LMFDB - Embedded newform 220.3.h.a.199.18

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			199.18
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20196 + 1.59852i) q^{2} +1.87168 q^{3} +(-1.11056 - 3.84274i) q^{4} +(3.84060 + 3.20153i) q^{5} +(-2.24970 + 2.99193i) q^{6} -11.6487 q^{7} +(7.47757 + 2.84358i) q^{8} -5.49681 q^{9} +(-9.73399 + 2.29116i) q^{10} +3.31662i q^{11} +(-2.07862 - 7.19239i) q^{12} +15.3665i q^{13} +(14.0013 - 18.6207i) q^{14} +(7.18837 + 5.99225i) q^{15} +(-13.5333 + 8.53520i) q^{16} +15.8071i q^{17} +(6.60697 - 8.78678i) q^{18} +14.1893i q^{19} +(8.03745 - 18.3139i) q^{20} -21.8026 q^{21} +(-5.30171 - 3.98647i) q^{22} +17.7274 q^{23} +(13.9956 + 5.32227i) q^{24} +(4.50035 + 24.5916i) q^{25} +(-24.5638 - 18.4700i) q^{26} -27.1334 q^{27} +(12.9366 + 44.7628i) q^{28} -20.6526 q^{29} +(-18.2189 + 4.28831i) q^{30} -10.1970i q^{31} +(2.62282 - 31.8923i) q^{32} +6.20767i q^{33} +(-25.2680 - 18.9996i) q^{34} +(-44.7378 - 37.2936i) q^{35} +(6.10455 + 21.1228i) q^{36} -43.4012i q^{37} +(-22.6820 - 17.0551i) q^{38} +28.7613i q^{39} +(19.6145 + 34.8607i) q^{40} +51.2365 q^{41} +(26.2059 - 34.8520i) q^{42} -50.3006 q^{43} +(12.7449 - 3.68332i) q^{44} +(-21.1110 - 17.5982i) q^{45} +(-21.3077 + 28.3377i) q^{46} -25.8323 q^{47} +(-25.3300 + 15.9752i) q^{48} +86.6912 q^{49} +(-44.7195 - 22.3643i) q^{50} +29.5858i q^{51} +(59.0496 - 17.0655i) q^{52} -36.3196i q^{53} +(32.6134 - 43.3734i) q^{54} +(-10.6183 + 12.7378i) q^{55} +(-87.1037 - 33.1239i) q^{56} +26.5579i q^{57} +(24.8237 - 33.0137i) q^{58} +76.2655i q^{59} +(15.0435 - 34.2778i) q^{60} +81.2888 q^{61} +(16.3001 + 12.2564i) q^{62} +64.0304 q^{63} +(47.8281 + 42.5261i) q^{64} +(-49.1965 + 59.0167i) q^{65} +(-9.92311 - 7.46140i) q^{66} +39.1221 q^{67} +(60.7425 - 17.5547i) q^{68} +33.1801 q^{69} +(113.388 - 26.6889i) q^{70} +26.8136i q^{71} +(-41.1028 - 15.6306i) q^{72} +40.7194i q^{73} +(69.3778 + 52.1667i) q^{74} +(8.42323 + 46.0276i) q^{75} +(54.5260 - 15.7581i) q^{76} -38.6342i q^{77} +(-45.9756 - 34.5700i) q^{78} -49.7047i q^{79} +(-79.3017 - 10.5471i) q^{80} -1.31384 q^{81} +(-61.5845 + 81.9028i) q^{82} +36.5271 q^{83} +(24.2131 + 83.7816i) q^{84} +(-50.6069 + 60.7086i) q^{85} +(60.4595 - 80.4067i) q^{86} -38.6551 q^{87} +(-9.43108 + 24.8003i) q^{88} +111.806 q^{89} +(53.5059 - 12.5940i) q^{90} -179.000i q^{91} +(-19.6874 - 68.1218i) q^{92} -19.0854i q^{93} +(31.0496 - 41.2936i) q^{94} +(-45.4277 + 54.4955i) q^{95} +(4.90909 - 59.6923i) q^{96} -35.6621i q^{97} +(-104.200 + 138.578i) q^{98} -18.2308i 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 $

$2$	−1.20196	+	1.59852i	−0.600982	+	0.799262i
$2$	−1.20196	+	1.59852i	−0.600982	+	0.799262i
$3$	1.87168			0.623894			0.311947	−	0.950100i	$-0.399019\pi$
$3$	1.87168			0.623894			0.311947	+	0.950100i	$0.399019\pi$
$4$	−1.11056	−	3.84274i	−0.277640	−	0.960685i
$5$	3.84060	+	3.20153i	0.768119	+	0.640307i
$5$	3.84060	+	3.20153i	0.768119	+	0.640307i
$6$	−2.24970	+	2.99193i	−0.374949	+	0.498655i
$7$	−11.6487			−1.66409			−0.832047	−	0.554705i	$-0.812831\pi$
$7$	−11.6487			−1.66409			−0.832047	+	0.554705i	$0.812831\pi$
$8$	7.47757	+	2.84358i	0.934696	+	0.355447i
$9$	−5.49681			−0.610756
$10$	−9.73399	+	2.29116i	−0.973399	+	0.229116i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	−2.07862	−	7.19239i	−0.173218	−	0.599366i
$13$			15.3665i			1.18204i	0.806656	+	0.591021i	$0.201275\pi$
$13$			15.3665i			1.18204i	−0.806656	+	0.591021i	$0.798725\pi$
$14$	14.0013	−	18.6207i	1.00009	−	1.33005i
$15$	7.18837	+	5.99225i	0.479225	+	0.399484i
$16$	−13.5333	+	8.53520i	−0.845832	+	0.533450i
$17$			15.8071i			0.929829i	0.885356	+	0.464914i	$0.153915\pi$
$17$			15.8071i			0.929829i	−0.885356	+	0.464914i	$0.846085\pi$
$18$	6.60697	−	8.78678i	0.367054	−	0.488155i
$19$			14.1893i			0.746808i	0.927669	+	0.373404i	$0.121809\pi$
$19$			14.1893i			0.746808i	−0.927669	+	0.373404i	$0.878191\pi$
$20$	8.03745	−	18.3139i	0.401872	−	0.915696i
$21$	−21.8026			−1.03822
$22$	−5.30171	−	3.98647i	−0.240987	−	0.181203i
$23$	17.7274			0.770757			0.385378	−	0.922759i	$-0.374071\pi$
$23$	17.7274			0.770757			0.385378	+	0.922759i	$0.374071\pi$
$24$	13.9956	+	5.32227i	0.583151	+	0.221761i
$25$	4.50035	+	24.5916i	0.180014	+	0.983664i
$26$	−24.5638	−	18.4700i	−0.944761	−	0.710386i
$27$	−27.1334			−1.00494
$28$	12.9366	+	44.7628i	0.462020	+	1.59867i
$29$	−20.6526			−0.712158			−0.356079	−	0.934456i	$-0.615887\pi$
$29$	−20.6526			−0.712158			−0.356079	+	0.934456i	$0.615887\pi$
$30$	−18.2189	+	4.28831i	−0.607298	+	0.142944i
$31$		−	10.1970i		−	0.328934i	−0.986383	−	0.164467i	$-0.947410\pi$
$31$		−	10.1970i		−	0.328934i	0.986383	−	0.164467i	$-0.0525904\pi$
$32$	2.62282	−	31.8923i	0.0819633	−	0.996635i
$33$			6.20767i			0.188111i
$34$	−25.2680	−	18.9996i	−0.743177	−	0.558811i
$35$	−44.7378	−	37.2936i	−1.27822	−	1.06553i
$36$	6.10455	+	21.1228i	0.169571	+	0.586745i
$37$		−	43.4012i		−	1.17300i	−0.809948	−	0.586502i	$-0.800505\pi$
$37$		−	43.4012i		−	1.17300i	0.809948	−	0.586502i	$-0.199495\pi$
$38$	−22.6820	−	17.0551i	−0.596895	−	0.448818i
$39$			28.7613i			0.737468i
$40$	19.6145	+	34.8607i	0.490363	+	0.871518i
$41$	51.2365			1.24967			0.624836	−	0.780756i	$-0.285166\pi$
$41$	51.2365			1.24967			0.624836	+	0.780756i	$0.285166\pi$
$42$	26.2059	−	34.8520i	0.623951	−	0.829808i
$43$	−50.3006			−1.16978			−0.584890	−	0.811113i	$-0.698862\pi$
$43$	−50.3006			−1.16978			−0.584890	+	0.811113i	$0.698862\pi$
$44$	12.7449	−	3.68332i	0.289657	−	0.0837118i
$45$	−21.1110	−	17.5982i	−0.469134	−	0.391072i
$46$	−21.3077	+	28.3377i	−0.463211	+	0.616037i
$47$	−25.8323			−0.549624			−0.274812	−	0.961498i	$-0.588616\pi$
$47$	−25.8323			−0.549624			−0.274812	+	0.961498i	$0.588616\pi$
$48$	−25.3300	+	15.9752i	−0.527709	+	0.332816i
$49$	86.6912			1.76921
$50$	−44.7195	−	22.3643i	−0.894391	−	0.447286i
$51$			29.5858i			0.580114i
$52$	59.0496	−	17.0655i	1.13557	−	0.328183i
$53$		−	36.3196i		−	0.685275i	−0.939468	−	0.342638i	$-0.888680\pi$
$53$		−	36.3196i		−	0.685275i	0.939468	−	0.342638i	$-0.111320\pi$
$54$	32.6134	−	43.3734i	0.603952	−	0.803212i
$55$	−10.6183	+	12.7378i	−0.193060	+	0.231597i
$56$	−87.1037	−	33.1239i	−1.55542	−	0.591497i
$57$			26.5579i			0.465929i
