LMFDB - Embedded newform 441.3.l.b.391.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(97,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("441.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$441 = 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	441.l (of order $6$ , degree $2$ , 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			391.6
Character	$\chi$	$=$	441.391
Dual form			441.3.l.b.97.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.227576 - 0.394173i) q^{2} +(-0.216177 - 2.99220i) q^{3} +(1.89642 - 3.28469i) q^{4} +(3.78523 + 2.18540i) q^{5} +(-1.13025 + 0.766164i) q^{6} -3.54692 q^{8} +(-8.90653 + 1.29369i) q^{9} -1.98938i q^{10} +(0.0697009 + 0.120725i) q^{11} +(-10.2384 - 4.96439i) q^{12} +(1.71085 + 0.987760i) q^{13} +(5.72089 - 11.7986i) q^{15} +(-6.77848 - 11.7407i) q^{16} -30.9273i q^{17} +(2.53685 + 3.21630i) q^{18} -29.1245i q^{19} +(14.3568 - 8.28888i) q^{20} +(0.0317245 - 0.0549484i) q^{22} +(-14.8892 + 25.7888i) q^{23} +(0.766764 + 10.6131i) q^{24} +(-2.94801 - 5.10610i) q^{25} -0.899161i q^{26} +(5.79637 + 26.3705i) q^{27} +(7.28707 + 12.6216i) q^{29} +(-5.95263 + 0.430059i) q^{30} +(-6.82604 - 3.94101i) q^{31} +(-10.1791 + 17.6307i) q^{32} +(0.346167 - 0.234657i) q^{33} +(-12.1907 + 7.03829i) q^{34} +(-12.6411 + 31.7086i) q^{36} +15.4652 q^{37} +(-11.4801 + 6.62804i) q^{38} +(2.58573 - 5.33274i) q^{39} +(-13.4259 - 7.75146i) q^{40} +(-0.747251 - 0.431426i) q^{41} +(-15.6629 - 27.1289i) q^{43} +0.528728 q^{44} +(-36.5405 - 14.5675i) q^{45} +13.5537 q^{46} +(58.0205 - 33.4982i) q^{47} +(-33.6651 + 22.8206i) q^{48} +(-1.34179 + 2.32405i) q^{50} +(-92.5406 + 6.68577i) q^{51} +(6.48898 - 3.74641i) q^{52} -33.8570 q^{53} +(9.07541 - 8.28605i) q^{54} +0.609299i q^{55} +(-87.1465 + 6.29606i) q^{57} +(3.31672 - 5.74473i) q^{58} +(57.4894 + 33.1915i) q^{59} +(-27.9056 - 41.1665i) q^{60} +(-35.9279 + 20.7430i) q^{61} +3.58752i q^{62} -44.9618 q^{64} +(4.31731 + 7.47781i) q^{65} +(-0.171275 - 0.0830474i) q^{66} +(-51.7774 + 89.6812i) q^{67} +(-101.587 - 58.6510i) q^{68} +(80.3841 + 38.9765i) q^{69} +86.4656 q^{71} +(31.5908 - 4.58862i) q^{72} -33.0384i q^{73} +(-3.51950 - 6.09595i) q^{74} +(-14.6412 + 9.92486i) q^{75} +(-95.6652 - 55.2323i) q^{76} +(-2.69047 + 0.194378i) q^{78} +(-24.3232 - 42.1291i) q^{79} -59.2549i q^{80} +(77.6527 - 23.0446i) q^{81} +0.392728i q^{82} +(102.894 - 59.4058i) q^{83} +(67.5886 - 117.067i) q^{85} +(-7.12897 + 12.3477i) q^{86} +(36.1910 - 24.5329i) q^{87} +(-0.247224 - 0.428204i) q^{88} +38.2703i q^{89} +(2.57364 + 17.7185i) q^{90} +(56.4723 + 97.8128i) q^{92} +(-10.3167 + 21.2768i) q^{93} +(-26.4081 - 15.2467i) q^{94} +(63.6489 - 110.243i) q^{95} +(54.9550 + 26.6465i) q^{96} +(-70.3678 + 40.6269i) q^{97} +(-0.776975 - 0.985074i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27}+ \cdots - 162 q^{99}+O(q^{100})$ 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$ .

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.227576	−	0.394173i	−0.113788	−	0.197086i	0.803507	−	0.595296i	$-0.202965\pi$
$2$	−0.227576	−	0.394173i	−0.113788	−	0.197086i	−0.917295	+	0.398209i	$0.869632\pi$
$3$	−0.216177	−	2.99220i	−0.0720591	−	0.997400i
$3$	−0.216177	−	2.99220i	−0.0720591	−	0.997400i
$4$	1.89642	−	3.28469i	0.474105	−	0.821173i
$5$	3.78523	+	2.18540i	0.757046	+	0.437081i	0.828234	−	0.560382i	$-0.189346\pi$
$5$	3.78523	+	2.18540i	0.757046	+	0.437081i	−0.0711878	+	0.997463i	$0.522679\pi$
$6$	−1.13025	+	0.766164i	−0.188375	+	0.127694i
$7$		0			0
$7$		0			0
$8$	−3.54692			−0.443365
$9$	−8.90653	+	1.29369i	−0.989615	+	0.143743i
$10$		−	1.98938i		−	0.198938i
$11$	0.0697009	+	0.120725i	0.00633644	+	0.0109750i	0.869176	−	0.494502i	$-0.164650\pi$
$11$	0.0697009	+	0.120725i	0.00633644	+	0.0109750i	−0.862840	+	0.505477i	$0.831316\pi$
$12$	−10.2384	−	4.96439i	−0.853202	−	0.413699i
$13$	1.71085	+	0.987760i	0.131604	+	0.0759816i	0.564357	−	0.825531i	$-0.309124\pi$
$13$	1.71085	+	0.987760i	0.131604	+	0.0759816i	−0.432753	+	0.901513i	$0.642458\pi$
$14$		0			0
$15$	5.72089	−	11.7986i	0.381393	−	0.786574i
$16$	−6.77848	−	11.7407i	−0.423655	−	0.733792i
$17$		−	30.9273i		−	1.81925i	−0.415430	−	0.909625i	$-0.636369\pi$
$17$		−	30.9273i		−	1.81925i	0.415430	−	0.909625i	$-0.363631\pi$
$18$	2.53685	+	3.21630i	0.140936	+	0.178683i
$19$		−	29.1245i		−	1.53287i	−0.642321	−	0.766435i	$-0.722029\pi$
$19$		−	29.1245i		−	1.53287i	0.642321	−	0.766435i	$-0.277971\pi$
$20$	14.3568	−	8.28888i	0.717838	−	0.414444i
$21$		0			0
$22$	0.0317245	−	0.0549484i	0.00144202	−	0.00249765i
$23$	−14.8892	+	25.7888i	−0.647356	+	1.12125i	0.336396	+	0.941721i	$0.390792\pi$
$23$	−14.8892	+	25.7888i	−0.647356	+	1.12125i	−0.983752	+	0.179533i	$0.942541\pi$
$24$	0.766764	+	10.6131i	0.0319485	+	0.442213i
$25$	−2.94801	−	5.10610i	−0.117920	−	0.204244i
$26$		−	0.899161i		−	0.0345831i
$27$	5.79637	+	26.3705i	0.214681	+	0.976684i
$28$		0			0
$29$	7.28707	+	12.6216i	0.251278	+	0.435227i	0.963878	−	0.266344i	$-0.0858157\pi$
$29$	7.28707	+	12.6216i	0.251278	+	0.435227i	−0.712600	+	0.701571i	$0.752482\pi$
$30$	−5.95263	+	0.430059i	−0.198421	+	0.0143353i
$31$	−6.82604	−	3.94101i	−0.220195	−	0.127129i	0.385846	−	0.922563i	$-0.373910\pi$
$31$	−6.82604	−	3.94101i	−0.220195	−	0.127129i	−0.606040	+	0.795434i	$0.707243\pi$
$32$	−10.1791	+	17.6307i	−0.318096	+	0.550959i
$33$	0.346167	−	0.234657i	0.0104899	−	0.00711082i
$34$	−12.1907	+	7.03829i	−0.358549	+	0.207009i
$35$		0			0
$36$	−12.6411	+	31.7086i	−0.351143	+	0.880795i
$37$	15.4652			0.417978			0.208989	−	0.977918i	$-0.432983\pi$
$37$	15.4652			0.417978			0.208989	+	0.977918i	$0.432983\pi$
$38$	−11.4801	+	6.62804i	−0.302108	+	0.174422i
$39$	2.58573	−	5.33274i	0.0663008	−	0.136737i
$40$	−13.4259	−	7.75146i	−0.335648	−	0.193787i
$41$	−0.747251	−	0.431426i	−0.0182256	−	0.0105226i	0.490859	−	0.871239i	$-0.336683\pi$
$41$	−0.747251	−	0.431426i	−0.0182256	−	0.0105226i	−0.509085	+	0.860716i	$0.670016\pi$
$42$		0			0
$43$	−15.6629	−	27.1289i	−0.364252	−	0.630904i	0.624403	−	0.781102i	$-0.285342\pi$
$43$	−15.6629	−	27.1289i	−0.364252	−	0.630904i	−0.988656	+	0.150198i	$0.952009\pi$
$44$	0.528728			0.0120165
$45$	−36.5405	−	14.5675i	−0.812012	−	0.323721i
$46$	13.5537			0.294645
$47$	58.0205	−	33.4982i	1.23448	−	0.712727i	0.266519	−	0.963830i	$-0.414127\pi$
$47$	58.0205	−	33.4982i	1.23448	−	0.712727i	0.967960	+	0.251103i	$0.0807932\pi$
$48$	−33.6651	+	22.8206i	−0.701356	+	0.475430i
$49$		0			0
$50$	−1.34179	+	2.32405i	−0.0268358	+	0.0464810i
$51$	−92.5406	+	6.68577i	−1.81452	+	0.131093i
$52$	6.48898	−	3.74641i	0.124788	−	0.0720464i
$53$	−33.8570			−0.638812			−0.319406	−	0.947618i	$-0.603483\pi$
$53$	−33.8570			−0.638812			−0.319406	+	0.947618i	$0.603483\pi$
$54$	9.07541	−	8.28605i	0.168063	−	0.153445i
$55$			0.609299i			0.0110782i
$56$		0			0
$57$	−87.1465	+	6.29606i	−1.52889	+	0.110457i
$58$	3.31672	−	5.74473i	0.0571849	−	0.0990471i
$59$	57.4894	+	33.1915i	0.974396	+	0.562568i	0.900574	−	0.434704i	$-0.143147\pi$
$59$	57.4894	+	33.1915i	0.974396	+	0.562568i	0.0738224	+	0.997271i	$0.476480\pi$
$60$	−27.9056	−	41.1665i	−0.465094	−	0.686108i
$61$	−35.9279	+	20.7430i	−0.588982	+	0.340049i	−0.764695	−	0.644393i	$-0.777110\pi$
$61$	−35.9279	+	20.7430i	−0.588982	+	0.340049i	0.175713	+	0.984441i	$0.443777\pi$
$62$			3.58752i			0.0578632i
$63$		0			0
$64$	−44.9618			−0.702528
$65$	4.31731	+	7.47781i	0.0664202	+	0.115043i
$66$	−0.171275	−	0.0830474i	−0.00259507	−	0.00125829i
$67$	−51.7774	+	89.6812i	−0.772798	+	1.33852i	0.163226	+	0.986589i	$0.447810\pi$
$67$	−51.7774	+	89.6812i	−0.772798	+	1.33852i	−0.936024	+	0.351936i	$0.885523\pi$
$68$	−101.587	−	58.6510i	−1.49392	−	0.862515i
$69$	80.3841	+	38.9765i	1.16499	+	0.564877i
$70$		0			0
$71$	86.4656			1.21783			0.608913	−	0.793237i	$-0.291606\pi$
$71$	86.4656			1.21783			0.608913	+	0.793237i	$0.291606\pi$
$72$	31.5908	−	4.58862i	0.438761	−	0.0637309i
