LMFDB - Embedded newform 99.3.l.a.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(26,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("99.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.l (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	99.53
Dual form			99.3.l.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28527 + 0.417608i) q^{2} +(-1.75856 - 1.27767i) q^{4} +(4.85485 - 1.57744i) q^{5} +(10.6531 + 7.73991i) q^{7} +(-4.90400 - 6.74978i) q^{8} +O(q^{10})$	\(q+(1.28527 + 0.417608i) q^{2} +(-1.75856 - 1.27767i) q^{4} +(4.85485 - 1.57744i) q^{5} +(10.6531 + 7.73991i) q^{7} +(-4.90400 - 6.74978i) q^{8} +6.89852 q^{10} +(4.16151 - 10.1824i) q^{11} +(-0.825159 + 2.53958i) q^{13} +(10.4598 + 14.3966i) q^{14} +(-0.797348 - 2.45398i) q^{16} +(-16.3735 + 5.32007i) q^{17} +(-24.7742 + 17.9995i) q^{19} +(-10.5530 - 3.42886i) q^{20} +(9.60091 - 11.3492i) q^{22} -15.5309i q^{23} +(0.855829 - 0.621796i) q^{25} +(-2.12110 + 2.91944i) q^{26} +(-8.84500 - 27.2221i) q^{28} +(-6.10287 + 8.39987i) q^{29} +(5.21245 - 16.0423i) q^{31} +29.8857i q^{32} -23.2660 q^{34} +(63.9282 + 20.7715i) q^{35} +(-15.1698 - 11.0215i) q^{37} +(-39.3582 + 12.7883i) q^{38} +(-34.4555 - 25.0334i) q^{40} +(7.85173 + 10.8070i) q^{41} +10.5356 q^{43} +(-20.3280 + 12.5893i) q^{44} +(6.48583 - 19.9613i) q^{46} +(-48.3198 - 66.5065i) q^{47} +(38.4399 + 118.306i) q^{49} +(1.35963 - 0.441772i) q^{50} +(4.69582 - 3.41171i) q^{52} +(59.9022 + 19.4634i) q^{53} +(4.14138 - 55.9987i) q^{55} -109.862i q^{56} +(-11.3517 + 8.24747i) q^{58} +(-38.7385 + 53.3189i) q^{59} +(11.2965 + 34.7670i) q^{61} +(13.3988 - 18.4418i) q^{62} +(-15.6699 + 48.2271i) q^{64} +13.6309i q^{65} +60.5815 q^{67} +(35.5909 + 11.5642i) q^{68} +(73.4904 + 53.3939i) q^{70} +(-46.7818 + 15.2003i) q^{71} +(-5.15593 - 3.74600i) q^{73} +(-14.8946 - 20.5007i) q^{74} +66.5643 q^{76} +(123.144 - 76.2644i) q^{77} +(35.5533 - 109.422i) q^{79} +(-7.74201 - 10.6560i) q^{80} +(5.57848 + 17.1688i) q^{82} +(38.5111 - 12.5130i) q^{83} +(-71.0987 + 51.6562i) q^{85} +(13.5411 + 4.39977i) q^{86} +(-89.1372 + 21.8454i) q^{88} -71.1308i q^{89} +(-28.4466 + 20.6676i) q^{91} +(-19.8433 + 27.3120i) q^{92} +(-34.3301 - 105.657i) q^{94} +(-91.8821 + 126.465i) q^{95} +(5.76879 - 17.7545i) q^{97} +168.107i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^7	$ 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	1.28527	+	0.417608i	0.642633	+	0.208804i	0.612163	−	0.790732i	$-0.290300\pi$
$2$	1.28527	+	0.417608i	0.642633	+	0.208804i	0.0304699	+	0.999536i	$0.490300\pi$
$3$		0			0
$3$		0			0
$4$	−1.75856	−	1.27767i	−0.439639	−	0.319416i
$5$	4.85485	−	1.57744i	0.970970	−	0.315487i	0.219762	−	0.975553i	$-0.429472\pi$
$5$	4.85485	−	1.57744i	0.970970	−	0.315487i	0.751207	+	0.660066i	$0.229472\pi$
$6$		0			0
$7$	10.6531	+	7.73991i	1.52187	+	1.10570i	0.960553	+	0.278098i	$0.0897040\pi$
$7$	10.6531	+	7.73991i	1.52187	+	1.10570i	0.561314	+	0.827603i	$0.310296\pi$
$8$	−4.90400	−	6.74978i	−0.613000	−	0.843722i
$9$		0			0
$10$	6.89852			0.689852
$11$	4.16151	−	10.1824i	0.378319	−	0.925675i
$11$	4.16151	−	10.1824i	0.378319	−	0.925675i
$12$		0			0
$13$	−0.825159	+	2.53958i	−0.0634737	+	0.195352i	−0.977764	−	0.209707i	$-0.932749\pi$
$13$	−0.825159	+	2.53958i	−0.0634737	+	0.195352i	0.914291	+	0.405059i	$0.132749\pi$
$14$	10.4598	+	14.3966i	0.747127	+	1.02833i
$15$		0			0
$16$	−0.797348	−	2.45398i	−0.0498342	−	0.153374i
$17$	−16.3735	+	5.32007i	−0.963146	+	0.312945i	−0.748046	−	0.663647i	$-0.769008\pi$
$17$	−16.3735	+	5.32007i	−0.963146	+	0.312945i	−0.215100	+	0.976592i	$0.569008\pi$
$18$		0			0
$19$	−24.7742	+	17.9995i	−1.30391	+	0.947344i	−0.999986	−	0.00535276i	$-0.998296\pi$
$19$	−24.7742	+	17.9995i	−1.30391	+	0.947344i	−0.303922	+	0.952697i	$0.598296\pi$
$20$	−10.5530	−	3.42886i	−0.527648	−	0.171443i
$21$		0			0
$22$	9.60091	−	11.3492i	0.436405	−	0.515875i
$23$		−	15.5309i		−	0.675257i	−0.941279	−	0.337628i	$-0.890375\pi$
$23$		−	15.5309i		−	0.675257i	0.941279	−	0.337628i	$-0.109625\pi$
$24$		0			0
$25$	0.855829	−	0.621796i	0.0342332	−	0.0248718i
$26$	−2.12110	+	2.91944i	−0.0815806	+	0.112286i
$27$		0			0
$28$	−8.84500	−	27.2221i	−0.315893	−	0.972218i
$29$	−6.10287	+	8.39987i	−0.210444	+	0.289651i	−0.901170	−	0.433465i	$-0.857291\pi$
$29$	−6.10287	+	8.39987i	−0.210444	+	0.289651i	0.690727	+	0.723116i	$0.257291\pi$
$30$		0			0
$31$	5.21245	−	16.0423i	0.168144	−	0.517493i	−0.831111	−	0.556107i	$-0.812294\pi$
$31$	5.21245	−	16.0423i	0.168144	−	0.517493i	0.999254	+	0.0386144i	$0.0122944\pi$
$32$			29.8857i			0.933929i
$33$		0			0
$34$	−23.2660			−0.684294
$35$	63.9282	+	20.7715i	1.82652	+	0.593473i
$36$		0			0
$37$	−15.1698	−	11.0215i	−0.409996	−	0.297879i	0.363604	−	0.931553i	$-0.381546\pi$
$37$	−15.1698	−	11.0215i	−0.409996	−	0.297879i	−0.773600	+	0.633674i	$0.781546\pi$
$38$	−39.3582	+	12.7883i	−1.03574	+	0.336533i
$39$		0			0
$40$	−34.4555	−	25.0334i	−0.861388	−	0.625835i
$41$	7.85173	+	10.8070i	0.191506	+	0.263585i	0.893963	−	0.448141i	$-0.147914\pi$
$41$	7.85173	+	10.8070i	0.191506	+	0.263585i	−0.702457	+	0.711726i	$0.747914\pi$
$42$		0			0
$43$	10.5356			0.245015			0.122507	−	0.992468i	$-0.460907\pi$
$43$	10.5356			0.245015			0.122507	+	0.992468i	$0.460907\pi$
$44$	−20.3280	+	12.5893i	−0.462000	+	0.286122i
$45$		0			0
$46$	6.48583	−	19.9613i	0.140996	−	0.433942i
$47$	−48.3198	−	66.5065i	−1.02808	−	1.41503i	−0.906380	−	0.422464i	$-0.861165\pi$
$47$	−48.3198	−	66.5065i	−1.02808	−	1.41503i	−0.121700	−	0.992567i	$-0.538835\pi$
$48$		0			0
$49$	38.4399	+	118.306i	0.784487	+	2.41440i
$50$	1.35963	−	0.441772i	0.0271927	−	0.00883544i
$51$		0			0
$52$	4.69582	−	3.41171i	0.0903042	−	0.0656098i
$53$	59.9022	+	19.4634i	1.13023	+	0.367234i	0.813663	−	0.581336i	$-0.197470\pi$
$53$	59.9022	+	19.4634i	1.13023	+	0.367234i	0.316567	+	0.948570i	$0.397470\pi$
$54$		0			0
$55$	4.14138	−	55.9987i	0.0752978	−	1.01816i
$56$		−	109.862i		−	1.96183i
$57$		0			0
$58$	−11.3517	+	8.24747i	−0.195718	+	0.142198i
$59$	−38.7385	+	53.3189i	−0.656584	+	0.903711i	−0.999362	−	0.0357057i	$-0.988632\pi$
$59$	−38.7385	+	53.3189i	−0.656584	+	0.903711i	0.342778	+	0.939416i	$0.388632\pi$
$60$		0			0
$61$	11.2965	+	34.7670i	0.185188	+	0.569951i	0.999952	−	0.00984300i	$-0.00313318\pi$
$61$	11.2965	+	34.7670i	0.185188	+	0.569951i	−0.814763	+	0.579794i	$0.803133\pi$
$62$	13.3988	−	18.4418i	0.216109	−	0.297449i
$63$		0			0
$64$	−15.6699	+	48.2271i	−0.244843	+	0.753548i
$65$			13.6309i			0.209706i
$66$		0			0
$67$	60.5815			0.904202			0.452101	−	0.891967i	$-0.350675\pi$
$67$	60.5815			0.904202			0.452101	+	0.891967i	$0.350675\pi$
$68$	35.5909	+	11.5642i	0.523396	+	0.170062i
$69$		0			0
$70$	73.4904	+	53.3939i	1.04986	+	0.762770i
$71$	−46.7818	+	15.2003i	−0.658899	+	0.214089i	−0.619334	−	0.785128i	$-0.712597\pi$
$71$	−46.7818	+	15.2003i	−0.658899	+	0.214089i	−0.0395649	+	0.999217i	$0.512597\pi$
$72$		0			0
$73$	−5.15593	−	3.74600i	−0.0706291	−	0.0513151i	0.551910	−	0.833903i	$-0.313899\pi$
$73$	−5.15593	−	3.74600i	−0.0706291	−	0.0513151i	−0.622540	+	0.782588i	$0.713899\pi$
$74$	−14.8946	−	20.5007i	−0.201278	−	0.277036i
$75$		0			0
$76$	66.5643			0.875846
$77$	123.144	−	76.2644i	1.59927	−	0.990447i
$78$		0			0
$79$	35.5533	−	109.422i	0.450042	−	1.38509i	−0.426817	−	0.904338i	$-0.640365\pi$
