LMFDB - Embedded newform 352.2.m.b.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(97,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("352.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			257.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	352.257
Dual form			352.2.m.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 1.53884i) q^{3} +(-2.61803 + 1.90211i) q^{5} +(1.38197 + 4.25325i) q^{7} +(0.309017 + 0.224514i) q^{9} +O(q^{10})$	\(q+(0.500000 - 1.53884i) q^{3} +(-2.61803 + 1.90211i) q^{5} +(1.38197 + 4.25325i) q^{7} +(0.309017 + 0.224514i) q^{9} +(3.30902 - 0.224514i) q^{11} +(-1.00000 - 0.726543i) q^{13} +(1.61803 + 4.97980i) q^{15} +(-1.50000 + 1.08981i) q^{17} +(-1.66312 + 5.11855i) q^{19} +7.23607 q^{21} +5.23607 q^{23} +(1.69098 - 5.20431i) q^{25} +(4.42705 - 3.21644i) q^{27} +(-2.61803 - 8.05748i) q^{29} +(-0.381966 - 0.277515i) q^{31} +(1.30902 - 5.20431i) q^{33} +(-11.7082 - 8.50651i) q^{35} +(2.85410 + 8.78402i) q^{37} +(-1.61803 + 1.17557i) q^{39} +(-2.26393 + 6.96767i) q^{41} +4.09017 q^{43} -1.23607 q^{45} +(2.00000 - 6.15537i) q^{47} +(-10.5172 + 7.64121i) q^{49} +(0.927051 + 2.85317i) q^{51} +(-5.23607 - 3.80423i) q^{53} +(-8.23607 + 6.88191i) q^{55} +(7.04508 + 5.11855i) q^{57} +(-2.80902 - 8.64527i) q^{59} +(-2.00000 + 1.45309i) q^{61} +(-0.527864 + 1.62460i) q^{63} +4.00000 q^{65} -1.38197 q^{67} +(2.61803 - 8.05748i) q^{69} +(-3.00000 + 2.17963i) q^{71} +(-1.26393 - 3.88998i) q^{73} +(-7.16312 - 5.20431i) q^{75} +(5.52786 + 13.7638i) q^{77} +(4.85410 + 3.52671i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(1.92705 - 1.40008i) q^{83} +(1.85410 - 5.70634i) q^{85} -13.7082 q^{87} +6.38197 q^{89} +(1.70820 - 5.25731i) q^{91} +(-0.618034 + 0.449028i) q^{93} +(-5.38197 - 16.5640i) q^{95} +(-4.54508 - 3.30220i) q^{97} +(1.07295 + 0.673542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 6 q^{5} + 10 q^{7} - q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 6 * q^5 + 10 * q^7 - q^9	$ 4 q + 2 q^{3} - 6 q^{5} + 10 q^{7} - q^{9} + 11 q^{11} - 4 q^{13} + 2 q^{15} - 6 q^{17} + 9 q^{19} + 20 q^{21} + 12 q^{23} + 9 q^{25} + 11 q^{27} - 6 q^{29} - 6 q^{31} + 3 q^{33} - 20 q^{35} - 2 q^{37} - 2 q^{39} - 18 q^{41} - 6 q^{43} + 4 q^{45} + 8 q^{47} - 13 q^{49} - 3 q^{51} - 12 q^{53} - 24 q^{55} + 17 q^{57} - 9 q^{59} - 8 q^{61} - 20 q^{63} + 16 q^{65} - 10 q^{67} + 6 q^{69} - 12 q^{71} - 14 q^{73} - 13 q^{75} + 40 q^{77} + 6 q^{79} - 14 q^{81} + q^{83} - 6 q^{85} - 28 q^{87} + 30 q^{89} - 20 q^{91} + 2 q^{93} - 26 q^{95} - 7 q^{97} + 11 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^5 + 10 * q^7 - q^9 + 11 * q^11 - 4 * q^13 + 2 * q^15 - 6 * q^17 + 9 * q^19 + 20 * q^21 + 12 * q^23 + 9 * q^25 + 11 * q^27 - 6 * q^29 - 6 * q^31 + 3 * q^33 - 20 * q^35 - 2 * q^37 - 2 * q^39 - 18 * q^41 - 6 * q^43 + 4 * q^45 + 8 * q^47 - 13 * q^49 - 3 * q^51 - 12 * q^53 - 24 * q^55 + 17 * q^57 - 9 * q^59 - 8 * q^61 - 20 * q^63 + 16 * q^65 - 10 * q^67 + 6 * q^69 - 12 * q^71 - 14 * q^73 - 13 * q^75 + 40 * q^77 + 6 * q^79 - 14 * q^81 + q^83 - 6 * q^85 - 28 * q^87 + 30 * q^89 - 20 * q^91 + 2 * q^93 - 26 * q^95 - 7 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	1.53884i	0.288675	−	0.888451i	−0.696598	−	0.717462i	$-0.745304\pi$
$3$	0.500000	−	1.53884i	0.288675	−	0.888451i	0.985273	−	0.170989i	$-0.0546962\pi$
$4$		0			0
$5$	−2.61803	+	1.90211i	−1.17082	+	0.850651i	−0.991107	−	0.133068i	$-0.957517\pi$
$5$	−2.61803	+	1.90211i	−1.17082	+	0.850651i	−0.179714	+	0.983719i	$0.557517\pi$
$6$		0			0
$7$	1.38197	+	4.25325i	0.522334	+	1.60758i	0.769528	+	0.638613i	$0.220491\pi$
$7$	1.38197	+	4.25325i	0.522334	+	1.60758i	−0.247194	+	0.968966i	$0.579509\pi$
$8$		0			0
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$		0			0
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$		0			0
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	0.440411	−	0.897796i	$-0.354833\pi$
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	−0.717761	+	0.696290i	$0.754833\pi$
$14$		0			0
$15$	1.61803	+	4.97980i	0.417775	+	1.28578i
$16$		0			0
$17$	−1.50000	+	1.08981i	−0.363803	+	0.264319i	−0.754637	−	0.656143i	$-0.772187\pi$
$17$	−1.50000	+	1.08981i	−0.363803	+	0.264319i	0.390833	+	0.920461i	$0.372187\pi$
$18$		0			0
$19$	−1.66312	+	5.11855i	−0.381546	+	1.17428i	0.557410	+	0.830238i	$0.311795\pi$
$19$	−1.66312	+	5.11855i	−0.381546	+	1.17428i	−0.938955	+	0.344039i	$0.888205\pi$
$20$		0			0
$21$	7.23607			1.57904
$22$		0			0
$23$	5.23607			1.09180			0.545898	−	0.837852i	$-0.316189\pi$
$23$	5.23607			1.09180			0.545898	+	0.837852i	$0.316189\pi$
$24$		0			0
$25$	1.69098	−	5.20431i	0.338197	−	1.04086i
$26$		0			0
$27$	4.42705	−	3.21644i	0.851986	−	0.619004i
$28$		0			0
$29$	−2.61803	−	8.05748i	−0.486157	−	1.49624i	−0.830299	−	0.557319i	$-0.811830\pi$
$29$	−2.61803	−	8.05748i	−0.486157	−	1.49624i	0.344142	−	0.938918i	$-0.388170\pi$
$30$		0			0
$31$	−0.381966	−	0.277515i	−0.0686031	−	0.0498431i	0.552955	−	0.833211i	$-0.313500\pi$
$31$	−0.381966	−	0.277515i	−0.0686031	−	0.0498431i	−0.621558	+	0.783368i	$0.713500\pi$
$32$		0			0
$33$	1.30902	−	5.20431i	0.227871	−	0.905954i
$34$		0			0
$35$	−11.7082	−	8.50651i	−1.97905	−	1.43786i
$36$		0			0
$37$	2.85410	+	8.78402i	0.469211	+	1.44408i	0.853608	+	0.520916i	$0.174410\pi$
$37$	2.85410	+	8.78402i	0.469211	+	1.44408i	−0.384396	+	0.923168i	$0.625590\pi$
$38$		0			0
$39$	−1.61803	+	1.17557i	−0.259093	+	0.188242i
$40$		0			0
$41$	−2.26393	+	6.96767i	−0.353567	+	1.08817i	0.603269	+	0.797538i	$0.293865\pi$
$41$	−2.26393	+	6.96767i	−0.353567	+	1.08817i	−0.956836	+	0.290629i	$0.906135\pi$
$42$		0			0
$43$	4.09017			0.623745			0.311873	−	0.950124i	$-0.399044\pi$
$43$	4.09017			0.623745			0.311873	+	0.950124i	$0.399044\pi$
$44$		0			0
$45$	−1.23607			−0.184262
$46$		0			0
$47$	2.00000	−	6.15537i	0.291730	−	0.897853i	−0.692570	−	0.721350i	$-0.743522\pi$
$47$	2.00000	−	6.15537i	0.291730	−	0.897853i	0.984300	−	0.176502i	$-0.0564783\pi$
$48$		0			0
$49$	−10.5172	+	7.64121i	−1.50246	+	1.09160i
$50$		0			0
$51$	0.927051	+	2.85317i	0.129813	+	0.399524i
$52$		0			0
$53$	−5.23607	−	3.80423i	−0.719229	−	0.522551i	0.166909	−	0.985972i	$-0.446622\pi$
$53$	−5.23607	−	3.80423i	−0.719229	−	0.522551i	−0.886138	+	0.463422i	$0.846622\pi$
$54$		0			0
$55$	−8.23607	+	6.88191i	−1.11055	+	0.927957i
$56$		0			0
$57$	7.04508	+	5.11855i	0.933144	+	0.677969i
$58$		0			0
$59$	−2.80902	−	8.64527i	−0.365703	−	1.12552i	−0.949540	−	0.313647i	$-0.898449\pi$
$59$	−2.80902	−	8.64527i	−0.365703	−	1.12552i	0.583837	−	0.811871i	$-0.301551\pi$
$60$		0			0
$61$	−2.00000	+	1.45309i	−0.256074	+	0.186048i	−0.708414	−	0.705797i	$-0.750589\pi$
$61$	−2.00000	+	1.45309i	−0.256074	+	0.186048i	0.452341	+	0.891845i	$0.350589\pi$
$62$		0			0
$63$	−0.527864	+	1.62460i	−0.0665046	+	0.204680i
$64$		0			0
$65$	4.00000			0.496139
$66$		0			0
