284441\pi$
$692$	1.77176	+	32.8251i	0.0673522	+	1.24782i
$693$		0			0
$694$	8.25308	+	3.16066i	0.313282	+	0.119977i
$695$			14.5115i			0.550452i
$696$	1.26366	+	0.407313i	0.0478988	+	0.0154391i
$697$		−	2.91880i		−	0.110557i
$698$	5.33901	−	13.9412i	0.202084	−	0.527681i
$699$	17.5695	+	17.5695i	0.664541	+	0.664541i
$700$		0			0
$701$	6.91144	−	6.91144i	0.261041	−	0.261041i	−0.564436	−	0.825477i	$-0.690906\pi$
$701$	6.91144	−	6.91144i	0.261041	−	0.261041i	0.825477	+	0.564436i	$0.190906\pi$
$702$	18.5751	−	8.28757i	0.701072	−	0.312794i
$703$	60.3642			2.27668
$704$	5.42440	+	33.2385i	0.204440	+	1.25272i
$705$	3.87995			0.146127
$706$	8.66191	−	3.86465i	0.325995	−	0.145448i
$707$		0			0
$708$	8.84163	−	9.85056i	0.332289	−	0.370207i
$709$	18.5092	+	18.5092i	0.695127	+	0.695127i	0.963355	−	0.268228i	$-0.0864381\pi$
$709$	18.5092	+	18.5092i	0.695127	+	0.695127i	−0.268228	+	0.963355i	$0.586438\pi$
$710$	5.61005	−	14.6489i	0.210541	−	0.549764i
$711$			24.8882i			0.933380i
$712$	29.5919	+	9.53831i	1.10900	+	0.357463i
$713$		−	9.33961i		−	0.349771i
$714$		0			0
$715$	10.4362	+	10.4362i	0.390290	+	0.390290i
$716$	−1.97290	−	36.5516i	−0.0737308	−	1.36600i
$717$	−20.9594	+	20.9594i	−0.782745	+	0.782745i
$718$	6.77292	+	15.1803i	0.252763	+	0.566523i
$719$	−14.5342			−0.542034			−0.271017	−	0.962575i	$-0.587360\pi$
$719$	−14.5342			−0.542034			−0.271017	+	0.962575i	$0.587360\pi$
$720$	−7.55976	−	6.08273i	−0.281736	−	0.226690i
$721$		0			0
$722$	−12.8012	−	28.6917i	−0.476413	−	1.06779i
$723$	−5.67950	+	5.67950i	−0.211223	+	0.211223i
$724$	−3.92775	+	0.212003i	−0.145974	+	0.00787904i
$725$	1.14652	+	1.14652i	0.0425807	+	0.0425807i
$726$	8.98044	+	3.43921i	0.333295	+	0.127641i
$727$			35.2605i			1.30774i	0.756607	+	0.653870i	$0.226856\pi$
$727$			35.2605i			1.30774i	−0.756607	+	0.653870i	$0.773144\pi$
$728$		0			0
$729$			13.6210i			0.504481i
$730$	−9.19484	+	24.0095i	−0.340316	+	0.888630i
$731$	−0.895286	−	0.895286i	−0.0331134	−	0.0331134i
$732$	10.3644	+	9.30282i	0.383078	+	0.343842i
$733$	4.68087	−	4.68087i	0.172892	−	0.172892i	−0.615357	−	0.788249i	$-0.710988\pi$
$733$	4.68087	−	4.68087i	0.172892	−	0.172892i	0.788249	+	0.615357i	$0.210988\pi$
$734$	−44.5184	+	19.8626i	−1.64320	+	0.733141i
$735$		0			0
$736$	7.55769	−	4.40291i	0.278580	−	0.162294i
$737$	−19.9070			−0.733285
$738$	−28.1663	+	12.5668i	−1.03682	+	0.462592i
$739$	11.1039	−	11.1039i	0.408464	−	0.408464i	−0.472739	−	0.881203i	$-0.656735\pi$
$739$	11.1039	−	11.1039i	0.408464	−	0.408464i	0.881203	+	0.472739i	$0.156735\pi$
$740$	−17.1734	−	15.4144i	−0.631306	−	0.566646i
$741$	−13.1192	−	13.1192i	−0.481946	−	0.481946i
$742$		0			0
$743$		−	9.88941i		−	0.362807i	−0.983409	−	0.181404i	$-0.941936\pi$
