LMFDB - Embedded newform 1040.2.bg.o.593.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(577,1040)] 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("1040.577"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-4,0,8,0,0,0,0,0,14,0,-2,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
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:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.1
Root			$2.10080 + 2.10080i$ of defining polynomial
Character	$\chi$	$=$	1040.593
Dual form			1040.2.bg.o.577.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10080 - 2.10080i) q^{3} +(-2.23468 + 0.0786365i) q^{5} +0.625152i q^{7} +5.82676i q^{9} +(1.43009 - 1.43009i) q^{11} +(-1.21252 + 3.39556i) q^{13} +(4.85984 + 4.52944i) q^{15} +(4.15605 + 4.15605i) q^{17} +(3.07381 - 3.07381i) q^{19} +(1.31332 - 1.31332i) q^{21} +(-1.05524 + 1.05524i) q^{23} +(4.98763 - 0.351456i) q^{25} +(5.93847 - 5.93847i) q^{27} -4.78242i q^{29} +(-4.05673 - 4.05673i) q^{31} -6.00869 q^{33} +(-0.0491597 - 1.39702i) q^{35} -2.88074i q^{37} +(9.68066 - 4.58614i) q^{39} +(-2.64372 - 2.64372i) q^{41} +(-5.55160 + 5.55160i) q^{43} +(-0.458196 - 13.0210i) q^{45} +6.93725i q^{47} +6.60919 q^{49} -17.4621i q^{51} +(-7.66949 - 7.66949i) q^{53} +(-3.08335 + 3.30826i) q^{55} -12.9150 q^{57} +(7.66332 + 7.66332i) q^{59} +10.3797 q^{61} -3.64261 q^{63} +(2.44258 - 7.68335i) q^{65} +4.43372 q^{67} +4.43372 q^{69} +(-6.97626 - 6.97626i) q^{71} +11.4091 q^{73} +(-11.2164 - 9.73970i) q^{75} +(0.894024 + 0.894024i) q^{77} -15.9184i q^{79} -7.47086 q^{81} -10.3232i q^{83} +(-9.61428 - 8.96064i) q^{85} +(-10.0469 + 10.0469i) q^{87} +(3.78962 + 3.78962i) q^{89} +(-2.12274 - 0.758007i) q^{91} +17.0448i q^{93} +(-6.62729 + 7.11072i) q^{95} +13.1745 q^{97} +(8.33280 + 8.33280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.10080	−	2.10080i	−1.21290	−	1.21290i	−0.970068	−	0.242832i	$-0.921924\pi$
$3$	−2.10080	−	2.10080i	−1.21290	−	1.21290i	−0.242832	−	0.970068i	$-0.578076\pi$
$4$		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	$0.0376940\pi$
$7$			0.625152i			0.236285i	−0.992997	+	0.118143i	$0.962306\pi$
$8$		0			0
$9$			5.82676i			1.94225i
$10$		0			0
$11$	1.43009	−	1.43009i	0.431189	−	0.431189i	−0.457844	−	0.889033i	$-0.651378\pi$
$11$	1.43009	−	1.43009i	0.431189	−	0.431189i	0.889033	+	0.457844i	$0.151378\pi$
$12$		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	−0.260337	−	0.965518i	$-0.583834\pi$
$19$	3.07381	−	3.07381i	0.705181	−	0.705181i	0.965518	+	0.260337i	$0.0838336\pi$
$20$		0			0
$21$	1.31332	−	1.31332i	0.286590	−	0.286590i
$22$		0			0
$23$	−1.05524	+	1.05524i	−0.220034	+	0.220034i	−0.808513	−	0.588479i	$-0.799727\pi$
$23$	−1.05524	+	1.05524i	−0.220034	+	0.220034i	0.588479	+	0.808513i	$0.299727\pi$
$24$		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	0.241732	−	0.970343i	$-0.422285\pi$
$31$	−4.05673	−	4.05673i	−0.728611	−	0.728611i	−0.970343	+	0.241732i	$0.922285\pi$
$32$		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	−0.989709	−	0.143097i	$-0.954294\pi$
$43$	−5.55160	+	5.55160i	−0.846612	+	0.846612i	0.143097	+	0.989709i	$0.454294\pi$
$44$		0			0
$45$	−0.458196	−	13.0210i	−0.0683038	−	1.94105i
$46$		0			0
$47$			6.93725i			1.01190i	0.862562	+	0.505951i	$0.168858\pi$
$47$			6.93725i			1.01190i	−0.862562	+	0.505951i	$0.831142\pi$
$48$		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	0.999997	−	0.00231846i	$-0.000737991\pi$
$59$	7.66332	+	7.66332i	0.997679	+	0.997679i	−0.00231846	+	0.999997i	$0.500738\pi$
$60$		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	$-0.412701\pi$
