LMFDB - Embedded newform 400.2.u.d.161.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			161.2
Root			$-0.357358 + 1.86824i$ of defining polynomial
Character	$\chi$	$=$	400.161
Dual form			400.2.u.d.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.720859 - 2.21858i) q^{3} +(-2.02373 + 0.951057i) q^{5} -3.77447 q^{7} +(-1.97539 - 1.43521i) q^{9} +O(q^{10})$	\(q+(0.720859 - 2.21858i) q^{3} +(-2.02373 + 0.951057i) q^{5} -3.77447 q^{7} +(-1.97539 - 1.43521i) q^{9} +(-3.05361 + 2.21858i) q^{11} +(-2.56969 - 1.86699i) q^{13} +(0.651166 + 5.17538i) q^{15} +(-0.430307 - 1.32435i) q^{17} +(-1.20945 - 3.72230i) q^{19} +(-2.72086 + 8.37394i) q^{21} +(0.720859 - 0.523735i) q^{23} +(3.19098 - 3.84937i) q^{25} +(1.05361 - 0.765491i) q^{27} +(0.0152089 - 0.0468081i) q^{29} +(1.72466 + 5.30795i) q^{31} +(2.72086 + 8.37394i) q^{33} +(7.63851 - 3.58973i) q^{35} +(-5.70152 - 4.14240i) q^{37} +(-5.99445 + 4.35522i) q^{39} +(1.20477 + 0.875319i) q^{41} -2.69767 q^{43} +(5.36263 + 1.02576i) q^{45} +(-1.16637 + 3.58973i) q^{47} +7.24660 q^{49} -3.24836 q^{51} +(3.58963 - 11.0477i) q^{53} +(4.06969 - 7.39396i) q^{55} -9.13004 q^{57} +(-0.558282 - 0.405615i) q^{59} +(-8.38168 + 6.08965i) q^{61} +(7.45605 + 5.41714i) q^{63} +(6.97599 + 1.33437i) q^{65} +(-4.73519 - 14.5734i) q^{67} +(-0.642308 - 1.97682i) q^{69} +(2.06969 - 6.36986i) q^{71} +(-4.18158 + 3.03810i) q^{73} +(-6.23987 - 9.85429i) q^{75} +(11.5257 - 8.37394i) q^{77} +(0.558282 - 1.71821i) q^{79} +(-3.20239 - 9.85596i) q^{81} +(3.08023 + 9.47997i) q^{83} +(2.13035 + 2.27088i) q^{85} +(-0.0928839 - 0.0674841i) q^{87} +(-11.7390 + 8.52891i) q^{89} +(9.69922 + 7.04690i) q^{91} +13.0193 q^{93} +(5.98771 + 6.38268i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +9.21619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 4 * q^7 - q^9	$ 8 q + 3 q^{3} - 4 q^{7} - q^{9} - q^{11} - 13 q^{13} + 10 q^{15} - 11 q^{17} - 20 q^{19} - 19 q^{21} + 3 q^{23} + 30 q^{25} - 15 q^{27} - 15 q^{29} + 9 q^{31} + 19 q^{33} + 15 q^{35} - 6 q^{37} + 12 q^{39} - 9 q^{41} - 12 q^{43} + 15 q^{45} + q^{47} - 4 q^{49} - 26 q^{51} + 7 q^{53} + 25 q^{55} - 10 q^{59} + 6 q^{61} + 8 q^{63} - 10 q^{65} + 11 q^{67} + 43 q^{69} + 9 q^{71} - 8 q^{73} - 30 q^{75} + 33 q^{77} + 10 q^{79} - 17 q^{81} - 27 q^{83} + 5 q^{85} - 15 q^{89} - q^{91} - 46 q^{93} + 30 q^{95} - 36 q^{97} + 42 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 4 * q^7 - q^9 - q^11 - 13 * q^13 + 10 * q^15 - 11 * q^17 - 20 * q^19 - 19 * q^21 + 3 * q^23 + 30 * q^25 - 15 * q^27 - 15 * q^29 + 9 * q^31 + 19 * q^33 + 15 * q^35 - 6 * q^37 + 12 * q^39 - 9 * q^41 - 12 * q^43 + 15 * q^45 + q^47 - 4 * q^49 - 26 * q^51 + 7 * q^53 + 25 * q^55 - 10 * q^59 + 6 * q^61 + 8 * q^63 - 10 * q^65 + 11 * q^67 + 43 * q^69 + 9 * q^71 - 8 * q^73 - 30 * q^75 + 33 * q^77 + 10 * q^79 - 17 * q^81 - 27 * q^83 + 5 * q^85 - 15 * q^89 - q^91 - 46 * q^93 + 30 * q^95 - 36 * q^97 + 42 * 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
$3$	0.720859	−	2.21858i	0.416188	−	1.28090i	−0.494996	−	0.868895i	$-0.664830\pi$
$3$	0.720859	−	2.21858i	0.416188	−	1.28090i	0.911184	−	0.412000i	$-0.135170\pi$
$4$		0			0
$5$	−2.02373	+	0.951057i	−0.905040	+	0.425325i
$5$	−2.02373	+	0.951057i	−0.905040	+	0.425325i
$6$		0			0
$7$	−3.77447			−1.42661			−0.713307	−	0.700851i	$-0.752804\pi$
$7$	−3.77447			−1.42661			−0.713307	+	0.700851i	$0.752804\pi$
$8$		0			0
$9$	−1.97539	−	1.43521i	−0.658464	−	0.478402i
$10$		0			0
$11$	−3.05361	+	2.21858i	−0.920698	+	0.668926i	−0.943698	−	0.330810i	$-0.892678\pi$
$11$	−3.05361	+	2.21858i	−0.920698	+	0.668926i	0.0230000	+	0.999735i	$0.492678\pi$
$12$		0			0
$13$	−2.56969	−	1.86699i	−0.712705	−	0.517810i	0.171340	−	0.985212i	$-0.445190\pi$
$13$	−2.56969	−	1.86699i	−0.712705	−	0.517810i	−0.884045	+	0.467402i	$0.845190\pi$
$14$		0			0
$15$	0.651166	+	5.17538i	0.168130	+	1.33628i
$16$		0			0
$17$	−0.430307	−	1.32435i	−0.104365	−	0.321201i	0.885216	−	0.465180i	$-0.154010\pi$
$17$	−0.430307	−	1.32435i	−0.104365	−	0.321201i	−0.989581	+	0.143979i	$0.954010\pi$
$18$		0			0
$19$	−1.20945	−	3.72230i	−0.277466	−	0.853953i	−0.988556	−	0.150852i	$-0.951798\pi$
$19$	−1.20945	−	3.72230i	−0.277466	−	0.853953i	0.711090	−	0.703101i	$-0.248202\pi$
$20$		0			0
$21$	−2.72086	+	8.37394i	−0.593740	+	1.82734i
$22$		0			0
$23$	0.720859	−	0.523735i	0.150310	−	0.109206i	−0.510089	−	0.860122i	$-0.670387\pi$
$23$	0.720859	−	0.523735i	0.150310	−	0.109206i	0.660398	+	0.750916i	$0.270387\pi$
$24$		0			0
$25$	3.19098	−	3.84937i	0.638197	−	0.769873i
$26$		0			0
$27$	1.05361	−	0.765491i	0.202767	−	0.147319i
$28$		0			0
$29$	0.0152089	−	0.0468081i	0.00282422	−	0.00869205i	−0.949634	−	0.313360i	$-0.898545\pi$
$29$	0.0152089	−	0.0468081i	0.00282422	−	0.00869205i	0.952459	+	0.304668i	$0.0985454\pi$
$30$		0			0
$31$	1.72466	+	5.30795i	0.309757	+	0.953335i	0.977859	+	0.209265i	$0.0671072\pi$
$31$	1.72466	+	5.30795i	0.309757	+	0.953335i	−0.668102	+	0.744070i	$0.732893\pi$
$32$		0			0
$33$	2.72086	+	8.37394i	0.473641	+	1.45772i
$34$		0			0
$35$	7.63851	−	3.58973i	1.29114	−	0.606775i
$36$		0			0
$37$	−5.70152	−	4.14240i	−0.937324	−	0.681006i	0.0104512	−	0.999945i	$-0.496673\pi$
$37$	−5.70152	−	4.14240i	−0.937324	−	0.681006i	−0.947775	+	0.318940i	$0.896673\pi$
$38$		0			0
$39$	−5.99445	+	4.35522i	−0.959880	+	0.697394i
$40$		0			0
$41$	1.20477	+	0.875319i	0.188154	+	0.136702i	0.677875	−	0.735178i	$-0.262901\pi$
$41$	1.20477	+	0.875319i	0.188154	+	0.136702i	−0.489721	+	0.871879i	$0.662901\pi$
$42$		0			0
$43$	−2.69767			−0.411391			−0.205695	−	0.978616i	$-0.565946\pi$
$43$	−2.69767			−0.411391			−0.205695	+	0.978616i	$0.565946\pi$
$44$		0			0
$45$	5.36263	+	1.02576i	0.799413	+	0.152912i
$46$		0			0
$47$	−1.16637	+	3.58973i	−0.170133	+	0.523616i	−0.999378	−	0.0352696i	$-0.988771\pi$
$47$	−1.16637	+	3.58973i	−0.170133	+	0.523616i	0.829245	+	0.558886i	$0.188771\pi$
$48$		0			0
$49$	7.24660			1.03523
$50$		0			0
$51$	−3.24836			−0.454861
$52$		0			0
$53$	3.58963	−	11.0477i	0.493073	−	1.51752i	−0.326864	−	0.945071i	$-0.605992\pi$
$53$	3.58963	−	11.0477i	0.493073	−	1.51752i	0.819938	−	0.572453i	$-0.194008\pi$
$54$		0			0
$55$	4.06969	−	7.39396i	0.548757	−	0.997001i
$56$		0			0
$57$	−9.13004			−1.20930
$58$		0			0
$59$	−0.558282	−	0.405615i	−0.0726821	−	0.0528066i	0.550851	−	0.834604i	$-0.314303\pi$
$59$	−0.558282	−	0.405615i	−0.0726821	−	0.0528066i	−0.623533	+	0.781797i	$0.714303\pi$
$60$		0			0
$61$	−8.38168	+	6.08965i	−1.07316	+	0.779700i	−0.976478	−	0.215615i	$-0.930824\pi$
$61$	−8.38168	+	6.08965i	−1.07316	+	0.779700i	−0.0966862	+	0.995315i	$0.530824\pi$
$62$		0			0
$63$	7.45605	+	5.41714i	0.939374	+	0.682495i
$64$		0			0
$65$	6.97599	+	1.33437i	0.865265	+	0.165508i
$66$		0			0
$67$	−4.73519	−	14.5734i	−0.578496	−	1.78043i	−0.623955	−	0.781461i	$-0.714475\pi$
$67$	−4.73519	−	14.5734i	−0.578496	−	1.78043i	0.0454589	−	0.998966i	$-0.485525\pi$
$68$		0			0
