LMFDB - Embedded newform 400.2.u.a.161.1

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:	$1$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			161.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	400.161
Dual form			400.2.u.a.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690983 + 2.12663i) q^{3} +(-1.80902 - 1.31433i) q^{5} -0.381966 q^{7} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(-0.690983 + 2.12663i) q^{3} +(-1.80902 - 1.31433i) q^{5} -0.381966 q^{7} +(-1.61803 - 1.17557i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(-4.54508 - 3.30220i) q^{13} +(4.04508 - 2.93893i) q^{15} +(0.236068 + 0.726543i) q^{17} +(-1.66312 - 5.11855i) q^{19} +(0.263932 - 0.812299i) q^{21} +(-2.80902 + 2.04087i) q^{23} +(1.54508 + 4.75528i) q^{25} +(-1.80902 + 1.31433i) q^{27} +(2.04508 - 6.29412i) q^{29} +(-2.69098 - 8.28199i) q^{31} +(-2.23607 - 6.88191i) q^{33} +(0.690983 + 0.502029i) q^{35} +(3.04508 + 2.21238i) q^{37} +(10.1631 - 7.38394i) q^{39} +(6.23607 + 4.53077i) q^{41} -6.61803 q^{43} +(1.38197 + 4.25325i) q^{45} +(-2.11803 + 6.51864i) q^{47} -6.85410 q^{49} -1.70820 q^{51} +(-3.07295 + 9.45756i) q^{53} +7.23607 q^{55} +12.0344 q^{57} +(3.73607 + 2.71441i) q^{59} +(-7.42705 + 5.39607i) q^{61} +(0.618034 + 0.449028i) q^{63} +(3.88197 + 11.9475i) q^{65} +(-0.0901699 - 0.277515i) q^{67} +(-2.39919 - 7.38394i) q^{69} +(1.97214 - 6.06961i) q^{71} +(-8.89919 + 6.46564i) q^{73} -11.1803 q^{75} +(1.00000 - 0.726543i) q^{77} +(-3.19098 + 9.82084i) q^{79} +(-3.39919 - 10.4616i) q^{81} +(4.16312 + 12.8128i) q^{83} +(0.527864 - 1.62460i) q^{85} +(11.9721 + 8.69827i) q^{87} +(-3.23607 + 2.35114i) q^{89} +(1.73607 + 1.26133i) q^{91} +19.4721 q^{93} +(-3.71885 + 11.4454i) q^{95} +(5.64590 - 17.3763i) q^{97} +6.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{3} - 5 q^{5} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 5 * q^3 - 5 * q^5 - 6 * q^7 - 2 * q^9	$ 4 q - 5 q^{3} - 5 q^{5} - 6 q^{7} - 2 q^{9} - 6 q^{11} - 7 q^{13} + 5 q^{15} - 8 q^{17} + 9 q^{19} + 10 q^{21} - 9 q^{23} - 5 q^{25} - 5 q^{27} - 3 q^{29} - 13 q^{31} + 5 q^{35} + q^{37} + 25 q^{39} + 16 q^{41} - 22 q^{43} + 10 q^{45} - 4 q^{47} - 14 q^{49} + 20 q^{51} - 19 q^{53} + 20 q^{55} - 10 q^{57} + 6 q^{59} - 23 q^{61} - 2 q^{63} + 20 q^{65} + 22 q^{67} + 15 q^{69} - 10 q^{71} - 11 q^{73} + 4 q^{77} - 15 q^{79} + 11 q^{81} + q^{83} + 20 q^{85} + 30 q^{87} - 4 q^{89} - 2 q^{91} + 60 q^{93} - 35 q^{95} + 36 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q - 5 * q^3 - 5 * q^5 - 6 * q^7 - 2 * q^9 - 6 * q^11 - 7 * q^13 + 5 * q^15 - 8 * q^17 + 9 * q^19 + 10 * q^21 - 9 * q^23 - 5 * q^25 - 5 * q^27 - 3 * q^29 - 13 * q^31 + 5 * q^35 + q^37 + 25 * q^39 + 16 * q^41 - 22 * q^43 + 10 * q^45 - 4 * q^47 - 14 * q^49 + 20 * q^51 - 19 * q^53 + 20 * q^55 - 10 * q^57 + 6 * q^59 - 23 * q^61 - 2 * q^63 + 20 * q^65 + 22 * q^67 + 15 * q^69 - 10 * q^71 - 11 * q^73 + 4 * q^77 - 15 * q^79 + 11 * q^81 + q^83 + 20 * q^85 + 30 * q^87 - 4 * q^89 - 2 * q^91 + 60 * q^93 - 35 * q^95 + 36 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	−0.690983	+	2.12663i	−0.398939	+	1.22781i	0.526912	+	0.849920i	$0.323350\pi$
$3$	−0.690983	+	2.12663i	−0.398939	+	1.22781i	−0.925851	+	0.377889i	$0.876650\pi$
$4$		0			0
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$		0			0
$7$	−0.381966			−0.144370			−0.0721848	−	0.997391i	$-0.522997\pi$
$7$	−0.381966			−0.144370			−0.0721848	+	0.997391i	$0.522997\pi$
$8$		0			0
$9$	−1.61803	−	1.17557i	−0.539345	−	0.391857i
$10$		0			0
$11$	−2.61803	+	1.90211i	−0.789367	+	0.573509i	−0.907776	−	0.419456i	$-0.862221\pi$
$11$	−2.61803	+	1.90211i	−0.789367	+	0.573509i	0.118409	+	0.992965i	$0.462221\pi$
$12$		0			0
$13$	−4.54508	−	3.30220i	−1.26058	−	0.915865i	−0.261794	−	0.965124i	$-0.584314\pi$
$13$	−4.54508	−	3.30220i	−1.26058	−	0.915865i	−0.998786	+	0.0492590i	$0.984314\pi$
$14$		0			0
$15$	4.04508	−	2.93893i	1.04444	−	0.758827i
$16$		0			0
$17$	0.236068	+	0.726543i	0.0572549	+	0.176212i	0.975594	−	0.219582i	$-0.0704693\pi$
$17$	0.236068	+	0.726543i	0.0572549	+	0.176212i	−0.918339	+	0.395794i	$0.870469\pi$
$18$		0			0
$19$	−1.66312	−	5.11855i	−0.381546	−	1.17428i	−0.938955	−	0.344039i	$-0.888205\pi$
$19$	−1.66312	−	5.11855i	−0.381546	−	1.17428i	0.557410	−	0.830238i	$-0.311795\pi$
$20$		0			0
$21$	0.263932	−	0.812299i	0.0575947	−	0.177258i
$22$		0			0
$23$	−2.80902	+	2.04087i	−0.585721	+	0.425551i	−0.840782	−	0.541374i	$-0.817904\pi$
$23$	−2.80902	+	2.04087i	−0.585721	+	0.425551i	0.255061	+	0.966925i	$0.417904\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$		0			0
$27$	−1.80902	+	1.31433i	−0.348145	+	0.252942i
$28$		0			0
$29$	2.04508	−	6.29412i	0.379763	−	1.16879i	−0.560446	−	0.828191i	$-0.689370\pi$
$29$	2.04508	−	6.29412i	0.379763	−	1.16879i	0.940209	−	0.340599i	$-0.110630\pi$
$30$		0			0
$31$	−2.69098	−	8.28199i	−0.483315	−	1.48749i	−0.834407	−	0.551149i	$-0.814190\pi$
$31$	−2.69098	−	8.28199i	−0.483315	−	1.48749i	0.351092	−	0.936341i	$-0.385810\pi$
$32$		0			0
$33$	−2.23607	−	6.88191i	−0.389249	−	1.19799i
$34$		0			0
$35$	0.690983	+	0.502029i	0.116797	+	0.0848583i
$36$		0			0
$37$	3.04508	+	2.21238i	0.500609	+	0.363714i	0.809250	−	0.587465i	$-0.199874\pi$
$37$	3.04508	+	2.21238i	0.500609	+	0.363714i	−0.308641	+	0.951179i	$0.599874\pi$
$38$		0			0
$39$	10.1631	−	7.38394i	1.62740	−	1.18238i
$40$		0			0
$41$	6.23607	+	4.53077i	0.973910	+	0.707587i	0.956339	−	0.292258i	$-0.0944067\pi$
$41$	6.23607	+	4.53077i	0.973910	+	0.707587i	0.0175708	+	0.999846i	$0.494407\pi$
$42$		0			0
$43$	−6.61803			−1.00924			−0.504620	−	0.863341i	$-0.668368\pi$
$43$	−6.61803			−1.00924			−0.504620	+	0.863341i	$0.668368\pi$
$44$		0			0
$45$	1.38197	+	4.25325i	0.206011	+	0.634038i
$46$		0			0
$47$	−2.11803	+	6.51864i	−0.308947	+	0.950841i	0.669228	+	0.743057i	$0.266625\pi$
$47$	−2.11803	+	6.51864i	−0.308947	+	0.950841i	−0.978175	+	0.207784i	$0.933375\pi$
$48$		0			0
$49$	−6.85410			−0.979157
$50$		0			0
$51$	−1.70820			−0.239196
$52$		0			0
$53$	−3.07295	+	9.45756i	−0.422102	+	1.29910i	0.483640	+	0.875267i	$0.339314\pi$
$53$	−3.07295	+	9.45756i	−0.422102	+	1.29910i	−0.905742	+	0.423829i	$0.860686\pi$
$54$		0			0
$55$	7.23607			0.975711
$56$		0			0
$57$	12.0344			1.59400
$58$		0			0
$59$	3.73607	+	2.71441i	0.486395	+	0.353386i	0.803796	−	0.594905i	$-0.202810\pi$
$59$	3.73607	+	2.71441i	0.486395	+	0.353386i	−0.317401	+	0.948291i	$0.602810\pi$
$60$		0			0
$61$	−7.42705	+	5.39607i	−0.950936	+	0.690896i	−0.951028	−	0.309104i	$-0.899971\pi$
$61$	−7.42705	+	5.39607i	−0.950936	+	0.690896i	9.17309e−5		1.00000i	$0.499971\pi$
$62$		0			0
$63$	0.618034	+	0.449028i	0.0778650	+	0.0565722i
$64$		0			0
$65$	3.88197	+	11.9475i	0.481499	+	1.48190i
$66$		0			0
$67$	−0.0901699	−	0.277515i	−0.0110160	−	0.0339038i	0.945397	−	0.325920i	$-0.105674\pi$