$58$	24.8237	−	33.0137i	0.427995	−	0.569201i
$59$			76.2655i			1.29263i	0.763069	+	0.646317i	$0.223692\pi$
$59$			76.2655i			1.29263i	−0.763069	+	0.646317i	$0.776308\pi$
$60$	15.0435	−	34.2778i	0.250726	−	0.571297i
$61$	81.2888			1.33260			0.666302	−	0.745682i	$-0.267876\pi$
$61$	81.2888			1.33260			0.666302	+	0.745682i	$0.267876\pi$
$62$	16.3001	+	12.2564i	0.262904	+	0.197683i
$63$	64.0304			1.01636
$64$	47.8281	+	42.5261i	0.747315	+	0.664470i
$65$	−49.1965	+	59.0167i	−0.756869	+	0.907949i
$66$	−9.92311	−	7.46140i	−0.150350	−	0.113051i
$67$	39.1221			0.583912			0.291956	−	0.956432i	$-0.405694\pi$
$67$	39.1221			0.583912			0.291956	+	0.956432i	$0.405694\pi$
$68$	60.7425	−	17.5547i	0.893273	−	0.258158i
$69$	33.1801			0.480870
$70$	113.388	−	26.6889i	1.61983	−	0.381270i
$71$			26.8136i			0.377657i	0.982010	+	0.188829i	$0.0604690\pi$
$71$			26.8136i			0.377657i	−0.982010	+	0.188829i	$0.939531\pi$
$72$	−41.1028	−	15.6306i	−0.570872	−	0.217092i
$73$			40.7194i			0.557801i	0.960320	+	0.278900i	$0.0899699\pi$
$73$			40.7194i			0.557801i	−0.960320	+	0.278900i	$0.910030\pi$
$74$	69.3778	+	52.1667i	0.937538	+	0.704955i
$75$	8.42323	+	46.0276i	0.112310	+	0.613702i
$76$	54.5260	−	15.7581i	0.717447	−	0.207344i
$77$		−	38.6342i		−	0.501743i
$78$	−45.9756	−	34.5700i	−0.589431	−	0.443205i
$79$		−	49.7047i		−	0.629173i	−0.949229	−	0.314587i	$-0.898134\pi$
$79$		−	49.7047i		−	0.629173i	0.949229	−	0.314587i	$-0.101866\pi$
$80$	−79.3017	−	10.5471i	−0.991271	−	0.131839i
$81$	−1.31384			−0.0162202
$82$	−61.5845	+	81.9028i	−0.751030	+	0.998815i
$83$	36.5271			0.440086			0.220043	−	0.975490i	$-0.429380\pi$
$83$	36.5271			0.440086			0.220043	+	0.975490i	$0.429380\pi$
$84$	24.2131	+	83.7816i	0.288251	+	0.997400i
$85$	−50.6069	+	60.7086i	−0.595376	+	0.714219i
$86$	60.4595	−	80.4067i	0.703017	−	0.934961i
$87$	−38.6551			−0.444311
$88$	−9.43108	+	24.8003i	−0.107171	+	0.281822i
$89$	111.806			1.25625			0.628125	−	0.778112i	$-0.283823\pi$
$89$	111.806			1.25625			0.628125	+	0.778112i	$0.283823\pi$
$90$	53.5059	−	12.5940i	0.594510	−	0.139934i
$91$		−	179.000i		−	1.96703i
$92$	−19.6874	−	68.1218i	−0.213993	−	0.740455i
$93$		−	19.0854i		−	0.205220i
$94$	31.0496	−	41.2936i	0.330314	−	0.439294i
$95$	−45.4277	+	54.4955i	−0.478186	+	0.573637i
$96$	4.90909	−	59.6923i	0.0511364	−	0.621795i
$97$		−	35.6621i		−	0.367651i	−0.982959	−	0.183825i	$-0.941152\pi$
$97$		−	35.6621i		−	0.367651i	0.982959	−	0.183825i	$-0.0588481\pi$
$98$	−104.200	+	138.578i	−1.06326	+	1.41406i
$99$		−	18.2308i		−	0.184150i
$100$	89.5012	−	44.6042i	0.895012	−	0.446042i
$101$	−189.155			−1.87282			−0.936409	−	0.350911i	$-0.885872\pi$
$101$	−189.155			−1.87282			−0.936409	+	0.350911i	$0.885872\pi$
$102$	−47.2937	−	35.5611i	−0.463664	−	0.348639i
$103$	124.305			1.20684			0.603420	−	0.797423i	$-0.293804\pi$
$103$	124.305			1.20684			0.603420	+	0.797423i	$0.293804\pi$
$104$	−43.6959	+	114.904i	−0.420153	+	1.10485i
$105$	−83.7349	−	69.8017i	−0.797475	−	0.664778i
$106$	58.0578	+	43.6549i	0.547715	+	0.411838i
$107$	30.8812			0.288610			0.144305	−	0.989533i	$-0.453905\pi$
$107$	30.8812			0.288610			0.144305	+	0.989533i	$0.453905\pi$
$108$	30.1333	+	104.267i	0.279012	+	0.965432i
$109$	123.311			1.13129			0.565647	−	0.824647i	$-0.308626\pi$
$109$	123.311			1.13129			0.565647	+	0.824647i	$0.308626\pi$
$110$	−7.59890	−	32.2840i	−0.0690809	−	0.293491i
$111$		−	81.2331i		−	0.731830i
$112$	157.645	−	99.4236i	1.40754	−	0.887711i
$113$		−	145.468i		−	1.28733i	−0.765308	−	0.643665i	$-0.777413\pi$
$113$		−	145.468i		−	1.28733i	0.765308	−	0.643665i	$-0.222587\pi$
$114$	−42.4535	−	31.9217i	−0.372399	−	0.280015i
$115$	68.0838	+	56.7549i	0.592033	+	0.493521i
$116$	22.9360	+	79.3626i	0.197724	+	0.684160i
$117$		−	84.4669i		−	0.721939i
$118$	−121.912	−	91.6684i	−1.03315	−	0.776851i
$119$		−	184.131i		−	1.54732i
$120$	36.7121	+	65.2482i	0.305934	+	0.543735i
$121$	−11.0000			−0.0909091
$122$	−97.7063	+	129.942i	−0.800871	+	1.06510i
$123$	95.8985			0.779662
$124$	−39.1842	+	11.3243i	−0.316002	+	0.0913254i
$125$	−61.4468	+	108.854i	−0.491575	+	0.870835i
$126$	−76.9623	+	102.354i	−0.610812	+	0.812335i
$127$	−168.227			−1.32462			−0.662310	−	0.749230i	$-0.730424\pi$
$127$	−168.227			−1.32462			−0.662310	+	0.749230i	$0.730424\pi$
$128$	−125.467	+	25.3396i	−0.980209	+	0.197965i
$129$	−94.1466			−0.729819
$130$	−35.2071	−	149.578i	−0.270824	−	1.15060i
$131$			108.405i			0.827522i	0.910385	+	0.413761i	$0.135785\pi$
$131$			108.405i			0.827522i	−0.910385	+	0.413761i	$0.864215\pi$
$132$	23.8544	−	6.89400i	0.180716	−	0.0522273i
$133$		−	165.287i		−	1.24276i
$134$	−47.0234	+	62.5377i	−0.350921	+	0.466699i
$135$	−104.208	−	86.8685i	−0.771915	−	0.643471i
$136$	−44.9487	+	118.199i	−0.330505	+	0.869107i
$137$			217.324i			1.58630i	0.609024	+	0.793152i	$0.291561\pi$
$137$			217.324i			1.58630i	−0.609024	+	0.793152i	$0.708439\pi$
$138$	−39.8813	+	53.0391i	−0.288995	+	0.384342i
$139$			219.762i			1.58102i	0.612449	+	0.790510i	$0.290185\pi$
$139$			219.762i			1.58102i	−0.612449	+	0.790510i	$0.709815\pi$
$140$	−93.6255	+	213.332i	−0.668753	+	1.52380i
$141$	−48.3499			−0.342907
$142$	−42.8623	−	32.2291i	−0.301847	−	0.226965i
$143$	−50.9650			−0.356399
$144$	74.3900	−	46.9164i	0.516597	−	0.325808i
$145$	−79.3183	−	66.1200i	−0.547023	−	0.456000i
$146$	−65.0910	−	48.9433i	−0.445829	−	0.335228i
$147$	162.258			1.10380
$148$	−166.779	+	48.1997i	−1.12689	+	0.325673i
$149$	−109.184			−0.732776			−0.366388	−	0.930462i	$-0.619406\pi$
$149$	−109.184			−0.732776			−0.366388	+	0.930462i	$0.619406\pi$
$150$	−83.7008	−	41.8589i	−0.558005	−	0.279059i
$151$			96.5663i			0.639512i	0.947500	+	0.319756i	$0.103601\pi$
$151$			96.5663i			0.639512i	−0.947500	+	0.319756i	$0.896399\pi$
$152$	−40.3485	+	106.102i	−0.265451	+	0.698038i
$153$		−	86.8885i		−	0.567899i
$154$	61.7578	+	46.4370i	0.401024	+	0.301539i
$155$	32.6459	−	39.1624i	0.210619	−	0.252660i
$156$	110.522	−	31.9412i	0.708475	−	0.204751i
$157$			265.012i			1.68798i	0.536362	+	0.843988i	$0.319798\pi$
$157$			265.012i			1.68798i	−0.536362	+	0.843988i	$0.680202\pi$
$158$	79.4542	+	59.7433i	0.502875	+	0.378122i
$159$		−	67.9787i		−	0.427539i
$160$	112.178	−	114.088i	0.701110	−	0.713053i
$161$	−206.500			−1.28261
