LMFDB - Embedded newform 177.3.b.a.119.32

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			119.32
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.97620i q^{2} +(-0.474775 - 2.96219i) q^{3} -4.85777 q^{4} +3.00594i q^{5} +(8.81608 - 1.41303i) q^{6} -3.67852 q^{7} -2.55289i q^{8} +(-8.54918 + 2.81275i) q^{9} +O(q^{10})$	\(q+2.97620i q^{2} +(-0.474775 - 2.96219i) q^{3} -4.85777 q^{4} +3.00594i q^{5} +(8.81608 - 1.41303i) q^{6} -3.67852 q^{7} -2.55289i q^{8} +(-8.54918 + 2.81275i) q^{9} -8.94628 q^{10} +14.3274i q^{11} +(2.30635 + 14.3896i) q^{12} -8.01457 q^{13} -10.9480i q^{14} +(8.90417 - 1.42715i) q^{15} -11.8332 q^{16} +0.828304i q^{17} +(-8.37131 - 25.4441i) q^{18} -25.2540 q^{19} -14.6022i q^{20} +(1.74647 + 10.8965i) q^{21} -42.6413 q^{22} +7.83517i q^{23} +(-7.56216 + 1.21205i) q^{24} +15.9643 q^{25} -23.8530i q^{26} +(12.3909 + 23.9889i) q^{27} +17.8694 q^{28} -2.34238i q^{29} +(4.24747 + 26.5006i) q^{30} +25.4893 q^{31} -45.4294i q^{32} +(42.4407 - 6.80232i) q^{33} -2.46520 q^{34} -11.0574i q^{35} +(41.5299 - 13.6637i) q^{36} -0.422862 q^{37} -75.1611i q^{38} +(3.80512 + 23.7407i) q^{39} +7.67384 q^{40} +6.28936i q^{41} +(-32.4301 + 5.19785i) q^{42} +48.4134 q^{43} -69.5994i q^{44} +(-8.45496 - 25.6983i) q^{45} -23.3190 q^{46} +63.1254i q^{47} +(5.61809 + 35.0521i) q^{48} -35.4685 q^{49} +47.5131i q^{50} +(2.45360 - 0.393258i) q^{51} +38.9329 q^{52} -24.6229i q^{53} +(-71.3957 + 36.8777i) q^{54} -43.0674 q^{55} +9.39087i q^{56} +(11.9900 + 74.8073i) q^{57} +6.97139 q^{58} +7.68115i q^{59} +(-43.2544 + 6.93274i) q^{60} +73.6703 q^{61} +75.8611i q^{62} +(31.4483 - 10.3468i) q^{63} +87.8744 q^{64} -24.0913i q^{65} +(20.2451 + 126.312i) q^{66} -100.685 q^{67} -4.02371i q^{68} +(23.2093 - 3.71995i) q^{69} +32.9091 q^{70} +47.9530i q^{71} +(7.18065 + 21.8251i) q^{72} +130.417 q^{73} -1.25852i q^{74} +(-7.57947 - 47.2894i) q^{75} +122.678 q^{76} -52.7038i q^{77} +(-70.6571 + 11.3248i) q^{78} -76.0894 q^{79} -35.5697i q^{80} +(65.1768 - 48.0934i) q^{81} -18.7184 q^{82} +142.865i q^{83} +(-8.48395 - 52.9326i) q^{84} -2.48983 q^{85} +144.088i q^{86} +(-6.93858 + 1.11210i) q^{87} +36.5764 q^{88} -73.4347i q^{89} +(76.4833 - 25.1637i) q^{90} +29.4818 q^{91} -38.0615i q^{92} +(-12.1017 - 75.5041i) q^{93} -187.874 q^{94} -75.9121i q^{95} +(-134.571 + 21.5688i) q^{96} +84.6768 q^{97} -105.561i q^{98} +(-40.2996 - 122.488i) 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 $

$2$			2.97620i			1.48810i	0.668124	+	0.744050i	$0.267098\pi$
$2$			2.97620i			1.48810i	−0.668124	+	0.744050i	$0.732902\pi$
$3$	−0.474775	−	2.96219i	−0.158258	−	0.987398i
$3$	−0.474775	−	2.96219i	−0.158258	−	0.987398i
$4$	−4.85777			−1.21444
$5$			3.00594i			0.601188i	0.953752	+	0.300594i	$0.0971849\pi$
$5$			3.00594i			0.601188i	−0.953752	+	0.300594i	$0.902815\pi$
$6$	8.81608	−	1.41303i	1.46935	−	0.235504i
$7$	−3.67852			−0.525503			−0.262752	−	0.964864i	$-0.584630\pi$
$7$	−3.67852			−0.525503			−0.262752	+	0.964864i	$0.584630\pi$
$8$		−	2.55289i		−	0.319111i
$9$	−8.54918	+	2.81275i	−0.949909	+	0.312528i
$10$	−8.94628			−0.894628
$11$			14.3274i			1.30249i	0.758865	+	0.651247i	$0.225754\pi$
$11$			14.3274i			1.30249i	−0.758865	+	0.651247i	$0.774246\pi$
$12$	2.30635	+	14.3896i	0.192196	+	1.19914i
$13$	−8.01457			−0.616505			−0.308253	−	0.951305i	$-0.599744\pi$
$13$	−8.01457			−0.616505			−0.308253	+	0.951305i	$0.599744\pi$
$14$		−	10.9480i		−	0.782001i
$15$	8.90417	−	1.42715i	0.593611	−	0.0951430i
$16$	−11.8332			−0.739572
$17$			0.828304i			0.0487238i	0.999703	+	0.0243619i	$0.00775540\pi$
$17$			0.828304i			0.0487238i	−0.999703	+	0.0243619i	$0.992245\pi$
$18$	−8.37131	−	25.4441i	−0.465073	−	1.41356i
$19$	−25.2540			−1.32916			−0.664580	−	0.747217i	$-0.731389\pi$
$19$	−25.2540			−1.32916			−0.664580	+	0.747217i	$0.731389\pi$
$20$		−	14.6022i		−	0.730108i
$21$	1.74647	+	10.8965i	0.0831653	+	0.518881i
$22$	−42.6413			−1.93824
$23$			7.83517i			0.340660i	0.985387	+	0.170330i	$0.0544833\pi$
$23$			7.83517i			0.340660i	−0.985387	+	0.170330i	$0.945517\pi$
$24$	−7.56216	+	1.21205i	−0.315090	+	0.0505021i
$25$	15.9643			0.638573
$26$		−	23.8530i		−	0.917421i
$27$	12.3909	+	23.9889i	0.458921	+	0.888477i
$28$	17.8694			0.638193
$29$		−	2.34238i		−	0.0807717i	−0.999184	−	0.0403858i	$-0.987141\pi$
$29$		−	2.34238i		−	0.0807717i	0.999184	−	0.0403858i	$-0.0128587\pi$
$30$	4.24747	+	26.5006i	0.141582	+	0.883353i
$31$	25.4893			0.822234			0.411117	−	0.911583i	$-0.365139\pi$
$31$	25.4893			0.822234			0.411117	+	0.911583i	$0.365139\pi$
$32$		−	45.4294i		−	1.41967i
$33$	42.4407	−	6.80232i	1.28608	−	0.206131i
$34$	−2.46520			−0.0725059
$35$		−	11.0574i		−	0.315926i
$36$	41.5299	−	13.6637i	1.15361	−	0.379547i
$37$	−0.422862			−0.0114287			−0.00571434	−	0.999984i	$-0.501819\pi$
$37$	−0.422862			−0.0114287			−0.00571434	+	0.999984i	$0.501819\pi$
$38$		−	75.1611i		−	1.97792i
$39$	3.80512	+	23.7407i	0.0975671	+	0.608736i
$40$	7.67384			0.191846
$41$			6.28936i			0.153399i	0.997054	+	0.0766995i	$0.0244382\pi$
$41$			6.28936i			0.153399i	−0.997054	+	0.0766995i	$0.975562\pi$
$42$	−32.4301	+	5.19785i	−0.772146	+	0.123758i
$43$	48.4134			1.12589			0.562946	−	0.826494i	$-0.309668\pi$
$43$	48.4134			1.12589			0.562946	+	0.826494i	$0.309668\pi$
$44$		−	69.5994i		−	1.58180i
$45$	−8.45496	−	25.6983i	−0.187888	−	0.571073i
$46$	−23.3190			−0.506936
$47$			63.1254i			1.34309i	0.740962	+	0.671547i	$0.234370\pi$
$47$			63.1254i			1.34309i	−0.740962	+	0.671547i	$0.765630\pi$
$48$	5.61809	+	35.0521i	0.117044	+	0.730252i
$49$	−35.4685			−0.723846
$50$			47.5131i			0.950261i
$51$	2.45360	−	0.393258i	0.0481098	−	0.00771095i
$52$	38.9329			0.748710
$53$		−	24.6229i		−	0.464583i	−0.972646	−	0.232291i	$-0.925378\pi$
$53$		−	24.6229i		−	0.464583i	0.972646	−	0.232291i	$-0.0746223\pi$
$54$	−71.3957	+	36.8777i	−1.32214	+	0.682920i
$55$	−43.0674			−0.783044
$56$			9.39087i			0.167694i
$57$	11.9900	+	74.8073i	0.210351	+	1.31241i
$58$	6.97139			0.120196
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	−43.2544	+	6.93274i	−0.720907	+	0.115546i
$61$	73.6703			1.20771			0.603855	−	0.797094i	$-0.293630\pi$
$61$	73.6703			1.20771			0.603855	+	0.797094i	$0.293630\pi$
$62$			75.8611i			1.22357i
$63$	31.4483	−	10.3468i	0.499180	−	0.164234i
$64$	87.8744			1.37304
$65$		−	24.0913i		−	0.370635i
$66$	20.2451	+	126.312i	0.306743	+	1.91382i
$67$	−100.685			−1.50276			−0.751379	−	0.659871i	$-0.770611\pi$
$67$	−100.685			−1.50276			−0.751379	+	0.659871i	$0.770611\pi$
$68$		−	4.02371i		−	0.0591722i
$69$	23.2093	−	3.71995i	0.336367	−	0.0539123i
$70$	32.9091			0.470130
$71$			47.9530i			0.675395i	0.941255	+	0.337697i	$0.109648\pi$
$71$			47.9530i			0.675395i	−0.941255	+	0.337697i	$0.890352\pi$
$72$	7.18065	+	21.8251i	0.0997313	+	0.303127i
$73$	130.417			1.78654			0.893268	−	0.449524i	$-0.148406\pi$
$73$	130.417			1.78654			0.893268	+	0.449524i	$0.148406\pi$
$74$		−	1.25852i		−	0.0170070i
$75$	−7.57947	−	47.2894i	−0.101060	−	0.630526i
$76$	122.678			1.61419
$77$		−	52.7038i		−	0.684465i
$78$	−70.6571	+	11.3248i	−0.905860	+	0.145190i
$79$	−76.0894			−0.963156			−0.481578	−	0.876403i	$-0.659936\pi$
