LMFDB - Embedded newform 400.2.u.g.241.1

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

Embedding invariants

Embedding label			241.1
Root			$0.772523 + 2.37758i$ of defining polynomial
Character	$\chi$	$=$	400.241
Dual form			400.2.u.g.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.772523 - 2.37758i) q^{3} +(1.16821 + 1.90664i) q^{5} +1.96923 q^{7} +(-2.62905 + 1.91012i) q^{9} +O(q^{10})$	\(q+(-0.772523 - 2.37758i) q^{3} +(1.16821 + 1.90664i) q^{5} +1.96923 q^{7} +(-2.62905 + 1.91012i) q^{9} +(2.80465 + 2.03770i) q^{11} +(4.32714 - 3.14385i) q^{13} +(3.63074 - 4.25043i) q^{15} +(-0.204922 + 0.630686i) q^{17} +(0.163997 - 0.504731i) q^{19} +(-1.52128 - 4.68201i) q^{21} +(-7.20196 - 5.23253i) q^{23} +(-2.27059 + 4.45471i) q^{25} +(0.504994 + 0.366899i) q^{27} +(-0.939405 - 2.89119i) q^{29} +(-0.921788 + 2.83697i) q^{31} +(2.67814 - 8.24246i) q^{33} +(2.30047 + 3.75463i) q^{35} +(9.46267 - 6.87504i) q^{37} +(-10.8176 - 7.85944i) q^{39} +(-0.662310 + 0.481196i) q^{41} +9.68524 q^{43} +(-6.71320 - 2.78126i) q^{45} +(2.52063 + 7.75769i) q^{47} -3.12212 q^{49} +1.65782 q^{51} +(2.88802 + 8.88842i) q^{53} +(-0.608757 + 7.72793i) q^{55} -1.32673 q^{57} +(-2.82290 + 2.05096i) q^{59} +(-9.24453 - 6.71654i) q^{61} +(-5.17722 + 3.76147i) q^{63} +(11.0492 + 4.57766i) q^{65} +(-2.91032 + 8.95703i) q^{67} +(-6.87709 + 21.1655i) q^{69} +(-1.27411 - 3.92130i) q^{71} +(-8.53720 - 6.20264i) q^{73} +(12.3455 + 1.95715i) q^{75} +(5.52301 + 4.01270i) q^{77} +(2.31326 + 7.11949i) q^{79} +(-2.53041 + 7.78781i) q^{81} +(1.17148 - 3.60543i) q^{83} +(-1.44189 + 0.346057i) q^{85} +(-6.14833 + 4.46702i) q^{87} +(11.3462 + 8.24351i) q^{89} +(8.52115 - 6.19098i) q^{91} +7.45723 q^{93} +(1.15392 - 0.276946i) q^{95} +(0.295759 + 0.910252i) q^{97} -11.2658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) $ 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9	$ 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9} + 10 q^{11} + q^{13} + 10 q^{15} - 4 q^{17} - 3 q^{21} - 11 q^{23} + 9 q^{25} - 13 q^{27} + 5 q^{29} + 9 q^{31} + 16 q^{33} - 24 q^{35} + 30 q^{37} - 14 q^{39} - 2 q^{41} + 42 q^{43} - 77 q^{45} + 16 q^{47} + 18 q^{49} - 100 q^{51} + 11 q^{53} + 24 q^{55} - 64 q^{57} + 53 q^{59} + 4 q^{61} + 38 q^{63} + 37 q^{65} + 14 q^{67} - 7 q^{69} + 6 q^{71} - 24 q^{73} + 15 q^{75} + 23 q^{77} + 22 q^{79} - 6 q^{81} - 33 q^{83} + 8 q^{85} - 37 q^{87} + 20 q^{89} + 27 q^{91} + 40 q^{93} + 24 q^{95} + 11 q^{97} - 122 q^{99}+O(q^{100}) $ 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9 + 10 * q^11 + q^13 + 10 * q^15 - 4 * q^17 - 3 * q^21 - 11 * q^23 + 9 * q^25 - 13 * q^27 + 5 * q^29 + 9 * q^31 + 16 * q^33 - 24 * q^35 + 30 * q^37 - 14 * q^39 - 2 * q^41 + 42 * q^43 - 77 * q^45 + 16 * q^47 + 18 * q^49 - 100 * q^51 + 11 * q^53 + 24 * q^55 - 64 * q^57 + 53 * q^59 + 4 * q^61 + 38 * q^63 + 37 * q^65 + 14 * q^67 - 7 * q^69 + 6 * q^71 - 24 * q^73 + 15 * q^75 + 23 * q^77 + 22 * q^79 - 6 * q^81 - 33 * q^83 + 8 * q^85 - 37 * q^87 + 20 * q^89 + 27 * q^91 + 40 * q^93 + 24 * q^95 + 11 * q^97 - 122 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.772523	−	2.37758i	−0.446017	−	1.37270i	−0.881365	−	0.472436i	$-0.843375\pi$
$3$	−0.772523	−	2.37758i	−0.446017	−	1.37270i	0.435349	−	0.900262i	$-0.356625\pi$
$4$		0			0
$5$	1.16821	+	1.90664i	0.522438	+	0.852677i
$5$	1.16821	+	1.90664i	0.522438	+	0.852677i
$6$		0			0
$7$	1.96923			0.744300			0.372150	−	0.928173i	$-0.378621\pi$
$7$	1.96923			0.744300			0.372150	+	0.928173i	$0.378621\pi$
$8$		0			0
$9$	−2.62905	+	1.91012i	−0.876351	+	0.636706i
$10$		0			0
$11$	2.80465	+	2.03770i	0.845635	+	0.614389i	0.923939	−	0.382540i	$-0.124951\pi$
$11$	2.80465	+	2.03770i	0.845635	+	0.614389i	−0.0783043	+	0.996930i	$0.524951\pi$
$12$		0			0
$13$	4.32714	−	3.14385i	1.20013	−	0.871948i	0.205836	−	0.978586i	$-0.434009\pi$
$13$	4.32714	−	3.14385i	1.20013	−	0.871948i	0.994298	+	0.106638i	$0.0340086\pi$
$14$		0			0
$15$	3.63074	−	4.25043i	0.937453	−	1.09746i
$16$		0			0
$17$	−0.204922	+	0.630686i	−0.0497010	+	0.152964i	−0.972827	−	0.231534i	$-0.925625\pi$
$17$	−0.204922	+	0.630686i	−0.0497010	+	0.152964i	0.923126	+	0.384498i	$0.125625\pi$
$18$		0			0
$19$	0.163997	−	0.504731i	0.0376235	−	0.115793i	−0.930481	−	0.366340i	$-0.880611\pi$
$19$	0.163997	−	0.504731i	0.0376235	−	0.115793i	0.968104	+	0.250547i	$0.0806106\pi$
$20$		0			0
$21$	−1.52128	−	4.68201i	−0.331970	−	1.02170i
$22$		0			0
$23$	−7.20196	−	5.23253i	−1.50171	−	1.09106i	−0.969693	−	0.244325i	$-0.921434\pi$
$23$	−7.20196	−	5.23253i	−1.50171	−	1.09106i	−0.532019	−	0.846733i	$-0.678566\pi$
$24$		0			0
$25$	−2.27059	+	4.45471i	−0.454118	+	0.890942i
$26$		0			0
$27$	0.504994	+	0.366899i	0.0971861	+	0.0706098i
$28$		0			0
$29$	−0.939405	−	2.89119i	−0.174443	−	0.536881i	0.825165	−	0.564892i	$-0.191082\pi$
$29$	−0.939405	−	2.89119i	−0.174443	−	0.536881i	−0.999608	+	0.0280119i	$0.991082\pi$
$30$		0			0
$31$	−0.921788	+	2.83697i	−0.165558	+	0.509535i	−0.999077	−	0.0429557i	$-0.986323\pi$
$31$	−0.921788	+	2.83697i	−0.165558	+	0.509535i	0.833519	+	0.552491i	$0.186323\pi$
$32$		0			0
$33$	2.67814	−	8.24246i	0.466204	−	1.43483i
$34$		0			0
$35$	2.30047	+	3.75463i	0.388850	+	0.634648i
$36$		0			0
$37$	9.46267	−	6.87504i	1.55565	−	1.13025i	0.616192	−	0.787596i	$-0.288674\pi$
$37$	9.46267	−	6.87504i	1.55565	−	1.13025i	0.939462	−	0.342653i	$-0.111326\pi$
$38$		0			0
$39$	−10.8176	−	7.85944i	−1.73220	−	1.25852i
$40$		0			0
$41$	−0.662310	+	0.481196i	−0.103435	+	0.0751502i	−0.638301	−	0.769787i	$-0.720362\pi$
$41$	−0.662310	+	0.481196i	−0.103435	+	0.0751502i	0.534865	+	0.844937i	$0.320362\pi$
$42$		0			0
$43$	9.68524			1.47699			0.738493	−	0.674261i	$-0.235538\pi$
$43$	9.68524			1.47699			0.738493	+	0.674261i	$0.235538\pi$
$44$		0			0
$45$	−6.71320	−	2.78126i	−1.00074	−	0.414606i
$46$		0			0
$47$	2.52063	+	7.75769i	0.367671	+	1.13158i	0.948291	+	0.317401i	$0.102810\pi$
$47$	2.52063	+	7.75769i	0.367671	+	1.13158i	−0.580620	+	0.814174i	$0.697190\pi$
$48$		0			0
$49$	−3.12212			−0.446018
$50$		0			0
$51$	1.65782			0.232141
$52$		0			0
$53$	2.88802	+	8.88842i	0.396700	+	1.22092i	0.927630	+	0.373502i	$0.121843\pi$
$53$	2.88802	+	8.88842i	0.396700	+	1.22092i	−0.530929	+	0.847416i	$0.678157\pi$
$54$		0			0
$55$	−0.608757	+	7.72793i	−0.0820848	+	1.04203i
$56$		0			0
$57$	−1.32673			−0.175730
$58$		0			0
$59$	−2.82290	+	2.05096i	−0.367511	+	0.267012i	−0.756178	−	0.654366i	$-0.772936\pi$
$59$	−2.82290	+	2.05096i	−0.367511	+	0.267012i	0.388667	+	0.921378i	$0.372936\pi$
$60$		0			0
$61$	−9.24453	−	6.71654i	−1.18364	−	0.859965i	−0.191063	−	0.981578i	$-0.561193\pi$
$61$	−9.24453	−	6.71654i	−1.18364	−	0.859965i	−0.992578	+	0.121613i	$0.961193\pi$
$62$		0			0
$63$	−5.17722	+	3.76147i	−0.652268	+	0.473900i
$64$		0			0
$65$	11.0492	+	4.57766i	1.37049	+	0.567789i
$66$		0			0
$67$	−2.91032	+	8.95703i	−0.355552	+	1.09428i	0.600137	+	0.799897i	$0.295113\pi$
