LMFDB - Embedded newform 656.2.u.h.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, 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("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			625.2
Root			$-1.29183 - 0.938568i$ of defining polynomial
Character	$\chi$	$=$	656.625
Dual form			656.2.u.h.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.59679 q^{3} +(-0.571528 - 1.75898i) q^{5} +(-1.03415 + 0.751356i) q^{7} -0.450271 q^{9} +O(q^{10})$	\(q-1.59679 q^{3} +(-0.571528 - 1.75898i) q^{5} +(-1.03415 + 0.751356i) q^{7} -0.450271 q^{9} +(-1.43165 + 4.40617i) q^{11} +(4.50781 + 3.27512i) q^{13} +(0.912609 + 2.80872i) q^{15} +(1.33199 - 4.09943i) q^{17} +(5.38615 - 3.91327i) q^{19} +(1.65132 - 1.19976i) q^{21} +(-2.53366 - 1.84081i) q^{23} +(1.27771 - 0.928311i) q^{25} +5.50935 q^{27} +(1.72141 + 5.29796i) q^{29} +(2.25091 - 6.92759i) q^{31} +(2.28604 - 7.03571i) q^{33} +(1.91267 + 1.38964i) q^{35} +(-1.60790 - 4.94861i) q^{37} +(-7.19802 - 5.22966i) q^{39} +(4.88418 + 4.14062i) q^{41} +(6.69051 + 4.86094i) q^{43} +(0.257343 + 0.792019i) q^{45} +(1.44780 + 1.05189i) q^{47} +(-1.65818 + 5.10336i) q^{49} +(-2.12690 + 6.54592i) q^{51} +(2.27067 + 6.98840i) q^{53} +8.56860 q^{55} +(-8.60054 + 6.24866i) q^{57} +(3.72589 + 2.70702i) q^{59} +(4.91155 - 3.56845i) q^{61} +(0.465649 - 0.338314i) q^{63} +(3.18453 - 9.80098i) q^{65} +(-1.10946 - 3.41457i) q^{67} +(4.04571 + 2.93938i) q^{69} +(1.34169 - 4.12930i) q^{71} -3.96550 q^{73} +(-2.04023 + 1.48231i) q^{75} +(-1.83005 - 5.63233i) q^{77} +0.450908 q^{79} -7.44644 q^{81} +6.52469 q^{83} -7.97210 q^{85} +(-2.74873 - 8.45971i) q^{87} +(-4.69418 + 3.41052i) q^{89} -7.12254 q^{91} +(-3.59423 + 11.0619i) q^{93} +(-9.96171 - 7.23761i) q^{95} +(4.32577 + 13.3133i) q^{97} +(0.644631 - 1.98397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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
$3$	−1.59679			−0.921905			−0.460953	−	0.887425i	$-0.652492\pi$
$3$	−1.59679			−0.921905			−0.460953	+	0.887425i	$0.652492\pi$
$4$		0			0
$5$	−0.571528	−	1.75898i	−0.255595	−	0.786641i	−0.993712	−	0.111968i	$-0.964285\pi$
$5$	−0.571528	−	1.75898i	−0.255595	−	0.786641i	0.738117	−	0.674673i	$-0.235715\pi$
$6$		0			0
$7$	−1.03415	+	0.751356i	−0.390873	+	0.283986i	−0.765813	−	0.643063i	$-0.777663\pi$
$7$	−1.03415	+	0.751356i	−0.390873	+	0.283986i	0.374940	+	0.927049i	$0.377663\pi$
$8$		0			0
$9$	−0.450271			−0.150090
$10$		0			0
$11$	−1.43165	+	4.40617i	−0.431659	+	1.32851i	0.464813	+	0.885409i	$0.346121\pi$
$11$	−1.43165	+	4.40617i	−0.431659	+	1.32851i	−0.896472	+	0.443100i	$0.853879\pi$
$12$		0			0
$13$	4.50781	+	3.27512i	1.25024	+	0.908354i	0.998236	−	0.0593715i	$-0.0189097\pi$
$13$	4.50781	+	3.27512i	1.25024	+	0.908354i	0.252006	+	0.967726i	$0.418910\pi$
$14$		0			0
$15$	0.912609	+	2.80872i	0.235635	+	0.725208i
$16$		0			0
$17$	1.33199	−	4.09943i	0.323054	−	0.994258i	−0.649257	−	0.760569i	$-0.724920\pi$
$17$	1.33199	−	4.09943i	0.323054	−	0.994258i	0.972311	−	0.233689i	$-0.0750799\pi$
$18$		0			0
$19$	5.38615	−	3.91327i	1.23567	−	0.897766i	0.238367	−	0.971175i	$-0.423388\pi$
$19$	5.38615	−	3.91327i	1.23567	−	0.897766i	0.997302	+	0.0734096i	$0.0233881\pi$
$20$		0			0
$21$	1.65132	−	1.19976i	0.360348	−	0.261808i
$22$		0			0
$23$	−2.53366	−	1.84081i	−0.528304	−	0.383836i	0.291419	−	0.956596i	$-0.405873\pi$
$23$	−2.53366	−	1.84081i	−0.528304	−	0.383836i	−0.819723	+	0.572760i	$0.805873\pi$
$24$		0			0
$25$	1.27771	−	0.928311i	0.255542	−	0.185662i
$26$		0			0
$27$	5.50935			1.06027
$28$		0			0
$29$	1.72141	+	5.29796i	0.319658	+	0.983806i	0.973795	+	0.227429i	$0.0730321\pi$
$29$	1.72141	+	5.29796i	0.319658	+	0.983806i	−0.654137	+	0.756376i	$0.726968\pi$
$30$		0			0
$31$	2.25091	−	6.92759i	0.404276	−	1.24423i	−0.517223	−	0.855851i	$-0.673034\pi$
$31$	2.25091	−	6.92759i	0.404276	−	1.24423i	0.921499	−	0.388382i	$-0.126966\pi$
$32$		0			0
$33$	2.28604	−	7.03571i	0.397949	−	1.22476i
$34$		0			0
$35$	1.91267	+	1.38964i	0.323300	+	0.234891i
$36$		0			0
$37$	−1.60790	−	4.94861i	−0.264337	−	0.813547i	−0.991845	−	0.127448i	$-0.959322\pi$
$37$	−1.60790	−	4.94861i	−0.264337	−	0.813547i	0.727508	−	0.686099i	$-0.240678\pi$
$38$		0			0
$39$	−7.19802	−	5.22966i	−1.15261	−	0.837417i
$40$		0			0
$41$	4.88418	+	4.14062i	0.762781	+	0.646657i
$41$	4.88418	+	4.14062i	0.762781	+	0.646657i
$42$		0			0
$43$	6.69051	+	4.86094i	1.02029	+	0.741286i	0.966343	−	0.257257i	$-0.0828188\pi$
$43$	6.69051	+	4.86094i	1.02029	+	0.741286i	0.0539502	+	0.998544i	$0.482819\pi$
$44$		0			0
$45$	0.257343	+	0.792019i	0.0383624	+	0.118067i
$46$		0			0
$47$	1.44780	+	1.05189i	0.211183	+	0.153433i	0.688349	−	0.725380i	$-0.258336\pi$
$47$	1.44780	+	1.05189i	0.211183	+	0.153433i	−0.477166	+	0.878813i	$0.658336\pi$
$48$		0			0
$49$	−1.65818	+	5.10336i	−0.236883	+	0.729052i
$50$		0			0
$51$	−2.12690	+	6.54592i	−0.297825	+	0.916612i
$52$		0			0
$53$	2.27067	+	6.98840i	0.311900	+	0.959931i	0.977012	+	0.213186i	$0.0683841\pi$
$53$	2.27067	+	6.98840i	0.311900	+	0.959931i	−0.665111	+	0.746744i	$0.731616\pi$
$54$		0			0
$55$	8.56860			1.15539
$56$		0			0
$57$	−8.60054	+	6.24866i	−1.13917	+	0.827655i
$58$		0			0
$59$	3.72589	+	2.70702i	0.485070	+	0.352424i	0.803285	−	0.595594i	$-0.203083\pi$
$59$	3.72589	+	2.70702i	0.485070	+	0.352424i	−0.318215	+	0.948019i	$0.603083\pi$
$60$		0			0
$61$	4.91155	−	3.56845i	0.628860	−	0.456893i	−0.227145	−	0.973861i	$-0.572939\pi$
$61$	4.91155	−	3.56845i	0.628860	−	0.456893i	0.856005	+	0.516968i	$0.172939\pi$
$62$		0			0
$63$	0.465649	−	0.338314i	0.0586663	−	0.0426236i
$64$		0			0
$65$	3.18453	−	9.80098i	0.394993	−	1.21566i
$66$		0			0
$67$	−1.10946	−	3.41457i	−0.135542	−	0.417156i	0.860132	−	0.510072i	$-0.170381\pi$
$67$	−1.10946	−	3.41457i	−0.135542	−	0.417156i	−0.995674	+	0.0929161i	$0.970381\pi$
$68$		0			0
$69$	4.04571	+	2.93938i	0.487047	+	0.353860i
$70$		0			0
$71$	1.34169	−	4.12930i	0.159230	−	0.490058i	−0.839335	−	0.543614i	$-0.817056\pi$
$71$	1.34169	−	4.12930i	0.159230	−	0.490058i	0.998565	+	0.0535559i	$0.0170555\pi$
$72$		0			0
$73$	−3.96550			−0.464127			−0.232064	−	0.972701i	$-0.574548\pi$
$73$	−3.96550			−0.464127			−0.232064	+	0.972701i	$0.574548\pi$
$74$		0			0
$75$	−2.04023	+	1.48231i	−0.235586	+	0.171163i
$76$		0			0
$77$	−1.83005	−	5.63233i	−0.208554	−	0.641863i
$78$		0			0
$79$	0.450908			0.0507311			0.0253655	−	0.999678i	$-0.491925\pi$
$79$	0.450908			0.0507311			0.0253655	+	0.999678i	$0.491925\pi$
$80$		0			0
