LMFDB - Embedded newform 110.5.h.a.51.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,5,Mod(41,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("110.41");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	110.h (of order $10$, degree $4$, 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:	$11.3706959392$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.7
Character	$\chi$	$=$	110.51
Dual form			110.5.h.a.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.66251 - 2.28825i) q^{2} +(-0.417925 + 1.28624i) q^{3} +(-2.47214 - 7.60845i) q^{4} +(-9.04508 + 6.57164i) q^{5} +(2.24843 + 3.09470i) q^{6} +(-34.7724 + 11.2982i) q^{7} +(-21.5200 - 6.99226i) q^{8} +(64.0506 + 46.5355i) q^{9} +31.6228i q^{10} +(-96.7298 - 72.6935i) q^{11} +10.8195 q^{12} +(-185.513 + 255.337i) q^{13} +(-31.9562 + 98.3511i) q^{14} +(-4.67254 - 14.3806i) q^{15} +(-51.7771 + 37.6183i) q^{16} +(250.794 + 345.188i) q^{17} +(212.969 - 69.1979i) q^{18} +(-297.041 - 96.5143i) q^{19} +(72.3607 + 52.5731i) q^{20} -49.4475i q^{21} +(-327.155 + 100.488i) q^{22} +48.1191 q^{23} +(17.9874 - 24.7576i) q^{24} +(38.6271 - 118.882i) q^{25} +(275.856 + 848.998i) q^{26} +(-175.250 + 127.326i) q^{27} +(171.924 + 236.633i) q^{28} +(-1157.94 + 376.238i) q^{29} +(-40.6745 - 13.2159i) q^{30} +(665.307 + 483.374i) q^{31} +181.019i q^{32} +(133.927 - 94.0373i) q^{33} +1206.82 q^{34} +(240.271 - 330.705i) q^{35} +(195.721 - 602.368i) q^{36} +(-475.103 - 1462.22i) q^{37} +(-714.681 + 519.246i) q^{38} +(-250.894 - 345.326i) q^{39} +(240.600 - 78.1758i) q^{40} +(1122.57 + 364.745i) q^{41} +(-113.148 - 82.2068i) q^{42} +2157.10i q^{43} +(-313.956 + 915.672i) q^{44} -885.158 q^{45} +(79.9984 - 110.108i) q^{46} +(1091.33 - 3358.78i) q^{47} +(-26.7472 - 82.3194i) q^{48} +(-860.982 + 625.540i) q^{49} +(-207.813 - 286.031i) q^{50} +(-548.808 + 178.319i) q^{51} +(2401.33 + 780.240i) q^{52} +(-598.091 - 434.538i) q^{53} +612.695i q^{54} +(1352.64 + 21.8460i) q^{55} +827.300 q^{56} +(248.281 - 341.730i) q^{57} +(-1064.16 + 3275.16i) q^{58} +(-1402.81 - 4317.42i) q^{59} +(-97.8630 + 71.1016i) q^{60} +(-3429.77 - 4720.67i) q^{61} +(2212.16 - 718.773i) q^{62} +(-2752.96 - 894.491i) q^{63} +(414.217 + 300.946i) q^{64} -3528.67i q^{65} +(7.47442 - 462.796i) q^{66} -3727.15 q^{67} +(2006.35 - 2761.50i) q^{68} +(-20.1102 + 61.8928i) q^{69} +(-357.281 - 1099.60i) q^{70} +(-4825.92 + 3506.23i) q^{71} +(-1052.98 - 1449.30i) q^{72} +(7011.80 - 2278.27i) q^{73} +(-4135.77 - 1343.79i) q^{74} +(136.768 + 99.3676i) q^{75} +2498.62i q^{76} +(4184.83 + 1434.85i) q^{77} -1207.30 q^{78} +(4529.72 - 6234.62i) q^{79} +(221.115 - 680.521i) q^{80} +(1891.15 + 5820.35i) q^{81} +(2700.91 - 1962.32i) q^{82} +(6383.72 + 8786.44i) q^{83} +(-376.219 + 122.241i) q^{84} +(-4536.90 - 1474.13i) q^{85} +(4935.97 + 3586.19i) q^{86} -1646.63i q^{87} +(1573.33 + 2240.72i) q^{88} -4875.33 q^{89} +(-1471.58 + 2025.46i) q^{90} +(3565.87 - 10974.6i) q^{91} +(-118.957 - 366.112i) q^{92} +(-899.783 + 653.731i) q^{93} +(-5871.36 - 8081.24i) q^{94} +(3321.01 - 1079.06i) q^{95} +(-232.834 - 75.6525i) q^{96} +(2652.84 + 1927.40i) q^{97} +3010.10i q^{98} +(-2812.77 - 9157.43i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) $ 32 * q - 18 * q^3 + 64 * q^4 - 200 * q^5 + 80 * q^6 - 60 * q^7 - 262 * q^9 - 258 * q^11 - 96 * q^12 - 570 * q^13 - 48 * q^14 + 150 * q^15 - 512 * q^16 + 150 * q^17 - 480 * q^18 - 1020 * q^19 + 1600 * q^20 - 480 * q^22 - 1536 * q^23 + 640 * q^24 - 1000 * q^25 + 448 * q^26 - 4194 * q^27 + 960 * q^28 - 4130 * q^29 - 800 * q^30 - 1936 * q^31 - 5852 * q^33 - 768 * q^34 + 1856 * q^36 + 2728 * q^37 - 1360 * q^38 + 7990 * q^39 - 4490 * q^41 - 2592 * q^42 + 1024 * q^44 + 300 * q^45 + 640 * q^46 - 2732 * q^47 - 1152 * q^48 + 3832 * q^49 + 12080 * q^51 + 5520 * q^52 + 1222 * q^53 - 550 * q^55 + 2304 * q^56 + 14580 * q^57 - 3104 * q^58 - 8340 * q^59 - 300 * q^61 + 11680 * q^62 + 32020 * q^63 + 4096 * q^64 + 29696 * q^66 - 9264 * q^67 + 1200 * q^68 - 25466 * q^69 - 1200 * q^70 - 7144 * q^71 - 20480 * q^72 - 7070 * q^73 + 19840 * q^74 + 1500 * q^75 + 34480 * q^77 - 5696 * q^78 + 57050 * q^79 + 12800 * q^80 - 63694 * q^81 + 13312 * q^82 + 580 * q^83 + 29520 * q^84 + 9750 * q^85 - 13360 * q^86 + 9600 * q^88 + 14368 * q^89 + 17600 * q^90 - 40158 * q^91 - 25712 * q^92 - 103942 * q^93 - 67600 * q^94 + 5700 * q^95 - 31458 * q^97 + 65268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	1.66251	−	2.28825i	0.415627	−	0.572061i
$2$	1.66251	−	2.28825i	0.415627	−	0.572061i
$3$	−0.417925	+	1.28624i	−0.0464361	+	0.142916i	−0.971586	−	0.236686i	$-0.923939\pi$
$3$	−0.417925	+	1.28624i	−0.0464361	+	0.142916i	0.925150	+	0.379601i	$0.123939\pi$
$4$	−2.47214	−	7.60845i	−0.154508	−	0.475528i
$5$	−9.04508	+	6.57164i	−0.361803	+	0.262866i
$5$	−9.04508	+	6.57164i	−0.361803	+	0.262866i
$6$	2.24843	+	3.09470i	0.0624564	+	0.0859639i
$7$	−34.7724	+	11.2982i	−0.709640	+	0.230576i	−0.641526	−	0.767101i	$-0.721698\pi$
$7$	−34.7724	+	11.2982i	−0.709640	+	0.230576i	−0.0681145	+	0.997678i	$0.521698\pi$
$8$	−21.5200	−	6.99226i	−0.336249	−	0.109254i
$9$	64.0506	+	46.5355i	0.790748	+	0.574512i
$10$			31.6228i			0.316228i
$11$	−96.7298	−	72.6935i	−0.799420	−	0.600773i
$11$	−96.7298	−	72.6935i	−0.799420	−	0.600773i
$12$	10.8195			0.0751352
$13$	−185.513	+	255.337i	−1.09771	+	1.51087i	−0.259324	+	0.965790i	$0.583500\pi$
$13$	−185.513	+	255.337i	−1.09771	+	1.51087i	−0.838385	+	0.545078i	$0.816500\pi$
$14$	−31.9562	+	98.3511i	−0.163042	+	0.501791i
$15$	−4.67254	−	14.3806i	−0.0207669	−	0.0639138i
$16$	−51.7771	+	37.6183i	−0.202254	+	0.146946i
$17$	250.794	+	345.188i	0.867799	+	1.19442i	0.979653	+	0.200698i	$0.0643209\pi$
$17$	250.794	+	345.188i	0.867799	+	1.19442i	−0.111855	+	0.993725i	$0.535679\pi$
$18$	212.969	−	69.1979i	0.657313	−	0.213574i
$19$	−297.041	−	96.5143i	−0.822827	−	0.267353i	−0.132806	−	0.991142i	$-0.542399\pi$
$19$	−297.041	−	96.5143i	−0.822827	−	0.267353i	−0.690021	+	0.723789i	$0.742399\pi$
$20$	72.3607	+	52.5731i	0.180902	+	0.131433i
$21$		−	49.4475i		−	0.112126i
$22$	−327.155	+	100.488i	−0.675939	+	0.207620i
$23$	48.1191			0.0909624			0.0454812	−	0.998965i	$-0.485518\pi$
$23$	48.1191			0.0909624			0.0454812	+	0.998965i	$0.485518\pi$
$24$	17.9874	−	24.7576i	0.0312282	−	0.0429819i
$25$	38.6271	−	118.882i	0.0618034	−	0.190211i
$26$	275.856	+	848.998i	0.408071	+	1.25591i
$27$	−175.250	+	127.326i	−0.240397	+	0.174659i
$28$	171.924	+	236.633i	0.219291	+	0.301828i
$29$	−1157.94	+	376.238i	−1.37686	+	0.447370i	−0.901637	−	0.432493i	$-0.857634\pi$
$29$	−1157.94	+	376.238i	−1.37686	+	0.447370i	−0.475227	+	0.879863i	$0.657634\pi$
$30$	−40.6745	−	13.2159i	−0.0451939	−	0.0146844i
$31$	665.307	+	483.374i	0.692307	+	0.502990i	0.877418	−	0.479727i	$-0.159264\pi$
$31$	665.307	+	483.374i	0.692307	+	0.502990i	−0.185111	+	0.982718i	$0.559264\pi$
$32$			181.019i			0.176777i
$33$	133.927	−	94.0373i	0.122982	−	0.0863520i
$34$	1206.82			1.04396
$35$	240.271	−	330.705i	0.196140	−	0.269963i
$36$	195.721	−	602.368i	0.151020	−	0.464790i
$37$	−475.103	−	1462.22i	−0.347044	−	1.06809i	−0.960481	−	0.278347i	$-0.910213\pi$
$37$	−475.103	−	1462.22i	−0.347044	−	1.06809i	0.613437	−	0.789744i	$-0.289787\pi$
$38$	−714.681	+	519.246i	−0.494931	+	0.359589i
$39$	−250.894	−	345.326i	−0.164953	−	0.227039i
$40$	240.600	−	78.1758i	0.150375	−	0.0488599i
$41$	1122.57	+	364.745i	0.667798	+	0.216981i	0.623246	−	0.782026i	$-0.285814\pi$
$41$	1122.57	+	364.745i	0.667798	+	0.216981i	0.0445528	+	0.999007i	$0.485814\pi$
$42$	−113.148	−	82.2068i	−0.0641428	−	0.0466025i
$43$			2157.10i			1.16663i	0.812246	+	0.583315i	$0.198245\pi$
$43$			2157.10i			1.16663i	−0.812246	+	0.583315i	$0.801755\pi$
$44$	−313.956	+	915.672i	−0.162167	+	0.472971i
$45$	−885.158			−0.437115
$46$	79.9984	−	110.108i	0.0378064	−	0.0520361i
$47$	1091.33	−	3358.78i	0.494040	−	1.52050i	−0.324408	−	0.945917i	$-0.605165\pi$
$47$	1091.33	−	3358.78i	0.494040	−	1.52050i	0.818448	−	0.574581i	$-0.194835\pi$
$48$	−26.7472	−	82.3194i	−0.0116090	−	0.0357289i
$49$	−860.982	+	625.540i	−0.358593	+	0.260533i
$50$	−207.813	−	286.031i	−0.0831254	−	0.114412i
$51$	−548.808	+	178.319i	−0.210999	+	0.0685577i
$52$	2401.33	+	780.240i	0.888066	+	0.288550i
$53$	−598.091	−	434.538i	−0.212919	−	0.154695i	0.476214	−	0.879329i	$-0.342009\pi$
$53$	−598.091	−	434.538i	−0.212919	−	0.154695i	−0.689134	+	0.724634i	$0.742009\pi$
$54$			612.695i			0.210115i
$55$	1352.64	+	21.8460i	0.447155	+	0.00722182i
$56$	827.300			0.263807
$57$	248.281	−	341.730i	0.0764178	−	0.105180i
$58$	−1064.16	+	3275.16i	−0.316339	+	0.973590i
$59$	−1402.81	−	4317.42i	−0.402992	−	1.24028i	−0.922561	−	0.385852i	$-0.873907\pi$
$59$	−1402.81	−	4317.42i	−0.402992	−	1.24028i	0.519569	−	0.854429i	$-0.326093\pi$
$60$	−97.8630	+	71.1016i	−0.0271842	+	0.0197505i
$61$	−3429.77	−	4720.67i	−0.921733	−	1.26866i	−0.962998	−	0.269509i	$-0.913139\pi$
$61$	−3429.77	−	4720.67i	−0.921733	−	1.26866i	0.0412647	−	0.999148i	$-0.486861\pi$
$62$	2212.16	−	718.773i	0.575483	−	0.186986i
$63$	−2752.96	−	894.491i	−0.693616	−	0.225369i
$64$	414.217	+	300.946i	0.101127	+	0.0734732i