$79$	35.5533	−	109.422i	0.450042	−	1.38509i	0.876859	−	0.480748i	$-0.159635\pi$
$80$	−7.74201	−	10.6560i	−0.0967751	−	0.133199i
$81$		0			0
$82$	5.57848	+	17.1688i	0.0680302	+	0.209375i
$83$	38.5111	−	12.5130i	0.463989	−	0.150759i	−0.0676879	−	0.997707i	$-0.521562\pi$
$83$	38.5111	−	12.5130i	0.463989	−	0.150759i	0.531677	+	0.846947i	$0.321562\pi$
$84$		0			0
$85$	−71.0987	+	51.6562i	−0.836455	+	0.607720i
$86$	13.5411	+	4.39977i	0.157454	+	0.0511601i
$87$		0			0
$88$	−89.1372	+	21.8454i	−1.01292	+	0.248243i
$89$		−	71.1308i		−	0.799222i	−0.916685	−	0.399611i	$-0.869145\pi$
$89$		−	71.1308i		−	0.799222i	0.916685	−	0.399611i	$-0.130855\pi$
$90$		0			0
$91$	−28.4466	+	20.6676i	−0.312600	+	0.227117i
$92$	−19.8433	+	27.3120i	−0.215688	+	0.296869i
$93$		0			0
$94$	−34.3301	−	105.657i	−0.365214	−	1.12401i
$95$	−91.8821	+	126.465i	−0.967180	+	1.33121i
$96$		0			0
$97$	5.76879	−	17.7545i	0.0594721	−	0.183036i	−0.916907	−	0.399101i	$-0.869322\pi$
$97$	5.76879	−	17.7545i	0.0594721	−	0.183036i	0.976379	+	0.216065i	$0.0693223\pi$
$98$			168.107i			1.71538i
$99$		0			0
$100$	−2.29947			−0.0229947
$101$	44.7592	+	14.5432i	0.443161	+	0.143992i	0.522093	−	0.852888i	$-0.325151\pi$
$101$	44.7592	+	14.5432i	0.443161	+	0.143992i	−0.0789326	+	0.996880i	$0.525151\pi$
$102$		0			0
$103$	−90.1550	−	65.5015i	−0.875292	−	0.635937i	0.0567100	−	0.998391i	$-0.481939\pi$
$103$	−90.1550	−	65.5015i	−0.875292	−	0.635937i	−0.932002	+	0.362454i	$0.881939\pi$
$104$	21.1882	−	6.88445i	0.203732	−	0.0661966i
$105$		0			0
$106$	68.8622	+	50.0313i	0.649643	+	0.471993i
$107$	−65.1737	−	89.7039i	−0.609100	−	0.838354i	0.387403	−	0.921910i	$-0.373372\pi$
$107$	−65.1737	−	89.7039i	−0.609100	−	0.838354i	−0.996503	+	0.0835565i	$0.973372\pi$
$108$		0			0
$109$	118.337			1.08566			0.542832	−	0.839841i	$-0.317352\pi$
$109$	118.337			1.08566			0.542832	+	0.839841i	$0.317352\pi$
$110$	28.7083	−	70.2437i	0.260984	−	0.638579i
$111$		0			0
$112$	10.4994	−	32.3139i	0.0937447	−	0.288517i
$113$	40.7594	+	56.1005i	0.360702	+	0.496464i	0.950344	−	0.311200i	$-0.100731\pi$
$113$	40.7594	+	56.1005i	0.360702	+	0.496464i	−0.589642	+	0.807665i	$0.700731\pi$
$114$		0			0
$115$	−24.4990	−	75.4002i	−0.213035	−	0.655654i
$116$	21.4645	−	6.97423i	0.185038	−	0.0601226i
$117$		0			0
$118$	−72.0557	+	52.3515i	−0.610641	+	0.443657i
$119$	−215.605	−	70.0542i	−1.81180	−	0.588691i
$120$		0			0
$121$	−86.3637	−	84.7486i	−0.713749	−	0.700401i
$122$			49.4023i			0.404937i
$123$		0			0
$124$	−29.6630	+	21.5515i	−0.239218	+	0.173802i
$125$	−71.8375	+	98.8758i	−0.574700	+	0.791006i
$126$		0			0
$127$	3.32960	+	10.2475i	0.0262174	+	0.0806887i	0.963309	−	0.268394i	$-0.0864931\pi$
$127$	3.32960	+	10.2475i	0.0262174	+	0.0806887i	−0.937092	+	0.349083i	$0.886493\pi$
$128$	29.9855	−	41.2716i	0.234262	−	0.322434i
$129$		0			0
$130$	−5.69237	+	17.5193i	−0.0437875	+	0.134764i
$131$			92.0724i			0.702843i	0.936217	+	0.351421i	$0.114302\pi$
$131$			92.0724i			0.702843i	−0.936217	+	0.351421i	$0.885698\pi$
$132$		0			0
$133$	−403.236			−3.03185
$134$	77.8633	+	25.2993i	0.581070	+	0.188801i
$135$		0			0
$136$	116.205	+	84.4277i	0.854447	+	0.620792i
$137$	−188.928	+	61.3865i	−1.37904	+	0.448077i	−0.902353	−	0.430998i	$-0.858162\pi$
$137$	−188.928	+	61.3865i	−1.37904	+	0.448077i	−0.476685	+	0.879074i	$0.658162\pi$
$138$		0			0
$139$	48.1649	+	34.9938i	0.346510	+	0.251754i	0.747403	−	0.664371i	$-0.231300\pi$
$139$	48.1649	+	34.9938i	0.346510	+	0.251754i	−0.400894	+	0.916125i	$0.631300\pi$
$140$	−85.8823	−	118.207i	−0.613445	−	0.844335i
$141$		0			0
$142$	−66.4748			−0.468133
$143$	22.4252	+	18.9706i	0.156819	+	0.132661i
$144$		0			0
$145$	−16.3782	+	50.4070i	−0.112953	+	0.347634i
$146$	−5.06238	−	6.96776i	−0.0346738	−	0.0477244i
$147$		0			0
$148$	12.5952	+	38.7640i	0.0851025	+	0.261919i
$149$	13.8516	−	4.50065i	0.0929636	−	0.0302057i	−0.262166	−	0.965023i	$-0.584437\pi$
$149$	13.8516	−	4.50065i	0.0929636	−	0.0302057i	0.355129	+	0.934817i	$0.384437\pi$
$150$		0			0
$151$	197.075	−	143.183i	1.30513	−	0.948234i	0.305140	−	0.952307i	$-0.401297\pi$
$151$	197.075	−	143.183i	1.30513	−	0.948234i	0.999992	+	0.00407377i	$0.00129672\pi$
$152$	242.986	+	78.9509i	1.59859	+	0.519414i
$153$		0			0
$154$	190.121	−	46.5941i	1.23455	−	0.302559i
$155$		−	86.1051i		−	0.555517i
$156$		0			0
$157$	89.8278	−	65.2637i	0.572151	−	0.415692i	−0.263735	−	0.964595i	$-0.584954\pi$
$157$	89.8278	−	65.2637i	0.572151	−	0.415692i	0.835886	+	0.548903i	$0.184954\pi$
$158$	91.3909	−	125.789i	0.578423	−	0.796131i
$159$		0			0
$160$	47.1428	+	145.091i	0.294643	+	0.906817i
$161$	120.208	−	165.452i	0.746632	−	1.02765i
$162$		0			0
$163$	38.0567	−	117.126i	0.233477	−	0.718567i	−0.763843	−	0.645402i	$-0.776690\pi$
$163$	38.0567	−	117.126i	0.233477	−	0.718567i	0.997320	−	0.0731653i	$-0.0233101\pi$
$164$		−	29.0365i		−	0.177052i
$165$		0			0
$166$	54.7225			0.329654
$167$	217.801	+	70.7679i	1.30420	+	0.423760i	0.877040	−	0.480417i	$-0.159515\pi$
$167$	217.801	+	70.7679i	1.30420	+	0.423760i	0.427159	+	0.904177i	$0.359515\pi$
$168$		0			0
$169$	130.955	+	95.1446i	0.774883	+	0.562986i
$170$	−112.953	+	36.7006i	−0.664428	+	0.215886i
$171$		0			0
$172$	−18.5275	−	13.4610i	−0.107718	−	0.0782617i
$173$	101.498	+	139.699i	0.586691	+	0.807511i	0.994409	−	0.105597i	$-0.0336754\pi$
$173$	101.498	+	139.699i	0.586691	+	0.807511i	−0.407718	+	0.913108i	$0.633675\pi$
$174$		0			0
$175$	13.9298			0.0795991
$176$	−28.3057	−	2.09335i	−0.160828	−	0.0118940i
$177$		0			0
$178$	29.7048	−	91.4220i	0.166881	−	0.513607i
$179$	−107.266	−	147.639i	−0.599252	−	0.824800i	0.396387	−	0.918083i	$-0.370264\pi$
$179$	−107.266	−	147.639i	−0.599252	−	0.824800i	−0.995640	+	0.0932832i	$0.970264\pi$
$180$		0			0
$181$	37.6199	+	115.782i	0.207845	+	0.639680i	0.999585	+	0.0288218i	$0.00917553\pi$
$181$	37.6199	+	115.782i	0.207845	+	0.639680i	−0.791740	+	0.610858i	$0.790824\pi$
$182$	−45.1924	+	14.6839i	−0.248310	+	0.0806807i
$183$		0			0
$184$	−104.830	+	76.1636i	−0.569729	+	0.413932i
$185$	−91.0330	−	29.5784i	−0.492071	−	0.159883i
$186$		0			0
$187$	−13.9672	+	188.861i	−0.0746910	+	1.00995i
$188$			178.692i			0.950488i
$189$		0			0
$190$	−170.906	+	124.170i	−0.899503	+	0.653528i
$191$	184.809	−	254.368i	0.967588	−	1.33177i	0.0243324	−	0.999704i	$-0.492254\pi$
$191$	184.809	−	254.368i	0.967588	−	1.33177i	0.943256	−	0.332067i	$-0.107746\pi$
$192$		0			0
$193$	38.4388	+	118.302i	0.199165	+	0.612966i	0.999903	+	0.0139512i	$0.00444094\pi$
$193$	38.4388	+	118.302i	0.199165	+	0.612966i	−0.800738	+	0.599015i	$0.795559\pi$
$194$	14.8289	−	20.4102i	0.0764374	−	0.105207i
$195$		0			0
$196$	83.5565	−	257.161i	0.426309	−	1.31204i
$197$		−	193.993i		−	0.984738i	−0.870387	−	0.492369i	$-0.836131\pi$
$197$		−	193.993i		−	0.984738i	0.870387	−	0.492369i	$-0.163869\pi$
$198$		0			0
$199$	−67.6934			−0.340168			−0.170084	−	0.985430i	$-0.554404\pi$
$199$	−67.6934			−0.340168			−0.170084	+	0.985430i	$0.554404\pi$
$200$	−8.39397	−	2.72737i	−0.0419699	−	0.0136368i
$201$		0			0
$202$	51.4542	+	37.3837i	0.254724	+	0.185068i
$203$	−130.028	+	42.2488i	−0.640534	+	0.208122i
$204$		0			0
$205$	55.1663	+	40.0806i	0.269104	+	0.195515i
$206$	−88.5193	−	121.836i	−0.429705	−	0.591438i
$207$		0			0
$208$	6.89002			0.0331251
$209$	80.1807	+	327.167i	0.383640	+	1.56539i
$210$		0			0
