LMFDB - Embedded newform 279.3.v.a.244.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,3,Mod(46,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.46"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	279.v (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,3,0,-11,14,0,-1,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60219937565$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			244.5
Root			$2.39225 + 1.73807i$ of defining polynomial
Character	$\chi$	$=$	279.244
Dual form			279.3.v.a.271.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.913758 + 2.81226i) q^{2} +(-3.83778 + 2.78831i) q^{4} +5.21585 q^{5} +(-5.08304 + 3.69304i) q^{7} +(-1.77924 - 1.29269i) q^{8} +(4.76602 + 14.6683i) q^{10} +(3.31109 + 4.55732i) q^{11} +(6.36975 + 2.06966i) q^{13} +(-15.0305 - 10.9203i) q^{14} +(-3.85401 + 11.8614i) q^{16} +(-13.9543 + 19.2065i) q^{17} +(-1.04359 - 3.21183i) q^{19} +(-20.0173 + 14.5434i) q^{20} +(-9.79083 + 13.4759i) q^{22} +(5.24664 - 7.22139i) q^{23} +2.20508 q^{25} +19.8046i q^{26} +(9.21022 - 28.3461i) q^{28} +(18.6515 - 6.06023i) q^{29} +(16.9290 - 25.9694i) q^{31} -45.6760 q^{32} +(-66.7644 - 21.6931i) q^{34} +(-26.5124 + 19.2624i) q^{35} -7.37919i q^{37} +(8.07892 - 5.86968i) q^{38} +(-9.28025 - 6.74249i) q^{40} +(8.96363 + 27.5872i) q^{41} +(10.2018 - 3.31478i) q^{43} +(-25.4144 - 8.25765i) q^{44} +(25.1026 + 8.15632i) q^{46} +(22.3601 - 68.8174i) q^{47} +(-2.94313 + 9.05803i) q^{49} +(2.01491 + 6.20127i) q^{50} +(-30.2165 + 9.81794i) q^{52} +(-7.30390 + 10.0530i) q^{53} +(17.2701 + 23.7703i) q^{55} +13.8179 q^{56} +(34.0859 + 46.9152i) q^{58} +(24.3552 - 74.9577i) q^{59} -61.8106i q^{61} +(88.5016 + 23.8791i) q^{62} +(-26.3208 - 81.0072i) q^{64} +(33.2237 + 10.7950i) q^{65} +63.5225 q^{67} -112.619i q^{68} +(-78.3966 - 56.9585i) q^{70} +(-20.4625 - 14.8669i) q^{71} +(73.0291 + 100.516i) q^{73} +(20.7522 - 6.74279i) q^{74} +(12.9606 + 9.41645i) q^{76} +(-33.6608 - 10.9370i) q^{77} +(40.3121 - 55.4848i) q^{79} +(-20.1019 + 61.8673i) q^{80} +(-69.3918 + 50.4161i) q^{82} +(14.4260 - 4.68729i) q^{83} +(-72.7836 + 100.178i) q^{85} +(18.6440 + 25.6613i) q^{86} -12.3888i q^{88} +(91.9646 + 126.578i) q^{89} +(-40.0210 + 13.0036i) q^{91} +42.3433i q^{92} +213.964 q^{94} +(-5.44320 - 16.7524i) q^{95} +(-75.4306 + 54.8035i) q^{97} -28.1628 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - 11 q^{4} + 14 q^{5} - q^{7} + 19 q^{8} + 12 q^{10} + 10 q^{11} + 10 q^{13} - 103 q^{16} - 35 q^{17} + 47 q^{19} + 125 q^{20} + 150 q^{22} - 75 q^{23} + 82 q^{25} + 88 q^{28} - 5 q^{29}+ \cdots + 1000 q^{98}+O(q^{100}) $ 20 * q + 3 * q^2 - 11 * q^4 + 14 * q^5 - q^7 + 19 * q^8 + 12 * q^10 + 10 * q^11 + 10 * q^13 - 103 * q^16 - 35 * q^17 + 47 * q^19 + 125 * q^20 + 150 * q^22 - 75 * q^23 + 82 * q^25 + 88 * q^28 - 5 * q^29 + 73 * q^31 - 226 * q^32 - 265 * q^34 + 50 * q^35 - 8 * q^38 - 466 * q^40 + 98 * q^41 + 245 * q^43 - 380 * q^44 - 445 * q^46 + 187 * q^47 + 328 * q^49 + 44 * q^50 - 15 * q^52 - 25 * q^53 + 190 * q^55 - 64 * q^56 - 85 * q^58 + 173 * q^59 + 40 * q^62 - 469 * q^64 + 345 * q^65 + 76 * q^67 - 11 * q^70 + 467 * q^71 - 15 * q^73 - 45 * q^74 + 55 * q^76 + 320 * q^77 + 500 * q^79 - 1030 * q^80 + 178 * q^82 + 50 * q^83 + 20 * q^85 - 1125 * q^86 - 55 * q^89 + 300 * q^91 + 62 * q^94 + 559 * q^95 - 405 * q^97 + 1000 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	0.913758	+	2.81226i	0.456879	+	1.40613i	0.868915	+	0.494962i	$0.164818\pi$
$2$	0.913758	+	2.81226i	0.456879	+	1.40613i	−0.412036	+	0.911168i	$0.635182\pi$
$3$		0			0
$3$		0			0
$4$	−3.83778	+	2.78831i	−0.959444	+	0.697077i
$5$	5.21585			1.04317			0.521585	−	0.853199i	$-0.325341\pi$
$5$	5.21585			1.04317			0.521585	+	0.853199i	$0.325341\pi$
$6$		0			0
$7$	−5.08304	+	3.69304i	−0.726148	+	0.527577i	−0.888343	−	0.459181i	$-0.848143\pi$
$7$	−5.08304	+	3.69304i	−0.726148	+	0.527577i	0.162194	+	0.986759i	$0.448143\pi$
$8$	−1.77924	−	1.29269i	−0.222405	−	0.161587i
$9$		0			0
$10$	4.76602	+	14.6683i	0.476602	+	1.46683i
$11$	3.31109	+	4.55732i	0.301008	+	0.414302i	0.932551	−	0.361039i	$-0.117578\pi$
$11$	3.31109	+	4.55732i	0.301008	+	0.414302i	−0.631543	+	0.775341i	$0.717578\pi$
$12$		0			0
$13$	6.36975	+	2.06966i	0.489981	+	0.159204i	0.543579	−	0.839358i	$-0.317069\pi$
$13$	6.36975	+	2.06966i	0.489981	+	0.159204i	−0.0535979	+	0.998563i	$0.517069\pi$
$14$	−15.0305	−	10.9203i	−1.07360	−	0.780019i
$15$		0			0
$16$	−3.85401	+	11.8614i	−0.240875	+	0.741338i
$17$	−13.9543	+	19.2065i	−0.820842	+	1.12979i	0.168717	+	0.985664i	$0.446038\pi$
$17$	−13.9543	+	19.2065i	−0.820842	+	1.12979i	−0.989559	+	0.144127i	$0.953962\pi$
$18$		0			0
$19$	−1.04359	−	3.21183i	−0.0549257	−	0.169044i	0.919830	−	0.392316i	$-0.128326\pi$
$19$	−1.04359	−	3.21183i	−0.0549257	−	0.169044i	−0.974756	+	0.223272i	$0.928326\pi$
$20$	−20.0173	+	14.5434i	−1.00086	+	0.727170i
$21$		0			0
$22$	−9.79083	+	13.4759i	−0.445038	+	0.612542i
$23$	5.24664	−	7.22139i	0.228115	−	0.313973i	−0.679582	−	0.733599i	$-0.737839\pi$
$23$	5.24664	−	7.22139i	0.228115	−	0.313973i	0.907697	+	0.419626i	$0.137839\pi$
$24$		0			0
$25$	2.20508			0.0882034
$26$			19.8046i			0.761714i
$27$		0			0
$28$	9.21022	−	28.3461i	0.328936	−	1.01236i
$29$	18.6515	−	6.06023i	0.643154	−	0.208973i	0.0307608	−	0.999527i	$-0.490207\pi$
$29$	18.6515	−	6.06023i	0.643154	−	0.208973i	0.612393	+	0.790553i	$0.290207\pi$
$30$		0			0
$31$	16.9290	−	25.9694i	0.546098	−	0.837721i
$31$	16.9290	−	25.9694i	0.546098	−	0.837721i
$32$	−45.6760			−1.42738
$33$		0			0
$34$	−66.7644	−	21.6931i	−1.96366	−	0.638031i
$35$	−26.5124	+	19.2624i	−0.757496	+	0.550353i
$36$		0			0
$37$		−	7.37919i		−	0.199438i	−0.995016	−	0.0997188i	$-0.968206\pi$
$37$		−	7.37919i		−	0.199438i	0.995016	−	0.0997188i	$-0.0317943\pi$
$38$	8.07892	−	5.86968i	0.212603	−	0.154465i
$39$		0			0
$40$	−9.28025	−	6.74249i	−0.232006	−	0.168562i
$41$	8.96363	+	27.5872i	0.218625	+	0.672859i	0.998876	+	0.0473927i	$0.0150912\pi$
$41$	8.96363	+	27.5872i	0.218625	+	0.672859i	−0.780251	+	0.625466i	$0.784909\pi$
$42$		0			0
$43$	10.2018	−	3.31478i	0.237252	−	0.0770879i	−0.187978	−	0.982173i	$-0.560193\pi$
$43$	10.2018	−	3.31478i	0.237252	−	0.0770879i	0.425230	+	0.905085i	$0.360193\pi$
$44$	−25.4144	−	8.25765i	−0.577601	−	0.187674i
$45$		0			0
$46$	25.1026	+	8.15632i	0.545708	+	0.177311i
$47$	22.3601	−	68.8174i	0.475747	−	1.46420i	−0.369200	−	0.929350i	$-0.620368\pi$
$47$	22.3601	−	68.8174i	0.475747	−	1.46420i	0.844947	−	0.534850i	$-0.179632\pi$
$48$		0			0
$49$	−2.94313	+	9.05803i	−0.0600639	+	0.184858i
$50$	2.01491	+	6.20127i	0.0402983	+	0.124025i
$51$		0			0
$52$	−30.2165	+	9.81794i	−0.581087	+	0.188807i
$53$	−7.30390	+	10.0530i	−0.137809	+	0.189678i	−0.872344	−	0.488893i	$-0.837401\pi$
$53$	−7.30390	+	10.0530i	−0.137809	+	0.189678i	0.734534	+	0.678572i	$0.237401\pi$
$54$		0			0
$55$	17.2701	+	23.7703i	0.314002	+	0.432187i
$56$	13.8179			0.246748
$57$		0			0
$58$	34.0859	+	46.9152i	0.587687	+	0.808882i
$59$	24.3552	−	74.9577i	0.412801	−	1.27047i	−0.501403	−	0.865214i	$-0.667183\pi$
$59$	24.3552	−	74.9577i	0.412801	−	1.27047i	0.914203	−	0.405255i	$-0.132817\pi$
$60$		0			0
$61$		−	61.8106i		−	1.01329i	−0.862155	−	0.506644i	$-0.830886\pi$
$61$		−	61.8106i		−	1.01329i	0.862155	−	0.506644i	$-0.169114\pi$
$62$	88.5016	+	23.8791i	1.42745	+	0.385147i
$63$		0			0
$64$	−26.3208	−	81.0072i	−0.411263	−	1.26574i
$65$	33.2237	+	10.7950i	0.511133	+	0.166077i
$66$		0			0
$67$	63.5225			0.948097			0.474049	−	0.880499i	$-0.342792\pi$