$69$	−0.642308	−	1.97682i	−0.0773248	−	0.237981i
$70$		0			0
$71$	2.06969	−	6.36986i	0.245627	−	0.755963i	−0.749905	−	0.661545i	$-0.769901\pi$
$71$	2.06969	−	6.36986i	0.245627	−	0.755963i	0.995533	−	0.0944182i	$-0.0300991\pi$
$72$		0			0
$73$	−4.18158	+	3.03810i	−0.489417	+	0.355582i	−0.804960	−	0.593329i	$-0.797813\pi$
$73$	−4.18158	+	3.03810i	−0.489417	+	0.355582i	0.315543	+	0.948911i	$0.397813\pi$
$74$		0			0
$75$	−6.23987	−	9.85429i	−0.720518	−	1.13788i
$76$		0			0
$77$	11.5257	−	8.37394i	1.31348	−	0.954299i
$78$		0			0
$79$	0.558282	−	1.71821i	0.0628116	−	0.193314i	−0.914726	−	0.404074i	$-0.867594\pi$
$79$	0.558282	−	1.71821i	0.0628116	−	0.193314i	0.977538	+	0.210760i	$0.0675938\pi$
$80$		0			0
$81$	−3.20239	−	9.85596i	−0.355822	−	1.09511i
$82$		0			0
$83$	3.08023	+	9.47997i	0.338099	+	1.04056i	0.965175	+	0.261604i	$0.0842514\pi$
$83$	3.08023	+	9.47997i	0.338099	+	1.04056i	−0.627076	+	0.778958i	$0.715749\pi$
$84$		0			0
$85$	2.13035	+	2.27088i	0.231069	+	0.246311i
$86$		0			0
$87$	−0.0928839	−	0.0674841i	−0.00995820	−	0.00723505i
$88$		0			0
$89$	−11.7390	+	8.52891i	−1.24434	+	0.904063i	−0.997879	−	0.0650909i	$-0.979266\pi$
$89$	−11.7390	+	8.52891i	−1.24434	+	0.904063i	−0.246457	+	0.969154i	$0.579266\pi$
$90$		0			0
$91$	9.69922	+	7.04690i	1.01675	+	0.738716i
$92$		0			0
$93$	13.0193			1.35004
$94$		0			0
$95$	5.98771	+	6.38268i	0.614326	+	0.654849i
$96$		0			0
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	−0.952461	−	0.304660i	$-0.901457\pi$
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	0.949632	+	0.313367i	$0.101457\pi$
$98$		0			0
$99$	9.21619			0.926261
$100$		0			0
$101$	16.3785			1.62972			0.814859	−	0.579659i	$-0.196814\pi$
$101$	16.3785			1.62972			0.814859	+	0.579659i	$0.196814\pi$
$102$		0			0
$103$	0.375822	−	1.15666i	0.0370308	−	0.113969i	−0.930832	−	0.365446i	$-0.880916\pi$
$103$	0.375822	−	1.15666i	0.0370308	−	0.113969i	0.967863	+	0.251477i	$0.0809163\pi$
$104$		0			0
$105$	−2.45780	−	19.5343i	−0.239857	−	1.90635i
$106$		0			0
$107$	10.8125			1.04528			0.522641	−	0.852553i	$-0.324947\pi$
$107$	10.8125			1.04528			0.522641	+	0.852553i	$0.324947\pi$
$108$		0			0
$109$	−9.23519	−	6.70976i	−0.884571	−	0.642678i	0.0498859	−	0.998755i	$-0.484114\pi$
$109$	−9.23519	−	6.70976i	−0.884571	−	0.642678i	−0.934457	+	0.356077i	$0.884114\pi$
$110$		0			0
$111$	−13.3002	+	9.66317i	−1.26240	+	0.917187i
$112$		0			0
$113$	8.43232	+	6.12644i	0.793246	+	0.576327i	0.908925	−	0.416960i	$-0.136904\pi$
$113$	8.43232	+	6.12644i	0.793246	+	0.576327i	−0.115679	+	0.993287i	$0.536904\pi$
$114$		0			0
$115$	−0.960724	+	1.74548i	−0.0895880	+	0.162767i
$116$		0			0
$117$	2.39663	+	7.37608i	0.221569	+	0.681919i
$118$		0			0
$119$	1.62418	+	4.99871i	0.148888	+	0.458231i
$120$		0			0
$121$	1.00326	−	3.08770i	0.0912051	−	0.280700i
$122$		0			0
$123$	2.81044	−	2.04190i	0.253408	−	0.184112i
$124$		0			0
$125$	−2.79673	+	10.8249i	−0.250147	+	0.968208i
$126$		0			0
$127$	−2.87115	+	2.08601i	−0.254773	+	0.185104i	−0.707840	−	0.706373i	$-0.750330\pi$
$127$	−2.87115	+	2.08601i	−0.254773	+	0.185104i	0.453066	+	0.891477i	$0.350330\pi$
$128$		0			0
$129$	−1.94464	+	5.98498i	−0.171216	+	0.526948i
$130$		0			0
$131$	−1.25252	−	3.85486i	−0.109433	−	0.336801i	0.881312	−	0.472535i	$-0.156661\pi$
$131$	−1.25252	−	3.85486i	−0.109433	−	0.336801i	−0.990745	+	0.135734i	$0.956661\pi$
$132$		0			0
$133$	4.56502	+	14.0497i	0.395837	+	1.21826i
$134$		0			0
$135$	−1.40420	+	2.55119i	−0.120854	+	0.219571i
$136$		0			0
$137$	2.88636	+	2.09706i	0.246598	+	0.179164i	0.704218	−	0.709984i	$-0.251298\pi$
$137$	2.88636	+	2.09706i	0.246598	+	0.179164i	−0.457620	+	0.889148i	$0.651298\pi$
$138$		0			0
$139$	−8.04650	+	5.84613i	−0.682495	+	0.495862i	−0.874185	−	0.485594i	$-0.838603\pi$
$139$	−8.04650	+	5.84613i	−0.682495	+	0.495862i	0.191689	+	0.981456i	$0.438603\pi$
$140$		0			0
$141$	7.12330	+	5.17538i	0.599890	+	0.435846i
$142$		0			0
$143$	11.9889			1.00256
$144$		0			0
$145$	0.0137385	+	0.109192i	0.00114092	+	0.00906786i
$146$		0			0
$147$	5.22378	−	16.0771i	0.430850	−	1.32602i
$148$		0			0
$149$	−19.5103			−1.59834			−0.799171	−	0.601104i	$-0.794728\pi$
$149$	−19.5103			−1.59834			−0.799171	+	0.601104i	$0.794728\pi$
$150$		0			0
$151$	18.4324			1.50001			0.750003	−	0.661435i	$-0.230052\pi$
$151$	18.4324			1.50001			0.750003	+	0.661435i	$0.230052\pi$
$152$		0			0
$153$	−1.05069	+	3.23368i	−0.0849430	+	0.261428i
$154$		0			0
$155$	−8.53840	−	9.10162i	−0.685821	−	0.731059i
$156$		0			0
$157$	10.1564			0.810572			0.405286	−	0.914190i	$-0.367172\pi$
$157$	10.1564			0.810572			0.405286	+	0.914190i	$0.367172\pi$
$158$		0			0
$159$	−21.9226	−	15.9277i	−1.73858	−	1.26315i
$160$		0			0
$161$	−2.72086	+	1.97682i	−0.214434	+	0.155795i
$162$		0			0
$163$	−15.0481	−	10.9331i	−1.17865	−	0.856343i	−0.186636	−	0.982429i	$-0.559758\pi$
$163$	−15.0481	−	10.9331i	−1.17865	−	0.856343i	−0.992019	+	0.126086i	$0.959758\pi$
$164$		0			0
$165$	−13.4704	−	14.3589i	−1.04867	−	1.11784i
$166$		0			0
$167$	−0.671048	−	2.06527i	−0.0519273	−	0.159816i	0.921730	−	0.387832i	$-0.126776\pi$
$167$	−0.671048	−	2.06527i	−0.0519273	−	0.159816i	−0.973657	+	0.228016i	$0.926776\pi$
$168$		0			0
$169$	−0.899554	−	2.76854i	−0.0691965	−	0.212965i
$170$		0			0
$171$	−2.95313	+	9.08880i	−0.225831	+	0.695038i
$172$		0			0
$173$	5.17306	−	3.75845i	0.393300	−	0.285750i	−0.373506	−	0.927628i	$-0.621845\pi$
$173$	5.17306	−	3.75845i	0.393300	−	0.285750i	0.766807	+	0.641878i	$0.221845\pi$
$174$		0			0
$175$	−12.0443	+	14.5293i	−0.910461	+	1.09831i
$176$		0			0
$177$	−1.30233	+	0.946199i	−0.0978892	+	0.0711207i
$178$		0			0
$179$	−2.47630	+	7.62127i	−0.185087	+	0.569640i	−0.999950	−	0.0100140i	$-0.996812\pi$
$179$	−2.47630	+	7.62127i	−0.185087	+	0.569640i	0.814862	+	0.579654i	$0.196812\pi$
$180$		0			0
$181$	−3.35682	−	10.3312i	−0.249510	−	0.767913i	−0.994862	−	0.101242i	$-0.967718\pi$
$181$	−3.35682	−	10.3312i	−0.249510	−	0.767913i	0.745352	−	0.666671i	$-0.232282\pi$
$182$		0			0
$183$	7.46834	+	22.9852i	0.552075	+	1.69911i
$184$		0			0
$185$	15.4780	+	2.96063i	1.13797	+	0.217670i
$186$		0			0
$187$	4.25215	+	3.08937i	0.310948	+	0.225917i
$188$		0			0
$189$	−3.97681	+	2.88932i	−0.289270	+	0.210167i
$190$		0			0
$191$	−6.62243	−	4.81147i	−0.479182	−	0.348146i	0.321827	−	0.946798i	$-0.395703\pi$
$191$	−6.62243	−	4.81147i	−0.479182	−	0.348146i	−0.801009	+	0.598652i	$0.795703\pi$
$192$		0			0
$193$	−17.5576			−1.26382			−0.631912	−	0.775040i	$-0.717730\pi$
$193$	−17.5576			−1.26382			−0.631912	+	0.775040i	$0.717730\pi$
$194$		0			0
$195$	7.98910	−	14.5149i	0.572111	−	1.03943i
$196$		0			0
$197$	1.47012	−	4.52458i	0.104742	−	0.322363i	−0.884928	−	0.465728i	$-0.845792\pi$
$197$	1.47012	−	4.52458i	0.104742	−	0.322363i	0.989670	+	0.143365i	$0.0457924\pi$
$198$		0			0
$199$	−14.5320			−1.03015			−0.515073	−	0.857146i	$-0.672235\pi$
$199$	−14.5320			−1.03015			−0.515073	+	0.857146i	$0.672235\pi$
$200$		0			0