$67$	−0.0901699	−	0.277515i	−0.0110160	−	0.0339038i	−0.956413	+	0.292016i	$0.905674\pi$
$68$		0			0
$69$	−2.39919	−	7.38394i	−0.288828	−	0.888922i
$70$		0			0
$71$	1.97214	−	6.06961i	0.234049	−	0.720330i	−0.763197	−	0.646166i	$-0.776371\pi$
$71$	1.97214	−	6.06961i	0.234049	−	0.720330i	0.997246	−	0.0741639i	$-0.0236288\pi$
$72$		0			0
$73$	−8.89919	+	6.46564i	−1.04157	+	0.756746i	−0.970592	−	0.240732i	$-0.922612\pi$
$73$	−8.89919	+	6.46564i	−1.04157	+	0.756746i	−0.0709795	+	0.997478i	$0.522612\pi$
$74$		0			0
$75$	−11.1803			−1.29099
$76$		0			0
$77$	1.00000	−	0.726543i	0.113961	−	0.0827972i
$78$		0			0
$79$	−3.19098	+	9.82084i	−0.359014	+	1.10493i	0.594632	+	0.803998i	$0.297298\pi$
$79$	−3.19098	+	9.82084i	−0.359014	+	1.10493i	−0.953646	+	0.300932i	$0.902702\pi$
$80$		0			0
$81$	−3.39919	−	10.4616i	−0.377687	−	1.16240i
$82$		0			0
$83$	4.16312	+	12.8128i	0.456962	+	1.40638i	0.868817	+	0.495134i	$0.164881\pi$
$83$	4.16312	+	12.8128i	0.456962	+	1.40638i	−0.411855	+	0.911249i	$0.635119\pi$
$84$		0			0
$85$	0.527864	−	1.62460i	0.0572549	−	0.176212i
$86$		0			0
$87$	11.9721	+	8.69827i	1.28355	+	0.932552i
$88$		0			0
$89$	−3.23607	+	2.35114i	−0.343023	+	0.249220i	−0.745936	−	0.666018i	$-0.767998\pi$
$89$	−3.23607	+	2.35114i	−0.343023	+	0.249220i	0.402913	+	0.915238i	$0.367998\pi$
$90$		0			0
$91$	1.73607	+	1.26133i	0.181989	+	0.132223i
$92$		0			0
$93$	19.4721			2.01917
$94$		0			0
$95$	−3.71885	+	11.4454i	−0.381546	+	1.17428i
$96$		0			0
$97$	5.64590	−	17.3763i	0.573254	−	1.76429i	−0.0687946	−	0.997631i	$-0.521915\pi$
$97$	5.64590	−	17.3763i	0.573254	−	1.76429i	0.642049	−	0.766664i	$-0.278085\pi$
$98$		0			0
$99$	6.47214			0.650474
$100$		0			0
$101$	−0.0557281			−0.00554515			−0.00277258	−	0.999996i	$-0.500883\pi$
$101$	−0.0557281			−0.00554515			−0.00277258	+	0.999996i	$0.500883\pi$
$102$		0			0
$103$	3.04508	−	9.37181i	0.300041	−	0.923432i	−0.681440	−	0.731874i	$-0.738646\pi$
$103$	3.04508	−	9.37181i	0.300041	−	0.923432i	0.981481	−	0.191558i	$-0.0613540\pi$
$104$		0			0
$105$	−1.54508	+	1.12257i	−0.150785	+	0.109552i
$106$		0			0
$107$	−3.29180			−0.318230			−0.159115	−	0.987260i	$-0.550864\pi$
$107$	−3.29180			−0.318230			−0.159115	+	0.987260i	$0.550864\pi$
$108$		0			0
$109$	12.0902	+	8.78402i	1.15803	+	0.841357i	0.989527	−	0.144345i	$-0.0461074\pi$
$109$	12.0902	+	8.78402i	1.15803	+	0.841357i	0.168501	+	0.985702i	$0.446107\pi$
$110$		0			0
$111$	−6.80902	+	4.94704i	−0.646283	+	0.469552i
$112$		0			0
$113$	−7.73607	−	5.62058i	−0.727748	−	0.528740i	0.161102	−	0.986938i	$-0.448495\pi$
$113$	−7.73607	−	5.62058i	−0.727748	−	0.528740i	−0.888850	+	0.458198i	$0.848495\pi$
$114$		0			0
$115$	7.76393			0.723990
$116$		0			0
$117$	3.47214	+	10.6861i	0.320999	+	0.987934i
$118$		0			0
$119$	−0.0901699	−	0.277515i	−0.00826587	−	0.0254397i
$120$		0			0
$121$	−0.163119	+	0.502029i	−0.0148290	+	0.0456390i
$122$		0			0
$123$	−13.9443	+	10.1311i	−1.25731	+	0.913491i
$124$		0			0
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$		0			0
$127$	13.3262	−	9.68208i	1.18251	−	0.859146i	0.190060	−	0.981773i	$-0.439132\pi$
$127$	13.3262	−	9.68208i	1.18251	−	0.859146i	0.992453	+	0.122627i	$0.0391319\pi$
$128$		0			0
$129$	4.57295	−	14.0741i	0.402626	−	1.23915i
$130$		0			0
$131$	−3.11803	−	9.59632i	−0.272424	−	0.838435i	−0.989890	−	0.141841i	$-0.954698\pi$
$131$	−3.11803	−	9.59632i	−0.272424	−	0.838435i	0.717466	−	0.696594i	$-0.245302\pi$
$132$		0			0
$133$	0.635255	+	1.95511i	0.0550836	+	0.169530i
$134$		0			0
$135$	5.00000			0.430331
$136$		0			0
$137$	−4.04508	−	2.93893i	−0.345595	−	0.251089i	0.401424	−	0.915892i	$-0.368515\pi$
$137$	−4.04508	−	2.93893i	−0.345595	−	0.251089i	−0.747019	+	0.664803i	$0.768515\pi$
$138$		0			0
$139$	11.5172	−	8.36775i	0.976878	−	0.709743i	0.0198692	−	0.999803i	$-0.493675\pi$
$139$	11.5172	−	8.36775i	0.976878	−	0.709743i	0.957009	+	0.290059i	$0.0936750\pi$
$140$		0			0
$141$	−12.3992	−	9.00854i	−1.04420	−	0.758656i
$142$		0			0
$143$	18.1803			1.52032
$144$		0			0
$145$	−11.9721	+	8.69827i	−0.994232	+	0.722352i
$146$		0			0
$147$	4.73607	−	14.5761i	0.390624	−	1.20222i
$148$		0			0
$149$	8.41641			0.689499			0.344749	−	0.938695i	$-0.387964\pi$
$149$	8.41641			0.689499			0.344749	+	0.938695i	$0.387964\pi$
$150$		0			0
$151$	−2.61803			−0.213053			−0.106526	−	0.994310i	$-0.533973\pi$
$151$	−2.61803			−0.213053			−0.106526	+	0.994310i	$0.533973\pi$
$152$		0			0
$153$	0.472136	−	1.45309i	0.0381699	−	0.117475i
$154$		0			0
$155$	−6.01722	+	18.5191i	−0.483315	+	1.48749i
$156$		0			0
$157$	−0.236068			−0.0188403			−0.00942014	−	0.999956i	$-0.502999\pi$
$157$	−0.236068			−0.0188403			−0.00942014	+	0.999956i	$0.502999\pi$
$158$		0			0
$159$	−17.9894	−	13.0700i	−1.42665	−	1.03652i
$160$		0			0
$161$	1.07295	−	0.779543i	0.0845602	−	0.0614366i
$162$		0			0
$163$	−5.80902	−	4.22050i	−0.454997	−	0.330575i	0.336568	−	0.941659i	$-0.390734\pi$
$163$	−5.80902	−	4.22050i	−0.454997	−	0.330575i	−0.791566	+	0.611084i	$0.790734\pi$
$164$		0			0
$165$	−5.00000	+	15.3884i	−0.389249	+	1.19799i
$166$		0			0
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	−0.996426	−	0.0844656i	$-0.973082\pi$
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	0.756478	−	0.654019i	$-0.226918\pi$
$168$		0			0
$169$	5.73607	+	17.6538i	0.441236	+	1.35798i
$170$		0			0
$171$	−3.32624	+	10.2371i	−0.254364	+	0.782851i
$172$		0			0
$173$	−12.5172	+	9.09429i	−0.951667	+	0.691426i	−0.951200	−	0.308574i	$-0.900148\pi$
$173$	−12.5172	+	9.09429i	−0.951667	+	0.691426i	−0.000466206		1.00000i	$0.500148\pi$
$174$		0			0
$175$	−0.590170	−	1.81636i	−0.0446127	−	0.137304i
$176$		0			0
$177$	−8.35410	+	6.06961i	−0.627933	+	0.456220i
$178$		0			0
$179$	−5.16312	+	15.8904i	−0.385910	+	1.18771i	0.549909	+	0.835225i	$0.314663\pi$
$179$	−5.16312	+	15.8904i	−0.385910	+	1.18771i	−0.935818	+	0.352483i	$0.885337\pi$
$180$		0			0
$181$	−6.70820	−	20.6457i	−0.498617	−	1.53458i	−0.811243	−	0.584709i	$-0.801209\pi$
$181$	−6.70820	−	20.6457i	−0.498617	−	1.53458i	0.312626	−	0.949876i	$-0.398791\pi$
$182$		0			0
$183$	−6.34346	−	19.5232i	−0.468922	−	1.44319i
$184$		0			0
$185$	−2.60081	−	8.00448i	−0.191216	−	0.588501i
$186$		0			0
$187$	−2.00000	−	1.45309i	−0.146254	−	0.106260i
$188$		0			0
$189$	0.690983	−	0.502029i	0.0502616	−	0.0365172i
$190$		0			0
$191$	−11.0902	−	8.05748i	−0.802457	−	0.583019i	0.109177	−	0.994022i	$-0.465178\pi$
$191$	−11.0902	−	8.05748i	−0.802457	−	0.583019i	−0.911634	+	0.411004i	$0.865178\pi$
$192$		0			0
$193$	5.70820			0.410886			0.205443	−	0.978669i	$-0.434137\pi$
$193$	5.70820			0.410886			0.205443	+	0.978669i	$0.434137\pi$
$194$		0			0
$195$	−28.0902			−2.01158
$196$		0			0
$197$	−5.94427	+	18.2946i	−0.423512	+	1.30344i	0.480900	+	0.876775i	$0.340310\pi$
$197$	−5.94427	+	18.2946i	−0.423512	+	1.30344i	−0.904412	+	0.426660i	$0.859690\pi$
$198$		0			0
$199$	−11.6180			−0.823581			−0.411790	−	0.911279i	$-0.635096\pi$
