LMFDB - Embedded newform 528.3.bf.c.145.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [528,3,Mod(145,528)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(528, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("528.145"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	528.bf (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,8,0,-60,0,-12,0,4,0,-60,0,-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:	$14.3869579582$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			145.1
Root			$0.304260 - 0.418778i$ of defining polynomial
Character	$\chi$	$=$	528.145
Dual form			528.3.bf.c.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40126 + 1.01807i) q^{3} +(0.109202 + 0.336090i) q^{5} +(-0.464787 + 0.639725i) q^{7} +(0.927051 - 2.85317i) q^{9} +(10.9281 - 1.25540i) q^{11} +(0.198988 + 0.0646551i) q^{13} +(-0.495185 - 0.359773i) q^{15} +(-14.2369 + 4.62586i) q^{17} +(1.27522 + 1.75519i) q^{19} -1.36961i q^{21} +24.1342 q^{23} +(20.1244 - 14.6212i) q^{25} +(1.60570 + 4.94183i) q^{27} +(-10.4767 + 14.4199i) q^{29} +(-10.4564 + 32.1814i) q^{31} +(-14.0350 + 12.8848i) q^{33} +(-0.265761 - 0.0863510i) q^{35} +(48.6102 + 35.3174i) q^{37} +(-0.344657 + 0.111986i) q^{39} +(31.4796 + 43.3280i) q^{41} +15.5727i q^{43} +1.06016 q^{45} +(-49.4759 + 35.9463i) q^{47} +(14.9486 + 46.0071i) q^{49} +(15.2402 - 20.9763i) q^{51} +(18.2219 - 56.0812i) q^{53} +(1.61531 + 3.53574i) q^{55} +(-3.57382 - 1.16121i) q^{57} +(-41.6528 - 30.2625i) q^{59} +(38.7576 - 12.5931i) q^{61} +(1.39436 + 1.91917i) q^{63} +0.0739383i q^{65} +72.9302 q^{67} +(-33.8182 + 24.5704i) q^{69} +(29.3727 + 90.3998i) q^{71} +(-66.7272 + 91.8421i) q^{73} +(-13.3140 + 40.9762i) q^{75} +(-4.27614 + 7.57449i) q^{77} +(139.926 + 45.4646i) q^{79} +(-7.28115 - 5.29007i) q^{81} +(18.9025 - 6.14179i) q^{83} +(-3.10941 - 4.27974i) q^{85} -30.8721i q^{87} -74.9710 q^{89} +(-0.133848 + 0.0972466i) q^{91} +(-18.1110 - 55.7399i) q^{93} +(-0.450645 + 0.620259i) q^{95} +(31.3671 - 96.5379i) q^{97} +(6.54905 - 32.3436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} - 60 q^{7} - 12 q^{9} + 4 q^{11} - 60 q^{13} - 12 q^{15} - 60 q^{17} + 8 q^{23} - 48 q^{25} - 160 q^{29} - 32 q^{31} + 36 q^{33} - 160 q^{35} - 84 q^{37} + 40 q^{41} + 24 q^{45} - 372 q^{47}+ \cdots - 48 q^{99}+O(q^{100}) $ 16 * q + 8 * q^5 - 60 * q^7 - 12 * q^9 + 4 * q^11 - 60 * q^13 - 12 * q^15 - 60 * q^17 + 8 * q^23 - 48 * q^25 - 160 * q^29 - 32 * q^31 + 36 * q^33 - 160 * q^35 - 84 * q^37 + 40 * q^41 + 24 * q^45 - 372 * q^47 + 96 * q^49 - 120 * q^51 - 124 * q^53 - 32 * q^55 - 120 * q^57 + 172 * q^59 + 100 * q^61 + 180 * q^63 - 248 * q^67 - 372 * q^69 - 48 * q^71 + 160 * q^73 - 192 * q^75 - 172 * q^77 + 460 * q^79 - 36 * q^81 + 420 * q^83 - 420 * q^85 - 360 * q^89 + 252 * q^91 - 24 * q^93 - 180 * q^95 + 324 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.40126	+	1.01807i	−0.467086	+	0.339358i
$3$	−1.40126	+	1.01807i	−0.467086	+	0.339358i
$4$		0			0
$5$	0.109202	+	0.336090i	0.0218405	+	0.0672180i	0.961383	−	0.275215i	$-0.0887490\pi$
$5$	0.109202	+	0.336090i	0.0218405	+	0.0672180i	−0.939542	+	0.342433i	$0.888749\pi$
$6$		0			0
$7$	−0.464787	+	0.639725i	−0.0663982	+	0.0913893i	−0.840925	−	0.541152i	$-0.817988\pi$
$7$	−0.464787	+	0.639725i	−0.0663982	+	0.0913893i	0.774526	+	0.632542i	$0.217988\pi$
$8$		0			0
$9$	0.927051	−	2.85317i	0.103006	−	0.317019i
$10$		0			0
$11$	10.9281	−	1.25540i	0.993466	−	0.114128i
$11$	10.9281	−	1.25540i	0.993466	−	0.114128i
$12$		0			0
$13$	0.198988	+	0.0646551i	0.0153068	+	0.00497347i	0.316660	−	0.948539i	$-0.397438\pi$
$13$	0.198988	+	0.0646551i	0.0153068	+	0.00497347i	−0.301354	+	0.953512i	$0.597438\pi$
$14$		0			0
$15$	−0.495185	−	0.359773i	−0.0330124	−	0.0239849i
$16$		0			0
$17$	−14.2369	+	4.62586i	−0.837467	+	0.272109i	−0.696187	−	0.717860i	$-0.745122\pi$
$17$	−14.2369	+	4.62586i	−0.837467	+	0.272109i	−0.141280	+	0.989970i	$0.545122\pi$
$18$		0			0
$19$	1.27522	+	1.75519i	0.0671168	+	0.0923783i	0.841256	−	0.540637i	$-0.181817\pi$
$19$	1.27522	+	1.75519i	0.0671168	+	0.0923783i	−0.774139	+	0.633016i	$0.781817\pi$
$20$		0			0
$21$		−	1.36961i		−	0.0652194i
$22$		0			0
$23$	24.1342			1.04931			0.524656	−	0.851314i	$-0.324194\pi$
$23$	24.1342			1.04931			0.524656	+	0.851314i	$0.324194\pi$
$24$		0			0
$25$	20.1244	−	14.6212i	0.804976	−	0.584849i
$26$		0			0
$27$	1.60570	+	4.94183i	0.0594703	+	0.183031i
$28$		0			0
$29$	−10.4767	+	14.4199i	−0.361265	+	0.497239i	−0.950501	−	0.310723i	$-0.899429\pi$
$29$	−10.4767	+	14.4199i	−0.361265	+	0.497239i	0.589236	+	0.807961i	$0.299429\pi$
$30$		0			0
$31$	−10.4564	+	32.1814i	−0.337303	+	1.03811i	0.628274	+	0.777992i	$0.283762\pi$
$31$	−10.4564	+	32.1814i	−0.337303	+	1.03811i	−0.965577	+	0.260119i	$0.916238\pi$
$32$		0			0
$33$	−14.0350	+	12.8848i	−0.425304	+	0.390448i
$34$		0			0
$35$	−0.265761	−	0.0863510i	−0.00759318	−	0.00246717i
$36$		0			0
$37$	48.6102	+	35.3174i	1.31379	+	0.954524i	0.999987	+	0.00503636i	$0.00160313\pi$
$37$	48.6102	+	35.3174i	1.31379	+	0.954524i	0.313803	+	0.949488i	$0.398397\pi$
$38$		0			0
$39$	−0.344657	+	0.111986i	−0.00883736	+	0.00287143i
$40$		0			0
$41$	31.4796	+	43.3280i	0.767796	+	1.05678i	0.996525	+	0.0832904i	$0.0265429\pi$
$41$	31.4796	+	43.3280i	0.767796	+	1.05678i	−0.228729	+	0.973490i	$0.573457\pi$
$42$		0			0
$43$			15.5727i			0.362157i	0.983469	+	0.181078i	$0.0579588\pi$
$43$			15.5727i			0.362157i	−0.983469	+	0.181078i	$0.942041\pi$
$44$		0			0
$45$	1.06016			0.0235591
$46$		0			0
$47$	−49.4759	+	35.9463i	−1.05268	+	0.764816i	−0.972720	−	0.231983i	$-0.925479\pi$
$47$	−49.4759	+	35.9463i	−1.05268	+	0.764816i	−0.0799585	+	0.996798i	$0.525479\pi$
$48$		0			0
$49$	14.9486	+	46.0071i	0.305074	+	0.938920i
$50$		0			0
$51$	15.2402	−	20.9763i	0.298827	−	0.411300i
$52$		0			0
$53$	18.2219	−	56.0812i	0.343809	−	1.05814i	−0.618409	−	0.785857i	$-0.712222\pi$
$53$	18.2219	−	56.0812i	0.343809	−	1.05814i	0.962218	−	0.272280i	$-0.0877776\pi$
$54$		0			0
$55$	1.61531	+	3.53574i	0.0293692	+	0.0642863i
$56$		0			0
$57$	−3.57382	−	1.16121i	−0.0626987	−	0.0203720i
$58$		0			0
$59$	−41.6528	−	30.2625i	−0.705980	−	0.512924i	0.175894	−	0.984409i	$-0.443718\pi$
$59$	−41.6528	−	30.2625i	−0.705980	−	0.512924i	−0.881874	+	0.471485i	$0.843718\pi$
$60$		0			0
$61$	38.7576	−	12.5931i	0.635371	−	0.206445i	0.0264182	−	0.999651i	$-0.491590\pi$
$61$	38.7576	−	12.5931i	0.635371	−	0.206445i	0.608953	+	0.793206i	$0.291590\pi$
$62$		0			0
$63$	1.39436	+	1.91917i	0.0221327	+	0.0304631i
$64$		0			0
$65$			0.0739383i			0.00113751i
$66$		0			0
$67$	72.9302			1.08851			0.544255	−	0.838920i	$-0.316812\pi$
$67$	72.9302			1.08851			0.544255	+	0.838920i	$0.316812\pi$
$68$		0			0
$69$	−33.8182	+	24.5704i	−0.490119	+	0.356092i
$70$		0			0
$71$	29.3727	+	90.3998i	0.413700	+	1.27324i	0.913409	+	0.407043i	$0.133440\pi$
