LMFDB - Embedded newform 400.2.u.g.241.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 12 x^{14} - 18 x^{13} + 100 x^{12} + 23 x^{11} + 567 x^{10} + 556 x^{9} + 3841 x^{8} + \cdots + 6400 $ x^16 - x^15 + 12x^14 - 18x^13 + 100x^12 + 23x^11 + 567x^10 + 556x^9 + 3841x^8 + 1155x^7 + 7575x^6 - 875x^5 + 7485x^4 + 900x^3 + 2000x^2 + 1600x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			241.3
Root			$-0.462625 - 1.42381i$ of defining polynomial
Character	$\chi$	$=$	400.241
Dual form			400.2.u.g.161.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.462625 + 1.42381i) q^{3} +(-2.22373 - 0.234601i) q^{5} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +O(q^{10})$	\(q+(0.462625 + 1.42381i) q^{3} +(-2.22373 - 0.234601i) q^{5} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +(1.04731 + 0.760912i) q^{11} +(-0.663861 + 0.482323i) q^{13} +(-0.694723 - 3.27470i) q^{15} +(-0.676707 + 2.08269i) q^{17} +(-1.98926 + 6.12233i) q^{19} +(2.28551 + 7.03407i) q^{21} +(1.79177 + 1.30180i) q^{23} +(4.88992 + 1.04338i) q^{25} +(4.55246 + 3.30755i) q^{27} +(-1.64801 - 5.07207i) q^{29} +(-0.218880 + 0.673643i) q^{31} +(-0.598887 + 1.84318i) q^{33} +(-10.9859 - 1.15900i) q^{35} +(5.78922 - 4.20612i) q^{37} +(-0.993856 - 0.722078i) q^{39} +(-8.19030 + 5.95060i) q^{41} -5.26985 q^{43} +(-1.46962 + 0.847721i) q^{45} +(-2.48612 - 7.65150i) q^{47} +17.4067 q^{49} -3.27842 q^{51} +(-4.08608 - 12.5757i) q^{53} +(-2.15041 - 1.93776i) q^{55} -9.63732 q^{57} +(7.76420 - 5.64102i) q^{59} +(5.29271 + 3.84538i) q^{61} +(3.03252 - 2.20325i) q^{63} +(1.58940 - 0.916812i) q^{65} +(2.26224 - 6.96246i) q^{67} +(-1.02460 + 3.15339i) q^{69} +(0.197864 + 0.608964i) q^{71} +(-9.68999 - 7.04019i) q^{73} +(0.776625 + 7.44503i) q^{75} +(5.17402 + 3.75914i) q^{77} +(0.692240 + 2.13050i) q^{79} +(-1.89987 + 5.84719i) q^{81} +(-3.53986 + 10.8946i) q^{83} +(1.99341 - 4.47258i) q^{85} +(6.45926 - 4.69293i) q^{87} +(2.56905 + 1.86652i) q^{89} +(-3.27968 + 2.38283i) q^{91} -1.06040 q^{93} +(5.85989 - 13.1477i) q^{95} +(-5.09821 - 15.6907i) q^{97} +0.982218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) $ 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9	$ 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9} + 10 q^{11} + q^{13} + 10 q^{15} - 4 q^{17} - 3 q^{21} - 11 q^{23} + 9 q^{25} - 13 q^{27} + 5 q^{29} + 9 q^{31} + 16 q^{33} - 24 q^{35} + 30 q^{37} - 14 q^{39} - 2 q^{41} + 42 q^{43} - 77 q^{45} + 16 q^{47} + 18 q^{49} - 100 q^{51} + 11 q^{53} + 24 q^{55} - 64 q^{57} + 53 q^{59} + 4 q^{61} + 38 q^{63} + 37 q^{65} + 14 q^{67} - 7 q^{69} + 6 q^{71} - 24 q^{73} + 15 q^{75} + 23 q^{77} + 22 q^{79} - 6 q^{81} - 33 q^{83} + 8 q^{85} - 37 q^{87} + 20 q^{89} + 27 q^{91} + 40 q^{93} + 24 q^{95} + 11 q^{97} - 122 q^{99}+O(q^{100}) $ 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9 + 10 * q^11 + q^13 + 10 * q^15 - 4 * q^17 - 3 * q^21 - 11 * q^23 + 9 * q^25 - 13 * q^27 + 5 * q^29 + 9 * q^31 + 16 * q^33 - 24 * q^35 + 30 * q^37 - 14 * q^39 - 2 * q^41 + 42 * q^43 - 77 * q^45 + 16 * q^47 + 18 * q^49 - 100 * q^51 + 11 * q^53 + 24 * q^55 - 64 * q^57 + 53 * q^59 + 4 * q^61 + 38 * q^63 + 37 * q^65 + 14 * q^67 - 7 * q^69 + 6 * q^71 - 24 * q^73 + 15 * q^75 + 23 * q^77 + 22 * q^79 - 6 * q^81 - 33 * q^83 + 8 * q^85 - 37 * q^87 + 20 * q^89 + 27 * q^91 + 40 * q^93 + 24 * q^95 + 11 * q^97 - 122 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.462625	+	1.42381i	0.267096	+	0.822038i	0.991203	+	0.132350i	$0.0422523\pi$
$3$	0.462625	+	1.42381i	0.267096	+	0.822038i	−0.724107	+	0.689688i	$0.757748\pi$
$4$		0			0
$5$	−2.22373	−	0.234601i	−0.994481	−	0.104917i
$5$	−2.22373	−	0.234601i	−0.994481	−	0.104917i
$6$		0			0
$7$	4.94031			1.86726			0.933631	−	0.358237i	$-0.116622\pi$
$7$	4.94031			1.86726			0.933631	+	0.358237i	$0.116622\pi$
$8$		0			0
$9$	0.613832	−	0.445975i	0.204611	−	0.148658i
$10$		0			0
$11$	1.04731	+	0.760912i	0.315775	+	0.229424i	0.734370	−	0.678749i	$-0.237478\pi$
$11$	1.04731	+	0.760912i	0.315775	+	0.229424i	−0.418596	+	0.908173i	$0.637478\pi$
$12$		0			0
$13$	−0.663861	+	0.482323i	−0.184122	+	0.133772i	−0.676028	−	0.736876i	$-0.736300\pi$
$13$	−0.663861	+	0.482323i	−0.184122	+	0.133772i	0.491906	+	0.870648i	$0.336300\pi$
$14$		0			0
$15$	−0.694723	−	3.27470i	−0.179377	−	0.845524i
$16$		0			0
$17$	−0.676707	+	2.08269i	−0.164126	+	0.505126i	−0.998971	−	0.0453583i	$-0.985557\pi$
$17$	−0.676707	+	2.08269i	−0.164126	+	0.505126i	0.834845	+	0.550485i	$0.185557\pi$
$18$		0			0
$19$	−1.98926	+	6.12233i	−0.456369	+	1.40456i	0.413152	+	0.910662i	$0.364428\pi$
$19$	−1.98926	+	6.12233i	−0.456369	+	1.40456i	−0.869521	+	0.493896i	$0.835572\pi$
$20$		0			0
$21$	2.28551	+	7.03407i	0.498739	+	1.53496i
$22$		0			0
$23$	1.79177	+	1.30180i	0.373610	+	0.271444i	0.758706	−	0.651433i	$-0.225832\pi$
$23$	1.79177	+	1.30180i	0.373610	+	0.271444i	−0.385096	+	0.922876i	$0.625832\pi$
$24$		0			0
$25$	4.88992	+	1.04338i	0.977985	+	0.208676i
$26$		0			0
$27$	4.55246	+	3.30755i	0.876121	+	0.636539i
$28$		0			0
$29$	−1.64801	−	5.07207i	−0.306029	−	0.941859i	−0.979291	−	0.202456i	$-0.935108\pi$
$29$	−1.64801	−	5.07207i	−0.306029	−	0.941859i	0.673263	−	0.739403i	$-0.264892\pi$
$30$		0			0
$31$	−0.218880	+	0.673643i	−0.0393120	+	0.120990i	−0.968787	−	0.247896i	$-0.920261\pi$
$31$	−0.218880	+	0.673643i	−0.0393120	+	0.120990i	0.929475	+	0.368886i	$0.120261\pi$
$32$		0			0
$33$	−0.598887	+	1.84318i	−0.104253	+	0.320857i
$34$		0			0
$35$	−10.9859	−	1.15900i	−1.85696	−	0.195907i
$36$		0			0
$37$	5.78922	−	4.20612i	0.951742	−	0.691481i	0.000523879	−	1.00000i	$-0.499833\pi$
$37$	5.78922	−	4.20612i	0.951742	−	0.691481i	0.951218	+	0.308519i	$0.0998332\pi$
$38$		0			0
$39$	−0.993856	−	0.722078i	−0.159144	−	0.115625i
$40$		0			0
$41$	−8.19030	+	5.95060i	−1.27911	+	0.929328i	−0.999526	−	0.0307933i	$-0.990197\pi$
$41$	−8.19030	+	5.95060i	−1.27911	+	0.929328i	−0.279584	+	0.960121i	$0.590197\pi$
$42$		0			0
$43$	−5.26985			−0.803645			−0.401823	−	0.915718i	$-0.631623\pi$
$43$	−5.26985			−0.803645			−0.401823	+	0.915718i	$0.631623\pi$
$44$		0			0
$45$	−1.46962	+	0.847721i	−0.219078	+	0.126371i
$46$		0			0
$47$	−2.48612	−	7.65150i	−0.362638	−	1.11609i	−0.951447	−	0.307813i	$-0.900403\pi$
$47$	−2.48612	−	7.65150i	−0.362638	−	1.11609i	0.588809	−	0.808273i	$-0.299597\pi$
$48$		0			0
$49$	17.4067			2.48667
$50$		0			0
$51$	−3.27842			−0.459071
$52$		0			0
$53$	−4.08608	−	12.5757i	−0.561266	−	1.72740i	−0.678792	−	0.734331i	$-0.737496\pi$
$53$	−4.08608	−	12.5757i	−0.561266	−	1.72740i	0.117526	−	0.993070i	$-0.462504\pi$
$54$		0			0
$55$	−2.15041	−	1.93776i	−0.289961	−	0.261288i
$56$		0			0
$57$	−9.63732			−1.27649
$58$		0			0
$59$	7.76420	−	5.64102i	1.01081	−	0.734398i	0.0464331	−	0.998921i	$-0.485215\pi$
$59$	7.76420	−	5.64102i	1.01081	−	0.734398i	0.964379	+	0.264523i	$0.0852146\pi$
$60$		0			0
$61$	5.29271	+	3.84538i	0.677662	+	0.492350i	0.872581	−	0.488469i	$-0.162445\pi$
$61$	5.29271	+	3.84538i	0.677662	+	0.492350i	−0.194919	+	0.980819i	$0.562445\pi$