$79$	−76.0894			−0.963156			−0.481578	+	0.876403i	$0.659936\pi$
$80$		−	35.5697i		−	0.444622i
$81$	65.1768	−	48.0934i	0.804652	−	0.593746i
$82$	−18.7184			−0.228273
$83$			142.865i			1.72127i	0.509226	+	0.860633i	$0.329932\pi$
$83$			142.865i			1.72127i	−0.509226	+	0.860633i	$0.670068\pi$
$84$	−8.48395	−	52.9326i	−0.100999	−	0.630151i
$85$	−2.48983			−0.0292921
$86$			144.088i			1.67544i
$87$	−6.93858	+	1.11210i	−0.0797538	+	0.0127828i
$88$	36.5764			0.415641
$89$		−	73.4347i		−	0.825109i	−0.910933	−	0.412554i	$-0.864637\pi$
$89$		−	73.4347i		−	0.825109i	0.910933	−	0.412554i	$-0.135363\pi$
$90$	76.4833	−	25.1637i	0.849814	−	0.279596i
$91$	29.4818			0.323975
$92$		−	38.0615i		−	0.413712i
$93$	−12.1017	−	75.5041i	−0.130125	−	0.811872i
$94$	−187.874			−1.99866
$95$		−	75.9121i		−	0.799074i
$96$	−134.571	+	21.5688i	−1.40178	+	0.224675i
$97$	84.6768			0.872957			0.436478	−	0.899715i	$-0.356226\pi$
$97$	84.6768			0.872957			0.436478	+	0.899715i	$0.356226\pi$
$98$		−	105.561i		−	1.07716i
$99$	−40.2996	−	122.488i	−0.407066	−	1.23725i
$100$	−77.5510			−0.775510
$101$		−	162.825i		−	1.61213i	−0.591825	−	0.806066i	$-0.701592\pi$
$101$		−	162.825i		−	1.61213i	0.591825	−	0.806066i	$-0.298408\pi$
$102$	1.17042	+	7.30240i	0.0114747	+	0.0715921i
$103$	−1.33089			−0.0129212			−0.00646062	−	0.999979i	$-0.502056\pi$
$103$	−1.33089			−0.0129212			−0.00646062	+	0.999979i	$0.502056\pi$
$104$			20.4603i			0.196734i
$105$	−32.7542	+	5.24979i	−0.311945	+	0.0499980i
$106$	73.2826			0.691346
$107$		−	101.598i		−	0.949518i	−0.880116	−	0.474759i	$-0.842535\pi$
$107$		−	101.598i		−	0.949518i	0.880116	−	0.474759i	$-0.157465\pi$
$108$	−60.1919	−	116.532i	−0.557332	−	1.07900i
$109$	−3.86290			−0.0354394			−0.0177197	−	0.999843i	$-0.505641\pi$
$109$	−3.86290			−0.0354394			−0.0177197	+	0.999843i	$0.505641\pi$
$110$		−	128.177i		−	1.16525i
$111$	0.200764	+	1.25260i	0.00180869	+	0.0112847i
$112$	43.5285			0.388648
$113$			67.2164i			0.594835i	0.954748	+	0.297417i	$0.0961253\pi$
$113$			67.2164i			0.594835i	−0.954748	+	0.297417i	$0.903875\pi$
$114$	−222.642	+	35.6846i	−1.95300	+	0.313023i
$115$	−23.5520			−0.204800
$116$			11.3787i			0.0980925i
$117$	68.5179	−	22.5430i	0.585623	−	0.192675i
$118$	−22.8606			−0.193734
$119$		−	3.04694i		−	0.0256045i
$120$	−3.64335	−	22.7314i	−0.0303612	−	0.189428i
$121$	−84.2757			−0.696493
$122$			219.258i			1.79719i
$123$	18.6303	−	2.98603i	0.151466	−	0.0242767i
$124$	−123.821			−0.998556
$125$			123.136i			0.985090i
$126$	30.7941	+	93.5966i	0.244397	+	0.742830i
$127$	−41.0103			−0.322916			−0.161458	−	0.986880i	$-0.551620\pi$
$127$	−41.0103			−0.322916			−0.161458	+	0.986880i	$0.551620\pi$
$128$			79.8142i			0.623548i
$129$	−22.9855	−	143.410i	−0.178182	−	1.11170i
$130$	71.7005			0.551542
$131$			57.1268i			0.436083i	0.975940	+	0.218041i	$0.0699667\pi$
$131$			57.1268i			0.436083i	−0.975940	+	0.218041i	$0.930033\pi$
$132$	−206.167	+	33.0441i	−1.56187	+	0.250334i
$133$	92.8975			0.698478
$134$		−	299.658i		−	2.23625i
$135$	−72.1091	+	37.2461i	−0.534142	+	0.275897i
$136$	2.11457			0.0155483
$137$			37.2566i			0.271946i	0.990713	+	0.135973i	$0.0434161\pi$
$137$			37.2566i			0.271946i	−0.990713	+	0.135973i	$0.956584\pi$
$138$	11.0713	+	69.0755i	0.0802269	+	0.500547i
$139$	151.905			1.09284			0.546421	−	0.837511i	$-0.315990\pi$
$139$	151.905			1.09284			0.546421	+	0.837511i	$0.315990\pi$
$140$			53.7144i			0.383674i
$141$	186.990	−	29.9704i	1.32617	−	0.212556i
$142$	−142.718			−1.00505
$143$		−	114.828i		−	0.802995i
$144$	101.164	−	33.2837i	0.702526	−	0.231137i
$145$	7.04105			0.0485589
$146$			388.148i			2.65855i
$147$	16.8396	+	105.064i	0.114555	+	0.714724i
$148$	2.05416			0.0138795
$149$			155.316i			1.04239i	0.853437	+	0.521196i	$0.174514\pi$
$149$			155.316i			1.04239i	−0.853437	+	0.521196i	$0.825486\pi$
$150$	140.743	−	22.5580i	0.938286	−	0.150387i
$151$	−100.269			−0.664036			−0.332018	−	0.943273i	$-0.607729\pi$
$151$	−100.269			−0.664036			−0.332018	+	0.943273i	$0.607729\pi$
$152$			64.4708i			0.424150i
$153$	−2.32981	−	7.08132i	−0.0152275	−	0.0462831i
$154$	156.857			1.01855
$155$			76.6191i			0.494317i
$156$	−18.4844	−	115.327i	−0.118490	−	0.739274i
$157$	−183.383			−1.16805			−0.584024	−	0.811737i	$-0.698522\pi$
$157$	−183.383			−1.16805			−0.584024	+	0.811737i	$0.698522\pi$
$158$		−	226.457i		−	1.43327i
$159$	−72.9377	+	11.6903i	−0.458728	+	0.0735241i
$160$	136.558			0.853488
$161$		−	28.8219i		−	0.179018i
$162$	143.136	+	193.979i	0.883554	+	1.19740i
$163$	−159.723			−0.979894			−0.489947	−	0.871752i	$-0.662984\pi$
$163$	−159.723			−0.979894			−0.489947	+	0.871752i	$0.662984\pi$
$164$		−	30.5523i		−	0.186294i
$165$	20.4473	+	127.574i	0.123923	+	0.773176i
$166$	−425.195			−2.56142
$167$			271.015i			1.62284i	0.584460	+	0.811422i	$0.301306\pi$
$167$			271.015i			1.62284i	−0.584460	+	0.811422i	$0.698694\pi$
$168$	27.8176	−	4.45855i	0.165581	−	0.0265390i
$169$	−104.767			−0.619921
$170$		−	7.41024i		−	0.0435896i
$171$	215.901	−	71.0333i	1.26258	−	0.415400i
$172$	−235.181			−1.36733
$173$			323.180i			1.86809i	0.357156	+	0.934045i	$0.383746\pi$
$173$			323.180i			1.86809i	−0.357156	+	0.934045i	$0.616254\pi$
$174$	−3.30984	−	20.6506i	−0.0190221	−	0.118682i
$175$	−58.7252			−0.335572
$176$		−	169.539i		−	0.963289i
$177$	22.7530	−	3.64682i	0.128548	−	0.0206035i
$178$	218.556			1.22784
$179$			6.98049i			0.0389972i	0.999810	+	0.0194986i	$0.00620698\pi$
$179$			6.98049i			0.0389972i	−0.999810	+	0.0194986i	$0.993793\pi$
$180$	41.0722	+	124.836i	0.228179	+	0.693536i
$181$	−23.0990			−0.127619			−0.0638095	−	0.997962i	$-0.520325\pi$
$181$	−23.0990			−0.127619			−0.0638095	+	0.997962i	$0.520325\pi$
$182$			87.7436i			0.482108i
$183$	−34.9769	−	218.226i	−0.191130	−	1.19249i
$184$	20.0024			0.108708
$185$		−	1.27110i		−	0.00687079i
$186$	224.715	−	36.0170i	1.20815	−	0.193640i
$187$	−11.8675			−0.0634625
$188$		−	306.649i		−	1.63111i
$189$	−45.5800	−	88.2437i	−0.241164	−	0.466898i
$190$	225.930			1.18910
$191$		−	317.561i		−	1.66262i	−0.555808	−	0.831311i	$-0.687591\pi$
$191$		−	317.561i		−	1.66262i	0.555808	−	0.831311i	$-0.312409\pi$
$192$	−41.7206	−	260.301i	−0.217295	−	1.35573i
$193$	−286.089			−1.48233			−0.741163	−	0.671325i	$-0.765726\pi$
$193$	−286.089			−1.48233			−0.741163	+	0.671325i	$0.765726\pi$
$194$			252.015i			1.29905i
$195$	−71.3631	+	11.4380i	−0.365964	+	0.0586562i
$196$	172.298			0.879070
$197$			258.325i			1.31129i	0.755068	+	0.655647i	$0.227604\pi$
$197$			258.325i			1.31129i	−0.755068	+	0.655647i	$0.772396\pi$
$198$	364.548	−	119.940i	1.84115	−	0.605755i
$199$	26.7086			0.134214			0.0671071	−	0.997746i	$-0.478623\pi$
$199$	26.7086			0.134214			0.0671071	+	0.997746i	$0.478623\pi$
$200$		−	40.7552i		−	0.203776i
$201$	47.8026	+	298.248i	0.237824	+	1.48382i
$202$	484.601			2.39901
$203$			8.61649i			0.0424458i
$204$	−11.9190	+	1.91036i	−0.0584265	+	0.00936450i
$205$	−18.9054			−0.0922216
$206$		−	3.96099i		−	0.0192281i
$207$	−22.0384	−	66.9843i	−0.106466	−	0.323596i
$208$	94.8376			0.455950
$209$		−	361.826i		−	1.73122i
$210$	−15.6244	−	97.4830i	−0.0744020	−	0.464205i