$67$	63.5225			0.948097			0.474049	+	0.880499i	$0.342792\pi$
$68$		−	112.619i		−	1.65616i
$69$		0			0
$70$	−78.3966	−	56.9585i	−1.11995	−	0.813692i
$71$	−20.4625	−	14.8669i	−0.288204	−	0.209392i	0.434284	−	0.900776i	$-0.357001\pi$
$71$	−20.4625	−	14.8669i	−0.288204	−	0.209392i	−0.722488	+	0.691384i	$0.757001\pi$
$72$		0			0
$73$	73.0291	+	100.516i	1.00040	+	1.37693i	0.925081	+	0.379771i	$0.123997\pi$
$73$	73.0291	+	100.516i	1.00040	+	1.37693i	0.0753179	+	0.997160i	$0.476003\pi$
$74$	20.7522	−	6.74279i	0.280435	−	0.0911188i
$75$		0			0
$76$	12.9606	+	9.41645i	0.170535	+	0.123901i
$77$	−33.6608	−	10.9370i	−0.437153	−	0.142040i
$78$		0			0
$79$	40.3121	−	55.4848i	0.510280	−	0.702340i	−0.473687	−	0.880693i	$-0.657077\pi$
$79$	40.3121	−	55.4848i	0.510280	−	0.702340i	0.983966	+	0.178354i	$0.0570771\pi$
$80$	−20.1019	+	61.8673i	−0.251274	+	0.773342i
$81$		0			0
$82$	−69.3918	+	50.4161i	−0.846241	+	0.614830i
$83$	14.4260	−	4.68729i	0.173807	−	0.0564734i	−0.220821	−	0.975314i	$-0.570874\pi$
$83$	14.4260	−	4.68729i	0.173807	−	0.0564734i	0.394628	+	0.918841i	$0.370874\pi$
$84$		0			0
$85$	−72.7836	+	100.178i	−0.856277	+	1.17856i
$86$	18.6440	+	25.6613i	0.216791	+	0.298387i
$87$		0			0
$88$		−	12.3888i		−	0.140782i
$89$	91.9646	+	126.578i	1.03331	+	1.42223i	0.902433	+	0.430831i	$0.141779\pi$
$89$	91.9646	+	126.578i	1.03331	+	1.42223i	0.130877	+	0.991399i	$0.458221\pi$
$90$		0			0
$91$	−40.0210	+	13.0036i	−0.439791	+	0.142897i
$92$			42.3433i			0.460253i
$93$		0			0
$94$	213.964			2.27621
$95$	−5.44320	−	16.7524i	−0.0572968	−	0.176342i
$96$		0			0
$97$	−75.4306	+	54.8035i	−0.777635	+	0.564985i	−0.904268	−	0.426965i	$-0.859583\pi$
$97$	−75.4306	+	54.8035i	−0.777635	+	0.564985i	0.126633	+	0.991950i	$0.459583\pi$
$98$	−28.1628			−0.287376
$99$		0			0
$100$	−8.46262	+	6.14845i	−0.0846262	+	0.0614845i
$101$	37.2606	+	27.0714i	0.368917	+	0.268034i	0.756762	−	0.653691i	$-0.226780\pi$
$101$	37.2606	+	27.0714i	0.368917	+	0.268034i	−0.387845	+	0.921725i	$0.626780\pi$
$102$		0			0
$103$	20.3131	+	62.5174i	0.197215	+	0.606965i	0.999944	+	0.0106204i	$0.00338064\pi$
$103$	20.3131	+	62.5174i	0.197215	+	0.606965i	−0.802729	+	0.596344i	$0.796619\pi$
$104$	−8.65788	−	11.9166i	−0.0832489	−	0.114582i
$105$		0			0
$106$	−34.9455	−	11.3545i	−0.329674	−	0.107118i
$107$	−73.7625	−	53.5916i	−0.689370	−	0.500856i	0.187083	−	0.982344i	$-0.440097\pi$
$107$	−73.7625	−	53.5916i	−0.689370	−	0.500856i	−0.876453	+	0.481488i	$0.840097\pi$
$108$		0			0
$109$	15.8725	−	48.8504i	0.145619	−	0.448169i	−0.851471	−	0.524402i	$-0.824289\pi$
$109$	15.8725	−	48.8504i	0.145619	−	0.448169i	0.997090	+	0.0762323i	$0.0242891\pi$
$110$	−51.0675	+	70.2884i	−0.464250	+	0.638985i
$111$		0			0
$112$	−24.2146	−	74.5250i	−0.216202	−	0.665402i
$113$	70.6470	−	51.3280i	0.625194	−	0.454230i	−0.229538	−	0.973300i	$-0.573721\pi$
$113$	70.6470	−	51.3280i	0.625194	−	0.454230i	0.854732	+	0.519069i	$0.173721\pi$
$114$		0			0
$115$	27.3657	−	37.6657i	0.237963	−	0.327527i
$116$	−54.6824	+	75.2638i	−0.471400	+	0.648826i
$117$		0			0
$118$	233.055			1.97504
$119$		−	149.161i		−	1.25345i
$120$		0			0
$121$	27.5852	−	84.8985i	0.227977	−	0.701640i
$122$	173.827	−	56.4800i	1.42482	−	0.462951i
$123$		0			0
$124$	7.44074	+	146.868i	0.0600060	+	1.18442i
$125$	−118.895			−0.951159
$126$		0			0
$127$	34.4876	+	11.2057i	0.271556	+	0.0882338i	0.441630	−	0.897198i	$-0.354401\pi$
$127$	34.4876	+	11.2057i	0.271556	+	0.0882338i	−0.170074	+	0.985431i	$0.554401\pi$
$128$	55.9515	−	40.6511i	0.437121	−	0.317587i
$129$		0			0
$130$			103.298i			0.794597i
$131$	147.918	−	107.469i	1.12915	−	0.820373i	0.143577	−	0.989639i	$-0.454140\pi$
$131$	147.918	−	107.469i	1.12915	−	0.820373i	0.985570	+	0.169266i	$0.0541396\pi$
$132$		0			0
$133$	17.1660	+	12.4719i	0.129068	+	0.0937733i
$134$	58.0442	+	178.642i	0.433166	+	1.33315i
$135$		0			0
$136$	49.6561	−	16.1343i	0.365119	−	0.118634i
$137$	−119.519	−	38.8342i	−0.872404	−	0.283461i	−0.161604	−	0.986856i	$-0.551667\pi$
$137$	−119.519	−	38.8342i	−0.872404	−	0.283461i	−0.710800	+	0.703394i	$0.751667\pi$
$138$		0			0
$139$	−236.072	−	76.7046i	−1.69836	−	0.551832i	−0.710034	−	0.704167i	$-0.751321\pi$
$139$	−236.072	−	76.7046i	−1.69836	−	0.551832i	−0.988329	+	0.152336i	$0.951321\pi$
$140$	48.0391	−	147.849i	0.343137	−	1.05607i
$141$		0			0
$142$	23.1117	−	71.1305i	0.162758	−	0.500919i
$143$	11.6587	+	35.8818i	0.0815295	+	0.250922i
$144$		0			0
$145$	97.2832	−	31.6092i	0.670919	−	0.217995i
$146$	−215.946	+	297.224i	−1.47908	+	2.03578i
$147$		0			0
$148$	20.5754	+	28.3197i	0.139023	+	0.191349i
$149$	196.177			1.31662			0.658310	−	0.752747i	$-0.271271\pi$
$149$	196.177			1.31662			0.658310	+	0.752747i	$0.271271\pi$
$150$		0			0
$151$	4.51948	+	6.22054i	0.0299304	+	0.0411956i	0.823720	−	0.566997i	$-0.191895\pi$
$151$	4.51948	+	6.22054i	0.0299304	+	0.0411956i	−0.793790	+	0.608193i	$0.791895\pi$
$152$	−2.29512	+	7.06366i	−0.0150995	+	0.0464715i
$153$		0			0
$154$		−	104.657i		−	0.679588i
$155$	88.2993	−	135.452i	0.569673	−	0.873886i
$156$		0			0
$157$	−85.2127	−	262.258i	−0.542756	−	1.67043i	−0.726266	−	0.687414i	$-0.758746\pi$
$157$	−85.2127	−	262.258i	−0.542756	−	1.67043i	0.183509	−	0.983018i	$-0.441254\pi$
$158$	192.873	+	62.6683i	1.22072	+	0.396635i
$159$		0			0
$160$	−238.239			−1.48900
$161$			56.0826i			0.348339i
$162$		0			0
$163$	−117.611	−	85.4491i	−0.721538	−	0.524228i	0.165338	−	0.986237i	$-0.447129\pi$
$163$	−117.611	−	85.4491i	−0.721538	−	0.524228i	−0.886875	+	0.462009i	$0.847129\pi$
$164$	−111.322	−	80.8802i	−0.678793	−	0.493172i
$165$		0			0
$166$	26.3638	+	36.2866i	0.158818	+	0.218594i
$167$	−271.725	+	88.2887i	−1.62709	+	0.528675i	−0.973601	−	0.228257i	$-0.926697\pi$
$167$	−271.725	+	88.2887i	−1.62709	+	0.528675i	−0.653494	+	0.756932i	$0.726697\pi$
$168$		0			0
$169$	−100.434	−	72.9693i	−0.594282	−	0.431771i
$170$	−348.233	−	113.148i	−2.04843	−	0.665575i
$171$		0			0
$172$	−29.9098	+	41.1673i	−0.173894	+	0.239345i
$173$	44.4941	−	136.939i	0.257191	−	0.791553i	−0.736199	−	0.676765i	$-0.763381\pi$
$173$	44.4941	−	136.939i	0.257191	−	0.791553i	0.993390	−	0.114788i	$-0.0366188\pi$
$174$		0			0
$175$	−11.2085	+	8.14347i	−0.0640487	+	0.0465341i
$176$	−66.8172	+	21.7102i	−0.379643	+	0.123354i
$177$		0			0
$178$	−271.938	+	374.290i	−1.52774	+	2.10275i
$179$	−120.316	−	165.601i	−0.672157	−	0.925144i	0.327650	−	0.944799i	$-0.393743\pi$
$179$	−120.316	−	165.601i	−0.672157	−	0.925144i	−0.999807	+	0.0196549i	$0.993743\pi$
$180$		0			0
$181$		−	124.758i		−	0.689272i	−0.938736	−	0.344636i	$-0.888002\pi$
$181$		−	124.758i		−	0.689272i	0.938736	−	0.344636i	$-0.111998\pi$
$182$	−73.1391	−	100.667i	−0.401863	−	0.553117i
$183$		0			0
$184$	−18.6701	+	6.06627i	−0.101468	+	0.0329689i
$185$		−	38.4887i		−	0.208047i
$186$		0			0
$187$	−133.734			−0.715155
$188$	106.071	+	326.453i	0.564207	+	1.73645i
$189$		0			0
$190$	42.1384	−	30.6154i	0.221781	−	0.161133i
$191$	−95.7014			−0.501055			−0.250527	−	0.968110i	$-0.580604\pi$
$191$	−95.7014			−0.501055			−0.250527	+	0.968110i	$0.580604\pi$
$192$		0			0
$193$	100.339	−	72.9004i	0.519890	−	0.377722i	−0.296672	−	0.954979i	$-0.595877\pi$
$193$	100.339	−	72.9004i	0.519890	−	0.377722i	0.816563	+	0.577257i	$0.195877\pi$
$194$	−223.047	−	162.053i	−1.14973	−	0.835326i
$195$		0			0
$196$	−13.9615	−	42.9690i	−0.0712321	−	0.219230i
$197$	90.5460	+	124.626i	0.459624	+	0.632618i	0.974431	−	0.224688i	$-0.0721363\pi$