$211$	23.1912	−	71.3752i	0.109911	−	0.338271i	−0.880941	−	0.473227i	$-0.843089\pi$
$211$	23.1912	−	71.3752i	0.109911	−	0.338271i	0.990852	+	0.134955i	$0.0430891\pi$
$212$	−80.4736	−	110.762i	−0.379593	−	0.522464i
$213$		0			0
$214$	−46.3044	−	142.510i	−0.216376	−	0.665936i
$215$	51.1489	−	16.6193i	0.237902	−	0.0772990i
$216$		0			0
$217$	179.694	−	130.556i	0.828084	−	0.601638i
$218$	152.095	+	49.4187i	0.697684	+	0.226691i
$219$		0			0
$220$	−78.8304	+	93.1855i	−0.358320	+	0.423570i
$221$		−	45.9716i		−	0.208016i
$222$		0			0
$223$	4.83651	−	3.51393i	0.0216884	−	0.0157575i	−0.576888	−	0.816823i	$-0.695733\pi$
$223$	4.83651	−	3.51393i	0.0216884	−	0.0157575i	0.598577	+	0.801066i	$0.295733\pi$
$224$	−231.313	+	318.375i	−1.03265	+	1.42132i
$225$		0			0
$226$	28.9586	+	89.1255i	0.128136	+	0.394361i
$227$	−98.9713	+	136.222i	−0.435997	+	0.600098i	−0.969317	−	0.245815i	$-0.920944\pi$
$227$	−98.9713	+	136.222i	−0.435997	+	0.600098i	0.533320	+	0.845914i	$0.320944\pi$
$228$		0			0
$229$	−108.832	+	334.950i	−0.475249	+	1.46267i	0.370373	+	0.928883i	$0.379230\pi$
$229$	−108.832	+	334.950i	−0.475249	+	1.46267i	−0.845622	+	0.533782i	$0.820770\pi$
$230$		−	107.140i		−	0.465827i
$231$		0			0
$232$	86.6257			0.373387
$233$	−338.664	−	110.039i	−1.45349	−	0.472268i	−0.527417	−	0.849606i	$-0.676840\pi$
$233$	−338.664	−	110.039i	−1.45349	−	0.472268i	−0.926076	+	0.377338i	$0.876840\pi$
$234$		0			0
$235$	−339.495	−	246.657i	−1.44466	−	1.04961i
$236$	136.248	−	44.2695i	0.577320	−	0.187583i
$237$		0			0
$238$	−247.854	−	180.077i	−1.04140	−	0.756624i
$239$	10.2500	+	14.1079i	0.0428871	+	0.0590290i	0.829922	−	0.557879i	$-0.188385\pi$
$239$	10.2500	+	14.1079i	0.0428871	+	0.0590290i	−0.787035	+	0.616908i	$0.788385\pi$
$240$		0			0
$241$	−98.6722			−0.409428			−0.204714	−	0.978822i	$-0.565626\pi$
$241$	−98.6722			−0.409428			−0.204714	+	0.978822i	$0.565626\pi$
$242$	−75.6086	−	144.991i	−0.312432	−	0.599135i
$243$		0			0
$244$	24.5551	−	75.5728i	0.100636	−	0.309725i
$245$	373.239	+	513.720i	1.52343	+	2.09682i
$246$		0			0
$247$	−25.2685	−	77.7686i	−0.102302	−	0.314852i
$248$	−133.844	+	43.4884i	−0.539692	+	0.175357i
$249$		0			0
$250$	−133.622	+	97.0818i	−0.534486	+	0.388327i
$251$	−168.627	−	54.7903i	−0.671821	−	0.218288i	−0.0468100	−	0.998904i	$-0.514906\pi$
$251$	−168.627	−	54.7903i	−0.671821	−	0.218288i	−0.625011	+	0.780616i	$0.714906\pi$
$252$		0			0
$253$	−158.142	−	64.6320i	−0.625068	−	0.255463i
$254$			14.5612i			0.0573275i
$255$		0			0
$256$	219.872	−	159.747i	0.858876	−	0.624010i
$257$	67.7862	−	93.2997i	0.263760	−	0.363034i	−0.656511	−	0.754316i	$-0.727968\pi$
$257$	67.7862	−	93.2997i	0.263760	−	0.363034i	0.920271	+	0.391283i	$0.127968\pi$
$258$		0			0
$259$	−76.2997	−	234.826i	−0.294593	−	0.906665i
$260$	17.4157	−	23.9707i	0.0669836	−	0.0921950i
$261$		0			0
$262$	−38.4502	+	118.338i	−0.146756	+	0.451670i
$263$			236.953i			0.900964i	0.892786	+	0.450482i	$0.148748\pi$
$263$			236.953i			0.900964i	−0.892786	+	0.450482i	$0.851252\pi$
$264$		0			0
$265$	321.518			1.21328
$266$	−518.266	−	168.395i	−1.94837	−	0.633063i
$267$		0			0
$268$	−106.536	−	77.4029i	−0.397522	−	0.288817i
$269$	502.614	−	163.309i	1.86845	−	0.607097i	0.876348	−	0.481678i	$-0.159973\pi$
$269$	502.614	−	163.309i	1.86845	−	0.607097i	0.992104	−	0.125419i	$-0.0400275\pi$
$270$		0			0
$271$	144.762	+	105.176i	0.534178	+	0.388103i	0.821918	−	0.569606i	$-0.192904\pi$
$271$	144.762	+	105.176i	0.534178	+	0.388103i	−0.287740	+	0.957708i	$0.592904\pi$
$272$	26.1107	+	35.9383i	0.0959953	+	0.132126i
$273$		0			0
$274$	−268.458			−0.979775
$275$	−2.76985	−	11.3020i	−0.0100722	−	0.0410983i
$276$		0			0
$277$	−88.4454	+	272.207i	−0.319297	+	0.982696i	0.654652	+	0.755930i	$0.272815\pi$
$277$	−88.4454	+	272.207i	−0.319297	+	0.982696i	−0.973949	+	0.226766i	$0.927185\pi$
$278$	47.2910	+	65.0904i	0.170111	+	0.234138i
$279$		0			0
$280$	−173.301	−	533.365i	−0.618932	−	1.90488i
$281$	241.030	−	78.3155i	0.857760	−	0.278703i	0.153067	−	0.988216i	$-0.451085\pi$
$281$	241.030	−	78.3155i	0.857760	−	0.278703i	0.704693	+	0.709513i	$0.251085\pi$
$282$		0			0
$283$	229.170	−	166.502i	0.809788	−	0.588346i	−0.103981	−	0.994579i	$-0.533158\pi$
$283$	229.170	−	166.502i	0.809788	−	0.588346i	0.913769	+	0.406234i	$0.133158\pi$
$284$	101.689	+	33.0409i	0.358061	+	0.116341i
$285$		0			0
$286$	20.9000	+	33.7472i	0.0730769	+	0.117997i
$287$			175.899i			0.612889i
$288$		0			0
$289$	5.98182	−	4.34605i	0.0206983	−	0.0150382i
$290$	−42.1008	+	57.9467i	−0.145175	+	0.199816i
$291$		0			0
$292$	4.28085	+	13.1751i	0.0146604	+	0.0451202i
$293$	−175.920	+	242.133i	−0.600409	+	0.826393i	−0.995746	−	0.0921437i	$-0.970628\pi$
$293$	−175.920	+	242.133i	−0.600409	+	0.826393i	0.395336	+	0.918536i	$0.370628\pi$
$294$		0			0
$295$	−103.962	+	319.963i	−0.352414	+	1.08462i
$296$			156.443i			0.528523i
$297$		0			0
$298$	19.6825			0.0660485
$299$	39.4419	+	12.8155i	0.131913	+	0.0428611i
$300$		0			0
$301$	112.237	+	81.5448i	0.372880	+	0.270913i
$302$	313.088	−	101.729i	1.03672	−	0.336849i
$303$		0			0
$304$	63.9243	+	46.4437i	0.210277	+	0.152775i
$305$	109.685	+	150.969i	0.359624	+	0.494980i
$306$		0			0
$307$	111.839			0.364296			0.182148	−	0.983271i	$-0.441695\pi$
$307$	111.839			0.364296			0.182148	+	0.983271i	$0.441695\pi$
$308$	−313.996	−	23.2215i	−1.01947	−	0.0753946i
$309$		0			0
$310$	35.9582	−	110.668i	0.115994	−	0.356993i
$311$	−209.419	−	288.240i	−0.673372	−	0.926817i	0.326459	−	0.945211i	$-0.394145\pi$
$311$	−209.419	−	288.240i	−0.673372	−	0.926817i	−0.999831	+	0.0183943i	$0.994145\pi$
$312$		0			0
$313$	104.677	+	322.163i	0.334431	+	1.02927i	0.967001	+	0.254771i	$0.0820000\pi$
$313$	104.677	+	322.163i	0.334431	+	1.02927i	−0.632570	+	0.774503i	$0.718000\pi$
$314$	142.707	−	46.3684i	0.454482	−	0.147670i
$315$		0			0
$316$	−202.327	+	146.999i	−0.640275	+	0.465187i
$317$	−384.837	−	125.041i	−1.21400	−	0.394452i	−0.369105	−	0.929388i	$-0.620336\pi$
$317$	−384.837	−	125.041i	−1.21400	−	0.394452i	−0.844893	+	0.534936i	$0.820336\pi$
$318$		0			0
$319$	60.1340	+	97.0982i	0.188508	+	0.304383i
$320$			258.853i			0.808917i
$321$		0			0
$322$	223.593	−	162.450i	0.694388	−	0.504502i
$323$	309.882	−	426.516i	0.959386	−	1.32048i
$324$		0			0
$325$	0.872904	+	2.68652i	0.00268586	+	0.00826623i
$326$	97.8259	−	134.646i	0.300080	−	0.413024i
$327$		0			0
$328$	34.4398	−	105.995i	0.104999	−	0.323155i
$329$		−	1082.49i		−	3.29024i
$330$		0			0
$331$	634.065			1.91561			0.957803	−	0.287426i	$-0.0927995\pi$
$331$	634.065			1.91561			0.957803	+	0.287426i	$0.0927995\pi$
$332$	−83.7113	−	27.1994i	−0.252142	−	0.0819260i
$333$		0			0
$334$	250.379	+	181.911i	0.749639	+	0.544644i
$335$	294.114	−	95.5634i	0.877952	−	0.285264i
$336$		0			0
$337$	−192.071	−	139.547i	−0.569942	−	0.414087i	0.265142	−	0.964209i	$-0.414581\pi$
$337$	−192.071	−	139.547i	−0.569942	−	0.414087i	−0.835084	+	0.550122i	$0.814581\pi$
$338$	128.579	+	176.974i	0.380412	+	0.523592i
$339$		0			0
$340$	191.030			0.561854
$341$	−141.658	−	119.835i	−0.415418	−	0.351424i
$342$		0			0
$343$	−306.786	+	944.192i	−0.894421	+	2.75275i
$344$	−51.6667	−	71.1132i	−0.150194	−	0.206724i
$345$		0			0
$346$	72.1117	+	221.937i	0.208415	+	0.641436i
$347$	−463.624	+	150.641i	−1.33609	+	0.434123i	−0.887992	−	0.459859i	$-0.847900\pi$
$347$	−463.624	+	150.641i	−1.33609	+	0.434123i	−0.448102	+	0.893983i	$0.647900\pi$