$211$	−372.105			−1.76353			−0.881766	−	0.471687i	$-0.843645\pi$
$211$	−372.105			−1.76353			−0.881766	+	0.471687i	$0.843645\pi$
$212$			119.612i			0.564209i
$213$	142.046	−	22.7669i	0.666883	−	0.106887i
$214$	302.377			1.41298
$215$			145.528i			0.676873i
$216$	61.2410	−	31.6325i	0.283523	−	0.146447i
$217$	−93.7628			−0.432087
$218$		−	11.4968i		−	0.0527374i
$219$	−61.9188	−	386.321i	−0.282734	−	1.76402i
$220$	209.212			0.950962
$221$		−	6.63850i		−	0.0300385i
$222$	−3.72798	+	0.597515i	−0.0167927	+	0.00269151i
$223$	312.508			1.40138			0.700690	−	0.713466i	$-0.252875\pi$
$223$	312.508			1.40138			0.700690	+	0.713466i	$0.252875\pi$
$224$			167.113i			0.746041i
$225$	−136.482	+	44.9037i	−0.606586	+	0.199572i
$226$	−200.049			−0.885174
$227$			11.4108i			0.0502677i	0.999684	+	0.0251339i	$0.00800120\pi$
$227$			11.4108i			0.0502677i	−0.999684	+	0.0251339i	$0.991999\pi$
$228$	−58.2446	−	363.397i	−0.255459	−	1.59384i
$229$	337.431			1.47350			0.736749	−	0.676166i	$-0.236360\pi$
$229$	337.431			1.47350			0.736749	+	0.676166i	$0.236360\pi$
$230$		−	70.0956i		−	0.304764i
$231$	−156.119	+	25.0225i	−0.675839	+	0.108322i
$232$	−5.97984			−0.0257752
$233$		−	246.547i		−	1.05814i	−0.848578	−	0.529071i	$-0.822541\pi$
$233$		−	246.547i		−	1.05814i	0.848578	−	0.529071i	$-0.177459\pi$
$234$	67.0925	+	203.923i	0.286720	+	0.871466i
$235$	−189.751			−0.807452
$236$		−	37.3132i		−	0.158107i
$237$	36.1253	+	225.391i	0.152428	+	0.951019i
$238$	9.06829			0.0381021
$239$			136.843i			0.572566i	0.958145	+	0.286283i	$0.0924198\pi$
$239$			136.843i			0.572566i	−0.958145	+	0.286283i	$0.907580\pi$
$240$	−105.364	+	16.8876i	−0.439019	+	0.0703651i
$241$	153.448			0.636715			0.318358	−	0.947971i	$-0.396869\pi$
$241$	153.448			0.636715			0.318358	+	0.947971i	$0.396869\pi$
$242$		−	250.821i		−	1.03645i
$243$	−173.406	−	170.233i	−0.713607	−	0.700547i
$244$	−357.873			−1.46669
$245$		−	106.616i		−	0.435168i
$246$	8.88703	+	55.4475i	0.0361261	+	0.225396i
$247$	202.400			0.819434
$248$		−	65.0713i		−	0.262384i
$249$	423.194	−	67.8288i	1.69957	−	0.272405i
$250$	−366.478			−1.46591
$251$		−	157.596i		−	0.627874i	−0.949444	−	0.313937i	$-0.898352\pi$
$251$		−	157.596i		−	0.627874i	0.949444	−	0.313937i	$-0.101648\pi$
$252$	−152.769	+	50.2622i	−0.606225	+	0.199453i
$253$	−112.258			−0.443708
$254$		−	122.055i		−	0.480531i
$255$	1.18211	+	7.37536i	0.00463573	+	0.0289230i
$256$	113.955			0.445135
$257$			379.854i			1.47803i	0.673689	+	0.739015i	$0.264709\pi$
$257$			379.854i			1.47803i	−0.673689	+	0.739015i	$0.735291\pi$
$258$	426.816	−	68.4094i	1.65433	−	0.265153i
$259$	1.55551			0.00600581
$260$			117.030i			0.450115i
$261$	6.58853	+	20.0254i	0.0252434	+	0.0767257i
$262$	−170.021			−0.648935
$263$			457.411i			1.73921i	0.493751	+	0.869603i	$0.335625\pi$
$263$			457.411i			1.73921i	−0.493751	+	0.869603i	$0.664375\pi$
$264$	−17.3656	−	108.346i	−0.0657787	−	0.410403i
$265$	74.0149			0.279301
$266$			276.482i			1.03940i
$267$	−217.528	+	34.8650i	−0.814710	+	0.130580i
$268$	489.103			1.82501
$269$			154.959i			0.576056i	0.957622	+	0.288028i	$0.0929996\pi$
$269$			154.959i			0.576056i	−0.957622	+	0.288028i	$0.907000\pi$
$270$	−110.852	−	214.611i	−0.410563	−	0.794856i
$271$	−53.5797			−0.197711			−0.0988555	−	0.995102i	$-0.531518\pi$
$271$	−53.5797			−0.197711			−0.0988555	+	0.995102i	$0.531518\pi$
$272$		−	9.80146i		−	0.0360348i
$273$	−13.9972	−	87.3307i	−0.0512718	−	0.319893i
$274$	−110.883			−0.404683
$275$			228.728i			0.831739i
$276$	−112.745	+	18.0706i	−0.408498	+	0.0654733i
$277$	363.311			1.31159			0.655797	−	0.754938i	$-0.272333\pi$
$277$	363.311			1.31159			0.655797	+	0.754938i	$0.272333\pi$
$278$			452.100i			1.62626i
$279$	−217.912	+	71.6950i	−0.781047	+	0.256971i
$280$	−28.2284			−0.100816
$281$		−	405.128i		−	1.44174i	−0.693072	−	0.720869i	$-0.743743\pi$
$281$		−	405.128i		−	1.44174i	0.693072	−	0.720869i	$-0.256257\pi$
$282$	89.1979	+	556.519i	0.316305	+	1.97347i
$283$	−375.399			−1.32650			−0.663250	−	0.748398i	$-0.730823\pi$
$283$	−375.399			−1.32650			−0.663250	+	0.748398i	$0.730823\pi$
$284$		−	232.945i		−	0.820228i
$285$	−224.866	+	36.0412i	−0.789004	+	0.126460i
$286$	341.752			1.19494
$287$		−	23.1356i		−	0.0806117i
$288$	127.782	+	388.384i	0.443686	+	1.34856i
$289$	288.314			0.997626
$290$			20.9556i			0.0722606i
$291$	−40.2024	−	250.829i	−0.138153	−	0.861955i
$292$	−633.536			−2.16965
$293$			21.8044i			0.0744176i	0.999308	+	0.0372088i	$0.0118467\pi$
$293$			21.8044i			0.0744176i	−0.999308	+	0.0372088i	$0.988153\pi$
$294$	−312.693	+	50.1179i	−1.06358	+	0.170469i
$295$	−23.0891			−0.0782680
$296$			1.07952i			0.00364703i
$297$	−343.699	+	177.529i	−1.15724	+	0.597742i
$298$	−462.253			−1.55118
$299$		−	62.7955i		−	0.210018i
$300$	36.8193	+	229.721i	0.122731	+	0.765737i
$301$	−178.090			−0.591660
$302$		−	298.422i		−	0.988152i
$303$	−482.320	+	77.3055i	−1.59182	+	0.255134i
$304$	298.835			0.983010
$305$			221.449i			0.726061i
$306$	21.0754	−	6.93400i	0.0688739	−	0.0226601i
$307$	−35.2986			−0.114979			−0.0574896	−	0.998346i	$-0.518310\pi$
$307$	−35.2986			−0.114979			−0.0574896	+	0.998346i	$0.518310\pi$
$308$			256.023i			0.831243i
$309$	0.631873	+	3.94235i	0.00204490	+	0.0127584i
$310$	−228.034			−0.735593
$311$		−	15.4570i		−	0.0497008i	−0.999691	−	0.0248504i	$-0.992089\pi$
$311$		−	15.4570i		−	0.0497008i	0.999691	−	0.0248504i	$-0.00791094\pi$
$312$	60.6074	−	9.71406i	0.194255	−	0.0311348i
$313$	453.370			1.44847			0.724233	−	0.689555i	$-0.242194\pi$
$313$	453.370			1.44847			0.724233	+	0.689555i	$0.242194\pi$
$314$		−	545.786i		−	1.73817i
$315$	31.1018	+	94.5318i	0.0987357	+	0.300101i
$316$	369.625			1.16970
$317$			11.2239i			0.0354068i	0.999843	+	0.0177034i	$0.00563546\pi$
$317$			11.2239i			0.0354068i	−0.999843	+	0.0177034i	$0.994365\pi$
$318$	−34.7928	−	217.077i	−0.109411	−	0.682633i
$319$	33.5603			0.105205
$320$			264.145i			0.825453i
$321$	−300.954	+	48.2364i	−0.937552	+	0.150269i
$322$	85.7796			0.266396
$323$		−	20.9180i		−	0.0647617i
$324$	−316.614	+	233.627i	−0.977204	+	0.721070i
$325$	−127.947			−0.393684
$326$		−	475.367i		−	1.45818i
$327$	1.83401	+	11.4426i	0.00560858	+	0.0349928i
$328$	16.0561			0.0489514
$329$		−	232.208i		−	0.705800i
$330$	−379.686	+	60.8554i	−1.15056	+	0.184410i
$331$	133.540			0.403443			0.201722	−	0.979443i	$-0.435346\pi$
$331$	133.540			0.403443			0.201722	+	0.979443i	$0.435346\pi$
$332$		−	694.006i		−	2.09038i
$333$	3.61512	−	1.18940i	0.0108562	−	0.00357179i
$334$	−806.595			−2.41496
$335$		−	302.652i		−	0.903439i
$336$	−20.6663	−	128.940i	−0.0615068	−	0.383750i
$337$	390.559			1.15893			0.579465	−	0.814997i	$-0.303262\pi$
$337$	390.559			1.15893			0.579465	+	0.814997i	$0.303262\pi$
$338$		−	311.807i		−	0.922505i
$339$	199.108	−	31.9127i	0.587339	−	0.0941376i
$340$	12.0950			0.0355736
$341$			365.196i			1.07096i
$342$	211.409	+	642.565i	0.618156	+	1.87885i
$343$	310.719			0.905887
$344$		−	123.594i		−	0.359285i
$345$	11.1819	+	69.7657i	0.0324114	+	0.202219i
$346$	−961.847			−2.77990
$347$		−	426.563i		−	1.22929i	−0.788805	−	0.614644i	$-0.789300\pi$
$347$		−	426.563i		−	1.22929i	0.788805	−	0.614644i	$-0.210700\pi$
