LMFDB - Embedded newform 756.2.bf.c.271.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.12
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.953127 - 1.04477i) q^{2} +(-0.183097 - 1.99160i) q^{4} +(-0.703801 - 0.406340i) q^{5} +(-2.60258 + 0.476010i) q^{7} +(-2.25528 - 1.70695i) q^{8} +O(q^{10})$	\(q+(0.953127 - 1.04477i) q^{2} +(-0.183097 - 1.99160i) q^{4} +(-0.703801 - 0.406340i) q^{5} +(-2.60258 + 0.476010i) q^{7} +(-2.25528 - 1.70695i) q^{8} +(-1.09534 + 0.348018i) q^{10} +(-1.86129 + 1.07462i) q^{11} -5.14045i q^{13} +(-1.98327 + 3.17280i) q^{14} +(-3.93295 + 0.729313i) q^{16} +(-1.78009 + 1.02773i) q^{17} +(-1.57359 + 2.72553i) q^{19} +(-0.680403 + 1.47609i) q^{20} +(-0.651317 + 2.96887i) q^{22} +(1.64186 + 0.947931i) q^{23} +(-2.16978 - 3.75816i) q^{25} +(-5.37059 - 4.89950i) q^{26} +(1.42455 + 5.09614i) q^{28} -7.65207 q^{29} +(0.513811 + 0.889946i) q^{31} +(-2.98664 + 4.80417i) q^{32} +(-0.622902 + 2.83935i) q^{34} +(2.02512 + 0.722515i) q^{35} +(2.94725 - 5.10478i) q^{37} +(1.34773 + 4.24182i) q^{38} +(0.893668 + 2.11777i) q^{40} +2.55145i q^{41} -10.2817i q^{43} +(2.48100 + 3.51019i) q^{44} +(2.55528 - 0.811875i) q^{46} +(-1.06224 + 1.83986i) q^{47} +(6.54683 - 2.47771i) q^{49} +(-5.99450 - 1.31509i) q^{50} +(-10.2377 + 0.941201i) q^{52} +(-3.32185 - 5.75361i) q^{53} +1.74664 q^{55} +(6.68208 + 3.36894i) q^{56} +(-7.29339 + 7.99467i) q^{58} +(6.32614 + 10.9572i) q^{59} +(5.15384 + 2.97557i) q^{61} +(1.41952 + 0.311417i) q^{62} +(2.17261 + 7.69933i) q^{64} +(-2.08877 + 3.61785i) q^{65} +(6.91842 - 3.99435i) q^{67} +(2.37277 + 3.35705i) q^{68} +(2.68506 - 1.42714i) q^{70} -11.0579i q^{71} +(8.64340 - 4.99027i) q^{73} +(-2.52423 - 7.94470i) q^{74} +(5.71629 + 2.63492i) q^{76} +(4.33262 - 3.68277i) q^{77} +(-6.82469 - 3.94024i) q^{79} +(3.06436 + 1.08482i) q^{80} +(2.66568 + 2.43185i) q^{82} -17.5056 q^{83} +1.67044 q^{85} +(-10.7421 - 9.79979i) q^{86} +(6.03206 + 0.753572i) q^{88} +(-0.484920 - 0.279969i) q^{89} +(2.44690 + 13.3784i) q^{91} +(1.58728 - 3.44350i) q^{92} +(0.909781 + 2.86342i) q^{94} +(2.21498 - 1.27882i) q^{95} -1.84737i q^{97} +(3.65132 - 9.20151i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) $ 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.953127	−	1.04477i	0.673963	−	0.738765i
$2$	0.953127	−	1.04477i	0.673963	−	0.738765i
$3$		0			0
$3$		0			0
$4$	−0.183097	−	1.99160i	−0.0915486	−	0.995801i
$5$	−0.703801	−	0.406340i	−0.314749	−	0.181721i	0.334300	−	0.942467i	$-0.391500\pi$
$5$	−0.703801	−	0.406340i	−0.314749	−	0.181721i	−0.649050	+	0.760746i	$0.724833\pi$
$6$		0			0
$7$	−2.60258	+	0.476010i	−0.983682	+	0.179915i
$7$	−2.60258	+	0.476010i	−0.983682	+	0.179915i
$8$	−2.25528	−	1.70695i	−0.797363	−	0.603500i
$9$		0			0
$10$	−1.09534	+	0.348018i	−0.346378	+	0.110053i
$11$	−1.86129	+	1.07462i	−0.561200	+	0.324009i	−0.753627	−	0.657302i	$-0.771697\pi$
$11$	−1.86129	+	1.07462i	−0.561200	+	0.324009i	0.192427	+	0.981311i	$0.438364\pi$
$12$		0			0
$13$		−	5.14045i		−	1.42570i	−0.701315	−	0.712852i	$-0.747403\pi$
$13$		−	5.14045i		−	1.42570i	0.701315	−	0.712852i	$-0.252597\pi$
$14$	−1.98327	+	3.17280i	−0.530050	+	0.847966i
$15$		0			0
$16$	−3.93295	+	0.729313i	−0.983238	+	0.182328i
$17$	−1.78009	+	1.02773i	−0.431735	+	0.249262i	−0.700085	−	0.714059i	$-0.746855\pi$
$17$	−1.78009	+	1.02773i	−0.431735	+	0.249262i	0.268351	+	0.963321i	$0.413521\pi$
$18$		0			0
$19$	−1.57359	+	2.72553i	−0.361005	+	0.625280i	−0.988127	−	0.153642i	$-0.950900\pi$
$19$	−1.57359	+	2.72553i	−0.361005	+	0.625280i	0.627121	+	0.778922i	$0.284233\pi$
$20$	−0.680403	+	1.47609i	−0.152143	+	0.330064i
$21$		0			0
$22$	−0.651317	+	2.96887i	−0.138861	+	0.632965i
$23$	1.64186	+	0.947931i	0.342352	+	0.197657i	0.661312	−	0.750111i	$-0.270000\pi$
$23$	1.64186	+	0.947931i	0.342352	+	0.197657i	−0.318959	+	0.947768i	$0.603333\pi$
$24$		0			0
$25$	−2.16978	−	3.75816i	−0.433955	−	0.751632i
$26$	−5.37059	−	4.89950i	−1.05326	−	0.960871i
$27$		0			0
$28$	1.42455	+	5.09614i	0.269214	+	0.963080i
$29$	−7.65207			−1.42095			−0.710477	−	0.703721i	$-0.751521\pi$
$29$	−7.65207			−1.42095			−0.710477	+	0.703721i	$0.751521\pi$
$30$		0			0
$31$	0.513811	+	0.889946i	0.0922831	+	0.159839i	0.908471	−	0.417947i	$-0.137250\pi$
$31$	0.513811	+	0.889946i	0.0922831	+	0.159839i	−0.816188	+	0.577786i	$0.803917\pi$
$32$	−2.98664	+	4.80417i	−0.527968	+	0.849264i
$33$		0			0
$34$	−0.622902	+	2.83935i	−0.106827	+	0.486944i
$35$	2.02512	+	0.722515i	0.342308	+	0.122127i
$36$		0			0
$37$	2.94725	−	5.10478i	0.484524	−	0.839221i	−0.515318	−	0.856999i	$-0.672326\pi$
$37$	2.94725	−	5.10478i	0.484524	−	0.839221i	0.999842	+	0.0177786i	$0.00565939\pi$
$38$	1.34773	+	4.24182i	0.218631	+	0.688113i
$39$		0			0
$40$	0.893668	+	2.11777i	0.141301	+	0.334849i
$41$			2.55145i			0.398469i	0.979952	+	0.199235i	$0.0638456\pi$
$41$			2.55145i			0.398469i	−0.979952	+	0.199235i	$0.936154\pi$
$42$		0			0
$43$		−	10.2817i		−	1.56795i	−0.620793	−	0.783974i	$-0.713189\pi$
$43$		−	10.2817i		−	1.56795i	0.620793	−	0.783974i	$-0.286811\pi$
$44$	2.48100	+	3.51019i	0.374025	+	0.529181i
$45$		0			0
$46$	2.55528	−	0.811875i	0.376755	−	0.119704i
$47$	−1.06224	+	1.83986i	−0.154944	+	0.268371i	−0.933039	−	0.359776i	$-0.882853\pi$
$47$	−1.06224	+	1.83986i	−0.154944	+	0.268371i	0.778095	+	0.628147i	$0.216186\pi$
$48$		0			0
$49$	6.54683	−	2.47771i	0.935261	−	0.353958i
$50$	−5.99450	−	1.31509i	−0.847750	−	0.185981i
$51$		0			0
$52$	−10.2377	+	0.941201i	−1.41972	+	0.130521i
$53$	−3.32185	−	5.75361i	−0.456291	−	0.790319i	0.542471	−	0.840075i	$-0.317489\pi$
$53$	−3.32185	−	5.75361i	−0.456291	−	0.790319i	−0.998761	+	0.0497559i	$0.984156\pi$
$54$		0			0
$55$	1.74664			0.235516
$56$	6.68208	+	3.36894i	0.892931	+	0.450194i
$57$		0			0
$58$	−7.29339	+	7.99467i	−0.957670	+	1.04975i
$59$	6.32614	+	10.9572i	0.823593	+	1.42651i	0.902990	+	0.429662i	$0.141367\pi$
$59$	6.32614	+	10.9572i	0.823593	+	1.42651i	−0.0793963	+	0.996843i	$0.525299\pi$
$60$		0			0
$61$	5.15384	+	2.97557i	0.659882	+	0.380983i	0.792232	−	0.610220i	$-0.208919\pi$
$61$	5.15384	+	2.97557i	0.659882	+	0.380983i	−0.132350	+	0.991203i	$0.542252\pi$
$62$	1.41952	+	0.311417i	0.180279	+	0.0395500i
$63$		0			0
$64$	2.17261	+	7.69933i	0.271577	+	0.962417i
$65$	−2.08877	+	3.61785i	−0.259080	+	0.448739i
$66$		0			0
$67$	6.91842	−	3.99435i	0.845220	−	0.487988i	−0.0138151	−	0.999905i	$-0.504398\pi$
$67$	6.91842	−	3.99435i	0.845220	−	0.487988i	0.859035	+	0.511917i	$0.171064\pi$
$68$	2.37277	+	3.35705i	0.287740	+	0.407102i
$69$		0			0
$70$	2.68506	−	1.42714i	0.320926	−	0.170576i
$71$		−	11.0579i		−	1.31234i	−0.754615	−	0.656168i	$-0.772176\pi$
$71$		−	11.0579i		−	1.31234i	0.754615	−	0.656168i	$-0.227824\pi$
$72$		0			0
$73$	8.64340	−	4.99027i	1.01163	−	0.584067i	0.0999643	−	0.994991i	$-0.468127\pi$
$73$	8.64340	−	4.99027i	1.01163	−	0.584067i	0.911670	+	0.410924i	$0.134794\pi$
$74$	−2.52423	−	7.94470i	−0.293436	−	0.923553i
$75$		0			0
$76$	5.71629	+	2.63492i	0.655703	+	0.302246i
$77$	4.33262	−	3.68277i	0.493748	−	0.419690i
$78$		0			0
$79$	−6.82469	−	3.94024i	−0.767837	−	0.443311i	0.0642652	−	0.997933i	$-0.479530\pi$
$79$	−6.82469	−	3.94024i	−0.767837	−	0.443311i	−0.832103	+	0.554622i	$0.812863\pi$
$80$	3.06436	+	1.08482i	0.342606	+	0.121287i
$81$		0			0
$82$	2.66568	+	2.43185i	0.294375	+	0.268553i