$201$	−35.7457			−2.52130
$202$		0			0
$203$	−0.0574054	+	0.176676i	−0.00402907	+	0.0124002i
$204$		0			0
$205$	−3.27062	−	0.625604i	−0.228430	−	0.0436941i
$206$		0			0
$207$	−2.17565			−0.151218
$208$		0			0
$209$	11.9514	+	8.68318i	0.826694	+	0.600628i
$210$		0			0
$211$	−11.4362	+	8.30886i	−0.787298	+	0.572006i	−0.907160	−	0.420785i	$-0.861755\pi$
$211$	−11.4362	+	8.30886i	−0.787298	+	0.572006i	0.119862	+	0.992791i	$0.461755\pi$
$212$		0			0
$213$	−12.6401	−	9.18355i	−0.866083	−	0.629246i
$214$		0			0
$215$	5.45936	−	2.56564i	0.372325	−	0.174975i
$216$		0			0
$217$	−6.50966	−	20.0347i	−0.441904	−	1.36004i
$218$		0			0
$219$	3.72592	+	11.4672i	0.251774	+	0.774882i
$220$		0			0
$221$	−1.36679	+	4.20655i	−0.0919402	+	0.282963i
$222$		0			0
$223$	3.73139	−	2.71102i	0.249873	−	0.181543i	−0.455798	−	0.890083i	$-0.650646\pi$
$223$	3.73139	−	2.71102i	0.249873	−	0.181543i	0.705670	+	0.708540i	$0.250646\pi$
$224$		0			0
$225$	−11.8281	+	3.02429i	−0.788538	+	0.201619i
$226$		0			0
$227$	−5.08578	+	3.69503i	−0.337555	+	0.245248i	−0.743630	−	0.668592i	$-0.766897\pi$
$227$	−5.08578	+	3.69503i	−0.337555	+	0.245248i	0.406075	+	0.913840i	$0.366897\pi$
$228$		0			0
$229$	5.48103	−	16.8689i	0.362196	−	1.11473i	−0.589522	−	0.807753i	$-0.700684\pi$
$229$	5.48103	−	16.8689i	0.362196	−	1.11473i	0.951718	−	0.306973i	$-0.0993163\pi$
$230$		0			0
$231$	−10.2698	−	31.6072i	−0.675703	−	2.07960i
$232$		0			0
$233$	0.792338	+	2.43856i	0.0519078	+	0.159756i	0.973650	−	0.228047i	$-0.0732341\pi$
$233$	0.792338	+	2.43856i	0.0519078	+	0.159756i	−0.921742	+	0.387803i	$0.873234\pi$
$234$		0			0
$235$	−1.05361	−	8.37394i	−0.0687298	−	0.546256i
$236$		0			0
$237$	−3.40955	−	2.47718i	−0.221474	−	0.160910i
$238$		0			0
$239$	7.63851	−	5.54970i	0.494094	−	0.358980i	−0.312662	−	0.949864i	$-0.601221\pi$
$239$	7.63851	−	5.54970i	0.494094	−	0.358980i	0.806757	+	0.590884i	$0.201221\pi$
$240$		0			0
$241$	23.8131	+	17.3012i	1.53394	+	1.11447i	0.953998	+	0.299812i	$0.0969240\pi$
$241$	23.8131	+	17.3012i	1.53394	+	1.11447i	0.579940	+	0.814659i	$0.303076\pi$
$242$		0			0
$243$	−20.2677			−1.30017
$244$		0			0
$245$	−14.6652	+	6.89193i	−0.936924	+	0.440309i
$246$		0			0
$247$	−3.84159	+	11.8232i	−0.244434	+	0.752292i
$248$		0			0
$249$	23.2524			1.47356
$250$		0			0
$251$	6.00759			0.379196			0.189598	−	0.981862i	$-0.439282\pi$
$251$	6.00759			0.379196			0.189598	+	0.981862i	$0.439282\pi$
$252$		0			0
$253$	−1.03928	+	3.19856i	−0.0653387	+	0.201092i
$254$		0			0
$255$	6.57380	−	3.08937i	0.411667	−	0.193464i
$256$		0			0
$257$	−13.6286			−0.850127			−0.425063	−	0.905164i	$-0.639748\pi$
$257$	−13.6286			−0.850127			−0.425063	+	0.905164i	$0.639748\pi$
$258$		0			0
$259$	21.5202	+	15.6353i	1.33720	+	0.971533i
$260$		0			0
$261$	−0.0972227	+	0.0706365i	−0.00601794	+	0.00437229i
$262$		0			0
$263$	−7.41298	−	5.38584i	−0.457104	−	0.332105i	0.335290	−	0.942115i	$-0.391166\pi$
$263$	−7.41298	−	5.38584i	−0.457104	−	0.332105i	−0.792394	+	0.610010i	$0.791166\pi$
$264$		0			0
$265$	3.24258	+	25.7716i	0.199190	+	1.58314i
$266$		0			0
$267$	10.4598	+	32.1921i	0.640132	+	1.97012i
$268$		0			0
$269$	8.68419	+	26.7272i	0.529484	+	1.62959i	0.755274	+	0.655409i	$0.227504\pi$
$269$	8.68419	+	26.7272i	0.529484	+	1.62959i	−0.225790	+	0.974176i	$0.572496\pi$
$270$		0			0
$271$	2.81162	−	8.65329i	0.170794	−	0.525650i	−0.828623	−	0.559808i	$-0.810875\pi$
$271$	2.81162	−	8.65329i	0.170794	−	0.525650i	0.999416	+	0.0341581i	$0.0108750\pi$
$272$		0			0
$273$	22.6259	−	16.4386i	1.36938	−	0.994912i
$274$		0			0
$275$	−1.20390	+	18.8339i	−0.0725977	+	1.13573i
$276$		0			0
$277$	−15.2006	+	11.0439i	−0.913318	+	0.663564i	−0.941852	−	0.336028i	$-0.890916\pi$
$277$	−15.2006	+	11.0439i	−0.913318	+	0.663564i	0.0285338	+	0.999593i	$0.490916\pi$
$278$		0			0
$279$	4.21112	−	12.9605i	0.252113	−	0.775925i
$280$		0			0
$281$	2.43554	+	7.49583i	0.145292	+	0.447164i	0.997048	−	0.0767748i	$-0.0244622\pi$
$281$	2.43554	+	7.49583i	0.145292	+	0.447164i	−0.851756	+	0.523938i	$0.824462\pi$
$282$		0			0
$283$	5.65496	+	17.4042i	0.336153	+	1.03457i	0.966151	+	0.257975i	$0.0830554\pi$
$283$	5.65496	+	17.4042i	0.336153	+	1.03457i	−0.629999	+	0.776596i	$0.716945\pi$
$284$		0			0
$285$	18.4768	−	8.68318i	1.09447	−	0.514347i
$286$		0			0
$287$	−4.54738	−	3.30386i	−0.268423	−	0.195021i
$288$		0			0
$289$	12.1846	−	8.85260i	0.716739	−	0.520741i
$290$		0			0
$291$	0.170172	+	0.123637i	0.00997564	+	0.00724773i
$292$		0			0
$293$	−29.4990			−1.72335			−0.861675	−	0.507461i	$-0.830584\pi$
$293$	−29.4990			−1.72335			−0.861675	+	0.507461i	$0.830584\pi$
$294$		0			0
$295$	1.51558	+	0.289899i	0.0882402	+	0.0168786i
$296$		0			0
$297$	−1.51901	+	4.67502i	−0.0881417	+	0.271272i
$298$		0			0
$299$	−2.83020			−0.163674
$300$		0			0
$301$	10.1823			0.586896
$302$		0			0
$303$	11.8066	−	36.3369i	0.678269	−	2.08750i
$304$		0			0
$305$	11.1707	−	20.2953i	0.639631	−	1.16210i
$306$		0			0
$307$	−13.9131			−0.794064			−0.397032	−	0.917805i	$-0.629960\pi$
$307$	−13.9131			−0.794064			−0.397032	+	0.917805i	$0.629960\pi$
$308$		0			0
$309$	−2.29523	−	1.66758i	−0.130571	−	0.0948653i
$310$		0			0
$311$	21.0050	−	15.2610i	1.19108	−	0.865373i	0.197705	−	0.980262i	$-0.436651\pi$
$311$	21.0050	−	15.2610i	1.19108	−	0.865373i	0.993378	+	0.114889i	$0.0366512\pi$
$312$		0			0
$313$	−7.66454	−	5.56861i	−0.433225	−	0.314757i	0.349712	−	0.936857i	$-0.386279\pi$
$313$	−7.66454	−	5.56861i	−0.433225	−	0.314757i	−0.782937	+	0.622101i	$0.786279\pi$
$314$		0			0
$315$	−20.2411	−	3.87171i	−1.14045	−	0.218146i
$316$		0			0
$317$	7.57321	+	23.3079i	0.425354	+	1.30910i	0.902655	+	0.430365i	$0.141615\pi$
$317$	7.57321	+	23.3079i	0.425354	+	1.30910i	−0.477301	+	0.878740i	$0.658385\pi$
$318$		0			0
$319$	0.0574054	+	0.176676i	0.00321408	+	0.00989194i
$320$		0			0
$321$	7.79427	−	23.9883i	0.435034	−	1.33890i
$322$		0			0
$323$	−4.40918	+	3.20346i	−0.245333	+	0.178245i
$324$		0			0
$325$	−15.3866	+	3.93416i	−0.853494	+	0.218228i
$326$		0			0
$327$	−21.5434	+	15.6522i	−1.19135	+	0.865568i
$328$		0			0
$329$	4.40244	−	13.5493i	0.242715	−	0.746998i
$330$		0			0
$331$	3.06247	+	9.42530i	0.168328	+	0.518061i	0.999266	−	0.0383039i	$-0.0121955\pi$
$331$	3.06247	+	9.42530i	0.168328	+	0.518061i	−0.830938	+	0.556365i	$0.812196\pi$
$332$		0			0
$333$	5.31754	+	16.3657i	0.291399	+	0.896835i
$334$		0			0
$335$	23.4429	+	24.9893i	1.28082	+	1.36531i
$336$		0			0
$337$	8.03812	+	5.84003i	0.437864	+	0.318127i	0.784786	−	0.619767i	$-0.212773\pi$
$337$	8.03812	+	5.84003i	0.437864	+	0.318127i	−0.346922	+	0.937894i	$0.612773\pi$
$338$		0			0
$339$	19.6705	−	14.2914i	1.06835	−	0.776205i
$340$		0			0
$341$	−17.0425	−	12.3821i	−0.922904	−	0.670529i
$342$		0			0
$343$	−0.930796			−0.0502583
$344$		0			0
$345$	3.17993	+	3.38968i	0.171201	+	0.182494i
$346$		0			0
$347$	6.06757	−	18.6741i	0.325724	−	1.00248i	−0.645388	−	0.763855i	$-0.723304\pi$