$348$	33.7060	−	5.40234i	0.0968563	−	0.0155240i
$349$	−484.515			−1.38830			−0.694148	−	0.719832i	$-0.744219\pi$
$349$	−484.515			−1.38830			−0.694148	+	0.719832i	$0.744219\pi$
$350$		−	174.778i		−	0.499365i
$351$	−99.3073	−	192.261i	−0.282927	−	0.547751i
$352$	650.887			1.84911
$353$		−	537.907i		−	1.52382i	−0.647685	−	0.761908i	$-0.724263\pi$
$353$		−	537.907i		−	1.52382i	0.647685	−	0.761908i	$-0.275737\pi$
$354$	10.8537	+	67.7176i	0.0306601	+	0.191293i
$355$	−144.144			−0.406039
$356$			356.729i			1.00205i
$357$	−9.02561	+	1.44661i	−0.0252818	+	0.00405213i
$358$	−20.7753			−0.0580317
$359$			59.8619i			0.166746i	0.996518	+	0.0833731i	$0.0265693\pi$
$359$			59.8619i			0.166746i	−0.996518	+	0.0833731i	$0.973431\pi$
$360$	−65.6050	+	21.5846i	−0.182236	+	0.0599572i
$361$	276.766			0.766665
$362$		−	68.7474i		−	0.189910i
$363$	40.0120	+	249.641i	0.110226	+	0.687716i
$364$	−143.216			−0.393449
$365$			392.026i			1.07404i
$366$	649.484	−	104.098i	1.77455	−	0.284421i
$367$	629.523			1.71532			0.857660	−	0.514217i	$-0.171917\pi$
$367$	629.523			1.71532			0.857660	+	0.514217i	$0.171917\pi$
$368$		−	92.7148i		−	0.251942i
$369$	−17.6904	−	53.7689i	−0.0479415	−	0.145715i
$370$	3.78304			0.0102244
$371$			90.5758i			0.244140i
$372$	58.7871	+	366.781i	0.158030	+	0.985972i
$373$	−80.1229			−0.214807			−0.107403	−	0.994216i	$-0.534254\pi$
$373$	−80.1229			−0.214807			−0.107403	+	0.994216i	$0.534254\pi$
$374$		−	35.3200i		−	0.0944385i
$375$	364.753	−	58.4621i	0.972676	−	0.155899i
$376$	161.152			0.428597
$377$			18.7731i			0.0497961i
$378$	262.631	−	135.655i	0.694791	−	0.358876i
$379$	149.480			0.394407			0.197204	−	0.980363i	$-0.436814\pi$
$379$	149.480			0.394407			0.197204	+	0.980363i	$0.436814\pi$
$380$			368.763i			0.970430i
$381$	19.4707	+	121.480i	0.0511041	+	0.318846i
$382$	945.124			2.47415
$383$			34.2467i			0.0894171i	0.999000	+	0.0447085i	$0.0142359\pi$
$383$			34.2467i			0.0894171i	−0.999000	+	0.0447085i	$0.985764\pi$
$384$	236.425	−	37.8938i	0.615690	−	0.0986818i
$385$	158.424			0.411492
$386$		−	851.458i		−	2.20585i
$387$	−413.894	+	136.175i	−1.06949	+	0.351873i
$388$	−411.340			−1.06016
$389$		−	70.7713i		−	0.181931i	−0.995854	−	0.0909657i	$-0.971005\pi$
$389$		−	70.7713i		−	0.181931i	0.995854	−	0.0909657i	$-0.0289954\pi$
$390$	−34.0416	−	212.391i	−0.0872862	−	0.544592i
$391$	−6.48991			−0.0165982
$392$			90.5472i			0.230988i
$393$	169.221	−	27.1224i	0.430587	−	0.0690137i
$394$	−768.827			−1.95134
$395$		−	228.720i		−	0.579038i
$396$	195.766	+	595.018i	0.494358	+	1.50257i
$397$	658.564			1.65885			0.829425	−	0.558618i	$-0.188668\pi$
$397$	658.564			1.65885			0.829425	+	0.558618i	$0.188668\pi$
$398$			79.4902i			0.199724i
$399$	−44.1054	−	275.180i	−0.110540	−	0.689675i
$400$	−188.908			−0.472271
$401$		−	394.424i		−	0.983602i	−0.870708	−	0.491801i	$-0.836339\pi$
$401$		−	394.424i		−	0.983602i	0.870708	−	0.491801i	$-0.163661\pi$
$402$	−887.645	+	142.270i	−2.20807	+	0.353906i
$403$	−204.285			−0.506911
$404$			790.968i			1.95784i
$405$	144.566	+	195.918i	0.356953	+	0.483747i
$406$	−25.6444			−0.0631636
$407$		−	6.05852i		−	0.0148858i
$408$	−1.00395	−	6.26377i	−0.00246065	−	0.0153524i
$409$	−501.659			−1.22655			−0.613275	−	0.789869i	$-0.710148\pi$
$409$	−501.659			−1.22655			−0.613275	+	0.789869i	$0.710148\pi$
$410$		−	56.2663i		−	0.137235i
$411$	110.361	−	17.6885i	0.268519	−	0.0430378i
$412$	6.46515			0.0156921
$413$		−	28.2553i		−	0.0684147i
$414$	199.359	−	65.5907i	0.481543	−	0.158432i
$415$	−429.444			−1.03480
$416$			364.097i			0.875233i
$417$	−72.1208	−	449.972i	−0.172952	−	1.07907i
$418$	1076.87			2.57623
$419$		−	383.331i		−	0.914870i	−0.889243	−	0.457435i	$-0.848768\pi$
$419$		−	383.331i		−	0.914870i	0.889243	−	0.457435i	$-0.151232\pi$
$420$	159.112	−	25.5022i	0.378839	−	0.0607196i
$421$	−439.790			−1.04463			−0.522316	−	0.852752i	$-0.674932\pi$
$421$	−439.790			−1.04463			−0.522316	+	0.852752i	$0.674932\pi$
$422$		−	1107.46i		−	2.62431i
$423$	−177.556	−	539.671i	−0.419755	−	1.27582i
$424$	−62.8596			−0.148254
$425$			13.2233i			0.0311137i
$426$	67.7589	+	422.758i	0.159058	+	0.992389i
$427$	−270.998			−0.634656
$428$			493.542i			1.15313i
$429$	−340.143	+	54.5176i	−0.792875	+	0.127081i
$430$	−433.119			−1.00725
$431$			643.243i			1.49244i	0.665697	+	0.746222i	$0.268134\pi$
$431$			643.243i			1.49244i	−0.665697	+	0.746222i	$0.731866\pi$
$432$	−146.623	−	283.864i	−0.339405	−	0.657093i
$433$	306.913			0.708805			0.354403	−	0.935093i	$-0.384684\pi$
$433$	306.913			0.708805			0.354403	+	0.935093i	$0.384684\pi$
$434$		−	279.057i		−	0.642988i
$435$	−3.34291	−	20.8569i	−0.00768486	−	0.0479470i
$436$	18.7651			0.0430391
$437$		−	197.870i		−	0.452791i
$438$	1149.77	−	184.283i	2.62504	−	0.420737i
$439$	−711.298			−1.62027			−0.810134	−	0.586244i	$-0.800606\pi$
$439$	−711.298			−1.62027			−0.810134	+	0.586244i	$0.800606\pi$
$440$			109.946i			0.249878i
$441$	303.226	−	99.7640i	0.687588	−	0.226222i
$442$	19.7575			0.0447002
$443$			305.524i			0.689671i	0.938663	+	0.344835i	$0.112065\pi$
$443$			305.524i			0.689671i	−0.938663	+	0.344835i	$0.887935\pi$
$444$	−0.975266	−	6.08483i	−0.00219655	−	0.0137046i
$445$	220.740			0.496045
$446$			930.086i			2.08539i
$447$	460.077	−	73.7404i	1.02926	−	0.164967i
$448$	−323.248			−0.721536
$449$			228.985i			0.509989i	0.966942	+	0.254995i	$0.0820737\pi$
$449$			228.985i			0.509989i	−0.966942	+	0.254995i	$0.917926\pi$
$450$	−133.642	−	406.198i	−0.296983	−	0.902661i
$451$	−90.1105			−0.199801
$452$		−	326.521i		−	0.722393i
$453$	47.6054	+	297.017i	0.105089	+	0.655668i
$454$	−33.9607			−0.0748034
$455$			88.6204i			0.194770i
$456$	190.975	−	30.6091i	0.418805	−	0.0671253i
$457$	−13.9561			−0.0305384			−0.0152692	−	0.999883i	$-0.504861\pi$
$457$	−13.9561			−0.0305384			−0.0152692	+	0.999883i	$0.504861\pi$
$458$			1004.26i			2.19271i
$459$	−19.8701	+	10.2634i	−0.0432900	+	0.0223603i
$460$	114.410			0.248718
$461$		−	518.730i		−	1.12523i	−0.826720	−	0.562614i	$-0.809796\pi$
$461$		−	518.730i		−	1.12523i	0.826720	−	0.562614i	$-0.190204\pi$
$462$	−74.4719	−	464.641i	−0.161195	−	1.00572i
$463$	873.381			1.88635			0.943177	−	0.332292i	$-0.107822\pi$
$463$	873.381			1.88635			0.943177	+	0.332292i	$0.107822\pi$
$464$			27.7177i			0.0597365i
$465$	226.961	−	36.3769i	0.488087	−	0.0782298i
$466$	733.773			1.57462
$467$		−	15.7070i		−	0.0336339i	−0.999859	−	0.0168169i	$-0.994647\pi$
$467$		−	15.7070i		−	0.0336339i	0.999859	−	0.0168169i	$-0.00535325\pi$
$468$	−332.844	+	109.509i	−0.711206	+	0.233993i
$469$	370.371			0.789704
$470$		−	564.738i		−	1.20157i
$471$	87.0659	+	543.217i	0.184853	+	1.15333i
$472$	19.6091			0.0415448
$473$			693.640i			1.46647i
$474$	−670.810	+	107.516i	−1.41521	+	0.226828i
$475$	−403.164			−0.848766
$476$			14.8013i			0.0310952i
$477$	69.2581	+	210.505i	0.145195	+	0.441311i
$478$	−407.273			−0.852036
$479$		−	375.998i		−	0.784964i	−0.919760	−	0.392482i	$-0.871617\pi$
$479$		−	375.998i		−	0.784964i	0.919760	−	0.392482i	$-0.128383\pi$
$480$	−64.8344	−	404.511i	−0.135072	−	0.842732i
$481$	3.38905			0.00704585
$482$			456.693i			0.947496i
$483$	−85.3759	+	13.6839i	−0.176762	+	0.0283311i