$83$	−17.5056			−1.92148			−0.960742	−	0.277443i	$-0.910513\pi$
$83$	−17.5056			−1.92148			−0.960742	+	0.277443i	$0.910513\pi$
$84$		0			0
$85$	1.67044			0.181184
$86$	−10.7421	−	9.79979i	−1.15835	−	1.05674i
$87$		0			0
$88$	6.03206	+	0.753572i	0.643020	+	0.0803311i
$89$	−0.484920	−	0.279969i	−0.0514014	−	0.0296766i	0.474079	−	0.880482i	$-0.342781\pi$
$89$	−0.484920	−	0.279969i	−0.0514014	−	0.0296766i	−0.525480	+	0.850806i	$0.676114\pi$
$90$		0			0
$91$	2.44690	+	13.3784i	0.256505	+	1.40244i
$92$	1.58728	−	3.44350i	0.165485	−	0.359010i
$93$		0			0
$94$	0.909781	+	2.86342i	0.0938368	+	0.295340i
$95$	2.21498	−	1.27882i	0.227252	−	0.131204i
$96$		0			0
$97$		−	1.84737i		−	0.187572i	−0.995592	−	0.0937859i	$-0.970103\pi$
$97$		−	1.84737i		−	0.187572i	0.995592	−	0.0937859i	$-0.0298969\pi$
$98$	3.65132	−	9.20151i	0.368839	−	0.929493i
$99$		0			0
$100$	−7.08748	+	5.00944i	−0.708748	+	0.500944i
$101$	14.1467	−	8.16763i	1.40765	−	0.812709i	0.412492	−	0.910961i	$-0.364658\pi$
$101$	14.1467	−	8.16763i	1.40765	−	0.812709i	0.995162	+	0.0982519i	$0.0313251\pi$
$102$		0			0
$103$	−2.38508	+	4.13108i	−0.235009	+	0.407048i	−0.959275	−	0.282473i	$-0.908845\pi$
$103$	−2.38508	+	4.13108i	−0.235009	+	0.407048i	0.724266	+	0.689520i	$0.242179\pi$
$104$	−8.77451	+	11.5932i	−0.860411	+	1.13680i
$105$		0			0
$106$	−9.17735	−	2.01335i	−0.891383	−	0.195554i
$107$	−4.05383	−	2.34048i	−0.391898	−	0.226263i	0.291084	−	0.956697i	$-0.405984\pi$
$107$	−4.05383	−	2.34048i	−0.391898	−	0.226263i	−0.682982	+	0.730435i	$0.739317\pi$
$108$		0			0
$109$	−4.19616	−	7.26796i	−0.401919	−	0.696144i	0.592038	−	0.805910i	$-0.298323\pi$
$109$	−4.19616	−	7.26796i	−0.401919	−	0.696144i	−0.993958	+	0.109765i	$0.964990\pi$
$110$	1.66477	−	1.82484i	0.158729	−	0.173991i
$111$		0			0
$112$	9.88865	−	3.77022i	0.934390	−	0.356252i
$113$	−2.60313			−0.244882			−0.122441	−	0.992476i	$-0.539072\pi$
$113$	−2.60313			−0.244882			−0.122441	+	0.992476i	$0.539072\pi$
$114$		0			0
$115$	−0.770364	−	1.33431i	−0.0718368	−	0.124425i
$116$	1.40107	+	15.2399i	0.130086	+	1.41499i
$117$		0			0
$118$	17.4774	+	3.83423i	1.60892	+	0.352969i
$119$	4.14361	−	3.52210i	0.379844	−	0.322870i
$120$		0			0
$121$	−3.19040	+	5.52594i	−0.290036	+	0.502358i
$122$	8.02106	−	2.54849i	0.726193	−	0.230730i
$123$		0			0
$124$	1.67834	−	1.18625i	0.150719	−	0.106529i
$125$			7.59006i			0.678876i
$126$		0			0
$127$		−	6.70221i		−	0.594725i	−0.954765	−	0.297363i	$-0.903893\pi$
$127$		−	6.70221i		−	0.594725i	0.954765	−	0.297363i	$-0.0961070\pi$
$128$	10.1148	+	5.06856i	0.894033	+	0.448002i
$129$		0			0
$130$	1.78897	+	5.63056i	0.156903	+	0.493833i
$131$	7.37529	−	12.7744i	0.644382	−	1.11610i	−0.340062	−	0.940403i	$-0.610448\pi$
$131$	7.37529	−	12.7744i	0.644382	−	1.11610i	0.984444	−	0.175699i	$-0.0562187\pi$
$132$		0			0
$133$	2.79800	−	7.84245i	0.242617	−	0.680027i
$134$	2.42095	−	11.0353i	0.209138	−	0.953305i
$135$		0			0
$136$	5.76890	+	0.720697i	0.494679	+	0.0617992i
$137$	10.0957	+	17.4863i	0.862534	+	1.49395i	0.869475	+	0.493977i	$0.164457\pi$
$137$	10.0957	+	17.4863i	0.862534	+	1.49395i	−0.00694033	+	0.999976i	$0.502209\pi$
$138$		0			0
$139$	−22.5005			−1.90847			−0.954235	−	0.299058i	$-0.903327\pi$
$139$	−22.5005			−1.90847			−0.954235	+	0.299058i	$0.903327\pi$
$140$	1.06817	−	4.16552i	0.0902766	−	0.352051i
$141$		0			0
$142$	−11.5530	−	10.5396i	−0.969509	−	0.884466i
$143$	5.52401	+	9.56786i	0.461941	+	0.800105i
$144$		0			0
$145$	5.38553	+	3.10934i	0.447244	+	0.258217i
$146$	3.02457	−	13.7868i	0.250315	−	1.14100i
$147$		0			0
$148$	−10.7063	−	4.93507i	−0.880054	−	0.405660i
$149$	5.94705	−	10.3006i	0.487201	−	0.843857i	−0.512691	−	0.858573i	$-0.671351\pi$
$149$	5.94705	−	10.3006i	0.487201	−	0.843857i	0.999892	+	0.0147163i	$0.00468451\pi$
$150$		0			0
$151$	8.34848	−	4.82000i	0.679390	−	0.392246i	−0.120235	−	0.992745i	$-0.538365\pi$
$151$	8.34848	−	4.82000i	0.679390	−	0.392246i	0.799625	+	0.600499i	$0.205032\pi$
$152$	8.20124	−	3.46081i	0.665208	−	0.280709i
$153$		0			0
$154$	0.281892	−	8.03675i	0.0227155	−	0.647620i
$155$		−	0.835127i		−	0.0670790i
$156$		0			0
$157$	5.18117	−	2.99135i	0.413503	−	0.238736i	−0.278791	−	0.960352i	$-0.589934\pi$
$157$	5.18117	−	2.99135i	0.413503	−	0.238736i	0.692294	+	0.721616i	$0.256600\pi$
$158$	−10.6214	+	3.37470i	−0.844997	+	0.268477i
$159$		0			0
$160$	4.05412	−	2.16759i	0.320506	−	0.171363i
$161$	−4.72430	−	1.68552i	−0.372327	−	0.132838i
$162$		0			0
$163$	8.53520	+	4.92780i	0.668528	+	0.385975i	0.795519	−	0.605929i	$-0.207198\pi$
$163$	8.53520	+	4.92780i	0.668528	+	0.385975i	−0.126990	+	0.991904i	$0.540532\pi$
$164$	5.08147	−	0.467163i	0.396796	−	0.0364793i
$165$		0			0
$166$	−16.6850	+	18.2893i	−1.29501	+	1.41953i
$167$	20.4794			1.58474			0.792371	−	0.610040i	$-0.208847\pi$
$167$	20.4794			1.58474			0.792371	+	0.610040i	$0.208847\pi$
$168$		0			0
$169$	−13.4242			−1.03263
$170$	1.59214	−	1.74523i	0.122112	−	0.133853i
$171$		0			0
$172$	−20.4771	+	1.88256i	−1.56136	+	0.143543i
$173$	3.46120	+	1.99833i	0.263150	+	0.151930i	0.625771	−	0.780007i	$-0.284785\pi$
$173$	3.46120	+	1.99833i	0.263150	+	0.151930i	−0.362620	+	0.931937i	$0.618118\pi$
$174$		0			0
$175$	7.43594	+	8.74808i	0.562104	+	0.661292i
$176$	6.53663	−	5.58388i	0.492717	−	0.420900i
$177$		0			0
$178$	−0.754694	+	0.239785i	−0.0565667	+	0.0179726i
$179$	−15.9493	+	9.20832i	−1.19211	+	0.688262i	−0.958784	−	0.284137i	$-0.908293\pi$
$179$	−15.9493	+	9.20832i	−1.19211	+	0.688262i	−0.233322	+	0.972400i	$0.574959\pi$
$180$		0			0
$181$			8.77700i			0.652389i	0.945303	+	0.326195i	$0.105767\pi$
$181$			8.77700i			0.652389i	−0.945303	+	0.326195i	$0.894233\pi$
$182$	16.3096	+	10.1949i	1.20895	+	0.755694i
$183$		0			0
$184$	−2.08480	−	4.94044i	−0.153693	−	0.364214i
$185$	−4.14855	+	2.39517i	−0.305007	+	0.176096i
$186$		0			0
$187$	2.20884	−	3.82582i	0.161526	−	0.279772i
$188$	3.85876	+	1.77869i	0.281429	+	0.129725i
$189$		0			0
$190$	0.775084	−	3.53303i	0.0562305	−	0.256313i
$191$	−19.0198	−	10.9811i	−1.37623	−	0.794565i	−0.384523	−	0.923115i	$-0.625634\pi$
$191$	−19.0198	−	10.9811i	−1.37623	−	0.794565i	−0.991703	+	0.128551i	$0.958968\pi$
$192$		0			0
$193$	−0.350671	−	0.607379i	−0.0252418	−	0.0437201i	0.853129	−	0.521701i	$-0.174702\pi$
$193$	−0.350671	−	0.607379i	−0.0252418	−	0.0437201i	−0.878370	+	0.477981i	$0.841369\pi$
$194$	−1.93008	−	1.76078i	−0.138572	−	0.126416i
$195$		0			0
$196$	−6.13331	−	12.5850i	−0.438094	−	0.898929i
$197$	23.9596			1.70705			0.853524	−	0.521053i	$-0.174461\pi$
$197$	23.9596			1.70705			0.853524	+	0.521053i	$0.174461\pi$
$198$		0			0
$199$	1.09676	+	1.89965i	0.0777473	+	0.134662i	0.902278	−	0.431155i	$-0.141894\pi$
$199$	1.09676	+	1.89965i	0.0777473	+	0.134662i	−0.824530	+	0.565818i	$0.808561\pi$
$200$	−1.52155	+	12.1794i	−0.107590	+	0.861216i
$201$		0			0
$202$	4.95034	−	22.5649i	0.348305	−	1.58766i
$203$	19.9151	−	3.64246i	1.39777	−	0.255651i
$204$		0			0
$205$	1.03675	−	1.79571i	0.0724101	−	0.125418i
$206$	2.04275	+	6.42931i	0.142325	+	0.447951i
$207$		0			0
$208$	3.74899	+	20.2171i	0.259946	+	1.40181i
$209$		−	6.76400i		−	0.467876i
$210$		0			0
$211$		−	11.0443i		−	0.760320i	−0.924921	−	0.380160i	$-0.875869\pi$
$211$		−	11.0443i		−	0.760320i	0.924921	−	0.380160i	$-0.124131\pi$
$212$	−10.8507	+	7.66926i	−0.745227	+	0.526727i
$213$		0			0
$214$	−6.30908	+	2.00455i	−0.431280	+	0.137028i