$73$		−	33.0384i		−	0.452580i	−0.974060	−	0.226290i	$-0.927340\pi$
$73$		−	33.0384i		−	0.452580i	0.974060	−	0.226290i	$-0.0726598\pi$
$74$	−3.51950	−	6.09595i	−0.0475608	−	0.0823777i
$75$	−14.6412	+	9.92486i	−0.195216	+	0.132332i
$76$	−95.6652	−	55.2323i	−1.25875	−	0.726741i
$77$		0			0
$78$	−2.69047	+	0.194378i	−0.0344932	+	0.00249203i
$79$	−24.3232	−	42.1291i	−0.307889	−	0.533279i	0.670011	−	0.742351i	$-0.266289\pi$
$79$	−24.3232	−	42.1291i	−0.307889	−	0.533279i	−0.977900	+	0.209071i	$0.932956\pi$
$80$		−	59.2549i		−	0.740686i
$81$	77.6527	−	23.0446i	0.958676	−	0.284501i
$82$			0.392728i			0.00478937i
$83$	102.894	−	59.4058i	1.23968	−	0.715732i	0.270655	−	0.962676i	$-0.412760\pi$
$83$	102.894	−	59.4058i	1.23968	−	0.715732i	0.969030	+	0.246944i	$0.0794264\pi$
$84$		0			0
$85$	67.5886	−	117.067i	0.795160	−	1.37726i
$86$	−7.12897	+	12.3477i	−0.0828950	+	0.143578i
$87$	36.1910	−	24.5329i	0.415989	−	0.281987i
$88$	−0.247224	−	0.428204i	−0.00280936	−	0.00486595i
$89$			38.2703i			0.430004i	0.976614	+	0.215002i	$0.0689758\pi$
$89$			38.2703i			0.430004i	−0.976614	+	0.215002i	$0.931024\pi$
$90$	2.57364	+	17.7185i	0.0285961	+	0.196872i
$91$		0			0
$92$	56.4723	+	97.8128i	0.613829	+	1.06318i
$93$	−10.3167	+	21.2768i	−0.110932	+	0.228783i
$94$	−26.4081	−	15.2467i	−0.280938	−	0.162199i
$95$	63.6489	−	110.243i	0.669989	−	1.16045i
$96$	54.9550	+	26.6465i	0.572448	+	0.277568i
$97$	−70.3678	+	40.6269i	−0.725441	+	0.418834i	−0.816752	−	0.576989i	$-0.804228\pi$
$97$	−70.3678	+	40.6269i	−0.725441	+	0.418834i	0.0913110	+	0.995822i	$0.470894\pi$
$98$		0			0
$99$	−0.776975	−	0.985074i	−0.00784823	−	0.00995024i
$100$	−22.3626			−0.223626
$101$	−22.0036	+	12.7038i	−0.217858	+	0.125780i	−0.604958	−	0.796257i	$-0.706810\pi$
$101$	−22.0036	+	12.7038i	−0.217858	+	0.125780i	0.387100	+	0.922038i	$0.373477\pi$
$102$	23.6953	+	34.9555i	0.232307	+	0.342701i
$103$	95.4563	+	55.1117i	0.926760	+	0.535065i	0.885786	−	0.464095i	$-0.153620\pi$
$103$	95.4563	+	55.1117i	0.926760	+	0.535065i	0.0409749	+	0.999160i	$0.486954\pi$
$104$	−6.06826	−	3.50351i	−0.0583486	−	0.0336876i
$105$		0			0
$106$	7.70504	+	13.3455i	0.0726891	+	0.125901i
$107$	156.837			1.46577			0.732885	−	0.680353i	$-0.238174\pi$
$107$	156.837			1.46577			0.732885	+	0.680353i	$0.238174\pi$
$108$	97.6113	+	30.9702i	0.903808	+	0.286761i
$109$	−24.9677			−0.229062			−0.114531	−	0.993420i	$-0.536536\pi$
$109$	−24.9677			−0.229062			−0.114531	+	0.993420i	$0.536536\pi$
$110$	0.240169	−	0.138662i	0.00218335	−	0.00126056i
$111$	−3.34322	−	46.2749i	−0.0301191	−	0.416891i
$112$		0			0
$113$	−50.2599	+	87.0526i	−0.444777	+	0.770377i	−0.998037	−	0.0626320i	$-0.980051\pi$
$113$	−50.2599	+	87.0526i	−0.444777	+	0.770377i	0.553259	+	0.833009i	$0.313384\pi$
$114$	22.3142	+	32.9179i	0.195738	+	0.288754i
$115$	−112.718	+	65.0778i	−0.980157	+	0.565894i
$116$	55.2774			0.476529
$117$	−16.5156	−	6.58421i	−0.141159	−	0.0562753i
$118$		−	30.2143i		−	0.256054i
$119$		0			0
$120$	−20.2916	+	41.8488i	−0.169096	+	0.348740i
$121$	60.4903	−	104.772i	0.499920	−	0.865886i
$122$	16.3526	+	9.44120i	0.134038	+	0.0773869i
$123$	−1.12937	+	2.32919i	−0.00918190	+	0.0189365i
$124$	−25.8900	+	14.9476i	−0.208791	+	0.120545i
$125$		−	135.041i		−	1.08033i
$126$		0			0
$127$	151.949			1.19645			0.598226	−	0.801327i	$-0.295872\pi$
$127$	151.949			1.19645			0.598226	+	0.801327i	$0.295872\pi$
$128$	50.9485	+	88.2455i	0.398035	+	0.689418i
$129$	−77.7891	+	52.7311i	−0.603016	+	0.408768i
$130$	1.96503	−	3.40353i	0.0151156	−	0.0261810i
$131$	110.832	+	63.9890i	0.846047	+	0.488466i	0.859315	−	0.511446i	$-0.170890\pi$
$131$	110.832	+	63.9890i	0.846047	+	0.488466i	−0.0132678	+	0.999912i	$0.504223\pi$
$132$	−0.114299	−	1.58206i	−0.000865901	−	0.0119853i
$133$		0			0
$134$	47.1332			0.351740
$135$	−35.6895	+	112.486i	−0.264367	+	0.833228i
$136$			109.697i			0.806592i
$137$	−9.92897	−	17.1975i	−0.0724743	−	0.125529i	0.827511	−	0.561450i	$-0.189756\pi$
$137$	−9.92897	−	17.1975i	−0.0724743	−	0.125529i	−0.899985	+	0.435921i	$0.856423\pi$
$138$	−2.92999	−	40.5553i	−0.0212318	−	0.293879i
$139$	−37.7617	−	21.8017i	−0.271667	−	0.156847i	0.357978	−	0.933730i	$-0.383466\pi$
$139$	−37.7617	−	21.8017i	−0.271667	−	0.156847i	−0.629645	+	0.776883i	$0.716800\pi$
$140$		0			0
$141$	−112.776	−	166.368i	−0.799830	−	1.17991i
$142$	−19.6775	−	34.0824i	−0.138574	−	0.240017i
$143$			0.275391i			0.00192581i
$144$	75.5616	+	95.7995i	0.524733	+	0.665274i
$145$			63.7008i			0.439316i
$146$	−13.0228	+	7.51873i	−0.0891974	+	0.0514982i
$147$		0			0
$148$	29.3284	−	50.7984i	0.198165	−	0.343232i
$149$	100.910	−	174.781i	0.677248	−	1.17303i	−0.298559	−	0.954391i	$-0.596506\pi$
$149$	100.910	−	174.781i	0.677248	−	1.17303i	0.975806	−	0.218636i	$-0.0701609\pi$
$150$	7.24409	+	3.51250i	0.0482940	+	0.0234167i
$151$	53.7144	+	93.0361i	0.355725	+	0.616133i	0.987242	−	0.159229i	$-0.0509008\pi$
$151$	53.7144	+	93.0361i	0.355725	+	0.616133i	−0.631517	+	0.775362i	$0.717567\pi$
$152$			103.302i			0.679622i
$153$	40.0103	+	275.455i	0.261505	+	1.80036i
$154$		0			0
$155$	−17.2254	−	29.8353i	−0.111132	−	0.192486i
$156$	−12.6128	−	18.6064i	−0.0808512	−	0.119272i
$157$	86.5180	+	49.9512i	0.551070	+	0.318160i	0.749553	−	0.661944i	$-0.230268\pi$
$157$	86.5180	+	49.9512i	0.551070	+	0.318160i	−0.198483	+	0.980104i	$0.563602\pi$
$158$	−11.0708	+	19.1751i	−0.0700681	+	0.121361i
$159$	7.31912	+	101.307i	0.0460322	+	0.637151i
$160$	−77.0604	+	44.4908i	−0.481627	+	0.278068i
$161$		0			0
$162$	−26.7554	−	25.3642i	−0.165157	−	0.156569i
$163$	124.888			0.766184			0.383092	−	0.923710i	$-0.374859\pi$
$163$	124.888			0.766184			0.383092	+	0.923710i	$0.374859\pi$
$164$	−2.83420	+	1.63633i	−0.0172817	+	0.00997761i
$165$	1.82314	−	0.131716i	0.0110494	−	0.000798282i
$166$	−46.8323	−	27.0386i	−0.282122	−	0.162883i
$167$	113.210	+	65.3618i	0.677904	+	0.391388i	0.799065	−	0.601245i	$-0.205328\pi$
$167$	113.210	+	65.3618i	0.677904	+	0.391388i	−0.121161	+	0.992633i	$0.538662\pi$
$168$		0			0
$169$	−82.5487	−	142.978i	−0.488454	−	0.846026i
$170$	−61.5261			−0.361918
$171$	37.6782	+	259.399i	0.220340	+	1.51695i
$172$	−118.813			−0.690775
$173$	−72.7886	+	42.0245i	−0.420743	+	0.242916i	−0.695395	−	0.718628i	$-0.744771\pi$
$173$	−72.7886	+	42.0245i	−0.420743	+	0.242916i	0.274652	+	0.961544i	$0.411437\pi$
$174$	−17.9064	−	8.68242i	−0.102910	−	0.0498990i
$175$		0			0
$176$	0.944932	−	1.63667i	0.00536893	−	0.00929926i
$177$	86.8878	−	179.195i	0.490891	−	1.01240i
$178$	15.0851	−	8.70940i	0.0847479	−	0.0489292i
$179$	−350.425			−1.95768			−0.978840	−	0.204625i	$-0.934402\pi$
$179$	−350.425			−1.95768			−0.978840	+	0.204625i	$0.934402\pi$
$180$	−117.146	+	92.3985i	−0.650810	+	0.513325i
$181$		−	138.049i		−	0.762703i	−0.924430	−	0.381351i	$-0.875459\pi$
$181$		−	138.049i		−	0.762703i	0.924430	−	0.381351i	$-0.124541\pi$
$182$		0			0
$183$	69.8340	+	103.019i	0.381606	+	0.562947i
$184$	52.8108	−	91.4710i	0.287015	−	0.497125i
$185$	58.5393	+	33.7977i	0.316429	+	0.182690i
$186$	10.7346	−	0.775539i	0.0577128	−	0.00416957i
$187$	3.73371	−	2.15566i	0.0199663	−	0.0115276i
$188$		−	254.106i		−	1.35163i
$189$		0			0
$190$	−57.9398			−0.304946
$191$	145.062	+	251.255i	0.759488	+	1.31547i	0.943112	+	0.332476i	$0.107884\pi$
$191$	145.062	+	251.255i	0.759488	+	1.31547i	−0.183624	+	0.982997i	$0.558783\pi$
$192$	9.71971	+	134.535i	0.0506235	+	0.700702i
$193$	110.240	−	190.941i	0.571192	−	0.989333i	−0.425252	−	0.905075i	$-0.639815\pi$
$193$	110.240	−	190.941i	0.571192	−	0.989333i	0.996444	−	0.0842581i	$-0.0268520\pi$
$194$	32.0280	+	18.4914i	0.165093	+	0.0953164i
$195$	21.4418	−	14.5348i	0.109958	−	0.0745374i
$196$		0			0
$197$	118.429			0.601163			0.300581	−	0.953756i	$-0.402819\pi$
$197$	118.429			0.601163			0.300581	+	0.953756i	$0.402819\pi$
$198$	−0.211469	+	0.530441i	−0.00106802	+	0.00267900i
$199$		−	175.694i		−	0.882885i	−0.897289	−	0.441443i	$-0.854467\pi$