$162$	1.57918	−	2.10020i	0.00974805	−	0.0129642i
$163$	22.4772			0.137897			0.0689485	−	0.997620i	$-0.478036\pi$
$163$	22.4772			0.137897			0.0689485	+	0.997620i	$0.478036\pi$
$164$	−56.9013	−	196.889i	−0.346959	−	1.20054i
$165$	−19.8741	+	23.8411i	−0.120449	+	0.144492i
$166$	−43.9043	+	58.3895i	−0.264484	+	0.351744i
$167$	177.972			1.06570			0.532849	−	0.846210i	$-0.321121\pi$
$167$	177.972			1.06570			0.532849	+	0.846210i	$0.321121\pi$
$168$	−163.030	−	61.9973i	−0.970419	−	0.369032i
$169$	−67.1305			−0.397222
$170$	−36.2165	−	153.866i	−0.213038	−	0.905095i
$171$		−	77.9961i		−	0.456118i
$172$	55.8619	+	193.292i	0.324778	+	1.12379i
$173$		−	31.7306i		−	0.183414i	−0.995786	−	0.0917071i	$-0.970768\pi$
$173$		−	31.7306i		−	0.183414i	0.995786	−	0.0917071i	$-0.0292323\pi$
$174$	46.4620	−	61.7911i	0.267023	−	0.355121i
$175$	−52.4231	−	286.459i	−0.299560	−	1.63691i
$176$	−28.3081	−	44.8849i	−0.160841	−	0.255028i
$177$			142.745i			0.806467i
$178$	−134.387	+	178.725i	−0.754984	+	1.00407i
$179$		−	246.725i		−	1.37835i	−0.724594	−	0.689176i	$-0.757973\pi$
$179$		−	246.725i		−	1.37835i	0.724594	−	0.689176i	$-0.242027\pi$
$180$	−44.1803	+	100.668i	−0.245446	+	0.559267i
$181$	167.071			0.923043			0.461522	−	0.887129i	$-0.347304\pi$
$181$	167.071			0.923043			0.461522	+	0.887129i	$0.347304\pi$
$182$	286.135	+	215.151i	1.57217	+	1.18215i
$183$	152.147			0.831403
$184$	132.558	+	50.4093i	0.720424	+	0.273963i
$185$	138.950	−	166.686i	0.751083	−	0.901007i
$186$	30.5086	+	22.9400i	0.164024	+	0.123334i
$187$	−52.4262			−0.280354
$188$	28.6884	+	99.2670i	0.152598	+	0.528016i
$189$	316.068			1.67232
$190$	−32.5100	−	138.119i	−0.171105	−	0.726942i
$191$		−	159.032i		−	0.832626i	−0.909221	−	0.416313i	$-0.863322\pi$
$191$		−	159.032i		−	0.832626i	0.909221	−	0.416313i	$-0.136678\pi$
$192$	89.5190	+	79.5953i	0.466245	+	0.414559i
$193$		−	166.756i		−	0.864020i	−0.901869	−	0.432010i	$-0.857805\pi$
$193$		−	166.756i		−	0.864020i	0.901869	−	0.432010i	$-0.142195\pi$
$194$	57.0068	+	42.8646i	0.293849	+	0.220952i
$195$	−92.0802	+	110.460i	−0.472206	+	0.566464i
$196$	−96.2759	−	333.132i	−0.491204	−	1.69965i
$197$		−	261.228i		−	1.32603i	−0.748607	−	0.663014i	$-0.769277\pi$
$197$		−	261.228i		−	1.32603i	0.748607	−	0.663014i	$-0.230723\pi$
$198$	29.1425	+	21.9128i	0.147184	+	0.110671i
$199$			264.882i			1.33107i	0.746368	+	0.665534i	$0.231796\pi$
$199$			264.882i			1.33107i	−0.746368	+	0.665534i	$0.768204\pi$
$200$	−36.2764	+	196.683i	−0.181382	+	0.983413i
$201$	73.2242			0.364299
$202$	227.357	−	302.368i	1.12553	−	1.49687i
$203$	240.575			1.18510
$204$	113.691	−	32.8569i	0.557307	−	0.161063i
$205$	196.779	+	164.035i	0.959896	+	0.800173i
$206$	−149.410	+	198.704i	−0.725290	+	0.964582i
$207$	−97.4441			−0.470745
$208$	−131.156	−	207.960i	−0.630560	−	0.999808i
$209$	−47.0607			−0.225171
$210$	212.226	−	49.9531i	1.01060	−	0.237872i
$211$			211.990i			1.00469i	0.864667	+	0.502345i	$0.167529\pi$
$211$			211.990i			1.00469i	−0.864667	+	0.502345i	$0.832471\pi$
$212$	−139.567	+	40.3351i	−0.658334	+	0.190260i
$213$			50.1866i			0.235618i
$214$	−37.1182	+	49.3644i	−0.173449	+	0.230675i
$215$	−193.184	−	161.039i	−0.898531	−	0.749018i
$216$	−202.892	−	77.1560i	−0.939315	−	0.357203i
$217$			118.781i			0.547377i
$218$	−148.216	+	197.116i	−0.679888	+	0.904201i
$219$			76.2138i			0.348008i
$220$	60.7404	+	26.6572i	0.276093	+	0.121169i
$221$	−242.900			−1.09910
$222$	129.853	+	97.6394i	0.584924	+	0.439817i
$223$	−166.223			−0.745397			−0.372698	−	0.927953i	$-0.621567\pi$
$223$	−166.223			−0.745397			−0.372698	+	0.927953i	$0.621567\pi$
$224$	−30.5524	+	371.503i	−0.136395	+	1.65849i
$225$	−24.7376	−	135.175i	−0.109945	−	0.600779i
$226$	232.535	+	174.848i	1.02891	+	0.773662i
$227$	−12.8157			−0.0564568			−0.0282284	−	0.999601i	$-0.508987\pi$
$227$	−12.8157			−0.0564568			−0.0282284	+	0.999601i	$0.508987\pi$
$228$	102.055	−	29.4942i	0.447611	−	0.129361i
$229$	−389.420			−1.70052			−0.850261	−	0.526361i	$-0.823556\pi$
$229$	−389.420			−1.70052			−0.850261	+	0.526361i	$0.823556\pi$
$230$	−172.558	+	40.6162i	−0.750254	+	0.176592i
$231$		−	72.3110i		−	0.313034i
$232$	−154.431	−	58.7273i	−0.665652	−	0.253135i
$233$			82.8772i			0.355696i	0.984058	+	0.177848i	$0.0569136\pi$
$233$			82.8772i			0.355696i	−0.984058	+	0.177848i	$0.943086\pi$
$234$	135.022	+	101.526i	0.577019	+	0.433873i
$235$	−99.2116	−	82.7031i	−0.422177	−	0.351928i
$236$	293.068	−	84.6975i	1.24181	−	0.358888i
$237$		−	93.0314i		−	0.392537i
$238$	294.338	+	221.319i	1.23672	+	0.929913i
$239$		−	402.695i		−	1.68492i	−0.538762	−	0.842458i	$-0.681108\pi$
$239$		−	402.695i		−	1.68492i	0.538762	−	0.842458i	$-0.318892\pi$
$240$	−148.428	−	19.7408i	−0.618448	−	0.0822533i
$241$	239.848			0.995219			0.497609	−	0.867401i	$-0.334211\pi$
$241$	239.848			0.995219			0.497609	+	0.867401i	$0.334211\pi$
$242$	13.2216	−	17.5838i	0.0546348	−	0.0726602i
$243$	241.742			0.994821
$244$	−90.2762	−	312.372i	−0.369985	−	1.28021i
$245$	332.946	+	277.545i	1.35896	+	1.13284i
$246$	−115.267	+	153.296i	−0.468563	+	0.623155i
$247$	−218.041			−0.882758
$248$	28.9958	−	76.2484i	0.116919	−	0.307453i
$249$	68.3672			0.274567
$250$	−100.150	−	229.063i	−0.400598	−	0.916254i
$251$			337.928i			1.34633i	0.739494	+	0.673163i	$0.235065\pi$
$251$			337.928i			1.34633i	−0.739494	+	0.673163i	$0.764935\pi$
$252$	−71.1097	−	246.052i	−0.282182	−	0.976398i
$253$			58.7952i			0.232392i
$254$	202.202	−	268.914i	0.796073	−	1.05872i
$255$	−94.7201	+	113.627i	−0.371451	+	0.445597i
$256$	110.301	−	231.019i	0.430862	−	0.902418i
$257$			265.980i			1.03494i	0.855701	+	0.517471i	$0.173126\pi$
$257$			265.980i			1.03494i	−0.855701	+	0.517471i	$0.826874\pi$
$258$	113.161	−	150.496i	0.438608	−	0.583317i
$259$			505.565i			1.95199i
$260$	281.421	+	123.508i	1.08239	+	0.475030i
$261$	113.523			0.434955
$262$	−173.289	−	130.300i	−0.661407	−	0.497326i
$263$	353.267			1.34322			0.671610	−	0.740905i	$-0.265603\pi$
$263$	353.267			1.34322			0.671610	+	0.740905i	$0.265603\pi$
$264$	−17.6520	+	46.4183i	−0.0668636	+	0.175827i
$265$	116.278	−	139.489i	0.438786	−	0.526373i
$266$	264.215	+	198.669i	0.993290	+	0.746876i
$267$	209.266			0.783767
$268$	−43.4475	−	150.336i	−0.162118	−	0.560956i