$71$	29.3727	+	90.3998i	0.413700	+	1.27324i	−0.499709	+	0.866193i	$0.666560\pi$
$72$		0			0
$73$	−66.7272	+	91.8421i	−0.914071	+	1.25811i	0.0516858	+	0.998663i	$0.483541\pi$
$73$	−66.7272	+	91.8421i	−0.914071	+	1.25811i	−0.965757	+	0.259448i	$0.916459\pi$
$74$		0			0
$75$	−13.3140	+	40.9762i	−0.177520	+	0.546350i
$76$		0			0
$77$	−4.27614	+	7.57449i	−0.0555343	+	0.0983700i
$78$		0			0
$79$	139.926	+	45.4646i	1.77121	+	0.575502i	0.998260	−	0.0589621i	$-0.0187791\pi$
$79$	139.926	+	45.4646i	1.77121	+	0.575502i	0.772952	+	0.634464i	$0.218779\pi$
$80$		0			0
$81$	−7.28115	−	5.29007i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	18.9025	−	6.14179i	0.227741	−	0.0739974i	−0.192924	−	0.981214i	$-0.561797\pi$
$83$	18.9025	−	6.14179i	0.227741	−	0.0739974i	0.420664	+	0.907216i	$0.361797\pi$
$84$		0			0
$85$	−3.10941	−	4.27974i	−0.0365813	−	0.0503499i
$86$		0			0
$87$		−	30.8721i		−	0.354851i
$88$		0			0
$89$	−74.9710			−0.842371			−0.421185	−	0.906975i	$-0.638386\pi$
$89$	−74.9710			−0.842371			−0.421185	+	0.906975i	$0.638386\pi$
$90$		0			0
$91$	−0.133848	+	0.0972466i	−0.00147086	+	0.00106864i
$92$		0			0
$93$	−18.1110	−	55.7399i	−0.194742	−	0.599353i
$94$		0			0
$95$	−0.450645	+	0.620259i	−0.00474363	+	0.00652905i
$96$		0			0
$97$	31.3671	−	96.5379i	0.323372	−	0.995236i	−0.648798	−	0.760960i	$-0.724728\pi$
$97$	31.3671	−	96.5379i	0.323372	−	0.995236i	0.972170	−	0.234276i	$-0.0752719\pi$
$98$		0			0
$99$	6.54905	−	32.3436i	0.0661521	−	0.326703i
$100$		0			0
$101$	24.8088	+	8.06086i	0.245631	+	0.0798105i	0.429245	−	0.903188i	$-0.358780\pi$
$101$	24.8088	+	8.06086i	0.245631	+	0.0798105i	−0.183614	+	0.982998i	$0.558780\pi$
$102$		0			0
$103$	−25.5133	−	18.5365i	−0.247702	−	0.179966i	0.457006	−	0.889464i	$-0.348922\pi$
$103$	−25.5133	−	18.5365i	−0.247702	−	0.179966i	−0.704708	+	0.709498i	$0.748922\pi$
$104$		0			0
$105$	0.460312	−	0.149564i	0.00438392	−	0.00142442i
$106$		0			0
$107$	−47.3389	−	65.1565i	−0.442420	−	0.608939i	0.528328	−	0.849040i	$-0.322819\pi$
$107$	−47.3389	−	65.1565i	−0.442420	−	0.608939i	−0.970748	+	0.240102i	$0.922819\pi$
$108$		0			0
$109$			32.1811i			0.295239i	0.989044	+	0.147620i	$0.0471612\pi$
$109$			32.1811i			0.295239i	−0.989044	+	0.147620i	$0.952839\pi$
$110$		0			0
$111$	−104.071			−0.937579
$112$		0			0
$113$	23.6264	−	17.1656i	0.209083	−	0.151908i	−0.478315	−	0.878188i	$-0.658752\pi$
$113$	23.6264	−	17.1656i	0.209083	−	0.151908i	0.687399	+	0.726280i	$0.258752\pi$
$114$		0			0
$115$	2.63551	+	8.11126i	0.0229175	+	0.0705327i
$116$		0			0
$117$	0.368944	−	0.507807i	0.00315336	−	0.00434023i
$118$		0			0
$119$	3.65787	−	11.2578i	0.0307384	−	0.0946031i
$120$		0			0
$121$	117.848	−	27.4384i	0.973950	−	0.226764i
$122$		0			0
$123$	−88.2222	−	28.6651i	−0.717254	−	0.233050i
$124$		0			0
$125$	14.2591	+	10.3598i	0.114073	+	0.0828786i
$126$		0			0
$127$	−141.757	+	46.0595i	−1.11619	+	0.362673i	−0.808314	−	0.588752i	$-0.799620\pi$
$127$	−141.757	+	46.0595i	−1.11619	+	0.362673i	−0.307880	+	0.951425i	$0.599620\pi$
$128$		0			0
$129$	−15.8542	−	21.8214i	−0.122901	−	0.169159i
$130$		0			0
$131$		−	165.965i		−	1.26691i	−0.773780	−	0.633454i	$-0.781636\pi$
$131$		−	165.965i		−	1.26691i	0.773780	−	0.633454i	$-0.218364\pi$
$132$		0			0
$133$	−1.71554			−0.0128988
$134$		0			0
$135$	−1.48556	+	1.07932i	−0.0110041	+	0.00799496i
$136$		0			0
$137$	−45.3846	−	139.680i	−0.331275	−	1.01956i	−0.968528	−	0.248904i	$-0.919930\pi$
$137$	−45.3846	−	139.680i	−0.331275	−	1.01956i	0.637253	−	0.770654i	$-0.280070\pi$
$138$		0			0
$139$	125.653	−	172.947i	0.903982	−	1.24422i	−0.0651984	−	0.997872i	$-0.520768\pi$
$139$	125.653	−	172.947i	0.903982	−	1.24422i	0.969180	−	0.246352i	$-0.0792320\pi$
$140$		0			0
$141$	32.7325	−	100.740i	0.232145	−	0.714470i
$142$		0			0
$143$	2.25573	+	0.456749i	0.0157744	+	0.00319405i
$144$		0			0
$145$	−5.99047	−	1.94642i	−0.0413136	−	0.0134236i
$146$		0			0
$147$	−67.7855	−	49.2490i	−0.461126	−	0.335028i
$148$		0			0
$149$	−219.924	+	71.4578i	−1.47600	+	0.479582i	−0.932916	−	0.360094i	$-0.882745\pi$
$149$	−219.924	+	71.4578i	−1.47600	+	0.479582i	−0.543087	+	0.839677i	$0.682745\pi$
$150$		0			0
$151$	156.589	+	215.527i	1.03701	+	1.42733i	0.899548	+	0.436822i	$0.143896\pi$
$151$	156.589	+	215.527i	1.03701	+	1.42733i	0.137467	+	0.990506i	$0.456104\pi$
$152$		0			0
$153$			44.9088i			0.293522i
$154$		0			0
$155$	−11.9577			−0.0771466
$156$		0			0
$157$	84.3629	−	61.2933i	0.537344	−	0.390403i	−0.285754	−	0.958303i	$-0.592244\pi$
$157$	84.3629	−	61.2933i	0.537344	−	0.390403i	0.823098	+	0.567900i	$0.192244\pi$
$158$		0			0
$159$	31.5612	+	97.1355i	0.198498	+	0.610915i
$160$		0			0
$161$	−11.2173	+	15.4392i	−0.0696724	+	0.0958959i
$162$		0			0
$163$	86.4221	−	265.980i	0.530197	−	1.63178i	−0.223607	−	0.974679i	$-0.571783\pi$
$163$	86.4221	−	265.980i	0.530197	−	1.63178i	0.753804	−	0.657099i	$-0.228217\pi$
$164$		0			0
$165$	−5.86311	−	3.30999i	−0.0355340	−	0.0200605i
$166$		0			0
$167$	−244.370	−	79.4006i	−1.46329	−	0.475453i	−0.534219	−	0.845346i	$-0.679394\pi$
$167$	−244.370	−	79.4006i	−1.46329	−	0.475453i	−0.929074	+	0.369893i	$0.879394\pi$
$168$		0			0
$169$	−136.688	−	99.3100i	−0.808807	−	0.587633i
$170$		0			0
$171$	6.19004	−	2.01127i	0.0361991	−	0.0117618i
$172$		0			0
$173$	−64.7673	−	89.1445i	−0.374377	−	0.515286i	0.579707	−	0.814825i	$-0.303167\pi$
$173$	−64.7673	−	89.1445i	−0.374377	−	0.515286i	−0.954084	+	0.299539i	$0.903167\pi$
$174$		0			0
$175$			19.6698i			0.112399i
$176$		0			0
$177$	89.1759			0.503819
$178$		0			0
$179$	21.9460	−	15.9447i	0.122603	−	0.0890764i	−0.524794	−	0.851229i	$-0.675858\pi$
$179$	21.9460	−	15.9447i	0.122603	−	0.0890764i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	80.2120	+	246.867i	0.443160	+	1.36391i	0.884489	+	0.466561i	$0.154507\pi$
$181$	80.2120	+	246.867i	0.443160	+	1.36391i	−0.441329	+	0.897345i	$0.645493\pi$
$182$		0			0
$183$	−41.4887	+	57.1044i	−0.226714	+	0.312046i
$184$		0			0
$185$	−6.56148	+	20.1942i	−0.0354675	+	0.109158i
$186$		0			0
$187$	−149.776	+	68.4251i	−0.800940	+	0.365910i
$188$		0			0
$189$	−3.90772	−	1.26970i	−0.0206758	−	0.00671797i
$190$		0			0
$191$	−100.951	−	73.3452i	−0.528539	−	0.384006i	0.291272	−	0.956640i	$-0.405922\pi$
$191$	−100.951	−	73.3452i	−0.528539	−	0.384006i	−0.819811	+	0.572634i	$0.805922\pi$
$192$		0			0
$193$	39.9341	−	12.9754i	0.206912	−	0.0672299i	−0.203727	−	0.979028i	$-0.565306\pi$
$193$	39.9341	−	12.9754i	0.206912	−	0.0672299i	0.410639	+	0.911798i	$0.365306\pi$
$194$		0			0
$195$	−0.0752747	−	0.103607i	−0.000386024	−	0.000531317i
$196$		0			0
$197$		−	274.338i		−	1.39258i	−0.717760	−	0.696290i	$-0.754833\pi$
$197$		−	274.338i		−	1.39258i	0.717760	−	0.696290i	$-0.245167\pi$
$198$		0			0
$199$	150.979			0.758690			0.379345	−	0.925255i	$-0.376149\pi$