$199$	−11.6180			−0.823581			−0.411790	+	0.911279i	$0.635096\pi$
$200$		0			0
$201$	0.652476			0.0460221
$202$		0			0
$203$	−0.781153	+	2.40414i	−0.0548262	+	0.168738i
$204$		0			0
$205$	−5.32624	−	16.3925i	−0.372001	−	1.14490i
$206$		0			0
$207$	6.94427			0.482660
$208$		0			0
$209$	14.0902	+	10.2371i	0.974637	+	0.708116i
$210$		0			0
$211$	1.66312	−	1.20833i	0.114494	−	0.0831846i	−0.529065	−	0.848581i	$-0.677457\pi$
$211$	1.66312	−	1.20833i	0.114494	−	0.0831846i	0.643559	+	0.765397i	$0.277457\pi$
$212$		0			0
$213$	11.5451	+	8.38800i	0.791056	+	0.574736i
$214$		0			0
$215$	11.9721	+	8.69827i	0.816493	+	0.593217i
$216$		0			0
$217$	1.02786	+	3.16344i	0.0697760	+	0.214748i
$218$		0			0
$219$	−7.60081	−	23.3929i	−0.513615	−	1.58075i
$220$		0			0
$221$	1.32624	−	4.08174i	0.0892124	−	0.274568i
$222$		0			0
$223$	−6.23607	+	4.53077i	−0.417598	+	0.303403i	−0.776671	−	0.629907i	$-0.783093\pi$
$223$	−6.23607	+	4.53077i	−0.417598	+	0.303403i	0.359073	+	0.933310i	$0.383093\pi$
$224$		0			0
$225$	3.09017	−	9.51057i	0.206011	−	0.634038i
$226$		0			0
$227$	19.0902	−	13.8698i	1.26706	−	0.920572i	0.267978	−	0.963425i	$-0.413645\pi$
$227$	19.0902	−	13.8698i	1.26706	−	0.920572i	0.999081	+	0.0428528i	$0.0136447\pi$
$228$		0			0
$229$	−0.673762	+	2.07363i	−0.0445235	+	0.137029i	−0.970847	−	0.239700i	$-0.922951\pi$
$229$	−0.673762	+	2.07363i	−0.0445235	+	0.137029i	0.926324	+	0.376729i	$0.122951\pi$
$230$		0			0
$231$	0.854102	+	2.62866i	0.0561958	+	0.172953i
$232$		0			0
$233$	1.85410	+	5.70634i	0.121466	+	0.373835i	0.993241	−	0.116073i	$-0.0370306\pi$
$233$	1.85410	+	5.70634i	0.121466	+	0.373835i	−0.871774	+	0.489907i	$0.837031\pi$
$234$		0			0
$235$	12.3992	−	9.00854i	0.808834	−	0.587652i
$236$		0			0
$237$	−18.6803	−	13.5721i	−1.21342	−	0.881600i
$238$		0			0
$239$	−14.3713	+	10.4414i	−0.929604	+	0.675397i	−0.945896	−	0.324471i	$-0.894814\pi$
$239$	−14.3713	+	10.4414i	−0.929604	+	0.675397i	0.0162921	+	0.999867i	$0.494814\pi$
$240$		0			0
$241$	−2.04508	−	1.48584i	−0.131736	−	0.0957114i	0.519966	−	0.854187i	$-0.325945\pi$
$241$	−2.04508	−	1.48584i	−0.131736	−	0.0957114i	−0.651702	+	0.758475i	$0.725945\pi$
$242$		0			0
$243$	17.8885			1.14755
$244$		0			0
$245$	12.3992	+	9.00854i	0.792155	+	0.575534i
$246$		0			0
$247$	−9.34346	+	28.7562i	−0.594510	+	1.82971i
$248$		0			0
$249$	−30.1246			−1.90907
$250$		0			0
$251$	25.9443			1.63759			0.818794	−	0.574087i	$-0.194643\pi$
$251$	25.9443			1.63759			0.818794	+	0.574087i	$0.194643\pi$
$252$		0			0
$253$	3.47214	−	10.6861i	0.218291	−	0.671832i
$254$		0			0
$255$	3.09017	+	2.24514i	0.193514	+	0.140596i
$256$		0			0
$257$	−1.38197			−0.0862047			−0.0431023	−	0.999071i	$-0.513724\pi$
$257$	−1.38197			−0.0862047			−0.0431023	+	0.999071i	$0.513724\pi$
$258$		0			0
$259$	−1.16312	−	0.845055i	−0.0722727	−	0.0525092i
$260$		0			0
$261$	−10.7082	+	7.77997i	−0.662821	+	0.481568i
$262$		0			0
$263$	−5.78115	−	4.20025i	−0.356481	−	0.258999i	0.395102	−	0.918637i	$-0.370709\pi$
$263$	−5.78115	−	4.20025i	−0.356481	−	0.258999i	−0.751583	+	0.659639i	$0.770709\pi$
$264$		0			0
$265$	17.9894	−	13.0700i	1.10508	−	0.802886i
$266$		0			0
$267$	−2.76393	−	8.50651i	−0.169150	−	0.520590i
$268$		0			0
$269$	−8.56231	−	26.3521i	−0.522053	−	1.60671i	−0.770071	−	0.637958i	$-0.779779\pi$
$269$	−8.56231	−	26.3521i	−0.522053	−	1.60671i	0.248018	−	0.968755i	$-0.420221\pi$
$270$		0			0
$271$	1.52786	−	4.70228i	0.0928111	−	0.285643i	−0.893866	−	0.448334i	$-0.852017\pi$
$271$	1.52786	−	4.70228i	0.0928111	−	0.285643i	0.986677	+	0.162691i	$0.0520174\pi$
$272$		0			0
$273$	−3.88197	+	2.82041i	−0.234947	+	0.170699i
$274$		0			0
$275$	−13.0902	−	9.51057i	−0.789367	−	0.573509i
$276$		0			0
$277$	0.954915	−	0.693786i	0.0573753	−	0.0416856i	−0.558728	−	0.829351i	$-0.688710\pi$
$277$	0.954915	−	0.693786i	0.0573753	−	0.0416856i	0.616103	+	0.787665i	$0.288710\pi$
$278$		0			0
$279$	−5.38197	+	16.5640i	−0.322210	+	0.991660i
$280$		0			0
$281$	4.89919	+	15.0781i	0.292261	+	0.899487i	0.984128	+	0.177462i	$0.0567886\pi$
$281$	4.89919	+	15.0781i	0.292261	+	0.899487i	−0.691867	+	0.722025i	$0.743211\pi$
$282$		0			0
$283$	−8.11803	−	24.9847i	−0.482567	−	1.48519i	−0.835474	−	0.549530i	$-0.814807\pi$
$283$	−8.11803	−	24.9847i	−0.482567	−	1.48519i	0.352907	−	0.935658i	$-0.385193\pi$
$284$		0			0
$285$	−21.7705	−	15.8172i	−1.28957	−	0.936930i
$286$		0			0
$287$	−2.38197	−	1.73060i	−0.140603	−	0.102154i
$288$		0			0
$289$	13.2812	−	9.64932i	0.781244	−	0.567607i
$290$		0			0
$291$	33.0517	+	24.0134i	1.93752	+	1.40769i
$292$		0			0
$293$	−8.47214			−0.494947			−0.247474	−	0.968895i	$-0.579600\pi$
$293$	−8.47214			−0.494947			−0.247474	+	0.968895i	$0.579600\pi$
$294$		0			0
$295$	−3.19098	−	9.82084i	−0.185786	−	0.571791i
$296$		0			0
$297$	2.23607	−	6.88191i	0.129750	−	0.399329i
$298$		0			0
$299$	19.5066			1.12809
$300$		0			0
$301$	2.52786			0.145704
$302$		0			0
$303$	0.0385072	−	0.118513i	0.00221218	−	0.00680839i
$304$		0			0
$305$	20.5279			1.17542
$306$		0			0
$307$	−15.2361			−0.869568			−0.434784	−	0.900535i	$-0.643175\pi$
$307$	−15.2361			−0.869568			−0.434784	+	0.900535i	$0.643175\pi$
$308$		0			0
$309$	17.8262	+	12.9515i	1.01410	+	0.736786i
$310$		0			0
$311$	−13.0172	+	9.45756i	−0.738139	+	0.536289i	−0.892128	−	0.451783i	$-0.850788\pi$
$311$	−13.0172	+	9.45756i	−0.738139	+	0.536289i	0.153989	+	0.988073i	$0.450788\pi$
$312$		0			0
$313$	6.23607	+	4.53077i	0.352483	+	0.256094i	0.749910	−	0.661540i	$-0.230097\pi$
$313$	6.23607	+	4.53077i	0.352483	+	0.256094i	−0.397427	+	0.917634i	$0.630097\pi$
$314$		0			0
$315$	−0.527864	−	1.62460i	−0.0297418	−	0.0915358i
$316$		0			0
$317$	−3.01722	−	9.28605i	−0.169464	−	0.521557i	0.829873	−	0.557952i	$-0.188413\pi$
$317$	−3.01722	−	9.28605i	−0.169464	−	0.521557i	−0.999337	+	0.0363950i	$0.988413\pi$
$318$		0			0
$319$	6.61803	+	20.3682i	0.370539	+	1.14040i
$320$		0			0
$321$	2.27458	−	7.00042i	0.126954	−	0.390725i
$322$		0			0
$323$	3.32624	−	2.41665i	0.185077	−	0.134466i
$324$		0			0
$325$	8.68034	−	26.7153i	0.481499	−	1.48190i
$326$		0			0
$327$	−27.0344	+	19.6417i	−1.49501	+	1.08619i
$328$		0			0
$329$	0.809017	−	2.48990i	0.0446026	−	0.137273i
$330$		0			0
$331$	8.05573	+	24.7930i	0.442783	+	1.36275i	0.884897	+	0.465787i	$0.154229\pi$
$331$	8.05573	+	24.7930i	0.442783	+	1.36275i	−0.442114	+	0.896959i	$0.645771\pi$
$332$		0			0
$333$	−2.32624	−	7.15942i	−0.127477	−	0.392334i
$334$		0			0
$335$	−0.201626	+	0.620541i	−0.0110160	+	0.0339038i
$336$		0			0
$337$	−1.69098	−	1.22857i	−0.0921137	−	0.0669245i	0.540775	−	0.841167i	$-0.318131\pi$
$337$	−1.69098	−	1.22857i	−0.0921137	−	0.0669245i	−0.632889	+	0.774243i	$0.718131\pi$
$338$		0			0
$339$	17.2984	−	12.5680i	0.939519	−	0.682600i
$340$		0			0
$341$	22.7984	+	16.5640i	1.23460	+	0.896990i
$342$		0			0
$343$	5.29180			0.285730
$344$		0			0
$345$	−5.36475	+	16.5110i	−0.288828	+	0.888922i