$197$	90.5460	+	124.626i	0.459624	+	0.632618i	−0.514807	+	0.857306i	$0.672136\pi$
$198$		0			0
$199$	262.101	+	85.1617i	1.31709	+	0.427948i	0.881494	−	0.472194i	$-0.156538\pi$
$199$	262.101	+	85.1617i	1.31709	+	0.427948i	0.435595	+	0.900143i	$0.356538\pi$
$200$	−3.92337	−	2.85050i	−0.0196169	−	0.0142525i
$201$		0			0
$202$	−42.0846	+	129.523i	−0.208340	+	0.641204i
$203$	−72.4254	+	99.6850i	−0.356775	+	0.491059i
$204$		0			0
$205$	46.7529	+	143.891i	0.228063	+	0.701906i
$206$	−157.254	+	114.251i	−0.763367	+	0.554619i
$207$		0			0
$208$	−49.0981	+	67.5778i	−0.236049	+	0.324893i
$209$	11.1819	−	15.3906i	0.0535021	−	0.0736394i
$210$		0			0
$211$	10.5159			0.0498383			0.0249191	−	0.999689i	$-0.492067\pi$
$211$	10.5159			0.0498383			0.0249191	+	0.999689i	$0.492067\pi$
$212$		−	58.9465i		−	0.278049i
$213$		0			0
$214$	83.3124	−	256.409i	0.389310	−	1.19817i
$215$	53.2113	−	17.2894i	0.247494	−	0.0804158i
$216$		0			0
$217$	9.85508	+	194.523i	0.0454151	+	0.896419i
$218$	151.884			0.696714
$219$		0			0
$220$	−132.558	−	43.0706i	−0.602536	−	0.195776i
$221$	−128.636	+	93.4597i	−0.582065	+	0.422895i
$222$		0			0
$223$			266.065i			1.19312i	0.802570	+	0.596558i	$0.203466\pi$
$223$			266.065i			1.19312i	−0.802570	+	0.596558i	$0.796534\pi$
$224$	232.173	−	168.684i	1.03649	−	0.753051i
$225$		0			0
$226$	208.902	+	151.776i	0.924345	+	0.671576i
$227$	3.84060	+	11.8202i	0.0169189	+	0.0520712i	0.959160	−	0.282866i	$-0.0912850\pi$
$227$	3.84060	+	11.8202i	0.0169189	+	0.0520712i	−0.942241	+	0.334937i	$0.891285\pi$
$228$		0			0
$229$	−261.591	+	84.9962i	−1.14232	+	0.371163i	−0.818246	−	0.574869i	$-0.805053\pi$
$229$	−261.591	+	84.9962i	−1.14232	+	0.371163i	−0.324075	+	0.946031i	$0.605053\pi$
$230$	130.931	+	42.5421i	0.569266	+	0.184966i
$231$		0			0
$232$	−41.0194	−	13.3280i	−0.176808	−	0.0574484i
$233$	−61.3553	+	188.832i	−0.263327	+	0.810438i	0.728747	+	0.684783i	$0.240103\pi$
$233$	−61.3553	+	188.832i	−0.263327	+	0.810438i	−0.992074	+	0.125655i	$0.959897\pi$
$234$		0			0
$235$	116.627	−	358.941i	0.496285	−	1.52741i
$236$	115.535	+	355.581i	0.489556	+	1.50670i
$237$		0			0
$238$	419.479	−	136.297i	1.76252	−	0.572677i
$239$	−129.225	+	177.863i	−0.540689	+	0.744195i	−0.988712	−	0.149827i	$-0.952128\pi$
$239$	−129.225	+	177.863i	−0.540689	+	0.744195i	0.448023	+	0.894022i	$0.352128\pi$
$240$		0			0
$241$	79.4670	+	109.377i	0.329739	+	0.453846i	0.941409	−	0.337266i	$-0.109502\pi$
$241$	79.4670	+	109.377i	0.329739	+	0.453846i	−0.611671	+	0.791112i	$0.709502\pi$
$242$	263.963			1.09075
$243$		0			0
$244$	172.347	+	237.215i	0.706340	+	0.972194i
$245$	−15.3509	+	47.2453i	−0.0626569	+	0.192838i
$246$		0			0
$247$		−	22.6185i		−	0.0915727i
$248$	−63.6912	+	24.3217i	−0.256819	+	0.0980713i
$249$		0			0
$250$	−108.641	−	334.363i	−0.434565	−	1.33745i
$251$	78.1627	+	25.3966i	0.311405	+	0.101182i	0.460550	−	0.887634i	$-0.347652\pi$
$251$	78.1627	+	25.3966i	0.311405	+	0.101182i	−0.149145	+	0.988815i	$0.547652\pi$
$252$		0			0
$253$	50.2823			0.198744
$254$			107.227i			0.422155i
$255$		0			0
$256$	−110.188	−	80.0560i	−0.430421	−	0.312719i
$257$	82.5128	+	59.9490i	0.321061	+	0.233265i	0.736628	−	0.676298i	$-0.236417\pi$
$257$	82.5128	+	59.9490i	0.321061	+	0.233265i	−0.415567	+	0.909563i	$0.636417\pi$
$258$		0			0
$259$	27.2517	+	37.5087i	0.105219	+	0.144821i
$260$	−157.605	+	51.2089i	−0.606172	+	0.196957i
$261$		0			0
$262$	437.392	+	317.784i	1.66943	+	1.21292i
$263$	166.458	+	54.0855i	0.632921	+	0.205648i	0.607868	−	0.794038i	$-0.292025\pi$
$263$	166.458	+	54.0855i	0.632921	+	0.205648i	0.0250522	+	0.999686i	$0.492025\pi$
$264$		0			0
$265$	−38.0960	+	52.4347i	−0.143759	+	0.197867i
$266$	−19.3885	+	59.6716i	−0.0728890	+	0.224329i
$267$		0			0
$268$	−243.785	+	177.120i	−0.909646	+	0.660897i
$269$	−184.972	+	60.1011i	−0.687629	+	0.223424i	−0.631932	−	0.775024i	$-0.717738\pi$
$269$	−184.972	+	60.1011i	−0.687629	+	0.223424i	−0.0556964	+	0.998448i	$0.517738\pi$
$270$		0			0
$271$	−54.2554	+	74.6762i	−0.200204	+	0.275558i	−0.897301	−	0.441420i	$-0.854475\pi$
$271$	−54.2554	+	74.6762i	−0.200204	+	0.275558i	0.697096	+	0.716978i	$0.254475\pi$
$272$	−174.036	−	239.540i	−0.639837	−	0.880661i
$273$		0			0
$274$		−	371.605i		−	1.35622i
$275$	7.30123	+	10.0493i	0.0265499	+	0.0365428i
$276$		0			0
$277$	−14.0177	+	4.55461i	−0.0506053	+	0.0164426i	−0.334210	−	0.942499i	$-0.608470\pi$
$277$	−14.0177	+	4.55461i	−0.0506053	+	0.0164426i	0.283605	+	0.958941i	$0.408470\pi$
$278$		−	733.986i		−	2.64024i
$279$		0			0
$280$	72.0722			0.257401
$281$	−31.0701	−	95.6241i	−0.110570	−	0.340299i	0.880427	−	0.474181i	$-0.157256\pi$
$281$	−31.0701	−	95.6241i	−0.110570	−	0.340299i	−0.990997	+	0.133882i	$0.957256\pi$
$282$		0			0
$283$	−150.671	+	109.469i	−0.532408	+	0.386817i	−0.821258	−	0.570558i	$-0.806727\pi$
$283$	−150.671	+	109.469i	−0.532408	+	0.386817i	0.288850	+	0.957374i	$0.406727\pi$
$284$	119.984			0.422478
$285$		0			0
$286$	−90.2557	+	65.5746i	−0.315579	+	0.229282i
$287$	−147.443	−	107.124i	−0.513739	−	0.373254i
$288$		0			0
$289$	−84.8595	−	261.171i	−0.293631	−	0.903704i
$290$	177.787	+	244.702i	0.613058	+	0.843801i
$291$		0			0
$292$	−560.539	−	182.130i	−1.91965	−	0.623733i
$293$	259.380	+	188.451i	0.885257	+	0.643177i	0.934637	−	0.355603i	$-0.115725\pi$
$293$	259.380	+	188.451i	0.885257	+	0.643177i	−0.0493799	+	0.998780i	$0.515725\pi$
$294$		0			0
$295$	127.033	−	390.968i	0.430621	−	1.32532i
$296$	−9.53903	+	13.1293i	−0.0322265	+	0.0443559i
$297$		0			0
$298$	179.258	+	551.699i	0.601537	+	1.85134i
$299$	48.3656	−	35.1397i	0.161758	−	0.117524i
$300$		0			0
$301$	−39.6147	+	54.5250i	−0.131610	+	0.181146i
$302$	−13.3640	+	18.3940i	−0.0442518	+	0.0609074i
$303$		0			0
$304$	42.1189			0.138549
$305$		−	322.395i		−	1.05703i
$306$		0			0
$307$	−153.090	+	471.163i	−0.498665	+	1.53473i	0.312502	+	0.949917i	$0.398833\pi$
$307$	−153.090	+	471.163i	−0.498665	+	1.53473i	−0.811167	+	0.584815i	$0.801167\pi$
$308$	159.678	−	51.8826i	0.518436	−	0.168450i
$309$		0			0
$310$	461.611	+	124.550i	1.48907	+	0.401773i
$311$	−321.930			−1.03514			−0.517572	−	0.855640i	$-0.673164\pi$
$311$	−321.930			−1.03514			−0.517572	+	0.855640i	$0.673164\pi$
$312$		0			0
$313$	−78.3120	−	25.4451i	−0.250198	−	0.0812943i	0.181233	−	0.983440i	$-0.441991\pi$
$313$	−78.3120	−	25.4451i	−0.250198	−	0.0812943i	−0.431431	+	0.902146i	$0.641991\pi$
$314$	659.673	−	479.280i	2.10087	−	1.52637i
$315$		0			0
$316$			325.341i			1.02956i
$317$	−433.663	+	315.075i	−1.36802	+	0.993927i	−0.370135	+	0.928978i	$0.620688\pi$
$317$	−433.663	+	315.075i	−1.36802	+	0.993927i	−0.997889	+	0.0649488i	$0.979312\pi$
$318$		0			0
$319$	89.3751	+	64.9348i	0.280173	+	0.203557i
$320$	−137.285	−	422.521i	−0.429017	−	1.32038i
$321$		0			0
$322$	−157.719	+	51.2460i	−0.489810	+	0.159149i
$323$	76.2505	+	24.7753i	0.236070	+	0.0767037i
$324$		0			0
$325$	14.0458	+	4.56377i	0.0432180	+	0.0140424i
$326$	132.837	−	408.831i	0.407476	−	1.25408i
$327$		0			0
$328$	19.7134	−	60.6715i	0.0601017	−	0.184974i
$329$	140.488	+	432.378i	0.427016	+	1.31422i
$330$		0			0
$331$	13.6662	−	4.44042i	0.0412876	−	0.0134152i	−0.288300	−	0.957540i	$-0.593090\pi$
$331$	13.6662	−	4.44042i	0.0412876	−	0.0134152i	0.329588	+	0.944125i	$0.393090\pi$
$332$	−42.2942	+	58.2129i	−0.127392	+	0.175340i
$333$		0			0
$334$	−496.582	−	683.486i	−1.48677	−	2.04636i
$335$	331.324			0.989027
$336$		0			0
$337$	377.588	+	519.705i	1.12044	+	1.54215i	0.805067	+	0.593184i	$0.202129\pi$