$81$	−7.44644			−0.827382
$82$		0			0
$83$	6.52469			0.716178			0.358089	−	0.933687i	$-0.383428\pi$
$83$	6.52469			0.716178			0.358089	+	0.933687i	$0.383428\pi$
$84$		0			0
$85$	−7.97210			−0.864695
$86$		0			0
$87$	−2.74873	−	8.45971i	−0.294694	−	0.906976i
$88$		0			0
$89$	−4.69418	+	3.41052i	−0.497582	+	0.361515i	−0.808093	−	0.589055i	$-0.799500\pi$
$89$	−4.69418	+	3.41052i	−0.497582	+	0.361515i	0.310511	+	0.950570i	$0.399500\pi$
$90$		0			0
$91$	−7.12254			−0.746646
$92$		0			0
$93$	−3.59423	+	11.0619i	−0.372704	+	1.14706i
$94$		0			0
$95$	−9.96171	−	7.23761i	−1.02205	−	0.742563i
$96$		0			0
$97$	4.32577	+	13.3133i	0.439215	+	1.35176i	0.888705	+	0.458479i	$0.151606\pi$
$97$	4.32577	+	13.3133i	0.439215	+	1.35176i	−0.449490	+	0.893285i	$0.648394\pi$
$98$		0			0
$99$	0.644631	−	1.98397i	0.0647878	−	0.199396i
$100$		0			0
$101$	−8.50884	+	6.18203i	−0.846661	+	0.615135i	−0.924223	−	0.381852i	$-0.875286\pi$
$101$	−8.50884	+	6.18203i	−0.846661	+	0.615135i	0.0775625	+	0.996987i	$0.475286\pi$
$102$		0			0
$103$	10.9714	−	7.97116i	1.08104	−	0.785422i	0.103176	−	0.994663i	$-0.467099\pi$
$103$	10.9714	−	7.97116i	1.08104	−	0.785422i	0.977864	+	0.209241i	$0.0670994\pi$
$104$		0			0
$105$	−3.05413	−	2.21895i	−0.298052	−	0.216548i
$106$		0			0
$107$	−8.65104	+	6.28535i	−0.836327	+	0.607627i	−0.921342	−	0.388752i	$-0.872906\pi$
$107$	−8.65104	+	6.28535i	−0.836327	+	0.607627i	0.0850151	+	0.996380i	$0.472906\pi$
$108$		0			0
$109$	−2.35099			−0.225184			−0.112592	−	0.993641i	$-0.535915\pi$
$109$	−2.35099			−0.225184			−0.112592	+	0.993641i	$0.535915\pi$
$110$		0			0
$111$	2.56748	+	7.90188i	0.243694	+	0.750013i
$112$		0			0
$113$	2.93526	−	9.03381i	0.276126	−	0.849829i	−0.712793	−	0.701374i	$-0.752570\pi$
$113$	2.93526	−	9.03381i	0.276126	−	0.849829i	0.988919	−	0.148455i	$-0.0474299\pi$
$114$		0			0
$115$	−1.78990	+	5.50874i	−0.166909	+	0.513692i
$116$		0			0
$117$	−2.02974	−	1.47469i	−0.187649	−	0.136335i
$118$		0			0
$119$	1.70266	+	5.24023i	0.156082	+	0.480372i
$120$		0			0
$121$	−8.46549	−	6.15054i	−0.769590	−	0.559140i
$122$		0			0
$123$	−7.79900	−	6.61169i	−0.703212	−	0.596156i
$124$		0			0
$125$	−9.84453	−	7.15247i	−0.880521	−	0.639736i
$126$		0			0
$127$	−2.81564	−	8.66566i	−0.249848	−	0.768953i	−0.994801	−	0.101836i	$-0.967528\pi$
$127$	−2.81564	−	8.66566i	−0.249848	−	0.768953i	0.744953	−	0.667117i	$-0.232472\pi$
$128$		0			0
$129$	−10.6833	−	7.76189i	−0.940614	−	0.683396i
$130$		0			0
$131$	−3.00689	+	9.25425i	−0.262713	+	0.808547i	0.729499	+	0.683982i	$0.239753\pi$
$131$	−3.00689	+	9.25425i	−0.262713	+	0.808547i	−0.992211	+	0.124565i	$0.960247\pi$
$132$		0			0
$133$	−2.62985	+	8.09384i	−0.228037	+	0.701825i
$134$		0			0
$135$	−3.14875	−	9.69085i	−0.271001	−	0.834055i
$136$		0			0
$137$	22.2741			1.90301			0.951503	−	0.307640i	$-0.0995391\pi$
$137$	22.2741			1.90301			0.951503	+	0.307640i	$0.0995391\pi$
$138$		0			0
$139$	−15.7327	+	11.4305i	−1.33443	+	0.969519i	−0.334799	+	0.942290i	$0.608668\pi$
$139$	−15.7327	+	11.4305i	−1.33443	+	0.969519i	−0.999629	+	0.0272290i	$0.991332\pi$
$140$		0			0
$141$	−2.31182	−	1.67964i	−0.194691	−	0.141451i
$142$		0			0
$143$	−20.8843	+	15.1733i	−1.74643	+	1.26886i
$144$		0			0
$145$	8.33518	−	6.05586i	0.692199	−	0.502912i
$146$		0			0
$147$	2.64776	−	8.14898i	0.218384	−	0.672117i
$148$		0			0
$149$	−2.47565	−	7.61925i	−0.202813	−	0.624194i	−0.999796	−	0.0201923i	$-0.993572\pi$
$149$	−2.47565	−	7.61925i	−0.202813	−	0.624194i	0.796983	−	0.604001i	$-0.206428\pi$
$150$		0			0
$151$	7.28946	+	5.29610i	0.593208	+	0.430991i	0.843462	−	0.537190i	$-0.180514\pi$
$151$	7.28946	+	5.29610i	0.593208	+	0.430991i	−0.250254	+	0.968180i	$0.580514\pi$
$152$		0			0
$153$	−0.599755	+	1.84586i	−0.0484873	+	0.149229i
$154$		0			0
$155$	−13.4720			−1.08209
$156$		0			0
$157$	18.8127	−	13.6682i	1.50142	−	1.09084i	0.531607	−	0.846991i	$-0.321588\pi$
$157$	18.8127	−	13.6682i	1.50142	−	1.09084i	0.969812	−	0.243854i	$-0.0784117\pi$
$158$		0			0
$159$	−3.62577	−	11.1590i	−0.287543	−	0.884965i
$160$		0			0
$161$	4.00329			0.315504
$162$		0			0
$163$	20.9625			1.64191			0.820954	−	0.570994i	$-0.193442\pi$
$163$	20.9625			1.64191			0.820954	+	0.570994i	$0.193442\pi$
$164$		0			0
$165$	−13.6822			−1.06516
$166$		0			0
$167$	−14.6078			−1.13039			−0.565194	−	0.824958i	$-0.691199\pi$
$167$	−14.6078			−1.13039			−0.565194	+	0.824958i	$0.691199\pi$
$168$		0			0
$169$	5.57676	+	17.1635i	0.428981	+	1.32027i
$170$		0			0
$171$	−2.42523	+	1.76203i	−0.185462	+	0.134746i
$172$		0			0
$173$	3.45171			0.262429			0.131214	−	0.991354i	$-0.458112\pi$
$173$	3.45171			0.262429			0.131214	+	0.991354i	$0.458112\pi$
$174$		0			0
$175$	−0.623855	+	1.92003i	−0.0471590	+	0.145141i
$176$		0			0
$177$	−5.94946	−	4.32254i	−0.447189	−	0.324902i
$178$		0			0
$179$	3.75572	+	11.5589i	0.280716	+	0.863954i	0.987650	+	0.156675i	$0.0500775\pi$
$179$	3.75572	+	11.5589i	0.280716	+	0.863954i	−0.706935	+	0.707279i	$0.749923\pi$
$180$		0			0
$181$	8.24793	−	25.3845i	0.613064	−	1.88682i	0.186158	−	0.982520i	$-0.440397\pi$
$181$	8.24793	−	25.3845i	0.613064	−	1.88682i	0.426906	−	0.904296i	$-0.359603\pi$
$182$		0			0
$183$	−7.84270	+	5.69806i	−0.579749	+	0.421212i
$184$		0			0
$185$	−7.78556	+	5.65654i	−0.572406	+	0.415877i
$186$		0			0
$187$	16.1558	+	11.7379i	1.18143	+	0.858361i
$188$		0			0
$189$	−5.69751	+	4.13948i	−0.414433	+	0.301103i
$190$		0			0
$191$	−7.34338			−0.531348			−0.265674	−	0.964063i	$-0.585594\pi$
$191$	−7.34338			−0.531348			−0.265674	+	0.964063i	$0.585594\pi$
$192$		0			0
$193$	1.89813	+	5.84183i	0.136630	+	0.420504i	0.995840	−	0.0911189i	$-0.0290443\pi$
$193$	1.89813	+	5.84183i	0.136630	+	0.420504i	−0.859210	+	0.511623i	$0.829044\pi$
$194$		0			0
$195$	−5.08502	+	15.6501i	−0.364146	+	1.12073i
$196$		0			0
$197$	0.602962	−	1.85573i	0.0429593	−	0.132215i	−0.927277	−	0.374377i	$-0.877857\pi$
$197$	0.602962	−	1.85573i	0.0429593	−	0.132215i	0.970236	+	0.242162i	$0.0778566\pi$
$198$		0			0
$199$	−8.72756	−	6.34094i	−0.618680	−	0.449497i	0.233780	−	0.972289i	$-0.424890\pi$
$199$	−8.72756	−	6.34094i	−0.618680	−	0.449497i	−0.852460	+	0.522792i	$0.824890\pi$
$200$		0			0
$201$	1.77157	+	5.45234i	0.124957	+	0.384578i
$202$		0			0
$203$	−5.76085	−	4.18550i	−0.404333	−	0.293765i
$204$		0			0
$205$	4.49184	−	10.9577i	0.313723	−	0.765317i
$206$		0			0
$207$	1.14083	+	0.828864i	0.0792934	+	0.0576100i
$208$		0			0
$209$	9.53143	+	29.3347i	0.659303	+	2.02912i
$210$		0			0
