LMFDB - Embedded newform 177.3.b.a.119.33

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			119.33
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.09739i q^{2} +(1.87116 - 2.34495i) q^{3} -5.59384 q^{4} -8.72041i q^{5} +(7.26322 + 5.79571i) q^{6} -11.2236 q^{7} -4.93675i q^{8} +(-1.99754 - 8.77552i) q^{9} +O(q^{10})$	\(q+3.09739i q^{2} +(1.87116 - 2.34495i) q^{3} -5.59384 q^{4} -8.72041i q^{5} +(7.26322 + 5.79571i) q^{6} -11.2236 q^{7} -4.93675i q^{8} +(-1.99754 - 8.77552i) q^{9} +27.0105 q^{10} -9.18062i q^{11} +(-10.4670 + 13.1173i) q^{12} +7.17130 q^{13} -34.7638i q^{14} +(-20.4489 - 16.3173i) q^{15} -7.08431 q^{16} -10.0383i q^{17} +(27.1812 - 6.18717i) q^{18} +27.7412 q^{19} +48.7806i q^{20} +(-21.0011 + 26.3187i) q^{21} +28.4360 q^{22} +2.46954i q^{23} +(-11.5764 - 9.23743i) q^{24} -51.0456 q^{25} +22.2123i q^{26} +(-24.3158 - 11.7363i) q^{27} +62.7829 q^{28} +42.9540i q^{29} +(50.5410 - 63.3383i) q^{30} +39.9367 q^{31} -41.6899i q^{32} +(-21.5280 - 17.1784i) q^{33} +31.0924 q^{34} +97.8742i q^{35} +(11.1739 + 49.0889i) q^{36} -42.6497 q^{37} +85.9253i q^{38} +(13.4186 - 16.8163i) q^{39} -43.0505 q^{40} +20.2872i q^{41} +(-81.5193 - 65.0486i) q^{42} +56.9139 q^{43} +51.3549i q^{44} +(-76.5262 + 17.4194i) q^{45} -7.64913 q^{46} -47.6938i q^{47} +(-13.2559 + 16.6123i) q^{48} +76.9687 q^{49} -158.108i q^{50} +(-23.5392 - 18.7832i) q^{51} -40.1151 q^{52} -68.4700i q^{53} +(36.3518 - 75.3157i) q^{54} -80.0588 q^{55} +55.4080i q^{56} +(51.9081 - 65.0515i) q^{57} -133.045 q^{58} -7.68115i q^{59} +(114.388 + 91.2762i) q^{60} -31.4105 q^{61} +123.700i q^{62} +(22.4196 + 98.4928i) q^{63} +100.793 q^{64} -62.5367i q^{65} +(53.2082 - 66.6808i) q^{66} +17.2244 q^{67} +56.1524i q^{68} +(5.79093 + 4.62089i) q^{69} -303.155 q^{70} -42.1176i q^{71} +(-43.3226 + 9.86136i) q^{72} +45.5157 q^{73} -132.103i q^{74} +(-95.5143 + 119.699i) q^{75} -155.180 q^{76} +103.039i q^{77} +(52.0867 + 41.5627i) q^{78} +27.8864 q^{79} +61.7781i q^{80} +(-73.0197 + 35.0590i) q^{81} -62.8373 q^{82} -0.101688i q^{83} +(117.477 - 147.222i) q^{84} -87.5378 q^{85} +176.285i q^{86} +(100.725 + 80.3736i) q^{87} -45.3224 q^{88} +34.2875i q^{89} +(-53.9547 - 237.032i) q^{90} -80.4876 q^{91} -13.8142i q^{92} +(74.7279 - 93.6495i) q^{93} +147.727 q^{94} -241.914i q^{95} +(-97.7605 - 78.0083i) q^{96} +59.1817 q^{97} +238.402i q^{98} +(-80.5647 + 18.3387i) 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 $

$2$			3.09739i			1.54870i	0.632760	+	0.774348i	$0.281922\pi$
$2$			3.09739i			1.54870i	−0.632760	+	0.774348i	$0.718078\pi$
$3$	1.87116	−	2.34495i	0.623719	−	0.781649i
$3$	1.87116	−	2.34495i	0.623719	−	0.781649i
$4$	−5.59384			−1.39846
$5$		−	8.72041i		−	1.74408i	−0.489432	−	0.872041i	$-0.662796\pi$
$5$		−	8.72041i		−	1.74408i	0.489432	−	0.872041i	$-0.337204\pi$
$6$	7.26322	+	5.79571i	1.21054	+	0.965951i
$7$	−11.2236			−1.60337			−0.801684	−	0.597748i	$-0.796062\pi$
$7$	−11.2236			−1.60337			−0.801684	+	0.597748i	$0.796062\pi$
$8$		−	4.93675i		−	0.617094i
$9$	−1.99754	−	8.77552i	−0.221949	−	0.975058i
$10$	27.0105			2.70105
$11$		−	9.18062i		−	0.834601i	−0.908768	−	0.417301i	$-0.862976\pi$
$11$		−	9.18062i		−	0.834601i	0.908768	−	0.417301i	$-0.137024\pi$
$12$	−10.4670	+	13.1173i	−0.872246	+	1.09310i
$13$	7.17130			0.551638			0.275819	−	0.961210i	$-0.411051\pi$
$13$	7.17130			0.551638			0.275819	+	0.961210i	$0.411051\pi$
$14$		−	34.7638i		−	2.48313i
$15$	−20.4489	−	16.3173i	−1.36326	−	1.08782i
$16$	−7.08431			−0.442770
$17$		−	10.0383i		−	0.590486i	−0.955422	−	0.295243i	$-0.904599\pi$
