LMFDB - Embedded newform 177.3.b.a.119.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("177.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.b (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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.27
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89638i q^{2} +(0.180746 + 2.99455i) q^{3} +0.403751 q^{4} -2.43864i q^{5} +(-5.67880 + 0.342762i) q^{6} -8.99368 q^{7} +8.35118i q^{8} +(-8.93466 + 1.08250i) q^{9} +O(q^{10})$	\(q+1.89638i q^{2} +(0.180746 + 2.99455i) q^{3} +0.403751 q^{4} -2.43864i q^{5} +(-5.67880 + 0.342762i) q^{6} -8.99368 q^{7} +8.35118i q^{8} +(-8.93466 + 1.08250i) q^{9} +4.62459 q^{10} +9.24832i q^{11} +(0.0729763 + 1.20905i) q^{12} -11.6512 q^{13} -17.0554i q^{14} +(7.30264 - 0.440774i) q^{15} -14.2220 q^{16} +27.6502i q^{17} +(-2.05284 - 16.9435i) q^{18} +29.8253 q^{19} -0.984604i q^{20} +(-1.62557 - 26.9320i) q^{21} -17.5383 q^{22} -29.8868i q^{23} +(-25.0080 + 1.50944i) q^{24} +19.0530 q^{25} -22.0950i q^{26} +(-4.85652 - 26.5596i) q^{27} -3.63121 q^{28} +16.6314i q^{29} +(0.835875 + 13.8486i) q^{30} -11.5203 q^{31} +6.43445i q^{32} +(-27.6946 + 1.67160i) q^{33} -52.4351 q^{34} +21.9324i q^{35} +(-3.60738 + 0.437062i) q^{36} +68.3024 q^{37} +56.5600i q^{38} +(-2.10590 - 34.8900i) q^{39} +20.3655 q^{40} +2.67565i q^{41} +(51.0733 - 3.08269i) q^{42} +14.6822 q^{43} +3.73402i q^{44} +(2.63984 + 21.7884i) q^{45} +56.6767 q^{46} +15.0479i q^{47} +(-2.57056 - 42.5884i) q^{48} +31.8863 q^{49} +36.1317i q^{50} +(-82.7998 + 4.99765i) q^{51} -4.70417 q^{52} +67.2208i q^{53} +(50.3671 - 9.20979i) q^{54} +22.5533 q^{55} -75.1078i q^{56} +(5.39080 + 89.3134i) q^{57} -31.5394 q^{58} -7.68115i q^{59} +(2.94845 - 0.177963i) q^{60} +102.337 q^{61} -21.8468i q^{62} +(80.3555 - 9.73570i) q^{63} -69.0901 q^{64} +28.4130i q^{65} +(-3.16998 - 52.5193i) q^{66} -55.2408 q^{67} +11.1638i q^{68} +(89.4976 - 5.40192i) q^{69} -41.5921 q^{70} -123.624i q^{71} +(-9.04019 - 74.6149i) q^{72} -81.1699 q^{73} +129.527i q^{74} +(3.44375 + 57.0552i) q^{75} +12.0420 q^{76} -83.1764i q^{77} +(66.1646 - 3.99358i) q^{78} -45.7843 q^{79} +34.6823i q^{80} +(78.6564 - 19.3436i) q^{81} -5.07404 q^{82} +144.462i q^{83} +(-0.656325 - 10.8738i) q^{84} +67.4288 q^{85} +27.8430i q^{86} +(-49.8036 + 3.00606i) q^{87} -77.2343 q^{88} +8.00625i q^{89} +(-41.3191 + 5.00614i) q^{90} +104.787 q^{91} -12.0668i q^{92} +(-2.08224 - 34.4980i) q^{93} -28.5365 q^{94} -72.7332i q^{95} +(-19.2683 + 1.16300i) q^{96} -41.6023 q^{97} +60.4684i q^{98} +(-10.0114 - 82.6306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.89638i			0.948189i	0.880474	+	0.474094i	$0.157224\pi$
$2$			1.89638i			0.948189i	−0.880474	+	0.474094i	$0.842776\pi$
$3$	0.180746	+	2.99455i	0.0602486	+	0.998183i
$3$	0.180746	+	2.99455i	0.0602486	+	0.998183i
$4$	0.403751			0.100938
$5$		−	2.43864i		−	0.487728i	−0.969809	−	0.243864i	$-0.921585\pi$
$5$		−	2.43864i		−	0.487728i	0.969809	−	0.243864i	$-0.0784151\pi$
$6$	−5.67880	+	0.342762i	−0.946466	+	0.0571271i
$7$	−8.99368			−1.28481			−0.642406	−	0.766365i	$-0.722064\pi$
$7$	−8.99368			−1.28481			−0.642406	+	0.766365i	$0.722064\pi$
$8$			8.35118i			1.04390i
$9$	−8.93466	+	1.08250i	−0.992740	+	0.120278i
$10$	4.62459			0.462459
$11$			9.24832i			0.840756i	0.907349	+	0.420378i	$0.138103\pi$
$11$			9.24832i			0.840756i	−0.907349	+	0.420378i	$0.861897\pi$
$12$	0.0729763	+	1.20905i	0.00608136	+	0.100754i
$13$	−11.6512			−0.896243			−0.448121	−	0.893973i	$-0.647907\pi$
$13$	−11.6512			−0.896243			−0.448121	+	0.893973i	$0.647907\pi$
$14$		−	17.0554i		−	1.21824i
$15$	7.30264	−	0.440774i	0.486842	−	0.0293850i
$16$	−14.2220			−0.888874
$17$			27.6502i			1.62648i	0.581929	+	0.813240i	$0.302298\pi$
$17$			27.6502i			1.62648i	−0.581929	+	0.813240i	$0.697702\pi$
$18$	−2.05284	−	16.9435i	−0.114047	−	0.941305i
$19$	29.8253			1.56975			0.784876	−	0.619652i	$-0.212726\pi$
$19$	29.8253			1.56975			0.784876	+	0.619652i	$0.212726\pi$
$20$		−	0.984604i		−	0.0492302i
$21$	−1.62557	−	26.9320i	−0.0774081	−	1.28248i
$22$	−17.5383			−0.797196
$23$		−	29.8868i		−	1.29943i	−0.760179	−	0.649714i	$-0.774889\pi$
$23$		−	29.8868i		−	1.29943i	0.760179	−	0.649714i	$-0.225111\pi$
$24$	−25.0080	+	1.50944i	−1.04200	+	0.0628933i
$25$	19.0530			0.762121
$26$		−	22.0950i		−	0.849807i
$27$	−4.85652	−	26.5596i	−0.179871	−	0.983690i
$28$	−3.63121			−0.129686
$29$			16.6314i			0.573497i	0.958006	+	0.286748i	$0.0925744\pi$
$29$			16.6314i			0.573497i	−0.958006	+	0.286748i	$0.907426\pi$
$30$	0.835875	+	13.8486i	0.0278625	+	0.461619i
$31$	−11.5203			−0.371621			−0.185811	−	0.982586i	$-0.559491\pi$
$31$	−11.5203			−0.371621			−0.185811	+	0.982586i	$0.559491\pi$
$32$			6.43445i			0.201077i
$33$	−27.6946	+	1.67160i	−0.839229	+	0.0506544i
$34$	−52.4351			−1.54221
$35$			21.9324i			0.626639i
$36$	−3.60738	+	0.437062i	−0.100205	+	0.0121406i
$37$	68.3024			1.84601			0.923006	−	0.384786i	$-0.125725\pi$
$37$	68.3024			1.84601			0.923006	+	0.384786i	$0.125725\pi$
$38$			56.5600i			1.48842i
$39$	−2.10590	−	34.8900i	−0.0539974	−	0.894615i
$40$	20.3655			0.509138
$41$			2.67565i			0.0652597i	0.999468	+	0.0326299i	$0.0103883\pi$
$41$			2.67565i			0.0652597i	−0.999468	+	0.0326299i	$0.989612\pi$
$42$	51.0733	−	3.08269i	1.21603	−	0.0733975i
$43$	14.6822			0.341447			0.170723	−	0.985319i	$-0.445390\pi$
$43$	14.6822			0.341447			0.170723	+	0.985319i	$0.445390\pi$
$44$			3.73402i			0.0848641i
$45$	2.63984	+	21.7884i	0.0586632	+	0.484188i
$46$	56.6767			1.23210
$47$			15.0479i			0.320169i	0.987103	+	0.160084i	$0.0511766\pi$
$47$			15.0479i			0.320169i	−0.987103	+	0.160084i	$0.948823\pi$
$48$	−2.57056	−	42.5884i	−0.0535534	−	0.887259i
$49$	31.8863			0.650740
$50$			36.1317i			0.722635i
$51$	−82.7998	+	4.99765i	−1.62353	+	0.0979931i
$52$	−4.70417			−0.0904647
$53$			67.2208i			1.26832i	0.773203	+	0.634159i	$0.218653\pi$
$53$			67.2208i			1.26832i	−0.773203	+	0.634159i	$0.781347\pi$
$54$	50.3671	−	9.20979i	0.932724	−	0.170552i
$55$	22.5533			0.410061
$56$		−	75.1078i		−	1.34121i
$57$	5.39080	+	89.3134i	0.0945754	+	1.56690i
$58$	−31.5394			−0.543783
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	2.94845	−	0.177963i	0.0491408	−	0.00296605i
$61$	102.337			1.67766			0.838830	−	0.544393i	$-0.183240\pi$
$61$	102.337			1.67766			0.838830	+	0.544393i	$0.183240\pi$
$62$		−	21.8468i		−	0.352367i
$63$	80.3555	−	9.73570i	1.27548	−	0.154535i
$64$	−69.0901			−1.07953
$65$			28.4130i			0.437123i
$66$	−3.16998	−	52.5193i	−0.0480299	−	0.795748i
$67$	−55.2408			−0.824489			−0.412245	−	0.911073i	$-0.635255\pi$
$67$	−55.2408			−0.824489			−0.412245	+	0.911073i	$0.635255\pi$
$68$			11.1638i			0.164173i
$69$	89.4976	−	5.40192i	1.29707	−	0.0782887i
$70$	−41.5921			−0.594172
$71$		−	123.624i		−	1.74118i	−0.492009	−	0.870590i	$-0.663737\pi$
$71$		−	123.624i		−	1.74118i	0.492009	−	0.870590i	$-0.336263\pi$
$72$	−9.04019	−	74.6149i	−0.125558	−	1.03632i
$73$	−81.1699			−1.11192			−0.555958	−	0.831210i	$-0.687649\pi$
$73$	−81.1699			−1.11192			−0.555958	+	0.831210i	$0.687649\pi$
$74$			129.527i			1.75037i
$75$	3.44375	+	57.0552i	0.0459167	+	0.760736i
$76$	12.0420			0.158447
