LMFDB - Embedded newform 520.2.w.e.73.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [520,2,Mod(57,520)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("520.57"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(520, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 6 x^{9} + 25 x^{8} - 106 x^{7} + 242 x^{6} + 268 x^{5} + 316 x^{4} + \cdots + 676 $ x^12 - 4x^11 + 8x^10 + 6x^9 + 25x^8 - 106x^7 + 242x^6 + 268x^5 + 316x^4 - 676x^3 + 1352x^2 + 1352*x + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.6
Root			$2.10080 + 2.10080i$ of defining polynomial
Character	$\chi$	$=$	520.73
Dual form			520.2.w.e.57.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.10080 + 2.10080i) q^{3} +(-2.23468 + 0.0786365i) q^{5} -0.625152i q^{7} +5.82676i q^{9} +(-1.43009 + 1.43009i) q^{11} +(-1.21252 + 3.39556i) q^{13} +(-4.85984 - 4.52944i) q^{15} +(4.15605 + 4.15605i) q^{17} +(-3.07381 + 3.07381i) q^{19} +(1.31332 - 1.31332i) q^{21} +(1.05524 - 1.05524i) q^{23} +(4.98763 - 0.351456i) q^{25} +(-5.93847 + 5.93847i) q^{27} -4.78242i q^{29} +(4.05673 + 4.05673i) q^{31} -6.00869 q^{33} +(0.0491597 + 1.39702i) q^{35} -2.88074i q^{37} +(-9.68066 + 4.58614i) q^{39} +(-2.64372 - 2.64372i) q^{41} +(5.55160 - 5.55160i) q^{43} +(-0.458196 - 13.0210i) q^{45} -6.93725i q^{47} +6.60919 q^{49} +17.4621i q^{51} +(-7.66949 - 7.66949i) q^{53} +(3.08335 - 3.30826i) q^{55} -12.9150 q^{57} +(-7.66332 - 7.66332i) q^{59} +10.3797 q^{61} +3.64261 q^{63} +(2.44258 - 7.68335i) q^{65} -4.43372 q^{67} +4.43372 q^{69} +(6.97626 + 6.97626i) q^{71} +11.4091 q^{73} +(11.2164 + 9.73970i) q^{75} +(0.894024 + 0.894024i) q^{77} +15.9184i q^{79} -7.47086 q^{81} +10.3232i q^{83} +(-9.61428 - 8.96064i) q^{85} +(10.0469 - 10.0469i) q^{87} +(3.78962 + 3.78962i) q^{89} +(2.12274 + 0.758007i) q^{91} +17.0448i q^{93} +(6.62729 - 7.11072i) q^{95} +13.1745 q^{97} +(-8.33280 - 8.33280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 8 q^{5} - 14 q^{11} - 2 q^{13} - 12 q^{15} + 14 q^{17} - 6 q^{19} - 18 q^{21} - 2 q^{23} + 2 q^{25} - 26 q^{27} - 22 q^{31} - 4 q^{33} - 12 q^{35} + 4 q^{39} - 4 q^{41} - 8 q^{43} + 16 q^{49}+ \cdots + 22 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 8 * q^5 - 14 * q^11 - 2 * q^13 - 12 * q^15 + 14 * q^17 - 6 * q^19 - 18 * q^21 - 2 * q^23 + 2 * q^25 - 26 * q^27 - 22 * q^31 - 4 * q^33 - 12 * q^35 + 4 * q^39 - 4 * q^41 - 8 * q^43 + 16 * q^49 - 36 * q^53 + 20 * q^55 - 32 * q^57 - 26 * q^59 + 12 * q^61 + 28 * q^63 + 12 * q^65 + 40 * q^67 - 40 * q^69 + 28 * q^71 + 60 * q^73 + 22 * q^75 - 40 * q^77 + 36 * q^81 + 10 * q^85 + 8 * q^87 + 24 * q^89 - 8 * q^91 + 34 * q^95 + 56 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	2.10080	+	2.10080i	1.21290	+	1.21290i	0.970068	+	0.242832i	$0.0780763\pi$
$3$	2.10080	+	2.10080i	1.21290	+	1.21290i	0.242832	+	0.970068i	$0.421924\pi$
$4$		0			0
$5$	−2.23468	+	0.0786365i	−0.999381	+	0.0351673i
$5$	−2.23468	+	0.0786365i	−0.999381	+	0.0351673i
$6$		0			0
$7$		−	0.625152i		−	0.236285i	−0.992997	−	0.118143i	$-0.962306\pi$
$7$		−	0.625152i		−	0.236285i	0.992997	−	0.118143i	$-0.0376940\pi$
$8$		0			0
$9$			5.82676i			1.94225i
$10$		0			0
$11$	−1.43009	+	1.43009i	−0.431189	+	0.431189i	−0.889033	−	0.457844i	$-0.848622\pi$
$11$	−1.43009	+	1.43009i	−0.431189	+	0.431189i	0.457844	+	0.889033i	$0.348622\pi$
$12$		0			0
$13$	−1.21252	+	3.39556i	−0.336292	+	0.941758i
$13$	−1.21252	+	3.39556i	−0.336292	+	0.941758i
$14$		0			0
$15$	−4.85984	−	4.52944i	−1.25480	−	1.16950i
$16$		0			0
$17$	4.15605	+	4.15605i	1.00799	+	1.00799i	0.999968	+	0.00802196i	$0.00255350\pi$
$17$	4.15605	+	4.15605i	1.00799	+	1.00799i	0.00802196	+	0.999968i	$0.497447\pi$
$18$		0			0
$19$	−3.07381	+	3.07381i	−0.705181	+	0.705181i	−0.965518	−	0.260337i	$-0.916166\pi$
$19$	−3.07381	+	3.07381i	−0.705181	+	0.705181i	0.260337	+	0.965518i	$0.416166\pi$
$20$		0			0
$21$	1.31332	−	1.31332i	0.286590	−	0.286590i
$22$		0			0
$23$	1.05524	−	1.05524i	0.220034	−	0.220034i	−0.588479	−	0.808513i	$-0.700273\pi$
$23$	1.05524	−	1.05524i	0.220034	−	0.220034i	0.808513	+	0.588479i	$0.200273\pi$
$24$		0			0
$25$	4.98763	−	0.351456i	0.997527	−	0.0702911i
$26$		0			0
$27$	−5.93847	+	5.93847i	−1.14286	+	1.14286i
$28$		0			0
$29$		−	4.78242i		−	0.888074i	−0.896008	−	0.444037i	$-0.853546\pi$
$29$		−	4.78242i		−	0.888074i	0.896008	−	0.444037i	$-0.146454\pi$
$30$		0			0
$31$	4.05673	+	4.05673i	0.728611	+	0.728611i	0.970343	−	0.241732i	$-0.0777155\pi$
$31$	4.05673	+	4.05673i	0.728611	+	0.728611i	−0.241732	+	0.970343i	$0.577715\pi$
$32$		0			0
$33$	−6.00869			−1.04598
$34$		0			0
$35$	0.0491597	+	1.39702i	0.00830951	+	0.236139i
$36$		0			0
$37$		−	2.88074i		−	0.473591i	−0.971559	−	0.236796i	$-0.923903\pi$
$37$		−	2.88074i		−	0.473591i	0.971559	−	0.236796i	$-0.0760972\pi$
$38$		0			0
$39$	−9.68066	+	4.58614i	−1.55015	+	0.734370i
$40$		0			0
$41$	−2.64372	−	2.64372i	−0.412880	−	0.412880i	0.469861	−	0.882741i	$-0.344304\pi$
$41$	−2.64372	−	2.64372i	−0.412880	−	0.412880i	−0.882741	+	0.469861i	$0.844304\pi$
$42$		0			0
$43$	5.55160	−	5.55160i	0.846612	−	0.846612i	−0.143097	−	0.989709i	$-0.545706\pi$
$43$	5.55160	−	5.55160i	0.846612	−	0.846612i	0.989709	+	0.143097i	$0.0457061\pi$
$44$		0			0
$45$	−0.458196	−	13.0210i	−0.0683038	−	1.94105i
$46$		0			0
$47$		−	6.93725i		−	1.01190i	−0.862562	−	0.505951i	$-0.831142\pi$
$47$		−	6.93725i		−	1.01190i	0.862562	−	0.505951i	$-0.168858\pi$
$48$		0			0
$49$	6.60919			0.944169
$50$		0			0
$51$			17.4621i			2.44518i
$52$		0			0
$53$	−7.66949	−	7.66949i	−1.05349	−	1.05349i	−0.998486	−	0.0549988i	$-0.982485\pi$
$53$	−7.66949	−	7.66949i	−1.05349	−	1.05349i	−0.0549988	−	0.998486i	$-0.517515\pi$
$54$		0			0
$55$	3.08335	−	3.30826i	0.415759	−	0.446086i
$56$		0			0
$57$	−12.9150			−1.71063
$58$		0			0
$59$	−7.66332	−	7.66332i	−0.997679	−	0.997679i	0.00231846	−	0.999997i	$-0.499262\pi$
$59$	−7.66332	−	7.66332i	−0.997679	−	0.997679i	−0.999997	+	0.00231846i	$0.999262\pi$
$60$		0			0
$61$	10.3797			1.32899			0.664495	−	0.747293i	$-0.268647\pi$
$61$	10.3797			1.32899			0.664495	+	0.747293i	$0.268647\pi$
$62$		0			0
$63$	3.64261			0.458926
$64$		0			0
$65$	2.44258	−	7.68335i	0.302964	−	0.953002i
$66$		0			0
$67$	−4.43372			−0.541665			−0.270833	−	0.962626i	$-0.587299\pi$
$67$	−4.43372			−0.541665			−0.270833	+	0.962626i	$0.587299\pi$
$68$		0			0
$69$	4.43372			0.533757
$70$		0			0