$211$	−2.15829	−	1.56809i	−0.148583	−	0.107952i	0.511010	−	0.859575i	$-0.329271\pi$
$211$	−2.15829	−	1.56809i	−0.148583	−	0.107952i	−0.659593	+	0.751623i	$0.729271\pi$
$212$		0			0
$213$	−2.14240	+	6.59362i	−0.146795	+	0.451787i
$214$		0			0
$215$	4.72649	−	14.5467i	0.322344	−	0.992074i
$216$		0			0
$217$	2.87730	+	8.85542i	0.195324	+	0.601145i
$218$		0			0
$219$	6.33206			0.427881
$220$		0			0
$221$	19.4305	−	14.1171i	1.30703	−	0.949616i
$222$		0			0
$223$	−6.76652	−	4.91617i	−0.453120	−	0.329211i	0.337706	−	0.941251i	$-0.390349\pi$
$223$	−6.76652	−	4.91617i	−0.453120	−	0.329211i	−0.790826	+	0.612041i	$0.790349\pi$
$224$		0			0
$225$	−0.575316	+	0.417992i	−0.0383544	+	0.0278661i
$226$		0			0
$227$	16.4534	−	11.9541i	1.09205	−	0.793424i	0.112309	−	0.993673i	$-0.464175\pi$
$227$	16.4534	−	11.9541i	1.09205	−	0.793424i	0.979745	+	0.200250i	$0.0641754\pi$
$228$		0			0
$229$	−6.80221	+	20.9350i	−0.449502	+	1.38343i	0.427967	+	0.903794i	$0.359230\pi$
$229$	−6.80221	+	20.9350i	−0.449502	+	1.38343i	−0.877470	+	0.479632i	$0.840770\pi$
$230$		0			0
$231$	2.92221	+	8.99363i	0.192267	+	0.591737i
$232$		0			0
$233$	−21.0383	−	15.2852i	−1.37826	−	1.00137i	−0.997040	−	0.0768857i	$-0.975502\pi$
$233$	−21.0383	−	15.2852i	−1.37826	−	1.00137i	−0.381225	−	0.924482i	$-0.624498\pi$
$234$		0			0
$235$	1.02279	−	3.14783i	0.0667196	−	0.205342i
$236$		0			0
$237$	−0.720004			−0.0467693
$238$		0			0
$239$	−0.162413	+	0.118000i	−0.0105057	+	0.00763280i	−0.593026	−	0.805184i	$-0.702067\pi$
$239$	−0.162413	+	0.118000i	−0.0105057	+	0.00763280i	0.582520	+	0.812816i	$0.302067\pi$
$240$		0			0
$241$	−1.12647	−	3.46691i	−0.0725620	−	0.223323i	0.908198	−	0.418541i	$-0.137458\pi$
$241$	−1.12647	−	3.46691i	−0.0725620	−	0.223323i	−0.980760	+	0.195218i	$0.937458\pi$
$242$		0			0
$243$	−4.63766			−0.297506
$244$		0			0
$245$	9.92442			0.634048
$246$		0			0
$247$	37.0962			2.36037
$248$		0			0
$249$	−10.4185			−0.660248
$250$		0			0
$251$	1.59174	+	4.89888i	0.100470	+	0.309215i	0.988641	−	0.150299i	$-0.0480237\pi$
$251$	1.59174	+	4.89888i	0.100470	+	0.309215i	−0.888171	+	0.459514i	$0.848024\pi$
$252$		0			0
$253$	11.7382	−	8.52832i	0.737976	−	0.536171i
$254$		0			0
$255$	12.7297			0.797167
$256$		0			0
$257$	1.95619	−	6.02053i	0.122024	−	0.375550i	−0.871323	−	0.490709i	$-0.836738\pi$
$257$	1.95619	−	6.02053i	0.122024	−	0.375550i	0.993347	+	0.115159i	$0.0367377\pi$
$258$		0			0
$259$	5.38098	+	3.90951i	0.334358	+	0.242925i
$260$		0			0
$261$	−0.775102	−	2.38552i	−0.0479776	−	0.147660i
$262$		0			0
$263$	2.69756	−	8.30224i	0.166339	−	0.511938i	−0.832794	−	0.553583i	$-0.813260\pi$
$263$	2.69756	−	8.30224i	0.166339	−	0.511938i	0.999132	+	0.0416454i	$0.0132600\pi$
$264$		0			0
$265$	10.9947	−	7.98813i	0.675400	−	0.490707i
$266$		0			0
$267$	7.49561	−	5.44588i	0.458724	−	0.333282i
$268$		0			0
$269$	−11.3028	−	8.21198i	−0.689145	−	0.500693i	0.187234	−	0.982315i	$-0.440048\pi$
$269$	−11.3028	−	8.21198i	−0.689145	−	0.500693i	−0.876379	+	0.481622i	$0.840048\pi$
$270$		0			0
$271$	0.234607	−	0.170452i	0.0142513	−	0.0103542i	−0.580637	−	0.814163i	$-0.697196\pi$
$271$	0.234607	−	0.170452i	0.0142513	−	0.0103542i	0.594888	+	0.803809i	$0.297196\pi$
$272$		0			0
$273$	11.3732			0.688337
$274$		0			0
$275$	2.26106	+	6.95882i	0.136347	+	0.419632i
$276$		0			0
$277$	−8.17877	+	25.1717i	−0.491415	+	1.51242i	0.331056	+	0.943611i	$0.392595\pi$
$277$	−8.17877	+	25.1717i	−0.491415	+	1.51242i	−0.822470	+	0.568808i	$0.807405\pi$
$278$		0			0
$279$	−1.01352	+	3.11930i	−0.0606779	+	0.186747i
$280$		0			0
$281$	−12.1316	−	8.81410i	−0.723709	−	0.525805i	0.163858	−	0.986484i	$-0.447606\pi$
$281$	−12.1316	−	8.81410i	−0.723709	−	0.525805i	−0.887567	+	0.460679i	$0.847606\pi$
$282$		0			0
$283$	1.15061	+	3.54123i	0.0683969	+	0.210504i	0.979413	−	0.201867i	$-0.0647008\pi$
$283$	1.15061	+	3.54123i	0.0683969	+	0.210504i	−0.911016	+	0.412371i	$0.864701\pi$
$284$		0			0
$285$	15.9067	+	11.5569i	0.942233	+	0.684573i
$286$		0			0
$287$	−8.16207	−	0.612278i	−0.481792	−	0.0361416i
$288$		0			0
$289$	−1.27787	−	0.928429i	−0.0751690	−	0.0546134i
$290$		0			0
$291$	−6.90733	−	21.2586i	−0.404915	−	1.24620i
$292$		0			0
$293$	−17.8094	−	12.9393i	−1.04044	−	0.755921i	−0.0700653	−	0.997542i	$-0.522321\pi$
$293$	−17.8094	−	12.9393i	−1.04044	−	0.755921i	−0.970371	+	0.241621i	$0.922321\pi$
$294$		0			0
$295$	2.63215	−	8.10092i	0.153250	−	0.471654i
$296$		0			0
$297$	−7.88746	+	24.2751i	−0.457677	+	1.40858i
$298$		0			0
$299$	−5.39239	−	16.5961i	−0.311850	−	0.959775i
$300$		0			0
$301$	−10.5713			−0.609320
$302$		0			0
$303$	13.5868	−	9.87139i	0.780541	−	0.567096i
$304$		0			0
$305$	−9.08393	−	6.59986i	−0.520144	−	0.377907i
$306$		0			0
$307$	−0.209699	+	0.152355i	−0.0119681	+	0.00869536i	−0.593753	−	0.804647i	$-0.702354\pi$
$307$	−0.209699	+	0.152355i	−0.0119681	+	0.00869536i	0.581785	+	0.813343i	$0.302354\pi$
$308$		0			0
$309$	−17.5189	+	12.7282i	−0.996617	+	0.724085i
$310$		0			0
$311$	−5.15827	+	15.8755i	−0.292498	+	0.900217i	0.691552	+	0.722327i	$0.256927\pi$
$311$	−5.15827	+	15.8755i	−0.292498	+	0.900217i	−0.984050	+	0.177891i	$0.943073\pi$
$312$		0			0
$313$	3.07286	+	9.45730i	0.173688	+	0.534558i	0.999571	−	0.0292839i	$-0.00932268\pi$
$313$	3.07286	+	9.45730i	0.173688	+	0.534558i	−0.825883	+	0.563842i	$0.809323\pi$
$314$		0			0
$315$	−0.861220	−	0.625713i	−0.0485242	−	0.0352549i
$316$		0			0
$317$	6.95686	−	21.4110i	0.390736	−	1.20256i	−0.541497	−	0.840703i	$-0.682142\pi$
$317$	6.95686	−	21.4110i	0.390736	−	1.20256i	0.932233	−	0.361859i	$-0.117858\pi$
$318$		0			0
$319$	−25.8081			−1.44498
$320$		0			0
$321$	13.8139	−	10.0364i	0.771015	−	0.560175i
$322$		0			0
$323$	−8.86790	−	27.2926i	−0.493423	−	1.51860i
$324$		0			0
$325$	8.80000			0.488136
$326$		0			0
$327$	3.75403			0.207599
$328$		0			0
$329$	−2.28758			−0.126119
$330$		0			0
$331$	35.5145			1.95205			0.976026	−	0.217655i	$-0.0698409\pi$
$331$	35.5145			1.95205			0.976026	+	0.217655i	$0.0698409\pi$
$332$		0			0
$333$	0.723992	+	2.22822i	0.0396745	+	0.122106i
$334$		0			0
$335$	−5.37208	+	3.90304i	−0.293508	+	0.213246i
$336$		0			0
$337$	25.7775			1.40419			0.702094	−	0.712084i	$-0.252248\pi$
$337$	25.7775			1.40419			0.702094	+	0.712084i	$0.252248\pi$
$338$		0			0
$339$	−4.68699	+	14.4251i	−0.254562	+	0.783462i
$340$		0			0
$341$	27.3016	+	19.8358i	1.47846	+	1.07417i
$342$		0			0
$343$	−4.88471	−	15.0336i	−0.263749	−	0.811737i
$344$		0			0
$345$	2.85808	−	8.79628i	0.153874	−	0.473576i