$62$		0			0
$63$	3.03252	−	2.20325i	0.382061	−	0.277584i
$64$		0			0
$65$	1.58940	−	0.916812i	0.197141	−	0.113717i
$66$		0			0
$67$	2.26224	−	6.96246i	0.276377	−	0.850600i	−0.712475	−	0.701697i	$-0.752426\pi$
$67$	2.26224	−	6.96246i	0.276377	−	0.850600i	0.988852	−	0.148903i	$-0.0475741\pi$
$68$		0			0
$69$	−1.02460	+	3.15339i	−0.123347	+	0.379624i
$70$		0			0
$71$	0.197864	+	0.608964i	0.0234822	+	0.0722707i	0.962111	−	0.272658i	$-0.0879029\pi$
$71$	0.197864	+	0.608964i	0.0234822	+	0.0722707i	−0.938629	+	0.344929i	$0.887903\pi$
$72$		0			0
$73$	−9.68999	−	7.04019i	−1.13413	−	0.823992i	−0.147837	−	0.989012i	$-0.547231\pi$
$73$	−9.68999	−	7.04019i	−1.13413	−	0.823992i	−0.986290	+	0.165020i	$0.947231\pi$
$74$		0			0
$75$	0.776625	+	7.44503i	0.0896769	+	0.859678i
$76$		0			0
$77$	5.17402	+	3.75914i	0.589634	+	0.428394i
$78$		0			0
$79$	0.692240	+	2.13050i	0.0778831	+	0.239700i	0.982416	−	0.186704i	$-0.0597804\pi$
$79$	0.692240	+	2.13050i	0.0778831	+	0.239700i	−0.904533	+	0.426403i	$0.859780\pi$
$80$		0			0
$81$	−1.89987	+	5.84719i	−0.211096	+	0.649688i
$82$		0			0
$83$	−3.53986	+	10.8946i	−0.388550	+	1.19583i	0.545322	+	0.838226i	$0.316407\pi$
$83$	−3.53986	+	10.8946i	−0.388550	+	1.19583i	−0.933872	+	0.357607i	$0.883593\pi$
$84$		0			0
$85$	1.99341	−	4.47258i	0.216216	−	0.485119i
$86$		0			0
$87$	6.45926	−	4.69293i	0.692505	−	0.503135i
$88$		0			0
$89$	2.56905	+	1.86652i	0.272319	+	0.197851i	0.715560	−	0.698551i	$-0.246172\pi$
$89$	2.56905	+	1.86652i	0.272319	+	0.197851i	−0.443241	+	0.896402i	$0.646172\pi$
$90$		0			0
$91$	−3.27968	+	2.38283i	−0.343804	+	0.249788i
$92$		0			0
$93$	−1.06040			−0.109958
$94$		0			0
$95$	5.85989	−	13.1477i	0.601212	−	1.34893i
$96$		0			0
$97$	−5.09821	−	15.6907i	−0.517645	−	1.59315i	−0.778418	−	0.627747i	$-0.783977\pi$
$97$	−5.09821	−	15.6907i	−0.517645	−	1.59315i	0.260773	−	0.965400i	$-0.416023\pi$
$98$		0			0
$99$	0.982218			0.0987166
$100$		0			0
$101$	−10.4077			−1.03561			−0.517804	−	0.855499i	$-0.673250\pi$
$101$	−10.4077			−1.03561			−0.517804	+	0.855499i	$0.673250\pi$
$102$		0			0
$103$	0.528090	+	1.62529i	0.0520343	+	0.160145i	0.973697	−	0.227847i	$-0.0731687\pi$
$103$	0.528090	+	1.62529i	0.0520343	+	0.160145i	−0.921663	+	0.387992i	$0.873169\pi$
$104$		0			0
$105$	−3.43215	−	16.1780i	−0.334943	−	1.57882i
$106$		0			0
$107$	−2.83747			−0.274308			−0.137154	−	0.990550i	$-0.543796\pi$
$107$	−2.83747			−0.274308			−0.137154	+	0.990550i	$0.543796\pi$
$108$		0			0
$109$	−6.66885	+	4.84520i	−0.638760	+	0.464086i	−0.859424	−	0.511264i	$-0.829178\pi$
$109$	−6.66885	+	4.84520i	−0.638760	+	0.464086i	0.220664	+	0.975350i	$0.429178\pi$
$110$		0			0
$111$	8.66695	+	6.29691i	0.822631	+	0.597676i
$112$		0			0
$113$	−3.16114	+	2.29670i	−0.297375	+	0.216055i	−0.726460	−	0.687208i	$-0.758836\pi$
$113$	−3.16114	+	2.29670i	−0.297375	+	0.216055i	0.429085	+	0.903264i	$0.358836\pi$
$114$		0			0
$115$	−3.67901	−	3.31520i	−0.343069	−	0.309144i
$116$		0			0
$117$	−0.192395	+	0.592130i	−0.0177869	+	0.0547425i
$118$		0			0
$119$	−3.34314	+	10.2891i	−0.306465	+	0.943203i
$120$		0			0
$121$	−2.88132	−	8.86781i	−0.261939	−	0.806164i
$122$		0			0
$123$	−12.2616	−	8.90855i	−1.10559	−	0.803257i
$124$		0			0
$125$	−10.6291	−	3.46737i	−0.950694	−	0.310131i
$126$		0			0
$127$	−11.5930	−	8.42282i	−1.02871	−	0.747404i	−0.0606629	−	0.998158i	$-0.519321\pi$
$127$	−11.5930	−	8.42282i	−1.02871	−	0.747404i	−0.968051	+	0.250754i	$0.919321\pi$
$128$		0			0
$129$	−2.43796	−	7.50328i	−0.214651	−	0.660627i
$130$		0			0
$131$	3.15766	−	9.71827i	0.275886	−	0.849089i	−0.713098	−	0.701065i	$-0.752708\pi$
$131$	3.15766	−	9.71827i	0.275886	−	0.849089i	0.988984	−	0.148025i	$-0.0472915\pi$
$132$		0			0
$133$	−9.82758	+	30.2462i	−0.852159	+	2.62268i
$134$		0			0
$135$	−9.34747	−	8.42311i	−0.804502	−	0.724946i
$136$		0			0
$137$	5.93150	−	4.30949i	0.506762	−	0.368184i	−0.304832	−	0.952406i	$-0.598600\pi$
$137$	5.93150	−	4.30949i	0.506762	−	0.368184i	0.811594	+	0.584222i	$0.198600\pi$
$138$		0			0
$139$	5.41640	+	3.93524i	0.459413	+	0.333783i	0.793301	−	0.608830i	$-0.208361\pi$
$139$	5.41640	+	3.93524i	0.459413	+	0.333783i	−0.333888	+	0.942613i	$0.608361\pi$
$140$		0			0
$141$	9.74415	−	7.07954i	0.820606	−	0.596205i
$142$		0			0
$143$	−1.06227			−0.0888316
$144$		0			0
$145$	2.47482	+	11.6655i	0.205523	+	0.968769i
$146$		0			0
$147$	8.05275	+	24.7838i	0.664180	+	2.04413i
$148$		0			0
$149$	−1.30424			−0.106847			−0.0534236	−	0.998572i	$-0.517013\pi$
$149$	−1.30424			−0.106847			−0.0534236	+	0.998572i	$0.517013\pi$
$150$		0			0
$151$	−0.227988			−0.0185534			−0.00927670	−	0.999957i	$-0.502953\pi$
$151$	−0.227988			−0.0185534			−0.00927670	+	0.999957i	$0.502953\pi$
$152$		0			0
$153$	0.513443	+	1.58022i	0.0415094	+	0.127753i
$154$		0			0
$155$	0.644767	−	1.44665i	0.0517889	−	0.116198i
$156$		0			0
$157$	7.75041			0.618550			0.309275	−	0.950973i	$-0.399914\pi$
$157$	7.75041			0.618550			0.309275	+	0.950973i	$0.399914\pi$
$158$		0			0
$159$	16.0151	−	11.6356i	1.27008	−	0.922765i
$160$		0			0
$161$	8.85191	+	6.43129i	0.697628	+	0.506856i
$162$		0			0
$163$	−6.78410	+	4.92893i	−0.531371	+	0.386064i	−0.820870	−	0.571114i	$-0.806511\pi$
$163$	−6.78410	+	4.92893i	−0.531371	+	0.386064i	0.289499	+	0.957178i	$0.406511\pi$
$164$		0			0
$165$	1.76417	−	3.95824i	0.137341	−	0.308148i
$166$		0			0
$167$	2.21859	−	6.82811i	0.171680	−	0.528375i	−0.827787	−	0.561043i	$-0.810400\pi$
$167$	2.21859	−	6.82811i	0.171680	−	0.528375i	0.999466	+	0.0326676i	$0.0104003\pi$
$168$		0			0
$169$	−3.80915	+	11.7233i	−0.293011	+	0.901796i
$170$		0			0
$171$	1.50933	+	4.64524i	0.115421	+	0.355230i
$172$		0			0
$173$	12.1252	+	8.80946i	0.921861	+	0.669771i	0.943986	−	0.329984i	$-0.107043\pi$
$173$	12.1252	+	8.80946i	0.921861	+	0.669771i	−0.0221258	+	0.999755i	$0.507043\pi$
$174$		0			0
$175$	24.1577	+	5.15461i	1.82615	+	0.389652i
$176$		0			0
$177$	11.6237	+	8.44508i	0.873688	+	0.634771i
$178$		0			0
$179$	5.70579	+	17.5606i	0.426471	+	1.31254i	0.901579	+	0.432615i	$0.142409\pi$
$179$	5.70579	+	17.5606i	0.426471	+	1.31254i	−0.475108	+	0.879927i	$0.657591\pi$
$180$		0			0
$181$	6.21242	−	19.1199i	0.461766	−	1.42117i	−0.401239	−	0.915973i	$-0.631420\pi$
$181$	6.21242	−	19.1199i	0.461766	−	1.42117i	0.863005	−	0.505195i	$-0.168580\pi$
$182$		0			0
$183$	−3.02656	+	9.31479i	−0.223730	+	0.688569i
$184$		0			0
$185$	−13.8604	+	7.99509i	−1.01904	+	0.587811i
$186$		0			0
$187$	−2.29346	+	1.66630i	−0.167715	+	0.121852i
$188$		0			0
$189$	22.4906	+	16.3403i	1.63595	+	1.18859i
$190$		0			0
$191$	−17.8233	+	12.9494i	−1.28965	+	0.936982i	−0.999798	−	0.0200904i	$-0.993605\pi$
$191$	−17.8233	+	12.9494i	−1.28965	+	0.936982i	−0.289848	+	0.957073i	$0.593605\pi$
$192$		0			0
$193$	16.9231			1.21815			0.609077	−	0.793111i	$-0.291540\pi$
$193$	16.9231			1.21815			0.609077	+	0.793111i	$0.291540\pi$
$194$		0			0
$195$	2.04066	+	1.83887i	0.146135	+	0.131684i
$196$		0			0