$67$	−1.38197			−0.168834			−0.0844170	−	0.996431i	$-0.526903\pi$
$67$	−1.38197			−0.168834			−0.0844170	+	0.996431i	$0.526903\pi$
$68$		0			0
$69$	2.61803	−	8.05748i	0.315174	−	0.970007i
$70$		0			0
$71$	−3.00000	+	2.17963i	−0.356034	+	0.258674i	−0.751396	−	0.659851i	$-0.770619\pi$
$71$	−3.00000	+	2.17963i	−0.356034	+	0.258674i	0.395362	+	0.918526i	$0.370619\pi$
$72$		0			0
$73$	−1.26393	−	3.88998i	−0.147932	−	0.455288i	0.849444	−	0.527678i	$-0.176937\pi$
$73$	−1.26393	−	3.88998i	−0.147932	−	0.455288i	−0.997376	+	0.0723902i	$0.976937\pi$
$74$		0			0
$75$	−7.16312	−	5.20431i	−0.827126	−	0.600942i
$76$		0			0
$77$	5.52786	+	13.7638i	0.629959	+	1.56853i
$78$		0			0
$79$	4.85410	+	3.52671i	0.546129	+	0.396786i	0.826356	−	0.563148i	$-0.190410\pi$
$79$	4.85410	+	3.52671i	0.546129	+	0.396786i	−0.280227	+	0.959934i	$0.590410\pi$
$80$		0			0
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$		0			0
$83$	1.92705	−	1.40008i	0.211521	−	0.153679i	−0.476980	−	0.878914i	$-0.658269\pi$
$83$	1.92705	−	1.40008i	0.211521	−	0.153679i	0.688502	+	0.725235i	$0.258269\pi$
$84$		0			0
$85$	1.85410	−	5.70634i	0.201106	−	0.618939i
$86$		0			0
$87$	−13.7082			−1.46967
$88$		0			0
$89$	6.38197			0.676487			0.338244	−	0.941059i	$-0.390167\pi$
$89$	6.38197			0.676487			0.338244	+	0.941059i	$0.390167\pi$
$90$		0			0
$91$	1.70820	−	5.25731i	0.179068	−	0.551116i
$92$		0			0
$93$	−0.618034	+	0.449028i	−0.0640871	+	0.0465620i
$94$		0			0
$95$	−5.38197	−	16.5640i	−0.552178	−	1.69943i
$96$		0			0
$97$	−4.54508	−	3.30220i	−0.461483	−	0.335287i	0.332629	−	0.943058i	$-0.392064\pi$
$97$	−4.54508	−	3.30220i	−0.461483	−	0.335287i	−0.794113	+	0.607770i	$0.792064\pi$
$98$		0			0
$99$	1.07295	+	0.673542i	0.107835	+	0.0676935i
$100$		0			0
$101$	1.85410	+	1.34708i	0.184490	+	0.134040i	0.676197	−	0.736721i	$-0.263627\pi$
$101$	1.85410	+	1.34708i	0.184490	+	0.134040i	−0.491707	+	0.870761i	$0.663627\pi$
$102$		0			0
$103$	−5.32624	−	16.3925i	−0.524810	−	1.61520i	−0.764692	−	0.644396i	$-0.777109\pi$
$103$	−5.32624	−	16.3925i	−0.524810	−	1.61520i	0.239882	−	0.970802i	$-0.422891\pi$
$104$		0			0
$105$	−18.9443	+	13.7638i	−1.84877	+	1.34321i
$106$		0			0
$107$	−1.02786	+	3.16344i	−0.0993674	+	0.305821i	−0.988367	−	0.152086i	$-0.951401\pi$
$107$	−1.02786	+	3.16344i	−0.0993674	+	0.305821i	0.889000	+	0.457907i	$0.151401\pi$
$108$		0			0
$109$	2.94427			0.282010			0.141005	−	0.990009i	$-0.454967\pi$
$109$	2.94427			0.282010			0.141005	+	0.990009i	$0.454967\pi$
$110$		0			0
$111$	14.9443			1.41845
$112$		0			0
$113$	5.89919	−	18.1558i	0.554949	−	1.70796i	−0.141130	−	0.989991i	$-0.545073\pi$
$113$	5.89919	−	18.1558i	0.554949	−	1.70796i	0.696078	−	0.717966i	$-0.254927\pi$
$114$		0			0
$115$	−13.7082	+	9.95959i	−1.27830	+	0.928737i
$116$		0			0
$117$	−0.145898	−	0.449028i	−0.0134883	−	0.0415127i
$118$		0			0
$119$	−6.70820	−	4.87380i	−0.614940	−	0.446780i
$120$		0			0
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$		0			0
$123$	9.59017	+	6.96767i	0.864717	+	0.628253i
$124$		0			0
$125$	0.472136	+	1.45309i	0.0422291	+	0.129968i
$126$		0			0
$127$	16.5623	−	12.0332i	1.46967	−	1.06778i	0.488957	−	0.872308i	$-0.337378\pi$
$127$	16.5623	−	12.0332i	1.46967	−	1.06778i	0.980710	−	0.195468i	$-0.0626224\pi$
$128$		0			0
$129$	2.04508	−	6.29412i	0.180060	−	0.554167i
$130$		0			0
$131$	−1.09017			−0.0952486			−0.0476243	−	0.998865i	$-0.515165\pi$
$131$	−1.09017			−0.0952486			−0.0476243	+	0.998865i	$0.515165\pi$
$132$		0			0
$133$	−24.0689			−2.08704
$134$		0			0
$135$	−5.47214	+	16.8415i	−0.470966	+	1.44949i
$136$		0			0
$137$	7.92705	−	5.75934i	0.677254	−	0.492054i	−0.195192	−	0.980765i	$-0.562533\pi$
$137$	7.92705	−	5.75934i	0.677254	−	0.492054i	0.872445	+	0.488711i	$0.162533\pi$
$138$		0			0
$139$	5.23607	+	16.1150i	0.444117	+	1.36685i	0.883449	+	0.468528i	$0.155215\pi$
$139$	5.23607	+	16.1150i	0.444117	+	1.36685i	−0.439331	+	0.898325i	$0.644785\pi$
$140$		0			0
$141$	−8.47214	−	6.15537i	−0.713483	−	0.518375i
$142$		0			0
$143$	−3.47214	−	2.17963i	−0.290355	−	0.182270i
$144$		0			0
$145$	22.1803	+	16.1150i	1.84198	+	1.33827i
$146$		0			0
$147$	6.50000	+	20.0049i	0.536111	+	1.64998i
$148$		0			0
$149$	3.47214	−	2.52265i	0.284448	−	0.206664i	−0.436407	−	0.899749i	$-0.643749\pi$
$149$	3.47214	−	2.52265i	0.284448	−	0.206664i	0.720855	+	0.693086i	$0.243749\pi$
$150$		0			0
$151$	4.00000	−	12.3107i	0.325515	−	1.00183i	−0.645692	−	0.763598i	$-0.723431\pi$
$151$	4.00000	−	12.3107i	0.325515	−	1.00183i	0.971207	−	0.238235i	$-0.0765690\pi$
$152$		0			0
$153$	−0.708204			−0.0572549
$154$		0			0
$155$	1.52786			0.122721
$156$		0			0
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$		0			0
$159$	−8.47214	+	6.15537i	−0.671884	+	0.488152i
$160$		0			0
$161$	7.23607	+	22.2703i	0.570282	+	1.75515i
$162$		0			0
$163$	17.0623	+	12.3965i	1.33642	+	0.970968i	0.999567	+	0.0294118i	$0.00936341\pi$
$163$	17.0623	+	12.3965i	1.33642	+	0.970968i	0.336856	+	0.941556i	$0.390637\pi$
$164$		0			0
$165$	6.47214	+	16.1150i	0.503855	+	1.25455i
$166$		0			0
$167$	10.2361	+	7.43694i	0.792091	+	0.575488i	0.908583	−	0.417704i	$-0.137165\pi$
$167$	10.2361	+	7.43694i	0.792091	+	0.575488i	−0.116492	+	0.993192i	$0.537165\pi$
$168$		0			0
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$		0			0
$171$	−1.66312	+	1.20833i	−0.127182	+	0.0924030i
$172$		0			0
$173$	−2.76393	+	8.50651i	−0.210138	+	0.646738i	0.789325	+	0.613975i	$0.210431\pi$
$173$	−2.76393	+	8.50651i	−0.210138	+	0.646738i	−0.999463	+	0.0327626i	$0.989569\pi$
$174$		0			0
$175$	24.4721			1.84992
$176$		0			0
$177$	−14.7082			−1.10554
$178$		0			0
$179$	−2.98936	+	9.20029i	−0.223435	+	0.687662i	0.775012	+	0.631947i	$0.217744\pi$
$179$	−2.98936	+	9.20029i	−0.223435	+	0.687662i	−0.998447	+	0.0557154i	$0.982256\pi$
$180$		0			0
$181$	−0.618034	+	0.449028i	−0.0459381	+	0.0333760i	−0.610517	−	0.792003i	$-0.709038\pi$
$181$	−0.618034	+	0.449028i	−0.0459381	+	0.0333760i	0.564579	+	0.825379i	$0.309038\pi$
$182$		0			0
$183$	1.23607	+	3.80423i	0.0913728	+	0.281216i
$184$		0			0
$185$	−24.1803	−	17.5680i	−1.77777	−	1.29163i
$186$		0			0
$187$	−4.71885	+	3.94298i	−0.345076	+	0.288339i
$188$		0			0
$189$	19.7984	+	14.3844i	1.44012	+	1.04631i
$190$		0			0
$191$	−1.76393	−	5.42882i	−0.127634	−	0.392816i	0.866738	−	0.498764i	$-0.166212\pi$
$191$	−1.76393	−	5.42882i	−0.127634	−	0.392816i	−0.994372	+	0.105948i	$0.966212\pi$
$192$		0			0
$193$	−14.0902	+	10.2371i	−1.01423	+	0.736883i	−0.965093	−	0.261909i	$-0.915648\pi$
$193$	−14.0902	+	10.2371i	−1.01423	+	0.736883i	−0.0491400	+	0.998792i	$0.515648\pi$
$194$		0			0
$195$	2.00000	−	6.15537i	0.143223	−	0.440795i
$196$		0			0
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$	−22.3607			−1.58511			−0.792553	−	0.609803i	$-0.791249\pi$
$199$	−22.3607			−1.58511			−0.792553	+	0.609803i	$0.791249\pi$
$200$		0			0
$201$	−0.690983	+	2.12663i	−0.0487382	+	0.150001i
$202$		0			0