$346$		0			0
$347$	−0.0450850	+	0.138757i	−0.00242029	+	0.00744888i	−0.952259	−	0.305290i	$-0.901247\pi$
$347$	−0.0450850	+	0.138757i	−0.00242029	+	0.00744888i	0.949839	+	0.312739i	$0.101247\pi$
$348$		0			0
$349$	−15.1246			−0.809602			−0.404801	−	0.914405i	$-0.632659\pi$
$349$	−15.1246			−0.809602			−0.404801	+	0.914405i	$0.632659\pi$
$350$		0			0
$351$	12.5623			0.670526
$352$		0			0
$353$	−2.91641	+	8.97578i	−0.155225	+	0.477733i	−0.998184	−	0.0602454i	$-0.980812\pi$
$353$	−2.91641	+	8.97578i	−0.155225	+	0.477733i	0.842959	+	0.537978i	$0.180812\pi$
$354$		0			0
$355$	−11.5451	+	8.38800i	−0.612749	+	0.445189i
$356$		0			0
$357$	0.652476			0.0345327
$358$		0			0
$359$	−6.69098	−	4.86128i	−0.353137	−	0.256569i	0.397047	−	0.917798i	$-0.370035\pi$
$359$	−6.69098	−	4.86128i	−0.353137	−	0.256569i	−0.750184	+	0.661229i	$0.770035\pi$
$360$		0			0
$361$	−8.06231	+	5.85761i	−0.424332	+	0.308295i
$362$		0			0
$363$	−0.954915	−	0.693786i	−0.0501200	−	0.0364143i
$364$		0			0
$365$	24.5967			1.28745
$366$		0			0
$367$	4.40983	+	13.5721i	0.230191	+	0.708456i	0.997723	+	0.0674449i	$0.0214847\pi$
$367$	4.40983	+	13.5721i	0.230191	+	0.708456i	−0.767532	+	0.641011i	$0.778515\pi$
$368$		0			0
$369$	−4.76393	−	14.6619i	−0.248000	−	0.763267i
$370$		0			0
$371$	1.17376	−	3.61247i	0.0609387	−	0.187550i
$372$		0			0
$373$	−3.97214	+	2.88593i	−0.205669	+	0.149428i	−0.685852	−	0.727741i	$-0.740570\pi$
$373$	−3.97214	+	2.88593i	−0.205669	+	0.149428i	0.480183	+	0.877168i	$0.340570\pi$
$374$		0			0
$375$	20.2254	+	14.6946i	1.04444	+	0.758827i
$376$		0			0
$377$	−30.0795	+	21.8541i	−1.54917	+	1.12554i
$378$		0			0
$379$	1.54508	−	4.75528i	0.0793657	−	0.244262i	−0.903499	−	0.428590i	$-0.859011\pi$
$379$	1.54508	−	4.75528i	0.0793657	−	0.244262i	0.982865	+	0.184327i	$0.0590106\pi$
$380$		0			0
$381$	11.3820	+	35.0301i	0.583116	+	1.79465i
$382$		0			0
$383$	−5.63525	−	17.3435i	−0.287948	−	0.886213i	−0.985500	−	0.169678i	$-0.945727\pi$
$383$	−5.63525	−	17.3435i	−0.287948	−	0.886213i	0.697551	−	0.716535i	$-0.254273\pi$
$384$		0			0
$385$	−2.76393			−0.140863
$386$		0			0
$387$	10.7082	+	7.77997i	0.544329	+	0.395478i
$388$		0			0
$389$	−11.6631	+	8.47375i	−0.591344	+	0.429636i	−0.842796	−	0.538233i	$-0.819092\pi$
$389$	−11.6631	+	8.47375i	−0.591344	+	0.429636i	0.251452	+	0.967870i	$0.419092\pi$
$390$		0			0
$391$	−2.14590	−	1.55909i	−0.108523	−	0.0788464i
$392$		0			0
$393$	22.5623			1.13812
$394$		0			0
$395$	18.6803	−	13.5721i	0.939910	−	0.682885i
$396$		0			0
$397$	2.75329	−	8.47375i	0.138184	−	0.425285i	−0.857888	−	0.513837i	$-0.828224\pi$
$397$	2.75329	−	8.47375i	0.138184	−	0.425285i	0.996072	+	0.0885513i	$0.0282237\pi$
$398$		0			0
$399$	−4.59675			−0.230125
$400$		0			0
$401$	12.5967			0.629052			0.314526	−	0.949249i	$-0.398155\pi$
$401$	12.5967			0.629052			0.314526	+	0.949249i	$0.398155\pi$
$402$		0			0
$403$	−15.1180	+	46.5285i	−0.753083	+	2.31775i
$404$		0			0
$405$	−7.60081	+	23.3929i	−0.377687	+	1.16240i
$406$		0			0
$407$	−12.1803			−0.603757
$408$		0			0
$409$	23.8435	+	17.3233i	1.17898	+	0.856581i	0.992057	−	0.125792i	$-0.0401473\pi$
$409$	23.8435	+	17.3233i	1.17898	+	0.856581i	0.186927	+	0.982374i	$0.440147\pi$
$410$		0			0
$411$	9.04508	−	6.57164i	0.446161	−	0.324155i
$412$		0			0
$413$	−1.42705	−	1.03681i	−0.0702206	−	0.0510182i
$414$		0			0
$415$	9.30902	−	28.6502i	0.456962	−	1.40638i
$416$		0			0
$417$	9.83688	+	30.2748i	0.481714	+	1.48256i
$418$		0			0
$419$	4.36475	+	13.4333i	0.213232	+	0.656260i	0.999274	+	0.0380876i	$0.0121266\pi$
$419$	4.36475	+	13.4333i	0.213232	+	0.656260i	−0.786043	+	0.618172i	$0.787873\pi$
$420$		0			0
$421$	−4.00000	+	12.3107i	−0.194948	+	0.599988i	0.805029	+	0.593235i	$0.202150\pi$
$421$	−4.00000	+	12.3107i	−0.194948	+	0.599988i	−0.999977	+	0.00675318i	$0.997850\pi$
$422$		0			0
$423$	11.0902	−	8.05748i	0.539223	−	0.391768i
$424$		0			0
$425$	−3.09017	+	2.24514i	−0.149895	+	0.108905i
$426$		0			0
$427$	2.83688	−	2.06111i	0.137286	−	0.0997443i
$428$		0			0
$429$	−12.5623	+	38.6628i	−0.606514	+	1.86666i
$430$		0			0
$431$	−5.16312	−	15.8904i	−0.248699	−	0.765416i	−0.995006	−	0.0998144i	$-0.968175\pi$
$431$	−5.16312	−	15.8904i	−0.248699	−	0.765416i	0.746307	−	0.665601i	$-0.231825\pi$
$432$		0			0
$433$	−9.66312	−	29.7400i	−0.464380	−	1.42921i	−0.859761	−	0.510697i	$-0.829387\pi$
$433$	−9.66312	−	29.7400i	−0.464380	−	1.42921i	0.395381	−	0.918517i	$-0.370613\pi$
$434$		0			0
$435$	−10.2254	−	31.4706i	−0.490272	−	1.50890i
$436$		0			0
$437$	15.1180	+	10.9839i	0.723194	+	0.525431i
$438$		0			0
$439$	−6.30902	+	4.58377i	−0.301113	+	0.218771i	−0.728074	−	0.685499i	$-0.759584\pi$
$439$	−6.30902	+	4.58377i	−0.301113	+	0.218771i	0.426961	+	0.904270i	$0.359584\pi$
$440$		0			0
$441$	11.0902	+	8.05748i	0.528103	+	0.383690i
$442$		0			0
$443$	39.6525			1.88395			0.941973	−	0.335689i	$-0.108969\pi$
$443$	39.6525			1.88395			0.941973	+	0.335689i	$0.108969\pi$
$444$		0			0
$445$	8.94427			0.423999
$446$		0			0
$447$	−5.81559	+	17.8986i	−0.275068	+	0.846573i
$448$		0			0
$449$	−35.0902			−1.65601			−0.828004	−	0.560723i	$-0.810523\pi$
$449$	−35.0902			−1.65601			−0.828004	+	0.560723i	$0.810523\pi$
$450$		0			0
$451$	−24.9443			−1.17458
$452$		0			0
$453$	1.80902	−	5.56758i	0.0849950	−	0.261588i
$454$		0			0
$455$	−1.48278	−	4.56352i	−0.0695138	−	0.213941i
$456$		0			0
$457$	4.47214			0.209198			0.104599	−	0.994514i	$-0.466644\pi$
$457$	4.47214			0.209198			0.104599	+	0.994514i	$0.466644\pi$
$458$		0			0
$459$	−1.38197	−	1.00406i	−0.0645046	−	0.0468654i
$460$		0			0
$461$	28.0795	−	20.4010i	1.30779	−	0.950168i	0.307795	−	0.951453i	$-0.400409\pi$
$461$	28.0795	−	20.4010i	1.30779	−	0.950168i	0.999999	+	0.00128485i	$0.000408982\pi$
$462$		0			0
$463$	1.57295	+	1.14281i	0.0731011	+	0.0531111i	0.623736	−	0.781635i	$-0.285614\pi$
$463$	1.57295	+	1.14281i	0.0731011	+	0.0531111i	−0.550634	+	0.834746i	$0.685614\pi$
$464$		0			0
$465$	−35.2254	−	25.5928i	−1.63354	−	1.18684i
$466$		0			0
$467$	−8.11803	−	24.9847i	−0.375658	−	1.15616i	−0.943034	−	0.332697i	$-0.892041\pi$
$467$	−8.11803	−	24.9847i	−0.375658	−	1.15616i	0.567376	−	0.823459i	$-0.307959\pi$
$468$		0			0
$469$	0.0344419	+	0.106001i	0.00159038	+	0.00489468i
$470$		0			0
$471$	0.163119	−	0.502029i	0.00751612	−	0.0231323i
$472$		0			0
$473$	17.3262	−	12.5882i	0.796661	−	0.578808i
$474$		0			0
$475$	21.7705	−	15.8172i	0.998899	−	0.725743i
$476$		0			0
$477$	16.0902	−	11.6902i	0.736718	−	0.535257i
$478$		0			0
$479$	−7.60739	+	23.4131i	−0.347591	+	1.06977i	0.612592	+	0.790400i	$0.290127\pi$
$479$	−7.60739	+	23.4131i	−0.347591	+	1.06977i	−0.960182	+	0.279374i	$0.909873\pi$
$480$		0			0
$481$	−6.53444	−	20.1109i	−0.297945	−	0.916980i
$482$		0			0
$483$	0.916408	+	2.82041i	0.0416980	+	0.128333i
$484$		0			0
$485$	−33.0517	+	24.0134i	−1.50080	+	1.09039i
$486$		0			0
