LMFDB - Embedded newform 121.3.d.f.40.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,3,Mod(40,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("121.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	121.d (of order $10$, degree $4$, not 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:	$3.29701119876$
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			40.4
Character	$\chi$	$=$	121.40
Dual form			121.3.d.f.118.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.867839 + 1.19448i) q^{2} +(1.41664 - 4.35997i) q^{3} +(0.562434 + 1.73099i) q^{4} +(3.42082 - 2.48537i) q^{5} +(3.97848 + 5.47590i) q^{6} +(2.09516 - 0.680759i) q^{7} +(-8.17251 - 2.65541i) q^{8} +(-9.72133 - 7.06296i) q^{9} +O(q^{10})$	\(q+(-0.867839 + 1.19448i) q^{2} +(1.41664 - 4.35997i) q^{3} +(0.562434 + 1.73099i) q^{4} +(3.42082 - 2.48537i) q^{5} +(3.97848 + 5.47590i) q^{6} +(2.09516 - 0.680759i) q^{7} +(-8.17251 - 2.65541i) q^{8} +(-9.72133 - 7.06296i) q^{9} +6.24301i q^{10} +8.34386 q^{12} +(12.6188 - 17.3683i) q^{13} +(-1.00511 + 3.09341i) q^{14} +(-5.99008 - 18.4356i) q^{15} +(4.37437 - 3.17817i) q^{16} +(5.94669 + 8.18492i) q^{17} +(16.8731 - 5.48241i) q^{18} +(3.79705 + 1.23374i) q^{19} +(6.22616 + 4.52357i) q^{20} -10.0992i q^{21} +0.0490953 q^{23} +(-23.1550 + 31.8702i) q^{24} +(-2.20047 + 6.77235i) q^{25} +(9.79498 + 30.1459i) q^{26} +(-11.1866 + 8.12756i) q^{27} +(2.35678 + 3.24383i) q^{28} +(-29.1064 + 9.45723i) q^{29} +(27.2193 + 8.84410i) q^{30} +(20.2945 + 14.7448i) q^{31} -26.3891i q^{32} -14.9375 q^{34} +(5.47523 - 7.53601i) q^{35} +(6.75834 - 20.8000i) q^{36} +(1.39407 + 4.29050i) q^{37} +(-4.76890 + 3.46481i) q^{38} +(-57.8491 - 79.6225i) q^{39} +(-34.5564 + 11.2281i) q^{40} +(-29.9834 - 9.74219i) q^{41} +(12.0633 + 8.76451i) q^{42} +74.2435i q^{43} -50.8091 q^{45} +(-0.0426068 + 0.0586433i) q^{46} +(-21.0255 + 64.7099i) q^{47} +(-7.65981 - 23.5745i) q^{48} +(-35.7156 + 25.9489i) q^{49} +(-6.17977 - 8.50573i) q^{50} +(44.1103 - 14.3323i) q^{51} +(37.1618 + 12.0746i) q^{52} +(-51.8725 - 37.6875i) q^{53} -20.4156i q^{54} -18.9304 q^{56} +(10.7581 - 14.8073i) q^{57} +(13.9632 - 42.9743i) q^{58} +(3.81740 + 11.7487i) q^{59} +(28.5429 - 20.7376i) q^{60} +(29.3105 + 40.3425i) q^{61} +(-35.2248 + 11.4452i) q^{62} +(-25.1759 - 8.18015i) q^{63} +(49.0187 + 35.6142i) q^{64} -90.7766i q^{65} +91.4910 q^{67} +(-10.8234 + 14.8972i) q^{68} +(0.0695504 - 0.214054i) q^{69} +(4.24998 + 13.0801i) q^{70} +(18.5592 - 13.4840i) q^{71} +(60.6927 + 83.5363i) q^{72} +(65.7368 - 21.3592i) q^{73} +(-6.33473 - 2.05828i) q^{74} +(26.4100 + 19.1880i) q^{75} +7.26657i q^{76} +145.311 q^{78} +(-20.8806 + 28.7397i) q^{79} +(7.06502 - 21.7439i) q^{80} +(-13.8305 - 42.5658i) q^{81} +(37.6576 - 27.3598i) q^{82} +(76.6149 + 105.451i) q^{83} +(17.4817 - 5.68015i) q^{84} +(40.6852 + 13.2194i) q^{85} +(-88.6823 - 64.4314i) q^{86} +140.300i q^{87} -128.031 q^{89} +(44.0941 - 60.6904i) q^{90} +(14.6148 - 44.9798i) q^{91} +(0.0276129 + 0.0849837i) q^{92} +(93.0372 - 67.5955i) q^{93} +(-59.0478 - 81.2724i) q^{94} +(16.0553 - 5.21670i) q^{95} +(-115.056 - 37.3839i) q^{96} +(-70.2327 - 51.0270i) q^{97} -65.1809i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 24 q^{4} + 4 q^{5} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 + 24 * q^4 + 4 * q^5 - 16 * q^9	$ 32 q + 4 q^{3} + 24 q^{4} + 4 q^{5} - 16 q^{9} + 208 q^{12} + 4 q^{14} + 68 q^{15} + 24 q^{16} - 52 q^{20} - 48 q^{23} + 16 q^{25} - 168 q^{26} - 104 q^{27} + 116 q^{31} - 720 q^{34} - 152 q^{36} + 4 q^{37} + 132 q^{38} + 176 q^{42} - 304 q^{45} + 244 q^{47} - 172 q^{48} - 88 q^{49} - 268 q^{53} - 48 q^{56} - 88 q^{58} + 56 q^{59} + 100 q^{60} + 40 q^{64} + 1136 q^{67} - 264 q^{69} + 188 q^{70} - 272 q^{71} + 96 q^{75} + 720 q^{78} + 356 q^{80} + 272 q^{81} + 180 q^{82} - 336 q^{86} - 96 q^{89} - 140 q^{91} + 156 q^{92} + 256 q^{93} - 152 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 24 * q^4 + 4 * q^5 - 16 * q^9 + 208 * q^12 + 4 * q^14 + 68 * q^15 + 24 * q^16 - 52 * q^20 - 48 * q^23 + 16 * q^25 - 168 * q^26 - 104 * q^27 + 116 * q^31 - 720 * q^34 - 152 * q^36 + 4 * q^37 + 132 * q^38 + 176 * q^42 - 304 * q^45 + 244 * q^47 - 172 * q^48 - 88 * q^49 - 268 * q^53 - 48 * q^56 - 88 * q^58 + 56 * q^59 + 100 * q^60 + 40 * q^64 + 1136 * q^67 - 264 * q^69 + 188 * q^70 - 272 * q^71 + 96 * q^75 + 720 * q^78 + 356 * q^80 + 272 * q^81 + 180 * q^82 - 336 * q^86 - 96 * q^89 - 140 * q^91 + 156 * q^92 + 256 * q^93 - 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.867839	+	1.19448i	−0.433920	+	0.597239i	−0.968847	−	0.247659i	$-0.920339\pi$
$2$	−0.867839	+	1.19448i	−0.433920	+	0.597239i	0.534928	+	0.844898i	$0.320339\pi$
$3$	1.41664	−	4.35997i	0.472214	−	1.45332i	−0.377465	−	0.926024i	$-0.623204\pi$
$3$	1.41664	−	4.35997i	0.472214	−	1.45332i	0.849679	−	0.527300i	$-0.176796\pi$
$4$	0.562434	+	1.73099i	0.140609	+	0.432749i
$5$	3.42082	−	2.48537i	0.684165	−	0.497075i	−0.190572	−	0.981673i	$-0.561034\pi$
$5$	3.42082	−	2.48537i	0.684165	−	0.497075i	0.874737	+	0.484598i	$0.161034\pi$
$6$	3.97848	+	5.47590i	0.663079	+	0.912650i
$7$	2.09516	−	0.680759i	0.299308	−	0.0972512i	−0.155513	−	0.987834i	$-0.549703\pi$
$7$	2.09516	−	0.680759i	0.299308	−	0.0972512i	0.454821	+	0.890583i	$0.349703\pi$
$8$	−8.17251	−	2.65541i	−1.02156	−	0.331926i
$9$	−9.72133	−	7.06296i	−1.08015	−	0.784774i
$10$			6.24301i			0.624301i
$11$		0			0
$11$		0			0
$12$	8.34386			0.695321
$13$	12.6188	−	17.3683i	0.970680	−	1.33603i	0.0289770	−	0.999580i	$-0.490775\pi$
$13$	12.6188	−	17.3683i	0.970680	−	1.33603i	0.941703	−	0.336446i	$-0.109225\pi$
$14$	−1.00511	+	3.09341i	−0.0717936	+	0.220958i
$15$	−5.99008	−	18.4356i	−0.399339	−	1.22904i
$16$	4.37437	−	3.17817i	0.273398	−	0.198635i
$17$	5.94669	+	8.18492i	0.349805	+	0.481466i	0.947273	−	0.320427i	$-0.103826\pi$
$17$	5.94669	+	8.18492i	0.349805	+	0.481466i	−0.597468	+	0.801893i	$0.703826\pi$
$18$	16.8731	−	5.48241i	0.937395	−	0.304578i
$19$	3.79705	+	1.23374i	0.199845	+	0.0649335i	0.407229	−	0.913326i	$-0.366495\pi$
$19$	3.79705	+	1.23374i	0.199845	+	0.0649335i	−0.207384	+	0.978260i	$0.566495\pi$
$20$	6.22616	+	4.52357i	0.311308	+	0.226179i
$21$		−	10.0992i		−	0.480916i
$22$		0			0
$23$	0.0490953			0.00213458			0.00106729	−	0.999999i	$-0.499660\pi$
$23$	0.0490953			0.00213458			0.00106729	+	0.999999i	$0.499660\pi$
$24$	−23.1550	+	31.8702i	−0.964793	+	1.32792i
$25$	−2.20047	+	6.77235i	−0.0880188	+	0.270894i
$26$	9.79498	+	30.1459i	0.376730	+	1.15946i
$27$	−11.1866	+	8.12756i	−0.414320	+	0.301021i
$28$	2.35678	+	3.24383i	0.0841707	+	0.115851i
$29$	−29.1064	+	9.45723i	−1.00367	+	0.326112i	−0.764330	−	0.644825i	$-0.776930\pi$
$29$	−29.1064	+	9.45723i	−1.00367	+	0.326112i	−0.239338	+	0.970936i	$0.576930\pi$
$30$	27.2193	+	8.84410i	0.907311	+	0.294803i
$31$	20.2945	+	14.7448i	0.654662	+	0.475640i	0.864856	−	0.502020i	$-0.167409\pi$
$31$	20.2945	+	14.7448i	0.654662	+	0.475640i	−0.210194	+	0.977660i	$0.567409\pi$
$32$		−	26.3891i		−	0.824660i
$33$		0			0
$34$	−14.9375			−0.439338
$35$	5.47523	−	7.53601i	0.156435	−	0.215315i
$36$	6.75834	−	20.8000i	0.187732	−	0.577779i
$37$	1.39407	+	4.29050i	0.0376775	+	0.115959i	0.968126	−	0.250463i	$-0.0805827\pi$
$37$	1.39407	+	4.29050i	0.0376775	+	0.115959i	−0.930449	+	0.366422i	$0.880583\pi$
$38$	−4.76890	+	3.46481i	−0.125497	+	0.0911792i
$39$	−57.8491	−	79.6225i	−1.48331	−	2.04160i
$40$	−34.5564	+	11.2281i	−0.863911	+	0.280702i
$41$	−29.9834	−	9.74219i	−0.731302	−	0.237614i	−0.0803854	−	0.996764i	$-0.525615\pi$
$41$	−29.9834	−	9.74219i	−0.731302	−	0.237614i	−0.650916	+	0.759150i	$0.725615\pi$
$42$	12.0633	+	8.76451i	0.287222	+	0.208679i
$43$			74.2435i			1.72659i	0.504697	+	0.863297i	$0.331604\pi$
$43$			74.2435i			1.72659i	−0.504697	+	0.863297i	$0.668396\pi$
$44$		0			0
$45$	−50.8091			−1.12909
$46$	−0.0426068	+	0.0586433i	−0.000926236	+	0.00127485i
$47$	−21.0255	+	64.7099i	−0.447352	+	1.37681i	0.432532	+	0.901618i	$0.357620\pi$
$47$	−21.0255	+	64.7099i	−0.447352	+	1.37681i	−0.879884	+	0.475189i	$0.842380\pi$
$48$	−7.65981	−	23.5745i	−0.159579	−	0.491135i
$49$	−35.7156	+	25.9489i	−0.728889	+	0.529569i
$50$	−6.17977	−	8.50573i	−0.123595	−	0.170115i
$51$	44.1103	−	14.3323i	0.864909	−	0.281026i
$52$	37.1618	+	12.0746i	0.714650	+	0.232204i
$53$	−51.8725	−	37.6875i	−0.978726	−	0.711086i	−0.0213022	−	0.999773i	$-0.506781\pi$
$53$	−51.8725	−	37.6875i	−0.978726	−	0.711086i	−0.957423	+	0.288687i	$0.906781\pi$
$54$		−	20.4156i		−	0.378067i
$55$		0			0
$56$	−18.9304			−0.338043
$57$	10.7581	−	14.8073i	0.188739	−	0.259777i
$58$	13.9632	−	42.9743i	0.240745	−	0.740936i
$59$	3.81740	+	11.7487i	0.0647016	+	0.199131i	0.978181	−	0.207753i	$-0.0666151\pi$
$59$	3.81740	+	11.7487i	0.0647016	+	0.199131i	−0.913480	+	0.406885i	$0.866615\pi$
$60$	28.5429	−	20.7376i	0.475715	−	0.345627i