$743$		−	9.88941i		−	0.362807i	0.983409	−	0.181404i	$-0.0580641\pi$
$744$	7.88196	+	15.3799i	0.288967	+	0.563856i
$745$			22.3494i			0.818817i
$746$	−16.4313	−	6.29266i	−0.601594	−	0.230391i
$747$	1.41393	+	1.41393i	0.0517330	+	0.0517330i
$748$	2.22423	−	0.120054i	0.0813258	−	0.00438963i
$749$		0			0
$750$	6.07564	+	13.6175i	0.221851	+	0.497239i
$751$	−3.91696			−0.142932			−0.0714659	−	0.997443i	$-0.522768\pi$
$751$	−3.91696			−0.142932			−0.0714659	+	0.997443i	$0.522768\pi$
$752$	1.34576	+	12.4300i	0.0490748	+	0.453276i
$753$	−9.91853			−0.361451
$754$	0.763926	+	1.71220i	0.0278205	+	0.0623547i
$755$	−11.2952	+	11.2952i	−0.411074	+	0.411074i
$756$		0			0
$757$	30.8256	+	30.8256i	1.12037	+	1.12037i	0.991685	+	0.128689i	$0.0410770\pi$
$757$	30.8256	+	30.8256i	1.12037	+	1.12037i	0.128689	+	0.991685i	$0.458923\pi$
$758$	−0.320503	−	0.122742i	−0.0116412	−	0.00445820i
$759$		−	6.58439i		−	0.238998i
$760$	−6.83607	+	21.2084i	−0.247970	+	0.769309i
$761$		−	30.8862i		−	1.11962i	−0.828620	−	0.559812i	$-0.810873\pi$
$761$		−	30.8862i		−	1.11962i	0.828620	−	0.559812i	$-0.189127\pi$
$762$	−5.49444	+	14.3470i	−0.199042	+	0.519737i
$763$		0			0
$764$	−4.63688	+	5.16599i	−0.167756	+	0.186899i
$765$	−0.453791	+	0.453791i	−0.0164069	+	0.0164069i
$766$	−28.0463	+	12.5133i	−1.01335	+	0.452123i
$767$	18.6922			0.674936
$768$	−8.72983	+	13.6286i	−0.315011	+	0.491780i
$769$	−32.1016			−1.15761			−0.578807	−	0.815465i	$-0.696481\pi$
$769$	−32.1016			−1.15761			−0.578807	+	0.815465i	$0.696481\pi$
$770$		0			0
$771$	5.94029	−	5.94029i	0.213934	−	0.213934i
$772$	−10.1351	+	11.2917i	−0.364771	+	0.406396i
$773$	30.9735	+	30.9735i	1.11404	+	1.11404i	0.992599	+	0.121439i	$0.0387509\pi$
$773$	30.9735	+	30.9735i	1.11404	+	1.11404i	0.121439	+	0.992599i	$0.461249\pi$
$774$	−4.78484	+	12.4941i	−0.171988	+	0.449092i
$775$			21.1057i			0.758137i
$776$	12.3608	−	38.3485i	0.443728	−	1.37663i
$777$		0			0
$778$	21.1650	+	8.10550i	0.758801	+	0.290596i
$779$	50.0840	+	50.0840i	1.79444	+	1.79444i
$780$	0.382281	+	7.08245i	0.0136879	+	0.253593i
$781$	26.9065	−	26.9065i	0.962790	−	0.962790i
$782$	−0.235711	−	0.528304i	−0.00842902	−	0.0188921i
$783$	−2.33612			−0.0834860
$784$		0			0
$785$	25.4364			0.907865
$786$	−10.6229	−	23.8092i	−0.378905	−	0.849247i
$787$	−24.5008	+	24.5008i	−0.873360	+	0.873360i	−0.992837	−	0.119477i	$-0.961878\pi$
$787$	−24.5008	+	24.5008i	−0.873360	+	0.873360i	0.119477	+	0.992837i	$0.461878\pi$
$788$	22.1083	−	1.19332i	0.787577	−	0.0425101i
$789$	9.90906	+	9.90906i	0.352772	+	0.352772i
$790$	−20.4047	−	7.81435i	−0.725968	−	0.278022i
$791$		0			0
$792$	−10.7349	−	20.9468i	−0.381448	−	0.744313i
$793$			19.6672i			0.698403i
$794$	10.5487	−	27.5445i	0.374358	−	0.977518i