$484$	409.392			0.845850
$485$			254.533i			0.524811i
$486$	506.647	−	516.092i	1.04248	−	1.06192i
$487$	789.687			1.62153			0.810767	−	0.585369i	$-0.199050\pi$
$487$	789.687			1.62153			0.810767	+	0.585369i	$0.199050\pi$
$488$		−	188.072i		−	0.385394i
$489$	75.8324	+	473.130i	0.155077	+	0.967546i
$490$	317.311			0.647573
$491$		−	613.979i		−	1.25047i	−0.780438	−	0.625233i	$-0.785004\pi$
$491$		−	613.979i		−	1.25047i	0.780438	−	0.625233i	$-0.214996\pi$
$492$	−90.5017	+	14.5055i	−0.183947	+	0.0294826i
$493$	1.94020			0.00393550
$494$			602.383i			1.21940i
$495$	368.191	−	121.138i	0.743820	−	0.244723i
$496$	−301.618			−0.608102
$497$		−	176.396i		−	0.354922i
$498$	201.872	+	1259.51i	0.405366	+	2.52914i
$499$	468.935			0.939750			0.469875	−	0.882733i	$-0.344299\pi$
$499$	468.935			0.939750			0.469875	+	0.882733i	$0.344299\pi$
$500$		−	598.168i		−	1.19634i
$501$	802.799	−	128.671i	1.60239	−	0.256829i
$502$	469.038			0.934339
$503$			803.692i			1.59780i	0.601466	+	0.798898i	$0.294584\pi$
$503$			803.692i			1.59780i	−0.601466	+	0.798898i	$0.705416\pi$
$504$	−26.4142	−	80.2842i	−0.0524091	−	0.159294i
$505$	489.443			0.969194
$506$		−	334.102i		−	0.660281i
$507$	49.7407	+	310.339i	0.0981078	+	0.612109i
$508$	199.219			0.392162
$509$			627.072i			1.23197i	0.787759	+	0.615984i	$0.211241\pi$
$509$			627.072i			1.23197i	−0.787759	+	0.615984i	$0.788759\pi$
$510$	−21.9506	+	3.51820i	−0.0430403	+	0.00689843i
$511$	−479.742			−0.938831
$512$			658.409i			1.28595i
$513$	−312.919	−	605.816i	−0.609979	−	1.18093i
$514$	−1130.52			−2.19946
$515$		−	4.00057i		−	0.00776810i
$516$	111.658	+	696.651i	0.216392	+	1.35010i
$517$	−904.426			−1.74937
$518$			4.62950i			0.00893725i
$519$	957.320	−	153.438i	1.84455	−	0.295641i
$520$	−61.5025			−0.118274
$521$		−	758.568i		−	1.45598i	−0.685586	−	0.727992i	$-0.740454\pi$
$521$		−	758.568i		−	1.45598i	0.685586	−	0.727992i	$-0.259546\pi$
$522$	−59.5996	+	19.6088i	−0.114176	+	0.0375647i
$523$	205.714			0.393334			0.196667	−	0.980470i	$-0.436988\pi$
$523$	205.714			0.393334			0.196667	+	0.980470i	$0.436988\pi$
$524$		−	277.509i		−	0.529597i
$525$	27.8813	+	173.955i	0.0531072	+	0.331343i
$526$	−1361.35			−2.58811
$527$			21.1129i			0.0400624i
$528$	−502.207	+	80.4929i	−0.951150	+	0.152449i
$529$	467.610			0.883951
$530$			220.283i			0.415628i
$531$	−21.6052	−	65.6675i	−0.0406877	−	0.123668i
$532$	−451.275			−0.848261
$533$		−	50.4065i		−	0.0945713i
$534$	−103.765	−	647.406i	−0.194317	−	1.21237i
$535$	305.399			0.570839
$536$			257.037i			0.479547i
$537$	20.6776	−	3.31417i	0.0385057	−	0.00617163i
$538$	−461.189			−0.857229
$539$		−	508.173i		−	0.942806i
$540$	350.289	−	180.933i	0.648684	−	0.335061i
$541$	231.135			0.427236			0.213618	−	0.976917i	$-0.431475\pi$
$541$	231.135			0.427236			0.213618	+	0.976917i	$0.431475\pi$
$542$		−	159.464i		−	0.294214i
$543$	10.9669	+	68.4238i	0.0201968	+	0.126011i
$544$	37.6294			0.0691717
$545$		−	11.6116i		−	0.0213057i
$546$	259.914	−	41.6585i	0.476032	−	0.0762976i
$547$	−978.215			−1.78833			−0.894164	−	0.447740i	$-0.852229\pi$
$547$	−978.215			−1.78833			−0.894164	+	0.447740i	$0.852229\pi$
$548$		−	180.984i		−	0.330263i
$549$	−629.821	+	207.216i	−1.14721	+	0.377443i
$550$	−680.741			−1.23771
$551$			59.1545i			0.107358i
$552$	−9.49662	−	59.2508i	−0.0172040	−	0.107338i
$553$	279.896			0.506142
$554$			1081.29i			1.95178i
$555$	−3.76523	+	0.603485i	−0.00678420	+	0.00108736i
$556$	−737.920			−1.32719
$557$		−	483.211i		−	0.867524i	−0.901027	−	0.433762i	$-0.857186\pi$
$557$		−	483.211i		−	0.867524i	0.901027	−	0.433762i	$-0.142814\pi$
$558$	−213.379	−	648.550i	−0.382399	−	1.16228i
$559$	−388.012			−0.694118
$560$			130.844i			0.233650i
$561$	5.63439	+	35.1538i	0.0100435	+	0.0626627i
$562$	1205.74			2.14545
$563$			918.492i			1.63142i	0.578458	+	0.815712i	$0.303655\pi$
$563$			918.492i			1.63142i	−0.578458	+	0.815712i	$0.696345\pi$
$564$	−908.353	+	145.589i	−1.61055	+	0.258137i
$565$	−202.048			−0.357607
$566$		−	1117.26i		−	1.97396i
$567$	−239.754	+	176.913i	−0.422847	+	0.312015i
$568$	122.419			0.215526
$569$		−	273.561i		−	0.480775i	−0.970677	−	0.240387i	$-0.922726\pi$
$569$		−	273.561i		−	0.480775i	0.970677	−	0.240387i	$-0.0772745\pi$
$570$	−107.266	−	669.247i	−0.188186	−	1.17412i
$571$	−678.503			−1.18827			−0.594135	−	0.804365i	$-0.702506\pi$
$571$	−678.503			−1.18827			−0.594135	+	0.804365i	$0.702506\pi$
$572$			557.809i			0.975191i
$573$	−940.676	+	150.770i	−1.64167	+	0.263124i
$574$	68.8560			0.119958
$575$			125.083i			0.217536i
$576$	−751.254	+	247.169i	−1.30426	+	0.429113i
$577$	313.594			0.543490			0.271745	−	0.962369i	$-0.412399\pi$
$577$	313.594			0.543490			0.271745	+	0.962369i	$0.412399\pi$
$578$			858.080i			1.48457i
$579$	135.828	+	847.451i	0.234591	+	1.46365i
$580$	−34.2038			−0.0589720
$581$		−	525.532i		−	0.904531i
$582$	746.517	−	119.651i	1.28268	−	0.205585i
$583$	352.783			0.605117
$584$		−	332.941i		−	0.570104i
$585$	67.7628	+	205.961i	0.115834	+	0.352070i
$586$	−64.8941			−0.110741
$587$		−	11.9241i		−	0.0203137i	−0.999948	−	0.0101568i	$-0.996767\pi$
$587$		−	11.9241i		−	0.0203137i	0.999948	−	0.0101568i	$-0.00323308\pi$
$588$	−81.8027	−	510.379i	−0.139120	−	0.867991i
$589$	−643.706			−1.09288
$590$		−	68.7176i		−	0.116471i
$591$	765.208	−	122.646i	1.29477	−	0.207523i
$592$	5.00379			0.00845234
$593$		−	310.201i		−	0.523104i	−0.965189	−	0.261552i	$-0.915766\pi$
$593$		−	310.201i		−	0.523104i	0.965189	−	0.261552i	$-0.0842344\pi$
$594$	−528.363	−	1022.92i	−0.889499	−	1.72208i
$595$	9.15890			0.0153931
$596$		−	754.491i		−	1.26593i
$597$	−12.6806	−	79.1161i	−0.0212405	−	0.132523i
$598$	186.892			0.312528
$599$		−	522.485i		−	0.872262i	−0.899883	−	0.436131i	$-0.856348\pi$
$599$		−	522.485i		−	0.872262i	0.899883	−	0.436131i	$-0.143652\pi$
$600$	−120.725	+	19.3496i	−0.201208	+	0.0322493i
$601$	−24.2214			−0.0403018			−0.0201509	−	0.999797i	$-0.506415\pi$
$601$	−24.2214			−0.0403018			−0.0201509	+	0.999797i	$0.506415\pi$
$602$		−	530.031i		−	0.880449i
$603$	860.772	−	283.201i	1.42748	−	0.469654i
$604$	487.086			0.806433
$605$		−	253.327i		−	0.418723i
$606$	−230.077	−	1435.48i	−0.379664	−	2.36878i
$607$	36.0443			0.0593810			0.0296905	−	0.999559i	$-0.490548\pi$
$607$	36.0443			0.0593810			0.0296905	+	0.999559i	$0.490548\pi$
$608$			1147.28i			1.88697i
$609$	25.5237	−	4.09090i	0.0419109	−	0.00671740i
$610$	−659.075			−1.08045
$611$		−	505.923i		−	0.828025i
$612$	11.3177	+	34.3994i	0.0184930	+	0.0562082i
$613$	185.688			0.302917			0.151458	−	0.988464i	$-0.451603\pi$
$613$	185.688			0.302917			0.151458	+	0.988464i	$0.451603\pi$
$614$		−	105.056i		−	0.171101i
$615$	8.97583	+	56.0015i	0.0145948	+	0.0910594i
$616$	−134.547			−0.218421
$617$		−	703.077i		−	1.13951i	−0.821815	−	0.569755i	$-0.807038\pi$
$617$		−	703.077i		−	1.13951i	0.821815	−	0.569755i	$-0.192962\pi$
$618$	−11.7332	+	1.88058i	−0.0189858	+	0.00304301i
$619$	−491.081			−0.793345			−0.396672	−	0.917960i	$-0.629835\pi$
$619$	−491.081			−0.793345			−0.396672	+	0.917960i	$0.629835\pi$
$620$		−	372.198i		−	0.600319i
$621$	−187.957	+	97.0845i	−0.302668	+	0.156336i
$622$	46.0030			0.0739598
