LMFDB - Embedded newform 220.3.i.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99978 - 0.0293959i) q^{2} +(1.37211 - 1.37211i) q^{3} +(3.99827 + 0.117571i) q^{4} +(-3.60976 - 3.45972i) q^{5} +(-2.78426 + 2.70359i) q^{6} +(-5.40554 + 5.40554i) q^{7} +(-7.99222 - 0.352649i) q^{8} +5.23463i q^{9} +(7.11703 + 7.02480i) q^{10} +(9.66660 + 5.24946i) q^{11} +(5.64738 - 5.32474i) q^{12} +(-13.3652 + 13.3652i) q^{13} +(10.9688 - 10.6510i) q^{14} +(-9.70009 + 0.205868i) q^{15} +(15.9724 + 0.940160i) q^{16} +(15.7700 + 15.7700i) q^{17} +(0.153877 - 10.4681i) q^{18} -23.8438i q^{19} +(-14.0260 - 14.2573i) q^{20} +14.8340i q^{21} +(-19.1768 - 10.7819i) q^{22} +(12.0954 - 12.0954i) q^{23} +(-11.4501 + 10.4823i) q^{24} +(1.06069 + 24.9775i) q^{25} +(27.1204 - 26.3346i) q^{26} +(19.5315 + 19.5315i) q^{27} +(-22.2484 + 20.9773i) q^{28} +2.11593 q^{29} +(19.4041 - 0.126548i) q^{30} +42.9394i q^{31} +(-31.9136 - 2.34964i) q^{32} +(20.4665 - 6.06080i) q^{33} +(-31.0730 - 32.0002i) q^{34} +(38.2144 - 0.811033i) q^{35} +(-0.615440 + 20.9295i) q^{36} +(-44.9716 + 44.9716i) q^{37} +(-0.700909 + 47.6824i) q^{38} +36.6770i q^{39} +(27.6299 + 28.9238i) q^{40} +13.2125i q^{41} +(0.436058 - 29.6648i) q^{42} +(-7.16475 - 7.16475i) q^{43} +(38.0325 + 22.1253i) q^{44} +(18.1104 - 18.8958i) q^{45} +(-24.5436 + 23.8325i) q^{46} +(26.0810 + 26.0810i) q^{47} +(23.2058 - 20.6258i) q^{48} -9.43982i q^{49} +(-1.38691 - 49.9808i) q^{50} +43.2763 q^{51} +(-55.0090 + 51.8663i) q^{52} +(-58.6533 - 58.6533i) q^{53} +(-38.4846 - 39.6329i) q^{54} +(-16.7324 - 52.3930i) q^{55} +(45.1086 - 41.2961i) q^{56} +(-32.7163 - 32.7163i) q^{57} +(-4.23141 - 0.0621997i) q^{58} -9.53643 q^{59} +(-38.8078 - 0.317333i) q^{60} -26.3635i q^{61} +(1.26224 - 85.8695i) q^{62} +(-28.2961 - 28.2961i) q^{63} +(63.7513 + 5.63690i) q^{64} +(94.4848 - 2.00528i) q^{65} +(-41.1067 + 11.5187i) q^{66} +(-48.5492 - 48.5492i) q^{67} +(61.1987 + 64.9069i) q^{68} -33.1923i q^{69} +(-76.4443 + 0.498547i) q^{70} +87.4983i q^{71} +(1.84599 - 41.8364i) q^{72} +(-64.7527 + 64.7527i) q^{73} +(91.2554 - 88.6114i) q^{74} +(35.7272 + 32.8165i) q^{75} +(2.80333 - 95.3339i) q^{76} +(-80.6294 + 23.8771i) q^{77} +(1.07815 - 73.3460i) q^{78} -33.6837i q^{79} +(-54.4036 - 58.6536i) q^{80} +6.48689 q^{81} +(0.388394 - 26.4222i) q^{82} +(24.7484 + 24.7484i) q^{83} +(-1.74404 + 59.3103i) q^{84} +(-2.36609 - 111.486i) q^{85} +(14.1173 + 14.5386i) q^{86} +(2.90329 - 2.90329i) q^{87} +(-75.4064 - 45.3637i) q^{88} -90.0902i q^{89} +(-36.7723 + 37.2551i) q^{90} -144.492i q^{91} +(49.7826 - 46.9384i) q^{92} +(58.9175 + 58.9175i) q^{93} +(-51.3897 - 52.9231i) q^{94} +(-82.4928 + 86.0703i) q^{95} +(-47.0129 + 40.5650i) q^{96} +(-76.9803 + 76.9803i) q^{97} +(-0.277492 + 18.8776i) q^{98} +(-27.4790 + 50.6011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.99978	−	0.0293959i	−0.999892	−	0.0146979i
$2$	−1.99978	−	0.0293959i	−0.999892	−	0.0146979i
$3$	1.37211	−	1.37211i	0.457370	−	0.457370i	−0.440422	−	0.897791i	$-0.645171\pi$
$3$	1.37211	−	1.37211i	0.457370	−	0.457370i	0.897791	+	0.440422i	$0.145171\pi$
$4$	3.99827	+	0.117571i	0.999568	+	0.0293927i
$5$	−3.60976	−	3.45972i	−0.721951	−	0.691944i
$5$	−3.60976	−	3.45972i	−0.721951	−	0.691944i
$6$	−2.78426	+	2.70359i	−0.464043	+	0.450598i
$7$	−5.40554	+	5.40554i	−0.772221	+	0.772221i	−0.978494	−	0.206274i	$-0.933866\pi$
$7$	−5.40554	+	5.40554i	−0.772221	+	0.772221i	0.206274	+	0.978494i	$0.433866\pi$
$8$	−7.99222	−	0.352649i	−0.999028	−	0.0440811i
$9$			5.23463i			0.581626i
$10$	7.11703	+	7.02480i	0.711703	+	0.702480i
$11$	9.66660	+	5.24946i	0.878782	+	0.477223i
$11$	9.66660	+	5.24946i	0.878782	+	0.477223i
$12$	5.64738	−	5.32474i	0.470615	−	0.443729i
$13$	−13.3652	+	13.3652i	−1.02809	+	1.02809i	−0.0284970	+	0.999594i	$0.509072\pi$
$13$	−13.3652	+	13.3652i	−1.02809	+	1.02809i	−0.999594	+	0.0284970i	$0.990928\pi$
$14$	10.9688	−	10.6510i	0.783487	−	0.760787i
$15$	−9.70009	+	0.205868i	−0.646673	+	0.0137245i
$16$	15.9724	+	0.940160i	0.998272	+	0.0587600i
$17$	15.7700	+	15.7700i	0.927648	+	0.927648i	0.997554	−	0.0699058i	$-0.0222699\pi$
$17$	15.7700	+	15.7700i	0.927648	+	0.927648i	−0.0699058	+	0.997554i	$0.522270\pi$
$18$	0.153877	−	10.4681i	0.00854870	−	0.581563i
$19$		−	23.8438i		−	1.25494i	−0.778642	−	0.627468i	$-0.784091\pi$
$19$		−	23.8438i		−	1.25494i	0.778642	−	0.627468i	$-0.215909\pi$
$20$	−14.0260	−	14.2573i	−0.701301	−	0.712865i
$21$			14.8340i			0.706381i
$22$	−19.1768	−	10.7819i	−0.871673	−	0.490088i
$23$	12.0954	−	12.0954i	0.525885	−	0.525885i	−0.393458	−	0.919343i	$-0.628721\pi$
$23$	12.0954	−	12.0954i	0.525885	−	0.525885i	0.919343	+	0.393458i	$0.128721\pi$
$24$	−11.4501	+	10.4823i	−0.477086	+	0.436764i
$25$	1.06069	+	24.9775i	0.0424274	+	0.999100i
$26$	27.1204	−	26.3346i	1.04309	−	1.01287i
$27$	19.5315	+	19.5315i	0.723388	+	0.723388i
$28$	−22.2484	+	20.9773i	−0.794585	+	0.749189i
$29$	2.11593			0.0729633			0.0364816	−	0.999334i	$-0.488385\pi$
$29$	2.11593			0.0729633			0.0364816	+	0.999334i	$0.488385\pi$
$30$	19.4041	−	0.126548i	0.646805	−	0.00421827i
$31$			42.9394i			1.38514i	0.721350	+	0.692571i	$0.243522\pi$
$31$			42.9394i			1.38514i	−0.721350	+	0.692571i	$0.756478\pi$
$32$	−31.9136	−	2.34964i	−0.997301	−	0.0734262i
$33$	20.4665	−	6.06080i	0.620196	−	0.183661i
$34$	−31.0730	−	32.0002i	−0.913913	−	0.941182i
$35$	38.2144	−	0.811033i	1.09184	−	0.0231724i
$36$	−0.615440	+	20.9295i	−0.0170956	+	0.581375i
$37$	−44.9716	+	44.9716i	−1.21545	+	1.21545i	−0.246239	+	0.969209i	$0.579195\pi$
$37$	−44.9716	+	44.9716i	−1.21545	+	1.21545i	−0.969209	+	0.246239i	$0.920805\pi$
$38$	−0.700909	+	47.6824i	−0.0184450	+	1.25480i
$39$			36.6770i			0.940435i
$40$	27.6299	+	28.9238i	0.690748	+	0.723096i
$41$			13.2125i			0.322257i	0.986933	+	0.161128i	$0.0515133\pi$
$41$			13.2125i			0.322257i	−0.986933	+	0.161128i	$0.948487\pi$
$42$	0.436058	−	29.6648i	0.0103823	−	0.706304i
$43$	−7.16475	−	7.16475i	−0.166622	−	0.166622i	0.618871	−	0.785493i	$-0.287590\pi$
$43$	−7.16475	−	7.16475i	−0.166622	−	0.166622i	−0.785493	+	0.618871i	$0.787590\pi$
$44$	38.0325	+	22.1253i	0.864375	+	0.502847i
$45$	18.1104	−	18.8958i	0.402453	−	0.419906i
$46$	−24.5436	+	23.8325i	−0.533557	+	0.518099i
$47$	26.0810	+	26.0810i	0.554915	+	0.554915i	0.927855	−	0.372940i	$-0.121650\pi$
$47$	26.0810	+	26.0810i	0.554915	+	0.554915i	−0.372940	+	0.927855i	$0.621650\pi$
$48$	23.2058	−	20.6258i	0.483454	−	0.429704i
$49$		−	9.43982i		−	0.192649i
$50$	−1.38691	−	49.9808i	−0.0277381	−	0.999615i
$51$	43.2763			0.848556
$52$	−55.0090	+	51.8663i	−1.05787	+	0.997428i
$53$	−58.6533	−	58.6533i	−1.10667	−	1.10667i	−0.993586	−	0.113080i	$-0.963928\pi$
$53$	−58.6533	−	58.6533i	−1.10667	−	1.10667i	−0.113080	−	0.993586i	$-0.536072\pi$
$54$	−38.4846	−	39.6329i	−0.712677	−	0.733942i
$55$	−16.7324	−	52.3930i	−0.304226	−	0.952600i
$56$	45.1086	−	41.2961i	0.805510	−	0.737430i