$348$		0			0
$349$	−30.7829	+	22.3651i	−0.0882033	+	0.0640834i	−0.631013	−	0.775772i	$-0.717361\pi$
$349$	−30.7829	+	22.3651i	−0.0882033	+	0.0640834i	0.542810	+	0.839856i	$0.317361\pi$
$350$	17.9036	+	5.81722i	0.0511530	+	0.0166206i
$351$		0			0
$352$	304.309	+	124.370i	0.864515	+	0.353323i
$353$			90.5379i			0.256481i	0.991743	+	0.128241i	$0.0409330\pi$
$353$			90.5379i			0.256481i	−0.991743	+	0.128241i	$0.959067\pi$
$354$		0			0
$355$	−203.141	+	147.591i	−0.572228	+	0.415748i
$356$	−90.8813	+	125.087i	−0.255285	+	0.351369i
$357$		0			0
$358$	−76.2102	−	234.551i	−0.212878	−	0.655170i
$359$	−65.8242	+	90.5992i	−0.183354	+	0.252366i	−0.890793	−	0.454409i	$-0.849850\pi$
$359$	−65.8242	+	90.5992i	−0.183354	+	0.252366i	0.707439	+	0.706775i	$0.249850\pi$
$360$		0			0
$361$	178.224	−	548.519i	0.493697	−	1.51944i
$362$			164.521i			0.454478i
$363$		0			0
$364$	76.4312			0.209976
$365$	−30.9403	−	10.0531i	−0.0847680	−	0.0275428i
$366$		0			0
$367$	−274.088	−	199.136i	−0.746833	−	0.542606i	0.148010	−	0.988986i	$-0.452713\pi$
$367$	−274.088	−	199.136i	−0.746833	−	0.542606i	−0.894844	+	0.446380i	$0.852713\pi$
$368$	−38.1126	+	12.3835i	−0.103567	+	0.0336509i
$369$		0			0
$370$	−104.649	−	76.0323i	−0.282836	−	0.205493i
$371$	487.497	+	670.982i	1.31401	+	1.80858i
$372$		0			0
$373$	−554.596			−1.48685			−0.743427	−	0.668818i	$-0.766801\pi$
$373$	−554.596			−1.48685			−0.743427	+	0.668818i	$0.766801\pi$
$374$	−96.8216	+	236.904i	−0.258881	+	0.633434i
$375$		0			0
$376$	−211.944	+	652.295i	−0.563680	+	1.73483i
$377$	−16.2963	−	22.4299i	−0.0432262	−	0.0594958i
$378$		0			0
$379$	−77.6587	−	239.009i	−0.204904	−	0.630631i	−0.999717	−	0.0237762i	$-0.992431\pi$
$379$	−77.6587	−	239.009i	−0.204904	−	0.630631i	0.794813	−	0.606854i	$-0.207569\pi$
$380$	323.160	−	105.001i	0.850420	−	0.276318i
$381$		0			0
$382$	343.755	−	249.753i	0.899883	−	0.653804i
$383$	489.046	+	158.901i	1.27688	+	0.414885i	0.867481	−	0.497470i	$-0.165737\pi$
$383$	489.046	+	158.901i	1.27688	+	0.414885i	0.409402	+	0.912354i	$0.365737\pi$
$384$		0			0
$385$	477.543	−	564.504i	1.24037	−	1.46624i
$386$			168.102i			0.435499i
$387$		0			0
$388$	−32.8291	+	23.8517i	−0.0846110	+	0.0614735i
$389$	−114.119	+	157.071i	−0.293365	+	0.403782i	−0.930103	−	0.367298i	$-0.880283\pi$
$389$	−114.119	+	157.071i	−0.293365	+	0.403782i	0.636739	+	0.771080i	$0.280283\pi$
$390$		0			0
$391$	82.6254	+	254.295i	0.211318	+	0.650371i
$392$	610.028	−	839.632i	1.55619	−	2.14192i
$393$		0			0
$394$	81.0132	−	249.333i	0.205617	−	0.632825i
$395$		−	587.309i		−	1.48686i
$396$		0			0
$397$	−260.248			−0.655537			−0.327769	−	0.944758i	$-0.606297\pi$
$397$	−260.248			−0.655537			−0.327769	+	0.944758i	$0.606297\pi$
$398$	−87.0041	−	28.2693i	−0.218603	−	0.0710285i
$399$		0			0
$400$	−2.20827	−	1.60440i	−0.00552068	−	0.00401101i
$401$	−360.802	+	117.232i	−0.899755	+	0.292348i	−0.722136	−	0.691751i	$-0.756840\pi$
$401$	−360.802	+	117.232i	−0.899755	+	0.292348i	−0.177619	+	0.984099i	$0.556840\pi$
$402$		0			0
$403$	36.4395	+	26.4748i	0.0904206	+	0.0656944i
$404$	−60.1303	−	82.7623i	−0.148837	−	0.204857i
$405$		0			0
$406$	−184.765			−0.455085
$407$	−175.355	+	108.600i	−0.430849	+	0.266829i
$408$		0			0
$409$	210.768	−	648.678i	0.515326	−	1.58601i	−0.267362	−	0.963596i	$-0.586152\pi$
$409$	210.768	−	648.678i	0.515326	−	1.58601i	0.782688	−	0.622415i	$-0.213848\pi$
$410$	54.1653	+	74.5522i	0.132111	+	0.181835i
$411$		0			0
$412$	74.8537	+	230.376i	0.181684	+	0.559165i
$413$	−825.367	+	268.178i	−1.99847	+	0.649342i
$414$		0			0
$415$	167.227	−	121.497i	0.402956	−	0.292765i
$416$	−75.8971	−	24.6605i	−0.182445	−	0.0592800i
$417$		0			0
$418$	−33.5741	+	453.981i	−0.0803209	+	1.08608i
$419$			275.319i			0.657085i	0.944489	+	0.328543i	$0.106557\pi$
$419$			275.319i			0.657085i	−0.944489	+	0.328543i	$0.893443\pi$
$420$		0			0
$421$	−98.2710	+	71.3981i	−0.233423	+	0.169592i	−0.698348	−	0.715758i	$-0.746081\pi$
$421$	−98.2710	+	71.3981i	−0.233423	+	0.169592i	0.464925	+	0.885350i	$0.346081\pi$
$422$	59.6138	−	82.0513i	0.141265	−	0.194434i
$423$		0			0
$424$	−162.387	−	499.775i	−0.382988	−	1.17871i
$425$	−10.7049	+	14.7340i	−0.0251880	+	0.0346683i
$426$		0			0
$427$	−148.751	+	457.809i	−0.348363	+	1.07215i
$428$			241.019i			0.563130i
$429$		0			0
$430$	72.6803			0.169024
$431$	−93.9131	−	30.5142i	−0.217896	−	0.0707987i	0.198035	−	0.980195i	$-0.436544\pi$
$431$	−93.9131	−	30.5142i	−0.217896	−	0.0707987i	−0.415931	+	0.909396i	$0.636544\pi$
$432$		0			0
$433$	−453.043	−	329.155i	−1.04629	−	0.760173i	−0.0747851	−	0.997200i	$-0.523827\pi$
$433$	−453.043	−	329.155i	−1.04629	−	0.760173i	−0.971503	+	0.237027i	$0.923827\pi$
$434$	285.476	−	92.7568i	0.657779	−	0.213725i
$435$		0			0
$436$	−208.103	−	151.196i	−0.477301	−	0.346779i
$437$	279.549	+	384.766i	0.639701	+	0.880472i
$438$		0			0
$439$	−577.439			−1.31535			−0.657676	−	0.753301i	$-0.728460\pi$
$439$	−577.439			−1.31535			−0.657676	+	0.753301i	$0.728460\pi$
$440$	−398.288	+	246.664i	−0.905200	+	0.560600i
$441$		0			0
$442$	19.1981	−	59.0857i	0.0434347	−	0.133678i
$443$	51.3607	+	70.6919i	0.115938	+	0.159575i	0.863042	−	0.505132i	$-0.168556\pi$
$443$	51.3607	+	70.6919i	0.115938	+	0.159575i	−0.747104	+	0.664707i	$0.768556\pi$
$444$		0			0
$445$	−112.204	−	345.329i	−0.252144	−	0.776021i
$446$	7.68364	−	2.49657i	0.0172279	−	0.00559768i
$447$		0			0
$448$	−540.206	+	392.482i	−1.20582	+	0.876077i
$449$	−91.5004	−	29.7303i	−0.203787	−	0.0662145i	0.205345	−	0.978690i	$-0.434168\pi$
$449$	−91.5004	−	29.7303i	−0.203787	−	0.0662145i	−0.409132	+	0.912475i	$0.634168\pi$
$450$		0			0
$451$	142.716	−	34.9763i	0.316444	−	0.0775528i
$452$		−	150.733i		−	0.333479i
$453$		0			0
$454$	−184.092	+	133.751i	−0.405489	+	0.294605i
$455$	−105.502	+	145.211i	−0.231872	+	0.319145i
$456$		0			0
$457$	−213.774	−	657.929i	−0.467777	−	1.43967i	−0.855456	−	0.517875i	$-0.826723\pi$
$457$	−213.774	−	657.929i	−0.467777	−	1.43967i	0.387679	−	0.921794i	$-0.373277\pi$
$458$	−279.756	+	385.051i	−0.610821	+	0.840723i
$459$		0			0
$460$	−53.2534	+	163.897i	−0.115768	+	0.356298i
$461$			70.5491i			0.153035i	0.997068	+	0.0765175i	$0.0243801\pi$
$461$			70.5491i			0.153035i	−0.997068	+	0.0765175i	$0.975620\pi$
$462$		0			0
$463$	248.292			0.536267			0.268134	−	0.963382i	$-0.413593\pi$
$463$	248.292			0.536267			0.268134	+	0.963382i	$0.413593\pi$
$464$	25.4793	+	8.27872i	0.0549122	+	0.0178421i
$465$		0			0
$466$	−389.320	−	282.858i	−0.835451	−	0.606991i
$467$	241.718	−	78.5391i	0.517598	−	0.168178i	−0.0385567	−	0.999256i	$-0.512276\pi$
$467$	241.718	−	78.5391i	0.517598	−	0.168178i	0.556155	+	0.831078i	$0.312276\pi$
$468$		0			0
$469$	645.379	+	468.895i	1.37607	+	0.999776i
$470$	−333.335	−	458.796i	−0.709223	−	0.976162i
$471$		0			0
$472$	549.864			1.16497
$473$	43.8441	−	107.278i	0.0926937	−	0.226804i
$474$		0			0
$475$	−10.0105	+	30.8091i	−0.0210747	+	0.0648612i
$476$	289.647	+	398.665i	0.608502	+	0.837531i
$477$		0			0
$478$	7.28241	+	22.4129i	0.0152352	+	0.0468890i
$479$	17.3840	−	5.64840i	0.0362922	−	0.0117921i	−0.290815	−	0.956779i	$-0.593926\pi$
$479$	17.3840	−	5.64840i	0.0362922	−	0.0117921i	0.327107	+	0.944987i	$0.393926\pi$
$480$		0			0
$481$	40.5076	−	29.4305i	0.0842153	−	0.0611860i
$482$	−126.820	−	41.2063i	−0.263112	−	0.0854903i
$483$		0			0