$65$		−	3528.67i		−	0.835187i
$66$	7.47442	−	462.796i	0.00171589	−	0.106243i
$67$	−3727.15			−0.830285			−0.415142	−	0.909757i	$-0.636268\pi$
$67$	−3727.15			−0.830285			−0.415142	+	0.909757i	$0.636268\pi$
$68$	2006.35	−	2761.50i	0.433899	−	0.597211i
$69$	−20.1102	+	61.8928i	−0.00422394	+	0.0130000i
$70$	−357.281	−	1099.60i	−0.0729146	−	0.224408i
$71$	−4825.92	+	3506.23i	−0.957333	+	0.695543i	−0.952530	−	0.304445i	$-0.901529\pi$
$71$	−4825.92	+	3506.23i	−0.957333	+	0.695543i	−0.00480321	+	0.999988i	$0.501529\pi$
$72$	−1052.98	−	1449.30i	−0.203121	−	0.279572i
$73$	7011.80	−	2278.27i	1.31578	−	0.427524i	0.434738	−	0.900557i	$-0.356841\pi$
$73$	7011.80	−	2278.27i	1.31578	−	0.427524i	0.881044	+	0.473034i	$0.156841\pi$
$74$	−4135.77	−	1343.79i	−0.755254	−	0.245397i
$75$	136.768	+	99.3676i	0.0243143	+	0.0176653i
$76$			2498.62i			0.432586i
$77$	4184.83	+	1434.85i	0.705824	+	0.242006i
$78$	−1207.30			−0.198439
$79$	4529.72	−	6234.62i	0.725800	−	0.998978i	−0.273511	−	0.961869i	$-0.588185\pi$
$79$	4529.72	−	6234.62i	0.725800	−	0.998978i	0.999311	−	0.0371092i	$-0.0118150\pi$
$80$	221.115	−	680.521i	0.0345492	−	0.106331i
$81$	1891.15	+	5820.35i	0.288241	+	0.887114i
$82$	2700.91	−	1962.32i	0.401681	−	0.291839i
$83$	6383.72	+	8786.44i	0.926655	+	1.27543i	0.961150	+	0.276026i	$0.0890175\pi$
$83$	6383.72	+	8786.44i	0.926655	+	1.27543i	−0.0344957	+	0.999405i	$0.510982\pi$
$84$	−376.219	+	122.241i	−0.0533190	+	0.0173244i
$85$	−4536.90	−	1474.13i	−0.627945	−	0.204032i
$86$	4935.97	+	3586.19i	0.667384	+	0.484883i
$87$		−	1646.63i		−	0.217550i
$88$	1573.33	+	2240.72i	0.203167	+	0.289349i
$89$	−4875.33			−0.615495			−0.307747	−	0.951468i	$-0.599575\pi$
$89$	−4875.33			−0.615495			−0.307747	+	0.951468i	$0.599575\pi$
$90$	−1471.58	+	2025.46i	−0.181677	+	0.250057i
$91$	3565.87	−	10974.6i	0.430609	−	1.32528i
$92$	−118.957	−	366.112i	−0.0140545	−	0.0432552i
$93$	−899.783	+	653.731i	−0.104033	+	0.0755846i
$94$	−5871.36	−	8081.24i	−0.664482	−	0.914581i
$95$	3321.01	−	1079.06i	0.367979	−	0.119564i
$96$	−232.834	−	75.6525i	−0.0252642	−	0.00820882i
$97$	2652.84	+	1927.40i	0.281947	+	0.204846i	0.719766	−	0.694217i	$-0.244249\pi$
$97$	2652.84	+	1927.40i	0.281947	+	0.204846i	−0.437819	+	0.899063i	$0.644249\pi$
$98$			3010.10i			0.313422i
$99$	−2812.77	−	9157.43i	−0.286988	−	0.934337i
$100$	−1000.00			−0.100000
$101$	−2424.50	+	3337.04i	−0.237673	+	0.327129i	−0.911147	−	0.412082i	$-0.864802\pi$
$101$	−2424.50	+	3337.04i	−0.237673	+	0.327129i	0.673473	+	0.739211i	$0.264802\pi$
$102$	−504.361	+	1552.26i	−0.0484776	+	0.149199i
$103$	2292.85	+	7056.67i	0.216123	+	0.665159i	0.999072	+	0.0430728i	$0.0137147\pi$
$103$	2292.85	+	7056.67i	0.216123	+	0.665159i	−0.782949	+	0.622086i	$0.786285\pi$
$104$	5777.61	−	4197.68i	0.534173	−	0.388099i
$105$	324.951	+	447.256i	0.0294740	+	0.0405675i
$106$	−1988.66	+	646.155i	−0.176990	+	0.0575076i
$107$	18238.6	+	5926.07i	1.59303	+	0.517606i	0.965370	−	0.260885i	$-0.0840142\pi$
$107$	18238.6	+	5926.07i	1.59303	+	0.517606i	0.627657	+	0.778490i	$0.284014\pi$
$108$	1402.00	+	1018.61i	0.120199	+	0.0873295i
$109$			12531.8i			1.05478i	0.849623	+	0.527390i	$0.176829\pi$
$109$			12531.8i			1.05478i	−0.849623	+	0.527390i	$0.823171\pi$
$110$	2298.77	−	3058.86i	0.189981	−	0.252799i
$111$	2079.32			0.168762
$112$	1375.39	−	1893.07i	0.109645	−	0.150914i
$113$	−6823.37	+	21000.2i	−0.534370	+	1.64462i	0.210637	+	0.977564i	$0.432446\pi$
$113$	−6823.37	+	21000.2i	−0.534370	+	1.64462i	−0.745007	+	0.667057i	$0.767554\pi$
$114$	−369.192	−	1136.26i	−0.0284081	−	0.0874313i
$115$	−435.242	+	316.222i	−0.0329105	+	0.0239109i
$116$	5725.18	+	7880.04i	0.425474	+	0.585615i
$117$	−23764.4	+	7721.54i	−1.73602	+	0.564069i
$118$	−12211.5	−	3967.76i	−0.877011	−	0.284958i
$119$	−12620.7	−	9169.48i	−0.891230	−	0.647517i
$120$			342.142i			0.0237598i
$121$	4072.30	+	14063.3i	0.278144	+	0.960539i
$122$	−16504.1			−1.10885
$123$	−938.299	+	1291.46i	−0.0620199	+	0.0853631i
$124$	2033.00	−	6256.92i	0.132219	−	0.406928i
$125$	431.864	+	1329.14i	0.0276393	+	0.0850651i
$126$	−6623.64	+	4812.35i	−0.417211	+	0.303121i
$127$	−1627.97	−	2240.71i	−0.100934	−	0.138924i	0.755562	−	0.655077i	$-0.227364\pi$
$127$	−1627.97	−	2240.71i	−0.100934	−	0.138924i	−0.856497	+	0.516152i	$0.827364\pi$
$128$	1377.28	−	447.504i	0.0840623	−	0.0273135i
$129$	−2774.55	−	901.505i	−0.166730	−	0.0541737i
$130$	−8074.46	−	5866.44i	−0.477778	−	0.347126i
$131$			26988.7i			1.57267i	0.617798	+	0.786337i	$0.288025\pi$
$131$			26988.7i			1.57267i	−0.617798	+	0.786337i	$0.711975\pi$
$132$	−1046.56	−	786.505i	−0.0600646	−	0.0451392i
$133$	11419.2			0.645556
$134$	−6196.41	+	8528.63i	−0.345089	+	0.474974i
$135$	748.406	−	2303.36i	0.0410648	−	0.126384i
$136$	−2983.43	−	9182.05i	−0.161301	−	0.496434i
$137$	−7096.99	+	5156.26i	−0.378123	+	0.274722i	−0.760571	−	0.649255i	$-0.775081\pi$
$137$	−7096.99	+	5156.26i	−0.378123	+	0.274722i	0.382448	+	0.923977i	$0.375081\pi$
$138$	108.193	+	148.914i	0.00568119	+	0.00781949i
$139$	13250.9	−	4305.49i	0.685831	−	0.222840i	0.0546844	−	0.998504i	$-0.482585\pi$
$139$	13250.9	−	4305.49i	0.685831	−	0.222840i	0.631146	+	0.775664i	$0.282585\pi$
$140$	−3110.14	−	1010.54i	−0.158680	−	0.0515584i
$141$	3864.10	+	2807.44i	0.194362	+	0.141212i
$142$			16872.0i			0.836740i
$143$	36506.0	−	11213.1i	1.78522	−	0.548343i
$144$	−5066.94			−0.244355
$145$	8001.19	−	11012.7i	0.380556	−	0.523790i
$146$	6443.93	−	19832.4i	0.302305	−	0.930399i
$147$	−444.769	−	1368.86i	−0.0205826	−	0.0633467i
$148$	−9950.68	+	7229.60i	−0.454286	+	0.330058i
$149$	−3868.97	−	5325.19i	−0.174270	−	0.239862i	0.712943	−	0.701222i	$-0.247362\pi$
$149$	−3868.97	−	5325.19i	−0.174270	−	0.239862i	−0.887213	+	0.461360i	$0.847362\pi$
$150$	454.755	−	147.759i	0.0202113	−	0.00656706i
$151$	−17507.5	−	5688.53i	−0.767839	−	0.249486i	−0.101199	−	0.994866i	$-0.532268\pi$
$151$	−17507.5	−	5688.53i	−0.767839	−	0.249486i	−0.666640	+	0.745380i	$0.732268\pi$
$152$	5717.44	+	4153.97i	0.247466	+	0.179794i
$153$			33780.3i			1.44305i
$154$	10240.6	−	7190.47i	0.431802	−	0.303191i
$155$	−9194.31			−0.382698
$156$	−2007.15	+	2762.61i	−0.0824766	+	0.113519i
$157$	−3291.86	+	10131.3i	−0.133549	+	0.411023i	−0.995362	−	0.0962047i	$-0.969330\pi$
$157$	−3291.86	+	10131.3i	−0.133549	+	0.411023i	0.861812	+	0.507228i	$0.169330\pi$
$158$	−6735.66	−	20730.2i	−0.269815	−	0.830404i
$159$	808.878	−	587.684i	0.0319955	−	0.0232461i
$160$	−1189.59	−	1637.34i	−0.0464685	−	0.0639584i
$161$	−1673.22	+	543.661i	−0.0645506	+	0.0209738i
$162$	16462.4	+	5348.97i	0.627284	+	0.203817i
$163$	12707.7	+	9232.68i	0.478290	+	0.347498i	0.800663	−	0.599114i	$-0.204481\pi$
$163$	12707.7	+	9232.68i	0.478290	+	0.347498i	−0.322373	+	0.946613i	$0.604481\pi$
$164$		−	9442.71i		−	0.351082i
$165$	−593.403	+	1730.70i	−0.0217963	+	0.0635701i
$166$	30718.5			1.11477
$167$	−10856.4	+	14942.6i	−0.389272	+	0.535787i	−0.958011	−	0.286731i	$-0.907431\pi$
$167$	−10856.4	+	14942.6i	−0.389272	+	0.535787i	0.568739	+	0.822518i	$0.307431\pi$
$168$	−345.749	+	1064.11i	−0.0122502	+	0.0377022i
$169$	−21955.9	−	67573.4i	−0.768738	−	2.36593i
$170$	−10915.8	+	7930.80i	−0.377710	+	0.274422i
$171$	−14534.3	−	20004.7i	−0.497052	−	0.684133i
$172$	16412.2	−	5332.64i	0.554765	−	0.180254i
$173$	16364.5	+	5317.14i	0.546777	+	0.177659i	0.569363	−	0.822086i	$-0.307190\pi$
$173$	16364.5	+	5317.14i	0.546777	+	0.177659i	−0.0225861	+	0.999745i	$0.507190\pi$
$174$	−3767.90	−	2737.54i	−0.124452	−	0.0904195i
$175$			4570.23i			0.149232i
$176$	7742.99	+	125.054i	0.249967	+	0.00403712i
$177$	6139.51			0.195969
$178$	−8105.28	+	11156.0i	−0.255816	+	0.352101i
$179$	12337.7	−	37971.4i	0.385058	−	1.18509i	−0.551379	−	0.834255i	$-0.685898\pi$
$179$	12337.7	−	37971.4i	0.385058	−	1.18509i	0.936438	−	0.350834i	$-0.114102\pi$
$180$	2188.23	+	6734.68i	0.0675380	+	0.207861i
$181$	25377.9	−	18438.2i	0.774639	−	0.562808i	−0.128726	−	0.991680i	$-0.541089\pi$
$181$	25377.9	−	18438.2i	0.774639	−	0.562808i	0.903365	+	0.428872i	$0.141089\pi$
$182$	−19184.4	−	26405.0i	−0.579168	−	0.797156i
$183$	7505.31	−	2438.62i	0.224113	−	0.0728186i
$184$	−1035.52	−	336.461i	−0.0305861	−	0.00993801i
$185$	13906.5	+	10103.7i	0.406326	+	0.295213i
$186$			3145.76i			0.0909284i
$187$	833.710	−	51621.1i	0.0238414	−	1.47619i
$188$	−28253.0			−0.799373
$189$	4655.29	−	6407.45i	0.130323	−	0.179375i
$190$	3052.05	−	9393.25i	0.0845443	−	0.260201i
$191$	4086.66	+	12577.5i	0.112022	+	0.344767i	0.991314	−	0.131515i	$-0.0419841\pi$
$191$	4086.66	+	12577.5i	0.112022	+	0.344767i	−0.879292	+	0.476282i	$0.841984\pi$
$192$	−560.201	+	407.010i	−0.0151964	+	0.0110408i
$193$	−3950.67	−	5437.64i	−0.106061	−	0.145981i	0.752687	−	0.658378i	$-0.228757\pi$
$193$	−3950.67	−	5437.64i	−0.106061	−	0.145981i	−0.858748	+	0.512398i	$0.828757\pi$
$194$	8820.72	−	2866.03i	0.234369	−	0.0761512i
$195$	4538.71	+	1474.72i	0.119361	+	0.0387828i
$196$	6887.85	+	5004.32i	0.179296	+	0.130267i
$197$			44731.0i			1.15259i	0.817240	+	0.576297i	$0.195503\pi$
$197$			44731.0i			1.15259i	−0.817240	+	0.576297i	$0.804497\pi$
$198$	−25630.7	−	8787.99i	−0.653778	−	0.224161i