$67$	−2.91032	+	8.95703i	−0.355552	+	1.09428i	−0.955689	+	0.294379i	$0.904887\pi$
$68$		0			0
$69$	−6.87709	+	21.1655i	−0.827904	+	2.54803i
$70$		0			0
$71$	−1.27411	−	3.92130i	−0.151209	−	0.465373i	0.846548	−	0.532312i	$-0.178677\pi$
$71$	−1.27411	−	3.92130i	−0.151209	−	0.465373i	−0.997757	+	0.0669389i	$0.978677\pi$
$72$		0			0
$73$	−8.53720	−	6.20264i	−0.999203	−	0.725964i	−0.0372862	−	0.999305i	$-0.511871\pi$
$73$	−8.53720	−	6.20264i	−0.999203	−	0.725964i	−0.961917	+	0.273341i	$0.911871\pi$
$74$		0			0
$75$	12.3455	+	1.95715i	1.42554	+	0.225992i
$76$		0			0
$77$	5.52301	+	4.01270i	0.629406	+	0.457290i
$78$		0			0
$79$	2.31326	+	7.11949i	0.260262	+	0.801005i	0.992747	+	0.120222i	$0.0383605\pi$
$79$	2.31326	+	7.11949i	0.260262	+	0.801005i	−0.732485	+	0.680783i	$0.761640\pi$
$80$		0			0
$81$	−2.53041	+	7.78781i	−0.281157	+	0.865312i
$82$		0			0
$83$	1.17148	−	3.60543i	0.128586	−	0.395748i	−0.865951	−	0.500129i	$-0.833286\pi$
$83$	1.17148	−	3.60543i	0.128586	−	0.395748i	0.994537	+	0.104381i	$0.0332861\pi$
$84$		0			0
$85$	−1.44189	+	0.346057i	−0.156395	+	0.0375352i
$86$		0			0
$87$	−6.14833	+	4.46702i	−0.659170	+	0.478915i
$88$		0			0
$89$	11.3462	+	8.24351i	1.20270	+	0.873810i	0.994547	−	0.104287i	$-0.0332561\pi$
$89$	11.3462	+	8.24351i	1.20270	+	0.873810i	0.208149	+	0.978097i	$0.433256\pi$
$90$		0			0
$91$	8.52115	−	6.19098i	0.893260	−	0.648991i
$92$		0			0
$93$	7.45723			0.773279
$94$		0			0
$95$	1.15392	−	0.276946i	0.118390	−	0.0284140i
$96$		0			0
$97$	0.295759	+	0.910252i	0.0300298	+	0.0924221i	0.964948	−	0.262441i	$-0.0845275\pi$
$97$	0.295759	+	0.910252i	0.0300298	+	0.0924221i	−0.934918	+	0.354863i	$0.884527\pi$
$98$		0			0
$99$	−11.2658			−1.13226
$100$		0			0
$101$	−10.7470			−1.06937			−0.534685	−	0.845052i	$-0.679570\pi$
$101$	−10.7470			−1.06937			−0.534685	+	0.845052i	$0.679570\pi$
$102$		0			0
$103$	−2.70909	−	8.33773i	−0.266935	−	0.821541i	−0.991241	−	0.132063i	$-0.957840\pi$
$103$	−2.70909	−	8.33773i	−0.266935	−	0.821541i	0.724306	−	0.689478i	$-0.242160\pi$
$104$		0			0
$105$	7.14977	−	8.37009i	0.697746	−	0.816837i
$106$		0			0
$107$	−4.50888			−0.435890			−0.217945	−	0.975961i	$-0.569935\pi$
$107$	−4.50888			−0.435890			−0.217945	+	0.975961i	$0.569935\pi$
$108$		0			0
$109$	−3.94816	+	2.86851i	−0.378165	+	0.274753i	−0.760589	−	0.649234i	$-0.775090\pi$
$109$	−3.94816	+	2.86851i	−0.378165	+	0.274753i	0.382423	+	0.923987i	$0.375090\pi$
$110$		0			0
$111$	−23.6561	−	17.1872i	−2.24534	−	1.63133i
$112$		0			0
$113$	−1.67560	+	1.21739i	−0.157627	+	0.114523i	−0.663803	−	0.747907i	$-0.731059\pi$
$113$	−1.67560	+	1.21739i	−0.157627	+	0.114523i	0.506176	+	0.862430i	$0.331059\pi$
$114$		0			0
$115$	1.56320	−	19.8442i	0.145769	−	1.85049i
$116$		0			0
$117$	−5.37116	+	16.5307i	−0.496564	+	1.52827i
$118$		0			0
$119$	−0.403540	+	1.24197i	−0.0369924	+	0.113851i
$120$		0			0
$121$	0.314671	+	0.968456i	0.0286064	+	0.0880415i
$122$		0			0
$123$	1.65573	+	1.20296i	0.149292	+	0.108467i
$124$		0			0
$125$	−11.1461	+	0.874810i	−0.996934	+	0.0782454i
$126$		0			0
$127$	−2.19062	−	1.59158i	−0.194386	−	0.141230i	0.486335	−	0.873772i	$-0.338333\pi$
$127$	−2.19062	−	1.59158i	−0.194386	−	0.141230i	−0.680721	+	0.732543i	$0.738333\pi$
$128$		0			0
$129$	−7.48208	−	23.0275i	−0.658760	−	2.02745i
$130$		0			0
$131$	−4.90254	+	15.0885i	−0.428337	+	1.31829i	0.471425	+	0.881906i	$0.343740\pi$
$131$	−4.90254	+	15.0885i	−0.428337	+	1.31829i	−0.899762	+	0.436381i	$0.856260\pi$
$132$		0			0
$133$	0.322948	−	0.993932i	0.0280032	−	0.0861849i
$134$		0			0
$135$	−0.109610	+	1.39146i	−0.00943374	+	0.119758i
$136$		0			0
$137$	−17.6241	+	12.8047i	−1.50573	+	1.09398i	−0.537700	+	0.843136i	$0.680707\pi$
$137$	−17.6241	+	12.8047i	−1.50573	+	1.09398i	−0.968029	+	0.250840i	$0.919293\pi$
$138$		0			0
$139$	10.1974	+	7.40882i	0.864930	+	0.628408i	0.929222	−	0.369523i	$-0.120479\pi$
$139$	10.1974	+	7.40882i	0.864930	+	0.628408i	−0.0642920	+	0.997931i	$0.520479\pi$
$140$		0			0
$141$	16.4973	−	11.9860i	1.38932	−	1.00940i
$142$		0			0
$143$	18.5424			1.55059
$144$		0			0
$145$	4.41505	−	5.16862i	0.366650	−	0.429230i
$146$		0			0
$147$	2.41191	+	7.42311i	0.198931	+	0.612247i
$148$		0			0
$149$	4.71325			0.386124			0.193062	−	0.981187i	$-0.438158\pi$
$149$	4.71325			0.386124			0.193062	+	0.981187i	$0.438158\pi$
$150$		0			0
$151$	−1.09617			−0.0892052			−0.0446026	−	0.999005i	$-0.514202\pi$
$151$	−1.09617			−0.0892052			−0.0446026	+	0.999005i	$0.514202\pi$
$152$		0			0
$153$	−0.665934	−	2.04953i	−0.0538376	−	0.165695i
$154$		0			0
$155$	−6.48593	+	1.55665i	−0.520963	+	0.125033i
$156$		0			0
$157$	−11.4429			−0.913245			−0.456623	−	0.889660i	$-0.650941\pi$
$157$	−11.4429			−0.913245			−0.456623	+	0.889660i	$0.650941\pi$
$158$		0			0
$159$	18.9019	−	13.7330i	1.49902	−	1.08910i
$160$		0			0
$161$	−14.1823	−	10.3041i	−1.11772	−	0.812074i
$162$		0			0
$163$	0.271579	−	0.197314i	0.0212717	−	0.0154548i	−0.577099	−	0.816674i	$-0.695815\pi$
$163$	0.271579	−	0.197314i	0.0212717	−	0.0154548i	0.598370	+	0.801220i	$0.295815\pi$
$164$		0			0
$165$	18.8441	−	4.52264i	1.46701	−	0.352087i
$166$		0			0
$167$	4.63310	−	14.2592i	0.358520	−	1.10341i	−0.595421	−	0.803414i	$-0.703015\pi$
$167$	4.63310	−	14.2592i	0.358520	−	1.10341i	0.953940	−	0.299996i	$-0.0969854\pi$
$168$		0			0
$169$	4.82314	−	14.8441i	0.371011	−	1.14185i
$170$		0			0
$171$	0.532939	+	1.64022i	0.0407549	+	0.125431i
$172$		0			0
$173$	2.94636	+	2.14066i	0.224008	+	0.162751i	0.694129	−	0.719851i	$-0.255790\pi$
$173$	2.94636	+	2.14066i	0.224008	+	0.162751i	−0.470121	+	0.882602i	$0.655790\pi$
$174$		0			0
$175$	−4.47132	+	8.77236i	−0.338000	+	0.663128i
$176$		0			0
$177$	7.05708	+	5.12727i	0.530443	+	0.385389i
$178$		0			0
$179$	5.71933	+	17.6023i	0.427482	+	1.31566i	0.900597	+	0.434655i	$0.143130\pi$
$179$	5.71933	+	17.6023i	0.427482	+	1.31566i	−0.473115	+	0.881001i	$0.656870\pi$
$180$		0			0
$181$	−0.0102245	+	0.0314676i	−0.000759978	+	0.00233897i	−0.951436	−	0.307847i	$-0.900391\pi$
$181$	−0.0102245	+	0.0314676i	−0.000759978	+	0.00233897i	0.950676	+	0.310186i	$0.100391\pi$
$182$		0			0
$183$	−8.82752	+	27.1683i	−0.652549	+	2.00834i
$184$		0			0
$185$	24.1626	+	10.0105i	1.77647	+	0.735987i
$186$		0			0
$187$	−1.85989	+	1.35129i	−0.136008	+	0.0988158i
$188$		0			0
$189$	0.994450	+	0.722510i	0.0723356	+	0.0525549i
$190$		0			0
$191$	−3.69432	+	2.68408i	−0.267311	+	0.194213i	−0.713364	−	0.700794i	$-0.752829\pi$
$191$	−3.69432	+	2.68408i	−0.267311	+	0.194213i	0.446053	+	0.895007i	$0.352829\pi$
$192$		0			0
$193$	9.48674			0.682870			0.341435	−	0.939905i	$-0.389087\pi$
$193$	9.48674			0.682870			0.341435	+	0.939905i	$0.389087\pi$
$194$		0			0
$195$	2.34799	−	29.8068i	0.168143	−	2.13451i
$196$		0			0
$197$	−3.89003	−	11.9723i	−0.277153	−	0.852989i	−0.988642	−	0.150292i	$-0.951979\pi$
$197$	−3.89003	−	11.9723i	−0.277153	−	0.852989i	0.711489	−	0.702698i	$-0.248021\pi$
$198$		0			0
$199$	−1.43593			−0.101791			−0.0508954	−	0.998704i	$-0.516207\pi$