$346$		0			0
$347$	22.5313	−	16.3699i	1.20954	−	0.878785i	0.214354	−	0.976756i	$-0.431235\pi$
$347$	22.5313	−	16.3699i	1.20954	−	0.878785i	0.995189	+	0.0979715i	$0.0312354\pi$
$348$		0			0
$349$	−28.4867	+	20.6968i	−1.52486	+	1.10788i	−0.565848	+	0.824510i	$0.691451\pi$
$349$	−28.4867	+	20.6968i	−1.52486	+	1.10788i	−0.959012	+	0.283366i	$0.908549\pi$
$350$		0			0
$351$	24.8351	+	18.0438i	1.32560	+	0.963105i
$352$		0			0
$353$	16.5323	−	12.0114i	0.879927	−	0.639304i	−0.0533052	−	0.998578i	$-0.516976\pi$
$353$	16.5323	−	12.0114i	0.879927	−	0.639304i	0.933232	+	0.359274i	$0.116976\pi$
$354$		0			0
$355$	−8.03019			−0.426198
$356$		0			0
$357$	−2.71878	−	8.36754i	−0.143893	−	0.442857i
$358$		0			0
$359$	−11.2364	+	34.5821i	−0.593035	+	1.82517i	−0.0287603	+	0.999586i	$0.509156\pi$
$359$	−11.2364	+	34.5821i	−0.593035	+	1.82517i	−0.564275	+	0.825587i	$0.690844\pi$
$360$		0			0
$361$	7.82565	−	24.0849i	0.411876	−	1.26762i
$362$		0			0
$363$	13.5176	+	9.82110i	0.709489	+	0.515474i
$364$		0			0
$365$	2.26640	+	6.97525i	0.118629	+	0.365101i
$366$		0			0
$367$	0.609095	+	0.442533i	0.0317945	+	0.0231000i	0.603569	−	0.797311i	$-0.293745\pi$
$367$	0.609095	+	0.442533i	0.0317945	+	0.0231000i	−0.571775	+	0.820411i	$0.693745\pi$
$368$		0			0
$369$	−2.19921	−	1.86440i	−0.114486	−	0.0970570i
$370$		0			0
$371$	−7.59899	−	5.52099i	−0.394520	−	0.286636i
$372$		0			0
$373$	1.31782	+	4.05582i	0.0682339	+	0.210002i	0.979359	−	0.202127i	$-0.0647853\pi$
$373$	1.31782	+	4.05582i	0.0682339	+	0.210002i	−0.911125	+	0.412129i	$0.864785\pi$
$374$		0			0
$375$	15.7196	+	11.4210i	0.811757	+	0.589776i
$376$		0			0
$377$	−9.59163	+	29.5200i	−0.493994	+	1.52036i
$378$		0			0
$379$	−6.29597	+	19.3770i	−0.323402	+	0.995330i	0.648754	+	0.760998i	$0.275290\pi$
$379$	−6.29597	+	19.3770i	−0.323402	+	0.995330i	−0.972157	+	0.234332i	$0.924710\pi$
$380$		0			0
$381$	4.49598	+	13.8372i	0.230336	+	0.708902i
$382$		0			0
$383$	19.5515			0.999036			0.499518	−	0.866304i	$-0.333510\pi$
$383$	19.5515			0.999036			0.499518	+	0.866304i	$0.333510\pi$
$384$		0			0
$385$	−8.86124	+	6.43807i	−0.451610	+	0.328114i
$386$		0			0
$387$	−3.01254	−	2.18874i	−0.153136	−	0.111260i
$388$		0			0
$389$	−18.0135	+	13.0876i	−0.913322	+	0.663567i	−0.941853	−	0.336026i	$-0.890917\pi$
$389$	−18.0135	+	13.0876i	−0.913322	+	0.663567i	0.0285309	+	0.999593i	$0.490917\pi$
$390$		0			0
$391$	−10.9211	+	7.93463i	−0.552303	+	0.401271i
$392$		0			0
$393$	4.80136	−	14.7771i	0.242196	−	0.745404i
$394$		0			0
$395$	−0.257706	−	0.793139i	−0.0129666	−	0.0399072i
$396$		0			0
$397$	15.2048	+	11.0470i	0.763109	+	0.554431i	0.899862	−	0.436174i	$-0.143667\pi$
$397$	15.2048	+	11.0470i	0.763109	+	0.554431i	−0.136753	+	0.990605i	$0.543667\pi$
$398$		0			0
$399$	4.19931	−	12.9241i	0.210228	−	0.647016i
$400$		0			0
$401$	−26.5301			−1.32485			−0.662424	−	0.749129i	$-0.730472\pi$
$401$	−26.5301			−1.32485			−0.662424	+	0.749129i	$0.730472\pi$
$402$		0			0
$403$	32.8354	−	23.8563i	1.63565	−	1.18837i
$404$		0			0
$405$	4.25585	+	13.0982i	0.211475	+	0.650853i
$406$		0			0
$407$	24.1064			1.19491
$408$		0			0
$409$	−0.757213			−0.0374418			−0.0187209	−	0.999825i	$-0.505959\pi$
$409$	−0.757213			−0.0374418			−0.0187209	+	0.999825i	$0.505959\pi$
$410$		0			0
$411$	−35.5670			−1.75439
$412$		0			0
$413$	−5.88708			−0.289684
$414$		0			0
$415$	−3.72904	−	11.4768i	−0.183052	−	0.563375i
$416$		0			0
$417$	25.1217	−	18.2520i	1.23022	−	0.893805i
$418$		0			0
$419$	−10.1749			−0.497075			−0.248537	−	0.968622i	$-0.579950\pi$
$419$	−10.1749			−0.497075			−0.248537	+	0.968622i	$0.579950\pi$
$420$		0			0
$421$	7.48442	−	23.0347i	0.364768	−	1.12264i	−0.585358	−	0.810775i	$-0.699046\pi$
$421$	7.48442	−	23.0347i	0.364768	−	1.12264i	0.950126	−	0.311866i	$-0.100954\pi$
$422$		0			0
$423$	−0.651901	−	0.473634i	−0.0316965	−	0.0230289i
$424$		0			0
$425$	−2.10365	−	6.47438i	−0.102042	−	0.314054i
$426$		0			0
$427$	−2.39812	+	7.38064i	−0.116053	+	0.357174i
$428$		0			0
$429$	33.3478	−	24.2286i	1.61005	−	1.16977i
$430$		0			0
$431$	5.51843	−	4.00937i	0.265813	−	0.193125i	−0.446893	−	0.894588i	$-0.647469\pi$
$431$	5.51843	−	4.00937i	0.265813	−	0.193125i	0.712706	+	0.701463i	$0.247469\pi$
$432$		0			0
$433$	1.62021	+	1.17715i	0.0778623	+	0.0565703i	0.626035	−	0.779795i	$-0.284677\pi$
$433$	1.62021	+	1.17715i	0.0778623	+	0.0565703i	−0.548173	+	0.836365i	$0.684677\pi$
$434$		0			0
$435$	−13.3095	+	9.66992i	−0.638142	+	0.463637i
$436$		0			0
$437$	−20.8503			−0.997403
$438$		0			0
$439$	−6.51090	−	20.0385i	−0.310748	−	0.956385i	−0.977469	−	0.211078i	$-0.932303\pi$
$439$	−6.51090	−	20.0385i	−0.310748	−	0.956385i	0.666721	−	0.745307i	$-0.267697\pi$
$440$		0			0
$441$	0.746632	−	2.29790i	0.0355539	−	0.109424i
$442$		0			0
$443$	−1.98282	+	6.10248i	−0.0942064	+	0.289938i	−0.987046	−	0.160437i	$-0.948710\pi$
$443$	−1.98282	+	6.10248i	−0.0942064	+	0.289938i	0.892840	+	0.450375i	$0.148710\pi$
$444$		0			0
$445$	8.68190	+	6.30777i	0.411562	+	0.299017i
$446$		0			0
$447$	3.95308	+	12.1663i	0.186974	+	0.575448i
$448$		0			0
$449$	13.7343	+	9.97852i	0.648160	+	0.470915i	0.862644	−	0.505812i	$-0.168807\pi$
$449$	13.7343	+	9.97852i	0.648160	+	0.470915i	−0.214484	+	0.976727i	$0.568807\pi$
$450$		0			0
$451$	−25.2367	+	15.5926i	−1.18835	+	0.734227i
$452$		0			0
$453$	−11.6397	−	8.45675i	−0.546881	−	0.397333i
$454$		0			0
$455$	4.07073	+	12.5284i	0.190839	+	0.587342i
$456$		0			0
$457$	−17.5677	−	12.7636i	−0.821780	−	0.597058i	0.0954418	−	0.995435i	$-0.469574\pi$
$457$	−17.5677	−	12.7636i	−0.821780	−	0.597058i	−0.917222	+	0.398377i	$0.869574\pi$
$458$		0			0
$459$	7.33838	−	22.5852i	0.342526	−	1.05419i
$460$		0			0
$461$	−1.18082	+	3.63420i	−0.0549964	+	0.169261i	−0.974782	−	0.223160i	$-0.928363\pi$
$461$	−1.18082	+	3.63420i	−0.0549964	+	0.169261i	0.919785	+	0.392422i	$0.128363\pi$
$462$		0			0
$463$	6.97903	+	21.4792i	0.324343	+	0.998225i	0.971736	+	0.236069i	$0.0758590\pi$
$463$	6.97903	+	21.4792i	0.324343	+	0.998225i	−0.647394	+	0.762156i	$0.724141\pi$
$464$		0			0
$465$	21.5119			0.997589
$466$		0			0
$467$	30.9209	−	22.4653i	1.43085	−	1.03957i	0.440990	−	0.897512i	$-0.354627\pi$
$467$	30.9209	−	22.4653i	1.43085	−	1.03957i	0.989858	−	0.142060i	$-0.0453727\pi$
$468$		0			0
$469$	3.71291	+	2.69758i	0.171446	+	0.124563i
$470$		0			0
$471$	−30.0399	+	21.8253i	−1.38417	+	1.00566i
$472$		0			0
$473$	−30.9966	+	22.5203i	−1.42522	+	1.03549i
$474$		0			0
$475$	3.24921	−	10.0000i	0.149084	−	0.458834i