$197$	−1.13633	−	3.49728i	−0.0809605	−	0.249171i	0.902381	−	0.430939i	$-0.141818\pi$
$197$	−1.13633	−	3.49728i	−0.0809605	−	0.249171i	−0.983341	+	0.181769i	$0.941818\pi$
$198$		0			0
$199$	−26.4847			−1.87745			−0.938724	−	0.344669i	$-0.887991\pi$
$199$	−26.4847			−1.87745			−0.938724	+	0.344669i	$0.887991\pi$
$200$		0			0
$201$	10.9598			0.773045
$202$		0			0
$203$	−8.14170	−	25.0576i	−0.571436	−	1.75870i
$204$		0			0
$205$	19.6090	−	11.3111i	1.36955	−	0.789999i
$206$		0			0
$207$	1.68042			0.116797
$208$		0			0
$209$	−6.74192	+	4.89829i	−0.466349	+	0.338822i
$210$		0			0
$211$	−2.51041	−	1.82392i	−0.172823	−	0.125564i	0.498011	−	0.867171i	$-0.334064\pi$
$211$	−2.51041	−	1.82392i	−0.172823	−	0.125564i	−0.670834	+	0.741607i	$0.734064\pi$
$212$		0			0
$213$	−0.775514	+	0.563444i	−0.0531373	+	0.0386065i
$214$		0			0
$215$	11.7187	+	1.23631i	0.799210	+	0.0843159i
$216$		0			0
$217$	−1.08133	+	3.32801i	−0.0734058	+	0.225920i
$218$		0			0
$219$	5.54108	−	17.0537i	0.374431	−	1.15238i
$220$		0			0
$221$	−0.555290	−	1.70901i	−0.0373529	−	0.114960i
$222$		0			0
$223$	6.61578	+	4.80665i	0.443026	+	0.321877i	0.786836	−	0.617162i	$-0.211718\pi$
$223$	6.61578	+	4.80665i	0.443026	+	0.321877i	−0.343810	+	0.939039i	$0.611718\pi$
$224$		0			0
$225$	3.46691	−	1.54032i	0.231127	−	0.102688i
$226$		0			0
$227$	−12.2020	−	8.86529i	−0.809877	−	0.588410i	0.103918	−	0.994586i	$-0.466862\pi$
$227$	−12.2020	−	8.86529i	−0.809877	−	0.588410i	−0.913795	+	0.406176i	$0.866862\pi$
$228$		0			0
$229$	−2.70693	−	8.33109i	−0.178879	−	0.550534i	0.820910	−	0.571057i	$-0.193467\pi$
$229$	−2.70693	−	8.33109i	−0.178879	−	0.550534i	−0.999789	+	0.0205237i	$0.993467\pi$
$230$		0			0
$231$	−2.95869	+	9.10590i	−0.194667	+	0.599124i
$232$		0			0
$233$	2.45112	−	7.54378i	0.160578	−	0.494209i	−0.838105	−	0.545509i	$-0.816336\pi$
$233$	2.45112	−	7.54378i	0.160578	−	0.494209i	0.998683	+	0.0512996i	$0.0163363\pi$
$234$		0			0
$235$	3.73341	+	17.5981i	0.243541	+	1.14797i
$236$		0			0
$237$	−2.71318	+	1.97124i	−0.176240	+	0.128046i
$238$		0			0
$239$	0.759253	+	0.551629i	0.0491120	+	0.0356819i	0.612070	−	0.790803i	$-0.290337\pi$
$239$	0.759253	+	0.551629i	0.0491120	+	0.0356819i	−0.562958	+	0.826485i	$0.690337\pi$
$240$		0			0
$241$	−8.86395	+	6.44003i	−0.570977	+	0.414839i	−0.835460	−	0.549551i	$-0.814799\pi$
$241$	−8.86395	+	6.44003i	−0.570977	+	0.414839i	0.264483	+	0.964390i	$0.414799\pi$
$242$		0			0
$243$	7.67721			0.492494
$244$		0			0
$245$	−38.7077	−	4.08362i	−2.47294	−	0.260893i
$246$		0			0
$247$	−1.63234	−	5.02384i	−0.103864	−	0.319659i
$248$		0			0
$249$	−17.1494			−1.08680
$250$		0			0
$251$	0.246980			0.0155893			0.00779463	−	0.999970i	$-0.497519\pi$
$251$	0.246980			0.0155893			0.00779463	+	0.999970i	$0.497519\pi$
$252$		0			0
$253$	0.885979	+	2.72676i	0.0557010	+	0.171430i
$254$		0			0
$255$	7.29031	+	0.769121i	0.456537	+	0.0481642i
$256$		0			0
$257$	7.97244			0.497307			0.248654	−	0.968592i	$-0.420012\pi$
$257$	7.97244			0.497307			0.248654	+	0.968592i	$0.420012\pi$
$258$		0			0
$259$	28.6005	−	20.7795i	1.77715	−	1.29118i
$260$		0			0
$261$	−3.27362	−	2.37842i	−0.202632	−	0.147221i
$262$		0			0
$263$	6.31136	−	4.58547i	0.389175	−	0.282752i	−0.375942	−	0.926643i	$-0.622681\pi$
$263$	6.31136	−	4.58547i	0.389175	−	0.282752i	0.765117	+	0.643891i	$0.222681\pi$
$264$		0			0
$265$	6.13606	+	28.9234i	0.376935	+	1.77675i
$266$		0			0
$267$	−1.46907	+	4.52135i	−0.0899059	+	0.276702i
$268$		0			0
$269$	0.440424	−	1.35549i	0.0268531	−	0.0826454i	−0.936732	−	0.350048i	$-0.886165\pi$
$269$	0.440424	−	1.35549i	0.0268531	−	0.0826454i	0.963585	+	0.267402i	$0.0861653\pi$
$270$		0			0
$271$	7.94569	+	24.4543i	0.482666	+	1.48549i	0.835333	+	0.549745i	$0.185275\pi$
$271$	7.94569	+	24.4543i	0.482666	+	1.48549i	−0.352667	+	0.935749i	$0.614725\pi$
$272$		0			0
$273$	−4.90996	−	3.56729i	−0.297164	−	0.215902i
$274$		0			0
$275$	4.32733	+	4.81354i	0.260948	+	0.290267i
$276$		0			0
$277$	−10.1633	−	7.38406i	−0.610652	−	0.443665i	0.238992	−	0.971022i	$-0.423183\pi$
$277$	−10.1633	−	7.38406i	−0.610652	−	0.443665i	−0.849644	+	0.527357i	$0.823183\pi$
$278$		0			0
$279$	0.166072	+	0.511118i	0.00994250	+	0.0305999i
$280$		0			0
$281$	−1.79351	+	5.51985i	−0.106992	+	0.329287i	−0.990193	−	0.139708i	$-0.955384\pi$
$281$	−1.79351	+	5.51985i	−0.106992	+	0.329287i	0.883201	+	0.468995i	$0.155384\pi$
$282$		0			0
$283$	1.05349	−	3.24232i	0.0626236	−	0.192736i	−0.914850	−	0.403794i	$-0.867691\pi$
$283$	1.05349	−	3.24232i	0.0626236	−	0.192736i	0.977473	+	0.211059i	$0.0676911\pi$
$284$		0			0
$285$	21.4308	+	2.26093i	1.26945	+	0.133926i
$286$		0			0
$287$	−40.4626	+	29.3978i	−2.38843	+	1.73530i
$288$		0			0
$289$	9.87363	+	7.17361i	0.580801	+	0.421977i
$290$		0			0
$291$	19.9820	−	14.5178i	1.17137	−	0.851048i
$292$		0			0
$293$	−0.336923			−0.0196832			−0.00984162	−	0.999952i	$-0.503133\pi$
$293$	−0.336923			−0.0196832			−0.00984162	+	0.999952i	$0.503133\pi$
$294$		0			0
$295$	−18.5888	+	10.7226i	−1.08228	+	0.624294i
$296$		0			0
$297$	2.25106	+	6.92804i	0.130620	+	0.402006i
$298$		0			0
$299$	−1.81737			−0.105101
$300$		0			0
$301$	−26.0347			−1.50062
$302$		0			0
$303$	−4.81487	−	14.8187i	−0.276607	−	0.851309i
$304$		0			0
$305$	−10.8674	−	9.79274i	−0.622266	−	0.560731i
$306$		0			0
$307$	23.5065			1.34159			0.670793	−	0.741645i	$-0.265954\pi$
$307$	23.5065			1.34159			0.670793	+	0.741645i	$0.265954\pi$
$308$		0			0
$309$	−2.06981	+	1.50380i	−0.117747	+	0.0855483i
$310$		0			0
$311$	5.87972	+	4.27187i	0.333408	+	0.242235i	0.741875	−	0.670538i	$-0.233937\pi$
$311$	5.87972	+	4.27187i	0.333408	+	0.242235i	−0.408467	+	0.912773i	$0.633937\pi$
$312$		0			0
$313$	9.58493	−	6.96386i	0.541772	−	0.393621i	−0.282971	−	0.959129i	$-0.591320\pi$
$313$	9.58493	−	6.96386i	0.541772	−	0.393621i	0.824743	+	0.565508i	$0.191320\pi$
$314$		0			0
$315$	−7.26038	+	4.18800i	−0.409076	+	0.235967i
$316$		0			0
$317$	−1.56828	+	4.82667i	−0.0880833	+	0.271093i	−0.985389	−	0.170316i	$-0.945521\pi$
$317$	−1.56828	+	4.82667i	−0.0880833	+	0.271093i	0.897306	+	0.441409i	$0.145521\pi$
$318$		0			0
$319$	2.13342	−	6.56600i	0.119449	−	0.367626i
$320$		0			0
$321$	−1.31268	−	4.04002i	−0.0732667	−	0.225492i
$322$		0			0
$323$	−11.4048	−	8.28604i	−0.634578	−	0.461048i
$324$		0			0
$325$	−3.74947	+	1.66587i	−0.207983	+	0.0924056i
$326$		0			0
$327$	−9.98383	−	7.25368i	−0.552107	−	0.401129i
$328$		0			0
$329$	−12.2822	−	37.8008i	−0.677140	−	2.08402i
$330$		0			0
$331$	−0.361461	+	1.11246i	−0.0198677	+	0.0611465i	−0.960499	−	0.278284i	$-0.910234\pi$
$331$	−0.361461	+	1.11246i	−0.0198677	+	0.0611465i	0.940631	+	0.339431i	$0.110234\pi$
$332$		0			0
$333$	1.67779	−	5.16369i	0.0919421	−	0.282969i
$334$		0			0
$335$	−6.66401	+	14.9519i	−0.364094	+	0.816909i
$336$		0			0
$337$	12.7113	−	9.23533i	0.692431	−	0.503081i	−0.185027	−	0.982733i	$-0.559237\pi$
$337$	12.7113	−	9.23533i	0.692431	−	0.503081i	0.877458	+	0.479653i	$0.159237\pi$
$338$		0			0