$199$	−30447.4			−0.768855			−0.384427	−	0.923155i	$-0.625601\pi$
$199$	−30447.4			−0.768855			−0.384427	+	0.923155i	$0.625601\pi$
$200$	−1662.51	+	2288.25i	−0.0415627	+	0.0572061i
$201$	1557.67	−	4794.01i	0.0385552	−	0.118661i
$202$	3605.22	+	11095.7i	0.0883545	+	0.271927i
$203$	36013.6	−	26165.4i	0.873926	−	0.634944i
$204$	2713.46	+	3734.75i	0.0652022	+	0.0897432i
$205$	−12550.7	+	4077.97i	−0.298648	+	0.0970368i
$206$	19959.3	+	6485.16i	0.470339	+	0.152822i
$207$	3082.06	+	2239.25i	0.0719284	+	0.0522591i
$208$		−	20199.3i		−	0.466884i
$209$	21716.7	+	30928.7i	0.497166	+	0.708059i
$210$	1563.67			0.0354573
$211$	37661.1	−	51836.0i	0.845917	−	1.16430i	−0.138831	−	0.990316i	$-0.544335\pi$
$211$	37661.1	−	51836.0i	0.845917	−	1.16430i	0.984748	−	0.173988i	$-0.0556655\pi$
$212$	−1827.60	+	5624.78i	−0.0406640	+	0.125151i
$213$	−2492.99	−	7672.63i	−0.0549492	−	0.169116i
$214$	43882.0	−	31882.2i	0.958207	−	0.696178i
$215$	−14175.7	−	19511.1i	−0.306667	−	0.422091i
$216$	4661.66	−	1514.67i	0.0999156	−	0.0324646i
$217$	−28595.6	−	9291.26i	−0.607266	−	0.197313i
$218$	28675.9	+	20834.3i	0.603399	+	0.438395i
$219$			9971.01i			0.207898i
$220$	−3177.71	−	10345.5i	−0.0656551	−	0.213751i
$221$	−134665.			−2.75721
$222$	3456.88	−	4757.99i	0.0701421	−	0.0965424i
$223$	20782.9	−	63963.0i	0.417922	−	1.28623i	−0.491689	−	0.870771i	$-0.663620\pi$
$223$	20782.9	−	63963.0i	0.417922	−	1.28623i	0.909611	−	0.415461i	$-0.136380\pi$
$224$	−2045.20	−	6294.47i	−0.0407605	−	0.125448i
$225$	8006.33	−	5816.94i	0.158150	−	0.114902i
$226$	36709.6	+	50526.5i	0.718726	+	0.989241i
$227$	−75351.1	+	24483.0i	−1.46230	+	0.475131i	−0.928773	−	0.370649i	$-0.879135\pi$
$227$	−75351.1	+	24483.0i	−1.46230	+	0.475131i	−0.533531	+	0.845780i	$0.679135\pi$
$228$	−3213.82	−	1044.23i	−0.0618233	−	0.0200876i
$229$	54163.8	+	39352.3i	1.03285	+	0.750411i	0.968877	−	0.247541i	$-0.0796225\pi$
$229$	54163.8	+	39352.3i	1.03285	+	0.750411i	0.0639742	+	0.997952i	$0.479622\pi$
$230$			1521.66i			0.0287649i
$231$	−3594.51	+	4783.04i	−0.0673621	+	0.0896355i
$232$	27549.6			0.511847
$233$	−24307.0	+	33455.7i	−0.447733	+	0.616251i	−0.971909	−	0.235359i	$-0.924373\pi$
$233$	−24307.0	+	33455.7i	−0.447733	+	0.616251i	0.524176	+	0.851610i	$0.324373\pi$
$234$	−21839.8	+	67216.0i	−0.398857	+	1.22755i
$235$	12201.5	+	37552.3i	0.220941	+	0.679987i
$236$	−29380.9	+	21346.5i	−0.527523	+	0.383268i
$237$	6126.14	+	8431.91i	0.109066	+	0.150117i
$238$	−41964.1	+	13634.9i	−0.740839	+	0.240713i
$239$	−45689.4	−	14845.4i	−0.799870	−	0.259894i	−0.119569	−	0.992826i	$-0.538151\pi$
$239$	−45689.4	−	14845.4i	−0.799870	−	0.259894i	−0.680301	+	0.732932i	$0.738151\pi$
$240$	782.904	+	568.813i	0.0135921	+	0.00987523i
$241$			49219.1i			0.847422i	0.905798	+	0.423711i	$0.139273\pi$
$241$			49219.1i			0.847422i	−0.905798	+	0.423711i	$0.860727\pi$
$242$	38950.4	+	14061.9i	0.665092	+	0.240111i
$243$	−25823.0			−0.437315
$244$	−27438.2	+	37765.4i	−0.460867	+	0.634328i
$245$	3676.83	−	11316.1i	0.0612550	−	0.188523i
$246$	1395.24	+	4294.12i	0.0230558	+	0.0709584i
$247$	79748.5	−	57940.7i	1.30716	−	0.949707i
$248$	−10937.5	−	15054.2i	−0.177834	−	0.244767i
$249$	−13969.4	+	4538.93i	−0.225309	+	0.0732074i
$250$	3759.38	+	1221.50i	0.0601501	+	0.0195440i
$251$	−37539.6	−	27274.1i	−0.595856	−	0.432915i	0.248549	−	0.968619i	$-0.420046\pi$
$251$	−37539.6	−	27274.1i	−0.595856	−	0.432915i	−0.844406	+	0.535704i	$0.820046\pi$
$252$			23157.1i			0.364655i
$253$	−4654.55	−	3497.95i	−0.0727172	−	0.0546478i
$254$	−7833.82			−0.121424
$255$	3792.17	−	5219.47i	0.0583186	−	0.0802687i
$256$	1265.73	−	3895.53i	0.0193136	−	0.0594410i
$257$	−16760.7	−	51584.1i	−0.253762	−	0.780998i	−0.994071	−	0.108732i	$-0.965321\pi$
$257$	−16760.7	−	51584.1i	−0.253762	−	0.780998i	0.740309	−	0.672266i	$-0.234679\pi$
$258$	−6675.57	+	4850.09i	−0.100288	+	0.0728635i
$259$	33040.9	+	45476.9i	0.492552	+	0.677940i
$260$	−26847.7	+	8723.34i	−0.397155	+	0.129044i
$261$	−91675.4	−	29787.1i	−1.34577	−	0.437268i
$262$	61756.7	+	44868.8i	0.899666	+	0.653646i
$263$			63790.6i			0.922243i	0.887337	+	0.461122i	$0.152553\pi$
$263$			63790.6i			0.922243i	−0.887337	+	0.461122i	$0.847447\pi$
$264$	−3539.64	+	1087.23i	−0.0507868	+	0.0155995i
$265$	8265.41			0.117699
$266$	18984.6	−	26130.0i	0.268311	−	0.369298i
$267$	2037.52	−	6270.85i	0.0285812	−	0.0879638i
$268$	9214.01	+	28357.8i	0.128286	+	0.394824i
$269$	−30841.2	+	22407.4i	−0.426212	+	0.309661i	−0.780133	−	0.625614i	$-0.784848\pi$
$269$	−30841.2	+	22407.4i	−0.426212	+	0.309661i	0.353920	+	0.935276i	$0.384848\pi$
$270$	−4026.41	−	5541.88i	−0.0552320	−	0.0760203i
$271$	19212.3	−	6242.46i	0.261602	−	0.0849996i	−0.175280	−	0.984519i	$-0.556083\pi$
$271$	19212.3	−	6242.46i	0.261602	−	0.0849996i	0.436881	+	0.899519i	$0.356083\pi$
$272$	−25970.7	−	8438.41i	−0.351032	−	0.114057i
$273$	12625.8	+	9173.15i	0.169407	+	0.123082i
$274$			24812.0i			0.330491i
$275$	−12378.4	+	8691.49i	−0.163681	+	0.114929i
$276$	520.623			0.00683448
$277$	32760.2	−	45090.6i	0.426960	−	0.587660i	−0.540292	−	0.841478i	$-0.681686\pi$
$277$	32760.2	−	45090.6i	0.426960	−	0.587660i	0.967252	+	0.253817i	$0.0816863\pi$
$278$	12177.8	−	37479.3i	0.157572	−	0.484956i
$279$	20119.3	+	61920.8i	0.258466	+	0.795478i
$280$	−7483.00	+	5436.72i	−0.0954464	+	0.0693459i
$281$	50547.0	+	69572.0i	0.640152	+	0.881093i	0.998624	−	0.0524473i	$-0.0167021\pi$
$281$	50547.0	+	69572.0i	0.640152	+	0.881093i	−0.358472	+	0.933540i	$0.616702\pi$
$282$	12848.2	−	4174.64i	0.161564	−	0.0524953i
$283$	4223.90	+	1372.43i	0.0527400	+	0.0171363i	0.335268	−	0.942123i	$-0.391173\pi$
$283$	4223.90	+	1372.43i	0.0527400	+	0.0171363i	−0.282528	+	0.959259i	$0.591173\pi$
$284$	38607.3	+	28049.9i	0.478667	+	0.347772i
$285$			4722.59i			0.0581421i
$286$	35033.2	−	102176.i	0.428299	−	1.24916i
$287$	−43155.4			−0.523927
$288$	−8423.83	+	11594.4i	−0.101560	+	0.139786i
$289$	−30447.9	+	93708.9i	−0.364553	+	1.12198i
$290$	−11897.7	−	36617.4i	−0.141471	−	0.435403i
$291$	−3587.78	+	2606.68i	−0.0423682	+	0.0307823i
$292$	−34668.3	−	47716.8i	−0.406599	−	0.559636i
$293$	−13384.5	+	4348.90i	−0.155908	+	0.0506576i	−0.385931	−	0.922528i	$-0.626120\pi$
$293$	−13384.5	+	4348.90i	−0.155908	+	0.0506576i	0.230023	+	0.973185i	$0.426120\pi$
$294$	−3871.72	−	1258.00i	−0.0447929	−	0.0145541i
$295$	41061.1	+	29832.6i	0.471831	+	0.342805i
$296$			34788.9i			0.397061i
$297$	26207.7	+	423.269i	0.297109	+	0.00479848i
$298$	−18617.5			−0.209647
$299$	−8926.72	+	12286.6i	−0.0998504	+	0.137432i
$300$	417.925	−	1286.24i	0.00464361	−	0.0142916i
$301$	−24371.4	−	75007.4i	−0.268997	−	0.827888i
$302$	−42123.1	+	30604.2i	−0.461856	+	0.335558i
$303$	−3278.98	−	4513.13i	−0.0357152	−	0.0491578i
$304$	19010.6	−	6176.92i	0.205707	−	0.0668382i
$305$	62045.1	+	20159.7i	0.666972	+	0.216712i
$306$	77297.7	+	56160.1i	0.825512	+	0.599770i
$307$		−	77483.0i		−	0.822110i	−0.911611	−	0.411055i	$-0.865161\pi$
$307$		−	77483.0i		−	0.822110i	0.911611	−	0.411055i	$-0.134839\pi$
$308$	571.524	−	35387.2i	0.00602467	−	0.373031i
$309$	−10034.8			−0.105098
$310$	−15285.6	+	21038.8i	−0.159060	+	0.218927i
$311$	−6456.32	+	19870.5i	−0.0667520	+	0.205441i	−0.978869	−	0.204489i	$-0.934447\pi$
$311$	−6456.32	+	19870.5i	−0.0667520	+	0.205441i	0.912117	+	0.409930i	$0.134447\pi$
$312$	2984.62	+	9185.71i	0.0306605	+	0.0943634i
$313$	4361.78	−	3169.02i	0.0445220	−	0.0323471i	−0.565302	−	0.824884i	$-0.691240\pi$
$313$	4361.78	−	3169.02i	0.0445220	−	0.0323471i	0.609824	+	0.792537i	$0.291240\pi$
$314$	17710.2	+	24376.0i	0.179624	+	0.247231i
$315$	30779.0	−	10000.7i	0.310194	−	0.100788i
$316$	−58633.9	−	19051.3i	−0.587185	−	0.190788i
$317$	21436.6	+	15574.6i	0.213323	+	0.154988i	0.689316	−	0.724461i	$-0.257911\pi$
$317$	21436.6	+	15574.6i	0.213323	+	0.154988i	−0.475993	+	0.879449i	$0.657911\pi$
$318$		−	2827.94i		−	0.0279651i
$319$	139358.	+	47781.5i	1.36946	+	0.469546i
$320$	−5724.33			−0.0559017
$321$	−15244.7	+	20982.5i	−0.147948	+	0.203633i
$322$	−1537.71	+	4732.57i	−0.0148307	+	0.0456442i
$323$	−41180.3	−	126740.i	−0.394716	−	1.21481i
$324$	39608.7	−	28777.4i	0.377312	−	0.274133i
$325$	23189.1	+	31917.1i	0.219542	+	0.302174i
$326$	42253.3	−	13728.9i	0.397581	−	0.129182i
$327$	−16119.0	−	5237.37i	−0.150745	−	0.0489799i
$328$	−21607.2	−	15698.6i	−0.200841	−	0.145919i
$329$			129123.i			1.19292i
$330$	2973.72	+	4235.15i	0.0273069	+	0.0388903i
$331$	−14821.3			−0.135279			−0.0676395	−	0.997710i	$-0.521547\pi$
$331$	−14821.3			−0.135279			−0.0676395	+	0.997710i	$0.521547\pi$
$332$	51069.8	−	70291.5i	0.463327	−	0.637715i
$333$	37614.3	−	115765.i	0.339207	−	1.04397i
$334$	16143.4	+	49684.2i	0.144711	+	0.445375i
$335$	33712.4	−	24493.5i	0.300400	−	0.218253i
$336$	1860.13	+	2560.25i	0.0164765	+	0.0226779i
$337$	−163253.	+	53044.1i	−1.43748	+	0.467065i	−0.921111	−	0.389301i	$-0.872717\pi$
$337$	−163253.	+	53044.1i	−1.43748	+	0.467065i	−0.516369	+	0.856366i	$0.672717\pi$
$338$	−191126.	−	62100.8i	−1.67297	−	0.543580i
$339$	−24159.6	−	17553.0i	−0.210228	−	0.152740i
$340$			38163.1i			0.330130i
$341$	−29216.8	−	95120.1i	−0.251261	−	0.818020i
$342$	−69939.1			−0.597954
