LMFDB - Embedded newform 220.3.h.a.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(199,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("220.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.h (of order $2$, degree $1$, 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:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97378 - 0.322758i) q^{2} -4.73469 q^{3} +(3.79165 + 1.27411i) q^{4} +(-1.42827 + 4.79166i) q^{5} +(9.34526 + 1.52816i) q^{6} +7.98176 q^{7} +(-7.07268 - 3.73861i) q^{8} +13.4173 q^{9} +(4.36565 - 8.99673i) q^{10} -3.31662i q^{11} +(-17.9523 - 6.03252i) q^{12} -16.6171i q^{13} +(-15.7543 - 2.57618i) q^{14} +(6.76243 - 22.6870i) q^{15} +(12.7533 + 9.66197i) q^{16} +27.0004i q^{17} +(-26.4829 - 4.33055i) q^{18} +32.7057i q^{19} +(-11.5206 + 16.3486i) q^{20} -37.7912 q^{21} +(-1.07047 + 6.54630i) q^{22} +4.15724 q^{23} +(33.4870 + 17.7012i) q^{24} +(-20.9201 - 13.6876i) q^{25} +(-5.36330 + 32.7986i) q^{26} -20.9146 q^{27} +(30.2641 + 10.1696i) q^{28} -57.6811 q^{29} +(-20.6700 + 42.5967i) q^{30} -14.8979i q^{31} +(-22.0538 - 23.1869i) q^{32} +15.7032i q^{33} +(8.71459 - 53.2929i) q^{34} +(-11.4001 + 38.2459i) q^{35} +(50.8738 + 17.0951i) q^{36} +4.84811i q^{37} +(10.5560 - 64.5541i) q^{38} +78.6768i q^{39} +(28.0159 - 28.5502i) q^{40} +6.17837 q^{41} +(74.5917 + 12.1974i) q^{42} -51.9995 q^{43} +(4.22575 - 12.5755i) q^{44} +(-19.1636 + 64.2912i) q^{45} +(-8.20550 - 1.34178i) q^{46} -42.9867 q^{47} +(-60.3829 - 45.7465i) q^{48} +14.7085 q^{49} +(36.8739 + 33.7685i) q^{50} -127.838i q^{51} +(21.1720 - 63.0063i) q^{52} +62.4688i q^{53} +(41.2809 + 6.75035i) q^{54} +(15.8921 + 4.73705i) q^{55} +(-56.4525 - 29.8407i) q^{56} -154.852i q^{57} +(113.850 + 18.6171i) q^{58} -15.6879i q^{59} +(54.5466 - 77.4054i) q^{60} -5.92632 q^{61} +(-4.80842 + 29.4052i) q^{62} +107.094 q^{63} +(36.0456 + 52.8840i) q^{64} +(79.6235 + 23.7337i) q^{65} +(5.06833 - 30.9947i) q^{66} -53.4975 q^{67} +(-34.4015 + 102.376i) q^{68} -19.6833 q^{69} +(34.8456 - 71.8097i) q^{70} +16.2442i q^{71} +(-94.8963 - 50.1620i) q^{72} +23.9582i q^{73} +(1.56477 - 9.56913i) q^{74} +(99.0501 + 64.8066i) q^{75} +(-41.6707 + 124.009i) q^{76} -26.4725i q^{77} +(25.3936 - 155.291i) q^{78} +27.9060i q^{79} +(-64.5121 + 47.3095i) q^{80} -21.7317 q^{81} +(-12.1948 - 1.99412i) q^{82} +24.0670 q^{83} +(-143.291 - 48.1501i) q^{84} +(-129.377 - 38.5639i) q^{85} +(102.636 + 16.7833i) q^{86} +273.102 q^{87} +(-12.3996 + 23.4574i) q^{88} +79.0905 q^{89} +(58.5753 - 120.712i) q^{90} -132.634i q^{91} +(15.7628 + 5.29679i) q^{92} +70.5369i q^{93} +(84.8465 + 13.8743i) q^{94} +(-156.715 - 46.7127i) q^{95} +(104.418 + 109.783i) q^{96} +69.4266i q^{97} +(-29.0314 - 4.74729i) q^{98} -44.5002i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) $ 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.97378	−	0.322758i	−0.986892	−	0.161379i
$2$	−1.97378	−	0.322758i	−0.986892	−	0.161379i
$3$	−4.73469			−1.57823			−0.789115	−	0.614245i	$-0.789461\pi$
$3$	−4.73469			−1.57823			−0.789115	+	0.614245i	$0.789461\pi$
$4$	3.79165	+	1.27411i	0.947914	+	0.318528i
$5$	−1.42827	+	4.79166i	−0.285655	+	0.958333i
$5$	−1.42827	+	4.79166i	−0.285655	+	0.958333i
$6$	9.34526	+	1.52816i	1.55754	+	0.254693i
$7$	7.98176			1.14025			0.570126	−	0.821557i	$-0.306894\pi$
$7$	7.98176			1.14025			0.570126	+	0.821557i	$0.306894\pi$
$8$	−7.07268	−	3.73861i	−0.884085	−	0.467326i
$9$	13.4173			1.49081
$10$	4.36565	−	8.99673i	0.436565	−	0.899673i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	−17.9523	−	6.03252i	−1.49603	−	0.502710i
$13$		−	16.6171i		−	1.27824i	−0.769108	−	0.639119i	$-0.779299\pi$
$13$		−	16.6171i		−	1.27824i	0.769108	−	0.639119i	$-0.220701\pi$
$14$	−15.7543	−	2.57618i	−1.12531	−	0.184013i
$15$	6.76243	−	22.6870i	0.450829	−	1.51247i
$16$	12.7533	+	9.66197i	0.797080	+	0.603873i
$17$			27.0004i			1.58826i	0.607750	+	0.794128i	$0.292072\pi$
$17$			27.0004i			1.58826i	−0.607750	+	0.794128i	$0.707928\pi$
$18$	−26.4829	−	4.33055i	−1.47127	−	0.240586i
$19$			32.7057i			1.72135i	0.509151	+	0.860677i	$0.329960\pi$
$19$			32.7057i			1.72135i	−0.509151	+	0.860677i	$0.670040\pi$
$20$	−11.5206	+	16.3486i	−0.576031	+	0.817428i
$21$	−37.7912			−1.79958
$22$	−1.07047	+	6.54630i	−0.0486576	+	0.297559i
$23$	4.15724			0.180750			0.0903748	−	0.995908i	$-0.471193\pi$
$23$	4.15724			0.180750			0.0903748	+	0.995908i	$0.471193\pi$
$24$	33.4870	+	17.7012i	1.39529	+	0.737548i
$25$	−20.9201	−	13.6876i	−0.836803	−	0.547504i
$26$	−5.36330	+	32.7986i	−0.206281	+	1.26148i
$27$	−20.9146			−0.774614
$28$	30.2641	+	10.1696i	1.08086	+	0.363202i
$29$	−57.6811			−1.98900			−0.994502	−	0.104715i	$-0.966607\pi$
$29$	−57.6811			−1.98900			−0.994502	+	0.104715i	$0.966607\pi$
$30$	−20.6700	+	42.5967i	−0.689001	+	1.41989i
$31$		−	14.8979i		−	0.480577i	−0.970702	−	0.240289i	$-0.922758\pi$
$31$		−	14.8979i		−	0.480577i	0.970702	−	0.240289i	$-0.0772421\pi$
$32$	−22.0538	−	23.1869i	−0.689180	−	0.724590i
$33$			15.7032i			0.475854i
$34$	8.71459	−	53.2929i	0.256311	−	1.56744i
$35$	−11.4001	+	38.2459i	−0.325718	+	1.09274i
$36$	50.8738	+	17.0951i	1.41316	+	0.474865i
$37$			4.84811i			0.131030i	0.997852	+	0.0655151i	$0.0208690\pi$
$37$			4.84811i			0.131030i	−0.997852	+	0.0655151i	$0.979131\pi$
$38$	10.5560	−	64.5541i	0.277791	−	1.69879i
$39$			78.6768i			2.01735i
$40$	28.0159	−	28.5502i	0.700397	−	0.713754i
$41$	6.17837			0.150692			0.0753460	−	0.997157i	$-0.475994\pi$
$41$	6.17837			0.150692			0.0753460	+	0.997157i	$0.475994\pi$
$42$	74.5917	+	12.1974i	1.77599	+	0.290415i
$43$	−51.9995			−1.20929			−0.604646	−	0.796494i	$-0.706685\pi$
$43$	−51.9995			−1.20929			−0.604646	+	0.796494i	$0.706685\pi$
$44$	4.22575	−	12.5755i	0.0960397	−	0.285807i
$45$	−19.1636	+	64.2912i	−0.425857	+	1.42869i
$46$	−8.20550	−	1.34178i	−0.178380	−	0.0291692i
$47$	−42.9867			−0.914610			−0.457305	−	0.889310i	$-0.651185\pi$
$47$	−42.9867			−0.914610			−0.457305	+	0.889310i	$0.651185\pi$
$48$	−60.3829	−	45.7465i	−1.25798	−	0.953051i
$49$	14.7085			0.300174
$50$	36.8739	+	33.7685i	0.737479	+	0.675370i
$51$		−	127.838i		−	2.50664i
$52$	21.1720	−	63.0063i	0.407154	−	1.21166i
$53$			62.4688i			1.17866i	0.807893	+	0.589329i	$0.200608\pi$
$53$			62.4688i			1.17866i	−0.807893	+	0.589329i	$0.799392\pi$