$199$	−1.43593			−0.101791			−0.0508954	+	0.998704i	$0.516207\pi$
$200$		0			0
$201$	23.5444			1.66069
$202$		0			0
$203$	−1.84991	−	5.69342i	−0.129838	−	0.399600i
$204$		0			0
$205$	−1.69118	−	0.700653i	−0.118117	−	0.0489357i
$206$		0			0
$207$	28.9291			2.01071
$208$		0			0
$209$	1.48844	−	1.08142i	0.102958	−	0.0748033i
$210$		0			0
$211$	−13.6070	−	9.88603i	−0.936741	−	0.680582i	0.0108927	−	0.999941i	$-0.496533\pi$
$211$	−13.6070	−	9.88603i	−0.936741	−	0.680582i	−0.947634	+	0.319358i	$0.896533\pi$
$212$		0			0
$213$	−8.33894	+	6.05860i	−0.571375	+	0.415128i
$214$		0			0
$215$	11.3144	+	18.4663i	0.771633	+	1.25939i
$216$		0			0
$217$	−1.81521	+	5.58666i	−0.123225	+	0.379247i
$218$		0			0
$219$	−8.15210	+	25.0896i	−0.550868	+	1.69540i
$220$		0			0
$221$	1.09606	+	3.37332i	0.0737288	+	0.226914i
$222$		0			0
$223$	−9.88804	−	7.18409i	−0.662152	−	0.481082i	0.205237	−	0.978712i	$-0.434204\pi$
$223$	−9.88804	−	7.18409i	−0.662152	−	0.481082i	−0.867389	+	0.497630i	$0.834204\pi$
$224$		0			0
$225$	−2.53952	−	16.0488i	−0.169302	−	1.06992i
$226$		0			0
$227$	−12.3318	−	8.95955i	−0.818488	−	0.594666i	0.0977912	−	0.995207i	$-0.468822\pi$
$227$	−12.3318	−	8.95955i	−0.818488	−	0.594666i	−0.916279	+	0.400541i	$0.868822\pi$
$228$		0			0
$229$	−6.01667	−	18.5174i	−0.397592	−	1.22366i	−0.926924	−	0.375249i	$-0.877557\pi$
$229$	−6.01667	−	18.5174i	−0.397592	−	1.22366i	0.529332	−	0.848415i	$-0.322443\pi$
$230$		0			0
$231$	5.27388	−	16.2313i	0.346996	−	1.06794i
$232$		0			0
$233$	−6.23396	+	19.1861i	−0.408400	+	1.25693i	0.509623	+	0.860398i	$0.329785\pi$
$233$	−6.23396	+	19.1861i	−0.408400	+	1.25693i	−0.918023	+	0.396528i	$0.870215\pi$
$234$		0			0
$235$	−11.8465	+	13.8685i	−0.772784	+	0.904682i
$236$		0			0
$237$	15.1401	−	10.9999i	0.983456	−	0.714523i
$238$		0			0
$239$	−0.0247410	−	0.0179754i	−0.00160036	−	0.00116273i	0.586985	−	0.809598i	$-0.300315\pi$
$239$	−0.0247410	−	0.0179754i	−0.00160036	−	0.00116273i	−0.588585	+	0.808435i	$0.700315\pi$
$240$		0			0
$241$	−7.54591	+	5.48242i	−0.486075	+	0.353154i	−0.803673	−	0.595071i	$-0.797124\pi$
$241$	−7.54591	+	5.48242i	−0.486075	+	0.353154i	0.317598	+	0.948225i	$0.397124\pi$
$242$		0			0
$243$	22.3436			1.43334
$244$		0			0
$245$	−3.64728	−	5.95278i	−0.233016	−	0.380309i
$246$		0			0
$247$	−0.877162	−	2.69963i	−0.0558125	−	0.171773i
$248$		0			0
$249$	−9.47721			−0.600594
$250$		0			0
$251$	9.20030			0.580718			0.290359	−	0.956918i	$-0.406225\pi$
$251$	9.20030			0.580718			0.290359	+	0.956918i	$0.406225\pi$
$252$		0			0
$253$	−9.53667	−	29.3509i	−0.599565	−	1.84527i
$254$		0			0
$255$	1.93667	+	3.16087i	0.121279	+	0.197941i
$256$		0			0
$257$	−4.27125			−0.266433			−0.133217	−	0.991087i	$-0.542531\pi$
$257$	−4.27125			−0.266433			−0.133217	+	0.991087i	$0.542531\pi$
$258$		0			0
$259$	18.6342	−	13.5385i	1.15787	−	0.841244i
$260$		0			0
$261$	7.99226	+	5.80672i	0.494709	+	0.359427i
$262$		0			0
$263$	7.22425	−	5.24873i	0.445467	−	0.323650i	−0.342337	−	0.939577i	$-0.611218\pi$
$263$	7.22425	−	5.24873i	0.445467	−	0.323650i	0.787803	+	0.615927i	$0.211218\pi$
$264$		0			0
$265$	−13.5732	+	15.8899i	−0.833798	+	0.976111i
$266$		0			0
$267$	10.8344	−	33.3449i	0.663054	−	2.04067i
$268$		0			0
$269$	0.957949	−	2.94826i	0.0584072	−	0.179759i	−0.917596	−	0.397513i	$-0.869873\pi$
$269$	0.957949	−	2.94826i	0.0584072	−	0.179759i	0.976004	+	0.217755i	$0.0698732\pi$
$270$		0			0
$271$	−2.38753	−	7.34805i	−0.145032	−	0.446362i	0.851983	−	0.523569i	$-0.175400\pi$
$271$	−2.38753	−	7.34805i	−0.145032	−	0.446362i	−0.997015	+	0.0772069i	$0.975400\pi$
$272$		0			0
$273$	−21.3024	−	15.4771i	−1.28928	−	0.936715i
$274$		0			0
$275$	−15.4456	+	7.86713i	−0.931403	+	0.474406i
$276$		0			0
$277$	13.1165	+	9.52967i	0.788092	+	0.572582i	0.907397	−	0.420276i	$-0.138067\pi$
$277$	13.1165	+	9.52967i	0.788092	+	0.572582i	−0.119305	+	0.992858i	$0.538067\pi$
$278$		0			0
$279$	−2.99552	−	9.21927i	−0.179337	−	0.551943i
$280$		0			0
$281$	−6.60078	+	20.3151i	−0.393770	+	1.21190i	0.536146	+	0.844125i	$0.319880\pi$
$281$	−6.60078	+	20.3151i	−0.393770	+	1.21190i	−0.929916	+	0.367773i	$0.880120\pi$
$282$		0			0
$283$	8.44812	−	26.0006i	0.502189	−	1.54558i	−0.303257	−	0.952909i	$-0.598074\pi$
$283$	8.44812	−	26.0006i	0.502189	−	1.54558i	0.805446	−	0.592669i	$-0.201926\pi$
$284$		0			0
$285$	−1.54989	−	2.52960i	−0.0918078	−	0.149841i
$286$		0			0
$287$	−1.30424	+	0.947587i	−0.0769870	+	0.0559343i
$288$		0			0
$289$	13.3975	+	9.73387i	0.788089	+	0.572580i
$290$		0			0
$291$	1.93572	−	1.40638i	0.113474	−	0.0824436i
$292$		0			0
$293$	15.7064			0.917578			0.458789	−	0.888545i	$-0.348283\pi$
$293$	15.7064			0.917578			0.458789	+	0.888545i	$0.348283\pi$
$294$		0			0
$295$	−7.20818	−	2.98633i	−0.419677	−	0.173871i
$296$		0			0
$297$	0.668701	+	2.05805i	0.0388020	+	0.119420i
$298$		0			0
$299$	−47.6142			−2.75360
$300$		0			0
$301$	19.0725			1.09932
$302$		0			0
$303$	8.30233	+	25.5520i	0.476957	+	1.46792i
$304$		0			0
$305$	2.00655	−	25.4723i	0.114895	−	1.45854i
$306$		0			0
$307$	−19.2486			−1.09858			−0.549288	−	0.835633i	$-0.685101\pi$
$307$	−19.2486			−1.09858			−0.549288	+	0.835633i	$0.685101\pi$
$308$		0			0
$309$	−17.7308	+	12.8822i	−1.00867	+	0.732842i
$310$		0			0
$311$	16.8369	+	12.2327i	0.954735	+	0.693656i	0.951922	−	0.306341i	$-0.0991046\pi$
$311$	16.8369	+	12.2327i	0.954735	+	0.693656i	0.00281293	+	0.999996i	$0.499105\pi$
$312$		0			0
$313$	−10.8335	+	7.87098i	−0.612344	+	0.444894i	−0.850239	−	0.526397i	$-0.823543\pi$
$313$	−10.8335	+	7.87098i	−0.612344	+	0.444894i	0.237895	+	0.971291i	$0.423543\pi$
$314$		0			0
$315$	−13.2198	−	5.47694i	−0.744854	−	0.308591i
$316$		0			0
$317$	3.31924	−	10.2156i	0.186427	−	0.573764i	−0.813543	−	0.581505i	$-0.802464\pi$
$317$	3.31924	−	10.2156i	0.186427	−	0.573764i	0.999970	+	0.00774123i	$0.00246413\pi$
$318$		0			0
$319$	3.25667	−	10.0230i	0.182339	−	0.561181i
$320$		0			0
$321$	3.48322	+	10.7202i	0.194414	+	0.598346i
$322$		0			0
$323$	0.284720	+	0.206861i	0.0158423	+	0.0115101i
$324$		0			0
$325$	4.17979	+	26.4146i	0.231853	+	1.46522i
$326$		0			0
$327$	9.87016	+	7.17109i	0.545821	+	0.396562i
$328$		0			0
$329$	4.96370	+	15.2767i	0.273658	+	0.842231i
$330$		0			0
$331$	−2.63127	+	8.09821i	−0.144627	+	0.445118i	−0.996963	−	0.0778779i	$-0.975186\pi$
$331$	−2.63127	+	8.09821i	−0.144627	+	0.445118i	0.852335	+	0.522996i	$0.175186\pi$
$332$		0			0
$333$	−11.7457	+	36.1497i	−0.643663	+	1.98099i
$334$		0			0
$335$	−20.4777	+	4.91472i	−1.11882	+	0.268520i
$336$		0			0
$337$	4.98308	−	3.62042i	0.271446	−	0.197217i	−0.443732	−	0.896160i	$-0.646346\pi$
$337$	4.98308	−	3.62042i	0.271446	−	0.197217i	0.715178	+	0.698943i	$0.246346\pi$
$338$		0			0
$339$	4.18889	+	3.04341i	0.227509	+	0.165295i
$340$		0			0
$341$	−8.36619	+	6.07839i	−0.453055	+	0.329163i
$342$		0			0
$343$	−19.9328			−1.07627
$344$		0			0
$345$	−48.3889	+	11.6135i	−2.60517	+	0.625250i
$346$		0			0