$343$	74469.6	−	102499.i	0.632981	−	0.871224i
$344$	15083.0	−	46420.7i	0.127459	−	0.392278i
$345$	−224.839	−	691.982i	−0.00188900	−	0.00581376i
$346$	39373.0	−	28606.2i	0.328887	−	0.238950i
$347$	67338.4	+	92683.4i	0.559247	+	0.769738i	0.991231	−	0.132144i	$-0.0421860\pi$
$347$	67338.4	+	92683.4i	0.559247	+	0.769738i	−0.431983	+	0.901882i	$0.642186\pi$
$348$	−12528.3	+	4070.70i	−0.103451	+	0.0336133i
$349$	−107379.	−	34889.7i	−0.881598	−	0.286448i	−0.166977	−	0.985961i	$-0.553401\pi$
$349$	−107379.	−	34889.7i	−0.881598	−	0.286448i	−0.714621	+	0.699512i	$0.753401\pi$
$350$	10457.8	+	7598.04i	0.0853699	+	0.0620248i
$351$		−	68368.4i		−	0.554934i
$352$	13158.9	−	17510.0i	0.106203	−	0.141319i
$353$	137291.			1.10177			0.550886	−	0.834580i	$-0.314290\pi$
$353$	137291.			1.10177			0.550886	+	0.834580i	$0.314290\pi$
$354$	10207.0	−	14048.7i	0.0814500	−	0.112106i
$355$	20609.1	−	63428.4i	0.163532	−	0.503300i
$356$	12052.5	+	37093.7i	0.0950992	+	0.292685i
$357$	17068.7	−	12401.1i	0.133926	−	0.0973026i
$358$	−66376.5	−	91359.4i	−0.517903	−	0.712832i
$359$	−102173.	+	33197.9i	−0.792768	+	0.257586i	−0.677282	−	0.735723i	$-0.736842\pi$
$359$	−102173.	+	33197.9i	−0.792768	+	0.257586i	−0.115485	+	0.993309i	$0.536842\pi$
$360$	19048.6	+	6189.25i	0.146980	+	0.0477566i
$361$	−26513.9	−	19263.4i	−0.203450	−	0.147815i
$362$		−	88724.5i		−	0.677059i
$363$	−19790.7	−	639.428i	−0.150192	−	0.00485264i
$364$	−92315.3			−0.696740
$365$	−48450.4	+	66686.2i	−0.363673	+	0.500553i
$366$	6897.47	−	21228.2i	0.0514905	−	0.158472i
$367$	26229.7	+	80726.7i	0.194743	+	0.599356i	0.999980	+	0.00640284i	$0.00203810\pi$
$367$	26229.7	+	80726.7i	0.194743	+	0.599356i	−0.805237	+	0.592953i	$0.797962\pi$
$368$	−2491.47	+	1810.16i	−0.0183975	+	0.0133666i
$369$	54927.7	+	75601.4i	0.403402	+	0.555236i
$370$	46239.3	−	15024.1i	0.337760	−	0.109745i
$371$	25706.5	+	8352.56i	0.186765	+	0.0606837i
$372$	7198.27	+	5229.85i	0.0520166	+	0.0377923i
$373$			15283.5i			0.109851i	0.998490	+	0.0549256i	$0.0174922\pi$
$373$			15283.5i			0.109851i	−0.998490	+	0.0549256i	$0.982508\pi$
$374$	−116736.	−	87728.1i	−0.834565	−	0.627185i
$375$	−1890.08			−0.0134406
$376$	−46970.9	+	64649.9i	−0.332241	+	0.457291i
$377$	118746.	−	365462.i	0.835480	−	2.57134i
$378$	−6922.37	−	21304.9i	−0.0484475	−	0.149106i
$379$	132541.	−	96297.0i	0.922727	−	0.670401i	−0.0214739	−	0.999769i	$-0.506836\pi$
$379$	132541.	−	96297.0i	0.922727	−	0.670401i	0.944201	+	0.329369i	$0.106836\pi$
$380$	−16420.0	−	22600.2i	−0.113712	−	0.156511i
$381$	3562.47	−	1157.52i	0.0245415	−	0.00797401i
$382$	35574.4	+	11558.8i	0.243787	+	0.0792113i
$383$	4146.07	+	3012.30i	0.0282644	+	0.0205353i	0.601828	−	0.798626i	$-0.294439\pi$
$383$	4146.07	+	3012.30i	0.0282644	+	0.0205353i	−0.573563	+	0.819161i	$0.694439\pi$
$384$			1958.53i			0.0132822i
$385$	−47281.5	+	14522.9i	−0.318985	+	0.0979784i
$386$	−19010.7			−0.127592
$387$	−100382.	+	138164.i	−0.670243	+	0.922511i
$388$	8106.34	−	24948.8i	0.0538470	−	0.165724i
$389$	57064.7	+	175627.i	0.377110	+	1.16063i	0.942044	+	0.335489i	$0.108902\pi$
$389$	57064.7	+	175627.i	0.377110	+	1.16063i	−0.564934	+	0.825136i	$0.691098\pi$
$390$	10920.2	−	7933.96i	0.0717960	−	0.0521628i
$391$	12068.0	+	16610.2i	0.0789371	+	0.108648i
$392$	22902.2	−	7441.38i	0.149041	−	0.0484263i
$393$	−34713.9	−	11279.2i	−0.224760	−	0.0730288i
$394$	102356.	+	74365.7i	0.659354	+	0.479049i
$395$			86160.4i			0.552221i
$396$	−62720.3	+	44039.3i	−0.399961	+	0.280834i
$397$	−6131.89			−0.0389057			−0.0194528	−	0.999811i	$-0.506192\pi$
$397$	−6131.89			−0.0389057			−0.0194528	+	0.999811i	$0.506192\pi$
$398$	−50619.1	+	69671.2i	−0.319557	+	0.439832i
$399$	−4772.39	+	14687.9i	−0.0299771	+	0.0922601i
$400$	2472.14	+	7608.45i	0.0154508	+	0.0475528i
$401$	136882.	−	99450.9i	0.851254	−	0.618472i	−0.0742377	−	0.997241i	$-0.523652\pi$
$401$	136882.	−	99450.9i	0.851254	−	0.618472i	0.925491	+	0.378769i	$0.123652\pi$
$402$	−8380.23	−	11534.4i	−0.0518566	−	0.0713745i
$403$	−246846.	+	80205.2i	−1.51990	+	0.493847i
$404$	31383.4	+	10197.1i	0.192282	+	0.0624761i
$405$	−55354.8	−	40217.6i	−0.337478	−	0.245192i
$406$		−	125908.i		−	0.763839i
$407$	−60337.1	+	175977.i	−0.364247	+	1.06235i
$408$	13057.2			0.0784384
$409$	167145.	−	230055.i	0.999187	−	1.37526i	0.0733638	−	0.997305i	$-0.476627\pi$
$409$	167145.	−	230055.i	0.999187	−	1.37526i	0.925823	−	0.377957i	$-0.123373\pi$
$410$	−11534.2	+	35498.7i	−0.0686154	+	0.211176i
$411$	−3666.19	−	11283.4i	−0.0217036	−	0.0667967i
$412$	48022.1	−	34890.1i	0.282909	−	0.205545i
$413$	97558.4	+	134278.i	0.571958	+	0.787233i
$414$	10247.9	−	3329.74i	0.0597908	−	0.0194272i
$415$	−115483.	−	37522.6i	−0.670534	−	0.217870i
$416$	−46220.9	−	33581.4i	−0.267086	−	0.194050i
$417$			18843.3i			0.108364i
$418$	106877.	+	1726.12i	0.611689	+	0.00987913i
$419$	11680.8			0.0665342			0.0332671	−	0.999446i	$-0.489409\pi$
$419$	11680.8			0.0665342			0.0332671	+	0.999446i	$0.489409\pi$
$420$	2599.61	−	3578.05i	0.0147370	−	0.0202837i
$421$	23906.2	−	73575.6i	0.134879	−	0.415116i	−0.860692	−	0.509126i	$-0.829969\pi$
$421$	23906.2	−	73575.6i	0.134879	−	0.415116i	0.995571	+	0.0940102i	$0.0299686\pi$
$422$	−56001.7	−	172355.i	−0.314468	−	0.967833i
$423$	226203.	−	164346.i	1.26421	−	0.918499i
$424$	9832.48	+	13533.2i	0.0546929	+	0.0752784i
$425$	50724.1	−	16481.3i	0.280826	−	0.0912458i
$426$	−21701.5	−	7051.24i	−0.119583	−	0.0388549i
$427$	172596.	+	125399.i	0.946621	+	0.687760i
$428$		−	153417.i		−	0.837504i
$429$	−834.043	+	51641.7i	−0.00453183	+	0.280599i
$430$	−68213.5			−0.368921
$431$	−50251.6	+	69165.4i	−0.270517	+	0.372335i	−0.922564	−	0.385843i	$-0.873911\pi$
$431$	−50251.6	+	69165.4i	−0.270517	+	0.372335i	0.652047	+	0.758179i	$0.273911\pi$
$432$	4284.12	−	13185.2i	0.0229559	−	0.0706510i
$433$	20845.1	+	64154.6i	0.111180	+	0.342178i	0.991131	−	0.132887i	$-0.0424247\pi$
$433$	20845.1	+	64154.6i	0.111180	+	0.342178i	−0.879951	+	0.475065i	$0.842425\pi$
$434$	−68801.0	+	49986.9i	−0.365271	+	0.265385i
$435$	10821.1	+	14893.9i	0.0571863	+	0.0787102i
$436$	95347.9	−	30980.4i	0.501578	−	0.162973i
$437$	−14293.3	−	4644.19i	−0.0748464	−	0.0243191i
$438$	22816.1	+	16576.9i	0.118931	+	0.0864082i
$439$			37975.9i			0.197051i	0.995135	+	0.0985256i	$0.0314126\pi$
$439$			37975.9i			0.197051i	−0.995135	+	0.0985256i	$0.968587\pi$
$440$	−28956.1	−	9928.16i	−0.149567	−	0.0512818i
$441$	−84256.2			−0.433236
$442$	−223881.	+	308146.i	−1.14597	+	1.57729i
$443$	−88181.1	+	271394.i	−0.449333	+	1.38290i	0.428329	+	0.903623i	$0.359103\pi$
$443$	−88181.1	+	271394.i	−0.449333	+	1.38290i	−0.877661	+	0.479281i	$0.840897\pi$
$444$	−5140.36	−	15820.4i	−0.0260752	−	0.0802512i
$445$	44097.8	−	32038.9i	0.222688	−	0.161792i
$446$	−111812.	−	153895.i	−0.562104	−	0.773670i
$447$	8466.41	−	2750.90i	0.0423725	−	0.0137677i
$448$	−17803.5	−	5784.69i	−0.0887050	−	0.0288220i
$449$	74272.9	+	53962.4i	0.368415	+	0.267669i	0.756553	−	0.653932i	$-0.226882\pi$
$449$	74272.9	+	53962.4i	0.368415	+	0.267669i	−0.388138	+	0.921601i	$0.626882\pi$
$450$		−	27991.1i		−	0.138228i
$451$	−82071.3	−	116885.i	−0.403495	−	0.574654i
$452$	176647.			0.864629
$453$	14633.6	−	20141.5i	0.0713109	−	0.0981510i
$454$	−69248.5	+	213125.i	−0.335969	+	1.03401i
$455$	39867.7	+	122700.i	0.192574	+	0.592683i
$456$	−7732.46	+	5617.96i	−0.0371868	+	0.0270178i
$457$	−110225.	−	151711.i	−0.527773	−	0.726417i	0.459016	−	0.888428i	$-0.348202\pi$
$457$	−110225.	−	151711.i	−0.527773	−	0.726417i	−0.986789	+	0.162011i	$0.948202\pi$
$458$	180095.	−	58516.5i	0.858562	−	0.278964i
$459$	−87903.1	−	28561.4i	−0.417233	−	0.135567i
$460$	3481.93	+	2529.77i	0.0164553	+	0.0119554i
$461$			410256.i			1.93043i	0.261463	+	0.965214i	$0.415795\pi$
$461$			410256.i			1.93043i	−0.261463	+	0.965214i	$0.584205\pi$
$462$	4968.87	+	16177.0i	0.0232795	+	0.0757902i
$463$	−205801.			−0.960031			−0.480015	−	0.877260i	$-0.659369\pi$
$463$	−205801.			−0.960031			−0.480015	+	0.877260i	$0.659369\pi$
$464$	45801.5	−	63040.3i	0.212737	−	0.292808i
$465$	3842.53	−	11826.1i	0.0177710	−	0.0546935i
$466$	36144.3	+	111241.i	0.166444	+	0.512261i
$467$	−94650.1	+	68767.3i	−0.433997	+	0.315318i	−0.783245	−	0.621713i	$-0.786437\pi$
$467$	−94650.1	+	68767.3i	−0.433997	+	0.315318i	0.349248	+	0.937030i	$0.386437\pi$
$468$	117498.	+	161722.i	0.536461	+	0.738375i
$469$	129602.	−	42110.2i	0.589203	−	0.191444i
$470$	106214.	+	34511.0i	0.480824	+	0.156229i
$471$	−11655.5	−	8468.25i	−0.0525401	−	0.0381726i
$472$			102719.i			0.461072i
$473$	156807.	−	208656.i	0.700880	−	0.932627i
$474$	29479.0			0.131207
$475$	−22947.6	+	31584.7i	−0.101707	+	0.139988i
$476$	−38565.5	+	118692.i	−0.170210	+	0.523852i
$477$	−18086.6	−	55664.9i	−0.0794915	−	0.244650i
$478$	−109929.	+	79868.0i	−0.481123	+	0.349556i
$479$	−189478.	−	260794.i	−0.825826	−	1.13665i	−0.988686	−	0.150002i	$-0.952072\pi$
$479$	−189478.	−	260794.i	−0.825826	−	1.13665i	0.162860	−	0.986649i	$-0.447928\pi$
$480$	2603.17	−	845.821i	0.0112985	−	0.00367110i
$481$	461495.	+	149949.i	1.99470	+	0.648117i
$482$	112625.	+	81827.1i	0.484777	+	0.352211i
$483$		−	2379.37i		−	0.0101992i