$484$	43.5950	+	259.379i	0.0900723	+	0.535907i
$485$		−	95.2954i		−	0.196485i
$486$		0			0
$487$	196.895	−	143.052i	0.404302	−	0.293742i	−0.366989	−	0.930225i	$-0.619611\pi$
$487$	196.895	−	143.052i	0.404302	−	0.293742i	0.771291	+	0.636483i	$0.219611\pi$
$488$	179.272	−	246.746i	0.367360	−	0.505627i
$489$		0			0
$490$	265.178	+	816.135i	0.541180	+	1.66558i
$491$	−185.960	+	255.952i	−0.378738	+	0.521288i	−0.955250	−	0.295801i	$-0.904413\pi$
$491$	−185.960	+	255.952i	−0.378738	+	0.521288i	0.576512	+	0.817089i	$0.304413\pi$
$492$		0			0
$493$	55.2373	−	170.003i	0.112043	−	0.344833i
$494$		−	110.506i		−	0.223696i
$495$		0			0
$496$	−43.5236			−0.0877493
$497$	−616.019	−	200.157i	−1.23947	−	0.402730i
$498$		0			0
$499$	−21.6847	−	15.7549i	−0.0434563	−	0.0315728i	0.565845	−	0.824512i	$-0.308550\pi$
$499$	−21.6847	−	15.7549i	−0.0434563	−	0.0315728i	−0.609301	+	0.792939i	$0.708550\pi$
$500$	252.660	−	82.0943i	0.505321	−	0.164189i
$501$		0			0
$502$	−193.850	−	140.840i	−0.386155	−	0.280558i
$503$	−107.344	−	147.746i	−0.213408	−	0.293730i	0.688871	−	0.724884i	$-0.258107\pi$
$503$	−107.344	−	147.746i	−0.213408	−	0.293730i	−0.902278	+	0.431154i	$0.858107\pi$
$504$		0			0
$505$	240.240			0.475723
$506$	−176.264	−	149.111i	−0.348348	−	0.294686i
$507$		0			0
$508$	7.23754	−	22.2749i	0.0142471	−	0.0438482i
$509$	127.165	+	175.027i	0.249832	+	0.343864i	0.915452	−	0.402426i	$-0.131833\pi$
$509$	127.165	+	175.027i	0.249832	+	0.343864i	−0.665620	+	0.746290i	$0.731833\pi$
$510$		0			0
$511$	−25.9327	−	79.8128i	−0.0507490	−	0.156189i
$512$	155.235	−	50.4390i	0.303194	−	0.0985137i
$513$		0			0
$514$	126.086	−	91.6069i	0.245304	−	0.178223i
$515$	−541.013	−	175.786i	−1.05051	−	0.341332i
$516$		0			0
$517$	−878.280	+	215.245i	−1.69880	+	0.416335i
$518$		−	333.678i		−	0.644165i
$519$		0			0
$520$	92.0055	−	66.8459i	0.176934	−	0.128550i
$521$	335.736	−	462.102i	0.644408	−	0.886951i	−0.354433	−	0.935081i	$-0.615326\pi$
$521$	335.736	−	462.102i	0.644408	−	0.886951i	0.998841	+	0.0481300i	$0.0153262\pi$
$522$		0			0
$523$	237.156	+	729.890i	0.453453	+	1.39558i	0.872942	+	0.487824i	$0.162209\pi$
$523$	237.156	+	729.890i	0.453453	+	1.39558i	−0.419490	+	0.907760i	$0.637791\pi$
$524$	117.638	−	161.914i	0.224500	−	0.308997i
$525$		0			0
$526$	−98.9537	+	304.548i	−0.188125	+	0.578989i
$527$			290.398i			0.551041i
$528$		0			0
$529$	287.791			0.544028
$530$	413.237	+	134.269i	0.779692	+	0.253337i
$531$		0			0
$532$	709.114	+	515.201i	1.33292	+	0.968424i
$533$	−33.9241	+	11.0226i	−0.0636474	+	0.0206803i
$534$		0			0
$535$	−457.910	−	332.691i	−0.855907	−	0.621853i
$536$	−297.092	−	408.912i	−0.554276	−	0.762895i
$537$		0			0
$538$	714.191			1.32749
$539$	1364.61	+	100.919i	2.53174	+	0.187235i
$540$		0			0
$541$	63.5980	−	195.735i	0.117556	−	0.361801i	−0.874915	−	0.484276i	$-0.839083\pi$
$541$	63.5980	−	195.735i	0.117556	−	0.361801i	0.992472	+	0.122475i	$0.0390830\pi$
$542$	142.136	+	195.633i	0.262243	+	0.360946i
$543$		0			0
$544$	−158.994	−	489.333i	−0.292269	−	0.899510i
$545$	574.510	−	186.670i	1.05415	−	0.342513i
$546$		0			0
$547$	−352.204	+	255.891i	−0.643883	+	0.467808i	−0.861182	−	0.508297i	$-0.830275\pi$
$547$	−352.204	+	255.891i	−0.643883	+	0.467808i	0.217299	+	0.976105i	$0.430275\pi$
$548$	410.672	+	133.435i	0.749402	+	0.243495i
$549$		0			0
$550$	1.15982	−	15.6828i	0.00210877	−	0.0285142i
$551$		−	317.949i		−	0.577040i
$552$		0			0
$553$	1225.67	−	890.498i	2.21639	−	1.61030i
$554$	−227.352	+	312.923i	−0.410382	+	0.564842i
$555$		0			0
$556$	−39.9902	−	123.077i	−0.0719248	−	0.221362i
$557$	−434.244	+	597.686i	−0.779612	+	1.07304i	0.215712	+	0.976457i	$0.430793\pi$
$557$	−434.244	+	597.686i	−0.779612	+	1.07304i	−0.995325	+	0.0965873i	$0.969207\pi$
$558$		0			0
$559$	−8.69356	+	26.7560i	−0.0155520	+	0.0478641i
$560$		−	173.441i		−	0.309716i
$561$		0			0
$562$	342.493			0.609419
$563$	62.6356	+	20.3515i	0.111253	+	0.0361484i	0.364115	−	0.931354i	$-0.381372\pi$
$563$	62.6356	+	20.3515i	0.111253	+	0.0361484i	−0.252861	+	0.967503i	$0.581372\pi$
$564$		0			0
$565$	286.376	+	208.064i	0.506859	+	0.368255i
$566$	364.077	−	118.296i	0.643246	−	0.209003i
$567$		0			0
$568$	332.017	+	241.224i	0.584537	+	0.424691i
$569$	−410.063	−	564.404i	−0.720673	−	0.991922i	−0.999501	−	0.0315808i	$-0.989946\pi$
$569$	−410.063	−	564.404i	−0.720673	−	0.991922i	0.278828	−	0.960341i	$-0.410054\pi$
$570$		0			0
$571$	−256.388			−0.449017			−0.224508	−	0.974472i	$-0.572078\pi$
$571$	−256.388			−0.449017			−0.224508	+	0.974472i	$0.572078\pi$
$572$	−15.1978	−	62.0127i	−0.0265696	−	0.108414i
$573$		0			0
$574$	−73.4569	+	226.077i	−0.127974	+	0.393862i
$575$	−9.65705	−	13.2918i	−0.0167949	−	0.0231162i
$576$		0			0
$577$	140.575	+	432.646i	0.243631	+	0.749819i	0.995859	+	0.0909159i	$0.0289794\pi$
$577$	140.575	+	432.646i	0.243631	+	0.749819i	−0.752227	+	0.658903i	$0.771021\pi$
$578$	9.50317	−	3.08777i	0.0164415	−	0.00534216i
$579$		0			0
$580$	93.2053	−	67.7176i	0.160699	−	0.116755i
$581$	507.110	+	164.770i	0.872823	+	0.283598i
$582$		0			0
$583$	447.468	−	528.952i	0.767527	−	0.907294i
$584$			53.1718i			0.0910475i
$585$		0			0
$586$	−327.221	+	237.740i	−0.558397	+	0.405699i
$587$	64.8291	−	89.2295i	0.110441	−	0.152009i	−0.750218	−	0.661190i	$-0.770052\pi$
$587$	64.8291	−	89.2295i	0.110441	−	0.152009i	0.860660	+	0.509181i	$0.170052\pi$
$588$		0			0
$589$	159.619	+	491.257i	0.271000	+	0.834052i
$590$	−267.238	+	367.822i	−0.452946	+	0.623427i
$591$		0			0
$592$	−14.9510	+	46.0146i	−0.0252551	+	0.0777273i
$593$			250.416i			0.422287i	0.977455	+	0.211144i	$0.0677188\pi$
$593$			250.416i			0.422287i	−0.977455	+	0.211144i	$0.932281\pi$
$594$		0			0
$595$	−1157.23			−1.94493
$596$	−30.1091	−	9.78303i	−0.0505186	−	0.0164145i
$597$		0			0
$598$	45.3415	+	32.9425i	0.0758219	+	0.0550879i
$599$	−271.473	+	88.2069i	−0.453210	+	0.147257i	−0.526722	−	0.850037i	$-0.676579\pi$
$599$	−271.473	+	88.2069i	−0.453210	+	0.147257i	0.0735122	+	0.997294i	$0.476579\pi$
$600$		0			0
$601$	180.803	+	131.361i	0.300836	+	0.218570i	0.727954	−	0.685625i	$-0.240471\pi$
$601$	180.803	+	131.361i	0.300836	+	0.218570i	−0.427118	+	0.904196i	$0.640471\pi$
$602$	110.200	+	151.678i	0.183057	+	0.251956i
$603$		0			0
$604$	−529.508			−0.876668
$605$	−552.968	−	275.208i	−0.913997	−	0.454890i
$606$		0			0
$607$	295.069	−	908.129i	0.486110	−	1.49609i	−0.344256	−	0.938876i	$-0.611869\pi$
$607$	295.069	−	908.129i	0.486110	−	1.49609i	0.830367	−	0.557218i	$-0.188131\pi$
$608$	−537.929	−	740.396i	−0.884752	−	1.21776i
$609$		0			0
$610$	77.9290	+	239.841i	0.127752	+	0.393182i
$611$	208.770	−	67.8334i	0.341685	−	0.111020i
$612$		0			0
$613$	275.176	−	199.927i	0.448901	−	0.326146i	−0.340261	−	0.940331i	$-0.610515\pi$
$613$	275.176	−	199.927i	0.448901	−	0.326146i	0.789162	+	0.614185i	$0.210515\pi$
$614$	143.743	+	46.7048i	0.234108	+	0.0760664i
$615$		0			0
$616$	−1118.67	−	457.193i	−1.81602	−	0.742197i
$617$			812.456i			1.31678i	0.752675	+	0.658392i	$0.228763\pi$
$617$			812.456i			1.31678i	−0.752675	+	0.658392i	$0.771237\pi$
$618$		0			0
$619$	−739.304	+	537.136i	−1.19435	+	0.867748i	−0.993717	−	0.111918i	$-0.964301\pi$
$619$	−739.304	+	537.136i	−1.19435	+	0.867748i	−0.200635	+	0.979666i	$0.564301\pi$
$620$	−110.014	+	151.421i	−0.177441	+	0.244227i
$621$		0			0
$622$	−148.787	−	457.920i	−0.239208	−	0.736206i