$77$		−	83.1764i		−	1.08021i
$78$	66.1646	−	3.99358i	0.848264	−	0.0511997i
$79$	−45.7843			−0.579549			−0.289774	−	0.957095i	$-0.593580\pi$
$79$	−45.7843			−0.579549			−0.289774	+	0.957095i	$0.593580\pi$
$80$			34.6823i			0.433529i
$81$	78.6564	−	19.3436i	0.971066	−	0.238810i
$82$	−5.07404			−0.0618786
$83$			144.462i			1.74051i	0.492606	+	0.870253i	$0.336044\pi$
$83$			144.462i			1.74051i	−0.492606	+	0.870253i	$0.663956\pi$
$84$	−0.656325	−	10.8738i	−0.00781340	−	0.129450i
$85$	67.4288			0.793280
$86$			27.8430i			0.323756i
$87$	−49.8036	+	3.00606i	−0.572455	+	0.0345524i
$88$	−77.2343			−0.877663
$89$			8.00625i			0.0899578i	0.998988	+	0.0449789i	$0.0143221\pi$
$89$			8.00625i			0.0899578i	−0.998988	+	0.0449789i	$0.985678\pi$
$90$	−41.3191	+	5.00614i	−0.459101	+	0.0556238i
$91$	104.787			1.15150
$92$		−	12.0668i		−	0.131161i
$93$	−2.08224	−	34.4980i	−0.0223897	−	0.370946i
$94$	−28.5365			−0.303580
$95$		−	72.7332i		−	0.765613i
$96$	−19.2683	+	1.16300i	−0.200711	+	0.0121146i
$97$	−41.6023			−0.428890			−0.214445	−	0.976736i	$-0.568794\pi$
$97$	−41.6023			−0.428890			−0.214445	+	0.976736i	$0.568794\pi$
$98$			60.4684i			0.617024i
$99$	−10.0114	−	82.6306i	−0.101125	−	0.834653i
$100$	7.69268			0.0769268
$101$			10.6631i			0.105575i	0.998606	+	0.0527874i	$0.0168106\pi$
$101$			10.6631i			0.105575i	−0.998606	+	0.0527874i	$0.983189\pi$
$102$	−9.47743	−	157.020i	−0.0929160	−	1.53941i
$103$	67.0506			0.650977			0.325488	−	0.945546i	$-0.394471\pi$
$103$	67.0506			0.650977			0.325488	+	0.945546i	$0.394471\pi$
$104$		−	97.3008i		−	0.935585i
$105$	−65.6776	+	3.96418i	−0.625501	+	0.0377541i
$106$	−127.476			−1.20260
$107$		−	52.2979i		−	0.488765i	−0.969679	−	0.244383i	$-0.921415\pi$
$107$		−	52.2979i		−	0.488765i	0.969679	−	0.244383i	$-0.0785853\pi$
$108$	−1.96082	−	10.7235i	−0.0181558	−	0.0992915i
$109$	−83.2905			−0.764133			−0.382066	−	0.924135i	$-0.624787\pi$
$109$	−83.2905			−0.764133			−0.382066	+	0.924135i	$0.624787\pi$
$110$			42.7697i			0.388815i
$111$	12.3454	+	204.535i	0.111220	+	1.84266i
$112$	127.908			1.14204
$113$			105.890i			0.937079i	0.883443	+	0.468539i	$0.155220\pi$
$113$			105.890i			0.937079i	−0.883443	+	0.468539i	$0.844780\pi$
$114$	−169.372	+	10.2230i	−1.48572	+	0.0896754i
$115$	−72.8833			−0.633768
$116$			6.71495i			0.0578875i
$117$	104.099	−	12.6124i	0.889736	−	0.107799i
$118$	14.5664			0.123444
$119$		−	248.677i		−	2.08972i
$120$	3.68098	+	60.9856i	0.0306749	+	0.508213i
$121$	35.4686			0.293129
$122$			194.070i			1.59074i
$123$	−8.01237	+	0.483612i	−0.0651412	+	0.00393181i
$124$	−4.65132			−0.0375106
$125$		−	107.430i		−	0.859437i
$126$	18.4626	+	152.384i	0.146528	+	1.20940i
$127$	−127.874			−1.00688			−0.503442	−	0.864029i	$-0.667933\pi$
$127$	−127.874			−1.00688			−0.503442	+	0.864029i	$0.667933\pi$
$128$		−	105.283i		−	0.822524i
$129$	2.65375	+	43.9666i	0.0205717	+	0.340826i
$130$	−53.8818			−0.414475
$131$		−	135.750i		−	1.03626i	−0.855302	−	0.518130i	$-0.826628\pi$
$131$		−	135.750i		−	1.03626i	0.855302	−	0.518130i	$-0.173372\pi$
$132$	−11.1817	+	0.674908i	−0.0847099	+	0.00511294i
$133$	−268.239			−2.01684
$134$		−	104.757i		−	0.781772i
$135$	−64.7695	+	11.8433i	−0.479774	+	0.0877282i
$136$	−230.911			−1.69788
$137$			0.886492i			0.00647074i	0.999995	+	0.00323537i	$0.00102985\pi$
$137$			0.886492i			0.00647074i	−0.999995	+	0.00323537i	$0.998970\pi$
$138$	10.2441	+	169.721i	0.0742324	+	1.22986i
$139$	−28.7731			−0.207001			−0.103500	−	0.994629i	$-0.533004\pi$
$139$	−28.7731			−0.207001			−0.103500	+	0.994629i	$0.533004\pi$
$140$			8.85522i			0.0632515i
$141$	−45.0618	+	2.71985i	−0.319587	+	0.0192897i
$142$	234.437			1.65097
$143$		−	107.754i		−	0.753522i
$144$	127.069	−	15.3954i	0.882421	−	0.106912i
$145$	40.5581			0.279711
$146$		−	153.929i		−	1.05431i
$147$	5.76331	+	95.4850i	0.0392062	+	0.649558i
$148$	27.5772			0.186332
$149$		−	134.861i		−	0.905106i	−0.891737	−	0.452553i	$-0.850513\pi$
$149$		−	134.861i		−	0.905106i	0.891737	−	0.452553i	$-0.149487\pi$
$150$	−108.198	+	6.53066i	−0.721322	+	0.0435377i
$151$	265.411			1.75769			0.878843	−	0.477110i	$-0.158316\pi$
$151$	265.411			1.75769			0.878843	+	0.477110i	$0.158316\pi$
$152$			249.076i			1.63866i
$153$	−29.9314	−	247.045i	−0.195630	−	1.61467i
$154$	157.734			1.02425
$155$			28.0938i			0.181250i
$156$	−0.850258	−	14.0869i	−0.00545037	−	0.0903004i
$157$	120.706			0.768826			0.384413	−	0.923161i	$-0.374404\pi$
$157$	120.706			0.768826			0.384413	+	0.923161i	$0.374404\pi$
$158$		−	86.8244i		−	0.549522i
$159$	−201.296	+	12.1499i	−1.26601	+	0.0764143i
$160$	15.6913			0.0980708
$161$			268.792i			1.66952i
$162$	36.6828	+	149.162i	0.226437	+	0.920754i
$163$	266.809			1.63686			0.818432	−	0.574603i	$-0.194844\pi$
$163$	266.809			1.63686			0.818432	+	0.574603i	$0.194844\pi$
$164$			1.08030i			0.00658717i
$165$	4.07642	+	67.5371i	0.0247056	+	0.409316i
$166$	−273.954			−1.65033
$167$			165.193i			0.989179i	0.869127	+	0.494589i	$0.164682\pi$
$167$			165.193i			0.989179i	−0.869127	+	0.494589i	$0.835318\pi$
$168$	224.914	−	13.5754i	1.33877	−	0.0808061i
$169$	−33.2506			−0.196749
$170$			127.871i			0.752180i
$171$	−266.479	+	32.2860i	−1.55836	+	0.188807i
$172$	5.92796			0.0344649
$173$			4.59582i			0.0265654i	0.999912	+	0.0132827i	$0.00422814\pi$
$173$			4.59582i			0.0265654i	−0.999912	+	0.0132827i	$0.995772\pi$
$174$	−5.70062	−	94.4464i	−0.0327622	−	0.542796i
$175$	−171.357			−0.979182
$176$		−	131.529i		−	0.747326i
$177$	23.0016	−	1.38833i	0.129952	−	0.00784370i
$178$	−15.1829			−0.0852970
$179$		−	201.860i		−	1.12771i	−0.825875	−	0.563854i	$-0.809318\pi$
$179$		−	201.860i		−	1.12771i	0.825875	−	0.563854i	$-0.190682\pi$
$180$	1.06584	+	8.79711i	0.00592133	+	0.0488728i
$181$	59.5716			0.329125			0.164562	−	0.986367i	$-0.447379\pi$
$181$	59.5716			0.329125			0.164562	+	0.986367i	$0.447379\pi$
$182$			198.715i			1.09184i
$183$	18.4970	+	306.454i	0.101077	+	1.67461i
$184$	249.590			1.35647
$185$		−	166.565i		−	0.900352i
$186$	65.4213	−	3.94871i	0.351727	−	0.0212296i
$187$	−255.717			−1.36747
$188$			6.07561i			0.0323171i
$189$	43.6780	+	238.869i	0.231100	+	1.26386i
$190$	137.930			0.725946
$191$		−	224.796i		−	1.17694i	−0.808519	−	0.588470i	$-0.799730\pi$
$191$		−	224.796i		−	1.17694i	0.808519	−	0.588470i	$-0.200270\pi$
$192$	−12.4877	−	206.894i	−0.0650403	−	1.07757i
$193$	120.501			0.624357			0.312178	−	0.950024i	$-0.398941\pi$
$193$	120.501			0.624357			0.312178	+	0.950024i	$0.398941\pi$
$194$		−	78.8937i		−	0.406669i
$195$	−85.0842	+	5.13553i	−0.436329	+	0.0263361i
$196$	12.8741			0.0656842
$197$			39.8294i			0.202180i	0.994877	+	0.101090i	$0.0322330\pi$
$197$			39.8294i			0.202180i	−0.994877	+	0.101090i	$0.967767\pi$
$198$	156.699	−	18.9853i	0.791408	−	0.0958854i
$199$	−74.5626			−0.374687			−0.187343	−	0.982295i	$-0.559988\pi$
$199$	−74.5626			−0.374687			−0.187343	+	0.982295i	$0.559988\pi$
$200$			159.115i			0.795576i
$201$	−9.98454	−	165.421i	−0.0496743	−	0.822991i
$202$	−20.2212			−0.100105
$203$		−	149.578i		−	0.736835i
$204$	−33.4305	+	2.01781i	−0.163875	+	0.00989121i
$205$	6.52495			0.0318290
$206$			127.153i			0.617249i
$207$	32.3526	+	267.029i	0.156293	+	1.28999i
$208$	165.702			0.796647