$484$	96932.4	−	65750.2i	0.413788	−	0.280677i
$485$	−36661.3			−0.155856
$486$	−42930.9	+	59089.4i	−0.181760	+	0.250171i
$487$	−49093.7	+	151095.i	−0.206999	+	0.637077i	0.792627	+	0.609707i	$0.208713\pi$
$487$	−49093.7	+	151095.i	−0.206999	+	0.637077i	−0.999625	+	0.0273694i	$0.991287\pi$
$488$	40800.3	+	125570.i	0.171326	+	0.527288i
$489$	−17186.3	+	12486.6i	−0.0718729	+	0.0522187i
$490$	−19781.3	−	27226.6i	−0.0823878	−	0.113397i
$491$	−248661.	+	80795.0i	−1.03144	+	0.335136i	−0.775361	−	0.631518i	$-0.782432\pi$
$491$	−248661.	+	80795.0i	−1.03144	+	0.335136i	−0.256083	+	0.966655i	$0.582432\pi$
$492$	12145.6	+	3946.34i	0.0501752	+	0.0163029i
$493$	−420278.	−	305350.i	−1.72919	−	1.25633i
$494$		−	278811.i		−	1.14250i
$495$	85621.1	+	64345.2i	0.349438	+	0.262607i
$496$	−52631.3			−0.213935
$497$	128194.	−	176444.i	0.518986	−	0.714324i
$498$	−12838.0	+	39511.4i	−0.0517654	+	0.159318i
$499$	1491.34	+	4589.87i	0.00598929	+	0.0184331i	0.954007	−	0.299786i	$-0.0969153\pi$
$499$	1491.34	+	4589.87i	0.00598929	+	0.0184331i	−0.948017	+	0.318219i	$0.896915\pi$
$500$	9045.08	−	6571.64i	0.0361803	−	0.0262866i
$501$	−14682.6	−	20208.8i	−0.0584960	−	0.0805129i
$502$	−124820.	+	40556.3i	−0.495308	+	0.160935i
$503$	6366.91	+	2068.73i	0.0251648	+	0.00817652i	0.321572	−	0.946885i	$-0.395789\pi$
$503$	6366.91	+	2068.73i	0.0251648	+	0.00817652i	−0.296408	+	0.955062i	$0.595789\pi$
$504$	52989.1	+	38498.8i	0.208605	+	0.151561i
$505$		−	46116.8i		−	0.180832i
$506$	−15742.4	+	4835.39i	−0.0614851	+	0.0188856i
$507$	96091.6			0.373826
$508$	−13023.8	+	17925.7i	−0.0504672	+	0.0694622i
$509$	12029.1	−	37021.8i	0.0464299	−	0.142896i	−0.925154	−	0.379592i	$-0.876064\pi$
$509$	12029.1	−	37021.8i	0.0464299	−	0.142896i	0.971584	+	0.236696i	$0.0760644\pi$
$510$	−5638.93	−	17354.8i	−0.0216798	−	0.0667237i
$511$	−218077.	+	158442.i	−0.835155	+	0.606776i
$512$	−6809.63	−	9372.65i	−0.0259767	−	0.0357538i
$513$	64345.1	−	20907.0i	0.244501	−	0.0794432i
$514$	−145902.	−	47406.4i	−0.552249	−	0.179437i
$515$	−67112.9	−	48760.4i	−0.253042	−	0.183845i
$516$			23338.7i			0.0876550i
$517$	−349726.	+	245561.i	−1.30842	+	0.918710i
$518$	158993.			0.592542
$519$	−13678.2	+	18826.5i	−0.0507804	+	0.0698932i
$520$	−24673.3	+	75936.7i	−0.0912476	+	0.280831i
$521$	−8921.33	−	27457.0i	−0.0328665	−	0.101153i	0.933277	−	0.359156i	$-0.116935\pi$
$521$	−8921.33	−	27457.0i	−0.0328665	−	0.101153i	−0.966144	+	0.258003i	$0.916935\pi$
$522$	−220571.	+	160254.i	−0.809484	+	0.588124i
$523$	233311.	+	321125.i	0.852966	+	1.17401i	0.983202	+	0.182523i	$0.0584265\pi$
$523$	233311.	+	321125.i	0.852966	+	1.17401i	−0.130236	+	0.991483i	$0.541573\pi$
$524$	205342.	−	66719.6i	0.747851	−	0.242991i
$525$	−5878.42	−	1910.01i	−0.0213276	−	0.00692975i
$526$	145969.	+	106052.i	0.527580	+	0.383309i
$527$			350883.i			1.26340i
$528$	−3396.84	+	9907.09i	−0.0121845	+	0.0355368i
$529$	−277526.			−0.991726
$530$	13741.3	−	18913.3i	0.0489189	−	0.0673310i
$531$	111062.	−	341814.i	0.393892	−	1.21227i
$532$	−28229.9	−	86882.8i	−0.0997439	−	0.306980i
$533$	−301384.	+	218968.i	−1.06088	+	0.770773i
$534$	−10961.9	−	15087.7i	−0.0384416	−	0.0529103i
$535$	−203913.	+	66255.5i	−0.712423	+	0.231480i
$536$	80208.0	+	26061.2i	0.279183	+	0.0907119i
$537$	43684.2	+	31738.4i	0.151487	+	0.110062i
$538$			107825.i			0.372523i
$539$	128755.	+	2079.47i	0.443187	+	0.00715773i
$540$	−19375.1			−0.0664442
$541$	35779.4	−	49246.2i	0.122247	−	0.168259i	−0.743507	−	0.668728i	$-0.766839\pi$
$541$	35779.4	−	49246.2i	0.122247	−	0.168259i	0.865754	+	0.500469i	$0.166839\pi$
$542$	17656.3	−	54340.6i	0.0601038	−	0.184981i
$543$	13109.8	+	40347.9i	0.0444629	+	0.136843i
$544$	−62485.7	+	45398.5i	−0.211146	+	0.153407i
$545$	−82354.8	−	113352.i	−0.277265	−	0.381623i
$546$	41980.8	−	13640.4i	0.140820	−	0.0457553i
$547$	206210.	+	67001.7i	0.689184	+	0.223930i	0.632612	−	0.774469i	$-0.281983\pi$
$547$	206210.	+	67001.7i	0.689184	+	0.223930i	0.0565723	+	0.998399i	$0.481983\pi$
$548$	56775.9	+	41250.1i	0.189061	+	0.137361i
$549$		−	461968.i		−	1.53274i
$550$	−690.831	+	42774.4i	−0.00228374	+	0.141403i
$551$	380268.			1.25253
$552$	865.541	−	1191.31i	0.00284059	−	0.00390974i
$553$	−87068.9	+	267970.i	−0.284717	+	0.876267i
$554$	−48714.2	−	149927.i	−0.158722	−	0.488495i
$555$	−18807.6	+	13664.5i	−0.0610588	+	0.0443618i
$556$	−65516.2	−	90175.4i	−0.211933	−	0.291701i
$557$	57276.2	−	18610.2i	0.184614	−	0.0599846i	−0.215251	−	0.976559i	$-0.569057\pi$
$557$	57276.2	−	18610.2i	0.184614	−	0.0599846i	0.399865	+	0.916574i	$0.369057\pi$
$558$	175138.	+	56905.9i	0.562488	+	0.182763i
$559$	−550786.	−	400170.i	−1.76262	−	1.28062i
$560$			26161.5i			0.0834232i
$561$	66048.7	+	22646.1i	0.209864	+	0.0719560i
$562$	243233.			0.770104
$563$	186886.	−	257227.i	0.589604	−	0.811520i	−0.405103	−	0.914271i	$-0.632764\pi$
$563$	186886.	−	257227.i	0.589604	−	0.811520i	0.994707	+	0.102751i	$0.0327643\pi$
$564$	11807.7	−	36340.2i	0.0371198	−	0.114243i
$565$	−76287.6	−	234789.i	−0.238977	−	0.735497i
$566$	10162.7	−	7383.64i	0.0317232	−	0.0230482i
$567$	−131519.	−	181021.i	−0.409094	−	0.563070i
$568$	128370.	−	41709.9i	0.397893	−	0.129283i
$569$	210022.	+	68240.3i	0.648695	+	0.210774i	0.614838	−	0.788653i	$-0.289221\pi$
$569$	210022.	+	68240.3i	0.648695	+	0.210774i	0.0338561	+	0.999427i	$0.489221\pi$
$570$	10806.4	+	7851.34i	0.0332608	+	0.0241654i
$571$		−	294471.i		−	0.903172i	−0.892228	−	0.451586i	$-0.850858\pi$
$571$		−	294471.i		−	0.903172i	0.892228	−	0.451586i	$-0.149142\pi$
$572$	−175562.	−	250034.i	−0.536584	−	0.764199i
$573$	−17885.6			−0.0544745
$574$	−71746.1	+	98750.1i	−0.217758	+	0.299719i
$575$	1858.70	−	5720.50i	0.00562179	−	0.0173021i
$576$	12526.2	+	38551.6i	0.0377549	+	0.116198i
$577$	315597.	−	229294.i	0.947940	−	0.688719i	−0.00237862	−	0.999997i	$-0.500757\pi$
$577$	315597.	−	229294.i	0.947940	−	0.688719i	0.950319	+	0.311278i	$0.100757\pi$
$578$	163809.	+	225464.i	0.490323	+	0.674872i
$579$	8645.19	−	2808.99i	0.0257880	−	0.00837903i
$580$	−103570.	−	33651.8i	−0.307876	−	0.100035i
$581$	−321248.	−	233401.i	−0.951675	−	0.691433i
$582$			12543.4i			0.0370312i
$583$	26265.1	+	85510.1i	0.0772754	+	0.251582i
$584$	−166824.			−0.489139
$585$	164208.	−	226013.i	0.479825	−	0.660423i
$586$	−12300.6	+	37857.2i	−0.0358203	+	0.110244i
$587$	−112979.	−	347712.i	−0.327884	−	1.00912i	−0.970122	−	0.242617i	$-0.921994\pi$
$587$	−112979.	−	347712.i	−0.327884	−	1.00912i	0.642238	−	0.766505i	$-0.278006\pi$
$588$	−9315.36	+	6768.01i	−0.0269430	+	0.0195752i
$589$	−150971.	−	207793.i	−0.435173	−	0.598964i
$590$	136529.	−	44360.9i	0.392211	−	0.127437i
$591$	−57534.9	−	18694.2i	−0.164724	−	0.0535220i
$592$	79605.5	+	57836.8i	0.227143	+	0.165029i
$593$		−	245753.i		−	0.698860i	−0.936962	−	0.349430i	$-0.886375\pi$
$593$		−	245753.i		−	0.698860i	0.936962	−	0.349430i	$-0.113625\pi$
$594$	44539.0	−	59265.9i	0.126231	−	0.167970i
$595$	174414.			0.492660
$596$	−30951.8	+	42601.5i	−0.0871351	+	0.119931i
$597$	12724.7	−	39162.7i	0.0357026	−	0.109881i
$598$	13274.0	+	40853.1i	0.0371192	+	0.114241i
$599$	350204.	−	254438.i	0.976039	−	0.709134i	0.0192189	−	0.999815i	$-0.493882\pi$
$599$	350204.	−	254438.i	0.976039	−	0.709134i	0.956820	+	0.290682i	$0.0938820\pi$
$600$	−2248.43	−	3094.70i	−0.00624564	−	0.00859639i
$601$	42511.5	−	13812.8i	0.117695	−	0.0382414i	−0.249577	−	0.968355i	$-0.580292\pi$
$601$	42511.5	−	13812.8i	0.117695	−	0.0382414i	0.367272	+	0.930113i	$0.380292\pi$
$602$	−212153.	−	68932.7i	−0.585405	−	0.190210i
$603$	−238726.	−	173445.i	−0.656546	−	0.477009i
$604$			147268.i			0.403677i
$605$	−129253.	−	100442.i	−0.353126	−	0.274412i
$606$	−15778.5			−0.0429655
$607$	−106328.	+	146348.i	−0.288583	+	0.397201i	−0.928553	−	0.371199i	$-0.878947\pi$
$607$	−106328.	+	146348.i	−0.288583	+	0.397201i	0.639970	+	0.768400i	$0.278947\pi$
$608$	17471.0	−	53770.1i	0.0472617	−	0.145457i
$609$	18604.0	+	57257.3i	0.0501617	+	0.154382i
$610$	149281.	−	108459.i	0.401185	−	0.291478i
$611$	655163.	+	901755.i	1.75496	+	2.41549i
$612$	257016.	−	83509.6i	0.686210	−	0.222963i
$613$	156654.	+	50899.9i	0.416888	+	0.135455i	0.509948	−	0.860205i	$-0.329665\pi$
$613$	156654.	+	50899.9i	0.416888	+	0.135455i	−0.0930596	+	0.995661i	$0.529665\pi$
$614$	−177300.	−	128816.i	−0.470297	−	0.341691i
$615$		−	17847.5i		−	0.0471875i
$616$	−80024.5	−	60139.4i	−0.210893	−	0.158488i
$617$	410674.			1.07877			0.539383	−	0.842060i	$-0.318657\pi$
$617$	410674.			1.07877			0.539383	+	0.842060i	$0.318657\pi$
$618$	−16683.0	+	22962.1i	−0.0436814	+	0.0601223i
$619$	−161311.	+	496465.i	−0.421001	+	1.29571i	0.485770	+	0.874086i	$0.338539\pi$
$619$	−161311.	+	496465.i	−0.421001	+	1.29571i	−0.906772	+	0.421622i	$0.861461\pi$
$620$	22729.6	+	69954.5i	0.0591301	+	0.181984i
$621$	−8432.86	+	6126.83i	−0.0218671	+	0.0158874i
$622$	34734.9	+	47808.5i	0.0897812	+	0.123573i
$623$	169527.	−	55082.6i	0.436780	−	0.141918i
$624$	25981.1	+	8441.78i	0.0667250	+	0.0216803i
$625$	−12640.9	−	9184.14i	−0.0323607	−	0.0235114i
$626$		−	15249.3i		−	0.0389137i
$627$	−48857.7	+	15007.0i	−0.124279	+	0.0381732i
$628$	85221.5			0.216088
$629$	385587.	−	530715.i	0.974587	−	1.34140i