$67$	4.43372			0.541665			0.270833	+	0.962626i	$0.412701\pi$
$68$		0			0
$69$	4.43372			0.533757
$70$		0			0
$71$	−6.97626	−	6.97626i	−0.827930	−	0.827930i	0.159300	−	0.987230i	$-0.449076\pi$
$71$	−6.97626	−	6.97626i	−0.827930	−	0.827930i	−0.987230	+	0.159300i	$0.949076\pi$
$72$		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	$-0.646834\pi$
$79$		−	15.9184i		−	1.79096i	0.445106	−	0.895478i	$-0.353166\pi$
$80$		0			0
$81$	−7.47086			−0.830096
$82$		0			0
$83$		−	10.3232i		−	1.13312i	−0.824020	−	0.566561i	$-0.808274\pi$
$83$		−	10.3232i		−	1.13312i	0.824020	−	0.566561i	$-0.191726\pi$
$84$		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	−0.458751	−	0.888565i	$-0.651703\pi$
$103$	4.36213	−	4.36213i	0.429814	−	0.429814i	0.888565	+	0.458751i	$0.151703\pi$
$104$		0			0
$105$	−2.83158	+	3.03813i	−0.276334	+	0.296492i
$106$		0			0
$107$	8.24089	−	8.24089i	0.796677	−	0.796677i	−0.185893	−	0.982570i	$-0.559518\pi$
$107$	8.24089	−	8.24089i	0.796677	−	0.796677i	0.982570	+	0.185893i	$0.0595179\pi$
$108$		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	$0.0536057\pi$
$127$	12.9989	+	12.9989i	1.15347	+	1.15347i	0.167612	+	0.985853i	$0.446394\pi$
$128$		0			0
$129$	23.3257			2.05371
$130$		0			0
$131$	0.0465615			0.00406810			0.00203405	−	0.999998i	$-0.499353\pi$
$131$	0.0465615			0.00406810			0.00203405	+	0.999998i	$0.499353\pi$
$132$		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	$0.284904\pi$
$139$			18.3978i			1.56049i	−0.625477	+	0.780243i	$0.715096\pi$
$140$		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	−0.780915	−	0.624637i	$-0.785247\pi$
$151$	−1.92037	+	1.92037i	−0.156277	+	0.156277i	0.624637	+	0.780915i	$0.285247\pi$
$152$		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	$-0.407023\pi$
$163$	7.35286			0.575920			0.287960	+	0.957642i	$0.407023\pi$
$164$		0			0
$165$	13.4275	−	0.472502i	1.04533	−	0.0367842i
$166$		0			0
$167$		−	8.16527i		−	0.631847i	−0.948785	−	0.315924i	$-0.897686\pi$
$167$		−	8.16527i		−	0.631847i	0.948785	−	0.315924i	$-0.102314\pi$
$168$		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	$-0.774542\pi$
$179$	−20.3221			−1.51894			−0.759471	+	0.650541i	$0.774542\pi$
$180$		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	$-0.328531\pi$
$191$	14.1798			1.02601			0.513007	+	0.858384i	$0.328531\pi$
$192$		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	$-0.338922\pi$
$199$	13.6756			0.969436			0.484718	+	0.874671i	$0.338922\pi$
$200$		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	$-0.444150\pi$
$211$	5.07122			0.349117			0.174558	+	0.984647i	$0.444150\pi$
$212$		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	$0.131232\pi$
$223$			11.9673i			0.801392i	−0.916211	+	0.400696i	$0.868768\pi$
$224$		0			0
$225$	2.04785	+	29.0617i	0.136523	+	1.93745i
$226$		0			0
$227$	22.4365			1.48916			0.744581	−	0.667532i	$-0.232649\pi$
$227$	22.4365			1.48916			0.744581	+	0.667532i	$0.232649\pi$
$228$		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	−0.880450	−	0.474140i	$-0.842759\pi$
$239$	−6.28140	+	6.28140i	−0.406310	+	0.406310i	0.474140	+	0.880450i	$0.342759\pi$
$240$		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	$-0.930004\pi$
$251$		−	6.91172i		−	0.436264i	0.975919	−	0.218132i	$-0.0699963\pi$
$252$		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	0.743187	−	0.669084i	$-0.233313\pi$
$263$	1.20176	+	1.20176i	0.0741035	+	0.0741035i	−0.669084	+	0.743187i	$0.733313\pi$
$264$		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	−0.468570	−	0.883426i	$-0.655231\pi$