$203$	30.6525	−	22.2703i	2.15138	−	1.56307i
$204$		0			0
$205$	−7.32624	−	22.5478i	−0.511687	−	1.57481i
$206$		0			0
$207$	1.61803	+	1.17557i	0.112461	+	0.0817078i
$208$		0			0
$209$	−4.35410	+	17.3108i	−0.301180	+	1.19741i
$210$		0			0
$211$	−0.0729490	−	0.0530006i	−0.00502202	−	0.00364871i	0.585271	−	0.810837i	$-0.300988\pi$
$211$	−0.0729490	−	0.0530006i	−0.00502202	−	0.00364871i	−0.590293	+	0.807189i	$0.700988\pi$
$212$		0			0
$213$	1.85410	+	5.70634i	0.127041	+	0.390992i
$214$		0			0
$215$	−10.7082	+	7.77997i	−0.730293	+	0.530589i
$216$		0			0
$217$	0.652476	−	2.00811i	0.0442929	−	0.136320i
$218$		0			0
$219$	−6.61803			−0.447205
$220$		0			0
$221$	2.29180			0.154163
$222$		0			0
$223$	0.708204	−	2.17963i	0.0474248	−	0.145959i	−0.924540	−	0.381085i	$-0.875550\pi$
$223$	0.708204	−	2.17963i	0.0474248	−	0.145959i	0.971965	+	0.235127i	$0.0755505\pi$
$224$		0			0
$225$	1.69098	−	1.22857i	0.112732	−	0.0819047i
$226$		0			0
$227$	−7.37132	−	22.6866i	−0.489252	−	1.50576i	−0.825727	−	0.564070i	$-0.809235\pi$
$227$	−7.37132	−	22.6866i	−0.489252	−	1.50576i	0.336475	−	0.941692i	$-0.390765\pi$
$228$		0			0
$229$	13.0902	+	9.51057i	0.865023	+	0.628476i	0.929247	−	0.369460i	$-0.120457\pi$
$229$	13.0902	+	9.51057i	0.865023	+	0.628476i	−0.0642240	+	0.997936i	$0.520457\pi$
$230$		0			0
$231$	23.9443	−	1.62460i	1.57542	−	0.106891i
$232$		0			0
$233$	−6.39919	−	4.64928i	−0.419225	−	0.304585i	0.358101	−	0.933683i	$-0.383424\pi$
$233$	−6.39919	−	4.64928i	−0.419225	−	0.304585i	−0.777326	+	0.629098i	$0.783424\pi$
$234$		0			0
$235$	6.47214	+	19.9192i	0.422196	+	1.29938i
$236$		0			0
$237$	7.85410	−	5.70634i	0.510179	−	0.370667i
$238$		0			0
$239$	−4.41641	+	13.5923i	−0.285674	+	0.879213i	0.700522	+	0.713631i	$0.252950\pi$
$239$	−4.41641	+	13.5923i	−0.285674	+	0.879213i	−0.986196	+	0.165583i	$0.947050\pi$
$240$		0			0
$241$	28.3262			1.82465			0.912327	−	0.409463i	$-0.134284\pi$
$241$	28.3262			1.82465			0.912327	+	0.409463i	$0.134284\pi$
$242$		0			0
$243$	3.94427			0.253025
$244$		0			0
$245$	13.0000	−	40.0099i	0.830540	−	2.55614i
$246$		0			0
$247$	5.38197	−	3.91023i	0.342446	−	0.248802i
$248$		0			0
$249$	−1.19098	−	3.66547i	−0.0754755	−	0.232290i
$250$		0			0
$251$	3.23607	+	2.35114i	0.204259	+	0.148403i	0.685212	−	0.728343i	$-0.259709\pi$
$251$	3.23607	+	2.35114i	0.204259	+	0.148403i	−0.480953	+	0.876746i	$0.659709\pi$
$252$		0			0
$253$	17.3262	−	1.17557i	1.08929	−	0.0739075i
$254$		0			0
$255$	−7.85410	−	5.70634i	−0.491843	−	0.357345i
$256$		0			0
$257$	−5.73607	−	17.6538i	−0.357806	−	1.10121i	−0.954365	−	0.298644i	$-0.903466\pi$
$257$	−5.73607	−	17.6538i	−0.357806	−	1.10121i	0.596558	−	0.802570i	$-0.296534\pi$
$258$		0			0
$259$	−33.4164	+	24.2784i	−2.07639	+	1.50859i
$260$		0			0
$261$	1.00000	−	3.07768i	0.0618984	−	0.190504i
$262$		0			0
$263$	0.180340			0.0111202			0.00556012	−	0.999985i	$-0.498230\pi$
$263$	0.180340			0.0111202			0.00556012	+	0.999985i	$0.498230\pi$
$264$		0			0
$265$	20.9443			1.28660
$266$		0			0
$267$	3.19098	−	9.82084i	0.195285	−	0.601025i
$268$		0			0
$269$	−11.4721	+	8.33499i	−0.699468	+	0.508194i	−0.879759	−	0.475420i	$-0.842296\pi$
$269$	−11.4721	+	8.33499i	−0.699468	+	0.508194i	0.180291	+	0.983613i	$0.442296\pi$
$270$		0			0
$271$	2.61803	+	8.05748i	0.159034	+	0.489457i	0.998547	−	0.0538825i	$-0.0171596\pi$
$271$	2.61803	+	8.05748i	0.159034	+	0.489457i	−0.839513	+	0.543340i	$0.817160\pi$
$272$		0			0
$273$	−7.23607	−	5.25731i	−0.437947	−	0.318187i
$274$		0			0
$275$	4.42705	−	17.6008i	0.266961	−	1.06137i
$276$		0			0
$277$	−8.23607	−	5.98385i	−0.494857	−	0.359535i	0.312192	−	0.950019i	$-0.398937\pi$
$277$	−8.23607	−	5.98385i	−0.494857	−	0.359535i	−0.807049	+	0.590484i	$0.798937\pi$
$278$		0			0
$279$	−0.0557281	−	0.171513i	−0.00333635	−	0.0102682i
$280$		0			0
$281$	−19.6353	+	14.2658i	−1.17134	+	0.851029i	−0.991169	−	0.132606i	$-0.957666\pi$
$281$	−19.6353	+	14.2658i	−1.17134	+	0.851029i	−0.180172	+	0.983635i	$0.557666\pi$
$282$		0			0
$283$	2.76393	−	8.50651i	0.164299	−	0.505659i	−0.834685	−	0.550727i	$-0.814350\pi$
$283$	2.76393	−	8.50651i	0.164299	−	0.505659i	0.998984	+	0.0450679i	$0.0143504\pi$
$284$		0			0
$285$	−28.1803			−1.66926
$286$		0			0
$287$	−32.7639			−1.93399
$288$		0			0
$289$	−4.19098	+	12.8985i	−0.246528	+	0.758736i
$290$		0			0
$291$	−7.35410	+	5.34307i	−0.431105	+	0.313216i
$292$		0			0
$293$	4.18034	+	12.8658i	0.244218	+	0.751626i	0.995764	+	0.0919452i	$0.0293085\pi$
$293$	4.18034	+	12.8658i	0.244218	+	0.751626i	−0.751546	+	0.659681i	$0.770692\pi$
$294$		0			0
$295$	23.7984	+	17.2905i	1.38559	+	1.00669i
$296$		0			0
$297$	13.9271	−	11.6372i	0.808129	−	0.675258i
$298$		0			0
$299$	−5.23607	−	3.80423i	−0.302810	−	0.220004i
$300$		0			0
$301$	5.65248	+	17.3965i	0.325803	+	1.00272i
$302$		0			0
$303$	3.00000	−	2.17963i	0.172345	−	0.125216i
$304$		0			0
$305$	2.47214	−	7.60845i	0.141554	−	0.435659i
$306$		0			0
$307$	−4.85410			−0.277038			−0.138519	−	0.990360i	$-0.544234\pi$
$307$	−4.85410			−0.277038			−0.138519	+	0.990360i	$0.544234\pi$
$308$		0			0
$309$	−27.8885			−1.58652
$310$		0			0
$311$	2.70820	−	8.33499i	0.153568	−	0.472634i	−0.844445	−	0.535643i	$-0.820069\pi$
$311$	2.70820	−	8.33499i	0.153568	−	0.472634i	0.998013	+	0.0630083i	$0.0200695\pi$
$312$		0			0
$313$	−12.4443	+	9.04129i	−0.703392	+	0.511044i	−0.881035	−	0.473051i	$-0.843153\pi$
$313$	−12.4443	+	9.04129i	−0.703392	+	0.511044i	0.177643	+	0.984095i	$0.443153\pi$
$314$		0			0
$315$	−1.70820	−	5.25731i	−0.0962464	−	0.296216i
$316$		0			0
$317$	1.47214	+	1.06957i	0.0826834	+	0.0600730i	0.628359	−	0.777923i	$-0.283727\pi$
$317$	1.47214	+	1.06957i	0.0826834	+	0.0600730i	−0.545676	+	0.837997i	$0.683727\pi$
$318$		0			0
$319$	−10.4721	−	26.0746i	−0.586327	−	1.45989i
$320$		0			0
$321$	4.35410	+	3.16344i	0.243022	+	0.176566i
$322$		0			0
$323$	−3.08359	−	9.49032i	−0.171576	−	0.528056i
$324$		0			0
$325$	−5.47214	+	3.97574i	−0.303539	+	0.220534i
$326$		0			0
$327$	1.47214	−	4.53077i	0.0814093	−	0.250552i
$328$		0			0
$329$	28.9443			1.59575
$330$		0			0
$331$	−29.7984			−1.63787			−0.818933	−	0.573889i	$-0.805434\pi$
$331$	−29.7984			−1.63787			−0.818933	+	0.573889i	$0.805434\pi$
$332$		0			0
$333$	−1.09017	+	3.35520i	−0.0597409	+	0.183864i
$334$		0			0
$335$	3.61803	−	2.62866i	0.197674	−	0.143619i
$336$		0			0
$337$	−6.75329	−	20.7845i	−0.367875	−	1.13220i	−0.948161	−	0.317790i	$-0.897059\pi$
$337$	−6.75329	−	20.7845i	−0.367875	−	1.13220i	0.580286	−	0.814413i	$-0.302941\pi$
$338$		0			0
$339$	−24.9894	−	18.1558i	−1.35724	−	0.986089i
$340$		0			0
$341$	−1.32624	−	0.832544i	−0.0718198	−	0.0450848i
$342$		0			0
$343$	−21.7082	−	15.7719i	−1.17213	−	0.851604i
$344$		0			0
$345$	8.47214	+	26.0746i	0.456124	+	1.40381i
$346$		0			0
$347$	11.5902	−	8.42075i	0.622193	−	0.452050i	−0.231494	−	0.972836i	$-0.574361\pi$
$347$	11.5902	−	8.42075i	0.622193	−	0.452050i	0.853687	+	0.520787i	$0.174361\pi$