$199$		−	175.694i		−	0.882885i	0.897289	−	0.441443i	$-0.145533\pi$
$200$	10.4564	+	18.1110i	0.0522818	+	0.0905548i
$201$	279.537	+	135.542i	1.39073	+	0.674336i
$202$	10.0150	+	5.78215i	0.0495791	+	0.0286245i
$203$		0			0
$204$	−153.535	+	316.646i	−0.752622	+	1.55219i
$205$	−1.88568	−	3.26609i	−0.00919844	−	0.0159322i
$206$		−	50.1684i		−	0.243536i
$207$	99.2483	−	248.951i	0.479460	−	1.20266i
$208$		−	26.7821i		−	0.128760i
$209$	3.51607	−	2.03001i	0.0168233	−	0.00971295i
$210$		0			0
$211$	−9.18761	+	15.9134i	−0.0435432	+	0.0754190i	−0.886976	−	0.461816i	$-0.847198\pi$
$211$	−9.18761	+	15.9134i	−0.0435432	+	0.0754190i	0.843432	+	0.537235i	$0.180531\pi$
$212$	−64.2071	+	111.210i	−0.302864	+	0.524575i
$213$	−18.6919	−	258.722i	−0.0877554	−	1.21466i
$214$	−35.6924	−	61.8210i	−0.166787	−	0.288883i
$215$		−	136.919i		−	0.636831i
$216$	−20.5593	−	93.5340i	−0.0951819	−	0.433028i
$217$		0			0
$218$	5.68205	+	9.84159i	0.0260644	+	0.0451449i
$219$	−98.8574	+	7.14214i	−0.451404	+	0.0326125i
$220$	2.00136	+	1.15549i	0.00909709	+	0.00525221i
$221$	30.5487	−	52.9119i	0.138229	−	0.239420i
$222$	−17.4795	+	11.8489i	−0.0787364	+	0.0533732i
$223$	142.303	−	82.1586i	0.638129	−	0.368424i	−0.145764	−	0.989319i	$-0.546564\pi$
$223$	142.303	−	82.1586i	0.638129	−	0.368424i	0.783894	+	0.620895i	$0.213231\pi$
$224$		0			0
$225$	32.8623	+	41.6639i	0.146055	+	0.185173i
$226$	45.7517			0.202441
$227$	−98.6637	+	56.9635i	−0.434642	+	0.250941i	−0.701322	−	0.712844i	$-0.747407\pi$
$227$	−98.6637	+	56.9635i	−0.434642	+	0.250941i	0.266680	+	0.963785i	$0.414073\pi$
$228$	−144.586	+	298.189i	−0.634147	+	1.30785i
$229$	−158.172	−	91.3208i	−0.690708	−	0.398781i	0.113169	−	0.993576i	$-0.463900\pi$
$229$	−158.172	−	91.3208i	−0.690708	−	0.398781i	−0.803877	+	0.594795i	$0.797233\pi$
$230$	51.3038	+	29.6203i	0.223060	+	0.128784i
$231$		0			0
$232$	−25.8467	−	44.7678i	−0.111408	−	0.192964i
$233$	−253.750			−1.08905			−0.544527	−	0.838743i	$-0.683291\pi$
$233$	−253.750			−1.08905			−0.544527	+	0.838743i	$0.683291\pi$
$234$	1.16324	+	8.00841i	0.00497110	+	0.0342240i
$235$	292.828			1.24608
$236$	218.048	−	125.890i	0.923931	−	0.533432i
$237$	−120.801	+	81.8874i	−0.509707	+	0.345516i
$238$		0			0
$239$	65.6961	−	113.789i	0.274879	−	0.476104i	−0.695226	−	0.718792i	$-0.744696\pi$
$239$	65.6961	−	113.789i	0.274879	−	0.476104i	0.970105	+	0.242687i	$0.0780289\pi$
$240$	−177.303	+	12.8096i	−0.738761	+	0.0533732i
$241$	225.576	−	130.236i	0.935999	−	0.540399i	0.0472950	−	0.998881i	$-0.484940\pi$
$241$	225.576	−	130.236i	0.935999	−	0.540399i	0.888704	+	0.458482i	$0.151607\pi$
$242$	−55.0645			−0.227539
$243$	−85.7409	−	227.371i	−0.352843	−	0.935683i
$244$			157.349i			0.644875i
$245$		0			0
$246$	1.17512	−	0.0848989i	0.00477692	−	0.000345117i
$247$	28.7681	−	49.8278i	0.116470	−	0.201732i
$248$	24.2114	+	13.9785i	0.0976267	+	0.0563648i
$249$	−199.997	−	295.037i	−0.803202	−	1.18489i
$250$	−53.2293	+	30.7320i	−0.212917	+	0.122928i
$251$			63.0463i			0.251181i	0.992082	+	0.125590i	$0.0400825\pi$
$251$			63.0463i			0.251181i	−0.992082	+	0.125590i	$0.959918\pi$
$252$		0			0
$253$	−4.15116			−0.0164077
$254$	−34.5800	−	59.8944i	−0.136142	−	0.235805i
$255$	−364.899	−	176.931i	−1.43098	−	0.693849i
$256$	−66.7343	+	115.587i	−0.260681	+	0.451512i
$257$	−106.641	−	61.5694i	−0.414947	−	0.239570i	0.277966	−	0.960591i	$-0.410340\pi$
$257$	−106.641	−	61.5694i	−0.414947	−	0.239570i	−0.692913	+	0.721021i	$0.743673\pi$
$258$	38.4881	+	18.6620i	0.149179	+	0.0723334i
$259$		0			0
$260$	32.7497			0.125960
$261$	−81.2310	−	102.987i	−0.311230	−	0.394587i
$262$		−	58.2494i		−	0.222326i
$263$	252.795	+	437.854i	0.961198	+	1.66484i	0.719499	+	0.694493i	$0.244371\pi$
$263$	252.795	+	437.854i	0.961198	+	1.66484i	0.241699	+	0.970351i	$0.422295\pi$
$264$	−1.22783	+	0.832311i	−0.00465086	+	0.00315269i
$265$	−128.157	−	73.9913i	−0.483610	−	0.279213i
$266$		0			0
$267$	114.513	−	8.27317i	0.428886	−	0.0309857i
$268$	196.383	+	340.146i	0.732774	+	1.26920i
$269$			8.87334i			0.0329864i	0.999864	+	0.0164932i	$0.00525018\pi$
$269$			8.87334i			0.0329864i	−0.999864	+	0.0164932i	$0.994750\pi$
$270$	52.4609	−	11.5312i	0.194300	−	0.0427081i
$271$		−	135.761i		−	0.500964i	−0.968121	−	0.250482i	$-0.919411\pi$
$271$		−	135.761i		−	0.500964i	0.968121	−	0.250482i	$-0.0805891\pi$
$272$	−363.107	+	209.640i	−1.33495	+	0.770735i
$273$		0			0
$274$	−4.51919	+	7.82746i	−0.0164934	+	0.0285674i
$275$	0.410958	−	0.711800i	0.00149439	−	0.00258836i
$276$	280.468	−	190.121i	1.01619	−	0.688845i
$277$	162.697	+	281.799i	0.587353	+	1.01733i	0.994578	+	0.103998i	$0.0331635\pi$
$277$	162.697	+	281.799i	0.587353	+	1.01733i	−0.407224	+	0.913328i	$0.633503\pi$
$278$			19.8462i			0.0713890i
$279$	65.8948	+	26.2700i	0.236182	+	0.0941577i
$280$		0			0
$281$	−7.89120	−	13.6680i	−0.0280826	−	0.0486404i	0.851643	−	0.524123i	$-0.175607\pi$
$281$	−7.89120	−	13.6680i	−0.0280826	−	0.0486404i	−0.879725	+	0.475483i	$0.842273\pi$
$282$	−39.9125	+	82.3144i	−0.141534	+	0.291895i
$283$	−273.509	−	157.910i	−0.966461	−	0.557987i	−0.0683057	−	0.997664i	$-0.521759\pi$
$283$	−273.509	−	157.910i	−0.966461	−	0.557987i	−0.898156	+	0.439678i	$0.855093\pi$
$284$	163.975	−	284.013i	0.577377	−	1.00005i
$285$	−343.629	−	166.618i	−1.20572	−	0.584626i
$286$	0.108552	−	0.0626723i	0.000379551	−	0.000219134i
$287$		0			0
$288$	67.8517	−	170.197i	0.235596	−	0.590961i
$289$	−667.495			−2.30967
$290$	25.1091	−	14.4968i	0.0865832	−	0.0499888i
$291$	136.776	+	201.772i	0.470019	+	0.693374i
$292$	−108.521	−	62.6546i	−0.371647	−	0.214570i
$293$	344.571	+	198.938i	1.17601	+	0.678969i	0.955088	−	0.296322i	$-0.0957602\pi$
$293$	344.571	+	198.938i	1.17601	+	0.678969i	0.220922	+	0.975292i	$0.429094\pi$
$294$		0			0
$295$	145.074	+	251.275i	0.491775	+	0.851780i
$296$	−54.8538			−0.185317
$297$	−2.77958	+	2.53782i	−0.00935884	+	0.00854483i
$298$	−91.8586			−0.308250
$299$	−50.9464	+	29.4139i	−0.170389	+	0.0983742i
$300$	4.83429	+	66.9135i	0.0161143	+	0.223045i
$301$		0			0
$302$	24.4482	−	42.3455i	0.0809543	−	0.140217i
$303$	42.7690	+	63.0930i	0.141152	+	0.208228i
$304$	−341.942	+	197.420i	−1.12481	+	0.649408i
$305$	−181.327			−0.594516
$306$	99.4714	−	78.4578i	0.325070	−	0.256398i
$307$			266.176i			0.867024i	0.901148	+	0.433512i	$0.142726\pi$
$307$			266.176i			0.867024i	−0.901148	+	0.433512i	$0.857274\pi$
$308$		0			0
$309$	144.270	−	297.538i	0.466893	−	0.962908i
$310$	−7.84018	+	13.5796i	−0.0252909	+	0.0438051i
$311$	110.220	+	63.6356i	0.354406	+	0.204616i	0.666624	−	0.745394i	$-0.267739\pi$
$311$	110.220	+	63.6356i	0.354406	+	0.204616i	−0.312218	+	0.950010i	$0.601072\pi$
$312$	−9.17139	+	18.9148i	−0.0293955	+	0.0606244i
$313$	432.327	−	249.604i	1.38124	−	0.797457i	0.388930	−	0.921267i	$-0.372845\pi$
$313$	432.327	−	249.604i	1.38124	−	0.797457i	0.992306	+	0.123810i	$0.0395113\pi$
$314$		−	45.4707i		−	0.144811i
$315$		0			0
$316$	−184.508			−0.583887
$317$	−98.4602	−	170.538i	−0.310600	−	0.537975i	0.667892	−	0.744258i	$-0.267197\pi$
$317$	−98.4602	−	170.538i	−0.310600	−	0.537975i	−0.978492	+	0.206283i	$0.933863\pi$
$318$	38.2668	−	25.9400i	0.120336	−	0.0815724i
$319$	−1.01583	+	1.75947i	−0.00318442	+	0.00551558i
$320$	−170.191	−	98.2597i	−0.531846	−	0.307062i
$321$	−33.9046	−	469.289i	−0.105622	−	1.46196i
$322$		0			0
$323$	−900.742			−2.78868
$324$	71.5676	−	298.768i	0.220888	−	0.922122i
$325$		−	11.6477i		−	0.0358391i
$326$	−28.4215	−	49.2275i	−0.0871825	−	0.151005i
$327$	5.39745	+	74.7084i	0.0165060	+	0.228466i
$328$	2.65044	+	1.53023i	0.00808061	+	0.00466535i
$329$		0			0
$330$	−0.466822	−	0.688658i	−0.00141461	−	0.00208684i
$331$	−96.3662	−	166.911i	−0.291137	−	0.504263i	0.682942	−	0.730472i	$-0.260700\pi$
$331$	−96.3662	−	166.911i	−0.291137	−	0.504263i	−0.974079	+	0.226209i	$0.927367\pi$
$332$		−	450.633i		−	1.35733i
$333$	−137.741	+	20.0072i	−0.413637	+	0.0600816i