$339$	−4.73249	−	3.43836i	−0.257034	−	0.186746i
$340$		0			0
$341$	−0.741818	+	0.538962i	−0.0401717	+	0.0291864i
$342$		0			0
$343$	51.4121			2.77599
$344$		0			0
$345$	3.01822	−	6.77191i	0.162495	−	0.364587i
$346$		0			0
$347$	1.95872	+	6.02832i	0.105150	+	0.323617i	0.989766	−	0.142703i	$-0.0455795\pi$
$347$	1.95872	+	6.02832i	0.105150	+	0.323617i	−0.884616	+	0.466320i	$0.845579\pi$
$348$		0			0
$349$	−32.3947			−1.73405			−0.867023	−	0.498268i	$-0.833970\pi$
$349$	−32.3947			−1.73405			−0.867023	+	0.498268i	$0.833970\pi$
$350$		0			0
$351$	−4.61751			−0.246464
$352$		0			0
$353$	−3.16369	−	9.73685i	−0.168386	−	0.518240i	0.830883	−	0.556447i	$-0.187836\pi$
$353$	−3.16369	−	9.73685i	−0.168386	−	0.518240i	−0.999270	+	0.0382063i	$0.987836\pi$
$354$		0			0
$355$	−0.297133	−	1.40059i	−0.0157702	−	0.0743356i
$356$		0			0
$357$	−16.1964			−0.857205
$358$		0			0
$359$	−23.2637	+	16.9020i	−1.22781	+	0.892056i	−0.996724	−	0.0808776i	$-0.974228\pi$
$359$	−23.2637	+	16.9020i	−1.22781	+	0.892056i	−0.231085	+	0.972933i	$0.574228\pi$
$360$		0			0
$361$	−18.1544	−	13.1899i	−0.955494	−	0.694207i
$362$		0			0
$363$	11.2931	−	8.20493i	0.592735	−	0.430647i
$364$		0			0
$365$	19.8963	+	17.9287i	1.04142	+	0.938433i
$366$		0			0
$367$	4.30732	−	13.2566i	0.224840	−	0.691988i	−0.773467	−	0.633836i	$-0.781479\pi$
$367$	4.30732	−	13.2566i	0.224840	−	0.691988i	0.998308	−	0.0581516i	$-0.0185207\pi$
$368$		0			0
$369$	−2.37365	+	7.30534i	−0.123567	+	0.380301i
$370$		0			0
$371$	−20.1865	−	62.1277i	−1.04803	−	3.22551i
$372$		0			0
$373$	−10.7964	−	7.84401i	−0.559014	−	0.406147i	0.272084	−	0.962274i	$-0.412287\pi$
$373$	−10.7964	−	7.84401i	−0.559014	−	0.406147i	−0.831098	+	0.556126i	$0.812287\pi$
$374$		0			0
$375$	0.0196112	−	16.7379i	0.00101272	−	0.864342i
$376$		0			0
$377$	3.54043	+	2.57227i	0.182341	+	0.132479i
$378$		0			0
$379$	−7.44745	−	22.9209i	−0.382550	−	1.17737i	−0.938242	−	0.345979i	$-0.887547\pi$
$379$	−7.44745	−	22.9209i	−0.382550	−	1.17737i	0.555693	−	0.831388i	$-0.312453\pi$
$380$		0			0
$381$	6.62930	−	20.4029i	0.339629	−	1.04527i
$382$		0			0
$383$	−10.6304	+	32.7170i	−0.543188	+	1.67176i	0.182072	+	0.983285i	$0.441720\pi$
$383$	−10.6304	+	32.7170i	−0.543188	+	1.67176i	−0.725260	+	0.688475i	$0.758280\pi$
$384$		0			0
$385$	−10.6237	−	9.57314i	−0.541434	−	0.487892i
$386$		0			0
$387$	−3.23480	+	2.35022i	−0.164434	+	0.119469i
$388$		0			0
$389$	2.77533	+	2.01639i	0.140715	+	0.102235i	0.655916	−	0.754834i	$-0.272283\pi$
$389$	2.77533	+	2.01639i	0.140715	+	0.102235i	−0.515201	+	0.857069i	$0.672283\pi$
$390$		0			0
$391$	−3.92375	+	2.85077i	−0.198432	+	0.144170i
$392$		0			0
$393$	15.2978			0.771672
$394$		0			0
$395$	−1.03954	−	4.90004i	−0.0523047	−	0.246548i
$396$		0			0
$397$	9.29725	+	28.6140i	0.466615	+	1.43609i	0.856940	+	0.515417i	$0.172363\pi$
$397$	9.29725	+	28.6140i	0.466615	+	1.43609i	−0.390324	+	0.920678i	$0.627637\pi$
$398$		0			0
$399$	−47.6114			−2.38355
$400$		0			0
$401$	36.3896			1.81721			0.908604	−	0.417658i	$-0.137149\pi$
$401$	36.3896			1.81721			0.908604	+	0.417658i	$0.137149\pi$
$402$		0			0
$403$	−0.179608	−	0.552776i	−0.00894690	−	0.0275357i
$404$		0			0
$405$	5.59655	−	12.5569i	0.278095	−	0.623955i
$406$		0			0
$407$	9.26357			0.459178
$408$		0			0
$409$	−2.97690	+	2.16284i	−0.147198	+	0.106946i	−0.658947	−	0.752189i	$-0.728998\pi$
$409$	−2.97690	+	2.16284i	−0.147198	+	0.106946i	0.511749	+	0.859135i	$0.328998\pi$
$410$		0			0
$411$	8.87996	+	6.45167i	0.438016	+	0.318237i
$412$		0			0
$413$	38.3575	−	27.8684i	1.88745	−	1.37131i
$414$		0			0
$415$	10.4276	−	23.3961i	0.511869	−	1.14847i
$416$		0			0
$417$	−3.09729	+	9.53247i	−0.151675	+	0.466807i
$418$		0			0
$419$	2.09891	−	6.45979i	0.102539	−	0.315582i	−0.886606	−	0.462525i	$-0.846944\pi$
$419$	2.09891	−	6.45979i	0.102539	−	0.315582i	0.989145	+	0.146943i	$0.0469435\pi$
$420$		0			0
$421$	6.70805	+	20.6452i	0.326930	+	1.00619i	0.970562	+	0.240852i	$0.0774269\pi$
$421$	6.70805	+	20.6452i	0.326930	+	1.00619i	−0.643632	+	0.765335i	$0.722573\pi$
$422$		0			0
$423$	−4.93844	−	3.58798i	−0.240115	−	0.174454i
$424$		0			0
$425$	−5.48208	+	9.47813i	−0.265920	+	0.459757i
$426$		0			0
$427$	26.1476	+	18.9974i	1.26537	+	0.919346i
$428$		0			0
$429$	−0.491433	−	1.51247i	−0.0237266	−	0.0730229i
$430$		0			0
$431$	5.17386	−	15.9235i	0.249216	−	0.767009i	−0.745698	−	0.666284i	$-0.767884\pi$
$431$	5.17386	−	15.9235i	0.249216	−	0.767009i	0.994914	−	0.100725i	$-0.0321161\pi$
$432$		0			0
$433$	−7.55488	+	23.2515i	−0.363065	+	1.11740i	0.588120	+	0.808774i	$0.299868\pi$
$433$	−7.55488	+	23.2515i	−0.363065	+	1.11740i	−0.951184	+	0.308624i	$0.900132\pi$
$434$		0			0
$435$	−15.4646	+	8.92044i	−0.741471	+	0.427702i
$436$		0			0
$437$	−11.5343	+	8.38019i	−0.551762	+	0.400879i
$438$		0			0
$439$	−18.4800	−	13.4265i	−0.882002	−	0.640812i	0.0517783	−	0.998659i	$-0.483511\pi$
$439$	−18.4800	−	13.4265i	−0.882002	−	0.640812i	−0.933780	+	0.357847i	$0.883511\pi$
$440$		0			0
$441$	10.6848	−	7.76293i	0.508798	−	0.369663i
$442$		0			0
$443$	8.95402			0.425418			0.212709	−	0.977116i	$-0.431771\pi$
$443$	8.95402			0.425418			0.212709	+	0.977116i	$0.431771\pi$
$444$		0			0
$445$	−5.27498	−	4.75334i	−0.250058	−	0.225330i
$446$		0			0
$447$	−0.603372	−	1.85699i	−0.0285385	−	0.0878325i
$448$		0			0
$449$	5.23228			0.246927			0.123463	−	0.992349i	$-0.460600\pi$
$449$	5.23228			0.246927			0.123463	+	0.992349i	$0.460600\pi$
$450$		0			0
$451$	−13.1056			−0.617120
$452$		0			0
$453$	−0.105473	−	0.324612i	−0.00495555	−	0.0152516i
$454$		0			0
$455$	7.85212	−	4.52934i	0.368113	−	0.212339i
$456$		0			0
$457$	−27.3114			−1.27758			−0.638788	−	0.769383i	$-0.720564\pi$
$457$	−27.3114			−1.27758			−0.638788	+	0.769383i	$0.720564\pi$
$458$		0			0
$459$	−9.96929	+	7.24311i	−0.465327	+	0.338080i
$460$		0			0
$461$	5.00159	+	3.63387i	0.232947	+	0.169246i	0.698135	−	0.715966i	$-0.254013\pi$
$461$	5.00159	+	3.63387i	0.232947	+	0.169246i	−0.465188	+	0.885212i	$0.654013\pi$
$462$		0			0
$463$	−5.22490	+	3.79611i	−0.242822	+	0.176420i	−0.702539	−	0.711645i	$-0.747951\pi$
$463$	−5.22490	+	3.79611i	−0.242822	+	0.176420i	0.459718	+	0.888065i	$0.347951\pi$
$464$		0			0
$465$	2.35804	+	0.248771i	0.109352	+	0.0115365i
$466$		0			0
$467$	0.120762	−	0.371668i	0.00558821	−	0.0171988i	−0.948224	−	0.317604i	$-0.897122\pi$
$467$	0.120762	−	0.371668i	0.00558821	−	0.0171988i	0.953812	+	0.300405i	$0.0971218\pi$
$468$		0			0
$469$	11.1762	−	34.3967i	0.516068	−	1.58829i
$470$		0			0
$471$	3.58553	+	11.0351i	0.165212	+	0.508472i
$472$		0			0
$473$	−5.51915	−	4.00990i	−0.253771	−	0.184375i
$474$		0			0
$475$	−16.1153	+	27.8622i	−0.739419	+	1.27840i
$476$		0			0
$477$	−8.11660	−	5.89705i	−0.371633	−	0.270008i
$478$		0			0
$479$	9.00958	+	27.7286i	0.411658	+	1.26695i	0.915206	+	0.402986i	$0.132028\pi$
$479$	9.00958	+	27.7286i	0.411658	+	1.26695i	−0.503548	+	0.863967i	$0.667972\pi$
$480$		0			0
$481$	−1.81453	+	5.58455i	−0.0827355	+	0.254634i
$482$		0			0