$347$	6.06757	−	18.6741i	0.325724	−	1.00248i	0.971113	−	0.238622i	$-0.0766956\pi$
$348$		0			0
$349$	1.48432			0.0794538			0.0397269	−	0.999211i	$-0.487351\pi$
$349$	1.48432			0.0794538			0.0397269	+	0.999211i	$0.487351\pi$
$350$		0			0
$351$	−4.13662			−0.220796
$352$		0			0
$353$	3.17632	−	9.77569i	0.169058	−	0.520308i	−0.830254	−	0.557385i	$-0.811805\pi$
$353$	3.17632	−	9.77569i	0.169058	−	0.520308i	0.999312	+	0.0370772i	$0.0118048\pi$
$354$		0			0
$355$	1.86959	+	14.8593i	0.0992277	+	0.788649i
$356$		0			0
$357$	12.2608			0.648911
$358$		0			0
$359$	−8.39154	−	6.09681i	−0.442889	−	0.321777i	0.343893	−	0.939009i	$-0.388254\pi$
$359$	−8.39154	−	6.09681i	−0.442889	−	0.321777i	−0.786782	+	0.617231i	$0.788254\pi$
$360$		0			0
$361$	2.97859	−	2.16408i	0.156768	−	0.113899i
$362$		0			0
$363$	−6.12710	−	4.45160i	−0.321589	−	0.233648i
$364$		0			0
$365$	5.57300	−	10.1252i	0.291704	−	0.529978i
$366$		0			0
$367$	−8.05741	−	24.7981i	−0.420593	−	1.29445i	−0.907151	−	0.420804i	$-0.861748\pi$
$367$	−8.05741	−	24.7981i	−0.420593	−	1.29445i	0.486558	−	0.873648i	$-0.338252\pi$
$368$		0			0
$369$	−1.12364	−	3.45820i	−0.0584942	−	0.180027i
$370$		0			0
$371$	−13.5489	+	41.6993i	−0.703426	+	2.16492i
$372$		0			0
$373$	−7.65001	+	5.55806i	−0.396102	+	0.287785i	−0.767952	−	0.640508i	$-0.778724\pi$
$373$	−7.65001	+	5.55806i	−0.396102	+	0.287785i	0.371849	+	0.928293i	$0.378724\pi$
$374$		0			0
$375$	21.9998	+	14.0080i	1.13606	+	0.723369i
$376$		0			0
$377$	−0.126472	+	0.0918876i	−0.00651366	+	0.00473245i
$378$		0			0
$379$	10.9163	−	33.5968i	0.560731	−	1.72575i	−0.119576	−	0.992825i	$-0.538154\pi$
$379$	10.9163	−	33.5968i	0.560731	−	1.72575i	0.680307	−	0.732927i	$-0.261846\pi$
$380$		0			0
$381$	2.55828	+	7.87358i	0.131065	+	0.403376i
$382$		0			0
$383$	−9.21407	−	28.3580i	−0.470817	−	1.44902i	−0.851517	−	0.524327i	$-0.824317\pi$
$383$	−9.21407	−	28.3580i	−0.470817	−	1.44902i	0.380700	−	0.924698i	$-0.375683\pi$
$384$		0			0
$385$	−15.3609	+	27.9083i	−0.782865	+	1.42234i
$386$		0			0
$387$	5.32895	+	3.87171i	0.270886	+	0.196810i
$388$		0			0
$389$	17.2942	−	12.5649i	0.876848	−	0.637068i	−0.0555675	−	0.998455i	$-0.517697\pi$
$389$	17.2942	−	12.5649i	0.876848	−	0.637068i	0.932416	+	0.361387i	$0.117697\pi$
$390$		0			0
$391$	−1.00380	−	0.729301i	−0.0507642	−	0.0368824i
$392$		0			0
$393$	−9.45519			−0.476951
$394$		0			0
$395$	0.504306	+	4.00816i	0.0253744	+	0.201673i
$396$		0			0
$397$	6.49555	−	19.9913i	0.326002	−	1.00333i	−0.644984	−	0.764196i	$-0.723136\pi$
$397$	6.49555	−	19.9913i	0.326002	−	1.00333i	0.970986	−	0.239136i	$-0.0768642\pi$
$398$		0			0
$399$	34.4610			1.72521
$400$		0			0
$401$	16.7820			0.838053			0.419026	−	0.907974i	$-0.362371\pi$
$401$	16.7820			0.838053			0.419026	+	0.907974i	$0.362371\pi$
$402$		0			0
$403$	5.47805	−	16.8597i	0.272881	−	0.839842i
$404$		0			0
$405$	15.8544	+	16.9002i	0.787810	+	0.839776i
$406$		0			0
$407$	26.6004			1.31853
$408$		0			0
$409$	−29.4165	−	21.3723i	−1.45455	−	1.05679i	−0.984741	−	0.174025i	$-0.944323\pi$
$409$	−29.4165	−	21.3723i	−1.45455	−	1.05679i	−0.469809	−	0.882768i	$-0.655677\pi$
$410$		0			0
$411$	6.73315	−	4.89192i	0.332122	−	0.241301i
$412$		0			0
$413$	2.10722	+	1.53098i	0.103689	+	0.0753347i
$414$		0			0
$415$	−15.2495	−	16.2554i	−0.748571	−	0.797948i
$416$		0			0
$417$	7.16968	+	22.0660i	0.351101	+	1.08058i
$418$		0			0
$419$	10.6731	+	32.8484i	0.521415	+	1.60475i	0.771298	+	0.636474i	$0.219608\pi$
$419$	10.6731	+	32.8484i	0.521415	+	1.60475i	−0.249884	+	0.968276i	$0.580392\pi$
$420$		0			0
$421$	3.00798	−	9.25762i	0.146600	−	0.451189i	−0.850613	−	0.525792i	$-0.823769\pi$
$421$	3.00798	−	9.25762i	0.146600	−	0.451189i	0.997213	+	0.0746033i	$0.0237691\pi$
$422$		0			0
$423$	7.45605	−	5.41714i	0.362526	−	0.263390i
$424$		0			0
$425$	−6.47100	−	2.56956i	−0.313890	−	0.124642i
$426$		0			0
$427$	31.6364	−	22.9852i	1.53099	−	1.11233i
$428$		0			0
$429$	8.64231	−	26.5983i	0.417255	−	1.28418i
$430$		0			0
$431$	0.956560	+	2.94399i	0.0460759	+	0.141807i	0.971448	−	0.237254i	$-0.0762472\pi$
$431$	0.956560	+	2.94399i	0.0460759	+	0.141807i	−0.925372	+	0.379061i	$0.876247\pi$
$432$		0			0
$433$	−5.63542	−	17.3440i	−0.270821	−	0.833501i	−0.990295	−	0.138981i	$-0.955617\pi$
$433$	−5.63542	−	17.3440i	−0.270821	−	0.833501i	0.719474	−	0.694519i	$-0.244383\pi$
$434$		0			0
$435$	0.252153	+	0.0482319i	0.0120898	+	0.00231254i
$436$		0			0
$437$	−2.82134	−	2.04982i	−0.134963	−	0.0980563i
$438$		0			0
$439$	−21.4595	+	15.5912i	−1.02421	+	0.744129i	−0.967141	−	0.254242i	$-0.918174\pi$
$439$	−21.4595	+	15.5912i	−1.02421	+	0.744129i	−0.0570645	+	0.998370i	$0.518174\pi$
$440$		0			0
$441$	−14.3149	−	10.4004i	−0.681661	−	0.495256i
$442$		0			0
$443$	−35.5267			−1.68793			−0.843963	−	0.536401i	$-0.819783\pi$
$443$	−35.5267			−1.68793			−0.843963	+	0.536401i	$0.819783\pi$
$444$		0			0
$445$	15.6452	−	28.4247i	0.741653	−	1.34746i
$446$		0			0
$447$	−14.0641	+	43.2850i	−0.665211	+	2.04731i
$448$		0			0
$449$	16.1841			0.763776			0.381888	−	0.924209i	$-0.375274\pi$
$449$	16.1841			0.763776			0.381888	+	0.924209i	$0.375274\pi$
$450$		0			0
$451$	−5.62087			−0.264676
$452$		0			0
$453$	13.2871	−	40.8936i	0.624284	−	1.92135i
$454$		0			0
$455$	−26.3306	−	5.03652i	−1.23440	−	0.236116i
$456$		0			0
$457$	23.7205			1.10960			0.554799	−	0.831984i	$-0.312795\pi$
$457$	23.7205			1.10960			0.554799	+	0.831984i	$0.312795\pi$
$458$		0			0
$459$	−1.46715	−	1.06595i	−0.0684807	−	0.0497542i
$460$		0			0
$461$	6.36936	−	4.62761i	0.296651	−	0.215529i	−0.429497	−	0.903068i	$-0.641309\pi$
$461$	6.36936	−	4.62761i	0.296651	−	0.215529i	0.726147	+	0.687539i	$0.241309\pi$
$462$		0			0
$463$	12.4775	+	9.06543i	0.579878	+	0.421306i	0.838680	−	0.544624i	$-0.183328\pi$
$463$	12.4775	+	9.06543i	0.579878	+	0.421306i	−0.258802	+	0.965930i	$0.583328\pi$
$464$		0			0
$465$	−26.3476	+	12.3821i	−1.22184	+	0.574206i
$466$		0			0
$467$	5.26481	+	16.2034i	0.243626	+	0.749805i	0.995859	+	0.0909075i	$0.0289768\pi$
$467$	5.26481	+	16.2034i	0.243626	+	0.749805i	−0.752233	+	0.658897i	$0.771023\pi$
$468$		0			0
$469$	17.8728	+	55.0069i	0.825290	+	2.53998i
$470$		0			0
$471$	7.32136	−	22.5328i	0.337350	−	1.03826i
$472$		0			0
$473$	8.23762	−	5.98498i	0.378766	−	0.275190i
$474$		0			0
$475$	−18.1878	−	7.22218i	−0.834514	−	0.331376i
$476$		0			0
$477$	−22.9467	+	16.6718i	−1.05066	+	0.763347i
$478$		0			0
$479$	7.75544	−	23.8688i	0.354355	−	1.09059i	−0.602027	−	0.798476i	$-0.705640\pi$
$479$	7.75544	−	23.8688i	0.354355	−	1.09059i	0.956382	−	0.292118i	$-0.0943598\pi$
$480$		0			0
$481$	6.91734	+	21.2894i	0.315403	+	0.970712i
$482$		0			0
$483$	2.42437	+	7.46144i	0.110313	+	0.339507i
$484$		0			0
$485$	−0.0251701	−	0.200049i	−0.00114292	−	0.00908375i
$486$		0			0
$487$	−11.0735	−	8.04536i	−0.501788	−	0.364570i	0.307912	−	0.951415i	$-0.400370\pi$
$487$	−11.0735	−	8.04536i	−0.501788	−	0.364570i	−0.809699	+	0.586845i	$0.800370\pi$
$488$		0			0