$209$			275.834i			1.31978i
$210$	−7.51759	−	124.549i	−0.0357980	−	0.593093i
$211$	400.704			1.89907			0.949536	−	0.313658i	$-0.101555\pi$
$211$	400.704			1.89907			0.949536	+	0.313658i	$0.101555\pi$
$212$			27.1405i			0.128021i
$213$	370.198	−	22.3445i	1.73802	−	0.104904i
$214$	99.1765			0.463442
$215$		−	35.8047i		−	0.166533i
$216$	221.804	−	40.5576i	1.02687	−	0.187767i
$217$	103.610			0.477463
$218$		−	157.950i		−	0.724542i
$219$	−14.6711	−	243.067i	−0.0669914	−	1.10990i
$220$	9.10594			0.0413906
$221$		−	322.156i		−	1.45772i
$222$	−387.876	+	23.4115i	−1.74719	+	0.105457i
$223$	−318.939			−1.43022			−0.715110	−	0.699012i	$-0.753623\pi$
$223$	−318.939			−1.43022			−0.715110	+	0.699012i	$0.753623\pi$
$224$		−	57.8694i		−	0.258346i
$225$	−170.232	+	20.6250i	−0.756588	+	0.0916666i
$226$	−200.807			−0.888528
$227$			13.1790i			0.0580573i	0.999579	+	0.0290287i	$0.00924141\pi$
$227$			13.1790i			0.0580573i	−0.999579	+	0.0290287i	$0.990759\pi$
$228$	2.17654	+	36.0604i	0.00954623	+	0.158160i
$229$	134.842			0.588832			0.294416	−	0.955677i	$-0.404875\pi$
$229$	134.842			0.588832			0.294416	+	0.955677i	$0.404875\pi$
$230$		−	138.214i		−	0.600931i
$231$	249.076	−	15.0338i	1.07825	−	0.0650813i
$232$	−138.892			−0.598672
$233$		−	67.8138i		−	0.291046i	−0.989355	−	0.145523i	$-0.953513\pi$
$233$		−	67.8138i		−	0.291046i	0.989355	−	0.145523i	$-0.0464865\pi$
$234$	23.9179	+	197.411i	0.102213	+	0.843638i
$235$	36.6965			0.156155
$236$		−	3.10127i		−	0.0131410i
$237$	−8.27533	−	137.104i	−0.0349170	−	0.578496i
$238$	471.585			1.98145
$239$			91.0150i			0.380816i	0.981705	+	0.190408i	$0.0609811\pi$
$239$			91.0150i			0.380816i	−0.981705	+	0.190408i	$0.939019\pi$
$240$	−103.858	+	6.26868i	−0.432742	+	0.0261195i
$241$	212.975			0.883714			0.441857	−	0.897086i	$-0.354320\pi$
$241$	212.975			0.883714			0.441857	+	0.897086i	$0.354320\pi$
$242$			67.2618i			0.277941i
$243$	72.1423	+	232.044i	0.296882	+	0.954914i
$244$	41.3188			0.169339
$245$		−	77.7592i		−	0.317384i
$246$	−0.917112	−	15.1945i	−0.00372810	−	0.0617662i
$247$	−347.499			−1.40688
$248$		−	96.2077i		−	0.387934i
$249$	−432.598	+	26.1109i	−1.73734	+	0.104863i
$250$	203.727			0.814908
$251$			198.118i			0.789314i	0.918829	+	0.394657i	$0.129137\pi$
$251$			198.118i			0.789314i	−0.918829	+	0.394657i	$0.870863\pi$
$252$	32.4436	−	3.93080i	0.128744	−	0.0155984i
$253$	276.403			1.09250
$254$		−	242.498i		−	0.954716i
$255$	12.1875	+	201.919i	0.0477940	+	0.791839i
$256$	−76.7038			−0.299624
$257$			269.943i			1.05036i	0.850991	+	0.525181i	$0.176002\pi$
$257$			269.943i			1.05036i	−0.850991	+	0.525181i	$0.823998\pi$
$258$	−83.3773	+	5.03251i	−0.323168	+	0.0195058i
$259$	−614.290			−2.37178
$260$			11.4718i			0.0441222i
$261$	−18.0036	−	148.596i	−0.0689792	−	0.569334i
$262$	257.433			0.982570
$263$		−	62.6176i		−	0.238090i	−0.992889	−	0.119045i	$-0.962017\pi$
$263$		−	62.6176i		−	0.238090i	0.992889	−	0.119045i	$-0.0379833\pi$
$264$	−13.9598	−	231.282i	−0.0528780	−	0.876069i
$265$	163.927			0.618594
$266$		−	508.683i		−	1.91234i
$267$	−23.9751	+	1.44710i	−0.0897944	+	0.00541983i
$268$	−22.3035			−0.0832221
$269$			103.492i			0.384728i	0.981324	+	0.192364i	$0.0616154\pi$
$269$			103.492i			0.384728i	−0.981324	+	0.192364i	$0.938385\pi$
$270$	−22.4594	−	122.827i	−0.0831829	−	0.454916i
$271$	−264.533			−0.976137			−0.488069	−	0.872805i	$-0.662298\pi$
$271$	−264.533			−0.976137			−0.488069	+	0.872805i	$0.662298\pi$
$272$		−	393.240i		−	1.44574i
$273$	18.9398	+	313.789i	0.0693764	+	1.14941i
$274$	−1.68112			−0.00613549
$275$			176.208i			0.640758i
$276$	36.1347	−	2.18103i	0.130923	−	0.00790228i
$277$	−47.1067			−0.170060			−0.0850301	−	0.996378i	$-0.527099\pi$
$277$	−47.1067			−0.170060			−0.0850301	+	0.996378i	$0.527099\pi$
$278$		−	54.5646i		−	0.196276i
$279$	102.930	−	12.4707i	0.368923	−	0.0446980i
$280$	−183.161			−0.654147
$281$			202.879i			0.721989i	0.932568	+	0.360995i	$0.117563\pi$
$281$			202.879i			0.721989i	−0.932568	+	0.360995i	$0.882437\pi$
$282$	−5.15786	−	85.4541i	−0.0182903	−	0.303029i
$283$	−71.1501			−0.251414			−0.125707	−	0.992067i	$-0.540120\pi$
$283$	−71.1501			−0.251414			−0.125707	+	0.992067i	$0.540120\pi$
$284$		−	49.9132i		−	0.175751i
$285$	217.803	−	13.1462i	0.764222	−	0.0461271i
$286$	204.342			0.714481
$287$		−	24.0639i		−	0.0838464i
$288$	−6.96533	−	57.4897i	−0.0241852	−	0.199617i
$289$	−475.531			−1.64544
$290$			76.9134i			0.265219i
$291$	−7.51944	−	124.580i	−0.0258400	−	0.428111i
$292$	−32.7724			−0.112234
$293$		−	224.865i		−	0.767458i	−0.923446	−	0.383729i	$-0.874640\pi$
$293$		−	224.865i		−	0.767458i	0.923446	−	0.383729i	$-0.125360\pi$
$294$	−181.076	+	10.9294i	−0.615903	+	0.0371749i
$295$	−18.7316			−0.0634968
$296$			570.406i			1.92705i
$297$	245.632	−	44.9146i	0.827044	−	0.151228i
$298$	255.747			0.858212
$299$			348.216i			1.16460i
$300$	1.39042	+	23.0361i	0.00463473	+	0.0767870i
$301$	−132.047			−0.438695
$302$			503.319i			1.66662i
$303$	−31.9310	+	1.92730i	−0.105383	+	0.00636073i
$304$	−424.175			−1.39531
$305$		−	249.564i		−	0.818243i
$306$	468.490	−	56.7613i	1.53101	−	0.185494i
$307$	−582.919			−1.89876			−0.949380	−	0.314130i	$-0.898287\pi$
$307$	−582.919			−1.89876			−0.949380	+	0.314130i	$0.898287\pi$
$308$		−	33.5826i		−	0.109034i
$309$	12.1191	+	200.786i	0.0392204	+	0.649794i
$310$	−53.2765			−0.171860
$311$			288.317i			0.927064i	0.886080	+	0.463532i	$0.153418\pi$
$311$			288.317i			0.927064i	−0.886080	+	0.463532i	$0.846582\pi$
$312$	291.372	−	17.5867i	0.933885	−	0.0563677i
$313$	45.4385			0.145171			0.0725855	−	0.997362i	$-0.476875\pi$
$313$	45.4385			0.145171			0.0725855	+	0.997362i	$0.476875\pi$
$314$			228.904i			0.728993i
$315$	−23.7419	−	195.958i	−0.0753711	−	0.622090i
$316$	−18.4855			−0.0584983
$317$		−	135.104i		−	0.426197i	−0.977031	−	0.213099i	$-0.931644\pi$
$317$		−	135.104i		−	0.426197i	0.977031	−	0.213099i	$-0.0683555\pi$
$318$	−23.0408	−	381.733i	−0.0724552	−	1.20042i
$319$	−153.813			−0.482171
$320$			168.486i			0.526519i
$321$	156.609	−	9.45262i	0.487877	−	0.0294474i
$322$	−509.732			−1.58302
$323$			824.674i			2.55317i
$324$	31.7576	−	7.81001i	0.0980173	−	0.0241050i
$325$	−221.990			−0.683045
$326$			505.971i			1.55206i
$327$	−15.0544	−	249.418i	−0.0460379	−	0.762745i
$328$	−22.3448			−0.0681244
$329$		−	135.336i		−	0.411356i
$330$	−128.076	+	7.73044i	−0.388109	+	0.0234256i
$331$	12.7021			0.0383748			0.0191874	−	0.999816i	$-0.493892\pi$
$331$	12.7021			0.0383748			0.0191874	+	0.999816i	$0.493892\pi$
$332$			58.3267i			0.175683i
$333$	−610.259	+	73.9377i	−1.83261	+	0.222035i
$334$	−313.268			−0.937928
$335$			134.712i			0.402127i
$336$	23.1188	+	383.027i	0.0688060	+	1.13996i
$337$	459.719			1.36415			0.682076	−	0.731281i	$-0.261077\pi$
$337$	459.719			1.36415			0.682076	+	0.731281i	$0.261077\pi$
$338$		−	63.0557i		−	0.186555i
$339$	−317.093	+	19.1392i	−0.935377	+	0.0564577i
$340$	27.2245			0.0800719
$341$		−	106.543i		−	0.312443i
$342$	−61.2265	−	505.345i	−0.179025	−	1.47762i
$343$	153.916			0.448733
$344$			122.614i			0.356435i
$345$	−13.1733	−	218.253i	−0.0381836	−	0.632616i
$346$	−8.71540			−0.0251890