$348$		0			0
$349$	−6.41641	+	19.7477i	−0.343462	+	1.05707i	0.618939	+	0.785439i	$0.287563\pi$
$349$	−6.41641	+	19.7477i	−0.343462	+	1.05707i	−0.962402	+	0.271630i	$0.912437\pi$
$350$		0			0
$351$	−6.76393			−0.361032
$352$		0			0
$353$	26.5066			1.41080			0.705401	−	0.708808i	$-0.250767\pi$
$353$	26.5066			1.41080			0.705401	+	0.708808i	$0.250767\pi$
$354$		0			0
$355$	3.70820	−	11.4127i	0.196811	−	0.605722i
$356$		0			0
$357$	−10.8541	+	7.88597i	−0.574460	+	0.417370i
$358$		0			0
$359$	1.76393	+	5.42882i	0.0930968	+	0.286522i	0.986753	−	0.162230i	$-0.0518686\pi$
$359$	1.76393	+	5.42882i	0.0930968	+	0.286522i	−0.893656	+	0.448752i	$0.851869\pi$
$360$		0			0
$361$	−8.06231	−	5.85761i	−0.424332	−	0.308295i
$362$		0			0
$363$	3.16312	−	17.5150i	0.166021	−	0.919301i
$364$		0			0
$365$	10.7082	+	7.77997i	0.560493	+	0.407222i
$366$		0			0
$367$	6.38197	+	19.6417i	0.333136	+	1.02529i	0.967633	+	0.252362i	$0.0812073\pi$
$367$	6.38197	+	19.6417i	0.333136	+	1.02529i	−0.634497	+	0.772925i	$0.718793\pi$
$368$		0			0
$369$	−2.26393	+	1.64484i	−0.117856	+	0.0856271i
$370$		0			0
$371$	8.94427	−	27.5276i	0.464363	−	1.42916i
$372$		0			0
$373$	16.6525			0.862233			0.431116	−	0.902296i	$-0.358120\pi$
$373$	16.6525			0.862233			0.431116	+	0.902296i	$0.358120\pi$
$374$		0			0
$375$	2.47214			0.127661
$376$		0			0
$377$	−3.23607	+	9.95959i	−0.166666	+	0.512945i
$378$		0			0
$379$	−0.836881	+	0.608030i	−0.0429877	+	0.0312324i	−0.609072	−	0.793115i	$-0.708458\pi$
$379$	−0.836881	+	0.608030i	−0.0429877	+	0.0312324i	0.566084	+	0.824348i	$0.308458\pi$
$380$		0			0
$381$	−10.2361	−	31.5034i	−0.524410	−	1.61397i
$382$		0			0
$383$	−6.00000	−	4.35926i	−0.306586	−	0.222748i	0.423844	−	0.905735i	$-0.360680\pi$
$383$	−6.00000	−	4.35926i	−0.306586	−	0.222748i	−0.730430	+	0.682987i	$0.760680\pi$
$384$		0			0
$385$	−40.6525	−	25.5195i	−2.07184	−	1.30060i
$386$		0			0
$387$	1.26393	+	0.918300i	0.0642493	+	0.0466798i
$388$		0			0
$389$	−1.18034	−	3.63271i	−0.0598456	−	0.184186i	0.916664	−	0.399658i	$-0.130871\pi$
$389$	−1.18034	−	3.63271i	−0.0598456	−	0.184186i	−0.976510	+	0.215472i	$0.930871\pi$
$390$		0			0
$391$	−7.85410	+	5.70634i	−0.397199	+	0.288582i
$392$		0			0
$393$	−0.545085	+	1.67760i	−0.0274959	+	0.0846237i
$394$		0			0
$395$	−19.4164			−0.976946
$396$		0			0
$397$	8.76393			0.439849			0.219925	−	0.975517i	$-0.429419\pi$
$397$	8.76393			0.439849			0.219925	+	0.975517i	$0.429419\pi$
$398$		0			0
$399$	−12.0344	+	37.0382i	−0.602476	+	1.85423i
$400$		0			0
$401$	−10.2533	+	7.44945i	−0.512025	+	0.372008i	−0.813591	−	0.581437i	$-0.802491\pi$
$401$	−10.2533	+	7.44945i	−0.512025	+	0.372008i	0.301566	+	0.953445i	$0.402491\pi$
$402$		0			0
$403$	0.180340	+	0.555029i	0.00898337	+	0.0276480i
$404$		0			0
$405$	20.1803	+	14.6619i	1.00277	+	0.728554i
$406$		0			0
$407$	11.4164	+	28.4257i	0.565890	+	1.40901i
$408$		0			0
$409$	−10.0902	−	7.33094i	−0.498927	−	0.362492i	0.309680	−	0.950841i	$-0.399778\pi$
$409$	−10.0902	−	7.33094i	−0.498927	−	0.362492i	−0.808607	+	0.588349i	$0.799778\pi$
$410$		0			0
$411$	−4.89919	−	15.0781i	−0.241659	−	0.743750i
$412$		0			0
$413$	32.8885	−	23.8949i	1.61834	−	1.17579i
$414$		0			0
$415$	−2.38197	+	7.33094i	−0.116926	+	0.359862i
$416$		0			0
$417$	27.4164			1.34259
$418$		0			0
$419$	26.3820			1.28884			0.644422	−	0.764670i	$-0.277098\pi$
$419$	26.3820			1.28884			0.644422	+	0.764670i	$0.277098\pi$
$420$		0			0
$421$	6.65248	−	20.4742i	0.324222	−	0.997852i	−0.647569	−	0.762007i	$-0.724214\pi$
$421$	6.65248	−	20.4742i	0.324222	−	0.997852i	0.971791	−	0.235845i	$-0.0757858\pi$
$422$		0			0
$423$	2.00000	−	1.45309i	0.0972433	−	0.0706514i
$424$		0			0
$425$	3.13525	+	9.64932i	0.152082	+	0.468061i
$426$		0			0
$427$	−8.94427	−	6.49839i	−0.432844	−	0.314479i
$428$		0			0
$429$	−5.09017	+	4.25325i	−0.245756	+	0.205349i
$430$		0			0
$431$	24.1803	+	17.5680i	1.16473	+	0.846223i	0.990368	−	0.138459i	$-0.0442150\pi$
$431$	24.1803	+	17.5680i	1.16473	+	0.846223i	0.174358	+	0.984682i	$0.444215\pi$
$432$		0			0
$433$	1.33688	+	4.11450i	0.0642464	+	0.197730i	0.978027	−	0.208478i	$-0.0668509\pi$
$433$	1.33688	+	4.11450i	0.0642464	+	0.197730i	−0.913781	+	0.406208i	$0.866851\pi$
$434$		0			0
$435$	35.8885	−	26.0746i	1.72072	−	1.25018i
$436$		0			0
$437$	−8.70820	+	26.8011i	−0.416570	+	1.28207i
$438$		0			0
$439$	6.00000			0.286364			0.143182	−	0.989696i	$-0.454267\pi$
$439$	6.00000			0.286364			0.143182	+	0.989696i	$0.454267\pi$
$440$		0			0
$441$	−4.96556			−0.236455
$442$		0			0
$443$	−10.7361	+	33.0422i	−0.510086	+	1.56988i	0.281963	+	0.959425i	$0.409015\pi$
$443$	−10.7361	+	33.0422i	−0.510086	+	1.56988i	−0.792049	+	0.610458i	$0.790985\pi$
$444$		0			0
$445$	−16.7082	+	12.1392i	−0.792045	+	0.575454i
$446$		0			0
$447$	−2.14590	−	6.60440i	−0.101497	−	0.312377i
$448$		0			0
$449$	−9.50000	−	6.90215i	−0.448333	−	0.325733i	0.340604	−	0.940207i	$-0.389368\pi$
$449$	−9.50000	−	6.90215i	−0.448333	−	0.325733i	−0.788937	+	0.614474i	$0.789368\pi$
$450$		0			0
$451$	−5.92705	+	23.5644i	−0.279094	+	1.10960i
$452$		0			0
$453$	−16.9443	−	12.3107i	−0.796111	−	0.578409i
$454$		0			0
$455$	5.52786	+	17.0130i	0.259150	+	0.797582i
$456$		0			0
$457$	−7.78115	+	5.65334i	−0.363987	+	0.264452i	−0.754713	−	0.656055i	$-0.772224\pi$
$457$	−7.78115	+	5.65334i	−0.363987	+	0.264452i	0.390726	+	0.920507i	$0.372224\pi$
$458$		0			0
$459$	−3.13525	+	9.64932i	−0.146341	+	0.450392i
$460$		0			0
$461$	−30.6525			−1.42763			−0.713814	−	0.700335i	$-0.753034\pi$
$461$	−30.6525			−1.42763			−0.713814	+	0.700335i	$0.753034\pi$
$462$		0			0
$463$	25.5279			1.18638			0.593190	−	0.805062i	$-0.297868\pi$
$463$	25.5279			1.18638			0.593190	+	0.805062i	$0.297868\pi$
$464$		0			0
$465$	0.763932	−	2.35114i	0.0354265	−	0.109032i
$466$		0			0
$467$	−20.6525	+	15.0049i	−0.955683	+	0.694344i	−0.952144	−	0.305650i	$-0.901126\pi$
$467$	−20.6525	+	15.0049i	−0.955683	+	0.694344i	−0.00353857	+	0.999994i	$0.501126\pi$
$468$		0			0
$469$	−1.90983	−	5.87785i	−0.0881878	−	0.271414i
$470$		0			0
$471$	−12.7082	−	9.23305i	−0.585563	−	0.425437i
$472$		0			0
$473$	13.5344	−	0.918300i	0.622314	−	0.0422235i
$474$		0			0
$475$	23.8262	+	17.3108i	1.09322	+	0.794273i
$476$		0			0
$477$	−0.763932	−	2.35114i	−0.0349780	−	0.107651i
$478$		0			0
$479$	−31.8885	+	23.1684i	−1.45702	+	1.05859i	−0.472899	+	0.881117i	$0.656793\pi$
$479$	−31.8885	+	23.1684i	−1.45702	+	1.05859i	−0.984125	+	0.177474i	$0.943207\pi$
$480$		0			0
$481$	3.52786	−	10.8576i	0.160857	−	0.495066i
$482$		0			0
$483$	37.8885			1.72399
$484$		0			0
$485$	18.1803			0.825527
$486$		0			0
$487$	10.2361	−	31.5034i	0.463841	−	1.42755i	−0.396594	−	0.917994i	$-0.629808\pi$
$487$	10.2361	−	31.5034i	0.463841	−	1.42755i	0.860435	−	0.509560i	$-0.170192\pi$
$488$		0			0
$489$	27.6074	−	20.0579i	1.24845	−	0.907052i
$490$		0			0