$61$	29.3105	+	40.3425i	0.480501	+	0.661352i	0.978601	−	0.205767i	$-0.0659689\pi$
$61$	29.3105	+	40.3425i	0.480501	+	0.661352i	−0.498100	+	0.867119i	$0.665969\pi$
$62$	−35.2248	+	11.4452i	−0.568142	+	0.184600i
$63$	−25.1759	−	8.18015i	−0.399618	−	0.129844i
$64$	49.0187	+	35.6142i	0.765918	+	0.556472i
$65$		−	90.7766i		−	1.39656i
$66$		0			0
$67$	91.4910			1.36554			0.682769	−	0.730635i	$-0.260776\pi$
$67$	91.4910			1.36554			0.682769	+	0.730635i	$0.260776\pi$
$68$	−10.8234	+	14.8972i	−0.159168	+	0.219076i
$69$	0.0695504	−	0.214054i	0.00100798	−	0.00310223i
$70$	4.24998	+	13.0801i	0.0607140	+	0.186859i
$71$	18.5592	−	13.4840i	0.261397	−	0.189916i	−0.449366	−	0.893348i	$-0.648350\pi$
$71$	18.5592	−	13.4840i	0.261397	−	0.189916i	0.710763	+	0.703432i	$0.248350\pi$
$72$	60.6927	+	83.5363i	0.842954	+	1.16023i
$73$	65.7368	−	21.3592i	0.900504	−	0.292591i	0.178059	−	0.984020i	$-0.443018\pi$
$73$	65.7368	−	21.3592i	0.900504	−	0.292591i	0.722445	+	0.691428i	$0.243018\pi$
$74$	−6.33473	−	2.05828i	−0.0856045	−	0.0278146i
$75$	26.4100	+	19.1880i	0.352133	+	0.255840i
$76$			7.26657i			0.0956128i
$77$		0			0
$78$	145.311			1.86296
$79$	−20.8806	+	28.7397i	−0.264311	+	0.363793i	−0.920459	−	0.390839i	$-0.872185\pi$
$79$	−20.8806	+	28.7397i	−0.264311	+	0.363793i	0.656148	+	0.754632i	$0.272185\pi$
$80$	7.06502	−	21.7439i	0.0883128	−	0.271799i
$81$	−13.8305	−	42.5658i	−0.170746	−	0.525503i
$82$	37.6576	−	27.3598i	0.459239	−	0.333656i
$83$	76.6149	+	105.451i	0.923071	+	1.27050i	0.962502	+	0.271276i	$0.0874455\pi$
$83$	76.6149	+	105.451i	0.923071	+	1.27050i	−0.0394310	+	0.999222i	$0.512555\pi$
$84$	17.4817	−	5.68015i	0.208116	−	0.0676209i
$85$	40.6852	+	13.2194i	0.478649	+	0.155523i
$86$	−88.6823	−	64.4314i	−1.03119	−	0.749203i
$87$			140.300i			1.61265i
$88$		0			0
$89$	−128.031			−1.43855			−0.719275	−	0.694725i	$-0.755526\pi$
$89$	−128.031			−1.43855			−0.719275	+	0.694725i	$0.755526\pi$
$90$	44.0941	−	60.6904i	0.489935	−	0.674337i
$91$	14.6148	−	44.9798i	0.160603	−	0.494284i
$92$	0.0276129	+	0.0849837i	0.000300140	+	0.000923736i
$93$	93.0372	−	67.5955i	1.00040	−	0.726833i
$94$	−59.0478	−	81.2724i	−0.628169	−	0.864600i
$95$	16.0553	−	5.21670i	0.169004	−	0.0549126i
$96$	−115.056	−	37.3839i	−1.19850	−	0.389416i
$97$	−70.2327	−	51.0270i	−0.724048	−	0.526052i	0.163627	−	0.986522i	$-0.447681\pi$
$97$	−70.2327	−	51.0270i	−0.724048	−	0.526052i	−0.887675	+	0.460471i	$0.847681\pi$
$98$		−	65.1809i		−	0.665112i
$99$		0			0
$100$	−12.9605			−0.129605
$101$	60.3939	−	83.1251i	0.597959	−	0.823020i	−0.397560	−	0.917576i	$-0.630143\pi$
$101$	60.3939	−	83.1251i	0.597959	−	0.823020i	0.995520	+	0.0945557i	$0.0301430\pi$
$102$	−21.1610	+	65.1270i	−0.207461	+	0.638500i
$103$	−16.8238	−	51.7782i	−0.163338	−	0.502701i	0.835572	−	0.549380i	$-0.185136\pi$
$103$	−16.8238	−	51.7782i	−0.163338	−	0.502701i	−0.998910	+	0.0466790i	$0.985136\pi$
$104$	−149.248	+	108.435i	−1.43507	+	1.04264i
$105$	−25.1004	−	34.5477i	−0.239051	−	0.329026i
$106$	90.0339	−	29.2538i	0.849377	−	0.275979i
$107$	−87.0112	−	28.2716i	−0.813188	−	0.264221i	−0.127241	−	0.991872i	$-0.540612\pi$
$107$	−87.0112	−	28.2716i	−0.813188	−	0.264221i	−0.685948	+	0.727651i	$0.740612\pi$
$108$	−20.3605	−	14.7928i	−0.188523	−	0.136970i
$109$		−	13.2988i		−	0.122007i	−0.998138	−	0.0610037i	$-0.980570\pi$
$109$		−	13.2988i		−	0.122007i	0.998138	−	0.0610037i	$-0.0194301\pi$
$110$		0			0
$111$	20.6813			0.186318
$112$	7.00144	−	9.63666i	0.0625129	−	0.0860416i
$113$	36.6856	−	112.907i	0.324651	−	0.999173i	−0.646947	−	0.762535i	$-0.723954\pi$
$113$	36.6856	−	112.907i	0.324651	−	0.999173i	0.971598	−	0.236638i	$-0.0760456\pi$
$114$	8.35066	+	25.7007i	0.0732514	+	0.225445i
$115$	0.167946	−	0.122020i	0.00146040	−	0.00106105i
$116$	−32.7409	−	45.0639i	−0.282249	−	0.388482i
$117$	−245.344	+	79.7170i	−2.09696	+	0.681342i
$118$	−17.3465	−	5.63622i	−0.147004	−	0.0477646i
$119$	18.0312	+	13.1004i	0.151523	+	0.110088i
$120$			166.571i			1.38809i
$121$		0			0
$122$	−73.6251			−0.603484
$123$	−84.9513	+	116.925i	−0.690661	+	0.950613i
$124$	−14.1089	+	43.4227i	−0.113781	+	0.350183i
$125$	41.9704	+	129.172i	0.335763	+	1.03337i
$126$	31.6197	−	22.9730i	0.250950	−	0.182326i
$127$	−37.1515	−	51.1346i	−0.292531	−	0.402635i	0.637303	−	0.770613i	$-0.280050\pi$
$127$	−37.1515	−	51.1346i	−0.292531	−	0.402635i	−0.929834	+	0.367979i	$0.880050\pi$
$128$	15.3094	−	4.97433i	0.119605	−	0.0388620i
$129$	323.700	+	105.176i	2.50930	+	0.815321i
$130$	108.431	+	78.7795i	0.834082	+	0.605996i
$131$		−	214.429i		−	1.63686i	−0.574607	−	0.818430i	$-0.694845\pi$
$131$		−	214.429i		−	1.63686i	0.574607	−	0.818430i	$-0.305155\pi$
$132$		0			0
$133$	8.79530			0.0661301
$134$	−79.3995	+	109.284i	−0.592534	+	0.815553i
$135$	−18.0675	+	55.6059i	−0.133833	+	0.411896i
$136$	−26.8651	−	82.6823i	−0.197537	−	0.607958i
$137$	9.95011	−	7.22918i	0.0726285	−	0.0527677i	−0.550879	−	0.834585i	$-0.685707\pi$
$137$	9.95011	−	7.22918i	0.0726285	−	0.0527677i	0.623507	+	0.781818i	$0.285707\pi$
$138$	0.195324	+	0.268841i	0.00141539	+	0.00194812i
$139$	52.0821	−	16.9225i	0.374691	−	0.121745i	−0.115616	−	0.993294i	$-0.536884\pi$
$139$	52.0821	−	16.9225i	0.374691	−	0.121745i	0.490308	+	0.871549i	$0.336884\pi$
$140$	16.1243	+	5.23909i	0.115173	+	0.0374221i
$141$	252.348	+	183.341i	1.78970	+	1.30029i
$142$			33.8705i			0.238525i
$143$		0			0
$144$	−64.9720			−0.451194
$145$	−76.0630	+	104.692i	−0.524573	+	0.722012i
$146$	−31.5359	+	97.0575i	−0.215999	+	0.664777i
$147$	62.5403	+	192.479i	0.425444	+	1.30938i
$148$	−6.64276	+	4.82624i	−0.0448835	+	0.0326098i
$149$	−7.59980	−	10.4602i	−0.0510054	−	0.0702029i	0.782752	−	0.622333i	$-0.213815\pi$
$149$	−7.59980	−	10.4602i	−0.0510054	−	0.0702029i	−0.833758	+	0.552130i	$0.813815\pi$
$150$	−45.8393	+	14.8941i	−0.305595	+	0.0992939i
$151$	−66.7109	−	21.6757i	−0.441794	−	0.143548i	0.0796690	−	0.996821i	$-0.474614\pi$
$151$	−66.7109	−	21.6757i	−0.441794	−	0.143548i	−0.521463	+	0.853274i	$0.674614\pi$
$152$	−27.7554	−	20.1655i	−0.182601	−	0.132668i
$153$		−	121.570i		−	0.794572i
$154$		0			0
$155$	106.071			0.684326
$156$	105.290	−	144.919i	0.674934	−	0.928968i
$157$	−10.2055	+	31.4094i	−0.0650035	+	0.200060i	−0.978283	−	0.207273i	$-0.933541\pi$
$157$	−10.2055	+	31.4094i	−0.0650035	+	0.200060i	0.913280	+	0.407333i	$0.133541\pi$
$158$	−16.2079	−	49.8828i	−0.102582	−	0.315714i
$159$	−237.801	+	172.773i	−1.49561	+	1.08662i
$160$	−65.5869	−	90.2726i	−0.409918	−	0.564204i
$161$	0.102862	−	0.0334220i	0.000638897	−	0.000207590i
$162$	62.8465	+	20.4201i	0.387942	+	0.126050i
$163$	−65.9602	−	47.9229i	−0.404664	−	0.294006i	0.366774	−	0.930310i	$-0.380462\pi$
$163$	−65.9602	−	47.9229i	−0.404664	−	0.294006i	−0.771438	+	0.636304i	$0.780462\pi$
$164$		−	57.3804i		−	0.349880i
$165$		0			0
$166$	−192.449			−1.15933
$167$	21.2756	−	29.2834i	0.127399	−	0.175349i	−0.740553	−	0.671998i	$-0.765436\pi$
$167$	21.2756	−	29.2834i	0.127399	−	0.175349i	0.867952	+	0.496649i	$0.165436\pi$
$168$	−26.8176	+	82.5361i	−0.159629	+	0.491286i
$169$	−90.2003	−	277.608i	−0.533730	−	1.64265i
$170$	−51.0985	+	37.1252i	−0.300579	+	0.218384i
$171$	−28.1986	−	38.8120i	−0.164904	−	0.226971i
$172$	−128.515	+	41.7571i	−0.747181	+	0.242774i
$173$	10.3028	+	3.34759i	0.0595539	+	0.0193502i	0.338642	−	0.940915i	$-0.390032\pi$
$173$	10.3028	+	3.34759i	0.0595539	+	0.0193502i	−0.279089	+	0.960265i	$0.590032\pi$
$174$	−167.586	−	121.758i	−0.963137	−	0.699760i
$175$			15.6871i			0.0896408i
$176$		0			0
$177$	56.6321			0.319955
$178$	111.110	−	152.930i	0.624216	−	0.859159i
$179$	−11.9209	+	36.6888i	−0.0665974	+	0.204966i	−0.978817	−	0.204735i	$-0.934367\pi$
$179$	−11.9209	+	36.6888i	−0.0665974	+	0.204966i	0.912220	+	0.409700i	$0.134367\pi$
$180$	−28.5768	−	87.9503i	−0.158760	−	0.488613i
$181$	140.658	−	102.194i	0.777117	−	0.564609i	−0.126995	−	0.991903i	$-0.540533\pi$
$181$	140.658	−	102.194i	0.777117	−	0.564609i	0.904112	+	0.427295i	$0.140533\pi$
$182$	41.0441	+	56.4924i	0.225517	+	0.310398i
$183$	217.415	−	70.6423i	1.18806	−	0.386023i
$184$	−0.401232	−	0.130368i	−0.00218061	−	0.000708523i
$185$	15.4323	+	11.2123i	0.0834181	+	0.0606068i
$186$			169.793i			0.912865i
$187$		0			0
$188$	−123.838			−0.658713
$189$	−17.9049	+	24.6439i	−0.0947347	+	0.130391i
$190$	−7.70223	+	23.7050i	−0.0405380	+	0.124763i
$191$	67.0886	+	206.477i	0.351249	+	1.08103i	0.958153	+	0.286258i	$0.0924114\pi$
$191$	67.0886	+	206.477i	0.351249	+	1.08103i	−0.606904	+	0.794775i	$0.707589\pi$
$192$	224.719	−	163.268i	1.17041	−	0.850353i
$193$	5.07480	+	6.98487i	0.0262943	+	0.0361910i	0.821962	−	0.569543i	$-0.192880\pi$
$193$	5.07480	+	6.98487i	0.0262943	+	0.0361910i	−0.795667	+	0.605734i	$0.792880\pi$
$194$	121.901	−	39.6082i	0.628358	−	0.204166i
$195$	−395.783	−	128.598i	−2.02966	−	0.659476i
$196$	−65.0050	−	47.2289i	−0.331658	−	0.240964i