$483$	−5.06183	+	15.5787i	−0.230321	+	0.708857i
$484$		0			0
$485$	7.65597	+	36.0878i	0.347640	+	1.63866i
$486$		0			0
$487$	16.6467	−	12.0945i	0.754333	−	0.548055i	−0.142834	−	0.989747i	$-0.545621\pi$
$487$	16.6467	−	12.0945i	0.754333	−	0.548055i	0.897167	+	0.441692i	$0.145621\pi$
$488$		0			0
$489$	−10.1564	−	7.37903i	−0.459287	−	0.333691i
$490$		0			0
$491$	25.9067	−	18.8223i	1.16915	−	0.849438i	0.178245	−	0.983986i	$-0.442958\pi$
$491$	25.9067	−	18.8223i	1.16915	−	0.849438i	0.990907	+	0.134548i	$0.0429582\pi$
$492$		0			0
$493$	11.6788			0.525985
$494$		0			0
$495$	−2.18418	−	0.230429i	−0.0981718	−	0.0103570i
$496$		0			0
$497$	0.977512	+	3.00847i	0.0438474	+	0.134948i
$498$		0			0
$499$	−9.59439			−0.429504			−0.214752	−	0.976669i	$-0.568894\pi$
$499$	−9.59439			−0.429504			−0.214752	+	0.976669i	$0.568894\pi$
$500$		0			0
$501$	10.7483			0.480200
$502$		0			0
$503$	3.29380	+	10.1373i	0.146863	+	0.451998i	0.997246	−	0.0741664i	$-0.0236296\pi$
$503$	3.29380	+	10.1373i	0.146863	+	0.451998i	−0.850383	+	0.526165i	$0.823630\pi$
$504$		0			0
$505$	23.1440	+	2.44167i	1.02989	+	0.108653i
$506$		0			0
$507$	−18.4540			−0.819573
$508$		0			0
$509$	14.0177	−	10.1844i	0.621323	−	0.451417i	−0.232061	−	0.972701i	$-0.574547\pi$
$509$	14.0177	−	10.1844i	0.621323	−	0.451417i	0.853383	+	0.521284i	$0.174547\pi$
$510$		0			0
$511$	−47.8715	−	34.7807i	−2.11771	−	1.53861i
$512$		0			0
$513$	−29.3060	+	21.2920i	−1.29389	+	0.940066i
$514$		0			0
$515$	−0.793032	−	3.73810i	−0.0349452	−	0.164720i
$516$		0			0
$517$	3.21839	−	9.90518i	0.141545	−	0.435629i
$518$		0			0
$519$	−6.93361	+	21.3395i	−0.304352	+	0.936698i
$520$		0			0
$521$	−10.1237	−	31.1575i	−0.443527	−	1.36504i	−0.884091	−	0.467315i	$-0.845221\pi$
$521$	−10.1237	−	31.1575i	−0.443527	−	1.36504i	0.440564	−	0.897721i	$-0.354779\pi$
$522$		0			0
$523$	−2.03218	−	1.47647i	−0.0888611	−	0.0645614i	0.542468	−	0.840077i	$-0.317490\pi$
$523$	−2.03218	−	1.47647i	−0.0888611	−	0.0645614i	−0.631329	+	0.775515i	$0.717490\pi$
$524$		0			0
$525$	3.83677	+	36.7807i	0.167450	+	1.60524i
$526$		0			0
$527$	−1.25487	−	0.911718i	−0.0546631	−	0.0397150i
$528$		0			0
$529$	−5.59162	−	17.2092i	−0.243114	−	0.748228i
$530$		0			0
$531$	2.25016	−	6.92527i	0.0976485	−	0.300531i
$532$		0			0
$533$	2.56711	−	7.90074i	0.111194	−	0.342219i
$534$		0			0
$535$	6.30975	+	0.665673i	0.272794	+	0.0287796i
$536$		0			0
$537$	−22.3634	+	16.2479i	−0.965051	+	0.701150i
$538$		0			0
$539$	18.2301	+	13.2449i	0.785226	+	0.570500i
$540$		0			0
$541$	−3.65744	+	2.65729i	−0.157246	+	0.114246i	−0.663626	−	0.748065i	$-0.730983\pi$
$541$	−3.65744	+	2.65729i	−0.157246	+	0.114246i	0.506380	+	0.862310i	$0.330983\pi$
$542$		0			0
$543$	30.0971			1.29159
$544$		0			0
$545$	15.9664	−	9.20989i	0.683925	−	0.394508i
$546$		0			0
$547$	10.6011	+	32.6267i	0.453269	+	1.39502i	0.873156	+	0.487441i	$0.162070\pi$
$547$	10.6011	+	32.6267i	0.453269	+	1.39502i	−0.419887	+	0.907576i	$0.637930\pi$
$548$		0			0
$549$	4.96377			0.211849
$550$		0			0
$551$	34.3312			1.46256
$552$		0			0
$553$	3.41988	+	10.5253i	0.145428	+	0.447582i
$554$		0			0
$555$	−17.7957	−	16.0359i	−0.755384	−	0.680686i
$556$		0			0
$557$	−2.34120			−0.0991997			−0.0495998	−	0.998769i	$-0.515795\pi$
$557$	−2.34120			−0.0991997			−0.0495998	+	0.998769i	$0.515795\pi$
$558$		0			0
$559$	3.49845	−	2.54177i	0.147969	−	0.107505i
$560$		0			0
$561$	−3.43351	−	2.49459i	−0.144963	−	0.105322i
$562$		0			0
$563$	1.40822	−	1.02313i	0.0593493	−	0.0431198i	−0.557715	−	0.830032i	$-0.688322\pi$
$563$	1.40822	−	1.02313i	0.0593493	−	0.0431198i	0.617064	+	0.786913i	$0.288322\pi$
$564$		0			0
$565$	7.56832	−	4.36563i	0.318401	−	0.183663i
$566$		0			0
$567$	−9.38594	+	28.8869i	−0.394172	+	1.21314i
$568$		0			0
$569$	−12.8853	+	39.6568i	−0.540178	+	1.66250i	0.192008	+	0.981393i	$0.438500\pi$
$569$	−12.8853	+	39.6568i	−0.540178	+	1.66250i	−0.732186	+	0.681105i	$0.761500\pi$
$570$		0			0
$571$	0.601693	+	1.85182i	0.0251801	+	0.0774963i	0.962857	−	0.270012i	$-0.0870278\pi$
$571$	0.601693	+	1.85182i	0.0251801	+	0.0774963i	−0.937677	+	0.347509i	$0.887028\pi$
$572$		0			0
$573$	−26.6829	−	19.3863i	−1.11470	−	0.809873i
$574$		0			0
$575$	7.40336	+	8.23519i	0.308742	+	0.343431i
$576$		0			0
$577$	−11.2592	−	8.18026i	−0.468725	−	0.340549i	0.328219	−	0.944602i	$-0.393552\pi$
$577$	−11.2592	−	8.18026i	−0.468725	−	0.340549i	−0.796944	+	0.604053i	$0.793552\pi$
$578$		0			0
$579$	7.82905	+	24.0954i	0.325364	+	1.00137i
$580$		0			0
$581$	−17.4880	+	53.8225i	−0.725524	+	2.23293i
$582$		0			0
$583$	5.28960	−	16.2797i	0.219073	−	0.674237i
$584$		0			0
$585$	0.566748	−	1.27160i	0.0234322	−	0.0525742i
$586$		0			0
$587$	13.9830	−	10.1593i	0.577142	−	0.419318i	−0.260551	−	0.965460i	$-0.583904\pi$
$587$	13.9830	−	10.1593i	0.577142	−	0.419318i	0.837693	+	0.546142i	$0.183904\pi$
$588$		0			0
$589$	−3.68885	−	2.68011i	−0.151996	−	0.110432i
$590$		0			0
$591$	4.45377	−	3.23585i	0.183204	−	0.133105i
$592$		0			0
$593$	26.1715			1.07474			0.537368	−	0.843348i	$-0.319419\pi$
$593$	26.1715			1.07474			0.537368	+	0.843348i	$0.319419\pi$
$594$		0			0
$595$	9.84808	−	22.0959i	0.403732	−	0.905844i
$596$		0			0
$597$	−12.2525	−	37.7092i	−0.501460	−	1.54333i
$598$		0			0
$599$	34.0712			1.39211			0.696055	−	0.717988i	$-0.254937\pi$
$599$	34.0712			1.39211			0.696055	+	0.717988i	$0.254937\pi$
$600$		0			0
$601$	−37.2599			−1.51986			−0.759931	−	0.650004i	$-0.774767\pi$
$601$	−37.2599			−1.51986			−0.759931	+	0.650004i	$0.774767\pi$
$602$		0			0
$603$	−1.71645	−	5.28268i	−0.0698991	−	0.215127i
$604$		0			0
$605$	4.32688	+	20.3955i	0.175913	+	0.829197i
$606$		0			0
$607$	0.110015			0.00446537			0.00223268	−	0.999998i	$-0.499289\pi$
$607$	0.110015			0.00446537			0.00223268	+	0.999998i	$0.499289\pi$
$608$		0			0
$609$	31.9107	−	23.1845i	1.29309	−	0.939484i
$610$		0			0
$611$	5.34093	+	3.88042i	0.216071	+	0.156985i
$612$		0			0
$613$	−2.40870	+	1.75003i	−0.0972866	+	0.0706829i	−0.635365	−	0.772212i	$-0.719150\pi$
$613$	−2.40870	+	1.75003i	−0.0972866	+	0.0706829i	0.538079	+	0.842895i	$0.319150\pi$
$614$		0			0
$615$	25.1764	+	22.6868i	1.01521	+	0.914819i
$616$		0			0
$617$	−11.2881	+	34.7412i	−0.454442	+	1.39863i	0.417347	+	0.908747i	$0.362960\pi$
$617$	−11.2881	+	34.7412i	−0.454442	+	1.39863i	−0.871789	+	0.489881i	$0.837040\pi$
$618$		0			0
$619$	−10.3624	+	31.8923i	−0.416501	+	1.28186i	0.494401	+	0.869234i	$0.335388\pi$
$619$	−10.3624	+	31.8923i	−0.416501	+	1.28186i	−0.910901	+	0.412624i	$0.864612\pi$
$620$		0			0
$621$	3.85120	+	11.8528i	0.154543	+	0.475635i
$622$		0			0
$623$	12.6919	+	9.22121i	0.508490	+	0.369440i
$624$		0			0
$625$	22.8227	+	10.2041i	0.912909	+	0.408163i
$626$		0			0
$627$	−10.0932	−	7.33316i	−0.403085	−	0.292858i
$628$		0			0
$629$	4.84243	+	14.9035i	0.193080	+	0.594240i
$630$		0			0
$631$	−4.01985	+	12.3718i	−0.160028	+	0.492515i	−0.998636	−	0.0522207i	$-0.983370\pi$
$631$	−4.01985	+	12.3718i	−0.160028	+	0.492515i	0.838608	+	0.544736i	$0.183370\pi$