$347$	−2.81658	−	8.66854i	−0.151202	−	0.465351i	0.846554	−	0.532302i	$-0.178673\pi$
$347$	−2.81658	−	8.66854i	−0.151202	−	0.465351i	−0.997756	+	0.0669508i	$0.978673\pi$
$348$		0			0
$349$	28.6909			1.53579			0.767893	−	0.640578i	$-0.221305\pi$
$349$	28.6909			1.53579			0.767893	+	0.640578i	$0.221305\pi$
$350$		0			0
$351$	3.33866			0.178204
$352$		0			0
$353$	−2.59408	−	7.98376i	−0.138069	−	0.424933i	0.857986	−	0.513673i	$-0.171716\pi$
$353$	−2.59408	−	7.98376i	−0.138069	−	0.424933i	−0.996055	+	0.0887408i	$0.971716\pi$
$354$		0			0
$355$	5.98811	−	7.01016i	0.317816	−	0.372061i
$356$		0			0
$357$	3.26462			0.172782
$358$		0			0
$359$	12.2475	−	8.89836i	0.646401	−	0.469638i	−0.215643	−	0.976472i	$-0.569185\pi$
$359$	12.2475	−	8.89836i	0.646401	−	0.469638i	0.862043	+	0.506835i	$0.169185\pi$
$360$		0			0
$361$	15.1435	+	11.0024i	0.797024	+	0.579072i
$362$		0			0
$363$	2.05949	−	1.49631i	0.108095	−	0.0785359i
$364$		0			0
$365$	1.85302	−	23.5234i	0.0969915	−	1.23127i
$366$		0			0
$367$	−5.47524	+	16.8511i	−0.285805	+	0.879618i	0.700351	+	0.713799i	$0.253027\pi$
$367$	−5.47524	+	16.8511i	−0.285805	+	0.879618i	−0.986156	+	0.165820i	$0.946973\pi$
$368$		0			0
$369$	0.822106	−	2.53018i	0.0427971	−	0.131716i
$370$		0			0
$371$	5.68718	+	17.5034i	0.295264	+	0.908729i
$372$		0			0
$373$	−21.9026	−	15.9132i	−1.13408	−	0.823954i	−0.147793	−	0.989018i	$-0.547217\pi$
$373$	−21.9026	−	15.9132i	−1.13408	−	0.823954i	−0.986283	+	0.165064i	$0.947217\pi$
$374$		0			0
$375$	10.6905	+	25.8249i	0.552056	+	1.33359i
$376$		0			0
$377$	−13.1544	−	9.55725i	−0.677487	−	0.492223i
$378$		0			0
$379$	−1.64450	−	5.06126i	−0.0844724	−	0.259979i	0.899895	−	0.436107i	$-0.143643\pi$
$379$	−1.64450	−	5.06126i	−0.0844724	−	0.259979i	−0.984367	+	0.176127i	$0.943643\pi$
$380$		0			0
$381$	−2.09180	+	6.43791i	−0.107166	+	0.329824i
$382$		0			0
$383$	−1.87276	+	5.76377i	−0.0956937	+	0.294515i	−0.987434	−	0.158033i	$-0.949485\pi$
$383$	−1.87276	+	5.76377i	−0.0956937	+	0.294515i	0.891740	+	0.452548i	$0.149485\pi$
$384$		0			0
$385$	−1.19878	+	15.2181i	−0.0610957	+	0.775586i
$386$		0			0
$387$	−25.4630	+	18.5000i	−1.29436	+	0.940406i
$388$		0			0
$389$	1.55863	+	1.13241i	0.0790259	+	0.0574156i	0.626597	−	0.779344i	$-0.284447\pi$
$389$	1.55863	+	1.13241i	0.0790259	+	0.0574156i	−0.547571	+	0.836759i	$0.684447\pi$
$390$		0			0
$391$	4.77593	−	3.46991i	0.241529	−	0.175481i
$392$		0			0
$393$	39.6614			2.00065
$394$		0			0
$395$	−10.8720	+	12.7276i	−0.547028	+	0.640395i
$396$		0			0
$397$	−4.10681	−	12.6395i	−0.206115	−	0.634357i	−0.999666	−	0.0258526i	$-0.991770\pi$
$397$	−4.10681	−	12.6395i	−0.206115	−	0.634357i	0.793551	−	0.608504i	$-0.208230\pi$
$398$		0			0
$399$	−2.61264			−0.130796
$400$		0			0
$401$	−7.73185			−0.386110			−0.193055	−	0.981188i	$-0.561840\pi$
$401$	−7.73185			−0.386110			−0.193055	+	0.981188i	$0.561840\pi$
$402$		0			0
$403$	4.93032	+	15.1740i	0.245597	+	0.755868i
$404$		0			0
$405$	−17.8046	+	4.27317i	−0.884719	+	0.212335i
$406$		0			0
$407$	40.5488			2.00993
$408$		0			0
$409$	3.26771	−	2.37413i	0.161578	−	0.117393i	−0.504058	−	0.863670i	$-0.668160\pi$
$409$	3.26771	−	2.37413i	0.161578	−	0.117393i	0.665636	+	0.746277i	$0.268160\pi$
$410$		0			0
$411$	44.0592	+	32.0109i	2.17328	+	1.57898i
$412$		0			0
$413$	−5.55895	+	4.03881i	−0.273538	+	0.198737i
$414$		0			0
$415$	8.24281	−	1.97830i	0.404624	−	0.0971109i
$416$		0			0
$417$	9.73738	−	29.9686i	0.476841	−	1.46757i
$418$		0			0
$419$	1.86222	−	5.73132i	0.0909754	−	0.279993i	−0.895209	−	0.445647i	$-0.852973\pi$
$419$	1.86222	−	5.73132i	0.0909754	−	0.279993i	0.986184	+	0.165654i	$0.0529735\pi$
$420$		0			0
$421$	7.28165	+	22.4106i	0.354886	+	1.09223i	0.956076	+	0.293120i	$0.0946936\pi$
$421$	7.28165	+	22.4106i	0.354886	+	1.09223i	−0.601190	+	0.799106i	$0.705306\pi$
$422$		0			0
$423$	−21.4450	−	15.5807i	−1.04269	−	0.757559i
$424$		0			0
$425$	−2.34423	−	2.34490i	−0.113712	−	0.113744i
$426$		0			0
$427$	−18.2046	−	13.2264i	−0.880983	−	0.640072i
$428$		0			0
$429$	−14.3244	−	44.0860i	−0.691589	−	2.12849i
$430$		0			0
$431$	−5.10679	+	15.7171i	−0.245985	+	0.757065i	0.749488	+	0.662018i	$0.230300\pi$
$431$	−5.10679	+	15.7171i	−0.245985	+	0.757065i	−0.995473	+	0.0950464i	$0.969700\pi$
$432$		0			0
$433$	−1.47609	+	4.54293i	−0.0709362	+	0.218319i	−0.980239	−	0.197815i	$-0.936615\pi$
$433$	−1.47609	+	4.54293i	−0.0709362	+	0.218319i	0.909303	+	0.416134i	$0.136615\pi$
$434$		0			0
$435$	−15.6995	−	6.50428i	−0.752735	−	0.311856i
$436$		0			0
$437$	−3.82212	+	2.77693i	−0.182837	+	0.132839i
$438$		0			0
$439$	20.7020	+	15.0409i	0.988054	+	0.717863i	0.959494	−	0.281729i	$-0.0909079\pi$
$439$	20.7020	+	15.0409i	0.988054	+	0.717863i	0.0285597	+	0.999592i	$0.490908\pi$
$440$		0			0
$441$	8.20823	−	5.96363i	0.390868	−	0.283982i
$442$		0			0
$443$	−29.2397			−1.38922			−0.694609	−	0.719387i	$-0.744423\pi$
$443$	−29.2397			−1.38922			−0.694609	+	0.719387i	$0.744423\pi$
$444$		0			0
$445$	−2.46272	+	31.2633i	−0.116744	+	1.48202i
$446$		0			0
$447$	−3.64109	−	11.2061i	−0.172218	−	0.530032i
$448$		0			0
$449$	−26.6658			−1.25844			−0.629219	−	0.777228i	$-0.716625\pi$
$449$	−26.6658			−1.25844			−0.629219	+	0.777228i	$0.716625\pi$
$450$		0			0
$451$	−2.83808			−0.133640
$452$		0			0
$453$	0.846819	+	2.60624i	0.0397870	+	0.122452i
$454$		0			0
$455$	21.7585	+	9.01447i	1.02005	+	0.422605i
$456$		0			0
$457$	14.8582			0.695037			0.347519	−	0.937673i	$-0.387024\pi$
$457$	14.8582			0.695037			0.347519	+	0.937673i	$0.387024\pi$
$458$		0			0
$459$	−0.334883	+	0.243307i	−0.0156310	+	0.0113566i
$460$		0			0
$461$	8.80835	+	6.39964i	0.410246	+	0.298061i	0.773701	−	0.633551i	$-0.218403\pi$
$461$	8.80835	+	6.39964i	0.410246	+	0.298061i	−0.363456	+	0.931612i	$0.618403\pi$
$462$		0			0
$463$	−25.2959	+	18.3786i	−1.17560	+	0.854124i	−0.991669	−	0.128815i	$-0.958883\pi$
$463$	−25.2959	+	18.3786i	−1.17560	+	0.854124i	−0.183932	+	0.982939i	$0.558883\pi$
$464$		0			0
$465$	8.71159	+	14.2183i	0.403990	+	0.659358i
$466$		0			0
$467$	3.24473	−	9.98625i	0.150148	−	0.462109i	−0.847489	−	0.530813i	$-0.821887\pi$
$467$	3.24473	−	9.98625i	0.150148	−	0.462109i	0.997637	+	0.0687046i	$0.0218866\pi$
$468$		0			0
$469$	−5.73109	+	17.6385i	−0.264637	+	0.814469i
$470$		0			0
$471$	8.83993	+	27.2065i	0.407323	+	1.25361i
$472$		0			0
$473$	27.1637	+	19.7356i	1.24899	+	0.907445i
$474$		0			0
$475$	1.87606	+	1.87660i	0.0860795	+	0.0861041i
$476$		0			0
$477$	−24.5707	−	17.8517i	−1.12501	−	0.817371i
$478$		0			0
$479$	−5.34884	−	16.4620i	−0.244395	−	0.752170i	−0.995735	−	0.0922552i	$-0.970592\pi$
$479$	−5.34884	−	16.4620i	−0.244395	−	0.752170i	0.751341	−	0.659915i	$-0.229408\pi$
$480$		0			0
$481$	19.3323	−	59.4985i	0.881475	−	2.71290i
$482$		0			0
$483$	−13.5426	+	41.6798i	−0.616209	+	1.89650i
$484$		0			0
$485$	−1.39002	+	1.62727i	−0.0631176	+	0.0738905i
$486$		0			0
$487$	25.5070	−	18.5319i	1.15583	−	0.839762i	0.166588	−	0.986027i	$-0.446725\pi$