$199$	150.979			0.758690			0.379345	+	0.925255i	$0.376149\pi$
$200$		0			0
$201$	−102.194	+	74.2483i	−0.508428	+	0.369395i
$202$		0			0
$203$	−4.35535	−	13.4044i	−0.0214549	−	0.0660315i
$204$		0			0
$205$	−11.1245	+	15.3115i	−0.0542657	+	0.0746903i
$206$		0			0
$207$	22.3736	−	68.8589i	0.108085	−	0.332652i
$208$		0			0
$209$	16.1392	+	17.5800i	0.0772212	+	0.0841149i
$210$		0			0
$211$	17.7693	+	5.77360i	0.0842147	+	0.0273630i	0.350821	−	0.936442i	$-0.385902\pi$
$211$	17.7693	+	5.77360i	0.0842147	+	0.0273630i	−0.266607	+	0.963805i	$0.585902\pi$
$212$		0			0
$213$	−133.192	−	96.7699i	−0.625316	−	0.454319i
$214$		0			0
$215$	−5.23385	+	1.70058i	−0.0243435	+	0.00790968i
$216$		0			0
$217$	−15.7273	−	21.6467i	−0.0724759	−	0.0997545i
$218$		0			0
$219$		−	196.628i		−	0.897844i
$220$		0			0
$221$	−3.13206			−0.0141722
$222$		0			0
$223$	−76.2747	+	55.4168i	−0.342039	+	0.248506i	−0.745522	−	0.666481i	$-0.767800\pi$
$223$	−76.2747	+	55.4168i	−0.342039	+	0.248506i	0.403483	+	0.914987i	$0.367800\pi$
$224$		0			0
$225$	−23.0605	−	70.9729i	−0.102491	−	0.315435i
$226$		0			0
$227$	−170.335	+	234.446i	−0.750374	+	1.03280i	0.247580	+	0.968867i	$0.420365\pi$
$227$	−170.335	+	234.446i	−0.750374	+	1.03280i	−0.997954	+	0.0639340i	$0.979635\pi$
$228$		0			0
$229$	−70.5265	+	217.058i	−0.307976	+	0.947852i	0.670574	+	0.741843i	$0.266048\pi$
$229$	−70.5265	+	217.058i	−0.307976	+	0.947852i	−0.978550	+	0.206010i	$0.933952\pi$
$230$		0			0
$231$	−1.71941	−	14.9673i	−0.00744333	−	0.0647933i
$232$		0			0
$233$	284.201	+	92.3427i	1.21975	+	0.396320i	0.846990	−	0.531608i	$-0.178412\pi$
$233$	284.201	+	92.3427i	1.21975	+	0.396320i	0.372758	+	0.927928i	$0.378412\pi$
$234$		0			0
$235$	−17.4841	−	12.7029i	−0.0744004	−	0.0540551i
$236$		0			0
$237$	−242.359	+	78.7471i	−1.02261	+	0.332266i
$238$		0			0
$239$	144.554	+	198.961i	0.604827	+	0.832473i	0.996139	−	0.0877850i	$-0.0279789\pi$
$239$	144.554	+	198.961i	0.604827	+	0.832473i	−0.391313	+	0.920258i	$0.627979\pi$
$240$		0			0
$241$		−	373.418i		−	1.54945i	−0.632297	−	0.774726i	$-0.717888\pi$
$241$		−	373.418i		−	1.54945i	0.632297	−	0.774726i	$-0.282112\pi$
$242$		0			0
$243$	15.5885			0.0641500
$244$		0			0
$245$	−13.8301	+	10.0482i	−0.0564494	+	0.0410129i
$246$		0			0
$247$	0.140271	+	0.431710i	0.000567900	+	0.00174782i
$248$		0			0
$249$	−20.2345	+	27.8504i	−0.0812629	+	0.111849i
$250$		0			0
$251$	111.067	−	341.831i	0.442500	−	1.36187i	−0.442702	−	0.896669i	$-0.645980\pi$
$251$	111.067	−	341.831i	0.442500	−	1.36187i	0.885202	−	0.465206i	$-0.154020\pi$
$252$		0			0
$253$	263.741	−	30.2981i	1.04246	−	0.119755i
$254$		0			0
$255$	8.71418	+	2.83141i	0.0341733	+	0.0111036i
$256$		0			0
$257$	28.9501	+	21.0334i	0.112646	+	0.0818422i	0.642682	−	0.766133i	$-0.277822\pi$
$257$	28.9501	+	21.0334i	0.112646	+	0.0818422i	−0.530036	+	0.847975i	$0.677822\pi$
$258$		0			0
$259$	−45.1869	+	14.6821i	−0.174467	+	0.0566876i
$260$		0			0
$261$	31.4301	+	43.2598i	0.120422	+	0.165746i
$262$		0			0
$263$			364.668i			1.38657i	0.720663	+	0.693286i	$0.243838\pi$
$263$			364.668i			1.38657i	−0.720663	+	0.693286i	$0.756162\pi$
$264$		0			0
$265$	20.8382			0.0786348
$266$		0			0
$267$	105.054	−	76.3260i	0.393460	−	0.285865i
$268$		0			0
$269$	−4.13369	−	12.7222i	−0.0153669	−	0.0472944i	0.943079	−	0.332569i	$-0.107915\pi$
$269$	−4.13369	−	12.7222i	−0.0153669	−	0.0472944i	−0.958446	+	0.285274i	$0.907915\pi$
$270$		0			0
$271$	−41.6402	+	57.3128i	−0.153654	+	0.211486i	−0.878904	−	0.477000i	$-0.841724\pi$
$271$	−41.6402	+	57.3128i	−0.153654	+	0.211486i	0.725250	+	0.688486i	$0.241724\pi$
$272$		0			0
$273$	0.0885521	−	0.272535i	0.000324367	−	0.000998298i
$274$		0			0
$275$	201.566	−	185.047i	0.732969	−	0.672898i
$276$		0			0
$277$	−75.4632	−	24.5195i	−0.272430	−	0.0885179i	0.169616	−	0.985510i	$-0.445747\pi$
$277$	−75.4632	−	24.5195i	−0.272430	−	0.0885179i	−0.442046	+	0.896992i	$0.645747\pi$
$278$		0			0
$279$	82.1255	+	59.6677i	0.294357	+	0.213863i
$280$		0			0
$281$	−326.300	+	106.021i	−1.16121	+	0.377300i	−0.825355	−	0.564614i	$-0.809025\pi$
$281$	−326.300	+	106.021i	−1.16121	+	0.377300i	−0.335854	+	0.941914i	$0.609025\pi$
$282$		0			0
$283$	70.3457	+	96.8225i	0.248571	+	0.342129i	0.915010	−	0.403430i	$-0.132182\pi$
$283$	70.3457	+	96.8225i	0.248571	+	0.342129i	−0.666439	+	0.745560i	$0.732182\pi$
$284$		0			0
$285$		−	1.32793i		−	0.00465942i
$286$		0			0
$287$	−42.3493			−0.147559
$288$		0			0
$289$	−52.5141	+	38.1538i	−0.181710	+	0.132020i
$290$		0			0
$291$	54.3294	+	167.209i	0.186699	+	0.574600i
$292$		0			0
$293$	6.76900	−	9.31673i	0.0231024	−	0.0317977i	−0.797310	−	0.603571i	$-0.793744\pi$
$293$	6.76900	−	9.31673i	0.0231024	−	0.0317977i	0.820412	+	0.571773i	$0.193744\pi$
$294$		0			0
$295$	5.62236	−	17.3038i	0.0190588	−	0.0586571i
$296$		0			0
$297$	23.7513	+	51.9892i	0.0799706	+	0.175048i
$298$		0			0
$299$	4.80241	+	1.56040i	0.0160616	+	0.00521872i
$300$		0			0
$301$	−9.96228	−	7.23802i	−0.0330973	−	0.0240466i
$302$		0			0
$303$	−42.9701	+	13.9618i	−0.141815	+	0.0460786i
$304$		0			0
$305$	8.46485	+	11.6509i	0.0277536	+	0.0381996i
$306$		0			0
$307$		−	196.858i		−	0.641231i	−0.947210	−	0.320615i	$-0.896110\pi$
$307$		−	196.858i		−	0.641231i	0.947210	−	0.320615i	$-0.103890\pi$
$308$		0			0
$309$	54.6223			0.176771
$310$		0			0
$311$	218.771	−	158.946i	0.703443	−	0.511082i	−0.177608	−	0.984101i	$-0.556836\pi$
$311$	218.771	−	158.946i	0.703443	−	0.511082i	0.881052	+	0.473020i	$0.156836\pi$
$312$		0			0
$313$	106.490	+	327.743i	0.340224	+	1.04710i	0.964091	+	0.265572i	$0.0855608\pi$
$313$	106.490	+	327.743i	0.340224	+	1.04710i	−0.623867	+	0.781531i	$0.714439\pi$
$314$		0			0
$315$	−0.492748	+	0.678210i	−0.00156428	+	0.00215305i
$316$		0			0
$317$	20.2627	−	62.3621i	0.0639201	−	0.196726i	−0.913996	−	0.405723i	$-0.867020\pi$
$317$	20.2627	−	62.3621i	0.0639201	−	0.196726i	0.977916	+	0.208997i	$0.0670198\pi$
$318$		0			0
$319$	−96.3877	+	170.735i	−0.302156	+	0.535220i
$320$		0			0
$321$	132.668	+	43.1065i	0.413297	+	0.134288i
$322$		0			0
$323$	−26.2745	−	19.0895i	−0.0813451	−	0.0591007i
$324$		0			0
$325$	4.94985	−	1.60830i	0.0152303	−	0.00494862i
$326$		0			0
$327$	−32.7627	−	45.0940i	−0.100192	−	0.137902i
$328$		0			0
$329$		−	48.3584i		−	0.146986i
$330$		0			0
$331$	−105.818			−0.319693			−0.159847	−	0.987142i	$-0.551100\pi$
$331$	−105.818			−0.319693			−0.159847	+	0.987142i	$0.551100\pi$
$332$		0			0
$333$	145.831	−	105.952i	0.437930	−	0.318175i
$334$		0			0
$335$	7.96415	+	24.5111i	0.0237736	+	0.0731675i
$336$		0			0
$337$	132.617	−	182.531i	0.393521	−	0.541635i	−0.565582	−	0.824692i	$-0.691348\pi$
$337$	132.617	−	182.531i	0.393521	−	0.541635i	0.959103	+	0.283057i	$0.0913485\pi$
$338$		0			0
$339$	−15.6309	+	48.1069i	−0.0461088	+	0.141908i
$340$		0			0
$341$	−73.8680	+	364.810i	−0.216622	+	1.06982i
$342$		0			0