$71$	6.97626	+	6.97626i	0.827930	+	0.827930i	0.987230	−	0.159300i	$-0.0509239\pi$
$71$	6.97626	+	6.97626i	0.827930	+	0.827930i	−0.159300	+	0.987230i	$0.550924\pi$
$72$		0			0
$73$	11.4091			1.33533			0.667665	−	0.744462i	$-0.267294\pi$
$73$	11.4091			1.33533			0.667665	+	0.744462i	$0.267294\pi$
$74$		0			0
$75$	11.2164	+	9.73970i	1.29516	+	1.12464i
$76$		0			0
$77$	0.894024	+	0.894024i	0.101884	+	0.101884i
$78$		0			0
$79$			15.9184i			1.79096i	0.445106	+	0.895478i	$0.353166\pi$
$79$			15.9184i			1.79096i	−0.445106	+	0.895478i	$0.646834\pi$
$80$		0			0
$81$	−7.47086			−0.830096
$82$		0			0
$83$			10.3232i			1.13312i	0.824020	+	0.566561i	$0.191726\pi$
$83$			10.3232i			1.13312i	−0.824020	+	0.566561i	$0.808274\pi$
$84$		0			0
$85$	−9.61428	−	8.96064i	−1.04281	−	0.971918i
$86$		0			0
$87$	10.0469	−	10.0469i	1.07715	−	1.07715i
$88$		0			0
$89$	3.78962	+	3.78962i	0.401699	+	0.401699i	0.878831	−	0.477132i	$-0.158324\pi$
$89$	3.78962	+	3.78962i	0.401699	+	0.401699i	−0.477132	+	0.878831i	$0.658324\pi$
$90$		0			0
$91$	2.12274	+	0.758007i	0.222523	+	0.0794607i
$92$		0			0
$93$			17.0448i			1.76746i
$94$		0			0
$95$	6.62729	−	7.11072i	0.679946	−	0.729544i
$96$		0			0
$97$	13.1745			1.33767			0.668834	−	0.743412i	$-0.266794\pi$
$97$	13.1745			1.33767			0.668834	+	0.743412i	$0.266794\pi$
$98$		0			0
$99$	−8.33280	−	8.33280i	−0.837478	−	0.837478i
$100$		0			0
$101$			0.366080i			0.0364263i	0.999834	+	0.0182131i	$0.00579774\pi$
$101$			0.366080i			0.0364263i	−0.999834	+	0.0182131i	$0.994202\pi$
$102$		0			0
$103$	−4.36213	+	4.36213i	−0.429814	+	0.429814i	−0.888565	−	0.458751i	$-0.848297\pi$
$103$	−4.36213	+	4.36213i	−0.429814	+	0.429814i	0.458751	+	0.888565i	$0.348297\pi$
$104$		0			0
$105$	−2.83158	+	3.03813i	−0.276334	+	0.296492i
$106$		0			0
$107$	−8.24089	+	8.24089i	−0.796677	+	0.796677i	−0.982570	−	0.185893i	$-0.940482\pi$
$107$	−8.24089	+	8.24089i	−0.796677	+	0.796677i	0.185893	+	0.982570i	$0.440482\pi$
$108$		0			0
$109$	10.5593	−	10.5593i	1.01139	−	1.01139i	0.0114600	−	0.999934i	$-0.496352\pi$
$109$	10.5593	−	10.5593i	1.01139	−	1.01139i	0.999934	−	0.0114600i	$-0.00364792\pi$
$110$		0			0
$111$	6.05188	−	6.05188i	0.574419	−	0.574419i
$112$		0			0
$113$	−7.12321	−	7.12321i	−0.670095	−	0.670095i	0.287643	−	0.957738i	$-0.407128\pi$
$113$	−7.12321	−	7.12321i	−0.670095	−	0.670095i	−0.957738	+	0.287643i	$0.907128\pi$
$114$		0			0
$115$	−2.27516	+	2.44112i	−0.212159	+	0.227635i
$116$		0			0
$117$	−19.7851	−	7.06504i	−1.82913	−	0.653164i
$118$		0			0
$119$	2.59816	−	2.59816i	0.238173	−	0.238173i
$120$		0			0
$121$			6.90967i			0.628152i
$122$		0			0
$123$		−	11.1079i		−	1.00156i
$124$		0			0
$125$	−11.1181	+	1.17760i	−0.994438	+	0.105328i
$126$		0			0
$127$	−12.9989	−	12.9989i	−1.15347	−	1.15347i	−0.985853	−	0.167612i	$-0.946394\pi$
$127$	−12.9989	−	12.9989i	−1.15347	−	1.15347i	−0.167612	−	0.985853i	$-0.553606\pi$
$128$		0			0
$129$	23.3257			2.05371
$130$		0			0
$131$	−0.0465615			−0.00406810			−0.00203405	−	0.999998i	$-0.500647\pi$
$131$	−0.0465615			−0.00406810			−0.00203405	+	0.999998i	$0.500647\pi$
$132$		0			0
$133$	1.92160	+	1.92160i	0.166624	+	0.166624i
$134$		0			0
$135$	12.8036	−	13.7376i	1.10196	−	1.18234i
$136$		0			0
$137$			2.98845i			0.255320i	0.991818	+	0.127660i	$0.0407467\pi$
$137$			2.98845i			0.255320i	−0.991818	+	0.127660i	$0.959253\pi$
$138$		0			0
$139$		−	18.3978i		−	1.56049i	−0.625477	−	0.780243i	$-0.715096\pi$
$139$		−	18.3978i		−	1.56049i	0.625477	−	0.780243i	$-0.284904\pi$
$140$		0			0
$141$	14.5738	−	14.5738i	1.22734	−	1.22734i
$142$		0			0
$143$	−3.12195	−	6.58997i	−0.261070	−	0.551081i
$144$		0			0
$145$	0.376073	+	10.6872i	0.0312312	+	0.887525i
$146$		0			0
$147$	13.8846	+	13.8846i	1.14518	+	1.14518i
$148$		0			0
$149$	9.92602	−	9.92602i	0.813171	−	0.813171i	−0.171937	−	0.985108i	$-0.555003\pi$
$149$	9.92602	−	9.92602i	0.813171	−	0.813171i	0.985108	+	0.171937i	$0.0550025\pi$
$150$		0			0
$151$	1.92037	−	1.92037i	0.156277	−	0.156277i	−0.624637	−	0.780915i	$-0.714753\pi$
$151$	1.92037	−	1.92037i	0.156277	−	0.156277i	0.780915	+	0.624637i	$0.214753\pi$
$152$		0			0
$153$	−24.2163	+	24.2163i	−1.95777	+	1.95777i
$154$		0			0
$155$	−9.38453	−	8.74652i	−0.753784	−	0.702537i
$156$		0			0
$157$	−2.67422	+	2.67422i	−0.213426	+	0.213426i	−0.805721	−	0.592295i	$-0.798222\pi$
$157$	−2.67422	+	2.67422i	−0.213426	+	0.213426i	0.592295	+	0.805721i	$0.298222\pi$
$158$		0			0
$159$		−	32.2242i		−	2.55554i
$160$		0			0
$161$	−0.659687	−	0.659687i	−0.0519906	−	0.0519906i
$162$		0			0
$163$	−7.35286			−0.575920			−0.287960	−	0.957642i	$-0.592977\pi$
$163$	−7.35286			−0.575920			−0.287960	+	0.957642i	$0.592977\pi$
$164$		0			0
$165$	13.4275	−	0.472502i	1.04533	−	0.0367842i
$166$		0			0
$167$			8.16527i			0.631847i	0.948785	+	0.315924i	$0.102314\pi$
$167$			8.16527i			0.631847i	−0.948785	+	0.315924i	$0.897686\pi$
$168$		0			0
$169$	−10.0596	−	8.23434i	−0.773816	−	0.633411i
$170$		0			0
$171$	−17.9104	−	17.9104i	−1.36964	−	1.36964i
$172$		0			0
$173$	0.911103	−	0.911103i	0.0692699	−	0.0692699i	−0.671623	−	0.740893i	$-0.734403\pi$
$173$	0.911103	−	0.911103i	0.0692699	−	0.0692699i	0.740893	+	0.671623i	$0.234403\pi$
$174$		0			0
$175$	−0.219713	−	3.11803i	−0.0166087	−	0.235701i
$176$		0			0
$177$		−	32.1983i		−	2.42017i
$178$		0			0
$179$	20.3221			1.51894			0.759471	−	0.650541i	$-0.225458\pi$
$179$	20.3221			1.51894			0.759471	+	0.650541i	$0.225458\pi$
$180$		0			0
$181$			20.9432i			1.55669i	0.627835	+	0.778346i	$0.283941\pi$
$181$			20.9432i			1.55669i	−0.627835	+	0.778346i	$0.716059\pi$
$182$		0			0
$183$	21.8058	+	21.8058i	1.61193	+	1.61193i
$184$		0			0
$185$	0.226532	+	6.43755i	0.0166549	+	0.473298i
$186$		0			0
$187$	−11.8871			−0.869268
$188$		0			0
$189$	3.71245	+	3.71245i	0.270041	+	0.270041i
$190$		0			0
$191$	−14.1798			−1.02601			−0.513007	−	0.858384i	$-0.671469\pi$
$191$	−14.1798			−1.02601			−0.513007	+	0.858384i	$0.671469\pi$
$192$		0			0
$193$	4.98622			0.358916			0.179458	−	0.983766i	$-0.442566\pi$
$193$	4.98622			0.358916			0.179458	+	0.983766i	$0.442566\pi$
$194$		0			0
$195$	21.2726	−	11.0098i	1.52336	−	0.788430i
$196$		0			0
$197$	−14.9509			−1.06521			−0.532604	−	0.846365i	$-0.678786\pi$
$197$	−14.9509			−1.06521			−0.532604	+	0.846365i	$0.678786\pi$
$198$		0			0
$199$	−13.6756			−0.969436			−0.484718	−	0.874671i	$-0.661078\pi$