$215$	−4.17787	+	7.23629i	−0.284929	+	0.493511i
$216$		0			0
$217$	−1.76086	−	2.07158i	−0.119535	−	0.140628i
$218$	−11.5928	−	2.54326i	−0.785166	−	0.172251i
$219$		0			0
$220$	−0.319804	−	3.47860i	−0.0215612	−	0.234527i
$221$	5.28301	+	9.15045i	0.355374	+	0.615526i
$222$		0			0
$223$	−20.4097			−1.36673			−0.683367	−	0.730075i	$-0.739485\pi$
$223$	−20.4097			−1.36673			−0.683367	+	0.730075i	$0.739485\pi$
$224$	5.48612	−	13.9249i	0.366557	−	0.930396i
$225$		0			0
$226$	−2.48111	+	2.71968i	−0.165041	+	0.180910i
$227$	−2.20721	−	3.82300i	−0.146498	−	0.253742i	0.783433	−	0.621476i	$-0.213467\pi$
$227$	−2.20721	−	3.82300i	−0.146498	−	0.253742i	−0.929931	+	0.367735i	$0.880133\pi$
$228$		0			0
$229$	−16.5530	−	9.55686i	−1.09385	−	0.631535i	−0.159252	−	0.987238i	$-0.550908\pi$
$229$	−16.5530	−	9.55686i	−1.09385	−	0.631535i	−0.934599	+	0.355703i	$0.884241\pi$
$230$	−2.12830	−	0.466912i	−0.140336	−	0.0307873i
$231$		0			0
$232$	17.2576	+	13.0617i	1.13302	+	0.857545i
$233$	−7.20579	+	12.4808i	−0.472067	+	0.817644i	−0.999489	−	0.0319592i	$-0.989825\pi$
$233$	−7.20579	+	12.4808i	−0.472067	+	0.817644i	0.527422	+	0.849603i	$0.323159\pi$
$234$		0			0
$235$	1.49522	−	0.863264i	0.0975372	−	0.0563131i
$236$	20.6641	−	14.6054i	1.34512	−	0.950729i
$237$		0			0
$238$	0.269594	−	7.68614i	0.0174752	−	0.498218i
$239$		−	13.3320i		−	0.862375i	−0.902262	−	0.431187i	$-0.858095\pi$
$239$		−	13.3320i		−	0.862375i	0.902262	−	0.431187i	$-0.141905\pi$
$240$		0			0
$241$	−21.3015	+	12.2984i	−1.37215	+	0.792210i	−0.991198	−	0.132386i	$-0.957736\pi$
$241$	−21.3015	+	12.2984i	−1.37215	+	0.792210i	−0.380950	+	0.924596i	$0.624403\pi$
$242$	2.73249	+	8.60016i	0.175651	+	0.552839i
$243$		0			0
$244$	4.98250	−	10.8092i	0.318972	−	0.691989i
$245$	−5.61446	−	0.916424i	−0.358694	−	0.0585482i
$246$		0			0
$247$	14.0104	+	8.08893i	0.891463	+	0.514687i
$248$	0.360309	−	2.88413i	0.0228796	−	0.183143i
$249$		0			0
$250$	7.92989	+	7.23430i	0.501530	+	0.457537i
$251$	−1.47312			−0.0929824			−0.0464912	−	0.998919i	$-0.514804\pi$
$251$	−1.47312			−0.0929824			−0.0464912	+	0.998919i	$0.514804\pi$
$252$		0			0
$253$	−4.07465			−0.256171
$254$	−7.00228	−	6.38806i	−0.439362	−	0.400823i
$255$		0			0
$256$	14.9362	−	5.73670i	0.933513	−	0.358544i
$257$	−9.23212	−	5.33017i	−0.575884	−	0.332487i	0.183612	−	0.982999i	$-0.441221\pi$
$257$	−9.23212	−	5.33017i	−0.575884	−	0.332487i	−0.759496	+	0.650512i	$0.774554\pi$
$258$		0			0
$259$	−5.24051	+	14.6885i	−0.325630	+	0.912700i
$260$	7.58777	+	3.49757i	0.470573	+	0.216910i
$261$		0			0
$262$	−6.31672	−	19.8811i	−0.390248	−	1.22826i
$263$	−23.1783	+	13.3820i	−1.42924	+	0.825170i	−0.997060	−	0.0766200i	$-0.975587\pi$
$263$	−23.1783	+	13.3820i	−1.42924	+	0.825170i	−0.432175	+	0.901790i	$0.642254\pi$
$264$		0			0
$265$			5.39919i			0.331670i
$266$	−5.52672	−	10.3981i	−0.338865	−	0.637550i
$267$		0			0
$268$	−9.22190	−	13.0474i	−0.563317	−	0.796996i
$269$	17.3592	−	10.0223i	1.05841	−	0.611073i	0.133418	−	0.991060i	$-0.457405\pi$
$269$	17.3592	−	10.0223i	1.05841	−	0.611073i	0.924992	+	0.379987i	$0.124071\pi$
$270$		0			0
$271$	4.36814	−	7.56584i	0.265346	−	0.459592i	−0.702309	−	0.711873i	$-0.747847\pi$
$271$	4.36814	−	7.56584i	0.265346	−	0.459592i	0.967654	+	0.252281i	$0.0811806\pi$
$272$	6.25146	−	5.34027i	0.379051	−	0.323802i
$273$		0			0
$274$	27.8917	+	6.11893i	1.68500	+	0.369658i
$275$	8.07716	+	4.66335i	0.487071	+	0.281211i
$276$		0			0
$277$	5.73771	+	9.93800i	0.344746	+	0.597117i	0.985308	−	0.170790i	$-0.0546319\pi$
$277$	5.73771	+	9.93800i	0.344746	+	0.597117i	−0.640562	+	0.767906i	$0.721299\pi$
$278$	−21.4459	+	23.5079i	−1.28624	+	1.40991i
$279$		0			0
$280$	−3.33392	−	5.08626i	−0.199240	−	0.303962i
$281$	−19.6940			−1.17484			−0.587422	−	0.809281i	$-0.699857\pi$
$281$	−19.6940			−1.17484			−0.587422	+	0.809281i	$0.699857\pi$
$282$		0			0
$283$	1.80656	+	3.12905i	0.107389	+	0.186003i	0.914712	−	0.404107i	$-0.132418\pi$
$283$	1.80656	+	3.12905i	0.107389	+	0.186003i	−0.807323	+	0.590110i	$0.799084\pi$
$284$	−22.0230	+	2.02468i	−1.30683	+	0.120143i
$285$		0			0
$286$	15.2613	+	3.34806i	0.902420	+	0.197975i
$287$	−1.21452	−	6.64034i	−0.0716906	−	0.391967i
$288$		0			0
$289$	−6.38752	+	11.0635i	−0.375737	+	0.650795i
$290$	8.38165	−	2.66306i	0.492188	−	0.156380i
$291$		0			0
$292$	−11.5212	−	16.3005i	−0.674228	−	0.953915i
$293$		−	26.8845i		−	1.57061i	−0.619110	−	0.785304i	$-0.712506\pi$
$293$		−	26.8845i		−	1.57061i	0.619110	−	0.785304i	$-0.287494\pi$
$294$		0			0
$295$		−	10.2822i		−	0.598656i
$296$	−15.3605	+	6.48191i	−0.892811	+	0.376754i
$297$		0			0
$298$	−5.09347	−	16.0311i	−0.295057	−	0.928656i
$299$	4.87279	−	8.43991i	0.281800	−	0.488093i
$300$		0			0
$301$	4.89421	+	26.7590i	0.282097	+	1.54236i
$302$	2.92137	−	13.3163i	0.168106	−	0.766269i
$303$		0			0
$304$	4.20107	−	11.8670i	0.240948	−	0.680620i
$305$	−2.41819	−	4.18842i	−0.138465	−	0.239828i
$306$		0			0
$307$	−9.99662			−0.570537			−0.285269	−	0.958448i	$-0.592083\pi$
$307$	−9.99662			−0.570537			−0.285269	+	0.958448i	$0.592083\pi$
$308$	−8.12789	−	7.95456i	−0.463130	−	0.453253i
$309$		0			0
$310$	−0.872517	−	0.795982i	−0.0495556	−	0.0452087i
$311$	9.81325	+	16.9970i	0.556458	+	0.963814i	0.997788	+	0.0664690i	$0.0211733\pi$
$311$	9.81325	+	16.9970i	0.556458	+	0.963814i	−0.441330	+	0.897345i	$0.645493\pi$
$312$		0			0
$313$	19.3657	+	11.1808i	1.09462	+	0.631977i	0.934802	−	0.355171i	$-0.115577\pi$
$313$	19.3657	+	11.1808i	1.09462	+	0.631977i	0.159814	+	0.987147i	$0.448911\pi$
$314$	1.81304	−	8.26428i	0.102316	−	0.466380i
$315$		0			0
$316$	−6.59780	+	14.3135i	−0.371155	+	0.805197i
$317$	1.16986	−	2.02626i	0.0657061	−	0.113806i	−0.831301	−	0.555823i	$-0.812403\pi$
$317$	1.16986	−	2.02626i	0.0657061	−	0.113806i	0.897007	+	0.442016i	$0.145737\pi$
$318$		0			0
$319$	14.2427	−	8.22304i	0.797439	−	0.460402i
$320$	1.59946	−	6.30162i	0.0894125	−	0.352271i
$321$		0			0
$322$	−6.26385	+	3.32931i	−0.349071	+	0.185535i
$323$		−	6.46892i		−	0.359940i
$324$		0			0
$325$	−19.3186	+	11.1536i	−1.07160	+	0.618691i
$326$	13.2836	−	4.22052i	0.735708	−	0.233753i
$327$		0			0
$328$	4.35521	−	5.75424i	0.240476	−	0.317725i
$329$	1.88878	−	5.29402i	0.104132	−	0.291869i
$330$		0			0
$331$	25.7526	+	14.8683i	1.41549	+	0.817234i	0.995898	−	0.0904788i	$-0.0288397\pi$
$331$	25.7526	+	14.8683i	1.41549	+	0.817234i	0.419592	+	0.907713i	$0.362173\pi$
$332$	3.20522	+	34.8641i	0.175909	+	1.91342i
$333$		0			0
$334$	19.5194	−	21.3963i	1.06806	−	1.17075i
$335$	−6.49226			−0.354710
$336$		0			0
$337$	−1.92824			−0.105038			−0.0525191	−	0.998620i	$-0.516725\pi$
$337$	−1.92824			−0.105038			−0.0525191	+	0.998620i	$0.516725\pi$
$338$	−12.7950	+	14.0252i	−0.695954	+	0.762871i
$339$		0			0
$340$	−0.305852	−	3.32685i	−0.0165872	−	0.180424i
$341$	−1.91270	−	1.10430i	−0.103579	−	0.0598011i
$342$		0			0
$343$	−15.8592	+	9.56478i	−0.856317	+	0.516450i
$344$	−17.5504	+	23.1882i	−0.946256	+	1.25022i
$345$		0			0
$346$	5.38676	−	1.71151i	0.289594	−	0.0920113i
$347$	11.6827	−	6.74504i	0.627163	−	0.362093i	−0.152490	−	0.988305i	$-0.548729\pi$
$347$	11.6827	−	6.74504i	0.627163	−	0.362093i	0.779652	+	0.626212i	$0.215396\pi$
$348$		0			0
$349$			22.7410i			1.21730i	0.793439	+	0.608650i	$0.208288\pi$
$349$			22.7410i			1.21730i	−0.793439	+	0.608650i	$0.791712\pi$