$487$	25.5070	−	18.5319i	1.15583	−	0.839762i	0.989246	+	0.146264i	$0.0467250\pi$
$488$		0			0
$489$	−0.678930	−	0.493272i	−0.0307023	−	0.0223065i
$490$		0			0
$491$	−6.25902	+	4.54744i	−0.282465	+	0.205223i	−0.719992	−	0.693982i	$-0.755855\pi$
$491$	−6.25902	+	4.54744i	−0.282465	+	0.205223i	0.437527	+	0.899205i	$0.355855\pi$
$492$		0			0
$493$	2.01594			0.0907933
$494$		0			0
$495$	−13.1608	−	21.4799i	−0.591534	−	0.965451i
$496$		0			0
$497$	−2.50902	−	7.72196i	−0.112545	−	0.346377i
$498$		0			0
$499$	21.6134			0.967551			0.483775	−	0.875192i	$-0.339265\pi$
$499$	21.6134			0.967551			0.483775	+	0.875192i	$0.339265\pi$
$500$		0			0
$501$	−37.4816			−1.67455
$502$		0			0
$503$	−6.51486	−	20.0507i	−0.290483	−	0.894015i	−0.984701	−	0.174250i	$-0.944250\pi$
$503$	−6.51486	−	20.0507i	−0.290483	−	0.894015i	0.694218	−	0.719764i	$-0.255750\pi$
$504$		0			0
$505$	−12.5547	−	20.4908i	−0.558679	−	0.911827i
$506$		0			0
$507$	−39.0190			−1.73290
$508$		0			0
$509$	26.9208	−	19.5591i	1.19324	−	0.866942i	0.199639	−	0.979869i	$-0.436023\pi$
$509$	26.9208	−	19.5591i	1.19324	−	0.866942i	0.993603	+	0.112928i	$0.0360229\pi$
$510$		0			0
$511$	−16.8117	−	12.2144i	−0.743707	−	0.540335i
$512$		0			0
$513$	0.268003	−	0.194715i	0.0118326	−	0.00859690i
$514$		0			0
$515$	12.7323	−	14.9055i	0.561053	−	0.656813i
$516$		0			0
$517$	−8.73836	+	26.8939i	−0.384313	+	1.18279i
$518$		0			0
$519$	2.81345	−	8.65892i	0.123497	−	0.380084i
$520$		0			0
$521$	−12.9310	−	39.7975i	−0.566517	−	1.74356i	−0.663402	−	0.748263i	$-0.730888\pi$
$521$	−12.9310	−	39.7975i	−0.566517	−	1.74356i	0.0968854	−	0.995296i	$-0.469112\pi$
$522$		0			0
$523$	−10.9408	−	7.94897i	−0.478408	−	0.347584i	0.322301	−	0.946637i	$-0.395544\pi$
$523$	−10.9408	−	7.94897i	−0.478408	−	0.347584i	−0.800709	+	0.599053i	$0.795544\pi$
$524$		0			0
$525$	24.3112	+	3.85408i	1.06103	+	0.168206i
$526$		0			0
$527$	−1.60034	−	1.16272i	−0.0697121	−	0.0506488i
$528$		0			0
$529$	17.3815	+	53.4946i	0.755715	+	2.32585i
$530$		0			0
$531$	3.50399	−	10.7842i	0.152060	−	0.467993i
$532$		0			0
$533$	−1.35310	+	4.16441i	−0.0586092	+	0.180381i
$534$		0			0
$535$	−5.26731	−	8.59684i	−0.227725	−	0.371674i
$536$		0			0
$537$	37.4325	−	27.1963i	1.61533	−	1.17361i
$538$		0			0
$539$	−8.75647	−	6.36195i	−0.377168	−	0.274029i
$540$		0			0
$541$	−12.5679	+	9.13114i	−0.540338	+	0.392578i	−0.824210	−	0.566284i	$-0.808381\pi$
$541$	−12.5679	+	9.13114i	−0.540338	+	0.392578i	0.283873	+	0.958862i	$0.408381\pi$
$542$		0			0
$543$	0.0827155			0.00354966
$544$		0			0
$545$	−10.0815	−	4.17673i	−0.431844	−	0.178912i
$546$		0			0
$547$	14.0680	+	43.2969i	0.601505	+	1.85124i	0.519237	+	0.854630i	$0.326216\pi$
$547$	14.0680	+	43.2969i	0.601505	+	1.85124i	0.0822677	+	0.996610i	$0.473784\pi$
$548$		0			0
$549$	37.1337			1.58483
$550$		0			0
$551$	−1.61333			−0.0687303
$552$		0			0
$553$	4.55535	+	14.0199i	0.193713	+	0.596188i
$554$		0			0
$555$	5.13462	−	65.1819i	0.217952	−	2.76682i
$556$		0			0
$557$	−42.5997			−1.80501			−0.902504	−	0.430681i	$-0.858274\pi$
$557$	−42.5997			−1.80501			−0.902504	+	0.430681i	$0.858274\pi$
$558$		0			0
$559$	41.9094	−	30.4490i	1.77258	−	1.28786i
$560$		0			0
$561$	4.64960	+	3.37813i	0.196306	+	0.142625i
$562$		0			0
$563$	30.8212	−	22.3929i	1.29896	−	0.943749i	0.299015	−	0.954248i	$-0.403342\pi$
$563$	30.8212	−	22.3929i	1.29896	−	0.943749i	0.999945	+	0.0104990i	$0.00334199\pi$
$564$		0			0
$565$	−4.27858	−	1.77261i	−0.180001	−	0.0745741i
$566$		0			0
$567$	−4.98297	+	15.3360i	−0.209265	+	0.644052i
$568$		0			0
$569$	7.50437	−	23.0961i	0.314600	−	0.968238i	−0.661319	−	0.750104i	$-0.730003\pi$
$569$	7.50437	−	23.0961i	0.314600	−	0.968238i	0.975919	−	0.218133i	$-0.0699968\pi$
$570$		0			0
$571$	−6.78385	−	20.8786i	−0.283895	−	0.873740i	−0.986728	−	0.162384i	$-0.948082\pi$
$571$	−6.78385	−	20.8786i	−0.283895	−	0.873740i	0.702832	−	0.711356i	$-0.251918\pi$
$572$		0			0
$573$	9.23556	+	6.71003i	0.385821	+	0.280315i
$574$		0			0
$575$	39.6621	−	20.2017i	1.65402	−	0.842469i
$576$		0			0
$577$	−0.771248	−	0.560344i	−0.0321075	−	0.0233274i	0.571616	−	0.820521i	$-0.306317\pi$
$577$	−0.771248	−	0.560344i	−0.0321075	−	0.0233274i	−0.603723	+	0.797194i	$0.706317\pi$
$578$		0			0
$579$	−7.32873	−	22.5555i	−0.304572	−	0.937375i
$580$		0			0
$581$	2.30691	−	7.09994i	0.0957067	−	0.294555i
$582$		0			0
$583$	−10.0120	+	30.8138i	−0.414656	+	1.27618i
$584$		0			0
$585$	−37.7928	+	9.07040i	−1.56254	+	0.375015i
$586$		0			0
$587$	27.9455	−	20.3036i	1.15343	−	0.838018i	0.164499	−	0.986377i	$-0.447399\pi$
$587$	27.9455	−	20.3036i	1.15343	−	0.838018i	0.988934	+	0.148359i	$0.0473992\pi$
$588$		0			0
$589$	1.28074	+	0.930510i	0.0527718	+	0.0383410i
$590$		0			0
$591$	−25.4599	+	18.4977i	−1.04728	+	0.760895i
$592$		0			0
$593$	6.57624			0.270054			0.135027	−	0.990842i	$-0.456888\pi$
$593$	6.57624			0.270054			0.135027	+	0.990842i	$0.456888\pi$
$594$		0			0
$595$	−2.83941	+	0.681467i	−0.116404	+	0.0279374i
$596$		0			0
$597$	1.10929	+	3.41405i	0.0454003	+	0.139728i
$598$		0			0
$599$	−12.2044			−0.498656			−0.249328	−	0.968419i	$-0.580210\pi$
$599$	−12.2044			−0.498656			−0.249328	+	0.968419i	$0.580210\pi$
$600$		0			0
$601$	−13.4214			−0.547470			−0.273735	−	0.961805i	$-0.588259\pi$
$601$	−13.4214			−0.547470			−0.273735	+	0.961805i	$0.588259\pi$
$602$		0			0
$603$	−9.45762	−	29.1076i	−0.385144	−	1.18535i
$604$		0			0
$605$	−1.47890	+	1.73132i	−0.0601259	+	0.0703882i
$606$		0			0
$607$	−9.33640			−0.378953			−0.189476	−	0.981885i	$-0.560679\pi$
$607$	−9.33640			−0.378953			−0.189476	+	0.981885i	$0.560679\pi$
$608$		0			0
$609$	−12.1075	+	8.79661i	−0.490620	+	0.356456i
$610$		0			0
$611$	35.2962	+	25.6442i	1.42793	+	1.03745i
$612$		0			0
$613$	33.8925	−	24.6243i	1.36890	−	0.994567i	0.371082	−	0.928600i	$-0.378987\pi$
$613$	33.8925	−	24.6243i	1.36890	−	0.994567i	0.997822	−	0.0659665i	$-0.0210131\pi$
$614$		0			0
$615$	−0.359381	+	4.56220i	−0.0144916	+	0.183966i
$616$		0			0
$617$	3.41880	−	10.5220i	0.137636	−	0.423599i	−0.858355	−	0.513056i	$-0.828513\pi$
$617$	3.41880	−	10.5220i	0.137636	−	0.423599i	0.995991	+	0.0894573i	$0.0285133\pi$
$618$		0			0
$619$	−8.91155	+	27.4269i	−0.358185	+	1.10238i	0.595954	+	0.803019i	$0.296774\pi$
$619$	−8.91155	+	27.4269i	−0.358185	+	1.10238i	−0.954139	+	0.299363i	$0.903226\pi$
$620$		0			0
$621$	−1.71713	−	5.28479i	−0.0689061	−	0.212071i
$622$		0			0
$623$	22.3433	+	16.2334i	0.895167	+	0.650377i
$624$		0			0
$625$	−14.6888	−	20.2296i	−0.587554	−	0.809185i
$626$		0			0
$627$	−3.72102	−	2.70348i	−0.148603	−	0.107967i
$628$		0			0
$629$	2.39688	+	7.37683i	0.0955697	+	0.294133i
$630$		0			0
$631$	9.34671	−	28.7662i	0.372087	−	1.14516i	−0.573337	−	0.819320i	$-0.694351\pi$
$631$	9.34671	−	28.7662i	0.372087	−	1.14516i	0.945423	−	0.325845i	$-0.105649\pi$
$632$		0			0
$633$	−12.9932	+	39.9888i	−0.516432	+	1.58941i
$634$		0			0
$635$	0.475480	−	6.03603i	0.0188688	−	0.239532i
$636$		0			0
$637$	−13.5099	+	9.81550i	−0.535281	+	0.388904i