$269$	−338.463			−1.25823			−0.629113	−	0.777314i	$-0.716582\pi$
$269$	−338.463			−1.25823			−0.629113	+	0.777314i	$0.716582\pi$
$270$	264.116	−	62.1669i	0.978209	−	0.230248i
$271$			371.846i			1.37213i	0.727542	+	0.686064i	$0.240663\pi$
$271$			371.846i			1.37213i	−0.727542	+	0.686064i	$0.759337\pi$
$272$	−134.917	−	213.922i	−0.496017	−	0.786478i
$273$		−	335.030i		−	1.22722i
$274$	−347.397	−	261.215i	−1.26787	−	0.953341i
$275$	−81.5611	+	14.9260i	−0.296586	+	0.0542763i
$276$	−36.8485	−	127.502i	−0.133509	−	0.461965i
$277$		−	147.634i		−	0.532976i	−0.963838	−	0.266488i	$-0.914137\pi$
$277$		−	147.634i		−	0.532976i	0.963838	−	0.266488i	$-0.0858632\pi$
$278$	−351.295	−	264.146i	−1.26365	−	0.950165i
$279$			56.0507i			0.200898i
$280$	−228.483	−	406.081i	−0.816010	−	1.45029i
$281$	−391.183			−1.39211			−0.696056	−	0.717988i	$-0.745063\pi$
$281$	−391.183			−1.39211			−0.696056	+	0.717988i	$0.745063\pi$
$282$	58.1149	−	77.2885i	0.206081	−	0.274073i
$283$	431.510			1.52477			0.762384	−	0.647124i	$-0.224029\pi$
$283$	431.510			1.52477			0.762384	+	0.647124i	$0.224029\pi$
$284$	103.038	−	29.7782i	0.362809	−	0.104853i
$285$	−85.0262	+	101.998i	−0.298337	+	0.357889i
$286$	61.2582	−	81.4689i	0.214189	−	0.284856i
$287$	−596.837			−2.07957
$288$	−14.4172	+	175.306i	−0.0500596	+	0.608701i
$289$	39.1360			0.135419
$290$	201.032	−	47.3183i	0.693214	−	0.163167i
$291$		−	66.7481i		−	0.229375i
$292$	156.474	−	45.2215i	0.535871	−	0.154868i
$293$		−	431.337i		−	1.47214i	−0.676905	−	0.736070i	$-0.736679\pi$
$293$		−	431.337i		−	1.47214i	0.676905	−	0.736070i	$-0.263321\pi$
$294$	−195.029	+	259.374i	−0.663363	+	0.882224i
$295$	−244.166	+	292.905i	−0.827683	+	0.992898i
$296$	123.415	−	324.535i	0.416941	−	1.09640i
$297$		−	89.9913i		−	0.303001i
$298$	131.235	−	174.533i	0.440386	−	0.585680i
$299$			272.409i			0.911066i
$300$	167.518	−	83.4848i	0.558393	−	0.278283i
$301$	585.934			1.94662
$302$	−154.364	−	116.069i	−0.511138	−	0.384335i
$303$	−354.037			−1.16844
$304$	−121.109	−	192.029i	−0.398385	−	0.631674i
$305$	312.197	+	260.249i	1.02360	+	0.853275i
$306$	138.893	+	104.437i	0.453900	+	0.341297i
$307$	−439.183			−1.43056			−0.715282	−	0.698836i	$-0.753702\pi$
$307$	−439.183			−1.43056			−0.715282	+	0.698836i	$0.753702\pi$
$308$	−148.461	+	42.9057i	−0.482017	+	0.139304i
$309$	232.659			0.752941
$310$	23.3628	+	99.2570i	0.0753639	+	0.320184i
$311$		−	147.247i		−	0.473463i	−0.971575	−	0.236731i	$-0.923924\pi$
$311$		−	147.247i		−	0.473463i	0.971575	−	0.236731i	$-0.0760761\pi$
$312$	−81.7849	+	215.064i	−0.262131	+	0.689309i
$313$			294.284i			0.940204i	0.882612	+	0.470102i	$0.155783\pi$
$313$			294.284i			0.940204i	−0.882612	+	0.470102i	$0.844217\pi$
$314$	−423.629	−	318.535i	−1.34914	−	1.01444i
$315$	245.915	+	204.996i	0.780682	+	0.650780i
$316$	−191.002	+	55.2001i	−0.604438	+	0.174684i
$317$			98.0368i			0.309264i	0.987972	+	0.154632i	$0.0494193\pi$
$317$			98.0368i			0.309264i	−0.987972	+	0.154632i	$0.950581\pi$
$318$	108.666	+	81.7080i	0.341716	+	0.256943i
$319$		−	68.4969i		−	0.214724i
$320$	47.5397	+	316.449i	0.148562	+	0.988903i
$321$	57.7999			0.180062
$322$	248.206	−	330.096i	0.770827	−	1.02514i
$323$	−224.292			−0.694403
$324$	1.45910	+	5.04873i	0.00450338	+	0.0155825i
$325$	−377.888	+	69.1548i	−1.16273	+	0.212784i
$326$	−27.0168	+	35.9304i	−0.0828736	+	0.110216i
$327$	230.799			0.705808
$328$	383.125	+	145.695i	1.16806	+	0.444192i
$329$	300.912			0.914626
$330$	−14.2227	−	60.4254i	−0.0430992	−	0.183107i
$331$		−	442.133i		−	1.33575i	−0.744274	−	0.667874i	$-0.767204\pi$
$331$		−	442.133i		−	1.33575i	0.744274	−	0.667874i	$-0.232796\pi$
$332$	−40.5657	−	140.364i	−0.122186	−	0.422784i
$333$			238.568i			0.716420i
$334$	−213.916	+	284.492i	−0.640466	+	0.851772i
$335$	150.252	+	125.251i	0.448514	+	0.373883i
$336$	295.061	−	186.089i	0.878157	−	0.553837i
$337$			86.8418i			0.257691i	0.991665	+	0.128845i	$0.0411271\pi$
$337$			86.8418i			0.257691i	−0.991665	+	0.128845i	$0.958873\pi$
$338$	80.6885	−	107.310i	0.238723	−	0.317484i
$339$		−	272.270i		−	0.803157i
$340$	289.490	+	127.049i	0.851440	+	0.373672i
$341$	33.8195			0.0991773
$342$	124.679	+	93.7486i	0.364558	+	0.274119i
$343$	−439.052			−1.28003
$344$	−376.126	−	143.034i	−1.09339	−	0.415795i
$345$	127.431	+	106.227i	0.369366	+	0.307905i
$346$	50.7222	+	38.1391i	0.146596	+	0.110229i
$347$	234.740			0.676485			0.338242	−	0.941059i	$-0.390168\pi$
$347$	234.740			0.676485			0.338242	+	0.941059i	$0.390168\pi$
$348$	42.9289	+	148.541i	0.123359	+	0.426843i
$349$	37.4021			0.107169			0.0535847	−	0.998563i	$-0.482935\pi$
$349$	37.4021			0.107169			0.0535847	+	0.998563i	$0.482935\pi$
$350$	520.923	+	260.514i	1.48835	+	0.744326i
$351$		−	416.947i		−	1.18788i
$352$	105.775	+	8.69892i	0.300497	+	0.0247129i
$353$			401.864i			1.13842i	0.822191	+	0.569212i	$0.192752\pi$
$353$			401.864i			1.13842i	−0.822191	+	0.569212i	$0.807248\pi$
$354$	−228.181	−	171.574i	−0.644579	−	0.484672i
$355$	−85.8448	+	102.980i	−0.241816	+	0.290086i
$356$	−124.168	−	429.642i	−0.348786	−	1.20686i
$357$		−	344.635i		−	0.965365i
$358$	394.396	+	296.555i	1.10167	+	0.828366i
$359$		−	433.553i		−	1.20767i	−0.797110	−	0.603834i	$-0.793639\pi$
$359$		−	433.553i		−	1.20767i	0.797110	−	0.603834i	$-0.206361\pi$
$360$	−107.817	−	191.623i	−0.299492	−	0.532285i
$361$	159.662			0.442278
$362$	−200.813	+	267.067i	−0.554733	+	0.737753i
$363$	−20.5885			−0.0567176
$364$	−687.849	+	198.790i	−1.88969	+	0.546126i
$365$	−130.365	+	156.387i	−0.357164	+	0.428457i
$366$	−182.875	+	243.210i	−0.499659	+	0.664509i
$367$	148.004			0.403280			0.201640	−	0.979460i	$-0.435373\pi$
$367$	148.004			0.403280			0.201640	+	0.979460i	$0.435373\pi$
$368$	−239.910	+	151.307i	−0.651930	+	0.411160i
$369$	−281.637			−0.763245
$370$	99.4388	+	422.466i	0.268753	+	1.14180i
$371$			423.074i			1.14036i
$372$	−73.3404	+	21.1956i	−0.197152	+	0.0569773i
$373$			367.813i			0.986094i	0.870003	+	0.493047i	$0.164117\pi$
$373$			367.813i			0.986094i	−0.870003	+	0.493047i	$0.835883\pi$
$374$	63.0144	−	83.8045i	0.168488	−	0.224076i
$375$	−115.009	+	203.741i	−0.306690	+	0.543309i
$376$	−193.163	−	73.4563i	−0.513732	−	0.195362i
$377$		−	317.359i		−	0.841801i