$347$		−	77.6938i		−	0.223901i	−0.993714	−	0.111951i	$-0.964290\pi$
$347$		−	77.6938i		−	0.223901i	0.993714	−	0.111951i	$-0.0357099\pi$
$348$	−20.1083	+	1.21370i	−0.0577823	+	0.00348764i
$349$	−263.372			−0.754649			−0.377324	−	0.926081i	$-0.623156\pi$
$349$	−263.372			−0.754649			−0.377324	+	0.926081i	$0.623156\pi$
$350$		−	324.957i		−	0.928449i
$351$	56.5840	+	309.450i	0.161208	+	0.881625i
$352$	−59.5079			−0.169057
$353$		−	314.961i		−	0.892242i	−0.894973	−	0.446121i	$-0.852805\pi$
$353$		−	314.961i		−	0.892242i	0.894973	−	0.446121i	$-0.147195\pi$
$354$	2.63281	+	43.6197i	0.00743731	+	0.123219i
$355$	−301.474			−0.849223
$356$			3.23253i			0.00908014i
$357$	744.675	−	44.9473i	2.08592	−	0.125903i
$358$	382.802			1.06928
$359$		−	373.835i		−	1.04132i	−0.853763	−	0.520661i	$-0.825685\pi$
$359$		−	373.835i		−	1.04132i	0.853763	−	0.520661i	$-0.174315\pi$
$360$	−181.959	+	22.0458i	−0.505442	+	0.0612383i
$361$	528.549			1.46412
$362$			112.970i			0.312073i
$363$	6.41080	+	106.212i	0.0176606	+	0.292596i
$364$	42.3078			0.116230
$365$			197.944i			0.542313i
$366$	−581.153	+	35.0774i	−1.58785	+	0.0958398i
$367$	−225.537			−0.614541			−0.307271	−	0.951622i	$-0.599416\pi$
$367$	−225.537			−0.614541			−0.307271	+	0.951622i	$0.599416\pi$
$368$			425.050i			1.15503i
$369$	−2.89640	−	23.9060i	−0.00784933	−	0.0647860i
$370$	315.871			0.853704
$371$		−	604.562i		−	1.62955i
$372$	−0.840706	−	13.9286i	−0.00225996	−	0.0374425i
$373$	400.892			1.07478			0.537389	−	0.843334i	$-0.319411\pi$
$373$	400.892			1.07478			0.537389	+	0.843334i	$0.319411\pi$
$374$		−	484.937i		−	1.29662i
$375$	321.703	−	19.4174i	0.857875	−	0.0517798i
$376$	−125.668			−0.334223
$377$		−	193.775i		−	0.513992i
$378$	−452.986	+	82.8299i	−1.19837	+	0.219127i
$379$	−335.706			−0.885769			−0.442884	−	0.896579i	$-0.646045\pi$
$379$	−335.706			−0.885769			−0.442884	+	0.896579i	$0.646045\pi$
$380$		−	29.3661i		−	0.0772793i
$381$	−23.1127	−	382.926i	−0.0606634	−	1.00506i
$382$	426.297			1.11596
$383$		−	599.733i		−	1.56588i	−0.622096	−	0.782941i	$-0.713719\pi$
$383$		−	599.733i		−	1.56588i	0.622096	−	0.782941i	$-0.286281\pi$
$384$	315.275	−	19.0295i	0.821030	−	0.0495559i
$385$	−202.838			−0.526851
$386$			228.515i			0.592008i
$387$	−131.181	+	15.8936i	−0.338968	+	0.0410686i
$388$	−16.7970			−0.0432912
$389$			107.907i			0.277397i	0.990335	+	0.138698i	$0.0442918\pi$
$389$			107.907i			0.277397i	−0.990335	+	0.138698i	$0.955708\pi$
$390$	−9.73891	−	161.352i	−0.0249716	−	0.413722i
$391$	826.375			2.11349
$392$			266.288i			0.679305i
$393$	406.510	−	24.5363i	1.03438	−	0.0624332i
$394$	−75.5316			−0.191705
$395$			111.652i			0.282662i
$396$	−4.04209	−	33.3622i	−0.0102073	−	0.0842480i
$397$	−178.931			−0.450707			−0.225353	−	0.974277i	$-0.572354\pi$
$397$	−178.931			−0.450707			−0.225353	+	0.974277i	$0.572354\pi$
$398$		−	141.399i		−	0.355274i
$399$	−48.4831	−	803.256i	−0.121512	−	2.01317i
$400$	−270.972			−0.677429
$401$		−	218.712i		−	0.545416i	−0.962097	−	0.272708i	$-0.912081\pi$
$401$		−	218.712i		−	0.545416i	0.962097	−	0.272708i	$-0.0879194\pi$
$402$	313.701	−	18.9345i	0.780351	−	0.0471006i
$403$	134.224			0.333063
$404$			4.30522i			0.0106565i
$405$	−47.1722	−	191.815i	−0.116475	−	0.473617i
$406$	283.656			0.698659
$407$			631.683i			1.55205i
$408$	−41.7362	−	691.475i	−0.102295	−	1.69479i
$409$	−149.540			−0.365623			−0.182812	−	0.983148i	$-0.558520\pi$
$409$	−149.540			−0.365623			−0.182812	+	0.983148i	$0.558520\pi$
$410$			12.3738i			0.0301799i
$411$	−2.65464	+	0.160230i	−0.00645899	+	0.000389853i
$412$	27.0717			0.0657081
$413$			69.0818i			0.167268i
$414$	−506.387	+	61.3528i	−1.22316	+	0.148195i
$415$	352.291			0.848894
$416$		−	74.9688i		−	0.180214i
$417$	−5.20061	−	86.1624i	−0.0124715	−	0.206625i
$418$	−523.085			−1.25140
$419$		−	481.158i		−	1.14835i	−0.818733	−	0.574174i	$-0.805323\pi$
$419$		−	481.158i		−	1.14835i	0.818733	−	0.574174i	$-0.194677\pi$
$420$	−26.5174	+	1.60054i	−0.0631366	+	0.00381082i
$421$	433.117			1.02878			0.514391	−	0.857556i	$-0.328018\pi$
$421$	433.117			1.02878			0.514391	+	0.857556i	$0.328018\pi$
$422$			759.886i			1.80068i
$423$	−16.2894	−	134.448i	−0.0385093	−	0.317844i
$424$	−561.373			−1.32399
$425$			526.819i			1.23957i
$426$	42.3736	+	702.035i	0.0994685	+	1.64797i
$427$	−920.389			−2.15548
$428$		−	21.1153i		−	0.0493349i
$429$	322.674	−	19.4760i	0.752153	−	0.0453986i
$430$	67.8992			0.157905
$431$		−	374.706i		−	0.869387i	−0.900578	−	0.434693i	$-0.856857\pi$
$431$		−	374.706i		−	0.869387i	0.900578	−	0.434693i	$-0.143143\pi$
$432$	69.0693	+	377.731i	0.159883	+	0.874376i
$433$	77.4189			0.178796			0.0893982	−	0.995996i	$-0.471506\pi$
$433$	77.4189			0.178796			0.0893982	+	0.995996i	$0.471506\pi$
$434$			196.483i			0.452725i
$435$	7.33070	+	121.453i	0.0168522	+	0.279203i
$436$	−33.6286			−0.0771299
$437$		−	891.384i		−	2.03978i
$438$	460.948	−	27.8220i	1.05239	−	0.0635205i
$439$	770.006			1.75400			0.877000	−	0.480490i	$-0.159541\pi$
$439$	770.006			1.75400			0.877000	+	0.480490i	$0.159541\pi$
$440$			188.347i			0.428061i
$441$	−284.893	+	34.5170i	−0.646016	+	0.0782699i
$442$	610.930			1.38219
$443$			139.287i			0.314417i	0.987565	+	0.157208i	$0.0502494\pi$
$443$			139.287i			0.314417i	−0.987565	+	0.157208i	$0.949751\pi$
$444$	4.98446	+	82.5812i	0.0112263	+	0.185994i
$445$	19.5244			0.0438750
$446$		−	604.829i		−	1.35612i
$447$	403.847	−	24.3755i	0.903462	−	0.0545314i
$448$	621.374			1.38700
$449$			667.731i			1.48715i	0.668652	+	0.743576i	$0.266872\pi$
$449$			667.731i			1.48715i	−0.668652	+	0.743576i	$0.733128\pi$
$450$	−39.1128	−	322.825i	−0.0869173	−	0.717388i
$451$	−24.7453			−0.0548675
$452$			42.7532i			0.0945867i
$453$	47.9719	+	794.786i	0.105898	+	1.75449i
$454$	−24.9924			−0.0550493
$455$		−	255.537i		−	0.561621i
$456$	−745.872	+	45.0195i	−1.63568	+	0.0987270i
$457$	694.295			1.51925			0.759623	−	0.650364i	$-0.225384\pi$
$457$	694.295			1.51925			0.759623	+	0.650364i	$0.225384\pi$
$458$			255.712i			0.558324i
$459$	734.378	−	134.283i	1.59995	−	0.292557i
$460$	−29.4267			−0.0639711
$461$			612.964i			1.32964i	0.747004	+	0.664820i	$0.231492\pi$
$461$			612.964i			1.32964i	−0.747004	+	0.664820i	$0.768508\pi$
$462$	28.5097	+	472.342i	0.0617094	+	1.02239i
$463$	189.967			0.410296			0.205148	−	0.978731i	$-0.434233\pi$
$463$	189.967			0.410296			0.205148	+	0.978731i	$0.434233\pi$
$464$		−	236.532i		−	0.509766i
$465$	−84.1283	+	5.07784i	−0.180921	+	0.0109201i
$466$	128.601			0.275967
$467$		−	338.134i		−	0.724056i	−0.932167	−	0.362028i	$-0.882084\pi$
$467$		−	338.134i		−	0.724056i	0.932167	−	0.362028i	$-0.117916\pi$
$468$	42.0301	−	5.09228i	0.0898080	−	0.0108809i
$469$	496.818			1.05931
$470$			69.5904i			0.148065i
$471$	21.8171	+	361.459i	0.0463207	+	0.767430i
$472$	64.1466			0.135904
$473$			135.786i			0.287074i
$474$	260.000	−	15.6931i	0.548523	−	0.0331079i
$475$	568.262			1.19634
$476$		−	100.403i		−	0.210932i
$477$	−72.7668	−	600.595i	−0.152551	−	1.25911i
$478$	−172.599			−0.361086
$479$			102.071i			0.213092i	0.994308	+	0.106546i	$0.0339791\pi$
$479$			102.071i			0.213092i	−0.994308	+	0.106546i	$0.966021\pi$
$480$	2.83614	+	46.9885i	0.00590863	+	0.0978927i
$481$	−795.802			−1.65447