$17$		−	10.0383i		−	0.590486i	0.955422	−	0.295243i	$-0.0954006\pi$
$18$	27.1812	−	6.18717i	1.51007	−	0.343732i
$19$	27.7412			1.46006			0.730031	−	0.683414i	$-0.239506\pi$
$19$	27.7412			1.46006			0.730031	+	0.683414i	$0.239506\pi$
$20$			48.7806i			2.43903i
$21$	−21.0011	+	26.3187i	−1.00005	+	1.25327i
$22$	28.4360			1.29254
$23$			2.46954i			0.107371i	0.998558	+	0.0536856i	$0.0170969\pi$
$23$			2.46954i			0.107371i	−0.998558	+	0.0536856i	$0.982903\pi$
$24$	−11.5764	−	9.23743i	−0.482350	−	0.384893i
$25$	−51.0456			−2.04182
$26$			22.2123i			0.854320i
$27$	−24.3158	−	11.7363i	−0.900587	−	0.434676i
$28$	62.7829			2.24225
$29$			42.9540i			1.48117i	0.671962	+	0.740586i	$0.265452\pi$
$29$			42.9540i			1.48117i	−0.671962	+	0.740586i	$0.734548\pi$
$30$	50.5410	−	63.3383i	1.68470	−	2.11128i
$31$	39.9367			1.28828			0.644141	−	0.764907i	$-0.277215\pi$
$31$	39.9367			1.28828			0.644141	+	0.764907i	$0.277215\pi$
$32$		−	41.6899i		−	1.30281i
$33$	−21.5280	−	17.1784i	−0.652365	−	0.520557i
$34$	31.0924			0.914484
$35$			97.8742i			2.79641i
$36$	11.1739	+	49.0889i	0.310387	+	1.36358i
$37$	−42.6497			−1.15269			−0.576347	−	0.817205i	$-0.695522\pi$
$37$	−42.6497			−1.15269			−0.576347	+	0.817205i	$0.695522\pi$
$38$			85.9253i			2.26119i
$39$	13.4186	−	16.8163i	0.344067	−	0.431187i
$40$	−43.0505			−1.07626
$41$			20.2872i			0.494809i	0.968912	+	0.247404i	$0.0795776\pi$
$41$			20.2872i			0.494809i	−0.968912	+	0.247404i	$0.920422\pi$
$42$	−81.5193	−	65.0486i	−1.94094	−	1.54878i
$43$	56.9139			1.32358			0.661790	−	0.749689i	$-0.269797\pi$
$43$	56.9139			1.32358			0.661790	+	0.749689i	$0.269797\pi$
$44$			51.3549i			1.16716i
$45$	−76.5262	+	17.4194i	−1.70058	+	0.387098i
$46$	−7.64913			−0.166285
$47$		−	47.6938i		−	1.01476i	−0.861722	−	0.507381i	$-0.830614\pi$
$47$		−	47.6938i		−	1.01476i	0.861722	−	0.507381i	$-0.169386\pi$
$48$	−13.2559	+	16.6123i	−0.276164	+	0.346090i
$49$	76.9687			1.57079
$50$		−	158.108i		−	3.16216i
$51$	−23.5392	−	18.7832i	−0.461553	−	0.368297i
$52$	−40.1151			−0.771444
$53$		−	68.4700i		−	1.29189i	−0.763386	−	0.645943i	$-0.776464\pi$
$53$		−	68.4700i		−	1.29189i	0.763386	−	0.645943i	$-0.223536\pi$
$54$	36.3518	−	75.3157i	0.673181	−	1.39474i
$55$	−80.0588			−1.45561
$56$			55.4080i			0.989428i
$57$	51.9081	−	65.0515i	0.910668	−	1.14125i
$58$	−133.045			−2.29388
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	114.388	+	91.2762i	1.90646	+	1.52127i
$61$	−31.4105			−0.514926			−0.257463	−	0.966288i	$-0.582887\pi$
$61$	−31.4105			−0.514926			−0.257463	+	0.966288i	$0.582887\pi$
$62$			123.700i			1.99516i
$63$	22.4196	+	98.4928i	0.355866	+	1.56338i
$64$	100.793			1.57489
$65$		−	62.5367i		−	0.962102i
$66$	53.2082	−	66.6808i	0.806184	−	1.01032i
$67$	17.2244			0.257081			0.128540	−	0.991704i	$-0.458971\pi$
$67$	17.2244			0.257081			0.128540	+	0.991704i	$0.458971\pi$
$68$			56.1524i			0.825771i
$69$	5.79093	+	4.62089i	0.0839266	+	0.0669695i
$70$	−303.155			−4.33078
$71$		−	42.1176i		−	0.593205i	−0.955001	−	0.296603i	$-0.904146\pi$
$71$		−	42.1176i		−	0.593205i	0.955001	−	0.296603i	$-0.0958536\pi$
$72$	−43.3226	+	9.86136i	−0.601702	+	0.136963i
$73$	45.5157			0.623503			0.311751	−	0.950164i	$-0.399084\pi$
$73$	45.5157			0.623503			0.311751	+	0.950164i	$0.399084\pi$
$74$		−	132.103i		−	1.78517i
$75$	−95.5143	+	119.699i	−1.27352	+	1.59599i
$76$	−155.180			−2.04184
$77$			103.039i			1.33817i
$78$	52.0867	+	41.5627i	0.667778	+	0.532856i
$79$	27.8864			0.352993			0.176496	−	0.984301i	$-0.443524\pi$
$79$	27.8864			0.352993			0.176496	+	0.984301i	$0.443524\pi$