$271$	6.82939	−	6.82939i	0.414856	−	0.414856i	0.883426	+	0.468570i	$0.155231\pi$
$272$		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	$0.541363\pi$
$283$	−18.8607	+	18.8607i	−1.12115	+	1.12115i	−0.991569	+	0.129582i	$0.958637\pi$
$284$		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	$-0.843915\pi$
$307$		−	16.5030i		−	0.941878i	0.882166	−	0.470939i	$-0.156085\pi$
$308$		0			0
$309$	−18.3280			−1.04264
$310$		0			0
$311$			1.19135i			0.0675552i	0.999429	+	0.0337776i	$0.0107538\pi$
$311$			1.19135i			0.0675552i	−0.999429	+	0.0337776i	$0.989246\pi$
$312$		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	0.292712	−	0.956201i	$-0.405442\pi$
$331$	−12.0711	−	12.0711i	−0.663489	−	0.663489i	−0.956201	+	0.292712i	$0.905442\pi$
$332$		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	$0.598895\pi$
$347$	−23.4309	+	23.4309i	−1.25784	+	1.25784i	−0.952124	+	0.305712i	$0.901105\pi$
$348$		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	0.763596	−	0.645694i	$-0.223432\pi$
$359$	2.23393	+	2.23393i	0.117902	+	0.117902i	−0.645694	+	0.763596i	$0.723432\pi$
$360$		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	−0.0996806	−	0.995019i	$-0.531782\pi$
$367$	17.1522	−	17.1522i	0.895339	−	0.895339i	0.995019	+	0.0996806i	$0.0317821\pi$
$368$		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	−0.345421	−	0.938448i	$-0.612264\pi$
$379$	11.5450	−	11.5450i	0.593026	−	0.593026i	0.938448	+	0.345421i	$0.112264\pi$
$380$		0			0
$381$		−	54.6163i		−	2.79808i
$382$		0			0
$383$		−	11.5813i		−	0.591775i	−0.955223	−	0.295888i	$-0.904385\pi$
$383$		−	11.5813i		−	0.591775i	0.955223	−	0.295888i	$-0.0956154\pi$
$384$		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	$-0.843914\pi$
$419$		−	19.2798i		−	0.941882i	0.882165	−	0.470941i	$-0.156086\pi$
$420$		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	0.951640	−	0.307216i	$-0.0993974\pi$
$431$	13.3786	+	13.3786i	0.644424	+	0.644424i	−0.307216	+	0.951640i	$0.599397\pi$
$432$		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	$-0.590291\pi$
$439$	−11.7278			−0.559737			−0.279869	+	0.960038i	$0.590291\pi$
$440$		0			0
$441$			38.5101i			1.83382i
$442$		0			0
$443$	20.8920	+	20.8920i	0.992608	+	0.992608i	0.999973	−	0.00736499i	$-0.00234437\pi$
$443$	20.8920	+	20.8920i	0.992608	+	0.992608i	−0.00736499	+	0.999973i	$0.502344\pi$
$444$		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	$-0.591205\pi$
$463$	−12.1627			−0.565251			−0.282625	+	0.959230i	$0.591205\pi$
$464$		0			0
$465$	−1.34034	−	38.0898i	−0.0621570	−	1.76637i
$466$		0			0
$467$	−8.81665	−	8.81665i	−0.407986	−	0.407986i	0.473050	−	0.881036i	$-0.343153\pi$
$467$	−8.81665	−	8.81665i	−0.407986	−	0.407986i	−0.881036	+	0.473050i	$0.843153\pi$
$468$		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	0.914417	−	0.404773i	$-0.132650\pi$
$479$	11.1541	+	11.1541i	0.509643	+	0.509643i	−0.404773	+	0.914417i	$0.632650\pi$
$480$		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	$-0.308721\pi$
$487$	24.9546			1.13080			0.565401	+	0.824816i	$0.308721\pi$
$488$		0			0
$489$	−15.4469	−	15.4469i	−0.698534	−	0.698534i
$490$		0			0
$491$			14.9353i			0.674020i	0.941501	+	0.337010i	$0.109416\pi$
$491$			14.9353i			0.674020i	−0.941501	+	0.337010i	$0.890584\pi$
$492$		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	−0.685330	−	0.728232i	$-0.740342\pi$
$499$	0.958355	−	0.958355i	0.0429019	−	0.0429019i	0.728232	+	0.685330i	$0.240342\pi$
$500$		0			0
$501$	−17.1536	+	17.1536i	−0.766368	+	0.766368i
$502$		0			0
$503$	−1.59172	−	1.59172i	−0.0709714	−	0.0709714i	0.670730	−	0.741701i	$-0.265981\pi$