$487$	−10.7533	−	7.81272i	−0.487278	−	0.354028i	0.316859	−	0.948473i	$-0.397372\pi$
$487$	−10.7533	−	7.81272i	−0.487278	−	0.354028i	−0.804137	+	0.594445i	$0.797372\pi$
$488$		0			0
$489$	12.9894	−	9.43732i	0.587399	−	0.426770i
$490$		0			0
$491$	6.66312	+	4.84104i	0.300702	+	0.218473i	0.727897	−	0.685687i	$-0.240498\pi$
$491$	6.66312	+	4.84104i	0.300702	+	0.218473i	−0.427194	+	0.904160i	$0.640498\pi$
$492$		0			0
$493$	5.05573			0.227699
$494$		0			0
$495$	−11.7082	−	8.50651i	−0.526245	−	0.382339i
$496$		0			0
$497$	−0.753289	+	2.31838i	−0.0337896	+	0.103994i
$498$		0			0
$499$	−9.43769			−0.422489			−0.211245	−	0.977433i	$-0.567752\pi$
$499$	−9.43769			−0.422489			−0.211245	+	0.977433i	$0.567752\pi$
$500$		0			0
$501$	22.4377			1.00244
$502$		0			0
$503$	−6.14590	+	18.9151i	−0.274032	+	0.843384i	0.715442	+	0.698672i	$0.246225\pi$
$503$	−6.14590	+	18.9151i	−0.274032	+	0.843384i	−0.989474	+	0.144712i	$0.953775\pi$
$504$		0			0
$505$	0.100813	+	0.0732450i	0.00448612	+	0.00325936i
$506$		0			0
$507$	−41.5066			−1.84337
$508$		0			0
$509$	−16.1074	−	11.7027i	−0.713948	−	0.518713i	0.170497	−	0.985358i	$-0.445463\pi$
$509$	−16.1074	−	11.7027i	−0.713948	−	0.518713i	−0.884445	+	0.466645i	$0.845463\pi$
$510$		0			0
$511$	3.39919	−	2.46965i	0.150371	−	0.109251i
$512$		0			0
$513$	9.73607	+	7.07367i	0.429858	+	0.312310i
$514$		0			0
$515$	−17.8262	+	12.9515i	−0.785518	+	0.570712i
$516$		0			0
$517$	−6.85410	−	21.0948i	−0.301443	−	0.927746i
$518$		0			0
$519$	−10.6910	−	32.9035i	−0.469282	−	1.44430i
$520$		0			0
$521$	−5.69098	+	17.5150i	−0.249326	+	0.767348i	0.745568	+	0.666429i	$0.232178\pi$
$521$	−5.69098	+	17.5150i	−0.249326	+	0.767348i	−0.994895	+	0.100919i	$0.967822\pi$
$522$		0			0
$523$	−16.6803	+	12.1190i	−0.729380	+	0.529926i	−0.889367	−	0.457193i	$-0.848855\pi$
$523$	−16.6803	+	12.1190i	−0.729380	+	0.529926i	0.159987	+	0.987119i	$0.448855\pi$
$524$		0			0
$525$	4.27051			0.186380
$526$		0			0
$527$	5.38197	−	3.91023i	0.234442	−	0.170332i
$528$		0			0
$529$	−3.38197	+	10.4086i	−0.147042	+	0.452549i
$530$		0			0
$531$	−2.85410	−	8.78402i	−0.123857	−	0.381194i
$532$		0			0
$533$	−13.3820	−	41.1855i	−0.579637	−	1.78394i
$534$		0			0
$535$	5.95492	+	4.32650i	0.257453	+	0.187051i
$536$		0			0
$537$	−30.2254	−	21.9601i	−1.30432	−	0.947646i
$538$		0			0
$539$	17.9443	−	13.0373i	0.772915	−	0.561555i
$540$		0			0
$541$	18.3262	+	13.3148i	0.787907	+	0.572448i	0.907341	−	0.420394i	$-0.138108\pi$
$541$	18.3262	+	13.3148i	0.787907	+	0.572448i	−0.119435	+	0.992842i	$0.538108\pi$
$542$		0			0
$543$	48.5410			2.08309
$544$		0			0
$545$	−10.3262	−	31.7809i	−0.442327	−	1.36134i
$546$		0			0
$547$	10.9271	−	33.6300i	0.467207	−	1.43792i	−0.388979	−	0.921247i	$-0.627172\pi$
$547$	10.9271	−	33.6300i	0.467207	−	1.43792i	0.856186	−	0.516668i	$-0.172828\pi$
$548$		0			0
$549$	18.3607			0.783615
$550$		0			0
$551$	−35.6180			−1.51738
$552$		0			0
$553$	1.21885	−	3.75123i	0.0518306	−	0.159518i
$554$		0			0
$555$	18.8197			0.798850
$556$		0			0
$557$	−30.1803			−1.27878			−0.639391	−	0.768882i	$-0.720813\pi$
$557$	−30.1803			−1.27878			−0.639391	+	0.768882i	$0.720813\pi$
$558$		0			0
$559$	30.0795	+	21.8541i	1.27223	+	0.924328i
$560$		0			0
$561$	4.47214	−	3.24920i	0.188814	−	0.137181i
$562$		0			0
$563$	25.1074	+	18.2416i	1.05815	+	0.768791i	0.973745	−	0.227640i	$-0.0731010\pi$
$563$	25.1074	+	18.2416i	1.05815	+	0.768791i	0.0844051	+	0.996432i	$0.473101\pi$
$564$		0			0
$565$	6.60739	+	20.3355i	0.277975	+	0.855519i
$566$		0			0
$567$	1.29837	+	3.99598i	0.0545266	+	0.167816i
$568$		0			0
$569$	2.63525	+	8.11048i	0.110476	+	0.340009i	0.990977	−	0.134035i	$-0.0427936\pi$
$569$	2.63525	+	8.11048i	0.110476	+	0.340009i	−0.880501	+	0.474044i	$0.842794\pi$
$570$		0			0
$571$	−9.36475	+	28.8217i	−0.391902	+	1.20615i	0.539445	+	0.842021i	$0.318634\pi$
$571$	−9.36475	+	28.8217i	−0.391902	+	1.20615i	−0.931348	+	0.364131i	$0.881366\pi$
$572$		0			0
$573$	24.7984	−	18.0171i	1.03597	−	0.752674i
$574$		0			0
$575$	−14.0451	−	10.2044i	−0.585721	−	0.425551i
$576$		0			0
$577$	16.0902	−	11.6902i	0.669843	−	0.486669i	−0.200130	−	0.979769i	$-0.564136\pi$
$577$	16.0902	−	11.6902i	0.669843	−	0.486669i	0.869972	+	0.493100i	$0.164136\pi$
$578$		0			0
$579$	−3.94427	+	12.1392i	−0.163918	+	0.504489i
$580$		0			0
$581$	−1.59017	−	4.89404i	−0.0659714	−	0.203039i
$582$		0			0
$583$	−9.94427	−	30.6053i	−0.411850	−	1.26754i
$584$		0			0
$585$	7.76393	−	23.8949i	0.320999	−	0.987934i
$586$		0			0
$587$	−18.2254	−	13.2415i	−0.752244	−	0.546537i	0.144278	−	0.989537i	$-0.453914\pi$
$587$	−18.2254	−	13.2415i	−0.752244	−	0.546537i	−0.896522	+	0.443000i	$0.853914\pi$
$588$		0			0
$589$	−37.9164	+	27.5479i	−1.56232	+	1.13509i
$590$		0			0
$591$	−34.7984	−	25.2825i	−1.43141	−	1.03998i
$592$		0			0
$593$	−0.562306			−0.0230911			−0.0115456	−	0.999933i	$-0.503675\pi$
$593$	−0.562306			−0.0230911			−0.0115456	+	0.999933i	$0.503675\pi$
$594$		0			0
$595$	−0.201626	+	0.620541i	−0.00826587	+	0.0254397i
$596$		0			0
$597$	8.02786	−	24.7072i	0.328559	−	1.01120i
$598$		0			0
$599$	−7.18034			−0.293381			−0.146690	−	0.989182i	$-0.546862\pi$
$599$	−7.18034			−0.293381			−0.146690	+	0.989182i	$0.546862\pi$
$600$		0			0
$601$	−42.5623			−1.73615			−0.868076	−	0.496431i	$-0.834644\pi$
$601$	−42.5623			−1.73615			−0.868076	+	0.496431i	$0.834644\pi$
$602$		0			0
$603$	−0.180340	+	0.555029i	−0.00734401	+	0.0226025i
$604$		0			0
$605$	0.954915	−	0.693786i	0.0388228	−	0.0282064i
$606$		0			0
$607$	32.2705			1.30982			0.654910	−	0.755707i	$-0.272707\pi$
$607$	32.2705			1.30982			0.654910	+	0.755707i	$0.272707\pi$
$608$		0			0
$609$	−4.57295	−	3.32244i	−0.185305	−	0.134632i
$610$		0			0
$611$	31.1525	−	22.6336i	1.26029	−	0.915657i
$612$		0			0
$613$	−15.3992	−	11.1882i	−0.621967	−	0.451886i	0.231641	−	0.972801i	$-0.425591\pi$
$613$	−15.3992	−	11.1882i	−0.621967	−	0.451886i	−0.853608	+	0.520916i	$0.825591\pi$
$614$		0			0
$615$	38.5410			1.55412
$616$		0			0
$617$	−5.74671	−	17.6866i	−0.231354	−	0.712034i	−0.997584	−	0.0694680i	$-0.977870\pi$
$617$	−5.74671	−	17.6866i	−0.231354	−	0.712034i	0.766230	−	0.642566i	$-0.222130\pi$
$618$		0			0
$619$	8.43363	+	25.9560i	0.338976	+	1.04326i	0.964730	+	0.263241i	$0.0847914\pi$
$619$	8.43363	+	25.9560i	0.338976	+	1.04326i	−0.625754	+	0.780020i	$0.715209\pi$
$620$		0			0
$621$	2.39919	−	7.38394i	0.0962761	−	0.296307i
$622$		0			0
$623$	1.23607	−	0.898056i	0.0495220	−	0.0359799i
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$	−31.5066	+	22.8909i	−1.25825	+	0.914173i
$628$		0			0
$629$	−0.888544	+	2.73466i	−0.0354286	+	0.109038i
$630$		0			0
$631$	14.1631	+	43.5896i	0.563825	+	1.73527i	0.671417	+	0.741079i	$0.265686\pi$
$631$	14.1631	+	43.5896i	0.563825	+	1.73527i	−0.107593	+	0.994195i	$0.534314\pi$
$632$		0			0
$633$	1.42047	+	4.37177i	0.0564587	+	0.173762i
$634$		0			0
$635$	−36.8328			−1.46167