$795$	−0.534452	−	0.534452i	−0.0189551	−	0.0189551i
$796$	29.2758	+	26.2773i	1.03765	+	0.931374i
$797$	10.8522	−	10.8522i	0.384403	−	0.384403i	−0.488283	−	0.872686i	$-0.662376\pi$
$797$	10.8522	−	10.8522i	0.384403	−	0.384403i	0.872686	+	0.488283i	$0.162376\pi$
$798$		0			0
$799$	0.826921			0.0292544
$800$	−17.0789	+	9.94971i	−0.603829	+	0.351775i
$801$	−21.7293			−0.767767
$802$	−0.189701	+	0.0846382i	−0.00669858	+	0.00298868i
$803$	−44.0996	+	44.0996i	−1.55624	+	1.55624i
$804$	−7.11951	−	6.39031i	−0.251086	−	0.225369i
$805$		0			0
$806$	−8.72813	+	22.7908i	−0.307435	+	0.802772i
$807$			1.83998i			0.0647703i
$808$	37.4839	−	19.2099i	1.31868	−	0.675801i
$809$			40.1576i			1.41186i	0.708279	+	0.705932i	$0.249472\pi$
$809$			40.1576i			1.41186i	−0.708279	+	0.705932i	$0.750528\pi$
$810$	1.35789	+	0.520029i	0.0477115	+	0.0182719i
$811$	15.7147	+	15.7147i	0.551819	+	0.551819i	0.926966	−	0.375147i	$-0.122408\pi$
$811$	15.7147	+	15.7147i	0.551819	+	0.551819i	−0.375147	+	0.926966i	$0.622408\pi$
$812$		0			0
$813$	11.7093	−	11.7093i	0.410662	−	0.410662i
$814$	−22.8085	−	51.1211i	−0.799437	−	1.79179i
$815$	−7.71862			−0.270372
$816$	0.834007	+	0.671058i	0.0291961	+	0.0234917i
$817$	30.7246			1.07492
$818$	−1.30897	−	2.93382i	−0.0457671	−	0.102579i
$819$		0			0
$820$	−1.45940	−	27.0380i	−0.0509644	−	0.944209i
$821$	−2.28780	−	2.28780i	−0.0798447	−	0.0798447i	0.666057	−	0.745901i	$-0.267981\pi$
$821$	−2.28780	−	2.28780i	−0.0798447	−	0.0798447i	−0.745901	+	0.666057i	$0.767981\pi$
$822$	9.81077	+	3.75720i	0.342190	+	0.131048i
$823$		−	10.5792i		−	0.368767i	−0.982854	−	0.184384i	$-0.940971\pi$
$823$		−	10.5792i		−	0.368767i	0.982854	−	0.184384i	$-0.0590288\pi$
$824$	−34.9594	−	11.2684i	−1.21787	−	0.392554i
$825$			14.8794i			0.518034i
$826$		0			0
$827$	16.8200	+	16.8200i	0.584887	+	0.584887i	0.936242	−	0.351355i	$-0.114279\pi$
$827$	16.8200	+	16.8200i	0.584887	+	0.584887i	−0.351355	+	0.936242i	$0.614279\pi$
$828$	−4.08327	+	4.54921i	−0.141903	+	0.158096i
$829$	−5.46840	+	5.46840i	−0.189925	+	0.189925i	−0.795664	−	0.605739i	$-0.792878\pi$
$829$	−5.46840	+	5.46840i	−0.189925	+	0.189925i	0.605739	+	0.795664i	$0.292878\pi$
$830$	−1.60316	+	0.715276i	−0.0556466	+	0.0248276i
$831$	11.8284			0.410323
$832$	−22.5572	+	3.68125i	−0.782029	+	0.127624i
$833$		0			0
$834$	−15.4490	+	6.89280i	−0.534954	+	0.238678i
$835$	−4.73571	+	4.73571i	−0.163886	+	0.163886i
$836$	−36.1057	+	40.2258i	−1.24874	+	1.39124i
$837$	−21.5021	−	21.5021i	−0.743222	−	0.743222i
$838$	−13.8516	+	36.1691i	−0.478495	+	1.24944i
$839$		−	6.99735i		−	0.241575i	−0.992678	−	0.120788i	$-0.961458\pi$
$839$		−	6.99735i		−	0.241575i	0.992678	−	0.120788i	$-0.0385420\pi$
$840$		0			0