$476$		0			0
$477$	−1.02242	−	3.14668i	−0.0468133	−	0.144076i
$478$		0			0
$479$	23.1454	+	16.8161i	1.05754	+	0.768349i	0.973632	−	0.228124i	$-0.0732592\pi$
$479$	23.1454	+	16.8161i	1.05754	+	0.768349i	0.0839100	+	0.996473i	$0.473259\pi$
$480$		0			0
$481$	8.95917	−	27.5735i	0.408503	−	1.25724i
$482$		0			0
$483$	−6.39241			−0.290865
$484$		0			0
$485$	20.9456	−	15.2179i	0.951092	−	0.691009i
$486$		0			0
$487$	−9.49919	−	29.2355i	−0.430449	−	1.32479i	−0.897679	−	0.440651i	$-0.854748\pi$
$487$	−9.49919	−	29.2355i	−0.430449	−	1.32479i	0.467229	−	0.884136i	$-0.345252\pi$
$488$		0			0
$489$	−33.4726			−1.51368
$490$		0			0
$491$	4.95876			0.223786			0.111893	−	0.993720i	$-0.464309\pi$
$491$	4.95876			0.223786			0.111893	+	0.993720i	$0.464309\pi$
$492$		0			0
$493$	24.0115			1.08142
$494$		0			0
$495$	−3.85819			−0.173413
$496$		0			0
$497$	1.71506	+	5.27842i	0.0769311	+	0.236769i
$498$		0			0
$499$	−26.5661	+	19.3014i	−1.18926	+	0.864049i	−0.993186	−	0.116539i	$-0.962820\pi$
$499$	−26.5661	+	19.3014i	−1.18926	+	0.864049i	−0.196076	+	0.980589i	$0.562820\pi$
$500$		0			0
$501$	23.3256			1.04211
$502$		0			0
$503$	2.80694	−	8.63888i	0.125155	−	0.385188i	−0.868774	−	0.495209i	$-0.835092\pi$
$503$	2.80694	−	8.63888i	0.125155	−	0.385188i	0.993929	+	0.110020i	$0.0350916\pi$
$504$		0			0
$505$	15.7371	+	11.4337i	0.700293	+	0.508792i
$506$		0			0
$507$	−8.90489	−	27.4064i	−0.395480	−	1.21716i
$508$		0			0
$509$	6.66689	−	20.5186i	0.295505	−	0.909469i	−0.687547	−	0.726140i	$-0.741312\pi$
$509$	6.66689	−	20.5186i	0.295505	−	0.909469i	0.983052	−	0.183330i	$-0.0586875\pi$
$510$		0			0
$511$	4.10094	−	2.97950i	0.181415	−	0.131806i
$512$		0			0
$513$	29.6742	−	21.5596i	1.31015	−	0.951878i
$514$		0			0
$515$	−20.2916	−	14.7427i	−0.894154	−	0.649641i
$516$		0			0
$517$	−6.70752	+	4.87330i	−0.294996	+	0.214327i
$518$		0			0
$519$	−5.51164			−0.241934
$520$		0			0
$521$	9.36230	+	28.8142i	0.410170	+	1.26237i	0.916501	+	0.400033i	$0.131001\pi$
$521$	9.36230	+	28.8142i	0.410170	+	1.26237i	−0.506331	+	0.862339i	$0.668999\pi$
$522$		0			0
$523$	−10.8802	+	33.4859i	−0.475759	+	1.46423i	0.369174	+	0.929360i	$0.379641\pi$
$523$	−10.8802	+	33.4859i	−0.475759	+	1.46423i	−0.844932	+	0.534874i	$0.820359\pi$
$524$		0			0
$525$	0.996164	−	3.06588i	0.0434762	−	0.133806i
$526$		0			0
$527$	−25.4010	−	18.4549i	−1.10649	−	0.803909i
$528$		0			0
$529$	−4.07655	−	12.5463i	−0.177241	−	0.545493i
$530$		0			0
$531$	−1.67766	−	1.21889i	−0.0728044	−	0.0528955i
$532$		0			0
$533$	8.45595	+	34.6614i	0.366268	+	1.50135i
$534$		0			0
$535$	16.0001	+	11.6248i	0.691746	+	0.502583i
$536$		0			0
$537$	−5.99708	−	18.4571i	−0.258793	−	0.796484i
$538$		0			0
$539$	−20.1123	−	14.6125i	−0.866299	−	0.629403i
$540$		0			0
$541$	6.39659	−	19.6867i	0.275011	−	0.846397i	−0.714205	−	0.699936i	$-0.753212\pi$
$541$	6.39659	−	19.6867i	0.275011	−	0.846397i	0.989216	−	0.146461i	$-0.0467882\pi$
$542$		0			0
$543$	−13.1702	+	40.5337i	−0.565187	+	1.73947i
$544$		0			0
$545$	1.34366	+	4.13536i	0.0575560	+	0.177139i
$546$		0			0
$547$	−3.52334			−0.150647			−0.0753236	−	0.997159i	$-0.523999\pi$
$547$	−3.52334			−0.150647			−0.0753236	+	0.997159i	$0.523999\pi$
$548$		0			0
$549$	−2.21153	+	1.60677i	−0.0943858	+	0.0685753i
$550$		0			0
$551$	30.0041	+	21.7993i	1.27822	+	0.928680i
$552$		0			0
$553$	−0.466308	+	0.338792i	−0.0198294	+	0.0144069i
$554$		0			0
$555$	12.4319	−	9.03229i	0.527704	−	0.383399i
$556$		0			0
$557$	−3.62466	+	11.1556i	−0.153582	+	0.472676i	−0.998014	−	0.0629855i	$-0.979938\pi$
$557$	−3.62466	+	11.1556i	−0.153582	+	0.472676i	0.844433	+	0.535662i	$0.179938\pi$
$558$		0			0
$559$	14.2394	+	43.8244i	0.602263	+	1.85358i
$560$		0			0
$561$	−25.7974	−	18.7429i	−1.08917	−	0.791327i
$562$		0			0
$563$	−9.93604	+	30.5800i	−0.418754	+	1.28879i	0.490095	+	0.871669i	$0.336962\pi$
$563$	−9.93604	+	30.5800i	−0.418754	+	1.28879i	−0.908850	+	0.417124i	$0.863038\pi$
$564$		0			0
$565$	−17.5679			−0.739087
$566$		0			0
$567$	7.70076	−	5.59493i	0.323401	−	0.234965i
$568$		0			0
$569$	−4.85926	−	14.9553i	−0.203711	−	0.626957i	−0.999764	−	0.0217303i	$-0.993082\pi$
$569$	−4.85926	−	14.9553i	−0.203711	−	0.626957i	0.796053	−	0.605227i	$-0.206918\pi$
$570$		0			0
$571$	4.42030			0.184984			0.0924919	−	0.995713i	$-0.470517\pi$
$571$	4.42030			0.184984			0.0924919	+	0.995713i	$0.470517\pi$
$572$		0			0
$573$	11.7258			0.489853
$574$		0			0
$575$	−4.94612			−0.206268
$576$		0			0
$577$	−27.1015			−1.12825			−0.564124	−	0.825690i	$-0.690786\pi$
$577$	−27.1015			−1.12825			−0.564124	+	0.825690i	$0.690786\pi$
$578$		0			0
$579$	−3.03090	−	9.32817i	−0.125960	−	0.387665i
$580$		0			0
$581$	−6.74753	+	4.90237i	−0.279935	+	0.203384i
$582$		0			0
$583$	−34.0429			−1.40991
$584$		0			0
$585$	−1.43390	+	4.41310i	−0.0592846	+	0.182459i
$586$		0			0
$587$	−31.8050	−	23.1077i	−1.31273	−	0.953756i	−0.999992	−	0.00391780i	$-0.998753\pi$
$587$	−31.8050	−	23.1077i	−1.31273	−	0.953756i	−0.312741	−	0.949839i	$-0.601247\pi$
$588$		0			0
$589$	−14.9858	−	46.1215i	−0.617478	−	1.90040i
$590$		0			0
$591$	−0.962803	+	2.96320i	−0.0396044	+	0.121890i
$592$		0			0
$593$	−19.7102	+	14.3203i	−0.809402	+	0.588065i	−0.913657	−	0.406485i	$-0.866754\pi$
$593$	−19.7102	+	14.3203i	−0.809402	+	0.588065i	0.104255	+	0.994551i	$0.466754\pi$
$594$		0			0
$595$	8.24437	−	5.98988i	0.337986	−	0.245561i
$596$		0			0
$597$	13.9360	+	10.1251i	0.570364	+	0.414394i
$598$		0			0
$599$	−1.32095	+	0.959724i	−0.0539724	+	0.0392133i	−0.614444	−	0.788960i	$-0.710620\pi$
$599$	−1.32095	+	0.959724i	−0.0539724	+	0.0392133i	0.560472	+	0.828173i	$0.310620\pi$
$600$		0			0
$601$	−4.95681			−0.202193			−0.101096	−	0.994877i	$-0.532235\pi$
$601$	−4.95681			−0.202193			−0.101096	+	0.994877i	$0.532235\pi$
$602$		0			0
$603$	0.499558	+	1.53748i	0.0203436	+	0.0626111i
$604$		0			0
$605$	−5.98042	+	18.4058i	−0.243139	+	0.748304i
$606$		0			0
$607$	4.27416	−	13.1545i	0.173483	−	0.533925i	−0.826078	−	0.563555i	$-0.809433\pi$
$607$	4.27416	−	13.1545i	0.173483	−	0.533925i	0.999561	+	0.0296307i	$0.00943312\pi$
$608$		0			0
$609$	9.19885	+	6.68336i	0.372756	+	0.270823i
$610$		0			0
$611$	3.08135	+	9.48341i	0.124658	+	0.383658i
$612$		0			0
$613$	−22.6693	−	16.4702i	−0.915605	−	0.665226i	0.0268209	−	0.999640i	$-0.491462\pi$
$613$	−22.6693	−	16.4702i	−0.915605	−	0.665226i	−0.942426	+	0.334414i	$0.891462\pi$
$614$		0			0
$615$	−7.17251	+	17.4971i	−0.289223	+	0.705550i
$616$		0			0