$54$	41.2809	+	6.75035i	0.764461	+	0.125007i
$55$	15.8921	+	4.73705i	0.288948	+	0.0861281i
$56$	−56.4525	−	29.8407i	−1.00808	−	0.532869i
$57$		−	154.852i		−	2.71669i
$58$	113.850	+	18.6171i	1.96293	+	0.320984i
$59$		−	15.6879i		−	0.265897i	−0.991123	−	0.132949i	$-0.957555\pi$
$59$		−	15.6879i		−	0.265897i	0.991123	−	0.132949i	$-0.0424445\pi$
$60$	54.5466	−	77.4054i	0.909110	−	1.29009i
$61$	−5.92632			−0.0971528			−0.0485764	−	0.998819i	$-0.515468\pi$
$61$	−5.92632			−0.0971528			−0.0485764	+	0.998819i	$0.515468\pi$
$62$	−4.80842	+	29.4052i	−0.0775551	+	0.474278i
$63$	107.094			1.69990
$64$	36.0456	+	52.8840i	0.563213	+	0.826312i
$65$	79.6235	+	23.7337i	1.22498	+	0.365134i
$66$	5.06833	−	30.9947i	0.0767930	−	0.469617i
$67$	−53.4975			−0.798469			−0.399235	−	0.916849i	$-0.630724\pi$
$67$	−53.4975			−0.798469			−0.399235	+	0.916849i	$0.630724\pi$
$68$	−34.4015	+	102.376i	−0.505904	+	1.50553i
$69$	−19.6833			−0.285265
$70$	34.8456	−	71.8097i	0.497794	−	1.02585i
$71$			16.2442i			0.228792i	0.993435	+	0.114396i	$0.0364933\pi$
$71$			16.2442i			0.228792i	−0.993435	+	0.114396i	$0.963507\pi$
$72$	−94.8963	−	50.1620i	−1.31800	−	0.696695i
$73$			23.9582i			0.328194i	0.986444	+	0.164097i	$0.0524710\pi$
$73$			23.9582i			0.328194i	−0.986444	+	0.164097i	$0.947529\pi$
$74$	1.56477	−	9.56913i	0.0211455	−	0.129313i
$75$	99.0501	+	64.8066i	1.32067	+	0.864088i
$76$	−41.6707	+	124.009i	−0.548299	+	1.63170i
$77$		−	26.4725i		−	0.343799i
$78$	25.3936	−	155.291i	0.325559	−	1.99091i
$79$			27.9060i			0.353241i	0.984279	+	0.176620i	$0.0565165\pi$
$79$			27.9060i			0.353241i	−0.984279	+	0.176620i	$0.943484\pi$
$80$	−64.5121	+	47.3095i	−0.806401	+	0.591369i
$81$	−21.7317			−0.268292
$82$	−12.1948	−	1.99412i	−0.148717	−	0.0243185i
$83$	24.0670			0.289964			0.144982	−	0.989434i	$-0.453688\pi$
$83$	24.0670			0.289964			0.144982	+	0.989434i	$0.453688\pi$
$84$	−143.291	−	48.1501i	−1.70585	−	0.573216i
$85$	−129.377	−	38.5639i	−1.52208	−	0.453693i
$86$	102.636	+	16.7833i	1.19344	+	0.195154i
$87$	273.102			3.13911
$88$	−12.3996	+	23.4574i	−0.140904	+	0.266562i
$89$	79.0905			0.888657			0.444329	−	0.895864i	$-0.353442\pi$
$89$	79.0905			0.888657			0.444329	+	0.895864i	$0.353442\pi$
$90$	58.5753	−	120.712i	0.650837	−	1.34124i
$91$		−	132.634i		−	1.45751i
$92$	15.7628	+	5.29679i	0.171335	+	0.0575738i
$93$			70.5369i			0.758461i
$94$	84.8465	+	13.8743i	0.902622	+	0.147599i
$95$	−156.715	−	46.7127i	−1.64963	−	0.491713i
$96$	104.418	+	109.783i	1.08769	+	1.14357i
$97$			69.4266i			0.715739i	0.933772	+	0.357869i	$0.116497\pi$
$97$			69.4266i			0.715739i	−0.933772	+	0.357869i	$0.883503\pi$
$98$	−29.0314	−	4.74729i	−0.296239	−	0.0484418i
$99$		−	44.5002i		−	0.449497i
$100$	−61.8822	−	78.5532i	−0.618822	−	0.785532i
$101$	−102.273			−1.01261			−0.506303	−	0.862356i	$-0.668988\pi$
$101$	−102.273			−1.01261			−0.506303	+	0.862356i	$0.668988\pi$
$102$	−41.2609	+	252.326i	−0.404519	+	2.47378i
$103$	56.6705			0.550199			0.275100	−	0.961416i	$-0.411289\pi$
$103$	56.6705			0.550199			0.275100	+	0.961416i	$0.411289\pi$
$104$	−62.1248	+	117.527i	−0.597354	+	1.13007i
$105$	53.9761	−	181.083i	0.514058	−	1.72460i
$106$	20.1623	−	123.300i	0.190211	−	1.16321i
$107$	−103.061			−0.963184			−0.481592	−	0.876396i	$-0.659941\pi$
$107$	−103.061			−0.963184			−0.481592	+	0.876396i	$0.659941\pi$
$108$	−79.3009	−	26.6475i	−0.734267	−	0.246736i
$109$	56.5755			0.519041			0.259520	−	0.965738i	$-0.416436\pi$
$109$	56.5755			0.519041			0.259520	+	0.965738i	$0.416436\pi$
$110$	−29.8388	−	14.4792i	−0.271262	−	0.131629i
$111$		−	22.9543i		−	0.206796i
$112$	101.794	+	77.1196i	0.908872	+	0.688568i
$113$			28.9693i			0.256365i	0.991751	+	0.128183i	$0.0409144\pi$
$113$			28.9693i			0.256365i	−0.991751	+	0.128183i	$0.959086\pi$
$114$	−49.9796	+	305.644i	−0.438418	+	2.68109i
$115$	−5.93768	+	19.9201i	−0.0516320	+	0.173218i
$116$	−218.707	−	73.4921i	−1.88540	−	0.633553i
$117$		−	222.957i		−	1.90561i
$118$	−5.06341	+	30.9646i	−0.0429102	+	0.262412i
$119$			215.511i			1.81101i
$120$	−132.646	+	135.176i	−1.10539	+	1.12647i
$121$	−11.0000			−0.0909091
$122$	11.6973	+	1.91277i	0.0958794	+	0.0156784i
$123$	−29.2527			−0.237827
$124$	18.9816	−	56.4876i	0.153077	−	0.455546i
$125$	95.4660	−	80.6923i	0.763728	−	0.645538i
$126$	−211.380	−	34.5654i	−1.67762	−	0.274328i
$127$	−83.0581			−0.654000			−0.327000	−	0.945024i	$-0.606038\pi$
$127$	−83.0581			−0.654000			−0.327000	+	0.945024i	$0.606038\pi$
$128$	−54.0776	−	116.016i	−0.422481	−	0.906372i
$129$	246.202			1.90854
$130$	−149.499	−	72.5444i	−1.15000	−	0.558034i
$131$		−	80.9381i		−	0.617848i	−0.951087	−	0.308924i	$-0.900031\pi$
$131$		−	80.9381i		−	0.617848i	0.951087	−	0.308924i	$-0.0999689\pi$
$132$	−20.0076	+	59.5411i	−0.151573	+	0.451069i
$133$			261.049i			1.96278i
$134$	105.592	+	17.2667i	0.788004	+	0.128856i
$135$	29.8717	−	100.216i	0.221272	−	0.742338i
$136$	100.944	−	190.965i	0.742234	−	1.40415i
$137$			164.303i			1.19929i	0.800266	+	0.599645i	$0.204691\pi$
$137$			164.303i			1.19929i	−0.800266	+	0.599645i	$0.795309\pi$
$138$	38.8505	+	6.35293i	0.281526	+	0.0460357i
$139$			196.202i			1.41152i	0.708449	+	0.705762i	$0.249395\pi$
$139$			196.202i			1.41152i	−0.708449	+	0.705762i	$0.750605\pi$
$140$	−91.9549	+	130.490i	−0.656821	+	0.932073i
$141$	203.529			1.44347
$142$	5.24296	−	32.0626i	0.0369222	−	0.225793i
$143$	−55.1127			−0.385403
$144$	171.115	+	129.638i	1.18830	+	0.900261i
$145$	82.3844	−	276.389i	0.568168	−	1.90613i
$146$	7.73269	−	47.2882i	0.0529636	−	0.323892i
$147$	−69.6403			−0.473743
$148$	−6.17703	+	18.3824i	−0.0417367	+	0.124205i
$149$	−22.8604			−0.153426			−0.0767129	−	0.997053i	$-0.524442\pi$
$149$	−22.8604			−0.153426			−0.0767129	+	0.997053i	$0.524442\pi$
$150$	−174.587	−	159.884i	−1.16391	−	1.06589i
$151$		−	104.875i		−	0.694540i	−0.937765	−	0.347270i	$-0.887109\pi$
$151$		−	104.875i		−	0.694540i	0.937765	−	0.347270i	$-0.112891\pi$
$152$	122.274	−	231.317i	0.804434	−	1.52182i
$153$			362.272i			2.36779i
$154$	−8.54422	+	52.2510i	−0.0554819	+	0.339292i
$155$	71.3857	+	21.2782i	0.460553	+	0.137279i
$156$	−100.243	+	298.315i	−0.642583	+	1.91228i
$157$		−	33.0112i		−	0.210262i	−0.994458	−	0.105131i	$-0.966474\pi$
$157$		−	33.0112i		−	0.210262i	0.994458	−	0.105131i	$-0.0335262\pi$