$343$	−73.2299	−	23.7938i	−0.213498	−	0.0693698i
$344$		0			0
$345$	−11.9509	−	8.68283i	−0.0346403	−	0.0251676i
$346$		0			0
$347$	−128.933	+	41.8930i	−0.371566	+	0.120729i	−0.488847	−	0.872370i	$-0.662582\pi$
$347$	−128.933	+	41.8930i	−0.371566	+	0.120729i	0.117281	+	0.993099i	$0.462582\pi$
$348$		0			0
$349$	293.983	+	404.633i	0.842358	+	1.15941i	0.985495	+	0.169704i	$0.0542811\pi$
$349$	293.983	+	404.633i	0.842358	+	1.15941i	−0.143137	+	0.989703i	$0.545719\pi$
$350$		0			0
$351$			1.08718i			0.00309738i
$352$		0			0
$353$	320.592			0.908192			0.454096	−	0.890953i	$-0.349962\pi$
$353$	320.592			0.908192			0.454096	+	0.890953i	$0.349962\pi$
$354$		0			0
$355$	−27.1749	+	19.7437i	−0.0765491	+	0.0556162i
$356$		0			0
$357$	6.33562	+	19.4990i	0.0177468	+	0.0546191i
$358$		0			0
$359$	−66.6745	+	91.7696i	−0.185723	+	0.255626i	−0.891718	−	0.452591i	$-0.850500\pi$
$359$	−66.6745	+	91.7696i	−0.185723	+	0.255626i	0.705996	+	0.708216i	$0.250500\pi$
$360$		0			0
$361$	110.101	−	338.855i	0.304988	−	0.938656i
$362$		0			0
$363$	−137.201	+	158.426i	−0.377964	+	0.436436i
$364$		0			0
$365$	−38.1540	−	12.3970i	−0.104532	−	0.0339644i
$366$		0			0
$367$	72.4621	+	52.6468i	0.197444	+	0.143452i	0.682115	−	0.731245i	$-0.261060\pi$
$367$	72.4621	+	52.6468i	0.197444	+	0.143452i	−0.484670	+	0.874697i	$0.661060\pi$
$368$		0			0
$369$	152.805	−	49.6495i	0.414107	−	0.134551i
$370$		0			0
$371$	27.4073	+	37.7228i	0.0738740	+	0.101679i
$372$		0			0
$373$			275.552i			0.738744i	0.929282	+	0.369372i	$0.120427\pi$
$373$			275.552i			0.738744i	−0.929282	+	0.369372i	$0.879573\pi$
$374$		0			0
$375$	−30.5277			−0.0814072
$376$		0			0
$377$	−3.01705	+	2.19202i	−0.00800279	+	0.00581437i
$378$		0			0
$379$	54.2463	+	166.953i	0.143130	+	0.440509i	0.996766	−	0.0803612i	$-0.0256074\pi$
$379$	54.2463	+	166.953i	0.143130	+	0.440509i	−0.853636	+	0.520871i	$0.825607\pi$
$380$		0			0
$381$	151.746	−	208.860i	0.398283	−	0.548189i
$382$		0			0
$383$	15.8151	−	48.6740i	0.0412928	−	0.127086i	−0.928285	−	0.371870i	$-0.878717\pi$
$383$	15.8151	−	48.6740i	0.0412928	−	0.127086i	0.969578	+	0.244783i	$0.0787169\pi$
$384$		0			0
$385$	−3.01268	−	0.610018i	−0.00782514	−	0.00158446i
$386$		0			0
$387$	44.4317	+	14.4367i	0.114811	+	0.0373042i
$388$		0			0
$389$	18.5317	+	13.4641i	0.0476393	+	0.0346120i	0.611350	−	0.791360i	$-0.290627\pi$
$389$	18.5317	+	13.4641i	0.0476393	+	0.0346120i	−0.563711	+	0.825972i	$0.690627\pi$
$390$		0			0
$391$	−343.597	+	111.641i	−0.878764	+	0.285528i
$392$		0			0
$393$	168.965	+	232.560i	0.429936	+	0.591755i
$394$		0			0
$395$			51.9925i			0.131627i
$396$		0			0
$397$	131.054			0.330112			0.165056	−	0.986284i	$-0.447220\pi$
$397$	131.054			0.330112			0.165056	+	0.986284i	$0.447220\pi$
$398$		0			0
$399$	2.40392	−	1.74655i	0.00602486	−	0.00437732i
$400$		0			0
$401$	239.751	+	737.877i	0.597882	+	1.84009i	0.539823	+	0.841778i	$0.318491\pi$
$401$	239.751	+	737.877i	0.597882	+	1.84009i	0.0580587	+	0.998313i	$0.481509\pi$
$402$		0			0
$403$	−4.16138	+	5.72765i	−0.0103260	+	0.0142125i
$404$		0			0
$405$	0.982821	−	3.02481i	0.00242672	−	0.00746867i
$406$		0			0
$407$	575.556	+	324.928i	1.41414	+	0.798348i
$408$		0			0
$409$	−710.800	−	230.953i	−1.73790	−	0.564677i	−0.743345	−	0.668909i	$-0.766762\pi$
$409$	−710.800	−	230.953i	−1.73790	−	0.564677i	−0.994553	+	0.104232i	$0.966762\pi$
$410$		0			0
$411$	205.800	+	149.522i	0.500729	+	0.363801i
$412$		0			0
$413$	38.7194	−	12.5807i	0.0937516	−	0.0304617i
$414$		0			0
$415$	4.12839	+	5.68224i	0.00994793	+	0.0136921i
$416$		0			0
$417$			370.268i			0.887934i
$418$		0			0
$419$	408.427			0.974765			0.487383	−	0.873189i	$-0.337952\pi$
$419$	408.427			0.974765			0.487383	+	0.873189i	$0.337952\pi$
$420$		0			0
$421$	−84.5514	+	61.4302i	−0.200835	+	0.145915i	−0.683657	−	0.729803i	$-0.739612\pi$
$421$	−84.5514	+	61.4302i	−0.200835	+	0.145915i	0.482823	+	0.875718i	$0.339612\pi$
$422$		0			0
$423$	56.6943	+	174.487i	0.134029	+	0.412499i
$424$		0			0
$425$	−218.874	+	301.254i	−0.514998	+	0.708833i
$426$		0			0
$427$	−9.95793	+	30.6473i	−0.0233207	+	0.0717737i
$428$		0			0
$429$	−3.62587	+	1.65648i	−0.00845191	+	0.00386126i
$430$		0			0
$431$	274.915	+	89.3253i	0.637854	+	0.207251i	0.610051	−	0.792362i	$-0.291149\pi$
$431$	274.915	+	89.3253i	0.637854	+	0.207251i	0.0278030	+	0.999613i	$0.491149\pi$
$432$		0			0
$433$	−445.768	−	323.869i	−1.02949	−	0.747966i	−0.0612810	−	0.998121i	$-0.519519\pi$
$433$	−445.768	−	323.869i	−1.02949	−	0.747966i	−0.968206	+	0.250154i	$0.919519\pi$
$434$		0			0
$435$	10.3758	−	3.37130i	0.0238524	−	0.00775012i
$436$		0			0
$437$	30.7764	+	42.3600i	0.0704265	+	0.0969337i
$438$		0			0
$439$		−	576.891i		−	1.31410i	−0.753846	−	0.657051i	$-0.771804\pi$
$439$		−	576.891i		−	1.31410i	0.753846	−	0.657051i	$-0.228196\pi$
$440$		0			0
$441$	145.124			0.329080
$442$		0			0
$443$	−144.200	+	104.767i	−0.325508	+	0.236495i	−0.738522	−	0.674229i	$-0.764476\pi$
$443$	−144.200	+	104.767i	−0.325508	+	0.236495i	0.413014	+	0.910724i	$0.364476\pi$
$444$		0			0
$445$	−8.18701	−	25.1970i	−0.0183978	−	0.0566225i
$446$		0			0
$447$	235.422	−	324.030i	0.526670	−	0.724900i
$448$		0			0
$449$	192.428	−	592.233i	0.428570	−	1.31900i	−0.470963	−	0.882153i	$-0.656094\pi$
$449$	192.428	−	592.233i	0.428570	−	1.31900i	0.899534	−	0.436851i	$-0.143906\pi$
$450$		0			0
$451$	398.408	+	433.974i	0.883387	+	0.962249i
$452$		0			0
$453$	−438.844	−	142.589i	−0.968750	−	0.314766i
$454$		0			0
$455$	−0.0473002	−	0.0343656i	−0.000103956	−	7.55288e-5i
$456$		0			0
$457$	−749.250	+	243.446i	−1.63950	+	0.532704i	−0.976426	−	0.215853i	$-0.930747\pi$
$457$	−749.250	+	243.446i	−1.63950	+	0.532704i	−0.663070	+	0.748557i	$0.730747\pi$
$458$		0			0
$459$	−45.7205	−	62.9288i	−0.0996089	−	0.137100i
$460$		0			0
$461$		−	377.985i		−	0.819924i	−0.912103	−	0.409962i	$-0.865542\pi$
$461$		−	377.985i		−	0.819924i	0.912103	−	0.409962i	$-0.134458\pi$
$462$		0			0
$463$	49.3159			0.106514			0.0532569	−	0.998581i	$-0.483040\pi$
$463$	49.3159			0.106514			0.0532569	+	0.998581i	$0.483040\pi$
$464$		0			0
$465$	16.7559	−	12.1738i	0.0360341	−	0.0261803i
$466$		0			0
$467$	36.2129	+	111.452i	0.0775436	+	0.238655i	0.982313	−	0.187248i	$-0.0599567\pi$
$467$	36.2129	+	111.452i	0.0775436	+	0.238655i	−0.904769	+	0.425902i	$0.859957\pi$
$468$		0			0
$469$	−33.8970	+	46.6553i	−0.0722751	+	0.0994782i
$470$		0			0
$471$	−55.8132	+	171.775i	−0.118499	+	0.364704i
$472$		0			0
$473$	19.5501	+	170.181i	0.0413321	+	0.359791i
$474$		0			0
$475$	51.3260	+	16.6768i	0.108055	+	0.0351091i
$476$		0			0
$477$	−143.117	−	103.980i	−0.300035	−	0.217988i
$478$		0			0
$479$	−875.668	+	284.522i	−1.82812	+	0.593991i	−0.828705	+	0.559686i	$0.810922\pi$
$479$	−875.668	+	284.522i	−1.82812	+	0.593991i	−0.999411	+	0.0343053i	$0.989078\pi$
$480$		0			0