$482$			403.881i			0.837927i
$483$	−804.913	+	48.5831i	−1.66649	+	0.100586i
$484$	14.3205			0.0295878
$485$			101.453i			0.209182i
$486$	−440.043	+	136.809i	−0.905439	+	0.281500i
$487$	776.399			1.59425			0.797125	−	0.603815i	$-0.206353\pi$
$487$	776.399			1.59425			0.797125	+	0.603815i	$0.206353\pi$
$488$			854.637i			1.75130i
$489$	48.2246	+	798.973i	0.0986188	+	1.63389i
$490$	147.461			0.300940
$491$			364.534i			0.742432i	0.928546	+	0.371216i	$0.121059\pi$
$491$			364.534i			0.742432i	−0.928546	+	0.371216i	$0.878941\pi$
$492$	−3.23500	+	0.195259i	−0.00657521	+	0.000396868i
$493$	−459.861			−0.932781
$494$		−	658.990i		−	1.33399i
$495$	−201.507	+	24.4141i	−0.407084	+	0.0493214i
$496$	163.841			0.330324
$497$			1111.83i			2.23709i
$498$	−49.5161	−	820.370i	−0.0994299	−	1.64733i
$499$	−323.663			−0.648624			−0.324312	−	0.945950i	$-0.605133\pi$
$499$	−323.663			−0.648624			−0.324312	+	0.945950i	$0.605133\pi$
$500$		−	43.3748i		−	0.0867496i
$501$	−494.678	+	29.8579i	−0.987382	+	0.0595966i
$502$	−375.706			−0.748418
$503$		−	241.598i		−	0.480314i	−0.970734	−	0.240157i	$-0.922801\pi$
$503$		−	241.598i		−	0.480314i	0.970734	−	0.240157i	$-0.0771990\pi$
$504$	81.3045	+	671.063i	0.161319	+	1.33147i
$505$	26.0034			0.0514918
$506$			524.164i			1.03590i
$507$	−6.00991	−	99.5706i	−0.0118539	−	0.196392i
$508$	−51.6294			−0.101633
$509$			18.3011i			0.0359549i	0.999838	+	0.0179775i	$0.00572271\pi$
$509$			18.3011i			0.0359549i	−0.999838	+	0.0179775i	$0.994277\pi$
$510$	−382.915	+	23.1121i	−0.750813	+	0.0453178i
$511$	730.016			1.42860
$512$		−	566.592i		−	1.10662i
$513$	−144.847	−	792.149i	−0.282353	−	1.54415i
$514$	−511.914			−0.995941
$515$		−	163.512i		−	0.317500i
$516$	1.07145	+	17.7516i	0.00207646	+	0.0344023i
$517$	−139.168			−0.269184
$518$		−	1164.93i		−	2.24889i
$519$	−13.7624	+	0.830674i	−0.0265171	+	0.00160053i
$520$	−237.282			−0.456311
$521$			513.675i			0.985941i	0.870046	+	0.492970i	$0.164089\pi$
$521$			513.675i			0.985941i	−0.870046	+	0.492970i	$0.835911\pi$
$522$	281.794	−	34.1416i	0.539836	−	0.0654054i
$523$	259.010			0.495239			0.247619	−	0.968857i	$-0.420352\pi$
$523$	259.010			0.495239			0.247619	+	0.968857i	$0.420352\pi$
$524$		−	54.8092i		−	0.104598i
$525$	−30.9720	−	513.136i	−0.0589943	−	0.977403i
$526$	118.747			0.225754
$527$		−	318.537i		−	0.604435i
$528$	393.871	−	23.7734i	0.745969	−	0.0450254i
$529$	−364.222			−0.688511
$530$			310.868i			0.586544i
$531$	8.31488	+	68.6284i	0.0156589	+	0.129244i
$532$	−108.302			−0.203575
$533$		−	31.1744i		−	0.0584886i
$534$	−2.74424	−	45.4659i	−0.00513903	−	0.0851421i
$535$	−127.536			−0.238385
$536$		−	461.325i		−	0.860682i
$537$	604.479	−	36.4853i	1.12566	−	0.0679428i
$538$	−196.259			−0.364794
$539$			294.894i			0.547114i
$540$	−26.1507	+	4.78175i	−0.0484273	+	0.00885509i
$541$	−314.149			−0.580682			−0.290341	−	0.956923i	$-0.593769\pi$
$541$	−314.149			−0.580682			−0.290341	+	0.956923i	$0.593769\pi$
$542$		−	501.655i		−	0.925563i
$543$	10.7673	+	178.390i	0.0198293	+	0.328527i
$544$	−177.914			−0.327047
$545$			203.116i			0.372689i
$546$	−595.063	+	35.9169i	−1.08986	+	0.0657820i
$547$	953.073			1.74236			0.871182	−	0.490961i	$-0.163354\pi$
$547$	953.073			1.74236			0.871182	+	0.490961i	$0.163354\pi$
$548$			0.357922i			0.000653142i
$549$	−914.349	+	110.781i	−1.66548	+	0.201786i
$550$	−334.158			−0.607560
$551$			496.037i			0.900249i
$552$	45.1124	+	747.410i	0.0817253	+	1.35400i
$553$	411.770			0.744611
$554$		−	89.3321i		−	0.161249i
$555$	498.788	−	30.1060i	0.898717	−	0.0542450i
$556$	−11.6172			−0.0208942
$557$		−	36.2728i		−	0.0651217i	−0.999470	−	0.0325608i	$-0.989634\pi$
$557$		−	36.2728i		−	0.0651217i	0.999470	−	0.0325608i	$-0.0103663\pi$
$558$	23.6492	+	195.194i	0.0423821	+	0.349809i
$559$	−171.065			−0.306019
$560$		−	311.922i		−	0.557003i
$561$	−46.2199	−	765.759i	−0.0823883	−	1.36499i
$562$	−384.735			−0.684582
$563$			661.989i			1.17582i	0.808925	+	0.587912i	$0.200050\pi$
$563$			661.989i			1.17582i	−0.808925	+	0.587912i	$0.799950\pi$
$564$	−18.1937	+	1.09814i	−0.0322584	+	0.00194706i
$565$	258.228			0.457040
$566$		−	134.927i		−	0.238388i
$567$	−707.410	+	173.970i	−1.24764	+	0.306826i
$568$	1032.40			1.81761
$569$		−	303.170i		−	0.532813i	−0.963861	−	0.266406i	$-0.914164\pi$
$569$		−	303.170i		−	0.532813i	0.963861	−	0.266406i	$-0.0858363\pi$
$570$	24.9302	+	413.037i	0.0437372	+	0.724627i
$571$	144.133			0.252422			0.126211	−	0.992003i	$-0.459718\pi$
$571$	144.133			0.252422			0.126211	+	0.992003i	$0.459718\pi$
$572$		−	43.5056i		−	0.0760588i
$573$	673.162	−	40.6309i	1.17480	−	0.0709090i
$574$	45.6343			0.0795023
$575$		−	569.434i		−	0.990321i
$576$	617.297	−	74.7903i	1.07170	−	0.129844i
$577$	−1009.11			−1.74889			−0.874445	−	0.485125i	$-0.838774\pi$
$577$	−1009.11			−1.74889			−0.874445	+	0.485125i	$0.838774\pi$
$578$		−	901.787i		−	1.56018i
$579$	21.7800	+	360.846i	0.0376166	+	0.623222i
$580$	16.3754			0.0282334
$581$		−	1299.24i		−	2.23622i
$582$	236.251	−	14.2597i	0.405930	−	0.0245012i
$583$	−621.680			−1.06635
$584$		−	677.864i		−	1.16073i
$585$	−30.7572	−	253.861i	−0.0525764	−	0.433950i
$586$	426.429			0.727695
$587$		−	516.896i		−	0.880573i	−0.897857	−	0.440286i	$-0.854877\pi$
$587$		−	516.896i		−	0.880573i	0.897857	−	0.440286i	$-0.145123\pi$
$588$	2.32694	+	38.5522i	0.00395738	+	0.0655649i
$589$	−343.595			−0.583354
$590$		−	35.5221i		−	0.0602070i
$591$	−119.271	+	7.19900i	−0.201812	+	0.0121810i
$592$	−971.396			−1.64087
$593$		−	560.953i		−	0.945957i	−0.881074	−	0.472979i	$-0.843179\pi$
$593$		−	560.953i		−	0.945957i	0.881074	−	0.472979i	$-0.156821\pi$
$594$	85.1751	+	465.811i	0.143392	+	0.784194i
$595$	−606.433			−1.01922
$596$		−	54.4502i		−	0.0913594i
$597$	−13.4769	−	223.282i	−0.0225743	−	0.374006i
$598$	−660.349			−1.10426
$599$			736.447i			1.22946i	0.788738	+	0.614730i	$0.210735\pi$
$599$			736.447i			1.22946i	−0.788738	+	0.614730i	$0.789265\pi$
$600$	−476.478	+	28.7594i	−0.794131	+	0.0479323i
$601$	935.818			1.55710			0.778550	−	0.627582i	$-0.215955\pi$
$601$	935.818			1.55710			0.778550	+	0.627582i	$0.215955\pi$
$602$		−	250.411i		−	0.415965i
$603$	493.558	−	59.7984i	0.818504	−	0.0991682i
$604$	107.160			0.177417
$605$		−	86.4952i		−	0.142967i
$606$	−3.65489	−	60.5533i	−0.00603118	−	0.0999230i
$607$	−137.313			−0.226216			−0.113108	−	0.993583i	$-0.536081\pi$
$607$	−137.313			−0.226216			−0.113108	+	0.993583i	$0.536081\pi$
$608$			191.910i			0.315641i
$609$	447.918	−	27.0355i	0.735497	−	0.0443933i
$610$	473.268			0.775849
$611$		−	175.326i		−	0.286949i
$612$	−12.0848	−	99.7446i	−0.0197465	−	0.162981i
$613$	−813.877			−1.32770			−0.663848	−	0.747868i	$-0.731078\pi$
$613$	−813.877			−1.32770			−0.663848	+	0.747868i	$0.731078\pi$
$614$		−	1105.44i		−	1.80038i
$615$	1.17936	+	19.5393i	0.00191765	+	0.0317712i
$616$	694.621			1.12763
$617$		−	657.088i		−	1.06497i	−0.846439	−	0.532486i	$-0.821258\pi$
$617$		−	657.088i		−	1.06497i	0.846439	−	0.532486i	$-0.178742\pi$
$618$	−380.767	+	22.9824i	−0.616128	+	0.0371884i
$619$	−775.722			−1.25319			−0.626593	−	0.779347i	$-0.715551\pi$
$619$	−775.722			−1.25319			−0.626593	+	0.779347i	$0.715551\pi$
$620$			11.3429i			0.0182950i