$80$			61.7781i			0.772227i
$81$	−73.0197	+	35.0590i	−0.901477	+	0.432827i
$82$	−62.8373			−0.766308
$83$		−	0.101688i		−	0.00122516i	−1.00000		0.000612579i	$-0.999805\pi$
$83$		−	0.101688i		−	0.00122516i	1.00000		0.000612579i	$-0.000194990\pi$
$84$	117.477	−	147.222i	1.39853	−	1.75265i
$85$	−87.5378			−1.02986
$86$			176.285i			2.04982i
$87$	100.725	+	80.3736i	1.15776	+	0.923835i
$88$	−45.3224			−0.515027
$89$			34.2875i			0.385252i	0.981272	+	0.192626i	$0.0617005\pi$
$89$			34.2875i			0.385252i	−0.981272	+	0.192626i	$0.938300\pi$
$90$	−53.9547	−	237.032i	−0.599496	−	2.63369i
$91$	−80.4876			−0.884479
$92$		−	13.8142i		−	0.150154i
$93$	74.7279	−	93.6495i	0.803526	−	1.00698i
$94$	147.727			1.57156
$95$		−	241.914i		−	2.54647i
$96$	−97.7605	−	78.0083i	−1.01834	−	0.812587i
$97$	59.1817			0.610121			0.305061	−	0.952333i	$-0.401323\pi$
$97$	59.1817			0.610121			0.305061	+	0.952333i	$0.401323\pi$
$98$			238.402i			2.43268i
$99$	−80.5647	+	18.3387i	−0.813785	+	0.185239i
$100$	285.541			2.85541
$101$			109.102i			1.08022i	0.841594	+	0.540110i	$0.181617\pi$
$101$			109.102i			1.08022i	−0.841594	+	0.540110i	$0.818383\pi$
$102$	58.1788	−	72.9101i	0.570381	−	0.714805i
$103$	84.9548			0.824804			0.412402	−	0.911002i	$-0.364690\pi$
$103$	84.9548			0.824804			0.412402	+	0.911002i	$0.364690\pi$
$104$		−	35.4029i		−	0.340412i
$105$	229.510	+	183.138i	2.18581	+	1.74417i
$106$	212.078			2.00074
$107$		−	132.466i		−	1.23800i	−0.785389	−	0.619002i	$-0.787537\pi$
$107$		−	132.466i		−	1.23800i	0.785389	−	0.619002i	$-0.212463\pi$
$108$	136.019	+	65.6508i	1.25943	+	0.607877i
$109$	42.8315			0.392950			0.196475	−	0.980509i	$-0.437051\pi$
$109$	42.8315			0.392950			0.196475	+	0.980509i	$0.437051\pi$
$110$		−	247.973i		−	2.25430i
$111$	−79.8042	+	100.011i	−0.718957	+	0.901001i
$112$	79.5113			0.709923
$113$		−	13.7032i		−	0.121267i	−0.998160	−	0.0606334i	$-0.980688\pi$
$113$		−	13.7032i		−	0.121267i	0.998160	−	0.0606334i	$-0.0193121\pi$
$114$	201.490	+	160.780i	1.76746	+	1.41035i
$115$	21.5354			0.187264
$116$		−	240.278i		−	2.07136i
$117$	−14.3250	−	62.9319i	−0.122436	−	0.537879i
$118$	23.7915			0.201623
$119$			112.665i			0.946766i
$120$	−80.5542	+	100.951i	−0.671285	+	0.841259i
$121$	36.7163			0.303440
$122$		−	97.2906i		−	0.797464i
$123$	47.5723	+	37.9605i	0.386767	+	0.308622i
$124$	−223.400			−1.80161
$125$			227.128i			1.81703i
$126$	−305.071	+	69.4422i	−2.42120	+	0.551128i
$127$	−54.3557			−0.427998			−0.213999	−	0.976834i	$-0.568649\pi$
$127$	−54.3557			−0.427998			−0.213999	+	0.976834i	$0.568649\pi$
$128$			145.435i			1.13621i
$129$	106.495	−	133.460i	0.825542	−	1.03457i
$130$	193.701			1.49000
$131$		−	85.5392i		−	0.652971i	−0.945202	−	0.326485i	$-0.894136\pi$
$131$		−	85.5392i		−	0.652971i	0.945202	−	0.326485i	$-0.105864\pi$
$132$	120.424	+	96.0931i	0.912306	+	0.727978i
$133$	−311.355			−2.34102
$134$			53.3507i			0.398140i
$135$	−102.345	+	212.044i	−0.758111	+	1.57070i
$136$	−49.5564			−0.364385
$137$			29.0403i			0.211973i	0.994368	+	0.105986i	$0.0338000\pi$
$137$			29.0403i			0.211973i	−0.994368	+	0.105986i	$0.966200\pi$
$138$	−14.3127	+	17.9368i	−0.103715	+	0.129977i
$139$	−2.50546			−0.0180249			−0.00901243	−	0.999959i	$-0.502869\pi$
$139$	−2.50546			−0.0180249			−0.00901243	+	0.999959i	$0.502869\pi$
$140$		−	547.493i		−	3.91066i
$141$	−111.839	−	89.2427i	−0.793188	−	0.632927i
$142$	130.455			0.918694
$143$		−	65.8369i		−	0.460398i
$144$	14.1512	+	62.1686i	0.0982723	+	0.431726i
$145$	374.576			2.58328
$146$			140.980i			0.965616i