$197$			387.582i			1.96742i	0.179757	+	0.983711i	$0.442469\pi$
$197$			387.582i			1.96742i	−0.179757	+	0.983711i	$0.557531\pi$
$198$		0			0
$199$	214.315			1.07696			0.538479	−	0.842639i	$-0.318999\pi$
$199$	214.315			1.07696			0.538479	+	0.842639i	$0.318999\pi$
$200$	35.9667	−	49.5040i	0.179834	−	0.247520i
$201$	129.610	−	398.898i	0.644825	−	1.98457i
$202$	46.8789	+	144.278i	0.232074	+	0.714250i
$203$	−54.5444	+	39.6288i	−0.268692	+	0.195216i
$204$	49.6183	+	68.2938i	0.243227	+	0.334774i
$205$	−126.781	+	41.1936i	−0.618443	+	0.200944i
$206$	76.4483	+	24.8396i	0.371108	+	0.120580i
$207$	−0.477272	−	0.346758i	−0.00230566	−	0.00167516i
$208$		−	116.080i		−	0.558079i
$209$		0			0
$210$	63.0495			0.300236
$211$	−147.854	+	203.503i	−0.700728	+	0.964470i	0.299219	+	0.954184i	$0.403274\pi$
$211$	−147.854	+	203.503i	−0.700728	+	0.964470i	−0.999947	+	0.0102851i	$0.996726\pi$
$212$	36.0621	−	110.988i	0.170104	−	0.523527i
$213$	−32.4983	−	100.020i	−0.152574	−	0.469576i
$214$	109.282	−	79.3977i	0.510662	−	0.371017i
$215$	184.523	+	253.974i	0.858246	+	1.18127i
$216$	113.005	−	36.7175i	0.523171	−	0.169988i
$217$	52.5580	+	17.0771i	0.242203	+	0.0786964i
$218$	15.8851	+	11.5412i	0.0728676	+	0.0529414i
$219$		−	316.869i		−	1.44689i
$220$		0			0
$221$	217.199			0.982800
$222$	−17.9481	+	24.7034i	−0.0808472	+	0.111277i
$223$	0.0907051	−	0.279162i	0.000406749	−	0.00125185i	−0.950853	−	0.309643i	$-0.899791\pi$
$223$	0.0907051	−	0.279162i	0.000406749	−	0.00125185i	0.951260	+	0.308391i	$0.0997905\pi$
$224$	−17.9646	−	55.2894i	−0.0801992	−	0.246828i
$225$	69.2244	−	50.2944i	0.307664	−	0.223531i
$226$	103.027	+	141.805i	0.455873	+	0.627455i
$227$	−290.719	+	94.4604i	−1.28070	+	0.416125i	−0.868827	−	0.495115i	$-0.835126\pi$
$227$	−290.719	+	94.4604i	−1.28070	+	0.416125i	−0.411874	+	0.911241i	$0.635126\pi$
$228$	31.6821	+	10.2941i	0.138956	+	0.0451497i
$229$	−177.028	−	128.619i	−0.773050	−	0.561654i	0.129835	−	0.991536i	$-0.458555\pi$
$229$	−177.028	−	128.619i	−0.773050	−	0.561654i	−0.902885	+	0.429882i	$0.858555\pi$
$230$			0.306502i			0.00133262i
$231$		0			0
$232$	262.985			1.13356
$233$	60.0428	−	82.6418i	0.257694	−	0.354686i	−0.660493	−	0.750832i	$-0.729653\pi$
$233$	60.0428	−	82.6418i	0.257694	−	0.354686i	0.918187	+	0.396146i	$0.129653\pi$
$234$	117.699	−	362.240i	0.502986	−	1.54803i
$235$	88.9038	+	273.618i	0.378314	+	1.16433i
$236$	−18.1900	+	13.2158i	−0.0770762	+	0.0559991i
$237$	95.7238	+	131.753i	0.403898	+	0.555918i
$238$	−31.2964	+	10.1688i	−0.131498	+	0.0427261i
$239$	−138.810	−	45.1021i	−0.580795	−	0.188712i	0.00386177	−	0.999993i	$-0.498771\pi$
$239$	−138.810	−	45.1021i	−0.580795	−	0.188712i	−0.584657	+	0.811281i	$0.698771\pi$
$240$	−84.7942	−	61.6066i	−0.353309	−	0.256694i
$241$		−	76.9429i		−	0.319265i	−0.987177	−	0.159633i	$-0.948969\pi$
$241$		−	76.9429i		−	0.319265i	0.987177	−	0.159633i	$-0.0510309\pi$
$242$		0			0
$243$	−329.625			−1.35648
$244$	−53.3474	+	73.4264i	−0.218637	+	0.300928i
$245$	−57.6840	+	177.533i	−0.235445	+	0.724625i
$246$	−65.9408	−	202.945i	−0.268052	−	0.824980i
$247$	69.3423	−	50.3802i	0.280738	−	0.203968i
$248$	−126.704	−	174.393i	−0.510902	−	0.703197i
$249$	568.301	−	184.652i	2.28233	−	0.741575i
$250$	−190.716	−	61.9674i	−0.762865	−	0.247870i
$251$	112.412	+	81.6718i	0.447855	+	0.325386i	0.788748	−	0.614716i	$-0.210730\pi$
$251$	112.412	+	81.6718i	0.447855	+	0.325386i	−0.340893	+	0.940102i	$0.610730\pi$
$252$		−	48.1802i		−	0.191191i
$253$		0			0
$254$	93.3207			0.367404
$255$	115.273	−	158.659i	0.452049	−	0.622193i
$256$	−82.2383	+	253.104i	−0.321244	+	0.988686i
$257$	−79.3142	−	244.104i	−0.308616	−	0.949821i	−0.978303	−	0.207178i	$-0.933572\pi$
$257$	−79.3142	−	244.104i	−0.308616	−	0.949821i	0.669688	−	0.742643i	$-0.266428\pi$
$258$	−406.550	+	295.376i	−1.57578	+	1.14487i
$259$	5.84158	+	8.04025i	0.0225544	+	0.0310434i
$260$	157.134	−	51.0559i	0.604361	−	0.196369i
$261$	349.749	+	113.640i	1.34003	+	0.435403i
$262$	256.130	+	186.090i	0.977597	+	0.710266i
$263$			341.497i			1.29847i	0.760588	+	0.649234i	$0.224911\pi$
$263$			341.497i			1.29847i	−0.760588	+	0.649234i	$0.775089\pi$
$264$		0			0
$265$	−271.114			−1.02307
$266$	−7.63291	+	10.5058i	−0.0286952	+	0.0394955i
$267$	−181.374	+	558.212i	−0.679303	+	2.09068i
$268$	51.4577	+	158.370i	0.192006	+	0.590935i
$269$	339.621	−	246.749i	1.26253	−	0.917284i	0.263654	−	0.964617i	$-0.415072\pi$
$269$	339.621	−	246.749i	1.26253	−	0.917284i	0.998879	+	0.0473332i	$0.0150722\pi$
$270$	−50.7404	−	69.8382i	−0.187928	−	0.258660i
$271$	−78.2810	+	25.4350i	−0.288860	+	0.0938562i	−0.449863	−	0.893098i	$-0.648527\pi$
$271$	−78.2810	+	25.4350i	−0.288860	+	0.0938562i	0.161003	+	0.986954i	$0.448527\pi$
$272$	52.0261	+	16.9043i	0.191272	+	0.0621482i
$273$	−175.407	−	127.440i	−0.642516	−	0.466815i
$274$			18.1590i			0.0662736i
$275$		0			0
$276$	0.409644			0.00148422
$277$	270.237	−	371.949i	0.975584	−	1.34278i	0.0364085	−	0.999337i	$-0.488408\pi$
$277$	270.237	−	371.949i	0.975584	−	1.34278i	0.939175	−	0.343439i	$-0.111592\pi$
$278$	−24.9853	+	76.8970i	−0.0898753	+	0.276608i
$279$	−93.1477	−	286.679i	−0.333863	−	1.02752i
$280$	−64.7576	+	47.0492i	−0.231277	+	0.168033i
$281$	−244.308	−	336.261i	−0.869424	−	1.19666i	−0.979239	−	0.202708i	$-0.935026\pi$
$281$	−244.308	−	336.261i	−0.869424	−	1.19666i	0.109815	−	0.993952i	$-0.464974\pi$
$282$	−437.995	+	142.313i	−1.55317	+	0.504657i
$283$	272.004	+	88.3796i	0.961147	+	0.312295i	0.747237	−	0.664558i	$-0.231380\pi$
$283$	272.004	+	88.3796i	0.961147	+	0.312295i	0.213910	+	0.976853i	$0.431380\pi$
$284$	33.7791	+	24.5420i	0.118941	+	0.0864154i
$285$		−	77.3910i		−	0.271548i
$286$		0			0
$287$	−69.4520			−0.241993
$288$	−186.385	+	256.537i	−0.647171	+	0.890755i
$289$	57.6762	−	177.509i	0.199571	−	0.614218i
$290$	−59.0416	−	181.711i	−0.203592	−	0.626591i
$291$	−321.971	+	233.926i	−1.10643	+	0.803868i
$292$	73.9452	+	101.777i	0.253237	+	0.348551i
$293$	−267.599	+	86.9483i	−0.913308	+	0.296752i	−0.727719	−	0.685876i	$-0.759419\pi$
$293$	−267.599	+	86.9483i	−0.913308	+	0.296752i	−0.185589	+	0.982627i	$0.559419\pi$
$294$	−284.187	−	92.3380i	−0.966623	−	0.314075i
$295$	42.2587	+	30.7027i	0.143250	+	0.104077i
$296$		−	38.7660i		−	0.130966i
$297$		0			0
$298$	19.0899			0.0640601
$299$	0.619526	−	0.852704i	0.00207199	−	0.00285185i
$300$	−18.3604	+	56.5075i	−0.0612014	+	0.188358i
$301$	50.5419	+	155.552i	0.167913	+	0.516784i
$302$	83.7855	−	60.8737i	0.277436	−	0.201569i
$303$	−276.867	−	381.074i	−0.913751	−	1.25767i
$304$	20.5307	−	6.67084i	0.0675353	−	0.0219436i
$305$	200.532	+	65.1569i	0.657483	+	0.213629i
$306$	145.212	+	105.503i	0.474550	+	0.344781i
$307$		−	95.7616i		−	0.311927i	−0.987763	−	0.155964i	$-0.950152\pi$
$307$		−	95.7616i		−	0.311927i	0.987763	−	0.155964i	$-0.0498482\pi$
$308$		0			0
$309$	−249.585			−0.807718
$310$	−92.0522	+	126.699i	−0.296942	+	0.408706i
$311$	44.0533	−	135.582i	0.141650	−	0.435955i	−0.854915	−	0.518769i	$-0.826391\pi$
$311$	44.0533	−	135.582i	0.141650	−	0.435955i	0.996565	+	0.0828136i	$0.0263906\pi$
$312$	261.342	+	804.329i	0.837636	+	2.57798i
$313$	−352.963	+	256.442i	−1.12768	+	0.819305i	−0.985355	−	0.170515i	$-0.945457\pi$
$313$	−352.963	+	256.442i	−1.12768	+	0.819305i	−0.142322	+	0.989820i	$0.545457\pi$
$314$	−28.6611	−	39.4487i	−0.0912775	−	0.125633i
$315$	−106.453	+	34.5887i	−0.337946	+	0.109805i
$316$	−61.4922	−	19.9800i	−0.194595	−	0.0632279i
$317$	336.648	+	244.589i	1.06198	+	0.771574i	0.974454	−	0.224589i	$-0.0721038\pi$
$317$	336.648	+	244.589i	1.06198	+	0.771574i	0.0875263	+	0.996162i	$0.472104\pi$
$318$		−	433.988i		−	1.36474i
$319$		0			0
$320$	256.199			0.800622
$321$	−246.527	+	339.316i	−0.767997	+	1.05706i
$322$	−0.0493462	+	0.151872i	−0.000153249	+	0.000471652i
$323$	12.4819	+	38.4152i	0.0386435	+	0.118933i
$324$	65.9024	−	47.8809i	0.203403	−	0.147781i
$325$	89.8571	+	123.678i	0.276483	+	0.380547i
$326$	114.486	−	37.1987i	0.351183	−	0.114106i
$327$	−57.9824	−	18.8396i	−0.177316	−	0.0576135i
$328$	219.170	+	159.236i	0.668201	+	0.485477i
$329$			149.891i			0.455596i
$330$		0			0
$331$	−468.374			−1.41503			−0.707514	−	0.706700i	$-0.750183\pi$
$331$	−468.374			−1.41503			−0.707514	+	0.706700i	$0.750183\pi$
$332$	−139.445	+	191.929i	−0.420015	+	0.578101i
$333$	16.7514	−	51.5556i	0.0503046	−	0.154822i
$334$	16.5145	+	50.8265i	0.0494447	+	0.152175i
$335$	312.975	−	227.389i	0.934253	−	0.678774i
$336$	−32.0970	−	44.1778i	−0.0955269	−	0.131481i
$337$	−74.9564	+	24.3548i	−0.222423	+	0.0722695i	−0.418108	−	0.908397i	$-0.637307\pi$
$337$	−74.9564	+	24.3548i	−0.222423	+	0.0722695i	0.195686	+	0.980667i	$0.437307\pi$
$338$	409.876	+	133.177i	1.21265	+	0.394014i
$339$	−440.299	−	319.896i	−1.29882	−	0.943647i
$340$			77.8609i			0.229003i
$341$		0			0
$342$	70.8319			0.207111
$343$	−120.614	+	166.011i	−0.351644	+	0.483997i