$617$	5.18446	+	3.76673i	0.208718	+	0.151643i	0.687234	−	0.726436i	$-0.258825\pi$
$617$	5.18446	+	3.76673i	0.208718	+	0.151643i	−0.478515	+	0.878079i	$0.658825\pi$
$618$		0			0
$619$	−12.8741	−	39.6224i	−0.517453	−	1.59256i	−0.778773	−	0.627305i	$-0.784158\pi$
$619$	−12.8741	−	39.6224i	−0.517453	−	1.59256i	0.261320	−	0.965252i	$-0.415842\pi$
$620$		0			0
$621$	−13.9588	−	10.1417i	−0.560148	−	0.406971i
$622$		0			0
$623$	2.29198	−	7.05400i	0.0918264	−	0.282613i
$624$		0			0
$625$	−4.51443	+	13.8940i	−0.180577	+	0.555760i
$626$		0			0
$627$	−15.2197	−	46.8413i	−0.607815	−	1.87066i
$628$		0			0
$629$	−22.4282			−0.894271
$630$		0			0
$631$	1.09391	−	0.794771i	0.0435478	−	0.0316393i	−0.565798	−	0.824544i	$-0.691432\pi$
$631$	1.09391	−	0.794771i	0.0435478	−	0.0316393i	0.609346	+	0.792904i	$0.291432\pi$
$632$		0			0
$633$	3.44633	+	2.50391i	0.136979	+	0.0995214i
$634$		0			0
$635$	−13.6335	+	9.90534i	−0.541030	+	0.393081i
$636$		0			0
$637$	−24.1889	+	17.5743i	−0.958399	+	0.696317i
$638$		0			0
$639$	−0.604125	+	1.85931i	−0.0238988	+	0.0735530i
$640$		0			0
$641$	−3.16214	−	9.73205i	−0.124897	−	0.384393i	0.868985	−	0.494838i	$-0.164772\pi$
$641$	−3.16214	−	9.73205i	−0.124897	−	0.384393i	−0.993882	+	0.110445i	$0.964772\pi$
$642$		0			0
$643$	19.2733	+	14.0029i	0.760066	+	0.552220i	0.898931	−	0.438091i	$-0.144345\pi$
$643$	19.2733	+	14.0029i	0.760066	+	0.552220i	−0.138864	+	0.990311i	$0.544345\pi$
$644$		0			0
$645$	−7.54720	+	23.2279i	−0.297171	+	0.914598i
$646$		0			0
$647$	3.73622			0.146886			0.0734430	−	0.997299i	$-0.476601\pi$
$647$	3.73622			0.146886			0.0734430	+	0.997299i	$0.476601\pi$
$648$		0			0
$649$	−17.2618	+	12.5414i	−0.677583	+	0.492293i
$650$		0			0
$651$	−4.59444	−	14.1402i	−0.180070	−	0.554199i
$652$		0			0
$653$	−39.0715			−1.52898			−0.764492	−	0.644633i	$-0.777010\pi$
$653$	−39.0715			−1.52898			−0.764492	+	0.644633i	$0.777010\pi$
$654$		0			0
$655$	17.9966			0.703184
$656$		0			0
$657$	1.78555			0.0696610
$658$		0			0
$659$	−10.9967			−0.428371			−0.214186	−	0.976793i	$-0.568710\pi$
$659$	−10.9967			−0.428371			−0.214186	+	0.976793i	$0.568710\pi$
$660$		0			0
$661$	14.1417	+	43.5236i	0.550047	+	1.69287i	0.708676	+	0.705534i	$0.249293\pi$
$661$	14.1417	+	43.5236i	0.550047	+	1.69287i	−0.158629	+	0.987338i	$0.550707\pi$
$662$		0			0
$663$	−31.0263	+	22.5419i	−1.20496	+	0.875456i
$664$		0			0
$665$	15.7399			0.610369
$666$		0			0
$667$	5.39107	−	16.5920i	0.208743	−	0.642445i
$668$		0			0
$669$	10.8047	+	7.85007i	0.417734	+	0.303501i
$670$		0			0
$671$	8.69156	+	26.7499i	0.335534	+	1.03267i
$672$		0			0
$673$	0.226646	−	0.697544i	0.00873656	−	0.0268884i	−0.946593	−	0.322430i	$-0.895500\pi$
$673$	0.226646	−	0.697544i	0.00873656	−	0.0268884i	0.955330	+	0.295542i	$0.0955002\pi$
$674$		0			0
$675$	7.03935	−	5.11439i	0.270945	−	0.196853i
$676$		0			0
$677$	−21.8378	+	15.8661i	−0.839295	+	0.609784i	−0.922174	−	0.386776i	$-0.873589\pi$
$677$	−21.8378	+	15.8661i	−0.839295	+	0.609784i	0.0828785	+	0.996560i	$0.473589\pi$
$678$		0			0
$679$	−14.4766	−	10.5178i	−0.555559	−	0.403637i
$680$		0			0
$681$	−26.2727	+	19.0882i	−1.00677	+	0.731461i
$682$		0			0
$683$	−35.0800			−1.34230			−0.671150	−	0.741322i	$-0.734199\pi$
$683$	−35.0800			−1.34230			−0.671150	+	0.741322i	$0.734199\pi$
$684$		0			0
$685$	−12.7303	−	39.1798i	−0.486399	−	1.49698i
$686$		0			0
$687$	10.8617	−	33.4288i	0.414399	−	1.27539i
$688$		0			0
$689$	−12.6521	+	38.9391i	−0.482006	+	1.48346i
$690$		0			0
$691$	−12.9830	−	9.43268i	−0.493895	−	0.358836i	0.312785	−	0.949824i	$-0.398738\pi$
$691$	−12.9830	−	9.43268i	−0.493895	−	0.358836i	−0.806680	+	0.590988i	$0.798738\pi$
$692$		0			0
$693$	0.824021	+	2.53607i	0.0313020	+	0.0963375i
$694$		0			0
$695$	29.0976	+	21.1407i	1.10374	+	0.801911i
$696$		0			0
$697$	23.4799	−	14.5071i	0.889364	−	0.549496i
$698$		0			0
$699$	33.5937	+	24.4072i	1.27063	+	0.923167i
$700$		0			0
$701$	−7.28884	−	22.4327i	−0.275296	−	0.847273i	−0.989141	−	0.146969i	$-0.953048\pi$
$701$	−7.28884	−	22.4327i	−0.275296	−	0.847273i	0.713845	−	0.700303i	$-0.246952\pi$
$702$		0			0
$703$	−28.0257	−	20.3618i	−1.05701	−	0.767961i
$704$		0			0
$705$	−1.63318	+	5.02642i	−0.0615092	+	0.189306i
$706$		0			0
$707$	4.15453	−	12.7863i	0.156247	−	0.480879i
$708$		0			0
$709$	−0.764286	−	2.35223i	−0.0287034	−	0.0883399i	0.935679	−	0.352853i	$-0.114789\pi$
$709$	−0.764286	−	2.35223i	−0.0287034	−	0.0883399i	−0.964382	+	0.264514i	$0.914789\pi$
$710$		0			0
$711$	−0.203031			−0.00761425
$712$		0			0
$713$	−18.4554	+	13.4087i	−0.691161	+	0.502158i
$714$		0			0
$715$	38.6256	+	28.0632i	1.44452	+	1.04950i
$716$		0			0
$717$	0.259340	−	0.188421i	0.00968522	−	0.00703672i
$718$		0			0
$719$	35.5701	−	25.8432i	1.32654	−	0.963789i	0.326716	−	0.945123i	$-0.394058\pi$
$719$	35.5701	−	25.8432i	1.32654	−	0.963789i	0.999826	−	0.0186663i	$-0.00594202\pi$
$720$		0			0
$721$	−5.35688	+	16.4868i	−0.199501	+	0.614000i
$722$		0			0
$723$	1.79873	+	5.53591i	0.0668953	+	0.205883i
$724$		0			0
$725$	7.11761	+	5.17125i	0.264341	+	0.192055i
$726$		0			0
$727$	−4.06898	+	12.5230i	−0.150910	+	0.464454i	−0.997724	−	0.0674363i	$-0.978518\pi$
$727$	−4.06898	+	12.5230i	−0.150910	+	0.464454i	0.846813	+	0.531890i	$0.178518\pi$
$728$		0			0
$729$	29.7447			1.10166
$730$		0			0
$731$	28.8388	−	20.9526i	1.06664	−	0.774960i
$732$		0			0
$733$	1.33504	+	4.10884i	0.0493109	+	0.151763i	0.972680	−	0.232150i	$-0.0745761\pi$
$733$	1.33504	+	4.10884i	0.0493109	+	0.151763i	−0.923369	+	0.383914i	$0.874576\pi$
$734$		0			0
$735$	−15.8472			−0.584532
$736$		0			0
$737$	16.6335			0.612703
$738$		0			0
$739$	−6.07440			−0.223450			−0.111725	−	0.993739i	$-0.535638\pi$
$739$	−6.07440			−0.223450			−0.111725	+	0.993739i	$0.535638\pi$
$740$		0			0
$741$	−59.2347			−2.17604
$742$		0			0
$743$	−15.2015	−	46.7855i	−0.557690	−	1.71639i	−0.688732	−	0.725016i	$-0.741832\pi$
$743$	−15.2015	−	46.7855i	−0.557690	−	1.71639i	0.131042	−	0.991377i	$-0.458168\pi$
$744$		0			0
$745$	−11.9872	+	8.70924i	−0.439178	+	0.319082i
$746$		0			0
$747$	−2.93788			−0.107491
$748$		0			0
$749$	4.22396	−	13.0000i	0.154340	−	0.475010i
$750$		0			0
$751$	−8.74919	−	6.35666i	−0.319262	−	0.231958i	0.416598	−	0.909091i	$-0.363222\pi$
$751$	−8.74919	−	6.35666i	−0.319262	−	0.231958i	−0.735861	+	0.677133i	$0.763222\pi$
$752$		0			0
$753$	−2.54167	−	7.82247i	−0.0926237	−	0.285067i
$754$		0			0
$755$	5.14962	−	15.8489i	0.187414	−	0.576801i
$756$		0			0