$158$	9.00690	−	55.0805i	0.0570057	−	0.348611i
$159$		−	295.771i		−	1.86019i
$160$	142.603	−	72.5570i	0.891266	−	0.453481i
$161$	33.1821			0.206100
$162$	42.8936	+	7.01407i	0.264775	+	0.0432967i
$163$	−11.6003			−0.0711676			−0.0355838	−	0.999367i	$-0.511329\pi$
$163$	−11.6003			−0.0711676			−0.0355838	+	0.999367i	$0.511329\pi$
$164$	23.4262	+	7.87192i	0.142843	+	0.0479995i
$165$	−75.2444	−	22.4284i	−0.456027	−	0.135930i
$166$	−47.5031	−	7.76782i	−0.286163	−	0.0467941i
$167$	−215.796			−1.29219			−0.646095	−	0.763257i	$-0.723599\pi$
$167$	−215.796			−1.29219			−0.646095	+	0.763257i	$0.723599\pi$
$168$	267.285	+	141.286i	1.59098	+	0.840990i
$169$	−107.128			−0.633892
$170$	242.915	+	117.874i	1.42891	+	0.693378i
$171$			438.823i			2.56622i
$172$	−197.164	−	66.2532i	−1.14630	−	0.385193i
$173$		−	241.675i		−	1.39697i	−0.715627	−	0.698483i	$-0.753859\pi$
$173$		−	241.675i		−	1.39697i	0.715627	−	0.698483i	$-0.246141\pi$
$174$	−539.045	−	88.1460i	−3.09796	−	0.506586i
$175$	−166.979	−	109.251i	−0.954166	−	0.624293i
$176$	32.0451	−	42.2979i	0.182075	−	0.240329i
$177$			74.2775i			0.419647i
$178$	−156.108	−	25.5271i	−0.877009	−	0.143411i
$179$			116.702i			0.651965i	0.945376	+	0.325983i	$0.105695\pi$
$179$			116.702i			0.651965i	−0.945376	+	0.325983i	$0.894305\pi$
$180$	−154.576	+	219.354i	−0.858754	+	1.21863i
$181$	58.1296			0.321158			0.160579	−	0.987023i	$-0.448664\pi$
$181$	58.1296			0.321158			0.160579	+	0.987023i	$0.448664\pi$
$182$	−42.8086	+	261.790i	−0.235212	+	1.43841i
$183$	28.0593			0.153330
$184$	−29.4028	−	15.5423i	−0.159798	−	0.0844690i
$185$	−23.2305	−	6.92443i	−0.125570	−	0.0374294i
$186$	22.7664	−	139.225i	0.122400	−	0.748520i
$187$	89.5501			0.478878
$188$	−162.991	−	54.7698i	−0.866971	−	0.291329i
$189$	−166.935			−0.883255
$190$	294.245	+	142.782i	1.54866	+	0.751484i
$191$			210.224i			1.10065i	0.834951	+	0.550325i	$0.185496\pi$
$191$			210.224i			1.10065i	−0.834951	+	0.550325i	$0.814504\pi$
$192$	−170.665	−	250.389i	−0.888880	−	1.30411i
$193$		−	11.9235i		−	0.0617797i	−0.999523	−	0.0308899i	$-0.990166\pi$
$193$		−	11.9235i		−	0.0617797i	0.999523	−	0.0308899i	$-0.00983412\pi$
$194$	22.4080	−	137.033i	0.115505	−	0.706357i
$195$	−376.993	−	112.372i	−1.93330	−	0.576266i
$196$	55.7696	+	18.7403i	0.284539	+	0.0956136i
$197$			314.359i			1.59573i	0.602837	+	0.797864i	$0.294037\pi$
$197$			314.359i			1.59573i	−0.602837	+	0.797864i	$0.705963\pi$
$198$	−14.3628	+	87.8338i	−0.0725394	+	0.443605i
$199$			9.66806i			0.0485832i	0.999705	+	0.0242916i	$0.00773302\pi$
$199$			9.66806i			0.0485832i	−0.999705	+	0.0242916i	$0.992267\pi$
$200$	96.7884	+	175.020i	0.483942	+	0.875100i
$201$	253.294			1.26017
$202$	201.865	+	33.0095i	0.999333	+	0.163413i
$203$	−460.397			−2.26797
$204$	162.880	−	484.719i	0.798433	−	2.37607i
$205$	−8.82440	+	29.6047i	−0.0430458	+	0.144413i
$206$	−111.855	−	18.2909i	−0.542987	−	0.0887906i
$207$	55.7790			0.269464
$208$	160.554	−	211.923i	0.771894	−	1.01886i
$209$	108.473			0.519008
$210$	−164.983	+	339.997i	−0.785634	+	1.61903i
$211$		−	0.857976i		−	0.00406624i	−0.999998	−	0.00203312i	$-0.999353\pi$
$211$		−	0.857976i		−	0.00406624i	0.999998	−	0.00203312i	$-0.000647162\pi$
$212$	−79.5922	+	236.860i	−0.375435	+	1.11727i
$213$		−	76.9114i		−	0.361086i
$214$	203.420	+	33.2637i	0.950559	+	0.155438i
$215$	74.2695	−	249.164i	0.345440	−	1.15890i
$216$	147.922	+	78.1914i	0.684825	+	0.361997i
$217$		−	118.911i		−	0.547979i
$218$	−111.668	−	18.2602i	−0.512238	−	0.0837623i
$219$		−	113.434i		−	0.517966i
$220$	54.2220	+	38.2096i	0.246464	+	0.173680i
$221$	448.668			2.03017
$222$	−7.40870	+	45.3069i	−0.0333725	+	0.204085i
$223$	246.978			1.10752			0.553762	−	0.832675i	$-0.313192\pi$
$223$	246.978			1.10752			0.553762	+	0.832675i	$0.313192\pi$
$224$	−176.028	−	185.072i	−0.785839	−	0.826215i
$225$	−280.691	−	183.651i	−1.24752	−	0.816226i
$226$	9.35007	−	57.1791i	0.0413720	−	0.253005i
$227$	317.663			1.39940			0.699698	−	0.714439i	$-0.253318\pi$
$227$	317.663			1.39940			0.699698	+	0.714439i	$0.253318\pi$
$228$	197.298	−	587.144i	0.865342	−	2.57519i
$229$	133.599			0.583401			0.291701	−	0.956510i	$-0.405779\pi$
$229$	133.599			0.583401			0.291701	+	0.956510i	$0.405779\pi$
$230$	18.1491	−	37.4016i	0.0789090	−	0.162616i
$231$			125.339i			0.542594i
$232$	407.960	+	215.647i	1.75845	+	0.929513i
$233$		−	195.429i		−	0.838753i	−0.907812	−	0.419376i	$-0.862249\pi$
$233$		−	195.429i		−	0.838753i	0.907812	−	0.419376i	$-0.137751\pi$
$234$	−71.9611	+	440.068i	−0.307526	+	1.88063i
$235$	61.3967	−	205.978i	0.261263	−	0.876501i
$236$	19.9882	−	59.4832i	0.0846956	−	0.252048i
$237$		−	132.126i		−	0.557495i
$238$	69.5578	−	425.371i	0.292260	−	1.78727i
$239$		−	417.886i		−	1.74847i	−0.485499	−	0.874237i	$-0.661362\pi$
$239$		−	417.886i		−	1.74847i	0.485499	−	0.874237i	$-0.338638\pi$
$240$	305.445	−	223.996i	1.27269	−	0.933317i
$241$	−321.343			−1.33337			−0.666687	−	0.745338i	$-0.732288\pi$
$241$	−321.343			−1.33337			−0.666687	+	0.745338i	$0.732288\pi$
$242$	21.7116	+	3.55034i	0.0897175	+	0.0146708i
$243$	291.124			1.19804
$244$	−22.4706	−	7.55079i	−0.0920925	−	0.0309459i
$245$	−21.0078	+	70.4783i	−0.0857460	+	0.287666i
$246$	57.7385	+	9.44154i	0.234709	+	0.0383802i
$247$	543.474			2.20030
$248$	−55.6974	+	105.368i	−0.224586	+	0.424871i
$249$	−113.950			−0.457630
$250$	−214.473	+	128.457i	−0.857894	+	0.513827i
$251$			276.231i			1.10052i	0.834993	+	0.550261i	$0.185472\pi$
$251$			276.231i			1.10052i	−0.834993	+	0.550261i	$0.814528\pi$
$252$	406.062	+	136.449i	1.61136	+	0.541465i
$253$		−	13.7880i		−	0.0544981i
$254$	163.939	+	26.8077i	0.645428	+	0.105542i
$255$	612.559	+	182.588i	2.40219	+	0.716032i
$256$	69.2926	+	246.444i	0.270674	+	0.962671i
$257$		−	460.052i		−	1.79008i	−0.445982	−	0.895042i	$-0.647145\pi$
$257$		−	460.052i		−	1.79008i	0.445982	−	0.895042i	$-0.352855\pi$
$258$	−485.949	−	79.4636i	−1.88352	−	0.307999i
$259$			38.6965i			0.149407i
$260$	271.665	+	191.439i	1.04487	+	0.736305i
$261$	−773.925			−2.96523
$262$	−26.1234	+	159.754i	−0.0997077	+	0.609749i
$263$	101.763			0.386932			0.193466	−	0.981107i	$-0.438027\pi$
$263$	101.763			0.386932			0.193466	+	0.981107i	$0.438027\pi$
$264$	58.7081	−	111.064i	0.222379	−	0.420696i