$147$	144.020	−	180.487i	0.979731	−	1.22781i
$148$	238.575			1.61200
$149$			133.203i			0.893978i	0.894540	+	0.446989i	$0.147504\pi$
$149$			133.203i			0.893978i	−0.894540	+	0.446989i	$0.852496\pi$
$150$	−370.755	−	295.845i	−2.47170	−	1.97230i
$151$	−34.6793			−0.229665			−0.114832	−	0.993385i	$-0.536633\pi$
$151$	−34.6793			−0.229665			−0.114832	+	0.993385i	$0.536633\pi$
$152$		−	136.951i		−	0.900995i
$153$	−88.0910	+	20.0518i	−0.575758	+	0.131058i
$154$	−319.153			−2.07242
$155$		−	348.265i		−	2.24687i
$156$	−75.0616	+	94.0677i	−0.481164	+	0.602998i
$157$	−269.832			−1.71867			−0.859336	−	0.511411i	$-0.829123\pi$
$157$	−269.832			−1.71867			−0.859336	+	0.511411i	$0.829123\pi$
$158$			86.3752i			0.546679i
$159$	−160.558	−	128.118i	−1.00980	−	0.805774i
$160$	−363.553			−2.27221
$161$		−	27.7171i		−	0.172156i
$162$	−108.591	−	226.171i	−0.670317	−	1.39611i
$163$	164.306			1.00801			0.504006	−	0.863700i	$-0.331859\pi$
$163$	164.306			1.00801			0.504006	+	0.863700i	$0.331859\pi$
$164$		−	113.483i		−	0.691970i
$165$	−149.803	+	187.733i	−0.907894	+	1.13778i
$166$	0.314968			0.00189740
$167$			268.971i			1.61060i	0.592864	+	0.805302i	$0.297997\pi$
$167$			268.971i			1.61060i	−0.592864	+	0.805302i	$0.702003\pi$
$168$	129.929	+	103.677i	0.773385	+	0.617125i
$169$	−117.573			−0.695695
$170$		−	271.139i		−	1.59493i
$171$	−55.4141	−	243.443i	−0.324059	−	1.42364i
$172$	−318.367			−1.85097
$173$		−	155.110i		−	0.896589i	−0.893886	−	0.448295i	$-0.852032\pi$
$173$		−	155.110i		−	0.896589i	0.893886	−	0.448295i	$-0.147968\pi$
$174$	−248.949	+	311.984i	−1.43074	+	1.79301i
$175$	572.914			3.27379
$176$			65.0384i			0.369536i
$177$	−18.0119	−	14.3726i	−0.101762	−	0.0812013i
$178$	−106.202			−0.596639
$179$			203.005i			1.13411i	0.823681	+	0.567053i	$0.191917\pi$
$179$			203.005i			1.13411i	−0.823681	+	0.567053i	$0.808083\pi$
$180$	428.075	−	97.4413i	2.37820	−	0.541340i
$181$	214.747			1.18645			0.593223	−	0.805038i	$-0.297855\pi$
$181$	214.747			1.18645			0.593223	+	0.805038i	$0.297855\pi$
$182$		−	249.302i		−	1.36979i
$183$	−58.7739	+	73.6559i	−0.321169	+	0.402491i
$184$	12.1915			0.0662581
$185$			371.923i			2.01039i
$186$	290.069	+	231.462i	1.55951	+	1.24442i
$187$	−92.1574			−0.492821
$188$			266.792i			1.41911i
$189$	272.911	+	131.723i	1.44397	+	0.696946i
$190$	749.304			3.94370
$191$			89.7848i			0.470078i	0.971986	+	0.235039i	$0.0755217\pi$
$191$			89.7848i			0.470078i	−0.971986	+	0.235039i	$0.924478\pi$
$192$	188.599	−	236.353i	0.982286	−	1.23101i
$193$	46.0334			0.238515			0.119258	−	0.992863i	$-0.461949\pi$
$193$	46.0334			0.238515			0.119258	+	0.992863i	$0.461949\pi$
$194$			183.309i			0.944892i
$195$	−146.645	−	117.016i	−0.752026	−	0.600082i
$196$	−430.550			−2.19669
$197$			202.962i			1.03026i	0.857111	+	0.515132i	$0.172257\pi$
$197$			202.962i			1.03026i	−0.857111	+	0.515132i	$0.827743\pi$
$198$	−56.8020	−	249.541i	−0.286879	−	1.26031i
$199$	−80.7470			−0.405764			−0.202882	−	0.979203i	$-0.565031\pi$
$199$	−80.7470			−0.405764			−0.202882	+	0.979203i	$0.565031\pi$
$200$			251.999i			1.26000i
$201$	32.2296	−	40.3903i	0.160346	−	0.200947i
$202$	−337.933			−1.67293
$203$		−	482.097i		−	2.37486i
$204$	131.674	+	105.070i	0.645463	+	0.515049i
$205$	176.912			0.862987
$206$			263.138i			1.27737i
$207$	21.6715	−	4.93301i	0.104693	−	0.0238309i
$208$	−50.8037			−0.244249
$209$		−	254.681i		−	1.21857i
$210$	−567.250	+	710.882i	−2.70119	+	3.38515i
$211$	−80.3144			−0.380637			−0.190318	−	0.981722i	$-0.560952\pi$
$211$	−80.3144			−0.380637			−0.190318	+	0.981722i	$0.560952\pi$