$638$		0			0
$639$	10.8399	+	7.87562i	0.428818	+	0.311555i
$640$		0			0
$641$	−3.27077	+	2.37635i	−0.129188	+	0.0938603i	−0.650503	−	0.759504i	$-0.725442\pi$
$641$	−3.27077	+	2.37635i	−0.129188	+	0.0938603i	0.521315	+	0.853364i	$0.325442\pi$
$642$		0			0
$643$	31.8273			1.25515			0.627573	−	0.778558i	$-0.284048\pi$
$643$	31.8273			1.25515			0.627573	+	0.778558i	$0.284048\pi$
$644$		0			0
$645$	35.1646	−	41.1665i	1.38460	−	1.62093i
$646$		0			0
$647$	−12.0407	−	37.0574i	−0.473369	−	1.45688i	−0.848145	−	0.529764i	$-0.822281\pi$
$647$	−12.0407	−	37.0574i	−0.473369	−	1.45688i	0.374777	−	0.927115i	$-0.377719\pi$
$648$		0			0
$649$	−12.0965			−0.474829
$650$		0			0
$651$	14.6850			0.575552
$652$		0			0
$653$	0.244228	+	0.751655i	0.00955736	+	0.0294145i	0.955721	−	0.294273i	$-0.0950774\pi$
$653$	0.244228	+	0.751655i	0.00955736	+	0.0294145i	−0.946164	+	0.323687i	$0.895077\pi$
$654$		0			0
$655$	−34.4956	+	8.27904i	−1.34785	+	0.323489i
$656$		0			0
$657$	34.2925			1.33788
$658$		0			0
$659$	1.76143	−	1.27975i	0.0686156	−	0.0498521i	−0.552949	−	0.833215i	$-0.686497\pi$
$659$	1.76143	−	1.27975i	0.0686156	−	0.0498521i	0.621564	+	0.783363i	$0.286497\pi$
$660$		0			0
$661$	11.5681	+	8.40468i	0.449945	+	0.326904i	0.789574	−	0.613655i	$-0.210302\pi$
$661$	11.5681	+	8.40468i	0.449945	+	0.326904i	−0.339629	+	0.940559i	$0.610302\pi$
$662$		0			0
$663$	7.17361	−	5.21193i	0.278600	−	0.202415i
$664$		0			0
$665$	2.27235	−	0.545370i	0.0881178	−	0.0211486i
$666$		0			0
$667$	−8.36268	+	25.7377i	−0.323804	+	0.996567i
$668$		0			0
$669$	−9.44201	+	29.0595i	−0.365049	+	1.12351i
$670$		0			0
$671$	−12.2414	−	37.6751i	−0.472574	−	1.45443i
$672$		0			0
$673$	9.48277	+	6.88964i	0.365534	+	0.265576i	0.755357	−	0.655314i	$-0.227464\pi$
$673$	9.48277	+	6.88964i	0.365534	+	0.265576i	−0.389823	+	0.920890i	$0.627464\pi$
$674$		0			0
$675$	−2.78106	+	1.41652i	−0.107043	+	0.0545219i
$676$		0			0
$677$	28.2613	+	20.5331i	1.08617	+	0.789149i	0.978749	−	0.205064i	$-0.0657403\pi$
$677$	28.2613	+	20.5331i	1.08617	+	0.789149i	0.107422	+	0.994213i	$0.465740\pi$
$678$		0			0
$679$	0.582418	+	1.79250i	0.0223511	+	0.0687897i
$680$		0			0
$681$	−11.7755	+	36.2412i	−0.451238	+	1.38877i
$682$		0			0
$683$	−12.1710	+	37.4584i	−0.465709	+	1.43330i	0.392380	+	0.919803i	$0.371652\pi$
$683$	−12.1710	+	37.4584i	−0.465709	+	1.43330i	−0.858089	+	0.513501i	$0.828348\pi$
$684$		0			0
$685$	−45.0025	−	18.6444i	−1.71946	−	0.712367i
$686$		0			0
$687$	−39.3786	+	28.6102i	−1.50239	+	1.09155i
$688$		0			0
$689$	40.4408	+	29.3819i	1.54067	+	1.11936i
$690$		0			0
$691$	25.2175	−	18.3216i	0.959318	−	0.696985i	0.00632573	−	0.999980i	$-0.497986\pi$
$691$	25.2175	−	18.3216i	0.959318	−	0.696985i	0.952992	+	0.302995i	$0.0979864\pi$
$692$		0			0
$693$	−22.1850			−0.842740
$694$		0			0
$695$	−2.21336	+	28.0978i	−0.0839577	+	1.06581i
$696$		0			0
$697$	−0.167762	−	0.516317i	−0.00635443	−	0.0195569i
$698$		0			0
$699$	50.4325			1.90753
$700$		0			0
$701$	29.1939			1.10264			0.551319	−	0.834295i	$-0.314125\pi$
$701$	29.1939			1.10264			0.551319	+	0.834295i	$0.314125\pi$
$702$		0			0
$703$	−1.91819	−	5.90359i	−0.0723460	−	0.222658i
$704$		0			0
$705$	42.1253	+	17.4524i	1.58653	+	0.657295i
$706$		0			0
$707$	−21.1634			−0.795932
$708$		0			0
$709$	38.5139	−	27.9820i	1.44642	−	1.05089i	0.459769	−	0.888039i	$-0.347932\pi$
$709$	38.5139	−	27.9820i	1.44642	−	1.05089i	0.986651	−	0.162847i	$-0.0520676\pi$
$710$		0			0
$711$	−19.6808	−	14.2989i	−0.738086	−	0.536251i
$712$		0			0
$713$	21.4832	−	15.6085i	0.804553	−	0.584542i
$714$		0			0
$715$	21.6613	+	35.3537i	0.810087	+	1.32215i
$716$		0			0
$717$	−0.0236250	+	0.0727102i	−0.000882291	+	0.00271541i
$718$		0			0
$719$	6.88230	−	21.1816i	0.256667	−	0.789939i	−0.736830	−	0.676078i	$-0.763678\pi$
$719$	6.88230	−	21.1816i	0.256667	−	0.789939i	0.993497	−	0.113861i	$-0.0363218\pi$
$720$		0			0
$721$	−5.33483	−	16.4189i	−0.198680	−	0.611473i
$722$		0			0
$723$	18.8643	+	13.7057i	0.701571	+	0.509721i
$724$		0			0
$725$	15.0124	+	2.37993i	0.557547	+	0.0883884i
$726$		0			0
$727$	−2.56712	−	1.86512i	−0.0952091	−	0.0691735i	0.539162	−	0.842202i	$-0.318741\pi$
$727$	−2.56712	−	1.86512i	−0.0952091	−	0.0691735i	−0.634371	+	0.773028i	$0.718741\pi$
$728$		0			0
$729$	−9.66970	−	29.7603i	−0.358137	−	1.10223i
$730$		0			0
$731$	−1.98472	+	6.10835i	−0.0734076	+	0.225925i
$732$		0			0
$733$	−6.09944	+	18.7721i	−0.225288	+	0.693365i	0.772974	+	0.634437i	$0.218768\pi$
$733$	−6.09944	+	18.7721i	−0.225288	+	0.693365i	−0.998262	+	0.0589275i	$0.981232\pi$
$734$		0			0
$735$	−11.3356	+	13.2704i	−0.418120	+	0.489485i
$736$		0			0
$737$	−26.4142	+	19.1910i	−0.972978	+	0.706910i
$738$		0			0
$739$	−12.3197	−	8.95076i	−0.453186	−	0.329259i	0.337666	−	0.941266i	$-0.390362\pi$
$739$	−12.3197	−	8.95076i	−0.453186	−	0.329259i	−0.790852	+	0.612007i	$0.790362\pi$
$740$		0			0
$741$	−5.74096	+	4.17105i	−0.210899	+	0.153227i
$742$		0			0
$743$	2.56670			0.0941631			0.0470816	−	0.998891i	$-0.485008\pi$
$743$	2.56670			0.0941631			0.0470816	+	0.998891i	$0.485008\pi$
$744$		0			0
$745$	5.50604	+	8.98649i	0.201726	+	0.329239i
$746$		0			0
$747$	3.80693	+	11.7165i	0.139288	+	0.428686i
$748$		0			0
$749$	−8.87904			−0.324433
$750$		0			0
$751$	2.25050			0.0821220			0.0410610	−	0.999157i	$-0.486926\pi$
$751$	2.25050			0.0821220			0.0410610	+	0.999157i	$0.486926\pi$
$752$		0			0
$753$	−7.10744	−	21.8745i	−0.259010	−	0.797150i
$754$		0			0
$755$	−1.28056	−	2.09001i	−0.0466042	−	0.0760633i
$756$		0			0
$757$	0.226086			0.00821722			0.00410861	−	0.999992i	$-0.498692\pi$
$757$	0.226086			0.00821722			0.00410861	+	0.999992i	$0.498692\pi$
$758$		0			0
$759$	−62.4168	+	45.3484i	−2.26558	+	1.64604i
$760$		0			0
$761$	−1.72984	−	1.25680i	−0.0627065	−	0.0455589i	0.555990	−	0.831189i	$-0.312339\pi$
$761$	−1.72984	−	1.25680i	−0.0627065	−	0.0455589i	−0.618697	+	0.785630i	$0.712339\pi$
$762$		0			0
$763$	−7.77485	+	5.64876i	−0.281468	+	0.204499i
$764$		0			0
$765$	3.12979	−	3.66398i	0.113158	−	0.132471i
$766$		0			0
$767$	−5.76719	+	17.7496i	−0.208241	+	0.640901i
$768$		0			0
$769$	−7.07289	+	21.7681i	−0.255055	+	0.784979i	0.738764	+	0.673964i	$0.235410\pi$
$769$	−7.07289	+	21.7681i	−0.255055	+	0.784979i	−0.993819	+	0.111014i	$0.964590\pi$
$770$		0			0
$771$	3.29964	+	10.1552i	0.118834	+	0.365732i
$772$		0			0
$773$	−18.6742	−	13.5676i	−0.671665	−	0.487993i	0.198917	−	0.980016i	$-0.436258\pi$
$773$	−18.6742	−	13.5676i	−0.671665	−	0.487993i	−0.870582	+	0.492023i	$0.836258\pi$
$774$		0			0
$775$	−10.5449	−	10.5479i	−0.378783	−	0.378891i
$776$		0			0
$777$	−46.5844	−	33.8455i	−1.67120	−	1.21420i
$778$		0			0
$779$	0.134258	+	0.413203i	0.00481028	+	0.0148045i
$780$		0			0
$781$	4.41701	−	13.5941i	0.158053	−	0.486437i
$782$		0			0
$783$	0.586382	−	1.80470i	0.0209556	−	0.0644947i
$784$		0			0
$785$	−13.3677	−	21.8176i	−0.477114	−	0.778704i
$786$		0			0
$787$	14.2972	−	10.3875i	0.509640	−	0.370275i	−0.303047	−	0.952976i	$-0.598004\pi$