$199$	−13.6756			−0.969436			−0.484718	+	0.874671i	$0.661078\pi$
$200$		0			0
$201$	−9.31438	−	9.31438i	−0.656986	−	0.656986i
$202$		0			0
$203$	−2.98974			−0.209839
$204$		0			0
$205$	6.11578	+	5.69999i	0.427144	+	0.398105i
$206$		0			0
$207$	6.14865	+	6.14865i	0.427361	+	0.427361i
$208$		0			0
$209$		−	8.79167i		−	0.608133i
$210$		0			0
$211$	−5.07122			−0.349117			−0.174558	−	0.984647i	$-0.555850\pi$
$211$	−5.07122			−0.349117			−0.174558	+	0.984647i	$0.555850\pi$
$212$		0			0
$213$			29.3115i			2.00839i
$214$		0			0
$215$	−11.9695	+	12.8426i	−0.816315	+	0.875861i
$216$		0			0
$217$	2.53607	−	2.53607i	0.172160	−	0.172160i
$218$		0			0
$219$	23.9682	+	23.9682i	1.61962	+	1.61962i
$220$		0			0
$221$	−19.1514	+	9.07282i	−1.28826	+	0.610304i
$222$		0			0
$223$		−	11.9673i		−	0.801392i	−0.916211	−	0.400696i	$-0.868768\pi$
$223$		−	11.9673i		−	0.801392i	0.916211	−	0.400696i	$-0.131232\pi$
$224$		0			0
$225$	2.04785	+	29.0617i	0.136523	+	1.93745i
$226$		0			0
$227$	−22.4365			−1.48916			−0.744581	−	0.667532i	$-0.767351\pi$
$227$	−22.4365			−1.48916			−0.744581	+	0.667532i	$0.767351\pi$
$228$		0			0
$229$	13.5075	+	13.5075i	0.892601	+	0.892601i	0.994767	−	0.102167i	$-0.0325775\pi$
$229$	13.5075	+	13.5075i	0.892601	+	0.892601i	−0.102167	+	0.994767i	$0.532577\pi$
$230$		0			0
$231$			3.75634i			0.247149i
$232$		0			0
$233$	3.80548	−	3.80548i	0.249305	−	0.249305i	−0.571380	−	0.820685i	$-0.693592\pi$
$233$	3.80548	−	3.80548i	0.249305	−	0.249305i	0.820685	+	0.571380i	$0.193592\pi$
$234$		0			0
$235$	0.545521	+	15.5026i	0.0355859	+	1.01128i
$236$		0			0
$237$	−33.4414	+	33.4414i	−2.17225	+	2.17225i
$238$		0			0
$239$	6.28140	−	6.28140i	0.406310	−	0.406310i	−0.474140	−	0.880450i	$-0.657241\pi$
$239$	6.28140	−	6.28140i	0.406310	−	0.406310i	0.880450	+	0.474140i	$0.157241\pi$
$240$		0			0
$241$	11.5260	−	11.5260i	0.742452	−	0.742452i	−0.230597	−	0.973049i	$-0.574068\pi$
$241$	11.5260	−	11.5260i	0.742452	−	0.742452i	0.973049	+	0.230597i	$0.0740680\pi$
$242$		0			0
$243$	2.12060	+	2.12060i	0.136036	+	0.136036i
$244$		0			0
$245$	−14.7694	+	0.519723i	−0.943585	+	0.0332039i
$246$		0			0
$247$	−6.71026	−	14.1644i	−0.426963	−	0.901256i
$248$		0			0
$249$	−21.6871	+	21.6871i	−1.37436	+	1.37436i
$250$		0			0
$251$			6.91172i			0.436264i	0.975919	+	0.218132i	$0.0699963\pi$
$251$			6.91172i			0.436264i	−0.975919	+	0.218132i	$0.930004\pi$
$252$		0			0
$253$			3.01819i			0.189752i
$254$		0			0
$255$	−1.37316	−	39.0223i	−0.0859905	−	2.44367i
$256$		0			0
$257$	−8.90543	−	8.90543i	−0.555505	−	0.555505i	0.372519	−	0.928025i	$-0.378494\pi$
$257$	−8.90543	−	8.90543i	−0.555505	−	0.555505i	−0.928025	+	0.372519i	$0.878494\pi$
$258$		0			0
$259$	−1.80090			−0.111903
$260$		0			0
$261$	27.8660			1.72486
$262$		0			0
$263$	−1.20176	−	1.20176i	−0.0741035	−	0.0741035i	0.669084	−	0.743187i	$-0.266687\pi$
$263$	−1.20176	−	1.20176i	−0.0741035	−	0.0741035i	−0.743187	+	0.669084i	$0.766687\pi$
$264$		0			0
$265$	17.7420	+	16.5358i	1.08988	+	1.01579i
$266$		0			0
$267$			15.9225i			0.974442i
$268$		0			0
$269$			18.3364i			1.11799i	0.829172	+	0.558994i	$0.188813\pi$
$269$			18.3364i			1.11799i	−0.829172	+	0.558994i	$0.811187\pi$
$270$		0			0
$271$	−6.82939	+	6.82939i	−0.414856	+	0.414856i	−0.883426	−	0.468570i	$-0.844769\pi$
$271$	−6.82939	+	6.82939i	−0.414856	+	0.414856i	0.468570	+	0.883426i	$0.344769\pi$
$272$		0			0
$273$	2.86703	+	6.05188i	0.173521	+	0.366276i
$274$		0			0
$275$	−6.63016	+	7.63539i	−0.399814	+	0.460431i
$276$		0			0
$277$	2.47038	+	2.47038i	0.148431	+	0.148431i	0.777417	−	0.628986i	$-0.216530\pi$
$277$	2.47038	+	2.47038i	0.148431	+	0.148431i	−0.628986	+	0.777417i	$0.716530\pi$
$278$		0			0
$279$	−23.6376	+	23.6376i	−1.41515	+	1.41515i
$280$		0			0
$281$	20.3045	−	20.3045i	1.21127	−	1.21127i	0.240654	−	0.970611i	$-0.422638\pi$
$281$	20.3045	−	20.3045i	1.21127	−	1.21127i	0.970611	−	0.240654i	$-0.0773619\pi$
$282$		0			0
$283$	18.8607	−	18.8607i	1.12115	−	1.12115i	0.129582	−	0.991569i	$-0.458637\pi$
$283$	18.8607	−	18.8607i	1.12115	−	1.12115i	0.991569	−	0.129582i	$-0.0413634\pi$
$284$		0			0
$285$	28.8609	−	1.01559i	1.70957	−	0.0601582i
$286$		0			0
$287$	−1.65273	+	1.65273i	−0.0975574	+	0.0975574i
$288$		0			0
$289$			17.5455i			1.03209i
$290$		0			0
$291$	27.6771	+	27.6771i	1.62246	+	1.62246i
$292$		0			0
$293$	26.4437			1.54486			0.772428	−	0.635102i	$-0.219042\pi$
$293$	26.4437			1.54486			0.772428	+	0.635102i	$0.219042\pi$
$294$		0			0
$295$	17.7277	+	16.5225i	1.03215	+	0.961976i
$296$		0			0
$297$		−	16.9851i		−	0.985577i
$298$		0			0
$299$	2.30364	+	4.86264i	0.133223	+	0.281214i
$300$		0			0
$301$	−3.47059	−	3.47059i	−0.200042	−	0.200042i
$302$		0			0
$303$	−0.769062	+	0.769062i	−0.0441815	+	0.0441815i
$304$		0			0
$305$	−23.1954	+	0.816226i	−1.32817	+	0.0467370i
$306$		0			0
$307$			16.5030i			0.941878i	0.882166	+	0.470939i	$0.156085\pi$
$307$			16.5030i			0.941878i	−0.882166	+	0.470939i	$0.843915\pi$
$308$		0			0
$309$	−18.3280			−1.04264
$310$		0			0
$311$		−	1.19135i		−	0.0675552i	−0.999429	−	0.0337776i	$-0.989246\pi$
$311$		−	1.19135i		−	0.0675552i	0.999429	−	0.0337776i	$-0.0107538\pi$
$312$		0			0
$313$	−23.9521	−	23.9521i	−1.35385	−	1.35385i	−0.881308	−	0.472542i	$-0.843337\pi$
$313$	−23.9521	−	23.9521i	−1.35385	−	1.35385i	−0.472542	−	0.881308i	$-0.656663\pi$
$314$		0			0
$315$	−8.14008	+	0.286442i	−0.458642	+	0.0161392i
$316$		0			0
$317$	−5.64869			−0.317262			−0.158631	−	0.987338i	$-0.550708\pi$
$317$	−5.64869			−0.317262			−0.158631	+	0.987338i	$0.550708\pi$
$318$		0			0
$319$	6.83931	+	6.83931i	0.382928	+	0.382928i
$320$		0			0
$321$	−34.6250			−1.93258
$322$		0			0
$323$	−25.5498			−1.42163
$324$		0			0
$325$	−4.85420	+	17.3619i	−0.269263	+	0.963067i
$326$		0			0
$327$	44.3659			2.45344
$328$		0			0
$329$	−4.33683			−0.239097
$330$		0			0
$331$	12.0711	+	12.0711i	0.663489	+	0.663489i	0.956201	−	0.292712i	$-0.0945576\pi$
$331$	12.0711	+	12.0711i	0.663489	+	0.663489i	−0.292712	+	0.956201i	$0.594558\pi$
$332$		0			0
$333$	16.7854			0.919835
$334$		0			0
$335$	9.90797	−	0.348652i	0.541330	−	0.0190489i
$336$		0			0
$337$	−10.2997	−	10.2997i	−0.561058	−	0.561058i	0.368550	−	0.929608i	$-0.379854\pi$
$337$	−10.2997	−	10.2997i	−0.561058	−	0.561058i	−0.929608	+	0.368550i	$0.879854\pi$
$338$		0			0
$339$		−	29.9289i		−	1.62552i
$340$		0			0
$341$	−11.6030			−0.628338