$212$			383.010i			1.80665i
$213$	−98.7634	−	78.8086i	−0.463678	−	0.369993i
$214$	410.301			1.91729
$215$		−	496.313i		−	2.30843i
$216$	−57.9390	+	120.041i	−0.268236	+	0.555746i
$217$	−448.233			−2.06559
$218$			132.666i			0.608560i
$219$	85.1670	−	106.732i	0.388891	−	0.487360i
$220$	447.836			2.03562
$221$		−	71.9874i		−	0.325735i
$222$	−309.774	−	247.185i	−1.39538	−	1.11345i
$223$	−1.92218			−0.00861964			−0.00430982	−	0.999991i	$-0.501372\pi$
$223$	−1.92218			−0.00861964			−0.00430982	+	0.999991i	$0.501372\pi$
$224$			467.910i			2.08888i
$225$	101.966	+	447.952i	0.453181	+	1.99090i
$226$	42.4440			0.187806
$227$		−	169.954i		−	0.748696i	−0.927288	−	0.374348i	$-0.877866\pi$
$227$		−	169.954i		−	0.748696i	0.927288	−	0.374348i	$-0.122134\pi$
$228$	−290.366	+	363.888i	−1.27353	+	1.59600i
$229$	112.375			0.490722			0.245361	−	0.969432i	$-0.421094\pi$
$229$	112.375			0.490722			0.245361	+	0.969432i	$0.421094\pi$
$230$			66.7036i			0.290016i
$231$	241.622	+	192.803i	1.04598	+	0.834644i
$232$	212.053			0.914021
$233$		−	342.532i		−	1.47010i	−0.678015	−	0.735048i	$-0.737160\pi$
$233$		−	342.532i		−	1.47010i	0.678015	−	0.735048i	$-0.262840\pi$
$234$	194.925	−	44.3700i	0.833012	−	0.189616i
$235$	−415.910			−1.76983
$236$			42.9671i			0.182064i
$237$	52.1799	−	65.3922i	0.220168	−	0.275916i
$238$	−348.968			−1.46625
$239$			61.3192i			0.256566i	0.991738	+	0.128283i	$0.0409466\pi$
$239$			61.3192i			0.256566i	−0.991738	+	0.128283i	$0.959053\pi$
$240$	144.866	+	115.597i	0.603610	+	0.481652i
$241$	−107.066			−0.444257			−0.222129	−	0.975017i	$-0.571300\pi$
$241$	−107.066			−0.444257			−0.222129	+	0.975017i	$0.571300\pi$
$242$			113.725i			0.469937i
$243$	−54.4199	+	236.828i	−0.223950	+	0.974601i
$244$	175.705			0.720103
$245$		−	671.199i		−	2.73959i
$246$	−117.578	+	147.350i	−0.477961	+	0.598984i
$247$	198.940			0.805426
$248$		−	197.158i		−	0.794991i
$249$	−0.238453	−	0.190274i	−0.000957643	−	0.000764154i
$250$	−703.506			−2.81402
$251$		−	82.0368i		−	0.326840i	−0.986557	−	0.163420i	$-0.947747\pi$
$251$		−	82.0368i		−	0.326840i	0.986557	−	0.163420i	$-0.0522525\pi$
$252$	−125.411	−	550.953i	−0.497664	−	2.18632i
$253$	22.6719			0.0896122
$254$		−	168.361i		−	0.662839i
$255$	−163.797	+	205.271i	−0.642341	+	0.804986i
$256$	−47.2985			−0.184760
$257$		−	499.557i		−	1.94380i	−0.235391	−	0.971901i	$-0.575637\pi$
$257$		−	499.557i		−	1.94380i	0.235391	−	0.971901i	$-0.424363\pi$
$258$	413.378	+	329.857i	1.60224	+	1.27851i
$259$	478.682			1.84819
$260$			349.820i			1.34546i
$261$	376.944	−	85.8023i	1.44423	−	0.328745i
$262$	264.948			1.01125
$263$			41.9833i			0.159632i	0.996810	+	0.0798161i	$0.0254333\pi$
$263$			41.9833i			0.159632i	−0.996810	+	0.0798161i	$0.974567\pi$
$264$	−84.8053	+	106.279i	−0.321232	+	0.402570i
$265$	−597.086			−2.25316
$266$		−	964.389i		−	3.62552i
$267$	80.4022	+	64.1572i	0.301132	+	0.240289i
$268$	−96.3506			−0.359517
$269$			246.564i			0.916596i	0.888799	+	0.458298i	$0.151541\pi$
$269$			246.564i			0.916596i	−0.888799	+	0.458298i	$0.848459\pi$
$270$	−656.784	−	317.003i	−2.43253	−	1.17408i
$271$	454.843			1.67839			0.839194	−	0.543831i	$-0.183027\pi$
$271$	454.843			1.67839			0.839194	+	0.543831i	$0.183027\pi$
$272$			71.1142i			0.261449i
$273$	−150.605	+	188.739i	−0.551666	+	0.691352i
$274$	−89.9492			−0.328282
$275$			468.630i			1.70411i
$276$	−32.3936	−	25.8485i	−0.117368	−	0.0936542i
$277$	−523.363			−1.88940			−0.944699	−	0.327939i	$-0.893646\pi$
$277$	−523.363			−1.88940			−0.944699	+	0.327939i	$0.893646\pi$
$278$		−	7.76038i		−	0.0279150i