$337$	377.588	+	519.705i	1.12044	+	1.54215i	0.315372	+	0.948968i	$0.397871\pi$
$338$	113.436	−	349.122i	0.335611	−	1.03290i
$339$		0			0
$340$		−	587.404i		−	1.72766i
$341$	174.404	−	8.83581i	0.511449	−	0.0259115i
$342$		0			0
$343$	−113.627	−	349.709i	−0.331275	−	1.01956i
$344$	−22.4365	−	7.29007i	−0.0652224	−	0.0211921i
$345$		0			0
$346$	425.764			1.23053
$347$			145.682i			0.419832i	0.977719	+	0.209916i	$0.0673191\pi$
$347$			145.682i			0.419832i	−0.977719	+	0.209916i	$0.932681\pi$
$348$		0			0
$349$	−376.007	−	273.185i	−1.07738	−	0.782765i	−0.100158	−	0.994972i	$-0.531935\pi$
$349$	−376.007	−	273.185i	−1.07738	−	0.782765i	−0.977225	+	0.212207i	$0.931935\pi$
$350$	−33.1434	−	24.0801i	−0.0946955	−	0.0688003i
$351$		0			0
$352$	−151.237	−	208.160i	−0.429652	−	0.591365i
$353$	−265.392	+	86.2310i	−0.751818	+	0.244281i	−0.659763	−	0.751473i	$-0.729344\pi$
$353$	−265.392	+	86.2310i	−0.751818	+	0.244281i	−0.0920548	+	0.995754i	$0.529344\pi$
$354$		0			0
$355$	−106.729	−	77.5433i	−0.300646	−	0.218432i
$356$	−705.879	−	229.354i	−1.98281	−	0.644253i
$357$		0			0
$358$	355.773	−	489.679i	0.993778	−	1.36782i
$359$	161.666	−	497.557i	0.450323	−	1.38595i	−0.426216	−	0.904621i	$-0.640154\pi$
$359$	161.666	−	497.557i	0.450323	−	1.38595i	0.876539	−	0.481330i	$-0.159846\pi$
$360$		0			0
$361$	282.828	−	205.487i	0.783458	−	0.569216i
$362$	350.852	−	113.999i	0.969205	−	0.314914i
$363$		0			0
$364$	117.334	−	161.496i	0.322345	−	0.443670i
$365$	380.909	+	524.276i	1.04359	+	1.43637i
$366$		0			0
$367$			330.694i			0.901074i	0.892758	+	0.450537i	$0.148767\pi$
$367$			330.694i			0.901074i	−0.892758	+	0.450537i	$0.851233\pi$
$368$	65.4352	+	90.0639i	0.177813	+	0.244739i
$369$		0			0
$370$	108.240	−	35.1694i	0.292541	−	0.0950524i
$371$		−	78.0731i		−	0.210440i
$372$		0			0
$373$	−65.8984			−0.176671			−0.0883356	−	0.996091i	$-0.528155\pi$
$373$	−65.8984			−0.176671			−0.0883356	+	0.996091i	$0.528155\pi$
$374$	−122.201	−	376.095i	−0.326739	−	1.00560i
$375$		0			0
$376$	−128.744	+	93.5378i	−0.342404	+	0.248771i
$377$	131.348			0.348403
$378$		0			0
$379$	402.911	−	292.732i	1.06309	−	0.772381i	0.0884330	−	0.996082i	$-0.471814\pi$
$379$	402.911	−	292.732i	1.06309	−	0.772381i	0.974658	+	0.223702i	$0.0718141\pi$
$380$	67.6007	+	49.1148i	0.177897	+	0.129249i
$381$		0			0
$382$	−87.4480	−	269.137i	−0.228921	−	0.704548i
$383$	154.922	+	213.231i	0.404495	+	0.556739i	0.961865	−	0.273525i	$-0.0881895\pi$
$383$	154.922	+	213.231i	0.404495	+	0.556739i	−0.557370	+	0.830264i	$0.688190\pi$
$384$		0			0
$385$	−175.569	−	57.0460i	−0.456025	−	0.148171i
$386$	296.700	+	215.565i	0.768654	+	0.558460i
$387$		0			0
$388$	136.677	−	420.647i	0.352259	−	1.08414i
$389$	416.464	−	573.214i	1.07060	−	1.47356i	0.201137	−	0.979563i	$-0.435536\pi$
$389$	416.464	−	573.214i	1.07060	−	1.47356i	0.869465	−	0.493995i	$-0.164464\pi$
$390$		0			0
$391$	65.4840	+	201.539i	0.167478	+	0.515445i
$392$	16.9458	−	12.3118i	0.0432291	−	0.0314078i
$393$		0			0
$394$	−267.743	+	368.516i	−0.679550	+	0.935321i
$395$	210.262	−	289.401i	0.532308	−	0.732660i
$396$		0			0
$397$	439.070			1.10597			0.552985	−	0.833191i	$-0.313489\pi$
$397$	439.070			1.10597			0.552985	+	0.833191i	$0.313489\pi$
$398$			814.912i			2.04752i
$399$		0			0
$400$	−8.49841	+	26.1554i	−0.0212460	+	0.0653885i
$401$	−380.052	+	123.486i	−0.947762	+	0.307946i	−0.741806	−	0.670615i	$-0.766030\pi$
$401$	−380.052	+	123.486i	−0.947762	+	0.307946i	−0.205956	+	0.978561i	$0.566030\pi$
$402$		0			0
$403$	161.581	−	130.381i	0.400946	−	0.323526i
$404$	−218.481			−0.540795
$405$		0			0
$406$	−346.519	−	112.591i	−0.853496	−	0.277318i
$407$	33.6293	−	24.4331i	0.0826274	−	0.0600323i
$408$		0			0
$409$			225.799i			0.552075i	0.961147	+	0.276037i	$0.0890214\pi$
$409$			225.799i			0.552075i	−0.961147	+	0.276037i	$0.910979\pi$
$410$	−361.937	+	262.963i	−0.882773	+	0.641372i
$411$		0			0
$412$	−252.275	−	183.288i	−0.612317	−	0.444875i
$413$	153.023	+	470.958i	0.370517	+	1.14033i
$414$		0			0
$415$	75.2439	−	24.4482i	0.181311	−	0.0589114i
$416$	−290.945	−	94.5338i	−0.699387	−	0.227245i
$417$		0			0
$418$	53.5000	+	17.3832i	0.127991	+	0.0415866i
$419$	−136.617	+	420.465i	−0.326056	+	1.00350i	0.644906	+	0.764262i	$0.276896\pi$
$419$	−136.617	+	420.465i	−0.326056	+	1.00350i	−0.970962	+	0.239234i	$0.923104\pi$
$420$		0			0
$421$	−134.613	+	414.296i	−0.319745	+	0.984075i	0.654012	+	0.756485i	$0.273085\pi$
$421$	−134.613	+	414.296i	−0.319745	+	0.984075i	−0.973757	+	0.227590i	$0.926915\pi$
$422$	9.60896	+	29.5733i	0.0227701	+	0.0700790i
$423$		0			0
$424$	25.9908	−	8.44491i	0.0612990	−	0.0199172i
$425$	−30.7704	+	42.3519i	−0.0724010	+	0.0996514i
$426$		0			0
$427$	228.269	+	314.186i	0.534588	+	0.735798i
$428$	432.514			1.01055
$429$		0			0
$430$	97.2445	+	133.846i	0.226150	+	0.311269i
$431$	79.0915	−	243.419i	0.183507	−	0.564776i	−0.816413	−	0.577469i	$-0.804040\pi$
$431$	79.0915	−	243.419i	0.183507	−	0.564776i	0.999919	+	0.0126929i	$0.00404037\pi$
$432$		0			0
$433$			135.443i			0.312801i	0.987694	+	0.156400i	$0.0499890\pi$
$433$			135.443i			0.312801i	−0.987694	+	0.156400i	$0.950011\pi$
$434$	−538.043	+	205.462i	−1.23973	+	0.473414i
$435$		0			0
$436$	75.2951	+	231.734i	0.172695	+	0.531501i
$437$	−28.6692	−	9.31520i	−0.0656046	−	0.0213162i
$438$		0			0
$439$	−285.701			−0.650800			−0.325400	−	0.945576i	$-0.605499\pi$
$439$	−285.701			−0.650800			−0.325400	+	0.945576i	$0.605499\pi$
$440$		−	64.6181i		−	0.146859i
$441$		0			0
$442$	−380.375	−	276.359i	−0.860578	−	0.625246i
$443$	−389.073	−	282.678i	−0.878269	−	0.638100i	0.0545242	−	0.998512i	$-0.482636\pi$
$443$	−389.073	−	282.678i	−0.878269	−	0.638100i	−0.932793	+	0.360413i	$0.882636\pi$
$444$		0			0
$445$	479.674	+	660.214i	1.07792	+	1.48363i
$446$	−748.244	+	243.119i	−1.67768	+	0.545110i
$447$		0			0
$448$	432.953	+	314.558i	0.966412	+	0.702139i
$449$	−141.577	−	46.0012i	−0.315316	−	0.102452i	0.147083	−	0.989124i	$-0.453011\pi$
$449$	−141.577	−	46.0012i	−0.315316	−	0.102452i	−0.462400	+	0.886672i	$0.653011\pi$
$450$		0			0
$451$	−96.0444	+	132.194i	−0.212959	+	0.293113i
$452$	−128.009	+	393.971i	−0.283206	+	0.871617i
$453$		0			0
$454$	−29.7320	+	21.6015i	−0.0654889	+	0.0475805i
$455$	−208.744	+	67.8249i	−0.458777	+	0.149066i
$456$		0			0
$457$	59.9116	−	82.4613i	0.131098	−	0.180440i	−0.738422	−	0.674339i	$-0.764429\pi$
$457$	59.9116	−	82.4613i	0.131098	−	0.180440i	0.869519	+	0.493899i	$0.164429\pi$
$458$	−478.063	−	657.997i	−1.04380	−	1.43667i
$459$		0			0
$460$			220.856i			0.480122i
$461$	−141.932	−	195.352i	−0.307878	−	0.423757i	0.626840	−	0.779148i	$-0.284348\pi$
$461$	−141.932	−	195.352i	−0.307878	−	0.423757i	−0.934718	+	0.355391i	$0.884348\pi$
$462$		0			0
$463$	408.512	−	132.734i	0.882315	−	0.286681i	0.167397	−	0.985890i	$-0.446464\pi$
$463$	408.512	−	132.734i	0.882315	−	0.286681i	0.714918	+	0.699208i	$0.246464\pi$
$464$			244.589i			0.527131i
$465$		0			0
$466$	−587.109			−1.25989
$467$	−175.611	−	540.474i	−0.376040	−	1.15733i	−0.942775	−	0.333431i	$-0.891794\pi$
$467$	−175.611	−	540.474i	−0.376040	−	1.15733i	0.566735	−	0.823900i	$-0.308206\pi$
$468$		0			0
$469$	−322.887	+	234.591i	−0.688459	+	0.500195i
$470$	1116.00			2.37448
$471$		0			0
$472$	−140.231	+	101.884i	−0.297100	+	0.215856i
$473$	48.8857	+	35.5176i	0.103352	+	0.0750900i
$474$		0			0
$475$	−2.30120	−	7.08236i	−0.00484463	−	0.0149102i
$476$	415.907	+	572.447i	0.873754	+	1.20262i
$477$		0			0
$478$	−618.276	−	200.890i	−1.29346	−	0.420272i