$632$		0			0
$633$	1.43554	−	4.41813i	0.0570576	−	0.175605i
$634$		0			0
$635$	23.8037	+	21.4498i	0.944621	+	0.851209i
$636$		0			0
$637$	−11.5556	+	8.39563i	−0.457849	+	0.332647i
$638$		0			0
$639$	0.393038	+	0.285559i	0.0155484	+	0.0112965i
$640$		0			0
$641$	16.5293	−	12.0092i	0.652867	−	0.474336i	−0.211379	−	0.977404i	$-0.567796\pi$
$641$	16.5293	−	12.0092i	0.652867	−	0.474336i	0.864247	+	0.503068i	$0.167796\pi$
$642$		0			0
$643$	9.64777			0.380471			0.190235	−	0.981738i	$-0.439075\pi$
$643$	9.64777			0.380471			0.190235	+	0.981738i	$0.439075\pi$
$644$		0			0
$645$	3.66109	+	17.2572i	0.144155	+	0.679501i
$646$		0			0
$647$	−12.8829	−	39.6496i	−0.506481	−	1.55879i	−0.798266	−	0.602304i	$-0.794249\pi$
$647$	−12.8829	−	39.6496i	−0.506481	−	1.55879i	0.291786	−	0.956484i	$-0.405751\pi$
$648$		0			0
$649$	12.4238			0.487677
$650$		0			0
$651$	−5.23871			−0.205321
$652$		0			0
$653$	−11.0289	−	33.9436i	−0.431596	−	1.32831i	−0.896535	−	0.442972i	$-0.853924\pi$
$653$	−11.0289	−	33.9436i	−0.431596	−	1.32831i	0.464940	−	0.885342i	$-0.346076\pi$
$654$		0			0
$655$	−9.30169	+	20.8700i	−0.363447	+	0.815458i
$656$		0			0
$657$	−9.08777			−0.354548
$658$		0			0
$659$	20.7470	−	15.0735i	0.808187	−	0.587182i	−0.105118	−	0.994460i	$-0.533522\pi$
$659$	20.7470	−	15.0735i	0.808187	−	0.587182i	0.913304	+	0.407278i	$0.133522\pi$
$660$		0			0
$661$	2.10868	+	1.53205i	0.0820182	+	0.0595897i	0.628039	−	0.778182i	$-0.283858\pi$
$661$	2.10868	+	1.53205i	0.0820182	+	0.0595897i	−0.546021	+	0.837772i	$0.683858\pi$
$662$		0			0
$663$	2.17641	−	1.58126i	0.0845249	−	0.0614110i
$664$		0			0
$665$	28.9497	−	64.9537i	1.12262	−	2.51880i
$666$		0			0
$667$	3.64994	−	11.2334i	0.141326	−	0.434958i
$668$		0			0
$669$	−3.78314	+	11.6433i	−0.146265	+	0.450156i
$670$		0			0
$671$	2.61709	+	8.05457i	0.101032	+	0.310943i
$672$		0			0
$673$	10.8025	+	7.84844i	0.416404	+	0.302535i	0.776189	−	0.630500i	$-0.217150\pi$
$673$	10.8025	+	7.84844i	0.416404	+	0.302535i	−0.359785	+	0.933035i	$0.617150\pi$
$674$		0			0
$675$	18.8101	+	20.9236i	0.724003	+	0.805351i
$676$		0			0
$677$	12.3250	+	8.95467i	0.473690	+	0.344156i	0.798878	−	0.601494i	$-0.205427\pi$
$677$	12.3250	+	8.95467i	0.473690	+	0.344156i	−0.325188	+	0.945650i	$0.605427\pi$
$678$		0			0
$679$	−25.1867	−	77.5168i	−0.966578	−	2.97482i
$680$		0			0
$681$	6.97755	−	21.4747i	0.267380	−	0.822912i
$682$		0			0
$683$	−6.86573	+	21.1306i	−0.262710	+	0.808538i	0.729502	+	0.683979i	$0.239752\pi$
$683$	−6.86573	+	21.1306i	−0.262710	+	0.808538i	−0.992212	+	0.124560i	$0.960248\pi$
$684$		0			0
$685$	−14.2010	+	8.19159i	−0.542594	+	0.312984i
$686$		0			0
$687$	10.6096	−	7.70833i	0.404782	−	0.294091i
$688$		0			0
$689$	8.77812	+	6.37768i	0.334420	+	0.242970i
$690$		0			0
$691$	−9.50955	+	6.90909i	−0.361760	+	0.262834i	−0.753786	−	0.657120i	$-0.771774\pi$
$691$	−9.50955	+	6.90909i	−0.361760	+	0.262834i	0.392026	+	0.919954i	$0.371774\pi$
$692$		0			0
$693$	4.85246			0.184330
$694$		0			0
$695$	−11.1214	−	10.0216i	−0.421858	−	0.380141i
$696$		0			0
$697$	−6.85082	−	21.0847i	−0.259493	−	0.798639i
$698$		0			0
$699$	11.8749			0.449149
$700$		0			0
$701$	11.7537			0.443932			0.221966	−	0.975054i	$-0.428753\pi$
$701$	11.7537			0.443932			0.221966	+	0.975054i	$0.428753\pi$
$702$		0			0
$703$	14.2349	+	43.8106i	0.536880	+	1.65235i
$704$		0			0
$705$	−23.3292	+	13.4570i	−0.878629	+	0.506819i
$706$		0			0
$707$	−51.4174			−1.93375
$708$		0			0
$709$	7.29158	−	5.29764i	0.273841	−	0.198957i	−0.442386	−	0.896825i	$-0.645868\pi$
$709$	7.29158	−	5.29764i	0.273841	−	0.198957i	0.716227	+	0.697868i	$0.245868\pi$
$710$		0			0
$711$	1.37507	+	0.999045i	0.0515690	+	0.0374671i
$712$		0			0
$713$	−1.26913	+	0.922077i	−0.0475293	+	0.0345321i
$714$		0			0
$715$	2.36220	+	0.249210i	0.0883413	+	0.00931993i
$716$		0			0
$717$	−0.434168	+	1.33623i	−0.0162143	+	0.0499025i
$718$		0			0
$719$	−13.6946	+	42.1476i	−0.510721	+	1.57184i	0.280213	+	0.959938i	$0.409595\pi$
$719$	−13.6946	+	42.1476i	−0.510721	+	1.57184i	−0.790934	+	0.611901i	$0.790405\pi$
$720$		0			0
$721$	2.60893	+	8.02946i	0.0971616	+	0.299033i
$722$		0			0
$723$	−13.2701	−	9.64128i	−0.493520	−	0.358563i
$724$		0			0
$725$	−2.76658	−	26.5215i	−0.102748	−	0.984985i
$726$		0			0
$727$	4.07391	+	2.95987i	0.151093	+	0.109775i	0.660763	−	0.750594i	$-0.270233\pi$
$727$	4.07391	+	2.95987i	0.151093	+	0.109775i	−0.509671	+	0.860370i	$0.670233\pi$
$728$		0			0
$729$	9.25127	+	28.4725i	0.342640	+	1.05454i
$730$		0			0
$731$	3.56615	−	10.9755i	0.131899	−	0.405942i
$732$		0			0
$733$	−2.00643	+	6.17517i	−0.0741094	+	0.228085i	−0.981249	−	0.192745i	$-0.938261\pi$
$733$	−2.00643	+	6.17517i	−0.0741094	+	0.228085i	0.907140	+	0.420830i	$0.138261\pi$
$734$		0			0
$735$	−12.0928	−	57.0016i	−0.446050	−	2.10254i
$736$		0			0
$737$	7.66708	−	5.57046i	0.282421	−	0.205191i
$738$		0			0
$739$	5.42854	+	3.94406i	0.199692	+	0.145085i	0.683138	−	0.730290i	$-0.260615\pi$
$739$	5.42854	+	3.94406i	0.199692	+	0.145085i	−0.483446	+	0.875374i	$0.660615\pi$
$740$		0			0
$741$	6.39784	−	4.64830i	0.235031	−	0.170760i
$742$		0			0
$743$	−27.9505			−1.02541			−0.512703	−	0.858566i	$-0.671356\pi$
$743$	−27.9505			−1.02541			−0.512703	+	0.858566i	$0.671356\pi$
$744$		0			0
$745$	2.90026	+	0.305975i	0.106257	+	0.0112101i
$746$		0			0
$747$	2.68582	+	8.26612i	0.0982692	+	0.302441i
$748$		0			0
$749$	−14.0180			−0.512205
$750$		0			0
$751$	16.0513			0.585719			0.292860	−	0.956155i	$-0.405393\pi$
$751$	16.0513			0.585719			0.292860	+	0.956155i	$0.405393\pi$
$752$		0			0
$753$	0.114259	+	0.351654i	0.00416384	+	0.0128150i
$754$		0			0
$755$	0.506983	+	0.0534863i	0.0184510	+	0.00194657i
$756$		0			0
$757$	37.5640			1.36529			0.682643	−	0.730752i	$-0.260831\pi$
$757$	37.5640			1.36529			0.682643	+	0.730752i	$0.260831\pi$
$758$		0			0
$759$	−3.47252	+	2.52294i	−0.126045	+	0.0915767i
$760$		0			0
$761$	7.57148	+	5.50100i	0.274466	+	0.199411i	0.716500	−	0.697587i	$-0.245743\pi$
$761$	7.57148	+	5.50100i	0.274466	+	0.199411i	−0.442034	+	0.896998i	$0.645743\pi$
$762$		0			0
$763$	−32.9462	+	23.9368i	−1.19273	+	0.866570i
$764$		0			0
$765$	−0.771037	−	3.63442i	−0.0278769	−	0.131403i
$766$		0			0
$767$	−2.43355	+	7.48970i	−0.0878705	+	0.270438i
$768$		0			0
$769$	−8.80986	+	27.1140i	−0.317692	+	0.977754i	0.656941	+	0.753942i	$0.271850\pi$
$769$	−8.80986	+	27.1140i	−0.317692	+	0.977754i	−0.974632	+	0.223812i	$0.928150\pi$
$770$		0			0
$771$	3.68825	+	11.3513i	0.132829	+	0.408806i
$772$		0			0
$773$	−8.69439	−	6.31684i	−0.312715	−	0.227201i	0.420345	−	0.907364i	$-0.361909\pi$
$773$	−8.69439	−	6.31684i	−0.312715	−	0.227201i	−0.733061	+	0.680163i	$0.761909\pi$
$774$		0			0
$775$	−1.77317	+	3.06569i	−0.0636942	+	0.110123i
$776$		0			0
$777$	42.8174	+	31.1087i	1.53607	+	1.11602i
$778$		0			0
$779$	−20.1388	−	61.9810i	−0.721549	−	2.22070i
$780$		0			0
$781$	−0.256144	+	0.788329i	−0.00916554	+	0.0282086i
$782$		0			0
$783$	9.27362	−	28.5413i	0.331412	−	1.01998i
$784$		0			0