$265$	−299.330	−	89.2226i	−1.12955	−	0.336689i
$266$	84.2558	−	515.255i	0.316751	−	1.93705i
$267$	−374.469			−1.40251
$268$	−202.844	−	68.1617i	−0.756880	−	0.254335i
$269$	−32.5721			−0.121086			−0.0605430	−	0.998166i	$-0.519283\pi$
$269$	−32.5721			−0.121086			−0.0605430	+	0.998166i	$0.519283\pi$
$270$	−91.3058	+	188.163i	−0.338170	+	0.696899i
$271$			328.890i			1.21362i	0.794849	+	0.606808i	$0.207550\pi$
$271$			328.890i			1.21362i	−0.794849	+	0.606808i	$0.792450\pi$
$272$	−260.877	+	344.343i	−0.959106	+	1.26597i
$273$			627.980i			2.30029i
$274$	53.0300	−	324.298i	0.193540	−	1.18357i
$275$	−45.3967	+	69.3840i	−0.165079	+	0.252306i
$276$	−74.6321	−	25.0786i	−0.270406	−	0.0908647i
$277$			253.434i			0.914922i	0.889230	+	0.457461i	$0.151241\pi$
$277$			253.434i			0.914922i	−0.889230	+	0.457461i	$0.848759\pi$
$278$	63.3258	−	387.260i	0.227791	−	1.39302i
$279$		−	199.890i		−	0.716450i
$280$	223.616	−	227.881i	0.798628	−	0.813859i
$281$	−5.26579			−0.0187395			−0.00936973	−	0.999956i	$-0.502983\pi$
$281$	−5.26579			−0.0187395			−0.00936973	+	0.999956i	$0.502983\pi$
$282$	−401.722	−	65.6905i	−1.42455	−	0.232945i
$283$	293.265			1.03627			0.518135	−	0.855299i	$-0.326626\pi$
$283$	293.265			1.03627			0.518135	+	0.855299i	$0.326626\pi$
$284$	−20.6969	+	61.5925i	−0.0728766	+	0.216875i
$285$	741.997	+	221.170i	2.60350	+	0.776036i
$286$	108.781	+	17.7881i	0.380352	+	0.0621960i
$287$	49.3143			0.171827
$288$	−295.902	−	311.106i	−1.02744	−	1.08023i
$289$	−440.020			−1.52256
$290$	−251.816	+	518.941i	−0.868330	+	1.78945i
$291$		−	328.714i		−	1.12960i
$292$	−30.5253	+	90.8410i	−0.104539	+	0.311099i
$293$		−	116.785i		−	0.398582i	−0.979940	−	0.199291i	$-0.936136\pi$
$293$		−	116.785i		−	0.398582i	0.979940	−	0.199291i	$-0.0638639\pi$
$294$	137.455	+	22.4770i	0.467534	+	0.0764523i
$295$	75.1713	+	22.4066i	0.254818	+	0.0759547i
$296$	18.1252	−	34.2892i	0.0612338	−	0.115842i
$297$			69.3658i			0.233555i
$298$	45.1216	+	7.37839i	0.151415	+	0.0247597i
$299$		−	69.0813i		−	0.231041i
$300$	292.993	+	371.925i	0.976643	+	1.23975i
$301$	−415.048			−1.37890
$302$	−33.8494	+	207.002i	−0.112084	+	0.685436i
$303$	484.232			1.59813
$304$	−316.002	+	417.106i	−1.03948	+	1.37206i
$305$	8.46441	−	28.3969i	0.0277522	−	0.0931047i
$306$	116.926	−	715.047i	0.382112	−	2.33676i
$307$	−251.246			−0.818390			−0.409195	−	0.912447i	$-0.634190\pi$
$307$	−251.246			−0.818390			−0.409195	+	0.912447i	$0.634190\pi$
$308$	33.7289	−	100.375i	0.109509	−	0.325892i
$309$	−268.317			−0.868341
$310$	−134.032	−	65.0390i	−0.432362	−	0.209803i
$311$		−	445.477i		−	1.43240i	−0.697894	−	0.716201i	$-0.745880\pi$
$311$		−	445.477i		−	1.43240i	0.697894	−	0.716201i	$-0.254120\pi$
$312$	294.142	−	556.456i	0.942762	−	1.78351i
$313$			424.911i			1.35754i	0.734349	+	0.678772i	$0.237488\pi$
$313$			424.911i			1.35754i	−0.734349	+	0.678772i	$0.762512\pi$
$314$	−10.6546	+	65.1570i	−0.0339319	+	0.207506i
$315$	−152.959	+	513.157i	−0.485584	+	1.62907i
$316$	−35.5553	+	105.810i	−0.112517	+	0.334842i
$317$		−	52.2687i		−	0.164886i	−0.996596	−	0.0824428i	$-0.973728\pi$
$317$		−	52.2687i		−	0.164886i	0.996596	−	0.0824428i	$-0.0262722\pi$
$318$	−95.4624	+	583.788i	−0.300196	+	1.83581i
$319$			191.307i			0.599707i
$320$	−304.885	+	97.1858i	−0.952766	+	0.303706i
$321$	487.961			1.52013
$322$	−65.4944	−	10.7098i	−0.203399	−	0.0332602i
$323$	−883.067			−2.73395
$324$	−82.3989	−	27.6885i	−0.254318	−	0.0854584i
$325$	−227.448	+	347.631i	−0.699841	+	1.06963i
$326$	22.8965	+	3.74410i	0.0702348	+	0.0114850i
$327$	−267.867			−0.819166
$328$	−43.6976	−	23.0985i	−0.133224	−	0.0704222i
$329$	−343.109			−1.04289
$330$	141.277	+	68.5547i	0.428113	+	0.207741i
$331$			204.652i			0.618283i	0.951016	+	0.309141i	$0.100042\pi$
$331$			204.652i			0.618283i	−0.951016	+	0.309141i	$0.899958\pi$
$332$	91.2537	+	30.6640i	0.274861	+	0.0923615i
$333$			65.0486i			0.195341i
$334$	425.934	+	69.6498i	1.27525	+	0.208532i
$335$	76.4090	−	256.342i	0.228086	−	0.765199i
$336$	−481.962	−	365.137i	−1.43441	−	1.08672i
$337$			24.2768i			0.0720379i	0.999351	+	0.0360190i	$0.0114677\pi$
$337$			24.2768i			0.0720379i	−0.999351	+	0.0360190i	$0.988532\pi$
$338$	211.447	+	34.5764i	0.625583	+	0.102297i
$339$		−	137.161i		−	0.404603i
$340$	−441.417	−	311.061i	−1.29829	−	0.914886i
$341$	−49.4107			−0.144899
$342$	141.634	−	866.142i	0.414134	−	2.53258i
$343$	−273.706			−0.797978
$344$	367.776	+	194.406i	1.06912	+	0.565133i
$345$	28.1131	−	94.3156i	0.0814871	−	0.273378i
$346$	−78.0026	+	477.014i	−0.225441	+	1.37865i
$347$	95.8193			0.276136			0.138068	−	0.990423i	$-0.455911\pi$
$347$	95.8193			0.276136			0.138068	+	0.990423i	$0.455911\pi$
$348$	1035.51	+	347.963i	2.97560	+	0.999892i
$349$	383.059			1.09759			0.548795	−	0.835957i	$-0.315087\pi$
$349$	383.059			1.09759			0.548795	+	0.835957i	$0.315087\pi$
$350$	294.319	+	269.532i	0.840911	+	0.770092i
$351$			347.540i			0.990141i
$352$	−76.9022	+	73.1441i	−0.218472	+	0.207796i
$353$		−	167.048i		−	0.473224i	−0.971604	−	0.236612i	$-0.923963\pi$
$353$		−	167.048i		−	0.473224i	0.971604	−	0.236612i	$-0.0760369\pi$
$354$	23.9737	−	146.608i	0.0677223	−	0.414147i
$355$	−77.8369	−	23.2012i	−0.219259	−	0.0653555i
$356$	299.884	+	100.770i	0.842370	+	0.283062i
$357$		−	1020.38i		−	2.85820i
$358$	37.6665	−	230.344i	0.105214	−	0.643420i
$359$			251.837i			0.701497i	0.936470	+	0.350748i	$0.114073\pi$
$359$			251.837i			0.701497i	−0.936470	+	0.350748i	$0.885927\pi$
$360$	375.897	−	383.066i	1.04416	−	1.06407i
$361$	−708.665			−1.96306
$362$	−114.735	−	18.7618i	−0.316949	−	0.0518282i
$363$	52.0816			0.143476
$364$	168.990	−	502.901i	0.464258	−	1.38160i
$365$	−114.799	−	34.2188i	−0.314519	−	0.0937501i
$366$	−55.3831	−	9.05637i	−0.151320	−	0.0247442i
$367$	−98.4658			−0.268299			−0.134150	−	0.990961i	$-0.542830\pi$
$367$	−98.4658			−0.268299			−0.134150	+	0.990961i	$0.542830\pi$
$368$	53.0185	+	40.1672i	0.144072	+	0.109150i
$369$	82.8971			0.224653
$370$	43.6172	+	21.1652i	0.117884	+	0.0572032i
$371$			498.611i			1.34397i
$372$	−89.8718	+	267.452i	−0.241591	+	0.718956i
$373$		−	106.337i		−	0.285087i	−0.989789	−	0.142543i	$-0.954472\pi$
$373$		−	106.337i		−	0.285087i	0.989789	−	0.142543i	$-0.0455280\pi$
$374$	−176.753	−	28.9030i	−0.472601	−	0.0772808i