$344$	197.147	−	606.756i	0.573102	−	1.76383i
$345$	−0.294085	−	0.905101i	−0.000852420	−	0.00262348i
$346$	−12.9398	+	9.40133i	−0.0373983	+	0.0271715i
$347$	−127.956	−	176.116i	−0.368748	−	0.507538i	0.583812	−	0.811889i	$-0.301561\pi$
$347$	−127.956	−	176.116i	−0.368748	−	0.507538i	−0.952560	+	0.304351i	$0.901561\pi$
$348$	−242.859	+	78.9098i	−0.697872	+	0.226752i
$349$	−390.034	−	126.730i	−1.11758	−	0.363122i	−0.308734	−	0.951149i	$-0.599905\pi$
$349$	−390.034	−	126.730i	−1.11758	−	0.363122i	−0.808842	+	0.588026i	$0.799905\pi$
$350$	−18.7380	−	13.6139i	−0.0535370	−	0.0388969i
$351$			296.854i			0.845737i
$352$		0			0
$353$	−91.7009			−0.259776			−0.129888	−	0.991529i	$-0.541462\pi$
$353$	−91.7009			−0.259776			−0.129888	+	0.991529i	$0.541462\pi$
$354$	−49.1475	+	67.6458i	−0.138835	+	0.191090i
$355$	29.9748	−	92.2531i	0.0844362	−	0.259868i
$356$	−72.0090	−	221.621i	−0.202273	−	0.622531i
$357$	82.6614	−	60.0570i	0.231544	−	0.168227i
$358$	−33.4786	−	46.0793i	−0.0935156	−	0.128713i
$359$	452.285	−	146.956i	1.25985	−	0.409349i	0.398407	−	0.917209i	$-0.369563\pi$
$359$	452.285	−	146.956i	1.25985	−	0.409349i	0.861440	+	0.507860i	$0.169563\pi$
$360$	415.238	+	134.919i	1.15344	+	0.374775i
$361$	−279.160	−	202.821i	−0.773295	−	0.561832i
$362$			256.701i			0.709120i
$363$		0			0
$364$	86.0797			0.236483
$365$	171.788	−	236.446i	0.470653	−	0.647799i
$366$	−104.300	+	321.003i	−0.284973	+	0.877058i
$367$	−129.487	−	398.519i	−0.352825	−	1.08588i	−0.957260	−	0.289229i	$-0.906601\pi$
$367$	−129.487	−	398.519i	−0.352825	−	1.08588i	0.604435	−	0.796655i	$-0.293399\pi$
$368$	0.214761	−	0.156033i	0.000583590	−	0.000424003i
$369$	222.670	+	306.478i	0.603441	+	0.830565i
$370$	−26.7856	+	8.70317i	−0.0723935	+	0.0235221i
$371$	−134.337	−	43.6488i	−0.362095	−	0.117652i
$372$	169.335	+	123.029i	0.455201	+	0.330723i
$373$		−	152.458i		−	0.408734i	−0.978894	−	0.204367i	$-0.934486\pi$
$373$		−	152.458i		−	0.408734i	0.978894	−	0.204367i	$-0.0655136\pi$
$374$		0			0
$375$	622.641			1.66038
$376$	343.663	−	473.011i	0.913997	−	1.25801i
$377$	−203.032	+	624.869i	−0.538547	+	1.65748i
$378$	−13.8981	−	42.7739i	−0.0367675	−	0.113159i
$379$	−445.956	+	324.006i	−1.17667	+	0.854897i	−0.991792	−	0.127865i	$-0.959188\pi$
$379$	−445.956	+	324.006i	−1.17667	+	0.854897i	−0.184873	+	0.982762i	$0.559188\pi$
$380$	18.0602	+	24.8577i	0.0475267	+	0.0654149i
$381$	−275.576	+	89.5400i	−0.723296	+	0.235013i
$382$	−304.855	−	99.0533i	−0.798049	−	0.259302i
$383$	239.441	+	173.964i	0.625171	+	0.454213i	0.854724	−	0.519083i	$-0.173726\pi$
$383$	239.441	+	173.964i	0.625171	+	0.454213i	−0.229553	+	0.973296i	$0.573726\pi$
$384$		−	73.7955i		−	0.192176i
$385$		0			0
$386$	−12.7474			−0.0330243
$387$	524.379	−	721.746i	1.35498	−	1.86498i
$388$	48.8263	−	150.272i	0.125841	−	0.387298i
$389$	−36.8307	−	113.353i	−0.0946805	−	0.291396i	0.892490	−	0.451068i	$-0.148957\pi$
$389$	−36.8307	−	113.353i	−0.0946805	−	0.291396i	−0.987170	+	0.159671i	$0.948957\pi$
$390$	497.084	−	361.152i	1.27457	−	0.926032i
$391$	0.291955	+	0.401841i	0.000746687	+	0.00102773i
$392$	360.791	−	117.228i	0.920385	−	0.299051i
$393$	−934.903	−	303.768i	−2.37889	−	0.772947i
$394$	−462.959	−	336.359i	−1.17502	−	0.853703i
$395$			150.209i			0.380277i
$396$		0			0
$397$	38.9263			0.0980512			0.0490256	−	0.998798i	$-0.484388\pi$
$397$	38.9263			0.0980512			0.0490256	+	0.998798i	$0.484388\pi$
$398$	−185.991	+	255.994i	−0.467313	+	0.643202i
$399$	12.4598	−	38.3473i	0.0312275	−	0.0961085i
$400$	11.8980	+	36.6182i	0.0297450	+	0.0915456i
$401$	−111.623	+	81.0991i	−0.278363	+	0.202242i	−0.718203	−	0.695834i	$-0.755035\pi$
$401$	−111.623	+	81.0991i	−0.278363	+	0.202242i	0.439840	+	0.898076i	$0.355035\pi$
$402$	363.995	+	500.996i	0.905460	+	1.24626i
$403$	512.187	−	166.420i	1.27094	−	0.412952i
$404$	177.857	+	57.7891i	0.440239	+	0.143042i
$405$	−153.103	−	111.236i	−0.378033	−	0.274657i
$406$		−	99.5436i		−	0.245181i
$407$		0			0
$408$	−398.551			−0.976840
$409$	170.849	−	235.154i	0.417724	−	0.574948i	−0.547357	−	0.836899i	$-0.684366\pi$
$409$	170.849	−	235.154i	0.417724	−	0.574948i	0.965081	+	0.261951i	$0.0843660\pi$
$410$	60.8205	−	187.186i	0.148343	−	0.456552i
$411$	−17.4233	−	53.6233i	−0.0423924	−	0.130470i
$412$	80.1656	−	58.2437i	0.194577	−	0.141368i
$413$	15.9961	+	22.0168i	0.0387315	+	0.0533093i
$414$	0.828391	−	0.269160i	0.00200094	−	0.000650146i
$415$	524.172	+	170.314i	1.26307	+	0.410395i
$416$	−458.335	−	333.000i	−1.10177	−	0.800481i
$417$		−	251.050i		−	0.602038i
$418$		0			0
$419$	668.534			1.59555			0.797773	−	0.602958i	$-0.206011\pi$
$419$	668.534			1.59555			0.797773	+	0.602958i	$0.206011\pi$
$420$	45.6846	−	62.8794i	0.108773	−	0.149713i
$421$	−111.723	+	343.849i	−0.265376	+	0.816744i	0.726230	+	0.687451i	$0.241271\pi$
$421$	−111.723	+	343.849i	−0.265376	+	0.816744i	−0.991607	+	0.129292i	$0.958729\pi$
$422$	−114.767	−	353.216i	−0.271959	−	0.837005i
$423$	661.440	−	480.564i	1.56369	−	1.13609i
$424$	323.852	+	445.745i	0.763803	+	1.05128i
$425$	−68.5167	+	22.2624i	−0.161216	+	0.0523822i
$426$	147.675	+	47.9824i	0.346654	+	0.112635i
$427$	88.8737	+	64.5705i	0.208135	+	0.151219i
$428$		−	166.517i		−	0.389058i
$429$		0			0
$430$	−463.503			−1.07791
$431$	−370.313	+	509.692i	−0.859194	+	1.18258i	0.122567	+	0.992460i	$0.460887\pi$
$431$	−370.313	+	509.692i	−0.859194	+	1.18258i	−0.981761	+	0.190119i	$0.939113\pi$
$432$	−23.1037	+	71.1060i	−0.0534808	+	0.164597i
$433$	141.361	+	435.064i	0.326468	+	1.00477i	0.970773	+	0.239998i	$0.0771467\pi$
$433$	141.361	+	435.064i	0.326468	+	1.00477i	−0.644305	+	0.764769i	$0.722853\pi$
$434$	−66.0101	+	47.9592i	−0.152097	+	0.110505i
$435$	348.699	+	479.943i	0.801608	+	1.10332i
$436$	23.0202	−	7.47970i	0.0527985	−	0.0171553i
$437$	0.186417	+	0.0605707i	0.000426584	+	0.000138606i
$438$	378.493	+	274.991i	0.864139	+	0.627834i
$439$			182.684i			0.416137i	0.978114	+	0.208068i	$0.0667176\pi$
$439$			182.684i			0.416137i	−0.978114	+	0.208068i	$0.933282\pi$
$440$		0			0
$441$	530.479			1.20290
$442$	−188.494	+	259.439i	−0.426456	+	0.586967i
$443$	149.853	−	461.201i	0.338269	−	1.04109i	−0.626820	−	0.779164i	$-0.715644\pi$
$443$	149.853	−	461.201i	0.338269	−	1.04109i	0.965089	−	0.261921i	$-0.0843561\pi$
$444$	11.6319	+	35.7993i	0.0261980	+	0.0806290i
$445$	−437.972	+	318.205i	−0.984206	+	0.715067i
$446$	0.254735	+	0.350613i	0.000571155	+	0.000786127i
$447$	−56.3725	+	18.3165i	−0.126113	+	0.0409766i
$448$	126.947	+	41.2475i	0.283363	+	0.0920703i
$449$	178.720	+	129.848i	0.398040	+	0.289193i	0.768742	−	0.639559i	$-0.220883\pi$
$449$	178.720	+	129.848i	0.398040	+	0.289193i	−0.370702	+	0.928752i	$0.620883\pi$
$450$			126.335i			0.280743i
$451$		0			0
$452$	216.074			0.478040
$453$	−189.011	+	260.151i	−0.417242	+	0.574285i
$454$	139.467	−	429.234i	0.307195	−	0.945450i
$455$	−61.7969	−	190.191i	−0.135817	−	0.418003i
$456$	−127.240	+	92.4455i	−0.279036	+	0.202731i
$457$	−202.102	−	278.170i	−0.442237	−	0.608687i	0.528470	−	0.848952i	$-0.322766\pi$
$457$	−202.102	−	278.170i	−0.442237	−	0.608687i	−0.970707	+	0.240265i	$0.922766\pi$
$458$	307.265	−	99.8363i	0.670883	−	0.217983i
$459$	−133.047	−	43.2295i	−0.289862	−	0.0941820i
$460$	0.305675	+	0.222086i	0.000664511	+	0.000482796i
$461$		−	3.68109i		−	0.00798501i	−0.999992	−	0.00399251i	$-0.998729\pi$
$461$		−	3.68109i		−	0.00798501i	0.999992	−	0.00399251i	$-0.00127086\pi$
$462$		0			0
$463$	373.943			0.807652			0.403826	−	0.914836i	$-0.367680\pi$
$463$	373.943			0.807652			0.403826	+	0.914836i	$0.367680\pi$
$464$	−97.2654	+	133.874i	−0.209624	+	0.288522i
$465$	150.264	−	462.464i	0.323148	−	0.994547i
$466$	46.6064	+	143.440i	0.100014	+	0.307810i
$467$	363.374	−	264.006i	0.778102	−	0.565324i	−0.126307	−	0.991991i	$-0.540312\pi$
$467$	363.374	−	264.006i	0.778102	−	0.565324i	0.904409	+	0.426667i	$0.140312\pi$
$468$	−275.980	−	379.853i	−0.589700	−	0.811652i
$469$	191.688	−	62.2833i	0.408717	−	0.132800i
$470$	−403.985	−	131.263i	−0.859542	−	0.279282i
$471$	122.487	+	88.9918i	0.260057	+	0.188942i
$472$		−	106.153i		−	0.224901i
$473$		0			0
$474$	−240.449			−0.507275
$475$	−16.7106	+	23.0002i	−0.0351802	+	0.0484214i
$476$	−12.5354	+	38.5801i	−0.0263349	+	0.0810506i
$477$	238.084	+	732.746i	0.499127	+	1.53616i
$478$	174.338	−	126.664i	0.364724	−	0.264988i
$479$	−206.179	−	283.781i	−0.430436	−	0.592445i	0.537617	−	0.843189i	$-0.319325\pi$
$479$	−206.179	−	283.781i	−0.430436	−	0.592445i	−0.968053	+	0.250745i	$0.919325\pi$
$480$	−486.499	+	158.073i	−1.01354	+	0.329319i
$481$	92.1103	+	29.9284i	0.191497	+	0.0622213i
$482$	91.9066	+	66.7741i	0.190678	+	0.138535i
$483$		−	0.495825i		−	0.00102655i
$484$		0			0
$485$	−367.075			−0.756855
$486$	286.062	−	393.730i	0.588605	−	0.810145i
$487$	156.665	−	482.166i	0.321695	−	0.990075i	−0.651216	−	0.758893i	$-0.725741\pi$