$841$			28.7847i			0.992575i
$842$	15.1473	+	5.80092i	0.522011	+	0.199913i
$843$	−21.6103	−	21.6103i	−0.744299	−	0.744299i
$844$	0.173619	+	3.21660i	0.00597620	+	0.110720i
$845$	4.19791	−	4.19791i	0.144413	−	0.144413i
$846$	−3.56030	−	7.97976i	−0.122406	−	0.274350i
$847$		0			0
$848$	1.52683	−	1.89758i	0.0524315	−	0.0651631i
$849$	16.8915			0.579715
$850$	0.532660	+	1.19386i	0.0182701	+	0.0409491i
$851$	−10.2802	+	10.2802i	−0.352400	+	0.352400i
$852$	18.2600	−	0.985597i	0.625577	−	0.0337660i
$853$	32.6377	+	32.6377i	1.11749	+	1.11749i	0.992108	+	0.125384i	$0.0400162\pi$
$853$	32.6377	+	32.6377i	1.11749	+	1.11749i	0.125384	+	0.992108i	$0.459984\pi$
$854$		0			0
$855$		−	15.5733i		−	0.532596i
$856$	−4.41880	+	2.26456i	−0.151031	+	0.0774010i
$857$			43.6532i			1.49116i	0.666414	+	0.745582i	$0.267828\pi$
$857$			43.6532i			1.49116i	−0.666414	+	0.745582i	$0.732172\pi$
$858$	−6.15330	+	16.0674i	−0.210070	+	0.548533i
$859$	−6.63555	−	6.63555i	−0.226402	−	0.226402i	0.584786	−	0.811188i	$-0.301179\pi$
$859$	−6.63555	−	6.63555i	−0.226402	−	0.226402i	−0.811188	+	0.584786i	$0.801179\pi$
$860$	−8.74105	−	7.84576i	−0.298067	−	0.267538i
$861$		0			0
$862$	−13.9040	+	6.20347i	−0.473571	+	0.211291i
$863$	−8.11592			−0.276269			−0.138135	−	0.990413i	$-0.544111\pi$
$863$	−8.11592			−0.276269			−0.138135	+	0.990413i	$0.544111\pi$
$864$	7.26308	−	27.5363i	0.247095	−	0.936804i
$865$	20.1699			0.685795
$866$	−6.45025	+	2.87788i	−0.219188	+	0.0977943i
$867$	−12.1096	+	12.1096i	−0.411265	+	0.411265i
$868$		0			0
$869$	−37.4786	−	37.4786i	−1.27137	−	1.27137i
$870$	0.291341	−	0.760746i	0.00987738	−	0.0257917i
$871$		−	13.5098i		−	0.457763i
$872$	19.9827	+	38.9919i	0.676699	+	1.32043i
$873$			28.1593i			0.953048i
$874$	13.1098	+	5.02063i	0.443446	+	0.169825i
$875$		0			0
$876$	−29.9280	+	1.61539i	−1.01117	+	0.0545789i
$877$	23.2126	−	23.2126i	0.783833	−	0.783833i	−0.196643	−	0.980475i	$-0.563004\pi$
$877$	23.2126	−	23.2126i	0.783833	−	0.783833i	0.980475	+	0.196643i	$0.0630039\pi$
$878$	0.979141	+	2.19457i	0.0330444	+	0.0740631i
$879$	−22.0088			−0.742340
$880$	20.5439	−	2.22423i	0.692535	−	0.0749787i
$881$	12.2614			0.413096			0.206548	−	0.978436i	$-0.433777\pi$
$881$	12.2614			0.413096			0.206548	+	0.978436i	$0.433777\pi$
$882$		0			0
$883$	4.12180	−	4.12180i	0.138710	−	0.138710i	−0.634342	−	0.773052i	$-0.718729\pi$
$883$	4.12180	−	4.12180i	0.138710	−	0.138710i	0.773052	+	0.634342i	$0.218729\pi$
$884$	0.0814744	+	1.50946i	0.00274028	+	0.0507687i
$885$	−5.74284	−	5.74284i	−0.193044	−	0.193044i
$886$	−14.7604	−	5.65276i	−0.495886	−	0.189908i
$887$			23.8826i			0.801899i	0.916100	+	0.400949i	$0.131320\pi$
$887$			23.8826i			0.801899i	−0.916100	+	0.400949i	$0.868680\pi$