$279$	−79.7753	−	350.466i	−0.285933	−	1.25615i
$280$	483.180			1.72564
$281$			327.127i			1.16415i	0.813134	+	0.582077i	$0.197760\pi$
$281$			327.127i			1.16415i	−0.813134	+	0.582077i	$0.802240\pi$
$282$	276.420	−	346.411i	0.980211	−	1.22841i
$283$	435.705			1.53959			0.769796	−	0.638290i	$-0.220358\pi$
$283$	435.705			1.53959			0.769796	+	0.638290i	$0.220358\pi$
$284$			235.599i			0.829574i
$285$	−567.276	−	452.660i	−1.99044	−	1.58828i
$286$	203.923			0.713017
$287$		−	227.694i		−	0.793361i
$288$	−365.851	+	83.2773i	−1.27031	+	0.289157i
$289$	188.233			0.651326
$290$			1160.21i			4.00072i
$291$	110.738	−	138.778i	0.380544	−	0.476900i
$292$	−254.608			−0.871944
$293$			228.463i			0.779736i	0.920871	+	0.389868i	$0.127479\pi$
$293$			228.463i			0.779736i	−0.920871	+	0.389868i	$0.872521\pi$
$294$	559.040	+	446.088i	1.90150	+	1.51731i
$295$	−66.9828			−0.227060
$296$			210.551i			0.711320i
$297$	−107.746	+	223.234i	−0.362781	+	0.751631i
$298$	−412.581			−1.38450
$299$			17.7098i			0.0592301i
$300$	534.292	−	669.578i	1.78097	−	2.23193i
$301$	−638.778			−2.12219
$302$		−	107.416i		−	0.355681i
$303$	255.839	+	204.147i	0.844353	+	0.673754i
$304$	−196.527			−0.646471
$305$			273.912i			0.898073i
$306$	−62.1084	−	272.852i	−0.202969	−	0.891675i
$307$	−374.581			−1.22013			−0.610067	−	0.792350i	$-0.708858\pi$
$307$	−374.581			−1.22013			−0.610067	+	0.792350i	$0.708858\pi$
$308$		−	576.386i		−	1.87138i
$309$	158.964	−	199.214i	0.514446	−	0.644707i
$310$	1078.71			3.47972
$311$		−	187.947i		−	0.604331i	−0.953256	−	0.302165i	$-0.902291\pi$
$311$		−	187.947i		−	0.604331i	0.953256	−	0.302165i	$-0.0977095\pi$
$312$	−83.0178	−	66.2444i	−0.266083	−	0.212322i
$313$	621.024			1.98410			0.992052	−	0.125832i	$-0.0401599\pi$
$313$	621.024			1.98410			0.992052	+	0.125832i	$0.0401599\pi$
$314$		−	835.774i		−	2.66170i
$315$	858.898	−	195.508i	2.72666	−	0.620660i
$316$	−155.992			−0.493646
$317$			313.420i			0.988706i	0.869261	+	0.494353i	$0.164595\pi$
$317$			313.420i			0.988706i	−0.869261	+	0.494353i	$0.835405\pi$
$318$	396.832	−	497.312i	1.24790	−	1.56388i
$319$	394.344			1.23619
$320$		−	878.954i		−	2.74673i
$321$	−310.627	−	247.866i	−0.967684	−	0.772167i
$322$	85.8506			0.266617
$323$		−	278.473i		−	0.862146i
$324$	408.460	−	196.114i	1.26068	−	0.605291i
$325$	−366.063			−1.12635
$326$			508.920i			1.56111i
$327$	80.1445	−	100.438i	0.245090	−	0.307149i
$328$	100.153			0.305343
$329$			535.296i			1.62704i
$330$	−581.484	−	463.997i	−1.76207	−	1.40605i
$331$	125.021			0.377707			0.188853	−	0.982005i	$-0.439523\pi$
$331$	125.021			0.377707			0.188853	+	0.982005i	$0.439523\pi$
$332$			0.568827i			0.00171333i
$333$	85.1945	+	374.273i	0.255839	+	1.12394i
$334$	−833.109			−2.49434
$335$		−	150.204i		−	0.448370i
$336$	148.778	−	186.450i	0.442792	−	0.554910i
$337$	−422.805			−1.25461			−0.627307	−	0.778772i	$-0.715843\pi$
$337$	−422.805			−1.25461			−0.627307	+	0.778772i	$0.715843\pi$
$338$		−	364.168i		−	1.07742i
$339$	−32.1332	−	25.6408i	−0.0947881	−	0.0756364i
$340$	489.672			1.44021
$341$		−	366.644i		−	1.07520i
$342$	754.039	−	171.639i	2.20479	−	0.501869i
$343$	−313.908			−0.915185
$344$		−	280.970i		−	0.816773i
$345$	40.2961	−	50.4993i	0.116800	−	0.146375i
$346$	480.436			1.38854
$347$		−	285.316i		−	0.822235i	−0.911582	−	0.411118i	$-0.865139\pi$
$347$		−	285.316i		−	0.822235i	0.911582	−	0.411118i	$-0.134861\pi$
$348$	−563.438	−	449.597i	−1.61907	−	1.29195i
$349$	−146.999			−0.421202			−0.210601	−	0.977572i	$-0.567542\pi$
$349$	−146.999			−0.421202			−0.210601	+	0.977572i	$0.567542\pi$