$57$	−32.7163	−	32.7163i	−0.573970	−	0.573970i
$58$	−4.23141	−	0.0621997i	−0.0729554	−	0.00107241i
$59$	−9.53643			−0.161634			−0.0808172	−	0.996729i	$-0.525753\pi$
$59$	−9.53643			−0.161634			−0.0808172	+	0.996729i	$0.525753\pi$
$60$	−38.8078	−	0.317333i	−0.646797	−	0.00528888i
$61$		−	26.3635i		−	0.432188i	−0.976373	−	0.216094i	$-0.930668\pi$
$61$		−	26.3635i		−	0.432188i	0.976373	−	0.216094i	$-0.0693318\pi$
$62$	1.26224	−	85.8695i	0.0203587	−	1.38499i
$63$	−28.2961	−	28.2961i	−0.449144	−	0.449144i
$64$	63.7513	+	5.63690i	0.996114	+	0.0880765i
$65$	94.4848	−	2.00528i	1.45361	−	0.0308504i
$66$	−41.1067	+	11.5187i	−0.622828	+	0.174525i
$67$	−48.5492	−	48.5492i	−0.724615	−	0.724615i	0.244926	−	0.969542i	$-0.421236\pi$
$67$	−48.5492	−	48.5492i	−0.724615	−	0.724615i	−0.969542	+	0.244926i	$0.921236\pi$
$68$	61.1987	+	64.9069i	0.899981	+	0.954513i
$69$		−	33.1923i		−	0.481047i
$70$	−76.4443	+	0.498547i	−1.09206	+	0.00712210i
$71$			87.4983i			1.23237i	0.787601	+	0.616185i	$0.211323\pi$
$71$			87.4983i			1.23237i	−0.787601	+	0.616185i	$0.788677\pi$
$72$	1.84599	−	41.8364i	0.0256387	−	0.581061i
$73$	−64.7527	+	64.7527i	−0.887024	+	0.887024i	−0.994236	−	0.107212i	$-0.965808\pi$
$73$	−64.7527	+	64.7527i	−0.887024	+	0.887024i	0.107212	+	0.994236i	$0.465808\pi$
$74$	91.2554	−	88.6114i	1.23318	−	1.19745i
$75$	35.7272	+	32.8165i	0.476363	+	0.437553i
$76$	2.80333	−	95.3339i	0.0368860	−	1.25439i
$77$	−80.6294	+	23.8771i	−1.04714	+	0.310092i
$78$	1.07815	−	73.3460i	0.0138225	−	0.940333i
$79$		−	33.6837i		−	0.426376i	−0.977011	−	0.213188i	$-0.931615\pi$
$79$		−	33.6837i		−	0.426376i	0.977011	−	0.213188i	$-0.0683846\pi$
$80$	−54.4036	−	58.6536i	−0.680045	−	0.733170i
$81$	6.48689			0.0800850
$82$	0.388394	−	26.4222i	0.00473651	−	0.322222i
$83$	24.7484	+	24.7484i	0.298173	+	0.298173i	0.840298	−	0.542125i	$-0.182380\pi$
$83$	24.7484	+	24.7484i	0.298173	+	0.298173i	−0.542125	+	0.840298i	$0.682380\pi$
$84$	−1.74404	+	59.3103i	−0.0207624	+	0.706075i
$85$	−2.36609	−	111.486i	−0.0278364	−	1.31160i
$86$	14.1173	+	14.5386i	0.164155	+	0.169053i
$87$	2.90329	−	2.90329i	0.0333712	−	0.0333712i
$88$	−75.4064	−	45.3637i	−0.856891	−	0.515497i
$89$		−	90.0902i		−	1.01225i	−0.862460	−	0.506125i	$-0.831077\pi$
$89$		−	90.0902i		−	1.01225i	0.862460	−	0.506125i	$-0.168923\pi$
$90$	−36.7723	+	37.2551i	−0.408581	+	0.413945i
$91$		−	144.492i		−	1.58783i
$92$	49.7826	−	46.9384i	0.541115	−	0.510200i
$93$	58.9175	+	58.9175i	0.633522	+	0.633522i
$94$	−51.3897	−	52.9231i	−0.546699	−	0.563011i
$95$	−82.4928	+	86.0703i	−0.868345	+	0.906003i
$96$	−47.0129	+	40.5650i	−0.489718	+	0.422552i
$97$	−76.9803	+	76.9803i	−0.793612	+	0.793612i	−0.982079	−	0.188468i	$-0.939648\pi$
$97$	−76.9803	+	76.9803i	−0.793612	+	0.793612i	0.188468	+	0.982079i	$0.439648\pi$
$98$	−0.277492	+	18.8776i	−0.00283155	+	0.192629i
$99$	−27.4790	+	50.6011i	−0.277566	+	0.511123i
$100$	1.30429	+	99.9915i	0.0130429	+	0.999915i
$101$			66.4437i			0.657858i	0.944355	+	0.328929i	$0.106688\pi$
$101$			66.4437i			0.657858i	−0.944355	+	0.328929i	$0.893312\pi$
$102$	−86.5433	−	1.27215i	−0.848464	−	0.0124720i
$103$	120.065	−	120.065i	1.16568	−	1.16568i	0.182469	−	0.983212i	$-0.441591\pi$
$103$	120.065	−	120.065i	1.16568	−	1.16568i	0.983212	−	0.182469i	$-0.0584090\pi$
$104$	111.531	−	102.104i	1.07241	−	0.981772i
$105$	51.3214	−	53.5471i	0.488776	−	0.509972i
$106$	115.570	+	119.018i	1.09028	+	1.12281i
$107$	100.381	−	100.381i	0.938136	−	0.938136i	−0.0600584	−	0.998195i	$-0.519129\pi$
$107$	100.381	−	100.381i	0.938136	−	0.938136i	0.998195	+	0.0600584i	$0.0191287\pi$
$108$	75.7958	+	80.3884i	0.701813	+	0.744337i
$109$	131.082			1.20259			0.601293	−	0.799029i	$-0.294652\pi$
$109$	131.082			1.20259			0.601293	+	0.799029i	$0.294652\pi$
$110$	31.9211	+	105.267i	0.290192	+	0.956968i
$111$			123.412i			1.11182i
$112$	−91.4213	+	81.2572i	−0.816262	+	0.725511i
$113$	18.1645	+	18.1645i	0.160748	+	0.160748i	0.782898	−	0.622150i	$-0.213741\pi$
$113$	18.1645	+	18.1645i	0.160748	+	0.160748i	−0.622150	+	0.782898i	$0.713741\pi$
$114$	64.4638	+	66.3872i	0.565472	+	0.582344i
$115$	−85.5078	+	1.81475i	−0.743546	+	0.0157805i
$116$	8.46008	+	0.248772i	0.0729317	+	0.00214459i
$117$	−69.9618	−	69.9618i	−0.597964	−	0.597964i
$118$	19.0708	+	0.280332i	0.161617	+	0.00237569i
$119$	−170.491			−1.43270
$120$	77.5979	+	1.77539i	0.646649	+	0.0147949i
$121$	65.8864	+	101.489i	0.544516	+	0.838751i
$122$	−0.774978	+	52.7213i	−0.00635228	+	0.432142i
$123$	18.1290	+	18.1290i	0.147390	+	0.147390i
$124$	−5.04842	+	171.683i	−0.0407131	+	1.38454i
$125$	82.5863	−	93.8323i	0.660690	−	0.750659i
$126$	55.7542	+	57.4178i	0.442494	+	0.455697i
$127$	−28.3396	+	28.3396i	−0.223147	+	0.223147i	−0.809822	−	0.586675i	$-0.800436\pi$
$127$	−28.3396	+	28.3396i	−0.223147	+	0.223147i	0.586675	+	0.809822i	$0.300436\pi$
$128$	−127.323	−	13.1466i	−0.994712	−	0.102708i
$129$	−19.6616			−0.152416
$130$	−189.008	+	1.23266i	−1.45391	+	0.00948197i
$131$	−118.186			−0.902180			−0.451090	−	0.892478i	$-0.648965\pi$
$131$	−118.186			−0.902180			−0.451090	+	0.892478i	$0.648965\pi$
$132$	82.5430	−	21.8265i	0.625326	−	0.165352i
$133$	128.889	+	128.889i	0.969088	+	0.969088i
$134$	95.6608	+	98.5151i	0.713887	+	0.735187i
$135$	−2.93045	−	138.077i	−0.0217070	−	1.02279i
$136$	−120.476	−	131.599i	−0.885854	−	0.967638i
$137$	79.6269	−	79.6269i	0.581218	−	0.581218i	−0.354020	−	0.935238i	$-0.615185\pi$
$137$	79.6269	−	79.6269i	0.581218	−	0.581218i	0.935238	+	0.354020i	$0.115185\pi$
$138$	−0.975716	+	66.3774i	−0.00707040	+	0.480996i
$139$			197.163i			1.41844i	0.704987	+	0.709220i	$0.250953\pi$
$139$			197.163i			1.41844i	−0.704987	+	0.709220i	$0.749047\pi$
$140$	152.887	+	1.25016i	1.09205	+	0.00892972i
$141$	71.5720			0.507603
$142$	2.57209	−	174.978i	0.0181133	−	1.23224i
$143$	−199.356	+	59.0360i	−1.39410	+	0.412839i
$144$	−4.92139	+	83.6094i	−0.0341763	+	0.580621i
$145$	−7.63801	−	7.32054i	−0.0526759	−	0.0504865i
$146$	131.395	−	127.588i	0.899965	−	0.873891i
$147$	−12.9525	−	12.9525i	−0.0881120	−	0.0881120i
$148$	−185.096	+	174.521i	−1.25065	+	1.17920i
$149$	−200.045			−1.34258			−0.671292	−	0.741193i	$-0.734260\pi$
$149$	−200.045			−1.34258			−0.671292	+	0.741193i	$0.734260\pi$
$150$	−70.4820	−	66.6761i	−0.469880	−	0.444507i
$151$	−20.3944			−0.135062			−0.0675312	−	0.997717i	$-0.521512\pi$
$151$	−20.3944			−0.135062			−0.0675312	+	0.997717i	$0.521512\pi$
$152$	−8.40848	+	190.565i	−0.0553190	+	1.25372i
$153$	−82.5503	+	82.5503i	−0.539544	+	0.539544i
$154$	161.943	−	45.3788i	1.05158	−	0.294668i
$155$	148.558	−	155.001i	0.958441	−	1.00001i
$156$	−4.31214	+	146.644i	−0.0276419	+	0.940029i
$157$	58.6993	−	58.6993i	0.373881	−	0.373881i	−0.495008	−	0.868889i	$-0.664835\pi$
$157$	58.6993	−	58.6993i	0.373881	−	0.373881i	0.868889	+	0.495008i	$0.164835\pi$
$158$	−0.990161	+	67.3601i	−0.00626684	+	0.426330i
$159$	−160.957			−1.01231