$334$		−	59.4991i		−	0.178141i
$335$	−391.979	+	226.309i	−1.17009	+	0.675550i
$336$		0			0
$337$	−189.897	+	328.912i	−0.563493	+	0.975999i	0.433695	+	0.901060i	$0.357210\pi$
$337$	−189.897	+	328.912i	−0.563493	+	0.975999i	−0.997188	+	0.0749390i	$0.976124\pi$
$338$	−37.5721	+	65.0769i	−0.111160	+	0.192535i
$339$	271.344	+	131.569i	0.800425	+	0.388109i
$340$	−256.352	−	444.015i	−0.753978	−	1.30593i
$341$		−	1.09877i		−	0.00322220i
$342$	93.6733	−	73.8846i	0.273899	−	0.216037i
$343$		0			0
$344$	55.5549	+	96.2240i	0.161497	+	0.279721i
$345$	219.093	+	323.207i	0.635052	+	0.936831i
$346$	33.1298	+	19.1275i	0.0957509	+	0.0552818i
$347$	96.1388	−	166.517i	0.277057	−	0.479877i	−0.693595	−	0.720365i	$-0.743974\pi$
$347$	96.1388	−	166.517i	0.277057	−	0.479877i	0.970652	+	0.240488i	$0.0773076\pi$
$348$	−11.9497	−	165.401i	−0.0343382	−	0.475290i
$349$	65.3195	−	37.7122i	0.187162	−	0.108058i	−0.403491	−	0.914983i	$-0.632203\pi$
$349$	65.3195	−	37.7122i	0.187162	−	0.108058i	0.590653	+	0.806926i	$0.298870\pi$
$350$		0			0
$351$	−16.1310	+	50.8414i	−0.0459572	+	0.144847i
$352$	−2.83796			−0.00806240
$353$	−490.119	+	282.970i	−1.38844	+	0.801616i	−0.993139	−	0.116937i	$-0.962693\pi$
$353$	−490.119	+	282.970i	−1.38844	+	0.801616i	−0.395300	+	0.918552i	$0.629359\pi$
$354$	−90.4073	+	6.53165i	−0.255388	+	0.0184510i
$355$	327.292	+	188.962i	0.921950	+	0.532288i
$356$	125.706	+	72.5766i	0.353108	+	0.203867i
$357$		0			0
$358$	79.7482	+	138.128i	0.222760	+	0.385832i
$359$	−36.6268			−0.102025			−0.0510123	−	0.998698i	$-0.516245\pi$
$359$	−36.6268			−0.102025			−0.0510123	+	0.998698i	$0.516245\pi$
$360$	129.606	+	51.6697i	0.360018	+	0.143527i
$361$	−487.239			−1.34969
$362$	−54.4152	+	31.4167i	−0.150318	+	0.0867863i
$363$	−326.576	−	158.350i	−0.899659	−	0.436225i
$364$		0			0
$365$	72.2022	−	125.058i	0.197814	−	0.342624i
$366$	24.7149	−	50.9713i	0.0675270	−	0.139266i
$367$	291.984	−	168.577i	0.795597	−	0.459338i	−0.0463322	−	0.998926i	$-0.514753\pi$
$367$	291.984	−	168.577i	0.795597	−	0.459338i	0.841929	+	0.539588i	$0.181420\pi$
$368$	403.704			1.09702
$369$	7.21355	+	2.87580i	0.0195489	+	0.00779348i
$370$		−	30.7661i		−	0.0831517i
$371$		0			0
$372$	50.3231	+	74.2369i	0.135277	+	0.199562i
$373$	−367.607	+	636.714i	−0.985541	+	1.70701i	−0.346034	+	0.938222i	$0.612472\pi$
$373$	−367.607	+	636.714i	−0.985541	+	1.70701i	−0.639507	+	0.768785i	$0.720862\pi$
$374$	−1.69940	−	0.981151i	−0.00454386	−	0.00262340i
$375$	−404.069	+	29.1927i	−1.07752	+	0.0778472i
$376$	−205.794	+	118.815i	−0.547325	+	0.315998i
$377$			28.7915i			0.0763701i
$378$		0			0
$379$	189.024			0.498745			0.249372	−	0.968408i	$-0.419776\pi$
$379$	189.024			0.498745			0.249372	+	0.968408i	$0.419776\pi$
$380$	−241.410	−	418.134i	−0.635290	−	1.10035i
$381$	−32.8480	−	454.663i	−0.0862153	−	1.19334i
$382$	66.0253	−	114.359i	0.172841	−	0.299370i
$383$	−12.2683	−	7.08313i	−0.0320322	−	0.0184938i	0.483898	−	0.875124i	$-0.339220\pi$
$383$	−12.2683	−	7.08313i	−0.0320322	−	0.0184938i	−0.515931	+	0.856630i	$0.672554\pi$
$384$	253.034	−	171.525i	0.658943	−	0.446679i
$385$		0			0
$386$	−100.352			−0.259979
$387$	174.598	+	221.361i	0.451158	+	0.571993i
$388$			308.182i			0.794284i
$389$	71.9971	+	124.703i	0.185082	+	0.320572i	0.943604	−	0.331075i	$-0.107411\pi$
$389$	71.9971	+	124.703i	0.185082	+	0.320572i	−0.758522	+	0.651648i	$0.774078\pi$
$390$	−10.6089	−	5.14400i	−0.0272022	−	0.0131898i
$391$	797.578	+	460.482i	2.03984	+	1.17770i
$392$		0			0
$393$	167.509	−	345.465i	0.426230	−	0.879046i
$394$	−26.9516	−	46.6815i	−0.0684050	−	0.118481i
$395$		−	212.624i		−	0.538290i
$396$	−4.70914	+	0.684011i	−0.0118918	+	0.00172730i
$397$			206.130i			0.519219i	0.965714	+	0.259610i	$0.0835939\pi$
$397$			206.130i			0.519219i	−0.965714	+	0.259610i	$0.916406\pi$
$398$	−69.2539	+	39.9837i	−0.174005	+	0.100462i
$399$		0			0
$400$	−39.9661	+	69.2233i	−0.0999152	+	0.173058i
$401$	178.201	−	308.654i	0.444393	−	0.769711i	−0.553617	−	0.832771i	$-0.686753\pi$
$401$	178.201	−	308.654i	0.444393	−	0.769711i	0.998010	+	0.0630606i	$0.0200861\pi$
$402$	−10.1891	−	141.032i	−0.0253461	−	0.350826i
$403$	−7.78556	−	13.4850i	−0.0193190	−	0.0334615i
$404$			96.3668i			0.238532i
$405$	344.295	+	82.4734i	0.850112	+	0.203638i
$406$		0			0
$407$	1.07794	+	1.86704i	0.00264849	+	0.00458732i
$408$	328.234	−	23.7139i	0.804495	−	0.0581223i
$409$	456.496	+	263.558i	1.11613	+	0.644396i	0.940409	−	0.340044i	$-0.110442\pi$
$409$	456.496	+	263.558i	1.11613	+	0.644396i	0.175718	+	0.984441i	$0.443775\pi$
$410$	−0.858270	+	1.48657i	−0.00209334	+	0.00362577i
$411$	−49.3119	+	33.4272i	−0.119980	+	0.0813314i
$412$	362.050	−	209.030i	0.878763	−	0.507354i
$413$		0			0
$414$	−120.716	+	17.5343i	−0.291585	+	0.0423533i
$415$	519.303			1.25133
$416$	−34.8298	+	20.1090i	−0.0837254	+	0.0483389i
$417$	−57.0719	+	117.703i	−0.136863	+	0.282263i
$418$	−1.60035	−	0.923961i	−0.00382858	−	0.00221043i
$419$	−274.217	−	158.319i	−0.654455	−	0.377850i	0.135706	−	0.990749i	$-0.456670\pi$
$419$	−274.217	−	158.319i	−0.654455	−	0.377850i	−0.790161	+	0.612899i	$0.790003\pi$
$420$		0			0
$421$	68.8293	+	119.216i	0.163490	+	0.283173i	0.936118	−	0.351686i	$-0.114391\pi$
$421$	68.8293	+	119.216i	0.163490	+	0.283173i	−0.772628	+	0.634859i	$0.781058\pi$
$422$	8.36351			0.0198187
$423$	−473.426	+	373.413i	−1.11921	+	0.882774i
$424$	120.088			0.283227
$425$	−157.918	+	91.1739i	−0.371571	+	0.214527i
$426$	−97.7275	+	66.2468i	−0.229407	+	0.155509i
$427$		0			0
$428$	297.429	−	515.162i	0.694928	−	1.20365i
$429$	0.824026	−	0.0595333i	0.00192081	−	0.000138772i
$430$	−53.9696	+	31.1594i	−0.125511	+	0.0724637i
$431$	−631.153			−1.46439			−0.732196	−	0.681094i	$-0.761504\pi$
$431$	−631.153			−1.46439			−0.732196	+	0.681094i	$0.761504\pi$
$432$	270.317	−	246.805i	0.625733	−	0.571308i
$433$		−	224.007i		−	0.517338i	−0.965966	−	0.258669i	$-0.916716\pi$
$433$		−	224.007i		−	0.517338i	0.965966	−	0.258669i	$-0.0832839\pi$
$434$		0			0
$435$	190.606	−	13.7707i	0.438174	−	0.0316567i
$436$	−47.3492	+	82.0113i	−0.108599	+	0.188099i
$437$	751.088	+	433.641i	1.71874	+	0.992313i
$438$	25.3128	+	37.3415i	0.0577918	+	0.0852546i
$439$	−196.906	+	113.684i	−0.448533	+	0.258961i	−0.707210	−	0.707003i	$-0.750047\pi$
$439$	−196.906	+	113.684i	−0.448533	+	0.258961i	0.258678	+	0.965964i	$0.416713\pi$
$440$		−	2.16113i		−	0.00491167i
$441$		0			0
$442$	−27.8086			−0.0629154
$443$	−47.0412	−	81.4778i	−0.106188	−	0.183923i	0.808035	−	0.589134i	$-0.200531\pi$
$443$	−47.0412	−	81.4778i	−0.106188	−	0.183923i	−0.914223	+	0.405212i	$0.867198\pi$
$444$	−158.339	−	76.7752i	−0.356620	−	0.172917i
$445$	−83.6362	+	144.862i	−0.187946	+	0.325533i
$446$	−64.7693	−	37.3946i	−0.145223	−	0.0838444i
$447$	−544.795	−	264.159i	−1.21878	−	0.590960i
$448$		0			0
$449$	−293.686			−0.654089			−0.327044	−	0.945009i	$-0.606053\pi$
$449$	−293.686			−0.654089			−0.327044	+	0.945009i	$0.606053\pi$
$450$	8.94411	−	22.4351i	0.0198758	−	0.0498558i
$451$		−	0.120283i		−	0.000266703i
$452$	190.627	+	330.176i	0.421742	+	0.730479i
$453$	266.771	−	180.837i	0.588898	−	0.399198i
$454$	44.9069	+	25.9270i	0.0989140	+	0.0571080i
$455$		0			0
$456$	309.102	−	22.3316i	0.677855	−	0.0489729i
$457$	142.012	+	245.972i	0.310749	+	0.538233i	0.978525	−	0.206130i	$-0.0660868\pi$
$457$	142.012	+	245.972i	0.310749	+	0.538233i	−0.667776	+	0.744363i	$0.732753\pi$
$458$			83.1296i			0.181506i
$459$	815.566	−	179.266i	1.77683	−	0.390558i
$460$			493.659i			1.07317i
$461$	−563.505	+	325.340i	−1.22235	+	0.705726i	−0.965419	−	0.260703i	$-0.916046\pi$
$461$	−563.505	+	325.340i	−1.22235	+	0.705726i	−0.256934	+	0.966429i	$0.582712\pi$
$462$		0			0
$463$	−215.001	+	372.393i	−0.464365	+	0.804304i	−0.999173	−	0.0406699i	$-0.987051\pi$
$463$	−215.001	+	372.393i	−0.464365	+	0.804304i	0.534807	+	0.844974i	$0.320384\pi$
$464$	98.7906	−	171.110i	0.212911	−	0.368772i