$487$	156.665	−	482.166i	0.321695	−	0.990075i	0.972911	−	0.231182i	$-0.0742593\pi$
$488$	−132.415	−	407.531i	−0.271342	−	0.835105i
$489$	−302.385	+	219.695i	−0.618373	+	0.449274i
$490$	−161.999	−	222.973i	−0.330610	−	0.455046i
$491$	−799.836	+	259.882i	−1.62899	+	0.529292i	−0.974040	−	0.226377i	$-0.927312\pi$
$491$	−799.836	+	259.882i	−1.62899	+	0.529292i	−0.654954	+	0.755669i	$0.727312\pi$
$492$	−250.177	−	81.2874i	−0.508490	−	0.165218i
$493$	−250.493	−	181.994i	−0.508100	−	0.369156i
$494$			126.550i			0.256174i
$495$		0			0
$496$	135.637			0.273463
$497$	29.7051	−	40.8855i	0.0597688	−	0.0822647i
$498$	−272.631	+	839.071i	−0.547451	+	1.68488i
$499$	−73.2356	−	225.396i	−0.146765	−	0.451695i	0.850469	−	0.526025i	$-0.176318\pi$
$499$	−73.2356	−	225.396i	−0.146765	−	0.451695i	−0.997234	+	0.0743299i	$0.976318\pi$
$500$	−199.990	+	145.301i	−0.399979	+	0.290602i
$501$	−97.5348	−	134.245i	−0.194680	−	0.267954i
$502$	−195.110	+	63.3952i	−0.388666	+	0.126285i
$503$	533.479	+	173.338i	1.06059	+	0.344608i	0.786818	−	0.617185i	$-0.211727\pi$
$503$	533.479	+	173.338i	1.06059	+	0.344608i	0.273777	+	0.961793i	$0.411727\pi$
$504$	184.029	+	133.705i	0.365137	+	0.265287i
$505$		−	434.458i		−	0.860312i
$506$		0			0
$507$	−1338.14			−2.63934
$508$	67.6185	−	93.0688i	0.133107	−	0.183206i
$509$	−166.478	+	512.366i	−0.327068	+	1.00661i	0.643430	+	0.765505i	$0.277511\pi$
$509$	−166.478	+	512.366i	−0.327068	+	1.00661i	−0.970498	+	0.241108i	$0.922489\pi$
$510$	89.4768	+	275.381i	0.175445	+	0.539963i
$511$	123.189	−	89.5017i	0.241074	−	0.175150i
$512$	−193.110	−	265.793i	−0.377168	−	0.519128i
$513$	−52.5035	+	17.0594i	−0.102346	+	0.0332542i
$514$	360.409	+	117.104i	0.701185	+	0.227829i
$515$	−186.239	−	135.311i	−0.361630	−	0.262740i
$516$			619.477i			1.20054i
$517$		0			0
$518$	−14.6735			−0.0283271
$519$	29.1908	−	40.1777i	0.0562443	−	0.0774137i
$520$	−241.049	+	741.873i	−0.463556	+	1.42668i
$521$	100.152	+	308.238i	0.192231	+	0.591627i	0.999998	+	0.00212431i	$0.000676189\pi$
$521$	100.152	+	308.238i	0.192231	+	0.591627i	−0.807767	+	0.589503i	$0.799324\pi$
$522$	−439.267	+	319.146i	−0.841507	+	0.611391i
$523$	−23.7889	−	32.7426i	−0.0454855	−	0.0626054i	0.785668	−	0.618648i	$-0.212319\pi$
$523$	−23.7889	−	32.7426i	−0.0454855	−	0.0626054i	−0.831154	+	0.556042i	$0.812319\pi$
$524$	371.175	−	120.602i	0.708349	−	0.230157i
$525$	68.3955	+	22.2230i	0.130277	+	0.0423296i
$526$	−407.911	−	296.365i	−0.775497	−	0.563431i
$527$			253.792i			0.481579i
$528$		0			0
$529$	−528.998			−0.999995
$530$	235.284	−	323.840i	0.443931	−	0.611019i
$531$	45.8707	−	141.176i	0.0863855	−	0.265867i
$532$	4.94678	+	15.2246i	0.00929846	+	0.0286177i
$533$	−547.561	+	397.826i	−1.02732	+	0.746391i
$534$	−509.368	−	701.085i	−0.953873	−	1.31289i
$535$	−367.916	+	119.543i	−0.687693	+	0.223445i
$536$	−747.712	−	242.946i	−1.39498	−	0.453258i
$537$	143.075	+	103.950i	0.266433	+	0.193575i
$538$			619.809i			1.15206i
$539$		0			0
$540$	−106.415			−0.197065
$541$	−526.715	+	724.960i	−0.973594	+	1.34004i	−0.0333843	+	0.999443i	$0.510629\pi$
$541$	−526.715	+	724.960i	−0.973594	+	1.34004i	−0.940210	+	0.340595i	$0.889371\pi$
$542$	37.5537	−	115.578i	0.0692873	−	0.213244i
$543$	−246.302	−	758.038i	−0.453594	−	1.39602i
$544$	215.993	−	156.928i	0.397046	−	0.288471i
$545$	−33.0525	−	45.4929i	−0.0606468	−	0.0834732i
$546$	304.450	−	98.9218i	0.557600	−	0.181175i
$547$	−44.7336	−	14.5348i	−0.0817800	−	0.0265719i	0.267841	−	0.963463i	$-0.413690\pi$
$547$	−44.7336	−	14.5348i	−0.0817800	−	0.0265719i	−0.349621	+	0.936891i	$0.613690\pi$
$548$	18.1100	+	13.1577i	0.0330474	+	0.0240103i
$549$		−	599.202i		−	1.09144i
$550$		0			0
$551$	−122.186			−0.221753
$552$	−1.13680	+	1.56468i	−0.00205943	+	0.00283456i
$553$	−24.1834	+	74.4288i	−0.0437313	+	0.134591i
$554$	209.763	+	645.584i	0.378633	+	1.16531i
$555$	70.7472	−	51.4009i	0.127472	−	0.0926142i
$556$	58.5855	+	80.6361i	0.105370	+	0.145029i
$557$	187.372	−	60.8808i	0.336394	−	0.109301i	−0.135949	−	0.990716i	$-0.543408\pi$
$557$	187.372	−	60.8808i	0.336394	−	0.109301i	0.472343	+	0.881415i	$0.343408\pi$
$558$	423.269	+	137.529i	0.758547	+	0.246467i
$559$	1289.49	+	936.867i	2.30677	+	1.67597i
$560$		−	50.3665i		−	0.0899402i
$561$		0			0
$562$	613.677			1.09195
$563$	378.943	−	521.570i	0.673078	−	0.926413i	−0.326747	−	0.945112i	$-0.605952\pi$
$563$	378.943	−	521.570i	0.673078	−	0.926413i	0.999825	+	0.0186992i	$0.00595248\pi$
$564$	−175.434	+	539.930i	−0.311053	+	0.957323i
$565$	−155.120	−	477.411i	−0.274549	−	0.844975i
$566$	−341.624	+	248.204i	−0.603576	+	0.438523i
$567$	−57.9540	−	79.7669i	−0.102212	−	0.140682i
$568$	−187.481	+	60.9162i	−0.330072	+	0.107247i
$569$	553.061	+	179.700i	0.971987	+	0.315818i	0.751618	−	0.659599i	$-0.229274\pi$
$569$	553.061	+	179.700i	0.971987	+	0.315818i	0.220369	+	0.975417i	$0.429274\pi$
$570$	92.4419	+	67.1630i	0.162179	+	0.117830i
$571$		−	971.767i		−	1.70187i	−0.525272	−	0.850934i	$-0.676036\pi$
$571$		−	971.767i		−	1.70187i	0.525272	−	0.850934i	$-0.323964\pi$
$572$		0			0
$573$	995.276			1.73696
$574$	60.2732	−	82.9589i	0.105006	−	0.144528i
$575$	−0.108033	+	0.332491i	−0.000187883	+	0.000578245i
$576$	−224.986	−	692.435i	−0.390600	−	1.20214i
$577$	590.066	−	428.708i	1.02265	−	0.742995i	0.0558219	−	0.998441i	$-0.482222\pi$
$577$	590.066	−	428.708i	1.02265	−	0.742995i	0.966824	+	0.255445i	$0.0822221\pi$
$578$	161.977	+	222.942i	0.280237	+	0.385713i
$579$	37.6430	−	12.2310i	0.0650138	−	0.0211243i
$580$	−224.001	−	72.7825i	−0.386209	−	0.125487i
$581$	232.307	+	168.781i	0.399840	+	0.290501i
$582$		−	587.597i		−	1.00962i
$583$		0			0
$584$	−593.952			−1.01704
$585$	−641.152	+	882.469i	−1.09599	+	1.50849i
$586$	128.375	−	395.099i	0.219071	−	0.674230i
$587$	213.859	+	658.191i	0.364326	+	1.12128i	0.950402	+	0.311024i	$0.100672\pi$
$587$	213.859	+	658.191i	0.364326	+	1.12128i	−0.586076	+	0.810256i	$0.699328\pi$
$588$	−298.006	+	216.514i	−0.506812	+	0.368221i
$589$	58.8681	+	81.0250i	0.0999459	+	0.137564i
$590$	−73.3475	+	23.8320i	−0.124318	+	0.0403933i
$591$	1689.85	+	549.065i	2.85930	+	0.929044i
$592$	19.7341	+	14.3376i	0.0333346	+	0.0242190i
$593$			240.570i			0.405684i	0.979212	+	0.202842i	$0.0650177\pi$
$593$			240.570i			0.405684i	−0.979212	+	0.202842i	$0.934982\pi$
$594$		0			0
$595$	94.2412			0.158389
$596$	13.8322	−	19.0384i	0.0232084	−	0.0319436i
$597$	303.607	−	934.406i	0.508554	−	1.56517i
$598$	0.480888	+	1.48002i	0.000804160	+	0.00247495i
$599$	299.620	−	217.686i	0.500200	−	0.363416i	−0.308894	−	0.951097i	$-0.599959\pi$
$599$	299.620	−	217.686i	0.500200	−	0.363416i	0.809093	+	0.587680i	$0.199959\pi$
$600$	−164.884	−	226.943i	−0.274807	−	0.378239i
$601$	220.103	−	71.5158i	0.366228	−	0.118995i	−0.120121	−	0.992759i	$-0.538328\pi$
$601$	220.103	−	71.5158i	0.366228	−	0.118995i	0.486349	+	0.873765i	$0.338328\pi$
$602$	−229.666	−	74.6229i	−0.381505	−	0.123958i
$603$	−889.415	−	646.198i	−1.47498	−	1.07164i
$604$		−	127.667i		−	0.211370i
$605$		0			0
$606$	695.460			1.14762
$607$	−299.131	+	411.718i	−0.492802	+	0.678283i	−0.980902	−	0.194505i	$-0.937690\pi$
$607$	−299.131	+	411.718i	−0.492802	+	0.678283i	0.488100	+	0.872788i	$0.337690\pi$
$608$	32.5572	−	100.201i	0.0535481	−	0.164804i
$609$	95.5108	+	293.952i	0.156832	+	0.482680i
$610$	−251.858	+	182.986i	−0.412883	+	0.299977i
$611$	858.586	+	1181.74i	1.40521	+	1.93411i
$612$	210.436	−	68.3749i	0.343850	−	0.111724i
$613$	−1002.44	−	325.712i	−1.63530	−	0.531341i	−0.659820	−	0.751424i	$-0.729367\pi$
$613$	−1002.44	−	325.712i	−1.63530	−	0.531341i	−0.975481	+	0.220083i	$0.929367\pi$
$614$	114.385	+	83.1057i	0.186295	+	0.135351i
$615$			611.117i			0.993687i
$616$		0			0
$617$	130.588			0.211650			0.105825	−	0.994385i	$-0.466252\pi$
$617$	130.588			0.211650			0.105825	+	0.994385i	$0.466252\pi$
$618$	216.600	−	298.124i	0.350485	−	0.482401i
$619$	−191.872	+	590.523i	−0.309972	+	0.953995i	0.667803	+	0.744338i	$0.267235\pi$
$619$	−191.872	+	590.523i	−0.309972	+	0.953995i	−0.977775	+	0.209657i	$0.932765\pi$
$620$	59.6577	+	183.608i	0.0962221	+	0.296141i
$621$	−0.549211	+	0.399025i	−0.000884398	+	0.000642552i
$622$	123.719	+	170.284i	0.198905	+	0.273769i
$623$	−268.245	+	87.1582i	−0.430570	+	0.139901i
$624$	−506.107	−	164.444i	−0.811069	−	0.263532i
$625$	320.590	+	232.922i	0.512944	+	0.372676i
$626$		−	644.157i		−	1.02901i
$627$		0			0
$628$	−60.1095			−0.0957158
$629$	−26.8273	+	36.9246i	−0.0426507	+	0.0587036i
$630$	51.0687	−	157.173i	0.0810615	−	0.249482i
$631$	232.404	+	715.265i	0.368310	+	1.13354i	0.947882	+	0.318621i	$0.103220\pi$
$631$	232.404	+	715.265i	0.368310	+	1.13354i	−0.579572	+	0.814921i	$0.696780\pi$
$632$	246.963	−	179.429i	0.390763	−	0.283906i
$633$	677.812	+	932.929i	1.07079	+	1.47382i
$634$	−584.312	+	189.855i	−0.921628	+	0.299455i
$635$	−254.177	−	82.5872i	−0.400279	−	0.130059i