$350$	16.2271	+	0.569172i	0.867377	+	0.0304235i
$351$		0			0
$352$	0.396363	−	12.1514i	0.0211262	−	0.647673i
$353$	−22.4215	+	12.9450i	−1.19337	+	0.688995i	−0.959070	−	0.283169i	$-0.908614\pi$
$353$	−22.4215	+	12.9450i	−1.19337	+	0.688995i	−0.234304	+	0.972163i	$0.575281\pi$
$354$		0			0
$355$	−4.49328	+	7.78259i	−0.238479	+	0.413057i
$356$	−0.468798	+	1.01703i	−0.0248463	+	0.0539024i
$357$		0			0
$358$	−5.58110	+	25.4401i	−0.294970	+	1.34455i
$359$	0.384185	+	0.221809i	0.0202765	+	0.0117066i	0.510104	−	0.860113i	$-0.329607\pi$
$359$	0.384185	+	0.221809i	0.0202765	+	0.0117066i	−0.489827	+	0.871819i	$0.662940\pi$
$360$		0			0
$361$	4.54765	+	7.87677i	0.239350	+	0.414567i
$362$	9.16997	+	8.36560i	0.481963	+	0.439686i
$363$		0			0
$364$	26.1964	−	7.32281i	1.37307	−	0.383819i
$365$	−8.11098			−0.424548
$366$		0			0
$367$	13.6052	+	23.5650i	0.710188	+	1.23008i	0.964786	+	0.263035i	$0.0847233\pi$
$367$	13.6052	+	23.5650i	0.710188	+	1.23008i	−0.254599	+	0.967047i	$0.581943\pi$
$368$	−7.14871	−	2.53073i	−0.372652	−	0.131924i
$369$		0			0
$370$	−1.45169	+	6.61719i	−0.0754699	+	0.344011i
$371$	11.3841	+	13.3930i	0.591035	+	0.695329i
$372$		0			0
$373$	−8.63311	+	14.9530i	−0.447005	+	0.774236i	−0.998189	−	0.0601476i	$-0.980843\pi$
$373$	−8.63311	+	14.9530i	−0.447005	+	0.774236i	0.551184	+	0.834384i	$0.314176\pi$
$374$	−1.89181	−	5.95423i	−0.0978231	−	0.307886i
$375$		0			0
$376$	5.53622	−	2.33621i	0.285509	−	0.120481i
$377$			39.3350i			2.02586i
$378$		0			0
$379$		−	30.0266i		−	1.54236i	−0.636616	−	0.771181i	$-0.719666\pi$
$379$		−	30.0266i		−	1.54236i	0.636616	−	0.771181i	$-0.280334\pi$
$380$	−2.95246	−	4.17721i	−0.151458	−	0.214287i
$381$		0			0
$382$	−29.6011	+	9.40500i	−1.51452	+	0.481201i
$383$	−10.5011	+	18.1884i	−0.536581	+	0.929386i	0.462504	+	0.886617i	$0.346951\pi$
$383$	−10.5011	+	18.1884i	−0.536581	+	0.929386i	−0.999085	+	0.0427689i	$0.986382\pi$
$384$		0			0
$385$	−4.54576	+	0.831417i	−0.231673	+	0.0423729i
$386$	−0.968807	−	0.212539i	−0.0493110	−	0.0108179i
$387$		0			0
$388$	−3.67922	+	0.338248i	−0.186784	+	0.0171719i
$389$	−4.55328	−	7.88652i	−0.230861	−	0.399862i	0.727201	−	0.686425i	$-0.240821\pi$
$389$	−4.55328	−	7.88652i	−0.230861	−	0.399862i	−0.958062	+	0.286562i	$0.907487\pi$
$390$		0			0
$391$	−3.89688			−0.197074
$392$	−18.9943	−	5.58720i	−0.959357	−	0.282196i
$393$		0			0
$394$	22.8365	−	25.0323i	1.15049	−	1.26111i
$395$	3.20215	+	5.54628i	0.161118	+	0.279064i
$396$		0			0
$397$	−3.92841	−	2.26807i	−0.197161	−	0.113831i	0.398169	−	0.917312i	$-0.369646\pi$
$397$	−3.92841	−	2.26807i	−0.197161	−	0.113831i	−0.595331	+	0.803481i	$0.702979\pi$
$398$	3.03005	+	0.664739i	0.151883	+	0.0333203i
$399$		0			0
$400$	11.2745	+	13.1982i	0.563725	+	0.659911i
$401$	−12.5118	+	21.6711i	−0.624810	+	1.08220i	0.363767	+	0.931490i	$0.381490\pi$
$401$	−12.5118	+	21.6711i	−0.624810	+	1.08220i	−0.988577	+	0.150714i	$0.951843\pi$
$402$		0			0
$403$	4.57472	−	2.64122i	0.227883	−	0.131568i
$404$	−18.8569	−	26.6792i	−0.938165	−	1.32734i
$405$		0			0
$406$	15.1761	−	24.2785i	0.753177	−	1.20492i
$407$			12.6686i			0.627961i
$408$		0			0
$409$	3.37147	−	1.94652i	0.166708	−	0.0962490i	−0.414325	−	0.910129i	$-0.635982\pi$
$409$	3.37147	−	1.94652i	0.166708	−	0.0962490i	0.581033	+	0.813880i	$0.302649\pi$
$410$	−0.887951	−	2.79471i	−0.0438527	−	0.138021i
$411$		0			0
$412$	8.66417	+	3.99374i	0.426853	+	0.196758i
$413$	−21.6800	−	25.5057i	−1.06680	−	1.25505i
$414$		0			0
$415$	12.3204	+	7.11320i	0.604786	+	0.349173i
$416$	24.6956	+	15.3526i	1.21080	+	0.752725i
$417$		0			0
$418$	−7.06684	−	6.44696i	−0.345651	−	0.315331i
$419$	−11.4873			−0.561192			−0.280596	−	0.959826i	$-0.590532\pi$
$419$	−11.4873			−0.561192			−0.280596	+	0.959826i	$0.590532\pi$
$420$		0			0
$421$	−7.14186			−0.348073			−0.174037	−	0.984739i	$-0.555681\pi$
$421$	−7.14186			−0.348073			−0.174037	+	0.984739i	$0.555681\pi$
$422$	−11.5388	−	10.5266i	−0.561698	−	0.512428i
$423$		0			0
$424$	−2.32944	+	18.6463i	−0.113128	+	0.905543i
$425$	7.72479	+	4.45991i	0.374707	+	0.216337i
$426$		0			0
$427$	−14.8297	−	5.29088i	−0.717659	−	0.256044i
$428$	−3.91905	+	8.50214i	−0.189435	+	0.410967i
$429$		0			0
$430$	3.57823	+	11.2620i	0.172558	+	0.543103i
$431$	−17.9137	+	10.3425i	−0.862873	+	0.498180i	−0.864973	−	0.501818i	$-0.832665\pi$
$431$	−17.9137	+	10.3425i	−0.862873	+	0.498180i	0.00210056	+	0.999998i	$0.499331\pi$
$432$		0			0
$433$			14.4701i			0.695389i	0.937608	+	0.347695i	$0.113035\pi$
$433$			14.4701i			0.695389i	−0.937608	+	0.347695i	$0.886965\pi$
$434$	−3.84264	−	0.134782i	−0.184453	−	0.00646974i
$435$		0			0
$436$	−13.7066	+	9.68782i	−0.656426	+	0.463962i
$437$	−5.16723	+	2.98330i	−0.247182	+	0.142711i
$438$		0			0
$439$	2.54215	−	4.40313i	0.121330	−	0.210150i	−0.798962	−	0.601381i	$-0.794617\pi$
$439$	2.54215	−	4.40313i	0.121330	−	0.210150i	0.920292	+	0.391231i	$0.127951\pi$
$440$	−3.93916	−	2.98143i	−0.187792	−	0.142134i
$441$		0			0
$442$	14.5955	+	3.20200i	0.694238	+	0.152303i
$443$	−4.97946	−	2.87489i	−0.236581	−	0.136590i	0.377023	−	0.926204i	$-0.376948\pi$
$443$	−4.97946	−	2.87489i	−0.236581	−	0.136590i	−0.613605	+	0.789614i	$0.710281\pi$
$444$		0			0
$445$	0.227525	+	0.394084i	0.0107857	+	0.0186814i
$446$	−19.4530	+	21.3235i	−0.921128	+	1.00970i
$447$		0			0
$448$	−9.31936	−	19.0039i	−0.440298	−	0.897852i
$449$	−18.3848			−0.867630			−0.433815	−	0.901002i	$-0.642833\pi$
$449$	−18.3848			−0.867630			−0.433815	+	0.901002i	$0.642833\pi$
$450$		0			0
$451$	−2.74183	−	4.74898i	−0.129108	−	0.223621i
$452$	0.476626	+	5.18440i	0.0224186	+	0.243854i
$453$		0			0
$454$	−6.09792	−	1.33777i	−0.286190	−	0.0627849i
$455$	3.71405	−	10.4100i	0.174117	−	0.488029i
$456$		0			0
$457$	14.5364	−	25.1777i	0.679982	−	1.17776i	−0.295003	−	0.955496i	$-0.595321\pi$
$457$	14.5364	−	25.1777i	0.679982	−	1.17776i	0.974986	−	0.222268i	$-0.0713459\pi$
$458$	−25.7618	+	8.18517i	−1.20377	+	0.382468i
$459$		0			0
$460$	−2.51636	+	1.77857i	−0.117326	+	0.0829261i
$461$		−	27.4011i		−	1.27620i	−0.769954	−	0.638099i	$-0.779721\pi$
$461$		−	27.4011i		−	1.27620i	0.769954	−	0.638099i	$-0.220279\pi$
$462$		0			0
$463$		−	33.6619i		−	1.56440i	−0.623027	−	0.782200i	$-0.714097\pi$
$463$		−	33.6619i		−	1.56440i	0.623027	−	0.782200i	$-0.285903\pi$
$464$	30.0952	−	5.58075i	1.39714	−	0.259080i
$465$		0			0
$466$	6.17155	+	19.4242i	0.285892	+	0.899809i
$467$	7.28260	−	12.6138i	0.336998	−	0.583698i	−0.646868	−	0.762602i	$-0.723922\pi$
$467$	7.28260	−	12.6138i	0.336998	−	0.583698i	0.983867	+	0.178903i	$0.0572549\pi$
$468$		0			0
$469$	−16.1044	+	13.6889i	−0.743632	+	0.632093i
$470$	0.523218	−	2.38496i	0.0241342	−	0.110010i
$471$		0			0
$472$	4.43619	−	35.5100i	0.204192	−	1.63448i
$473$	11.0489	+	19.1373i	0.508029	+	0.879933i
$474$		0			0
$475$	13.6573			0.626641
$476$	−7.77330	−	7.60753i	−0.356289	−	0.348691i
$477$		0			0
$478$	−13.9289	−	12.7071i	−0.637093	−	0.581209i
$479$	3.36750	+	5.83269i	0.153865	+	0.266502i	0.932645	−	0.360795i	$-0.117495\pi$
$479$	3.36750	+	5.83269i	0.153865	+	0.266502i	−0.778780	+	0.627297i	$0.784161\pi$
$480$		0			0
$481$	−26.2408	−	15.1502i	−1.19648	−	0.690788i
$482$	−7.45398	+	33.9771i	−0.339519	+	1.54762i
$483$		0			0
$484$	11.5896	+	5.34222i	0.526801	+	0.242828i
$485$	−0.750659	+	1.30018i	−0.0340857	+	0.0590381i
$486$		0			0