$378$	−379.902	+	505.242i	−1.00503	+	1.33662i
$379$		−	266.654i		−	0.703571i	−0.936081	−	0.351786i	$-0.885575\pi$
$379$		−	266.654i		−	0.703571i	0.936081	−	0.351786i	$-0.114425\pi$
$380$	259.862	+	114.046i	0.683849	+	0.300121i
$381$	−314.867			−0.826422
$382$	254.216	+	191.150i	0.665486	+	0.500393i
$383$	−406.879			−1.06235			−0.531174	−	0.847263i	$-0.678249\pi$
$383$	−406.879			−1.06235			−0.531174	+	0.847263i	$0.678249\pi$
$384$	−234.834	+	47.4276i	−0.611546	+	0.123509i
$385$	123.689	−	148.378i	0.321270	−	0.385399i
$386$	266.563	+	200.435i	0.690578	+	0.519261i
$387$	276.492			0.714451
$388$	−137.040	+	39.6050i	−0.353197	+	0.102075i
$389$	−80.3605			−0.206582			−0.103291	−	0.994651i	$-0.532937\pi$
$389$	−80.3605			−0.206582			−0.103291	+	0.994651i	$0.532937\pi$
$390$	−65.8965	−	279.962i	−0.168965	−	0.717851i
$391$			280.219i			0.716672i
$392$	648.240	+	246.513i	1.65367	+	0.628860i
$393$			202.900i			0.516286i
$394$	417.579	+	313.986i	1.05984	+	0.796919i
$395$	159.131	−	190.896i	0.402864	−	0.483280i
$396$	−70.0564	+	20.2465i	−0.176910	+	0.0511275i
$397$			183.692i			0.462701i	0.972870	+	0.231350i	$0.0743144\pi$
$397$			183.692i			0.462701i	−0.972870	+	0.231350i	$0.925686\pi$
$398$	−423.421	−	318.379i	−1.06387	−	0.799948i
$399$		−	309.364i		−	0.775349i
$400$	−270.799	−	294.394i	−0.676997	−	0.735986i
$401$	131.109			0.326955			0.163478	−	0.986547i	$-0.447729\pi$
$401$	131.109			0.326955			0.163478	+	0.986547i	$0.447729\pi$
$402$	−88.0129	+	117.051i	−0.218937	+	0.291171i
$403$	156.692			0.388813
$404$	210.068	+	726.872i	0.519970	+	1.79919i
$405$	−5.04591	−	4.20629i	−0.0124590	−	0.0103859i
$406$	−289.163	+	384.565i	−0.712223	+	0.947204i
$407$	143.945			0.353674
$408$	−84.1296	+	221.230i	−0.206200	+	0.542231i
$409$	−513.687			−1.25596			−0.627979	−	0.778231i	$-0.716118\pi$
$409$	−513.687			−1.25596			−0.627979	+	0.778231i	$0.716118\pi$
$410$	−498.736	+	117.391i	−1.21643	+	0.286319i
$411$			406.761i			0.989685i
$412$	−138.048	−	477.670i	−0.335068	−	1.15939i
$413$		−	888.390i		−	2.15107i
$414$	117.124	−	155.767i	0.282909	−	0.376248i
$415$	140.286	+	116.943i	0.338039	+	0.281790i
$416$	490.075	+	40.3037i	1.17806	+	0.0968840i
$417$			411.324i			0.986389i
$418$	56.5653	−	75.2277i	0.135324	−	0.179971i
$419$			534.713i			1.27616i	0.769968	+	0.638082i	$0.220272\pi$
$419$			534.713i			1.27616i	−0.769968	+	0.638082i	$0.779728\pi$
$420$	−175.237	+	399.291i	−0.417231	+	0.950692i
$421$	−95.6323			−0.227155			−0.113578	−	0.993529i	$-0.536231\pi$
$421$	−95.6323			−0.227155			−0.113578	+	0.993529i	$0.536231\pi$
$422$	−338.871	−	254.804i	−0.803011	−	0.603801i
$423$	141.995			0.335687
$424$	103.278	−	271.582i	0.243579	−	0.640524i
$425$	−388.722	+	71.1375i	−0.914639	+	0.167382i
$426$	−80.2245	−	60.3225i	−0.188321	−	0.141602i
$427$	−946.905			−2.21758
$428$	−34.2955	−	118.669i	−0.0801297	−	0.277263i
$429$	−95.3903			−0.222355
$430$	489.625	−	115.246i	1.13866	−	0.268015i
$431$		−	351.962i		−	0.816617i	−0.912844	−	0.408308i	$-0.866119\pi$
$431$		−	351.962i		−	0.816617i	0.912844	−	0.408308i	$-0.133881\pi$
$432$	367.205	−	231.589i	0.850011	−	0.536086i
$433$			103.965i			0.240103i	0.992768	+	0.120052i	$0.0383060\pi$
$433$			103.965i			0.240103i	−0.992768	+	0.120052i	$0.961694\pi$
$434$	−189.874	−	142.770i	−0.437498	−	0.328964i
$435$	−148.459	−	123.756i	−0.341284	−	0.284496i
$436$	−136.945	−	473.853i	−0.314093	−	1.08682i
$437$			251.540i			0.575607i
$438$	−121.830	−	91.6063i	−0.278150	−	0.209147i
$439$		−	673.854i		−	1.53498i	−0.641064	−	0.767488i	$-0.721507\pi$
$439$		−	673.854i		−	1.53498i	0.641064	−	0.767488i	$-0.278493\pi$
$440$	−115.620	+	65.0540i	−0.262773	+	0.147850i
$441$	−476.525			−1.08056
$442$	291.957	−	388.282i	0.660537	−	0.878466i
$443$	535.342			1.20845			0.604223	−	0.796815i	$-0.293484\pi$
$443$	535.342			1.20845			0.604223	+	0.796815i	$0.293484\pi$
$444$	−312.158	+	90.2144i	−0.703058	+	0.203186i
$445$	429.403	+	357.952i	0.964950	+	0.804386i
$446$	199.795	−	265.712i	0.447970	−	0.595768i
$447$	−204.357			−0.457175
$448$	−557.134	−	495.372i	−1.24360	−	1.10574i
$449$	−290.972			−0.648045			−0.324022	−	0.946049i	$-0.605035\pi$
$449$	−290.972			−0.648045			−0.324022	+	0.946049i	$0.605035\pi$
$450$	245.815	+	122.932i	0.546255	+	0.273183i
$451$			169.932i			0.376790i
$452$	−558.997	+	161.551i	−1.23672	+	0.357415i
$453$			180.741i			0.398987i
$454$	15.4040	−	20.4862i	0.0339295	−	0.0451238i
$455$	573.073	−	687.465i	1.25950	−	1.51091i
$456$	−75.5196	+	198.589i	−0.165613	+	0.435502i
$457$		−	733.910i		−	1.60593i	−0.596026	−	0.802965i	$-0.703255\pi$
$457$		−	733.910i		−	1.60593i	0.596026	−	0.802965i	$-0.296745\pi$
$458$	468.069	−	622.497i	1.02198	−	1.35916i
$459$		−	428.900i		−	0.934423i
$460$	142.483	−	324.658i	0.309746	−	0.705779i
$461$	127.878			0.277392			0.138696	−	0.990335i	$-0.455709\pi$
$461$	127.878			0.277392			0.138696	+	0.990335i	$0.455709\pi$
$462$	115.591	+	86.9152i	0.250197	+	0.188128i
$463$	173.856			0.375499			0.187749	−	0.982217i	$-0.439881\pi$
$463$	173.856			0.375499			0.187749	+	0.982217i	$0.439881\pi$
$464$	279.498	−	176.274i	0.602366	−	0.379901i
$465$	61.1027	−	73.2995i	0.131404	−	0.157633i
$466$	−132.481	−	99.6155i	−0.284295	−	0.213767i
$467$	670.447			1.43565			0.717823	−	0.696225i	$-0.245138\pi$
$467$	670.447			1.43565			0.717823	+	0.696225i	$0.245138\pi$
$468$	−324.584	+	93.8057i	−0.693556	+	0.200440i
$469$	−455.720			−0.971685
$470$	251.452	−	59.1859i	0.535004	−	0.125927i
$471$			496.019i			1.05312i
$472$	−216.867	+	570.280i	−0.459463	+	1.20822i
$473$		−	166.828i		−	0.352702i
$474$	148.713	+	111.820i	0.313740	+	0.235908i
$475$	−348.939	+	63.8571i	−0.734608	+	0.134436i
$476$	−707.569	+	204.489i	−1.48649	+	0.429599i
$477$			199.642i			0.418536i
$478$	643.718	+	484.025i	1.34669	+	1.01260i
$479$			729.204i			1.52235i	0.648549	+	0.761173i	$0.275376\pi$
$479$			729.204i			1.52235i	−0.648549	+	0.761173i	$0.724624\pi$
$480$	209.961	−	213.537i	0.437418	−	0.444869i
$481$	666.925			1.38654
$482$	−288.289	+	383.403i	−0.598109	+	0.795441i
$483$	−386.503			−0.800214
$484$	12.2162	+	42.2701i	0.0252400	+	0.0873350i
$485$	114.174	−	136.964i	0.235409	−	0.282400i
$486$	−290.565	+	386.430i	−0.597870	+	0.795123i
$487$	456.198			0.936752			0.468376	−	0.883529i	$-0.344839\pi$