$160$	107.071	+	118.894i	0.669196	+	0.743086i
$161$			130.764i			0.812198i
$162$	−12.9724	−	0.190688i	−0.0800764	−	0.00117708i
$163$	69.4946	−	69.4946i	0.426347	−	0.426347i	−0.461035	−	0.887382i	$-0.652522\pi$
$163$	69.4946	−	69.4946i	0.426347	−	0.426347i	0.887382	+	0.461035i	$0.152522\pi$
$164$	−1.55341	+	52.8273i	−0.00947199	+	0.322117i
$165$	−94.8476	−	48.9302i	−0.574834	−	0.296546i
$166$	−48.7639	−	50.2189i	−0.293759	−	0.302524i
$167$	9.68845	−	9.68845i	0.0580147	−	0.0580147i	−0.677504	−	0.735519i	$-0.736938\pi$
$167$	9.68845	−	9.68845i	0.0580147	−	0.0580147i	0.735519	+	0.677504i	$0.236938\pi$
$168$	5.23119	−	118.557i	0.0311380	−	0.705694i
$169$		−	188.256i		−	1.11394i
$170$	1.45445	+	223.017i	0.00855559	+	1.31186i
$171$	124.814			0.729904
$172$	−27.8043	−	29.4890i	−0.161653	−	0.171448i
$173$	147.049	−	147.049i	0.849997	−	0.849997i	−0.140136	−	0.990132i	$-0.544754\pi$
$173$	147.049	−	147.049i	0.849997	−	0.849997i	0.990132	+	0.140136i	$0.0447538\pi$
$174$	−5.89130	+	5.72061i	−0.0338581	+	0.0328771i
$175$	−140.751	−	129.283i	−0.804289	−	0.738762i
$176$	149.463	+	92.9343i	0.849222	+	0.528036i
$177$	−13.0850	+	13.0850i	−0.0739266	+	0.0739266i
$178$	−2.64828	+	180.161i	−0.0148780	+	1.01214i
$179$	10.0156			0.0559533			0.0279767	−	0.999609i	$-0.491094\pi$
$179$	10.0156			0.0559533			0.0279767	+	0.999609i	$0.491094\pi$
$180$	74.6318	−	73.4211i	0.414621	−	0.407895i
$181$	−129.338			−0.714576			−0.357288	−	0.933994i	$-0.616299\pi$
$181$	−129.338			−0.714576			−0.357288	+	0.933994i	$0.616299\pi$
$182$	−4.24747	+	288.953i	−0.0233378	+	1.58765i
$183$	−36.1736	−	36.1736i	−0.197670	−	0.197670i
$184$	−100.934	+	92.4033i	−0.548555	+	0.502192i
$185$	317.925	−	6.74741i	1.71852	−	0.0364725i
$186$	−116.090	−	119.554i	−0.624142	−	0.642765i
$187$	69.6584	+	235.226i	0.372505	+	1.25790i
$188$	101.213	+	107.345i	0.538365	+	0.570986i
$189$	−211.156			−1.11723
$190$	167.498	−	169.697i	0.881568	−	0.893142i
$191$		−	309.845i		−	1.62223i	−0.584888	−	0.811114i	$-0.698862\pi$
$191$		−	309.845i		−	1.62223i	0.584888	−	0.811114i	$-0.301138\pi$
$192$	95.2081	−	79.7393i	0.495876	−	0.415309i
$193$	−13.6957	+	13.6957i	−0.0709620	+	0.0709620i	−0.741697	−	0.670735i	$-0.765979\pi$
$193$	−13.6957	+	13.6957i	−0.0709620	+	0.0709620i	0.670735	+	0.741697i	$0.265979\pi$
$194$	156.207	−	151.681i	0.805190	−	0.781862i
$195$	126.892	−	132.395i	0.650728	−	0.678948i
$196$	1.10985	−	37.7430i	0.00566249	−	0.192566i
$197$	238.001	+	238.001i	1.20813	+	1.20813i	0.971632	+	0.236496i	$0.0759991\pi$
$197$	238.001	+	238.001i	1.20813	+	1.20813i	0.236496	+	0.971632i	$0.424001\pi$
$198$	56.4395	−	100.384i	0.285048	−	0.506988i
$199$	29.7932			0.149715			0.0748573	−	0.997194i	$-0.476150\pi$
$199$	29.7932			0.149715			0.0748573	+	0.997194i	$0.476150\pi$
$200$	0.331048	−	200.000i	0.00165524	−	0.999999i
$201$	−133.230			−0.662834
$202$	1.95317	−	132.873i	0.00966916	−	0.657787i
$203$	−11.4378	+	11.4378i	−0.0563437	+	0.0563437i
$204$	173.031	+	5.08803i	0.848189	+	0.0249413i
$205$	45.7116	−	47.6940i	0.222984	−	0.232654i
$206$	−243.634	+	236.575i	−1.18269	+	1.14842i
$207$	63.3147	+	63.3147i	0.305868	+	0.305868i
$208$	−226.039	+	200.908i	−1.08673	+	0.965904i
$209$	125.167	−	230.488i	0.598885	−	1.10282i
$210$	−104.206	+	105.574i	−0.496218	+	0.502733i
$211$	209.002			0.990530			0.495265	−	0.868742i	$-0.335071\pi$
$211$	209.002			0.990530			0.495265	+	0.868742i	$0.335071\pi$
$212$	−227.616	−	241.408i	−1.07366	−	1.13872i
$213$	120.057	+	120.057i	0.563649	+	0.563649i
$214$	−203.690	+	197.789i	−0.951824	+	0.924246i
$215$	1.07498	+	50.6510i	0.00499991	+	0.235586i
$216$	−149.212	−	162.988i	−0.690797	−	0.754572i
$217$	−232.111	−	232.111i	−1.06964	−	1.06964i
$218$	−262.135	−	3.85327i	−1.20246	−	0.0176755i
$219$			177.696i			0.811395i
$220$	−60.7409	−	211.449i	−0.276095	−	0.961130i
$221$	−421.538			−1.90741
$222$	3.62780	−	246.797i	0.0163414	−	1.11170i
$223$	16.9302	−	16.9302i	0.0759202	−	0.0759202i	−0.668127	−	0.744047i	$-0.732904\pi$
$223$	16.9302	−	16.9302i	0.0759202	−	0.0759202i	0.744047	+	0.668127i	$0.232904\pi$
$224$	185.212	−	159.809i	0.826837	−	0.713435i
$225$	−130.748	+	5.55230i	−0.581102	+	0.0246769i
$226$	−35.7912	−	36.8591i	−0.158368	−	0.163093i
$227$	−3.69520	+	3.69520i	−0.0162784	+	0.0162784i	−0.715199	−	0.698921i	$-0.753664\pi$
$227$	−3.69520	+	3.69520i	−0.0162784	+	0.0162784i	0.698921	+	0.715199i	$0.253664\pi$
$228$	−126.962	−	134.655i	−0.556851	−	0.590592i
$229$			210.110i			0.917509i	0.888563	+	0.458755i	$0.151704\pi$
$229$			210.110i			0.917509i	−0.888563	+	0.458755i	$0.848296\pi$
$230$	171.050	−	1.11554i	0.743698	−	0.00485018i
$231$	−77.8704	+	143.394i	−0.337101	+	0.620755i
$232$	−16.9110	−	0.746182i	−0.0728923	−	0.00321630i
$233$	133.713	−	133.713i	0.573875	−	0.573875i	−0.359334	−	0.933209i	$-0.616996\pi$
$233$	133.713	−	133.713i	0.573875	−	0.573875i	0.933209	+	0.359334i	$0.116996\pi$
$234$	137.852	+	141.965i	0.589111	+	0.606689i
$235$	−3.91313	−	184.379i	−0.0166516	−	0.784592i
$236$	−38.1292	−	1.12120i	−0.161565	−	0.00475087i
$237$	−46.2177	−	46.2177i	−0.195011	−	0.195011i
$238$	340.945	+	5.01173i	1.43254	+	0.0210577i
$239$		−	11.3879i		−	0.0476482i	−0.999716	−	0.0238241i	$-0.992416\pi$
$239$		−	11.3879i		−	0.0476482i	0.999716	−	0.0238241i	$-0.00758416\pi$
$240$	−155.127	−	5.83144i	−0.646362	−	0.0242977i
$241$		−	105.735i		−	0.438736i	−0.975642	−	0.219368i	$-0.929600\pi$
$241$		−	105.735i		−	0.438736i	0.975642	−	0.219368i	$-0.0703995\pi$
$242$	−128.775	−	204.893i	−0.532129	−	0.846663i
$243$	−166.882	+	166.882i	−0.686759	+	0.686759i
$244$	3.09958	−	105.408i	0.0127032	−	0.432002i
$245$	−32.6591	+	34.0755i	−0.133303	+	0.139084i
$246$	−35.7212	−	36.7870i	−0.145208	−	0.149541i
$247$	318.677	+	318.677i	1.29019	+	1.29019i
$248$	15.1425	−	343.181i	0.0610586	−	1.38380i
$249$	67.9149			0.272751
$250$	−167.913	+	185.217i	−0.671652	+	0.740867i
$251$			114.817i			0.457440i	0.973492	+	0.228720i	$0.0734540\pi$
$251$			114.817i			0.457440i	−0.973492	+	0.228720i	$0.926546\pi$
$252$	−109.809	−	116.462i	−0.435748	−	0.462151i
$253$	180.415	−	53.4269i	0.713103	−	0.211174i
$254$	57.5062	−	55.8401i	0.226402	−	0.219843i
$255$	−156.217	−	149.724i	−0.612616	−	0.587153i
$256$	254.232	+	30.0331i	0.993095	+	0.117317i
$257$	−214.818	+	214.818i	−0.835869	+	0.835869i	−0.988312	−	0.152443i	$-0.951286\pi$
$257$	−214.818	+	214.818i	−0.835869	+	0.835869i	0.152443	+	0.988312i	$0.451286\pi$
$258$	39.3190	+	0.577971i	0.152399	+	0.00224020i
$259$		−	486.192i		−	1.87719i
$260$	378.012	+	3.09101i	1.45389	+	0.0118885i
$261$			11.0761i			0.0424373i
$262$	236.346	+	3.47417i	0.902083	+	0.0132602i
$263$	62.0971	+	62.0971i	0.236111	+	0.236111i	0.815238	−	0.579127i	$-0.196606\pi$
$263$	62.0971	+	62.0971i	0.236111	+	0.236111i	−0.579127	+	0.815238i	$0.696606\pi$
$264$	−165.710	+	41.2218i	−0.627689	+	0.156143i
$265$	8.80019	+	414.648i	0.0332082	+	1.56471i