$636$	−432.816	−	314.460i	−0.680529	−	0.494433i
$637$			947.765i			1.48786i
$638$		0			0
$639$	−275.657			−0.431389
$640$	40.0078	−	55.0660i	0.0625122	−	0.0860406i
$641$	−209.862	+	645.890i	−0.327399	+	1.00763i	0.642948	+	0.765910i	$0.277711\pi$
$641$	−209.862	+	645.890i	−0.327399	+	1.00763i	−0.970346	+	0.241719i	$0.922289\pi$
$642$	−191.359	−	588.943i	−0.298067	−	0.917356i
$643$	718.796	−	522.236i	1.11788	−	0.812186i	0.133992	−	0.990982i	$-0.457220\pi$
$643$	718.796	−	522.236i	1.11788	−	0.812186i	0.983886	+	0.178796i	$0.0572202\pi$
$644$	0.115707	+	0.159257i	0.000179669	+	0.000247293i
$645$	1368.72	−	444.725i	2.12205	−	0.689496i
$646$	−56.7184	−	18.4289i	−0.0877994	−	0.0285277i
$647$	−559.357	−	406.397i	−0.864540	−	0.628125i	0.0645766	−	0.997913i	$-0.479430\pi$
$647$	−559.357	−	406.397i	−0.864540	−	0.628125i	−0.929116	+	0.369788i	$0.879430\pi$
$648$			384.595i			0.593511i
$649$		0			0
$650$	−225.712			−0.347249
$651$	148.912	−	204.959i	0.228743	−	0.314837i
$652$	45.8560	−	141.130i	0.0703313	−	0.216458i
$653$	59.1532	+	182.055i	0.0905868	+	0.278798i	0.986078	−	0.166281i	$-0.0531758\pi$
$653$	59.1532	+	182.055i	0.0905868	+	0.278798i	−0.895492	+	0.445078i	$0.853176\pi$
$654$	72.8229	−	52.9090i	0.111350	−	0.0809006i
$655$	−532.935	−	733.523i	−0.813642	−	1.11988i
$656$	−162.121	+	52.6762i	−0.247135	+	0.0802991i
$657$	−789.908	−	256.657i	−1.20230	−	0.390649i
$658$	−179.041	−	130.081i	−0.272100	−	0.197692i
$659$		−	1009.37i		−	1.53167i	−0.643036	−	0.765836i	$-0.722325\pi$
$659$		−	1009.37i		−	1.53167i	0.643036	−	0.765836i	$-0.277675\pi$
$660$		0			0
$661$	329.349			0.498259			0.249129	−	0.968470i	$-0.419856\pi$
$661$	329.349			0.498259			0.249129	+	0.968470i	$0.419856\pi$
$662$	406.473	−	559.463i	0.614008	−	0.845110i
$663$	307.693	−	946.981i	0.464092	−	1.42833i
$664$	−346.120	−	1065.25i	−0.521264	−	1.60429i
$665$	30.0872	−	21.8596i	0.0452439	−	0.0328716i
$666$	47.0445	+	64.7512i	0.0706374	+	0.0972240i
$667$	−1.42899	+	0.464306i	−0.00214241	+	0.000696111i
$668$	62.6555	+	20.3580i	0.0937956	+	0.0304761i
$669$	−1.08864	−	0.790943i	−0.00162726	−	0.00118228i
$670$			571.179i			0.852506i
$671$		0			0
$672$	−266.510			−0.396592
$673$	724.287	−	996.895i	1.07621	−	1.48127i	0.212576	−	0.977145i	$-0.431815\pi$
$673$	724.287	−	996.895i	1.07621	−	1.48127i	0.863630	−	0.504126i	$-0.168185\pi$
$674$	35.9588	−	110.670i	0.0533514	−	0.164199i
$675$	−30.4269	−	93.6442i	−0.0450768	−	0.138732i
$676$	429.806	−	312.272i	0.635808	−	0.461942i
$677$	−253.602	−	349.053i	−0.374597	−	0.515589i	0.579546	−	0.814939i	$-0.303230\pi$
$677$	−253.602	−	349.053i	−0.374597	−	0.515589i	−0.954143	+	0.299351i	$0.903230\pi$
$678$	764.218	−	248.310i	1.12717	−	0.366238i
$679$	−181.886	−	59.0983i	−0.267873	−	0.0870372i
$680$	−297.397	−	216.072i	−0.437349	−	0.317753i
$681$			1401.34i			2.05777i
$682$		0			0
$683$	−223.916			−0.327841			−0.163921	−	0.986474i	$-0.552414\pi$
$683$	−223.916			−0.327841			−0.163921	+	0.986474i	$0.552414\pi$
$684$	51.3235	−	70.6408i	0.0750344	−	0.103276i
$685$	16.0704	−	49.4595i	0.0234604	−	0.0722036i
$686$	−93.6229	−	288.142i	−0.136477	−	0.420032i
$687$	−811.560	+	589.633i	−1.18131	+	0.858272i
$688$	235.958	+	324.769i	0.342963	+	0.472048i
$689$	−1309.14	+	425.365i	−1.90006	+	0.617366i
$690$	1.33634	+	0.434204i	0.00193673	+	0.000629281i
$691$	−763.716	−	554.872i	−1.10523	−	0.802998i	−0.123326	−	0.992366i	$-0.539356\pi$
$691$	−763.716	−	554.872i	−1.10523	−	0.802998i	−0.981906	+	0.189368i	$0.939356\pi$
$692$			19.7169i			0.0284927i
$693$		0			0
$694$	321.412			0.463129
$695$	136.105	−	187.332i	0.195835	−	0.269543i
$696$	372.555	−	1146.61i	0.535281	−	1.64742i
$697$	−98.5628	−	303.345i	−0.141410	−	0.435216i
$698$	489.863	−	355.906i	0.701809	−	0.509894i
$699$	−275.257	−	378.859i	−0.393787	−	0.542001i
$700$	−27.1544	+	8.82299i	−0.0387920	+	0.0126043i
$701$	−967.101	−	314.230i	−1.37960	−	0.448260i	−0.477063	−	0.878869i	$-0.658299\pi$
$701$	−967.101	−	314.230i	−1.37960	−	0.448260i	−0.902538	+	0.430609i	$0.858299\pi$
$702$	−354.585	−	257.621i	−0.505107	−	0.366982i
$703$			18.0111i			0.0256204i
$704$		0			0
$705$	1318.91			1.87079
$706$	79.5817	−	109.535i	0.112722	−	0.155148i
$707$	69.9467	−	215.274i	0.0989346	−	0.304489i
$708$	31.8518	+	98.0298i	0.0449884	+	0.138460i
$709$	137.405	−	99.8306i	0.193801	−	0.140805i	−0.486653	−	0.873595i	$-0.661782\pi$
$709$	137.405	−	99.8306i	0.193801	−	0.140805i	0.680454	+	0.732790i	$0.261782\pi$
$710$	84.1810	+	115.865i	0.118565	+	0.163190i
$711$	405.974	−	131.909i	0.570991	−	0.185526i
$712$	1046.34	+	339.975i	1.46957	+	0.477493i
$713$	0.996366	+	0.723903i	0.00139743	+	0.00101529i
$714$			150.857i			0.211284i
$715$		0			0
$716$	−70.2130			−0.0980628
$717$	−393.288	+	541.314i	−0.548518	+	0.754971i
$718$	−216.975	+	667.779i	−0.302193	+	0.930054i
$719$	149.619	+	460.481i	0.208093	+	0.640446i	0.999572	+	0.0292491i	$0.00931160\pi$
$719$	149.619	+	460.481i	0.208093	+	0.640446i	−0.791479	+	0.611197i	$0.790688\pi$
$720$	−222.258	+	161.480i	−0.308691	+	0.224277i
$721$	−70.4970	−	97.0307i	−0.0977766	−	0.134578i
$722$	484.531	−	157.434i	0.671096	−	0.218052i
$723$	−335.469	−	109.000i	−0.463996	−	0.150761i
$724$	256.009	+	186.001i	0.353603	+	0.256908i
$725$		−	217.929i		−	0.300592i
$726$		0			0
$727$	−112.022			−0.154088			−0.0770441	−	0.997028i	$-0.524548\pi$
$727$	−112.022			−0.154088			−0.0770441	+	0.997028i	$0.524548\pi$
$728$	−238.880	+	328.790i	−0.328132	+	0.451634i
$729$	−342.487	+	1054.07i	−0.469803	+	1.44591i
$730$	133.345	+	410.395i	0.182665	+	0.562185i
$731$	−607.677	+	441.503i	−0.831296	+	0.603972i
$732$	244.563	+	336.612i	0.334102	+	0.459852i
$733$	1091.95	−	354.796i	1.48970	−	0.484033i	0.552706	−	0.833377i	$-0.313595\pi$
$733$	1091.95	−	354.796i	1.48970	−	0.484033i	0.936995	+	0.349344i	$0.113595\pi$
$734$	588.397	+	191.182i	0.801630	+	0.260465i
$735$	692.322	+	503.001i	0.941935	+	0.684356i
$736$		−	1.29558i		−	0.00176030i
$737$		0			0
$738$	−559.323			−0.757891
$739$	−449.205	+	618.278i	−0.607856	+	0.836641i	−0.996399	−	0.0847891i	$-0.972978\pi$
$739$	−449.205	+	618.278i	−0.607856	+	0.836641i	0.388543	+	0.921430i	$0.372978\pi$
$740$	−10.7287	+	33.0195i	−0.0144982	+	0.0446209i
$741$	−121.423	−	373.701i	−0.163864	−	0.504320i
$742$	168.721	−	122.583i	0.227386	−	0.165206i
$743$	810.468	+	1115.51i	1.09080	+	1.50136i	0.847040	+	0.531530i	$0.178383\pi$
$743$	810.468	+	1115.51i	1.09080	+	1.50136i	0.243765	+	0.969834i	$0.421617\pi$
$744$	−939.841	+	305.373i	−1.26323	+	0.410448i
$745$	−51.9952	−	16.8943i	−0.0697922	−	0.0226768i
$746$	182.107	+	132.309i	0.244112	+	0.177358i
$747$		−	1566.26i		−	2.09673i
$748$		0			0
$749$	−201.548			−0.269090
$750$	−540.353	+	743.732i	−0.720470	+	0.991642i
$751$	32.3035	−	99.4198i	0.0430139	−	0.132383i	−0.927243	−	0.374459i	$-0.877828\pi$
$751$	32.3035	−	99.4198i	0.0430139	−	0.132383i	0.970257	+	0.242076i	$0.0778283\pi$
$752$	113.685	+	349.888i	0.151178	+	0.465277i
$753$	515.334	−	374.412i	0.684374	−	0.497227i
$754$	−570.193	−	784.803i	−0.756224	−	1.04085i
$755$	−282.079	+	91.6529i	−0.373614	+	0.121395i
$756$	−52.7288	−	17.1326i	−0.0697471	−	0.0226622i
$757$	244.860	+	177.901i	0.323461	+	0.235008i	0.737651	−	0.675183i	$-0.235935\pi$
$757$	244.860	+	177.901i	0.323461	+	0.235008i	−0.414190	+	0.910190i	$0.635935\pi$
$758$		−	813.870i		−	1.07371i
$759$		0			0
$760$	−145.065			−0.190875
$761$	−14.3199	+	19.7096i	−0.0188172	+	0.0258996i	−0.818322	−	0.574760i	$-0.805095\pi$
$761$	−14.3199	+	19.7096i	−0.0188172	+	0.0258996i	0.799505	+	0.600660i	$0.205095\pi$
$762$	132.202	−	406.875i	0.173493	−	0.533957i
$763$	−9.05327	−	27.8631i	−0.0118654	−	0.0365178i
$764$	−319.678	+	232.260i	−0.418427	+	0.304005i
$765$	−302.146	−	415.868i	−0.394962	−	0.543619i
$766$	−415.592	+	135.034i	−0.542548	+	0.176285i
$767$	252.227	+	81.9536i	0.328849	+	0.106850i
$768$	987.022	+	717.114i	1.28519	+	0.933742i
$769$			926.837i			1.20525i	0.798025	+	0.602625i	$0.205878\pi$
$769$			926.837i			1.20525i	−0.798025	+	0.602625i	$0.794122\pi$
$770$		0			0
$771$	−1176.65			−1.52613
$772$	−9.23652	+	12.7130i	−0.0119644	+	0.0164676i
$773$	160.581	−	494.217i	0.207737	−	0.639349i	−0.791853	−	0.610712i	$-0.790883\pi$
$773$	160.581	−	494.217i	0.207737	−	0.639349i	0.999590	−	0.0286369i	$-0.00911664\pi$
$774$	407.033	+	1252.72i	0.525883	+	1.61850i
$775$	−144.515	+	104.996i	−0.186471	+	0.135479i
$776$	438.480	+	603.516i	0.565051	+	0.777726i
$777$	43.3307	−	14.0790i	0.0557667	−	0.0181197i
$778$	167.361	+	54.3789i	0.215117	+	0.0698958i
$779$	−101.829	−	73.9832i	−0.130718	−	0.0949720i
$780$		−	757.427i		−	0.971060i
$781$		0			0
$782$	−0.733360			−0.000937801
$783$	248.738	−	342.358i	0.317673	−	0.437239i
$784$	−73.7633	+	227.020i	−0.0940859	+	0.289566i
$785$	43.1528	+	132.811i	0.0549718	+	0.169186i
$786$	1174.19	−	853.099i	1.49388	−	1.08537i