$487$	456.198			0.936752			0.468376	+	0.883529i	$0.344839\pi$
$488$	607.843	+	231.151i	1.24558	+	0.473670i
$489$	42.0702			0.0860330
$490$	−843.851	+	198.623i	−1.72215	+	0.405353i
$491$		−	612.698i		−	1.24786i	−0.781482	−	0.623928i	$-0.785536\pi$
$491$		−	612.698i		−	1.24786i	0.781482	−	0.623928i	$-0.214464\pi$
$492$	−106.501	−	368.513i	−0.216466	−	0.749010i
$493$		−	326.457i		−	0.662185i
$494$	262.078	−	348.544i	0.530522	−	0.705555i
$495$	58.3667	−	70.0173i	0.117913	−	0.141449i
$496$	87.0330	+	137.998i	0.175470	+	0.278223i
$497$		−	312.343i		−	0.628457i
$498$	−82.1749	+	109.287i	−0.165010	+	0.219451i
$499$			922.765i			1.84923i	0.380904	+	0.924614i	$0.375613\pi$
$499$			922.765i			1.84923i	−0.380904	+	0.924614i	$0.624387\pi$
$500$	486.540	+	115.235i	0.973080	+	0.230469i
$501$	333.106			0.664883
$502$	−540.186	−	406.177i	−1.07607	−	0.809118i
$503$	−197.816			−0.393272			−0.196636	−	0.980477i	$-0.563002\pi$
$503$	−197.816			−0.393272			−0.196636	+	0.980477i	$0.563002\pi$
$504$	478.792	+	182.075i	0.949984	+	0.361261i
$505$	−726.466	−	605.585i	−1.43855	−	1.19918i
$506$	−93.9855	−	70.6697i	−0.185742	−	0.139663i
$507$	−125.647			−0.247824
$508$	186.826	+	646.451i	0.367768	+	1.27254i
$509$	652.830			1.28257			0.641287	−	0.767301i	$-0.278401\pi$
$509$	652.830			1.28257			0.641287	+	0.767301i	$0.278401\pi$
$510$	−67.7858	−	287.988i	−0.132913	−	0.564683i
$511$		−	474.327i		−	0.928233i
$512$	236.712	+	453.995i	0.462328	+	0.886709i
$513$		−	385.005i		−	0.750498i
$514$	−425.176	−	319.699i	−0.827190	−	0.621982i
$515$	477.404	+	397.966i	0.926998	+	0.772749i
$516$	104.556	+	361.781i	0.202627	+	0.701126i
$517$		−	85.6762i		−	0.165718i
$518$	−808.158	−	607.671i	−1.56015	−	1.17311i
$519$		−	59.3897i		−	0.114431i
$520$	−535.689	+	301.407i	−1.03017	+	0.579629i
$521$	−317.045			−0.608531			−0.304266	−	0.952587i	$-0.598411\pi$
$521$	−317.045			−0.608531			−0.304266	+	0.952587i	$0.598411\pi$
$522$	−136.451	+	181.470i	−0.261400	+	0.347643i
$523$	−57.7480			−0.110417			−0.0552084	−	0.998475i	$-0.517582\pi$
$523$	−57.7480			−0.110417			−0.0552084	+	0.998475i	$0.517582\pi$
$524$	416.574	−	120.391i	0.794988	−	0.229754i
$525$	−98.1193	−	536.160i	−0.186894	−	1.02126i
$526$	−424.614	+	564.706i	−0.807252	+	1.07359i
$527$	161.184			0.305852
$528$	−52.9837	−	84.0102i	−0.100348	−	0.159110i
$529$	−214.739			−0.405934
$530$	83.2138	+	353.535i	0.157007	+	0.667046i
$531$		−	419.217i		−	0.789485i
$532$	−635.154	+	183.561i	−1.19390	+	0.345040i
$533$			787.328i			1.47716i
$534$	−251.530	+	334.516i	−0.471030	+	0.626435i
$535$	118.602	+	98.8674i	0.221687	+	0.184799i
$536$	292.539	+	111.247i	0.545781	+	0.207550i
$537$		−	461.791i		−	0.859946i
$538$	406.821	−	541.041i	0.756172	−	1.00565i
$539$			287.522i			0.533436i
$540$	−218.083	+	496.919i	−0.403858	+	0.920220i
$541$	77.7702			0.143753			0.0718764	−	0.997414i	$-0.477101\pi$
$541$	77.7702			0.143753			0.0718764	+	0.997414i	$0.477101\pi$
$542$	−594.406	−	446.946i	−1.09669	−	0.824624i
$543$	312.703			0.575881
$544$	504.125	+	41.4592i	0.926700	+	0.0762118i
$545$	473.588	+	394.785i	0.868969	+	0.724376i
$546$	535.554	+	402.694i	0.980868	+	0.737535i
$547$	156.036			0.285257			0.142629	−	0.989776i	$-0.454445\pi$
$547$	156.036			0.285257			0.142629	+	0.989776i	$0.454445\pi$
$548$	835.118	−	241.351i	1.52394	−	0.440422i
$549$	−446.829			−0.813896
$550$	74.1740	−	148.318i	0.134862	−	0.269669i
$551$		−	293.047i		−	0.531845i
$552$	248.106	+	94.3501i	0.449468	+	0.170924i
$553$			578.993i			1.04700i
$554$	235.997	+	177.451i	0.425987	+	0.320309i
$555$	260.071	−	311.984i	0.468596	−	0.562133i
$556$	844.488	−	244.059i	1.51886	−	0.438955i
$557$		−	274.108i		−	0.492116i	−0.969255	−	0.246058i	$-0.920865\pi$
$557$		−	274.108i		−	0.492116i	0.969255	−	0.246058i	$-0.0791353\pi$
$558$	−89.5984	−	67.3709i	−0.160571	−	0.120736i
$559$		−	772.945i		−	1.38273i
$560$	923.758	+	122.859i	1.64957	+	0.219392i
$561$	−98.1251			−0.174911
$562$	470.189	−	625.316i	0.836635	−	1.11266i
$563$	−31.2910			−0.0555790			−0.0277895	−	0.999614i	$-0.508847\pi$
$563$	−31.2910			−0.0555790			−0.0277895	+	0.999614i	$0.508847\pi$
$564$	53.6956	+	185.796i	0.0952049	+	0.329426i
$565$	465.722	−	558.685i	0.824286	−	0.988823i
$566$	−518.659	+	689.779i	−0.916359	+	1.21869i
$567$	15.3044			0.0269919
$568$	−76.2467	+	200.501i	−0.134237	+	0.352995i
$569$	−363.431			−0.638719			−0.319360	−	0.947634i	$-0.603468\pi$
$569$	−363.431			−0.638719			−0.319360	+	0.947634i	$0.603468\pi$
$570$	−60.8484	−	258.515i	−0.106752	−	0.453535i
$571$			694.121i			1.21562i	0.794081	+	0.607812i	$0.207953\pi$
$571$			694.121i			1.21562i	−0.794081	+	0.607812i	$0.792047\pi$
$572$	56.5998	+	195.845i	0.0989508	+	0.342387i
$573$		−	297.656i		−	0.519470i
$574$	717.376	−	954.058i	1.24978	−	1.66212i
$575$	79.7796	+	435.945i	0.138747	+	0.758166i
$576$	−262.902	−	233.758i	−0.456427	−	0.405830i
$577$			6.57594i			0.0113968i	0.999984	+	0.00569839i	$0.00181386\pi$
$577$			6.57594i			0.0113968i	−0.999984	+	0.00569839i	$0.998186\pi$
$578$	−47.0401	+	62.5598i	−0.0813842	+	0.108235i
$579$		−	312.114i		−	0.539057i
$580$	−165.994	+	378.230i	−0.286197	+	0.652120i
$581$	−425.492			−0.732344
$582$	106.699	+	80.2289i	0.183331	+	0.137850i
$583$	120.458			0.206618
$584$	−115.789	+	304.483i	−0.198269	+	0.521374i
$585$	270.424	−	324.403i	0.462263	−	0.554535i
$586$	689.503	+	518.452i	1.17663	+	0.884731i
$587$	78.5744			0.133858			0.0669288	−	0.997758i	$-0.478680\pi$
$587$	78.5744			0.133858			0.0669288	+	0.997758i	$0.478680\pi$
$588$	−180.198	−	623.517i	−0.306459	−	1.06040i
$589$	144.688			0.245650
$590$	−174.736	−	742.367i	−0.296163	−	1.25825i
$591$		−	488.935i		−	0.827301i
$592$	370.438	+	587.361i	0.625739	+	0.992164i
$593$		−	493.290i		−	0.831855i	−0.909398	−	0.415927i	$-0.863457\pi$
$593$		−	493.290i		−	0.831855i	0.909398	−	0.415927i	$-0.136543\pi$
$594$	143.853	+	108.166i	0.242177	+	0.182098i
$595$	589.503	−	707.174i	0.990761	−	1.18853i
$596$	121.255	+	419.564i	0.203448	+	0.703967i
$597$			495.776i			0.830445i
$598$	−435.452	−	327.426i	−0.728181	−	0.547535i
$599$			90.0018i			0.150253i	0.997174	+	0.0751267i	$0.0239361\pi$
$599$			90.0018i			0.150253i	−0.997174	+	0.0751267i	$0.976064\pi$
