LMFDB - Embedded newform 177.3.b.a.119.12

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

$q$-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	$-0.842776\pi$
$2$		−	1.89638i		−	0.948189i	0.880474	−	0.474094i	$-0.157224\pi$
$3$	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	$0.0784151\pi$
$5$			2.43864i			0.487728i	−0.969809	+	0.243864i	$0.921585\pi$
$6$	−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	$-0.861897\pi$
$11$		−	9.24832i		−	0.840756i	0.907349	−	0.420378i	$-0.138103\pi$
$12$	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	$-0.697702\pi$
$17$		−	27.6502i		−	1.62648i	0.581929	−	0.813240i	$-0.302298\pi$
$18$	−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	$0.225111\pi$
$23$			29.8868i			1.29943i	−0.760179	+	0.649714i	$0.774889\pi$
$24$	−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	$-0.907426\pi$
$29$		−	16.6314i		−	0.573497i	0.958006	−	0.286748i	$-0.0925744\pi$
$30$	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	$-0.989612\pi$
$41$		−	2.67565i		−	0.0652597i	0.999468	−	0.0326299i	$-0.0103883\pi$
$42$	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	$-0.948823\pi$
$47$		−	15.0479i		−	0.320169i	0.987103	−	0.160084i	$-0.0511766\pi$
$48$	−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	$-0.781347\pi$
$53$		−	67.2208i		−	1.26832i	0.773203	−	0.634159i	$-0.218653\pi$
$54$	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	$0.336263\pi$
$71$			123.624i			1.74118i	−0.492009	+	0.870590i	$0.663737\pi$
$72$	−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	$-0.663956\pi$
$83$		−	144.462i		−	1.74051i	0.492606	−	0.870253i	$-0.336044\pi$
$84$	−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	$-0.985678\pi$
$89$		−	8.00625i		−	0.0899578i	0.998988	−	0.0449789i	$-0.0143221\pi$
$90$	−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	$-0.983189\pi$
$101$		−	10.6631i		−	0.105575i	0.998606	−	0.0527874i	$-0.0168106\pi$
$102$	−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	$0.0785853\pi$
$107$			52.2979i			0.488765i	−0.969679	+	0.244383i	$0.921415\pi$
$108$	−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	$-0.844780\pi$
$113$		−	105.890i		−	0.937079i	0.883443	−	0.468539i	$-0.155220\pi$
$114$	−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	$0.173372\pi$
$131$			135.750i			1.03626i	−0.855302	+	0.518130i	$0.826628\pi$
$132$	−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	$-0.998970\pi$
$137$		−	0.886492i		−	0.00647074i	0.999995	−	0.00323537i	$-0.00102985\pi$
$138$	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	$0.149487\pi$
$149$			134.861i			0.905106i	−0.891737	+	0.452553i	$0.850513\pi$
$150$	−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	$-0.835318\pi$
$167$		−	165.193i		−	0.989179i	0.869127	−	0.494589i	$-0.164682\pi$
$168$	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	$-0.995772\pi$
$173$		−	4.59582i		−	0.0265654i	0.999912	−	0.0132827i	$-0.00422814\pi$
$174$	−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	$0.190682\pi$
$179$			201.860i			1.12771i	−0.825875	+	0.563854i	$0.809318\pi$
$180$	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	$0.200270\pi$
$191$			224.796i			1.17694i	−0.808519	+	0.588470i	$0.799730\pi$
$192$	−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	$-0.967767\pi$
$197$		−	39.8294i		−	0.202180i	0.994877	−	0.101090i	$-0.0322330\pi$
$198$	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	$-0.990759\pi$
$227$		−	13.1790i		−	0.0580573i	0.999579	−	0.0290287i	$-0.00924141\pi$
$228$	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	$0.0464865\pi$
$233$			67.8138i			0.291046i	−0.989355	+	0.145523i	$0.953513\pi$
$234$	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	$-0.939019\pi$
$239$		−	91.0150i		−	0.380816i	0.981705	−	0.190408i	$-0.0609811\pi$
$240$	−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	$-0.870863\pi$
$251$		−	198.118i		−	0.789314i	0.918829	−	0.394657i	$-0.129137\pi$
$252$	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	$-0.823998\pi$
$257$		−	269.943i		−	1.05036i	0.850991	−	0.525181i	$-0.176002\pi$
$258$	−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	$0.0379833\pi$