$350$			1774.54i			5.07011i
$351$	−174.376	−	84.1642i	−0.496798	−	0.239784i
$352$	−382.739			−1.08733
$353$			372.881i			1.05632i	0.849145	+	0.528160i	$0.177118\pi$
$353$			372.881i			1.05632i	−0.849145	+	0.528160i	$0.822882\pi$
$354$	44.5177	−	55.7898i	0.125756	−	0.157598i
$355$	−367.282			−1.03460
$356$		−	191.799i		−	0.538760i
$357$	264.194	+	210.814i	0.740039	+	0.590516i
$358$	−628.787			−1.75639
$359$			74.5446i			0.207645i	0.994596	+	0.103823i	$0.0331074\pi$
$359$			74.5446i			0.207645i	−0.994596	+	0.103823i	$0.966893\pi$
$360$	85.9951	+	377.791i	0.238875	+	1.04942i
$361$	408.572			1.13178
$362$			665.154i			1.83744i
$363$	68.7019	−	86.0977i	0.189262	−	0.237184i
$364$	450.235			1.23691
$365$		−	396.916i		−	1.08744i
$366$	−228.141	−	182.046i	−0.623336	−	0.497393i
$367$	639.738			1.74316			0.871578	−	0.490257i	$-0.163097\pi$
$367$	639.738			1.74316			0.871578	+	0.490257i	$0.163097\pi$
$368$		−	17.4950i		−	0.0475407i
$369$	178.030	−	40.5244i	0.482467	−	0.109822i
$370$	−1151.99			−3.11349
$371$			768.478i			2.07137i
$372$	−418.016	+	523.860i	−1.12370	+	1.40823i
$373$	−272.666			−0.731008			−0.365504	−	0.930810i	$-0.619103\pi$
$373$	−272.666			−0.731008			−0.365504	+	0.930810i	$0.619103\pi$
$374$		−	285.448i		−	0.763229i
$375$	532.604	+	424.993i	1.42028	+	1.13331i
$376$	−235.453			−0.626204
$377$			308.036i			0.817071i
$378$	−407.997	+	845.312i	−1.07936	+	2.23627i
$379$	473.984			1.25062			0.625309	−	0.780377i	$-0.284973\pi$
$379$	473.984			1.25062			0.625309	+	0.780377i	$0.284973\pi$
$380$			1353.23i			3.56113i
$381$	−101.708	+	127.461i	−0.266950	+	0.334544i
$382$	−278.099			−0.728007
$383$			297.241i			0.776086i	0.921641	+	0.388043i	$0.126849\pi$
$383$			297.241i			0.776086i	−0.921641	+	0.388043i	$0.873151\pi$
$384$	341.037	+	272.132i	0.888118	+	0.708676i
$385$	898.546			2.33388
$386$			142.584i			0.369388i
$387$	−113.688	−	499.450i	−0.293767	−	1.29057i
$388$	−331.053			−0.853230
$389$		−	147.396i		−	0.378910i	−0.981889	−	0.189455i	$-0.939328\pi$
$389$		−	147.396i		−	0.378910i	0.981889	−	0.189455i	$-0.0606721\pi$
$390$	362.444	−	454.217i	0.929344	−	1.16466i
$391$	24.7899			0.0634012
$392$		−	379.975i		−	0.969324i
$393$	−200.585	−	160.057i	−0.510394	−	0.407270i
$394$	−628.653			−1.59557
$395$		−	243.181i		−	0.615649i
$396$	450.666	−	102.584i	1.13805	−	0.259049i
$397$	−671.197			−1.69067			−0.845336	−	0.534235i	$-0.820600\pi$
$397$	−671.197			−1.69067			−0.845336	+	0.534235i	$0.820600\pi$
$398$		−	250.105i		−	0.628405i
$399$	−582.594	+	730.111i	−1.46014	+	1.82985i
$400$	361.623			0.904057
$401$		−	420.309i		−	1.04815i	−0.851671	−	0.524076i	$-0.824411\pi$
$401$		−	420.309i		−	1.04815i	0.851671	−	0.524076i	$-0.175589\pi$
$402$	125.105	+	99.8276i	0.311205	+	0.248327i
$403$	286.398			0.710666
$404$		−	610.301i		−	1.51065i
$405$	305.729	+	636.762i	0.754885	+	1.57225i
$406$	1493.24			3.67794
$407$			391.550i			0.962040i
$408$	−92.7278	+	116.207i	−0.227274	+	0.284821i
$409$	−119.098			−0.291193			−0.145597	−	0.989344i	$-0.546510\pi$
$409$	−119.098			−0.291193			−0.145597	+	0.989344i	$0.546510\pi$
$410$			547.967i			1.33651i
$411$	68.0979	+	54.3389i	0.165688	+	0.132212i
$412$	−475.223			−1.15345
$413$			86.2099i			0.208741i
$414$	15.2795	+	67.1251i	0.0369069	+	0.162138i
$415$	−0.886762			−0.00213678
$416$		−	298.971i		−	0.718679i
$417$	−4.68810	+	5.87516i	−0.0112424	+	0.0140891i
$418$	788.847			1.88719
$419$		−	744.229i		−	1.77620i	−0.459648	−	0.888101i	$-0.652025\pi$
$419$		−	744.229i		−	1.77620i	0.459648	−	0.888101i	$-0.347975\pi$