$491$	−2.55573	−	7.86572i	−0.115338	−	0.354975i	0.876679	−	0.481076i	$-0.159754\pi$
$491$	−2.55573	−	7.86572i	−0.115338	−	0.354975i	−0.992017	+	0.126101i	$0.959754\pi$
$492$		0			0
$493$	12.7082	+	9.23305i	0.572349	+	0.415836i
$494$		0			0
$495$	−4.09017	+	0.277515i	−0.183839	+	0.0124734i
$496$		0			0
$497$	−13.4164	−	9.74759i	−0.601808	−	0.437239i
$498$		0			0
$499$	−12.8607	−	39.5811i	−0.575723	−	1.77189i	−0.633704	−	0.773576i	$-0.718466\pi$
$499$	−12.8607	−	39.5811i	−0.575723	−	1.77189i	0.0579807	−	0.998318i	$-0.481534\pi$
$500$		0			0
$501$	16.5623	−	12.0332i	0.739949	−	0.537605i
$502$		0			0
$503$	3.18034	−	9.78808i	0.141804	−	0.436429i	−0.854782	−	0.518987i	$-0.826309\pi$
$503$	3.18034	−	9.78808i	0.141804	−	0.436429i	0.996586	+	0.0825585i	$0.0263091\pi$
$504$		0			0
$505$	−7.41641			−0.330026
$506$		0			0
$507$	−18.5623			−0.824381
$508$		0			0
$509$	−4.09017	+	12.5882i	−0.181294	+	0.557964i	−0.999865	−	0.0164407i	$-0.994767\pi$
$509$	−4.09017	+	12.5882i	−0.181294	+	0.557964i	0.818571	+	0.574405i	$0.194767\pi$
$510$		0			0
$511$	14.7984	−	10.7516i	0.654642	−	0.475625i
$512$		0			0
$513$	9.10081	+	28.0094i	0.401811	+	1.23665i
$514$		0			0
$515$	45.1246	+	32.7849i	1.98843	+	1.44468i
$516$		0			0
$517$	5.23607	−	20.8172i	0.230282	−	0.915541i
$518$		0			0
$519$	11.7082	+	8.50651i	0.513933	+	0.373394i
$520$		0			0
$521$	−3.13525	−	9.64932i	−0.137358	−	0.422744i	0.858591	−	0.512661i	$-0.171340\pi$
$521$	−3.13525	−	9.64932i	−0.137358	−	0.422744i	−0.995949	+	0.0899161i	$0.971340\pi$
$522$		0			0
$523$	20.0623	−	14.5761i	0.877263	−	0.637369i	−0.0552627	−	0.998472i	$-0.517600\pi$
$523$	20.0623	−	14.5761i	0.877263	−	0.637369i	0.932526	+	0.361103i	$0.117600\pi$
$524$		0			0
$525$	12.2361	−	37.6587i	0.534026	−	1.64356i
$526$		0			0
$527$	0.875388			0.0381325
$528$		0			0
$529$	4.41641			0.192018
$530$		0			0
$531$	1.07295	−	3.30220i	0.0465620	−	0.143303i
$532$		0			0
$533$	7.32624	−	5.32282i	0.317335	−	0.230557i
$534$		0			0
$535$	−3.32624	−	10.2371i	−0.143806	−	0.442589i
$536$		0			0
$537$	12.6631	+	9.20029i	0.546454	+	0.397022i
$538$		0			0
$539$	−33.0861	+	27.6462i	−1.42512	+	1.19080i
$540$		0			0
$541$	−19.9443	−	14.4904i	−0.857471	−	0.622989i	0.0697246	−	0.997566i	$-0.477788\pi$
$541$	−19.9443	−	14.4904i	−0.857471	−	0.622989i	−0.927196	+	0.374577i	$0.877788\pi$
$542$		0			0
$543$	0.381966	+	1.17557i	0.0163917	+	0.0504486i
$544$		0			0
$545$	−7.70820	+	5.60034i	−0.330183	+	0.239892i
$546$		0			0
$547$	−6.33688	+	19.5029i	−0.270945	+	0.833884i	0.719318	+	0.694681i	$0.244454\pi$
$547$	−6.33688	+	19.5029i	−0.270945	+	0.833884i	−0.990264	+	0.139204i	$0.955546\pi$
$548$		0			0
$549$	−0.944272			−0.0403005
$550$		0			0
$551$	45.5967			1.94249
$552$		0			0
$553$	−8.29180	+	25.5195i	−0.352603	+	1.08520i
$554$		0			0
$555$	−39.1246	+	28.4257i	−1.66075	+	1.20660i
$556$		0			0
$557$	0.0557281	+	0.171513i	0.00236127	+	0.00726726i	0.952230	−	0.305381i	$-0.0987839\pi$
$557$	0.0557281	+	0.171513i	0.00236127	+	0.00726726i	−0.949869	+	0.312648i	$0.898784\pi$
$558$		0			0
$559$	−4.09017	−	2.97168i	−0.172996	−	0.125689i
$560$		0			0
$561$	3.70820	+	9.23305i	0.156560	+	0.389820i
$562$		0			0
$563$	14.1074	+	10.2496i	0.594556	+	0.431970i	0.843942	−	0.536434i	$-0.180229\pi$
$563$	14.1074	+	10.2496i	0.594556	+	0.431970i	−0.249387	+	0.968404i	$0.580229\pi$
$564$		0			0
$565$	19.0902	+	58.7535i	0.803129	+	2.47178i
$566$		0			0
$567$	27.8885	−	20.2622i	1.17121	−	0.850933i
$568$		0			0
$569$	−4.19098	+	12.8985i	−0.175695	+	0.540734i	−0.999665	−	0.0259003i	$-0.991755\pi$
$569$	−4.19098	+	12.8985i	−0.175695	+	0.540734i	0.823969	+	0.566634i	$0.191755\pi$
$570$		0			0
$571$	22.4721			0.940430			0.470215	−	0.882552i	$-0.344176\pi$
$571$	22.4721			0.940430			0.470215	+	0.882552i	$0.344176\pi$
$572$		0			0
$573$	−9.23607			−0.385842
$574$		0			0
$575$	8.85410	−	27.2501i	0.369242	−	1.13641i
$576$		0			0
$577$	−27.4443	+	19.9394i	−1.14252	+	0.830089i	−0.987468	−	0.157817i	$-0.949554\pi$
$577$	−27.4443	+	19.9394i	−1.14252	+	0.830089i	−0.155052	+	0.987906i	$0.549554\pi$
$578$		0			0
$579$	8.70820	+	26.8011i	0.361901	+	1.11382i
$580$		0			0
$581$	8.61803	+	6.26137i	0.357536	+	0.259765i
$582$		0			0
$583$	−18.1803	−	11.4127i	−0.752953	−	0.472665i
$584$		0			0
$585$	1.23607	+	0.898056i	0.0511051	+	0.0371300i
$586$		0			0
$587$	−0.607391	−	1.86936i	−0.0250697	−	0.0771566i	0.937739	−	0.347341i	$-0.112915\pi$
$587$	−0.607391	−	1.86936i	−0.0250697	−	0.0771566i	−0.962809	+	0.270184i	$0.912915\pi$
$588$		0			0
$589$	2.05573	−	1.49357i	0.0847048	−	0.0615416i
$590$		0			0
$591$	−4.00000	+	12.3107i	−0.164538	+	0.506396i
$592$		0			0
$593$	−34.7984			−1.42900			−0.714499	−	0.699636i	$-0.753345\pi$
$593$	−34.7984			−1.42900			−0.714499	+	0.699636i	$0.753345\pi$
$594$		0			0
$595$	26.8328			1.10004
$596$		0			0
$597$	−11.1803	+	34.4095i	−0.457581	+	1.40829i
$598$		0			0
$599$	−10.3820	+	7.54294i	−0.424196	+	0.308196i	−0.779324	−	0.626621i	$-0.784437\pi$
$599$	−10.3820	+	7.54294i	−0.424196	+	0.308196i	0.355128	+	0.934818i	$0.384437\pi$
$600$		0			0
$601$	1.02786	+	3.16344i	0.0419274	+	0.129039i	0.969829	−	0.243785i	$-0.0783892\pi$
$601$	1.02786	+	3.16344i	0.0419274	+	0.129039i	−0.927902	+	0.372825i	$0.878389\pi$
$602$		0			0
$603$	−0.427051	−	0.310271i	−0.0173909	−	0.0126352i
$604$		0			0
$605$	−25.7082	+	24.6215i	−1.04519	+	1.00101i
$606$		0			0
$607$	−16.4164	−	11.9272i	−0.666321	−	0.484111i	0.202470	−	0.979288i	$-0.435103\pi$
$607$	−16.4164	−	11.9272i	−0.666321	−	0.484111i	−0.868792	+	0.495178i	$0.835103\pi$
$608$		0			0
$609$	−18.9443	−	58.3045i	−0.767661	−	2.36262i
$610$		0			0
$611$	−6.47214	+	4.70228i	−0.261835	+	0.190234i
$612$		0			0
$613$	2.09017	−	6.43288i	0.0844212	−	0.259822i	−0.899931	−	0.436031i	$-0.856384\pi$
$613$	2.09017	−	6.43288i	0.0844212	−	0.259822i	0.984353	+	0.176210i	$0.0563837\pi$
$614$		0			0
$615$	−38.3607			−1.54685
$616$		0			0
$617$	−4.90983			−0.197662			−0.0988312	−	0.995104i	$-0.531510\pi$
$617$	−4.90983			−0.197662			−0.0988312	+	0.995104i	$0.531510\pi$
$618$		0			0
$619$	−4.89919	+	15.0781i	−0.196915	+	0.606042i	0.803034	+	0.595933i	$0.203218\pi$
$619$	−4.89919	+	15.0781i	−0.196915	+	0.606042i	−0.999949	+	0.0101086i	$0.996782\pi$
$620$		0			0
$621$	23.1803	−	16.8415i	0.930195	−	0.675826i
$622$		0			0
$623$	8.81966	+	27.1441i	0.353352	+	1.08751i
$624$		0			0
$625$	18.1353	+	13.1760i	0.725410	+	0.527041i
$626$		0			0
$627$	24.4615	+	15.3557i	0.976898	+	0.613246i
$628$		0			0
$629$	−13.8541	−	10.0656i	−0.552399	−	0.401342i
$630$		0			0
$631$	−1.90983	−	5.87785i	−0.0760291	−	0.233994i	0.905818	−	0.423667i	$-0.139257\pi$
$631$	−1.90983	−	5.87785i	−0.0760291	−	0.233994i	−0.981847	+	0.189673i	$0.939257\pi$
$632$		0			0
$633$	−0.118034	+	0.0857567i	−0.00469143	+	0.00340852i
$634$		0			0
$635$	−20.4721	+	63.0068i	−0.812412	+	2.50035i
$636$		0			0
$637$	16.0689			0.636672
$638$		0			0