$266$	−253.961	−	261.538i	−0.954739	−	0.983227i
$267$	−123.614	−	123.614i	−0.462972	−	0.462972i
$268$	−188.405	−	199.821i	−0.703004	−	0.745600i
$269$		−	141.951i		−	0.527699i	−0.964564	−	0.263849i	$-0.915008\pi$
$269$		−	141.951i		−	0.527699i	0.964564	−	0.263849i	$-0.0849922\pi$
$270$	1.80137	+	276.211i	0.00667172	+	1.02300i
$271$	−57.6866			−0.212866			−0.106433	−	0.994320i	$-0.533943\pi$
$271$	−57.6866			−0.212866			−0.106433	+	0.994320i	$0.533943\pi$
$272$	237.058	+	266.711i	0.871536	+	0.980554i
$273$	−198.259	−	198.259i	−0.726223	−	0.726223i
$274$	−161.577	+	156.896i	−0.589698	+	0.572613i
$275$	−120.865	+	247.015i	−0.439509	+	0.898238i
$276$	3.90244	−	132.712i	0.0141393	−	0.480840i
$277$	287.942	+	287.942i	1.03950	+	1.03950i	0.999187	+	0.0403151i	$0.0128362\pi$
$277$	287.942	+	287.942i	1.03950	+	1.03950i	0.0403151	+	0.999187i	$0.487164\pi$
$278$	5.79578	−	394.284i	0.0208481	−	1.41829i
$279$	−224.772			−0.805635
$280$	−305.704	−	6.99429i	−1.09180	−	0.0249796i
$281$		−	257.615i		−	0.916778i	−0.888752	−	0.458389i	$-0.848427\pi$
$281$		−	257.615i		−	0.916778i	0.888752	−	0.458389i	$-0.151573\pi$
$282$	−143.129	−	2.10392i	−0.507548	−	0.00746071i
$283$	182.273	+	182.273i	0.644074	+	0.644074i	0.951554	−	0.307480i	$-0.0994858\pi$
$283$	182.273	+	182.273i	0.644074	+	0.644074i	−0.307480	+	0.951554i	$0.599486\pi$
$284$	−10.2872	+	349.842i	−0.0362227	+	1.23184i
$285$	4.90866	+	231.287i	0.0172234	+	0.811533i
$286$	400.404	−	112.199i	1.40001	−	0.392304i
$287$	−71.4209	−	71.4209i	−0.248853	−	0.248853i
$288$	12.2995	−	167.056i	0.0427066	−	0.580056i
$289$			208.387i			0.721061i
$290$	15.0592	+	14.8640i	0.0519282	+	0.0512553i
$291$			211.251i			0.725948i
$292$	−266.512	+	251.286i	−0.912713	+	0.860569i
$293$	70.5399	−	70.5399i	0.240750	−	0.240750i	−0.576410	−	0.817161i	$-0.695547\pi$
$293$	70.5399	−	70.5399i	0.240750	−	0.240750i	0.817161	+	0.576410i	$0.195547\pi$
$294$	25.5214	+	26.2829i	0.0868074	+	0.0893975i
$295$	34.4242	+	32.9934i	0.116692	+	0.111842i
$296$	375.282	−	343.564i	1.26784	−	1.16069i
$297$	86.2733	+	291.333i	0.290483	+	0.980918i
$298$	400.047	+	5.88049i	1.34244	+	0.0197332i
$299$			323.313i			1.08131i
$300$	138.989	+	135.410i	0.463296	+	0.451365i
$301$	77.4588			0.257338
$302$	40.7844	+	0.599512i	0.135048	+	0.00198514i
$303$	91.1679	+	91.1679i	0.300884	+	0.300884i
$304$	22.4170	−	380.841i	0.0737400	−	1.25277i
$305$	−91.2103	+	95.1658i	−0.299050	+	0.312019i
$306$	167.509	−	162.656i	0.547416	−	0.531556i
$307$	130.177	−	130.177i	0.424030	−	0.424030i	−0.462558	−	0.886589i	$-0.653068\pi$
$307$	130.177	−	130.177i	0.424030	−	0.424030i	0.886589	+	0.462558i	$0.153068\pi$
$308$	−325.186	+	85.9874i	−1.05580	+	0.279180i
$309$		−	329.485i		−	1.06629i
$310$	−301.641	+	305.601i	−0.973035	+	0.985810i
$311$			429.813i			1.38203i	0.722838	+	0.691017i	$0.242837\pi$
$311$			429.813i			1.38203i	−0.722838	+	0.691017i	$0.757163\pi$
$312$	12.9341	−	293.131i	0.0414554	−	0.939521i
$313$	154.139	+	154.139i	0.492456	+	0.492456i	0.909079	−	0.416623i	$-0.136787\pi$
$313$	154.139	+	154.139i	0.492456	+	0.492456i	−0.416623	+	0.909079i	$0.636787\pi$
$314$	−119.111	+	115.660i	−0.379336	+	0.368345i
$315$	4.24546	+	200.038i	0.0134777	+	0.635042i
$316$	3.96022	−	134.677i	0.0125323	−	0.426192i
$317$	150.396	−	150.396i	0.474435	−	0.474435i	−0.428911	−	0.903347i	$-0.641103\pi$
$317$	150.396	−	150.396i	0.474435	−	0.474435i	0.903347	+	0.428911i	$0.141103\pi$
$318$	321.880	+	4.73148i	1.01220	+	0.0148789i
$319$	20.4539	+	11.1075i	0.0641188	+	0.0348198i
$320$	−210.625	−	240.909i	−0.658202	−	0.752842i
$321$		−	275.466i		−	0.858150i
$322$	3.84392	−	261.500i	0.0119376	−	0.812111i
$323$	376.017	−	376.017i	1.16414	−	1.16414i
$324$	25.9363	+	0.762668i	0.0800504	+	0.00235391i
$325$	−348.005	−	319.652i	−1.07078	−	0.983546i
$326$	−141.017	+	136.931i	−0.432567	+	0.420034i
$327$	179.859	−	179.859i	0.550026	−	0.550026i
$328$	4.65938	−	105.597i	0.0142054	−	0.321943i
$329$	−281.964			−0.857034
$330$	188.236	+	100.638i	0.570413	+	0.304963i
$331$			70.1476i			0.211926i	0.994370	+	0.105963i	$0.0337926\pi$
$331$			70.1476i			0.211926i	−0.994370	+	0.105963i	$0.966207\pi$
$332$	96.0411	+	101.860i	0.289280	+	0.306809i
$333$	−235.410	−	235.410i	−0.706936	−	0.706936i
$334$	−19.6596	+	19.0900i	−0.0588611	+	0.0571557i
$335$	7.28419	+	343.218i	0.0217439	+	1.02453i
$336$	−13.9463	+	236.934i	−0.0415069	+	0.705160i
$337$	240.883	+	240.883i	0.714785	+	0.714785i	0.967532	−	0.252747i	$-0.0813340\pi$
$337$	240.883	+	240.883i	0.714785	+	0.714785i	−0.252747	+	0.967532i	$0.581334\pi$
$338$	−5.53395	+	376.472i	−0.0163726	+	1.11382i
$339$	49.8475			0.147043
$340$	3.64719	−	446.028i	0.0107270	−	1.31185i
$341$	−225.409	+	415.078i	−0.661022	+	1.21724i
$342$	−249.600	−	3.66900i	−0.729825	−	0.0107281i
$343$	−213.844	−	213.844i	−0.623453	−	0.623453i
$344$	54.7357	+	59.7890i	0.159115	+	0.173805i
$345$	−114.836	+	119.816i	−0.332858	+	0.347293i
$346$	−298.390	+	289.744i	−0.862398	+	0.837412i
$347$	364.291	−	364.291i	1.04983	−	1.04983i	0.0511387	−	0.998692i	$-0.483715\pi$
$347$	364.291	−	364.291i	1.04983	−	1.04983i	0.998692	−	0.0511387i	$-0.0162851\pi$
$348$	11.9495	−	11.2668i	0.0343376	−	0.0323759i
$349$	−258.483			−0.740639			−0.370319	−	0.928905i	$-0.620752\pi$
$349$	−258.483			−0.740639			−0.370319	+	0.928905i	$0.620752\pi$
$350$	277.670	+	262.676i	0.793343	+	0.750504i
$351$	−522.083			−1.48742
$352$	−296.162	−	190.242i	−0.841369	−	0.540461i
$353$	−42.8688	−	42.8688i	−0.121441	−	0.121441i	0.643774	−	0.765216i	$-0.277368\pi$
$353$	−42.8688	−	42.8688i	−0.121441	−	0.121441i	−0.765216	+	0.643774i	$0.777368\pi$
$354$	26.5518	−	25.7826i	0.0750052	−	0.0728321i
$355$	302.720	−	315.848i	0.852732	−	0.889712i
$356$	10.5920	−	360.205i	0.0297528	−	1.01181i
$357$	−233.932	+	233.932i	−0.655272	+	0.655272i
$358$	−20.0291	−	0.294419i	−0.0559473	−	0.000822398i
$359$		−	424.185i		−	1.18157i	−0.806828	−	0.590787i	$-0.798817\pi$
$359$		−	424.185i		−	1.18157i	0.806828	−	0.590787i	$-0.201183\pi$
$360$	−151.406	+	144.633i	−0.420571	+	0.401757i
$361$	−207.526			−0.574865
$362$	258.649	+	3.80201i	0.714499	+	0.0105028i
$363$	229.657	+	48.8504i	0.632664	+	0.134574i
$364$	16.9881	−	577.719i	0.0466705	−	1.58714i
$365$	457.768	−	9.71533i	1.25416	−	0.0266173i
$366$	71.2760	+	73.4027i	0.194743	+	0.200554i
$367$	334.946	+	334.946i	0.912659	+	0.912659i	0.996481	−	0.0838218i	$-0.0267127\pi$
$367$	334.946	+	334.946i	0.912659	+	0.912659i	−0.0838218	+	0.996481i	$0.526713\pi$
$368$	204.563	−	181.820i	0.555877	−	0.494075i
$369$	−69.1627			−0.187433
$370$	−635.981	+	4.14768i	−1.71887	+	0.0112099i
$371$	634.106			1.70918
$372$	228.641	+	242.495i	0.614627	+	0.651869i
$373$	−161.062	+	161.062i	−0.431802	+	0.431802i	−0.889241	−	0.457439i	$-0.848767\pi$
$373$	−161.062	+	161.062i	−0.431802	+	0.431802i	0.457439	+	0.889241i	$0.348767\pi$
$374$	−132.387	−	472.450i	−0.353976	−	1.26323i