$375$	−452.002	+	382.053i	−1.20534	+	1.01881i
$376$	304.031	+	160.710i	0.808593	+	0.427421i
$377$			958.493i			2.54242i
$378$	329.494	+	53.8797i	0.871678	+	0.142539i
$379$			22.1653i			0.0584837i	0.999572	+	0.0292418i	$0.00930929\pi$
$379$			22.1653i			0.0584837i	−0.999572	+	0.0292418i	$0.990691\pi$
$380$	−534.692	−	376.791i	−1.40708	−	0.991554i
$381$	393.254			1.03216
$382$	67.8515	−	414.937i	0.177622	−	1.08622i
$383$	280.276			0.731790			0.365895	−	0.930656i	$-0.380763\pi$
$383$	280.276			0.731790			0.365895	+	0.930656i	$0.380763\pi$
$384$	256.041	+	549.298i	0.666773	+	1.43046i
$385$	126.847	+	37.8100i	0.329474	+	0.0982077i
$386$	−3.84840	+	23.5344i	−0.00996996	+	0.0609700i
$387$	−697.694			−1.80283
$388$	−88.4572	+	263.242i	−0.227982	+	0.678458i
$389$	352.236			0.905490			0.452745	−	0.891640i	$-0.350445\pi$
$389$	352.236			0.905490			0.452745	+	0.891640i	$0.350445\pi$
$390$	707.834	+	343.476i	1.81496	+	0.880707i
$391$			112.247i			0.287077i
$392$	−104.029	−	54.9894i	−0.265379	−	0.140279i
$393$			383.217i			0.975106i
$394$	101.462	−	620.476i	0.257517	−	1.57481i
$395$	−133.716	−	39.8574i	−0.338522	−	0.100905i
$396$	56.6981	−	168.729i	0.143177	−	0.426084i
$397$		−	216.236i		−	0.544676i	−0.962202	−	0.272338i	$-0.912203\pi$
$397$		−	216.236i		−	0.544676i	0.962202	−	0.272338i	$-0.0877968\pi$
$398$	3.12044	−	19.0827i	0.00784031	−	0.0479464i
$399$		−	1235.99i		−	3.09772i
$400$	−134.550	−	376.691i	−0.336376	−	0.941728i
$401$	548.165			1.36700			0.683498	−	0.729952i	$-0.260458\pi$
$401$	548.165			1.36700			0.683498	+	0.729952i	$0.260458\pi$
$402$	−499.948	−	81.7527i	−1.24365	−	0.203365i
$403$	−247.560			−0.614292
$404$	−387.784	−	130.307i	−0.959863	−	0.322543i
$405$	31.0387	−	104.131i	0.0766388	−	0.257113i
$406$	908.725	+	148.597i	2.23824	+	0.366002i
$407$	16.0794			0.0395071
$408$	−477.938	+	904.160i	−1.17142	+	2.21608i
$409$	−715.299			−1.74890			−0.874448	−	0.485119i	$-0.838776\pi$
$409$	−715.299			−1.74890			−0.874448	+	0.485119i	$0.838776\pi$
$410$	26.9726	−	55.5851i	0.0657869	−	0.135573i
$411$		−	777.923i		−	1.89276i
$412$	214.875	+	72.2045i	0.521541	+	0.175254i
$413$		−	125.217i		−	0.303190i
$414$	−110.096	−	18.0031i	−0.265932	−	0.0434858i
$415$	−34.3742	+	115.321i	−0.0828295	+	0.277882i
$416$	−385.299	+	366.469i	−0.926198	+	0.880936i
$417$		−	928.956i		−	2.22771i
$418$	−214.102	−	35.0104i	−0.512205	−	0.0837570i
$419$		−	122.220i		−	0.291695i	−0.989307	−	0.145848i	$-0.953409\pi$
$419$		−	122.220i		−	0.291695i	0.989307	−	0.145848i	$-0.0465909\pi$
$420$	435.378	−	617.831i	1.03661	−	1.47103i
$421$	252.558			0.599900			0.299950	−	0.953955i	$-0.403030\pi$
$421$	252.558			0.599900			0.299950	+	0.953955i	$0.403030\pi$
$422$	−0.276919	+	1.69346i	−0.000656206	+	0.00401294i
$423$	−576.765			−1.36351
$424$	233.546	−	441.822i	0.550817	−	1.04203i
$425$	369.570	−	564.850i	0.869577	−	1.32906i
$426$	−24.8238	+	151.807i	−0.0582718	+	0.356354i
$427$	−47.3025			−0.110779
$428$	−390.770	−	131.311i	−0.913015	−	0.306801i
$429$	260.941			0.608255
$430$	−227.012	+	467.826i	−0.527935	+	1.08797i
$431$		−	342.069i		−	0.793663i	−0.917892	−	0.396831i	$-0.870110\pi$
$431$		−	342.069i		−	0.793663i	0.917892	−	0.396831i	$-0.129890\pi$
$432$	−266.730	−	202.076i	−0.617430	−	0.467769i
$433$			736.676i			1.70133i	0.525707	+	0.850666i	$0.323801\pi$
$433$			736.676i			1.70133i	−0.525707	+	0.850666i	$0.676199\pi$
$434$	−38.3796	+	234.706i	−0.0884323	+	0.540796i
$435$	−390.065	+	1308.61i	−0.896700	+	3.00831i
$436$	214.515	+	72.0834i	0.492006	+	0.165329i
$437$			135.966i			0.311134i
$438$	−36.6119	+	223.895i	−0.0835888	+	0.511176i
$439$			358.512i			0.816656i	0.912835	+	0.408328i	$0.133888\pi$
$439$			358.512i			0.816656i	−0.912835	+	0.408328i	$0.866112\pi$
$440$	−94.6901	−	92.9181i	−0.215205	−	0.211178i
$441$	197.349			0.447503
$442$	−885.573	−	144.811i	−2.00356	−	0.327627i
$443$	673.951			1.52133			0.760667	−	0.649142i	$-0.224872\pi$
$443$	673.951			1.52133			0.760667	+	0.649142i	$0.224872\pi$
$444$	29.2463	−	87.0349i	0.0658702	−	0.196024i
$445$	−112.963	+	378.975i	−0.253849	+	0.851629i
$446$	−487.481	−	79.7142i	−1.09301	−	0.178731i
$447$	108.237			0.242141
$448$	287.708	+	422.107i	0.642204	+	0.942203i
$449$	506.931			1.12902			0.564511	−	0.825425i	$-0.309065\pi$
$449$	506.931			1.12902			0.564511	+	0.825425i	$0.309065\pi$
$450$	494.749	+	453.082i	1.09944	+	1.00685i
$451$		−	20.4913i		−	0.0454353i
$452$	−36.9101	+	109.841i	−0.0816594	+	0.243012i
$453$			496.553i			1.09614i
$454$	−626.998	−	102.528i	−1.38105	−	0.225833i
$455$	635.536	+	189.437i	1.39678	+	0.416345i
$456$	−578.929	+	1095.22i	−1.26958	+	2.40179i
$457$			130.803i			0.286221i	0.989707	+	0.143110i	$0.0457104\pi$
$457$			130.803i			0.286221i	−0.989707	+	0.143110i	$0.954290\pi$
$458$	−263.695	−	43.1201i	−0.575754	−	0.0941488i
$459$		−	564.701i		−	1.23029i
$460$	−47.8940	+	67.9649i	−0.104117	+	0.147750i
$461$	−232.740			−0.504859			−0.252430	−	0.967615i	$-0.581230\pi$
$461$	−232.740			−0.504859			−0.252430	+	0.967615i	$0.581230\pi$
$462$	40.4542	−	247.393i	0.0875633	−	0.535482i
$463$	49.3198			0.106522			0.0532611	−	0.998581i	$-0.483038\pi$
$463$	49.3198			0.106522			0.0532611	+	0.998581i	$0.483038\pi$
$464$	−735.624	−	557.314i	−1.58540	−	1.20111i
$465$	−337.989	−	100.746i	−0.726858	−	0.216658i
$466$	−63.0764	+	385.736i	−0.135357	+	0.827759i
$467$	521.442			1.11658			0.558289	−	0.829647i	$-0.311458\pi$
$467$	521.442			1.11658			0.558289	+	0.829647i	$0.311458\pi$
$468$	284.071	−	845.374i	0.606990	−	1.80636i
$469$	−427.004			−0.910456
$470$	−187.665	+	386.739i	−0.399287	+	0.822850i
$471$			156.298i			0.331842i
$472$	−58.6510	+	110.956i	−0.124261	+	0.235076i
$473$			172.463i			0.364615i
$474$	−42.6449	+	260.789i	−0.0899681	+	0.550188i
$475$	447.663	−	684.206i	0.942449	−	1.44043i
$476$	−274.584	+	817.141i	−0.576858	+	1.71668i
$477$			838.164i			1.75716i
$478$	−134.876	+	824.816i	−0.282167	+	1.72556i
$479$			473.099i			0.987681i	0.869552	+	0.493841i	$0.164407\pi$
$479$			473.099i			0.987681i	−0.869552	+	0.493841i	$0.835593\pi$
$480$	−675.179	+	343.535i	−1.40662	+	0.715698i
$481$	80.5616			0.167488
$482$	634.262	+	103.716i	1.31590	+	0.215179i
$483$	−157.107			−0.325273
$484$	−41.7082	−	14.0152i	−0.0861740	−	0.0289571i
$485$	−332.669	−	99.1602i	−0.685916	−	0.204454i