$630$	28286.3	−	87056.3i	0.0712681	−	0.219341i
$631$	−42805.0	−	131740.i	−0.107507	−	0.330872i	0.882804	−	0.469742i	$-0.155653\pi$
$631$	−42805.0	−	131740.i	−0.107507	−	0.330872i	−0.990311	+	0.138870i	$0.955653\pi$
$632$	−141073.	+	102496.i	−0.353192	+	0.256609i
$633$	50934.1	+	70104.7i	0.127116	+	0.174960i
$634$	71277.0	−	23159.3i	0.177325	−	0.0576165i
$635$	29450.3	+	9568.98i	0.0730369	+	0.0237311i
$636$	−6471.02	−	4701.47i	−0.0159977	−	0.0116230i
$637$		−	335886.i		−	0.827776i
$638$	341019.	−	239447.i	0.837794	−	0.588259i
$639$	−472267.			−1.15661
$640$	−9516.75	+	13098.7i	−0.0232343	+	0.0319792i
$641$	−57272.8	+	176268.i	−0.139390	+	0.428999i	−0.996247	−	0.0865554i	$-0.972414\pi$
$641$	−57272.8	+	176268.i	−0.139390	+	0.428999i	0.856857	+	0.515555i	$0.172414\pi$
$642$	22668.7	+	69767.2i	0.0549993	+	0.169271i
$643$	−479739.	+	348551.i	−1.16033	+	0.843032i	−0.989820	−	0.142324i	$-0.954543\pi$
$643$	−479739.	+	348551.i	−1.16033	+	0.843032i	−0.170513	+	0.985355i	$0.554543\pi$
$644$	8272.84	+	11386.6i	0.0199472	+	0.0274550i
$645$	31020.4	−	10079.1i	0.0745638	−	0.0242272i
$646$	−358475.	−	116476.i	−0.859001	−	0.279106i
$647$	−201889.	−	146681.i	−0.482286	−	0.350401i	0.319924	−	0.947443i	$-0.396343\pi$
$647$	−201889.	−	146681.i	−0.482286	−	0.350401i	−0.802210	+	0.597042i	$0.796343\pi$
$648$		−	138477.i		−	0.329783i
$649$	−178154.	+	519598.i	−0.422968	+	1.23361i
$650$	111586.			0.264109
$651$	23901.6	−	32897.7i	0.0563982	−	0.0776254i
$652$	38831.3	−	119510.i	0.0913453	−	0.281132i
$653$	58706.8	+	180681.i	0.137677	+	0.423727i	0.995997	−	0.0893884i	$-0.0284912\pi$
$653$	58706.8	+	180681.i	0.137677	+	0.423727i	−0.858320	+	0.513116i	$0.828491\pi$
$654$	−38782.3	+	28177.0i	−0.0906730	+	0.0658778i
$655$	−177360.	−	244115.i	−0.413402	−	0.568999i
$656$	−71844.4	+	23343.7i	−0.166950	+	0.0542452i
$657$	555131.	+	180373.i	1.28607	+	0.417870i
$658$	295465.	+	214668.i	0.682424	+	0.495810i
$659$		−	647680.i		−	1.49139i	−0.666290	−	0.745693i	$-0.732119\pi$
$659$		−	647680.i		−	1.49139i	0.666290	−	0.745693i	$-0.267881\pi$
$660$	14634.9	+	236.362i	0.0335971	+	0.000542613i
$661$	636359.			1.45646			0.728231	−	0.685331i	$-0.240343\pi$
$661$	636359.			1.45646			0.728231	+	0.685331i	$0.240343\pi$
$662$	−24640.5	+	33914.8i	−0.0562256	+	0.0773879i
$663$	56279.7	−	173211.i	0.128034	−	0.394048i
$664$	−75940.4	−	233720.i	−0.172241	−	0.530103i
$665$	−103288.	+	75043.2i	−0.233564	+	0.169695i
$666$	−202365.	−	278531.i	−0.456233	−	0.627950i
$667$	−55719.2	+	18104.3i	−0.125243	+	0.0406939i
$668$	140528.	+	45660.4i	0.314927	+	0.102326i
$669$	73586.2	+	53463.5i	0.164416	+	0.119455i
$670$		−	117863.i		−	0.262559i
$671$	−11401.5	+	705952.i	−0.0253232	+	1.56794i
$672$	8950.95			0.0198212
$673$	−429143.	+	590664.i	−0.947483	+	1.30410i	0.00515272	+	0.999987i	$0.498360\pi$
$673$	−429143.	+	590664.i	−0.947483	+	1.30410i	−0.952636	+	0.304112i	$0.901640\pi$
$674$	−150031.	+	461749.i	−0.330265	+	1.01645i
$675$	8367.43	+	25752.3i	0.0183647	+	0.0565208i
$676$	−459851.	+	334101.i	−1.00629	+	0.731114i
$677$	−462304.	−	636306.i	−1.00867	−	1.38832i	−0.919850	−	0.392270i	$-0.871690\pi$
$677$	−462304.	−	636306.i	−1.00867	−	1.38832i	−0.0888216	−	0.996048i	$-0.528310\pi$
$678$	−80331.1	+	26101.2i	−0.174753	+	0.0567806i
$679$	−114022.	−	37047.9i	−0.247313	−	0.0803570i
$680$	87326.4	+	63446.4i	0.188855	+	0.137211i
$681$		−	107152.i		−	0.231049i
$682$	−266231.	−	91282.7i	−0.572388	−	0.196254i
$683$	116433.			0.249595			0.124798	−	0.992182i	$-0.460172\pi$
$683$	116433.			0.249595			0.124798	+	0.992182i	$0.460172\pi$
$684$	−116274.	+	160038.i	−0.248526	+	0.342066i
$685$	30307.7	−	93277.7i	0.0645911	−	0.198791i
$686$	−110736.	−	340809.i	−0.235310	−	0.724208i
$687$	−73252.9	+	53221.3i	−0.155207	+	0.112764i
$688$	−81146.3	−	111688.i	−0.171432	−	0.235956i
$689$	221907.	−	72102.0i	0.467447	−	0.151883i
$690$	−1957.22	−	635.940i	−0.00411095	−	0.00133573i
$691$	215206.	+	156356.i	0.450710	+	0.327460i	0.789876	−	0.613267i	$-0.210145\pi$
$691$	215206.	+	156356.i	0.450710	+	0.327460i	−0.339166	+	0.940727i	$0.610145\pi$
$692$		−	137653.i		−	0.287458i
$693$	201270.	+	286646.i	0.419094	+	0.596870i
$694$	324033.			0.672776
$695$	−91561.7	+	126024.i	−0.189559	+	0.260906i
$696$	−11513.7	+	35435.5i	−0.0237682	+	0.0731509i
$697$	155628.	+	478973.i	0.320348	+	0.985929i
$698$	−258355.	+	187706.i	−0.530282	+	0.385272i
$699$	−32873.5	−	45246.5i	−0.0672810	−	0.0926043i
$700$	34772.4	−	11298.2i	0.0709640	−	0.0230576i
$701$	158266.	+	51423.8i	0.322071	+	0.104647i	0.465591	−	0.885000i	$-0.345842\pi$
$701$	158266.	+	51423.8i	0.322071	+	0.104647i	−0.143519	+	0.989648i	$0.545842\pi$
$702$	−156444.	−	113663.i	−0.317456	−	0.230645i
$703$			480192.i			0.971637i
$704$	−18190.3	−	59221.3i	−0.0367023	−	0.119490i
$705$	−53400.6			−0.107440
$706$	228247.	−	314155.i	0.457926	−	0.630281i
$707$	46603.1	−	143430.i	0.0932343	−	0.286946i
$708$	−15177.7	−	46712.2i	−0.0302789	−	0.0931888i
$709$	−391107.	+	284156.i	−0.778043	+	0.565281i	−0.904391	−	0.426705i	$-0.859674\pi$
$709$	−391107.	+	284156.i	−0.778043	+	0.565281i	0.126348	+	0.991986i	$0.459674\pi$
$710$	−110877.	−	152609.i	−0.219950	−	0.302735i
$711$	580263.	−	188539.i	1.14785	−	0.372959i
$712$	104917.	+	34089.6i	0.206960	+	0.0672453i
$713$	32014.0	+	23259.5i	0.0629739	+	0.0457532i
$714$		−	59674.3i		−	0.117055i
$715$	−256511.	+	341327.i	−0.501758	+	0.667665i
$716$	−319404.			−0.623038
$717$	38189.5	−	52563.3i	0.0742857	−	0.102245i
$718$	−93897.9	+	288988.i	−0.182141	+	0.560571i
$719$	132677.	+	408337.i	0.256647	+	0.789879i	0.993501	+	0.113827i	$0.0363109\pi$
$719$	132677.	+	408337.i	0.256647	+	0.789879i	−0.736853	+	0.676053i	$0.763689\pi$
$720$	45830.9	−	33298.1i	0.0884084	−	0.0642324i
$721$	−159456.	−	219472.i	−0.306740	−	0.422191i
$722$	−88159.0	+	28644.6i	−0.169119	+	0.0549501i
$723$	−63307.6	−	20569.9i	−0.121110	−	0.0393510i
$724$	−203024.	−	147505.i	−0.387319	−	0.281404i
$725$			152192.i			0.289544i
$726$	−34365.3	+	44222.8i	−0.0651999	+	0.0839022i
$727$	173195.			0.327692			0.163846	−	0.986486i	$-0.447610\pi$
$727$	173195.			0.327692			0.163846	+	0.986486i	$0.447610\pi$
$728$	−153475.	+	211240.i	−0.289584	+	0.398578i
$729$	−142391.	+	438234.i	−0.267933	+	0.824614i
$730$	72045.3	+	221733.i	0.135195	+	0.416087i
$731$	−744605.	+	540987.i	−1.39345	+	1.01240i
$732$	−37108.3	−	51075.2i	−0.0692546	−	0.0953208i
$733$	−906097.	+	294409.i	−1.68642	+	0.547952i	−0.986140	−	0.165913i	$-0.946943\pi$
$733$	−906097.	+	294409.i	−1.68642	+	0.547952i	−0.700283	+	0.713865i	$0.746943\pi$
$734$	228329.	+	74188.7i	0.423809	+	0.137704i
$735$	13018.6	+	9458.58i	0.0240985	+	0.0175086i
$736$			8710.49i			0.0160800i
$737$	360526.	+	270939.i	0.663746	+	0.498813i
$738$	264312.			0.485294
$739$	230234.	−	316890.i	0.421581	−	0.580256i	−0.544414	−	0.838816i	$-0.683248\pi$
$739$	230234.	−	316890.i	0.421581	−	0.580256i	0.965995	+	0.258560i	$0.0832480\pi$
$740$	42494.5	−	130785.i	0.0776013	−	0.238832i
$741$	41196.8	+	126791.i	0.0750286	+	0.230914i
$742$	61850.0	−	44936.7i	0.112339	−	0.0816194i
$743$	11337.0	+	15604.0i	0.0205362	+	0.0282656i	0.819162	−	0.573563i	$-0.194439\pi$
$743$	11337.0	+	15604.0i	0.0205362	+	0.0282656i	−0.798625	+	0.601828i	$0.794439\pi$
$744$	23934.3	−	7776.74i	0.0432390	−	0.0140492i
$745$	69990.4	+	22741.3i	0.126103	+	0.0409734i
$746$	34972.4	+	25408.9i	0.0628417	+	0.0456571i
$747$			859847.i			1.54092i
$748$	−394817.	+	121271.i	−0.705656	+	0.216747i
$749$	−701152.			−1.24982
$750$	−3142.28	+	4324.97i	−0.00558627	+	0.00768884i
$751$	−111170.	+	342145.i	−0.197109	+	0.606638i	0.802837	+	0.596199i	$0.203323\pi$
$751$	−111170.	+	342145.i	−0.197109	+	0.606638i	−0.999946	+	0.0104395i	$0.996677\pi$
$752$	69845.4	+	214962.i	0.123510	+	0.380125i
$753$	50769.7	−	36886.4i	0.0895396	−	0.0650543i
$754$	−638852.	−	879304.i	−1.12372	−	1.54667i
$755$	195740.	−	63599.7i	0.343388	−	0.111574i
$756$	−60259.3	−	19579.4i	−0.105434	−	0.0342576i
$757$	−588909.	−	427867.i	−1.02768	−	0.746651i	−0.0598341	−	0.998208i	$-0.519057\pi$
$757$	−588909.	−	427867.i	−1.02768	−	0.746651i	−0.967842	+	0.251558i	$0.919057\pi$
$758$		−	463382.i		−	0.806493i
$759$	6444.46	−	4525.00i	0.0111867	−	0.00785479i
$760$	−79013.1			−0.136796
$761$	−43667.9	+	60103.7i	−0.0754038	+	0.103784i	−0.845053	−	0.534683i	$-0.820431\pi$
$761$	−43667.9	+	60103.7i	−0.0754038	+	0.103784i	0.769649	+	0.638467i	$0.220431\pi$
$762$	3273.95	−	10076.2i	0.00563848	−	0.0173534i
$763$	−141588.	−	435762.i	−0.243207	−	0.748515i
$764$	85592.2	−	62186.4i	0.146638	−	0.106539i
$765$	−221992.	−	305546.i	−0.379328	−	0.522100i
$766$	13785.8	−	4479.27i	0.0234949	−	0.00763395i
$767$	1.36264e6	+	442747.i	2.31627	+	0.752601i
$768$	4481.60	+	3256.08i	0.00759821	+	0.00552042i
$769$			829019.i			1.40188i	0.713219	+	0.700942i	$0.247237\pi$
$769$			829019.i			1.40188i	−0.713219	+	0.700942i	$0.752763\pi$
$770$	−45374.0	+	132336.i	−0.0765289	+	0.223201i
$771$	73354.3			0.123401
$772$	−31605.4	+	43501.1i	−0.0530306	+	0.0729904i
$773$	158751.	−	488586.i	0.265679	−	0.817677i	−0.725857	−	0.687846i	$-0.758557\pi$