$479$	−401.431	−	291.657i	−0.838061	−	0.608887i	0.0837673	−	0.996485i	$-0.473305\pi$
$479$	−401.431	−	291.657i	−0.838061	−	0.608887i	−0.921828	+	0.387598i	$0.873305\pi$
$480$		0			0
$481$	15.2724	−	47.0036i	0.0317513	−	0.0977206i
$482$	−234.983	+	323.426i	−0.487516	+	0.671008i
$483$		0			0
$484$	130.857	+	402.737i	0.270366	+	0.832102i
$485$	−393.435	+	285.847i	−0.811206	+	0.589375i
$486$		0			0
$487$	−155.153	+	213.550i	−0.318590	+	0.438501i	−0.938036	−	0.346538i	$-0.887357\pi$
$487$	−155.153	+	213.550i	−0.318590	+	0.438501i	0.619446	+	0.785039i	$0.287357\pi$
$488$	−79.9022	+	109.976i	−0.163734	+	0.225361i
$489$		0			0
$490$	−146.893			−0.299782
$491$			482.796i			0.983290i	0.870796	+	0.491645i	$0.163604\pi$
$491$			482.796i			0.983290i	−0.870796	+	0.491645i	$0.836396\pi$
$492$		0			0
$493$	−143.873	+	442.795i	−0.291831	+	0.898164i
$494$	63.6089	−	20.6678i	0.128763	−	0.0418376i
$495$		0			0
$496$	242.789	+	300.888i	0.489493	+	0.606630i
$497$	158.915			0.319749
$498$		0			0
$499$	−319.557	−	103.830i	−0.640394	−	0.208077i	−0.0292203	−	0.999573i	$-0.509302\pi$
$499$	−319.557	−	103.830i	−0.640394	−	0.208077i	−0.611174	+	0.791496i	$0.709302\pi$
$500$	456.292	−	331.515i	0.912584	−	0.663031i
$501$		0			0
$502$			243.020i			0.484104i
$503$	−10.4474	+	7.59051i	−0.0207703	+	0.0150905i	−0.598122	−	0.801405i	$-0.704086\pi$
$503$	−10.4474	+	7.59051i	−0.0207703	+	0.0150905i	0.577352	+	0.816496i	$0.304086\pi$
$504$		0			0
$505$	194.346	+	141.200i	0.384843	+	0.279605i
$506$	45.9458	+	141.407i	0.0908020	+	0.279460i
$507$		0			0
$508$	−163.601	+	53.1570i	−0.322048	+	0.104640i
$509$	−387.512	−	125.910i	−0.761320	−	0.247368i	−0.0974751	−	0.995238i	$-0.531077\pi$
$509$	−387.512	−	125.910i	−0.761320	−	0.247368i	−0.663845	+	0.747870i	$0.731077\pi$
$510$		0			0
$511$	−742.419	−	241.227i	−1.45288	−	0.472068i
$512$	209.940	−	646.128i	0.410038	−	1.26197i
$513$		0			0
$514$	−93.1955	+	286.826i	−0.181314	+	0.558028i
$515$	105.950	+	326.081i	0.205728	+	0.633167i
$516$		0			0
$517$	387.659	−	125.958i	0.749824	−	0.243633i
$518$	−80.5827	+	110.913i	−0.155565	+	0.214117i
$519$		0			0
$520$	−45.1582	−	62.1549i	−0.0868427	−	0.119529i
$521$	−248.737			−0.477423			−0.238711	−	0.971091i	$-0.576725\pi$
$521$	−248.737			−0.477423			−0.238711	+	0.971091i	$0.576725\pi$
$522$		0			0
$523$	−480.687	−	661.609i	−0.919095	−	1.26503i	−0.963964	−	0.266033i	$-0.914287\pi$
$523$	−480.687	−	661.609i	−0.919095	−	1.26503i	0.0448683	−	0.998993i	$-0.485713\pi$
$524$	−268.021	+	824.883i	−0.511490	+	1.57420i
$525$		0			0
$526$			517.544i			0.983925i
$527$	262.547	+	687.531i	0.498191	+	1.30461i
$528$		0			0
$529$	138.849	+	427.333i	0.262474	+	0.807813i
$530$	−182.270	−	59.2232i	−0.343906	−	0.111742i
$531$		0			0
$532$	−100.655			−0.189201
$533$			194.275i			0.364494i
$534$		0			0
$535$	−384.734	−	279.526i	−0.719130	−	0.522478i
$536$	−113.022	−	82.1151i	−0.210862	−	0.153200i
$537$		0			0
$538$	−338.040	−	465.271i	−0.628326	−	0.864817i
$539$	−51.0253	+	16.5791i	−0.0946666	+	0.0307591i
$540$		0			0
$541$	513.683	+	373.212i	0.949506	+	0.689856i	0.950690	−	0.310143i	$-0.100377\pi$
$541$	513.683	+	373.212i	0.949506	+	0.689856i	−0.00118419	+	0.999999i	$0.500377\pi$
$542$	−259.585	−	84.3443i	−0.478939	−	0.155617i
$543$		0			0
$544$	637.378	−	877.275i	1.17165	−	1.61264i
$545$	82.7884	−	254.797i	0.151905	−	0.467517i
$546$		0			0
$547$	511.421	−	371.569i	0.934957	−	0.679286i	−0.0122447	−	0.999925i	$-0.503898\pi$
$547$	511.421	−	371.569i	0.934957	−	0.679286i	0.947201	+	0.320639i	$0.103898\pi$
$548$	566.970	−	184.220i	1.03462	−	0.336168i
$549$		0			0
$550$	−21.5896	+	29.7155i	−0.0392538	+	0.0540283i
$551$	−38.9289	−	53.5810i	−0.0706514	−	0.0972432i
$552$		0			0
$553$			430.906i			0.779215i
$554$	−25.6175	−	35.2595i	−0.0462410	−	0.0636452i
$555$		0			0
$556$	1119.87	−	363.868i	2.01415	−	0.654438i
$557$		−	46.8846i		−	0.0841734i	−0.999114	−	0.0420867i	$-0.986599\pi$
$557$		−	46.8846i		−	0.0841734i	0.999114	−	0.0420867i	$-0.0134006\pi$
$558$		0			0
$559$	71.8437			0.128522
$560$	−126.300	−	388.711i	−0.225536	−	0.694127i
$561$		0			0
$562$	240.529	−	174.755i	0.427987	−	0.310951i
$563$	807.800			1.43481			0.717407	−	0.696655i	$-0.245329\pi$
$563$	807.800			1.43481			0.717407	+	0.696655i	$0.245329\pi$
$564$		0			0
$565$	368.484	−	267.719i	0.652184	−	0.473839i
$566$	−445.533	−	323.699i	−0.787160	−	0.571905i
$567$		0			0
$568$	17.1894	+	52.9034i	0.0302630	+	0.0931398i
$569$	145.543	+	200.323i	0.255788	+	0.352061i	0.917528	−	0.397672i	$-0.130182\pi$
$569$	145.543	+	200.323i	0.255788	+	0.352061i	−0.661740	+	0.749733i	$0.730182\pi$
$570$		0			0
$571$	−903.094	−	293.433i	−1.58160	−	0.513893i	−0.619132	−	0.785287i	$-0.712515\pi$
$571$	−903.094	−	293.433i	−1.58160	−	0.513893i	−0.962468	+	0.271394i	$0.912515\pi$
$572$	−144.793	−	105.198i	−0.253135	−	0.183913i
$573$		0			0
$574$	166.532	−	512.534i	0.290126	−	0.892916i
$575$	11.5693	−	15.9238i	0.0201205	−	0.0276935i
$576$		0			0
$577$	10.8420	+	33.3682i	0.0187903	+	0.0578306i	0.960012	−	0.279959i	$-0.0903208\pi$
$577$	10.8420	+	33.3682i	0.0187903	+	0.0578306i	−0.941222	+	0.337789i	$0.890321\pi$
$578$	656.938	−	477.294i	1.13657	−	0.825767i
$579$		0			0
$580$	−285.215	+	392.565i	−0.491750	+	0.676836i
$581$	−56.0176	+	77.1016i	−0.0964158	+	0.132705i
$582$		0			0
$583$	−69.9984			−0.120066
$584$		−	273.246i		−	0.467887i
$585$		0			0
$586$	−292.962	+	901.643i	−0.499934	+	1.53864i
$587$	220.922	−	71.7818i	0.376357	−	0.122286i	−0.114729	−	0.993397i	$-0.536600\pi$
$587$	220.922	−	71.7818i	0.376357	−	0.122286i	0.491086	+	0.871111i	$0.336600\pi$
$588$		0			0
$589$	−101.076	−	27.2719i	−0.171606	−	0.0463021i
$590$	1215.58			2.06031
$591$		0			0
$592$	87.5276	+	28.4394i	0.147851	+	0.0480396i
$593$	−143.431	+	104.208i	−0.241873	+	0.175731i	−0.702117	−	0.712061i	$-0.747762\pi$
$593$	−143.431	+	104.208i	−0.241873	+	0.175731i	0.460244	+	0.887792i	$0.347762\pi$
$594$		0			0
$595$		−	778.001i		−	1.30757i
$596$	−752.881	+	547.000i	−1.26322	+	0.917786i
$597$		0			0
$598$	143.016	+	103.907i	0.239158	+	0.173758i
$599$	−173.180	−	532.995i	−0.289116	−	0.889807i	−0.985135	−	0.171784i	$-0.945047\pi$
$599$	−173.180	−	532.995i	−0.289116	−	0.889807i	0.696019	−	0.718024i	$-0.254953\pi$
$600$		0			0
$601$	−966.674	+	314.091i	−1.60844	+	0.522614i	−0.969176	−	0.246371i	$-0.920762\pi$
$601$	−966.674	+	314.091i	−1.60844	+	0.522614i	−0.639266	+	0.768985i	$0.720762\pi$
$602$	−189.537	−	61.5842i	−0.314845	−	0.102299i
$603$		0			0
$604$	−34.6895	−	11.2713i	−0.0574330	−	0.0186611i
$605$	143.880	−	442.818i	0.237818	−	0.731930i
$606$		0			0
$607$	96.6970	−	297.603i	0.159303	−	0.490285i	−0.839268	−	0.543717i	$-0.817016\pi$
$607$	96.6970	−	297.603i	0.159303	−	0.490285i	0.998571	+	0.0534329i	$0.0170163\pi$
$608$	47.6670	+	146.704i	0.0783996	+	0.241289i
$609$		0			0
$610$	906.658	−	294.591i	1.48632	−	0.482936i
$611$	284.857	−	392.072i	0.466214	−	0.641689i
$612$		0			0
$613$	32.4139	+	44.6139i	0.0528775	+	0.0727797i	0.834637	−	0.550801i	$-0.185677\pi$
$613$	32.4139	+	44.6139i	0.0528775	+	0.0727797i	−0.781759	+	0.623580i	$0.785677\pi$
$614$	−1464.92			−2.38586
$615$		0			0
$616$	45.7523	+	62.9727i	0.0742733	+	0.102228i
$617$	34.9324	−	107.511i	0.0566165	−	0.174248i	−0.918749	−	0.394841i	$-0.870800\pi$
$617$	34.9324	−	107.511i	0.0566165	−	0.174248i	0.975366	+	0.220594i	$0.0707995\pi$
$618$		0			0
$619$		−	451.076i		−	0.728717i	−0.931259	−	0.364359i	$-0.881288\pi$
$619$		−	451.076i		−	0.728717i	0.931259	−	0.364359i	$-0.118712\pi$