$481$	7.38940	+	10.1706i	0.0153626	+	0.0211448i
$482$		0			0
$483$		−	33.0544i		−	0.0684355i
$484$		0			0
$485$	35.8708			0.0739604
$486$		0			0
$487$	313.986	−	228.124i	0.644735	−	0.468427i	−0.216739	−	0.976230i	$-0.569542\pi$
$487$	313.986	−	228.124i	0.644735	−	0.468427i	0.861474	+	0.507802i	$0.169542\pi$
$488$		0			0
$489$	149.688	+	460.691i	0.306109	+	0.942108i
$490$		0			0
$491$	−214.526	+	295.270i	−0.436917	+	0.601365i	−0.969523	−	0.244998i	$-0.921213\pi$
$491$	−214.526	+	295.270i	−0.436917	+	0.601365i	0.532607	+	0.846363i	$0.321213\pi$
$492$		0			0
$493$	82.4513	−	253.759i	0.167244	−	0.514724i
$494$		0			0
$495$	11.5855	−	1.33093i	0.0234051	−	0.00268874i
$496$		0			0
$497$	−71.4830	−	23.2262i	−0.143829	−	0.0467329i
$498$		0			0
$499$	−198.310	−	144.081i	−0.397415	−	0.288739i	0.371072	−	0.928604i	$-0.378990\pi$
$499$	−198.310	−	144.081i	−0.397415	−	0.288739i	−0.768487	+	0.639865i	$0.778990\pi$
$500$		0			0
$501$	423.261	−	137.526i	0.844833	−	0.274503i
$502$		0			0
$503$	−172.959	−	238.058i	−0.343855	−	0.473276i	0.601707	−	0.798717i	$-0.294487\pi$
$503$	−172.959	−	238.058i	−0.343855	−	0.473276i	−0.945563	+	0.325440i	$0.894487\pi$
$504$		0			0
$505$			9.21825i			0.0182540i
$506$		0			0
$507$	292.641			0.577201
$508$		0			0
$509$	691.862	−	502.667i	1.35926	−	0.987558i	0.360766	−	0.932656i	$-0.382515\pi$
$509$	691.862	−	502.667i	1.35926	−	0.987558i	0.998492	−	0.0549019i	$-0.0174846\pi$
$510$		0			0
$511$	−27.7397	−	85.3741i	−0.0542852	−	0.167073i
$512$		0			0
$513$	−6.62623	+	9.12023i	−0.0129166	+	0.0177782i
$514$		0			0
$515$	3.44383	−	10.5990i	0.00668704	−	0.0205806i
$516$		0			0
$517$	−495.552	+	454.938i	−0.958514	+	0.879958i
$518$		0			0
$519$	181.511	+	58.9766i	0.349733	+	0.113635i
$520$		0			0
$521$	491.143	+	356.836i	0.942693	+	0.684907i	0.949068	−	0.315073i	$-0.102029\pi$
$521$	491.143	+	356.836i	0.942693	+	0.684907i	−0.00637404	+	0.999980i	$0.502029\pi$
$522$		0			0
$523$	−641.901	+	208.566i	−1.22734	+	0.398788i	−0.849752	−	0.527183i	$-0.823248\pi$
$523$	−641.901	+	208.566i	−1.22734	+	0.398788i	−0.377593	+	0.925972i	$0.623248\pi$
$524$		0			0
$525$	−20.0254	−	27.5625i	−0.0381435	−	0.0525001i
$526$		0			0
$527$		−	506.535i		−	0.961166i
$528$		0			0
$529$	53.4586			0.101056
$530$		0			0
$531$	−124.958	+	90.7876i	−0.235327	+	0.170975i
$532$		0			0
$533$	3.46269	+	10.6571i	0.00649660	+	0.0199945i
$534$		0			0
$535$	16.7289	−	23.0254i	0.0312690	−	0.0430381i
$536$		0			0
$537$	−14.5191	+	44.6852i	−0.0270375	+	0.0832127i
$538$		0			0
$539$	221.118	+	484.005i	0.410237	+	0.897968i
$540$		0			0
$541$	−222.251	−	72.2137i	−0.410815	−	0.133482i	0.0963161	−	0.995351i	$-0.469294\pi$
$541$	−222.251	−	72.2137i	−0.410815	−	0.133482i	−0.507131	+	0.861869i	$0.669294\pi$
$542$		0			0
$543$	−363.727	−	264.263i	−0.669846	−	0.486672i
$544$		0			0
$545$	−10.8157	+	3.51425i	−0.0198454	+	0.00644816i
$546$		0			0
$547$	−560.308	−	771.198i	−1.02433	−	1.40987i	−0.909123	−	0.416527i	$-0.863247\pi$
$547$	−560.308	−	771.198i	−1.02433	−	1.40987i	−0.115207	−	0.993342i	$-0.536753\pi$
$548$		0			0
$549$		−	122.257i		−	0.222690i
$550$		0			0
$551$	−38.6697			−0.0701810
$552$		0			0
$553$	−94.1206	+	68.3826i	−0.170200	+	0.123658i
$554$		0			0
$555$	−11.3648	−	34.9773i	−0.0204772	−	0.0630222i
$556$		0			0
$557$	264.552	−	364.125i	0.474959	−	0.653725i	−0.502567	−	0.864538i	$-0.667611\pi$
$557$	264.552	−	364.125i	0.474959	−	0.653725i	0.977526	+	0.210813i	$0.0676110\pi$
$558$		0			0
$559$	−1.00686	+	3.09879i	−0.00180118	+	0.00554345i
$560$		0			0
$561$	140.213	−	248.364i	0.249934	−	0.442717i
$562$		0			0
$563$	−297.055	−	96.5192i	−0.527630	−	0.171437i	0.0330754	−	0.999453i	$-0.489470\pi$
$563$	−297.055	−	96.5192i	−0.527630	−	0.171437i	−0.560705	+	0.828016i	$0.689470\pi$
$564$		0			0
$565$	8.34926	+	6.06609i	0.0147774	+	0.0107364i
$566$		0			0
$567$	6.76838	−	2.19918i	0.0119372	−	0.00387862i
$568$		0			0
$569$	331.841	+	456.740i	0.583200	+	0.802706i	0.994042	−	0.109000i	$-0.0347650\pi$
$569$	331.841	+	456.740i	0.583200	+	0.802706i	−0.410841	+	0.911707i	$0.634765\pi$
$570$		0			0
$571$		−	224.552i		−	0.393260i	−0.980478	−	0.196630i	$-0.937000\pi$
$571$		−	224.552i		−	0.393260i	0.980478	−	0.196630i	$-0.0629998\pi$
$572$		0			0
$573$	216.129			0.377189
$574$		0			0
$575$	485.686	−	352.871i	0.844671	−	0.613689i
$576$		0			0
$577$	−326.124	−	1003.71i	−0.565207	−	1.73953i	−0.667337	−	0.744756i	$-0.732566\pi$
$577$	−326.124	−	1003.71i	−0.565207	−	1.73953i	0.102130	−	0.994771i	$-0.467434\pi$
$578$		0			0
$579$	−42.7481	+	58.8377i	−0.0738309	+	0.101619i
$580$		0			0
$581$	−4.85658	+	14.9470i	−0.00835900	+	0.0257264i
$582$		0			0
$583$	128.727	−	635.739i	0.220800	−	1.09046i
$584$		0			0
$585$	0.210959	+	0.0685446i	0.000360613	+	0.000117170i
$586$		0			0
$587$	−64.2470	−	46.6782i	−0.109450	−	0.0795200i	0.531714	−	0.846924i	$-0.321548\pi$
$587$	−64.2470	−	46.6782i	−0.109450	−	0.0795200i	−0.641164	+	0.767404i	$0.721548\pi$
$588$		0			0
$589$	−69.8186	+	22.6855i	−0.118538	+	0.0385152i
$590$		0			0
$591$	279.297	+	384.419i	0.472583	+	0.650455i
$592$		0			0
$593$		−	709.519i		−	1.19649i	−0.801313	−	0.598245i	$-0.795865\pi$
$593$		−	709.519i		−	1.19649i	0.801313	−	0.598245i	$-0.204135\pi$
$594$		0			0
$595$	4.18307			0.00703037
$596$		0			0
$597$	−211.561	+	153.708i	−0.354374	+	0.257468i
$598$		0			0
$599$	−215.771	−	664.076i	−0.360219	−	1.10864i	−0.952921	−	0.303219i	$-0.901939\pi$
$599$	−215.771	−	664.076i	−0.360219	−	1.10864i	0.592702	−	0.805422i	$-0.298061\pi$
$600$		0			0
$601$	131.365	−	180.808i	0.218577	−	0.300845i	−0.685621	−	0.727958i	$-0.740469\pi$
$601$	131.365	−	180.808i	0.218577	−	0.300845i	0.904198	+	0.427113i	$0.140469\pi$
$602$		0			0
$603$	67.6100	−	208.082i	0.112123	−	0.345078i
$604$		0			0
$605$	22.0911	+	36.6112i	0.0365141	+	0.0605144i
$606$		0			0
$607$	−906.706	−	294.607i	−1.49375	−	0.485348i	−0.555561	−	0.831476i	$-0.687497\pi$
$607$	−906.706	−	294.607i	−1.49375	−	0.485348i	−0.938188	+	0.346127i	$0.887497\pi$
$608$		0			0
$609$	19.7496	+	14.3490i	0.0324296	+	0.0235615i
$610$		0			0
$611$	−12.1692	+	3.95402i	−0.0199169	+	0.00647139i
$612$		0			0
$613$	−16.3918	−	22.5614i	−0.0267403	−	0.0368049i	0.795438	−	0.606036i	$-0.207241\pi$
$613$	−16.3918	−	22.5614i	−0.0267403	−	0.0368049i	−0.822178	+	0.569231i	$0.807241\pi$
$614$		0			0
$615$		−	32.7809i		−	0.0533023i
$616$		0			0
$617$	−997.165			−1.61615			−0.808075	−	0.589079i	$-0.799491\pi$
$617$	−997.165			−1.61615			−0.808075	+	0.589079i	$0.799491\pi$
$618$		0			0
$619$	−18.8208	+	13.6741i	−0.0304052	+	0.0220907i	−0.602884	−	0.797829i	$-0.705982\pi$
$619$	−18.8208	+	13.6741i	−0.0304052	+	0.0220907i	0.572479	+	0.819919i	$0.305982\pi$
$620$		0			0
$621$	38.7522	+	119.267i	0.0624030	+	0.192057i
$622$		0			0
$623$	34.8456	−	47.9608i	0.0559319	−	0.0769837i
$624$		0			0