$375$	−15.4308	−	242.066i	−0.0411488	−	0.645508i
$376$	−199.248	−	217.643i	−0.529915	−	0.578837i
$377$	−28.2799	+	28.2799i	−0.0750129	+	0.0750129i
$378$	422.267	+	6.20713i	1.11711	+	0.0164210i
$379$	−111.445			−0.294050			−0.147025	−	0.989133i	$-0.546970\pi$
$379$	−111.445			−0.294050			−0.147025	+	0.989133i	$0.546970\pi$
$380$	−339.948	+	334.434i	−0.894600	+	0.880088i
$381$			77.7701i			0.204121i
$382$	−9.10818	+	619.624i	−0.0238434	+	1.62205i
$383$	−157.375	+	157.375i	−0.410902	+	0.410902i	−0.882053	−	0.471151i	$-0.843839\pi$
$383$	−157.375	+	157.375i	−0.410902	+	0.410902i	0.471151	+	0.882053i	$0.343839\pi$
$384$	−192.740	+	156.663i	−0.501926	+	0.407975i
$385$	373.661	+	192.765i	0.970547	+	0.500688i
$386$	27.7910	−	26.9858i	0.0719973	−	0.0699113i
$387$	37.5049	−	37.5049i	0.0969118	−	0.0969118i
$388$	−316.839	+	298.738i	−0.816595	+	0.769942i
$389$			36.5877i			0.0940559i	0.998894	+	0.0470279i	$0.0149750\pi$
$389$			36.5877i			0.0940559i	−0.998894	+	0.0470279i	$0.985025\pi$
$390$	−257.648	+	261.031i	−0.660637	+	0.669311i
$391$	381.488			0.975672
$392$	−3.32894	+	75.4452i	−0.00849220	+	0.192462i
$393$	−162.164	+	162.164i	−0.412630	+	0.412630i
$394$	−468.955	−	482.948i	−1.19024	−	1.22576i
$395$	−116.536	+	121.590i	−0.295028	+	0.307823i
$396$	−115.818	+	199.086i	−0.292469	+	0.502743i
$397$	359.312	−	359.312i	0.905067	−	0.905067i	−0.0908021	−	0.995869i	$-0.528943\pi$
$397$	359.312	−	359.312i	0.905067	−	0.905067i	0.995869	+	0.0908021i	$0.0289431\pi$
$398$	−59.5800	−	0.875797i	−0.149698	−	0.00220049i
$399$	353.699			0.886462
$400$	−6.54119	+	399.947i	−0.0163530	+	0.999866i
$401$	324.116			0.808269			0.404134	−	0.914700i	$-0.367573\pi$
$401$	324.116			0.808269			0.404134	+	0.914700i	$0.367573\pi$
$402$	266.430	+	3.91640i	0.662762	+	0.00974229i
$403$	−573.893	−	573.893i	−1.42405	−	1.42405i
$404$	−7.81183	+	265.660i	−0.0193362	+	0.657574i
$405$	−23.4161	−	22.4428i	−0.0578175	−	0.0554143i
$406$	23.2093	−	22.5369i	0.0571658	−	0.0555095i
$407$	−670.799	+	198.646i	−1.64815	+	0.488074i
$408$	−345.874	−	15.2614i	−0.847731	−	0.0374053i
$409$	91.6119			0.223990			0.111995	−	0.993709i	$-0.464276\pi$
$409$	91.6119			0.223990			0.111995	+	0.993709i	$0.464276\pi$
$410$	−92.8154	+	94.0340i	−0.226379	+	0.229351i
$411$		−	218.514i		−	0.531663i
$412$	494.169	−	465.937i	1.19944	−	1.13091i
$413$	51.5496	−	51.5496i	0.124817	−	0.124817i
$414$	−124.755	−	128.477i	−0.301340	−	0.310331i
$415$	−3.71318	−	174.958i	−0.00894742	−	0.421586i
$416$	457.935	−	395.128i	1.10080	−	0.949827i
$417$	270.529	+	270.529i	0.648751	+	0.648751i
$418$	−257.082	+	457.248i	−0.615029	+	1.09389i
$419$	225.194			0.537455			0.268728	−	0.963216i	$-0.413397\pi$
$419$	225.194			0.537455			0.268728	+	0.963216i	$0.413397\pi$
$420$	211.493	−	208.062i	0.503554	−	0.495386i
$421$	683.540			1.62361			0.811805	−	0.583928i	$-0.198485\pi$
$421$	683.540			1.62361			0.811805	+	0.583928i	$0.198485\pi$
$422$	−417.959	−	6.14379i	−0.990423	−	0.0145587i
$423$	−136.525	+	136.525i	−0.322753	+	0.322753i
$424$	448.086	+	489.454i	1.05681	+	1.15437i
$425$	−377.168	+	410.622i	−0.887455	+	0.966170i
$426$	−236.559	−	243.618i	−0.555304	−	0.571873i
$427$	142.509	+	142.509i	0.333745	+	0.333745i
$428$	413.151	−	389.547i	0.965306	−	0.910157i
$429$	−192.534	+	354.542i	−0.448798	+	0.826437i
$430$	−0.660797	−	101.323i	−0.00153674	−	0.235634i
$431$	−515.599			−1.19629			−0.598143	−	0.801390i	$-0.704094\pi$
$431$	−515.599			−1.19629			−0.598143	+	0.801390i	$0.704094\pi$
$432$	293.601	+	330.326i	0.679632	+	0.764644i
$433$	−113.047	−	113.047i	−0.261078	−	0.261078i	0.564414	−	0.825492i	$-0.309102\pi$
$433$	−113.047	−	113.047i	−0.261078	−	0.261078i	−0.825492	+	0.564414i	$0.809102\pi$
$434$	457.348	+	470.995i	1.05380	+	1.08524i
$435$	−20.5248	+	0.435602i	−0.0471833	+	0.00100138i
$436$	524.101	+	15.4114i	1.20207	+	0.0353472i
$437$	−288.399	−	288.399i	−0.659952	−	0.659952i
$438$	5.22352	−	355.353i	0.0119258	−	0.811308i
$439$			651.024i			1.48297i	0.670969	+	0.741486i	$0.265878\pi$
$439$			651.024i			1.48297i	−0.670969	+	0.741486i	$0.734122\pi$
$440$	115.253	+	424.637i	0.261939	+	0.965085i
$441$	49.4140			0.112050
$442$	842.985	+	12.3915i	1.90721	+	0.0280350i
$443$	−13.9233	+	13.9233i	−0.0314295	+	0.0314295i	−0.722647	−	0.691217i	$-0.757075\pi$
$443$	−13.9233	+	13.9233i	−0.0314295	+	0.0314295i	0.691217	+	0.722647i	$0.257075\pi$
$444$	−14.5096	+	493.434i	−0.0326793	+	1.11134i
$445$	−311.687	+	325.204i	−0.700420	+	0.730795i
$446$	−34.3544	+	33.3591i	−0.0770279	+	0.0747961i
$447$	−274.483	+	274.483i	−0.614057	+	0.614057i
$448$	−375.081	+	314.140i	−0.837234	+	0.701205i
$449$			6.37868i			0.0142064i	0.999975	+	0.00710321i	$0.00226104\pi$
$449$			6.37868i			0.0142064i	−0.999975	+	0.00710321i	$0.997739\pi$
$450$	261.631	−	7.25995i	0.581402	−	0.0161332i
$451$	−69.3586	+	127.720i	−0.153788	+	0.283193i
$452$	70.4911	+	74.7624i	0.155954	+	0.165404i
$453$	−27.9834	+	27.9834i	−0.0617734	+	0.0617734i
$454$	7.49822	−	7.28098i	0.0165159	−	0.0160374i
$455$	−499.902	+	521.582i	−1.09869	+	1.14633i
$456$	249.938	+	273.013i	0.548111	+	0.598713i
$457$	11.7490	+	11.7490i	0.0257091	+	0.0257091i	0.719844	−	0.694135i	$-0.244213\pi$
$457$	11.7490	+	11.7490i	0.0257091	+	0.0257091i	−0.694135	+	0.719844i	$0.744213\pi$
$458$	6.17635	−	420.174i	0.0134855	−	0.917410i
$459$			616.023i			1.34210i
$460$	−342.097	−	2.79734i	−0.743689	−	0.00608117i
$461$			383.674i			0.832265i	0.909304	+	0.416133i	$0.136615\pi$
$461$			383.674i			0.832265i	−0.909304	+	0.416133i	$0.863385\pi$
$462$	159.939	−	284.469i	0.346189	−	0.615733i
$463$	92.7118	−	92.7118i	0.200241	−	0.200241i	−0.599862	−	0.800103i	$-0.704778\pi$
$463$	92.7118	−	92.7118i	0.200241	−	0.200241i	0.800103	+	0.599862i	$0.204778\pi$
$464$	33.7965	+	1.98932i	0.0728372	+	0.00428732i
$465$	−8.83983	−	416.516i	−0.0190104	−	0.895734i
$466$	−271.328	+	263.466i	−0.582248	+	0.565378i
$467$	−514.758	−	514.758i	−1.10227	−	1.10227i	−0.994137	−	0.108128i	$-0.965514\pi$
$467$	−514.758	−	514.758i	−1.10227	−	1.10227i	−0.108128	−	0.994137i	$-0.534486\pi$
$468$	−271.501	−	287.952i	−0.580130	−	0.615282i
$469$	524.870			1.11913
$470$	2.40542	+	368.833i	0.00511792	+	0.784752i
$471$		−	161.084i		−	0.342003i
$472$	76.2173	+	3.36301i	0.161477	+	0.00712502i
$473$	−31.6478	−	106.870i	−0.0669086	−	0.225941i
$474$	91.0668	+	93.7840i	0.192124	+	0.197857i
$475$	595.558	−	25.2908i	1.25381	−	0.0532437i
$476$	−681.669	−	20.0448i	−1.43208	−	0.0421108i
$477$	307.029	−	307.029i	0.643666	−	0.643666i
$478$	−0.334758	+	22.7734i	−0.000700330	+	0.0476431i
$479$		−	300.009i		−	0.626324i	−0.949700	−	0.313162i	$-0.898612\pi$
$479$		−	300.009i		−	0.626324i	0.949700	−	0.313162i	$-0.101388\pi$
$480$	310.049	+	16.2217i	0.645935	+	0.0337952i
$481$		−	1202.11i		−	2.49918i
$482$	−3.10818	+	211.448i	−0.00644851	+	0.438688i
$483$	179.422	+	179.422i	0.371475	+	0.371475i
$484$	251.500	+	413.526i	0.519627	+	0.854393i