$489$	−35.1033	+	25.5041i	−1.58743	+	1.15333i
$490$		0			0
$491$	−2.08733	−	1.51654i	−0.0942001	−	0.0684403i	0.539688	−	0.841865i	$-0.318542\pi$
$491$	−2.08733	−	1.51654i	−0.0942001	−	0.0684403i	−0.633888	+	0.773425i	$0.718542\pi$
$492$		0			0
$493$	−0.0685347			−0.00308665
$494$		0			0
$495$	−18.6511	+	8.76511i	−0.838304	+	0.393963i
$496$		0			0
$497$	−7.81199	+	24.0428i	−0.350416	+	1.07847i
$498$		0			0
$499$	39.0539			1.74829			0.874146	−	0.485664i	$-0.161422\pi$
$499$	39.0539			1.74829			0.874146	+	0.485664i	$0.161422\pi$
$500$		0			0
$501$	−5.06570			−0.226319
$502$		0			0
$503$	−3.69387	+	11.3686i	−0.164702	+	0.506899i	−0.999014	−	0.0443923i	$-0.985865\pi$
$503$	−3.69387	+	11.3686i	−0.164702	+	0.506899i	0.834313	+	0.551292i	$0.185865\pi$
$504$		0			0
$505$	−33.1456	+	15.5768i	−1.47496	+	0.693160i
$506$		0			0
$507$	−6.79067			−0.301584
$508$		0			0
$509$	3.94254	+	2.86442i	0.174750	+	0.126963i	0.671722	−	0.740803i	$-0.265555\pi$
$509$	3.94254	+	2.86442i	0.174750	+	0.126963i	−0.496972	+	0.867767i	$0.665555\pi$
$510$		0			0
$511$	15.7832	−	11.4672i	0.698210	−	0.507279i
$512$		0			0
$513$	−4.12367	−	2.99602i	−0.182064	−	0.132278i
$514$		0			0
$515$	0.339487	+	2.69820i	0.0149596	+	0.118897i
$516$		0			0
$517$	−4.40244	−	13.5493i	−0.193619	−	0.595899i
$518$		0			0
$519$	−4.60936	−	14.1861i	−0.202328	−	0.622702i
$520$		0			0
$521$	−2.70131	+	8.31378i	−0.118347	+	0.364233i	−0.992630	−	0.121182i	$-0.961332\pi$
$521$	−2.70131	+	8.31378i	−0.118347	+	0.364233i	0.874284	+	0.485415i	$0.161332\pi$
$522$		0			0
$523$	−17.0534	+	12.3900i	−0.745694	+	0.541778i	−0.894489	−	0.447090i	$-0.852460\pi$
$523$	−17.0534	+	12.3900i	−0.745694	+	0.541778i	0.148795	+	0.988868i	$0.452460\pi$
$524$		0			0
$525$	23.5522	+	37.1947i	1.02790	+	1.62331i
$526$		0			0
$527$	6.28743	−	4.56809i	0.273885	−	0.198989i
$528$		0			0
$529$	−6.86205	+	21.1192i	−0.298350	+	0.918227i
$530$		0			0
$531$	0.520683	+	1.60250i	0.0225957	+	0.0695425i
$532$		0			0
$533$	−1.46169	−	4.49861i	−0.0633126	−	0.194856i
$534$		0			0
$535$	−21.8816	+	10.2833i	−0.946022	+	0.444585i
$536$		0			0
$537$	15.1233	+	10.9877i	0.652619	+	0.474155i
$538$		0			0
$539$	−22.1283	+	16.0771i	−0.953133	+	0.692492i
$540$		0			0
$541$	−26.5406	−	19.2829i	−1.14107	−	0.829036i	−0.153802	−	0.988102i	$-0.549152\pi$
$541$	−26.5406	−	19.2829i	−1.14107	−	0.829036i	−0.987268	+	0.159066i	$0.949152\pi$
$542$		0			0
$543$	−25.3404			−1.08746
$544$		0			0
$545$	25.0709	+	4.79557i	1.07392	+	0.205419i
$546$		0			0
$547$	1.69044	−	5.20264i	0.0722781	−	0.222449i	−0.908391	−	0.418121i	$-0.862689\pi$
$547$	1.69044	−	5.20264i	0.0722781	−	0.222449i	0.980669	+	0.195672i	$0.0626888\pi$
$548$		0			0
$549$	25.2970			1.07965
$550$		0			0
$551$	−0.192628			−0.00820623
$552$		0			0
$553$	−2.10722	+	6.48535i	−0.0896080	+	0.275785i
$554$		0			0
$555$	17.7258	−	32.2049i	0.752420	−	1.36702i
$556$		0			0
$557$	−5.19840			−0.220263			−0.110132	−	0.993917i	$-0.535127\pi$
$557$	−5.19840			−0.220263			−0.110132	+	0.993917i	$0.535127\pi$
$558$		0			0
$559$	6.93218	+	5.03652i	0.293200	+	0.213022i
$560$		0			0
$561$	9.91921	−	7.20673i	0.418789	−	0.304268i
$562$		0			0
$563$	−4.05741	−	2.94788i	−0.170999	−	0.124238i	0.498994	−	0.866605i	$-0.333703\pi$
$563$	−4.05741	−	2.94788i	−0.170999	−	0.124238i	−0.669993	+	0.742367i	$0.733703\pi$
$564$		0			0
$565$	−22.8913	−	4.37866i	−0.963046	−	0.184212i
$566$		0			0
$567$	12.0873	+	37.2010i	0.507620	+	1.56229i
$568$		0			0
$569$	−12.9303	−	39.7952i	−0.542064	−	1.66830i	−0.727869	−	0.685716i	$-0.759489\pi$
$569$	−12.9303	−	39.7952i	−0.542064	−	1.66830i	0.185805	−	0.982587i	$-0.440511\pi$
$570$		0			0
$571$	13.7723	−	42.3869i	0.576355	−	1.77384i	−0.0551642	−	0.998477i	$-0.517568\pi$
$571$	13.7723	−	42.3869i	0.576355	−	1.77384i	0.631519	−	0.775360i	$-0.282432\pi$
$572$		0			0
$573$	−15.4485	+	11.2240i	−0.645369	+	0.468888i
$574$		0			0
$575$	0.284202	−	4.44608i	0.0118520	−	0.185414i
$576$		0			0
$577$	20.3401	−	14.7779i	0.846769	−	0.615213i	−0.0774845	−	0.996994i	$-0.524689\pi$
$577$	20.3401	−	14.7779i	0.846769	−	0.615213i	0.924253	+	0.381780i	$0.124689\pi$
$578$		0			0
$579$	−12.6566	+	38.9529i	−0.525989	+	1.61883i
$580$		0			0
$581$	−11.6262	−	35.7818i	−0.482337	−	1.48448i
$582$		0			0
$583$	13.5489	+	41.6993i	0.561140	+	1.72701i
$584$		0			0
$585$	−11.8652	−	12.6479i	−0.490566	−	0.522925i
$586$		0			0
$587$	17.2770	+	12.5525i	0.713099	+	0.518097i	0.884172	−	0.467162i	$-0.154723\pi$
$587$	17.2770	+	12.5525i	0.713099	+	0.518097i	−0.171073	+	0.985258i	$0.554723\pi$
$588$		0			0
$589$	17.6719	−	12.8394i	0.728157	−	0.529037i
$590$		0			0
$591$	−8.97836	−	6.52316i	−0.369321	−	0.268327i
$592$		0			0
$593$	−33.4430			−1.37334			−0.686669	−	0.726970i	$-0.740928\pi$
$593$	−33.4430			−1.37334			−0.686669	+	0.726970i	$0.740928\pi$
$594$		0			0
$595$	−8.04095	−	8.57136i	−0.329647	−	0.351391i
$596$		0			0
$597$	−10.4755	+	32.2403i	−0.428734	+	1.31951i
$598$		0			0
$599$	−26.3174			−1.07530			−0.537650	−	0.843168i	$-0.680688\pi$
$599$	−26.3174			−1.07530			−0.537650	+	0.843168i	$0.680688\pi$
$600$		0			0
$601$	20.9964			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$601$	20.9964			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$602$		0			0
$603$	−11.5620	+	35.5842i	−0.470841	+	1.44910i
$604$		0			0
$605$	0.906260	+	7.20284i	0.0368447	+	0.292837i
$606$		0			0
$607$	−9.32822			−0.378621			−0.189310	−	0.981917i	$-0.560625\pi$
$607$	−9.32822			−0.378621			−0.189310	+	0.981917i	$0.560625\pi$
$608$		0			0
$609$	0.350587	+	0.254716i	0.0142065	+	0.0103216i
$610$		0			0
$611$	9.69922	−	7.04690i	0.392389	−	0.285087i
$612$		0			0
$613$	25.9724	+	18.8700i	1.04902	+	0.762154i	0.972025	−	0.234878i	$-0.0754690\pi$
$613$	25.9724	+	18.8700i	1.04902	+	0.762154i	0.0769902	+	0.997032i	$0.475469\pi$
$614$		0			0
$615$	−3.74560	+	6.80514i	−0.151037	+	0.274410i
$616$		0			0
$617$	−9.86557	−	30.3631i	−0.397173	−	1.22237i	−0.927257	−	0.374427i	$-0.877840\pi$
$617$	−9.86557	−	30.3631i	−0.397173	−	1.22237i	0.530084	−	0.847945i	$-0.322160\pi$
$618$		0			0
$619$	1.40420	+	4.32167i	0.0564394	+	0.173703i	0.975302	−	0.220875i	$-0.0708911\pi$
$619$	1.40420	+	4.32167i	0.0564394	+	0.173703i	−0.918863	+	0.394577i	$0.870891\pi$
$620$		0			0
$621$	0.358589	−	1.10362i	0.0143897	−	0.0442868i
$622$		0			0
$623$	44.3086	−	32.1921i	1.77519	−	1.28975i
$624$		0			0
$625$	−4.63525	−	24.5665i	−0.185410	−	0.982661i
$626$		0			0
$627$	27.8796	−	20.2557i	1.11340	−	0.808934i
$628$		0			0
$629$	−3.03257	+	9.33329i	−0.120916	+	0.372143i
$630$		0			0
$631$	8.31756	+	25.5988i	0.331117	+	1.01907i	0.968603	+	0.248611i	$0.0799742\pi$
$631$	8.31756	+	25.5988i	0.331117	+	1.01907i	−0.637486	+	0.770462i	$0.720026\pi$
$632$		0			0
$633$	10.1900	+	31.3615i	0.405015	+	1.24651i
$634$		0			0
$635$	3.82652	−	6.95215i	0.151851	−	0.275888i
$636$		0			0
$637$	−18.6215	−	13.5293i	−0.737813	−	0.536052i
$638$		0			0
$639$	−13.2305	+	9.61253i	−0.523391	+	0.380266i