$465$	−85.5495	+	57.9916i	−0.183977	+	0.124713i
$466$	57.7473	+	100.021i	0.123921	+	0.214638i
$467$			250.455i			0.536306i	0.963376	+	0.268153i	$0.0864132\pi$
$467$			250.455i			0.536306i	−0.963376	+	0.268153i	$0.913587\pi$
$468$	−52.9476	+	41.7623i	−0.113136	+	0.0892357i
$469$		0			0
$470$	−66.6406	−	115.425i	−0.141789	−	0.245585i
$471$	130.761	−	269.678i	0.277624	−	0.572564i
$472$	−203.910	−	117.728i	−0.432013	−	0.249423i
$473$	2.18343	−	3.78181i	0.00461613	−	0.00799537i
$474$	59.7690	+	28.9807i	0.126095	+	0.0611407i
$475$	−148.713	+	85.8595i	−0.313080	+	0.180757i
$476$		0			0
$477$	301.549	−	43.8006i	0.632178	−	0.0918251i
$478$	−59.8033			−0.125112
$479$	−463.619	+	267.671i	−0.967889	+	0.558811i	−0.898592	−	0.438785i	$-0.855409\pi$
$479$	−463.619	+	267.671i	−0.967889	+	0.558811i	−0.0692973	+	0.997596i	$0.522076\pi$
$480$	149.784	+	220.962i	0.312050	+	0.460338i
$481$	26.4586	+	15.2759i	0.0550075	+	0.0317586i
$482$	−102.671	−	59.2772i	−0.213011	−	0.122982i
$483$		0			0
$484$	−229.430	−	397.384i	−0.474028	−	0.821041i
$485$	−355.145			−0.732257
$486$	−70.1109	+	85.5408i	−0.144261	+	0.176010i
$487$	733.392			1.50594			0.752969	−	0.658056i	$-0.228621\pi$
$487$	733.392			1.50594			0.752969	+	0.658056i	$0.228621\pi$
$488$	127.433	−	73.5737i	0.261134	−	0.150766i
$489$	−26.9979	−	373.690i	−0.0552105	−	0.764193i
$490$		0			0
$491$	−69.4113	+	120.224i	−0.141367	+	0.244855i	−0.928012	−	0.372551i	$-0.878483\pi$
$491$	−69.4113	+	120.224i	−0.141367	+	0.244855i	0.786645	+	0.617406i	$0.211816\pi$
$492$	5.50891	+	8.12677i	0.0111970	+	0.0165178i
$493$	390.351	−	225.369i	0.791787	−	0.457138i
$494$	−26.1877			−0.0530115
$495$	−0.788244	−	5.42674i	−0.00159241	−	0.0109631i
$496$			106.856i			0.215436i
$497$		0			0
$498$	−70.7809	+	145.977i	−0.142130	+	0.293126i
$499$	47.9299	−	83.0170i	0.0960519	−	0.166367i	−0.813995	−	0.580872i	$-0.802712\pi$
$499$	47.9299	−	83.0170i	0.0960519	−	0.166367i	0.910047	+	0.414505i	$0.136045\pi$
$500$	−443.567	−	256.094i	−0.887134	−	0.512187i
$501$	171.102	−	352.877i	0.341522	−	0.704345i
$502$	24.8511	−	14.3478i	0.0495043	−	0.0285813i
$503$			41.5091i			0.0825231i	0.999148	+	0.0412615i	$0.0131377\pi$
$503$			41.5091i			0.0825231i	−0.999148	+	0.0412615i	$0.986862\pi$
$504$		0			0
$505$	−111.052			−0.219904
$506$	0.944703	+	1.63627i	0.00186700	+	0.00323374i
$507$	−409.975	+	277.911i	−0.808630	+	0.548148i
$508$	288.160	−	499.107i	0.567244	−	0.982495i
$509$	−75.2739	−	43.4594i	−0.147886	−	0.0853819i	0.424231	−	0.905554i	$-0.360544\pi$
$509$	−75.2739	−	43.4594i	−0.147886	−	0.0853819i	−0.572117	+	0.820172i	$0.693878\pi$
$510$	13.3005	+	184.098i	0.0260795	+	0.360977i
$511$		0			0
$512$	468.337			0.914720
$513$	768.028	−	168.817i	1.49713	−	0.329078i
$514$			56.0468i			0.109040i
$515$	240.883	+	417.221i	0.467734	+	0.810139i
$516$	25.6847	+	355.513i	0.0497766	+	0.688979i
$517$	8.08816	+	4.66970i	0.0156444	+	0.00903231i
$518$		0			0
$519$	141.481	+	208.713i	0.272603	+	0.402145i
$520$	−15.3132	−	26.5232i	−0.0294484	−	0.0510061i
$521$		−	180.917i		−	0.347249i	−0.984812	−	0.173624i	$-0.944452\pi$
$521$		−	180.917i		−	0.347249i	0.984812	−	0.173624i	$-0.0555479\pi$
$522$	−22.1086	+	55.4565i	−0.0423536	+	0.106238i
$523$		−	453.302i		−	0.866734i	−0.901217	−	0.433367i	$-0.857325\pi$
$523$		−	453.302i		−	0.866734i	0.901217	−	0.433367i	$-0.142675\pi$
$524$	420.369	−	242.700i	0.802230	−	0.463168i
$525$		0			0
$526$	115.060	−	199.290i	0.218745	−	0.378878i
$527$	−121.885	+	211.111i	−0.231280	+	0.400589i
$528$	−5.10152	−	2.47362i	−0.00966197	−	0.00468488i
$529$	−178.876	−	309.822i	−0.338139	−	0.585675i
$530$			67.3546i			0.127084i
$531$	−554.971	−	221.248i	−1.04514	−	0.416662i
$532$		0			0
$533$	−0.852290	−	1.47621i	−0.00159904	−	0.00276963i
$534$	−29.3213	−	43.2549i	−0.0549089	−	0.0810018i
$535$	593.666	+	342.753i	1.10966	+	0.640660i
$536$	183.651	−	318.092i	0.342632	−	0.593455i
$537$	75.7539	+	1048.54i	0.141069	+	1.95259i
$538$	3.49763	−	2.01936i	0.00650117	−	0.00375345i
$539$		0			0
$540$	301.799	+	330.549i	0.558887	+	0.612128i
$541$	385.783			0.713093			0.356546	−	0.934278i	$-0.383954\pi$
$541$	385.783			0.713093			0.356546	+	0.934278i	$0.383954\pi$
$542$	−53.5134	+	30.8960i	−0.0987333	+	0.0570037i
$543$	−413.071	+	29.8431i	−0.760720	+	0.0549597i
$544$	545.269	+	314.811i	1.00233	+	0.578697i
$545$	−94.5086	−	54.5646i	−0.173410	−	0.100118i
$546$		0			0
$547$	341.808	+	592.029i	0.624877	+	1.08232i	0.988565	+	0.150798i	$0.0481843\pi$
$547$	341.808	+	592.029i	0.624877	+	1.08232i	−0.363687	+	0.931521i	$0.618482\pi$
$548$	−75.3180			−0.137442
$549$	293.158	−	231.228i	0.533985	−	0.421180i
$550$	−0.374096			−0.000680175
$551$	367.598	−	212.233i	0.667147	−	0.385177i
$552$	−285.116	−	138.247i	−0.516514	−	0.250447i
$553$		0			0
$554$	74.0518	−	128.261i	0.133667	−	0.231519i
$555$	88.4746	−	182.468i	0.159414	−	0.328770i
$556$	−143.224	+	82.6903i	−0.257597	+	0.148724i
$557$	161.119			0.289262			0.144631	−	0.989486i	$-0.453800\pi$
$557$	161.119			0.289262			0.144631	+	0.989486i	$0.453800\pi$
$558$	−4.64114	−	31.9523i	−0.00831745	−	0.0572623i
$559$		−	61.8846i		−	0.110706i
$560$		0			0
$561$	−7.25730	−	10.7060i	−0.0129364	−	0.0190838i
$562$	−3.59169	+	6.22099i	−0.00639091	+	0.0110694i
$563$	473.617	+	273.443i	0.841239	+	0.485689i	0.857685	−	0.514175i	$-0.171902\pi$
$563$	473.617	+	273.443i	0.841239	+	0.485689i	−0.0164464	+	0.999865i	$0.505235\pi$
$564$	−760.337	+	54.9320i	−1.34811	+	0.0973971i
$565$	−380.490	+	219.676i	−0.673434	+	0.388808i
$566$			143.746i			0.253969i
$567$		0			0
$568$	−306.687			−0.539941
$569$	301.145	+	521.599i	0.529253	+	0.916694i	0.999418	+	0.0341151i	$0.0108613\pi$
$569$	301.145	+	521.599i	0.529253	+	0.916694i	−0.470164	+	0.882579i	$0.655805\pi$
$570$	12.5253	+	173.368i	0.0219742	+	0.304154i
$571$	−160.184	+	277.446i	−0.280532	+	0.485895i	−0.971516	−	0.236975i	$-0.923844\pi$
$571$	−160.184	+	277.446i	−0.280532	+	0.485895i	0.690984	+	0.722870i	$0.257177\pi$
$572$	0.904575	+	0.522257i	0.00158143	+	0.000913036i
$573$	720.447	−	488.371i	1.25732	−	0.852306i
$574$		0			0
$575$	175.574			0.305346
$576$	400.454	−	58.1667i	0.695232	−	0.100984i
$577$		−	106.843i		−	0.185170i	−0.995705	−	0.0925849i	$-0.970487\pi$
$577$		−	106.843i		−	0.185170i	0.995705	−	0.0925849i	$-0.0295129\pi$
$578$	151.906	+	263.108i	0.262813	+	0.455205i
$579$	−595.166	−	288.583i	−1.02792	−	0.498416i
$580$	209.238	+	120.803i	0.360755	+	0.208282i
$581$		0			0
$582$	48.4062	−	99.8316i	0.0831721	−	0.171532i
$583$	−2.35987	−	4.08741i	−0.00404780	−	0.00701099i
$584$			117.184i			0.200658i
$585$	−48.1263	−	61.0161i	−0.0822671	−	0.104301i
$586$		−	181.094i		−	0.309034i
$587$	−269.081	+	155.354i	−0.458400	+	0.264657i	−0.711371	−	0.702816i	$-0.751926\pi$
$587$	−269.081	+	155.354i	−0.458400	+	0.264657i	0.252971	+	0.967474i	$0.418592\pi$
$588$		0			0
$589$	−114.780	+	198.805i	−0.194873	+	0.337530i
$590$	66.0305	−	114.368i	0.111916	−	0.193844i
$591$	−25.6017	−	354.364i	−0.0433192	−	0.599600i
$592$	−104.830	−	181.572i	−0.177078	−	0.306709i
$593$			848.638i			1.43109i	0.698565	+	0.715546i	$0.253822\pi$
$593$			848.638i			1.43109i	−0.698565	+	0.715546i	$0.746178\pi$
$594$	1.63290	+	0.518088i	0.00274899	+	0.000872202i
$595$		0			0
$596$	−382.735	−	662.916i	−0.642173	−	1.11228i
$597$	−525.712	+	37.9811i	−0.880590	+	0.0636199i
$598$	23.1883	+	13.3878i	0.0387764	+	0.0223876i
$599$	−176.616	+	305.907i	−0.294851	+	0.510697i	−0.974950	−	0.222423i	$-0.928603\pi$
$599$	−176.616	+	305.907i	−0.294851	+	0.510697i	0.680099	+	0.733120i	$0.261937\pi$
$600$	51.9312	−	35.2027i	0.0865520	−	0.0586712i
$601$	582.924	−	336.552i	0.969924	−	0.559986i	0.0707111	−	0.997497i	$-0.477473\pi$
$601$	582.924	−	336.552i	0.969924	−	0.559986i	0.899213	+	0.437511i	$0.144140\pi$
$602$		0			0
$603$	345.138	−	865.732i	0.572368	−	1.43571i
$604$	407.460			0.674603
$605$	457.940	−	264.392i	0.756925	−	0.437011i
$606$	15.1363	−	31.2168i	0.0249775	−	0.0515129i