$342$		0			0
$343$		−	8.50780i		−	0.459378i
$344$		0			0
$345$	−9.90797	+	0.348652i	−0.533427	+	0.0187708i
$346$		0			0
$347$	23.4309	−	23.4309i	1.25784	−	1.25784i	0.305712	−	0.952124i	$-0.401105\pi$
$347$	23.4309	−	23.4309i	1.25784	−	1.25784i	0.952124	−	0.305712i	$-0.0988945\pi$
$348$		0			0
$349$	−21.2807	−	21.2807i	−1.13913	−	1.13913i	−0.988607	−	0.150521i	$-0.951905\pi$
$349$	−21.2807	−	21.2807i	−1.13913	−	1.13913i	−0.150521	−	0.988607i	$-0.548095\pi$
$350$		0			0
$351$	−12.9639	−	27.3649i	−0.691963	−	1.46063i
$352$		0			0
$353$		−	34.0709i		−	1.81341i	−0.421762	−	0.906706i	$-0.638588\pi$
$353$		−	34.0709i		−	1.81341i	0.421762	−	0.906706i	$-0.361412\pi$
$354$		0			0
$355$	−16.1383	−	15.0412i	−0.856534	−	0.798301i
$356$		0			0
$357$	10.9165			0.577760
$358$		0			0
$359$	−2.23393	−	2.23393i	−0.117902	−	0.117902i	0.645694	−	0.763596i	$-0.276568\pi$
$359$	−2.23393	−	2.23393i	−0.117902	−	0.117902i	−0.763596	+	0.645694i	$0.776568\pi$
$360$		0			0
$361$			0.103344i			0.00543918i
$362$		0			0
$363$	−14.5159	+	14.5159i	−0.761886	+	0.761886i
$364$		0			0
$365$	−25.4957	+	0.897169i	−1.33450	+	0.0469600i
$366$		0			0
$367$	−17.1522	+	17.1522i	−0.895339	+	0.895339i	−0.995019	−	0.0996806i	$-0.968218\pi$
$367$	−17.1522	+	17.1522i	−0.895339	+	0.895339i	0.0996806	+	0.995019i	$0.468218\pi$
$368$		0			0
$369$	15.4043	−	15.4043i	0.801917	−	0.801917i
$370$		0			0
$371$	−4.79459	+	4.79459i	−0.248923	+	0.248923i
$372$		0			0
$373$	−9.22477	−	9.22477i	−0.477641	−	0.477641i	0.426736	−	0.904376i	$-0.359663\pi$
$373$	−9.22477	−	9.22477i	−0.477641	−	0.477641i	−0.904376	+	0.426736i	$0.859663\pi$
$374$		0			0
$375$	−25.8310	−	20.8831i	−1.33391	−	1.07840i
$376$		0			0
$377$	16.2390	+	5.79877i	0.836351	+	0.298652i
$378$		0			0
$379$	−11.5450	+	11.5450i	−0.593026	+	0.593026i	−0.938448	−	0.345421i	$-0.887736\pi$
$379$	−11.5450	+	11.5450i	−0.593026	+	0.593026i	0.345421	+	0.938448i	$0.387736\pi$
$380$		0			0
$381$		−	54.6163i		−	2.79808i
$382$		0			0
$383$			11.5813i			0.591775i	0.955223	+	0.295888i	$0.0956154\pi$
$383$			11.5813i			0.591775i	−0.955223	+	0.295888i	$0.904385\pi$
$384$		0			0
$385$	−2.06817	−	1.92756i	−0.105403	−	0.0982375i
$386$		0			0
$387$	32.3479	+	32.3479i	1.64433	+	1.64433i
$388$		0			0
$389$	1.68545			0.0854559			0.0427280	−	0.999087i	$-0.486395\pi$
$389$	1.68545			0.0854559			0.0427280	+	0.999087i	$0.486395\pi$
$390$		0			0
$391$	8.77129			0.443583
$392$		0			0
$393$	−0.0978166	−	0.0978166i	−0.00493419	−	0.00493419i
$394$		0			0
$395$	−1.25176	−	35.5725i	−0.0629831	−	1.78985i
$396$		0			0
$397$			22.5437i			1.13144i	0.824599	+	0.565718i	$0.191401\pi$
$397$			22.5437i			1.13144i	−0.824599	+	0.565718i	$0.808599\pi$
$398$		0			0
$399$			8.07381i			0.404196i
$400$		0			0
$401$	−22.0230	+	22.0230i	−1.09978	+	1.09978i	−0.105340	+	0.994436i	$0.533593\pi$
$401$	−22.0230	+	22.0230i	−1.09978	+	1.09978i	−0.994436	+	0.105340i	$0.966407\pi$
$402$		0			0
$403$	−18.6937	+	8.85601i	−0.931201	+	0.441149i
$404$		0			0
$405$	16.6950	−	0.587482i	0.829582	−	0.0291922i
$406$		0			0
$407$	4.11973	+	4.11973i	0.204207	+	0.204207i
$408$		0			0
$409$	−1.20825	+	1.20825i	−0.0597443	+	0.0597443i	−0.736348	−	0.676603i	$-0.763451\pi$
$409$	−1.20825	+	1.20825i	−0.0597443	+	0.0597443i	0.676603	+	0.736348i	$0.263451\pi$
$410$		0			0
$411$	−6.27814	+	6.27814i	−0.309678	+	0.309678i
$412$		0			0
$413$	−4.79073	+	4.79073i	−0.235737	+	0.235737i
$414$		0			0
$415$	−0.811783	−	23.0692i	−0.0398489	−	1.13242i
$416$		0			0
$417$	38.6503	−	38.6503i	1.89271	−	1.89271i
$418$		0			0
$419$			19.2798i			0.941882i	0.882165	+	0.470941i	$0.156086\pi$
$419$			19.2798i			0.941882i	−0.882165	+	0.470941i	$0.843914\pi$
$420$		0			0
$421$	19.9104	+	19.9104i	0.970374	+	0.970374i	0.999574	−	0.0291995i	$-0.00929582\pi$
$421$	19.9104	+	19.9104i	0.970374	+	0.970374i	−0.0291995	+	0.999574i	$0.509296\pi$
$422$		0			0
$423$	40.4217			1.96537
$424$		0			0
$425$	22.1895	+	19.2682i	1.07635	+	0.934644i
$426$		0			0
$427$		−	6.48891i		−	0.314020i
$428$		0			0
$429$	7.28563	−	20.4028i	0.351754	−	0.985058i
$430$		0			0
$431$	−13.3786	−	13.3786i	−0.644424	−	0.644424i	0.307216	−	0.951640i	$-0.400603\pi$
$431$	−13.3786	−	13.3786i	−0.644424	−	0.644424i	−0.951640	+	0.307216i	$0.900603\pi$
$432$		0			0
$433$	11.1481	−	11.1481i	0.535745	−	0.535745i	−0.386531	−	0.922276i	$-0.626327\pi$
$433$	11.1481	−	11.1481i	0.535745	−	0.535745i	0.922276	+	0.386531i	$0.126327\pi$
$434$		0			0
$435$	−21.6617	+	23.2418i	−1.03860	+	1.11436i
$436$		0			0
$437$			6.48724i			0.310327i
$438$		0			0
$439$	11.7278			0.559737			0.279869	−	0.960038i	$-0.409709\pi$
$439$	11.7278			0.559737			0.279869	+	0.960038i	$0.409709\pi$
$440$		0			0
$441$			38.5101i			1.83382i
$442$		0			0
$443$	−20.8920	−	20.8920i	−0.992608	−	0.992608i	0.00736499	−	0.999973i	$-0.497656\pi$
$443$	−20.8920	−	20.8920i	−0.992608	−	0.992608i	−0.999973	+	0.00736499i	$0.997656\pi$
$444$		0			0
$445$	−8.76661	−	8.17061i	−0.415577	−	0.387324i
$446$		0			0
$447$	41.7053			1.97259
$448$		0			0
$449$	1.81112	+	1.81112i	0.0854720	+	0.0854720i	0.748550	−	0.663078i	$-0.230750\pi$
$449$	1.81112	+	1.81112i	0.0854720	+	0.0854720i	−0.663078	+	0.748550i	$0.730750\pi$
$450$		0			0
$451$	7.56153			0.356059
$452$		0			0
$453$	8.06864			0.379098
$454$		0			0
$455$	−4.80326	−	1.52698i	−0.225180	−	0.0715860i
$456$		0			0
$457$	9.50414			0.444585			0.222292	−	0.974980i	$-0.428646\pi$
$457$	9.50414			0.444585			0.222292	+	0.974980i	$0.428646\pi$
$458$		0			0
$459$	−49.3612			−2.30398
$460$		0			0
$461$	6.71519	+	6.71519i	0.312758	+	0.312758i	0.845977	−	0.533219i	$-0.179018\pi$
$461$	6.71519	+	6.71519i	0.312758	+	0.312758i	−0.533219	+	0.845977i	$0.679018\pi$
$462$		0			0
$463$	12.1627			0.565251			0.282625	−	0.959230i	$-0.408795\pi$
$463$	12.1627			0.565251			0.282625	+	0.959230i	$0.408795\pi$
$464$		0			0
$465$	−1.34034	−	38.0898i	−0.0621570	−	1.76637i
$466$		0			0
$467$	8.81665	+	8.81665i	0.407986	+	0.407986i	0.881036	−	0.473050i	$-0.156847\pi$
$467$	8.81665	+	8.81665i	0.407986	+	0.407986i	−0.473050	+	0.881036i	$0.656847\pi$
$468$		0			0
$469$			2.77175i			0.127987i
$470$		0			0
$471$	−11.2360			−0.517730
$472$		0			0
$473$			15.8786i			0.730099i
$474$		0			0
$475$	−14.2507	+	16.4114i	−0.653869	+	0.753005i
$476$		0			0
$477$	44.6883	−	44.6883i	2.04614	−	2.04614i
$478$		0			0