$623$	550.546	−	757.761i	0.883701	−	1.21631i
$624$		0			0
$625$	−200.962	+	618.498i	−0.321540	+	0.989597i
$626$			457.779i			0.731276i
$627$		0			0
$628$	−241.352			−0.384319
$629$	307.018	+	99.7563i	0.488105	+	0.158595i
$630$		0			0
$631$	488.541	+	354.946i	0.774233	+	0.562513i	0.903243	−	0.429130i	$-0.141180\pi$
$631$	488.541	+	354.946i	0.774233	+	0.562513i	−0.129010	+	0.991643i	$0.541180\pi$
$632$	−912.926	+	296.628i	−1.44450	+	0.469348i
$633$		0			0
$634$	−442.400	−	321.423i	−0.697792	−	0.506976i
$635$	32.3295	+	44.4977i	0.0509125	+	0.0700751i
$636$		0			0
$637$	−332.165			−0.521453
$638$	36.7392	+	149.909i	0.0575849	+	0.234968i
$639$		0			0
$640$	80.4720	−	247.667i	0.125738	−	0.386980i
$641$	−633.628	−	872.114i	−0.988499	−	1.36055i	−0.932122	−	0.362143i	$-0.882045\pi$
$641$	−633.628	−	872.114i	−0.988499	−	1.36055i	−0.0563769	−	0.998410i	$-0.517955\pi$
$642$		0			0
$643$	118.832	+	365.726i	0.184808	+	0.568781i	0.999945	−	0.0104874i	$-0.00333831\pi$
$643$	118.832	+	365.726i	0.184808	+	0.568781i	−0.815137	+	0.579268i	$0.803338\pi$
$644$	−422.784	+	137.371i	−0.656497	+	0.213309i
$645$		0			0
$646$	576.397	−	418.777i	0.892255	−	0.648262i
$647$	−566.074	−	183.929i	−0.874921	−	0.284279i	−0.163074	−	0.986614i	$-0.552141\pi$
$647$	−566.074	−	183.929i	−0.874921	−	0.284279i	−0.711847	+	0.702335i	$0.752141\pi$
$648$		0			0
$649$	381.706	+	616.339i	0.588144	+	0.949675i
$650$			3.81743i			0.00587297i
$651$		0			0
$652$	−216.573	+	157.350i	−0.332168	+	0.241334i
$653$	246.058	−	338.670i	0.376812	−	0.518637i	−0.577924	−	0.816090i	$-0.696137\pi$
$653$	246.058	−	338.670i	0.376812	−	0.518637i	0.954736	+	0.297453i	$0.0961372\pi$
$654$		0			0
$655$	145.238	+	446.998i	0.221738	+	0.682439i
$656$	20.2596	−	27.8849i	0.0308835	−	0.0425075i
$657$		0			0
$658$	452.056	−	1391.29i	0.687015	−	2.11442i
$659$			1112.39i			1.68800i	0.536347	+	0.843998i	$0.319804\pi$
$659$			1112.39i			1.68800i	−0.536347	+	0.843998i	$0.680196\pi$
$660$		0			0
$661$	−736.025			−1.11350			−0.556751	−	0.830679i	$-0.687952\pi$
$661$	−736.025			−1.11350			−0.556751	+	0.830679i	$0.687952\pi$
$662$	814.943	+	264.791i	1.23103	+	0.399986i
$663$		0			0
$664$	−273.318	−	198.577i	−0.411624	−	0.299062i
$665$	−1957.65	+	636.080i	−2.94384	+	0.956511i
$666$		0			0
$667$	130.458	+	94.7830i	0.195589	+	0.142103i
$668$	−292.598	−	402.727i	−0.438021	−	0.602884i
$669$		0			0
$670$	417.923			0.623765
$671$	401.023	+	29.6576i	0.597649	+	0.0441991i
$672$		0			0
$673$	168.609	−	518.924i	0.250533	−	0.771061i	−0.744144	−	0.668019i	$-0.767142\pi$
$673$	168.609	−	518.924i	0.250533	−	0.771061i	0.994677	−	0.103042i	$-0.0328576\pi$
$674$	−188.586	−	259.566i	−0.279801	−	0.385113i
$675$		0			0
$676$	−108.729	−	334.634i	−0.160842	−	0.495021i
$677$	936.672	−	304.343i	1.38356	−	0.449547i	0.479724	−	0.877420i	$-0.340737\pi$
$677$	936.672	−	304.343i	1.38356	−	0.449547i	0.903839	+	0.427873i	$0.140737\pi$
$678$		0			0
$679$	198.874	−	144.490i	0.292892	−	0.212798i
$680$	697.336	+	226.578i	1.02549	+	0.333203i
$681$		0			0
$682$	−132.023	−	213.178i	−0.193583	−	0.312578i
$683$		−	924.817i		−	1.35405i	−0.735959	−	0.677026i	$-0.763269\pi$
$683$		−	924.817i		−	1.35405i	0.735959	−	0.677026i	$-0.236731\pi$
$684$		0			0
$685$	−820.385	+	596.044i	−1.19764	+	0.870138i
$686$	−788.604	+	1085.42i	−1.14957	+	1.58225i
$687$		0			0
$688$	−8.40056	−	25.8543i	−0.0122101	−	0.0375789i
$689$	−98.8576	+	136.066i	−0.143480	+	0.197483i
$690$		0			0
$691$	−24.4525	+	75.2570i	−0.0353871	+	0.108910i	−0.967190	−	0.254055i	$-0.918236\pi$
$691$	−24.4525	+	75.2570i	−0.0353871	+	0.108910i	0.931803	+	0.362965i	$0.118236\pi$
$692$		−	375.349i		−	0.542412i
$693$		0			0
$694$	−658.790			−0.949265
$695$	289.034	+	93.9127i	0.415876	+	0.135126i
$696$		0			0
$697$	−186.054	−	135.176i	−0.266935	−	0.193940i
$698$	−48.9041	+	15.8899i	−0.0700632	+	0.0227649i
$699$		0			0
$700$	−24.4964	−	17.7977i	−0.0349949	−	0.0254253i
$701$	724.322	+	996.943i	1.03327	+	1.42217i	0.902464	+	0.430765i	$0.141756\pi$
$701$	724.322	+	996.943i	1.03327	+	1.42217i	0.130805	+	0.991408i	$0.458244\pi$
$702$		0			0
$703$	574.204			0.816791
$704$	425.858	+	360.255i	0.604912	+	0.511726i
$705$		0			0
$706$	−37.8094	+	116.365i	−0.0535544	+	0.164823i
$707$	364.261	+	501.362i	0.515220	+	0.709140i
$708$		0			0
$709$	−82.6830	−	254.472i	−0.116619	−	0.358917i	0.875662	−	0.482924i	$-0.160425\pi$
$709$	−82.6830	−	254.472i	−0.116619	−	0.358917i	−0.992281	+	0.124007i	$0.960425\pi$
$710$	−322.725	+	104.860i	−0.454543	+	0.147690i
$711$		0			0
$712$	−480.117	+	348.825i	−0.674322	+	0.489923i
$713$	−249.151	−	80.9541i	−0.349440	−	0.113540i
$714$		0			0
$715$	138.796	+	56.7251i	0.194120	+	0.0793358i
$716$			396.682i			0.554025i
$717$		0			0
$718$	−122.437	+	88.9554i	−0.170525	+	0.123893i
$719$	−403.585	+	555.487i	−0.561314	+	0.772583i	−0.991493	−	0.130161i	$-0.958451\pi$
$719$	−403.585	+	555.487i	−0.561314	+	0.772583i	0.430179	+	0.902744i	$0.358451\pi$
$720$		0			0
$721$	−453.452	−	1395.58i	−0.628922	−	1.93562i
$722$	458.132	−	630.564i	0.634531	−	0.873358i
$723$		0			0
$724$	81.7742	−	251.675i	0.112948	−	0.347617i
$725$			10.9836i			0.0151498i
$726$		0			0
$727$	−1265.58			−1.74082			−0.870410	−	0.492327i	$-0.836146\pi$
$727$	−1265.58			−1.74082			−0.870410	+	0.492327i	$0.836146\pi$
$728$	279.004	+	90.6539i	0.383247	+	0.124525i
$729$		0			0
$730$	−35.5683	−	25.8419i	−0.0487237	−	0.0353998i
$731$	−172.505	+	56.0502i	−0.235985	+	0.0766761i
$732$		0			0
$733$	−80.5752	−	58.5413i	−0.109925	−	0.0798654i	0.531465	−	0.847081i	$-0.321642\pi$
$733$	−80.5752	−	58.5413i	−0.109925	−	0.0798654i	−0.641390	+	0.767215i	$0.721642\pi$
$734$	−269.115	−	370.405i	−0.366641	−	0.504638i
$735$		0			0
$736$	464.152			0.630642
$737$	252.111	−	616.867i	0.342077	−	0.836997i
$738$		0			0
$739$	−99.0512	+	304.848i	−0.134034	+	0.412515i	−0.995439	−	0.0954052i	$-0.969585\pi$
$739$	−99.0512	+	304.848i	−0.134034	+	0.412515i	0.861404	+	0.507920i	$0.169585\pi$
$740$	122.295	+	168.325i	0.165264	+	0.227466i
$741$		0			0
$742$	346.356	+	1065.97i	0.466787	+	1.43662i
$743$	51.9858	−	16.8912i	0.0699674	−	0.0227338i	−0.273824	−	0.961780i	$-0.588289\pi$
$743$	51.9858	−	16.8912i	0.0699674	−	0.0227338i	0.343792	+	0.939046i	$0.388289\pi$
$744$		0			0
$745$	60.1478	−	43.6999i	0.0807353	−	0.0586576i
$746$	−712.804	−	231.604i	−0.955501	−	0.310461i
$747$		0			0
$748$	265.864	−	314.278i	0.355433	−	0.420157i
$749$		−	1460.06i		−	1.94935i
$750$		0			0
$751$	−117.339	+	85.2520i	−0.156244	+	0.113518i	−0.663160	−	0.748477i	$-0.730785\pi$
$751$	−117.339	+	85.2520i	−0.156244	+	0.113518i	0.506916	+	0.861995i	$0.330785\pi$
$752$	−124.678	+	171.605i	−0.165795	+	0.228198i
$753$		0			0
$754$	−11.5782	−	35.6339i	−0.0153556	−	0.0472598i
$755$	730.906	−	1006.01i	0.968088	−	1.33246i
$756$		0			0
$757$	80.8537	−	248.842i	0.106808	−	0.328721i	−0.883343	−	0.468728i	$-0.844712\pi$
$757$	80.8537	−	248.842i	0.106808	−	0.328721i	0.990151	+	0.140007i	$0.0447124\pi$
$758$		−	339.621i		−	0.448049i
$759$		0			0
$760$	1304.20			1.71605
$761$	955.456	+	310.446i	1.25553	+	0.407945i	0.859898	−	0.510465i	$-0.170527\pi$
$761$	955.456	+	310.446i	1.25553	+	0.407945i	0.395629	+	0.918411i	$0.370527\pi$
$762$		0			0
$763$	1260.66	+	915.921i	1.65224	+	1.20042i
$764$	−649.995	+	211.196i	−0.850779	+	0.276435i
$765$		0			0