$623$			270.131i			0.433597i
$624$	−45.0266	−	280.927i	−0.0721580	−	0.450204i
$625$	28.9683			0.0463493
$626$			1349.32i			2.15546i
$627$	−1071.80	+	171.786i	−1.70941	+	0.273981i
$628$	890.834			1.41853
$629$		−	0.350258i		−	0.000556849i
$630$	−281.345	+	92.5651i	−0.446580	+	0.146929i
$631$	1125.02			1.78291			0.891456	−	0.453107i	$-0.149684\pi$
$631$	1125.02			1.78291			0.891456	+	0.453107i	$0.149684\pi$
$632$			194.248i			0.307354i
$633$	176.666	+	1102.25i	0.279094	+	1.74131i
$634$	−33.4047			−0.0526888
$635$		−	123.274i		−	0.194133i
$636$	354.315	−	56.7890i	0.557099	−	0.0892908i
$637$	284.264			0.446255
$638$			99.8822i			0.156555i
$639$	−134.880	−	409.959i	−0.211080	−	0.641563i
$640$	−239.917			−0.374870
$641$			904.406i			1.41093i	0.708745	+	0.705465i	$0.249262\pi$
$641$			904.406i			1.41093i	−0.708745	+	0.705465i	$0.750738\pi$
$642$	−143.561	−	895.700i	−0.223616	−	1.39517i
$643$	275.235			0.428048			0.214024	−	0.976828i	$-0.431343\pi$
$643$	275.235			0.428048			0.214024	+	0.976828i	$0.431343\pi$
$644$			140.010i			0.217407i
$645$	431.081	−	69.0929i	0.668342	−	0.107121i
$646$	62.2562			0.0963719
$647$		−	206.877i		−	0.319748i	−0.987137	−	0.159874i	$-0.948891\pi$
$647$		−	206.877i		−	0.319748i	0.987137	−	0.159874i	$-0.0511087\pi$
$648$	−122.777	−	166.389i	−0.189471	−	0.256774i
$649$	−110.051			−0.169570
$650$		−	380.797i		−	0.585841i
$651$	44.5163	+	277.744i	0.0683813	+	0.426641i
$652$	775.896			1.19003
$653$		−	1076.47i		−	1.64850i	−0.566223	−	0.824252i	$-0.691596\pi$
$653$		−	1076.47i		−	1.64850i	0.566223	−	0.824252i	$-0.308404\pi$
$654$	−34.0556	+	5.45837i	−0.0520728	+	0.00834614i
$655$	−171.720			−0.262167
$656$		−	74.4230i		−	0.113450i
$657$	−1114.96	+	366.831i	−1.69705	+	0.558343i
$658$	691.099			1.05030
$659$			926.569i			1.40602i	0.711179	+	0.703011i	$0.248162\pi$
$659$			926.569i			1.40602i	−0.711179	+	0.703011i	$0.751838\pi$
$660$	−99.3285	−	619.725i	−0.150498	−	0.938977i
$661$	−164.989			−0.249605			−0.124803	−	0.992182i	$-0.539830\pi$
$661$	−164.989			−0.249605			−0.124803	+	0.992182i	$0.539830\pi$
$662$			397.441i			0.600364i
$663$	−19.6645	+	3.15180i	−0.0296599	+	0.00475384i
$664$	364.719			0.549276
$665$			279.244i			0.419916i
$666$	3.53991	+	10.7593i	0.00531518	+	0.0161551i
$667$	18.3529			0.0275157
$668$		−	1316.53i		−	1.97085i
$669$	−148.371	−	925.709i	−0.221780	−	1.38372i
$670$	900.753			1.34441
$671$			1055.51i			1.57304i
$672$	495.021	−	79.3412i	0.736639	−	0.118067i
$673$	−1140.47			−1.69460			−0.847302	−	0.531112i	$-0.821775\pi$
$673$	−1140.47			−1.69460			−0.847302	+	0.531112i	$0.821775\pi$
$674$			1162.38i			1.72460i
$675$	197.812	+	382.967i	0.293054	+	0.567358i
$676$	508.933			0.752859
$677$		−	21.8653i		−	0.0322973i	−0.999870	−	0.0161486i	$-0.994860\pi$
$677$		−	21.8653i		−	0.0322973i	0.999870	−	0.0161486i	$-0.00514050\pi$
$678$	94.9785	+	592.585i	0.140086	+	0.874019i
$679$	−311.485			−0.458741
$680$			6.35627i			0.00934746i
$681$	33.8009	−	5.41755i	0.0496342	−	0.00795529i
$682$	−1086.90			−1.59369
$683$			856.622i			1.25421i	0.778937	+	0.627103i	$0.215759\pi$
$683$			856.622i			1.25421i	−0.778937	+	0.627103i	$0.784241\pi$
$684$	−1048.80	+	345.064i	−1.53333	+	0.504479i
$685$	−111.991			−0.163491
$686$			924.763i			1.34805i
$687$	−160.204	−	999.536i	−0.233193	−	1.45493i
$688$	−572.883			−0.832679
$689$			197.342i			0.286418i
$690$	−207.637	+	33.2797i	−0.300923	+	0.0482314i
$691$	−497.476			−0.719937			−0.359968	−	0.932965i	$-0.617212\pi$
$691$	−497.476			−0.719937			−0.359968	+	0.932965i	$0.617212\pi$
$692$		−	1569.93i		−	2.26869i
$693$	148.243	+	450.574i	0.213915	+	0.650179i
$694$	1269.54			1.82930
$695$			456.617i			0.657003i
$696$	2.83908	+	17.7134i	0.00407914	+	0.0254503i
$697$	−5.20950			−0.00747418
$698$		−	1442.02i		−	2.06592i
$699$	−730.320	+	117.054i	−1.04481	+	0.167460i
$700$	285.273			0.407533
$701$		−	510.239i		−	0.727873i	−0.931424	−	0.363937i	$-0.881432\pi$
$701$		−	510.239i		−	0.727873i	0.931424	−	0.363937i	$-0.118568\pi$
$702$	572.206	−	295.558i	0.815108	−	0.421023i
$703$	10.6790			0.0151906
$704$			1259.02i			1.78837i
$705$	90.0892	+	562.080i	0.127786	+	0.797276i
$706$	1600.92			2.26759
$707$			598.957i			0.847181i
$708$	−110.529	+	17.7154i	−0.156114	+	0.0250218i
$709$	−21.4011			−0.0301849			−0.0150925	−	0.999886i	$-0.504804\pi$
$709$	−21.4011			−0.0301849			−0.0150925	+	0.999886i	$0.504804\pi$
$710$		−	429.001i		−	0.604227i
$711$	650.501	−	214.021i	0.914911	−	0.301013i
$712$	−187.471			−0.263302
$713$			199.713i			0.280102i
$714$	−4.30540	−	26.8620i	−0.00602997	−	0.0376219i
$715$	345.167			0.482751
$716$		−	33.9096i		−	0.0473598i
$717$	405.356	−	64.9698i	0.565351	−	0.0906134i
$718$	−178.161			−0.248135
$719$			271.790i			0.378012i	0.981976	+	0.189006i	$0.0605265\pi$
$719$			271.790i			0.378012i	−0.981976	+	0.189006i	$0.939473\pi$
$720$	100.049	+	304.092i	0.138957	+	0.422350i
$721$	4.89570			0.00679016
$722$			823.711i			1.14087i
$723$	−72.8535	−	454.544i	−0.100766	−	0.628691i
$724$	112.210			0.154986
$725$		−	37.3945i		−	0.0515786i
$726$	−742.981	+	119.084i	−1.02339	+	0.164027i
$727$	−520.902			−0.716509			−0.358254	−	0.933624i	$-0.616628\pi$
$727$	−520.902			−0.716509			−0.358254	+	0.933624i	$0.616628\pi$
$728$		−	75.2638i		−	0.103384i
$729$	−421.933	+	594.486i	−0.578784	+	0.815481i
$730$	−1166.75			−1.59828
$731$			40.1010i			0.0548577i
$732$	169.909	+	1060.09i	0.232117	+	1.44821i
$733$	655.583			0.894383			0.447192	−	0.894438i	$-0.352424\pi$
$733$	655.583			0.894383			0.447192	+	0.894438i	$0.352424\pi$
$734$			1873.59i			2.55257i
$735$	−315.817	+	50.6187i	−0.429683	+	0.0688689i
$736$	355.947			0.483624
$737$		−	1442.56i		−	1.95733i
$738$	160.027	−	52.6502i	0.216839	−	0.0713417i
$739$	160.286			0.216895			0.108448	−	0.994102i	$-0.465412\pi$
$739$	160.286			0.216895			0.108448	+	0.994102i	$0.465412\pi$
$740$			6.17469i			0.00834417i
$741$	−96.0946	−	599.548i	−0.129682	−	0.809107i
$742$	−269.572			−0.363304
$743$			1101.61i			1.48265i	0.671145	+	0.741326i	$0.265803\pi$
$743$			1101.61i			1.48265i	−0.671145	+	0.741326i	$0.734197\pi$
$744$	−192.754	+	30.8943i	−0.259078	+	0.0415245i
$745$	−466.872			−0.626673
$746$		−	238.462i		−	0.319654i
$747$	−401.844	−	1221.38i	−0.537944	−	1.63505i
$748$	57.6495			0.0770715
$749$			373.732i			0.498975i
$750$	173.995	+	1085.58i	0.231993	+	1.44744i
$751$	1083.43			1.44265			0.721323	−	0.692598i	$-0.243534\pi$
$751$	1083.43			1.44265			0.721323	+	0.692598i	$0.243534\pi$
$752$		−	746.973i		−	0.993315i
$753$	−466.831	+	74.8229i	−0.619961	+	0.0993663i
$754$	−55.8726			−0.0741017
$755$		−	301.404i		−	0.399210i
$756$	221.417	+	428.667i	0.292880	+	0.567020i
$757$	601.996			0.795239			0.397620	−	0.917550i	$-0.369836\pi$
$757$	601.996			0.795239			0.397620	+	0.917550i	$0.369836\pi$
$758$			444.883i			0.586917i
$759$	53.2973	+	332.530i	0.0702205	+	0.438116i
$760$	−193.795			−0.254994
$761$		−	33.3091i		−	0.0437702i	−0.999760	−	0.0218851i	$-0.993033\pi$
$761$		−	33.3091i		−	0.0437702i	0.999760	−	0.0218851i	$-0.00696680\pi$
$762$	−361.550	+	57.9486i	−0.474475	+	0.0760481i
$763$	14.2097			0.0186235
$764$			1542.64i			2.01916i