$479$	−11.1541	−	11.1541i	−0.509643	−	0.509643i	0.404773	−	0.914417i	$-0.367350\pi$
$479$	−11.1541	−	11.1541i	−0.509643	−	0.509643i	−0.914417	+	0.404773i	$0.867350\pi$
$480$		0			0
$481$	9.78173	+	3.49295i	0.446008	+	0.159265i
$482$		0			0
$483$		−	2.77175i		−	0.126119i
$484$		0			0
$485$	−29.4409	+	1.03600i	−1.33684	+	0.0470422i
$486$		0			0
$487$	−24.9546			−1.13080			−0.565401	−	0.824816i	$-0.691279\pi$
$487$	−24.9546			−1.13080			−0.565401	+	0.824816i	$0.691279\pi$
$488$		0			0
$489$	−15.4469	−	15.4469i	−0.698534	−	0.698534i
$490$		0			0
$491$		−	14.9353i		−	0.674020i	−0.941501	−	0.337010i	$-0.890584\pi$
$491$		−	14.9353i		−	0.674020i	0.941501	−	0.337010i	$-0.109416\pi$
$492$		0			0
$493$	19.8760	−	19.8760i	0.895169	−	0.895169i
$494$		0			0
$495$	19.2765	+	17.9659i	0.866412	+	0.807508i
$496$		0			0
$497$	4.36122	−	4.36122i	0.195627	−	0.195627i
$498$		0			0
$499$	−0.958355	+	0.958355i	−0.0429019	+	0.0429019i	−0.728232	−	0.685330i	$-0.759658\pi$
$499$	−0.958355	+	0.958355i	−0.0429019	+	0.0429019i	0.685330	+	0.728232i	$0.259658\pi$
$500$		0			0
$501$	−17.1536	+	17.1536i	−0.766368	+	0.766368i
$502$		0			0
$503$	1.59172	+	1.59172i	0.0709714	+	0.0709714i	0.741701	−	0.670730i	$-0.234019\pi$
$503$	1.59172	+	1.59172i	0.0709714	+	0.0709714i	−0.670730	+	0.741701i	$0.734019\pi$
$504$		0			0
$505$	−0.0287872	−	0.818073i	−0.00128101	−	0.0364038i
$506$		0			0
$507$	−3.83454	−	38.4320i	−0.170298	−	1.70683i
$508$		0			0
$509$	10.4868	−	10.4868i	0.464820	−	0.464820i	−0.435411	−	0.900232i	$-0.643397\pi$
$509$	10.4868	−	10.4868i	0.464820	−	0.464820i	0.900232	+	0.435411i	$0.143397\pi$
$510$		0			0
$511$		−	7.13240i		−	0.315519i
$512$		0			0
$513$		−	36.5075i		−	1.61185i
$514$		0			0
$515$	9.40497	−	10.0910i	0.414433	−	0.444663i
$516$		0			0
$517$	9.92090	+	9.92090i	0.436321	+	0.436321i
$518$		0			0
$519$	3.82810			0.168035
$520$		0			0
$521$	3.91703			0.171608			0.0858041	−	0.996312i	$-0.472654\pi$
$521$	3.91703			0.171608			0.0858041	+	0.996312i	$0.472654\pi$
$522$		0			0
$523$	−12.5403	−	12.5403i	−0.548347	−	0.548347i	0.377615	−	0.925963i	$-0.376744\pi$
$523$	−12.5403	−	12.5403i	−0.548347	−	0.548347i	−0.925963	+	0.377615i	$0.876744\pi$
$524$		0			0
$525$	6.08879	−	7.01194i	0.265737	−	0.306026i
$526$		0			0
$527$			33.7200i			1.46887i
$528$		0			0
$529$			20.7729i			0.903171i
$530$		0			0
$531$	44.6523	−	44.6523i	1.93775	−	1.93775i
$532$		0			0
$533$	12.1825	−	5.77135i	0.527681	−	0.249985i
$534$		0			0
$535$	17.7678	−	19.0638i	0.768167	−	0.824201i
$536$		0			0
$537$	42.6927	+	42.6927i	1.84232	+	1.84232i
$538$		0			0
$539$	−9.45174	+	9.45174i	−0.407115	+	0.407115i
$540$		0			0
$541$	12.8645	−	12.8645i	0.553090	−	0.553090i	−0.374241	−	0.927331i	$-0.622097\pi$
$541$	12.8645	−	12.8645i	0.553090	−	0.553090i	0.927331	+	0.374241i	$0.122097\pi$
$542$		0			0
$543$	−43.9975	+	43.9975i	−1.88811	+	1.88811i
$544$		0			0
$545$	−22.7663	+	24.4270i	−0.975201	+	1.04634i
$546$		0			0
$547$	−0.897666	+	0.897666i	−0.0383814	+	0.0383814i	−0.726037	−	0.687656i	$-0.758640\pi$
$547$	−0.897666	+	0.897666i	−0.0383814	+	0.0383814i	0.687656	+	0.726037i	$0.258640\pi$
$548$		0			0
$549$			60.4803i			2.58123i
$550$		0			0
$551$	14.7003	+	14.7003i	0.626253	+	0.626253i
$552$		0			0
$553$	9.95139			0.423176
$554$		0			0
$555$	−13.0481	+	13.9999i	−0.553863	+	0.594265i
$556$		0			0
$557$		−	12.1237i		−	0.513697i	−0.966452	−	0.256848i	$-0.917316\pi$
$557$		−	12.1237i		−	0.513697i	0.966452	−	0.256848i	$-0.0826841\pi$
$558$		0			0
$559$	12.1194	+	25.5822i	0.512595	+	1.08201i
$560$		0			0
$561$	−24.9724	−	24.9724i	−1.05434	−	1.05434i
$562$		0			0
$563$	−5.13582	+	5.13582i	−0.216449	+	0.216449i	−0.807000	−	0.590551i	$-0.798910\pi$
$563$	−5.13582	+	5.13582i	−0.216449	+	0.216449i	0.590551	+	0.807000i	$0.298910\pi$
$564$		0			0
$565$	16.4783	+	15.3580i	0.693246	+	0.646115i
$566$		0			0
$567$			4.67042i			0.196139i
$568$		0			0
$569$	−33.3065			−1.39628			−0.698142	−	0.715960i	$-0.745989\pi$
$569$	−33.3065			−1.39628			−0.698142	+	0.715960i	$0.745989\pi$
$570$		0			0
$571$			16.1774i			0.677003i	0.940966	+	0.338502i	$0.109920\pi$
$571$			16.1774i			0.677003i	−0.940966	+	0.338502i	$0.890080\pi$
$572$		0			0
$573$	−29.7890	−	29.7890i	−1.24445	−	1.24445i
$574$		0			0
$575$	4.89230	−	5.63404i	0.204023	−	0.234956i
$576$		0			0
$577$	−17.8546			−0.743298			−0.371649	−	0.928373i	$-0.621208\pi$
$577$	−17.8546			−0.743298			−0.371649	+	0.928373i	$0.621208\pi$
$578$		0			0
$579$	10.4751	+	10.4751i	0.435329	+	0.435329i
$580$		0			0
$581$	6.45359			0.267740
$582$		0			0
$583$	21.9361			0.908502
$584$		0			0
$585$	44.7690	+	14.2323i	1.85097	+	0.588434i
$586$		0			0
$587$	30.4634			1.25736			0.628680	−	0.777664i	$-0.283595\pi$
$587$	30.4634			1.25736			0.628680	+	0.777664i	$0.283595\pi$
$588$		0			0
$589$	−24.9393			−1.02761
$590$		0			0
$591$	−31.4089	−	31.4089i	−1.29199	−	1.29199i
$592$		0			0
$593$	10.5132			0.431724			0.215862	−	0.976424i	$-0.430744\pi$
$593$	10.5132			0.431724			0.215862	+	0.976424i	$0.430744\pi$
$594$		0			0
$595$	−5.60176	+	6.01038i	−0.229650	+	0.246402i
$596$		0			0
$597$	−28.7297	−	28.7297i	−1.17583	−	1.17583i
$598$		0			0
$599$		−	43.0711i		−	1.75984i	−0.475126	−	0.879918i	$-0.657598\pi$
$599$		−	43.0711i		−	1.75984i	0.475126	−	0.879918i	$-0.342402\pi$
$600$		0			0
$601$	23.2359			0.947813			0.473907	−	0.880575i	$-0.342843\pi$
$601$	23.2359			0.947813			0.473907	+	0.880575i	$0.342843\pi$
$602$		0			0
$603$		−	25.8342i		−	1.05205i
$604$		0			0
$605$	−0.543352	−	15.4409i	−0.0220904	−	0.627764i
$606$		0			0
$607$	24.5847	−	24.5847i	0.997861	−	0.997861i	−0.00213629	−	0.999998i	$-0.500680\pi$
$607$	24.5847	−	24.5847i	0.997861	−	0.997861i	0.999998	+	0.00213629i	$0.000680002\pi$
$608$		0			0
$609$	−6.28086	−	6.28086i	−0.254513	−	0.254513i
$610$		0			0
$611$	23.5558	+	8.41153i	0.952966	+	0.340294i
$612$		0			0
$613$			0.669386i			0.0270363i	0.999909	+	0.0135181i	$0.00430308\pi$
$613$			0.669386i			0.0270363i	−0.999909	+	0.0135181i	$0.995697\pi$
$614$		0			0
$615$	0.873485	+	24.8226i	0.0352223	+	1.00094i
$616$		0			0
$617$	−19.4299			−0.782217			−0.391108	−	0.920345i	$-0.627908\pi$
$617$	−19.4299			−0.782217			−0.391108	+	0.920345i	$0.627908\pi$
$618$		0			0
$619$	−15.3796	−	15.3796i	−0.618160	−	0.618160i	0.326899	−	0.945059i	$-0.393996\pi$
$619$	−15.3796	−	15.3796i	−0.618160	−	0.618160i	−0.945059	+	0.326899i	$0.893996\pi$