$600$	−67.8979	+	368.127i	−0.113163	+	0.613545i
$601$	525.158			0.873807			0.436903	−	0.899509i	$-0.356075\pi$
$601$	525.158			0.873807			0.436903	+	0.899509i	$0.356075\pi$
$602$	−704.272	+	936.630i	−1.16989	+	1.55586i
$603$	−215.047			−0.356628
$604$	371.079	−	107.243i	0.614369	−	0.177554i
$605$	−42.2466	−	35.2169i	−0.0698290	−	0.0582097i
$606$	425.540	−	565.937i	0.702212	−	0.933890i
$607$	852.633			1.40467			0.702334	−	0.711848i	$-0.252141\pi$
$607$	852.633			1.40467			0.702334	+	0.711848i	$0.252141\pi$
$608$	452.531	+	37.2162i	0.744295	+	0.0612108i
$609$	450.280			0.739376
$610$	−791.265	+	186.245i	−1.29715	+	0.305320i
$611$		−	396.954i		−	0.649679i
$612$	−333.890	+	96.4951i	−0.545572	+	0.157672i
$613$			640.325i			1.04458i	0.852769	+	0.522288i	$0.174922\pi$
$613$			640.325i			1.04458i	−0.852769	+	0.522288i	$0.825078\pi$
$614$	527.883	−	702.045i	0.859744	−	1.14340i
$615$	368.307	+	307.022i	0.598873	+	0.499223i
$616$	109.859	−	288.890i	0.178343	−	0.468978i
$617$		−	687.291i		−	1.11392i	−0.830538	−	0.556962i	$-0.811967\pi$
$617$		−	687.291i		−	1.11392i	0.830538	−	0.556962i	$-0.188033\pi$
$618$	−279.648	+	371.911i	−0.452504	+	0.601797i
$619$			455.133i			0.735271i	0.929970	+	0.367635i	$0.119833\pi$
$619$			455.133i			0.735271i	−0.929970	+	0.367635i	$0.880167\pi$
$620$	−186.746	−	81.9574i	−0.301203	−	0.132189i
$621$	−481.005			−0.774565
$622$	235.378	+	176.986i	0.378421	+	0.284543i
$623$	−1302.39			−2.09052
$624$	−245.483	−	389.235i	−0.393403	−	0.623774i
$625$	−584.494	+	221.342i	−0.935190	+	0.354147i
$626$	−470.420	−	353.719i	−0.751469	−	0.565046i
$627$	−88.0827			−0.140483
$628$	1018.37	−	294.313i	1.62161	−	0.468650i
$629$	686.046			1.09069
$630$	−623.272	+	146.704i	−0.989320	+	0.232863i
$631$		−	319.662i		−	0.506596i	−0.967388	−	0.253298i	$-0.918485\pi$
$631$		−	319.662i		−	0.506596i	0.967388	−	0.253298i	$-0.0815153\pi$
$632$	141.339	−	371.670i	0.223638	−	0.588086i
$633$			396.777i			0.626820i
$634$	−156.714	−	117.837i	−0.247183	−	0.185862i
$635$	−646.091	−	538.583i	−1.01747	−	0.848163i
$636$	−261.224	+	75.4946i	−0.410730	+	0.118702i
$637$			1332.14i			2.09128i
$638$	109.494	+	82.3309i	0.171621	+	0.129045i
$639$		−	147.389i		−	0.230656i
$640$	−562.993	−	304.367i	−0.879676	−	0.475574i
$641$	800.239			1.24842			0.624211	−	0.781256i	$-0.285420\pi$
$641$	800.239			1.24842			0.624211	+	0.781256i	$0.285420\pi$
$642$	−69.4734	+	92.3945i	−0.108214	+	0.143917i
$643$	−363.629			−0.565519			−0.282759	−	0.959191i	$-0.591250\pi$
$643$	−363.629			−0.565519			−0.282759	+	0.959191i	$0.591250\pi$
$644$	229.332	+	793.528i	0.356105	+	1.23219i
$645$	−361.579	−	301.414i	−0.560588	−	0.467308i
$646$	269.591	−	358.537i	0.417324	−	0.555010i
$647$	467.325			0.722296			0.361148	−	0.932509i	$-0.382385\pi$
$647$	467.325			0.722296			0.361148	+	0.932509i	$0.382385\pi$
$648$	−9.82430	−	3.73599i	−0.0151610	−	0.00576542i
$649$	−252.944			−0.389744
$650$	343.662	−	687.185i	0.528711	−	1.05721i
$651$			222.320i			0.341505i
$652$	−24.9623	−	86.3740i	−0.0382858	−	0.132476i
$653$		−	517.515i		−	0.792520i	−0.918138	−	0.396260i	$-0.870308\pi$
$653$		−	517.515i		−	0.792520i	0.918138	−	0.396260i	$-0.129692\pi$
$654$	−277.412	+	368.938i	−0.424178	+	0.564126i
$655$	−347.064	+	416.341i	−0.529868	+	0.635636i
$656$	−693.399	+	437.314i	−1.05701	+	0.666637i
$657$		−	223.827i		−	0.340680i
$658$	−361.686	+	481.015i	−0.549674	+	0.731026i
$659$			880.339i			1.33587i	0.744219	+	0.667936i	$0.232822\pi$
$659$			880.339i			1.33587i	−0.744219	+	0.667936i	$0.767178\pi$
$660$	113.687	+	49.8938i	0.172253	+	0.0755966i
$661$	382.765			0.579069			0.289535	−	0.957168i	$-0.406499\pi$
$661$	382.765			0.579069			0.289535	+	0.957168i	$0.406499\pi$
$662$	706.760	+	531.428i	1.06761	+	0.802762i
$663$	−454.632			−0.685719
$664$	273.134	+	103.868i	0.411347	+	0.156427i
$665$	529.171	−	634.800i	0.795747	−	0.954586i
$666$	−381.356	−	286.750i	−0.572607	−	0.430556i
$667$	−366.117			−0.548901
$668$	−197.648	−	683.899i	−0.295881	−	1.02380i
$669$	−311.117			−0.465049
$670$	−380.815	+	89.6349i	−0.568380	+	0.133783i
$671$			269.604i			0.401795i
$672$	−57.1843	+	695.335i	−0.0850957	+	1.03472i
$673$			751.235i			1.11625i	0.829757	+	0.558124i	$0.188479\pi$
$673$			751.235i			1.11625i	−0.829757	+	0.558124i	$0.811521\pi$
$674$	−138.819	−	104.381i	−0.205962	−	0.154868i
$675$	−122.110	−	667.254i	−0.180904	−	0.988524i
$676$	74.5526	+	257.965i	0.110285	+	0.381605i
$677$		−	302.142i		−	0.446296i	−0.974785	−	0.223148i	$-0.928367\pi$
$677$		−	302.142i		−	0.446296i	0.974785	−	0.223148i	$-0.0716333\pi$
$678$	435.231	+	327.259i	0.641933	+	0.482683i
$679$			415.416i			0.611805i
$680$	−551.047	+	310.048i	−0.810363	+	0.455953i
$681$	−23.9869			−0.0352230
$682$	−40.6498	+	54.0612i	−0.0596038	+	0.0792687i
$683$	−338.096			−0.495017			−0.247508	−	0.968886i	$-0.579612\pi$
$683$	−338.096			−0.495017			−0.247508	+	0.968886i	$0.579612\pi$
$684$	−299.719	+	86.6195i	−0.438185	+	0.126637i
$685$	−695.769	+	834.652i	−1.01572	+	1.21847i
$686$	527.725	−	701.835i	0.769278	−	1.02308i
$687$	−728.870			−1.06095
$688$	680.733	−	429.325i	0.989437	−	0.624019i
$689$	558.106			0.810024
$690$	−322.974	+	76.0207i	−0.468079	+	0.110175i
$691$		−	176.823i		−	0.255894i	−0.991781	−	0.127947i	$-0.959161\pi$
$691$		−	176.823i		−	0.255894i	0.991781	−	0.127947i	$-0.0408387\pi$
$692$	−121.933	+	35.2389i	−0.176203	+	0.0509232i
$693$			212.365i			0.306443i
$694$	−282.150	+	375.238i	−0.406556	+	0.540689i
$695$	−703.575	+	844.016i	−1.01234	+	1.21441i
$696$	−289.046	−	109.919i	−0.415296	−	0.157929i
$697$			809.900i			1.16198i
$698$	−44.9560	+	59.7882i	−0.0644069	+	0.0856565i
$699$			155.120i			0.221917i
$700$	−1042.57	+	519.579i	−1.48938	+	0.742255i
$701$	34.8582			0.0497263			0.0248632	−	0.999691i	$-0.492085\pi$
$701$	34.8582			0.0497263			0.0248632	+	0.999691i	$0.492085\pi$
$702$	666.499	+	501.155i	0.949429	+	0.713896i
$703$	615.834			0.876009
$704$	−141.043	+	158.628i	−0.200345	+	0.225324i
$705$	−185.693	−	154.794i	−0.263394	−	0.219566i
$706$	−642.389	−	483.026i	−0.909899	−	0.684173i
$707$	2203.40			3.11654
$708$	548.531	−	158.527i	0.774761	−	0.223908i
$709$	1065.71			1.50312			0.751561	−	0.659664i	$-0.229301\pi$
$709$	1065.71			1.50312			0.751561	+	0.659664i	$0.229301\pi$