$620$	38.8098	+	766.041i	0.0625964	+	1.23555i
$621$		0			0
$622$	−294.166	−	905.349i	−0.472935	−	1.45555i
$623$	−934.919	−	303.774i	−1.50067	−	0.487598i
$624$		0			0
$625$	−675.265			−1.08042
$626$		−	243.484i		−	0.388952i
$627$		0			0
$628$	1058.28	+	768.887i	1.68516	+	1.22434i
$629$	141.728	+	102.972i	0.225323	+	0.163707i
$630$		0			0
$631$	183.378	+	252.399i	0.290616	+	0.399998i	0.929214	−	0.369542i	$-0.120485\pi$
$631$	183.378	+	252.399i	0.290616	+	0.399998i	−0.638598	+	0.769540i	$0.720485\pi$
$632$	−143.450	+	46.6097i	−0.226978	+	0.0737495i
$633$		0			0
$634$	−1282.34	−	931.671i	−2.02261	−	1.46951i
$635$	179.882	+	58.4472i	0.283279	+	0.0920429i
$636$		0			0
$637$	−37.4940	+	51.6061i	−0.0588603	+	0.0810143i
$638$	−100.946	+	310.680i	−0.158223	+	0.486960i
$639$		0			0
$640$	291.834	−	212.030i	0.455991	−	0.331297i
$641$	−34.3584	+	11.1637i	−0.0536012	+	0.0174161i	−0.335695	−	0.941971i	$-0.608971\pi$
$641$	−34.3584	+	11.1637i	−0.0536012	+	0.0174161i	0.282094	+	0.959387i	$0.408971\pi$
$642$		0			0
$643$	−148.338	+	204.170i	−0.230697	+	0.317527i	−0.908634	−	0.417592i	$-0.862874\pi$
$643$	−148.338	+	204.170i	−0.230697	+	0.317527i	0.677938	+	0.735120i	$0.262874\pi$
$644$	−156.376	−	215.233i	−0.242819	−	0.334212i
$645$		0			0
$646$			237.075i			0.366989i
$647$	114.418	+	157.483i	0.176844	+	0.243405i	0.888233	−	0.459394i	$-0.151933\pi$
$647$	114.418	+	157.483i	0.176844	+	0.243405i	−0.711389	+	0.702799i	$0.751933\pi$
$648$		0			0
$649$	422.249	−	137.197i	0.650614	−	0.211397i
$650$			43.6707i			0.0671857i
$651$		0			0
$652$	689.622			1.05770
$653$	−3.50040	−	10.7731i	−0.00536049	−	0.0164979i	0.948340	−	0.317254i	$-0.102761\pi$
$653$	−3.50040	−	10.7731i	−0.00536049	−	0.0164979i	−0.953701	+	0.300756i	$0.902761\pi$
$654$		0			0
$655$	771.519	−	560.542i	1.17789	−	0.855789i
$656$	−361.769			−0.551477
$657$		0			0
$658$	−1087.59	+	790.178i	−1.65287	+	1.20088i
$659$	97.3577	+	70.7345i	0.147736	+	0.107336i	0.659198	−	0.751970i	$-0.270896\pi$
$659$	97.3577	+	70.7345i	0.147736	+	0.107336i	−0.511462	+	0.859306i	$0.670896\pi$
$660$		0			0
$661$	−371.810	−	1144.31i	−0.562496	−	1.73119i	−0.675275	−	0.737566i	$-0.735975\pi$
$661$	−371.810	−	1144.31i	−0.562496	−	1.73119i	0.112779	−	0.993620i	$-0.464025\pi$
$662$	24.9752	+	34.3754i	0.0377269	+	0.0519266i
$663$		0			0
$664$	−31.7266	−	10.3086i	−0.0477810	−	0.0155250i
$665$	89.5355	+	65.0513i	0.134640	+	0.0978215i
$666$		0			0
$667$	54.0943	−	166.485i	0.0811010	−	0.249603i
$668$	796.643	−	1096.48i	1.19258	−	1.64144i
$669$		0			0
$670$	302.750	+	931.768i	0.451866	+	1.39070i
$671$	281.691	−	204.660i	0.419808	−	0.305008i
$672$		0			0
$673$	632.418	−	870.448i	0.939699	−	1.29339i	−0.0162545	−	0.999868i	$-0.505174\pi$
$673$	632.418	−	870.448i	0.939699	−	1.29339i	0.955954	−	0.293517i	$-0.0948258\pi$
$674$	−1116.52	+	1536.76i	−1.65656	+	2.28006i
$675$		0			0
$676$	588.903			0.871158
$677$			294.316i			0.434736i	0.976090	+	0.217368i	$0.0697471\pi$
$677$			294.316i			0.434736i	−0.976090	+	0.217368i	$0.930253\pi$
$678$		0			0
$679$	181.025	−	557.137i	0.266605	−	0.820526i
$680$	258.999	−	84.1539i	0.380881	−	0.123756i
$681$		0			0
$682$	184.212	+	482.396i	0.270105	+	0.707326i
$683$	1037.16			1.51853			0.759264	−	0.650782i	$-0.225559\pi$
$683$	1037.16			1.51853			0.759264	+	0.650782i	$0.225559\pi$
$684$		0			0
$685$	−623.395	−	202.553i	−0.910066	−	0.295698i
$686$	879.645	−	639.100i	1.28228	−	0.931632i
$687$		0			0
$688$			133.783i			0.194453i
$689$	−67.3302	+	48.9182i	−0.0977216	+	0.0709989i
$690$		0			0
$691$	−634.771	−	461.188i	−0.918627	−	0.667422i	0.0245548	−	0.999698i	$-0.492183\pi$
$691$	−634.771	−	461.188i	−0.918627	−	0.667422i	−0.943182	+	0.332277i	$0.892183\pi$
$692$	211.069	+	649.603i	0.305013	+	0.938733i
$693$		0			0
$694$	−409.695	+	133.118i	−0.590338	+	0.191813i
$695$	−1231.32	−	400.080i	−1.77168	−	0.575654i
$696$		0			0
$697$	−654.934	−	212.801i	−0.939647	−	0.305310i
$698$	424.687	−	1307.05i	0.608434	−	1.87257i
$699$		0			0
$700$	20.3093	−	62.5056i	0.0290133	−	0.0892937i
$701$	210.137	+	646.736i	0.299768	+	0.922591i	0.981578	+	0.191062i	$0.0611930\pi$
$701$	210.137	+	646.736i	0.299768	+	0.922591i	−0.681810	+	0.731529i	$0.738807\pi$
$702$		0			0
$703$	−23.7007	+	7.70083i	−0.0337137	+	0.0109542i
$704$	282.025	−	388.174i	0.400604	−	0.551384i
$705$		0			0
$706$	−485.008	−	667.556i	−0.686980	−	0.945547i
$707$	−289.373			−0.409297
$708$		0			0
$709$	429.911	+	591.722i	0.606363	+	0.834587i	0.996272	−	0.0862665i	$-0.0274937\pi$
$709$	429.911	+	591.722i	0.606363	+	0.834587i	−0.389909	+	0.920853i	$0.627494\pi$
$710$	120.547	−	371.006i	0.169785	−	0.522543i
$711$		0			0
$712$		−	344.095i		−	0.483280i
$713$	−98.7142	−	258.503i	−0.138449	−	0.362557i
$714$		0			0
$715$	60.8101	+	187.154i	0.0850491	+	0.261754i
$716$	923.492	+	300.061i	1.28979	+	0.419079i
$717$		0			0
$718$	1546.98			2.15457
$719$		−	919.406i		−	1.27873i	−0.768904	−	0.639364i	$-0.779198\pi$
$719$		−	919.406i		−	1.27873i	0.768904	−	0.639364i	$-0.220802\pi$
$720$		0			0
$721$	−334.132	−	242.761i	−0.463428	−	0.336700i
$722$	836.319	+	607.621i	1.15834	+	0.841581i
$723$		0			0
$724$	347.864	+	478.794i	0.480475	+	0.661318i
$725$	41.1280	−	13.3633i	0.0567283	−	0.0184322i
$726$		0			0
$727$	184.984	+	134.399i	0.254449	+	0.184868i	0.707696	−	0.706517i	$-0.249735\pi$
$727$	184.984	+	134.399i	0.254449	+	0.184868i	−0.453247	+	0.891385i	$0.649735\pi$
$728$	88.0167	+	28.5984i	0.120902	+	0.0392834i
$729$		0			0
$730$	−1126.34	+	1550.28i	−1.54293	+	2.12366i
$731$	−78.6945	+	242.197i	−0.107653	+	0.331323i
$732$		0			0
$733$	−94.7309	+	68.8261i	−0.129237	+	0.0938964i	−0.650526	−	0.759484i	$-0.725451\pi$
$733$	−94.7309	+	68.8261i	−0.129237	+	0.0938964i	0.521289	+	0.853380i	$0.325451\pi$
$734$	−929.997	+	302.174i	−1.26703	+	0.411682i
$735$		0			0
$736$	−239.646	+	329.844i	−0.325606	+	0.448158i
$737$	210.329	+	289.493i	0.285385	+	0.392799i
$738$		0			0
$739$			942.715i			1.27566i	0.770176	+	0.637832i	$0.220168\pi$
$739$			942.715i			1.27566i	−0.770176	+	0.637832i	$0.779832\pi$
$740$	107.318	+	147.711i	0.145025	+	0.199610i
$741$		0			0
$742$	219.562	−	71.3399i	0.295905	−	0.0961455i
$743$		−	759.232i		−	1.02185i	−0.859626	−	0.510923i	$-0.829304\pi$
$743$		−	759.232i		−	1.02185i	0.859626	−	0.510923i	$-0.170696\pi$
$744$		0			0
$745$	1023.23			1.37346
$746$	−60.2152	−	185.323i	−0.0807174	−	0.248423i
$747$		0			0
$748$	513.241	−	372.891i	0.686151	−	0.498518i
$749$	572.854			0.764825
$750$		0			0
$751$	326.330	−	237.093i	0.434527	−	0.315703i	−0.348929	−	0.937149i	$-0.613455\pi$
$751$	326.330	−	237.093i	0.434527	−	0.315703i	0.783457	+	0.621446i	$0.213455\pi$
$752$	730.095	+	530.445i	0.970871	+	0.705379i
$753$		0			0
$754$	120.020	+	369.384i	0.159178	+	0.489899i
$755$	23.5729	+	32.4454i	0.0312224	+	0.0429740i
$756$		0			0
$757$	766.011	+	248.892i	1.01190	+	0.328787i	0.767612	−	0.640915i	$-0.221445\pi$
$757$	766.011	+	248.892i	1.01190	+	0.328787i	0.244291	+	0.969702i	$0.421445\pi$
$758$	1191.40	+	865.604i	1.57177	+	1.14196i
$759$		0			0
$760$	−11.9710	+	36.8430i	−0.0157513	+	0.0484776i
$761$	182.899	−	251.739i	0.240340	−	0.330800i	−0.671759	−	0.740770i	$-0.734461\pi$
$761$	182.899	−	251.739i	0.240340	−	0.330800i	0.912099	+	0.409970i	$0.134461\pi$
$762$		0			0
$763$	99.7264	+	306.926i	0.130703	+	0.402263i
$764$	367.281	−	266.845i	0.480734	−	0.349274i
$765$		0			0
$766$	−458.100	+	630.521i	−0.598042	+	0.823135i
$767$	310.274	−	427.055i	0.404529	−	0.556786i
$768$		0			0