$620$		0			0
$621$			12.5331i			0.502935i
$622$		0			0
$623$	2.36909	−	2.36909i	0.0949155	−	0.0949155i
$624$		0			0
$625$	24.7530	−	3.50586i	0.990118	−	0.140234i
$626$		0			0
$627$	18.4696	−	18.4696i	0.737604	−	0.737604i
$628$		0			0
$629$	11.9725	−	11.9725i	0.477375	−	0.477375i
$630$		0			0
$631$	−16.6091	+	16.6091i	−0.661197	+	0.661197i	−0.955662	−	0.294466i	$-0.904858\pi$
$631$	−16.6091	+	16.6091i	−0.661197	+	0.661197i	0.294466	+	0.955662i	$0.404858\pi$
$632$		0			0
$633$	−10.6536	−	10.6536i	−0.423444	−	0.423444i
$634$		0			0
$635$	30.0706	+	28.0262i	1.19332	+	1.11219i
$636$		0			0
$637$	−8.01375	+	22.4419i	−0.317516	+	0.889179i
$638$		0			0
$639$	−40.6490	+	40.6490i	−1.60805	+	1.60805i
$640$		0			0
$641$		−	5.60958i		−	0.221565i	−0.993845	−	0.110783i	$-0.964664\pi$
$641$		−	5.60958i		−	0.221565i	0.993845	−	0.110783i	$-0.0353357\pi$
$642$		0			0
$643$		−	32.7184i		−	1.29029i	−0.764061	−	0.645144i	$-0.776798\pi$
$643$		−	32.7184i		−	1.29029i	0.764061	−	0.645144i	$-0.223202\pi$
$644$		0			0
$645$	−52.1255	+	1.83425i	−2.05244	+	0.0722235i
$646$		0			0
$647$	−19.6159	−	19.6159i	−0.771180	−	0.771180i	0.207133	−	0.978313i	$-0.433587\pi$
$647$	−19.6159	−	19.6159i	−0.771180	−	0.771180i	−0.978313	+	0.207133i	$0.933587\pi$
$648$		0			0
$649$	21.9185			0.860376
$650$		0			0
$651$	10.6556			0.417626
$652$		0			0
$653$	−3.70498	−	3.70498i	−0.144987	−	0.144987i	0.630887	−	0.775874i	$-0.282691\pi$
$653$	−3.70498	−	3.70498i	−0.144987	−	0.144987i	−0.775874	+	0.630887i	$0.782691\pi$
$654$		0			0
$655$	0.104050	−	0.00366143i	0.00406558	−	0.000143064i
$656$		0			0
$657$			66.4779i			2.59355i
$658$		0			0
$659$			0.600315i			0.0233850i	0.999932	+	0.0116925i	$0.00372192\pi$
$659$			0.600315i			0.0233850i	−0.999932	+	0.0116925i	$0.996278\pi$
$660$		0			0
$661$	−13.3229	+	13.3229i	−0.518199	+	0.518199i	−0.917026	−	0.398827i	$-0.869417\pi$
$661$	−13.3229	+	13.3229i	−0.518199	+	0.518199i	0.398827	+	0.917026i	$0.369417\pi$
$662$		0			0
$663$	−59.2935	−	21.1731i	−2.30277	−	0.822294i
$664$		0			0
$665$	−4.44528	−	4.14306i	−0.172380	−	0.160661i
$666$		0			0
$667$	−5.04662	−	5.04662i	−0.195406	−	0.195406i
$668$		0			0
$669$	25.1410	−	25.1410i	0.972008	−	0.972008i
$670$		0			0
$671$	−14.8440	+	14.8440i	−0.573046	+	0.573046i
$672$		0			0
$673$	17.9518	−	17.9518i	0.691989	−	0.691989i	−0.270680	−	0.962669i	$-0.587249\pi$
$673$	17.9518	−	17.9518i	0.691989	−	0.691989i	0.962669	+	0.270680i	$0.0872485\pi$
$674$		0			0
$675$	−27.5318	+	31.7060i	−1.05970	+	1.22037i
$676$		0			0
$677$	−4.11061	+	4.11061i	−0.157983	+	0.157983i	−0.781673	−	0.623689i	$-0.785633\pi$
$677$	−4.11061	+	4.11061i	−0.157983	+	0.157983i	0.623689	+	0.781673i	$0.285633\pi$
$678$		0			0
$679$		−	8.23606i		−	0.316071i
$680$		0			0
$681$	−47.1347	−	47.1347i	−1.80620	−	1.80620i
$682$		0			0
$683$	41.5283			1.58904			0.794518	−	0.607241i	$-0.207724\pi$
$683$	41.5283			1.58904			0.794518	+	0.607241i	$0.207724\pi$
$684$		0			0
$685$	−0.235001	−	6.67823i	−0.00897892	−	0.255162i
$686$		0			0
$687$			56.7532i			2.16527i
$688$		0			0
$689$	35.3416	−	16.7428i	1.34641	−	0.637850i
$690$		0			0
$691$	−21.7721	−	21.7721i	−0.828251	−	0.828251i	0.159024	−	0.987275i	$-0.449165\pi$
$691$	−21.7721	−	21.7721i	−0.828251	−	0.828251i	−0.987275	+	0.159024i	$0.949165\pi$
$692$		0			0
$693$	−5.20927	+	5.20927i	−0.197884	+	0.197884i
$694$		0			0
$695$	1.44674	+	41.1134i	0.0548781	+	1.55952i
$696$		0			0
$697$		−	21.9749i		−	0.832357i
$698$		0			0
$699$	15.9891			0.604764
$700$		0			0
$701$			9.81277i			0.370623i	0.982680	+	0.185312i	$0.0593295\pi$
$701$			9.81277i			0.370623i	−0.982680	+	0.185312i	$0.940671\pi$
$702$		0			0
$703$	8.85487	+	8.85487i	0.333968	+	0.333968i
$704$		0			0
$705$	−31.4218	+	33.7139i	−1.18341	+	1.26974i
$706$		0			0
$707$	0.228855			0.00860699
$708$		0			0
$709$	−20.4477	−	20.4477i	−0.767931	−	0.767931i	0.209811	−	0.977742i	$-0.432715\pi$
$709$	−20.4477	−	20.4477i	−0.767931	−	0.767931i	−0.977742	+	0.209811i	$0.932715\pi$
$710$		0			0
$711$	−92.7525			−3.47849
$712$		0			0
$713$	8.56169			0.320638
$714$		0			0
$715$	7.49478	+	14.4810i	0.280289	+	0.541559i
$716$		0			0
$717$	26.3920			0.985626
$718$		0			0
$719$	8.51967			0.317730			0.158865	−	0.987300i	$-0.449216\pi$
$719$	8.51967			0.317730			0.158865	+	0.987300i	$0.449216\pi$
$720$		0			0
$721$	2.72699	+	2.72699i	0.101559	+	0.101559i
$722$		0			0
$723$	48.4276			1.80104
$724$		0			0
$725$	−1.68081	−	23.8530i	−0.0624237	−	0.885877i
$726$		0			0
$727$	−24.6182	−	24.6182i	−0.913038	−	0.913038i	0.0834725	−	0.996510i	$-0.473399\pi$
$727$	−24.6182	−	24.6182i	−0.913038	−	0.913038i	−0.996510	+	0.0834725i	$0.973399\pi$
$728$		0			0
$729$			31.3225i			1.16009i
$730$		0			0
$731$	46.1455			1.70675
$732$		0			0
$733$		−	25.4304i		−	0.939293i	−0.882855	−	0.469646i	$-0.844381\pi$
$733$		−	25.4304i		−	0.939293i	0.882855	−	0.469646i	$-0.155619\pi$
$734$		0			0
$735$	−32.1196	−	29.9359i	−1.18475	−	1.10420i
$736$		0			0
$737$	6.34063	−	6.34063i	0.233560	−	0.233560i
$738$		0			0
$739$	0.982511	+	0.982511i	0.0361422	+	0.0361422i	0.724947	−	0.688805i	$-0.241864\pi$
$739$	0.982511	+	0.982511i	0.0361422	+	0.0361422i	−0.688805	+	0.724947i	$0.741864\pi$
$740$		0			0
$741$	15.6596	−	43.8535i	0.575270	−	1.61100i
$742$		0			0
$743$			26.0191i			0.954548i	0.878755	+	0.477274i	$0.158375\pi$
$743$			26.0191i			0.954548i	−0.878755	+	0.477274i	$0.841625\pi$
$744$		0			0
$745$	−21.4010	+	22.9621i	−0.784071	+	0.841265i
$746$		0			0
$747$	−60.1510			−2.20081
$748$		0			0
$749$	5.15180	+	5.15180i	0.188243	+	0.188243i
$750$		0			0
$751$			24.4105i			0.890751i	0.895344	+	0.445375i	$0.146930\pi$
$751$			24.4105i			0.890751i	−0.895344	+	0.445375i	$0.853070\pi$
$752$		0			0
$753$	−14.5202	+	14.5202i	−0.529144	+	0.529144i
$754$		0			0
$755$	−4.14041	+	4.44243i	−0.150685	+	0.161677i
$756$		0			0
$757$	−5.21745	+	5.21745i	−0.189632	+	0.189632i	−0.795537	−	0.605905i	$-0.792811\pi$
$757$	−5.21745	+	5.21745i	−0.189632	+	0.189632i	0.605905	+	0.795537i	$0.292811\pi$
$758$		0			0
$759$	−6.34063	+	6.34063i	−0.230150	+	0.230150i
$760$		0			0
$761$	23.7644	−	23.7644i	0.861459	−	0.861459i	−0.130049	−	0.991508i	$-0.541513\pi$
$761$	23.7644	−	23.7644i	0.861459	−	0.861459i	0.991508	+	0.130049i	$0.0415134\pi$
$762$		0			0
$763$	−6.60114	−	6.60114i	−0.238977	−	0.238977i
$764$		0			0
$765$	52.2115	−	56.0201i	1.88771	−	2.02541i