$640$		0			0
$641$	−28.9303	−	21.0191i	−1.14268	−	0.830205i	−0.155189	−	0.987885i	$-0.549599\pi$
$641$	−28.9303	−	21.0191i	−1.14268	−	0.830205i	−0.987490	+	0.157679i	$0.949599\pi$
$642$		0			0
$643$	−28.2255			−1.11311			−0.556553	−	0.830812i	$-0.687876\pi$
$643$	−28.2255			−1.11311			−0.556553	+	0.830812i	$0.687876\pi$
$644$		0			0
$645$	−1.75663	−	13.9615i	−0.0691672	−	0.549732i
$646$		0			0
$647$	−0.394848	+	1.21522i	−0.0155231	+	0.0477751i	−0.958518	−	0.285032i	$-0.907996\pi$
$647$	−0.394848	+	1.21522i	−0.0155231	+	0.0477751i	0.942995	+	0.332807i	$0.107996\pi$
$648$		0			0
$649$	2.60466			0.102242
$650$		0			0
$651$	−49.1410			−1.92599
$652$		0			0
$653$	−8.47040	+	26.0692i	−0.331472	+	1.02017i	0.636961	+	0.770896i	$0.280191\pi$
$653$	−8.47040	+	26.0692i	−0.331472	+	1.02017i	−0.968434	+	0.249272i	$0.919809\pi$
$654$		0			0
$655$	6.20096	+	6.60999i	0.242291	+	0.258274i
$656$		0			0
$657$	12.6206			0.492375
$658$		0			0
$659$	−33.3535	−	24.2327i	−1.29927	−	0.943972i	−0.299318	−	0.954153i	$-0.596759\pi$
$659$	−33.3535	−	24.2327i	−1.29927	−	0.943972i	−0.999948	+	0.0101814i	$0.996759\pi$
$660$		0			0
$661$	21.4653	−	15.5955i	0.834904	−	0.606593i	−0.0860388	−	0.996292i	$-0.527421\pi$
$661$	21.4653	−	15.5955i	0.834904	−	0.606593i	0.920942	+	0.389699i	$0.127421\pi$
$662$		0			0
$663$	8.34728	+	6.06465i	0.324181	+	0.235532i
$664$		0			0
$665$	−22.6004	−	24.0912i	−0.876407	−	0.934217i
$666$		0			0
$667$	−0.0135516	−	0.0417075i	−0.000524719	−	0.00161492i
$668$		0			0
$669$	−3.32479	−	10.2326i	−0.128544	−	0.395617i
$670$		0			0
$671$	12.0840	−	37.1908i	0.466499	−	1.43574i
$672$		0			0
$673$	6.42142	−	4.66543i	0.247527	−	0.179839i	−0.457103	−	0.889414i	$-0.651113\pi$
$673$	6.42142	−	4.66543i	0.247527	−	0.179839i	0.704630	+	0.709575i	$0.251113\pi$
$674$		0			0
$675$	0.415389	−	6.49839i	0.0159883	−	0.250123i
$676$		0			0
$677$	−23.8667	+	17.3402i	−0.917271	+	0.666436i	−0.942843	−	0.333237i	$-0.891859\pi$
$677$	−23.8667	+	17.3402i	−0.917271	+	0.666436i	0.0255722	+	0.999673i	$0.491859\pi$
$678$		0			0
$679$	0.105172	−	0.323686i	0.00403613	−	0.0124219i
$680$		0			0
$681$	4.53159	+	13.9468i	0.173651	+	0.534442i
$682$		0			0
$683$	−11.6650	−	35.9012i	−0.446349	−	1.37372i	−0.880997	−	0.473121i	$-0.843127\pi$
$683$	−11.6650	−	35.9012i	−0.446349	−	1.37372i	0.434648	−	0.900600i	$-0.356873\pi$
$684$		0			0
$685$	−7.83564	−	1.49880i	−0.299384	−	0.0572663i
$686$		0			0
$687$	−33.4738	−	24.3201i	−1.27711	−	0.927872i
$688$		0			0
$689$	−29.8503	+	21.6875i	−1.13721	+	0.826228i
$690$		0			0
$691$	14.2843	+	10.3782i	0.543401	+	0.394804i	0.825347	−	0.564626i	$-0.190980\pi$
$691$	14.2843	+	10.3782i	0.543401	+	0.394804i	−0.281945	+	0.959430i	$0.590980\pi$
$692$		0			0
$693$	−34.7862			−1.32142
$694$		0			0
$695$	10.7240	−	19.4837i	0.406783	−	0.739058i
$696$		0			0
$697$	0.640805	−	1.97219i	0.0242722	−	0.0747022i
$698$		0			0
$699$	5.98131			0.226234
$700$		0			0
$701$	−16.8372			−0.635931			−0.317965	−	0.948102i	$-0.603000\pi$
$701$	−16.8372			−0.635931			−0.317965	+	0.948102i	$0.603000\pi$
$702$		0			0
$703$	−8.52354	+	26.2328i	−0.321471	+	0.989387i
$704$		0			0
$705$	−19.3377	−	3.69892i	−0.728301	−	0.139310i
$706$		0			0
$707$	−61.8200			−2.32498
$708$		0			0
$709$	23.1615	+	16.8278i	0.869849	+	0.631982i	0.930546	−	0.366174i	$-0.119333\pi$
$709$	23.1615	+	16.8278i	0.869849	+	0.631982i	−0.0606978	+	0.998156i	$0.519333\pi$
$710$		0			0
$711$	−3.56882	+	2.59290i	−0.133841	+	0.0972412i
$712$		0			0
$713$	4.02319	+	2.92302i	0.150670	+	0.109468i
$714$		0			0
$715$	−24.2623	+	11.4021i	−0.907359	+	0.426415i
$716$		0			0
$717$	−6.80615	−	20.9472i	−0.254180	−	0.782286i
$718$		0			0
$719$	2.54857	+	7.84368i	0.0950455	+	0.292520i	0.987266	−	0.159081i	$-0.0508531\pi$
$719$	2.54857	+	7.84368i	0.0950455	+	0.292520i	−0.892220	+	0.451601i	$0.850853\pi$
$720$		0			0
$721$	−1.41853	+	4.36578i	−0.0528287	+	0.162590i
$722$		0			0
$723$	55.5500	−	40.3595i	2.06593	−	1.50098i
$724$		0			0
$725$	−0.131650	−	0.207908i	−0.00488937	−	0.00772152i
$726$		0			0
$727$	−1.71013	+	1.24248i	−0.0634251	+	0.0460810i	−0.619046	−	0.785355i	$-0.712481\pi$
$727$	−1.71013	+	1.24248i	−0.0634251	+	0.0460810i	0.555621	+	0.831436i	$0.312481\pi$
$728$		0			0
$729$	−5.00295	+	15.3975i	−0.185295	+	0.570278i
$730$		0			0
$731$	1.16082	+	3.57265i	0.0429346	+	0.132139i
$732$		0			0
$733$	13.9537	+	42.9451i	0.515393	+	1.58622i	0.782567	+	0.622567i	$0.213910\pi$
$733$	13.9537	+	42.9451i	0.515393	+	1.58622i	−0.267174	+	0.963648i	$0.586090\pi$
$734$		0			0
$735$	4.71874	+	37.5039i	0.174053	+	1.38335i
$736$		0			0
$737$	46.7917	+	33.9961i	1.72359	+	1.25226i
$738$		0			0
$739$	24.2478	−	17.6171i	0.891969	−	0.648054i	−0.0444213	−	0.999013i	$-0.514144\pi$
$739$	24.2478	−	17.6171i	0.891969	−	0.648054i	0.936391	+	0.350959i	$0.114144\pi$
$740$		0			0
$741$	23.4614	+	17.0457i	0.861876	+	0.626190i
$742$		0			0
$743$	−17.6562			−0.647741			−0.323871	−	0.946101i	$-0.604984\pi$
$743$	−17.6562			−0.647741			−0.323871	+	0.946101i	$0.604984\pi$
$744$		0			0
$745$	39.4835	−	18.5554i	1.44656	−	0.679816i
$746$		0			0
$747$	7.52105	−	23.1474i	0.275181	−	0.846920i
$748$		0			0
$749$	−40.8113			−1.49121
$750$		0			0
$751$	−30.1342			−1.09961			−0.549806	−	0.835293i	$-0.685298\pi$
$751$	−30.1342			−1.09961			−0.549806	+	0.835293i	$0.685298\pi$
$752$		0			0
$753$	4.33063	−	13.3283i	0.157817	−	0.485710i
$754$		0			0
$755$	−37.3022	+	17.5302i	−1.35757	+	0.637990i
$756$		0			0
$757$	−4.90706			−0.178350			−0.0891750	−	0.996016i	$-0.528423\pi$
$757$	−4.90706			−0.178350			−0.0891750	+	0.996016i	$0.528423\pi$
$758$		0			0
$759$	6.34708	+	4.61142i	0.230384	+	0.167384i
$760$		0			0
$761$	−10.7466	+	7.80786i	−0.389564	+	0.283035i	−0.765277	−	0.643701i	$-0.777398\pi$
$761$	−10.7466	+	7.80786i	−0.389564	+	0.283035i	0.375713	+	0.926736i	$0.377398\pi$
$762$		0			0
$763$	34.8579	+	25.3258i	1.26194	+	0.916854i
$764$		0			0
$765$	−0.949106	−	7.54337i	−0.0343150	−	0.272731i
$766$		0			0
$767$	0.677332	+	2.08461i	0.0244571	+	0.0752711i
$768$		0			0
$769$	−8.83716	−	27.1980i	−0.318676	−	0.980784i	−0.974215	−	0.225623i	$-0.927558\pi$
$769$	−8.83716	−	27.1980i	−0.318676	−	0.980784i	0.655539	−	0.755162i	$-0.272442\pi$
$770$		0			0
$771$	−9.82428	+	30.2360i	−0.353813	+	1.08892i
$772$		0			0
$773$	36.4564	−	26.4871i	1.31124	−	0.952675i	0.311247	−	0.950329i	$-0.399253\pi$
$773$	36.4564	−	26.4871i	1.31124	−	0.952675i	0.999997	−	0.00234562i	$-0.000746636\pi$
$774$		0			0
$775$	25.9356	+	10.2987i	0.931634	+	0.369941i
$776$		0			0
$777$	50.2012	−	36.4733i	1.80096	−	1.30847i
$778$		0			0
$779$	1.80109	−	5.54318i	0.0645307	−	0.198605i
$780$		0			0
$781$	7.81199	+	24.0428i	0.279535	+	0.860320i
$782$		0			0
$783$	−0.0198070	−	0.0609596i	−0.000707844	−	0.00217852i
$784$		0			0
$785$	−20.5539	+	9.65934i	−0.733600	+	0.344757i
$786$		0			0
$787$	20.8458	+	15.1454i	0.743074	+	0.539875i	0.893672	−	0.448720i	$-0.148120\pi$