$487$	4.48186	−	2.58760i	0.203093	−	0.117256i	−0.395005	−	0.918679i	$-0.629257\pi$
$487$	4.48186	−	2.58760i	0.203093	−	0.117256i	0.598097	+	0.801424i	$0.295924\pi$
$488$	−6.54421	−	15.5081i	−0.296243	−	0.702021i
$489$		0			0
$490$	−6.30874	+	4.99236i	−0.285000	+	0.225532i
$491$			4.23104i			0.190944i	0.995432	+	0.0954720i	$0.0304360\pi$
$491$			4.23104i			0.190944i	−0.995432	+	0.0954720i	$0.969564\pi$
$492$		0			0
$493$	13.6214	−	7.86430i	0.613475	−	0.354190i
$494$	21.8048	−	6.92794i	0.981046	−	0.311703i
$495$		0			0
$496$	−2.66984	−	3.12539i	−0.119879	−	0.140334i
$497$	5.26369	+	28.7792i	0.236109	+	1.29092i
$498$		0			0
$499$	24.9498	+	14.4048i	1.11691	+	0.644846i	0.940609	−	0.339491i	$-0.110255\pi$
$499$	24.9498	+	14.4048i	1.11691	+	0.644846i	0.176297	+	0.984337i	$0.443588\pi$
$500$	15.1164	−	1.38972i	0.676025	−	0.0621501i
$501$		0			0
$502$	−1.40407	+	1.53907i	−0.0626667	+	0.0686922i
$503$	33.0972			1.47573			0.737865	−	0.674948i	$-0.235834\pi$
$503$	33.0972			1.47573			0.737865	+	0.674948i	$0.235834\pi$
$504$		0			0
$505$	−13.2753			−0.590744
$506$	−3.88366	+	4.25708i	−0.172650	+	0.189250i
$507$		0			0
$508$	−13.3481	+	1.22716i	−0.592228	+	0.0544462i
$509$	−16.1832	−	9.34337i	−0.717308	−	0.414138i	0.0964533	−	0.995338i	$-0.469250\pi$
$509$	−16.1832	−	9.34337i	−0.717308	−	0.414138i	−0.813761	+	0.581200i	$0.802584\pi$
$510$		0			0
$511$	−20.1197	+	17.1019i	−0.890044	+	0.756544i
$512$	8.24255	−	21.0727i	0.364273	−	0.931292i
$513$		0			0
$514$	−14.3682	+	4.56513i	−0.633754	+	0.201359i
$515$	3.35725	−	1.93831i	0.147938	−	0.0854120i
$516$		0			0
$517$		−	4.56602i		−	0.200813i
$518$	10.3513	+	19.4752i	0.454809	+	0.855689i
$519$		0			0
$520$	10.8863	−	4.59385i	0.477395	−	0.201454i
$521$	17.4125	−	10.0531i	0.762855	−	0.440435i	−0.0674646	−	0.997722i	$-0.521491\pi$
$521$	17.4125	−	10.0531i	0.762855	−	0.440435i	0.830320	+	0.557287i	$0.188158\pi$
$522$		0			0
$523$	10.3935	−	18.0021i	0.454476	−	0.787175i	−0.544182	−	0.838967i	$-0.683160\pi$
$523$	10.3935	−	18.0021i	0.454476	−	0.787175i	0.998658	+	0.0517922i	$0.0164933\pi$
$524$	−26.7919	−	12.3497i	−1.17041	−	0.539499i
$525$		0			0
$526$	−8.11073	+	36.9708i	−0.353645	+	1.61200i
$527$	−1.82926	−	1.05612i	−0.0796837	−	0.0460054i
$528$		0			0
$529$	−9.70286	−	16.8058i	−0.421863	−	0.730689i
$530$	5.64093	+	5.14612i	0.245026	+	0.223533i
$531$		0			0
$532$	−16.1313	−	4.13657i	−0.699382	−	0.179343i
$533$	13.1156			0.568099
$534$		0			0
$535$	1.90206	+	3.29446i	0.0822332	+	0.142432i
$536$	−22.4212	−	2.80103i	−0.968448	−	0.120986i
$537$		0			0
$538$	6.07447	−	27.6890i	0.261889	−	1.19376i
$539$	−9.52296	+	11.6471i	−0.410183	+	0.501674i
$540$		0			0
$541$	15.1843	−	26.3000i	0.652824	−	1.13072i	−0.329611	−	0.944117i	$-0.606917\pi$
$541$	15.1843	−	26.3000i	0.652824	−	1.13072i	0.982435	−	0.186607i	$-0.0597492\pi$
$542$	−3.74118	−	11.7749i	−0.160698	−	0.505776i
$543$		0			0
$544$	0.379071	−	11.6213i	0.0162525	−	0.498260i
$545$			6.82026i			0.292148i
$546$		0			0
$547$			13.2770i			0.567685i	0.958871	+	0.283842i	$0.0916092\pi$
$547$			13.2770i			0.567685i	−0.958871	+	0.283842i	$0.908391\pi$
$548$	32.9772	−	23.3083i	1.40872	−	0.995682i
$549$		0			0
$550$	12.5707	−	3.99403i	0.536017	−	0.170306i
$551$	12.0412	−	20.8560i	0.512972	−	0.888493i
$552$		0			0
$553$	19.6374	+	7.00615i	0.835066	+	0.297932i
$554$	15.8517	+	3.47758i	0.673475	+	0.147748i
$555$		0			0
$556$	4.11978	+	44.8121i	0.174718	+	1.90046i
$557$	−15.4608	−	26.7788i	−0.655093	−	1.13465i	−0.981870	−	0.189553i	$-0.939296\pi$
$557$	−15.4608	−	26.7788i	−0.655093	−	1.13465i	0.326777	−	0.945101i	$-0.394037\pi$
$558$		0			0
$559$	−52.8527			−2.23543
$560$	−8.49163	−	1.36467i	−0.358837	−	0.0576678i
$561$		0			0
$562$	−18.7709	+	20.5757i	−0.791801	+	0.867934i
$563$	−11.6019	−	20.0950i	−0.488960	−	0.846904i	0.510959	−	0.859605i	$-0.329290\pi$
$563$	−11.6019	−	20.0950i	−0.488960	−	0.846904i	−0.999919	+	0.0127010i	$0.995957\pi$
$564$		0			0
$565$	1.83209	+	1.05776i	0.0770764	+	0.0445001i
$566$	4.99102	+	1.09494i	0.209788	+	0.0460238i
$567$		0			0
$568$	−18.8754	+	24.9388i	−0.791994	+	1.04641i
$569$	6.30064	−	10.9130i	0.264137	−	0.457498i	−0.703200	−	0.710992i	$-0.748246\pi$
$569$	6.30064	−	10.9130i	0.264137	−	0.457498i	0.967337	+	0.253494i	$0.0815797\pi$
$570$		0			0
$571$	−36.0513	+	20.8142i	−1.50870	+	0.871049i	−0.508752	+	0.860913i	$0.669893\pi$
$571$	−36.0513	+	20.8142i	−1.50870	+	0.871049i	−0.999949	+	0.0101362i	$0.996774\pi$
$572$	18.0439	−	12.7535i	0.754455	−	0.533249i
$573$		0			0
$574$	−8.09523	−	5.06020i	−0.337888	−	0.211209i
$575$		−	8.22719i		−	0.343097i
$576$		0			0
$577$	19.5101	−	11.2642i	0.812218	−	0.468934i	−0.0355075	−	0.999369i	$-0.511305\pi$
$577$	19.5101	−	11.2642i	0.812218	−	0.468934i	0.847726	+	0.530435i	$0.177971\pi$
$578$	5.47073	+	17.2184i	0.227552	+	0.716193i
$579$		0			0
$580$	5.20649	−	11.2951i	0.216188	−	0.469006i
$581$	45.5596	−	8.33282i	1.89013	−	0.345704i
$582$		0			0
$583$	12.3658	+	7.13942i	0.512141	+	0.295685i
$584$	−28.0115	−	3.49942i	−1.15912	−	0.144807i
$585$		0			0
$586$	−28.0882	−	25.6243i	−1.16031	−	1.05853i
$587$	−8.49214			−0.350508			−0.175254	−	0.984523i	$-0.556075\pi$
$587$	−8.49214			−0.350508			−0.175254	+	0.984523i	$0.556075\pi$
$588$		0			0
$589$	−3.23410			−0.133259
$590$	−10.7426	−	9.80029i	−0.442266	−	0.403472i
$591$		0			0
$592$	−7.86839	+	22.2263i	−0.323389	+	0.913496i
$593$	−0.699256	−	0.403715i	−0.0287150	−	0.0165786i	0.485574	−	0.874196i	$-0.338611\pi$
$593$	−0.699256	−	0.403715i	−0.0287150	−	0.0165786i	−0.514289	+	0.857617i	$0.671944\pi$
$594$		0			0
$595$	−4.34745	+	0.795145i	−0.178228	+	0.0325978i
$596$	−21.6036	−	9.95814i	−0.884916	−	0.407901i
$597$		0			0
$598$	−4.17340	−	13.1353i	−0.170663	−	0.537141i
$599$	−27.9459	+	16.1346i	−1.14184	+	0.659240i	−0.946885	−	0.321572i	$-0.895789\pi$
$599$	−27.9459	+	16.1346i	−1.14184	+	0.659240i	−0.194953	+	0.980813i	$0.562455\pi$
$600$		0			0
$601$			2.37514i			0.0968838i	0.998826	+	0.0484419i	$0.0154256\pi$
$601$			2.37514i			0.0968838i	−0.998826	+	0.0484419i	$0.984574\pi$
$602$	32.6219	+	20.3914i	1.32957	+	0.831092i
$603$		0			0
$604$	−11.1281	−	15.7443i	−0.452796	−	0.640627i
$605$	4.49082	−	2.59277i	0.182578	−	0.105411i
$606$		0			0
$607$	8.99848	−	15.5858i	0.365237	−	0.632609i	−0.623577	−	0.781762i	$-0.714321\pi$
$607$	8.99848	−	15.5858i	0.365237	−	0.632609i	0.988814	+	0.149153i	$0.0476545\pi$
$608$	−8.39417	−	15.6999i	−0.340429	−	0.636717i
$609$		0			0
$610$	−6.68079	−	1.46565i	−0.270497	−	0.0593423i
$611$	9.45770	+	5.46041i	0.382618	+	0.220904i
$612$		0			0
$613$	8.95667	+	15.5134i	0.361757	+	0.626581i	0.988250	−	0.152846i	$-0.0488438\pi$
$613$	8.95667	+	15.5134i	0.361757	+	0.626581i	−0.626493	+	0.779427i	$0.715510\pi$
$614$	−9.52805	+	10.4442i	−0.384521	+	0.421493i
$615$		0			0
$616$	−16.0576	+	0.910090i	−0.646980	+	0.0366686i
$617$	7.48143			0.301191			0.150596	−	0.988595i	$-0.451881\pi$
$617$	7.48143			0.301191			0.150596	+	0.988595i	$0.451881\pi$
$618$		0			0
$619$	14.6007	+	25.2892i	0.586852	+	1.01646i	0.994642	+	0.103381i	$0.0329662\pi$
$619$	14.6007	+	25.2892i	0.586852	+	1.01646i	−0.407790	+	0.913076i	$0.633700\pi$
$620$	−1.66324	+	0.152909i	−0.0667973	+	0.00614099i
$621$		0			0
$622$	27.1113	+	5.94774i	1.08706	+	0.238482i
$623$	1.39531	+	0.497814i	0.0559019	+	0.0199445i
$624$		0			0
$625$	−7.76474	+	13.4489i	−0.310589	+	0.537957i