$766$	562.196	+	408.460i	0.733938	+	0.533237i
$767$	−103.442	−	142.376i	−0.134866	−	0.185627i
$768$		0			0
$769$	1067.91			1.38869			0.694347	−	0.719641i	$-0.255693\pi$
$769$	1067.91			1.38869			0.694347	+	0.719641i	$0.255693\pi$
$770$	849.511	−	526.112i	1.10326	−	0.683262i
$771$		0			0
$772$	83.5542	−	257.153i	0.108231	−	0.333100i
$773$	104.322	+	143.587i	0.134957	+	0.185753i	0.871147	−	0.491023i	$-0.163377\pi$
$773$	104.322	+	143.587i	0.134957	+	0.185753i	−0.736190	+	0.676775i	$0.763377\pi$
$774$		0			0
$775$	−5.51406	−	16.9705i	−0.00711491	−	0.0218974i
$776$	−148.129	+	48.1301i	−0.190888	+	0.0620233i
$777$		0			0
$778$	−212.267	+	154.221i	−0.272837	+	0.198228i
$779$	−389.041	−	126.407i	−0.499411	−	0.162268i
$780$		0			0
$781$	−39.9067	+	539.609i	−0.0510970	+	0.690920i
$782$			361.342i			0.462074i
$783$		0			0
$784$	259.670	−	188.662i	0.331212	−	0.240640i
$785$	333.151	−	458.543i	0.424396	−	0.584131i
$786$		0			0
$787$	204.108	+	628.179i	0.259349	+	0.798194i	0.992942	+	0.118605i	$0.0378421\pi$
$787$	204.108	+	628.179i	0.259349	+	0.798194i	−0.733592	+	0.679590i	$0.762158\pi$
$788$	−247.859	+	341.148i	−0.314541	+	0.432929i
$789$		0			0
$790$	245.265	−	754.849i	0.310462	−	0.955505i
$791$			913.116i			1.15438i
$792$		0			0
$793$	−97.6148			−0.123096
$794$	−334.488	−	108.682i	−0.421270	−	0.136879i
$795$		0			0
$796$	119.043	+	86.4896i	0.149551	+	0.108655i
$797$	379.061	−	123.164i	0.475610	−	0.154535i	−0.0613960	−	0.998113i	$-0.519555\pi$
$797$	379.061	−	123.164i	0.475610	−	0.154535i	0.537006	+	0.843578i	$0.319555\pi$
$798$		0			0
$799$	1144.98	+	831.878i	1.43302	+	1.04115i
$800$	18.5828	+	25.5771i	0.0232285	+	0.0319713i
$801$		0			0
$802$	−512.683			−0.639256
$803$	−59.5998	+	36.9108i	−0.0742215	+	0.0459662i
$804$		0			0
$805$	322.601	−	992.863i	0.400746	−	1.23337i
$806$	35.7783	+	49.2446i	0.0443900	+	0.0610976i
$807$		0			0
$808$	−121.336	−	373.435i	−0.150169	−	0.462172i
$809$	716.122	−	232.682i	0.885194	−	0.287617i	0.169082	−	0.985602i	$-0.445920\pi$
$809$	716.122	−	232.682i	0.885194	−	0.287617i	0.716112	+	0.697985i	$0.245920\pi$
$810$		0			0
$811$	−811.310	+	589.451i	−1.00038	+	0.726820i	−0.962170	−	0.272450i	$-0.912166\pi$
$811$	−811.310	+	589.451i	−1.00038	+	0.726820i	−0.0382118	+	0.999270i	$0.512166\pi$
$812$	282.642	+	91.8360i	0.348082	+	0.113099i
$813$		0			0
$814$	−270.730	+	66.3495i	−0.332593	+	0.0815104i
$815$		−	628.663i		−	0.771366i
$816$		0			0
$817$	−261.012	+	189.636i	−0.319476	+	0.232113i
$818$	541.787	−	745.706i	0.662331	−	0.911621i
$819$		0			0
$820$	−45.8033	−	140.968i	−0.0558577	−	0.171912i
$821$	−804.527	+	1107.34i	−0.979936	+	1.34877i	−0.0430718	+	0.999072i	$0.513714\pi$
$821$	−804.527	+	1107.34i	−0.979936	+	1.34877i	−0.936864	+	0.349694i	$0.886286\pi$
$822$		0			0
$823$	−431.321	+	1327.47i	−0.524084	+	1.61296i	0.242037	+	0.970267i	$0.422185\pi$
$823$	−431.321	+	1327.47i	−0.524084	+	1.61296i	−0.766120	+	0.642697i	$0.777815\pi$
$824$			929.746i			1.12833i
$825$		0			0
$826$	−1172.81			−1.41987
$827$	−192.907	−	62.6792i	−0.233261	−	0.0757910i	0.190054	−	0.981774i	$-0.439134\pi$
$827$	−192.907	−	62.6792i	−0.233261	−	0.0757910i	−0.423315	+	0.905983i	$0.639134\pi$
$828$		0			0
$829$	−461.108	−	335.015i	−0.556222	−	0.404119i	0.273852	−	0.961772i	$-0.411702\pi$
$829$	−461.108	−	335.015i	−0.556222	−	0.404119i	−0.830074	+	0.557653i	$0.811702\pi$
$830$	265.669	−	86.3212i	0.320084	−	0.104001i
$831$		0			0
$832$	−109.546	−	79.5899i	−0.131666	−	0.0956610i
$833$	−1258.79	−	1732.57i	−1.51115	−	2.07992i
$834$		0			0
$835$	1169.02			1.40003
$836$	277.008	−	677.786i	0.331349	−	0.810749i
$837$		0			0
$838$	−114.975	+	353.858i	−0.137202	+	0.422265i
$839$	76.3914	+	105.144i	0.0910505	+	0.125320i	0.852112	−	0.523359i	$-0.175321\pi$
$839$	76.3914	+	105.144i	0.0910505	+	0.125320i	−0.761062	+	0.648680i	$0.775321\pi$
$840$		0			0
$841$	226.570	+	697.312i	0.269406	+	0.829146i
$842$	−156.121	+	50.7267i	−0.185417	+	0.0602455i
$843$		0			0
$844$	−131.977	+	95.8867i	−0.156371	+	0.113610i
$845$	785.853	+	255.339i	0.930003	+	0.302176i
$846$		0			0
$847$	−264.092	−	1571.28i	−0.311797	−	1.85511i
$848$		−	162.518i		−	0.191649i
$849$		0			0
$850$	−19.9117	+	14.4667i	−0.0234255	+	0.0170196i
$851$	−171.174	+	235.601i	−0.201145	+	0.276852i
$852$		0			0
$853$	99.5966	+	306.527i	0.116760	+	0.359351i	0.992310	−	0.123777i	$-0.0395006\pi$
$853$	99.5966	+	306.527i	0.116760	+	0.359351i	−0.875550	+	0.483128i	$0.839501\pi$
$854$	−382.369	+	526.286i	−0.447739	+	0.616260i
$855$		0			0
$856$	−285.869	+	879.816i	−0.333960	+	1.02782i
$857$			634.845i			0.740776i	0.928877	+	0.370388i	$0.120775\pi$
$857$			634.845i			0.740776i	−0.928877	+	0.370388i	$0.879225\pi$
$858$		0			0
$859$	1658.25			1.93044			0.965219	−	0.261443i	$-0.0841984\pi$
$859$	1658.25			1.93044			0.965219	+	0.261443i	$0.0841984\pi$
$860$	−111.182	−	36.1252i	−0.129281	−	0.0420061i
$861$		0			0
$862$	−107.960	−	78.4378i	−0.125244	−	0.0909951i
$863$	820.127	−	266.475i	0.950321	−	0.308778i	0.207475	−	0.978240i	$-0.433475\pi$
$863$	820.127	−	266.475i	0.950321	−	0.308778i	0.742846	+	0.669462i	$0.233475\pi$
$864$		0			0
$865$	713.122	+	518.113i	0.824418	+	0.598975i
$866$	−444.823	−	612.246i	−0.513652	−	0.706981i
$867$		0			0
$868$	−482.809			−0.556231
$869$	−966.224	−	817.379i	−1.11188	−	0.940597i
$870$		0			0
$871$	−49.9893	+	153.851i	−0.0573930	+	0.176638i
$872$	−580.327	−	798.752i	−0.665513	−	0.916000i
$873$		0			0
$874$	198.613	+	611.269i	0.227246	+	0.699393i
$875$	−1530.58	+	497.315i	−1.74923	+	0.568360i
$876$		0			0
$877$	−554.481	+	402.854i	−0.632247	+	0.459354i	−0.857178	−	0.515020i	$-0.827784\pi$
$877$	−554.481	+	402.854i	−0.632247	+	0.459354i	0.224931	+	0.974375i	$0.427784\pi$
$878$	−742.163	−	241.143i	−0.845288	−	0.274651i
$879$		0			0
$880$	−140.722	+	34.4875i	−0.159911	+	0.0391904i
$881$			551.003i			0.625429i	0.949847	+	0.312715i	$0.101238\pi$
$881$			551.003i			0.625429i	−0.949847	+	0.312715i	$0.898762\pi$
$882$		0			0
$883$	1288.51	−	936.160i	1.45924	−	1.06020i	0.475686	−	0.879615i	$-0.342200\pi$
$883$	1288.51	−	936.160i	1.45924	−	1.06020i	0.983559	−	0.180588i	$-0.0578002\pi$
$884$	−58.7363	+	80.8436i	−0.0664438	+	0.0914521i
$885$		0			0
$886$	36.4906	+	112.307i	0.0411858	+	0.126757i
$887$	−225.726	+	310.686i	−0.254483	+	0.350266i	−0.917075	−	0.398715i	$-0.869456\pi$
$887$	−225.726	+	310.686i	−0.254483	+	0.350266i	0.662592	+	0.748981i	$0.269456\pi$
$888$		0			0
$889$	−43.8439	+	134.938i	−0.0493183	+	0.151786i
$890$		−	490.697i		−	0.551345i
$891$		0			0
$892$	−12.9949			−0.0145683
$893$	2394.17	+	777.913i	2.68104	+	0.871124i
$894$		0			0
$895$	−753.653	−	547.561i	−0.842070	−	0.611800i
$896$	638.876	−	207.583i	0.713031	−	0.231678i
$897$		0			0
$898$	−105.187	−	76.4227i	−0.117134	−	0.0851032i
$899$	102.942	+	141.688i	0.114507	+	0.157606i
$900$		0			0
$901$	−1084.35			−1.20350
$902$	198.035	+	14.6456i	0.219551	+	0.0162369i
$903$		0			0
$904$	178.782	−	550.234i	0.197767	−	0.608665i
$905$	365.278	+	502.762i	0.403622	+	0.555538i
$906$		0			0
$907$	−438.054	−	1348.19i	−0.482970	−	1.48643i	−0.834899	−	0.550403i	$-0.814474\pi$
$907$	−438.054	−	1348.19i	−0.482970	−	1.48643i	0.351929	−	0.936027i	$-0.385526\pi$
$908$	348.093	−	113.102i	0.383363	−	0.124562i
$909$		0			0
$910$	−196.239	+	142.576i	−0.215647	+	0.156677i