$263$			62.6176i			0.238090i	−0.992889	+	0.119045i	$0.962017\pi$
$264$	−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	$-0.938385\pi$
$269$		−	103.492i		−	0.384728i	0.981324	−	0.192364i	$-0.0616154\pi$
$270$	−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	$-0.882437\pi$
$281$		−	202.879i		−	0.721989i	0.932568	−	0.360995i	$-0.117563\pi$
$282$	−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	$0.125360\pi$
$293$			224.865i			0.767458i	−0.923446	+	0.383729i	$0.874640\pi$
$294$	−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	$-0.846582\pi$
$311$		−	288.317i		−	0.927064i	0.886080	−	0.463532i	$-0.153418\pi$
$312$	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	$0.0683555\pi$
$317$			135.104i			0.426197i	−0.977031	+	0.213099i	$0.931644\pi$
$318$	−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	$0.0357099\pi$
$347$			77.6938i			0.223901i	−0.993714	+	0.111951i	$0.964290\pi$
$348$	−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	$0.147195\pi$
$353$			314.961i			0.892242i	−0.894973	+	0.446121i	$0.852805\pi$
$354$	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	$0.174315\pi$
$359$			373.835i			1.04132i	−0.853763	+	0.520661i	$0.825685\pi$
$360$	−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	$0.286281\pi$
$383$			599.733i			1.56588i	−0.622096	+	0.782941i	$0.713719\pi$
$384$	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	$-0.955708\pi$
$389$		−	107.907i		−	0.277397i	0.990335	−	0.138698i	$-0.0442918\pi$
$390$	−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	$0.0879194\pi$
$401$			218.712i			0.545416i	−0.962097	+	0.272708i	$0.912081\pi$
$402$	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	$0.194677\pi$
$419$			481.158i			1.14835i	−0.818733	+	0.574174i	$0.805323\pi$
$420$	−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	$0.143143\pi$
$431$			374.706i			0.869387i	−0.900578	+	0.434693i	$0.856857\pi$
$432$	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	$-0.949751\pi$
$443$		−	139.287i		−	0.314417i	0.987565	−	0.157208i	$-0.0502494\pi$
$444$	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	$-0.733128\pi$
$449$		−	667.731i		−	1.48715i	0.668652	−	0.743576i	$-0.266872\pi$
$450$	−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	$-0.768508\pi$
$461$		−	612.964i		−	1.32964i	0.747004	−	0.664820i	$-0.231492\pi$
$462$	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	$0.117916\pi$
$467$			338.134i			0.724056i	−0.932167	+	0.362028i	$0.882084\pi$
$468$	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	$-0.966021\pi$
$479$		−	102.071i		−	0.213092i	0.994308	−	0.106546i	$-0.0339791\pi$
$480$	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	$-0.878941\pi$
$491$		−	364.534i		−	0.742432i	0.928546	−	0.371216i	$-0.121059\pi$
$492$	−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	$0.0771990\pi$
$503$			241.598i			0.480314i	−0.970734	+	0.240157i	$0.922801\pi$
$504$	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	$-0.994277\pi$
$509$		−	18.3011i		−	0.0359549i	0.999838	−	0.0179775i	$-0.00572271\pi$
$510$	−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	$-0.835911\pi$
$521$		−	513.675i		−	0.985941i	0.870046	−	0.492970i	$-0.164089\pi$
$522$	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	$0.0103663\pi$
$557$			36.2728i			0.0651217i	−0.999470	+	0.0325608i	$0.989634\pi$
$558$	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	$-0.799950\pi$
$563$		−	661.989i		−	1.17582i	0.808925	−	0.587912i	$-0.200050\pi$
$564$	−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	$0.0858363\pi$
$569$			303.170i			0.532813i	−0.963861	+	0.266406i	$0.914164\pi$
$570$	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	$0.145123\pi$
$587$			516.896i			0.880573i	−0.897857	+	0.440286i	$0.854877\pi$
$588$	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	$0.156821\pi$
$593$			560.953i			0.945957i	−0.881074	+	0.472979i	$0.843179\pi$
$594$	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	$-0.789265\pi$
$599$		−	736.447i		−	1.22946i	0.788738	−	0.614730i	$-0.210735\pi$
$600$	−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	$0.178742\pi$
$617$			657.088i			1.06497i	−0.846439	+	0.532486i	$0.821258\pi$