$626$	30.1394	−	9.57604i	1.20461	−	0.382735i
$627$		0			0
$628$	−6.90624	−	9.77112i	−0.275589	−	0.389910i
$629$			12.1159i			0.483094i
$630$		0			0
$631$		−	3.89890i		−	0.155213i	−0.996984	−	0.0776063i	$-0.975272\pi$
$631$		−	3.89890i		−	0.155213i	0.996984	−	0.0776063i	$-0.0247277\pi$
$632$	8.66581	+	20.5358i	0.344707	+	0.816870i
$633$		0			0
$634$	−1.00195	−	3.15353i	−0.0397927	−	0.125243i
$635$	−2.72338	+	4.71702i	−0.108074	+	0.187189i
$636$		0			0
$637$	−12.7365	−	33.6536i	−0.504639	−	1.33341i
$638$	4.98392	−	22.7180i	0.197315	−	0.899414i
$639$		0			0
$640$	−5.05927	−	7.67731i	−0.199985	−	0.303472i
$641$	−1.10624	−	1.91606i	−0.0436938	−	0.0756799i	0.843351	−	0.537362i	$-0.180579\pi$
$641$	−1.10624	−	1.91606i	−0.0436938	−	0.0756799i	−0.887045	+	0.461683i	$0.847246\pi$
$642$		0			0
$643$	−32.8438			−1.29523			−0.647616	−	0.761967i	$-0.724234\pi$
$643$	−32.8438			−1.29523			−0.647616	+	0.761967i	$0.724234\pi$
$644$	−2.49188	+	9.71754i	−0.0981937	+	0.382925i
$645$		0			0
$646$	−6.75854	−	6.16570i	−0.265911	−	0.242586i
$647$	−16.0315	−	27.7674i	−0.630263	−	1.09165i	−0.987498	−	0.157633i	$-0.949614\pi$
$647$	−16.0315	−	27.7674i	−0.630263	−	1.09165i	0.357234	−	0.934015i	$-0.383720\pi$
$648$		0			0
$649$	−23.5496	−	13.5963i	−0.924401	−	0.533703i
$650$	−6.76013	+	30.8144i	−0.265154	+	1.20864i
$651$		0			0
$652$	8.25144	−	17.9010i	0.323151	−	0.701056i
$653$	15.9326	−	27.5961i	0.623491	−	1.07992i	−0.365340	−	0.930874i	$-0.619047\pi$
$653$	15.9326	−	27.5961i	0.623491	−	1.07992i	0.988831	−	0.149044i	$-0.0476195\pi$
$654$		0			0
$655$	−10.3815	+	5.99375i	−0.405638	+	0.234195i
$656$	−1.86080	−	10.0347i	−0.0726522	−	0.391790i
$657$		0			0
$658$	−3.73080	−	7.01922i	−0.145442	−	0.273638i
$659$		−	16.2660i		−	0.633634i	−0.948487	−	0.316817i	$-0.897386\pi$
$659$		−	16.2660i		−	0.633634i	0.948487	−	0.316817i	$-0.102614\pi$
$660$		0			0
$661$	37.3471	−	21.5624i	1.45263	−	0.838679i	0.454004	−	0.891000i	$-0.349995\pi$
$661$	37.3471	−	21.5624i	1.45263	−	0.838679i	0.998630	+	0.0523206i	$0.0166618\pi$
$662$	40.0794	−	12.7342i	1.55773	−	0.494930i
$663$		0			0
$664$	39.4800	+	29.8812i	1.53212	+	1.15961i
$665$	−5.15594	+	4.38259i	−0.199939	+	0.169949i
$666$		0			0
$667$	−12.5637	−	7.25363i	−0.486467	−	0.280862i
$668$	−3.74971	−	40.7867i	−0.145081	−	1.57809i
$669$		0			0
$670$	−6.18795	+	6.78293i	−0.239061	+	0.262048i
$671$	−12.7904			−0.493768
$672$		0			0
$673$	20.3814			0.785645			0.392822	−	0.919614i	$-0.371499\pi$
$673$	20.3814			0.785645			0.392822	+	0.919614i	$0.371499\pi$
$674$	−1.83786	+	2.01458i	−0.0707918	+	0.0775986i
$675$		0			0
$676$	2.45793	+	26.7356i	0.0945358	+	1.02829i
$677$	31.8523	+	18.3900i	1.22419	+	0.706784i	0.965807	−	0.259260i	$-0.0834788\pi$
$677$	31.8523	+	18.3900i	1.22419	+	0.706784i	0.258378	+	0.966044i	$0.416812\pi$
$678$		0			0
$679$	0.879366	+	4.80792i	0.0337470	+	0.184511i
$680$	−3.76731	−	2.85136i	−0.144470	−	0.109345i
$681$		0			0
$682$	−2.97679	+	0.945800i	−0.113987	+	0.0362165i
$683$	29.7576	−	17.1805i	1.13864	−	0.657395i	0.192548	−	0.981288i	$-0.438325\pi$
$683$	29.7576	−	17.1805i	1.13864	−	0.657395i	0.946094	+	0.323892i	$0.104992\pi$
$684$		0			0
$685$		−	16.4091i		−	0.626961i
$686$	−5.12283	+	25.6857i	−0.195591	+	0.980686i
$687$		0			0
$688$	7.49860	+	40.4375i	0.285881	+	1.54167i
$689$	−29.5761	+	17.0758i	−1.12676	+	0.650535i
$690$		0			0
$691$	24.0149	−	41.5950i	0.913568	−	1.58235i	0.104584	−	0.994516i	$-0.466649\pi$
$691$	24.0149	−	41.5950i	0.913568	−	1.58235i	0.808984	−	0.587830i	$-0.200018\pi$
$692$	3.34613	−	7.25923i	0.127201	−	0.275954i
$693$		0			0
$694$	4.08812	−	18.6347i	0.155183	−	0.707363i
$695$	15.8359	+	9.14286i	0.600690	+	0.346808i
$696$		0			0
$697$	−2.62221	−	4.54180i	−0.0993234	−	0.172033i
$698$	23.7592	+	21.6751i	0.899298	+	0.820414i
$699$		0			0
$700$	16.0612	−	16.4112i	0.607056	−	0.620284i
$701$	−1.33206			−0.0503111			−0.0251555	−	0.999684i	$-0.508008\pi$
$701$	−1.33206			−0.0503111			−0.0251555	+	0.999684i	$0.508008\pi$
$702$		0			0
$703$	9.27549	+	16.0656i	0.349832	+	0.605926i
$704$	−12.3177	−	11.9960i	−0.464240	−	0.452115i
$705$		0			0
$706$	−7.84589	+	35.7636i	−0.295284	+	1.34598i
$707$	−32.9301	+	27.9909i	−1.23847	+	1.05271i
$708$		0			0
$709$	15.9986	−	27.7104i	0.600840	−	1.04068i	−0.391855	−	0.920027i	$-0.628166\pi$
$709$	15.9986	−	27.7104i	0.600840	−	1.04068i	0.992694	−	0.120658i	$-0.0385003\pi$
$710$	3.84837	+	12.1123i	0.144427	+	0.454565i
$711$		0			0
$712$	0.615738	+	1.45915i	0.0230758	+	0.0546838i
$713$			1.94823i			0.0729617i
$714$		0			0
$715$		−	8.97849i		−	0.335777i
$716$	21.2596	+	30.0786i	0.794507	+	1.12409i
$717$		0			0
$718$	0.597917	−	0.189973i	0.0223141	−	0.00708973i
$719$	1.60377	−	2.77780i	0.0598104	−	0.103595i	−0.834570	−	0.550902i	$-0.814284\pi$
$719$	1.60377	−	2.77780i	0.0598104	−	0.103595i	0.894380	+	0.447308i	$0.147617\pi$
$720$		0			0
$721$	4.24092	−	11.8868i	0.157940	−	0.442687i
$722$	12.5639	+	2.75630i	0.467581	+	0.102579i
$723$		0			0
$724$	17.4803	−	1.60704i	0.649650	−	0.0597253i
$725$	16.6033	+	28.7577i	0.616630	+	1.06803i
$726$		0			0
$727$	−50.4852			−1.87239			−0.936197	−	0.351477i	$-0.885680\pi$
$727$	−50.4852			−1.87239			−0.936197	+	0.351477i	$0.885680\pi$
$728$	17.3179	−	34.3489i	0.641843	−	1.27305i
$729$		0			0
$730$	−7.73080	+	8.47413i	−0.286130	+	0.313642i
$731$	10.5669	+	18.3024i	0.390830	+	0.676938i
$732$		0			0
$733$	−4.98706	−	2.87928i	−0.184201	−	0.106349i	0.405064	−	0.914288i	$-0.367249\pi$
$733$	−4.98706	−	2.87928i	−0.184201	−	0.106349i	−0.589265	+	0.807940i	$0.700583\pi$
$734$	37.5875	+	8.24604i	1.38738	+	0.304367i
$735$		0			0
$736$	−9.45767	+	5.05666i	−0.348614	+	0.186391i
$737$	−8.58479	+	14.8693i	−0.316225	+	0.547718i
$738$		0			0
$739$	22.7520	−	13.1359i	0.836945	−	0.483210i	−0.0192796	−	0.999814i	$-0.506137\pi$
$739$	22.7520	−	13.1359i	0.836945	−	0.483210i	0.856225	+	0.516604i	$0.172804\pi$
$740$	5.52980	+	7.82371i	0.203280	+	0.287605i
$741$		0			0
$742$	24.8432	+	0.871382i	0.912021	+	0.0319894i
$743$			1.42155i			0.0521516i	0.999660	+	0.0260758i	$0.00830112\pi$
$743$			1.42155i			0.0521516i	−0.999660	+	0.0260758i	$0.991699\pi$
$744$		0			0
$745$	−8.37108	+	4.83304i	−0.306693	+	0.177069i
$746$	7.39401	+	23.2717i	0.270714	+	0.852038i
$747$		0			0
$748$	−8.02395	−	3.69863i	−0.293385	−	0.135235i
$749$	11.6645	+	4.16162i	0.426211	+	0.152062i
$750$		0			0
$751$	41.4368	+	23.9235i	1.51205	+	0.872982i	0.999901	+	0.0140857i	$0.00448377\pi$
$751$	41.4368	+	23.9235i	1.51205	+	0.872982i	0.512149	+	0.858897i	$0.328850\pi$
$752$	2.83592	−	8.01079i	0.103415	−	0.292123i
$753$		0			0
$754$	41.0962	+	37.4913i	1.49663	+	1.36535i
$755$	−7.83423			−0.285117
$756$		0			0
$757$	31.0162			1.12730			0.563651	−	0.826013i	$-0.309396\pi$
$757$	31.0162			1.12730			0.563651	+	0.826013i	$0.309396\pi$
$758$	−31.3709	−	28.6191i	−1.13944	−	1.03949i
$759$		0			0
$760$	−7.17831	−	0.896771i	−0.260385	−	0.0325293i
$761$	10.0676	+	5.81256i	0.364952	+	0.210705i	0.671251	−	0.741230i	$-0.265757\pi$
$761$	10.0676	+	5.81256i	0.364952	+	0.210705i	−0.306299	+	0.951935i	$0.599091\pi$
$762$		0			0
$763$	14.3805	+	16.9180i	0.520607	+	0.612473i
$764$	−18.3875	+	39.8905i	−0.665236	+	1.44319i
$765$		0			0
$766$	8.99389	+	28.3072i	0.324963	+	1.02278i
$767$	56.3249	−	32.5192i	2.03377	−	1.17420i
$768$		0			0