$787$	20.8458	+	15.1454i	0.743074	+	0.539875i	−0.150598	+	0.988595i	$0.548120\pi$
$788$		0			0
$789$	−17.2926	+	12.5638i	−0.615633	+	0.447284i
$790$		0			0
$791$	−31.8275	−	23.1240i	−1.13166	−	0.822196i
$792$		0			0
$793$	32.9077			1.16859
$794$		0			0
$795$	59.5137	+	11.3838i	2.11073	+	0.403741i
$796$		0			0
$797$	15.5882	−	47.9757i	0.552164	−	1.69939i	−0.151154	−	0.988510i	$-0.548299\pi$
$797$	15.5882	−	47.9757i	0.552164	−	1.69939i	0.703318	−	0.710875i	$-0.251701\pi$
$798$		0			0
$799$	5.25595			0.185942
$800$		0			0
$801$	35.4299			1.25186
$802$		0			0
$803$	6.02866	−	18.5543i	0.212747	−	0.654768i
$804$		0			0
$805$	3.62622	−	6.58824i	0.127808	−	0.232205i
$806$		0			0
$807$	65.5564			2.30769
$808$		0			0
$809$	2.92626	+	2.12605i	0.102882	+	0.0747480i	0.638037	−	0.770006i	$-0.279747\pi$
$809$	2.92626	+	2.12605i	0.102882	+	0.0747480i	−0.535155	+	0.844754i	$0.679747\pi$
$810$		0			0
$811$	40.8026	−	29.6448i	1.43277	−	1.04097i	0.443280	−	0.896383i	$-0.353815\pi$
$811$	40.8026	−	29.6448i	1.43277	−	1.04097i	0.989492	−	0.144586i	$-0.0461852\pi$
$812$		0			0
$813$	−17.1712	−	12.4756i	−0.602220	−	0.437538i
$814$		0			0
$815$	40.8512	+	7.81402i	1.43095	+	0.273713i
$816$		0			0
$817$	3.26269	+	10.0415i	0.114147	+	0.351308i
$818$		0			0
$819$	−9.04601	−	27.8408i	−0.316093	−	0.972835i
$820$		0			0
$821$	−3.48714	+	10.7323i	−0.121702	+	0.374560i	−0.993286	−	0.115686i	$-0.963093\pi$
$821$	−3.48714	+	10.7323i	−0.121702	+	0.374560i	0.871584	+	0.490246i	$0.163093\pi$
$822$		0			0
$823$	0.871148	−	0.632926i	0.0303663	−	0.0220624i	−0.572499	−	0.819906i	$-0.694026\pi$
$823$	0.871148	−	0.632926i	0.0303663	−	0.0220624i	0.602865	+	0.797843i	$0.294026\pi$
$824$		0			0
$825$	40.9166	+	16.2475i	1.42453	+	0.565666i
$826$		0			0
$827$	−23.7689	+	17.2691i	−0.826526	+	0.600506i	−0.918574	−	0.395248i	$-0.870659\pi$
$827$	−23.7689	+	17.2691i	−0.826526	+	0.600506i	0.0920482	+	0.995755i	$0.470659\pi$
$828$		0			0
$829$	6.51402	−	20.0481i	0.226241	−	0.696299i	−0.771922	−	0.635717i	$-0.780704\pi$
$829$	6.51402	−	20.0481i	0.226241	−	0.696299i	0.998163	−	0.0605816i	$-0.0192955\pi$
$830$		0			0
$831$	13.5442	+	41.6849i	0.469845	+	1.44603i
$832$		0			0
$833$	−3.11826	−	9.59702i	−0.108041	−	0.332517i
$834$		0			0
$835$	3.32221	+	3.54136i	0.114970	+	0.122554i
$836$		0			0
$837$	5.88030	+	4.27229i	0.203253	+	0.147672i
$838$		0			0
$839$	−2.76181	+	2.00657i	−0.0953483	+	0.0692746i	−0.634438	−	0.772974i	$-0.718768\pi$
$839$	−2.76181	+	2.00657i	−0.0953483	+	0.0692746i	0.539090	+	0.842248i	$0.318768\pi$
$840$		0			0
$841$	23.4595	+	17.0443i	0.808949	+	0.587736i
$842$		0			0
$843$	18.3857			0.633239
$844$		0			0
$845$	4.45350	+	4.74726i	0.153205	+	0.163311i
$846$		0			0
$847$	−3.78676	+	11.6544i	−0.130114	+	0.400451i
$848$		0			0
$849$	42.6889			1.46508
$850$		0			0
$851$	−6.27951			−0.215259
$852$		0			0
$853$	−12.5449	+	38.6094i	−0.429531	+	1.32196i	0.469058	+	0.883167i	$0.344594\pi$
$853$	−12.5449	+	38.6094i	−0.429531	+	1.32196i	−0.898589	+	0.438792i	$0.855406\pi$
$854$		0			0
$855$	−2.66762	−	21.2019i	−0.0912306	−	0.725089i
$856$		0			0
$857$	−43.0463			−1.47043			−0.735216	−	0.677833i	$-0.762919\pi$
$857$	−43.0463			−1.47043			−0.735216	+	0.677833i	$0.762919\pi$
$858$		0			0
$859$	6.17691	+	4.48779i	0.210753	+	0.153121i	0.688155	−	0.725564i	$-0.258421\pi$
$859$	6.17691	+	4.48779i	0.210753	+	0.153121i	−0.477401	+	0.878685i	$0.658421\pi$
$860$		0			0
$861$	−10.6079	+	7.70709i	−0.361516	+	0.262657i
$862$		0			0
$863$	5.23799	+	3.80562i	0.178303	+	0.129545i	0.673357	−	0.739317i	$-0.264852\pi$
$863$	5.23799	+	3.80562i	0.178303	+	0.129545i	−0.495054	+	0.868862i	$0.664852\pi$
$864$		0			0
$865$	−6.89439	+	12.5260i	−0.234416	+	0.425896i
$866$		0			0
$867$	−10.8568	−	33.4138i	−0.368717	−	1.13479i
$868$		0			0
$869$	2.10722	+	6.48535i	0.0714824	+	0.220000i
$870$		0			0
$871$	−15.0405	+	46.2898i	−0.509627	+	1.56847i
$872$		0			0
$873$	0.178121	−	0.129412i	0.00602848	−	0.00437995i
$874$		0			0
$875$	10.5562	−	40.8582i	0.356863	−	1.38126i
$876$		0			0
$877$	6.36784	−	4.62651i	0.215027	−	0.156226i	−0.475058	−	0.879954i	$-0.657573\pi$
$877$	6.36784	−	4.62651i	0.215027	−	0.156226i	0.690085	+	0.723728i	$0.257573\pi$
$878$		0			0
$879$	−21.2646	+	65.4457i	−0.717238	+	2.20743i
$880$		0			0
$881$	5.95327	+	18.3223i	0.200571	+	0.617293i	0.999866	+	0.0163551i	$0.00520623\pi$
$881$	5.95327	+	18.3223i	0.200571	+	0.617293i	−0.799295	+	0.600938i	$0.794794\pi$
$882$		0			0
$883$	−1.93876	−	5.96688i	−0.0652444	−	0.200802i	0.913120	−	0.407691i	$-0.133666\pi$
$883$	−1.93876	−	5.96688i	−0.0652444	−	0.200802i	−0.978364	+	0.206889i	$0.933666\pi$
$884$		0			0
$885$	1.73568	−	3.15344i	0.0583443	−	0.106002i
$886$		0			0
$887$	18.8281	+	13.6794i	0.632185	+	0.459309i	0.857156	−	0.515056i	$-0.172229\pi$
$887$	18.8281	+	13.6794i	0.632185	+	0.459309i	−0.224972	+	0.974365i	$0.572229\pi$
$888$		0			0
$889$	10.8371	−	7.87358i	0.363463	−	0.264071i
$890$		0			0
$891$	31.6451	+	22.9915i	1.06015	+	0.770243i
$892$		0			0
$893$	14.7727			0.494350
$894$		0			0
$895$	−2.23689	−	17.7785i	−0.0747709	−	0.594270i
$896$		0			0
$897$	−2.04017	+	6.27900i	−0.0681194	+	0.209650i
$898$		0			0
$899$	0.274685			0.00916126
$900$		0			0
$901$	−16.1757			−0.538890
$902$		0			0
$903$	7.33998	−	22.5901i	0.244259	−	0.751752i
$904$		0			0
$905$	16.6189	+	17.7151i	0.552430	+	0.588870i
$906$		0			0
$907$	17.6544			0.586206			0.293103	−	0.956081i	$-0.405312\pi$
$907$	17.6544			0.586206			0.293103	+	0.956081i	$0.405312\pi$
$908$		0			0
$909$	−32.3539	−	23.5065i	−1.07311	−	0.779660i
$910$		0			0
$911$	−28.2767	+	20.5442i	−0.936847	+	0.680659i	−0.947660	−	0.319282i	$-0.896558\pi$
$911$	−28.2767	+	20.5442i	−0.936847	+	0.680659i	0.0108124	+	0.999942i	$0.496558\pi$
$912$		0			0
$913$	−30.4378	−	22.1144i	−1.00735	−	0.731879i
$914$		0			0
$915$	−36.9741	−	39.4130i	−1.22233	−	1.30295i
$916$		0			0
$917$	4.72760	+	14.5500i	0.156119	+	0.480485i
$918$		0			0
$919$	−11.2243	−	34.5449i	−0.370256	−	1.13953i	−0.946624	−	0.322340i	$-0.895531\pi$
$919$	−11.2243	−	34.5449i	−0.370256	−	1.13953i	0.576368	−	0.817190i	$-0.304469\pi$
$920$		0			0
$921$	−10.0294	+	30.8673i	−0.330480	+	1.01711i
$922$		0			0
$923$	−17.2110	+	12.5045i	−0.566505	+	0.411590i
$924$		0			0
$925$	−34.1390	+	8.72892i	−1.12249	+	0.287005i
$926$		0			0
$927$	−2.40244	+	1.74548i	−0.0789066	+	0.0573290i
$928$		0			0
$929$	5.88811	−	18.1217i	0.193183	−	0.594555i	−0.806810	−	0.590810i	$-0.798808\pi$
$929$	5.88811	−	18.1217i	0.193183	−	0.594555i	0.999993	−	0.00374449i	$-0.00119191\pi$
$930$		0			0
$931$	−8.76439	−	26.9740i	−0.287241	−	0.884037i
$932$		0			0
$933$	−18.7161	−	57.6022i	−0.612737	−	1.88581i
$934$		0			0
$935$	−11.5434	−	2.20802i	−0.377509	−	0.0722100i
$936$		0			0
$937$	−48.1590	−	34.9896i	−1.57329	−	1.14306i	−0.923920	−	0.382586i	$-0.875034\pi$
$937$	−48.1590	−	34.9896i	−1.57329	−	1.14306i	−0.649367	−	0.760475i	$-0.724966\pi$
$938$		0			0