$785$	−17.2348	−	1.81826i	−0.615136	−	0.0648963i
$786$		0			0
$787$	11.9226	−	8.66229i	0.424995	−	0.308777i	−0.354649	−	0.934999i	$-0.615400\pi$
$787$	11.9226	−	8.66229i	0.424995	−	0.308777i	0.779645	+	0.626222i	$0.215400\pi$
$788$		0			0
$789$	9.44863	+	6.86483i	0.336380	+	0.244395i
$790$		0			0
$791$	−15.6170	+	11.3464i	−0.555277	+	0.403432i
$792$		0			0
$793$	−5.36833			−0.190635
$794$		0			0
$795$	−38.3429	+	22.1173i	−1.35988	+	0.784420i
$796$		0			0
$797$	1.73244	+	5.33189i	0.0613660	+	0.188865i	0.977040	−	0.213057i	$-0.0683421\pi$
$797$	1.73244	+	5.33189i	0.0613660	+	0.188865i	−0.915674	+	0.401923i	$0.868342\pi$
$798$		0			0
$799$	17.6181			0.623283
$800$		0			0
$801$	2.40939			0.0851315
$802$		0			0
$803$	−4.79142	−	14.7465i	−0.169085	−	0.520391i
$804$		0			0
$805$	−18.1754	−	16.3781i	−0.640600	−	0.577252i
$806$		0			0
$807$	2.13371			0.0751100
$808$		0			0
$809$	−18.8090	+	13.6655i	−0.661290	+	0.480455i	−0.867098	−	0.498137i	$-0.834018\pi$
$809$	−18.8090	+	13.6655i	−0.661290	+	0.480455i	0.205809	+	0.978592i	$0.434018\pi$
$810$		0			0
$811$	−27.9935	−	20.3385i	−0.982984	−	0.714180i	−0.0246104	−	0.999697i	$-0.507835\pi$
$811$	−27.9935	−	20.3385i	−0.982984	−	0.714180i	−0.958373	+	0.285518i	$0.907835\pi$
$812$		0			0
$813$	−31.1425	+	22.6263i	−1.09221	+	0.793540i
$814$		0			0
$815$	16.2423	−	9.36905i	0.568943	−	0.328183i
$816$		0			0
$817$	10.4831	−	32.2638i	0.366758	−	1.12877i
$818$		0			0
$819$	−0.950490	+	2.92531i	−0.0332128	+	0.102219i
$820$		0			0
$821$	−8.45765	−	26.0300i	−0.295174	−	0.908452i	−0.983163	−	0.182731i	$-0.941506\pi$
$821$	−8.45765	−	26.0300i	−0.295174	−	0.908452i	0.687989	−	0.725721i	$-0.258494\pi$
$822$		0			0
$823$	−34.9184	−	25.3697i	−1.21718	−	0.884331i	−0.221315	−	0.975202i	$-0.571035\pi$
$823$	−34.9184	−	25.3697i	−1.21718	−	0.884331i	−0.995863	+	0.0908711i	$0.971035\pi$
$824$		0			0
$825$	−4.85165	+	8.38816i	−0.168913	+	0.292038i
$826$		0			0
$827$	25.6576	+	18.6413i	0.892202	+	0.648223i	0.936451	−	0.350798i	$-0.114090\pi$
$827$	25.6576	+	18.6413i	0.892202	+	0.648223i	−0.0442493	+	0.999021i	$0.514090\pi$
$828$		0			0
$829$	−7.62684	−	23.4730i	−0.264891	−	0.815251i	−0.991718	−	0.128431i	$-0.959006\pi$
$829$	−7.62684	−	23.4730i	−0.264891	−	0.815251i	0.726827	−	0.686820i	$-0.240994\pi$
$830$		0			0
$831$	5.81172	−	17.8866i	0.201606	−	0.620481i
$832$		0			0
$833$	−11.7792	+	36.2527i	−0.408125	+	1.25608i
$834$		0			0
$835$	−6.53542	+	14.6634i	−0.226168	+	0.507447i
$836$		0			0
$837$	−3.22455	+	2.34277i	−0.111457	+	0.0809781i
$838$		0			0
$839$	31.3138	+	22.7508i	1.08107	+	0.785444i	0.977869	−	0.209216i	$-0.0670911\pi$
$839$	31.3138	+	22.7508i	1.08107	+	0.785444i	0.103202	+	0.994660i	$0.467091\pi$
$840$		0			0
$841$	0.451574	−	0.328088i	0.0155715	−	0.0113134i
$842$		0			0
$843$	−8.68895			−0.299263
$844$		0			0
$845$	11.2208	−	25.1759i	0.386008	−	0.866077i
$846$		0			0
$847$	−14.2346	−	43.8097i	−0.489108	−	1.50532i
$848$		0			0
$849$	5.10382			0.175163
$850$		0			0
$851$	15.8485			0.543279
$852$		0			0
$853$	4.75488	+	14.6340i	0.162804	+	0.501059i	0.998868	−	0.0475731i	$-0.0151487\pi$
$853$	4.75488	+	14.6340i	0.162804	+	0.501059i	−0.836064	+	0.548632i	$0.815149\pi$
$854$		0			0
$855$	−2.26656	−	10.6838i	−0.0775147	−	0.365380i
$856$		0			0
$857$	39.2764			1.34166			0.670829	−	0.741612i	$-0.265939\pi$
$857$	39.2764			1.34166			0.670829	+	0.741612i	$0.265939\pi$
$858$		0			0
$859$	−35.1666	+	25.5500i	−1.19987	+	0.871755i	−0.994272	−	0.106882i	$-0.965913\pi$
$859$	−35.1666	+	25.5500i	−1.19987	+	0.871755i	−0.205596	+	0.978637i	$0.565913\pi$
$860$		0			0
$861$	−60.5760	−	44.0110i	−2.06442	−	1.49989i
$862$		0			0
$863$	14.8393	−	10.7814i	0.505134	−	0.367002i	−0.305840	−	0.952083i	$-0.598937\pi$
$863$	14.8393	−	10.7814i	0.505134	−	0.367002i	0.810975	+	0.585081i	$0.198937\pi$
$864$		0			0
$865$	−24.8964	−	22.4344i	−0.846503	−	0.762793i
$866$		0			0
$867$	−5.64609	+	17.3769i	−0.191751	+	0.590150i
$868$		0			0
$869$	−0.896134	+	2.75802i	−0.0303993	+	0.0935593i
$870$		0			0
$871$	1.85634	+	5.71324i	0.0628998	+	0.193586i
$872$		0			0
$873$	−10.1271	−	7.35776i	−0.342750	−	0.249023i
$874$		0			0
$875$	−52.5109	−	17.1299i	−1.77519	−	0.579096i
$876$		0			0
$877$	−17.2904	−	12.5622i	−0.583855	−	0.424196i	0.256257	−	0.966609i	$-0.417511\pi$
$877$	−17.2904	−	12.5622i	−0.583855	−	0.424196i	−0.840112	+	0.542413i	$0.817511\pi$
$878$		0			0
$879$	−0.155869	−	0.479715i	−0.00525732	−	0.0161804i
$880$		0			0
$881$	−3.08008	+	9.47952i	−0.103771	+	0.319373i	−0.989440	−	0.144943i	$-0.953700\pi$
$881$	−3.08008	+	9.47952i	−0.103771	+	0.319373i	0.885669	+	0.464317i	$0.153700\pi$
$882$		0			0
$883$	1.77903	−	5.47528i	0.0598690	−	0.184258i	−0.916649	−	0.399693i	$-0.869117\pi$
$883$	1.77903	−	5.47528i	0.0598690	−	0.184258i	0.976518	+	0.215435i	$0.0691168\pi$
$884$		0			0
$885$	−23.8666	−	21.5065i	−0.802268	−	0.722933i
$886$		0			0
$887$	−8.61165	+	6.25673i	−0.289151	+	0.210080i	−0.722899	−	0.690954i	$-0.757191\pi$
$887$	−8.61165	+	6.25673i	−0.289151	+	0.210080i	0.433748	+	0.901034i	$0.357191\pi$
$888$		0			0
$889$	−57.2731	−	41.6113i	−1.92088	−	1.39560i
$890$		0			0
$891$	−6.43895	+	4.67817i	−0.215713	+	0.156725i
$892$		0			0
$893$	51.7905			1.73310
$894$		0			0
$895$	−8.56838	−	40.3886i	−0.286409	−	1.35004i
$896$		0			0
$897$	−0.840762	−	2.58760i	−0.0280722	−	0.0863974i
$898$		0			0
$899$	3.77748			0.125986
$900$		0			0
$901$	28.9563			0.964674
$902$		0			0
$903$	−12.0443	−	37.0685i	−0.400809	−	1.23356i
$904$		0			0
$905$	−18.3003	+	41.0599i	−0.608322	+	1.36488i
$906$		0			0
$907$	−23.4462			−0.778518			−0.389259	−	0.921128i	$-0.627269\pi$
$907$	−23.4462			−0.778518			−0.389259	+	0.921128i	$0.627269\pi$
$908$		0			0
$909$	−6.38860	+	4.64159i	−0.211896	+	0.153952i
$910$		0			0
$911$	27.6056	+	20.0567i	0.914616	+	0.664507i	0.942178	−	0.335113i	$-0.108774\pi$
$911$	27.6056	+	20.0567i	0.914616	+	0.664507i	−0.0275624	+	0.999620i	$0.508774\pi$
$912$		0			0
$913$	−11.9971	+	8.71642i	−0.397047	+	0.288471i
$914$		0			0
$915$	8.91550	−	20.0035i	0.294737	−	0.661296i
$916$		0			0
$917$	15.5998	−	48.0113i	0.515151	−	1.58547i
$918$		0			0
$919$	14.9065	−	45.8775i	0.491720	−	1.51336i	−0.330286	−	0.943881i	$-0.607145\pi$
$919$	14.9065	−	45.8775i	0.491720	−	1.51336i	0.822006	−	0.569479i	$-0.192855\pi$
$920$		0			0
$921$	10.8747	+	33.4688i	0.358333	+	1.10283i
$922$		0			0
$923$	−0.425072	−	0.308833i	−0.0139914	−	0.0101654i
$924$		0			0
$925$	32.6974	−	14.5272i	1.07508	−	0.477653i
$926$		0			0
$927$	1.04900	+	0.762142i	0.0344536	+	0.0250320i
$928$		0			0
$929$	3.84435	+	11.8317i	0.126129	+	0.388186i	0.994105	−	0.108421i	$-0.0345793\pi$
$929$	3.84435	+	11.8317i	0.126129	+	0.388186i	−0.867976	+	0.496606i	$0.834579\pi$
$930$		0			0
$931$	−34.6264	+	106.569i	−1.13484	+	3.49267i
$932$		0			0
$933$	−3.36223	+	10.3479i	−0.110075	+	0.338775i
$934$		0			0
$935$	5.49095	−	3.16734i	0.179573	−	0.103583i
$936$		0			0
$937$	48.2420	−	35.0499i	1.57600	−	1.14503i	0.654890	−	0.755724i	$-0.272715\pi$