$769$		−	27.9395i		−	1.00752i	−0.863843	−	0.503762i	$-0.831949\pi$
$769$		−	27.9395i		−	1.00752i	0.863843	−	0.503762i	$-0.168051\pi$
$770$	−3.46405	+	5.54173i	−0.124836	+	0.199710i
$771$		0			0
$772$	−1.14545	+	0.809605i	−0.0412257	+	0.0291383i
$773$	46.4286	−	26.8056i	1.66992	−	0.964129i	0.702243	−	0.711938i	$-0.252182\pi$
$773$	46.4286	−	26.8056i	1.66992	−	0.964129i	0.967677	−	0.252191i	$-0.0811512\pi$
$774$		0			0
$775$	2.22971	−	3.86197i	0.0800935	−	0.138726i
$776$	−3.15337	+	4.16634i	−0.113200	+	0.149563i
$777$		0			0
$778$	−12.5795	−	2.75971i	−0.450996	−	0.0989404i
$779$	−6.95405	−	4.01492i	−0.249155	−	0.143850i
$780$		0			0
$781$	11.8830	+	20.5820i	0.425209	+	0.736483i
$782$	−3.71423	+	4.07136i	−0.132820	+	0.145591i
$783$		0			0
$784$	−23.9413	+	14.5194i	−0.855048	+	0.518550i
$785$	−4.86202			−0.173533
$786$		0			0
$787$	−20.7021	−	35.8571i	−0.737950	−	1.27817i	−0.953417	−	0.301656i	$-0.902461\pi$
$787$	−20.7021	−	35.8571i	−0.737950	−	1.27817i	0.215467	−	0.976511i	$-0.430873\pi$
$788$	−4.38693	−	47.7179i	−0.156278	−	1.69988i
$789$		0			0
$790$	8.84666	+	1.94080i	0.314750	+	0.0690505i
$791$	6.77485	−	1.23912i	0.240886	−	0.0440579i
$792$		0			0
$793$	15.2958	−	26.4931i	0.543169	−	0.940796i
$794$	−6.11389	+	1.94254i	−0.216974	+	0.0689380i
$795$		0			0
$796$	3.58252	−	2.53213i	0.126979	−	0.0897490i
$797$		−	10.5390i		−	0.373311i	−0.982425	−	0.186656i	$-0.940235\pi$
$797$		−	10.5390i		−	0.373311i	0.982425	−	0.186656i	$-0.0597648\pi$
$798$		0			0
$799$		−	4.36682i		−	0.154487i
$800$	24.5352	+	0.800303i	0.867449	+	0.0282950i
$801$		0			0
$802$	10.7160	+	33.7273i	0.378396	+	1.19095i
$803$	−10.7253	+	18.5767i	−0.378486	+	0.655557i
$804$		0			0
$805$	2.64008	+	3.10594i	0.0930505	+	0.109470i
$806$	1.60082	−	7.29695i	0.0563865	−	0.257024i
$807$		0			0
$808$	−45.8467	−	5.72753i	−1.61288	−	0.201494i
$809$	−19.6904	−	34.1047i	−0.692276	−	1.19906i	−0.971090	−	0.238712i	$-0.923275\pi$
$809$	−19.6904	−	34.1047i	−0.692276	−	1.19906i	0.278814	−	0.960345i	$-0.410059\pi$
$810$		0			0
$811$	5.44942			0.191355			0.0956775	−	0.995412i	$-0.469498\pi$
$811$	5.44942			0.191355			0.0956775	+	0.995412i	$0.469498\pi$
$812$	−10.9007	−	38.9960i	−0.382541	−	1.36849i
$813$		0			0
$814$	13.2358	+	12.0748i	0.463916	+	0.423222i
$815$	−4.00472	−	6.93638i	−0.140279	−	0.242971i
$816$		0			0
$817$	28.0232	+	16.1792i	0.980407	+	0.566038i
$818$	1.17977	−	5.37769i	0.0412497	−	0.188027i
$819$		0			0
$820$	−3.76617	−	1.73601i	−0.131520	−	0.0606242i
$821$	16.0464	−	27.7932i	0.560024	−	0.969990i	−0.437469	−	0.899233i	$-0.644125\pi$
$821$	16.0464	−	27.7932i	0.560024	−	0.969990i	0.997494	−	0.0707570i	$-0.0225415\pi$
$822$		0			0
$823$	28.0465	−	16.1927i	0.977640	−	0.564440i	0.0760829	−	0.997101i	$-0.475759\pi$
$823$	28.0465	−	16.1927i	0.977640	−	0.564440i	0.901557	+	0.432661i	$0.142425\pi$
$824$	12.4306	−	5.24554i	0.433041	−	0.182737i
$825$		0			0
$826$	−47.3114	−	1.65946i	−1.64617	−	0.0577401i
$827$		−	15.1100i		−	0.525426i	−0.964874	−	0.262713i	$-0.915383\pi$
$827$		−	15.1100i		−	0.525426i	0.964874	−	0.262713i	$-0.0846173\pi$
$828$		0			0
$829$	−26.0615	+	15.0466i	−0.905153	+	0.522590i	−0.878868	−	0.477064i	$-0.841701\pi$
$829$	−26.0615	+	15.0466i	−0.905153	+	0.522590i	−0.0262843	+	0.999655i	$0.508368\pi$
$830$	19.1746	−	6.09225i	0.665561	−	0.211465i
$831$		0			0
$832$	39.5780	−	11.1682i	1.37212	−	0.387188i
$833$	−9.10751	+	11.1389i	−0.315557	+	0.385941i
$834$		0			0
$835$	−14.4134	−	8.32158i	−0.498796	−	0.287980i
$836$	−13.4712	+	1.23847i	−0.465911	+	0.0428334i
$837$		0			0
$838$	−10.9489	+	12.0016i	−0.378222	+	0.414589i
$839$	14.7609			0.509602			0.254801	−	0.966993i	$-0.417990\pi$
$839$	14.7609			0.509602			0.254801	+	0.966993i	$0.417990\pi$
$840$		0			0
$841$	29.5542			1.01911
$842$	−6.80710	+	7.46162i	−0.234588	+	0.257144i
$843$		0			0
$844$	−21.9958	+	2.02218i	−0.757128	+	0.0696063i
$845$	9.44796	+	5.45478i	0.325020	+	0.187650i
$846$		0			0
$847$	5.67287	−	15.9003i	0.194922	−	0.546342i
$848$	17.2608	+	20.2060i	0.592740	+	0.693877i
$849$		0			0
$850$	12.0223	−	3.81978i	0.412361	−	0.131017i
$851$	9.67795	−	5.58757i	0.331756	−	0.191539i
$852$		0			0
$853$			6.60254i			0.226067i	0.993591	+	0.113033i	$0.0360567\pi$
$853$			6.60254i			0.226067i	−0.993591	+	0.113033i	$0.963943\pi$
$854$	−19.6623	+	10.4508i	−0.672831	+	0.357618i
$855$		0			0
$856$	5.14744	+	12.1981i	0.175936	+	0.416924i
$857$	−2.44768	+	1.41317i	−0.0836111	+	0.0482729i	−0.541223	−	0.840879i	$-0.682038\pi$
$857$	−2.44768	+	1.41317i	−0.0836111	+	0.0482729i	0.457612	+	0.889152i	$0.348705\pi$
$858$		0			0
$859$	−8.29006	+	14.3588i	−0.282853	+	0.489916i	−0.972086	−	0.234624i	$-0.924614\pi$
$859$	−8.29006	+	14.3588i	−0.282853	+	0.489916i	0.689233	+	0.724540i	$0.257948\pi$
$860$	15.1768	+	6.99572i	0.517523	+	0.238552i
$861$		0			0
$862$	−6.26850	+	28.5734i	−0.213506	+	0.973215i
$863$	3.90041	+	2.25190i	0.132771	+	0.0766557i	0.564915	−	0.825149i	$-0.308909\pi$
$863$	3.90041	+	2.25190i	0.132771	+	0.0766557i	−0.432143	+	0.901805i	$0.642242\pi$
$864$		0			0
$865$	−1.62400	−	2.81285i	−0.0552176	−	0.0956397i
$866$	15.1180	+	13.7919i	0.513729	+	0.468666i
$867$		0			0
$868$	−3.80334	+	3.88622i	−0.129094	+	0.131907i
$869$	16.9370			0.574547
$870$		0			0
$871$	−20.5328	−	35.5638i	−0.695726	−	1.20503i
$872$	−2.94255	+	23.5540i	−0.0996472	+	0.797638i
$873$		0			0
$874$	−1.80816	+	8.24204i	−0.0611618	+	0.278791i
$875$	−3.61295	−	19.7537i	−0.122140	−	0.667798i
$876$		0			0
$877$	−1.22271	+	2.11780i	−0.0412880	+	0.0715130i	−0.885931	−	0.463817i	$-0.846479\pi$
$877$	−1.22271	+	2.11780i	−0.0412880	+	0.0715130i	0.844643	+	0.535330i	$0.179813\pi$
$878$	−2.17727	−	6.85270i	−0.0734795	−	0.231268i
$879$		0			0
$880$	−6.86944	+	1.27385i	−0.231569	+	0.0429413i
$881$			46.1550i			1.55500i	0.628883	+	0.777500i	$0.283513\pi$
$881$			46.1550i			1.55500i	−0.628883	+	0.777500i	$0.716487\pi$
$882$		0			0
$883$			6.58454i			0.221587i	0.993843	+	0.110794i	$0.0353393\pi$
$883$			6.58454i			0.221587i	−0.993843	+	0.110794i	$0.964661\pi$
$884$	17.2567	−	12.1971i	0.580407	−	0.410232i
$885$		0			0
$886$	−7.74967	+	2.46226i	−0.260355	+	0.0827214i
$887$	3.75381	−	6.50180i	0.126041	−	0.218309i	−0.796099	−	0.605167i	$-0.793106\pi$
$887$	3.75381	−	6.50180i	0.126041	−	0.218309i	0.922139	+	0.386858i	$0.126440\pi$
$888$		0			0
$889$	3.19032	+	17.4430i	0.107000	+	0.585021i
$890$	0.628589	+	0.137901i	0.0210703	+	0.00462246i
$891$		0			0
$892$	3.73696	+	40.6480i	0.125123	+	1.36100i
$893$	−3.34306	−	5.79036i	−0.111871	−	0.193767i
$894$		0			0
$895$	14.9668			0.500286
$896$	−28.7373	−	8.37657i	−0.960046	−	0.279841i
$897$		0			0
$898$	−17.5230	+	19.2079i	−0.584750	+	0.640975i
$899$	−3.93171	−	6.80993i	−0.131130	−	0.227124i
$900$		0			0
$901$	11.8264	+	6.82796i	0.393993	+	0.227472i
$902$	−7.57492	−	1.66180i	−0.252217	−	0.0553319i
$903$		0			0
$904$	5.87080	+	4.44343i	0.195260	+	0.147786i
$905$	3.56645	−	6.17726i	0.118553	−	0.205339i
$906$		0			0
$907$	22.8284	−	13.1800i	0.758005	−	0.437634i	−0.0705742	−	0.997507i	$-0.522483\pi$
$907$	22.8284	−	13.1800i	0.758005	−	0.437634i	0.828579	+	0.559872i	$0.189150\pi$
$908$	−7.20976	+	5.09587i	−0.239264	+	0.169112i
$909$		0			0
$910$	−7.33614	−	13.8024i	−0.243191	−	0.457545i
$911$			41.7614i			1.38362i	0.722081	+	0.691808i	$0.243186\pi$
$911$			41.7614i			1.38362i	−0.722081	+	0.691808i	$0.756814\pi$