$773$	158751.	−	488586.i	0.265679	−	0.817677i	0.991536	−	0.129831i	$-0.0414435\pi$
$774$	149267.	+	459396.i	0.249162	+	0.766841i
$775$	83163.3	−	60421.7i	0.138461	−	0.100598i
$776$	−43612.0	−	60026.8i	−0.0724241	−	0.0996832i
$777$	−72302.9	+	23492.6i	−0.119760	+	0.0389125i
$778$	496748.	+	161403.i	0.820686	+	0.266657i
$779$	−298245.	−	216688.i	−0.491472	−	0.357075i
$780$		−	38178.3i		−	0.0627520i
$781$	721690.	+	11655.7i	1.18317	+	0.0191089i
$782$	58071.2			0.0949615
$783$	155024.	−	213372.i	0.252857	−	0.348028i
$784$	21047.4	−	64777.3i	0.0342426	−	0.105388i
$785$	−36804.1	−	113271.i	−0.0597251	−	0.183815i
$786$	−83521.8	+	60682.1i	−0.135193	+	0.0982236i
$787$	512066.	+	704798.i	0.826754	+	1.13793i	0.988518	+	0.151100i	$0.0482817\pi$
$787$	512066.	+	704798.i	0.826754	+	1.13793i	−0.161764	+	0.986829i	$0.551718\pi$
$788$	340334.	−	110581.i	0.548091	−	0.178086i
$789$	−82050.1	−	26659.7i	−0.131803	−	0.0428254i
$790$	197156.	+	143242.i	0.315905	+	0.229518i
$791$		−	807318.i		−	1.29030i
$792$	−3500.40	+	216735.i	−0.00558042	+	0.345525i
$793$	1.84163e6			2.92857
$794$	−10194.3	+	14031.3i	−0.0161702	+	0.0222564i
$795$	−3454.32	+	10631.3i	−0.00546548	+	0.0168210i
$796$	75270.1	+	231658.i	0.118795	+	0.365612i
$797$	−369769.	+	268653.i	−0.582122	+	0.422937i	−0.839489	−	0.543377i	$-0.817145\pi$
$797$	−369769.	+	268653.i	−0.582122	+	0.422937i	0.257366	+	0.966314i	$0.417145\pi$
$798$	25675.4	+	35339.1i	0.0403191	+	0.0554945i
$799$	1.43311e6	−	465646.i	2.24484	−	0.729394i
$800$	21520.0	+	6992.26i	0.0336249	+	0.0109254i
$801$	−312268.	−	226876.i	−0.486701	−	0.353609i
$802$		−	478559.i		−	0.744023i
$803$	−843866.	−	289336.i	−1.30871	−	0.448716i
$804$	−40325.8			−0.0623836
$805$	11561.6	−	15913.2i	0.0178414	−	0.0245565i
$806$	−226854.	+	698186.i	−0.349202	+	1.07473i
$807$	−15932.0	−	49033.8i	−0.0244638	−	0.0752919i
$808$	75508.7	−	54860.3i	0.115658	−	0.0840301i
$809$	662041.	+	911222.i	1.01155	+	1.39228i	0.917961	+	0.396670i	$0.129834\pi$
$809$	662041.	+	911222.i	1.01155	+	1.39228i	0.0935904	+	0.995611i	$0.470166\pi$
$810$	−184056.	+	59803.3i	−0.280530	+	0.0911497i
$811$	−714645.	−	232202.i	−1.08655	−	0.353041i	−0.289636	−	0.957137i	$-0.593534\pi$
$811$	−714645.	−	232202.i	−1.08655	−	0.353041i	−0.796911	+	0.604096i	$0.793534\pi$
$812$	−288109.	−	209323.i	−0.436963	−	0.317472i
$813$			27320.5i			0.0413341i
$814$	302367.	+	430629.i	0.456337	+	0.649912i
$815$	−175616.			−0.264392
$816$	21707.6	−	29878.0i	0.0326011	−	0.0448716i
$817$	208191.	−	640746.i	0.311902	−	0.959934i
$818$	−248543.	−	764937.i	−0.371446	−	1.14319i
$819$	739106.	−	536992.i	1.10189	−	0.800572i
$820$	62054.1	+	85410.1i	0.0922875	+	0.127023i
$821$	−1.06998e6	+	347657.i	−1.58741	+	0.515780i	−0.963952	−	0.266077i	$-0.914272\pi$
$821$	−1.06998e6	+	347657.i	−1.58741	+	0.515780i	−0.623457	+	0.781858i	$0.714272\pi$
$822$	−31914.2	−	10369.5i	−0.0472324	−	0.0153467i
$823$	−852899.	−	619668.i	−1.25921	−	0.914870i	−0.260491	−	0.965476i	$-0.583885\pi$
$823$	−852899.	−	619668.i	−1.25921	−	0.914870i	−0.998719	+	0.0506066i	$0.983885\pi$
$824$		−	167891.i		−	0.247272i
$825$	−6006.13	−	19553.9i	−0.00882444	−	0.0287294i
$826$	469452.			0.688067
$827$	−116616.	+	160508.i	−0.170509	+	0.234685i	−0.885716	−	0.464227i	$-0.846332\pi$
$827$	−116616.	+	160508.i	−0.170509	+	0.234685i	0.715208	+	0.698912i	$0.246332\pi$
$828$	9417.94	−	28985.4i	0.0137371	−	0.0422785i
$829$	152806.	+	470287.i	0.222346	+	0.684312i	0.998550	+	0.0538295i	$0.0171428\pi$
$829$	152806.	+	470287.i	0.222346	+	0.684312i	−0.776204	+	0.630482i	$0.782857\pi$
$830$	−277852.	+	201871.i	−0.403327	+	0.293034i
$831$	44306.0	+	60982.0i	0.0641594	+	0.0883079i
$832$	−153685.	+	49935.3i	−0.222016	+	0.0721375i
$833$	−431858.	−	140319.i	−0.622373	−	0.202221i
$834$	43118.0	+	31327.1i	0.0619907	+	0.0450389i
$835$		−	206501.i		−	0.296176i
$836$	181633.	−	241690.i	0.259886	−	0.345818i
$837$	−178141.			−0.254280
$838$	19419.4	−	26728.6i	0.0276534	−	0.0380616i
$839$	−63986.1	+	196929.i	−0.0908996	+	0.279760i	−0.986163	−	0.165776i	$-0.946987\pi$
$839$	−63986.1	+	196929.i	−0.0908996	+	0.279760i	0.895264	+	0.445536i	$0.146987\pi$
$840$	−3865.59	−	11897.1i	−0.00547845	−	0.0168609i
$841$	627074.	−	455596.i	0.886598	−	0.644151i
$842$	−128615.	−	177023.i	−0.181412	−	0.249693i
$843$	−110611.	+	35939.8i	−0.155648	+	0.0505731i
$844$	−487495.	−	158397.i	−0.684361	−	0.222362i
$845$	642661.	+	466921.i	0.900054	+	0.653928i
$846$		−	790835.i		−	1.10496i
$847$	−300494.	−	443003.i	−0.418859	−	0.617504i
$848$	47314.0			0.0657957
$849$	−3530.54	+	4859.38i	−0.00489808	+	0.00674164i
$850$	46616.1	−	143469.i	0.0645205	−	0.198574i
$851$	−22861.5	−	70360.6i	−0.0315679	−	0.0971562i
$852$	−52213.8	+	37935.6i	−0.0719294	+	0.0522598i
$853$	−327891.	−	451303.i	−0.450642	−	0.620256i	0.521893	−	0.853011i	$-0.325226\pi$
$853$	−327891.	−	451303.i	−0.450642	−	0.620256i	−0.972535	+	0.232755i	$0.925226\pi$
$854$	573886.	−	186467.i	0.786882	−	0.255674i
$855$	262928.	+	85430.4i	0.359670	+	0.116864i
$856$	−351056.	−	255057.i	−0.479104	−	0.348089i
$857$		−	1.05604e6i		−	1.43787i	−0.695076	−	0.718936i	$-0.744629\pi$
$857$		−	1.05604e6i		−	1.43787i	0.695076	−	0.718936i	$-0.255371\pi$
$858$	116782.	+	87763.2i	0.158636	+	0.119217i
$859$	850619.			1.15279			0.576393	−	0.817173i	$-0.304460\pi$
$859$	850619.			1.15279			0.576393	+	0.817173i	$0.304460\pi$
$860$	−113405.	+	156089.i	−0.153333	+	0.211045i
$861$	18035.7	−	55508.2i	0.0243291	−	0.0748774i
$862$	74723.7	+	229976.i	0.100564	+	0.309505i
$863$	−275561.	+	200207.i	−0.369995	+	0.268817i	−0.757209	−	0.653173i	$-0.773438\pi$
$863$	−275561.	+	200207.i	−0.369995	+	0.268817i	0.387214	+	0.921990i	$0.373438\pi$
$864$	−23048.5	−	31723.6i	−0.0308756	−	0.0424967i
$865$	−182960.	+	59447.5i	−0.244526	+	0.0794513i
$866$	181457.	+	58958.8i	0.241956	+	0.0786164i
$867$	−107807.	−	78326.6i	−0.143420	−	0.104201i
$868$			240537.i			0.319259i
$869$	−891375.	+	273792.i	−1.18038	+	0.362562i
$870$	52071.1			0.0687952
$871$	691434.	−	951677.i	0.911412	−	1.25445i
$872$	87625.9	−	269685.i	0.115239	−	0.354669i
$873$	80223.4	+	246902.i	0.105262	+	0.323964i
$874$	−34389.8	+	24985.7i	−0.0450202	+	0.0327091i
$875$	−30033.9	−	41338.1i	−0.0392280	−	0.0539926i
$876$	75864.0	−	24649.7i	0.0988616	−	0.0321221i
$877$	−420930.	−	136768.i	−0.547281	−	0.177822i	0.0223091	−	0.999751i	$-0.492898\pi$
$877$	−420930.	−	136768.i	−0.547281	−	0.177822i	−0.569590	+	0.821929i	$0.692898\pi$
$878$	86898.2	+	63135.3i	0.112725	+	0.0818998i
$879$		−	19033.3i		−	0.0246340i
$880$	−70857.8	+	49753.0i	−0.0915003	+	0.0642472i
$881$	−7081.47			−0.00912372			−0.00456186	−	0.999990i	$-0.501452\pi$
$881$	−7081.47			−0.00912372			−0.00456186	+	0.999990i	$0.501452\pi$
$882$	−140077.	+	192799.i	−0.180065	+	0.247838i
$883$	183264.	−	564028.i	0.235047	−	0.723401i	−0.762068	−	0.647497i	$-0.775816\pi$
$883$	183264.	−	564028.i	0.235047	−	0.723401i	0.997115	−	0.0759037i	$-0.0241842\pi$
$884$	332909.	+	1.02459e6i	0.426012	+	1.31113i
$885$	−55532.4	+	40346.6i	−0.0709022	+	0.0515135i
$886$	474413.	+	652974.i	0.604351	+	0.831818i
$887$	−191863.	+	62340.1i	−0.243862	+	0.0792356i	−0.428398	−	0.903590i	$-0.640922\pi$
$887$	−191863.	+	62340.1i	−0.243862	+	0.0792356i	0.184536	+	0.982826i	$0.440922\pi$
$888$	−44746.9	−	14539.1i	−0.0567462	−	0.0184380i
$889$	81924.5	+	59521.7i	0.103660	+	0.0753133i
$890$		−	154172.i		−	0.194636i
$891$	240172.	−	700475.i	0.302529	−	0.882343i
$892$	−538038.			−0.676212
$893$	−648341.	+	892364.i	−0.813018	+	1.11902i
$894$	7780.73	−	23946.6i	0.00973521	−	0.0299619i
$895$	137939.	+	424533.i	0.172203	+	0.529988i
$896$	−42835.2	+	31121.6i	−0.0533562	+	0.0387655i
$897$	−12072.8	−	16616.8i	−0.0150046	−	0.0206520i
$898$	246958.	−	80241.6i	0.306246	−	0.0995055i
$899$	−952251.	−	309405.i	−1.17824	−	0.382832i
$900$	−64050.6	−	46535.5i	−0.0790748	−	0.0574512i
$901$		−	315433.i		−	0.388560i
$902$	−403906.	−	6523.32i	−0.496441	−	0.00801780i
$903$	106663.			0.130809
$904$	293677.	−	404212.i	0.359363	−	0.494621i
$905$	−108377.	+	333549.i	−0.132324	+	0.407252i
$906$	−21760.1	−	66970.7i	−0.0265097	−	0.0815884i
$907$	−277769.	+	201811.i	−0.337652	+	0.245319i	−0.743671	−	0.668546i	$-0.766917\pi$
$907$	−277769.	+	201811.i	−0.337652	+	0.245319i	0.406018	+	0.913865i	$0.366917\pi$
$908$	372556.	+	512780.i	0.451877	+	0.621955i
$909$	−310582.	+	100914.i	−0.375879	+	0.122131i
$910$	347048.	+	112763.i	0.419090	+	0.136171i
$911$	−93023.6	−	67585.6i	−0.112087	−	0.0814362i	0.530330	−	0.847792i	$-0.322068\pi$
$911$	−93023.6	−	67585.6i	−0.112087	−	0.0814362i	−0.642417	+	0.766355i	$0.722068\pi$
$912$			27033.7i			0.0325024i
$913$	21221.3	−	1.31397e6i	0.0254584	−	1.57631i
$914$	−530403.			−0.634912
$915$	−51860.4	+	71379.7i	−0.0619432	+	0.0852575i
$916$	165510.	−	509387.i	0.197257	−	0.607095i
$917$	−304924.	−	938460.i	−0.362621	−	1.11603i
$918$	−211495.	+	153660.i	−0.250966	+	0.182338i
$919$	−685573.	−	943611.i	−0.811751	−	1.11728i	−0.991051	−	0.133485i	$-0.957383\pi$
$919$	−685573.	−	943611.i	−0.811751	−	1.11728i	0.179300	−	0.983794i	$-0.442617\pi$
$920$	11577.5	−	3761.75i	0.0136785	−	0.00444441i
$921$	99661.8	+	32382.1i	0.117492	+	0.0381756i