$787$	−43.8258	−	60.3210i	−0.0556872	−	0.0766468i	0.780265	−	0.625449i	$-0.215084\pi$
$787$	−43.8258	−	60.3210i	−0.0556872	−	0.0766468i	−0.835952	+	0.548802i	$0.815084\pi$
$788$	−670.903	+	217.990i	−0.851399	+	0.276636i
$789$	1488.92	+	483.779i	1.88710	+	0.613155i
$790$	−179.422	−	130.358i	−0.227116	−	0.165010i
$791$		−	261.531i		−	0.330634i
$792$		0			0
$793$	1070.55			1.35000
$794$	−33.7818	+	46.4967i	−0.0425464	+	0.0585601i
$795$	−384.072	+	1182.05i	−0.483109	+	1.48686i
$796$	120.538	+	370.978i	0.151430	+	0.466052i
$797$	−1123.79	+	816.480i	−1.41002	+	1.02444i	−0.416705	+	0.909042i	$0.636815\pi$
$797$	−1123.79	+	816.480i	−1.41002	+	1.02444i	−0.993319	+	0.115400i	$0.963185\pi$
$798$	34.9919	+	48.1622i	0.0438495	+	0.0603537i
$799$	−654.678	+	212.718i	−0.819372	+	0.266230i
$800$	178.716	+	58.0685i	0.223396	+	0.0725856i
$801$	1244.63	+	904.278i	1.55385	+	1.12894i
$802$		−	203.713i		−	0.254006i
$803$		0			0
$804$	763.388			0.949488
$805$	0.268808	−	0.369983i	0.000333923	−	0.000459606i
$806$	−245.711	+	756.222i	−0.304853	+	0.938240i
$807$	−594.699	−	1830.30i	−0.736926	−	2.26802i
$808$	−714.301	+	518.970i	−0.884036	+	0.642290i
$809$	−559.545	−	770.147i	−0.691650	−	0.951974i	−1.00000		0.000701300i	$-0.999777\pi$
$809$	−559.545	−	770.147i	−0.691650	−	0.951974i	0.308350	−	0.951273i	$-0.400223\pi$
$810$	265.739	−	86.3437i	0.328072	−	0.106597i
$811$	195.516	+	63.5272i	0.241081	+	0.0783319i	0.427065	−	0.904221i	$-0.359547\pi$
$811$	195.516	+	63.5272i	0.241081	+	0.0783319i	−0.185985	+	0.982553i	$0.559547\pi$
$812$	−99.2749	−	72.1275i	−0.122260	−	0.0888269i
$813$			377.335i			0.464127i
$814$		0			0
$815$	−344.745			−0.423000
$816$	147.405	−	202.885i	0.180643	−	0.248634i
$817$	−91.5970	+	281.906i	−0.112114	+	0.345051i
$818$	132.616	+	408.151i	0.162123	+	0.498963i
$819$	−459.766	+	334.040i	−0.561375	+	0.407863i
$820$	−142.612	−	196.288i	−0.173917	−	0.239376i
$821$	364.224	−	118.343i	0.443634	−	0.144146i	−0.0786775	−	0.996900i	$-0.525070\pi$
$821$	364.224	−	118.343i	0.443634	−	0.144146i	0.522312	+	0.852755i	$0.325070\pi$
$822$	79.1725	+	25.7247i	0.0963170	+	0.0312953i
$823$	−211.377	−	153.575i	−0.256838	−	0.186603i	0.451914	−	0.892061i	$-0.350741\pi$
$823$	−211.377	−	153.575i	−0.256838	−	0.186603i	−0.708752	+	0.705458i	$0.750741\pi$
$824$			467.832i			0.567758i
$825$		0			0
$826$	−40.1806			−0.0486448
$827$	24.8516	−	34.2054i	0.0300504	−	0.0413608i	−0.793727	−	0.608274i	$-0.791862\pi$
$827$	24.8516	−	34.2054i	0.0300504	−	0.0413608i	0.823778	+	0.566913i	$0.191862\pi$
$828$	0.331803	−	1.02118i	0.000400728	−	0.00123331i
$829$	−259.489	−	798.624i	−0.313014	−	0.963359i	−0.976564	−	0.215227i	$-0.930951\pi$
$829$	−259.489	−	798.624i	−0.313014	−	0.963359i	0.663550	−	0.748132i	$-0.269049\pi$
$830$	−658.333	+	478.307i	−0.793173	+	0.576274i
$831$	−1238.86	−	1705.14i	−1.49080	−	2.05192i
$832$	1237.12	−	401.964i	1.48692	−	0.483130i
$833$	−424.779	−	138.019i	−0.509939	−	0.165689i
$834$	299.873	+	217.871i	0.359560	+	0.261236i
$835$		−	153.051i		−	0.183295i
$836$		0			0
$837$	−346.867			−0.414417
$838$	−580.180	+	798.550i	−0.692339	+	0.952923i
$839$	−90.8616	+	279.643i	−0.108298	+	0.333305i	−0.990490	−	0.137583i	$-0.956067\pi$
$839$	−90.8616	+	279.643i	−0.108298	+	0.333305i	0.882193	+	0.470889i	$0.156067\pi$
$840$	113.395	+	348.993i	0.134994	+	0.415468i
$841$	77.3585	−	56.2042i	0.0919839	−	0.0668302i
$842$	−313.762	−	431.857i	−0.372639	−	0.512894i
$843$	−1812.19	+	588.815i	−2.14969	+	0.698476i
$844$	−435.421	−	141.477i	−0.515901	−	0.167627i
$845$	−998.519	−	725.467i	−1.18168	−	0.858540i
$846$			1207.13i			1.42687i
$847$		0			0
$848$	−346.687			−0.408829
$849$	770.665	−	1060.73i	0.907733	−	1.24939i
$850$	32.8695	−	101.162i	0.0386700	−	0.119014i
$851$	0.0684421	+	0.210643i	8.04255e−5	+	0.000247524i
$852$	154.855	−	112.509i	0.181755	−	0.132053i
$853$	−426.215	−	586.634i	−0.499665	−	0.687730i	0.482469	−	0.875913i	$-0.339740\pi$
$853$	−426.215	−	586.634i	−0.499665	−	0.687730i	−0.982134	+	0.188183i	$0.939740\pi$
$854$	−154.256	+	50.1209i	−0.180628	+	0.0586896i
$855$	−192.925	−	62.6850i	−0.225643	−	0.0733158i
$856$	636.027	+	462.101i	0.743022	+	0.539837i
$857$		−	381.946i		−	0.445678i	−0.974855	−	0.222839i	$-0.928468\pi$
$857$		−	381.946i		−	0.445678i	0.974855	−	0.222839i	$-0.0715325\pi$
$858$		0			0
$859$	−1181.72			−1.37569			−0.687846	−	0.725857i	$-0.741443\pi$
$859$	−1181.72			−1.37569			−0.687846	+	0.725857i	$0.741443\pi$
$860$	−335.846	+	462.252i	−0.390518	+	0.537502i
$861$	−98.3885	+	302.809i	−0.114272	+	0.351694i
$862$	−287.444	−	884.661i	−0.333461	−	1.02629i
$863$	700.178	−	508.709i	0.811330	−	0.589466i	−0.102886	−	0.994693i	$-0.532808\pi$
$863$	700.178	−	508.709i	0.811330	−	0.589466i	0.914216	+	0.405227i	$0.132808\pi$
$864$	214.479	+	295.205i	0.248240	+	0.341673i
$865$	43.5642	−	14.1549i	0.0503632	−	0.0163640i
$866$	−642.353	−	208.713i	−0.741747	−	0.241008i
$867$	−692.228	−	502.933i	−0.798417	−	0.580084i
$868$			100.582i			0.115878i
$869$		0			0
$870$	−875.897			−1.00678
$871$	1154.51	−	1589.05i	1.32550	−	1.82439i
$872$	−35.3138	+	108.685i	−0.0404975	+	0.124638i
$873$	322.353	+	992.101i	0.369248	+	1.13643i
$874$	−0.234131	+	0.170106i	−0.000267884	+	0.000194629i
$875$	175.869	+	242.063i	0.200993	+	0.276644i
$876$	548.498	−	178.218i	0.626140	−	0.203445i
$877$	877.427	+	285.093i	1.00049	+	0.325078i	0.763060	−	0.646328i	$-0.223696\pi$
$877$	877.427	+	285.093i	1.00049	+	0.325078i	0.237427	+	0.971405i	$0.423696\pi$
$878$	−218.212	−	158.540i	−0.248533	−	0.180570i
$879$			1289.90i			1.46746i
$880$		0			0
$881$	−1102.13			−1.25100			−0.625500	−	0.780224i	$-0.715105\pi$
$881$	−1102.13			−1.25100			−0.625500	+	0.780224i	$0.715105\pi$
$882$	−460.371	+	633.646i	−0.521962	+	0.718419i
$883$	394.286	−	1213.49i	0.446530	−	1.37428i	−0.434267	−	0.900784i	$-0.642993\pi$
$883$	394.286	−	1213.49i	0.446530	−	1.37428i	0.880797	−	0.473494i	$-0.157007\pi$
$884$	122.160	+	375.970i	0.138190	+	0.425305i
$885$	193.728	−	140.752i	0.218902	−	0.159042i
$886$	420.846	+	579.245i	0.474995	+	0.653775i
$887$	1313.62	−	426.821i	1.48097	−	0.481196i	0.546566	−	0.837416i	$-0.315935\pi$
$887$	1313.62	−	426.821i	1.48097	−	0.481196i	0.934402	+	0.356220i	$0.115935\pi$
$888$	−169.018	−	54.9174i	−0.190336	−	0.0618440i
$889$	−112.649	−	81.8439i	−0.126714	−	0.0920629i
$890$		−	799.299i		−	0.898088i
$891$		0			0
$892$	0.534243			0.000598927
$893$	−159.670	+	219.767i	−0.178802	+	0.246100i
$894$	27.0436	−	83.2315i	0.0302501	−	0.0931001i
$895$	50.4061	+	155.134i	0.0563197	+	0.173334i
$896$	28.6894	−	20.8440i	0.0320194	−	0.0232634i
$897$	−2.84012	−	3.90909i	−0.00316624	−	0.00435796i
$898$	−310.200	+	100.790i	−0.345435	+	0.112239i
$899$	−730.146	−	237.239i	−0.812176	−	0.263892i
$900$	125.994	+	91.5397i	0.139993	+	0.101711i
$901$		−	648.688i		−	0.719965i
$902$		0			0
$903$	749.802			0.830346
$904$	−599.627	+	825.315i	−0.663304	+	0.912960i
$905$	227.176	−	699.177i	0.251023	−	0.772571i
$906$	−146.714	−	451.539i	−0.161936	−	0.498387i
$907$	−768.005	+	557.989i	−0.846753	+	0.615202i	−0.924249	−	0.381790i	$-0.875308\pi$
$907$	−768.005	+	557.989i	−0.846753	+	0.615202i	0.0774956	+	0.996993i	$0.475308\pi$
$908$	−327.021	−	450.106i	−0.360155	−	0.495711i
$909$	−1174.22	+	381.527i	−1.29177	+	0.419721i
$910$	280.809	+	91.2405i	0.308582	+	0.100264i
$911$	−446.583	−	324.462i	−0.490212	−	0.356160i	0.315054	−	0.949074i	$-0.397977\pi$
$911$	−446.583	−	324.462i	−0.490212	−	0.356160i	−0.805266	+	0.592914i	$0.797977\pi$
$912$		−	98.9636i		−	0.108513i
$913$		0			0
$914$	507.660			0.555427
$915$	568.165	−	782.012i	0.620945	−	0.854658i
$916$	123.071	−	378.775i	0.134357	−	0.413510i
$917$	−145.974	−	449.262i	−0.159187	−	0.489926i
$918$	167.100	−	121.405i	0.182026	−	0.132250i
$919$	1028.85	+	1416.09i	1.11953	+	1.54090i	0.806572	+	0.591136i	$0.201320\pi$
$919$	1028.85	+	1416.09i	1.11953	+	1.54090i	0.312960	+	0.949766i	$0.398680\pi$
$920$	−1.69656	+	0.551245i	−0.00184408	+	0.000599180i
$921$	−417.518	−	135.660i	−0.453331	−	0.147296i
$922$	4.39698	+	3.19460i	0.00476896	+	0.00346485i
$923$		−	492.495i		−	0.533581i
$924$		0			0
$925$	−32.1243			−0.0347290
$926$	−324.522	+	446.667i	−0.350456	+	0.482362i
$927$	−202.158	+	622.179i	−0.218078	+	0.671175i
$928$	249.568	+	768.092i	0.268931	+	0.827685i
$929$	574.527	−	417.418i	0.618435	−	0.449320i	−0.233939	−	0.972251i	$-0.575162\pi$
$929$	574.527	−	417.418i	0.618435	−	0.449320i	0.852375	+	0.522932i	$0.175162\pi$
$930$	421.999	+	580.832i	0.453762	+	0.624550i
$931$	−167.628	+	54.4656i	−0.180052	+	0.0585023i
$932$	176.823	+	57.4532i	0.189724	+	0.0616451i
$933$	−528.726	−	384.142i	−0.566695	−	0.411728i
$934$			663.157i			0.710018i
$935$		0			0
$936$	2216.76			2.36833
$937$	−503.433	+	692.917i	−0.537282	+	0.739506i	−0.988218	−	0.153051i	$-0.951090\pi$
$937$	−503.433	+	692.917i	−0.537282	+	0.739506i	0.450936	+	0.892556i	$0.351090\pi$