$486$	−574.616	−	93.9626i	−1.18234	−	0.193339i
$487$	−100.945			−0.207280			−0.103640	−	0.994615i	$-0.533049\pi$
$487$	−100.945			−0.207280			−0.103640	+	0.994615i	$0.533049\pi$
$488$	41.9150	+	22.1562i	0.0858914	+	0.0454020i
$489$	54.9240			0.112319
$490$	64.2123	−	132.328i	0.131045	−	0.270058i
$491$			18.4996i			0.0376773i	0.999823	+	0.0188387i	$0.00599689\pi$
$491$			18.4996i			0.0376773i	−0.999823	+	0.0188387i	$0.994003\pi$
$492$	−110.916	−	37.2711i	−0.225439	−	0.0757543i
$493$		−	1557.41i		−	3.15905i
$494$	−1072.70	−	175.411i	−2.17146	−	0.355083i
$495$	213.230	+	63.5584i	0.430767	+	0.128401i
$496$	143.943	−	189.997i	0.290208	−	0.383059i
$497$			129.658i			0.260880i
$498$	224.912	+	36.7782i	0.451631	+	0.0738519i
$499$		−	764.191i		−	1.53145i	−0.643171	−	0.765723i	$-0.722382\pi$
$499$		−	764.191i		−	1.53145i	0.643171	−	0.765723i	$-0.277618\pi$
$500$	464.785	−	184.323i	0.929570	−	0.368646i
$501$	1021.73			2.03937
$502$	89.1558	−	545.221i	0.177601	−	1.08610i
$503$	519.882			1.03356			0.516781	−	0.856118i	$-0.327130\pi$
$503$	519.882			1.03356			0.516781	+	0.856118i	$0.327130\pi$
$504$	−757.440	−	400.381i	−1.50286	−	0.794408i
$505$	146.074	−	490.059i	0.289255	−	0.970413i
$506$	−4.45019	+	27.2146i	−0.00879485	+	0.0537837i
$507$	507.217			1.00043
$508$	−314.927	−	105.825i	−0.619936	−	0.208317i
$509$	731.539			1.43721			0.718604	−	0.695420i	$-0.244781\pi$
$509$	731.539			1.43721			0.718604	+	0.695420i	$0.244781\pi$
$510$	−1150.13	−	558.098i	−2.25515	−	1.09431i
$511$			191.228i			0.374224i
$512$	−57.2269	−	508.792i	−0.111771	−	0.993734i
$513$		−	684.027i		−	1.33339i
$514$	−148.485	+	908.043i	−0.288882	+	1.76662i
$515$	−80.9409	+	271.546i	−0.157167	+	0.527274i
$516$	933.512	+	313.688i	1.80913	+	0.607923i
$517$			142.571i			0.275765i
$518$	12.4896	−	76.3786i	0.0241112	−	0.147449i
$519$			1144.26i			2.20473i
$520$	−474.421	−	465.542i	−0.912347	−	0.895273i
$521$	−913.393			−1.75315			−0.876577	−	0.481262i	$-0.840179\pi$
$521$	−913.393			−1.75315			−0.876577	+	0.481262i	$0.840179\pi$
$522$	1527.56	+	249.791i	2.92636	+	0.478526i
$523$	662.576			1.26688			0.633438	−	0.773793i	$-0.281643\pi$
$523$	662.576			1.26688			0.633438	+	0.773793i	$0.281643\pi$
$524$	103.124	−	306.889i	0.196802	−	0.585666i
$525$	790.594	+	517.271i	1.50589	+	0.985278i
$526$	−200.859	−	32.8449i	−0.381861	−	0.0624428i
$527$	402.248			0.763280
$528$	−151.724	+	200.267i	−0.287356	+	0.379294i
$529$	−511.717			−0.967330
$530$	562.015	+	272.717i	1.06041	+	0.514561i
$531$		−	210.490i		−	0.396403i
$532$	−332.606	+	989.809i	−0.625199	+	1.86054i
$533$		−	102.667i		−	0.192620i
$534$	739.121	+	120.863i	1.38412	+	0.226335i
$535$	147.199	−	493.832i	0.275138	−	0.923051i
$536$	378.370	+	200.006i	0.705915	+	0.373145i
$537$		−	552.547i		−	1.02895i
$538$	64.2904	+	10.5129i	0.119499	+	0.0195407i
$539$		−	48.7826i		−	0.0905058i
$540$	240.949	−	341.923i	0.446202	−	0.633191i
$541$	334.290			0.617912			0.308956	−	0.951076i	$-0.400020\pi$
$541$	334.290			0.617912			0.308956	+	0.951076i	$0.400020\pi$
$542$	106.152	−	649.158i	0.195852	−	1.19771i
$543$	−275.226			−0.506862
$544$	626.054	−	595.460i	1.15084	−	1.09460i
$545$	−80.8052	+	271.091i	−0.148266	+	0.497414i
$546$	202.686	−	1239.50i	0.371219	−	2.27014i
$547$	−750.195			−1.37147			−0.685736	−	0.727851i	$-0.740519\pi$
$547$	−750.195			−1.37147			−0.685736	+	0.727851i	$0.740519\pi$
$548$	−209.340	+	622.979i	−0.382007	+	1.13682i
$549$	−79.5153			−0.144837
$550$	111.997	−	122.297i	0.203632	−	0.222358i
$551$		−	1886.50i		−	3.42378i
$552$	139.213	+	73.5880i	0.252198	+	0.133312i
$553$			222.739i			0.402783i
$554$	81.7977	−	500.223i	0.147649	−	0.902930i
$555$	109.989	+	32.7850i	0.198179	+	0.0590721i
$556$	−249.983	+	743.930i	−0.449610	+	1.33800i
$557$			599.474i			1.07626i	0.842863	+	0.538128i	$0.180868\pi$
$557$			599.474i			1.07626i	−0.842863	+	0.538128i	$0.819132\pi$
$558$	−64.5160	+	394.539i	−0.115620	+	0.707059i
$559$			864.081i			1.54576i
$560$	−514.920	+	377.613i	−0.919500	+	0.674309i
$561$	−423.992			−0.755779
$562$	10.3935	+	1.69958i	0.0184938	+	0.00302416i
$563$	123.380			0.219147			0.109573	−	0.993979i	$-0.465052\pi$
$563$	123.380			0.219147			0.109573	+	0.993979i	$0.465052\pi$
$564$	771.710	+	259.318i	1.36828	+	0.459784i
$565$	−138.811	−	41.3760i	−0.245683	−	0.0732319i
$566$	−578.841	−	94.6536i	−1.02269	−	0.167232i
$567$	−173.457			−0.305920
$568$	60.7308	−	114.890i	0.106920	−	0.202272i
$569$	−357.450			−0.628208			−0.314104	−	0.949389i	$-0.601704\pi$
$569$	−357.450			−0.628208			−0.314104	+	0.949389i	$0.601704\pi$
$570$	−1393.16	−	676.028i	−2.44414	−	1.18601i
$571$		−	146.201i		−	0.256045i	−0.991771	−	0.128022i	$-0.959137\pi$
$571$		−	146.201i		−	0.256045i	0.991771	−	0.128022i	$-0.0408629\pi$
$572$	−208.968	−	70.2196i	−0.365329	−	0.122762i
$573$		−	995.346i		−	1.73708i
$574$	−97.3358	−	15.9166i	−0.169574	−	0.0277292i
$575$	−86.9698	−	56.9027i	−0.151252	−	0.0989612i
$576$	483.635	+	709.560i	0.839644	+	1.23188i
$577$			243.693i			0.422345i	0.977449	+	0.211172i	$0.0677281\pi$
$577$			243.693i			0.422345i	−0.977449	+	0.211172i	$0.932272\pi$
$578$	868.505	+	142.020i	1.50260	+	0.245709i
$579$			56.4540i			0.0975027i
$580$	664.523	−	943.003i	1.14573	−	1.62587i
$581$	192.097			0.330632
$582$	−106.095	+	648.810i	−0.182294	+	1.11479i
$583$	207.186			0.355379
$584$	89.5701	−	169.448i	0.153374	−	0.290151i
$585$	1068.33	+	318.443i	1.82621	+	0.544347i
$586$	−37.6932	+	230.508i	−0.0643228	+	0.393358i
$587$	367.994			0.626906			0.313453	−	0.949604i	$-0.398514\pi$
$587$	367.994			0.626906			0.313453	+	0.949604i	$0.398514\pi$
$588$	−264.052	−	88.7294i	−0.449068	−	0.150900i
$589$	487.246			0.827244
$590$	−141.140	−	68.4881i	−0.239220	−	0.116081i
$591$		−	1488.39i		−	2.51843i
$592$	−46.8423	+	61.8294i	−0.0791256	+	0.104442i
$593$		−	590.301i		−	0.995448i	−0.867335	−	0.497724i	$-0.834169\pi$
$593$		−	590.301i		−	0.995448i	0.867335	−	0.497724i	$-0.165831\pi$
$594$	22.3884	−	136.913i	0.0376909	−	0.230494i
$595$	−1032.65	−	307.808i	−1.73555	−	0.517324i
$596$	−86.6789	−	29.1267i	−0.145434	−	0.0488703i
$597$		−	45.7753i		−	0.0766755i
$598$	−22.2965	+	136.352i	−0.0372852	+	0.228013i
$599$			805.119i			1.34410i	0.740504	+	0.672052i	$0.234587\pi$
$599$			805.119i			1.34410i	−0.740504	+	0.672052i	$0.765413\pi$