$621$	−793.783	+	145.146i	−1.27823	+	0.233729i
$622$	−546.758			−0.879031
$623$		−	72.0056i		−	0.115579i
$624$	29.9500	+	496.204i	0.0479968	+	0.795199i
$625$	214.343			0.342949
$626$			86.1686i			0.137650i
$627$	−825.999	+	49.8558i	−1.31738	+	0.0795149i
$628$	48.7351			0.0776036
$629$			1888.57i			3.00250i
$630$	371.611	−	45.0236i	0.589859	−	0.0714660i
$631$	−214.389			−0.339761			−0.169881	−	0.985465i	$-0.554338\pi$
$631$	−214.389			−0.339761			−0.169881	+	0.985465i	$0.554338\pi$
$632$		−	382.353i		−	0.604989i
$633$	72.4256	+	1199.93i	0.114416	+	1.89562i
$634$	256.209			0.404115
$635$			311.840i			0.491086i
$636$	−81.2735	+	4.90553i	−0.127789	+	0.00771309i
$637$	−371.512			−0.583221
$638$		−	291.687i		−	0.457189i
$639$	133.823	+	1104.54i	0.209426	+	1.72854i
$640$	−256.748			−0.401168
$641$			832.235i			1.29834i	0.760644	+	0.649169i	$0.224883\pi$
$641$			832.235i			1.29834i	−0.760644	+	0.649169i	$0.775117\pi$
$642$	17.9257	+	296.989i	0.0279217	+	0.462600i
$643$	−874.064			−1.35935			−0.679676	−	0.733512i	$-0.737880\pi$
$643$	−874.064			−1.35935			−0.679676	+	0.733512i	$0.737880\pi$
$644$			108.525i			0.168517i
$645$	107.219	−	6.47154i	0.166231	−	0.0100334i
$646$	−1563.89			−2.42089
$647$		−	505.000i		−	0.780526i	−0.920704	−	0.390263i	$-0.872384\pi$
$647$		−	505.000i		−	0.780526i	0.920704	−	0.390263i	$-0.127616\pi$
$648$	161.542	+	656.873i	0.249293	+	1.01369i
$649$	71.0377			0.109457
$650$		−	420.976i		−	0.647656i
$651$	18.7270	+	310.264i	0.0287665	+	0.476596i
$652$	107.724			0.165221
$653$			469.638i			0.719201i	0.933106	+	0.359600i	$0.117087\pi$
$653$			469.638i			0.719201i	−0.933106	+	0.359600i	$0.882913\pi$
$654$	472.990	−	28.5488i	0.723226	−	0.0436527i
$655$	−331.046			−0.505414
$656$		−	38.0530i		−	0.0580077i
$657$	725.226	−	87.8668i	1.10384	−	0.133739i
$658$	256.649			0.390043
$659$		−	1147.55i		−	1.74135i	−0.491862	−	0.870673i	$-0.663683\pi$
$659$		−	1147.55i		−	1.74135i	0.491862	−	0.870673i	$-0.336317\pi$
$660$	1.64586	+	27.2682i	0.00249373	+	0.0413154i
$661$	286.508			0.433446			0.216723	−	0.976233i	$-0.430463\pi$
$661$	286.508			0.433446			0.216723	+	0.976233i	$0.430463\pi$
$662$			24.0879i			0.0363866i
$663$	964.713	−	58.2284i	1.45507	−	0.0878256i
$664$	−1206.43			−1.81691
$665$			654.139i			0.983668i
$666$	−140.214	−	1157.28i	−0.210531	−	1.73766i
$667$	497.060			0.745217
$668$			66.6968i			0.0998455i
$669$	−57.6469	−	955.079i	−0.0861687	−	1.42762i
$670$	−255.466			−0.381292
$671$			946.448i			1.41050i
$672$	173.293	−	10.4597i	0.257876	−	0.0155650i
$673$	614.908			0.913682			0.456841	−	0.889548i	$-0.348981\pi$
$673$	614.908			0.913682			0.456841	+	0.889548i	$0.348981\pi$
$674$			871.801i			1.29347i
$675$	−92.5313	−	506.041i	−0.137083	−	0.749691i
$676$	−13.4250			−0.0198594
$677$		−	203.554i		−	0.300671i	−0.988635	−	0.150336i	$-0.951965\pi$
$677$		−	203.554i		−	0.300671i	0.988635	−	0.150336i	$-0.0480354\pi$
$678$	−36.2951	−	601.328i	−0.0535326	−	0.886914i
$679$	374.158			0.551042
$680$			563.110i			0.828103i
$681$	−39.4652	+	2.38205i	−0.0579519	+	0.00349787i
$682$	202.046			0.296255
$683$		−	1206.46i		−	1.76641i	−0.468990	−	0.883203i	$-0.655382\pi$
$683$		−	1206.46i		−	1.76641i	0.468990	−	0.883203i	$-0.344618\pi$
$684$	−107.591	+	13.0355i	−0.157297	+	0.0190578i
$685$	2.16184			0.00315597
$686$			291.882i			0.425484i
$687$	24.3722	+	403.793i	0.0354763	+	0.587762i
$688$	−208.810			−0.303503
$689$		−	783.200i		−	1.13672i
$690$	413.889	−	24.9816i	0.599840	−	0.0362053i
$691$	−220.368			−0.318911			−0.159456	−	0.987205i	$-0.550974\pi$
$691$	−220.368			−0.318911			−0.159456	+	0.987205i	$0.550974\pi$
$692$			1.85557i			0.00268145i
$693$	90.0389	+	743.153i	0.129926	+	1.07237i
$694$	147.337			0.212301
$695$			70.1672i			0.100960i
$696$	−25.1041	−	415.919i	−0.0360691	−	0.597584i
$697$	−73.9821			−0.106144
$698$		−	499.454i		−	0.715550i
$699$	203.072	−	12.2571i	0.290518	−	0.0175351i
$700$	−69.1855			−0.0988364
$701$			1139.10i			1.62496i	0.582986	+	0.812482i	$0.301884\pi$
$701$			1139.10i			1.62496i	−0.582986	+	0.812482i	$0.698116\pi$
$702$	−586.835	+	107.305i	−0.835947	+	0.152856i
$703$	2037.14			2.89778
$704$		−	638.967i		−	0.907624i
$705$	6.63274	+	109.890i	0.00940814	+	0.155872i
$706$	597.286			0.846014
$707$		−	95.9001i		−	0.135644i
$708$	9.28691	−	0.560542i	0.0131171	−	0.000791725i
$709$	729.352			1.02870			0.514352	−	0.857579i	$-0.328032\pi$
$709$	729.352			1.02870			0.514352	+	0.857579i	$0.328032\pi$
$710$		−	571.709i		−	0.805224i
$711$	409.068	−	49.5618i	0.575341	−	0.0697071i
$712$	−66.8616			−0.0939067
$713$			344.304i			0.482895i
$714$	85.2370	+	1412.18i	0.119380	+	1.97785i
$715$	−262.773			−0.367514
$716$		−	81.5010i		−	0.113828i
$717$	−272.549	+	16.4506i	−0.380124	+	0.0229436i
$718$	708.932			0.987370
$719$			815.315i			1.13396i	0.823733	+	0.566978i	$0.191888\pi$
$719$			815.315i			1.13396i	−0.823733	+	0.566978i	$0.808112\pi$
$720$	−37.5438	−	309.875i	−0.0521441	−	0.430382i
$721$	−603.031			−0.836382
$722$			1002.33i			1.38827i
$723$	38.4943	+	637.764i	0.0532425	+	0.882108i
$724$	24.0521			0.0332211
$725$			316.879i			0.437074i
$726$	−201.419	+	12.1573i	−0.277436	+	0.0167456i
$727$	244.795			0.336719			0.168359	−	0.985726i	$-0.446153\pi$
$727$	244.795			0.336719			0.168359	+	0.985726i	$0.446153\pi$
$728$			875.092i			1.20205i
$729$	−681.828	+	257.975i	−0.935293	+	0.353875i
$730$	−375.377			−0.514215
$731$			405.965i			0.555356i
$732$	7.46820	+	123.731i	0.0102025	+	0.169032i
$733$	−1169.54			−1.59556			−0.797779	−	0.602950i	$-0.793992\pi$
$733$	−1169.54			−1.59556			−0.797779	+	0.602950i	$0.793992\pi$
$734$		−	427.703i		−	0.582701i
$735$	232.854	−	14.0546i	0.316808	−	0.0191220i
$736$	192.305			0.261284
$737$		−	510.884i		−	0.693195i
$738$	45.3348	−	5.49267i	0.0614293	−	0.00744265i
$739$	75.1506			0.101692			0.0508461	−	0.998706i	$-0.483808\pi$
$739$	75.1506			0.101692			0.0508461	+	0.998706i	$0.483808\pi$
$740$		−	67.2509i		−	0.0908795i
$741$	−62.8090	−	1040.60i	−0.0847625	−	1.40432i
$742$	1146.48			1.54512
$743$		−	1357.17i		−	1.82661i	−0.407271	−	0.913307i	$-0.633520\pi$
$743$		−	1357.17i		−	1.82661i	0.407271	−	0.913307i	$-0.366480\pi$
$744$	288.099	−	17.3891i	0.387230	−	0.0233725i
$745$	−328.877			−0.441446
$746$			760.243i			1.01909i
$747$	−156.381	−	1290.72i	−0.209345	−	1.72787i
$748$	−103.246			−0.138030
$749$			470.350i			0.627971i
$750$	36.8228	+	610.071i	0.0490971	+	0.813428i
$751$	524.167			0.697958			0.348979	−	0.937131i	$-0.386528\pi$
$751$	524.167			0.697958			0.348979	+	0.937131i	$0.386528\pi$
$752$		−	214.011i		−	0.284589i
$753$	−593.273	+	35.8089i	−0.787880	+	0.0475550i
$754$	367.471			0.487362
$755$		−	647.242i		−	0.857274i
$756$	17.6350	+	96.4435i	0.0233267	+	0.127571i
$757$	−406.400			−0.536855			−0.268428	−	0.963300i	$-0.586504\pi$
$757$	−406.400			−0.536855			−0.268428	+	0.963300i	$0.586504\pi$
$758$		−	636.626i		−	0.839876i
$759$	49.9587	+	827.702i	0.0658217	+	1.09052i
$760$	607.408			0.799221
$761$			1447.41i			1.90199i	0.309210	+	0.950994i	$0.399935\pi$
$761$			1447.41i			1.90199i	−0.309210	+	0.950994i	$0.600065\pi$
$762$	726.172	−	43.8305i	0.952982	−	0.0575203i
$763$	749.088			0.981766