$765$	21.2860	−	7.00328i	0.0278249	−	0.00915461i
$766$	−101.925			−0.133062
$767$		−	61.5611i		−	0.0802621i
$768$	−54.1028	−	337.555i	−0.0704464	−	0.439525i
$769$	231.879			0.301533			0.150766	−	0.988569i	$-0.451826\pi$
$769$	231.879			0.301533			0.150766	+	0.988569i	$0.451826\pi$
$770$			471.503i			0.612341i
$771$	1125.20	−	180.345i	1.45940	−	0.233911i
$772$	1389.75			1.80020
$773$		−	444.880i		−	0.575524i	−0.957702	−	0.287762i	$-0.907089\pi$
$773$		−	444.880i		−	0.575524i	0.957702	−	0.287762i	$-0.0929113\pi$
$774$	−405.284	−	1231.83i	−0.523622	−	1.59152i
$775$	406.919			0.525057
$776$		−	216.171i		−	0.278570i
$777$	−0.738516	−	4.60771i	−0.000950471	−	0.00593013i
$778$	210.630			0.270732
$779$		−	158.832i		−	0.203892i
$780$	346.665	−	55.5629i	0.444443	−	0.0712345i
$781$	−687.044			−0.879698
$782$		−	19.3153i		−	0.0246998i
$783$	56.1911	−	29.0241i	0.0717638	−	0.0370678i
$784$	419.704			0.535337
$785$		−	551.239i		−	0.702216i
$786$	80.7217	+	503.635i	0.102699	+	0.640757i
$787$	−344.088			−0.437215			−0.218607	−	0.975813i	$-0.570151\pi$
$787$	−344.088			−0.437215			−0.218607	+	0.975813i	$0.570151\pi$
$788$		−	1254.88i		−	1.59249i
$789$	1354.94	−	217.168i	1.71729	−	0.275244i
$790$	680.716			0.861666
$791$		−	247.257i		−	0.312588i
$792$	−312.698	+	102.880i	−0.394821	+	0.129899i
$793$	−590.436			−0.744560
$794$			1960.02i			2.46854i
$795$	−35.1404	−	219.246i	−0.0442018	−	0.275782i
$796$	−129.744			−0.162995
$797$			1010.66i			1.26808i	0.773302	+	0.634038i	$0.218604\pi$
$797$			1010.66i			1.26808i	−0.773302	+	0.634038i	$0.781396\pi$
$798$	818.992	−	131.267i	1.02631	−	0.164495i
$799$	−52.2871			−0.0654406
$800$		−	725.250i		−	0.906563i
$801$	206.554	+	627.806i	0.257870	+	0.783778i
$802$	1173.89			1.46370
$803$			1868.54i			2.32695i
$804$	−232.214	−	1448.82i	−0.288824	−	1.80201i
$805$	86.6367			0.107623
$806$		−	607.994i		−	0.754335i
$807$	459.019	−	73.5707i	0.568796	−	0.0911657i
$808$	−415.676			−0.514450
$809$			887.084i			1.09652i	0.836308	+	0.548260i	$0.184709\pi$
$809$			887.084i			1.09652i	−0.836308	+	0.548260i	$0.815291\pi$
$810$	−583.090	+	430.257i	−0.719864	+	0.531182i
$811$	95.4437			0.117686			0.0588432	−	0.998267i	$-0.481259\pi$
$811$	95.4437			0.117686			0.0588432	+	0.998267i	$0.481259\pi$
$812$		−	41.8569i		−	0.0515479i
$813$	25.4383	+	158.713i	0.0312894	+	0.195219i
$814$	18.0314			0.0221516
$815$		−	480.117i		−	0.589100i
$816$	−29.0338	+	4.65349i	−0.0355806	+	0.00570280i
$817$	−1222.63			−1.49649
$818$		−	1493.04i		−	1.82523i
$819$	−252.045	+	82.9249i	−0.307747	+	0.101251i
$820$	91.8382			0.111998
$821$			342.926i			0.417693i	0.977948	+	0.208847i	$0.0669710\pi$
$821$			342.926i			0.417693i	−0.977948	+	0.208847i	$0.933029\pi$
$822$	52.6446	+	328.457i	0.0640445	+	0.399583i
$823$	−480.308			−0.583606			−0.291803	−	0.956478i	$-0.594255\pi$
$823$	−480.308			−0.583606			−0.291803	+	0.956478i	$0.594255\pi$
$824$			3.39762i			0.00412332i
$825$	677.537	−	108.594i	0.821257	−	0.131630i
$826$	84.0933			0.101808
$827$		−	551.486i		−	0.666851i	−0.942776	−	0.333426i	$-0.891795\pi$
$827$		−	551.486i		−	0.666851i	0.942776	−	0.333426i	$-0.108205\pi$
$828$	107.057	+	325.394i	0.129296	+	0.392988i
$829$	−1375.90			−1.65971			−0.829853	−	0.557982i	$-0.811576\pi$
$829$	−1375.90			−1.65971			−0.829853	+	0.557982i	$0.811576\pi$
$830$		−	1278.11i		−	1.53989i
$831$	−172.491	−	1076.20i	−0.207571	−	1.29506i
$832$	−704.275			−0.846485
$833$		−	29.3787i		−	0.0352685i
$834$	1339.21	−	214.646i	1.60576	−	0.257369i
$835$	−814.655			−0.975634
$836$			1757.67i			2.10247i
$837$	315.834	+	611.459i	0.377340	+	0.730536i
$838$	1140.87			1.36142
$839$		−	1542.80i		−	1.83886i	−0.393256	−	0.919429i	$-0.628651\pi$
$839$		−	1542.80i		−	1.83886i	0.393256	−	0.919429i	$-0.371349\pi$
$840$	13.4021	+	83.6179i	0.0159549	+	0.0995451i
$841$	835.513			0.993476
$842$		−	1308.90i		−	1.55452i
$843$	−1200.07	+	192.345i	−1.42357	+	0.228167i
$844$	1807.60			2.14171
$845$		−	314.922i		−	0.372689i
$846$	1606.17	−	528.443i	1.89854	−	0.624637i
$847$	310.010			0.366009
$848$			291.366i			0.343593i
$849$	178.230	+	1112.01i	0.209930	+	1.30978i
$850$	−39.3553			−0.0463003
$851$		−	3.31319i		−	0.00389329i
$852$	−690.027	+	110.596i	−0.809891	+	0.129808i
$853$	628.277			0.736550			0.368275	−	0.929717i	$-0.379949\pi$
$853$	628.277			0.736550			0.368275	+	0.929717i	$0.379949\pi$
$854$		−	806.544i		−	0.944431i
$855$	213.522	+	648.986i	0.249733	+	0.759048i
$856$	−259.370			−0.303002
$857$		−	1466.23i		−	1.71089i	−0.517894	−	0.855445i	$-0.673284\pi$
$857$		−	1466.23i		−	1.71089i	0.517894	−	0.855445i	$-0.326716\pi$
$858$	−162.255	−	1012.34i	−0.189109	−	1.17988i
$859$	454.895			0.529563			0.264782	−	0.964308i	$-0.414700\pi$
$859$	454.895			0.529563			0.264782	+	0.964308i	$0.414700\pi$
$860$		−	706.939i		−	0.822023i
$861$	−68.5320	+	10.9842i	−0.0795958	+	0.0127575i
$862$	−1914.42			−2.22091
$863$		−	598.566i		−	0.693587i	−0.937942	−	0.346794i	$-0.887270\pi$
$863$		−	598.566i		−	0.693587i	0.937942	−	0.346794i	$-0.112730\pi$
$864$	1089.80	−	562.909i	1.26134	−	0.651515i
$865$	−971.458			−1.12307
$866$			913.433i			1.05477i
$867$	−136.884	−	854.042i	−0.157883	−	0.985054i
$868$	455.478			0.524744
$869$		−	1090.17i		−	1.25451i
$870$	62.0744	−	9.94918i	0.0713499	−	0.0114358i
$871$	806.945			0.926458
$872$			9.86155i			0.0113091i
$873$	−723.917	+	238.175i	−0.829229	+	0.272823i
$874$	588.900			0.673798
$875$		−	452.960i		−	0.517668i
$876$	300.787	+	1876.66i	0.343365	+	2.14230i
$877$	−853.750			−0.973489			−0.486745	−	0.873544i	$-0.661816\pi$
$877$	−853.750			−0.973489			−0.486745	+	0.873544i	$0.661816\pi$
$878$		−	2116.96i		−	2.41112i
$879$	64.5887	−	10.3522i	0.0734798	−	0.0117772i
$880$	509.624			0.579118
$881$		−	648.926i		−	0.736579i	−0.929711	−	0.368290i	$-0.879944\pi$
$881$		−	648.926i		−	0.736579i	0.929711	−	0.368290i	$-0.120056\pi$
$882$	296.918	+	902.462i	0.336641	+	1.02320i
$883$	−417.090			−0.472355			−0.236178	−	0.971710i	$-0.575895\pi$
$883$	−417.090			−0.472355			−0.236178	+	0.971710i	$0.575895\pi$
$884$			32.2483i			0.0364800i
$885$	10.9621	+	68.3942i	0.0123866	+	0.0772816i
$886$	−909.301			−1.02630
$887$		−	868.327i		−	0.978948i	−0.872018	−	0.489474i	$-0.837189\pi$
$887$		−	868.327i		−	0.978948i	0.872018	−	0.489474i	$-0.162811\pi$
$888$	3.19775	−	0.512529i	0.00360107	−	0.000577173i
$889$	150.857			0.169693
$890$			656.967i			0.738165i
$891$	689.056	+	933.818i	0.773351	+	1.04806i
$892$	−1518.09			−1.70190
$893$		−	1594.17i		−	1.78519i
$894$	219.466	+	1369.28i	0.245488	+	1.53164i
$895$	−20.9829			−0.0234446
$896$		−	293.598i		−	0.327677i
$897$	−186.012	+	29.8138i	−0.207372	+	0.0332372i
$898$	−681.506			−0.758915
$899$		−	59.7055i		−	0.0664132i
$900$	662.998	−	218.132i	0.736664	−	0.242369i
$901$	20.3952			0.0226362
$902$		−	268.187i		−	0.297325i
$903$	84.5526	+	527.536i	0.0936352	+	0.584204i
$904$	171.596			0.189819
$905$		−	69.4343i		−	0.0767230i
$906$	−883.983	+	141.683i	−0.975699	+	0.156383i
$907$	−1302.76			−1.43634			−0.718171	−	0.695867i	$-0.755020\pi$
$907$	−1302.76			−1.43634			−0.718171	+	0.695867i	$0.755020\pi$
$908$		−	55.4309i		−	0.0610472i
$909$	457.988	+	1392.02i	0.503837	+	1.53138i