$607$	−671.609	−	387.754i	−1.10644	−	0.638804i	−0.168535	−	0.985696i	$-0.553904\pi$
$607$	−671.609	−	387.754i	−1.10644	−	0.638804i	−0.937905	+	0.346892i	$0.887237\pi$
$608$	513.486	+	296.461i	0.844549	+	0.487600i
$609$		0			0
$610$	41.2657	+	71.4743i	0.0676487	+	0.117171i
$611$	132.353			0.216616
$612$	980.660	+	390.956i	1.60239	+	0.638817i
$613$	−133.357			−0.217549			−0.108774	−	0.994066i	$-0.534693\pi$
$613$	−133.357			−0.217549			−0.108774	+	0.994066i	$0.534693\pi$
$614$	104.920	−	60.5753i	0.170879	−	0.0986569i
$615$	−9.36517	+	6.34839i	−0.0152279	+	0.0103226i
$616$		0			0
$617$	−496.756	+	860.406i	−0.805115	+	1.39450i	0.111099	+	0.993809i	$0.464563\pi$
$617$	−496.756	+	860.406i	−0.805115	+	1.39450i	−0.916214	+	0.400690i	$0.868770\pi$
$618$	−150.114	+	10.8453i	−0.242903	+	0.0175490i
$619$	−687.090	+	396.691i	−1.11000	+	0.640859i	−0.938829	−	0.344383i	$-0.888088\pi$
$619$	−687.090	+	396.691i	−1.11000	+	0.640859i	−0.171170	+	0.985241i	$0.554755\pi$
$620$	−130.666			−0.210752
$621$	−766.367	−	243.153i	−1.23409	−	0.391551i
$622$		−	57.9277i		−	0.0931314i
$623$		0			0
$624$	−80.1373	+	5.78967i	−0.128425	+	0.00927832i
$625$	221.418	−	383.508i	0.354269	−	0.613612i
$626$	−196.774	−	113.608i	−0.314336	−	0.181482i
$627$	−6.83428	−	10.0820i	−0.0109000	−	0.0160797i
$628$	328.149	−	189.457i	0.522530	−	0.301683i
$629$		−	478.295i		−	0.760406i
$630$		0			0
$631$	−124.394			−0.197137			−0.0985687	−	0.995130i	$-0.531426\pi$
$631$	−124.394			−0.197137			−0.0985687	+	0.995130i	$0.531426\pi$
$632$	86.2726	+	149.429i	0.136507	+	0.236438i
$633$	49.6023	+	24.0511i	0.0783606	+	0.0379954i
$634$	−44.8143	+	77.6206i	−0.0706850	+	0.122430i
$635$	575.164	+	332.071i	0.905770	+	0.522947i
$636$	346.643	+	168.080i	0.545036	+	0.264276i
$637$		0			0
$638$	0.924714			0.00144939
$639$	−770.109	+	111.860i	−1.20518	+	0.175054i
$640$			445.373i			0.695895i
$641$	−430.255	−	745.224i	−0.671225	−	1.16260i	−0.977557	−	0.210671i	$-0.932435\pi$
$641$	−430.255	−	745.224i	−0.671225	−	1.16260i	0.306332	−	0.951925i	$-0.400898\pi$
$642$	−177.265	+	120.163i	−0.276114	+	0.187170i
$643$	−847.964	−	489.572i	−1.31876	−	0.761387i	−0.335232	−	0.942135i	$-0.608815\pi$
$643$	−847.964	−	489.572i	−1.31876	−	0.761387i	−0.983529	+	0.180748i	$0.942148\pi$
$644$		0			0
$645$	−409.688	+	29.5987i	−0.635176	+	0.0458895i
$646$	204.987	+	355.048i	0.317318	+	0.549610i
$647$			706.721i			1.09231i	0.837686	+	0.546153i	$0.183908\pi$
$647$			706.721i			1.09231i	−0.837686	+	0.546153i	$0.816092\pi$
$648$	−275.428	+	81.7374i	−0.425043	+	0.126138i
$649$			9.25391i			0.0142587i
$650$	−4.59121	+	2.65074i	−0.00706340	+	0.00407806i
$651$		0			0
$652$	236.840	−	410.219i	0.363252	−	0.629170i
$653$	420.493	−	728.315i	0.643940	−	1.11534i	−0.340605	−	0.940207i	$-0.610632\pi$
$653$	420.493	−	728.315i	0.643940	−	1.11534i	0.984545	−	0.175131i	$-0.0560348\pi$
$654$	28.2197	−	19.1294i	0.0431494	−	0.0292498i
$655$	279.684	+	484.427i	0.426998	+	0.739582i
$656$			11.6976i			0.0178318i
$657$	42.7414	+	294.257i	0.0650555	+	0.447880i
$658$		0			0
$659$	−241.065	−	417.537i	−0.365804	−	0.633591i	0.623101	−	0.782141i	$-0.285873\pi$
$659$	−241.065	−	417.537i	−0.365804	−	0.633591i	−0.988905	+	0.148550i	$0.952539\pi$
$660$	3.02480	−	6.23826i	0.00458302	−	0.00945191i
$661$	−716.914	−	413.911i	−1.08459	−	0.626189i	−0.152460	−	0.988310i	$-0.548719\pi$
$661$	−716.914	−	413.911i	−1.08459	−	0.626189i	−0.932131	+	0.362121i	$0.882053\pi$
$662$	−43.8612	+	75.9699i	−0.0662556	+	0.114758i
$663$	−164.927	−	79.9696i	−0.248759	−	0.120618i
$664$	−364.956	+	210.708i	−0.549633	+	0.317331i
$665$		0			0
$666$	39.2328	+	49.7407i	0.0589081	+	0.0746857i
$667$	−433.994			−0.650666
$668$	429.387	−	247.907i	0.642795	−	0.371118i
$669$	−276.598	−	408.038i	−0.413449	−	0.609922i
$670$	178.410	+	103.005i	0.266284	+	0.153739i
$671$	−5.00841	−	2.89161i	−0.00746410	−	0.00430940i
$672$		0			0
$673$	325.267	+	563.379i	0.483309	+	0.837116i	0.999816	−	0.0191670i	$-0.00610143\pi$
$673$	325.267	+	563.379i	0.483309	+	0.837116i	−0.516507	+	0.856283i	$0.672768\pi$
$674$	172.864			0.256475
$675$	117.563	−	107.337i	0.174167	−	0.159018i
$676$	−626.187			−0.926312
$677$	−366.544	+	211.624i	−0.541424	+	0.312591i	−0.745656	−	0.666331i	$-0.767864\pi$
$677$	−366.544	+	211.624i	−0.541424	+	0.312591i	0.204232	+	0.978923i	$0.434530\pi$
$678$	−9.89047	−	136.898i	−0.0145877	−	0.201915i
$679$		0			0
$680$	−239.731	+	415.227i	−0.352546	+	0.610628i
$681$	191.775	+	282.907i	0.281608	+	0.415429i
$682$	−0.433105	+	0.250053i	−0.000635051	+	0.000366647i
$683$	439.670			0.643734			0.321867	−	0.946785i	$-0.395690\pi$
$683$	439.670			0.643734			0.321867	+	0.946785i	$0.395690\pi$
$684$	923.499	+	368.167i	1.35014	+	0.538256i
$685$		−	86.7953i		−	0.126709i
$686$		0			0
$687$	−239.057	+	493.024i	−0.347972	+	0.717648i
$688$	−212.341	+	367.785i	−0.308635	+	0.534571i
$689$	−57.9244	−	33.4426i	−0.0840702	−	0.0485379i
$690$	77.5391	−	159.915i	0.112375	−	0.231760i
$691$	700.681	−	404.539i	1.01401	−	0.585439i	0.101647	−	0.994821i	$-0.467589\pi$
$691$	700.681	−	404.539i	1.01401	−	0.585439i	0.912363	+	0.409381i	$0.134255\pi$
$692$			318.784i			0.460671i
$693$		0			0
$694$	−87.5155			−0.126103
$695$	−95.2911	−	165.049i	−0.137109	−	0.237481i
$696$	−128.367	+	87.0162i	−0.184435	+	0.125023i
$697$	−13.3428	+	23.1104i	−0.0191432	+	0.0331570i
$698$	−29.7303	−	17.1648i	−0.0425935	−	0.0245914i
$699$	54.8549	+	759.270i	0.0784763	+	1.08622i
$700$		0			0
$701$	−14.5407			−0.0207428			−0.0103714	−	0.999946i	$-0.503301\pi$
$701$	−14.5407			−0.0207428			−0.0103714	+	0.999946i	$0.503301\pi$
$702$	23.7113	−	5.21188i	0.0337768	−	0.00742432i
$703$		−	450.416i		−	0.640706i
$704$	−3.13388	−	5.42803i	−0.00445153	−	0.00771028i
$705$	−63.3028	−	876.201i	−0.0897912	−	1.24284i
$706$	223.078	+	128.794i	0.315975	+	0.182428i
$707$		0			0
$708$	−423.825	−	625.228i	−0.598623	−	0.883091i
$709$	−475.616	−	823.790i	−0.670826	−	1.16190i	−0.977670	−	0.210145i	$-0.932606\pi$
$709$	−475.616	−	823.790i	−0.670826	−	1.16190i	0.306844	−	0.951760i	$-0.400727\pi$
$710$		−	172.013i		−	0.242272i
$711$	271.138	+	343.757i	0.381347	+	0.483484i
$712$		−	135.742i		−	0.190649i
$713$	203.268	−	117.357i	0.285089	−	0.164596i
$714$		0			0
$715$	−0.601841	+	1.04242i	−0.000841736	+	0.00145793i
$716$	−664.552	+	1151.04i	−0.928145	+	1.60760i
$717$	−354.681	−	171.977i	−0.494674	−	0.239857i
$718$	8.33538	+	14.4373i	0.0116092	+	0.0201077i
$719$		−	1057.31i		−	1.47052i	−0.677783	−	0.735262i	$-0.737059\pi$
$719$		−	1057.31i		−	1.47052i	0.677783	−	0.735262i	$-0.262941\pi$
$720$	76.6575	+	527.756i	0.106469	+	0.732994i
$721$		0			0
$722$	110.884	+	192.056i	0.153579	+	0.266006i
$723$	−438.457	−	646.814i	−0.606441	−	0.894625i
$724$	−453.449	−	261.799i	−0.626311	−	0.361601i
$725$	42.9647	−	74.4171i	0.0592617	−	0.102644i
$726$	11.9037	+	164.764i	0.0163963	+	0.226948i
$727$	−1105.69	+	638.372i	−1.52090	+	0.878091i	−0.521202	+	0.853434i	$0.674516\pi$
$727$	−1105.69	+	638.372i	−1.52090	+	0.878091i	−0.999696	+	0.0246570i	$0.992151\pi$
$728$		0			0
$729$	−661.804	+	305.706i	−0.907825	+	0.419350i
$730$	−65.7259			−0.0900355
$731$	−839.021	+	484.409i	−1.14777	+	0.662666i
$732$	470.821	−	34.0154i	0.643198	−	0.0464691i
$733$	75.3308	+	43.4922i	0.102770	+	0.0593346i	0.550504	−	0.834832i	$-0.314435\pi$
$733$	75.3308	+	43.4922i	0.102770	+	0.0593346i	−0.447734	+	0.894167i	$0.647769\pi$
$734$	−132.897	−	76.7281i	−0.181059	−	0.104534i
$735$		0			0
$736$	−303.116	−	525.013i	−0.411843	−	0.713333i
$737$	−14.4357			−0.0195872
$738$	−0.508069	−	3.49785i	−0.000688440	−	0.00473963i
$739$	777.826			1.05254			0.526269	−	0.850318i	$-0.323590\pi$
$739$	777.826			1.05254			0.526269	+	0.850318i	$0.323590\pi$
$740$	222.030	−	128.189i	0.300041	−	0.173228i
$741$	−155.314	−	75.3082i	−0.209600	−	0.101631i
$742$		0			0
$743$	162.682	−	281.774i	0.218953	−	0.379238i	−0.735535	−	0.677487i	$-0.763069\pi$