$503$	−1.59172	−	1.59172i	−0.0709714	−	0.0709714i	−0.741701	+	0.670730i	$0.765981\pi$
$504$		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	0.925963	−	0.377615i	$-0.123256\pi$
$523$	12.5403	+	12.5403i	0.548347	+	0.548347i	−0.377615	+	0.925963i	$0.623256\pi$
$524$		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	−0.687656	−	0.726037i	$-0.741360\pi$
$547$	0.897666	−	0.897666i	0.0383814	−	0.0383814i	0.726037	+	0.687656i	$0.241360\pi$
$548$		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	−0.590551	−	0.807000i	$-0.701090\pi$
$563$	5.13582	−	5.13582i	0.216449	−	0.216449i	0.807000	+	0.590551i	$0.201090\pi$
$564$		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	$-0.890080\pi$
$571$		−	16.1774i		−	0.677003i	0.940966	−	0.338502i	$-0.109920\pi$
$572$		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	$-0.716405\pi$
$587$	−30.4634			−1.25736			−0.628680	+	0.777664i	$0.716405\pi$
$588$		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	$0.342402\pi$
$599$			43.0711i			1.75984i	−0.475126	+	0.879918i	$0.657598\pi$
$600$		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	−0.999998	−	0.00213629i	$-0.999320\pi$
$607$	−24.5847	+	24.5847i	−0.997861	+	0.997861i	0.00213629	+	0.999998i	$0.499320\pi$
$608$		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	0.945059	−	0.326899i	$-0.106004\pi$
$619$	15.3796	+	15.3796i	0.618160	+	0.618160i	−0.326899	+	0.945059i	$0.606004\pi$
$620$		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	−0.294466	−	0.955662i	$-0.595142\pi$
$631$	16.6091	−	16.6091i	0.661197	−	0.661197i	0.955662	+	0.294466i	$0.0951416\pi$
$632$		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	$0.223202\pi$
$643$			32.7184i			1.29029i	−0.764061	+	0.645144i	$0.776798\pi$
$644$		0			0
$645$	−52.1255	+	1.83425i	−2.05244	+	0.0722235i
$646$		0			0
$647$	19.6159	+	19.6159i	0.771180	+	0.771180i	0.978313	−	0.207133i	$-0.0664132\pi$
$647$	19.6159	+	19.6159i	0.771180	+	0.771180i	−0.207133	+	0.978313i	$0.566413\pi$
$648$		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	$-0.996278\pi$
$659$		−	0.600315i		−	0.0233850i	0.999932	−	0.0116925i	$-0.00372192\pi$
$660$		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	$-0.792276\pi$
$683$	−41.5283			−1.58904			−0.794518	+	0.607241i	$0.792276\pi$
$684$		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	0.987275	−	0.159024i	$-0.0508347\pi$
$691$	21.7721	+	21.7721i	0.828251	+	0.828251i	−0.159024	+	0.987275i	$0.550835\pi$
$692$		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	$-0.550784\pi$
$719$	−8.51967			−0.317730			−0.158865	+	0.987300i	$0.550784\pi$
$720$		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	0.996510	−	0.0834725i	$-0.0266011\pi$
$727$	24.6182	+	24.6182i	0.913038	+	0.913038i	−0.0834725	+	0.996510i	$0.526601\pi$
$728$		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	0.688805	−	0.724947i	$-0.258136\pi$
$739$	−0.982511	−	0.982511i	−0.0361422	−	0.0361422i	−0.724947	+	0.688805i	$0.758136\pi$
$740$		0			0
$741$	15.6596	−	43.8535i	0.575270	−	1.61100i
$742$		0			0
$743$		−	26.0191i		−	0.954548i	−0.878755	−	0.477274i	$-0.841625\pi$
$743$		−	26.0191i		−	0.954548i	0.878755	−	0.477274i	$-0.158375\pi$
$744$		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	$-0.853070\pi$
$751$		−	24.4105i		−	0.890751i	0.895344	−	0.445375i	$-0.146930\pi$
$752$		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	$0.131458\pi$
$787$			22.5183i			0.802692i	−0.915926	+	0.401346i	$0.868542\pi$
$788$		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	0.191036	−	0.981583i	$-0.438815\pi$