$625$	190.246	−	585.517i	0.304394	−	0.936828i
$626$		0			0
$627$	−40.5130	−	8.20321i	−0.0646140	−	0.0130833i
$628$		0			0
$629$	−855.434	−	277.947i	−1.35999	−	0.441888i
$630$		0			0
$631$	−423.736	−	307.862i	−0.671531	−	0.487896i	0.199006	−	0.979998i	$-0.436229\pi$
$631$	−423.736	−	307.862i	−0.671531	−	0.487896i	−0.870537	+	0.492103i	$0.836229\pi$
$632$		0			0
$633$	−30.7773	+	10.0002i	−0.0486214	+	0.0157980i
$634$		0			0
$635$	−30.9603	−	42.6132i	−0.0487564	−	0.0671074i
$636$		0			0
$637$			10.1214i			0.0158891i
$638$		0			0
$639$	285.156			0.446253
$640$		0			0
$641$	54.5371	−	39.6235i	0.0850813	−	0.0618152i	−0.544431	−	0.838805i	$-0.683255\pi$
$641$	54.5371	−	39.6235i	0.0850813	−	0.0618152i	0.629513	+	0.776990i	$0.283255\pi$
$642$		0			0
$643$	249.209	+	766.988i	0.387573	+	1.19283i	0.934597	+	0.355710i	$0.115761\pi$
$643$	249.209	+	766.988i	0.387573	+	1.19283i	−0.547024	+	0.837117i	$0.684239\pi$
$644$		0			0
$645$	5.60266	−	7.71140i	0.00868629	−	0.0119557i
$646$		0			0
$647$	300.028	−	923.392i	0.463722	−	1.42719i	−0.396860	−	0.917879i	$-0.629900\pi$
$647$	300.028	−	923.392i	0.463722	−	1.42719i	0.860582	−	0.509311i	$-0.170100\pi$
$648$		0			0
$649$	−493.179	−	278.422i	−0.759906	−	0.429001i
$650$		0			0
$651$	44.0759	+	14.3211i	0.0677050	+	0.0219987i
$652$		0			0
$653$	−22.6871	−	16.4831i	−0.0347429	−	0.0252422i	0.570278	−	0.821452i	$-0.306835\pi$
$653$	−22.6871	−	16.4831i	−0.0347429	−	0.0252422i	−0.605021	+	0.796209i	$0.706835\pi$
$654$		0			0
$655$	55.7792	−	18.1238i	0.0851591	−	0.0276699i
$656$		0			0
$657$	200.182	+	275.526i	0.304690	+	0.419370i
$658$		0			0
$659$			570.449i			0.865628i	0.901483	+	0.432814i	$0.142479\pi$
$659$			570.449i			0.865628i	−0.901483	+	0.432814i	$0.857521\pi$
$660$		0			0
$661$	854.772			1.29315			0.646575	−	0.762851i	$-0.276201\pi$
$661$	854.772			1.29315			0.646575	+	0.762851i	$0.276201\pi$
$662$		0			0
$663$	4.38883	−	3.18867i	0.00661965	−	0.00480946i
$664$		0			0
$665$	−0.187341	−	0.576577i	−0.000281716	−	0.000867034i
$666$		0			0
$667$	−252.846	+	348.013i	−0.379080	+	0.521758i
$668$		0			0
$669$	50.4622	−	155.307i	0.0754293	−	0.232147i
$670$		0			0
$671$	407.739	−	186.276i	0.607659	−	0.277609i
$672$		0			0
$673$	336.109	+	109.208i	0.499418	+	0.162271i	0.547885	−	0.836554i	$-0.315433\pi$
$673$	336.109	+	109.208i	0.499418	+	0.162271i	−0.0484662	+	0.998825i	$0.515433\pi$
$674$		0			0
$675$	104.569	+	75.9741i	0.154918	+	0.112554i
$676$		0			0
$677$	−1181.53	+	383.903i	−1.74525	+	0.567065i	−0.995509	−	0.0946695i	$-0.969821\pi$
$677$	−1181.53	+	383.903i	−1.74525	+	0.567065i	−0.749738	+	0.661735i	$0.769821\pi$
$678$		0			0
$679$	47.1787	+	64.9359i	0.0694826	+	0.0956346i
$680$		0			0
$681$		−	501.933i		−	0.737053i
$682$		0			0
$683$	818.617			1.19856			0.599281	−	0.800539i	$-0.295453\pi$
$683$	818.617			1.19856			0.599281	+	0.800539i	$0.295453\pi$
$684$		0			0
$685$	41.9888	−	30.5067i	0.0612975	−	0.0445353i
$686$		0			0
$687$	−122.155	−	375.956i	−0.177810	−	0.547243i
$688$		0			0
$689$	7.25187	−	9.98134i	0.0105252	−	0.0144867i
$690$		0			0
$691$	−84.5050	+	260.080i	−0.122294	+	0.376381i	−0.993398	−	0.114716i	$-0.963404\pi$
$691$	−84.5050	+	260.080i	−0.122294	+	0.376381i	0.871105	+	0.491098i	$0.163404\pi$
$692$		0			0
$693$	17.6471	+	19.2225i	0.0254648	+	0.0277381i
$694$		0			0
$695$	71.8475	+	23.3447i	0.103378	+	0.0335895i
$696$		0			0
$697$	−648.603	−	471.238i	−0.930564	−	0.676094i
$698$		0			0
$699$	−492.251	+	159.942i	−0.704222	+	0.228816i
$700$		0			0
$701$	−298.072	−	410.262i	−0.425210	−	0.585252i	0.541635	−	0.840614i	$-0.317805\pi$
$701$	−298.072	−	410.262i	−0.425210	−	0.585252i	−0.966846	+	0.255362i	$0.917805\pi$
$702$		0			0
$703$			130.358i			0.185430i
$704$		0			0
$705$	37.4323			0.0530954
$706$		0			0
$707$	−16.6875	+	12.1242i	−0.0236033	+	0.0171488i
$708$		0			0
$709$	178.793	+	550.269i	0.252177	+	0.776119i	0.994373	+	0.105937i	$0.0337842\pi$
$709$	178.793	+	550.269i	0.252177	+	0.776119i	−0.742196	+	0.670183i	$0.766216\pi$
$710$		0			0
$711$	259.437	−	357.084i	0.364890	−	0.502228i
$712$		0			0
$713$	−252.356	+	776.672i	−0.353936	+	1.08930i
$714$		0			0
$715$	0.0928224	+	0.808008i	0.000129822	+	0.00113008i
$716$		0			0
$717$	−405.114	−	131.630i	−0.565013	−	0.183584i
$718$		0			0
$719$	31.7569	+	23.0727i	0.0441681	+	0.0320900i	0.609650	−	0.792671i	$-0.291310\pi$
$719$	31.7569	+	23.0727i	0.0441681	+	0.0320900i	−0.565482	+	0.824761i	$0.691310\pi$
$720$		0			0
$721$	23.7165	−	7.70597i	0.0328940	−	0.0106879i
$722$		0			0
$723$	380.167	+	523.255i	0.525819	+	0.723728i
$724$		0			0
$725$			443.374i			0.611550i
$726$		0			0
$727$	−918.828			−1.26386			−0.631932	−	0.775024i	$-0.717738\pi$
$727$	−918.828			−1.26386			−0.631932	+	0.775024i	$0.717738\pi$
$728$		0			0
$729$	−21.8435	+	15.8702i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−72.0374	−	221.708i	−0.0985463	−	0.303294i
$732$		0			0
$733$	434.317	−	597.786i	0.592520	−	0.815534i	−0.402478	−	0.915430i	$-0.631851\pi$
$733$	434.317	−	597.786i	0.592520	−	0.815534i	0.994998	+	0.0998958i	$0.0318509\pi$
$734$		0			0
$735$	9.14979	−	28.1602i	0.0124487	−	0.0383131i
$736$		0			0
$737$	796.990	−	91.5568i	1.08140	−	0.124229i
$738$		0			0
$739$	−1082.21	−	351.633i	−1.46443	−	0.475822i	−0.535011	−	0.844845i	$-0.679692\pi$
$739$	−1082.21	−	351.633i	−1.46443	−	0.475822i	−0.929420	+	0.369023i	$0.879692\pi$
$740$		0			0
$741$	−0.636069	−	0.462131i	−0.000858393	−	0.000623659i
$742$		0			0
$743$	−179.099	+	58.1929i	−0.241049	+	0.0783215i	−0.427050	−	0.904228i	$-0.640447\pi$
$743$	−179.099	+	58.1929i	−0.241049	+	0.0783215i	0.186001	+	0.982550i	$0.440447\pi$
$744$		0			0
$745$	−48.0325	−	66.1111i	−0.0644732	−	0.0887397i
$746$		0			0
$747$		−	59.6257i		−	0.0798203i
$748$		0			0
$749$	63.6848			0.0850264
$750$		0			0
$751$	489.777	−	355.844i	0.652166	−	0.473827i	−0.211842	−	0.977304i	$-0.567946\pi$
$751$	489.777	−	355.844i	0.652166	−	0.473827i	0.864008	+	0.503477i	$0.167946\pi$
$752$		0			0
$753$	192.375	+	592.068i	0.255477	+	0.786279i
$754$		0			0
$755$	−55.3365	+	76.1641i	−0.0732933	+	0.100880i
$756$		0			0
$757$	−120.088	+	369.594i	−0.158637	+	0.488235i	−0.998511	−	0.0545462i	$-0.982629\pi$
$757$	−120.088	+	369.594i	−0.158637	+	0.488235i	0.839874	+	0.542781i	$0.182629\pi$
$758$		0			0
$759$	−338.724	+	310.964i	−0.446277	+	0.409702i
$760$		0			0
$761$	664.937	+	216.051i	0.873768	+	0.283904i	0.711367	−	0.702821i	$-0.248076\pi$
$761$	664.937	+	216.051i	0.873768	+	0.283904i	0.162400	+	0.986725i	$0.448076\pi$
$762$		0			0
$763$	−20.5870	−	14.9574i	−0.0269817	−	0.0196034i
$764$		0			0
$765$	−15.0934	+	4.90415i	−0.0197299	+	0.00641065i
$766$		0			0
$767$	−6.33178	−	8.71494i	−0.00825525	−	0.0113624i
$768$		0			0
$769$		−	337.074i		−	0.438328i	−0.975688	−	0.219164i	$-0.929667\pi$
$769$		−	337.074i		−	0.438328i	0.975688	−	0.219164i	$-0.0703330\pi$