$766$		0			0
$767$	35.3131	−	16.7293i	1.27508	−	0.604061i
$768$		0			0
$769$	−5.72519	+	5.72519i	−0.206456	+	0.206456i	−0.802759	−	0.596304i	$-0.796635\pi$
$769$	−5.72519	+	5.72519i	−0.206456	+	0.206456i	0.596304	+	0.802759i	$0.296635\pi$
$770$		0			0
$771$		−	37.4171i		−	1.34755i
$772$		0			0
$773$			43.6133i			1.56866i	0.620344	+	0.784330i	$0.286993\pi$
$773$			43.6133i			1.56866i	−0.620344	+	0.784330i	$0.713007\pi$
$774$		0			0
$775$	21.6593	+	18.8077i	0.778024	+	0.675594i
$776$		0			0
$777$	−3.78334	−	3.78334i	−0.135727	−	0.135727i
$778$		0			0
$779$	16.2526			0.582310
$780$		0			0
$781$	−19.9534			−0.713988
$782$		0			0
$783$	28.4003	+	28.4003i	1.01494	+	1.01494i
$784$		0			0
$785$	5.76576	−	6.18634i	0.205789	−	0.220800i
$786$		0			0
$787$		−	22.5183i		−	0.802692i	−0.915926	−	0.401346i	$-0.868542\pi$
$787$		−	22.5183i		−	0.802692i	0.915926	−	0.401346i	$-0.131458\pi$
$788$		0			0
$789$		−	5.04932i		−	0.179760i
$790$		0			0
$791$	−4.45308	+	4.45308i	−0.158333	+	0.158333i
$792$		0			0
$793$	−12.5856	+	35.2450i	−0.446928	+	1.25159i
$794$		0			0
$795$	2.53400	+	72.0109i	0.0898716	+	2.55396i
$796$		0			0
$797$	−5.28800	−	5.28800i	−0.187311	−	0.187311i	0.607222	−	0.794532i	$-0.292284\pi$
$797$	−5.28800	−	5.28800i	−0.187311	−	0.187311i	−0.794532	+	0.607222i	$0.792284\pi$
$798$		0			0
$799$	28.8315	−	28.8315i	1.01999	−	1.01999i
$800$		0			0
$801$	−22.0812	+	22.0812i	−0.780202	+	0.780202i
$802$		0			0
$803$	−16.3160	+	16.3160i	−0.575780	+	0.575780i
$804$		0			0
$805$	1.52607	+	1.42232i	0.0537868	+	0.0501301i
$806$		0			0
$807$	−38.5211	+	38.5211i	−1.35601	+	1.35601i
$808$		0			0
$809$			30.1040i			1.05840i	0.848497	+	0.529199i	$0.177508\pi$
$809$			30.1040i			1.05840i	−0.848497	+	0.529199i	$0.822492\pi$
$810$		0			0
$811$	22.5132	+	22.5132i	0.790547	+	0.790547i	0.981583	−	0.191036i	$-0.0611848\pi$
$811$	22.5132	+	22.5132i	0.790547	+	0.790547i	−0.191036	+	0.981583i	$0.561185\pi$
$812$		0			0
$813$	−28.6944			−1.00636
$814$		0			0
$815$	16.4313	−	0.578203i	0.575564	−	0.0202536i
$816$		0			0
$817$			34.1292i			1.19403i
$818$		0			0
$819$	−4.41672	+	12.3687i	−0.154333	+	0.432197i
$820$		0			0
$821$	−23.1426	−	23.1426i	−0.807682	−	0.807682i	0.176600	−	0.984283i	$-0.443490\pi$
$821$	−23.1426	−	23.1426i	−0.807682	−	0.807682i	−0.984283	+	0.176600i	$0.943490\pi$
$822$		0			0
$823$	−2.54836	+	2.54836i	−0.0888301	+	0.0888301i	−0.750126	−	0.661295i	$-0.770007\pi$
$823$	−2.54836	+	2.54836i	−0.0888301	+	0.0888301i	0.661295	+	0.750126i	$0.270007\pi$
$824$		0			0
$825$	−29.9691	+	2.11179i	−1.04339	+	0.0735230i
$826$		0			0
$827$		−	7.98441i		−	0.277645i	−0.990317	−	0.138823i	$-0.955668\pi$
$827$		−	7.98441i		−	0.277645i	0.990317	−	0.138823i	$-0.0443318\pi$
$828$		0			0
$829$	−32.6036			−1.13237			−0.566186	−	0.824278i	$-0.691581\pi$
$829$	−32.6036			−1.13237			−0.566186	+	0.824278i	$0.691581\pi$
$830$		0			0
$831$			10.3796i			0.360064i
$832$		0			0
$833$	27.4681	+	27.4681i	0.951713	+	0.951713i
$834$		0			0
$835$	−0.642088	−	18.2468i	−0.0222204	−	0.631456i
$836$		0			0
$837$	−48.1816			−1.66540
$838$		0			0
$839$	17.7214	+	17.7214i	0.611810	+	0.611810i	0.943418	−	0.331607i	$-0.107591\pi$
$839$	17.7214	+	17.7214i	0.611810	+	0.611810i	−0.331607	+	0.943418i	$0.607591\pi$
$840$		0			0
$841$	6.12842			0.211325
$842$		0			0
$843$	85.3116			2.93829
$844$		0			0
$845$	23.1276	+	17.6101i	0.795613	+	0.605806i
$846$		0			0
$847$	4.31959			0.148423
$848$		0			0
$849$	79.2452			2.71969
$850$		0			0
$851$	−3.03989	−	3.03989i	−0.104206	−	0.104206i
$852$		0			0
$853$	−40.3100			−1.38019			−0.690095	−	0.723719i	$-0.742431\pi$
$853$	−40.3100			−1.38019			−0.690095	+	0.723719i	$0.742431\pi$
$854$		0			0
$855$	41.4325	+	38.6156i	1.41696	+	1.32063i
$856$		0			0
$857$	10.2248	+	10.2248i	0.349274	+	0.349274i	0.859839	−	0.510565i	$-0.170564\pi$
$857$	10.2248	+	10.2248i	0.349274	+	0.349274i	−0.510565	+	0.859839i	$0.670564\pi$
$858$		0			0
$859$		−	30.9345i		−	1.05547i	−0.849409	−	0.527735i	$-0.823041\pi$
$859$		−	30.9345i		−	1.05547i	0.849409	−	0.527735i	$-0.176959\pi$
$860$		0			0
$861$	−6.94411			−0.236655
$862$		0			0
$863$			4.54648i			0.154764i	0.997002	+	0.0773820i	$0.0246561\pi$
$863$			4.54648i			0.154764i	−0.997002	+	0.0773820i	$0.975344\pi$
$864$		0			0
$865$	−1.96438	+	2.10767i	−0.0667910	+	0.0716630i
$866$		0			0
$867$	−36.8596	+	36.8596i	−1.25182	+	1.25182i
$868$		0			0
$869$	−22.7647	−	22.7647i	−0.772240	−	0.772240i
$870$		0			0
$871$	5.37596	−	15.0550i	0.182157	−	0.510118i
$872$		0			0
$873$			76.7647i			2.59809i
$874$		0			0
$875$	0.736180	+	6.95053i	0.0248874	+	0.234971i
$876$		0			0
$877$	52.1926			1.76242			0.881210	−	0.472725i	$-0.156730\pi$
$877$	52.1926			1.76242			0.881210	+	0.472725i	$0.156730\pi$
$878$		0			0
$879$	55.5530	+	55.5530i	1.87376	+	1.87376i
$880$		0			0
$881$		−	13.1925i		−	0.444466i	−0.974994	−	0.222233i	$-0.928665\pi$
$881$		−	13.1925i		−	0.444466i	0.974994	−	0.222233i	$-0.0713346\pi$
$882$		0			0
$883$	−8.85507	+	8.85507i	−0.297997	+	0.297997i	−0.840229	−	0.542232i	$-0.817579\pi$
$883$	−8.85507	+	8.85507i	−0.297997	+	0.297997i	0.542232	+	0.840229i	$0.317579\pi$
$884$		0			0
$885$	2.53196	+	71.9530i	0.0851109	+	2.41867i
$886$		0			0
$887$	8.82709	−	8.82709i	0.296385	−	0.296385i	−0.543211	−	0.839596i	$-0.682792\pi$
$887$	8.82709	−	8.82709i	0.296385	−	0.296385i	0.839596	+	0.543211i	$0.182792\pi$
$888$		0			0
$889$	−8.12628	+	8.12628i	−0.272547	+	0.272547i
$890$		0			0
$891$	10.6840	−	10.6840i	0.357928	−	0.357928i
$892$		0			0
$893$	21.3238	+	21.3238i	0.713574	+	0.713574i
$894$		0			0
$895$	−45.4134	+	1.59805i	−1.51800	+	0.0534171i
$896$		0			0
$897$	−5.37596	+	15.0550i	−0.179498	+	0.502670i
$898$		0			0
$899$	19.4010	−	19.4010i	0.647061	−	0.647061i
$900$		0			0
$901$		−	63.7495i		−	2.12380i
$902$		0			0
$903$		−	14.5821i		−	0.485261i
$904$		0			0
$905$	−1.64690	−	46.8013i	−0.0547447	−	1.55573i
$906$		0			0
$907$	−21.0591	−	21.0591i	−0.699256	−	0.699256i	0.264994	−	0.964250i	$-0.414630\pi$
$907$	−21.0591	−	21.0591i	−0.699256	−	0.699256i	−0.964250	+	0.264994i	$0.914630\pi$
$908$		0			0
$909$	−2.13306			−0.0707491
$910$		0			0
$911$	−13.2480			−0.438925			−0.219463	−	0.975621i	$-0.570430\pi$
$911$	−13.2480			−0.438925			−0.219463	+	0.975621i	$0.570430\pi$
$912$		0			0
$913$	−14.7632	−	14.7632i	−0.488590	−	0.488590i
$914$		0			0
$915$	−50.4438	−	47.0144i	−1.66762	−	1.55425i