$743$	162.682	−	281.774i	0.218953	−	0.379238i	0.954488	+	0.298249i	$0.0964025\pi$
$744$	36.5924	−	75.4673i	0.0491834	−	0.101434i
$745$	763.935	−	441.058i	1.02542	−	0.592024i
$746$	334.634			0.448571
$747$	−839.575	+	662.212i	−1.12393	+	0.886496i
$748$		−	16.3521i		−	0.0218611i
$749$		0			0
$750$	103.463	+	152.629i	0.137951	+	0.203506i
$751$	−160.798	+	278.510i	−0.214112	+	0.370852i	−0.952997	−	0.302979i	$-0.902019\pi$
$751$	−160.798	+	278.510i	−0.214112	+	0.370852i	0.738886	+	0.673831i	$0.235352\pi$
$752$	−786.582	−	454.133i	−1.04599	−	0.603901i
$753$	188.647	−	13.6292i	0.250528	−	0.0180998i
$754$	11.3488	−	6.55225i	0.0150515	−	0.00868999i
$755$			469.551i			0.621922i
$756$		0			0
$757$	1029.44			1.35989			0.679946	−	0.733263i	$-0.262003\pi$
$757$	1029.44			1.35989			0.679946	+	0.733263i	$0.262003\pi$
$758$	−43.0174	−	74.5083i	−0.0567511	−	0.0982958i
$759$	0.897386	+	12.4211i	0.00118233	+	0.0163651i
$760$	−225.758	+	391.024i	−0.297050	+	0.514505i
$761$	−936.211	−	540.522i	−1.23024	−	0.710278i	−0.263158	−	0.964753i	$-0.584764\pi$
$761$	−936.211	−	540.522i	−1.23024	−	0.710278i	−0.967079	+	0.254475i	$0.918097\pi$
$762$	−171.741	+	116.418i	−0.225381	+	0.152780i
$763$		0			0
$764$	1100.40			1.44031
$765$	−450.532	+	1130.10i	−0.588930	+	1.47725i
$766$			6.44780i			0.00841749i
$767$	65.5705	+	113.571i	0.0854896	+	0.148072i
$768$	360.287	+	174.695i	0.469123	+	0.227468i
$769$	345.681	+	199.579i	0.449520	+	0.259531i	0.707627	−	0.706586i	$-0.249766\pi$
$769$	345.681	+	199.579i	0.449520	+	0.259531i	−0.258107	+	0.966116i	$0.583099\pi$
$770$		0			0
$771$	−161.175	+	332.402i	−0.209046	+	0.431131i
$772$	−418.122	−	724.209i	−0.541609	−	0.938095i
$773$		−	696.903i		−	0.901557i	−0.892636	−	0.450778i	$-0.851146\pi$
$773$		−	696.903i		−	0.901557i	0.892636	−	0.450778i	$-0.148854\pi$
$774$	47.5203	−	119.198i	0.0613957	−	0.154003i
$775$			46.4726i			0.0599646i
$776$	249.589	−	144.100i	0.321635	−	0.185696i
$777$		0			0
$778$	32.7696	−	56.7586i	0.0421203	−	0.0729544i
$779$	−12.5651	+	21.7634i	−0.0161298	+	0.0279376i
$780$	−7.07974	−	97.9938i	−0.00907660	−	0.125633i
$781$	6.02673	+	10.4386i	0.00771668	+	0.0133657i
$782$		−	419.178i		−	0.536033i
$783$	−290.598	+	265.323i	−0.371135	+	0.338854i
$784$		0			0
$785$	218.327	+	378.154i	0.278124	+	0.481725i
$786$	−174.294	+	12.5922i	−0.221748	+	0.0160206i
$787$	−68.7086	−	39.6689i	−0.0873044	−	0.0504052i	0.455712	−	0.890127i	$-0.349385\pi$
$787$	−68.7086	−	39.6689i	−0.0873044	−	0.0504052i	−0.543017	+	0.839722i	$0.682718\pi$
$788$	224.591	−	389.003i	0.285014	−	0.493659i
$789$	1255.50	−	851.068i	1.59125	−	1.07867i
$790$	−83.8108	+	48.3882i	−0.106090	+	0.0612509i
$791$		0			0
$792$	2.75587	+	3.49398i	0.00347963	+	0.00441159i
$793$	−81.9564			−0.103350
$794$	81.2509	−	46.9102i	0.102331	−	0.0590809i
$795$	−193.692	+	399.466i	−0.243638	+	0.502473i
$796$	−577.101	−	333.190i	−0.725002	−	0.418580i
$797$	−79.3190	−	45.7948i	−0.0995219	−	0.0574590i	0.449413	−	0.893324i	$-0.351633\pi$
$797$	−79.3190	−	45.7948i	−0.0995219	−	0.0574590i	−0.548935	+	0.835865i	$0.684967\pi$
$798$		0			0
$799$	−1036.01	−	1794.42i	−1.29663	−	2.24583i
$800$	120.032			0.150040
$801$	−49.5100	−	340.856i	−0.0618102	−	0.425538i
$802$	−162.217			−0.202266
$803$	3.98857	−	2.30280i	0.00496709	−	0.00286775i
$804$	975.332	−	661.150i	1.21310	−	0.822326i
$805$		0			0
$806$	−3.54361	+	6.13771i	−0.00439654	+	0.00761502i
$807$	26.5508	−	1.91821i	0.0329006	−	0.00237697i
$808$	78.0451	−	45.0594i	0.0965905	−	0.0557665i
$809$	−1278.01			−1.57974			−0.789871	−	0.613273i	$-0.789852\pi$
$809$	−1278.01			−1.57974			−0.789871	+	0.613273i	$0.789852\pi$
$810$	−45.8445	−	154.481i	−0.0565982	−	0.190717i
$811$		−	176.218i		−	0.217285i	−0.994081	−	0.108642i	$-0.965350\pi$
$811$		−	176.218i		−	0.217285i	0.994081	−	0.108642i	$-0.0346503\pi$
$812$		0			0
$813$	−406.225	+	29.3485i	−0.499662	+	0.0360990i
$814$	0.490624	−	0.849787i	0.000602733	−	0.00104396i
$815$	472.730	+	272.931i	0.580037	+	0.334885i
$816$	705.780	+	1041.17i	0.864926	+	1.27594i
$817$	−790.116	+	456.174i	−0.967094	+	0.558352i
$818$		−	239.918i		−	0.293298i
$819$		0			0
$820$	−14.3042			−0.0174441
$821$	195.125	+	337.966i	0.237667	+	0.411651i	0.960044	−	0.279848i	$-0.0902840\pi$
$821$	195.125	+	337.966i	0.237667	+	0.411651i	−0.722377	+	0.691499i	$0.756951\pi$
$822$	24.3983	+	11.8302i	0.0296816	+	0.0143920i
$823$	49.6717	−	86.0339i	0.0603544	−	0.104537i	−0.834269	−	0.551357i	$-0.814110\pi$
$823$	49.6717	−	86.0339i	0.0603544	−	0.104537i	0.894624	+	0.446820i	$0.147444\pi$
$824$	−338.576	−	195.477i	−0.410893	−	0.237229i
$825$	−2.21869	−	1.07579i	−0.00268932	−	0.00130399i
$826$		0			0
$827$	494.422			0.597850			0.298925	−	0.954277i	$-0.403372\pi$
$827$	494.422			0.597850			0.298925	+	0.954277i	$0.403372\pi$
$828$	−629.512	−	798.116i	−0.760280	−	0.963908i
$829$		−	756.983i		−	0.913128i	−0.889690	−	0.456564i	$-0.849080\pi$
$829$		−	756.983i		−	0.913128i	0.889690	−	0.456564i	$-0.150920\pi$
$830$	−118.181	−	204.695i	−0.142386	−	0.246620i
$831$	808.029	−	547.740i	0.972357	−	0.659134i
$832$	−76.9229	−	44.4115i	−0.0924555	−	0.0533792i
$833$		0			0
$834$	59.3837	−	4.29029i	0.0712035	−	0.00514423i
$835$	285.684	+	494.819i	0.342137	+	0.592598i
$836$		−	15.3990i		−	0.0184198i
$837$	64.3602	−	202.849i	0.0768939	−	0.242353i
$838$			144.118i			0.171979i
$839$	1345.92	−	777.067i	1.60419	−	0.926182i	0.613559	−	0.789649i	$-0.289737\pi$
$839$	1345.92	−	777.067i	1.60419	−	0.926182i	0.990636	−	0.136533i	$-0.0435960\pi$
$840$		0			0
$841$	314.297	−	544.379i	0.373718	−	0.647299i
$842$	31.3278	−	54.2613i	0.0372064	−	0.0644433i
$843$	−39.1914	+	26.5667i	−0.0464904	+	0.0315145i
$844$	34.8471	+	60.3570i	0.0412880	+	0.0715130i
$845$		−	721.609i		−	0.853975i
$846$	254.930	+	101.632i	0.301335	+	0.120132i
$847$		0			0
$848$	229.499	+	397.504i	0.270636	+	0.468755i
$849$	−413.373	+	852.529i	−0.486894	+	1.00416i
$850$	71.8765	+	41.4979i	0.0845606	+	0.0488211i
$851$	−230.264	+	398.829i	−0.270580	+	0.468659i
$852$	−885.272	−	429.249i	−1.03905	−	0.503813i
$853$	667.098	−	385.149i	0.782061	−	0.451523i	−0.0550992	−	0.998481i	$-0.517548\pi$
$853$	667.098	−	385.149i	0.782061	−	0.451523i	0.837160	+	0.546958i	$0.184214\pi$
$854$		0			0
$855$	−424.271	+	1064.23i	−0.496223	+	1.24471i
$856$	−556.290			−0.649871
$857$	982.010	−	566.964i	1.14587	−	0.661568i	0.197992	−	0.980204i	$-0.436558\pi$
$857$	982.010	−	566.964i	1.14587	−	0.661568i	0.947877	+	0.318635i	$0.103225\pi$
$858$	−0.210995	−	0.311260i	−0.000245915	−	0.000362774i
$859$	−610.092	−	352.237i	−0.710235	−	0.410054i	0.100913	−	0.994895i	$-0.467824\pi$
$859$	−610.092	−	352.237i	−0.710235	−	0.410054i	−0.811148	+	0.584841i	$0.801157\pi$
$860$	−449.736	−	259.655i	−0.522949	−	0.301925i
$861$		0			0
$862$	143.635	+	248.783i	0.166630	+	0.288612i
$863$	−550.428			−0.637807			−0.318904	−	0.947787i	$-0.603315\pi$
$863$	−550.428			−0.637807			−0.318904	+	0.947787i	$0.603315\pi$
$864$	−523.931	−	166.233i	−0.606402	−	0.192399i
$865$	−367.362			−0.424696
$866$	−88.2976	+	50.9786i	−0.101960	+	0.0588668i
$867$	144.297	+	1997.28i	0.166433	+	2.30367i
$868$		0			0
$869$	3.39070	−	5.87287i	0.00390184	−	0.00675819i
$870$	−48.8053	−	71.9977i	−0.0560980	−	0.0827560i
$871$	−177.167	+	102.287i	−0.203406	+	0.117437i
$872$	88.5585			0.101558
$873$	574.174	−	452.879i	0.657703	−	0.518761i
$874$		−	394.745i		−	0.451653i
$875$		0			0
$876$	−164.015	+	338.261i	−0.187232	+	0.386142i
$877$	−11.2603	+	19.5034i	−0.0128396	+	0.0222388i	−0.872374	−	0.488839i	$-0.837420\pi$
$877$	−11.2603	+	19.5034i	−0.0128396	+	0.0222388i	0.859534	+	0.511078i	$0.170754\pi$
$878$	89.6220	+	51.7433i	0.102075	+	0.0589331i
$879$	520.774	−	1074.03i	0.592462	−	1.22188i
$880$	7.15358	−	4.13012i	0.00812906	−	0.00469332i
$881$		−	443.014i		−	0.502854i	−0.967876	−	0.251427i	$-0.919100\pi$
$881$		−	443.014i		−	0.502854i	0.967876	−	0.251427i	$-0.0808998\pi$