$636$		0			0
$637$	31.1525	+	22.6336i	1.23431	+	0.896776i
$638$		0			0
$639$	−10.3262	+	7.50245i	−0.408500	+	0.296792i
$640$		0			0
$641$	−31.1074	−	22.6008i	−1.22867	−	0.892680i	−0.231878	−	0.972745i	$-0.574487\pi$
$641$	−31.1074	−	22.6008i	−1.22867	−	0.892680i	−0.996790	+	0.0800652i	$0.974487\pi$
$642$		0			0
$643$	−36.9443			−1.45694			−0.728470	−	0.685078i	$-0.759768\pi$
$643$	−36.9443			−1.45694			−0.728470	+	0.685078i	$0.759768\pi$
$644$		0			0
$645$	−26.7705	+	19.4499i	−1.05409	+	0.765840i
$646$		0			0
$647$	−2.67376	+	8.22899i	−0.105116	+	0.323515i	−0.989758	−	0.142757i	$-0.954403\pi$
$647$	−2.67376	+	8.22899i	−0.105116	+	0.323515i	0.884641	+	0.466272i	$0.154403\pi$
$648$		0			0
$649$	−14.9443			−0.586614
$650$		0			0
$651$	−7.43769			−0.291506
$652$		0			0
$653$	−2.31966	+	7.13918i	−0.0907753	+	0.279378i	−0.986130	−	0.165977i	$-0.946922\pi$
$653$	−2.31966	+	7.13918i	−0.0907753	+	0.279378i	0.895354	+	0.445354i	$0.146922\pi$
$654$		0			0
$655$	−6.97214	+	21.4580i	−0.272424	+	0.838435i
$656$		0			0
$657$	22.0000			0.858302
$658$		0			0
$659$	29.0344	+	21.0948i	1.13102	+	0.821735i	0.985843	−	0.167670i	$-0.0536245\pi$
$659$	29.0344	+	21.0948i	1.13102	+	0.821735i	0.145178	+	0.989406i	$0.453624\pi$
$660$		0			0
$661$	11.6803	−	8.48626i	0.454313	−	0.330077i	−0.336984	−	0.941511i	$-0.609407\pi$
$661$	11.6803	−	8.48626i	0.454313	−	0.330077i	0.791296	+	0.611433i	$0.209407\pi$
$662$		0			0
$663$	7.76393	+	5.64083i	0.301526	+	0.219072i
$664$		0			0
$665$	1.42047	−	4.37177i	0.0550836	−	0.169530i
$666$		0			0
$667$	7.10081	+	21.8541i	0.274945	+	0.846192i
$668$		0			0
$669$	−5.32624	−	16.3925i	−0.205924	−	0.633770i
$670$		0			0
$671$	9.18034	−	28.2542i	0.354403	−	1.09074i
$672$		0			0
$673$	−5.76393	+	4.18774i	−0.222183	+	0.161426i	−0.693309	−	0.720641i	$-0.743848\pi$
$673$	−5.76393	+	4.18774i	−0.222183	+	0.161426i	0.471126	+	0.882066i	$0.343848\pi$
$674$		0			0
$675$	−9.04508	−	6.57164i	−0.348145	−	0.252942i
$676$		0			0
$677$	0.927051	−	0.673542i	0.0356295	−	0.0258863i	−0.569828	−	0.821764i	$-0.692990\pi$
$677$	0.927051	−	0.673542i	0.0356295	−	0.0258863i	0.605457	+	0.795878i	$0.292990\pi$
$678$		0			0
$679$	−2.15654	+	6.63715i	−0.0827605	+	0.254710i
$680$		0			0
$681$	16.3050	+	50.1815i	0.624807	+	1.92296i
$682$		0			0
$683$	2.25329	+	6.93491i	0.0862197	+	0.265357i	0.984866	−	0.173317i	$-0.0554484\pi$
$683$	2.25329	+	6.93491i	0.0862197	+	0.265357i	−0.898646	+	0.438674i	$0.855448\pi$
$684$		0			0
$685$	3.45492	+	10.6331i	0.132006	+	0.406271i
$686$		0			0
$687$	−3.94427	−	2.86568i	−0.150483	−	0.109333i
$688$		0			0
$689$	45.1976	−	32.8380i	1.72189	−	1.25103i
$690$		0			0
$691$	−32.4787	−	23.5972i	−1.23555	−	0.897679i	−0.238255	−	0.971203i	$-0.576575\pi$
$691$	−32.4787	−	23.5972i	−1.23555	−	0.897679i	−0.997293	+	0.0735241i	$0.976575\pi$
$692$		0			0
$693$	−2.47214			−0.0939087
$694$		0			0
$695$	−31.8328			−1.20749
$696$		0			0
$697$	−1.81966	+	5.60034i	−0.0689245	+	0.212128i
$698$		0			0
$699$	−13.4164			−0.507455
$700$		0			0
$701$	−20.1803			−0.762201			−0.381100	−	0.924534i	$-0.624455\pi$
$701$	−20.1803			−0.762201			−0.381100	+	0.924534i	$0.624455\pi$
$702$		0			0
$703$	6.25987	−	19.2659i	0.236095	−	0.726627i
$704$		0			0
$705$	10.5902	+	32.5932i	0.398849	+	1.22753i
$706$		0			0
$707$	0.0212862			0.000800551
$708$		0			0
$709$	−10.1910	−	7.40418i	−0.382730	−	0.278070i	0.379740	−	0.925093i	$-0.376014\pi$
$709$	−10.1910	−	7.40418i	−0.382730	−	0.278070i	−0.762470	+	0.647023i	$0.776014\pi$
$710$		0			0
$711$	16.7082	−	12.1392i	0.626607	−	0.455256i
$712$		0			0
$713$	24.4615	+	17.7723i	0.916090	+	0.665578i
$714$		0			0
$715$	−32.8885	−	23.8949i	−1.22996	−	0.893620i
$716$		0			0
$717$	−12.2746	−	37.7773i	−0.458402	−	1.41082i
$718$		0			0
$719$	−7.51064	−	23.1154i	−0.280100	−	0.862058i	−0.987825	−	0.155570i	$-0.950278\pi$
$719$	−7.51064	−	23.1154i	−0.280100	−	0.862058i	0.707725	−	0.706488i	$-0.249722\pi$
$720$		0			0
$721$	−1.16312	+	3.57971i	−0.0433168	+	0.133315i
$722$		0			0
$723$	4.57295	−	3.32244i	0.170070	−	0.123563i
$724$		0			0
$725$	33.0902			1.22894
$726$		0			0
$727$	−3.50000	+	2.54290i	−0.129808	+	0.0943109i	−0.650795	−	0.759254i	$-0.725564\pi$
$727$	−3.50000	+	2.54290i	−0.129808	+	0.0943109i	0.520987	+	0.853565i	$0.325564\pi$
$728$		0			0
$729$	−2.16312	+	6.65740i	−0.0801155	+	0.246570i
$730$		0			0
$731$	−1.56231	−	4.80828i	−0.0577840	−	0.177841i
$732$		0			0
$733$	1.28115	+	3.94298i	0.0473205	+	0.145637i	0.971925	−	0.235291i	$-0.0756044\pi$
$733$	1.28115	+	3.94298i	0.0473205	+	0.145637i	−0.924604	+	0.380929i	$0.875604\pi$
$734$		0			0
$735$	−27.7254	+	20.1437i	−1.02267	+	0.743012i
$736$		0			0
$737$	0.763932	+	0.555029i	0.0281398	+	0.0204448i
$738$		0			0
$739$	−3.50000	+	2.54290i	−0.128750	+	0.0935420i	−0.650296	−	0.759681i	$-0.725355\pi$
$739$	−3.50000	+	2.54290i	−0.128750	+	0.0935420i	0.521547	+	0.853223i	$0.325355\pi$
$740$		0			0
$741$	−54.6976	−	39.7401i	−2.00937	−	1.45989i
$742$		0			0
$743$	−34.2492			−1.25648			−0.628241	−	0.778019i	$-0.716225\pi$
$743$	−34.2492			−1.25648			−0.628241	+	0.778019i	$0.716225\pi$
$744$		0			0
$745$	−15.2254	−	11.0619i	−0.557816	−	0.405277i
$746$		0			0
$747$	8.32624	−	25.6255i	0.304641	−	0.937589i
$748$		0			0
$749$	1.25735			0.0459427
$750$		0			0
$751$	36.2361			1.32227			0.661136	−	0.750266i	$-0.270074\pi$
$751$	36.2361			1.32227			0.661136	+	0.750266i	$0.270074\pi$
$752$		0			0
$753$	−17.9271	+	55.1738i	−0.653298	+	2.01064i
$754$		0			0
$755$	4.73607	+	3.44095i	0.172363	+	0.125229i
$756$		0			0
$757$	15.0000			0.545184			0.272592	−	0.962130i	$-0.412119\pi$
$757$	15.0000			0.545184			0.272592	+	0.962130i	$0.412119\pi$
$758$		0			0
$759$	20.3262	+	14.7679i	0.737796	+	0.536040i
$760$		0			0
$761$	25.7705	−	18.7234i	0.934180	−	0.678722i	−0.0128325	−	0.999918i	$-0.504085\pi$
$761$	25.7705	−	18.7234i	0.934180	−	0.678722i	0.947013	+	0.321196i	$0.104085\pi$
$762$		0			0
$763$	−4.61803	−	3.35520i	−0.167184	−	0.121466i
$764$		0			0
$765$	−2.76393	+	2.00811i	−0.0999302	+	0.0726035i
$766$		0			0
$767$	−8.01722	−	24.6745i	−0.289485	−	0.890943i
$768$		0			0
$769$	14.9787	+	46.0997i	0.540146	+	1.66240i	0.732259	+	0.681026i	$0.238466\pi$
$769$	14.9787	+	46.0997i	0.540146	+	1.66240i	−0.192113	+	0.981373i	$0.561534\pi$
$770$		0			0
$771$	0.954915	−	2.93893i	0.0343904	−	0.105843i
$772$		0			0
$773$	−34.2426	+	24.8787i	−1.23162	+	0.894826i	−0.997011	−	0.0772632i	$-0.975382\pi$
$773$	−34.2426	+	24.8787i	−1.23162	+	0.894826i	−0.234612	+	0.972089i	$0.575382\pi$
$774$		0			0
$775$	35.2254	−	25.5928i	1.26533	−	0.919319i
$776$		0			0
$777$	2.60081	−	1.88960i	0.0933036	−	0.0677891i
$778$		0			0
$779$	12.8197	−	39.4549i	0.459312	−	1.41362i
$780$		0			0
$781$	6.38197	+	19.6417i	0.228365	+	0.702834i
$782$		0			0
$783$	4.57295	+	14.0741i	0.163424	+	0.502967i
$784$		0			0
$785$	0.427051	+	0.310271i	0.0152421	+	0.0110740i