$937$	48.2420	−	35.0499i	1.57600	−	1.14503i	0.921109	−	0.389306i	$-0.127285\pi$
$938$		0			0
$939$	14.3494	+	10.4255i	0.468277	+	0.340223i
$940$		0			0
$941$	−5.16826	+	3.75496i	−0.168480	+	0.122408i	−0.668830	−	0.743415i	$-0.733205\pi$
$941$	−5.16826	+	3.75496i	−0.168480	+	0.122408i	0.500350	+	0.865823i	$0.333205\pi$
$942$		0			0
$943$	−22.4216			−0.730149
$944$		0			0
$945$	−46.1794	−	41.6128i	−1.50222	−	1.35366i
$946$		0			0
$947$	0.704405	+	2.16794i	0.0228901	+	0.0704485i	0.961849	−	0.273581i	$-0.0882081\pi$
$947$	0.704405	+	2.16794i	0.0228901	+	0.0704485i	−0.938959	+	0.344029i	$0.888208\pi$
$948$		0			0
$949$	9.82845			0.319045
$950$		0			0
$951$	−7.59779			−0.246375
$952$		0			0
$953$	−1.25775	−	3.87094i	−0.0407424	−	0.125392i	0.928617	−	0.371041i	$-0.120999\pi$
$953$	−1.25775	−	3.87094i	−0.0407424	−	0.125392i	−0.969359	+	0.245649i	$0.920999\pi$
$954$		0			0
$955$	42.6720	−	24.6145i	1.38083	−	0.796506i
$956$		0			0
$957$	10.3357			0.334107
$958$		0			0
$959$	29.3034	−	21.2902i	0.946258	−	0.687496i
$960$		0			0
$961$	24.6736	+	17.9264i	0.795924	+	0.578273i
$962$		0			0
$963$	−1.74173	+	1.26544i	−0.0561264	+	0.0407782i
$964$		0			0
$965$	−37.6324	−	3.97019i	−1.21143	−	0.127805i
$966$		0			0
$967$	−10.9040	+	33.5590i	−0.350649	+	1.07919i	0.607841	+	0.794059i	$0.292036\pi$
$967$	−10.9040	+	33.5590i	−0.350649	+	1.07919i	−0.958490	+	0.285127i	$0.907964\pi$
$968$		0			0
$969$	6.52164	−	20.0716i	0.209505	−	0.644791i
$970$		0			0
$971$	5.31316	+	16.3522i	0.170508	+	0.524768i	0.999400	−	0.0346399i	$-0.0110284\pi$
$971$	5.31316	+	16.3522i	0.170508	+	0.524768i	−0.828892	+	0.559408i	$0.811028\pi$
$972$		0			0
$973$	26.7587	+	19.4413i	0.857844	+	0.623260i
$974$		0			0
$975$	−4.10648	−	4.56788i	−0.131513	−	0.146289i
$976$		0			0
$977$	−36.6659	−	26.6394i	−1.17305	−	0.852269i	−0.181677	−	0.983358i	$-0.558152\pi$
$977$	−36.6659	−	26.6394i	−1.17305	−	0.852269i	−0.991371	+	0.131089i	$0.958152\pi$
$978$		0			0
$979$	1.27032	+	3.90965i	0.0405996	+	0.124953i
$980$		0			0
$981$	−1.93271	+	5.94828i	−0.0617068	+	0.189914i
$982$		0			0
$983$	−1.22263	+	3.76288i	−0.0389960	+	0.120017i	−0.968659	−	0.248393i	$-0.920098\pi$
$983$	−1.22263	+	3.76288i	−0.0389960	+	0.120017i	0.929663	+	0.368410i	$0.120098\pi$
$984$		0			0
$985$	1.70643	+	8.04357i	0.0543714	+	0.256290i
$986$		0			0
$987$	48.1391	−	34.9751i	1.53229	−	1.11327i
$988$		0			0
$989$	−9.44237	−	6.86029i	−0.300250	−	0.218144i
$990$		0			0
$991$	20.2739	−	14.7298i	0.644020	−	0.467908i	−0.217209	−	0.976125i	$-0.569695\pi$
$991$	20.2739	−	14.7298i	0.644020	−	0.467908i	0.861229	+	0.508217i	$0.169695\pi$
$992$		0			0
$993$	−1.75116			−0.0555713
$994$		0			0
$995$	58.8947	+	6.21334i	1.86709	+	0.196976i
$996$		0			0
$997$	15.8857	+	48.8913i	0.503106	+	1.54840i	0.803931	+	0.594722i	$0.202738\pi$
$997$	15.8857	+	48.8913i	0.503106	+	1.54840i	−0.300825	+	0.953679i	$0.597262\pi$
$998$		0			0
$999$	40.2671			1.27400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.g.241.3		16
4.3	odd	2		200.2.m.c.41.2	✓	16
20.3	even	4		1000.2.q.d.49.6		32
20.7	even	4		1000.2.q.d.49.3		32
20.19	odd	2		1000.2.m.c.201.3		16
25.6	even	5		10000.2.a.bk.1.6		8
25.11	even	5	inner	400.2.u.g.161.3		16
25.19	even	10		10000.2.a.bh.1.3		8
100.11	odd	10		200.2.m.c.161.2	yes	16
100.19	odd	10		5000.2.a.m.1.6		8
100.23	even	20		1000.2.q.d.449.3		32
100.27	even	20		1000.2.q.d.449.6		32
100.31	odd	10		5000.2.a.l.1.3		8
100.39	odd	10		1000.2.m.c.801.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.c.41.2	✓	16	4.3	odd	2
200.2.m.c.161.2	yes	16	100.11	odd	10
400.2.u.g.161.3		16	25.11	even	5	inner
400.2.u.g.241.3		16	1.1	even	1	trivial
1000.2.m.c.201.3		16	20.19	odd	2
1000.2.m.c.801.3		16	100.39	odd	10
1000.2.q.d.49.3		32	20.7	even	4
1000.2.q.d.49.6		32	20.3	even	4
1000.2.q.d.449.3		32	100.23	even	20
1000.2.q.d.449.6		32	100.27	even	20
5000.2.a.l.1.3		8	100.31	odd	10
5000.2.a.m.1.6		8	100.19	odd	10
10000.2.a.bh.1.3		8	25.19	even	10
10000.2.a.bk.1.6		8	25.6	even	5

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.462625 + 1.42381i) q^{3} +(-2.22373 - 0.234601i) q^{5} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +O(q^{10})\)	\(q+(0.462625 + 1.42381i) q^{3} +(-2.22373 - 0.234601i) q^{5} +4.94031 q^{7} +(0.613832 - 0.445975i) q^{9} +(1.04731 + 0.760912i) q^{11} +(-0.663861 + 0.482323i) q^{13} +(-0.694723 - 3.27470i) q^{15} +(-0.676707 + 2.08269i) q^{17} +(-1.98926 + 6.12233i) q^{19} +(2.28551 + 7.03407i) q^{21} +(1.79177 + 1.30180i) q^{23} +(4.88992 + 1.04338i) q^{25} +(4.55246 + 3.30755i) q^{27} +(-1.64801 - 5.07207i) q^{29} +(-0.218880 + 0.673643i) q^{31} +(-0.598887 + 1.84318i) q^{33} +(-10.9859 - 1.15900i) q^{35} +(5.78922 - 4.20612i) q^{37} +(-0.993856 - 0.722078i) q^{39} +(-8.19030 + 5.95060i) q^{41} -5.26985 q^{43} +(-1.46962 + 0.847721i) q^{45} +(-2.48612 - 7.65150i) q^{47} +17.4067 q^{49} -3.27842 q^{51} +(-4.08608 - 12.5757i) q^{53} +(-2.15041 - 1.93776i) q^{55} -9.63732 q^{57} +(7.76420 - 5.64102i) q^{59} +(5.29271 + 3.84538i) q^{61} +(3.03252 - 2.20325i) q^{63} +(1.58940 - 0.916812i) q^{65} +(2.26224 - 6.96246i) q^{67} +(-1.02460 + 3.15339i) q^{69} +(0.197864 + 0.608964i) q^{71} +(-9.68999 - 7.04019i) q^{73} +(0.776625 + 7.44503i) q^{75} +(5.17402 + 3.75914i) q^{77} +(0.692240 + 2.13050i) q^{79} +(-1.89987 + 5.84719i) q^{81} +(-3.53986 + 10.8946i) q^{83} +(1.99341 - 4.47258i) q^{85} +(6.45926 - 4.69293i) q^{87} +(2.56905 + 1.86652i) q^{89} +(-3.27968 + 2.38283i) q^{91} -1.06040 q^{93} +(5.85989 - 13.1477i) q^{95} +(-5.09821 - 15.6907i) q^{97} +0.982218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) \) 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9	\( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9} + 10 q^{11} + q^{13} + 10 q^{15} - 4 q^{17} - 3 q^{21} - 11 q^{23} + 9 q^{25} - 13 q^{27} + 5 q^{29} + 9 q^{31} + 16 q^{33} - 24 q^{35} + 30 q^{37} - 14 q^{39} - 2 q^{41} + 42 q^{43} - 77 q^{45} + 16 q^{47} + 18 q^{49} - 100 q^{51} + 11 q^{53} + 24 q^{55} - 64 q^{57} + 53 q^{59} + 4 q^{61} + 38 q^{63} + 37 q^{65} + 14 q^{67} - 7 q^{69} + 6 q^{71} - 24 q^{73} + 15 q^{75} + 23 q^{77} + 22 q^{79} - 6 q^{81} - 33 q^{83} + 8 q^{85} - 37 q^{87} + 20 q^{89} + 27 q^{91} + 40 q^{93} + 24 q^{95} + 11 q^{97} - 122 q^{99}+O(q^{100}) \) 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9 + 10 * q^11 + q^13 + 10 * q^15 - 4 * q^17 - 3 * q^21 - 11 * q^23 + 9 * q^25 - 13 * q^27 + 5 * q^29 + 9 * q^31 + 16 * q^33 - 24 * q^35 + 30 * q^37 - 14 * q^39 - 2 * q^41 + 42 * q^43 - 77 * q^45 + 16 * q^47 + 18 * q^49 - 100 * q^51 + 11 * q^53 + 24 * q^55 - 64 * q^57 + 53 * q^59 + 4 * q^61 + 38 * q^63 + 37 * q^65 + 14 * q^67 - 7 * q^69 + 6 * q^71 - 24 * q^73 + 15 * q^75 + 23 * q^77 + 22 * q^79 - 6 * q^81 - 33 * q^83 + 8 * q^85 - 37 * q^87 + 20 * q^89 + 27 * q^91 + 40 * q^93 + 24 * q^95 + 11 * q^97 - 122 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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