$600$	−458.263	−	828.666i	−0.763772	−	1.38111i
$601$	−448.802			−0.746759			−0.373380	−	0.927679i	$-0.621801\pi$
$601$	−448.802			−0.746759			−0.373380	+	0.927679i	$0.621801\pi$
$602$	819.215	+	133.960i	1.36082	+	0.222525i
$603$	−717.792			−1.19037
$604$	133.623	−	397.652i	0.221230	−	0.658364i
$605$	15.7110	−	52.7083i	0.0259686	−	0.0871211i
$606$	−955.770	−	156.290i	−1.57718	−	0.257904i
$607$	988.361			1.62827			0.814136	−	0.580675i	$-0.197211\pi$
$607$	988.361			1.62827			0.814136	+	0.580675i	$0.197211\pi$
$608$	758.344	−	721.285i	1.24728	−	1.18632i
$609$	2179.84			3.57937
$610$	−25.8723	+	53.3175i	−0.0424135	+	0.0874057i
$611$			714.314i			1.16909i
$612$	−461.575	+	1373.61i	−0.754207	+	2.24446i
$613$		−	872.852i		−	1.42390i	−0.702229	−	0.711951i	$-0.747812\pi$
$613$		−	872.852i		−	1.42390i	0.702229	−	0.711951i	$-0.252188\pi$
$614$	495.905	+	81.0916i	0.807663	+	0.132071i
$615$	41.7808	−	140.169i	0.0679363	−	0.227917i
$616$	−98.9703	+	187.232i	−0.160666	+	0.303947i
$617$		−	717.022i		−	1.16211i	−0.813864	−	0.581055i	$-0.802640\pi$
$617$		−	717.022i		−	1.16211i	0.813864	−	0.581055i	$-0.197360\pi$
$618$	529.601	+	86.6016i	0.856959	+	0.140132i
$619$			233.773i			0.377662i	0.982010	+	0.188831i	$0.0604699\pi$
$619$			233.773i			0.377662i	−0.982010	+	0.188831i	$0.939530\pi$
$620$	243.559	+	171.633i	0.392837	+	0.276827i
$621$	−86.9470			−0.140011
$622$	−143.781	+	879.275i	−0.231160	+	1.41363i
$623$	631.281			1.01329
$624$	−760.173	+	1003.39i	−1.21823	+	1.60799i
$625$	250.299	+	572.691i	0.400478	+	0.916306i
$626$	137.144	−	838.683i	0.219079	−	1.33975i
$627$	−513.585			−0.819114
$628$	42.0599	−	125.167i	0.0669744	−	0.199311i
$629$	−130.901			−0.208109
$630$	467.534	−	963.493i	0.742117	−	1.52935i
$631$			51.5454i			0.0816884i	0.999166	+	0.0408442i	$0.0130047\pi$
$631$			51.5454i			0.0816884i	−0.999166	+	0.0408442i	$0.986995\pi$
$632$	104.330	−	197.370i	0.165079	−	0.312295i
$633$			4.06225i			0.00641746i
$634$	−16.8702	+	103.167i	−0.0266091	+	0.162724i
$635$	118.630	−	397.986i	0.186818	−	0.626750i
$636$	376.845	−	1121.46i	0.592523	−	1.76330i
$637$		−	244.413i		−	0.383694i
$638$	61.7458	−	377.598i	0.0967802	−	0.591847i
$639$			217.954i			0.341086i
$640$	633.145	−	93.4197i	0.989289	−	0.145968i
$641$	558.971			0.872030			0.436015	−	0.899939i	$-0.356390\pi$
$641$	558.971			0.872030			0.436015	+	0.899939i	$0.356390\pi$
$642$	−963.129	−	157.493i	−1.50020	−	0.245317i
$643$	−732.573			−1.13930			−0.569652	−	0.821886i	$-0.692922\pi$
$643$	−732.573			−1.13930			−0.569652	+	0.821886i	$0.692922\pi$
$644$	125.815	+	42.2777i	0.195365	+	0.0656486i
$645$	−351.643	+	1179.72i	−0.545184	+	1.82902i
$646$	1742.98	+	285.017i	2.69812	+	0.441203i
$647$	787.541			1.21722			0.608610	−	0.793470i	$-0.291728\pi$
$647$	787.541			1.21722			0.608610	+	0.793470i	$0.291728\pi$
$648$	153.701	+	81.2461i	0.237193	+	0.125380i
$649$	−52.0310			−0.0801710
$650$	561.135	−	612.738i	0.863284	−	0.942673i
$651$			563.009i			0.864837i
$652$	−43.9844	−	14.7801i	−0.0674608	−	0.0226689i
$653$		−	1098.35i		−	1.68201i	−0.541026	−	0.841006i	$-0.681964\pi$
$653$		−	1098.35i		−	1.68201i	0.541026	−	0.841006i	$-0.318036\pi$
$654$	528.713	+	86.4564i	0.808429	+	0.132196i
$655$	387.828	+	115.602i	0.592104	+	0.176491i
$656$	78.7945	+	59.6952i	0.120114	+	0.0909988i
$657$			321.454i			0.489275i
$658$	677.224	+	110.741i	1.02922	+	0.168300i
$659$		−	606.310i		−	0.920046i	−0.887907	−	0.460023i	$-0.847841\pi$
$659$		−	606.310i		−	0.920046i	0.887907	−	0.460023i	$-0.152159\pi$
$660$	−256.725	−	180.911i	−0.388977	−	0.274107i
$661$	1154.82			1.74708			0.873538	−	0.486757i	$-0.161820\pi$
$661$	1154.82			1.74708			0.873538	+	0.486757i	$0.161820\pi$
$662$	66.0530	−	403.938i	0.0997779	−	0.610179i
$663$	−2124.30			−3.20408
$664$	−170.218	−	89.9770i	−0.256353	−	0.135508i
$665$	−1250.86	−	372.850i	−1.88099	−	0.560676i
$666$	20.9950	−	128.392i	0.0315240	−	0.192781i
$667$	−239.794			−0.359512
$668$	−818.223	−	274.948i	−1.22488	−	0.411598i
$669$	−1169.36			−1.74793
$670$	−233.551	+	481.302i	−0.348584	+	0.718361i
$671$			19.6554i			0.0292927i
$672$	833.438	+	876.260i	1.24023	+	1.30396i
$673$			782.062i			1.16205i	0.813884	+	0.581027i	$0.197349\pi$
$673$			782.062i			1.16205i	−0.813884	+	0.581027i	$0.802651\pi$
$674$	7.83553	−	47.9171i	0.0116254	−	0.0710937i
$675$	437.535	+	286.271i	0.648199	+	0.424105i
$676$	−406.191	−	136.493i	−0.600875	−	0.201912i
$677$			746.901i			1.10325i	0.834092	+	0.551626i	$0.185992\pi$
$677$			746.901i			1.10325i	−0.834092	+	0.551626i	$0.814008\pi$
$678$	−44.2697	+	270.725i	−0.0652945	+	0.399300i
$679$			554.147i			0.816122i
$680$	770.865	+	756.439i	1.13362	+	1.11241i
$681$	−1504.04			−2.20857
$682$	97.5261	+	15.9477i	0.143000	+	0.0233837i
$683$	−953.904			−1.39664			−0.698319	−	0.715786i	$-0.746068\pi$
$683$	−953.904			−1.39664			−0.698319	+	0.715786i	$0.746068\pi$
$684$	−559.109	+	1663.86i	−0.817411	+	2.43255i
$685$	−787.283	−	234.669i	−1.14932	−	0.342583i
$686$	540.238	+	88.3410i	0.787518	+	0.128777i
$687$	−632.550			−0.920742
$688$	−663.165	−	502.418i	−0.963903	−	0.730259i
$689$	1038.05			1.50660
$690$	−85.9303	+	177.085i	−0.124537	+	0.256645i
$691$			1086.54i			1.57241i	0.617964	+	0.786206i	$0.287958\pi$
$691$			1086.54i			1.57241i	−0.617964	+	0.786206i	$0.712042\pi$
$692$	307.921	−	916.348i	0.444972	−	1.32420i
$693$		−	355.190i		−	0.512539i
$694$	−189.127	−	30.9265i	−0.272517	−	0.0445626i
$695$	−940.134	−	280.230i	−1.35271	−	0.403209i
$696$	−1931.57	−	1021.02i	−2.77524	−	1.46699i
$697$			166.818i			0.239338i
$698$	−756.075	−	123.635i	−1.08320	−	0.177128i
$699$			925.298i			1.32375i
$700$	−493.929	−	626.993i	−0.705612	−	0.895704i
$701$	−520.512			−0.742528			−0.371264	−	0.928527i	$-0.621076\pi$
$701$	−520.512			−0.742528			−0.371264	+	0.928527i	$0.621076\pi$
$702$	112.171	−	685.968i	0.159788	−	0.977163i
$703$	−158.561			−0.225549
$704$	175.396	−	119.550i	0.249142	−	0.169815i
$705$	−290.695	+	975.241i	−0.412333	+	1.38332i
$706$	−53.9161	+	329.717i	−0.0763684	+	0.467021i
$707$	−816.320			−1.15463
$708$	−94.6378	+	281.635i	−0.133669	+	0.397789i
$709$	−419.440			−0.591594			−0.295797	−	0.955251i	$-0.595585\pi$
$709$	−419.440			−0.591594			−0.295797	+	0.955251i	$0.595585\pi$