$786$		0			0
$787$	35.3607	+	25.6910i	1.26047	+	0.915787i	0.998781	−	0.0493650i	$-0.0157198\pi$
$787$	35.3607	+	25.6910i	1.26047	+	0.915787i	0.261691	+	0.965152i	$0.415720\pi$
$788$		0			0
$789$	12.9271	−	9.39205i	0.460215	−	0.334366i
$790$		0			0
$791$	2.95492	+	2.14687i	0.105065	+	0.0763340i
$792$		0			0
$793$	51.5755			1.83150
$794$		0			0
$795$	15.3647	+	47.2878i	0.544931	+	1.67713i
$796$		0			0
$797$	−5.78115	+	17.7926i	−0.204779	+	0.630245i	0.794943	+	0.606684i	$0.207500\pi$
$797$	−5.78115	+	17.7926i	−0.204779	+	0.630245i	−0.999722	+	0.0235613i	$0.992500\pi$
$798$		0			0
$799$	−5.23607			−0.185239
$800$		0			0
$801$	8.00000			0.282666
$802$		0			0
$803$	11.0000	−	33.8545i	0.388182	−	1.19470i
$804$		0			0
$805$	−2.96556			−0.104522
$806$		0			0
$807$	61.9574			2.18100
$808$		0			0
$809$	−25.7254	−	18.6906i	−0.904458	−	0.657127i	0.0351493	−	0.999382i	$-0.488809\pi$
$809$	−25.7254	−	18.6906i	−0.904458	−	0.657127i	−0.939607	+	0.342255i	$0.888809\pi$
$810$		0			0
$811$	−0.517221	+	0.375783i	−0.0181621	+	0.0131955i	−0.596829	−	0.802368i	$-0.703573\pi$
$811$	−0.517221	+	0.375783i	−0.0181621	+	0.0131955i	0.578667	+	0.815564i	$0.303573\pi$
$812$		0			0
$813$	8.94427	+	6.49839i	0.313689	+	0.227909i
$814$		0			0
$815$	4.96149	+	15.2699i	0.173794	+	0.534881i
$816$		0			0
$817$	11.0066	+	33.8748i	0.385071	+	1.18513i
$818$		0			0
$819$	−1.32624	−	4.08174i	−0.0463425	−	0.142628i
$820$		0			0
$821$	−2.20820	+	6.79615i	−0.0770668	+	0.237187i	−0.982167	−	0.188011i	$-0.939796\pi$
$821$	−2.20820	+	6.79615i	−0.0770668	+	0.237187i	0.905100	+	0.425199i	$0.139796\pi$
$822$		0			0
$823$	28.7984	−	20.9232i	1.00385	−	0.729338i	0.0409383	−	0.999162i	$-0.486965\pi$
$823$	28.7984	−	20.9232i	1.00385	−	0.729338i	0.962910	+	0.269823i	$0.0869653\pi$
$824$		0			0
$825$	29.2705	−	21.2663i	1.01907	−	0.740396i
$826$		0			0
$827$	21.1525	−	15.3682i	0.735544	−	0.534404i	−0.155769	−	0.987794i	$-0.549785\pi$
$827$	21.1525	−	15.3682i	0.735544	−	0.534404i	0.891312	+	0.453390i	$0.149785\pi$
$828$		0			0
$829$	−7.59017	+	23.3601i	−0.263617	+	0.811331i	0.728391	+	0.685162i	$0.240268\pi$
$829$	−7.59017	+	23.3601i	−0.263617	+	0.811331i	−0.992009	+	0.126170i	$0.959732\pi$
$830$		0			0
$831$	0.815595	+	2.51014i	0.0282927	+	0.0870759i
$832$		0			0
$833$	−1.61803	−	4.97980i	−0.0560616	−	0.172540i
$834$		0			0
$835$	−6.93363	+	21.3395i	−0.239948	+	0.738484i
$836$		0			0
$837$	15.7533	+	11.4454i	0.544513	+	0.395612i
$838$		0			0
$839$	11.9721	−	8.69827i	0.413324	−	0.300297i	−0.361622	−	0.932325i	$-0.617777\pi$
$839$	11.9721	−	8.69827i	0.413324	−	0.300297i	0.774946	+	0.632027i	$0.217777\pi$
$840$		0			0
$841$	−11.9721	−	8.69827i	−0.412832	−	0.299940i
$842$		0			0
$843$	−35.4508			−1.22099
$844$		0			0
$845$	12.8262	−	39.4751i	0.441236	−	1.35798i
$846$		0			0
$847$	0.0623059	−	0.191758i	0.00214086	−	0.00658888i
$848$		0			0
$849$	58.7426			2.01604
$850$		0			0
$851$	−13.0689			−0.447996
$852$		0			0
$853$	−6.61803	+	20.3682i	−0.226597	+	0.697394i	0.771528	+	0.636195i	$0.219493\pi$
$853$	−6.61803	+	20.3682i	−0.226597	+	0.697394i	−0.998126	+	0.0611995i	$0.980507\pi$
$854$		0			0
$855$	19.4721	−	14.1473i	0.665933	−	0.483829i
$856$		0			0
$857$	−9.85410			−0.336610			−0.168305	−	0.985735i	$-0.553829\pi$
$857$	−9.85410			−0.336610			−0.168305	+	0.985735i	$0.553829\pi$
$858$		0			0
$859$	−15.0451	−	10.9309i	−0.513332	−	0.372957i	0.300754	−	0.953702i	$-0.402762\pi$
$859$	−15.0451	−	10.9309i	−0.513332	−	0.372957i	−0.814086	+	0.580744i	$0.802762\pi$
$860$		0			0
$861$	5.32624	−	3.86974i	0.181518	−	0.131880i
$862$		0			0
$863$	19.8262	+	14.4046i	0.674893	+	0.490338i	0.871660	−	0.490112i	$-0.163044\pi$
$863$	19.8262	+	14.4046i	0.674893	+	0.490338i	−0.196767	+	0.980450i	$0.563044\pi$
$864$		0			0
$865$	34.5967			1.17632
$866$		0			0
$867$	11.3435	+	34.9116i	0.385244	+	1.18566i
$868$		0			0
$869$	−10.3262	−	31.7809i	−0.350294	−	1.07809i
$870$		0			0
$871$	−0.506578	+	1.55909i	−0.0171647	+	0.0528276i
$872$		0			0
$873$	−29.5623	+	21.4783i	−1.00053	+	0.726929i
$874$		0			0
$875$	−1.31966	+	4.06150i	−0.0446127	+	0.137304i
$876$		0			0
$877$	−2.70820	+	1.96763i	−0.0914495	+	0.0664420i	−0.632570	−	0.774503i	$-0.718000\pi$
$877$	−2.70820	+	1.96763i	−0.0914495	+	0.0664420i	0.541121	+	0.840945i	$0.318000\pi$
$878$		0			0
$879$	5.85410	−	18.0171i	0.197454	−	0.607701i
$880$		0			0
$881$	−5.12461	−	15.7719i	−0.172653	−	0.531370i	0.826866	−	0.562399i	$-0.190122\pi$
$881$	−5.12461	−	15.7719i	−0.172653	−	0.531370i	−0.999518	+	0.0310292i	$0.990122\pi$
$882$		0			0
$883$	−6.65248	−	20.4742i	−0.223874	−	0.689012i	−0.998404	−	0.0564755i	$-0.982014\pi$
$883$	−6.65248	−	20.4742i	−0.223874	−	0.689012i	0.774530	−	0.632537i	$-0.217986\pi$
$884$		0			0
$885$	23.0902			0.776168
$886$		0			0
$887$	−30.6525	−	22.2703i	−1.02921	−	0.747764i	−0.0610591	−	0.998134i	$-0.519448\pi$
$887$	−30.6525	−	22.2703i	−1.02921	−	0.747764i	−0.968150	+	0.250370i	$0.919448\pi$
$888$		0			0
$889$	−5.09017	+	3.69822i	−0.170719	+	0.124034i
$890$		0			0
$891$	28.7984	+	20.9232i	0.964782	+	0.700955i
$892$		0			0
$893$	36.8885			1.23443
$894$		0			0
$895$	30.2254	−	21.9601i	1.01032	−	0.734044i
$896$		0			0
$897$	−13.4787	+	41.4832i	−0.450041	+	1.38508i
$898$		0			0
$899$	−57.6312			−1.92211
$900$		0			0
$901$	−7.59675			−0.253084
$902$		0			0
$903$	−1.74671	+	5.37582i	−0.0581269	+	0.178896i
$904$		0			0
$905$	−15.0000	+	46.1653i	−0.498617	+	1.53458i
$906$		0			0
$907$	−10.8197			−0.359261			−0.179630	−	0.983734i	$-0.557490\pi$
$907$	−10.8197			−0.359261			−0.179630	+	0.983734i	$0.557490\pi$
$908$		0			0
$909$	0.0901699	+	0.0655123i	0.00299075	+	0.00217291i
$910$		0			0
$911$	−14.0451	+	10.2044i	−0.465334	+	0.338085i	−0.795620	−	0.605796i	$-0.792855\pi$
$911$	−14.0451	+	10.2044i	−0.465334	+	0.338085i	0.330286	+	0.943881i	$0.392855\pi$
$912$		0			0
$913$	−35.2705	−	25.6255i	−1.16728	−	0.848081i
$914$		0			0
$915$	−14.1844	+	43.6551i	−0.468922	+	1.44319i
$916$		0			0
$917$	1.19098	+	3.66547i	0.0393297	+	0.121044i
$918$		0			0
$919$	−4.80902	−	14.8006i	−0.158635	−	0.488228i	0.839876	−	0.542778i	$-0.182628\pi$
$919$	−4.80902	−	14.8006i	−0.158635	−	0.488228i	−0.998511	+	0.0545502i	$0.982628\pi$
$920$		0			0
$921$	10.5279	−	32.4014i	0.346905	−	1.06766i
$922$		0			0
$923$	−29.0066	+	21.0745i	−0.954763	+	0.693676i
$924$		0			0
$925$	−5.81559	+	17.8986i	−0.191216	+	0.588501i
$926$		0			0
$927$	−15.9443	+	11.5842i	−0.523679	+	0.380475i
$928$		0			0
$929$	18.0967	−	55.6961i	0.593735	−	1.82733i	0.0328105	−	0.999462i	$-0.489554\pi$
$929$	18.0967	−	55.6961i	0.593735	−	1.82733i	0.560925	−	0.827867i	$-0.310446\pi$
$930$		0			0
$931$	11.3992	+	35.0831i	0.373593	+	1.14980i
$932$		0			0
$933$	−11.1180	−	34.2178i	−0.363988	−	1.12024i
$934$		0			0
$935$	1.70820	+	5.25731i	0.0558642	+	0.171932i
$936$		0			0
$937$	−0.354102	−	0.257270i	−0.0115680	−	0.00840465i	0.581986	−	0.813199i	$-0.302276\pi$