$769$	−1316.21			−1.71159			−0.855794	−	0.517316i	$-0.826931\pi$
$769$	−1316.21			−1.71159			−0.855794	+	0.517316i	$0.826931\pi$
$770$		−	545.873i		−	0.708926i
$771$		0			0
$772$	−181.809	+	559.551i	−0.235504	+	0.724807i
$773$	621.647	−	201.985i	0.804200	−	0.261300i	0.122061	−	0.992523i	$-0.461050\pi$
$773$	621.647	−	201.985i	0.804200	−	0.261300i	0.682139	+	0.731222i	$0.261050\pi$
$774$		0			0
$775$	37.3299	−	57.2646i	0.0481677	−	0.0738898i
$776$	205.053			0.264244
$777$		0			0
$778$	1992.57	+	647.426i	2.56115	+	0.832167i
$779$	79.2512	−	57.5794i	0.101735	−	0.0739145i
$780$		0			0
$781$		−	142.480i		−	0.182432i
$782$	−506.943	+	368.316i	−0.648265	+	0.470992i
$783$		0			0
$784$	−96.0982	−	69.8194i	−0.122574	−	0.0890554i
$785$	−444.457	−	1367.90i	−0.566187	−	1.74254i
$786$		0			0
$787$	−519.575	+	168.820i	−0.660197	+	0.214511i	−0.619905	−	0.784677i	$-0.712829\pi$
$787$	−519.575	+	168.820i	−0.660197	+	0.214511i	−0.0402920	+	0.999188i	$0.512829\pi$
$788$	−694.990	−	225.816i	−0.881967	−	0.286568i
$789$		0			0
$790$	1006.00	+	326.868i	1.27341	+	0.413758i
$791$	−169.545	+	521.805i	−0.214342	+	0.659677i
$792$		0			0
$793$	127.927	−	393.718i	0.161320	−	0.496492i
$794$	401.204	+	1234.78i	0.505295	+	1.55514i
$795$		0			0
$796$	−1243.34	+	403.986i	−1.56199	+	0.507520i
$797$	272.719	−	375.365i	0.342182	−	0.470973i	−0.602895	−	0.797820i	$-0.705986\pi$
$797$	272.719	−	375.365i	0.342182	−	0.470973i	0.945077	+	0.326848i	$0.105986\pi$
$798$		0			0
$799$	1009.72	+	1389.76i	1.26373	+	1.73937i
$800$	−100.719			−0.125899
$801$		0			0
$802$	−694.552	−	955.969i	−0.866025	−	1.19198i
$803$	−216.278	+	665.634i	−0.269337	+	0.828934i
$804$		0			0
$805$			292.519i			0.363377i
$806$	514.312	+	335.272i	0.638104	+	0.415970i
$807$		0			0
$808$	−31.3005	−	96.3330i	−0.0387382	−	0.119224i
$809$	−244.661	−	79.4951i	−0.302424	−	0.0982634i	0.153874	−	0.988090i	$-0.450825\pi$
$809$	−244.661	−	79.4951i	−0.302424	−	0.0982634i	−0.456298	+	0.889827i	$0.650825\pi$
$810$		0			0
$811$	1305.17			1.60933			0.804666	−	0.593728i	$-0.202345\pi$
$811$	1305.17			1.60933			0.804666	+	0.593728i	$0.202345\pi$
$812$		−	584.513i		−	0.719844i
$813$		0			0
$814$	99.4414	+	72.2484i	0.122164	+	0.0887573i
$815$	−613.439	−	445.690i	−0.752686	−	0.546859i
$816$		0			0
$817$	−21.2930	−	29.3074i	−0.0260625	−	0.0358719i
$818$	−635.004	+	206.325i	−0.776289	+	0.252232i
$819$		0			0
$820$	−580.639	−	421.859i	−0.708096	−	0.514462i
$821$	1015.78	+	330.047i	1.23725	+	0.402007i	0.853335	−	0.521362i	$-0.174576\pi$
$821$	1015.78	+	330.047i	1.23725	+	0.402007i	0.383914	+	0.923369i	$0.374576\pi$
$822$		0			0
$823$	230.119	−	316.732i	0.279610	−	0.384850i	−0.645995	−	0.763342i	$-0.723557\pi$
$823$	230.119	−	316.732i	0.279610	−	0.384850i	0.925605	+	0.378492i	$0.123557\pi$
$824$	44.6739	−	137.492i	0.0542158	−	0.166859i
$825$		0			0
$826$	−1184.63	+	860.683i	−1.43417	+	1.04199i
$827$	−431.848	+	140.316i	−0.522186	+	0.169669i	−0.558237	−	0.829681i	$-0.688522\pi$
$827$	−431.848	+	140.316i	−0.522186	+	0.169669i	0.0360511	+	0.999350i	$0.488522\pi$
$828$		0			0
$829$	629.022	−	865.774i	0.758772	−	1.04436i	−0.238543	−	0.971132i	$-0.576670\pi$
$829$	629.022	−	865.774i	0.758772	−	1.04436i	0.997315	−	0.0732281i	$-0.0233301\pi$
$830$	137.509	+	189.265i	0.165674	+	0.228031i
$831$		0			0
$832$		−	570.471i		−	0.685662i
$833$	−132.903	−	182.926i	−0.159548	−	0.219599i
$834$		0			0
$835$	−1417.28	+	460.501i	−1.69734	+	0.551498i
$836$			90.2445i			0.107948i
$837$		0			0
$838$	−1307.29			−1.56001
$839$	286.883	+	882.936i	0.341935	+	1.05237i	0.963204	+	0.268770i	$0.0866172\pi$
$839$	286.883	+	882.936i	0.341935	+	1.05237i	−0.621270	+	0.783597i	$0.713383\pi$
$840$		0			0
$841$	−369.232	+	268.263i	−0.439040	+	0.318981i
$842$	−1288.11			−1.52982
$843$		0			0
$844$	−40.3576	+	29.3215i	−0.0478170	+	0.0347411i
$845$	−523.847	−	380.597i	−0.619937	−	0.450410i
$846$		0			0
$847$	173.317	+	533.415i	0.204625	+	0.629770i
$848$	−91.0929	−	125.379i	−0.107421	−	0.147852i
$849$		0			0
$850$	−147.221	−	47.8350i	−0.173201	−	0.0562765i
$851$	−53.2880	−	38.7160i	−0.0626181	−	0.0454947i
$852$		0			0
$853$	90.7019	−	279.152i	0.106333	−	0.327259i	−0.883708	−	0.468038i	$-0.844961\pi$
$853$	90.7019	−	279.152i	0.106333	−	0.327259i	0.990041	+	0.140780i	$0.0449609\pi$
$854$	−674.988	+	929.042i	−0.790385	+	1.08787i
$855$		0			0
$856$	61.9637	+	190.705i	0.0723875	+	0.222786i
$857$	−633.842	+	460.513i	−0.739605	+	0.537355i	−0.892587	−	0.450874i	$-0.851112\pi$
$857$	−633.842	+	460.513i	−0.739605	+	0.537355i	0.152982	+	0.988229i	$0.451112\pi$
$858$		0			0
$859$	50.7728	−	69.8827i	0.0591069	−	0.0813536i	−0.778440	−	0.627719i	$-0.783989\pi$
$859$	50.7728	−	69.8827i	0.0591069	−	0.0813536i	0.837547	+	0.546365i	$0.183989\pi$
$860$	−156.005	+	214.722i	−0.181401	+	0.249677i
$861$		0			0
$862$	756.826			0.877989
$863$			104.362i			0.120930i	0.998170	+	0.0604648i	$0.0192583\pi$
$863$			104.362i			0.120930i	−0.998170	+	0.0604648i	$0.980742\pi$
$864$		0			0
$865$	232.074	−	714.252i	0.268294	−	0.825724i
$866$	−380.900	+	123.762i	−0.439839	+	0.142912i
$867$		0			0
$868$	−580.211	−	719.056i	−0.668446	−	0.828406i
$869$	386.339			0.444579
$870$		0			0
$871$	404.623	+	131.470i	0.464550	+	0.150941i
$872$	−91.3896	+	66.3984i	−0.104805	+	0.0761450i
$873$		0			0
$874$		−	89.1371i		−	0.101988i
$875$	604.347	−	439.084i	0.690682	−	0.501810i
$876$		0			0
$877$	385.885	+	280.362i	0.440006	+	0.319683i	0.785637	−	0.618687i	$-0.212335\pi$
$877$	385.885	+	280.362i	0.440006	+	0.319683i	−0.345631	+	0.938370i	$0.612335\pi$
$878$	−261.062	−	803.466i	−0.297337	−	0.915110i
$879$		0			0
$880$	−348.509	+	113.237i	−0.396032	+	0.128679i
$881$	−132.919	−	43.1879i	−0.150872	−	0.0490214i	0.232607	−	0.972571i	$-0.425274\pi$
$881$	−132.919	−	43.1879i	−0.150872	−	0.0490214i	−0.383480	+	0.923549i	$0.625274\pi$
$882$		0			0
$883$	−1251.19	−	406.536i	−1.41698	−	0.460403i	−0.502336	−	0.864672i	$-0.667526\pi$
$883$	−1251.19	−	406.536i	−1.41698	−	0.460403i	−0.914640	+	0.404269i	$0.867526\pi$
$884$	233.083	−	717.355i	0.263668	−	0.811488i
$885$		0			0
$886$	439.445	−	1352.47i	0.495988	−	1.52649i
$887$	188.419	+	579.895i	0.212423	+	0.653771i	0.999327	+	0.0366948i	$0.0116830\pi$
$887$	188.419	+	579.895i	0.212423	+	0.653771i	−0.786903	+	0.617076i	$0.788317\pi$
$888$		0			0
$889$	−216.685	+	70.4052i	−0.243740	+	0.0791959i
$890$	−1418.39	+	1952.24i	−1.59369	+	2.19353i
$891$		0			0
$892$	−741.871	−	1021.10i	−0.831694	−	1.14473i
$893$	−244.365			−0.273645
$894$		0			0
$895$	−627.550	−	863.749i	−0.701173	−	0.965083i
$896$	−134.277	+	413.262i	−0.149863	+	0.461230i
$897$		0			0
$898$		−	440.185i		−	0.490184i
$899$	158.371	−	586.961i	0.176163	−	0.652904i
$900$		0			0
$901$	−91.1608	−	280.564i	−0.101177	−	0.311392i
$902$	−459.525	−	149.309i	−0.509451	−	0.165531i
$903$		0			0
$904$	−192.049			−0.212444
$905$		−	650.720i		−	0.719028i
$906$		0			0
$907$	1126.58	+	818.508i	1.24209	+	0.902435i	0.997736	−	0.0672504i	$-0.0214226\pi$
$907$	1126.58	+	818.508i	1.24209	+	0.902435i	0.244359	+	0.969685i	$0.421423\pi$
$908$	−47.6976	−	34.6543i	−0.0525304	−	0.0381656i
$909$		0			0
$910$	−381.482	−	525.065i	−0.419211	−	0.576995i
$911$	−994.153	+	323.020i	−1.09128	+	0.354577i	−0.798740	−	0.601677i	$-0.794499\pi$
$911$	−994.153	+	323.020i	−1.09128	+	0.354577i	−0.292537	+	0.956254i	$0.594499\pi$
$912$		0			0
$913$	69.1273	+	50.2239i	0.0757144	+	0.0550098i
$914$	286.647	+	93.1373i	0.313618	+	0.101901i
$915$		0			0