$939$	−17.8794	+	12.9902i	−0.583474	+	0.423918i
$940$		0			0
$941$	−12.2598	−	8.90727i	−0.399658	−	0.290369i	0.369744	−	0.929134i	$-0.379446\pi$
$941$	−12.2598	−	8.90727i	−0.399658	−	0.290369i	−0.769402	+	0.638765i	$0.779446\pi$
$942$		0			0
$943$	1.32691			0.0432101
$944$		0			0
$945$	5.30009	−	9.62938i	0.172412	−	0.313244i
$946$		0			0
$947$	−0.778999	+	2.39751i	−0.0253141	+	0.0779087i	−0.962915	−	0.269803i	$-0.913041\pi$
$947$	−0.778999	+	2.39751i	−0.0253141	+	0.0779087i	0.937601	+	0.347712i	$0.113041\pi$
$948$		0			0
$949$	16.4175			0.532934
$950$		0			0
$951$	57.1697			1.85385
$952$		0			0
$953$	9.69336	−	29.8331i	0.313999	−	0.966389i	−0.662166	−	0.749357i	$-0.730363\pi$
$953$	9.69336	−	29.8331i	0.313999	−	0.966389i	0.976165	−	0.217032i	$-0.0696375\pi$
$954$		0			0
$955$	17.9780	+	3.43883i	0.581754	+	0.111278i
$956$		0			0
$957$	0.433350			0.0140082
$958$		0			0
$959$	−10.8945	−	7.91529i	−0.351800	−	0.255598i
$960$		0			0
$961$	−0.120328	+	0.0874237i	−0.00388156	+	0.00282012i
$962$		0			0
$963$	−21.3589	−	15.5181i	−0.688280	−	0.500065i
$964$		0			0
$965$	35.5319	−	16.6983i	1.14381	−	0.537537i
$966$		0			0
$967$	−15.1746	−	46.7027i	−0.487983	−	1.50186i	−0.827613	−	0.561299i	$-0.810302\pi$
$967$	−15.1746	−	46.7027i	−0.487983	−	1.50186i	0.339630	−	0.940559i	$-0.389698\pi$
$968$		0			0
$969$	3.92872	+	12.0913i	0.126209	+	0.388430i
$970$		0			0
$971$	−7.72049	+	23.7612i	−0.247762	+	0.762534i	0.747407	+	0.664366i	$0.231298\pi$
$971$	−7.72049	+	23.7612i	−0.247762	+	0.762534i	−0.995170	+	0.0981683i	$0.968702\pi$
$972$		0			0
$973$	30.3713	−	22.0660i	0.973658	−	0.707404i
$974$		0			0
$975$	−2.36334	+	36.9723i	−0.0756873	+	1.18406i
$976$		0			0
$977$	−12.6095	+	9.16131i	−0.403412	+	0.293096i	−0.770929	−	0.636921i	$-0.780208\pi$
$977$	−12.6095	+	9.16131i	−0.403412	+	0.293096i	0.367517	+	0.930017i	$0.380208\pi$
$978$		0			0
$979$	16.9244	−	52.0879i	0.540906	−	1.66474i
$980$		0			0
$981$	8.61323	+	26.5088i	0.274999	+	0.846361i
$982$		0			0
$983$	4.18993	+	12.8953i	0.133638	+	0.411296i	0.995376	−	0.0960585i	$-0.0306236\pi$
$983$	4.18993	+	12.8953i	0.133638	+	0.411296i	−0.861738	+	0.507354i	$0.830624\pi$
$984$		0			0
$985$	1.32799	+	10.5547i	0.0423133	+	0.336301i
$986$		0			0
$987$	−26.8867	−	19.5343i	−0.855812	−	0.621784i
$988$		0			0
$989$	−1.94464	+	1.41286i	−0.0618359	+	0.0449264i
$990$		0			0
$991$	25.1120	+	18.2449i	0.797709	+	0.579570i	0.910241	−	0.414079i	$-0.135896\pi$
$991$	25.1120	+	18.2449i	0.797709	+	0.579570i	−0.112532	+	0.993648i	$0.535896\pi$
$992$		0			0
$993$	23.1184			0.733639
$994$		0			0
$995$	29.4089	−	13.8207i	0.932324	−	0.438147i
$996$		0			0
$997$	0.478723	−	1.47336i	0.0151613	−	0.0466617i	−0.943190	−	0.332255i	$-0.892191\pi$
$997$	0.478723	−	1.47336i	0.0151613	−	0.0466617i	0.958351	+	0.285593i	$0.0921906\pi$
$998$		0			0
$999$	−9.17813			−0.290383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.d.161.2		8
4.3	odd	2		50.2.d.b.11.1	✓	8
12.11	even	2		450.2.h.e.361.2		8
20.3	even	4		250.2.e.c.199.3		16
20.7	even	4		250.2.e.c.199.2		16
20.19	odd	2		250.2.d.d.51.2		8
25.4	even	10		10000.2.a.x.1.1		4
25.16	even	5	inner	400.2.u.d.241.2		8
25.21	even	5		10000.2.a.t.1.4		4
100.3	even	20		1250.2.b.e.1249.1		8
100.47	even	20		1250.2.b.e.1249.8		8
100.59	odd	10		250.2.d.d.201.2		8
100.63	even	20		250.2.e.c.49.2		16
100.71	odd	10		1250.2.a.l.1.1		4
100.79	odd	10		1250.2.a.f.1.4		4
100.87	even	20		250.2.e.c.49.3		16
100.91	odd	10		50.2.d.b.41.1	yes	8
300.191	even	10		450.2.h.e.91.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.1	✓	8	4.3	odd	2
50.2.d.b.41.1	yes	8	100.91	odd	10
250.2.d.d.51.2		8	20.19	odd	2
250.2.d.d.201.2		8	100.59	odd	10
250.2.e.c.49.2		16	100.63	even	20
250.2.e.c.49.3		16	100.87	even	20
250.2.e.c.199.2		16	20.7	even	4
250.2.e.c.199.3		16	20.3	even	4
400.2.u.d.161.2		8	1.1	even	1	trivial
400.2.u.d.241.2		8	25.16	even	5	inner
450.2.h.e.91.2		8	300.191	even	10
450.2.h.e.361.2		8	12.11	even	2
1250.2.a.f.1.4		4	100.79	odd	10
1250.2.a.l.1.1		4	100.71	odd	10
1250.2.b.e.1249.1		8	100.3	even	20
1250.2.b.e.1249.8		8	100.47	even	20
10000.2.a.t.1.4		4	25.21	even	5
10000.2.a.x.1.1		4	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)

\(f(q)\)	\(=\)	\(q+(0.720859 - 2.21858i) q^{3} +(-2.02373 + 0.951057i) q^{5} -3.77447 q^{7} +(-1.97539 - 1.43521i) q^{9} +O(q^{10})\)	\(q+(0.720859 - 2.21858i) q^{3} +(-2.02373 + 0.951057i) q^{5} -3.77447 q^{7} +(-1.97539 - 1.43521i) q^{9} +(-3.05361 + 2.21858i) q^{11} +(-2.56969 - 1.86699i) q^{13} +(0.651166 + 5.17538i) q^{15} +(-0.430307 - 1.32435i) q^{17} +(-1.20945 - 3.72230i) q^{19} +(-2.72086 + 8.37394i) q^{21} +(0.720859 - 0.523735i) q^{23} +(3.19098 - 3.84937i) q^{25} +(1.05361 - 0.765491i) q^{27} +(0.0152089 - 0.0468081i) q^{29} +(1.72466 + 5.30795i) q^{31} +(2.72086 + 8.37394i) q^{33} +(7.63851 - 3.58973i) q^{35} +(-5.70152 - 4.14240i) q^{37} +(-5.99445 + 4.35522i) q^{39} +(1.20477 + 0.875319i) q^{41} -2.69767 q^{43} +(5.36263 + 1.02576i) q^{45} +(-1.16637 + 3.58973i) q^{47} +7.24660 q^{49} -3.24836 q^{51} +(3.58963 - 11.0477i) q^{53} +(4.06969 - 7.39396i) q^{55} -9.13004 q^{57} +(-0.558282 - 0.405615i) q^{59} +(-8.38168 + 6.08965i) q^{61} +(7.45605 + 5.41714i) q^{63} +(6.97599 + 1.33437i) q^{65} +(-4.73519 - 14.5734i) q^{67} +(-0.642308 - 1.97682i) q^{69} +(2.06969 - 6.36986i) q^{71} +(-4.18158 + 3.03810i) q^{73} +(-6.23987 - 9.85429i) q^{75} +(11.5257 - 8.37394i) q^{77} +(0.558282 - 1.71821i) q^{79} +(-3.20239 - 9.85596i) q^{81} +(3.08023 + 9.47997i) q^{83} +(2.13035 + 2.27088i) q^{85} +(-0.0928839 - 0.0674841i) q^{87} +(-11.7390 + 8.52891i) q^{89} +(9.69922 + 7.04690i) q^{91} +13.0193 q^{93} +(5.98771 + 6.38268i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +9.21619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 4 * q^7 - q^9	\( 8 q + 3 q^{3} - 4 q^{7} - q^{9} - q^{11} - 13 q^{13} + 10 q^{15} - 11 q^{17} - 20 q^{19} - 19 q^{21} + 3 q^{23} + 30 q^{25} - 15 q^{27} - 15 q^{29} + 9 q^{31} + 19 q^{33} + 15 q^{35} - 6 q^{37} + 12 q^{39} - 9 q^{41} - 12 q^{43} + 15 q^{45} + q^{47} - 4 q^{49} - 26 q^{51} + 7 q^{53} + 25 q^{55} - 10 q^{59} + 6 q^{61} + 8 q^{63} - 10 q^{65} + 11 q^{67} + 43 q^{69} + 9 q^{71} - 8 q^{73} - 30 q^{75} + 33 q^{77} + 10 q^{79} - 17 q^{81} - 27 q^{83} + 5 q^{85} - 15 q^{89} - q^{91} - 46 q^{93} + 30 q^{95} - 36 q^{97} + 42 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 4 * q^7 - q^9 - q^11 - 13 * q^13 + 10 * q^15 - 11 * q^17 - 20 * q^19 - 19 * q^21 + 3 * q^23 + 30 * q^25 - 15 * q^27 - 15 * q^29 + 9 * q^31 + 19 * q^33 + 15 * q^35 - 6 * q^37 + 12 * q^39 - 9 * q^41 - 12 * q^43 + 15 * q^45 + q^47 - 4 * q^49 - 26 * q^51 + 7 * q^53 + 25 * q^55 - 10 * q^59 + 6 * q^61 + 8 * q^63 - 10 * q^65 + 11 * q^67 + 43 * q^69 + 9 * q^71 - 8 * q^73 - 30 * q^75 + 33 * q^77 + 10 * q^79 - 17 * q^81 - 27 * q^83 + 5 * q^85 - 15 * q^89 - q^91 - 46 * q^93 + 30 * q^95 - 36 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more