$910$	−263.752			−0.289837
$911$		−	353.839i		−	0.388407i	−0.980961	−	0.194203i	$-0.937788\pi$
$911$		−	353.839i		−	0.388407i	0.980961	−	0.194203i	$-0.0622122\pi$
$912$	−141.879	−	885.207i	−0.155570	−	0.970621i
$913$	−2046.89			−2.24194
$914$		−	41.5360i		−	0.0454443i
$915$	655.973	−	105.138i	0.716911	−	0.114905i
$916$	−1639.16			−1.78948
$917$		−	210.142i		−	0.229163i
$918$	−30.5459	−	59.1374i	−0.0332744	−	0.0644198i
$919$	−422.773			−0.460036			−0.230018	−	0.973186i	$-0.573879\pi$
$919$	−422.773			−0.460036			−0.230018	+	0.973186i	$0.573879\pi$
$920$			60.1258i			0.0653542i
$921$	16.7589	+	104.561i	0.0181964	+	0.113530i
$922$	1543.85			1.67445
$923$		−	384.323i		−	0.416384i
$924$	758.390	−	121.553i	0.820768	−	0.131551i
$925$	−6.75070			−0.00729806
$926$			2599.36i			2.80708i
$927$	11.3780	−	3.74346i	0.0122740	−	0.00403825i
$928$	−106.413			−0.114669
$929$		−	621.240i		−	0.668719i	−0.942446	−	0.334359i	$-0.891480\pi$
$929$		−	621.240i		−	0.668719i	0.942446	−	0.334359i	$-0.108520\pi$
$930$	108.265	+	675.480i	0.116414	+	0.726323i
$931$	895.722			0.962107
$932$			1197.67i			1.28505i
$933$	−45.7865	+	7.33858i	−0.0490745	+	0.00786557i
$934$	46.7473			0.0500506
$935$		−	35.6729i		−	0.0381529i
$936$	−57.5498	−	174.919i	−0.0614848	−	0.186879i
$937$	1193.75			1.27402			0.637008	−	0.770858i	$-0.280172\pi$
$937$	1193.75			1.27402			0.637008	+	0.770858i	$0.280172\pi$
$938$			1102.30i			1.17516i
$939$	−215.249	−	1342.97i	−0.229232	−	1.43021i
$940$	921.767			0.980604
$941$			1131.16i			1.20208i	0.799217	+	0.601042i	$0.205248\pi$
$941$			1131.16i			1.20208i	−0.799217	+	0.601042i	$0.794752\pi$
$942$	−1616.72	+	259.126i	−1.71627	+	0.275080i
$943$	−49.2782			−0.0522569
$944$		−	90.8922i		−	0.0962841i
$945$	265.255	−	137.011i	0.280693	−	0.144985i
$946$	−2064.41			−2.18225
$947$		−	766.712i		−	0.809622i	−0.914400	−	0.404811i	$-0.867337\pi$
$947$		−	766.712i		−	0.809622i	0.914400	−	0.404811i	$-0.132663\pi$
$948$	−175.489	−	1094.90i	−0.185115	−	1.15496i
$949$	−1045.24			−1.10141
$950$		−	1199.90i		−	1.26305i
$951$	33.2475	−	5.32885i	0.0349606	−	0.00560342i
$952$	−7.77850			−0.00817069
$953$		−	239.940i		−	0.251773i	−0.992045	−	0.125887i	$-0.959822\pi$
$953$		−	239.940i		−	0.251773i	0.992045	−	0.125887i	$-0.0401776\pi$
$954$	−626.506	+	206.126i	−0.656715	+	0.216065i
$955$	954.568			0.999547
$956$		−	664.753i		−	0.695349i
$957$	−15.9336	−	99.4121i	−0.0166495	−	0.103879i
$958$	1119.04			1.16810
$959$		−	137.049i		−	0.142909i
$960$	782.449	−	125.410i	0.815051	−	0.130635i
$961$	−311.298			−0.323931
$962$			10.0865i			0.0104849i
$963$	285.771	+	868.583i	0.296751	+	0.901955i
$964$	−745.416			−0.773254
$965$		−	859.966i		−	0.891156i
$966$	−40.7260	−	254.096i	−0.0421595	−	0.263039i
$967$	−1856.93			−1.92030			−0.960150	−	0.279484i	$-0.909837\pi$
$967$	−1856.93			−1.92030			−0.960150	+	0.279484i	$0.909837\pi$
$968$			215.147i			0.222259i
$969$	−61.9632	+	9.93136i	−0.0639455	+	0.0102491i
$970$	−757.542			−0.780971
$971$			407.887i			0.420069i	0.977694	+	0.210034i	$0.0673576\pi$
$971$			407.887i			0.420069i	−0.977694	+	0.210034i	$0.932642\pi$
$972$	842.368	+	826.952i	0.866634	+	0.850773i
$973$	−558.786			−0.574292
$974$			2350.27i			2.41300i
$975$	60.7462	+	379.004i	0.0623038	+	0.388722i
$976$	−871.753			−0.893189
$977$			531.210i			0.543716i	0.962337	+	0.271858i	$0.0876380\pi$
$977$			531.210i			0.543716i	−0.962337	+	0.271858i	$0.912362\pi$
$978$	−1408.13	+	225.693i	−1.43980	+	0.230769i
$979$	1052.13			1.07470
$980$			517.916i			0.528486i
$981$	33.0246	−	10.8654i	0.0336642	−	0.0110758i
$982$	1827.32			1.86082
$983$			707.841i			0.720082i	0.932936	+	0.360041i	$0.117237\pi$
$983$			707.841i			0.720082i	−0.932936	+	0.360041i	$0.882763\pi$
$984$	−7.62302	−	47.5611i	−0.00774697	−	0.0483345i
$985$	−776.509			−0.788334
$986$			5.77443i			0.00585642i
$987$	−687.846	+	110.247i	−0.696906	+	0.111699i
$988$	−983.213			−0.995155
$989$			379.327i			0.383546i
$990$	360.531	+	1095.81i	0.364173	+	1.10688i
$991$	237.797			0.239957			0.119978	−	0.992777i	$-0.461717\pi$
$991$	237.797			0.239957			0.119978	+	0.992777i	$0.461717\pi$
$992$		−	1157.96i		−	1.16730i
$993$	−63.4014	−	395.570i	−0.0638483	−	0.398359i
$994$	524.991			0.528160
$995$			80.2845i			0.0806879i
$996$	−2055.78	+	329.497i	−2.06403	+	0.330820i
$997$	−1298.45			−1.30235			−0.651176	−	0.758927i	$-0.725724\pi$
$997$	−1298.45			−1.30235			−0.651176	+	0.758927i	$0.725724\pi$
$998$			1395.65i			1.39844i
$999$	−5.23962	−	10.1440i	−0.00524486	−	0.0101541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.32	yes	38
3.2	odd	2	inner	177.3.b.a.119.7	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.7	✓	38	3.2	odd	2	inner
177.3.b.a.119.32	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)

\(f(q)\)	\(=\)	\(q+2.97620i q^{2} +(-0.474775 - 2.96219i) q^{3} -4.85777 q^{4} +3.00594i q^{5} +(8.81608 - 1.41303i) q^{6} -3.67852 q^{7} -2.55289i q^{8} +(-8.54918 + 2.81275i) q^{9} +O(q^{10})\)	\(q+2.97620i q^{2} +(-0.474775 - 2.96219i) q^{3} -4.85777 q^{4} +3.00594i q^{5} +(8.81608 - 1.41303i) q^{6} -3.67852 q^{7} -2.55289i q^{8} +(-8.54918 + 2.81275i) q^{9} -8.94628 q^{10} +14.3274i q^{11} +(2.30635 + 14.3896i) q^{12} -8.01457 q^{13} -10.9480i q^{14} +(8.90417 - 1.42715i) q^{15} -11.8332 q^{16} +0.828304i q^{17} +(-8.37131 - 25.4441i) q^{18} -25.2540 q^{19} -14.6022i q^{20} +(1.74647 + 10.8965i) q^{21} -42.6413 q^{22} +7.83517i q^{23} +(-7.56216 + 1.21205i) q^{24} +15.9643 q^{25} -23.8530i q^{26} +(12.3909 + 23.9889i) q^{27} +17.8694 q^{28} -2.34238i q^{29} +(4.24747 + 26.5006i) q^{30} +25.4893 q^{31} -45.4294i q^{32} +(42.4407 - 6.80232i) q^{33} -2.46520 q^{34} -11.0574i q^{35} +(41.5299 - 13.6637i) q^{36} -0.422862 q^{37} -75.1611i q^{38} +(3.80512 + 23.7407i) q^{39} +7.67384 q^{40} +6.28936i q^{41} +(-32.4301 + 5.19785i) q^{42} +48.4134 q^{43} -69.5994i q^{44} +(-8.45496 - 25.6983i) q^{45} -23.3190 q^{46} +63.1254i q^{47} +(5.61809 + 35.0521i) q^{48} -35.4685 q^{49} +47.5131i q^{50} +(2.45360 - 0.393258i) q^{51} +38.9329 q^{52} -24.6229i q^{53} +(-71.3957 + 36.8777i) q^{54} -43.0674 q^{55} +9.39087i q^{56} +(11.9900 + 74.8073i) q^{57} +6.97139 q^{58} +7.68115i q^{59} +(-43.2544 + 6.93274i) q^{60} +73.6703 q^{61} +75.8611i q^{62} +(31.4483 - 10.3468i) q^{63} +87.8744 q^{64} -24.0913i q^{65} +(20.2451 + 126.312i) q^{66} -100.685 q^{67} -4.02371i q^{68} +(23.2093 - 3.71995i) q^{69} +32.9091 q^{70} +47.9530i q^{71} +(7.18065 + 21.8251i) q^{72} +130.417 q^{73} -1.25852i q^{74} +(-7.57947 - 47.2894i) q^{75} +122.678 q^{76} -52.7038i q^{77} +(-70.6571 + 11.3248i) q^{78} -76.0894 q^{79} -35.5697i q^{80} +(65.1768 - 48.0934i) q^{81} -18.7184 q^{82} +142.865i q^{83} +(-8.48395 - 52.9326i) q^{84} -2.48983 q^{85} +144.088i q^{86} +(-6.93858 + 1.11210i) q^{87} +36.5764 q^{88} -73.4347i q^{89} +(76.4833 - 25.1637i) q^{90} +29.4818 q^{91} -38.0615i q^{92} +(-12.1017 - 75.5041i) q^{93} -187.874 q^{94} -75.9121i q^{95} +(-134.571 + 21.5688i) q^{96} +84.6768 q^{97} -105.561i q^{98} +(-40.2996 - 122.488i) 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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