$888$	8.25308	−	25.6045i	0.276955	−	0.859232i
$889$		0			0
$890$	6.82252	−	17.8149i	0.228692	−	0.597157i
$891$	2.49412	+	2.49412i	0.0835562	+	0.0835562i
$892$	10.7237	−	11.9474i	0.359056	−	0.400028i
$893$	−14.1892	+	14.1892i	−0.474825	+	0.474825i
$894$	−23.7932	+	10.6157i	−0.795763	+	0.355042i
$895$	−22.4597			−0.750744
$896$		0			0
$897$	4.46847			0.149198
$898$	5.23598	−	2.33612i	0.174727	−	0.0779572i
$899$	1.98201	−	1.98201i	0.0661036	−	0.0661036i
$900$	9.22736	−	10.2803i	0.307579	−	0.342677i
$901$	−0.113906	−	0.113906i	−0.00379477	−	0.00379477i
$902$	23.4909	−	61.3392i	0.782161	−	2.04237i
$903$		0			0
$904$	6.62333	−	20.5484i	0.220289	−	0.683428i
$905$			2.41346i			0.0802261i
$906$	−17.3900	−	6.65980i	−0.577744	−	0.221257i
$907$	33.8412	+	33.8412i	1.12368	+	1.12368i	0.991184	+	0.132494i	$0.0422986\pi$
$907$	33.8412	+	33.8412i	1.12368	+	1.12368i	0.132494	+	0.991184i	$0.457701\pi$
$908$	−0.544885	−	10.0950i	−0.0180826	−	0.335014i
$909$	−20.8151	+	20.8151i	−0.690393	+	0.690393i
$910$		0			0
$911$	0.866439			0.0287064			0.0143532	−	0.999897i	$-0.495431\pi$
$911$	0.866439			0.0287064			0.0143532	+	0.999897i	$0.495431\pi$
$912$	−25.8256	+	2.79606i	−0.855170	+	0.0925867i
$913$	−4.25841			−0.140933
$914$	−5.84856	−	13.1085i	−0.193453	−	0.433591i
$915$	6.04240	−	6.04240i	0.199755	−	0.199755i
$916$	−1.79653	+	0.0969689i	−0.0593589	+	0.00320394i
$917$		0			0
$918$	−1.75895	−	0.673622i	−0.0580541	−	0.0222328i
$919$			32.5204i			1.07275i	0.843980	+	0.536375i	$0.180207\pi$
$919$			32.5204i			1.07275i	−0.843980	+	0.536375i	$0.819793\pi$
$920$	−2.44764	−	4.77605i	−0.0806964	−	0.157462i
$921$		−	11.6632i		−	0.384314i
$922$	−0.733936	+	1.91645i	−0.0241709	+	0.0631148i
$923$	18.2600	+	18.2600i	0.601034	+	0.601034i
$924$		0			0
$925$	23.2311	−	23.2311i	0.763835	−	0.763835i
$926$	13.6828	−	6.10480i	0.449645	−	0.200616i
$927$	25.6707			0.843135
$928$	2.53822	+	0.669491i	0.0833212	+	0.0219771i
$929$	−10.2017			−0.334705			−0.167353	−	0.985897i	$-0.553522\pi$
$929$	−10.2017			−0.334705			−0.167353	+	0.985897i	$0.553522\pi$
$930$	9.68363	−	4.32050i	0.317539	−	0.141675i
$931$		0			0
$932$	36.5595	+	32.8150i	1.19755	+	1.07489i
$933$	−22.2502	−	22.2502i	−0.728440	−	0.728440i
$934$	−6.62875	+	17.3089i	−0.216899	+	0.566365i
$935$		−	1.36671i		−	0.0446962i
$936$	14.2155	−	7.28519i	0.464647	−	0.238124i
$937$		−	5.06532i		−	0.165477i	−0.996571	−	0.0827384i	$-0.973633\pi$
$937$		−	5.06532i		−	0.165477i	0.996571	−	0.0827384i	$-0.0263666\pi$
$938$		0			0
$939$	−2.27447	−	2.27447i	−0.0742247	−	0.0742247i
$940$	7.66011	−	0.413461i	0.249845	−	0.0134856i
$941$	29.4222	−	29.4222i	0.959137	−	0.959137i	−0.0400599	−	0.999197i	$-0.512755\pi$