$639$	−1.41641			−0.0560322
$640$		0			0
$641$	−10.1525	+	31.2461i	−0.400999	+	1.23415i	0.523192	+	0.852215i	$0.324741\pi$
$641$	−10.1525	+	31.2461i	−0.400999	+	1.23415i	−0.924190	+	0.381932i	$0.875259\pi$
$642$		0			0
$643$	28.7254	−	20.8702i	1.13282	−	0.823042i	0.146717	−	0.989178i	$-0.453129\pi$
$643$	28.7254	−	20.8702i	1.13282	−	0.823042i	0.986103	+	0.166136i	$0.0531292\pi$
$644$		0			0
$645$	6.61803	+	20.3682i	0.260585	+	0.801998i
$646$		0			0
$647$	19.0344	+	13.8293i	0.748321	+	0.543687i	0.895306	−	0.445452i	$-0.146957\pi$
$647$	19.0344	+	13.8293i	0.748321	+	0.543687i	−0.146985	+	0.989139i	$0.546957\pi$
$648$		0			0
$649$	−11.2361	−	27.9767i	−0.441054	−	1.09818i
$650$		0			0
$651$	−2.76393	−	2.00811i	−0.108327	−	0.0787042i
$652$		0			0
$653$	−13.9098	−	42.8101i	−0.544334	−	1.67529i	−0.722569	−	0.691299i	$-0.757039\pi$
$653$	−13.9098	−	42.8101i	−0.544334	−	1.67529i	0.178235	−	0.983988i	$-0.442961\pi$
$654$		0			0
$655$	2.85410	−	2.07363i	0.111519	−	0.0810233i
$656$		0			0
$657$	0.482779	−	1.48584i	0.0188350	−	0.0579682i
$658$		0			0
$659$	−11.4934			−0.447720			−0.223860	−	0.974621i	$-0.571866\pi$
$659$	−11.4934			−0.447720			−0.223860	+	0.974621i	$0.571866\pi$
$660$		0			0
$661$	−21.4164			−0.833002			−0.416501	−	0.909135i	$-0.636744\pi$
$661$	−21.4164			−0.833002			−0.416501	+	0.909135i	$0.636744\pi$
$662$		0			0
$663$	1.14590	−	3.52671i	0.0445030	−	0.136966i
$664$		0			0
$665$	63.0132	−	45.7817i	2.44355	−	1.77534i
$666$		0			0
$667$	−13.7082	−	42.1895i	−0.530784	−	1.63358i
$668$		0			0
$669$	−3.00000	−	2.17963i	−0.115987	−	0.0842693i
$670$		0			0
$671$	−6.29180	+	5.25731i	−0.242892	+	0.202956i
$672$		0			0
$673$	35.9164	+	26.0948i	1.38448	+	1.00588i	0.996446	+	0.0842337i	$0.0268442\pi$
$673$	35.9164	+	26.0948i	1.38448	+	1.00588i	0.388030	+	0.921647i	$0.373156\pi$
$674$		0			0
$675$	−9.25329	−	28.4787i	−0.356159	−	1.09615i
$676$		0			0
$677$	10.0902	−	7.33094i	0.387797	−	0.281751i	−0.376755	−	0.926313i	$-0.622960\pi$
$677$	10.0902	−	7.33094i	0.387797	−	0.281751i	0.764552	+	0.644562i	$0.222960\pi$
$678$		0			0
$679$	7.76393	−	23.8949i	0.297952	−	0.917003i
$680$		0			0
$681$	−38.5967			−1.47903
$682$		0			0
$683$	27.4164			1.04906			0.524530	−	0.851392i	$-0.324241\pi$
$683$	27.4164			1.04906			0.524530	+	0.851392i	$0.324241\pi$
$684$		0			0
$685$	−9.79837	+	30.1563i	−0.374377	+	1.15221i
$686$		0			0
$687$	21.1803	−	15.3884i	0.808080	−	0.587105i
$688$		0			0
$689$	2.47214	+	7.60845i	0.0941809	+	0.289859i
$690$		0			0
$691$	−31.5344	−	22.9111i	−1.19963	−	0.871580i	−0.205379	−	0.978683i	$-0.565843\pi$
$691$	−31.5344	−	22.9111i	−1.19963	−	0.871580i	−0.994248	+	0.107103i	$0.965843\pi$
$692$		0			0
$693$	−1.38197	+	5.49434i	−0.0524965	+	0.208713i
$694$		0			0
$695$	−44.3607	−	32.2299i	−1.68270	−	1.22255i
$696$		0			0
$697$	−4.19756	−	12.9188i	−0.158994	−	0.489333i
$698$		0			0
$699$	−10.3541	+	7.52270i	−0.391628	+	0.284534i
$700$		0			0
$701$	2.11146	−	6.49839i	0.0797486	−	0.245441i	−0.903231	−	0.429154i	$-0.858812\pi$
$701$	2.11146	−	6.49839i	0.0797486	−	0.245441i	0.982980	+	0.183713i	$0.0588117\pi$
$702$		0			0
$703$	−49.7082			−1.87478
$704$		0			0
$705$	33.8885			1.27632
$706$		0			0
$707$	−3.16718	+	9.74759i	−0.119114	+	0.366596i
$708$		0			0
$709$	42.4508	−	30.8423i	1.59428	−	1.15831i	0.696779	−	0.717285i	$-0.254616\pi$
$709$	42.4508	−	30.8423i	1.59428	−	1.15831i	0.897496	−	0.441023i	$-0.145384\pi$
$710$		0			0
$711$	0.708204	+	2.17963i	0.0265597	+	0.0817424i
$712$		0			0
$713$	−2.00000	−	1.45309i	−0.0749006	−	0.0544185i
$714$		0			0
$715$	13.2361	−	0.898056i	0.495001	−	0.0335854i
$716$		0			0
$717$	18.7082	+	13.5923i	0.698671	+	0.507614i
$718$		0			0
$719$	3.70820	+	11.4127i	0.138293	+	0.425621i	0.996088	−	0.0883709i	$-0.0281661\pi$
$719$	3.70820	+	11.4127i	0.138293	+	0.425621i	−0.857795	+	0.513992i	$0.828166\pi$
$720$		0			0
$721$	62.3607	−	45.3077i	2.32243	−	1.68735i
$722$		0			0
$723$	14.1631	−	43.5896i	0.526732	−	1.62111i
$724$		0			0
$725$	−46.3607			−1.72179
$726$		0			0
$727$	−6.87539			−0.254994			−0.127497	−	0.991839i	$-0.540694\pi$
$727$	−6.87539			−0.254994			−0.127497	+	0.991839i	$0.540694\pi$
$728$		0			0
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$		0			0
$731$	−6.13525	+	4.45752i	−0.226921	+	0.164867i
$732$		0			0
$733$	3.20163	+	9.85359i	0.118255	+	0.363951i	0.992612	−	0.121332i	$-0.0387166\pi$
$733$	3.20163	+	9.85359i	0.118255	+	0.363951i	−0.874357	+	0.485283i	$0.838717\pi$
$734$		0			0
$735$	−55.0689	−	40.0099i	−2.03125	−	1.47579i
$736$		0			0
$737$	−4.57295	+	0.310271i	−0.168447	+	0.0114290i
$738$		0			0
$739$	−20.5344	−	14.9191i	−0.755372	−	0.548810i	0.142116	−	0.989850i	$-0.454610\pi$
$739$	−20.5344	−	14.9191i	−0.755372	−	0.548810i	−0.897487	+	0.441040i	$0.854610\pi$
$740$		0			0
$741$	−3.32624	−	10.2371i	−0.122192	−	0.376070i
$742$		0			0
$743$	2.61803	−	1.90211i	0.0960464	−	0.0697818i	−0.538726	−	0.842481i	$-0.681094\pi$
$743$	2.61803	−	1.90211i	0.0960464	−	0.0697818i	0.634772	+	0.772700i	$0.281094\pi$
$744$		0			0
$745$	−4.29180	+	13.2088i	−0.157239	+	0.483933i
$746$		0			0
$747$	0.909830			0.0332889
$748$		0			0
$749$	−14.8754			−0.543535
$750$		0			0
$751$	10.6180	−	32.6789i	0.387458	−	1.19247i	−0.547224	−	0.836986i	$-0.684315\pi$
$751$	10.6180	−	32.6789i	0.387458	−	1.19247i	0.934682	−	0.355486i	$-0.115685\pi$
$752$		0			0
$753$	5.23607	−	3.80423i	0.190813	−	0.138634i
$754$		0			0
$755$	12.9443	+	39.8384i	0.471090	+	1.44987i
$756$		0			0
$757$	−27.7426	−	20.1562i	−1.00832	−	0.732590i	−0.0444668	−	0.999011i	$-0.514159\pi$
$757$	−27.7426	−	20.1562i	−1.00832	−	0.732590i	−0.963857	+	0.266421i	$0.914159\pi$
$758$		0			0
$759$	6.85410	−	27.2501i	0.248788	−	0.989117i
$760$		0			0
$761$	−31.3885	−	22.8051i	−1.13783	−	0.826685i	−0.151018	−	0.988531i	$-0.548255\pi$
$761$	−31.3885	−	22.8051i	−1.13783	−	0.826685i	−0.986816	+	0.161846i	$0.948255\pi$
$762$		0			0
$763$	4.06888	+	12.5227i	0.147303	+	0.453353i
$764$		0			0
$765$	1.85410	−	1.34708i	0.0670352	−	0.0487039i
$766$		0			0
$767$	−3.47214	+	10.6861i	−0.125372	+	0.385854i
$768$		0			0
$769$	−18.5836			−0.670141			−0.335071	−	0.942193i	$-0.608760\pi$
$769$	−18.5836			−0.670141			−0.335071	+	0.942193i	$0.608760\pi$
$770$		0			0
$771$	−30.0344			−1.08166
$772$		0			0
$773$	−7.67376	+	23.6174i	−0.276006	+	0.849459i	0.712945	+	0.701220i	$0.247361\pi$
$773$	−7.67376	+	23.6174i	−0.276006	+	0.849459i	−0.988951	+	0.148240i	$0.952639\pi$
$774$		0			0
$775$	−2.09017	+	1.51860i	−0.0750811	+	0.0545496i
$776$		0			0
$777$	20.6525	+	63.5618i	0.740903	+	2.28027i
$778$		0			0
$779$	−31.8992	−	23.1761i	−1.14291	−	0.830371i
$780$		0			0
$781$	−9.43769	+	7.88597i	−0.337707	+	0.282182i
$782$		0			0
$783$	−37.5066	−	27.2501i	−1.34038	−	0.973840i
$784$		0			0
$785$	9.70820	+	29.8788i	0.346501	+	1.06642i
$786$		0			0
$787$	1.17376	−	0.852788i	0.0418401	−	0.0303986i	−0.566669	−	0.823946i	$-0.691768\pi$