$787$	14.2972	−	10.3875i	0.509640	−	0.370275i	0.812687	+	0.582700i	$0.198004\pi$
$788$		0			0
$789$	−18.0602	−	13.1215i	−0.642960	−	0.467138i
$790$		0			0
$791$	−3.29964	+	2.39733i	−0.117322	+	0.0852393i
$792$		0			0
$793$	−61.1182			−2.17037
$794$		0			0
$795$	48.2653	+	19.9962i	1.71179	+	0.709191i
$796$		0			0
$797$	−11.8102	−	36.3480i	−0.418339	−	1.28751i	−0.909230	−	0.416293i	$-0.863329\pi$
$797$	−11.8102	−	36.3480i	−0.418339	−	1.28751i	0.490892	−	0.871221i	$-0.336671\pi$
$798$		0			0
$799$	−5.40920			−0.191364
$800$		0			0
$801$	−45.5759			−1.61034
$802$		0			0
$803$	−11.3048	−	34.7925i	−0.398936	−	1.22780i
$804$		0			0
$805$	3.07831	−	39.0779i	0.108496	−	1.37732i
$806$		0			0
$807$	−7.74977			−0.272805
$808$		0			0
$809$	9.35284	−	6.79523i	0.328828	−	0.238908i	−0.411105	−	0.911588i	$-0.634857\pi$
$809$	9.35284	−	6.79523i	0.328828	−	0.238908i	0.739933	+	0.672680i	$0.234857\pi$
$810$		0			0
$811$	−11.1233	−	8.08153i	−0.390591	−	0.283781i	0.375107	−	0.926982i	$-0.377606\pi$
$811$	−11.1233	−	8.08153i	−0.390591	−	0.283781i	−0.765698	+	0.643201i	$0.777606\pi$
$812$		0			0
$813$	−15.6262	+	11.3531i	−0.548034	+	0.398170i
$814$		0			0
$815$	0.693467	+	0.287302i	0.0242911	+	0.0100637i
$816$		0			0
$817$	1.58835	−	4.88844i	0.0555694	−	0.171025i
$818$		0			0
$819$	−10.5771	+	32.5528i	−0.369592	+	1.13749i
$820$		0			0
$821$	3.66994	+	11.2949i	0.128082	+	0.394195i	0.994450	−	0.105211i	$-0.0335517\pi$
$821$	3.66994	+	11.2949i	0.128082	+	0.394195i	−0.866368	+	0.499406i	$0.833552\pi$
$822$		0			0
$823$	−0.660171	−	0.479642i	−0.0230121	−	0.0167193i	0.576220	−	0.817295i	$-0.304527\pi$
$823$	−0.660171	−	0.479642i	−0.0230121	−	0.0167193i	−0.599232	+	0.800576i	$0.704527\pi$
$824$		0			0
$825$	30.6368	+	30.6456i	1.06664	+	1.06694i
$826$		0			0
$827$	25.6601	+	18.6431i	0.892288	+	0.648285i	0.936474	−	0.350738i	$-0.114069\pi$
$827$	25.6601	+	18.6431i	0.892288	+	0.648285i	−0.0441855	+	0.999023i	$0.514069\pi$
$828$		0			0
$829$	−5.21242	−	16.0422i	−0.181035	−	0.557168i	0.818823	−	0.574046i	$-0.194627\pi$
$829$	−5.21242	−	16.0422i	−0.181035	−	0.557168i	−0.999858	+	0.0168788i	$0.994627\pi$
$830$		0			0
$831$	12.5248	−	38.5473i	0.434480	−	1.33719i
$832$		0			0
$833$	0.639793	−	1.96908i	0.0221675	−	0.0682246i
$834$		0			0
$835$	32.5996	−	7.82402i	1.12816	−	0.270761i
$836$		0			0
$837$	−1.50638	+	1.09445i	−0.0520681	+	0.0378297i
$838$		0			0
$839$	−10.4252	−	7.57437i	−0.359919	−	0.261496i	0.393099	−	0.919496i	$-0.371403\pi$
$839$	−10.4252	−	7.57437i	−0.359919	−	0.261496i	−0.753018	+	0.658000i	$0.771403\pi$
$840$		0			0
$841$	15.9850	−	11.6138i	0.551207	−	0.400475i
$842$		0			0
$843$	53.4001			1.83920
$844$		0			0
$845$	33.9368	−	8.14495i	1.16746	−	0.280195i
$846$		0			0
$847$	0.619659	+	1.90712i	0.0212917	+	0.0655293i
$848$		0			0
$849$	−68.3450			−2.34560
$850$		0			0
$851$	−104.124			−3.56931
$852$		0			0
$853$	−16.6069	−	51.1109i	−0.568610	−	1.75000i	−0.656972	−	0.753915i	$-0.728163\pi$
$853$	−16.6069	−	51.1109i	−0.568610	−	1.75000i	0.0883619	−	0.996088i	$-0.471837\pi$
$854$		0			0
$855$	−2.50473	+	2.93224i	−0.0856600	+	0.100280i
$856$		0			0
$857$	26.0296			0.889154			0.444577	−	0.895741i	$-0.353354\pi$
$857$	26.0296			0.889154			0.444577	+	0.895741i	$0.353354\pi$
$858$		0			0
$859$	−29.6664	+	21.5539i	−1.01221	+	0.735410i	−0.964670	−	0.263459i	$-0.915137\pi$
$859$	−29.6664	+	21.5539i	−1.01221	+	0.735410i	−0.0475348	+	0.998870i	$0.515137\pi$
$860$		0			0
$861$	3.26052	+	2.36891i	0.111118	+	0.0807322i
$862$		0			0
$863$	−8.00400	+	5.81525i	−0.272459	+	0.197953i	−0.715622	−	0.698488i	$-0.753857\pi$
$863$	−8.00400	+	5.81525i	−0.272459	+	0.197953i	0.443162	+	0.896441i	$0.353857\pi$
$864$		0			0
$865$	−0.639515	+	8.11839i	−0.0217442	+	0.276034i
$866$		0			0
$867$	12.7932	−	39.3733i	0.434479	−	1.33719i
$868$		0			0
$869$	−8.01948	+	24.6814i	−0.272042	+	0.837260i
$870$		0			0
$871$	15.5663	+	47.9080i	0.527442	+	1.62330i
$872$		0			0
$873$	−2.51626	−	1.82817i	−0.0851623	−	0.0618741i
$874$		0			0
$875$	−21.9492	+	1.72270i	−0.742018	+	0.0582380i
$876$		0			0
$877$	44.8420	+	32.5796i	1.51421	+	1.10014i	0.964267	+	0.264933i	$0.0853498\pi$
$877$	44.8420	+	32.5796i	1.51421	+	1.10014i	0.549941	+	0.835203i	$0.314650\pi$
$878$		0			0
$879$	−12.1336	−	37.3433i	−0.409255	−	1.25956i
$880$		0			0
$881$	0.808559	−	2.48849i	0.0272410	−	0.0838393i	−0.936512	−	0.350636i	$-0.885965\pi$
$881$	0.808559	−	2.48849i	0.0272410	−	0.0838393i	0.963753	+	0.266797i	$0.0859653\pi$
$882$		0			0
$883$	−1.55524	+	4.78654i	−0.0523380	+	0.161080i	−0.973809	−	0.227367i	$-0.926988\pi$
$883$	−1.55524	+	4.78654i	−0.0523380	+	0.161080i	0.921471	+	0.388447i	$0.126988\pi$
$884$		0			0
$885$	−1.53176	+	19.4451i	−0.0514894	+	0.653638i
$886$		0			0
$887$	19.7742	−	14.3668i	0.663954	−	0.482391i	−0.204042	−	0.978962i	$-0.565408\pi$
$887$	19.7742	−	14.3668i	0.663954	−	0.482391i	0.867996	+	0.496571i	$0.165408\pi$
$888$		0			0
$889$	−4.31384	−	3.13419i	−0.144682	−	0.105117i
$890$		0			0
$891$	−22.9661	+	16.6859i	−0.769395	+	0.558998i
$892$		0			0
$893$	4.32892			0.144862
$894$		0			0
$895$	−26.8799	+	31.4678i	−0.898497	+	1.05185i
$896$		0			0
$897$	36.7831	+	113.207i	1.22815	+	3.77986i
$898$		0			0
$899$	9.06816			0.302440
$900$		0			0
$901$	−6.19762			−0.206473
$902$		0			0
$903$	−14.7339	−	45.3464i	−0.490315	−	1.50903i
$904$		0			0
$905$	−0.0719419	+	0.0172663i	−0.00239143	+	0.000573951i
$906$		0			0
$907$	25.7407			0.854705			0.427353	−	0.904085i	$-0.359446\pi$
$907$	25.7407			0.854705			0.427353	+	0.904085i	$0.359446\pi$
$908$		0			0
$909$	28.2545	−	20.5281i	0.937143	−	0.680874i
$910$		0			0
$911$	23.5524	+	17.1119i	0.780327	+	0.566941i	0.905077	−	0.425247i	$-0.139813\pi$
$911$	23.5524	+	17.1119i	0.780327	+	0.566941i	−0.124750	+	0.992188i	$0.539813\pi$
$912$		0			0
$913$	10.6324	−	7.72487i	0.351880	−	0.255656i
$914$		0			0
$915$	−62.1127	+	14.9072i	−2.05338	+	0.492818i
$916$		0			0
$917$	−9.65425	+	29.7127i	−0.318811	+	0.981201i
$918$		0			0
$919$	−3.40072	+	10.4664i	−0.112180	+	0.345253i	−0.991348	−	0.131257i	$-0.958099\pi$
$919$	−3.40072	+	10.4664i	−0.112180	+	0.345253i	0.879169	+	0.476510i	$0.158099\pi$
$920$		0			0
$921$	14.8700	+	45.7651i	0.489983	+	1.50801i
$922$		0			0
$923$	−17.8413	−	12.9624i	−0.587252	−	0.426664i
$924$		0			0
$925$	9.14043	+	57.7638i	0.300536	+	1.89926i
$926$		0			0
$927$	23.0484	+	16.7456i	0.757009	+	0.549999i
$928$		0			0
$929$	−6.10267	−	18.7821i	−0.200222	−	0.616221i	−0.999876	−	0.0157591i	$-0.994984\pi$
$929$	−6.10267	−	18.7821i	−0.200222	−	0.616221i	0.799654	−	0.600462i	$-0.205016\pi$
$930$		0			0
$931$	−0.512019	+	1.57583i	−0.0167807	+	0.0516458i
$932$		0			0
$933$	16.0774	−	49.4813i	0.526352	−	1.61994i
$934$		0			0
$935$	−4.74915	−	1.96756i	−0.155314	−	0.0643461i
$936$		0			0
$937$	−42.9514	+	31.2061i	−1.40316	+	1.01946i	−0.408890	+	0.912584i	$0.634084\pi$
$937$	−42.9514	+	31.2061i	−1.40316	+	1.01946i	−0.994273	+	0.106874i	$0.965916\pi$