$941$	29.4222	−	29.4222i	0.959137	−	0.959137i	0.999197	+	0.0400599i	$0.0127549\pi$
$942$	12.0820	+	27.0797i	0.393654	+	0.882304i
$943$	−17.0589			−0.555513
$944$	16.4062	−	20.3900i	0.533976	−	0.663638i
$945$		0			0
$946$	−11.6092	−	26.0200i	−0.377449	−	0.845984i
$947$	19.0039	−	19.0039i	0.617542	−	0.617542i	−0.327358	−	0.944900i	$-0.606158\pi$
$947$	19.0039	−	19.0039i	0.617542	−	0.617542i	0.944900	+	0.327358i	$0.106158\pi$
$948$	−1.37286	−	25.4347i	−0.0445883	−	0.826080i
$949$	−29.9280	−	29.9280i	−0.971504	−	0.971504i
$950$	−29.6256	−	11.3456i	−0.961181	−	0.368101i
$951$		−	2.24518i		−	0.0728049i
$952$		0			0
$953$			39.1113i			1.26694i	0.773767	+	0.633470i	$0.218370\pi$
$953$			39.1113i			1.26694i	−0.773767	+	0.633470i	$0.781630\pi$
$954$	−0.608770	+	1.58961i	−0.0197097	+	0.0514656i
$955$	3.01176	+	3.01176i	0.0974581	+	0.0974581i
$956$	−39.1464	+	43.6134i	−1.26608	+	1.41056i
$957$	1.39731	−	1.39731i	0.0451685	−	0.0451685i
$958$	−43.2349	+	19.2900i	−1.39686	+	0.623230i
$959$		0			0
$960$	8.06128	+	5.79928i	0.260177	+	0.187171i
$961$	5.48559			0.176955
$962$	34.6931	−	15.4789i	1.11855	−	0.499059i
$963$	2.45379	−	2.45379i	0.0790723	−	0.0790723i
$964$	−10.6077	+	11.8182i	−0.341651	+	0.380638i
$965$	6.58300	+	6.58300i	0.211914	+	0.211914i
$966$		0			0
$967$			53.9124i			1.73371i	0.498565	+	0.866853i	$0.333861\pi$
$967$			53.9124i			1.73371i	−0.498565	+	0.866853i	$0.666139\pi$
$968$	18.0964	+	5.83300i	0.581641	+	0.187480i
$969$			1.71808i			0.0551926i
$970$	−23.0866	−	8.84141i	−0.741266	−	0.283880i
$971$	−26.1105	−	26.1105i	−0.837926	−	0.837926i	0.150659	−	0.988586i	$-0.451860\pi$
$971$	−26.1105	−	26.1105i	−0.837926	−	0.837926i	−0.988586	+	0.150659i	$0.951860\pi$
$972$	1.71936	+	31.8543i	0.0551485	+	1.02173i
$973$		0			0
$974$	−13.2674	−	29.7365i	−0.425115	−	0.952819i
$975$	−10.0978			−0.323390
$976$	21.4536	+	17.2620i	0.686712	+	0.552542i
$977$	−57.0755			−1.82601			−0.913004	−	0.407950i	$-0.866244\pi$
$977$	−57.0755			−1.82601			−0.913004	+	0.407950i	$0.866244\pi$
$978$	−3.66626	−	8.21727i	−0.117234	−	0.262759i
$979$	32.7217	−	32.7217i	1.04579	−	1.04579i
$980$		0			0
$981$	−21.6525	−	21.6525i	−0.691311	−	0.691311i
$982$	−40.9668	−	15.6890i	−1.30730	−	0.500655i
$983$		−	46.5572i		−	1.48494i	−0.669878	−	0.742471i	$-0.733654\pi$
$983$		−	46.5572i		−	1.48494i	0.669878	−	0.742471i	$-0.266346\pi$
$984$	28.0916	−	14.3965i	0.895527	−	0.458942i
$985$		−	13.5848i		−	0.432847i
$986$	0.0620926	−	0.162136i	0.00197743	−	0.00516345i
$987$		0			0
$988$	−27.2991	−	24.5030i	−0.868499	−	0.779544i
$989$	−5.23248	+	5.23248i	−0.166383	+	0.166383i
$990$	−13.1887	+	5.88434i	−0.419164	+	0.187017i
$991$	52.9443			1.68183			0.840915	−	0.541167i	$-0.182017\pi$