$485$	544.211	−	11.5499i	1.12208	−	0.0238143i
$486$	338.635	−	328.823i	0.696779	−	0.676591i
$487$	−603.738	−	603.738i	−1.23971	−	1.23971i	−0.960120	−	0.279587i	$-0.909802\pi$
$487$	−603.738	−	603.738i	−1.23971	−	1.23971i	−0.279587	−	0.960120i	$-0.590198\pi$
$488$	−9.29705	+	210.703i	−0.0190513	+	0.431768i
$489$		−	190.708i		−	0.389996i
$490$	66.3129	−	67.1835i	0.135332	−	0.137109i
$491$	628.029			1.27908			0.639541	−	0.768757i	$-0.279124\pi$
$491$	628.029			1.27908			0.639541	+	0.768757i	$0.279124\pi$
$492$	70.3533	+	74.6162i	0.142995	+	0.151659i
$493$	33.3683	+	33.3683i	0.0676842	+	0.0676842i
$494$	−627.917	−	646.652i	−1.27109	−	1.30901i
$495$	274.258	−	87.5882i	0.554057	−	0.176946i
$496$	−40.3699	+	685.843i	−0.0813909	+	1.38275i
$497$	−472.976	−	472.976i	−0.951662	−	0.951662i
$498$	−135.815	−	1.99642i	−0.272721	−	0.00400887i
$499$	−260.768			−0.522582			−0.261291	−	0.965260i	$-0.584148\pi$
$499$	−260.768			−0.522582			−0.261291	+	0.965260i	$0.584148\pi$
$500$	341.234	−	365.457i	0.682469	−	0.730915i
$501$		−	26.5872i		−	0.0530683i
$502$	3.37516	−	229.610i	0.00672342	−	0.457390i
$503$	−210.359	−	210.359i	−0.418209	−	0.418209i	0.466377	−	0.884586i	$-0.345559\pi$
$503$	−210.359	−	210.359i	−0.418209	−	0.418209i	−0.884586	+	0.466377i	$0.845559\pi$
$504$	216.170	+	236.127i	0.428908	+	0.468506i
$505$	229.876	−	239.845i	0.455201	−	0.474942i
$506$	−362.362	+	101.539i	−0.716129	+	0.200670i
$507$	−258.308	−	258.308i	−0.509483	−	0.509483i
$508$	−116.641	+	109.978i	−0.229609	+	0.216491i
$509$			349.415i			0.686473i	0.939249	+	0.343236i	$0.111523\pi$
$509$			349.415i			0.686473i	−0.939249	+	0.343236i	$0.888477\pi$
$510$	307.999	+	304.008i	0.603920	+	0.596094i
$511$		−	700.048i		−	1.36996i
$512$	−507.527	−	67.5331i	−0.991263	−	0.131901i
$513$	465.704	−	465.704i	0.907805	−	0.907805i
$514$	435.905	−	423.275i	0.848064	−	0.823493i
$515$	−848.797	+	18.0142i	−1.64815	+	0.0349791i
$516$	−78.6126	−	2.31163i	−0.152350	−	0.00447991i
$517$	115.204	+	389.026i	0.222831	+	0.752468i
$518$	−14.2920	+	972.278i	−0.0275908	+	1.87699i
$519$		−	403.536i		−	0.777525i
$520$	−755.851	−	17.2933i	−1.45356	−	0.0332564i
$521$	−377.707			−0.724965			−0.362483	−	0.931991i	$-0.618071\pi$
$521$	−377.707			−0.724965			−0.362483	+	0.931991i	$0.618071\pi$
$522$	0.325593	−	22.1499i	0.000623741	−	0.0424328i
$523$	179.347	+	179.347i	0.342919	+	0.342919i	0.857464	−	0.514545i	$-0.172039\pi$
$523$	179.347	+	179.347i	0.342919	+	0.342919i	−0.514545	+	0.857464i	$0.672039\pi$
$524$	−472.538	−	13.8952i	−0.901791	−	0.0265175i
$525$	−370.516	+	15.7342i	−0.705744	+	0.0299699i
$526$	−122.355	−	126.006i	−0.232615	−	0.239556i
$527$	−677.155	+	677.155i	−1.28492	+	1.28492i
$528$	332.596	−	77.5636i	0.629916	−	0.146901i
$529$			236.405i			0.446890i
$530$	−5.40953	−	829.465i	−0.0102067	−	1.56503i
$531$		−	49.9197i		−	0.0940108i
$532$	500.178	+	530.485i	0.940185	+	0.997153i
$533$	−176.588	−	176.588i	−0.331309	−	0.331309i
$534$	243.567	+	250.834i	0.456118	+	0.469727i
$535$	−709.638	+	15.0608i	−1.32643	+	0.0281511i
$536$	370.895	+	405.137i	0.691969	+	0.755853i
$537$	13.7426	−	13.7426i	0.0255913	−	0.0255913i
$538$	−4.17277	+	283.871i	−0.00775608	+	0.527642i
$539$	49.5539	−	91.2510i	0.0919368	−	0.169297i
$540$	4.51711	−	552.415i	0.00836503	−	1.02299i
$541$		−	769.268i		−	1.42194i	−0.703224	−	0.710968i	$-0.748257\pi$
$541$		−	769.268i		−	1.42194i	0.703224	−	0.710968i	$-0.251743\pi$
$542$	115.361	+	1.69575i	0.212843	+	0.00312868i
$543$	−177.466	+	177.466i	−0.326825	+	0.326825i
$544$	−466.224	−	540.332i	−0.857030	−	0.993257i
$545$	−473.174	−	453.507i	−0.868209	−	0.832122i
$546$	390.647	+	402.303i	0.715471	+	0.736819i
$547$	430.049	−	430.049i	0.786196	−	0.786196i	−0.194672	−	0.980868i	$-0.562364\pi$
$547$	430.049	−	430.049i	0.786196	−	0.786196i	0.980868	+	0.194672i	$0.0623642\pi$
$548$	327.732	−	309.008i	0.598051	−	0.563884i
$549$	138.003			0.251372
$550$	248.965	−	490.425i	0.452664	−	0.891681i
$551$		−	50.4519i		−	0.0915642i
$552$	−11.7052	+	265.280i	−0.0212051	+	0.480580i
$553$	182.079	+	182.079i	0.329256	+	0.329256i
$554$	−567.358	−	584.286i	−1.02411	−	1.05467i
$555$	426.970	−	445.486i	0.769315	−	0.802678i
$556$	−23.1806	+	788.312i	−0.0416918	+	1.41783i
$557$	−40.6884	−	40.6884i	−0.0730492	−	0.0730492i	0.669638	−	0.742687i	$-0.266449\pi$
$557$	−40.6884	−	40.6884i	−0.0730492	−	0.0730492i	−0.742687	+	0.669638i	$0.766449\pi$
$558$	449.496	+	6.60737i	0.805548	+	0.0118412i
$559$	191.516			0.342605
$560$	611.136	+	22.9735i	1.09131	+	0.0410241i
$561$	418.335	+	227.177i	0.745696	+	0.404951i
$562$	−7.57281	+	515.174i	−0.0134747	+	0.916679i
$563$	356.621	+	356.621i	0.633429	+	0.633429i	0.948927	−	0.315497i	$-0.102171\pi$
$563$	356.621	+	356.621i	0.633429	+	0.633429i	−0.315497	+	0.948927i	$0.602171\pi$
$564$	286.164	+	8.41477i	0.507383	+	0.0149198i
$565$	−2.72536	−	128.414i	−0.00482364	−	0.227281i
$566$	−359.149	−	369.865i	−0.634538	−	0.653471i
$567$	−35.0651	+	35.0651i	−0.0618433	+	0.0618433i
$568$	30.8562	−	699.306i	0.0543243	−	1.23117i
$569$	−65.3391			−0.114832			−0.0574158	−	0.998350i	$-0.518286\pi$
$569$	−65.3391			−0.114832			−0.0574158	+	0.998350i	$0.518286\pi$
$570$	−3.01738	−	462.668i	−0.00529366	−	0.811698i
$571$	−989.702			−1.73328			−0.866640	−	0.498935i	$-0.833725\pi$
$571$	−989.702			−1.73328			−0.866640	+	0.498935i	$0.833725\pi$
$572$	−804.020	+	212.603i	−1.40563	+	0.371684i
$573$	−425.142	−	425.142i	−0.741958	−	0.741958i
$574$	140.727	+	144.926i	0.245169	+	0.252484i
$575$	314.941	+	289.282i	0.547723	+	0.503099i
$576$	−29.5071	+	333.715i	−0.0512276	+	0.579366i
$577$	601.472	−	601.472i	1.04241	−	1.04241i	0.0433523	−	0.999060i	$-0.486196\pi$
$577$	601.472	−	601.472i	1.04241	−	1.04241i	0.999060	−	0.0433523i	$-0.0138038\pi$
$578$	6.12571	−	416.728i	0.0105981	−	0.720983i
$579$			37.5839i			0.0649117i
$580$	−29.6782	−	30.1675i	−0.0511692	−	0.0520130i
$581$	−267.557			−0.460511
$582$	6.20990	−	422.456i	0.0106699	−	0.725869i
$583$	−259.080	−	874.876i	−0.444391	−	1.50065i
$584$	540.353	−	494.683i	0.925263	−	0.847061i
$585$	10.4969	+	494.594i	0.0179434	+	0.845459i
$586$	−143.138	+	138.991i	−0.244263	+	0.237186i
$587$	540.157	+	540.157i	0.920199	+	0.920199i	0.997043	−	0.0768444i	$-0.0244845\pi$
$587$	540.157	+	540.157i	0.920199	+	0.920199i	−0.0768444	+	0.997043i	$0.524484\pi$
$588$	−50.2646	−	53.3103i	−0.0854841	−	0.0906638i
$589$	1023.84			1.73826
$590$	−67.8710	−	66.9915i	−0.115036	−	0.113545i
$591$	653.128			1.10512
$592$	−760.582	+	676.021i	−1.28477	+	1.14193i
$593$	−498.341	+	498.341i	−0.840372	+	0.840372i	−0.988907	−	0.148535i	$-0.952544\pi$
$593$	−498.341	+	498.341i	−0.840372	+	0.840372i	0.148535	+	0.988907i	$0.452544\pi$
$594$	−163.964	−	585.138i	−0.276034	−	0.985081i
$595$	615.431	+	589.851i	1.03434	+	0.991346i
$596$	−799.834	−	23.5194i	−1.34200	−	0.0394621i
$597$	40.8795	−	40.8795i	0.0684749	−	0.0684749i