$911$	831.997	+	270.332i	0.913279	+	0.296742i	0.727707	−	0.685888i	$-0.240586\pi$
$911$	831.997	+	270.332i	0.913279	+	0.296742i	0.185572	+	0.982631i	$0.440586\pi$
$912$		0			0
$913$	32.8515	−	444.209i	0.0359819	−	0.486538i
$914$		−	934.888i		−	1.02285i
$915$		0			0
$916$	619.342	−	449.978i	0.676137	−	0.491242i
$917$	−712.632	+	980.854i	−0.777134	+	1.06963i
$918$		0			0
$919$	−359.359	−	1105.99i	−0.391033	−	1.20348i	−0.932008	−	0.362437i	$-0.881945\pi$
$919$	−359.359	−	1105.99i	−0.391033	−	1.20348i	0.540975	−	0.841039i	$-0.318055\pi$
$920$	−388.791	+	535.125i	−0.422599	+	0.581658i
$921$		0			0
$922$	−29.4619	+	90.6744i	−0.0319543	+	0.0983453i
$923$		−	131.349i		−	0.142306i
$924$		0			0
$925$	−19.8359			−0.0214443
$926$	319.121	+	103.689i	0.344623	+	0.111975i
$927$		0			0
$928$	−251.036	−	182.389i	−0.270513	−	0.196539i
$929$	−527.156	+	171.283i	−0.567444	+	0.184374i	−0.578668	−	0.815563i	$-0.696427\pi$
$929$	−527.156	+	171.283i	−0.567444	+	0.184374i	0.0112238	+	0.999937i	$0.496427\pi$
$930$		0			0
$931$	−3081.77	−	2239.03i	−3.31017	−	2.40498i
$932$	454.967	+	626.208i	0.488162	+	0.671897i
$933$		0			0
$934$	343.471			0.367742
$935$	230.108	+	938.925i	0.246105	+	1.00420i
$936$		0			0
$937$	−265.097	+	815.885i	−0.282921	+	0.870742i	0.704093	+	0.710108i	$0.251354\pi$
$937$	−265.097	+	815.885i	−0.282921	+	0.870742i	−0.987014	+	0.160634i	$0.948646\pi$
$938$	633.669	+	872.170i	0.675553	+	0.929819i
$939$		0			0
$940$	281.875	+	867.522i	0.299867	+	0.922896i
$941$	320.582	−	104.163i	0.340682	−	0.110694i	−0.133679	−	0.991025i	$-0.542679\pi$
$941$	320.582	−	104.163i	0.340682	−	0.110694i	0.474361	+	0.880330i	$0.342679\pi$
$942$		0			0
$943$	167.842	−	121.944i	0.177987	−	0.129315i
$944$	161.732	+	52.5499i	0.171326	+	0.0556672i
$945$		0			0
$946$	101.152	−	119.571i	0.106926	−	0.126397i
$947$			405.388i			0.428076i	0.976825	+	0.214038i	$0.0686616\pi$
$947$			405.388i			0.428076i	−0.976825	+	0.214038i	$0.931338\pi$
$948$		0			0
$949$	13.7677	−	10.0028i	0.0145076	−	0.0105404i
$950$	−25.7322	+	35.4174i	−0.0270866	+	0.0372814i
$951$		0			0
$952$	584.475	+	1798.83i	0.613944	+	1.88953i
$953$	−439.632	+	605.102i	−0.461314	+	0.634944i	−0.974781	−	0.223166i	$-0.928361\pi$
$953$	−439.632	+	605.102i	−0.461314	+	0.634944i	0.513467	+	0.858109i	$0.328361\pi$
$954$		0			0
$955$	495.972	−	1526.44i	0.519342	−	1.59837i
$956$		−	37.9057i		−	0.0396503i
$957$		0			0
$958$	24.7019			0.0257848
$959$	−2487.79	−	808.332i	−2.59415	−	0.842891i
$960$		0			0
$961$	547.280	+	397.623i	0.569491	+	0.413759i
$962$	64.3534	−	20.9097i	0.0668954	−	0.0217356i
$963$		0			0
$964$	173.521	+	126.070i	0.180001	+	0.130778i
$965$	373.229	+	513.706i	0.386766	+	0.532338i
$966$		0			0
$967$	−284.479			−0.294187			−0.147094	−	0.989123i	$-0.546992\pi$
$967$	−284.479			−0.294187			−0.147094	+	0.989123i	$0.546992\pi$
$968$	−148.507	+	998.543i	−0.153416	+	1.03155i
$969$		0			0
$970$	39.7961	−	122.480i	0.0410269	−	0.126268i
$971$	−693.245	−	954.170i	−0.713949	−	0.982667i	−0.999703	−	0.0243639i	$-0.992244\pi$
$971$	−693.245	−	954.170i	−0.713949	−	0.982667i	0.285754	−	0.958303i	$-0.407756\pi$
$972$		0			0
$973$	242.255	+	745.583i	0.248977	+	0.766272i
$974$	312.802	−	101.636i	0.321152	−	0.104349i
$975$		0			0
$976$	76.3104	−	55.4428i	0.0781869	−	0.0568061i
$977$	−12.9784	−	4.21695i	−0.0132840	−	0.00431622i	0.302367	−	0.953191i	$-0.402223\pi$
$977$	−12.9784	−	4.21695i	−0.0132840	−	0.00431622i	−0.315651	+	0.948875i	$0.602223\pi$
$978$		0			0
$979$	−724.284	−	296.011i	−0.739820	−	0.302361i
$980$		−	1380.28i		−	1.40845i
$981$		0			0
$982$	−345.896	+	251.308i	−0.352236	+	0.255915i
$983$	294.641	−	405.539i	0.299737	−	0.412552i	−0.632409	−	0.774634i	$-0.717934\pi$
$983$	294.641	−	405.539i	0.299737	−	0.412552i	0.932146	+	0.362082i	$0.117934\pi$
$984$		0			0
$985$	−306.012	−	941.808i	−0.310672	−	0.956151i
$986$	141.989	−	195.431i	0.144005	−	0.198206i
$987$		0			0
$988$	−54.9261	+	169.045i	−0.0555932	+	0.171098i
$989$		−	163.628i		−	0.165448i
$990$		0			0
$991$	118.253			0.119327			0.0596635	−	0.998219i	$-0.480997\pi$
$991$	118.253			0.119327			0.0596635	+	0.998219i	$0.480997\pi$
$992$	479.435	+	155.778i	0.483302	+	0.157034i
$993$		0			0
$994$	−708.161	−	514.509i	−0.712436	−	0.517615i
$995$	−328.641	+	106.782i	−0.330293	+	0.107319i
$996$		0			0
$997$	−401.180	−	291.474i	−0.402387	−	0.292351i	0.368126	−	0.929776i	$-0.380000\pi$
$997$	−401.180	−	291.474i	−0.402387	−	0.292351i	−0.770512	+	0.637425i	$0.780000\pi$
$998$	−21.2912	−	29.3049i	−0.0213339	−	0.0293636i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.53.6	yes	32
3.2	odd	2	inner	99.3.l.a.53.3	✓	32
11.4	even	5		1089.3.b.i.485.11		16
11.5	even	5	inner	99.3.l.a.71.3	yes	32
11.7	odd	10		1089.3.b.j.485.6		16
33.5	odd	10	inner	99.3.l.a.71.6	yes	32
33.26	odd	10		1089.3.b.i.485.6		16
33.29	even	10		1089.3.b.j.485.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.53.3	✓	32	3.2	odd	2	inner
99.3.l.a.53.6	yes	32	1.1	even	1	trivial
99.3.l.a.71.3	yes	32	11.5	even	5	inner
99.3.l.a.71.6	yes	32	33.5	odd	10	inner
1089.3.b.i.485.6		16	33.26	odd	10
1089.3.b.i.485.11		16	11.4	even	5
1089.3.b.j.485.6		16	11.7	odd	10
1089.3.b.j.485.11		16	33.29	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28527 + 0.417608i) q^{2} +(-1.75856 - 1.27767i) q^{4} +(4.85485 - 1.57744i) q^{5} +(10.6531 + 7.73991i) q^{7} +(-4.90400 - 6.74978i) q^{8} +O(q^{10})\)	\(q+(1.28527 + 0.417608i) q^{2} +(-1.75856 - 1.27767i) q^{4} +(4.85485 - 1.57744i) q^{5} +(10.6531 + 7.73991i) q^{7} +(-4.90400 - 6.74978i) q^{8} +6.89852 q^{10} +(4.16151 - 10.1824i) q^{11} +(-0.825159 + 2.53958i) q^{13} +(10.4598 + 14.3966i) q^{14} +(-0.797348 - 2.45398i) q^{16} +(-16.3735 + 5.32007i) q^{17} +(-24.7742 + 17.9995i) q^{19} +(-10.5530 - 3.42886i) q^{20} +(9.60091 - 11.3492i) q^{22} -15.5309i q^{23} +(0.855829 - 0.621796i) q^{25} +(-2.12110 + 2.91944i) q^{26} +(-8.84500 - 27.2221i) q^{28} +(-6.10287 + 8.39987i) q^{29} +(5.21245 - 16.0423i) q^{31} +29.8857i q^{32} -23.2660 q^{34} +(63.9282 + 20.7715i) q^{35} +(-15.1698 - 11.0215i) q^{37} +(-39.3582 + 12.7883i) q^{38} +(-34.4555 - 25.0334i) q^{40} +(7.85173 + 10.8070i) q^{41} +10.5356 q^{43} +(-20.3280 + 12.5893i) q^{44} +(6.48583 - 19.9613i) q^{46} +(-48.3198 - 66.5065i) q^{47} +(38.4399 + 118.306i) q^{49} +(1.35963 - 0.441772i) q^{50} +(4.69582 - 3.41171i) q^{52} +(59.9022 + 19.4634i) q^{53} +(4.14138 - 55.9987i) q^{55} -109.862i q^{56} +(-11.3517 + 8.24747i) q^{58} +(-38.7385 + 53.3189i) q^{59} +(11.2965 + 34.7670i) q^{61} +(13.3988 - 18.4418i) q^{62} +(-15.6699 + 48.2271i) q^{64} +13.6309i q^{65} +60.5815 q^{67} +(35.5909 + 11.5642i) q^{68} +(73.4904 + 53.3939i) q^{70} +(-46.7818 + 15.2003i) q^{71} +(-5.15593 - 3.74600i) q^{73} +(-14.8946 - 20.5007i) q^{74} +66.5643 q^{76} +(123.144 - 76.2644i) q^{77} +(35.5533 - 109.422i) q^{79} +(-7.74201 - 10.6560i) q^{80} +(5.57848 + 17.1688i) q^{82} +(38.5111 - 12.5130i) q^{83} +(-71.0987 + 51.6562i) q^{85} +(13.5411 + 4.39977i) q^{86} +(-89.1372 + 21.8454i) q^{88} -71.1308i q^{89} +(-28.4466 + 20.6676i) q^{91} +(-19.8433 + 27.3120i) q^{92} +(-34.3301 - 105.657i) q^{94} +(-91.8821 + 126.465i) q^{95} +(5.76879 - 17.7545i) q^{97} +168.107i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^7	\( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

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