$991$	52.9443			1.68183			0.840915	+	0.541167i	$0.182017\pi$
$992$	17.2002	+	29.5244i	0.546106	+	0.937402i
$993$	2.80341			0.0889635
$994$		0			0
$995$	17.0677	−	17.0677i	0.541082	−	0.541082i
$996$	−1.52297	−	1.36698i	−0.0482571	−	0.0433145i
$997$	−16.0449	−	16.0449i	−0.508148	−	0.508148i	0.405810	−	0.913958i	$-0.366990\pi$
$997$	−16.0449	−	16.0449i	−0.508148	−	0.508148i	−0.913958	+	0.405810i	$0.866990\pi$
$998$	4.37878	−	11.4338i	0.138608	−	0.361931i
$999$			47.3350i			1.49761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.g.197.4		8
7.2	even	3		784.2.x.j.165.2		16
7.3	odd	6		784.2.x.k.373.2		16
7.4	even	3		784.2.x.j.373.2		16
7.5	odd	6		784.2.x.k.165.2		16
7.6	odd	2		112.2.m.c.85.4	yes	8
16.13	even	4	inner	784.2.m.g.589.4		8
28.27	even	2		448.2.m.c.113.3		8
56.13	odd	2		896.2.m.e.225.3		8
56.27	even	2		896.2.m.f.225.2		8
112.13	odd	4		112.2.m.c.29.4	✓	8
112.27	even	4		896.2.m.f.673.2		8
112.45	odd	12		784.2.x.k.765.2		16
112.61	odd	12		784.2.x.k.557.2		16
112.69	odd	4		896.2.m.e.673.3		8
112.83	even	4		448.2.m.c.337.3		8
112.93	even	12		784.2.x.j.557.2		16
112.109	even	12		784.2.x.j.765.2		16
224.13	odd	8		7168.2.a.bc.1.5		8
224.83	even	8		7168.2.a.bd.1.4		8
224.125	odd	8		7168.2.a.bc.1.4		8
224.195	even	8		7168.2.a.bd.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.4	✓	8	112.13	odd	4
112.2.m.c.85.4	yes	8	7.6	odd	2
448.2.m.c.113.3		8	28.27	even	2
448.2.m.c.337.3		8	112.83	even	4
784.2.m.g.197.4		8	1.1	even	1	trivial
784.2.m.g.589.4		8	16.13	even	4	inner
784.2.x.j.165.2		16	7.2	even	3
784.2.x.j.373.2		16	7.4	even	3
784.2.x.j.557.2		16	112.93	even	12
784.2.x.j.765.2		16	112.109	even	12
784.2.x.k.165.2		16	7.5	odd	6
784.2.x.k.373.2		16	7.3	odd	6
784.2.x.k.557.2		16	112.61	odd	12
784.2.x.k.765.2		16	112.45	odd	12
896.2.m.e.225.3		8	56.13	odd	2
896.2.m.e.673.3		8	112.69	odd	4
896.2.m.f.225.2		8	56.27	even	2
896.2.m.f.673.2		8	112.27	even	4
7168.2.a.bc.1.4		8	224.125	odd	8
7168.2.a.bc.1.5		8	224.13	odd	8
7168.2.a.bd.1.4		8	224.83	even	8
7168.2.a.bd.1.5		8	224.195	even	8

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29150 - 0.576222i) q^{2} +(0.715276 - 0.715276i) q^{3} +(1.33594 - 1.48838i) q^{4} +(-0.867721 - 0.867721i) q^{5} +(0.511620 - 1.33594i) q^{6} +(0.867721 - 2.69204i) q^{8} +1.97676i q^{9} +(-1.62066 - 0.620660i) q^{10} +(-2.97676 - 2.97676i) q^{11} +(-0.109040 - 2.02017i) q^{12} +(2.02017 - 2.02017i) q^{13} -1.24132 q^{15} +(-0.430552 - 3.97676i) q^{16} -0.264559 q^{17} +(1.13905 + 2.55298i) q^{18} +(4.53959 - 4.53959i) q^{19} +(-2.45072 + 0.132279i) q^{20} +(-5.55976 - 2.12921i) q^{22} +1.54621i q^{23} +(-1.30489 - 2.54621i) q^{24} -3.49412i q^{25} +(1.44498 - 3.77310i) q^{26} +(3.55976 + 3.55976i) q^{27} +(-0.328129 + 0.328129i) q^{29} +(-1.60316 + 0.715276i) q^{30} -6.04033 q^{31} +(-2.84756 - 4.88789i) q^{32} -4.25841 q^{33} +(-0.341677 + 0.152445i) q^{34} +(2.94217 + 2.64082i) q^{36} +(6.64863 + 6.64863i) q^{37} +(3.24706 - 8.47869i) q^{38} -2.88995i q^{39} +(-3.08887 + 1.58300i) q^{40} +11.0327i q^{41} +(3.38407 + 3.38407i) q^{43} +(-8.40731 + 0.453791i) q^{44} +(1.71528 - 1.71528i) q^{45} +(0.890960 + 1.99693i) q^{46} -3.12566 q^{47} +(-3.15244 - 2.53652i) q^{48} +(-2.01339 - 4.51265i) q^{50} +(-0.189233 + 0.189233i) q^{51} +(-0.307963 - 5.70559i) q^{52} +(0.430552 + 0.430552i) q^{53} +(6.64863 + 2.54621i) q^{54} +5.16599i q^{55} -6.49412i q^{57} +(-0.234703 + 0.612853i) q^{58} +(4.62640 + 4.62640i) q^{59} +(-1.65832 + 1.84756i) q^{60} +(-4.86772 + 4.86772i) q^{61} +(-7.80108 + 3.48057i) q^{62} +(-6.49412 - 4.67187i) q^{64} -3.50588 q^{65} +(-5.49973 + 2.45379i) q^{66} +(3.34374 - 3.34374i) q^{67} +(-0.353433 + 0.393764i) q^{68} +(1.10597 + 1.10597i) q^{69} +9.03885i q^{71} +(5.32151 + 1.71528i) q^{72} -14.8146i q^{73} +(12.4178 + 4.75561i) q^{74} +(-2.49926 - 2.49926i) q^{75} +(-0.692037 - 12.8212i) q^{76} +(-1.66525 - 3.73237i) q^{78} +12.5904 q^{79} +(-3.07712 + 3.82432i) q^{80} -0.837864 q^{81} +(6.35729 + 14.2487i) q^{82} +(0.715276 - 0.715276i) q^{83} +(0.229563 + 0.229563i) q^{85} +(6.32050 + 2.42055i) q^{86} +0.469405i q^{87} +(-10.5965 + 5.43055i) q^{88} +10.9924i q^{89} +(1.22690 - 3.20366i) q^{90} +(2.30135 + 2.06564i) q^{92} +(-4.32050 + 4.32050i) q^{93} +(-4.03679 + 1.80108i) q^{94} -7.87820 q^{95} +(-5.53298 - 1.45940i) q^{96} +14.2452 q^{97} +(5.88434 - 5.88434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{4} + 4 q^{5} + 16 q^{6} - 4 q^{8} - 12 q^{10} + 12 q^{12} - 8 q^{15} + 8 q^{16} - 24 q^{17} + 6 q^{18} + 12 q^{19} + 8 q^{20} - 4 q^{22} - 8 q^{26} - 12 q^{27} - 16 q^{29} + 20 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^4 + 4 * q^5 + 16 * q^6 - 4 * q^8 - 12 * q^10 + 12 * q^12 - 8 * q^15 + 8 * q^16 - 24 * q^17 + 6 * q^18 + 12 * q^19 + 8 * q^20 - 4 * q^22 - 8 * q^26 - 12 * q^27 - 16 * q^29 + 20 * q^30 - 16 * q^31 - 28 * q^32 + 24 * q^33 + 12 * q^34 + 24 * q^36 + 16 * q^37 + 16 * q^38 - 28 * q^40 - 32 * q^43 - 32 * q^44 + 8 * q^45 + 20 * q^46 - 24 * q^47 - 20 * q^48 - 14 * q^50 + 8 * q^51 - 32 * q^52 - 8 * q^53 + 16 * q^54 + 12 * q^58 + 28 * q^59 - 28 * q^60 - 28 * q^61 - 20 * q^62 - 32 * q^64 - 48 * q^65 + 16 * q^66 - 28 * q^68 - 44 * q^69 + 44 * q^72 - 4 * q^74 - 28 * q^75 + 24 * q^76 + 12 * q^78 - 24 * q^79 + 12 * q^80 + 40 * q^81 - 4 * q^82 - 40 * q^85 - 40 * q^88 + 16 * q^90 + 36 * q^92 + 16 * q^93 - 28 * q^94 + 16 * q^95 - 8 * q^96 + 32 * q^97 + 48 * q^99

Introduction

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