$710$	−61.4342	−	261.004i	−0.0865271	−	0.367611i
$711$			273.217i			0.384272i
$712$	836.039	+	317.930i	1.17421	+	0.446531i
$713$		−	180.765i		−	0.253528i
$714$	550.908	+	414.239i	0.771580	+	0.580167i
$715$	−195.736	−	163.166i	−0.273757	−	0.228205i
$716$	−948.101	+	274.004i	−1.32416	+	0.382686i
$717$		−	753.717i		−	1.05121i
$718$	693.045	+	521.115i	0.965244	+	0.725787i
$719$		−	620.988i		−	0.863683i	−0.901949	−	0.431842i	$-0.857864\pi$
$719$		−	620.988i		−	0.863683i	0.901949	−	0.431842i	$-0.142136\pi$
$720$	435.906	+	57.9753i	0.605425	+	0.0805212i
$721$	−1447.98			−2.00830
$722$	−191.909	+	255.224i	−0.265801	+	0.353496i
$723$	448.919			0.620911
$724$	−185.542	−	642.010i	−0.256274	−	0.886754i
$725$	−92.9440	−	507.880i	−0.128199	−	0.700525i
$726$	24.7466	−	32.9112i	0.0340863	−	0.0453323i
$727$	−471.311			−0.648295			−0.324148	−	0.946006i	$-0.605077\pi$
$727$	−471.311			−0.648295			−0.324148	+	0.946006i	$0.605077\pi$
$728$	508.999	−	1338.48i	0.699174	−	1.83857i
$729$	464.288			0.636883
$730$	−93.2946	−	396.363i	−0.127801	−	0.542963i
$731$		−	795.105i		−	1.08770i
$732$	−168.968	−	584.660i	−0.230831	−	0.798716i
$733$		−	382.451i		−	0.521761i	−0.965371	−	0.260880i	$-0.915987\pi$
$733$		−	382.451i		−	0.521761i	0.965371	−	0.260880i	$-0.0840128\pi$
$734$	−177.895	+	236.587i	−0.242364	+	0.322326i
$735$	623.169	+	519.476i	0.847849	+	0.706770i
$736$	46.4959	−	565.368i	0.0631737	−	0.768163i
$737$			129.753i			0.176056i
$738$	338.518	−	450.204i	0.458697	−	0.610033i
$739$		−	1273.04i		−	1.72265i	−0.508051	−	0.861327i	$-0.669634\pi$
$739$		−	1273.04i		−	1.72265i	0.508051	−	0.861327i	$-0.330366\pi$
$740$	−794.845	−	348.834i	−1.07411	−	0.471398i
$741$	−408.104			−0.550747
$742$	−676.295	−	508.520i	−0.911449	−	0.685338i
$743$	−754.743			−1.01580			−0.507902	−	0.861415i	$-0.669579\pi$
$743$	−754.743			−1.01580			−0.507902	+	0.861415i	$0.669579\pi$
$744$	54.2709	−	142.713i	0.0729448	−	0.191818i
$745$	−419.330	−	349.555i	−0.562860	−	0.469202i
$746$	−587.958	−	442.098i	−0.788147	−	0.592625i
$747$	−200.783			−0.268785
$748$	58.2225	+	201.460i	0.0778376	+	0.269332i
$749$	−359.725			−0.480274
$750$	−187.448	−	428.734i	−0.249931	−	0.571645i
$751$			951.384i			1.26682i	0.773815	+	0.633412i	$0.218346\pi$
$751$			951.384i			1.26682i	−0.773815	+	0.633412i	$0.781654\pi$
$752$	349.597	−	220.484i	0.464890	−	0.293197i
$753$			632.493i			0.839964i
$754$	507.306	+	381.454i	0.672820	+	0.505907i
$755$	−309.160	+	370.872i	−0.409484	+	0.491221i
$756$	−351.013	−	1214.57i	−0.464303	−	1.60657i
$757$			925.077i			1.22203i	0.791619	+	0.611015i	$0.209238\pi$
$757$			925.077i			1.22203i	−0.791619	+	0.611015i	$0.790762\pi$
$758$	426.252	+	320.508i	0.562338	+	0.422834i
$759$			110.046i			0.144988i
$760$	−494.651	+	278.317i	−0.650857	+	0.366207i
$761$	365.227			0.479930			0.239965	−	0.970782i	$-0.422864\pi$
$761$	365.227			0.479930			0.239965	+	0.970782i	$0.422864\pi$
$762$	378.459	−	503.322i	0.496665	−	0.660528i
$763$	−1436.41			−1.88258
$764$	−611.117	+	176.614i	−0.799891	+	0.231171i
$765$	278.177	−	333.704i	0.363630	−	0.436214i
$766$	489.055	−	650.407i	0.638453	−	0.849095i
$767$	−1171.94			−1.52795
$768$	206.448	−	432.394i	0.268812	−	0.563013i
$769$	230.757			0.300074			0.150037	−	0.988680i	$-0.452061\pi$
$769$	230.757			0.300074			0.150037	+	0.988680i	$0.452061\pi$
$770$	88.5170	+	376.065i	0.114957	+	0.488396i
$771$			497.830i			0.645694i
$772$	−640.799	+	185.193i	−0.830051	+	0.239887i
$773$		−	490.699i		−	0.634799i	−0.948292	−	0.317399i	$-0.897190\pi$
$773$		−	490.699i		−	0.634799i	0.948292	−	0.317399i	$-0.102810\pi$
$774$	−332.334	+	441.980i	−0.429372	+	0.571034i
$775$	250.759	−

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+(-1.20196 + 1.59852i) q^{2} +1.87168 q^{3} +(-1.11056 - 3.84274i) q^{4} +(3.84060 + 3.20153i) q^{5} +(-2.24970 + 2.99193i) q^{6} -11.6487 q^{7} +(7.47757 + 2.84358i) q^{8} -5.49681 q^{9} +(-9.73399 + 2.29116i) q^{10} +3.31662i q^{11} +(-2.07862 - 7.19239i) q^{12} +15.3665i q^{13} +(14.0013 - 18.6207i) q^{14} +(7.18837 + 5.99225i) q^{15} +(-13.5333 + 8.53520i) q^{16} +15.8071i q^{17} +(6.60697 - 8.78678i) q^{18} +14.1893i q^{19} +(8.03745 - 18.3139i) q^{20} -21.8026 q^{21} +(-5.30171 - 3.98647i) q^{22} +17.7274 q^{23} +(13.9956 + 5.32227i) q^{24} +(4.50035 + 24.5916i) q^{25} +(-24.5638 - 18.4700i) q^{26} -27.1334 q^{27} +(12.9366 + 44.7628i) q^{28} -20.6526 q^{29} +(-18.2189 + 4.28831i) q^{30} -10.1970i q^{31} +(2.62282 - 31.8923i) q^{32} +6.20767i q^{33} +(-25.2680 - 18.9996i) q^{34} +(-44.7378 - 37.2936i) q^{35} +(6.10455 + 21.1228i) q^{36} -43.4012i q^{37} +(-22.6820 - 17.0551i) q^{38} +28.7613i q^{39} +(19.6145 + 34.8607i) q^{40} +51.2365 q^{41} +(26.2059 - 34.8520i) q^{42} -50.3006 q^{43} +(12.7449 - 3.68332i) q^{44} +(-21.1110 - 17.5982i) q^{45} +(-21.3077 + 28.3377i) q^{46} -25.8323 q^{47} +(-25.3300 + 15.9752i) q^{48} +86.6912 q^{49} +(-44.7195 - 22.3643i) q^{50} +29.5858i q^{51} +(59.0496 - 17.0655i) q^{52} -36.3196i q^{53} +(32.6134 - 43.3734i) q^{54} +(-10.6183 + 12.7378i) q^{55} +(-87.1037 - 33.1239i) q^{56} +26.5579i q^{57} +(24.8237 - 33.0137i) q^{58} +76.2655i q^{59} +(15.0435 - 34.2778i) q^{60} +81.2888 q^{61} +(16.3001 + 12.2564i) q^{62} +64.0304 q^{63} +(47.8281 + 42.5261i) q^{64} +(-49.1965 + 59.0167i) q^{65} +(-9.92311 - 7.46140i) q^{66} +39.1221 q^{67} +(60.7425 - 17.5547i) q^{68} +33.1801 q^{69} +(113.388 - 26.6889i) q^{70} +26.8136i q^{71} +(-41.1028 - 15.6306i) q^{72} +40.7194i q^{73} +(69.3778 + 52.1667i) q^{74} +(8.42323 + 46.0276i) q^{75} +(54.5260 - 15.7581i) q^{76} -38.6342i q^{77} +(-45.9756 - 34.5700i) q^{78} -49.7047i q^{79} +(-79.3017 - 10.5471i) q^{80} -1.31384 q^{81} +(-61.5845 + 81.9028i) q^{82} +36.5271 q^{83} +(24.2131 + 83.7816i) q^{84} +(-50.6069 + 60.7086i) q^{85} +(60.4595 - 80.4067i) q^{86} -38.6551 q^{87} +(-9.43108 + 24.8003i) q^{88} +111.806 q^{89} +(53.5059 - 12.5940i) q^{90} -179.000i q^{91} +(-19.6874 - 68.1218i) q^{92} -19.0854i q^{93} +(31.0496 - 41.2936i) q^{94} +(-45.4277 + 54.4955i) q^{95} +(4.90909 - 59.6923i) q^{96} -35.6621i q^{97} +(-104.200 + 138.578i) q^{98} -18.2308i 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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