$912$		0			0
$913$	32.5829	−	18.8118i	1.07834	−	0.622578i
$914$	−12.4500	−	39.1848i	−0.411809	−	1.29612i
$915$		0			0
$916$	−16.0026	+	34.7167i	−0.528742	+	1.14707i
$917$	−13.1140	+	36.7570i	−0.433064	+	1.21382i
$918$		0			0
$919$	17.1773	+	9.91735i	0.566628	+	0.327143i	0.755802	−	0.654801i	$-0.227247\pi$
$919$	17.1773	+	9.91735i	0.566628	+	0.327143i	−0.189173	+	0.981944i	$0.560581\pi$
$920$	−0.540216	+	4.32422i	−0.0178104	+	0.142565i
$921$		0			0
$922$	−28.6280	−	26.1168i	−0.942811	−	0.860110i
$923$	−56.8428			−1.87100
$924$		0			0
$925$	−25.5795			−0.841047
$926$	−35.1690	−	32.0840i	−1.15572	−	1.05435i
$927$		0			0
$928$	22.8539	−	36.7618i	0.750218	−	1.20677i
$929$	−48.7429	−	28.1417i	−1.59920	−	0.923301i	−0.991641	−	0.129029i	$-0.958814\pi$
$929$	−48.7429	−	28.1417i	−1.59920	−	0.923301i	−0.607563	−	0.794271i	$-0.707853\pi$
$930$		0			0
$931$	−3.54893	+	21.7425i	−0.116311	+	0.712581i
$932$	26.1761	+	12.0659i	0.857428	+	0.395231i
$933$		0			0
$934$	−6.23733	−	19.6312i	−0.204092	−	0.642354i
$935$	−3.10917	+	1.79508i	−0.101681	+	0.0587054i
$936$		0			0
$937$		−	2.78557i		−	0.0910006i	−0.998964	−	0.0455003i	$-0.985512\pi$
$937$		−	2.78557i		−	0.0910006i	0.998964	−	0.0455003i	$-0.0144882\pi$
$938$	−1.04779	+	29.8726i	−0.0342116	+	0.975376i
$939$		0			0
$940$	−1.99305	−	2.81981i	−0.0650060	−	0.0919722i
$941$	−42.7539	+	24.6840i	−1.39374	+	0.804674i	−0.993727	−	0.111837i	$-0.964326\pi$
$941$	−42.7539	+	24.6840i	−1.39374	+	0.804674i	−0.400009	+	0.916511i	$0.630993\pi$
$942$		0			0
$943$	−2.41860	+	4.18913i	−0.0787603	+	0.136417i
$944$	−32.8716	−	38.4804i	−1.06988	−	1.25243i
$945$		0			0
$946$	30.5251	+	6.69666i	0.992457	+	0.217727i
$947$	42.7332	+	24.6720i	1.38864	+	0.801734i	0.993162	−	0.116740i	$-0.0372445\pi$
$947$	42.7332	+	24.6720i	1.38864	+	0.801734i	0.395481	+	0.918474i	$0.370578\pi$
$948$		0			0
$949$	−25.6522	−	44.4310i	−0.832706	−	1.44229i
$950$	13.0172	−	14.2688i	0.422332	−	0.462940i
$951$		0			0
$952$	−15.3571	+	0.870386i	−0.497726	+	0.0282094i
$953$	34.4944			1.11738			0.558691	−	0.829376i	$-0.311304\pi$
$953$	34.4944			1.11738			0.558691	+	0.829376i	$0.311304\pi$
$954$		0			0
$955$	8.92412	+	15.4570i	0.288778	+	0.500178i
$956$	−26.5520	+	2.44105i	−0.858753	+	0.0789492i
$957$		0			0
$958$	9.30349	+	2.04102i	0.300582	+	0.0659423i
$959$	−34.5985	−	40.7037i	−1.11724	−	1.31439i
$960$		0			0
$961$	14.9720	−	25.9323i	0.482968	−	0.836525i
$962$	−40.8393	+	12.9757i	−1.31671	+	0.418353i
$963$		0			0
$964$	28.3938	+	40.1722i	0.914502	+	1.29386i
$965$			0.569966i			0.0183478i
$966$		0			0
$967$		−	5.11586i		−	0.164515i	−0.996611	−	0.0822575i	$-0.973787\pi$
$967$		−	5.11586i		−	0.164515i	0.996611	−	0.0822575i	$-0.0262130\pi$
$968$	16.6278	−	7.01669i	0.534437	−	0.225525i
$969$		0			0
$970$	0.642918	+	2.02350i	0.0206429	+	0.0649708i
$971$	−21.5432	+	37.3139i	−0.691354	+	1.19746i	0.280040	+	0.959988i	$0.409652\pi$
$971$	−21.5432	+	37.3139i	−0.691354	+	1.19746i	−0.971394	+	0.237472i	$0.923681\pi$
$972$		0			0
$973$	58.5594	−	10.7105i	1.87733	−	0.343362i
$974$	1.56833	−	7.14884i	0.0502525	−	0.229064i
$975$		0			0
$976$	−22.4399	−	7.94402i	−0.718285	−	0.254282i
$977$	11.9965	+	20.7786i	0.383803	+	0.664766i	0.991602	−	0.129325i	$-0.0412809\pi$
$977$	11.9965	+	20.7786i	0.383803	+	0.664766i	−0.607800	+	0.794090i	$0.707948\pi$
$978$		0			0
$979$	1.20344			0.0384620
$980$	−0.797159	+	11.3496i	−0.0254643	+	0.362548i
$981$		0			0
$982$	4.42047	+	4.03272i	0.141063	+	0.128689i
$983$	−17.1303	−	29.6706i	−0.546372	−	0.946344i	−0.998519	−	0.0544009i	$-0.982675\pi$
$983$	−17.1303	−	29.6706i	−0.546372	−	0.946344i	0.452147	−	0.891943i	$-0.350658\pi$
$984$		0			0
$985$	−16.8628	−	9.73572i	−0.537292	−	0.310206i
$986$	4.76649	−	21.7269i	0.151796	−	0.691925i
$987$		0			0
$988$	13.5447	−	29.3843i	0.430913	−	0.934839i
$989$	9.74636	−	16.8812i	0.309916	−	0.536791i
$990$		0			0
$991$	−2.24015	+	1.29335i	−0.0711608	+	0.0410847i	−0.535158	−	0.844752i	$-0.679748\pi$
$991$	−2.24015	+	1.29335i	−0.0711608	+	0.0410847i	0.463997	+	0.885837i	$0.346415\pi$
$992$	−5.81001	−	0.189514i	−0.184468	−	0.00601709i
$993$		0			0
$994$	35.0846	+	21.9308i	1.11282	+	0.695604i
$995$		−	1.78263i		−	0.0565132i
$996$		0			0
$997$	−17.1394	+	9.89541i	−0.542809	+	0.313391i	−0.746217	−	0.665703i	$-0.768132\pi$
$997$	−17.1394	+	9.89541i	−0.542809	+	0.313391i	0.203408	+	0.979094i	$0.434798\pi$
$998$	38.8300	−	12.3373i	1.22914	−	0.390529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.c.271.12	yes	32
3.2	odd	2		756.2.bf.b.271.5	✓	32
4.3	odd	2		756.2.bf.b.271.10	yes	32
7.3	odd	6		756.2.bf.b.703.10	yes	32
12.11	even	2	inner	756.2.bf.c.271.7	yes	32
21.17	even	6	inner	756.2.bf.c.703.7	yes	32
28.3	even	6	inner	756.2.bf.c.703.12	yes	32
84.59	odd	6		756.2.bf.b.703.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.5	✓	32	3.2	odd	2
756.2.bf.b.271.10	yes	32	4.3	odd	2
756.2.bf.b.703.5	yes	32	84.59	odd	6
756.2.bf.b.703.10	yes	32	7.3	odd	6
756.2.bf.c.271.7	yes	32	12.11	even	2	inner
756.2.bf.c.271.12	yes	32	1.1	even	1	trivial
756.2.bf.c.703.7	yes	32	21.17	even	6	inner
756.2.bf.c.703.12	yes	32	28.3	even	6	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.953127 - 1.04477i) q^{2} +(-0.183097 - 1.99160i) q^{4} +(-0.703801 - 0.406340i) q^{5} +(-2.60258 + 0.476010i) q^{7} +(-2.25528 - 1.70695i) q^{8} +O(q^{10})\)	\(q+(0.953127 - 1.04477i) q^{2} +(-0.183097 - 1.99160i) q^{4} +(-0.703801 - 0.406340i) q^{5} +(-2.60258 + 0.476010i) q^{7} +(-2.25528 - 1.70695i) q^{8} +(-1.09534 + 0.348018i) q^{10} +(-1.86129 + 1.07462i) q^{11} -5.14045i q^{13} +(-1.98327 + 3.17280i) q^{14} +(-3.93295 + 0.729313i) q^{16} +(-1.78009 + 1.02773i) q^{17} +(-1.57359 + 2.72553i) q^{19} +(-0.680403 + 1.47609i) q^{20} +(-0.651317 + 2.96887i) q^{22} +(1.64186 + 0.947931i) q^{23} +(-2.16978 - 3.75816i) q^{25} +(-5.37059 - 4.89950i) q^{26} +(1.42455 + 5.09614i) q^{28} -7.65207 q^{29} +(0.513811 + 0.889946i) q^{31} +(-2.98664 + 4.80417i) q^{32} +(-0.622902 + 2.83935i) q^{34} +(2.02512 + 0.722515i) q^{35} +(2.94725 - 5.10478i) q^{37} +(1.34773 + 4.24182i) q^{38} +(0.893668 + 2.11777i) q^{40} +2.55145i q^{41} -10.2817i q^{43} +(2.48100 + 3.51019i) q^{44} +(2.55528 - 0.811875i) q^{46} +(-1.06224 + 1.83986i) q^{47} +(6.54683 - 2.47771i) q^{49} +(-5.99450 - 1.31509i) q^{50} +(-10.2377 + 0.941201i) q^{52} +(-3.32185 - 5.75361i) q^{53} +1.74664 q^{55} +(6.68208 + 3.36894i) q^{56} +(-7.29339 + 7.99467i) q^{58} +(6.32614 + 10.9572i) q^{59} +(5.15384 + 2.97557i) q^{61} +(1.41952 + 0.311417i) q^{62} +(2.17261 + 7.69933i) q^{64} +(-2.08877 + 3.61785i) q^{65} +(6.91842 - 3.99435i) q^{67} +(2.37277 + 3.35705i) q^{68} +(2.68506 - 1.42714i) q^{70} -11.0579i q^{71} +(8.64340 - 4.99027i) q^{73} +(-2.52423 - 7.94470i) q^{74} +(5.71629 + 2.63492i) q^{76} +(4.33262 - 3.68277i) q^{77} +(-6.82469 - 3.94024i) q^{79} +(3.06436 + 1.08482i) q^{80} +(2.66568 + 2.43185i) q^{82} -17.5056 q^{83} +1.67044 q^{85} +(-10.7421 - 9.79979i) q^{86} +(6.03206 + 0.753572i) q^{88} +(-0.484920 - 0.279969i) q^{89} +(2.44690 + 13.3784i) q^{91} +(1.58728 - 3.44350i) q^{92} +(0.909781 + 2.86342i) q^{94} +(2.21498 - 1.27882i) q^{95} -1.84737i q^{97} +(3.65132 - 9.20151i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) \) 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

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