$938$	−91.9586	+	283.019i	−0.0980369	+	0.301726i
$939$	618.061	+	1902.19i	0.658211	+	2.02577i
$940$	−423.628	+	307.784i	−0.450668	+	0.327430i
$941$	−430.320	−	592.284i	−0.457301	−	0.629420i	0.516646	−	0.856199i	$-0.327180\pi$
$941$	−430.320	−	592.284i	−0.457301	−	0.629420i	−0.973946	+	0.226779i	$0.927180\pi$
$942$	−212.598	+	69.0771i	−0.225687	+	0.0733303i
$943$	−1.47204	−	0.478296i	−0.00156102	−	0.000507206i
$944$	54.0382	+	39.2610i	0.0572438	+	0.0415901i
$945$			128.803i			0.136299i
$946$		0			0
$947$	1396.71			1.47488			0.737438	−	0.675415i	$-0.236036\pi$
$947$	1396.71			1.47488			0.737438	+	0.675415i	$0.236036\pi$
$948$	−174.225	+	239.800i	−0.183781	+	0.252953i
$949$	458.548	−	1411.27i	0.483191	−	1.48711i
$950$	−12.9711	−	39.9209i	−0.0136538	−	0.0420220i
$951$	1543.31	−	1121.28i	1.62283	−	1.17905i
$952$	−112.573	−	154.944i	−0.118249	−	0.162756i
$953$	−87.0293	+	28.2775i	−0.0913214	+	0.0296721i	−0.354321	−	0.935124i	$-0.615288\pi$
$953$	−87.0293	+	28.2775i	−0.0913214	+	0.0296721i	0.263000	+	0.964796i	$0.415288\pi$
$954$	−1081.87	−	351.520i	−1.13403	−	0.368470i
$955$	742.672	+	539.583i	0.777667	+	0.565008i
$956$		−	265.646i		−	0.277873i
$957$		0			0
$958$	517.900			0.540606
$959$	15.9257	−	21.9199i	0.0166066	−	0.0228570i
$960$	362.942	−	1117.02i	0.378065	−	1.16356i
$961$	−102.508	−	315.486i	−0.106668	−	0.328289i
$962$	−115.686	+	84.0507i	−0.120256	+	0.0873708i
$963$	646.183	+	889.395i	0.671010	+	0.923567i
$964$	133.188	−	43.2753i	0.138162	−	0.0448914i
$965$	34.7200	+	11.2812i	0.0359793	+	0.0116904i
$966$	0.592252	+	0.430296i	0.000613097	+	0.000445441i
$967$			780.874i			0.807522i	0.914864	+	0.403761i	$0.132297\pi$
$967$			780.874i			0.807522i	−0.914864	+	0.403761i	$0.867703\pi$
$968$		0			0
$969$	185.172			0.191096
$970$	318.562	−	438.463i	0.328415	−	0.452024i
$971$	4.65069	−	14.3134i	0.00478959	−	0.0147408i	−0.948633	−	0.316378i	$-0.897533\pi$
$971$	4.65069	−	14.3134i	0.00478959	−	0.0147408i	0.953423	+	0.301637i	$0.0975332\pi$
$972$	−185.393	−	570.580i	−0.190733	−	0.587016i
$973$	97.6002	−	70.9107i	0.100309	−	0.0728784i
$974$	439.977	+	605.576i	0.451722	+	0.621742i
$975$	666.527	−	216.568i	0.683617	−	0.222121i
$976$	256.430	+	83.3193i	0.262736	+	0.0853681i
$977$	−26.8968	−	19.5416i	−0.0275300	−	0.0200017i	0.573935	−	0.818901i	$-0.305416\pi$
$977$	−26.8968	−	19.5416i	−0.0275300	−	0.0200017i	−0.601465	+	0.798899i	$0.705416\pi$
$978$		−	551.852i		−	0.564266i
$979$		0			0
$980$	−339.752			−0.346686
$981$	−93.9289	+	129.282i	−0.0957481	+	0.131786i
$982$	383.705	−	1180.92i	0.390738	−	1.20257i
$983$	−488.147	−	1502.36i	−0.496589	−	1.52834i	−0.814466	−	0.580211i	$-0.802970\pi$
$983$	−488.147	−	1502.36i	−0.496589	−	1.52834i	0.317878	−	0.948132i	$-0.397030\pi$
$984$	1004.75	−	729.994i	1.02109	−	0.741864i
$985$	963.287	+	1325.85i	0.977956	+	1.34604i
$986$	434.776	−	141.267i	0.440949	−	0.143273i
$987$	653.520	+	212.342i	0.662128	+	0.215138i
$988$	126.208	+	91.6957i	0.127741	+	0.0928094i
$989$			3.64501i			0.00368555i
$990$		0			0
$991$	33.3255			0.0336282			0.0168141	−	0.999859i	$-0.494648\pi$
$991$	33.3255			0.0336282			0.0168141	+	0.999859i	$0.494648\pi$
$992$	389.104	−	535.555i	0.392241	−	0.539874i
$993$	−663.518	+	2042.10i	−0.668195	+	2.05649i
$994$	23.0577	+	70.9642i	0.0231968	+	0.0713925i
$995$	733.133	−	532.652i	0.736817	−	0.535329i
$996$	639.264	+	879.871i	0.641831	+	0.883404i
$997$	1448.24	−	470.561i	1.45259	−	0.471976i	0.526795	−	0.849992i	$-0.323394\pi$
$997$	1448.24	−	470.561i	1.45259	−	0.471976i	0.925799	+	0.378016i	$0.123394\pi$
$998$	332.787	+	108.129i	0.333454	+	0.108346i
$999$	−50.4662	−	36.6658i	−0.0505167	−	0.0367025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.3.d.f.40.4		32
11.2	odd	10	inner	121.3.d.f.94.4		32
11.3	even	5	inner	121.3.d.f.118.5		32
11.4	even	5	inner	121.3.d.f.112.4		32
11.5	even	5		121.3.b.c.120.4	✓	8
11.6	odd	10		121.3.b.c.120.5	yes	8
11.7	odd	10	inner	121.3.d.f.112.5		32
11.8	odd	10	inner	121.3.d.f.118.4		32
11.9	even	5	inner	121.3.d.f.94.5		32
11.10	odd	2	inner	121.3.d.f.40.5		32
33.5	odd	10		1089.3.c.k.604.5		8
33.17	even	10		1089.3.c.k.604.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.3.b.c.120.4	✓	8	11.5	even	5
121.3.b.c.120.5	yes	8	11.6	odd	10
121.3.d.f.40.4		32	1.1	even	1	trivial
121.3.d.f.40.5		32	11.10	odd	2	inner
121.3.d.f.94.4		32	11.2	odd	10	inner
121.3.d.f.94.5		32	11.9	even	5	inner
121.3.d.f.112.4		32	11.4	even	5	inner
121.3.d.f.112.5		32	11.7	odd	10	inner
121.3.d.f.118.4		32	11.8	odd	10	inner
121.3.d.f.118.5		32	11.3	even	5	inner
1089.3.c.k.604.4		8	33.17	even	10
1089.3.c.k.604.5		8	33.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	121.d (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.867839 + 1.19448i) q^{2} +(1.41664 - 4.35997i) q^{3} +(0.562434 + 1.73099i) q^{4} +(3.42082 - 2.48537i) q^{5} +(3.97848 + 5.47590i) q^{6} +(2.09516 - 0.680759i) q^{7} +(-8.17251 - 2.65541i) q^{8} +(-9.72133 - 7.06296i) q^{9} +O(q^{10})\)	\(q+(-0.867839 + 1.19448i) q^{2} +(1.41664 - 4.35997i) q^{3} +(0.562434 + 1.73099i) q^{4} +(3.42082 - 2.48537i) q^{5} +(3.97848 + 5.47590i) q^{6} +(2.09516 - 0.680759i) q^{7} +(-8.17251 - 2.65541i) q^{8} +(-9.72133 - 7.06296i) q^{9} +6.24301i q^{10} +8.34386 q^{12} +(12.6188 - 17.3683i) q^{13} +(-1.00511 + 3.09341i) q^{14} +(-5.99008 - 18.4356i) q^{15} +(4.37437 - 3.17817i) q^{16} +(5.94669 + 8.18492i) q^{17} +(16.8731 - 5.48241i) q^{18} +(3.79705 + 1.23374i) q^{19} +(6.22616 + 4.52357i) q^{20} -10.0992i q^{21} +0.0490953 q^{23} +(-23.1550 + 31.8702i) q^{24} +(-2.20047 + 6.77235i) q^{25} +(9.79498 + 30.1459i) q^{26} +(-11.1866 + 8.12756i) q^{27} +(2.35678 + 3.24383i) q^{28} +(-29.1064 + 9.45723i) q^{29} +(27.2193 + 8.84410i) q^{30} +(20.2945 + 14.7448i) q^{31} -26.3891i q^{32} -14.9375 q^{34} +(5.47523 - 7.53601i) q^{35} +(6.75834 - 20.8000i) q^{36} +(1.39407 + 4.29050i) q^{37} +(-4.76890 + 3.46481i) q^{38} +(-57.8491 - 79.6225i) q^{39} +(-34.5564 + 11.2281i) q^{40} +(-29.9834 - 9.74219i) q^{41} +(12.0633 + 8.76451i) q^{42} +74.2435i q^{43} -50.8091 q^{45} +(-0.0426068 + 0.0586433i) q^{46} +(-21.0255 + 64.7099i) q^{47} +(-7.65981 - 23.5745i) q^{48} +(-35.7156 + 25.9489i) q^{49} +(-6.17977 - 8.50573i) q^{50} +(44.1103 - 14.3323i) q^{51} +(37.1618 + 12.0746i) q^{52} +(-51.8725 - 37.6875i) q^{53} -20.4156i q^{54} -18.9304 q^{56} +(10.7581 - 14.8073i) q^{57} +(13.9632 - 42.9743i) q^{58} +(3.81740 + 11.7487i) q^{59} +(28.5429 - 20.7376i) q^{60} +(29.3105 + 40.3425i) q^{61} +(-35.2248 + 11.4452i) q^{62} +(-25.1759 - 8.18015i) q^{63} +(49.0187 + 35.6142i) q^{64} -90.7766i q^{65} +91.4910 q^{67} +(-10.8234 + 14.8972i) q^{68} +(0.0695504 - 0.214054i) q^{69} +(4.24998 + 13.0801i) q^{70} +(18.5592 - 13.4840i) q^{71} +(60.6927 + 83.5363i) q^{72} +(65.7368 - 21.3592i) q^{73} +(-6.33473 - 2.05828i) q^{74} +(26.4100 + 19.1880i) q^{75} +7.26657i q^{76} +145.311 q^{78} +(-20.8806 + 28.7397i) q^{79} +(7.06502 - 21.7439i) q^{80} +(-13.8305 - 42.5658i) q^{81} +(37.6576 - 27.3598i) q^{82} +(76.6149 + 105.451i) q^{83} +(17.4817 - 5.68015i) q^{84} +(40.6852 + 13.2194i) q^{85} +(-88.6823 - 64.4314i) q^{86} +140.300i q^{87} -128.031 q^{89} +(44.0941 - 60.6904i) q^{90} +(14.6148 - 44.9798i) q^{91} +(0.0276129 + 0.0849837i) q^{92} +(93.0372 - 67.5955i) q^{93} +(-59.0478 - 81.2724i) q^{94} +(16.0553 - 5.21670i) q^{95} +(-115.056 - 37.3839i) q^{96} +(-70.2327 - 51.0270i) q^{97} -65.1809i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 24 q^{4} + 4 q^{5} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 + 24 * q^4 + 4 * q^5 - 16 * q^9	\( 32 q + 4 q^{3} + 24 q^{4} + 4 q^{5} - 16 q^{9} + 208 q^{12} + 4 q^{14} + 68 q^{15} + 24 q^{16} - 52 q^{20} - 48 q^{23} + 16 q^{25} - 168 q^{26} - 104 q^{27} + 116 q^{31} - 720 q^{34} - 152 q^{36} + 4 q^{37} + 132 q^{38} + 176 q^{42} - 304 q^{45} + 244 q^{47} - 172 q^{48} - 88 q^{49} - 268 q^{53} - 48 q^{56} - 88 q^{58} + 56 q^{59} + 100 q^{60} + 40 q^{64} + 1136 q^{67} - 264 q^{69} + 188 q^{70} - 272 q^{71} + 96 q^{75} + 720 q^{78} + 356 q^{80} + 272 q^{81} + 180 q^{82} - 336 q^{86} - 96 q^{89} - 140 q^{91} + 156 q^{92} + 256 q^{93} - 152 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 24 * q^4 + 4 * q^5 - 16 * q^9 + 208 * q^12 + 4 * q^14 + 68 * q^15 + 24 * q^16 - 52 * q^20 - 48 * q^23 + 16 * q^25 - 168 * q^26 - 104 * q^27 + 116 * q^31 - 720 * q^34 - 152 * q^36 + 4 * q^37 + 132 * q^38 + 176 * q^42 - 304 * q^45 + 244 * q^47 - 172 * q^48 - 88 * q^49 - 268 * q^53 - 48 * q^56 - 88 * q^58 + 56 * q^59 + 100 * q^60 + 40 * q^64 + 1136 * q^67 - 264 * q^69 + 188 * q^70 - 272 * q^71 + 96 * q^75 + 720 * q^78 + 356 * q^80 + 272 * q^81 + 180 * q^82 - 336 * q^86 - 96 * q^89 - 140 * q^91 + 156 * q^92 + 256 * q^93 - 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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