$787$	1.17376	−	0.852788i	0.0418401	−	0.0303986i	0.608509	+	0.793547i	$0.291768\pi$
$788$		0			0
$789$	0.0901699	−	0.277515i	0.00321014	−	0.00987978i
$790$		0			0
$791$	85.3738			3.03554
$792$		0			0
$793$	3.05573			0.108512
$794$		0			0
$795$	10.4721	−	32.2299i	0.371408	−	1.14308i
$796$		0			0
$797$	21.5623	−	15.6659i	0.763776	−	0.554916i	−0.136290	−	0.990669i	$-0.543518\pi$
$797$	21.5623	−	15.6659i	0.763776	−	0.554916i	0.900066	+	0.435753i	$0.143518\pi$
$798$		0			0
$799$	3.70820	+	11.4127i	0.131187	+	0.403752i
$800$		0			0
$801$	1.97214	+	1.43284i	0.0696820	+	0.0506269i
$802$		0			0
$803$	−5.05573	−	12.5882i	−0.178413	−	0.444230i
$804$		0			0
$805$	−61.3050	−	44.5407i	−2.16072	−	1.56985i
$806$		0			0
$807$	7.09017	+	21.8213i	0.249586	+	0.768146i
$808$		0			0
$809$	−17.6803	+	12.8455i	−0.621608	+	0.451624i	−0.853483	−	0.521121i	$-0.825514\pi$
$809$	−17.6803	+	12.8455i	−0.621608	+	0.451624i	0.231875	+	0.972746i	$0.425514\pi$
$810$		0			0
$811$	−6.44427	+	19.8334i	−0.226289	+	0.696446i	0.771869	+	0.635781i	$0.219322\pi$
$811$	−6.44427	+	19.8334i	−0.226289	+	0.696446i	−0.998158	+	0.0606646i	$0.980678\pi$
$812$		0			0
$813$	13.7082			0.480768
$814$		0			0
$815$	−68.2492			−2.39067
$816$		0			0
$817$	−6.80244	+	20.9358i	−0.237987	+	0.732449i
$818$		0			0
$819$	1.70820	−	1.24108i	0.0596895	−	0.0433669i
$820$		0			0
$821$	9.43769	+	29.0462i	0.329378	+	1.01372i	0.969426	+	0.245386i	$0.0789145\pi$
$821$	9.43769	+	29.0462i	0.329378	+	1.01372i	−0.640048	+	0.768335i	$0.721085\pi$
$822$		0			0
$823$	2.32624	+	1.69011i	0.0810876	+	0.0589136i	0.627590	−	0.778544i	$-0.284041\pi$
$823$	2.32624	+	1.69011i	0.0810876	+	0.0589136i	−0.546503	+	0.837457i	$0.684041\pi$
$824$		0			0
$825$	−24.8713	−	15.6129i	−0.865908	−	0.543573i
$826$		0			0
$827$	−22.5344	−	16.3722i	−0.783599	−	0.569318i	0.122458	−	0.992474i	$-0.460922\pi$
$827$	−22.5344	−	16.3722i	−0.783599	−	0.569318i	−0.906057	+	0.423155i	$0.860922\pi$
$828$		0			0
$829$	0.875388	+	2.69417i	0.0304035	+	0.0935723i	0.965107	−	0.261857i	$-0.0843348\pi$
$829$	0.875388	+	2.69417i	0.0304035	+	0.0935723i	−0.934703	+	0.355429i	$0.884335\pi$
$830$		0			0
$831$	−13.3262	+	9.68208i	−0.462282	+	0.335868i
$832$		0			0
$833$	7.44834	−	22.9236i	0.258070	−	0.794257i
$834$		0			0
$835$	−40.9443			−1.41693
$836$		0			0
$837$	−2.58359			−0.0893020
$838$		0			0
$839$	7.85410	−	24.1724i	0.271154	−	0.834525i	−0.719058	−	0.694950i	$-0.755426\pi$
$839$	7.85410	−	24.1724i	0.271154	−	0.834525i	0.990211	−	0.139575i	$-0.0445736\pi$
$840$		0			0
$841$	−34.6074	+	25.1437i	−1.19336	+	0.867026i
$842$		0			0
$843$	12.1353	+	37.3485i	0.417960	+	1.28635i
$844$		0			0
$845$	30.0344	+	21.8213i	1.03322	+	0.750676i
$846$		0			0
$847$	21.3820	+	44.3036i	0.734693	+	1.52229i
$848$		0			0
$849$	−11.7082	−	8.50651i	−0.401825	−	0.291943i
$850$		0			0
$851$	14.9443	+	45.9937i	0.512283	+	1.57665i
$852$		0			0
$853$	13.2361	−	9.61657i	0.453194	−	0.329265i	−0.337661	−	0.941268i	$-0.609636\pi$
$853$	13.2361	−	9.61657i	0.453194	−	0.329265i	0.790856	+	0.612003i	$0.209636\pi$
$854$		0			0
$855$	2.05573	−	6.32688i	0.0703044	−	0.216375i
$856$		0			0
$857$	−10.7426			−0.366962			−0.183481	−	0.983023i	$-0.558737\pi$
$857$	−10.7426			−0.366962			−0.183481	+	0.983023i	$0.558737\pi$
$858$		0			0
$859$	44.5066			1.51854			0.759272	−	0.650773i	$-0.225555\pi$
$859$	44.5066			1.51854			0.759272	+	0.650773i	$0.225555\pi$
$860$		0			0
$861$	−16.3820	+	50.4185i	−0.558296	+	1.71826i
$862$		0			0
$863$	1.76393	−	1.28157i	0.0600449	−	0.0436252i	−0.557358	−	0.830272i	$-0.688185\pi$
$863$	1.76393	−	1.28157i	0.0600449	−	0.0436252i	0.617403	+	0.786647i	$0.288185\pi$
$864$		0			0
$865$	−8.94427	−	27.5276i	−0.304114	−	0.935968i
$866$		0			0
$867$	17.7533	+	12.8985i	0.602933	+	0.438057i
$868$		0			0
$869$	16.8541	+	10.5801i	0.571736	+	0.358906i
$870$		0			0
$871$	1.38197	+	1.00406i	0.0468261	+	0.0340212i
$872$		0			0
$873$	−0.663119	−	2.04087i	−0.0224432	−	0.0690730i
$874$		0			0
$875$	−5.52786	+	4.01623i	−0.186876	+	0.135773i
$876$		0			0
$877$	3.87539	−	11.9272i	0.130863	−	0.402754i	−0.864061	−	0.503387i	$-0.832087\pi$
$877$	3.87539	−	11.9272i	0.130863	−	0.402754i	0.994924	+	0.100634i	$0.0320870\pi$
$878$		0			0
$879$	21.8885			0.738282
$880$		0			0
$881$	−29.6180			−0.997857			−0.498928	−	0.866643i	$-0.666273\pi$
$881$	−29.6180			−0.997857			−0.498928	+	0.866643i	$0.666273\pi$
$882$		0			0
$883$	−6.86068	+	21.1150i	−0.230880	+	0.710576i	0.766761	+	0.641933i	$0.221867\pi$
$883$	−6.86068	+	21.1150i	−0.230880	+	0.710576i	−0.997641	+	0.0686437i	$0.978133\pi$
$884$		0			0
$885$	38.5066	−	27.9767i	1.29438	−	0.940425i
$886$		0			0
$887$	−2.61803	−	8.05748i	−0.0879050	−	0.270544i	0.897435	−	0.441147i	$-0.145428\pi$
$887$	−2.61803	−	8.05748i	−0.0879050	−	0.270544i	−0.985340	+	0.170603i	$0.945428\pi$
$888$		0			0
$889$	74.0689	+	53.8142i	2.48419	+	1.80487i
$890$		0			0
$891$	−9.52786	−	23.7234i	−0.319195	−	0.794764i
$892$		0			0
$893$	28.1803	+	20.4742i	0.943019	+	0.685143i
$894$		0			0
$895$	−9.67376	−	29.7728i	−0.323358	−	0.995194i
$896$		0			0
$897$	−8.47214	+	6.15537i	−0.282876	+	0.205522i
$898$		0			0
$899$	−1.23607	+	3.80423i	−0.0412252	+	0.126878i
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$	29.5967			0.984918
$904$		0			0
$905$	0.763932	−	2.35114i	0.0253940	−	0.0781546i
$906$		0			0
$907$	−3.11803	+	2.26538i	−0.103533	+	0.0752209i	−0.638347	−	0.769749i	$-0.720382\pi$
$907$	−3.11803	+	2.26538i	−0.103533	+	0.0752209i	0.534814	+	0.844970i	$0.320382\pi$
$908$		0			0
$909$	0.270510	+	0.832544i	0.00897224	+	0.0276137i
$910$		0			0
$911$	23.9443	+	17.3965i	0.793309	+	0.576373i	0.908944	−	0.416919i	$-0.136890\pi$
$911$	23.9443	+	17.3965i	0.793309	+	0.576373i	−0.115635	+	0.993292i	$0.536890\pi$
$912$		0			0
$913$	6.06231	−	5.06555i	0.200633	−	0.167645i
$914$		0			0
$915$	−10.4721	−	7.60845i	−0.346198	−	0.251528i
$916$		0			0
$917$	−1.50658	−	4.63677i	−0.0497516	−	0.153120i
$918$		0			0
$919$	−35.1246	+	25.5195i	−1.15865	+	0.841811i	−0.989607	−	0.143797i	$-0.954069\pi$
$919$	−35.1246	+	25.5195i	−1.15865	+	0.841811i	−0.169047	+	0.985608i	$0.554069\pi$
$920$		0			0
$921$	−2.42705	+	7.46969i	−0.0799740	+	0.246135i
$922$		0			0
$923$	4.58359			0.150871
$924$		0			0
$925$	50.5410			1.66178
$926$		0			0
$927$	2.03444	−	6.26137i	0.0668198	−	0.205650i
$928$		0			0
$929$	22.2082	−	16.1352i	0.728628	−	0.529379i	−0.160501	−	0.987036i	$-0.551311\pi$
$929$	22.2082	−	16.1352i	0.728628	−	0.529379i	0.889129	+	0.457657i	$0.151311\pi$
$930$		0			0
$931$	−21.6205	−	66.5412i	−0.708585	−	2.18080i
$932$		0			0
$933$	−11.4721	−	8.33499i	−0.375581	−	0.272875i
$934$		0			0
$935$	4.85410	−	19.2986i	0.158746	−	0.631133i
$936$		0			0
$937$	−35.1525	−	25.5398i	−1.14838	−	0.834348i	−0.160117	−	0.987098i	$-0.551187\pi$
$937$	−35.1525	−	25.5398i	−1.14838	−	0.834348i	−0.988265	+	0.152750i	$0.951187\pi$