$598$	9.50407	−	646.556i	0.0158931	−	1.08120i
$599$	382.377			0.638359			0.319179	−	0.947694i	$-0.396593\pi$
$599$	382.377			0.638359			0.319179	+	0.947694i	$0.396593\pi$
$600$	−273.967	−	274.876i	−0.456612	−	0.458126i
$601$			298.411i			0.496525i	0.968693	+	0.248262i	$0.0798595\pi$
$601$			298.411i			0.496525i	−0.968693	+	0.248262i	$0.920140\pi$
$602$	−154.901	−	2.27697i	−0.257310	−	0.00378234i
$603$	254.137	−	254.137i	0.421455	−	0.421455i
$604$	−81.5425	−	2.39779i	−0.135004	−	0.00396985i
$605$	113.289	−	594.298i	0.187254	−	0.982311i
$606$	−179.636	−	184.996i	−0.296429	−	0.305274i
$607$	−257.024	+	257.024i	−0.423433	+	0.423433i	−0.886384	−	0.462951i	$-0.846791\pi$
$607$	−257.024	+	257.024i	−0.423433	+	0.423433i	0.462951	+	0.886384i	$0.346791\pi$
$608$	−56.0243	+	760.942i	−0.0921452	+	1.25155i
$609$			31.3878i			0.0515398i
$610$	185.198	−	187.630i	0.303604	−	0.307590i
$611$	−697.155			−1.14101
$612$	−339.764	+	320.353i	−0.555170	+	0.523452i
$613$	30.8327	−	30.8327i	0.0502980	−	0.0502980i	−0.681510	−	0.731808i	$-0.738677\pi$
$613$	30.8327	−	30.8327i	0.0502980	−	0.0502980i	0.731808	+	0.681510i	$0.238677\pi$
$614$	−264.153	+	256.500i	−0.430217	+	0.417752i
$615$	−2.72003	−	128.163i	−0.00442281	−	0.208395i
$616$	652.829	−	162.397i	1.05979	−	0.263632i
$617$	−175.339	+	175.339i	−0.284181	+	0.284181i	−0.834774	−	0.550593i	$-0.814402\pi$
$617$	−175.339	+	175.339i	−0.284181	+	0.284181i	0.550593	+	0.834774i	$0.314402\pi$
$618$	−9.68549	+	658.898i	−0.0156723	+	1.06618i
$619$	−310.013			−0.500829			−0.250415	−	0.968139i	$-0.580567\pi$
$619$	−310.013			−0.500829			−0.250415	+	0.968139i	$0.580567\pi$
$620$	612.200	−	602.269i	0.987419	−	0.971402i
$621$	472.480			0.760837
$622$	12.6347	−	859.533i	0.0203131	−	1.38189i
$623$	486.987	+	486.987i	0.781680	+	0.781680i
$624$	−34.4822	+	585.818i	−0.0552599	+	0.938810i
$625$	−622.750	+	52.9865i	−0.996400	+	0.0847784i
$626$	−303.713	−	312.775i	−0.485165	−	0.499641i
$627$	−144.513	−	487.998i	−0.230483	−	0.778306i
$628$	241.597	−	227.794i	0.384708	−	0.362730i
$629$	−1418.40			−2.25502
$630$	−2.60971	−	400.158i	−0.00414240	−	0.635172i
$631$		−	260.205i		−	0.412370i	−0.978513	−	0.206185i	$-0.933895\pi$
$631$		−	260.205i		−	0.412370i	0.978513	−	0.206185i	$-0.0661048\pi$
$632$	−11.8785	+	269.208i	−0.0187951	+	0.425961i
$633$	286.773	−	286.773i	0.453038	−	0.453038i
$634$	−305.180	+	296.338i	−0.481357	+	0.467411i
$635$	200.346	−	4.25200i	0.315506	−	0.00669607i
$636$	−643.552	−	18.9239i	−1.01187	−	0.0297545i
$637$	126.165	+	126.165i	0.198061	+	0.198061i
$638$	−40.5769	−	22.8139i	−0.0636001	−	0.0357584i
$639$	−458.022			−0.716779
$640$	414.122	+	487.958i	0.647065	+	0.762435i
$641$	−272.859			−0.425677			−0.212839	−	0.977087i	$-0.568271\pi$
$641$	−272.859			−0.425677			−0.212839	+	0.977087i	$0.568271\pi$
$642$	−8.09757	+	550.873i	−0.0126130	+	0.858058i
$643$	126.133	−	126.133i	0.196163	−	0.196163i	−0.602190	−	0.798353i	$-0.705705\pi$
$643$	126.133	−	126.133i	0.196163	−	0.196163i	0.798353	+	0.602190i	$0.205705\pi$
$644$	−15.3740	+	522.830i	−0.0238727	+	0.811847i
$645$	70.9737	+	68.0238i	0.110037	+	0.105463i
$646$	−763.006	+	740.899i	−1.18112	+	1.14690i
$647$	513.203	+	513.203i	0.793204	+	0.793204i	0.982014	−	0.188810i	$-0.0604631\pi$
$647$	513.203	+	513.203i	0.793204	+	0.793204i	−0.188810	+	0.982014i	$0.560463\pi$
$648$	−51.8446	−	2.28759i	−0.0800072	−	0.00353023i
$649$	−92.1848	−	50.0611i	−0.142041	−	0.0771357i
$650$	686.538	+	649.466i	1.05621	+	0.999178i
$651$	−636.963			−0.978437
$652$	286.029	−	269.688i	0.438694	−	0.413631i
$653$	376.550	+	376.550i	0.576647	+	0.576647i	0.933978	−	0.357331i	$-0.116313\pi$
$653$	376.550	+	376.550i	0.576647	+	0.576647i	−0.357331	+	0.933978i	$0.616313\pi$
$654$	−364.965	+	354.391i	−0.558051	+	0.541883i
$655$	426.621	+	408.889i	0.651330	+	0.624258i
$656$	−12.4219	+	211.035i	−0.0189358	+	0.321700i
$657$	−338.957	−	338.957i	−0.515916	−	0.515916i
$658$	563.867	+	8.28858i	0.856941	+	0.0125966i
$659$		−	594.010i		−	0.901382i	−0.892680	−	0.450691i	$-0.851178\pi$
$659$		−	594.010i		−	0.901382i	0.892680	−	0.450691i	$-0.148822\pi$
$660$	−373.474	−	206.787i	−0.565869	−	0.313314i
$661$	318.260			0.481483			0.240742	−	0.970589i	$-0.422609\pi$
$661$	318.260			0.481483			0.240742	+	0.970589i	$0.422609\pi$
$662$	2.06205	−	140.280i	0.00311488	−	0.211904i
$663$	−578.396	+	578.396i	−0.872393	+	0.872393i
$664$	−189.067	−	206.522i	−0.284740	−	0.311027i
$665$	−19.3381	−	911.175i	−0.0290799	−	1.37019i
$666$	463.849	+	477.689i	0.696469	+	0.717250i
$667$	25.5930	−	25.5930i	0.0383703	−	0.0383703i
$668$	39.8761	−	37.5980i	0.0596948	−	0.0562844i
$669$		−	46.4602i		−	0.0694472i
$670$	−4.47764	−	686.575i	−0.00668304	−	1.02474i
$671$	138.394	−	254.845i	0.206250	−	0.379799i
$672$	34.8545	−	473.406i	0.0518668	−	0.704474i
$673$	−470.399	+	470.399i	−0.698959	+	0.698959i	−0.964186	−	0.265227i	$-0.914553\pi$
$673$	−470.399	+	470.399i	−0.698959	+	0.698959i	0.265227	+	0.964186i	$0.414553\pi$
$674$	−474.632	−	488.794i	−0.704202	−	0.725214i
$675$	−467.130	+	508.564i	−0.692045	+	0.753428i
$676$	22.1334	−	752.699i	0.0327417	−	1.11346i
$677$	−468.594	−	468.594i	−0.692163	−	0.692163i	0.270545	−	0.962707i	$-0.412796\pi$
$677$	−468.594	−	468.594i	−0.692163	−	0.692163i	−0.962707	+	0.270545i	$0.912796\pi$
$678$	−99.6841	−	1.46531i	−0.147027	−	0.00216122i
$679$		−	832.241i		−	1.22569i
$680$	−20.4050	+	891.853i	−0.0300073	+	1.31155i
$681$			10.1404i			0.0148905i
$682$	462.970	−	823.441i	0.678842	−	1.20739i
$683$	−345.217	+	345.217i	−0.505442	+	0.505442i	−0.913124	−	0.407682i	$-0.866337\pi$
$683$	−345.217	+	345.217i	−0.505442	+	0.505442i	0.407682	+	0.913124i	$0.366337\pi$
$684$	499.038	+	14.6744i	0.729588	+	0.0214538i
$685$	−562.921	+	11.9470i	−0.821782	+	0.0174409i
$686$	421.356	+	433.929i	0.614222	+	0.632549i
$687$	288.293	+	288.293i	0.419641	+	0.419641i
$688$	−107.702	−	121.174i	−0.156544	−	0.176125i
$689$	1567.82			2.27551
$690$	233.169	−	236.230i	0.337926	−	0.342363i
$691$		−	1319.79i		−	1.90997i	−0.296660	−	0.954983i	$-0.595873\pi$
$691$		−	1319.79i		−	1.90997i	0.296660	−	0.954983i	$-0.404127\pi$
$692$	605.232	−	570.655i	0.874613	−	0.824646i
$693$	−124.988	−	422.066i	−0.180358	−	0.609041i
$694$	−739.212	+	717.795i	−1.06515	+	1.03429i
$695$	682.129	−	711.711i	0.981481	−	1.02404i
$696$	−24.2276	+	22.1799i	−0.0348098	+	0.0318677i
$697$	−208.362	+	208.362i	−0.298941	+	0.298941i
$698$	516.910	+	7.59833i	0.740559	+	0.0108859i
$699$		−	366.937i		−	0.524946i
$700$	−547.559	−	533.458i	−0.782227	−	0.762083i
$701$		−	108.292i		−	0.154482i	−0.997012	−	0.0772411i	$-0.975389\pi$
$701$		−	108.292i		−	0.154482i	0.997012	−	0.0772411i	$-0.0246111\pi$
$702$	1044.05	+	15.3471i	1.48726	+	0.0218620i
$703$	1072.29	+	1072.29i	1.52531	+	1.52531i
$704$	586.668	+	389.149i	0.833335	+	0.552769i
$705$	−258.357	−	247.619i	−0.366464	−	0.351233i
$706$	84.4682	+	86.9885i	0.119643	+	0.123213i