$770$		0			0
$771$	−61.9801			−0.0803892
$772$		0			0
$773$	643.324	−	467.403i	0.832244	−	0.604660i	−0.0879495	−	0.996125i	$-0.528031\pi$
$773$	643.324	−	467.403i	0.832244	−	0.604660i	0.920193	+	0.391464i	$0.128031\pi$
$774$		0			0
$775$	260.104	+	800.517i	0.335618	+	1.03292i
$776$		0			0
$777$	48.3710	−	66.5770i	0.0622535	−	0.0856846i
$778$		0			0
$779$	−35.9054	+	110.505i	−0.0460916	+	0.141855i
$780$		0			0
$781$	434.476	+	951.026i	0.556308	+	1.21770i
$782$		0			0
$783$	−88.0833	−	28.6200i	−0.112495	−	0.0365517i
$784$		0			0
$785$	29.8127	+	21.6602i	0.0379780	+	0.0275926i
$786$		0			0
$787$	508.815	−	165.324i	0.646525	−	0.210069i	0.0326436	−	0.999467i	$-0.489607\pi$
$787$	508.815	−	165.324i	0.646525	−	0.210069i	0.613881	+	0.789398i	$0.289607\pi$
$788$		0			0
$789$	−371.259	−	510.994i	−0.470544	−	0.647648i
$790$		0			0
$791$			23.0928i			0.0291944i
$792$		0			0
$793$	8.52651			0.0107522
$794$		0			0
$795$	−29.1997	+	21.2149i	−0.0367292	+	0.0266854i
$796$		0			0
$797$	−219.724	−	676.242i	−0.275689	−	0.848484i	−0.989036	−	0.147673i	$-0.952822\pi$
$797$	−219.724	−	676.242i	−0.275689	−	0.848484i	0.713347	−	0.700811i	$-0.247178\pi$
$798$		0			0
$799$	538.102	−	740.634i	0.673470	−	0.926952i
$800$		0			0
$801$	−69.5020	+	213.905i	−0.0867690	+	0.267047i
$802$		0			0
$803$	−613.905	+	1087.43i	−0.764514	+	1.35421i
$804$		0			0
$805$	−6.41393	−	2.08401i	−0.00796761	−	0.00258883i
$806$		0			0
$807$	18.7445	+	13.6187i	0.0232274	+	0.0168757i
$808$		0			0
$809$	−102.321	+	33.2462i	−0.126479	+	0.0410954i	−0.371572	−	0.928404i	$-0.621181\pi$
$809$	−102.321	+	33.2462i	−0.126479	+	0.0410954i	0.245094	+	0.969499i	$0.421181\pi$
$810$		0			0
$811$	738.698	+	1016.73i	0.910848	+	1.25368i	0.966876	+	0.255246i	$0.0821564\pi$
$811$	738.698	+	1016.73i	0.910848	+	1.25368i	−0.0560279	+	0.998429i	$0.517844\pi$
$812$		0			0
$813$		−	122.703i		−	0.150926i
$814$		0			0
$815$	98.8308			0.121265
$816$		0			0
$817$	−27.3331	+	19.8587i	−0.0334555	+	0.0243068i
$818$		0			0
$819$	0.153377	+	0.472045i	0.000187273	+	0.000576367i
$820$		0			0
$821$	−608.067	+	836.933i	−0.740642	+	1.01941i	0.257939	+	0.966161i	$0.416957\pi$
$821$	−608.067	+	836.933i	−0.740642	+	1.01941i	−0.998581	+	0.0532455i	$0.983043\pi$
$822$		0			0
$823$	165.580	−	509.603i	0.201191	−	0.619202i	−0.798657	−	0.601786i	$-0.794456\pi$
$823$	165.580	−	509.603i	0.201191	−	0.619202i	0.999848	−	0.0174160i	$-0.00554397\pi$
$824$		0			0
$825$	−94.0552	+	464.508i	−0.114006	+	0.563040i
$826$		0			0
$827$	−131.119	−	42.6030i	−0.158547	−	0.0515151i	0.228668	−	0.973504i	$-0.426563\pi$
$827$	−131.119	−	42.6030i	−0.158547	−	0.0515151i	−0.387215	+	0.921989i	$0.626563\pi$
$828$		0			0
$829$	7.75076	+	5.63126i	0.00934954	+	0.00679283i	0.592450	−	0.805607i	$-0.298161\pi$
$829$	7.75076	+	5.63126i	0.00934954	+	0.00679283i	−0.583101	+	0.812400i	$0.698161\pi$
$830$		0			0
$831$	130.706	−	42.4690i	0.157288	−	0.0511059i
$832$		0			0
$833$	−425.645	−	585.850i	−0.510978	−	0.703301i
$834$		0			0
$835$		−	90.8011i		−	0.108744i
$836$		0			0
$837$	−175.825			−0.210066
$838$		0			0
$839$	−388.855	+	282.520i	−0.463474	+	0.336734i	−0.794893	−	0.606750i	$-0.792473\pi$
$839$	−388.855	+	282.520i	−0.463474	+	0.336734i	0.331418	+	0.943484i	$0.392473\pi$
$840$		0			0
$841$	161.710	+	497.693i	0.192283	+	0.591787i
$842$		0			0
$843$	349.293	−	480.760i	0.414345	−	0.570297i
$844$		0			0
$845$	18.4504	−	56.7845i	0.0218348	−	0.0672006i
$846$		0			0
$847$	−37.2212	+	88.1433i	−0.0439447	+	0.104065i
$848$		0			0
$849$	−197.145	−	64.0563i	−0.232209	−	0.0754491i
$850$		0			0
$851$	1173.17	+	852.357i	1.37858	+	1.00159i
$852$		0			0
$853$	−1443.72	+	469.094i	−1.69252	+	0.549934i	−0.987274	−	0.159026i	$-0.949165\pi$
$853$	−1443.72	+	469.094i	−1.69252	+	0.549934i	−0.705248	+	0.708960i	$0.749165\pi$
$854$		0			0
$855$	1.35193	+	1.86078i	0.00158121	+	0.00217635i
$856$		0			0
$857$			229.336i			0.267603i	0.991008	+	0.133802i	$0.0427185\pi$
$857$			229.336i			0.267603i	−0.991008	+	0.133802i	$0.957282\pi$
$858$		0			0
$859$	308.792			0.359478			0.179739	−	0.983714i	$-0.442475\pi$
$859$	308.792			0.359478			0.179739	+	0.983714i	$0.442475\pi$
$860$		0			0
$861$	59.3424	−	43.1148i	0.0689226	−	0.0500752i
$862$		0			0
$863$	−159.802	−	491.821i	−0.185171	−	0.569897i	0.814781	−	0.579770i	$-0.196857\pi$
$863$	−159.802	−	491.821i	−0.185171	−	0.569897i	−0.999951	+	0.00987257i	$0.996857\pi$
$864$		0			0
$865$	22.8879	−	31.5024i	0.0264600	−	0.0364190i
$866$		0			0
$867$	34.7425	−	106.927i	0.0400721	−	0.123329i
$868$		0			0
$869$	1586.20	+	321.180i	1.82532	+	0.369597i
$870$		0			0
$871$	14.5122	+	4.71530i	0.0166616	+	0.00541367i
$872$		0			0
$873$	−246.360	−	178.991i	−0.282199	−	0.205030i
$874$		0			0
$875$	−13.2549	+	4.30677i	−0.0151484	+	0.00492202i
$876$		0			0
$877$	148.255	+	204.056i	0.169048	+	0.232675i	0.885133	−	0.465339i	$-0.154067\pi$
$877$	148.255	+	204.056i	0.169048	+	0.232675i	−0.716084	+	0.698014i	$0.754067\pi$
$878$		0			0
$879$			19.9465i			0.0226923i
$880$		0			0
$881$	830.794			0.943012			0.471506	−	0.881863i	$-0.343711\pi$
$881$	830.794			0.943012			0.471506	+	0.881863i	$0.343711\pi$
$882$		0			0
$883$	435.210	−	316.199i	0.492877	−	0.358096i	−0.313413	−	0.949617i	$-0.601472\pi$
$883$	435.210	−	316.199i	0.492877	−	0.358096i	0.806290	+	0.591521i	$0.201472\pi$
$884$		0			0
$885$	9.73821	+	29.9711i	0.0110036	+	0.0338657i
$886$		0			0
$887$	−840.566	+	1156.94i	−0.947651	+	1.30433i	0.00491261	+	0.999988i	$0.498436\pi$
$887$	−840.566	+	1156.94i	−0.947651	+	1.30433i	−0.952563	+	0.304341i	$0.901564\pi$
$888$		0			0
$889$	36.4213	−	112.093i	0.0409688	−	0.126089i
$890$		0			0
$891$	−86.2105	−	48.6697i	−0.0967571	−	0.0546237i
$892$		0			0
$893$	−126.185	−	41.0001i	−0.141305	−	0.0459127i
$894$		0			0
$895$	7.75540	+	5.63463i	0.00866525	+	0.00629567i
$896$		0			0
$897$	−8.31801	+	2.70269i	−0.00927315	+	0.00301303i
$898$		0			0
$899$	−354.505	−	487.935i	−0.394333	−	0.542753i
$900$		0			0
$901$			882.717i			0.979708i
$902$		0			0
$903$	21.3286			0.0236197
$904$		0			0
$905$	−74.2103	+	53.9169i	−0.0820003	+	0.0595767i
$906$		0			0
$907$	418.026	+	1286.55i	0.460889	+	1.41847i	0.864080	+	0.503355i	$0.167901\pi$
$907$	418.026	+	1286.55i	0.460889	+	1.41847i	−0.403191	+	0.915116i	$0.632099\pi$
$908$		0			0
$909$	45.9980	−	63.3108i	0.0506029	−	0.0696489i
$910$		0			0
$911$	263.965	−	812.400i	0.289753	−	0.891768i	−0.695181	−	0.718835i	$-0.744676\pi$
$911$	263.965	−	812.400i	0.289753	−	0.891768i	0.984934	−	0.172933i	$-0.0553243\pi$
$912$		0			0
$913$	198.858	−	90.8485i	0.217808	−	0.0995054i
$914$		0			0
$915$	−23.7229	−	7.70803i	−0.0259266	−	0.00842408i
$916$		0			0
$917$	106.172	+	77.1385i	0.115782	+	0.0841204i
$918$		0			0
$919$	314.056	−	102.043i	0.341737	−	0.111037i	−0.133120	−	0.991100i	$-0.542500\pi$