$916$		0			0
$917$			0.0291080i			0.000961230i
$918$		0			0
$919$			49.3292i			1.62722i	0.581412	+	0.813610i	$0.302501\pi$
$919$			49.3292i			1.62722i	−0.581412	+	0.813610i	$0.697499\pi$
$920$		0			0
$921$	−34.6696	+	34.6696i	−1.14240	+	1.14240i
$922$		0			0
$923$	−32.1471	+	15.2295i	−1.05814	+	0.501284i
$924$		0			0
$925$	−1.01245	−	14.3681i	−0.0332893	−	0.472420i
$926$		0			0
$927$	−25.4171	−	25.4171i	−0.834807	−	0.834807i
$928$		0			0
$929$	8.16689	−	8.16689i	0.267947	−	0.267947i	−0.560325	−	0.828273i	$-0.689324\pi$
$929$	8.16689	−	8.16689i	0.267947	−	0.267947i	0.828273	+	0.560325i	$0.189324\pi$
$930$		0			0
$931$	−20.3154	+	20.3154i	−0.665810	+	0.665810i
$932$		0			0
$933$	2.50279	−	2.50279i	0.0819378	−	0.0819378i
$934$		0			0
$935$	26.5638	−	0.934757i	0.868730	−	0.0305698i
$936$		0			0
$937$	−29.6443	+	29.6443i	−0.968438	+	0.968438i	−0.999517	−	0.0310793i	$-0.990106\pi$
$937$	−29.6443	+	29.6443i	−0.968438	+	0.968438i	0.0310793	+	0.999517i	$0.490106\pi$
$938$		0			0
$939$		−	100.637i		−	3.28417i
$940$		0			0
$941$	25.5489	+	25.5489i	0.832871	+	0.832871i	0.987909	−	0.155038i	$-0.0495499\pi$
$941$	25.5489	+	25.5489i	0.832871	+	0.832871i	−0.155038	+	0.987909i	$0.549550\pi$
$942$		0			0
$943$	−5.57954			−0.181695
$944$		0			0
$945$	−8.58808	−	8.00421i	−0.279370	−	0.260377i
$946$		0			0
$947$		−	37.4564i		−	1.21717i	−0.793489	−	0.608585i	$-0.791738\pi$
$947$		−	37.4564i		−	1.21717i	0.793489	−	0.608585i	$-0.208262\pi$
$948$		0			0
$949$	−13.8337	+	38.7401i	−0.449060	+	1.25756i
$950$		0			0
$951$	−11.8668	−	11.8668i	−0.384807	−	0.384807i
$952$		0			0
$953$	−1.64519	+	1.64519i	−0.0532930	+	0.0532930i	−0.733251	−	0.679958i	$-0.761998\pi$
$953$	−1.64519	+	1.64519i	−0.0532930	+	0.0532930i	0.679958	+	0.733251i	$0.261998\pi$
$954$		0			0
$955$	31.6874	−	1.11505i	1.02538	−	0.0360822i
$956$		0			0
$957$			28.7361i			0.928906i
$958$		0			0
$959$	1.86823			0.0603283
$960$		0			0
$961$			1.91419i			0.0617482i
$962$		0			0
$963$	−48.0177	−	48.0177i	−1.54735	−	1.54735i
$964$		0			0
$965$	−11.1426	+	0.392099i	−0.358694	+	0.0126221i
$966$		0			0
$967$	−15.1821			−0.488223			−0.244111	−	0.969747i	$-0.578496\pi$
$967$	−15.1821			−0.488223			−0.244111	+	0.969747i	$0.578496\pi$
$968$		0			0
$969$	−53.6752	−	53.6752i	−1.72430	−	1.72430i
$970$		0			0
$971$	45.4645			1.45902			0.729512	−	0.683968i	$-0.239747\pi$
$971$	45.4645			1.45902			0.729512	+	0.683968i	$0.239747\pi$
$972$		0			0
$973$	−11.5014			−0.368719
$974$		0			0
$975$	−46.6718	+	26.2763i	−1.49469	+	0.841515i
$976$		0			0
$977$	−3.47995			−0.111334			−0.0556668	−	0.998449i	$-0.517728\pi$
$977$	−3.47995			−0.111334			−0.0556668	+	0.998449i	$0.517728\pi$
$978$		0			0
$979$	−10.8390			−0.346416
$980$		0			0
$981$	61.5263	+	61.5263i	1.96438	+	1.96438i
$982$		0			0
$983$	30.8871			0.985145			0.492572	−	0.870271i	$-0.336057\pi$
$983$	30.8871			0.985145			0.492572	+	0.870271i	$0.336057\pi$
$984$		0			0
$985$	33.4106	−	1.17569i	1.06455	−	0.0374605i
$986$		0			0
$987$	−9.11084	−	9.11084i	−0.290001	−	0.290001i
$988$		0			0
$989$		−	11.7166i		−	0.372566i
$990$		0			0
$991$	−16.6535			−0.529014			−0.264507	−	0.964384i	$-0.585209\pi$
$991$	−16.6535			−0.529014			−0.264507	+	0.964384i	$0.585209\pi$
$992$		0			0
$993$			50.7182i			1.60949i
$994$		0			0
$995$	30.5606	−	1.07540i	0.968836	−	0.0340924i
$996$		0			0
$997$	28.4391	−	28.4391i	0.900675	−	0.900675i	−0.0948197	−	0.995494i	$-0.530227\pi$
$997$	28.4391	−	28.4391i	0.900675	−	0.900675i	0.995494	+	0.0948197i	$0.0302275\pi$
$998$		0			0
$999$	17.1072	+	17.1072i	0.541248	+	0.541248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.w.e.73.6	yes	12
4.3	odd	2		1040.2.bg.o.593.1		12
5.2	odd	4		520.2.bh.e.177.6	yes	12
13.5	odd	4		520.2.bh.e.473.6	yes	12
20.7	even	4		1040.2.cd.o.177.1		12
52.31	even	4		1040.2.cd.o.993.1		12
65.57	even	4	inner	520.2.w.e.57.6	✓	12
260.187	odd	4		1040.2.bg.o.577.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.w.e.57.6	✓	12	65.57	even	4	inner
520.2.w.e.73.6	yes	12	1.1	even	1	trivial
520.2.bh.e.177.6	yes	12	5.2	odd	4
520.2.bh.e.473.6	yes	12	13.5	odd	4
1040.2.bg.o.577.1		12	260.187	odd	4
1040.2.bg.o.593.1		12	4.3	odd	2
1040.2.cd.o.177.1		12	20.7	even	4
1040.2.cd.o.993.1		12	52.31	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10080 + 2.10080i) q^{3} +(-2.23468 + 0.0786365i) q^{5} -0.625152i q^{7} +5.82676i q^{9} +(-1.43009 + 1.43009i) q^{11} +(-1.21252 + 3.39556i) q^{13} +(-4.85984 - 4.52944i) q^{15} +(4.15605 + 4.15605i) q^{17} +(-3.07381 + 3.07381i) q^{19} +(1.31332 - 1.31332i) q^{21} +(1.05524 - 1.05524i) q^{23} +(4.98763 - 0.351456i) q^{25} +(-5.93847 + 5.93847i) q^{27} -4.78242i q^{29} +(4.05673 + 4.05673i) q^{31} -6.00869 q^{33} +(0.0491597 + 1.39702i) q^{35} -2.88074i q^{37} +(-9.68066 + 4.58614i) q^{39} +(-2.64372 - 2.64372i) q^{41} +(5.55160 - 5.55160i) q^{43} +(-0.458196 - 13.0210i) q^{45} -6.93725i q^{47} +6.60919 q^{49} +17.4621i q^{51} +(-7.66949 - 7.66949i) q^{53} +(3.08335 - 3.30826i) q^{55} -12.9150 q^{57} +(-7.66332 - 7.66332i) q^{59} +10.3797 q^{61} +3.64261 q^{63} +(2.44258 - 7.68335i) q^{65} -4.43372 q^{67} +4.43372 q^{69} +(6.97626 + 6.97626i) q^{71} +11.4091 q^{73} +(11.2164 + 9.73970i) q^{75} +(0.894024 + 0.894024i) q^{77} +15.9184i q^{79} -7.47086 q^{81} +10.3232i q^{83} +(-9.61428 - 8.96064i) q^{85} +(10.0469 - 10.0469i) q^{87} +(3.78962 + 3.78962i) q^{89} +(2.12274 + 0.758007i) q^{91} +17.0448i q^{93} +(6.62729 - 7.11072i) q^{95} +13.1745 q^{97} +(-8.33280 - 8.33280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 8 q^{5} - 14 q^{11} - 2 q^{13} - 12 q^{15} + 14 q^{17} - 6 q^{19} - 18 q^{21} - 2 q^{23} + 2 q^{25} - 26 q^{27} - 22 q^{31} - 4 q^{33} - 12 q^{35} + 4 q^{39} - 4 q^{41} - 8 q^{43} + 16 q^{49}+ \cdots + 22 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 8 * q^5 - 14 * q^11 - 2 * q^13 - 12 * q^15 + 14 * q^17 - 6 * q^19 - 18 * q^21 - 2 * q^23 + 2 * q^25 - 26 * q^27 - 22 * q^31 - 4 * q^33 - 12 * q^35 + 4 * q^39 - 4 * q^41 - 8 * q^43 + 16 * q^49 - 36 * q^53 + 20 * q^55 - 32 * q^57 - 26 * q^59 + 12 * q^61 + 28 * q^63 + 12 * q^65 + 40 * q^67 - 40 * q^69 + 28 * q^71 + 60 * q^73 + 22 * q^75 - 40 * q^77 + 36 * q^81 + 10 * q^85 + 8 * q^87 + 24 * q^89 - 8 * q^91 + 34 * q^95 + 56 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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