$938$		0			0
$939$	27.0830	+	19.6770i	0.883820	+	0.642133i
$940$		0			0
$941$	−19.0947	+	13.8731i	−0.622469	+	0.452250i	−0.853783	−	0.520629i	$-0.825698\pi$
$941$	−19.0947	+	13.8731i	−0.622469	+	0.452250i	0.231314	+	0.972879i	$0.425698\pi$
$942$		0			0
$943$	7.28780			0.237323
$944$		0			0
$945$	−0.215848	+	2.74010i	−0.00702153	+	0.0891356i
$946$		0			0
$947$	−6.12449	−	18.8492i	−0.199019	−	0.612518i	−0.999906	−	0.0137025i	$-0.995638\pi$
$947$	−6.12449	−	18.8492i	−0.199019	−	0.612518i	0.800887	−	0.598816i	$-0.204362\pi$
$948$		0			0
$949$	−56.4419			−1.83218
$950$		0			0
$951$	−26.8525			−0.870754
$952$		0			0
$953$	5.88467	+	18.1111i	0.190623	+	0.586678i	1.00000		0.000612273i	$-0.000194893\pi$
$953$	5.88467	+	18.1111i	0.190623	+	0.586678i	−0.809377	+	0.587290i	$0.800195\pi$
$954$		0			0
$955$	−9.43331	−	3.90819i	−0.305255	−	0.126466i
$956$		0			0
$957$	−26.3464			−0.851658
$958$		0			0
$959$	−34.7060	+	25.2154i	−1.12071	+	0.814246i
$960$		0			0
$961$	17.8808	+	12.9912i	0.576800	+	0.419070i
$962$		0			0
$963$	11.8541	−	8.61251i	0.381993	−	0.277534i
$964$		0			0
$965$	11.0825	+	18.0878i	0.356757	+	0.582268i
$966$		0			0
$967$	−9.31375	+	28.6648i	−0.299510	+	0.921798i	0.682159	+	0.731204i	$0.261041\pi$
$967$	−9.31375	+	28.6648i	−0.299510	+	0.921798i	−0.981669	+	0.190594i	$0.938959\pi$
$968$		0			0
$969$	0.271877	−	0.836751i	0.00873394	−	0.0268803i
$970$		0			0
$971$	−8.52605	−	26.2405i	−0.273614	−	0.842097i	−0.989583	−	0.143965i	$-0.954015\pi$
$971$	−8.52605	−	26.2405i	−0.273614	−	0.842097i	0.715969	−	0.698132i	$-0.245985\pi$
$972$		0			0
$973$	20.0810	+	14.5897i	0.643767	+	0.467724i
$974$		0			0
$975$	59.5738	−	30.3437i	1.90789	−	0.971775i
$976$		0			0
$977$	8.20867	+	5.96395i	0.262619	+	0.190804i	0.711301	−	0.702888i	$-0.248106\pi$
$977$	8.20867	+	5.96395i	0.262619	+	0.190804i	−0.448682	+	0.893691i	$0.648106\pi$
$978$		0			0
$979$	15.0244	+	46.2403i	0.480182	+	1.47785i
$980$		0			0
$981$	4.90074	−	15.0829i	0.156468	−	0.481560i
$982$		0			0
$983$	7.55672	−	23.2572i	0.241022	−	0.741789i	−0.755243	−	0.655445i	$-0.772481\pi$
$983$	7.55672	−	23.2572i	0.241022	−	0.741789i	0.996265	−	0.0863449i	$-0.0275187\pi$
$984$		0			0
$985$	18.2825	−	21.4030i	0.582530	−	0.681956i
$986$		0			0
$987$	32.4870	−	23.6032i	1.03407	−	0.751298i
$988$		0			0
$989$	−69.7527	−	50.6783i	−2.21801	−	1.61148i
$990$		0			0
$991$	−26.5943	+	19.3219i	−0.844797	+	0.613781i	−0.923706	−	0.383101i	$-0.874856\pi$
$991$	−26.5943	+	19.3219i	−0.844797	+	0.613781i	0.0789097	+	0.996882i	$0.474856\pi$
$992$		0			0
$993$	21.2869			0.675518
$994$		0			0
$995$	−1.67747	−	2.73782i	−0.0531793	−	0.0867947i
$996$		0			0
$997$	8.16684	+	25.1350i	0.258647	+	0.796032i	0.993089	+	0.117362i	$0.0374436\pi$
$997$	8.16684	+	25.1350i	0.258647	+	0.796032i	−0.734443	+	0.678671i	$0.762556\pi$
$998$		0			0
$999$	7.30104			0.230995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.g.241.1		16
4.3	odd	2		200.2.m.c.41.4	✓	16
20.3	even	4		1000.2.q.d.49.2		32
20.7	even	4		1000.2.q.d.49.7		32
20.19	odd	2		1000.2.m.c.201.1		16
25.6	even	5		10000.2.a.bk.1.1		8
25.11	even	5	inner	400.2.u.g.161.1		16
25.19	even	10		10000.2.a.bh.1.8		8
100.11	odd	10		200.2.m.c.161.4	yes	16
100.19	odd	10		5000.2.a.m.1.1		8
100.23	even	20		1000.2.q.d.449.7		32
100.27	even	20		1000.2.q.d.449.2		32
100.31	odd	10		5000.2.a.l.1.8		8
100.39	odd	10		1000.2.m.c.801.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.c.41.4	✓	16	4.3	odd	2
200.2.m.c.161.4	yes	16	100.11	odd	10
400.2.u.g.161.1		16	25.11	even	5	inner
400.2.u.g.241.1		16	1.1	even	1	trivial
1000.2.m.c.201.1		16	20.19	odd	2
1000.2.m.c.801.1		16	100.39	odd	10
1000.2.q.d.49.2		32	20.3	even	4
1000.2.q.d.49.7		32	20.7	even	4
1000.2.q.d.449.2		32	100.27	even	20
1000.2.q.d.449.7		32	100.23	even	20
5000.2.a.l.1.8		8	100.31	odd	10
5000.2.a.m.1.1		8	100.19	odd	10
10000.2.a.bh.1.8		8	25.19	even	10
10000.2.a.bk.1.1		8	25.6	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.772523 - 2.37758i) q^{3} +(1.16821 + 1.90664i) q^{5} +1.96923 q^{7} +(-2.62905 + 1.91012i) q^{9} +O(q^{10})\)	\(q+(-0.772523 - 2.37758i) q^{3} +(1.16821 + 1.90664i) q^{5} +1.96923 q^{7} +(-2.62905 + 1.91012i) q^{9} +(2.80465 + 2.03770i) q^{11} +(4.32714 - 3.14385i) q^{13} +(3.63074 - 4.25043i) q^{15} +(-0.204922 + 0.630686i) q^{17} +(0.163997 - 0.504731i) q^{19} +(-1.52128 - 4.68201i) q^{21} +(-7.20196 - 5.23253i) q^{23} +(-2.27059 + 4.45471i) q^{25} +(0.504994 + 0.366899i) q^{27} +(-0.939405 - 2.89119i) q^{29} +(-0.921788 + 2.83697i) q^{31} +(2.67814 - 8.24246i) q^{33} +(2.30047 + 3.75463i) q^{35} +(9.46267 - 6.87504i) q^{37} +(-10.8176 - 7.85944i) q^{39} +(-0.662310 + 0.481196i) q^{41} +9.68524 q^{43} +(-6.71320 - 2.78126i) q^{45} +(2.52063 + 7.75769i) q^{47} -3.12212 q^{49} +1.65782 q^{51} +(2.88802 + 8.88842i) q^{53} +(-0.608757 + 7.72793i) q^{55} -1.32673 q^{57} +(-2.82290 + 2.05096i) q^{59} +(-9.24453 - 6.71654i) q^{61} +(-5.17722 + 3.76147i) q^{63} +(11.0492 + 4.57766i) q^{65} +(-2.91032 + 8.95703i) q^{67} +(-6.87709 + 21.1655i) q^{69} +(-1.27411 - 3.92130i) q^{71} +(-8.53720 - 6.20264i) q^{73} +(12.3455 + 1.95715i) q^{75} +(5.52301 + 4.01270i) q^{77} +(2.31326 + 7.11949i) q^{79} +(-2.53041 + 7.78781i) q^{81} +(1.17148 - 3.60543i) q^{83} +(-1.44189 + 0.346057i) q^{85} +(-6.14833 + 4.46702i) q^{87} +(11.3462 + 8.24351i) q^{89} +(8.52115 - 6.19098i) q^{91} +7.45723 q^{93} +(1.15392 - 0.276946i) q^{95} +(0.295759 + 0.910252i) q^{97} -11.2658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) \) 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9	\( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9} + 10 q^{11} + q^{13} + 10 q^{15} - 4 q^{17} - 3 q^{21} - 11 q^{23} + 9 q^{25} - 13 q^{27} + 5 q^{29} + 9 q^{31} + 16 q^{33} - 24 q^{35} + 30 q^{37} - 14 q^{39} - 2 q^{41} + 42 q^{43} - 77 q^{45} + 16 q^{47} + 18 q^{49} - 100 q^{51} + 11 q^{53} + 24 q^{55} - 64 q^{57} + 53 q^{59} + 4 q^{61} + 38 q^{63} + 37 q^{65} + 14 q^{67} - 7 q^{69} + 6 q^{71} - 24 q^{73} + 15 q^{75} + 23 q^{77} + 22 q^{79} - 6 q^{81} - 33 q^{83} + 8 q^{85} - 37 q^{87} + 20 q^{89} + 27 q^{91} + 40 q^{93} + 24 q^{95} + 11 q^{97} - 122 q^{99}+O(q^{100}) \) 16 * q - q^3 - q^5 + 6 * q^7 - 11 * q^9 + 10 * q^11 + q^13 + 10 * q^15 - 4 * q^17 - 3 * q^21 - 11 * q^23 + 9 * q^25 - 13 * q^27 + 5 * q^29 + 9 * q^31 + 16 * q^33 - 24 * q^35 + 30 * q^37 - 14 * q^39 - 2 * q^41 + 42 * q^43 - 77 * q^45 + 16 * q^47 + 18 * q^49 - 100 * q^51 + 11 * q^53 + 24 * q^55 - 64 * q^57 + 53 * q^59 + 4 * q^61 + 38 * q^63 + 37 * q^65 + 14 * q^67 - 7 * q^69 + 6 * q^71 - 24 * q^73 + 15 * q^75 + 23 * q^77 + 22 * q^79 - 6 * q^81 - 33 * q^83 + 8 * q^85 - 37 * q^87 + 20 * q^89 + 27 * q^91 + 40 * q^93 + 24 * q^95 + 11 * q^97 - 122 * q^99

Introduction

L-functions

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Varieties

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Database

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