$757$	26.4995	−	19.2530i	0.963142	−	0.699764i	0.00926370	−	0.999957i	$-0.497051\pi$
$757$	26.4995	−	19.2530i	0.963142	−	0.699764i	0.953878	+	0.300193i	$0.0970512\pi$
$758$		0			0
$759$	−18.7435	+	13.6179i	−0.680344	+	0.494299i
$760$		0			0
$761$	−7.49569	−	5.44594i	−0.271719	−	0.197415i	0.443579	−	0.896235i	$-0.353709\pi$
$761$	−7.49569	−	5.44594i	−0.271719	−	0.197415i	−0.715297	+	0.698820i	$0.753709\pi$
$762$		0			0
$763$	2.43129	−	1.76643i	0.0880184	−	0.0639491i
$764$		0			0
$765$	3.58961			0.129783
$766$		0			0
$767$	7.92982	+	24.4055i	0.286329	+	0.881231i
$768$		0			0
$769$	−3.81322	+	11.7359i	−0.137508	+	0.423207i	−0.995972	−	0.0896679i	$-0.971419\pi$
$769$	−3.81322	+	11.7359i	−0.137508	+	0.423207i	0.858463	+	0.512875i	$0.171419\pi$
$770$		0			0
$771$	−3.12362	+	9.61350i	−0.112494	+	0.346222i
$772$		0			0
$773$	−19.4756	−	14.1498i	−0.700487	−	0.508934i	0.179604	−	0.983739i	$-0.442518\pi$
$773$	−19.4756	−	14.1498i	−0.700487	−	0.508934i	−0.880091	+	0.474806i	$0.842518\pi$
$774$		0			0
$775$	−3.55495	−	10.9410i	−0.127697	−	0.393012i
$776$		0			0
$777$	−8.59229	−	6.24266i	−0.308247	−	0.223954i
$778$		0			0
$779$	42.5103	+	3.18891i	1.52309	+	0.114255i
$780$		0			0
$781$	16.2736	+	11.8234i	0.582314	+	0.423076i
$782$		0			0
$783$	9.48385	+	29.1883i	0.338925	+	1.04310i
$784$		0			0
$785$	−34.7942	−	25.2795i	−1.24186	−	0.902263i
$786$		0			0
$787$	−2.86698	+	8.82366i	−0.102197	+	0.314529i	−0.989062	−	0.147498i	$-0.952878\pi$
$787$	−2.86698	+	8.82366i	−0.102197	+	0.314529i	0.886866	+	0.462028i	$0.152878\pi$
$788$		0			0
$789$	−4.30743	+	13.2569i	−0.153349	+	0.471958i
$790$		0			0
$791$	3.75209	+	11.5478i	0.133409	+	0.410591i
$792$		0			0
$793$	33.8274			1.20125
$794$		0			0
$795$	−17.5562	+	12.7553i	−0.622655	+	0.452386i
$796$		0			0
$797$	14.4218	+	10.4781i	0.510847	+	0.371152i	0.813145	−	0.582061i	$-0.197754\pi$
$797$	14.4218	+	10.4781i	0.510847	+	0.371152i	−0.302298	+	0.953214i	$0.597754\pi$
$798$		0			0
$799$	6.24058	−	4.53405i	0.220776	−	0.160403i
$800$		0			0
$801$	2.11365	−	1.53566i	0.0746823	−	0.0542599i
$802$		0			0
$803$	5.67721	−	17.4727i	0.200345	−	0.616597i
$804$		0			0
$805$	−2.28799	−	7.04172i	−0.0806412	−	0.248188i
$806$		0			0
$807$	18.0482	+	13.1128i	0.635327	+	0.461592i
$808$		0			0
$809$	9.88518	−	30.4234i	0.347544	−	1.06963i	−0.612663	−	0.790344i	$-0.709902\pi$
$809$	9.88518	−	30.4234i	0.347544	−	1.06963i	0.960208	−	0.279287i	$-0.0900982\pi$
$810$		0			0
$811$	−0.627343			−0.0220290			−0.0110145	−	0.999939i	$-0.503506\pi$
$811$	−0.627343			−0.0220290			−0.0110145	+	0.999939i	$0.503506\pi$
$812$		0			0
$813$	−0.374617	+	0.272175i	−0.0131384	+	0.00954560i
$814$		0			0
$815$	−11.9806	−	36.8726i	−0.419664	−	1.29159i
$816$		0			0
$817$	55.0583			1.92625
$818$		0			0
$819$	3.20708			0.112064
$820$		0			0
$821$	−3.04573			−0.106297			−0.0531484	−	0.998587i	$-0.516926\pi$
$821$	−3.04573			−0.106297			−0.0531484	+	0.998587i	$0.516926\pi$
$822$		0			0
$823$	−14.1863			−0.494504			−0.247252	−	0.968951i	$-0.579527\pi$
$823$	−14.1863			−0.494504			−0.247252	+	0.968951i	$0.579527\pi$
$824$		0			0
$825$	−3.61043	−	11.1117i	−0.125699	−	0.386861i
$826$		0			0
$827$	9.18149	−	6.67075i	0.319272	−	0.231965i	−0.416593	−	0.909093i	$-0.636776\pi$
$827$	9.18149	−	6.67075i	0.319272	−	0.231965i	0.735865	+	0.677129i	$0.236776\pi$
$828$		0			0
$829$	46.0074			1.59790			0.798952	−	0.601395i	$-0.205388\pi$
$829$	46.0074			1.59790			0.798952	+	0.601395i	$0.205388\pi$
$830$		0			0
$831$	13.0598	−	40.1938i	0.453038	−	1.39431i
$832$		0			0
$833$	18.7122	+	13.5952i	0.648340	+	0.471046i
$834$		0			0
$835$	8.34878	+	25.6949i	0.288921	+	0.889209i
$836$		0			0
$837$	12.4011	−	38.1665i	0.428643	−	1.31923i
$838$		0			0
$839$	−45.1285	+	32.7878i	−1.55801	+	1.13196i	−0.620393	+	0.784291i	$0.713027\pi$
$839$	−45.1285	+	32.7878i	−1.55801	+	1.13196i	−0.937617	+	0.347669i	$0.886973\pi$
$840$		0			0
$841$	−1.64359	+	1.19414i	−0.0566757	+	0.0411773i
$842$		0			0
$843$	19.3715	+	14.0742i	0.667191	+	0.484743i
$844$		0			0
$845$	27.0030	−	19.6188i	0.928932	−	0.674908i
$846$		0			0
$847$	13.3758			0.459600
$848$		0			0
$849$	−1.83729	−	5.65458i	−0.0630555	−	0.194065i
$850$		0			0
$851$	−5.03558	+	15.4979i	−0.172618	+	0.531262i
$852$		0			0
$853$	−3.68086	+	11.3285i	−0.126030	+	0.387881i	−0.994087	−	0.108583i	$-0.965369\pi$
$853$	−3.68086	+	11.3285i	−0.126030	+	0.387881i	0.868057	+	0.496464i	$0.165369\pi$
$854$		0			0
$855$	4.48547	+	3.25889i	0.153400	+	0.111452i
$856$		0			0
$857$	1.32493	+	4.07772i	0.0452588	+	0.139292i	0.971132	−	0.238541i	$-0.0766692\pi$
$857$	1.32493	+	4.07772i	0.0452588	+	0.139292i	−0.925874	+	0.377833i	$0.876669\pi$
$858$		0			0
$859$	−43.4543	−	31.5714i	−1.48264	−	1.07720i	−0.976694	−	0.214637i	$-0.931143\pi$
$859$	−43.4543	−	31.5714i	−1.48264	−	1.07720i	−0.505947	−	0.862564i	$-0.668857\pi$
$860$		0			0
$861$	13.0331	+	0.977677i	0.444167	+	0.0333191i
$862$		0			0
$863$	−14.2445	−	10.3492i	−0.484887	−	0.352291i	0.318327	−	0.947981i	$-0.396879\pi$
$863$	−14.2445	−	10.3492i	−0.484887	−	0.352291i	−0.803215	+	0.595690i	$0.796879\pi$
$864$		0			0
$865$	−1.97275	−	6.07149i	−0.0670754	−	0.206437i
$866$		0			0
$867$	2.04049	+	1.48250i	0.0692987	+	0.0503484i
$868$		0			0
$869$	−0.645542	+	1.98677i	−0.0218985	+	0.0673967i
$870$		0			0
$871$	6.18187	−	19.0258i	0.209465	−	0.644666i
$872$		0			0
$873$	−1.94777	−	5.99461i	−0.0659220	−	0.202887i
$874$		0			0
$875$	15.5548			0.525848
$876$		0			0
$877$	−32.7046	+	23.7613i	−1.10436	+	0.802362i	−0.981766	−	0.190095i	$-0.939120\pi$
$877$	−32.7046	+	23.7613i	−1.10436	+	0.802362i	−0.122591	+	0.992457i	$0.539120\pi$
$878$		0			0
$879$	28.4378	+	20.6613i	0.959183	+	0.696888i
$880$		0			0
$881$	45.3087	−	32.9187i	1.52649	−	1.10906i	0.568336	−	0.822797i	$-0.307588\pi$
$881$	45.3087	−	32.9187i	1.52649	−	1.10906i	0.958152	−	0.286261i	$-0.0924124\pi$
$882$		0			0
$883$	−28.2719	+	20.5408i	−0.951426	+	0.691252i	−0.951144	−	0.308748i	$-0.900090\pi$
$883$	−28.2719	+	20.5408i	−0.951426	+	0.691252i	−0.000282373		1.00000i	$0.500090\pi$
$884$		0			0
$885$	−4.20298	+	12.9354i	−0.141282	+	0.434820i
$886$		0			0
$887$	3.02081	+	9.29710i	0.101429	+	0.312166i	0.988876	−	0.148744i	$-0.0475231\pi$
$887$	3.02081	+	9.29710i	0.101429	+	0.312166i	−0.887447	+	0.460910i	$0.847523\pi$
$888$		0			0
$889$	9.42280	+	6.84607i	0.316031	+	0.229610i
$890$		0			0
$891$	10.6607	−	32.8103i	0.357147	−	1.09919i
$892$		0			0
$893$	11.9144			0.398699
$894$		0			0
$895$	18.1854	−	13.2125i	0.607872	−	0.441645i