$922$	938767.	+	682054.i	1.10432	+	0.802337i
$923$		−	1.88269e6i		−	2.20991i
$924$	45277.7	+	15524.3i	0.0530323	+	0.0181831i
$925$	−192183.			−0.224611
$926$	−342145.	+	470923.i	−0.399015	+	0.549196i
$927$	−181527.	+	558683.i	−0.211243	+	0.650139i
$928$	−68106.4	−	209610.i	−0.0790847	−	0.243398i
$929$	1.05351e6	−	765422.i	1.22070	−	0.886890i	0.224541	−	0.974465i	$-0.427912\pi$
$929$	1.05351e6	−	765422.i	1.22070	−	0.886890i	0.996158	+	0.0875750i	$0.0279117\pi$
$930$	−20672.8	−	28453.6i	−0.0239019	−	0.0328982i
$931$	316120.	−	102714.i	0.364714	−	0.118503i
$932$	314636.	+	102231.i	0.362223	+	0.117693i
$933$	−22860.0	−	16608.8i	−0.0262611	−	0.0190798i
$934$			330909.i			0.379328i
$935$	331694.	+	472396.i	0.379415	+	0.540359i
$936$	565401.			0.645364
$937$	−417190.	+	574212.i	−0.475176	+	0.654024i	−0.977569	−	0.210616i	$-0.932453\pi$
$937$	−417190.	+	574212.i	−0.475176	+	0.654024i	0.502393	+	0.864639i	$0.332453\pi$
$938$	119106.	−	366569.i	0.135371	−	0.416630i
$939$	2253.22	+	6934.71i	0.00255548	+	0.00786497i
$940$	255551.	−	185669.i	0.289216	−	0.210128i
$941$	473260.	+	651386.i	0.534466	+	0.735630i	0.987803	−	0.155710i	$-0.0497664\pi$
$941$	473260.	+	651386.i	0.534466	+	0.735630i	−0.453337	+	0.891339i	$0.649766\pi$
$942$	−38754.9	+	12592.2i	−0.0436742	+	0.0141906i
$943$	54017.0	+	17551.2i	0.0607446	+	0.0197371i
$944$	235047.	+	170772.i	0.263762	+	0.191634i
$945$			88548.8i			0.0991560i
$946$	−216762.	−	705705.i	−0.242215	−	0.788571i
$947$	−543595.			−0.606143			−0.303072	−	0.952968i	$-0.598012\pi$
$947$	−543595.			−0.606143			−0.303072	+	0.952968i	$0.598012\pi$
$948$	49009.1	−	67455.3i	0.0545331	−	0.0750584i
$949$	−719054.	+	2.21302e6i	−0.798415	+	2.45727i
$950$	34123.0	+	105020.i	0.0378094	+	0.116365i
$951$	−28991.6	+	21063.6i	−0.0320561	+	0.0232901i
$952$	207482.	+	285574.i	0.228932	+	0.315097i
$953$	269139.	−	87448.7i	0.296341	−	0.0962870i	−0.157073	−	0.987587i	$-0.550206\pi$
$953$	269139.	−	87448.7i	0.296341	−	0.0962870i	0.453414	+	0.891300i	$0.350206\pi$
$954$	−157444.	−	51156.7i	−0.172993	−	0.0562090i
$955$	−119619.	−	86908.1i	−0.131157	−	0.0952914i
$956$			384325.i			0.420517i
$957$	−119700.	+	159278.i	−0.130698	+	0.173913i
$958$	−911771.			−0.993470
$959$	188522.	−	259479.i	0.204987	−	0.282140i
$960$	2392.34	−	7362.87i	0.00259586	−	0.00798923i
$961$	−76400.7	−	235137.i	−0.0827276	−	0.254609i
$962$	1.11036e6	−	806723.i	1.19981	−	0.871715i
$963$	892419.	+	1.22831e6i	0.962312	+	1.32451i
$964$	374481.	−	121676.i	0.402973	−	0.130934i
$965$	71468.4	+	23221.5i	0.0767466	+	0.0249365i
$966$	−5444.58	−	3955.72i	−0.00583459	−	0.00423908i
$967$			155371.i			0.166156i	0.996543	+	0.0830780i	$0.0264751\pi$
$967$			155371.i			0.166156i	−0.996543	+	0.0830780i	$0.973525\pi$
$968$	10698.2	−	331115.i	0.0114172	−	0.353369i
$969$	180228.			0.191945
$970$	−60949.7	+	83890.0i	−0.0647781	+	0.0891594i
$971$	67311.1	−	207162.i	0.0713918	−	0.219721i	−0.908994	−	0.416809i	$-0.863148\pi$
$971$	67311.1	−	207162.i	0.0713918	−	0.219721i	0.980386	+	0.197088i	$0.0631484\pi$
$972$	63838.0	+	196473.i	0.0675688	+	0.207955i
$973$	−412122.	+	299424.i	−0.435312	+	0.316272i
$974$	264124.	+	363535.i	0.278413	+	0.383202i
$975$	−50744.4	+	16487.8i	−0.0533800	+	0.0173442i
$976$	355167.	+	115401.i	0.372849	+	0.121146i
$977$	−158481.	−	115143.i	−0.166031	−	0.120628i	0.501667	−	0.865061i	$-0.332720\pi$
$977$	−158481.	−	115143.i	−0.166031	−	0.120628i	−0.667698	+	0.744432i	$0.732720\pi$
$978$			60085.5i			0.0628192i
$979$	471590.	+	354405.i	0.492039	+	0.369773i
$980$	−95187.8			−0.0991127
$981$	−583176.	+	802672.i	−0.605984	+	0.834066i
$982$	−228523.	+	703321.i	−0.236977	+	0.729341i
$983$	−480200.	−	1.47790e6i	−0.496952	−	1.52946i	−0.813892	−	0.581016i	$-0.802655\pi$
$983$	−480200.	−	1.47790e6i	−0.496952	−	1.52946i	0.316939	−	0.948446i	$-0.397345\pi$
$984$	29222.4	−	21231.3i	0.0301804	−	0.0219273i
$985$	−293956.	−	404596.i	−0.302977	−	0.417012i
$986$	−1.39743e6	+	454053.i	−1.43740	+	0.467038i
$987$	−166083.	−	53963.7i	−0.170487	−	0.0553946i
$988$	−637988.	−	463526.i	−0.653580	−	0.474854i
$989$			103798.i			0.106120i
$990$	289584.	−	88947.7i	0.295463	−	0.0907537i
$991$	−451707.			−0.459949			−0.229975	−	0.973197i	$-0.573864\pi$
$991$	−451707.			−0.459949			−0.229975	+	0.973197i	$0.573864\pi$
$992$	−87500.0	+	120433.i	−0.0889170	+	0.122384i
$993$	6194.19	−	19063.8i	0.00628183	−	0.0193335i
$994$	−190624.	−	586680.i	−0.192932	−	0.593784i
$995$	275399.	−	200089.i	0.278174	−	0.202105i
$996$	69068.5	+	95064.6i	0.0696244	+	0.0958297i
$997$	−269307.	+	87503.1i	−0.270930	+	0.0880305i	−0.441331	−	0.897344i	$-0.645494\pi$
$997$	−269307.	+	87503.1i	−0.270930	+	0.0880305i	0.170401	+	0.985375i	$0.445494\pi$
$998$	12982.1	+	4218.14i	0.0130342	+	0.00423507i
$999$	269440.	+	195760.i	0.269980	+	0.196152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.5.h.a.51.7	yes	32
11.8	odd	10	inner	110.5.h.a.41.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.5.h.a.41.7	✓	32	11.8	odd	10	inner
110.5.h.a.51.7	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	110.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66251 - 2.28825i) q^{2} +(-0.417925 + 1.28624i) q^{3} +(-2.47214 - 7.60845i) q^{4} +(-9.04508 + 6.57164i) q^{5} +(2.24843 + 3.09470i) q^{6} +(-34.7724 + 11.2982i) q^{7} +(-21.5200 - 6.99226i) q^{8} +(64.0506 + 46.5355i) q^{9} +31.6228i q^{10} +(-96.7298 - 72.6935i) q^{11} +10.8195 q^{12} +(-185.513 + 255.337i) q^{13} +(-31.9562 + 98.3511i) q^{14} +(-4.67254 - 14.3806i) q^{15} +(-51.7771 + 37.6183i) q^{16} +(250.794 + 345.188i) q^{17} +(212.969 - 69.1979i) q^{18} +(-297.041 - 96.5143i) q^{19} +(72.3607 + 52.5731i) q^{20} -49.4475i q^{21} +(-327.155 + 100.488i) q^{22} +48.1191 q^{23} +(17.9874 - 24.7576i) q^{24} +(38.6271 - 118.882i) q^{25} +(275.856 + 848.998i) q^{26} +(-175.250 + 127.326i) q^{27} +(171.924 + 236.633i) q^{28} +(-1157.94 + 376.238i) q^{29} +(-40.6745 - 13.2159i) q^{30} +(665.307 + 483.374i) q^{31} +181.019i q^{32} +(133.927 - 94.0373i) q^{33} +1206.82 q^{34} +(240.271 - 330.705i) q^{35} +(195.721 - 602.368i) q^{36} +(-475.103 - 1462.22i) q^{37} +(-714.681 + 519.246i) q^{38} +(-250.894 - 345.326i) q^{39} +(240.600 - 78.1758i) q^{40} +(1122.57 + 364.745i) q^{41} +(-113.148 - 82.2068i) q^{42} +2157.10i q^{43} +(-313.956 + 915.672i) q^{44} -885.158 q^{45} +(79.9984 - 110.108i) q^{46} +(1091.33 - 3358.78i) q^{47} +(-26.7472 - 82.3194i) q^{48} +(-860.982 + 625.540i) q^{49} +(-207.813 - 286.031i) q^{50} +(-548.808 + 178.319i) q^{51} +(2401.33 + 780.240i) q^{52} +(-598.091 - 434.538i) q^{53} +612.695i q^{54} +(1352.64 + 21.8460i) q^{55} +827.300 q^{56} +(248.281 - 341.730i) q^{57} +(-1064.16 + 3275.16i) q^{58} +(-1402.81 - 4317.42i) q^{59} +(-97.8630 + 71.1016i) q^{60} +(-3429.77 - 4720.67i) q^{61} +(2212.16 - 718.773i) q^{62} +(-2752.96 - 894.491i) q^{63} +(414.217 + 300.946i) q^{64} -3528.67i q^{65} +(7.47442 - 462.796i) q^{66} -3727.15 q^{67} +(2006.35 - 2761.50i) q^{68} +(-20.1102 + 61.8928i) q^{69} +(-357.281 - 1099.60i) q^{70} +(-4825.92 + 3506.23i) q^{71} +(-1052.98 - 1449.30i) q^{72} +(7011.80 - 2278.27i) q^{73} +(-4135.77 - 1343.79i) q^{74} +(136.768 + 99.3676i) q^{75} +2498.62i q^{76} +(4184.83 + 1434.85i) q^{77} -1207.30 q^{78} +(4529.72 - 6234.62i) q^{79} +(221.115 - 680.521i) q^{80} +(1891.15 + 5820.35i) q^{81} +(2700.91 - 1962.32i) q^{82} +(6383.72 + 8786.44i) q^{83} +(-376.219 + 122.241i) q^{84} +(-4536.90 - 1474.13i) q^{85} +(4935.97 + 3586.19i) q^{86} -1646.63i q^{87} +(1573.33 + 2240.72i) q^{88} -4875.33 q^{89} +(-1471.58 + 2025.46i) q^{90} +(3565.87 - 10974.6i) q^{91} +(-118.957 - 366.112i) q^{92} +(-899.783 + 653.731i) q^{93} +(-5871.36 - 8081.24i) q^{94} +(3321.01 - 1079.06i) q^{95} +(-232.834 - 75.6525i) q^{96} +(2652.84 + 1927.40i) q^{97} +3010.10i q^{98} +(-2812.77 - 9157.43i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) \) 32 * q - 18 * q^3 + 64 * q^4 - 200 * q^5 + 80 * q^6 - 60 * q^7 - 262 * q^9 - 258 * q^11 - 96 * q^12 - 570 * q^13 - 48 * q^14 + 150 * q^15 - 512 * q^16 + 150 * q^17 - 480 * q^18 - 1020 * q^19 + 1600 * q^20 - 480 * q^22 - 1536 * q^23 + 640 * q^24 - 1000 * q^25 + 448 * q^26 - 4194 * q^27 + 960 * q^28 - 4130 * q^29 - 800 * q^30 - 1936 * q^31 - 5852 * q^33 - 768 * q^34 + 1856 * q^36 + 2728 * q^37 - 1360 * q^38 + 7990 * q^39 - 4490 * q^41 - 2592 * q^42 + 1024 * q^44 + 300 * q^45 + 640 * q^46 - 2732 * q^47 - 1152 * q^48 + 3832 * q^49 + 12080 * q^51 + 5520 * q^52 + 1222 * q^53 - 550 * q^55 + 2304 * q^56 + 14580 * q^57 - 3104 * q^58 - 8340 * q^59 - 300 * q^61 + 11680 * q^62 + 32020 * q^63 + 4096 * q^64 + 29696 * q^66 - 9264 * q^67 + 1200 * q^68 - 25466 * q^69 - 1200 * q^70 - 7144 * q^71 - 20480 * q^72 - 7070 * q^73 + 19840 * q^74 + 1500 * q^75 + 34480 * q^77 - 5696 * q^78 + 57050 * q^79 + 12800 * q^80 - 63694 * q^81 + 13312 * q^82 + 580 * q^83 + 29520 * q^84 + 9750 * q^85 - 13360 * q^86 + 9600 * q^88 + 14368 * q^89 + 17600 * q^90 - 40158 * q^91 - 25712 * q^92 - 103942 * q^93 - 67600 * q^94 + 5700 * q^95 - 31458 * q^97 + 65268 * q^99

Introduction

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