$707$	−359.164	−	359.164i	−0.508012	−	0.508012i
$708$	−53.8559	+	50.7790i	−0.0760676	+	0.0717218i
$709$			844.657i			1.19134i	0.803231	+	0.595668i	$0.203113\pi$
$709$			844.657i			1.19134i	−0.803231	+	0.595668i	$0.796887\pi$
$710$	−614.659	+	622.728i	−0.865716	+	0.877082i
$711$	176.322			0.247991
$712$	−31.7702	+	720.021i	−0.0446211	+	1.01127i
$713$	519.367	+	519.367i	0.728425	+	0.728425i
$714$	474.691	−	460.937i	0.664833	−	0.645570i
$715$	923.874	+	476.610i	1.29213	+	0.666587i
$716$	40.0453	+	1.17755i	0.0559291	+	0.00164462i
$717$	−15.6255	−	15.6255i	−0.0217928	−	0.0217928i
$718$	−12.4693	+	848.278i	−0.0173667	+	1.18145i
$719$	459.476			0.639049			0.319524	−	0.947578i	$-0.396477\pi$
$719$	459.476			0.639049			0.319524	+	0.947578i	$0.396477\pi$
$720$	307.030	−	284.783i	0.426431	−	0.395532i
$721$			1298.03i			1.80033i
$722$	415.008	+	6.10041i	0.574803	+	0.00844933i
$723$	−145.080	−	145.080i	−0.200664	−	0.200664i
$724$	−517.129	−	15.2064i	−0.714267	−	0.0210033i
$725$	2.24434	+	52.8507i	0.00309564	+	0.0728976i
$726$	−457.828	−	104.441i	−0.630618	−	0.143858i
$727$	−77.1065	−	77.1065i	−0.106061	−	0.106061i	0.652085	−	0.758146i	$-0.273895\pi$
$727$	−77.1065	−	77.1065i	−0.106061	−	0.106061i	−0.758146	+	0.652085i	$0.773895\pi$
$728$	−50.9550	+	1154.81i	−0.0699931	+	1.58628i
$729$			516.344i			0.708291i
$730$	−915.723	+	5.97207i	−1.25441	+	0.00818092i
$731$		−	225.977i		−	0.309133i
$732$	−140.379	−	148.885i	−0.191774	−	0.203395i
$733$	−908.588	+	908.588i	−1.23955	+	1.23955i	−0.279361	+	0.960186i	$0.590123\pi$
$733$	−908.588	+	908.588i	−1.23955	+	1.23955i	−0.960186	+	0.279361i	$0.909877\pi$
$734$	−659.973	−	679.665i	−0.899146	−	0.925975i
$735$	1.94335	+	91.5671i	0.00264402	+	0.124581i
$736$	−414.426	+	357.587i	−0.563079	+	0.485852i
$737$	−214.449	−	724.163i	−0.290976	−	0.982582i
$738$	138.311	+	2.03310i	0.187413	+	0.00275488i
$739$			377.105i			0.510291i	0.966903	+	0.255146i	$0.0821234\pi$
$739$			377.105i			0.510291i	−0.966903	+	0.255146i	$0.917877\pi$
$740$	1271.95	+	10.4007i	1.71885	+	0.0140551i
$741$	874.518			1.18019
$742$	−1268.08	−	18.6401i	−1.70900	−	0.0251214i
$743$	36.1901	+	36.1901i	0.0487080	+	0.0487080i	0.731041	−	0.682333i	$-0.239035\pi$
$743$	36.1901	+	36.1901i	0.0487080	+	0.0487080i	−0.682333	+	0.731041i	$0.739035\pi$
$744$	−450.105	−	491.659i	−0.604980	−	0.660832i
$745$	722.113	+	692.099i	0.969280	+	0.928992i
$746$	326.824	−	317.355i	0.438102	−	0.425409i
$747$	−129.549	+	129.549i	−0.173425	+	0.173425i
$748$	250.858	+	948.689i	0.335371	+	1.26830i
$749$			1085.22i			1.44890i
$750$	23.7425	+	484.532i	0.0316567	+	0.646043i
$751$			1317.50i			1.75433i	0.480187	+	0.877166i	$0.340569\pi$
$751$			1317.50i			1.75433i	−0.480187	+	0.877166i	$0.659431\pi$
$752$	392.055	+	441.096i	0.521350	+	0.586563i
$753$	157.542	+	157.542i	0.209219	+	0.209219i
$754$	57.3849	−	55.7223i	0.0761073	−	0.0739022i
$755$	73.6189	+	70.5590i	0.0975085	+	0.0934556i
$756$	−844.261	−	24.8258i	−1.11675	−	0.0328384i
$757$	218.159	−	218.159i	0.288189	−	0.288189i	−0.548175	−	0.836364i	$-0.684677\pi$
$757$	218.159	−	218.159i	0.288189	−	0.288189i	0.836364	+	0.548175i	$0.184677\pi$
$758$	222.866	+	3.27602i	0.294018	+	0.00432193i
$759$	174.241	−	320.857i	0.229567	−	0.422736i
$760$	689.654	−	658.802i	0.907439	−	0.866845i
$761$			1116.86i			1.46762i	0.679353	+	0.733812i	$0.262261\pi$
$761$			1116.86i			1.46762i	−0.679353	+	0.733812i	$0.737739\pi$
$762$	2.28612	−	155.523i	0.00300016	−	0.204099i
$763$	−708.569	+	708.569i	−0.928662	+	0.928662i
$764$	36.4288	−	1238.85i	0.0476816	−	1.62153i
$765$	583.587	−	12.3856i	0.762859	−	0.0161904i
$766$	319.343	−	310.091i	0.416897	−	0.404818i
$767$	127.456	−	127.456i	0.166175	−	0.166175i
$768$	390.043	−	307.626i	0.507868	−	0.400554i
$769$	1167.60			1.51833			0.759167	−	0.650896i	$-0.225607\pi$
$769$	1167.60			1.51833			0.759167	+	0.650896i	$0.225607\pi$
$770$	−741.574	−	396.472i	−0.963083	−	0.514899i
$771$			589.508i			0.764602i
$772$	−56.3692	+	53.1488i	−0.0730171	+	0.0688456i

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99978 - 0.0293959i) q^{2} +(1.37211 - 1.37211i) q^{3} +(3.99827 + 0.117571i) q^{4} +(-3.60976 - 3.45972i) q^{5} +(-2.78426 + 2.70359i) q^{6} +(-5.40554 + 5.40554i) q^{7} +(-7.99222 - 0.352649i) q^{8} +5.23463i q^{9} +(7.11703 + 7.02480i) q^{10} +(9.66660 + 5.24946i) q^{11} +(5.64738 - 5.32474i) q^{12} +(-13.3652 + 13.3652i) q^{13} +(10.9688 - 10.6510i) q^{14} +(-9.70009 + 0.205868i) q^{15} +(15.9724 + 0.940160i) q^{16} +(15.7700 + 15.7700i) q^{17} +(0.153877 - 10.4681i) q^{18} -23.8438i q^{19} +(-14.0260 - 14.2573i) q^{20} +14.8340i q^{21} +(-19.1768 - 10.7819i) q^{22} +(12.0954 - 12.0954i) q^{23} +(-11.4501 + 10.4823i) q^{24} +(1.06069 + 24.9775i) q^{25} +(27.1204 - 26.3346i) q^{26} +(19.5315 + 19.5315i) q^{27} +(-22.2484 + 20.9773i) q^{28} +2.11593 q^{29} +(19.4041 - 0.126548i) q^{30} +42.9394i q^{31} +(-31.9136 - 2.34964i) q^{32} +(20.4665 - 6.06080i) q^{33} +(-31.0730 - 32.0002i) q^{34} +(38.2144 - 0.811033i) q^{35} +(-0.615440 + 20.9295i) q^{36} +(-44.9716 + 44.9716i) q^{37} +(-0.700909 + 47.6824i) q^{38} +36.6770i q^{39} +(27.6299 + 28.9238i) q^{40} +13.2125i q^{41} +(0.436058 - 29.6648i) q^{42} +(-7.16475 - 7.16475i) q^{43} +(38.0325 + 22.1253i) q^{44} +(18.1104 - 18.8958i) q^{45} +(-24.5436 + 23.8325i) q^{46} +(26.0810 + 26.0810i) q^{47} +(23.2058 - 20.6258i) q^{48} -9.43982i q^{49} +(-1.38691 - 49.9808i) q^{50} +43.2763 q^{51} +(-55.0090 + 51.8663i) q^{52} +(-58.6533 - 58.6533i) q^{53} +(-38.4846 - 39.6329i) q^{54} +(-16.7324 - 52.3930i) q^{55} +(45.1086 - 41.2961i) q^{56} +(-32.7163 - 32.7163i) q^{57} +(-4.23141 - 0.0621997i) q^{58} -9.53643 q^{59} +(-38.8078 - 0.317333i) q^{60} -26.3635i q^{61} +(1.26224 - 85.8695i) q^{62} +(-28.2961 - 28.2961i) q^{63} +(63.7513 + 5.63690i) q^{64} +(94.4848 - 2.00528i) q^{65} +(-41.1067 + 11.5187i) q^{66} +(-48.5492 - 48.5492i) q^{67} +(61.1987 + 64.9069i) q^{68} -33.1923i q^{69} +(-76.4443 + 0.498547i) q^{70} +87.4983i q^{71} +(1.84599 - 41.8364i) q^{72} +(-64.7527 + 64.7527i) q^{73} +(91.2554 - 88.6114i) q^{74} +(35.7272 + 32.8165i) q^{75} +(2.80333 - 95.3339i) q^{76} +(-80.6294 + 23.8771i) q^{77} +(1.07815 - 73.3460i) q^{78} -33.6837i q^{79} +(-54.4036 - 58.6536i) q^{80} +6.48689 q^{81} +(0.388394 - 26.4222i) q^{82} +(24.7484 + 24.7484i) q^{83} +(-1.74404 + 59.3103i) q^{84} +(-2.36609 - 111.486i) q^{85} +(14.1173 + 14.5386i) q^{86} +(2.90329 - 2.90329i) q^{87} +(-75.4064 - 45.3637i) q^{88} -90.0902i q^{89} +(-36.7723 + 37.2551i) q^{90} -144.492i q^{91} +(49.7826 - 46.9384i) q^{92} +(58.9175 + 58.9175i) q^{93} +(-51.3897 - 52.9231i) q^{94} +(-82.4928 + 86.0703i) q^{95} +(-47.0129 + 40.5650i) q^{96} +(-76.9803 + 76.9803i) q^{97} +(-0.277492 + 18.8776i) q^{98} +(-27.4790 + 50.6011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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