$896$		0			0
$897$	8.61049	+	26.5004i	0.287496	+	0.884822i
$898$		0			0
$899$	40.5768			1.35331
$900$		0			0
$901$	31.6730			1.05518
$902$		0			0
$903$	16.8801			0.561735
$904$		0			0
$905$	−49.3648			−1.64094
$906$		0			0
$907$	0.839601	+	2.58402i	0.0278785	+	0.0858011i	0.964028	−	0.265802i	$-0.0856367\pi$
$907$	0.839601	+	2.58402i	0.0278785	+	0.0858011i	−0.936149	+	0.351603i	$0.885637\pi$
$908$		0			0
$909$	3.83128	−	2.78359i	0.127076	−	0.0923259i
$910$		0			0
$911$	31.2047			1.03386			0.516929	−	0.856028i	$-0.327075\pi$
$911$	31.2047			1.03386			0.516929	+	0.856028i	$0.327075\pi$
$912$		0			0
$913$	−9.34108	+	28.7489i	−0.309144	+	0.951449i
$914$		0			0
$915$	14.5051	+	10.5386i	0.479524	+	0.348395i
$916$		0			0
$917$	−3.84365	−	11.8295i	−0.126929	−	0.390646i
$918$		0			0
$919$	−13.0714	+	40.2295i	−0.431184	+	1.32705i	0.465762	+	0.884910i	$0.345780\pi$
$919$	−13.0714	+	40.2295i	−0.431184	+	1.32705i	−0.896947	+	0.442139i	$0.854220\pi$
$920$		0			0
$921$	0.334844	−	0.243279i	0.0110335	−	0.00801630i
$922$		0			0
$923$	19.5721	−	14.2199i	0.644222	−	0.468055i
$924$		0			0
$925$	−6.64828	−	4.83026i	−0.218594	−	0.158818i
$926$		0			0
$927$	−4.94009	+	3.58919i	−0.162254	+	0.117884i
$928$		0			0
$929$	46.7477			1.53374			0.766872	−	0.641800i	$-0.221812\pi$
$929$	46.7477			1.53374			0.766872	+	0.641800i	$0.221812\pi$
$930$		0			0
$931$	11.0396	+	33.9764i	0.361808	+	1.11353i
$932$		0			0
$933$	8.23665	−	25.3498i	0.269656	−	0.829915i
$934$		0			0
$935$	11.4133	−	35.1264i	0.373253	−	1.14876i
$936$		0			0
$937$	8.69980	+	6.32078i	0.284210	+	0.206491i	0.720752	−	0.693193i	$-0.243797\pi$
$937$	8.69980	+	6.32078i	0.284210	+	0.206491i	−0.436542	+	0.899684i	$0.643797\pi$
$938$		0			0
$939$	−4.90671	−	15.1013i	−0.160124	−	0.492812i
$940$		0			0
$941$	40.1065	+	29.1391i	1.30743	+	0.949906i	0.999999	−	0.00166276i	$-0.000529272\pi$
$941$	40.1065	+	29.1391i	1.30743	+	0.949906i	0.307435	+	0.951569i	$0.400529\pi$
$942$		0			0
$943$	−4.75275	−	19.4818i	−0.154771	−	0.634414i
$944$		0			0
$945$	10.5376	+	7.65599i	0.342787	+	0.249049i
$946$		0			0
$947$	2.33809	+	7.19590i	0.0759778	+	0.233835i	0.981831	−	0.189755i	$-0.0607695\pi$
$947$	2.33809	+	7.19590i	0.0759778	+	0.233835i	−0.905854	+	0.423591i	$0.860769\pi$
$948$		0			0
$949$	−17.8757	−	12.9875i	−0.580271	−	0.421592i
$950$		0			0
$951$	−11.1086	+	34.1888i	−0.360222	+	1.10865i
$952$		0			0
$953$	−10.1577	+	31.2621i	−0.329039	+	1.01268i	0.640545	+	0.767921i	$0.278709\pi$
$953$	−10.1577	+	31.2621i	−0.329039	+	1.01268i	−0.969584	+	0.244758i	$0.921291\pi$
$954$		0			0
$955$	4.19695	+	12.9169i	0.135810	+	0.417980i
$956$		0			0
$957$	41.2101			1.33213
$958$		0			0
$959$	−23.0348	+	16.7358i	−0.743834	+	0.540427i
$960$		0			0
$961$	−17.8454	−	12.9654i	−0.575658	−	0.418240i
$962$		0			0
$963$	3.89531	−	2.83011i	0.125525	−	0.0911990i
$964$		0			0
$965$	9.19085	−	6.67754i	0.295864	−	0.214958i
$966$		0			0
$967$	−12.7939	+	39.3756i	−0.411425	+	1.26623i	0.503985	+	0.863712i	$0.331867\pi$
$967$	−12.7939	+	39.3756i	−0.411425	+	1.26623i	−0.915410	+	0.402523i	$0.868133\pi$
$968$		0			0
$969$	14.1602	+	43.5805i	0.454890	+	1.40001i
$970$		0			0
$971$	−38.0053	−	27.6125i	−1.21965	−	0.886127i	−0.223578	−	0.974686i	$-0.571774\pi$
$971$	−38.0053	−	27.6125i	−1.21965	−	0.886127i	−0.996071	+	0.0885595i	$0.971774\pi$
$972$		0			0
$973$	7.68165	−	23.6417i	0.246262	−	0.757917i
$974$		0			0
$975$	−14.0517			−0.450016
$976$		0			0
$977$	20.7055	−	15.0434i	0.662428	−	0.481282i	−0.205054	−	0.978751i	$-0.565737\pi$
$977$	20.7055	−	15.0434i	0.662428	−	0.481282i	0.867482	+	0.497468i	$0.165737\pi$
$978$		0			0
$979$	−8.30690	−	25.5660i	−0.265490	−	0.817093i
$980$		0			0
$981$	1.05858			0.0337980
$982$		0			0
$983$	36.2444			1.15602			0.578008	−	0.816031i	$-0.303830\pi$
$983$	36.2444			1.15602			0.578008	+	0.816031i	$0.303830\pi$
$984$		0			0
$985$	−3.60880			−0.114986
$986$		0			0
$987$	3.65278			0.116269
$988$		0			0
$989$	−8.00340	−	24.6319i	−0.254493	−	0.783250i
$990$		0			0
$991$	−36.3154	+	26.3847i	−1.15360	+	0.838138i	−0.988955	−	0.148216i	$-0.952647\pi$
$991$	−36.3154	+	26.3847i	−1.15360	+	0.838138i	−0.164642	+	0.986353i	$0.552647\pi$
$992$		0			0
$993$	−56.7090			−1.79961
$994$		0			0
$995$	−6.16556	+	18.9756i	−0.195461	+	0.601568i
$996$		0			0
$997$	−45.2861	−	32.9023i	−1.43423	−	1.04203i	−0.989210	−	0.146503i	$-0.953198\pi$
$997$	−45.2861	−	32.9023i	−1.43423	−	1.04203i	−0.445015	−	0.895523i	$-0.646802\pi$
$998$		0			0
$999$	−8.85849	−	27.2636i	−0.280270	−	0.862583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.625.2		20
4.3	odd	2		328.2.m.c.297.4	yes	20
41.37	even	5	inner	656.2.u.h.529.2		20
164.119	odd	10		328.2.m.c.201.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.201.4	✓	20	164.119	odd	10
328.2.m.c.297.4	yes	20	4.3	odd	2
656.2.u.h.529.2		20	41.37	even	5	inner
656.2.u.h.625.2		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q-1.59679 q^{3} +(-0.571528 - 1.75898i) q^{5} +(-1.03415 + 0.751356i) q^{7} -0.450271 q^{9} +O(q^{10})\)	\(q-1.59679 q^{3} +(-0.571528 - 1.75898i) q^{5} +(-1.03415 + 0.751356i) q^{7} -0.450271 q^{9} +(-1.43165 + 4.40617i) q^{11} +(4.50781 + 3.27512i) q^{13} +(0.912609 + 2.80872i) q^{15} +(1.33199 - 4.09943i) q^{17} +(5.38615 - 3.91327i) q^{19} +(1.65132 - 1.19976i) q^{21} +(-2.53366 - 1.84081i) q^{23} +(1.27771 - 0.928311i) q^{25} +5.50935 q^{27} +(1.72141 + 5.29796i) q^{29} +(2.25091 - 6.92759i) q^{31} +(2.28604 - 7.03571i) q^{33} +(1.91267 + 1.38964i) q^{35} +(-1.60790 - 4.94861i) q^{37} +(-7.19802 - 5.22966i) q^{39} +(4.88418 + 4.14062i) q^{41} +(6.69051 + 4.86094i) q^{43} +(0.257343 + 0.792019i) q^{45} +(1.44780 + 1.05189i) q^{47} +(-1.65818 + 5.10336i) q^{49} +(-2.12690 + 6.54592i) q^{51} +(2.27067 + 6.98840i) q^{53} +8.56860 q^{55} +(-8.60054 + 6.24866i) q^{57} +(3.72589 + 2.70702i) q^{59} +(4.91155 - 3.56845i) q^{61} +(0.465649 - 0.338314i) q^{63} +(3.18453 - 9.80098i) q^{65} +(-1.10946 - 3.41457i) q^{67} +(4.04571 + 2.93938i) q^{69} +(1.34169 - 4.12930i) q^{71} -3.96550 q^{73} +(-2.04023 + 1.48231i) q^{75} +(-1.83005 - 5.63233i) q^{77} +0.450908 q^{79} -7.44644 q^{81} +6.52469 q^{83} -7.97210 q^{85} +(-2.74873 - 8.45971i) q^{87} +(-4.69418 + 3.41052i) q^{89} -7.12254 q^{91} +(-3.59423 + 11.0619i) q^{93} +(-9.96171 - 7.23761i) q^{95} +(4.32577 + 13.3133i) q^{97} +(0.644631 - 1.98397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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