$710$	146.145	+	70.9167i	0.205838	+	0.0998826i
$711$			374.424i			0.526615i
$712$	−559.382	−	295.688i	−0.785649	−	0.415293i
$713$		−	61.9341i		−	0.0868641i
$714$	−329.335	+	2014.00i	−0.461253	+	2.82073i
$715$	78.7159	−	264.081i	0.110092	−	0.369344i
$716$	−148.691	+	442.493i	−0.207669	+	0.618007i
$717$			1978.56i			2.75950i
$718$	81.2825	−	497.073i	0.113207	−	0.692302i
$719$			674.291i			0.937818i	0.883246	+	0.468909i	$0.155353\pi$
$719$			674.291i			0.937818i	−0.883246	+	0.468909i	$0.844647\pi$
$720$	−865.578	+	634.766i	−1.20219	+	0.881620i
$721$	452.330			0.627365
$722$	1398.75	+	228.728i	1.93733	+	0.316797i
$723$	1521.46			2.10437
$724$	220.408	+	74.0636i	0.304430	+	0.102298i
$725$	1206.69	+	789.517i	1.66440	+	1.08899i
$726$	−102.798	−	16.8098i	−0.141595	−	0.0231539i
$727$	268.034			0.368685			0.184342	−	0.982862i	$-0.440985\pi$
$727$	268.034			0.368685			0.184342	+	0.982862i	$0.440985\pi$
$728$	−495.865	+	938.076i	−0.681134	+	1.28857i
$729$	−1182.80			−1.62249
$730$	215.545	+	104.593i	0.295267	+	0.143278i
$731$		−	1404.01i		−	1.92067i
$732$	106.391	+	35.7507i	0.145343	+	0.0488397i
$733$			1208.37i			1.64852i	0.566212	+	0.824260i	$0.308409\pi$
$733$			1208.37i			1.64852i	−0.566212	+	0.824260i	$0.691591\pi$
$734$	194.350	+	31.7807i	0.264783	+	0.0432979i
$735$	99.4653	−	333.693i	0.135327	−	0.454004i
$736$	−91.6828	−	96.3935i	−0.124569	−	0.130969i
$737$			177.431i			0.240748i
$738$	−163.621	−	26.7557i	−0.221709	−	0.0362543i
$739$		−	1108.28i		−	1.49970i	−0.661605	−	0.749852i	$-0.730125\pi$
$739$		−	1108.28i		−	1.49970i	0.661605	−	0.749852i	$-0.269875\pi$
$740$	−79.2597	−	55.8533i	−0.107108	−	0.0754774i
$741$	−2573.18			−3.47258
$742$	160.931	−	984.152i	0.216888	−	1.32635i
$743$	−441.298			−0.593940			−0.296970	−	0.954887i	$-0.595976\pi$
$743$	−441.298			−0.593940			−0.296970	+	0.954887i	$0.595976\pi$
$744$	263.710	−	498.885i	0.354449	−	0.670544i
$745$	32.6509	−	109.539i	0.0438268	−	0.147033i
$746$	−34.3212	+	209.887i	−0.0460070	+	0.281350i
$747$	322.914			0.432281
$748$	339.543	+	114.097i	0.453934	+	0.152536i
$749$	−822.606			−1.09827
$750$	1015.47	−	608.204i	1.35395	−	0.810938i
$751$		−	381.181i		−	0.507565i	−0.967261	−	0.253782i	$-0.918325\pi$
$751$		−	381.181i		−	0.507565i	0.967261	−	0.253782i	$-0.0816747\pi$
$752$	−548.221	−	415.336i	−0.729018	−	0.552309i
$753$		−	1307.87i		−	1.73688i
$754$	309.361	−	1891.86i	0.410294	−	2.50910i
$755$	502.528	+	149.791i	0.665600	+	0.198398i
$756$	−632.961	−	212.694i	−0.837249	−	0.281341i
$757$		−	8.07063i		−	0.0106613i	−0.999986	−	0.00533066i	$-0.998303\pi$
$757$		−	8.07063i		−	0.0106613i	0.999986	−	0.00533066i	$-0.00169681\pi$
$758$	7.15403	−	43.7496i	0.00943804	−	0.0577171i
$759$			65.2820i			0.0860105i
$760$	933.754	+	916.280i	1.22862	+	1.20563i
$761$	514.328			0.675858			0.337929	−	0.941172i	$-0.390274\pi$
$761$	514.328			0.675858			0.337929	+	0.941172i	$0.390274\pi$
$762$	−776.199	−	126.926i	−1.01863	−	0.166570i
$763$	451.572			0.591837
$764$	−267.849	+	797.097i	−0.350587	+	1.04332i
$765$	−1735.89	−	517.424i	−2.26913	−	0.676371i
$766$	−553.204	−	90.4612i	−0.722198	−	0.118096i
$767$	−260.688			−0.339880
$768$	−328.079	−	1166.84i	−0.427186	−	1.51932i
$769$	428.701			0.557479			0.278739	−	0.960367i	$-0.410083\pi$
$769$	428.701			0.557479			0.278739	+	0.960367i	$0.410083\pi$
$770$	−238.166	−	115.570i	−0.309306	−	0.150091i
$771$			2178.20i			2.82517i
$772$	15.1918	−	45.2098i	0.0196786	−	0.0585619i
$773$		−	710.711i		−	0.919419i	−0.888069	−	0.459709i	$-0.847954\pi$
$773$		−	710.711i		−	0.919419i	0.888069	−	0.459709i	$-0.152046\pi$
$774$	1377.10	+	225.186i	1.77920	+	0.290938i
$775$	−203.916	+	311.665i	−0.263118

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97378 - 0.322758i) q^{2} -4.73469 q^{3} +(3.79165 + 1.27411i) q^{4} +(-1.42827 + 4.79166i) q^{5} +(9.34526 + 1.52816i) q^{6} +7.98176 q^{7} +(-7.07268 - 3.73861i) q^{8} +13.4173 q^{9} +(4.36565 - 8.99673i) q^{10} -3.31662i q^{11} +(-17.9523 - 6.03252i) q^{12} -16.6171i q^{13} +(-15.7543 - 2.57618i) q^{14} +(6.76243 - 22.6870i) q^{15} +(12.7533 + 9.66197i) q^{16} +27.0004i q^{17} +(-26.4829 - 4.33055i) q^{18} +32.7057i q^{19} +(-11.5206 + 16.3486i) q^{20} -37.7912 q^{21} +(-1.07047 + 6.54630i) q^{22} +4.15724 q^{23} +(33.4870 + 17.7012i) q^{24} +(-20.9201 - 13.6876i) q^{25} +(-5.36330 + 32.7986i) q^{26} -20.9146 q^{27} +(30.2641 + 10.1696i) q^{28} -57.6811 q^{29} +(-20.6700 + 42.5967i) q^{30} -14.8979i q^{31} +(-22.0538 - 23.1869i) q^{32} +15.7032i q^{33} +(8.71459 - 53.2929i) q^{34} +(-11.4001 + 38.2459i) q^{35} +(50.8738 + 17.0951i) q^{36} +4.84811i q^{37} +(10.5560 - 64.5541i) q^{38} +78.6768i q^{39} +(28.0159 - 28.5502i) q^{40} +6.17837 q^{41} +(74.5917 + 12.1974i) q^{42} -51.9995 q^{43} +(4.22575 - 12.5755i) q^{44} +(-19.1636 + 64.2912i) q^{45} +(-8.20550 - 1.34178i) q^{46} -42.9867 q^{47} +(-60.3829 - 45.7465i) q^{48} +14.7085 q^{49} +(36.8739 + 33.7685i) q^{50} -127.838i q^{51} +(21.1720 - 63.0063i) q^{52} +62.4688i q^{53} +(41.2809 + 6.75035i) q^{54} +(15.8921 + 4.73705i) q^{55} +(-56.4525 - 29.8407i) q^{56} -154.852i q^{57} +(113.850 + 18.6171i) q^{58} -15.6879i q^{59} +(54.5466 - 77.4054i) q^{60} -5.92632 q^{61} +(-4.80842 + 29.4052i) q^{62} +107.094 q^{63} +(36.0456 + 52.8840i) q^{64} +(79.6235 + 23.7337i) q^{65} +(5.06833 - 30.9947i) q^{66} -53.4975 q^{67} +(-34.4015 + 102.376i) q^{68} -19.6833 q^{69} +(34.8456 - 71.8097i) q^{70} +16.2442i q^{71} +(-94.8963 - 50.1620i) q^{72} +23.9582i q^{73} +(1.56477 - 9.56913i) q^{74} +(99.0501 + 64.8066i) q^{75} +(-41.6707 + 124.009i) q^{76} -26.4725i q^{77} +(25.3936 - 155.291i) q^{78} +27.9060i q^{79} +(-64.5121 + 47.3095i) q^{80} -21.7317 q^{81} +(-12.1948 - 1.99412i) q^{82} +24.0670 q^{83} +(-143.291 - 48.1501i) q^{84} +(-129.377 - 38.5639i) q^{85} +(102.636 + 16.7833i) q^{86} +273.102 q^{87} +(-12.3996 + 23.4574i) q^{88} +79.0905 q^{89} +(58.5753 - 120.712i) q^{90} -132.634i q^{91} +(15.7628 + 5.29679i) q^{92} +70.5369i q^{93} +(84.8465 + 13.8743i) q^{94} +(-156.715 - 46.7127i) q^{95} +(104.418 + 109.783i) q^{96} +69.4266i q^{97} +(-29.0314 - 4.74729i) q^{98} -44.5002i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) \) 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

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