$764$		−	90.7614i		−	0.118798i
$765$	−602.454	+	72.9920i	−0.787521	+	0.0954144i
$766$	1137.32			1.48475
$767$			89.4942i			0.116681i
$768$	−13.8639	−	229.693i	−0.0180519	−	0.299080i
$769$	1021.92			1.32889			0.664447	−	0.747335i	$-0.268667\pi$
$769$	1021.92			1.32889			0.664447	+	0.747335i	$0.268667\pi$
$770$		−	384.657i		−	0.499554i
$771$	−808.357	+	48.7910i	−1.04845	+	0.0632828i
$772$	48.6523			0.0630211
$773$			757.370i			0.979780i	0.871784	+	0.489890i	$0.162963\pi$
$773$			757.370i			0.979780i	−0.871784	+	0.489890i	$0.837037\pi$
$774$	−30.1402	−	248.768i	−0.0389408	−	0.321406i
$775$	−219.496			−0.283220
$776$		−	347.428i		−	0.447717i
$777$	−111.030	−	1839.52i	−0.142896	−	2.36747i
$778$	−204.633			−0.263024
$779$			79.8021i			0.102442i
$780$	−34.3528	+	2.07348i	−0.0440421	+	0.00265830i
$781$	1143.31			1.46391
$782$			1567.12i			2.00399i
$783$	441.724	−	80.7707i	0.564143	−	0.103155i
$784$	−453.486			−0.578426
$785$		−	294.358i		−	0.374978i
$786$	46.5300	+	770.897i	0.0591985	+	0.980785i
$787$	−906.536			−1.15189			−0.575944	−	0.817489i	$-0.695365\pi$
$787$	−906.536			−1.15189			−0.575944	+	0.817489i	$0.695365\pi$
$788$			16.0812i			0.0204076i
$789$	187.512	−	11.3179i	0.237657	−	0.0143446i
$790$	−211.734			−0.268017
$791$		−	952.340i		−	1.20397i
$792$	690.063	−	83.6065i	0.871291	−	0.105564i
$793$	−1192.35			−1.50359
$794$		−	339.320i		−	0.427355i
$795$	29.6292	+	490.889i	0.0372694	+	0.617471i
$796$	−30.1047			−0.0378200
$797$		−	1385.97i		−	1.73899i	−0.493946	−	0.869493i	$-0.664446\pi$
$797$		−	1385.97i		−	1.73899i	0.493946	−	0.869493i	$-0.335554\pi$
$798$	1523.28	−	91.9423i	1.90887	−	0.115216i
$799$	−416.077			−0.520748
$800$			122.596i			0.153245i
$801$	−8.66680	−	71.5331i	−0.0108200	−	0.0893047i
$802$	414.761			0.517158
$803$		−	750.685i		−	0.934851i
$804$	−4.03127	−	66.7890i	−0.00501401	−	0.0830709i
$805$	655.489			0.814272
$806$			254.540i			0.315807i
$807$	−309.911	+	18.7057i	−0.384029	+	0.0231793i
$808$	−89.0490			−0.110209
$809$		−	539.451i		−	0.666812i	−0.942783	−	0.333406i	$-0.891802\pi$
$809$		−	539.451i		−	0.666812i	0.942783	−	0.333406i	$-0.108198\pi$
$810$	363.753	−	89.4563i	0.449078	−	0.110440i
$811$	−1246.88			−1.53746			−0.768731	−	0.639572i	$-0.779112\pi$
$811$	−1246.88			−1.53746			−0.768731	+	0.639572i	$0.779112\pi$
$812$		−	60.3921i		−	0.0743745i
$813$	−47.8133	−	792.158i	−0.0588109	−	0.974364i
$814$	−1197.91			−1.47163
$815$		−	650.652i		−	0.798345i
$816$	1177.58	−	71.0765i	1.44311	−	0.0871035i
$817$	437.901			0.535987
$818$		−	283.584i		−	0.346680i
$819$	−936.234	+	113.432i	−1.14314	+	0.138501i
$820$	2.63446			0.00321275
$821$		−	5.03563i		−	0.00613353i	−0.999995	−	0.00306677i	$-0.999024\pi$
$821$		−	5.03563i		−	0.00613353i	0.999995	−	0.00306677i	$-0.000976183\pi$
$822$	−0.303856	−	5.03421i	−0.000369654	−	0.00612434i
$823$	539.459			0.655479			0.327739	−	0.944768i	$-0.393713\pi$
$823$	539.459			0.655479			0.327739	+	0.944768i	$0.393713\pi$
$824$			559.951i			0.679553i
$825$	−527.665	+	31.8489i	−0.639594	+	0.0386048i
$826$	−131.005			−0.158602
$827$		−	138.744i		−	0.167768i	−0.996476	−	0.0838841i	$-0.973267\pi$
$827$		−	138.744i		−	0.167768i	0.996476	−	0.0838841i	$-0.0267325\pi$
$828$	13.0624	+	107.813i	0.0157759	+	0.130209i
$829$	−1083.08			−1.30648			−0.653242	−	0.757149i	$-0.726592\pi$
$829$	−1083.08			−1.30648			−0.653242	+	0.757149i	$0.726592\pi$
$830$			668.077i			0.804912i
$831$	−8.51434	−	141.063i	−0.0102459	−	0.169751i
$832$	804.979			0.967523
$833$			881.660i			1.05842i
$834$	163.396	−	9.86233i	0.195919	−	0.0118253i
$835$	402.846			0.482451
$836$			111.368i			0.133216i
$837$	55.9484	+	305.974i	0.0668439	+	0.365560i
$838$	912.457			1.08885
$839$			579.384i			0.690564i	0.938499	+	0.345282i	$0.112217\pi$
$839$			579.384i			0.690564i	−0.938499	+	0.345282i	$0.887783\pi$
$840$	−33.1056	−	548.485i	−0.0394114	−	0.652958i
$841$	564.396			0.671101
$842$			821.354i			0.975479i
$843$	−607.531	+	36.6695i	−0.720678	+	0.0434988i
$844$	161.785			0.191688
$845$			81.0863i			0.0959601i
$846$	254.964	−	30.8909i	0.301376	−	0.0365141i
$847$	−318.993			−0.376615
$848$		−	956.013i		−	1.12737i
$849$	−12.8601	−	213.062i	−0.0151473	−	0.250957i
$850$	−999.048			−1.17535
$851$		−	2041.34i		−	2.39876i
$852$	149.468	−	9.02161i	0.175432	−	0.0105887i
$853$	180.029			0.211054			0.105527	−	0.994416i	$-0.466347\pi$
$853$	180.029			0.211054			0.105527	+	0.994416i	$0.466347\pi$
$854$		−	1745.40i		−	2.04380i
$855$	78.7341	+	649.847i	0.0920867	+	0.760055i
$856$	436.749			0.510221
$857$			713.388i			0.832425i	0.909267	+	0.416212i	$0.136643\pi$
$857$			713.388i			0.832425i	−0.909267	+	0.416212i	$0.863357\pi$
$858$	36.9339	+	611.911i	0.0430465	+	0.713183i
$859$	819.160			0.953621			0.476810	−	0.879006i	$-0.341793\pi$
$859$	819.160			0.953621			0.476810	+	0.879006i	$0.341793\pi$
$860$		−	14.4562i		−	0.0168095i
$861$	72.0606	−	4.34945i	0.0836941	−	0.00505163i
$862$	710.584			0.824343
$863$			1234.06i			1.42997i	0.699140	+	0.714985i	$0.253566\pi$
$863$			1234.06i			1.42997i	−0.699140	+	0.714985i	$0.746434\pi$
$864$	170.897	−	31.2490i	0.197797	−	0.0361679i
$865$	11.2076			0.0129567
$866$			146.815i			0.169533i
$867$	−85.9502	−	1424.00i	−0.0991352	−	1.64245i
$868$	41.8325			0.0481941
$869$		−	423.428i		−	0.487259i
$870$	−230.321	+	13.9018i	−0.264737	+	0.0159791i
$871$	643.619			0.738942
$872$		−	695.573i		−	0.797676i
$873$	371.703	−	45.0347i	0.425776	−	0.0515861i
$874$	1690.40			1.93410
$875$			966.187i			1.10421i
$876$	−5.92348	−	98.1387i	−0.00676196	−	0.112030i
$877$	−455.374			−0.519240			−0.259620	−	0.965711i	$-0.583597\pi$
$877$	−455.374			−0.519240			−0.259620	+	0.965711i	$0.583597\pi$
$878$			1460.22i			1.66312i
$879$	673.370	−	40.6434i	0.766064	−	0.0462383i
$880$	−320.753			−0.364492
$881$			732.548i			0.831497i	0.909480	+	0.415748i	$0.136480\pi$
$881$			732.548i			0.831497i	−0.909480	+	0.415748i	$0.863520\pi$
$882$	−65.4573	−	540.265i	−0.0742146	−	0.612545i
$883$	835.925			0.946687			0.473344	−	0.880878i	$-0.343047\pi$
$883$	835.925			0.946687			0.473344	+	0.880878i	$0.343047\pi$
$884$		−	130.071i		−	0.147139i
$885$	−3.38565	−	56.0926i	−0.00382560	−	0.0633815i
$886$	−264.140			−0.298127
$887$			194.117i			0.218847i	0.993995	+	0.109423i	$0.0349004\pi$
$887$			194.117i			0.218847i	−0.993995	+	0.109423i	$0.965100\pi$
$888$	−1708.11	+	103.098i	−1.92355	+	0.116102i
$889$	1150.06			1.29366
$890$			37.0256i			0.0416018i
$891$	178.896	+	727.439i	0.200781	+	0.816430i
$892$	−128.772			−0.144363
$893$			448.809i			0.502586i
$894$	46.2252	+	765.847i	0.0517060	+	0.856653i
$895$	−492.263			−0.550015
$896$			946.882i			1.05679i
$897$	−1042.75	+	62.9386i	−1.16249	+	0.0701656i
$898$	−1266.27			−1.41010
$899$		−	191.598i		−	0.213124i
$900$	−68.7315	+	8.32736i	−0.0763683	+	0.00925262i
$901$	−1858.67			−2.06289
$902$		−	46.9264i		−	0.0520248i
$903$	−23.8670	−	395.422i	−0.0264307	−	0.437898i
$904$	−884.305			−0.978214
$905$		−	145.274i		−	0.160524i
$906$	−1507.21	+	90.9728i	−1.66359	+	0.100411i
$907$	−1128.23			−1.24391			−0.621957	−	0.783051i	$-0.713662\pi$
$907$	−1128.23			−1.24391			−0.621957	+	0.783051i	$0.713662\pi$
$908$			5.32104i			0.00586018i