$882$		0			0
$883$	331.418			0.375332			0.187666	−	0.982233i	$-0.439908\pi$
$883$	331.418			0.375332			0.187666	+	0.982233i	$0.439908\pi$
$884$	−115.866	−	200.686i	−0.131070	−	0.227021i
$885$	720.504	−	488.410i	0.814129	−	0.551875i
$886$	−21.4109	+	37.0847i	−0.0241658	+	0.0418564i
$887$	328.087	+	189.421i	0.369883	+	0.213552i	0.673408	−	0.739271i	$-0.264830\pi$
$887$	328.087	+	189.421i	0.369883	+	0.213552i	−0.303524	+	0.952824i	$0.598163\pi$
$888$	11.8581	+	164.134i	0.0133538	+	0.184835i
$889$		0			0
$890$	76.1343			0.0855441
$891$	8.19454	+	7.76843i	0.00919701	+	0.00871878i
$892$		−	623.228i		−	0.698686i
$893$	−975.619	−	1689.82i	−1.09252	−	1.89230i
$894$	19.8577	+	274.859i	0.0222122	+	0.307449i
$895$	−1326.44	−	765.820i	−1.48206	−	0.855665i
$896$		0			0
$897$	99.0257	+	146.083i	0.110397	+	0.162857i
$898$	66.8358	+	115.763i	0.0744274	+	0.128912i
$899$		−	114.874i		−	0.127780i
$900$	199.174	−	28.9304i	0.221304	−	0.0321448i
$901$			1047.11i			1.16216i
$902$	−0.0474123	+	0.0273735i	−5.25635e−5	+	3.03476e-5i
$903$		0			0
$904$	178.268	−	308.769i	0.197199	−	0.341558i
$905$	301.693	−	522.548i	0.333363	−	0.577402i
$906$	−131.991	−	63.9998i	−0.145686	−	0.0706400i
$907$	196.898	+	341.037i	0.217087	+	0.376006i	0.953916	−	0.300073i	$-0.0970111\pi$
$907$	196.898	+	341.037i	0.217087	+	0.376006i	−0.736829	+	0.676079i	$0.763678\pi$
$908$			432.107i			0.475888i
$909$	179.541	−	141.613i	0.197515	−	0.155790i
$910$		0			0
$911$	571.193	+	989.335i	0.626995	+	1.08599i	0.988151	+	0.153482i	$0.0490488\pi$
$911$	571.193	+	989.335i	0.626995	+	1.08599i	−0.361156	+	0.932505i	$0.617618\pi$
$912$	664.641	+	980.481i	0.728773	+	1.07509i
$913$	14.3436	+	8.28127i	0.0157104	+	0.00907039i
$914$	64.6371	−	111.955i	0.0707189	−	0.122489i
$915$	39.1988	+	542.568i	0.0428402	+	0.592970i
$916$	−599.921	+	346.365i	−0.654936	+	0.378127i
$917$		0			0
$918$	−256.265	−	280.678i	−0.279156	−	0.305749i
$919$	−375.149			−0.408214			−0.204107	−	0.978949i	$-0.565429\pi$
$919$	−375.149			−0.408214			−0.204107	+	0.978949i	$0.565429\pi$
$920$	399.802	−	230.826i	0.434568	−	0.250898i
$921$	796.454	−	57.5413i	0.864770	−	0.0624770i
$922$	256.480	+	148.079i	0.278178	+	0.160606i
$923$	147.930	+	85.4073i	0.160271	+	0.0925323i
$924$		0			0
$925$	−45.5915	−	78.9668i	−0.0492881	−	0.0853695i
$926$	195.716			0.211357
$927$	−921.483	−	367.364i	−0.994048	−	0.396293i
$928$	−296.703			−0.319723
$929$	56.1689	−	32.4291i	0.0604617	−	0.0349076i	−0.469464	−	0.882951i	$-0.655553\pi$
$929$	56.1689	−	32.4291i	0.0604617	−	0.0349076i	0.529926	+	0.848044i	$0.322220\pi$
$930$	42.3277	+	20.5238i	0.0455137	+	0.0220686i
$931$		0			0
$932$	−481.216	+	833.490i	−0.516326	+	0.894303i
$933$	166.584	−	343.557i	0.178546	−	0.368229i
$934$	98.7224	−	56.9974i	0.105699	−	0.0610251i
$935$	18.8439			0.0201539
$936$	58.5796	+	23.3537i	0.0625850	+	0.0249505i
$937$			1198.08i			1.27863i	0.768944	+	0.639316i	$0.220783\pi$
$937$			1198.08i			1.27863i	−0.768944	+	0.639316i	$0.779217\pi$
$938$		0			0
$939$	−840.325	−	1239.65i	−0.894915	−	1.32018i
$940$	555.325	−	961.851i	0.590771	−	1.02325i
$941$	−671.665	−	387.786i	−0.713778	−	0.412100i	0.0986805	−	0.995119i	$-0.468538\pi$
$941$	−671.665	−	387.786i	−0.713778	−	0.412100i	−0.812458	+	0.583019i	$0.801871\pi$
$942$	−136.058	+	9.82973i	−0.144435	+	0.0104350i
$943$	22.2519	−	12.8472i	0.0235969	−	0.0136237i
$944$		−	899.952i		−	0.953339i
$945$		0			0
$946$	−1.98758			−0.00210104
$947$	424.142	+	734.636i	0.447880	+	0.775751i	0.998248	−	0.0591714i	$-0.0188458\pi$
$947$	424.142	+	734.636i	0.447880	+	0.775751i	−0.550368	+	0.834922i	$0.685513\pi$
$948$	39.8864	+	552.085i	0.0420743	+	0.582369i
$949$	32.6340	−	56.5237i	0.0343878	−	0.0595614i
$950$	67.6869	+	39.0791i	0.0712494	+	0.0411359i
$951$	−488.999	+	331.479i	−0.514195	+	0.348558i
$952$		0			0
$953$	−846.104			−0.887832			−0.443916	−	0.896068i	$-0.646411\pi$
$953$	−846.104			−0.887832			−0.443916	+	0.896068i	$0.646411\pi$
$954$	−85.8902	−	108.894i	−0.0900317	−	0.114145i
$955$			1268.08i			1.32783i
$956$	−249.174	−	431.583i	−0.260643	−	0.451447i
$957$	5.48429	+	2.65921i	0.00573071	+	0.00277870i
$958$	211.017	+	121.831i	0.220268	+	0.127172i
$959$		0			0
$960$	−257.222	+	530.487i	−0.267939	+	0.552590i
$961$	−449.437	−	778.447i	−0.467676	−	0.810039i
$962$		−	13.9057i		−	0.0144550i
$963$	−1396.88	+	202.899i	−1.45055	+	0.210695i
$964$		−	987.929i		−	1.02482i
$965$	834.568	−	481.838i	0.864837	−	0.499314i
$966$		0			0
$967$	84.2016	−	145.842i	0.0870751	−	0.150819i	−0.819198	−	0.573510i	$-0.805581\pi$
$967$	84.2016	−	145.842i	0.0870751	−	0.150819i	0.906274	+	0.422692i	$0.138915\pi$
$968$	−214.554	+	371.619i	−0.221647	+	0.383904i
$969$	194.720	+	2695.20i	0.200949	+	2.78143i
$970$	80.8223	+	139.988i	0.0833219	+	0.144318i
$971$			1029.28i			1.06002i	0.847992	+	0.530010i	$0.177812\pi$
$971$			1029.28i			1.06002i	−0.847992	+	0.530010i	$0.822188\pi$
$972$	−909.444	−	149.558i	−0.935642	−	0.153866i
$973$		0			0
$974$	−166.902	−	289.083i	−0.171358	−	0.296800i
$975$	−34.8523	+	2.51797i	−0.0357459	+	0.00258253i
$976$	487.073	+	281.212i	0.499050	+	0.288127i
$977$	−486.819	+	843.195i	−0.498279	+	0.863045i	−0.999998	−	0.00198578i	$-0.999368\pi$
$977$	−486.819	+	843.195i	−0.498279	+	0.863045i	0.501719	+	0.865031i	$0.332701\pi$
$978$	−141.154	+	95.6847i	−0.144330	+	0.0978371i
$979$	−4.62020	+	2.66748i	−0.00471931	+	0.00272469i
$980$		0			0
$981$	222.376	−	32.3005i	0.226683	−	0.0329261i
$982$	63.1853			0.0643435
$983$	−530.517	+	306.294i	−0.539692	+	0.311591i	−0.744954	−	0.667116i	$-0.767529\pi$
$983$	−530.517	+	306.294i	−0.539692	+	0.311591i	0.205262	+	0.978707i	$0.434195\pi$
$984$	4.00580	−	8.26146i	0.00407094	−	0.00839579i
$985$	448.282	+	258.815i	0.455108	+	0.262757i
$986$	−177.669	−	102.577i	−0.180191	−	0.104034i
$987$		0			0
$988$	−109.113	−	188.989i	−0.110438	−	0.191284i
$989$	932.829			0.943204
$990$	−1.95969	+	1.54570i	−0.00197948	+	0.00156131i
$991$	−205.562			−0.207429			−0.103714	−	0.994607i	$-0.533073\pi$
$991$	−205.562			−0.207429			−0.103714	+	0.994607i	$0.533073\pi$
$992$	138.966	−	80.2318i	0.140086	−	0.0808788i
$993$	−478.600	+	324.429i	−0.481973	+	0.326716i
$994$		0			0
$995$	383.963	−	665.043i	0.385892	−	0.668385i
$996$	−1348.38	+	97.4165i	−1.35380	+	0.0978078i
$997$	−197.186	+	113.845i	−0.197779	+	0.114188i	−0.595619	−	0.803267i	$-0.703093\pi$
$997$	−197.186	+	113.845i	−0.197779	+	0.114188i	0.397840	+	0.917455i	$0.369760\pi$
$998$	−43.6307			−0.0437182
$999$	89.6420	+	407.824i	0.0897317	+	0.408232i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.l.b.391.6		28
7.2	even	3		441.3.k.b.31.6		28
7.3	odd	6		441.3.t.a.166.9		28
7.4	even	3		63.3.t.a.40.9	yes	28
7.5	odd	6		63.3.k.a.31.6	✓	28
7.6	odd	2		441.3.l.a.391.6		28
9.7	even	3		441.3.l.a.97.6		28
21.5	even	6		189.3.k.a.10.9		28
21.11	odd	6		189.3.t.a.145.6		28
63.11	odd	6		189.3.k.a.19.9		28
63.16	even	3		441.3.t.a.178.9		28
63.25	even	3		63.3.k.a.61.6	yes	28
63.34	odd	6	inner	441.3.l.b.97.6		28
63.47	even	6		189.3.t.a.73.6		28
63.52	odd	6		441.3.k.b.313.6		28
63.61	odd	6		63.3.t.a.52.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.6	✓	28	7.5	odd	6
63.3.k.a.61.6	yes	28	63.25	even	3
63.3.t.a.40.9	yes	28	7.4	even	3
63.3.t.a.52.9	yes	28	63.61	odd	6
189.3.k.a.10.9		28	21.5	even	6
189.3.k.a.19.9		28	63.11	odd	6
189.3.t.a.73.6		28	63.47	even	6
189.3.t.a.145.6		28	21.11	odd	6
441.3.k.b.31.6		28	7.2	even	3
441.3.k.b.313.6		28	63.52	odd	6
441.3.l.a.97.6		28	9.7	even	3
441.3.l.a.391.6		28	7.6	odd	2
441.3.l.b.97.6		28	63.34	odd	6	inner
441.3.l.b.391.6		28	1.1	even	1	trivial
441.3.t.a.166.9		28	7.3	odd	6
441.3.t.a.178.9		28	63.16	even	3

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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	441.3.l.b.391.6

Level	$441$
Weight	$3$
Character	441.391
Analytic conductor	$12.016$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$