$916$	766.934	−	1055.59i	0.837264	−	1.15239i
$917$	−354.987	+	1092.54i	−0.387117	+	1.19143i
$918$		0			0
$919$	−94.1551	+	68.4077i	−0.102454	+	0.0744371i	−0.637833	−	0.770175i	$-0.720169\pi$
$919$	−94.1551	+	68.4077i	−0.102454	+	0.0744371i	0.535379	+	0.844612i	$0.320169\pi$
$920$	−97.3803	+	31.6408i	−0.105848	+	0.0343921i
$921$		0			0
$922$	419.689	−	577.653i	0.455194	−	0.626521i
$923$	−99.5716	−	137.048i	−0.107878	−	0.148482i
$924$		0			0
$925$		−	16.2717i		−	0.0175911i
$926$	746.562	+	1027.55i	0.806222	+	1.10967i
$927$		0			0
$928$	−851.925	+	276.807i	−0.918023	+	0.298284i
$929$			16.8619i			0.0181506i	0.999959	+	0.00907531i	$0.00288880\pi$
$929$			16.8619i			0.0181506i	−0.999959	+	0.00907531i	$0.997111\pi$
$930$		0			0
$931$	32.1643			0.0345481
$932$	−291.054	−	895.773i	−0.312290	−	0.961130i
$933$		0			0
$934$	1359.49	−	987.724i	1.45555	−	1.05752i
$935$	−697.536			−0.746028
$936$		0			0
$937$	−229.398	+	166.668i	−0.244822	+	0.177874i	−0.703429	−	0.710766i	$-0.748349\pi$
$937$	−229.398	+	166.668i	−0.244822	+	0.177874i	0.458607	+	0.888639i	$0.348349\pi$
$938$	−954.772	−	693.683i	−1.01788	−	0.739534i
$939$		0			0
$940$	553.250	+	1702.73i	0.588563	+	1.81141i
$941$	−631.597	−	869.318i	−0.671197	−	0.923824i	0.328590	−	0.944473i	$-0.393427\pi$
$941$	−631.597	−	869.318i	−0.671197	−	0.923824i	−0.999787	+	0.0206491i	$0.993427\pi$
$942$		0			0
$943$	246.247	+	80.0105i	0.261131	+	0.0848467i
$944$	795.239	+	577.775i	0.842414	+	0.612050i
$945$		0			0
$946$	−55.2148	+	169.934i	−0.0583666	+	0.179634i
$947$	−69.0430	+	95.0295i	−0.0729071	+	0.100348i	−0.843913	−	0.536480i	$-0.819754\pi$
$947$	−69.0430	+	95.0295i	−0.0729071	+	0.100348i	0.771006	+	0.636828i	$0.219754\pi$
$948$		0			0
$949$	257.144	+	791.407i	0.270963	+	0.833937i
$950$	17.8147	−	12.9431i	0.0187523	−	0.0136244i
$951$		0			0
$952$	−192.819	+	265.393i	−0.202541	+	0.278774i
$953$	326.856	−	449.879i	0.342976	−	0.472066i	−0.602332	−	0.798246i	$-0.705762\pi$
$953$	326.856	−	449.879i	0.342976	−	0.472066i	0.945308	+	0.326180i	$0.105762\pi$
$954$		0			0
$955$	−499.164			−0.522685
$956$		−	1042.91i		−	1.09091i
$957$		0			0
$958$	453.403	−	1395.43i	0.473281	−	1.45661i
$959$	750.938	−	243.995i	0.783043	−	0.254426i
$960$		0			0
$961$	−387.816	−	879.272i	−0.403554	−	0.914956i
$962$	146.142			0.151914
$963$		0			0
$964$	−609.953	−	198.186i	−0.632731	−	0.205587i
$965$	523.352	−	380.238i	0.542334	−	0.394029i
$966$		0			0
$967$		−	441.345i		−	0.456406i	−0.973614	−	0.228203i	$-0.926715\pi$
$967$		−	441.345i		−	0.456406i	0.973614	−	0.228203i	$-0.0732850\pi$
$968$	−158.828	+	115.396i	−0.164079	+	0.119210i
$969$		0			0
$970$	−1163.38	−	845.245i	−1.19936	−	0.871387i
$971$	86.3666	+	265.809i	0.0889461	+	0.273748i	0.985629	−	0.168926i	$-0.0540299\pi$
$971$	86.3666	+	265.809i	0.0889461	+	0.273748i	−0.896683	+	0.442674i	$0.854030\pi$
$972$		0			0
$973$	1483.24	−	481.933i	1.52440	−	0.495307i
$974$	−742.331	−	241.198i	−0.762147	−	0.247636i
$975$		0			0
$976$	733.161	+	238.219i	0.751190	+	0.244076i
$977$	−369.006	+	1135.68i	−0.377693	+	1.16242i	0.563951	+	0.825808i	$0.309281\pi$
$977$	−369.006	+	1135.68i	−0.377693	+	1.16242i	−0.941644	+	0.336611i	$0.890719\pi$
$978$		0			0
$979$	−272.356	+	838.225i	−0.278198	+	0.856205i
$980$	−72.8210	−	224.120i	−0.0743072	−	0.228694i
$981$		0			0
$982$	−1357.75	+	441.158i	−1.38263	+	0.449245i
$983$	724.460	−	997.133i	0.736989	−	1.01438i	−0.261798	−	0.965123i	$-0.584315\pi$
$983$	724.460	−	997.133i	0.736989	−	1.01438i	0.998786	−	0.0492549i	$-0.0156847\pi$
$984$		0			0
$985$	472.274	+	650.029i	0.479466	+	0.659928i
$986$	−1376.72			−1.39627
$987$		0			0
$988$	63.0672	+	86.8046i	0.0638332	+	0.0878589i
$989$	29.5881	−	91.0629i	0.0299172	−	0.0920757i
$990$		0			0
$991$			875.612i			0.883564i	0.897122	+	0.441782i	$0.145654\pi$
$991$			875.612i			0.883564i	−0.897122	+	0.441782i	$0.854346\pi$
$992$	−773.251	+	1186.18i	−0.779487	+	1.19574i
$993$		0			0
$994$	145.210	+	446.911i	0.146087	+	0.449609i
$995$	1367.08	+	444.191i	1.37395	+	0.446423i
$996$		0			0
$997$	−1277.59			−1.28144			−0.640719	−	0.767776i	$-0.721363\pi$
$997$	−1277.59			−1.28144			−0.640719	+	0.767776i	$0.721363\pi$
$998$		−	993.552i		−	0.995543i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.3.v.a.244.5		20
3.2	odd	2		31.3.f.a.27.1	yes	20
31.23	odd	10	inner	279.3.v.a.271.5		20
93.23	even	10		31.3.f.a.23.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.23.1	✓	20	93.23	even	10
31.3.f.a.27.1	yes	20	3.2	odd	2
279.3.v.a.244.5		20	1.1	even	1	trivial
279.3.v.a.271.5		20	31.23	odd	10	inner

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	279.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913758 + 2.81226i) q^{2} +(-3.83778 + 2.78831i) q^{4} +5.21585 q^{5} +(-5.08304 + 3.69304i) q^{7} +(-1.77924 - 1.29269i) q^{8} +(4.76602 + 14.6683i) q^{10} +(3.31109 + 4.55732i) q^{11} +(6.36975 + 2.06966i) q^{13} +(-15.0305 - 10.9203i) q^{14} +(-3.85401 + 11.8614i) q^{16} +(-13.9543 + 19.2065i) q^{17} +(-1.04359 - 3.21183i) q^{19} +(-20.0173 + 14.5434i) q^{20} +(-9.79083 + 13.4759i) q^{22} +(5.24664 - 7.22139i) q^{23} +2.20508 q^{25} +19.8046i q^{26} +(9.21022 - 28.3461i) q^{28} +(18.6515 - 6.06023i) q^{29} +(16.9290 - 25.9694i) q^{31} -45.6760 q^{32} +(-66.7644 - 21.6931i) q^{34} +(-26.5124 + 19.2624i) q^{35} -7.37919i q^{37} +(8.07892 - 5.86968i) q^{38} +(-9.28025 - 6.74249i) q^{40} +(8.96363 + 27.5872i) q^{41} +(10.2018 - 3.31478i) q^{43} +(-25.4144 - 8.25765i) q^{44} +(25.1026 + 8.15632i) q^{46} +(22.3601 - 68.8174i) q^{47} +(-2.94313 + 9.05803i) q^{49} +(2.01491 + 6.20127i) q^{50} +(-30.2165 + 9.81794i) q^{52} +(-7.30390 + 10.0530i) q^{53} +(17.2701 + 23.7703i) q^{55} +13.8179 q^{56} +(34.0859 + 46.9152i) q^{58} +(24.3552 - 74.9577i) q^{59} -61.8106i q^{61} +(88.5016 + 23.8791i) q^{62} +(-26.3208 - 81.0072i) q^{64} +(33.2237 + 10.7950i) q^{65} +63.5225 q^{67} -112.619i q^{68} +(-78.3966 - 56.9585i) q^{70} +(-20.4625 - 14.8669i) q^{71} +(73.0291 + 100.516i) q^{73} +(20.7522 - 6.74279i) q^{74} +(12.9606 + 9.41645i) q^{76} +(-33.6608 - 10.9370i) q^{77} +(40.3121 - 55.4848i) q^{79} +(-20.1019 + 61.8673i) q^{80} +(-69.3918 + 50.4161i) q^{82} +(14.4260 - 4.68729i) q^{83} +(-72.7836 + 100.178i) q^{85} +(18.6440 + 25.6613i) q^{86} -12.3888i q^{88} +(91.9646 + 126.578i) q^{89} +(-40.0210 + 13.0036i) q^{91} +42.3433i q^{92} +213.964 q^{94} +(-5.44320 - 16.7524i) q^{95} +(-75.4306 + 54.8035i) q^{97} -28.1628 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - 11 q^{4} + 14 q^{5} - q^{7} + 19 q^{8} + 12 q^{10} + 10 q^{11} + 10 q^{13} - 103 q^{16} - 35 q^{17} + 47 q^{19} + 125 q^{20} + 150 q^{22} - 75 q^{23} + 82 q^{25} + 88 q^{28} - 5 q^{29}+ \cdots + 1000 q^{98}+O(q^{100}) \) 20 * q + 3 * q^2 - 11 * q^4 + 14 * q^5 - q^7 + 19 * q^8 + 12 * q^10 + 10 * q^11 + 10 * q^13 - 103 * q^16 - 35 * q^17 + 47 * q^19 + 125 * q^20 + 150 * q^22 - 75 * q^23 + 82 * q^25 + 88 * q^28 - 5 * q^29 + 73 * q^31 - 226 * q^32 - 265 * q^34 + 50 * q^35 - 8 * q^38 - 466 * q^40 + 98 * q^41 + 245 * q^43 - 380 * q^44 - 445 * q^46 + 187 * q^47 + 328 * q^49 + 44 * q^50 - 15 * q^52 - 25 * q^53 + 190 * q^55 - 64 * q^56 - 85 * q^58 + 173 * q^59 + 40 * q^62 - 469 * q^64 + 345 * q^65 + 76 * q^67 - 11 * q^70 + 467 * q^71 - 15 * q^73 - 45 * q^74 + 55 * q^76 + 320 * q^77 + 500 * q^79 - 1030 * q^80 + 178 * q^82 + 50 * q^83 + 20 * q^85 - 1125 * q^86 - 55 * q^89 + 300 * q^91 + 62 * q^94 + 559 * q^95 - 405 * q^97 + 1000 * q^98

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