$919$	314.056	−	102.043i	0.341737	−	0.111037i	0.474857	+	0.880063i	$0.342500\pi$
$920$		0			0
$921$	200.416	+	275.849i	0.217607	+	0.299510i
$922$		0			0
$923$			19.8875i			0.0215466i
$924$		0			0
$925$	1494.64			1.61582
$926$		0			0
$927$	−76.5400	+	55.6096i	−0.0825674	+	0.0599887i
$928$		0			0
$929$	−35.3551	−	108.812i	−0.0380572	−	0.117128i	0.930223	−	0.366995i	$-0.119613\pi$
$929$	−35.3551	−	108.812i	−0.0380572	−	0.117128i	−0.968280	+	0.249867i	$0.919613\pi$
$930$		0			0
$931$	−61.6884	+	84.9068i	−0.0662603	+	0.0911995i
$932$		0			0
$933$	−144.735	+	445.450i	−0.155129	+	0.477438i
$934$		0			0
$935$	−39.3529	−	42.8660i	−0.0420886	−	0.0458460i
$936$		0			0
$937$	1540.46	+	500.527i	1.64404	+	0.534181i	0.977436	−	0.211233i	$-0.0677478\pi$
$937$	1540.46	+	500.527i	1.64404	+	0.534181i	0.666603	+	0.745413i	$0.267748\pi$
$938$		0			0
$939$	−482.887	−	350.838i	−0.514257	−	0.373629i
$940$		0			0
$941$	722.085	−	234.620i	0.767359	−	0.249330i	0.100925	−	0.994894i	$-0.467820\pi$
$941$	722.085	−	234.620i	0.767359	−	0.249330i	0.666434	+	0.745564i	$0.267820\pi$
$942$		0			0
$943$	759.735	+	1045.69i	0.805658	+	1.10889i
$944$		0			0
$945$		−	1.45200i		−	0.00153651i
$946$		0			0
$947$	−1855.32			−1.95915			−0.979575	−	0.201079i	$-0.935555\pi$
$947$	−1855.32			−1.95915			−0.979575	+	0.201079i	$0.935555\pi$
$948$		0			0
$949$	−19.2160	+	13.9612i	−0.0202486	+	0.0147115i
$950$		0			0
$951$	35.0960	+	108.014i	0.0369043	+	0.113580i
$952$		0			0
$953$	−955.025	+	1314.48i	−1.00212	+	1.37931i	−0.0781115	+	0.996945i	$0.524889\pi$
$953$	−955.025	+	1314.48i	−1.00212	+	1.37931i	−0.924013	+	0.382361i	$0.875111\pi$
$954$		0			0
$955$	13.6265	−	41.9381i	0.0142686	−	0.0439142i
$956$		0			0
$957$	−38.7569	−	337.374i	−0.0404983	−	0.352533i
$958$		0			0
$959$	110.451	+	35.8876i	0.115173	+	0.0374219i
$960$		0			0
$961$	−148.843	−	108.141i	−0.154884	−	0.112530i
$962$		0			0
$963$	−229.788	+	74.6627i	−0.238617	+	0.0775313i
$964$		0			0
$965$	8.72179	+	12.0045i	0.00903812	+	0.0124399i
$966$		0			0
$967$		−	325.104i		−	0.336199i	−0.985770	−	0.168099i	$-0.946237\pi$
$967$		−	325.104i		−	0.336199i	0.985770	−	0.168099i	$-0.0537629\pi$
$968$		0			0
$969$	56.2519			0.0580515
$970$		0			0
$971$	227.145	−	165.031i	0.233929	−	0.169960i	−0.464645	−	0.885497i	$-0.653818\pi$
$971$	227.145	−	165.031i	0.233929	−	0.169960i	0.698574	+	0.715537i	$0.253818\pi$
$972$		0			0
$973$	52.2365	+	160.767i	0.0536860	+	0.165229i
$974$		0			0
$975$	−5.29864	+	7.29296i	−0.00543450	+	0.00747995i
$976$		0			0
$977$	497.452	−	1531.00i	0.509163	−	1.56704i	−0.284495	−	0.958678i	$-0.591826\pi$
$977$	497.452	−	1531.00i	0.509163	−	1.56704i	0.793658	−	0.608364i	$-0.208174\pi$
$978$		0			0
$979$	−819.293	+	94.1188i	−0.836867	+	0.0961377i
$980$		0			0
$981$	91.8181	+	29.8335i	0.0935964	+	0.0304113i
$982$		0			0
$983$	−302.881	−	220.056i	−0.308119	−	0.223862i	0.422970	−	0.906144i	$-0.360988\pi$
$983$	−302.881	−	220.056i	−0.308119	−	0.223862i	−0.731089	+	0.682282i	$0.760988\pi$
$984$		0			0
$985$	92.2025	−	29.9584i	0.0936066	−	0.0304146i
$986$		0			0
$987$	49.2324	+	67.7626i	0.0498808	+	0.0686551i
$988$		0			0
$989$			375.836i			0.380016i
$990$		0			0
$991$	943.875			0.952447			0.476223	−	0.879324i	$-0.342005\pi$
$991$	943.875			0.952447			0.476223	+	0.879324i	$0.342005\pi$
$992$		0			0
$993$	148.279	−	107.731i	0.149324	−	0.108490i
$994$		0			0
$995$	16.4873	+	50.7427i	0.0165702	+	0.0509977i
$996$		0			0
$997$	400.666	−	551.470i	0.401872	−	0.553129i	−0.559341	−	0.828938i	$-0.688946\pi$
$997$	400.666	−	551.470i	0.401872	−	0.553129i	0.961213	+	0.275809i	$0.0889457\pi$
$998$		0			0
$999$	−96.4793	+	296.933i	−0.0965759	+	0.297230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.3.bf.c.145.1		16
4.3	odd	2		66.3.f.a.13.4	✓	16
11.6	odd	10	inner	528.3.bf.c.193.1		16
12.11	even	2		198.3.j.b.145.2		16
44.7	even	10		726.3.d.e.241.2		16
44.15	odd	10		726.3.d.e.241.10		16
44.39	even	10		66.3.f.a.61.4	yes	16
132.59	even	10		2178.3.d.m.1693.4		16
132.83	odd	10		198.3.j.b.127.2		16
132.95	odd	10		2178.3.d.m.1693.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.f.a.13.4	✓	16	4.3	odd	2
66.3.f.a.61.4	yes	16	44.39	even	10
198.3.j.b.127.2		16	132.83	odd	10
198.3.j.b.145.2		16	12.11	even	2
528.3.bf.c.145.1		16	1.1	even	1	trivial
528.3.bf.c.193.1		16	11.6	odd	10	inner
726.3.d.e.241.2		16	44.7	even	10
726.3.d.e.241.10		16	44.15	odd	10
2178.3.d.m.1693.4		16	132.59	even	10
2178.3.d.m.1693.12		16	132.95	odd	10

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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	528.bf (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40126 + 1.01807i) q^{3} +(0.109202 + 0.336090i) q^{5} +(-0.464787 + 0.639725i) q^{7} +(0.927051 - 2.85317i) q^{9} +(10.9281 - 1.25540i) q^{11} +(0.198988 + 0.0646551i) q^{13} +(-0.495185 - 0.359773i) q^{15} +(-14.2369 + 4.62586i) q^{17} +(1.27522 + 1.75519i) q^{19} -1.36961i q^{21} +24.1342 q^{23} +(20.1244 - 14.6212i) q^{25} +(1.60570 + 4.94183i) q^{27} +(-10.4767 + 14.4199i) q^{29} +(-10.4564 + 32.1814i) q^{31} +(-14.0350 + 12.8848i) q^{33} +(-0.265761 - 0.0863510i) q^{35} +(48.6102 + 35.3174i) q^{37} +(-0.344657 + 0.111986i) q^{39} +(31.4796 + 43.3280i) q^{41} +15.5727i q^{43} +1.06016 q^{45} +(-49.4759 + 35.9463i) q^{47} +(14.9486 + 46.0071i) q^{49} +(15.2402 - 20.9763i) q^{51} +(18.2219 - 56.0812i) q^{53} +(1.61531 + 3.53574i) q^{55} +(-3.57382 - 1.16121i) q^{57} +(-41.6528 - 30.2625i) q^{59} +(38.7576 - 12.5931i) q^{61} +(1.39436 + 1.91917i) q^{63} +0.0739383i q^{65} +72.9302 q^{67} +(-33.8182 + 24.5704i) q^{69} +(29.3727 + 90.3998i) q^{71} +(-66.7272 + 91.8421i) q^{73} +(-13.3140 + 40.9762i) q^{75} +(-4.27614 + 7.57449i) q^{77} +(139.926 + 45.4646i) q^{79} +(-7.28115 - 5.29007i) q^{81} +(18.9025 - 6.14179i) q^{83} +(-3.10941 - 4.27974i) q^{85} -30.8721i q^{87} -74.9710 q^{89} +(-0.133848 + 0.0972466i) q^{91} +(-18.1110 - 55.7399i) q^{93} +(-0.450645 + 0.620259i) q^{95} +(31.3671 - 96.5379i) q^{97} +(6.54905 - 32.3436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 60 q^{7} - 12 q^{9} + 4 q^{11} - 60 q^{13} - 12 q^{15} - 60 q^{17} + 8 q^{23} - 48 q^{25} - 160 q^{29} - 32 q^{31} + 36 q^{33} - 160 q^{35} - 84 q^{37} + 40 q^{41} + 24 q^{45} - 372 q^{47}+ \cdots - 48 q^{99}+O(q^{100}) \) 16 * q + 8 * q^5 - 60 * q^7 - 12 * q^9 + 4 * q^11 - 60 * q^13 - 12 * q^15 - 60 * q^17 + 8 * q^23 - 48 * q^25 - 160 * q^29 - 32 * q^31 + 36 * q^33 - 160 * q^35 - 84 * q^37 + 40 * q^41 + 24 * q^45 - 372 * q^47 + 96 * q^49 - 120 * q^51 - 124 * q^53 - 32 * q^55 - 120 * q^57 + 172 * q^59 + 100 * q^61 + 180 * q^63 - 248 * q^67 - 372 * q^69 - 48 * q^71 + 160 * q^73 - 192 * q^75 - 172 * q^77 + 460 * q^79 - 36 * q^81 + 420 * q^83 - 420 * q^85 - 360 * q^89 + 252 * q^91 - 24 * q^93 - 180 * q^95 + 324 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more