$909$	−11.5428	−	95.2708i	−0.0126984	−	0.104808i
$910$	484.595			0.532522
$911$		−	1482.59i		−	1.62744i	−0.581260	−	0.813718i	$-0.697440\pi$
$911$		−	1482.59i		−	1.62744i	0.581260	−	0.813718i	$-0.302560\pi$
$912$	−76.6678	−	1270.21i	−0.0840656	−	1.39278i
$913$	−1336.03			−1.46334
$914$			1316.65i			1.44053i
$915$	747.332	−	45.1077i	0.816756	−	0.0492980i
$916$	54.4428			0.0594354
$917$			1220.89i			1.33140i
$918$	254.652	+	1392.66i	0.277399	+	1.51706i
$919$	−462.705			−0.503487			−0.251743	−	0.967794i	$-0.581004\pi$
$919$	−462.705			−0.503487			−0.251743	+	0.967794i	$0.581004\pi$
$920$		−	608.661i		−	0.661588i
$921$	−105.360	−	1745.58i	−0.114398	−	1.89531i
$922$	−1162.41			−1.26075
$923$			1440.36i			1.56052i
$924$	100.565	−	6.06991i	0.108836	−	0.00656916i
$925$	1301.37			1.40688
$926$			360.249i			0.389038i
$927$	−599.074	+	72.5826i	−0.646251	+	0.0782984i
$928$	−107.014			−0.115317
$929$		−	1431.98i		−	1.54143i	−0.637183	−	0.770713i	$-0.719900\pi$
$929$		−	1431.98i		−	1.54143i	0.637183	−	0.770713i	$-0.280100\pi$
$930$	−9.62950	−	159.539i	−0.0103543	−	0.171547i
$931$	951.017			1.02150
$932$		−	27.3799i		−	0.0293776i
$933$	−863.379	+	52.1120i	−0.925379	+	0.0558543i
$934$	641.230			0.686542
$935$			623.603i			0.666956i
$936$	105.329	+	869.350i	0.112531	+	0.928793i
$937$	−1183.14			−1.26269			−0.631343	−	0.775504i	$-0.717496\pi$
$937$	−1183.14			−1.26269			−0.631343	+	0.775504i	$0.717496\pi$
$938$			942.154i			1.00443i
$939$	8.21282	+	136.068i	0.00874635	+	0.144907i
$940$	14.8163			0.0157620
$941$		−	1632.81i		−	1.73519i	−0.497274	−	0.867594i	$-0.665666\pi$
$941$		−	1632.81i		−	1.73519i	0.497274	−	0.867594i	$-0.334334\pi$
$942$	−685.464	+	41.3734i	−0.727668	+	0.0439208i
$943$	79.9667			0.0848003
$944$			109.241i			0.115722i
$945$	582.516	−	106.515i	0.616419	−	0.112714i
$946$	−257.501			−0.272200
$947$			249.865i			0.263849i	0.991260	+	0.131925i	$0.0421157\pi$
$947$			249.865i			0.263849i	−0.991260	+	0.131925i	$0.957884\pi$
$948$	−3.34117	−	55.3557i	−0.00352444	−	0.0583921i
$949$	945.723			0.996547
$950$			1077.64i			1.13436i
$951$	404.577	−	24.4196i	0.425423	−	0.0256778i
$952$	2076.74			2.18145
$953$		−	492.377i		−	0.516660i	−0.966057	−	0.258330i	$-0.916828\pi$
$953$		−	492.377i		−	0.516660i	0.966057	−	0.258330i	$-0.0831722\pi$
$954$	1138.96	−	137.993i	1.19387	−	0.144647i
$955$	−548.196			−0.574027
$956$			36.7474i			0.0384387i
$957$	−27.8010	−	460.600i	−0.0290501	−	0.481295i
$958$	−193.565			−0.202051
$959$		−	7.97282i		−	0.00831368i
$960$	−504.540	+	30.4531i	−0.525562	+	0.0317220i
$961$	−828.284			−0.861898
$962$		−	1509.14i		−	1.56875i
$963$	56.6127	+	467.264i	0.0587879	+	0.485217i
$964$	85.9889			0.0892001
$965$		−	293.858i		−	0.304516i
$966$	−92.1319	−	1526.42i	−0.0953747	−	1.58014i
$967$	478.893			0.495236			0.247618	−	0.968858i	$-0.420352\pi$
$967$	478.893			0.495236			0.247618	+	0.968858i	$0.420352\pi$
$968$			296.204i			0.305996i
$969$	−2469.53	+	149.056i	−2.54853	+	0.153825i
$970$	−192.393			−0.198344
$971$		−	214.648i		−	0.221059i	−0.993873	−	0.110529i	$-0.964745\pi$
$971$		−	214.648i		−	0.221059i	0.993873	−	0.110529i	$-0.0352546\pi$
$972$	29.1275	+	93.6881i	0.0299666	+	0.0963869i
$973$	258.776			0.265957
$974$			1472.35i			1.51165i
$975$	−40.1237	−	664.759i	−0.0411525	−	0.681804i
$976$	−1455.44			−1.49123
$977$		−	13.6869i		−	0.0140091i	−0.999975	−	0.00700456i	$-0.997770\pi$
$977$		−	13.6869i		−	0.0140091i	0.999975	−	0.00700456i	$-0.00222964\pi$
$978$	−1515.15	+	91.4520i	−1.54924	+	0.0935093i
$979$	−74.0443			−0.0756326
$980$		−	31.3953i		−	0.0320361i
$981$	744.172	−	90.1623i	0.758585	−	0.0919086i
$982$	−691.295			−0.703966
$983$			297.768i			0.302917i	0.988464	+	0.151459i	$0.0483971\pi$
$983$			297.768i			0.302917i	−0.988464	+	0.151459i	$0.951603\pi$
$984$	−4.03873	−	66.9127i	−0.00410440	−	0.0680007i
$985$	97.1297			0.0986088
$986$		−	872.070i		−	0.884453i
$987$	405.271	−	24.4614i	0.410609	−	0.0247836i
$988$	−140.303			−0.142007
$989$		−	438.805i		−	0.443685i
$990$	−46.2984	−	382.132i	−0.0467660	−	0.385992i
$991$	922.960			0.931342			0.465671	−	0.884958i	$-0.345813\pi$
$991$	922.960			0.931342			0.465671	+	0.884958i	$0.345813\pi$
$992$		−	74.1266i		−	0.0747244i
$993$	2.29585	+	38.0370i	0.00231203	+	0.0383051i
$994$	−2108.45			−2.12118
$995$			181.832i			0.182745i
$996$	−174.662	+	10.5423i	−0.175364	+	0.0105846i
$997$	943.403			0.946242			0.473121	−	0.880997i	$-0.343127\pi$
$997$	943.403			0.946242			0.473121	+	0.880997i	$0.343127\pi$
$998$		−	613.788i		−	0.615018i
$999$	−331.712	−	1814.09i	−0.332044	−	1.81590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.27	yes	38
3.2	odd	2	inner	177.3.b.a.119.12	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.12	✓	38	3.2	odd	2	inner
177.3.b.a.119.27	yes	38	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.89638i q^{2} +(0.180746 + 2.99455i) q^{3} +0.403751 q^{4} -2.43864i q^{5} +(-5.67880 + 0.342762i) q^{6} -8.99368 q^{7} +8.35118i q^{8} +(-8.93466 + 1.08250i) q^{9} +O(q^{10})\)	\(q+1.89638i q^{2} +(0.180746 + 2.99455i) q^{3} +0.403751 q^{4} -2.43864i q^{5} +(-5.67880 + 0.342762i) q^{6} -8.99368 q^{7} +8.35118i q^{8} +(-8.93466 + 1.08250i) q^{9} +4.62459 q^{10} +9.24832i q^{11} +(0.0729763 + 1.20905i) q^{12} -11.6512 q^{13} -17.0554i q^{14} +(7.30264 - 0.440774i) q^{15} -14.2220 q^{16} +27.6502i q^{17} +(-2.05284 - 16.9435i) q^{18} +29.8253 q^{19} -0.984604i q^{20} +(-1.62557 - 26.9320i) q^{21} -17.5383 q^{22} -29.8868i q^{23} +(-25.0080 + 1.50944i) q^{24} +19.0530 q^{25} -22.0950i q^{26} +(-4.85652 - 26.5596i) q^{27} -3.63121 q^{28} +16.6314i q^{29} +(0.835875 + 13.8486i) q^{30} -11.5203 q^{31} +6.43445i q^{32} +(-27.6946 + 1.67160i) q^{33} -52.4351 q^{34} +21.9324i q^{35} +(-3.60738 + 0.437062i) q^{36} +68.3024 q^{37} +56.5600i q^{38} +(-2.10590 - 34.8900i) q^{39} +20.3655 q^{40} +2.67565i q^{41} +(51.0733 - 3.08269i) q^{42} +14.6822 q^{43} +3.73402i q^{44} +(2.63984 + 21.7884i) q^{45} +56.6767 q^{46} +15.0479i q^{47} +(-2.57056 - 42.5884i) q^{48} +31.8863 q^{49} +36.1317i q^{50} +(-82.7998 + 4.99765i) q^{51} -4.70417 q^{52} +67.2208i q^{53} +(50.3671 - 9.20979i) q^{54} +22.5533 q^{55} -75.1078i q^{56} +(5.39080 + 89.3134i) q^{57} -31.5394 q^{58} -7.68115i q^{59} +(2.94845 - 0.177963i) q^{60} +102.337 q^{61} -21.8468i q^{62} +(80.3555 - 9.73570i) q^{63} -69.0901 q^{64} +28.4130i q^{65} +(-3.16998 - 52.5193i) q^{66} -55.2408 q^{67} +11.1638i q^{68} +(89.4976 - 5.40192i) q^{69} -41.5921 q^{70} -123.624i q^{71} +(-9.04019 - 74.6149i) q^{72} -81.1699 q^{73} +129.527i q^{74} +(3.44375 + 57.0552i) q^{75} +12.0420 q^{76} -83.1764i q^{77} +(66.1646 - 3.99358i) q^{78} -45.7843 q^{79} +34.6823i q^{80} +(78.6564 - 19.3436i) q^{81} -5.07404 q^{82} +144.462i q^{83} +(-0.656325 - 10.8738i) q^{84} +67.4288 q^{85} +27.8430i q^{86} +(-49.8036 + 3.00606i) q^{87} -77.2343 q^{88} +8.00625i q^{89} +(-41.3191 + 5.00614i) q^{90} +104.787 q^{91} -12.0668i q^{92} +(-2.08224 - 34.4980i) q^{93} -28.5365 q^{94} -72.7332i q^{95} +(-19.2683 + 1.16300i) q^{96} -41.6023 q^{97} +60.4684i q^{98} +(-10.0114 - 82.6306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

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