$937$	−0.354102	−	0.257270i	−0.0115680	−	0.00840465i	−0.593554	+	0.804794i	$0.702276\pi$
$938$		0			0
$939$	−13.9443	+	10.1311i	−0.455054	+	0.330616i
$940$		0			0
$941$	24.3156	+	17.6663i	0.792666	+	0.575905i	0.908753	−	0.417334i	$-0.137035\pi$
$941$	24.3156	+	17.6663i	0.792666	+	0.575905i	−0.116088	+	0.993239i	$0.537035\pi$
$942$		0			0
$943$	−26.7639			−0.871554
$944$		0			0
$945$	−1.90983			−0.0621268
$946$		0			0
$947$	−6.49342	+	19.9847i	−0.211008	+	0.649415i	0.788405	+	0.615156i	$0.210907\pi$
$947$	−6.49342	+	19.9847i	−0.211008	+	0.649415i	−0.999413	+	0.0342591i	$0.989093\pi$
$948$		0			0
$949$	61.7984			2.00606
$950$		0			0
$951$	21.8328			0.707978
$952$		0			0
$953$	2.84752	−	8.76378i	0.0922404	−	0.283887i	−0.894284	−	0.447499i	$-0.852315\pi$
$953$	2.84752	−	8.76378i	0.0922404	−	0.283887i	0.986525	+	0.163613i	$0.0523147\pi$
$954$		0			0
$955$	9.47214	+	29.1522i	0.306511	+	0.943344i
$956$		0			0
$957$	−47.8885			−1.54802
$958$		0			0
$959$	1.54508	+	1.12257i	0.0498934	+	0.0362497i
$960$		0			0
$961$	−36.2705	+	26.3521i	−1.17002	+	0.850067i
$962$		0			0
$963$	5.32624	+	3.86974i	0.171636	+	0.124701i
$964$		0			0
$965$	−10.3262	−	7.50245i	−0.332413	−	0.241512i
$966$		0			0
$967$	2.61803	+	8.05748i	0.0841903	+	0.259111i	0.984286	−	0.176581i	$-0.0565037\pi$
$967$	2.61803	+	8.05748i	0.0841903	+	0.259111i	−0.900096	+	0.435692i	$0.856504\pi$
$968$		0			0
$969$	2.84095	+	8.74353i	0.0912643	+	0.280883i
$970$		0			0
$971$	−14.6976	+	45.2344i	−0.471667	+	1.45164i	0.378733	+	0.925506i	$0.376360\pi$
$971$	−14.6976	+	45.2344i	−0.471667	+	1.45164i	−0.850400	+	0.526136i	$0.823640\pi$
$972$		0			0
$973$	−4.39919	+	3.19620i	−0.141031	+	0.102465i
$974$		0			0
$975$	50.8156	+	36.9197i	1.62740	+	1.18238i
$976$		0			0
$977$	4.28115	−	3.11044i	0.136966	−	0.0995118i	−0.517192	−	0.855869i	$-0.673023\pi$
$977$	4.28115	−	3.11044i	0.136966	−	0.0995118i	0.654159	+	0.756357i	$0.273023\pi$
$978$		0			0
$979$	4.00000	−	12.3107i	0.127841	−	0.393453i
$980$		0			0
$981$	−9.23607	−	28.4257i	−0.294885	−	0.907563i
$982$		0			0
$983$	6.42705	+	19.7804i	0.204991	+	0.630898i	0.999714	+	0.0239250i	$0.00761629\pi$
$983$	6.42705	+	19.7804i	0.204991	+	0.630898i	−0.794723	+	0.606973i	$0.792384\pi$
$984$		0			0
$985$	34.7984	−	25.2825i	1.10877	−	0.805567i
$986$		0			0
$987$	4.73607	+	3.44095i	0.150751	+	0.109527i
$988$		0			0
$989$	18.5902	−	13.5065i	0.591133	−	0.429483i
$990$		0			0
$991$	−23.3156	−	16.9398i	−0.740644	−	0.538110i	0.152269	−	0.988339i	$-0.451342\pi$
$991$	−23.3156	−	16.9398i	−0.740644	−	0.538110i	−0.892913	+	0.450230i	$0.851342\pi$
$992$		0			0
$993$	−58.2918			−1.84983
$994$		0			0
$995$	21.0172	+	15.2699i	0.666291	+	0.484089i
$996$		0			0
$997$	−14.6697	+	45.1487i	−0.464594	+	1.42987i	0.394899	+	0.918725i	$0.370780\pi$
$997$	−14.6697	+	45.1487i	−0.464594	+	1.42987i	−0.859492	+	0.511148i	$0.829220\pi$
$998$		0			0
$999$	−8.41641			−0.266283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.a.161.1		4
4.3	odd	2		200.2.m.a.161.1	yes	4
20.3	even	4		1000.2.q.a.449.2		8
20.7	even	4		1000.2.q.a.449.1		8
20.19	odd	2		1000.2.m.a.801.1		4
25.4	even	10		10000.2.a.i.1.2		2
25.16	even	5	inner	400.2.u.a.241.1		4
25.21	even	5		10000.2.a.g.1.1		2
100.59	odd	10		1000.2.m.a.201.1		4
100.63	even	20		1000.2.q.a.49.1		8
100.71	odd	10		5000.2.a.c.1.2		2
100.79	odd	10		5000.2.a.a.1.1		2
100.87	even	20		1000.2.q.a.49.2		8
100.91	odd	10		200.2.m.a.41.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.a.41.1	✓	4	100.91	odd	10
200.2.m.a.161.1	yes	4	4.3	odd	2
400.2.u.a.161.1		4	1.1	even	1	trivial
400.2.u.a.241.1		4	25.16	even	5	inner
1000.2.m.a.201.1		4	100.59	odd	10
1000.2.m.a.801.1		4	20.19	odd	2
1000.2.q.a.49.1		8	100.63	even	20
1000.2.q.a.49.2		8	100.87	even	20
1000.2.q.a.449.1		8	20.7	even	4
1000.2.q.a.449.2		8	20.3	even	4
5000.2.a.a.1.1		2	100.79	odd	10
5000.2.a.c.1.2		2	100.71	odd	10
10000.2.a.g.1.1		2	25.21	even	5
10000.2.a.i.1.2		2	25.4	even	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.690983 + 2.12663i) q^{3} +(-1.80902 - 1.31433i) q^{5} -0.381966 q^{7} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(-0.690983 + 2.12663i) q^{3} +(-1.80902 - 1.31433i) q^{5} -0.381966 q^{7} +(-1.61803 - 1.17557i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(-4.54508 - 3.30220i) q^{13} +(4.04508 - 2.93893i) q^{15} +(0.236068 + 0.726543i) q^{17} +(-1.66312 - 5.11855i) q^{19} +(0.263932 - 0.812299i) q^{21} +(-2.80902 + 2.04087i) q^{23} +(1.54508 + 4.75528i) q^{25} +(-1.80902 + 1.31433i) q^{27} +(2.04508 - 6.29412i) q^{29} +(-2.69098 - 8.28199i) q^{31} +(-2.23607 - 6.88191i) q^{33} +(0.690983 + 0.502029i) q^{35} +(3.04508 + 2.21238i) q^{37} +(10.1631 - 7.38394i) q^{39} +(6.23607 + 4.53077i) q^{41} -6.61803 q^{43} +(1.38197 + 4.25325i) q^{45} +(-2.11803 + 6.51864i) q^{47} -6.85410 q^{49} -1.70820 q^{51} +(-3.07295 + 9.45756i) q^{53} +7.23607 q^{55} +12.0344 q^{57} +(3.73607 + 2.71441i) q^{59} +(-7.42705 + 5.39607i) q^{61} +(0.618034 + 0.449028i) q^{63} +(3.88197 + 11.9475i) q^{65} +(-0.0901699 - 0.277515i) q^{67} +(-2.39919 - 7.38394i) q^{69} +(1.97214 - 6.06961i) q^{71} +(-8.89919 + 6.46564i) q^{73} -11.1803 q^{75} +(1.00000 - 0.726543i) q^{77} +(-3.19098 + 9.82084i) q^{79} +(-3.39919 - 10.4616i) q^{81} +(4.16312 + 12.8128i) q^{83} +(0.527864 - 1.62460i) q^{85} +(11.9721 + 8.69827i) q^{87} +(-3.23607 + 2.35114i) q^{89} +(1.73607 + 1.26133i) q^{91} +19.4721 q^{93} +(-3.71885 + 11.4454i) q^{95} +(5.64590 - 17.3763i) q^{97} +6.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{3} - 5 q^{5} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 5 * q^3 - 5 * q^5 - 6 * q^7 - 2 * q^9	\( 4 q - 5 q^{3} - 5 q^{5} - 6 q^{7} - 2 q^{9} - 6 q^{11} - 7 q^{13} + 5 q^{15} - 8 q^{17} + 9 q^{19} + 10 q^{21} - 9 q^{23} - 5 q^{25} - 5 q^{27} - 3 q^{29} - 13 q^{31} + 5 q^{35} + q^{37} + 25 q^{39} + 16 q^{41} - 22 q^{43} + 10 q^{45} - 4 q^{47} - 14 q^{49} + 20 q^{51} - 19 q^{53} + 20 q^{55} - 10 q^{57} + 6 q^{59} - 23 q^{61} - 2 q^{63} + 20 q^{65} + 22 q^{67} + 15 q^{69} - 10 q^{71} - 11 q^{73} + 4 q^{77} - 15 q^{79} + 11 q^{81} + q^{83} + 20 q^{85} + 30 q^{87} - 4 q^{89} - 2 q^{91} + 60 q^{93} - 35 q^{95} + 36 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q - 5 * q^3 - 5 * q^5 - 6 * q^7 - 2 * q^9 - 6 * q^11 - 7 * q^13 + 5 * q^15 - 8 * q^17 + 9 * q^19 + 10 * q^21 - 9 * q^23 - 5 * q^25 - 5 * q^27 - 3 * q^29 - 13 * q^31 + 5 * q^35 + q^37 + 25 * q^39 + 16 * q^41 - 22 * q^43 + 10 * q^45 - 4 * q^47 - 14 * q^49 + 20 * q^51 - 19 * q^53 + 20 * q^55 - 10 * q^57 + 6 * q^59 - 23 * q^61 - 2 * q^63 + 20 * q^65 + 22 * q^67 + 15 * q^69 - 10 * q^71 - 11 * q^73 + 4 * q^77 - 15 * q^79 + 11 * q^81 + q^83 + 20 * q^85 + 30 * q^87 - 4 * q^89 - 2 * q^91 + 60 * q^93 - 35 * q^95 + 36 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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