$938$		0			0
$939$	7.69098	+	23.6704i	0.250986	+	0.772455i
$940$		0			0
$941$	24.7984	−	18.0171i	0.808404	−	0.587340i	−0.104964	−	0.994476i	$-0.533473\pi$
$941$	24.7984	−	18.0171i	0.808404	−	0.587340i	0.913367	+	0.407136i	$0.133473\pi$
$942$		0			0
$943$	−11.8541	+	36.4832i	−0.386023	+	1.18806i
$944$		0			0
$945$	−79.1935			−2.57616
$946$		0			0
$947$	−24.7984			−0.805839			−0.402919	−	0.915235i	$-0.632005\pi$
$947$	−24.7984			−0.805839			−0.402919	+	0.915235i	$0.632005\pi$
$948$		0			0
$949$	−1.56231	+	4.80828i	−0.0507146	+	0.156083i
$950$		0			0
$951$	2.38197	−	1.73060i	0.0772405	−	0.0561185i
$952$		0			0
$953$	1.44427	+	4.44501i	0.0467846	+	0.143988i	0.971720	−	0.236136i	$-0.0758812\pi$
$953$	1.44427	+	4.44501i	0.0467846	+	0.143988i	−0.924935	+	0.380124i	$0.875881\pi$
$954$		0			0
$955$	14.9443	+	10.8576i	0.483585	+	0.351345i
$956$		0			0
$957$	−45.3607	+	3.07768i	−1.46630	+	0.0994874i
$958$		0			0
$959$	35.4508	+	25.7565i	1.14477	+	0.831722i
$960$		0			0
$961$	−9.51064	−	29.2707i	−0.306795	−	0.944218i
$962$		0			0
$963$	−1.02786	+	0.746787i	−0.0331225	+	0.0240649i
$964$		0			0
$965$	17.4164	−	53.6022i	0.560654	−	1.72552i
$966$		0			0
$967$	−10.3607			−0.333177			−0.166589	−	0.986027i	$-0.553275\pi$
$967$	−10.3607			−0.333177			−0.166589	+	0.986027i	$0.553275\pi$
$968$		0			0
$969$	−16.1459			−0.518681
$970$		0			0
$971$	11.0557	−	34.0260i	0.354795	−	1.09195i	−0.601333	−	0.798999i	$-0.705363\pi$
$971$	11.0557	−	34.0260i	0.354795	−	1.09195i	0.956128	−	0.292949i	$-0.0946365\pi$
$972$		0			0
$973$	−61.3050	+	44.5407i	−1.96535	+	1.42791i
$974$		0			0
$975$	3.38197	+	10.4086i	0.108310	+	0.333343i
$976$		0			0
$977$	19.0344	+	13.8293i	0.608966	+	0.442440i	0.849050	−	0.528313i	$-0.177175\pi$
$977$	19.0344	+	13.8293i	0.608966	+	0.442440i	−0.240084	+	0.970752i	$0.577175\pi$
$978$		0			0
$979$	21.1180	−	1.43284i	0.674935	−	0.0457938i
$980$		0			0
$981$	0.909830	+	0.661030i	0.0290486	+	0.0211051i
$982$		0			0
$983$	−8.21478	−	25.2825i	−0.262011	−	0.806386i	−0.992367	−	0.123320i	$-0.960646\pi$
$983$	−8.21478	−	25.2825i	−0.262011	−	0.806386i	0.730356	−	0.683067i	$-0.239354\pi$
$984$		0			0
$985$	20.9443	−	15.2169i	0.667340	−	0.484851i
$986$		0			0
$987$	14.4721	−	44.5407i	0.460653	−	1.41774i
$988$		0			0
$989$	21.4164			0.681002
$990$		0			0
$991$	11.7082			0.371923			0.185962	−	0.982557i	$-0.440460\pi$
$991$	11.7082			0.371923			0.185962	+	0.982557i	$0.440460\pi$
$992$		0			0
$993$	−14.8992	+	45.8550i	−0.472811	+	1.45516i
$994$		0			0
$995$	58.5410	−	42.5325i	1.85588	−	1.34837i
$996$		0			0
$997$	−8.38197	−	25.7970i	−0.265460	−	0.817000i	−0.991587	−	0.129441i	$-0.958682\pi$
$997$	−8.38197	−	25.7970i	−0.265460	−	0.817000i	0.726128	−	0.687560i	$-0.241318\pi$
$998$		0			0
$999$	40.8885	+	29.7073i	1.29366	+	0.939896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.b.257.1	yes	4
4.3	odd	2		352.2.m.a.257.1	✓	4
8.3	odd	2		704.2.m.f.257.1		4
8.5	even	2		704.2.m.c.257.1		4
11.3	even	5	inner	352.2.m.b.289.1	yes	4
11.5	even	5		3872.2.a.y.1.2		2
11.6	odd	10		3872.2.a.z.1.2		2
44.3	odd	10		352.2.m.a.289.1	yes	4
44.27	odd	10		3872.2.a.n.1.1		2
44.39	even	10		3872.2.a.o.1.1		2
88.3	odd	10		704.2.m.f.641.1		4
88.5	even	10		7744.2.a.ca.1.1		2
88.27	odd	10		7744.2.a.cp.1.2		2
88.61	odd	10		7744.2.a.bz.1.1		2
88.69	even	10		704.2.m.c.641.1		4
88.83	even	10		7744.2.a.co.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.a.257.1	✓	4	4.3	odd	2
352.2.m.a.289.1	yes	4	44.3	odd	10
352.2.m.b.257.1	yes	4	1.1	even	1	trivial
352.2.m.b.289.1	yes	4	11.3	even	5	inner
704.2.m.c.257.1		4	8.5	even	2
704.2.m.c.641.1		4	88.69	even	10
704.2.m.f.257.1		4	8.3	odd	2
704.2.m.f.641.1		4	88.3	odd	10
3872.2.a.n.1.1		2	44.27	odd	10
3872.2.a.o.1.1		2	44.39	even	10
3872.2.a.y.1.2		2	11.5	even	5
3872.2.a.z.1.2		2	11.6	odd	10
7744.2.a.bz.1.1		2	88.61	odd	10
7744.2.a.ca.1.1		2	88.5	even	10
7744.2.a.co.1.2		2	88.83	even	10
7744.2.a.cp.1.2		2	88.27	odd	10

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 1.53884i) q^{3} +(-2.61803 + 1.90211i) q^{5} +(1.38197 + 4.25325i) q^{7} +(0.309017 + 0.224514i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 1.53884i) q^{3} +(-2.61803 + 1.90211i) q^{5} +(1.38197 + 4.25325i) q^{7} +(0.309017 + 0.224514i) q^{9} +(3.30902 - 0.224514i) q^{11} +(-1.00000 - 0.726543i) q^{13} +(1.61803 + 4.97980i) q^{15} +(-1.50000 + 1.08981i) q^{17} +(-1.66312 + 5.11855i) q^{19} +7.23607 q^{21} +5.23607 q^{23} +(1.69098 - 5.20431i) q^{25} +(4.42705 - 3.21644i) q^{27} +(-2.61803 - 8.05748i) q^{29} +(-0.381966 - 0.277515i) q^{31} +(1.30902 - 5.20431i) q^{33} +(-11.7082 - 8.50651i) q^{35} +(2.85410 + 8.78402i) q^{37} +(-1.61803 + 1.17557i) q^{39} +(-2.26393 + 6.96767i) q^{41} +4.09017 q^{43} -1.23607 q^{45} +(2.00000 - 6.15537i) q^{47} +(-10.5172 + 7.64121i) q^{49} +(0.927051 + 2.85317i) q^{51} +(-5.23607 - 3.80423i) q^{53} +(-8.23607 + 6.88191i) q^{55} +(7.04508 + 5.11855i) q^{57} +(-2.80902 - 8.64527i) q^{59} +(-2.00000 + 1.45309i) q^{61} +(-0.527864 + 1.62460i) q^{63} +4.00000 q^{65} -1.38197 q^{67} +(2.61803 - 8.05748i) q^{69} +(-3.00000 + 2.17963i) q^{71} +(-1.26393 - 3.88998i) q^{73} +(-7.16312 - 5.20431i) q^{75} +(5.52786 + 13.7638i) q^{77} +(4.85410 + 3.52671i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(1.92705 - 1.40008i) q^{83} +(1.85410 - 5.70634i) q^{85} -13.7082 q^{87} +6.38197 q^{89} +(1.70820 - 5.25731i) q^{91} +(-0.618034 + 0.449028i) q^{93} +(-5.38197 - 16.5640i) q^{95} +(-4.54508 - 3.30220i) q^{97} +(1.07295 + 0.673542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 6 q^{5} + 10 q^{7} - q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 6 * q^5 + 10 * q^7 - q^9	\( 4 q + 2 q^{3} - 6 q^{5} + 10 q^{7} - q^{9} + 11 q^{11} - 4 q^{13} + 2 q^{15} - 6 q^{17} + 9 q^{19} + 20 q^{21} + 12 q^{23} + 9 q^{25} + 11 q^{27} - 6 q^{29} - 6 q^{31} + 3 q^{33} - 20 q^{35} - 2 q^{37} - 2 q^{39} - 18 q^{41} - 6 q^{43} + 4 q^{45} + 8 q^{47} - 13 q^{49} - 3 q^{51} - 12 q^{53} - 24 q^{55} + 17 q^{57} - 9 q^{59} - 8 q^{61} - 20 q^{63} + 16 q^{65} - 10 q^{67} + 6 q^{69} - 12 q^{71} - 14 q^{73} - 13 q^{75} + 40 q^{77} + 6 q^{79} - 14 q^{81} + q^{83} - 6 q^{85} - 28 q^{87} + 30 q^{89} - 20 q^{91} + 2 q^{93} - 26 q^{95} - 7 q^{97} + 11 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^5 + 10 * q^7 - q^9 + 11 * q^11 - 4 * q^13 + 2 * q^15 - 6 * q^17 + 9 * q^19 + 20 * q^21 + 12 * q^23 + 9 * q^25 + 11 * q^27 - 6 * q^29 - 6 * q^31 + 3 * q^33 - 20 * q^35 - 2 * q^37 - 2 * q^39 - 18 * q^41 - 6 * q^43 + 4 * q^45 + 8 * q^47 - 13 * q^49 - 3 * q^51 - 12 * q^53 - 24 * q^55 + 17 * q^57 - 9 * q^59 - 8 * q^61 - 20 * q^63 + 16 * q^65 - 10 * q^67 + 6 * q^69 - 12 * q^71 - 14 * q^73 - 13 * q^75 + 40 * q^77 + 6 * q^79 - 14 * q^81 + q^83 - 6 * q^85 - 28 * q^87 + 30 * q^89 - 20 * q^91 + 2 * q^93 - 26 * q^95 - 7 * q^97 + 11 * q^99

Introduction

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