$811$	−22.5132	−	22.5132i	−0.790547	−	0.790547i	−0.981583	+	0.191036i	$0.938815\pi$
$812$		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	−0.661295	−	0.750126i	$-0.729993\pi$
$823$	2.54836	−	2.54836i	0.0888301	−	0.0888301i	0.750126	+	0.661295i	$0.229993\pi$
$824$		0			0
$825$	−29.9691	+	2.11179i	−1.04339	+	0.0735230i
$826$		0			0
$827$			7.98441i			0.277645i	0.990317	+	0.138823i	$0.0443318\pi$
$827$			7.98441i			0.277645i	−0.990317	+	0.138823i	$0.955668\pi$
$828$		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	0.331607	−	0.943418i	$-0.392409\pi$
$839$	−17.7214	−	17.7214i	−0.611810	−	0.611810i	−0.943418	+	0.331607i	$0.892409\pi$
$840$		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	$0.176959\pi$
$859$			30.9345i			1.05547i	−0.849409	+	0.527735i	$0.823041\pi$
$860$		0			0
$861$	−6.94411			−0.236655
$862$		0			0
$863$		−	4.54648i		−	0.154764i	−0.997002	−	0.0773820i	$-0.975344\pi$
$863$		−	4.54648i		−	0.154764i	0.997002	−	0.0773820i	$-0.0246561\pi$
$864$		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	−0.542232	−	0.840229i	$-0.682421\pi$
$883$	8.85507	−	8.85507i	0.297997	−	0.297997i	0.840229	+	0.542232i	$0.182421\pi$
$884$		0			0
$885$	2.53196	+	71.9530i	0.0851109	+	2.41867i
$886$		0			0
$887$	−8.82709	+	8.82709i	−0.296385	+	0.296385i	−0.839596	−	0.543211i	$-0.817208\pi$
$887$	−8.82709	+	8.82709i	−0.296385	+	0.296385i	0.543211	+	0.839596i	$0.317208\pi$
$888$		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	0.964250	−	0.264994i	$-0.0853699\pi$
$907$	21.0591	+	21.0591i	0.699256	+	0.699256i	−0.264994	+	0.964250i	$0.585370\pi$
$908$		0			0
$909$	−2.13306			−0.0707491
$910$		0			0
$911$	13.2480			0.438925			0.219463	−	0.975621i	$-0.429570\pi$
$911$	13.2480			0.438925			0.219463	+	0.975621i	$0.429570\pi$
$912$		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	$-0.697499\pi$
$919$		−	49.3292i		−	1.62722i	0.581412	−	0.813610i	$-0.302501\pi$
$920$		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	$0.208262\pi$
$947$			37.4564i			1.21717i	−0.793489	+	0.608585i	$0.791738\pi$
$948$		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	$-0.421504\pi$
$967$	15.1821			0.488223			0.244111	+	0.969747i	$0.421504\pi$
$968$		0			0
$969$	−53.6752	−	53.6752i	−1.72430	−	1.72430i
$970$		0			0
$971$	−45.4645			−1.45902			−0.729512	−	0.683968i	$-0.760253\pi$
$971$	−45.4645			−1.45902			−0.729512	+	0.683968i	$0.760253\pi$
$972$		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	$-0.663943\pi$
$983$	−30.8871			−0.985145			−0.492572	+	0.870271i	$0.663943\pi$
$984$		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	$-0.414791\pi$
$991$	16.6535			0.529014			0.264507	+	0.964384i	$0.414791\pi$
$992$		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	1040.2.bg.o.593.1		12
4.3	odd	2		520.2.w.e.73.6	yes	12
5.2	odd	4		1040.2.cd.o.177.1		12
13.5	odd	4		1040.2.cd.o.993.1		12
20.7	even	4		520.2.bh.e.177.6	yes	12
52.31	even	4		520.2.bh.e.473.6	yes	12
65.57	even	4	inner	1040.2.bg.o.577.1		12
260.187	odd	4		520.2.w.e.57.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.w.e.57.6	✓	12	260.187	odd	4
520.2.w.e.73.6	yes	12	4.3	odd	2
520.2.bh.e.177.6	yes	12	20.7	even	4
520.2.bh.e.473.6	yes	12	52.31	even	4
1040.2.bg.o.577.1		12	65.57	even	4	inner
1040.2.bg.o.593.1		12	1.1	even	1	trivial
1040.2.cd.o.177.1		12	5.2	odd	4
1040.2.cd.o.993.1		12	13.5	odd	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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.bg (of order \(4\), degree \(2\), not 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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