$618$	−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	$-0.775117\pi$
$641$		−	832.235i		−	1.29834i	0.760644	−	0.649169i	$-0.224883\pi$
$642$	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	$0.127616\pi$
$647$			505.000i			0.780526i	−0.920704	+	0.390263i	$0.872384\pi$
$648$	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	$-0.882913\pi$
$653$		−	469.638i		−	0.719201i	0.933106	−	0.359600i	$-0.117087\pi$
$654$	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	$0.336317\pi$
$659$			1147.55i			1.74135i	−0.491862	+	0.870673i	$0.663683\pi$
$660$	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	$0.0480354\pi$
$677$			203.554i			0.300671i	−0.988635	+	0.150336i	$0.951965\pi$
$678$	−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	$0.344618\pi$
$683$			1206.46i			1.76641i	−0.468990	+	0.883203i	$0.655382\pi$
$684$	−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	$-0.698116\pi$
$701$		−	1139.10i		−	1.62496i	0.582986	−	0.812482i	$-0.301884\pi$
$702$	−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	$-0.808112\pi$
$719$		−	815.315i		−	1.13396i	0.823733	−	0.566978i	$-0.191888\pi$
$720$	−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	$0.366480\pi$
$743$			1357.17i			1.82661i	−0.407271	+	0.913307i	$0.633520\pi$
$744$	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	$-0.600065\pi$
$761$		−	1447.41i		−	1.90199i	0.309210	−	0.950994i	$-0.399935\pi$
$762$	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	$-0.837037\pi$
$773$		−	757.370i		−	0.979780i	0.871784	−	0.489890i	$-0.162963\pi$
$774$	−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	$0.335554\pi$
$797$			1385.97i			1.73899i	−0.493946	+	0.869493i	$0.664446\pi$
$798$	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	$0.108198\pi$
$809$			539.451i			0.666812i	−0.942783	+	0.333406i	$0.891802\pi$
$810$	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	$0.000976183\pi$
$821$			5.03563i			0.00613353i	−0.999995	+	0.00306677i	$0.999024\pi$
$822$	−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	$0.0267325\pi$
$827$			138.744i			0.167768i	−0.996476	+	0.0838841i	$0.973267\pi$
$828$	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	$-0.887783\pi$
$839$		−	579.384i		−	0.690564i	0.938499	−	0.345282i	$-0.112217\pi$
$840$	−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	$-0.863357\pi$
$857$		−	713.388i		−	0.832425i	0.909267	−	0.416212i	$-0.136643\pi$
$858$	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	$-0.746434\pi$
$863$		−	1234.06i		−	1.42997i	0.699140	−	0.714985i	$-0.253566\pi$
$864$	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	$-0.863520\pi$
$881$		−	732.548i		−	0.831497i	0.909480	−	0.415748i	$-0.136480\pi$
$882$	−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	$-0.965100\pi$
$887$		−	194.117i		−	0.218847i	0.993995	−	0.109423i	$-0.0349004\pi$
$888$	−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	$0.302560\pi$
$911$			1482.59i			1.62744i	−0.581260	+	0.813718i	$0.697440\pi$
$912$	−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	$0.280100\pi$
$929$			1431.98i			1.54143i	−0.637183	+	0.770713i	$0.719900\pi$
$930$	−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	$0.334334\pi$
$941$			1632.81i			1.73519i	−0.497274	+	0.867594i	$0.665666\pi$
$942$	−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	$-0.957884\pi$
$947$		−	249.865i		−	0.263849i	0.991260	−	0.131925i	$-0.0421157\pi$
$948$	−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	$0.0831722\pi$
$953$			492.377i			0.516660i	−0.966057	+	0.258330i	$0.916828\pi$
$954$	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	$0.0352546\pi$
$971$			214.648i			0.221059i	−0.993873	+	0.110529i	$0.964745\pi$
$972$	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	$0.00222964\pi$
$977$			13.6869i			0.0140091i	−0.999975	+	0.00700456i	$0.997770\pi$
$978$	−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	$-0.951603\pi$
$983$		−	297.768i		−	0.302917i	0.988464	−	0.151459i	$-0.0483971\pi$
$984$	−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.119.12	✓	38
3.2	odd	2	inner	177.3.b.a.119.27	yes	38

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more