$420$	−1283.84	−	1024.44i	−3.05676	−	2.43915i
$421$	−364.752			−0.866393			−0.433197	−	0.901299i	$-0.642614\pi$
$421$	−364.752			−0.866393			−0.433197	+	0.901299i	$0.642614\pi$
$422$		−	248.765i		−	0.589491i
$423$	−418.539	+	95.2704i	−0.989453	+	0.225226i
$424$	−338.019			−0.797215
$425$			512.409i			1.20567i
$426$	244.101	−	305.909i	0.573007	−	0.718096i
$427$	352.538			0.825616
$428$			740.996i			1.73130i
$429$	−154.384	−	123.191i	−0.359869	−	0.287159i
$430$	1537.28			3.57506
$431$		−	64.3549i		−	0.149315i	−0.997209	−	0.0746576i	$-0.976214\pi$
$431$		−	64.3549i		−	0.149315i	0.997209	−	0.0746576i	$-0.0237864\pi$
$432$	172.261	+	83.1433i	0.398752	+	0.192461i
$433$	−399.530			−0.922701			−0.461351	−	0.887218i	$-0.652635\pi$
$433$	−399.530			−0.922701			−0.461351	+	0.887218i	$0.652635\pi$
$434$		−	1388.35i		−	3.19897i
$435$	700.891	−	878.361i	1.61124	−	2.01922i
$436$	−239.593			−0.549524
$437$			68.5079i			0.156769i
$438$	330.590	+	263.796i	0.754773	+	0.602273i
$439$	−757.730			−1.72604			−0.863019	−	0.505172i	$-0.831429\pi$
$439$	−757.730			−1.72604			−0.863019	+	0.505172i	$0.831429\pi$
$440$			395.230i			0.898250i
$441$	−153.748	−	675.440i	−0.348635	−	1.53161i
$442$	222.973			0.504464
$443$			397.689i			0.897717i	0.893603	+	0.448859i	$0.148169\pi$
$443$			397.689i			0.897717i	−0.893603	+	0.448859i	$0.851831\pi$
$444$	446.412	−	559.446i	1.00543	−	1.26001i
$445$	299.001			0.671912
$446$		−	5.95374i		−	0.0133492i
$447$	312.353	+	249.243i	0.698776	+	0.557591i
$448$	−1131.25			−2.52512
$449$		−	219.751i		−	0.489424i	−0.969596	−	0.244712i	$-0.921307\pi$
$449$		−	219.751i		−	0.489424i	0.969596	−	0.244712i	$-0.0786934\pi$
$450$	−1387.48	+	315.828i	−3.08329	+	0.701840i
$451$	186.249			0.412968
$452$			76.6533i			0.169587i
$453$	−64.8905	+	81.3212i	−0.143246	+	0.179517i
$454$	526.414			1.15950
$455$			701.885i			1.54260i
$456$	−321.143	−	256.257i	−0.704261	−	0.561967i
$457$	416.283			0.910903			0.455451	−	0.890261i	$-0.349478\pi$
$457$	416.283			0.910903			0.455451	+	0.890261i	$0.349478\pi$
$458$			348.070i			0.759979i
$459$	−117.812	+	244.089i	−0.256670	+	0.531784i
$460$	−120.466			−0.261882
$461$			387.495i			0.840554i	0.907396	+	0.420277i	$0.138067\pi$
$461$			387.495i			0.840554i	−0.907396	+	0.420277i	$0.861933\pi$
$462$	−597.186	+	748.397i	−1.29261	+	1.61991i
$463$	−445.696			−0.962626			−0.481313	−	0.876549i	$-0.659840\pi$
$463$	−445.696			−0.962626			−0.481313	+	0.876549i	$0.659840\pi$
$464$		−	304.299i		−	0.655817i
$465$	−816.662	−	651.658i	−1.75626	−	1.40142i
$466$	1060.96			2.27673
$467$			805.049i			1.72387i	0.507016	+	0.861937i	$0.330749\pi$
$467$			805.049i			1.72387i	−0.507016	+	0.861937i	$0.669251\pi$
$468$	80.1316	+	352.031i	0.171221	+	0.752203i
$469$	−193.319			−0.412195
$470$		−	1288.24i		−	2.74093i
$471$	−504.897	+	632.741i	−1.07197	+	1.34340i
$472$	−37.9199			−0.0803387
$473$		−	522.505i		−	1.10466i
$474$	202.545	+	161.622i	0.427311	+	0.340974i
$475$	−1416.06			−2.98119
$476$		−	630.231i		−	1.32402i
$477$	−600.860	+	136.772i	−1.25966	+	0.286733i
$478$	−189.930			−0.397343
$479$		−	199.257i		−	0.415986i	−0.978130	−	0.207993i	$-0.933307\pi$
$479$		−	199.257i		−	0.415986i	0.978130	−	0.207993i	$-0.0666931\pi$
$480$	−680.265	+	852.512i	−1.41722	+	1.77607i
$481$	−305.853			−0.635870
$482$		−	331.625i		−	0.688019i
$483$	−64.9950	−	51.8630i	−0.134565	−	0.107377i
$484$	−205.385			−0.424349
$485$		−	516.089i		−	1.06410i
$486$	−733.549	−	168.560i	−1.50936	−	0.346831i
$487$	−558.507			−1.14683			−0.573416	−	0.819264i	$-0.694382\pi$
$487$	−558.507			−1.14683			−0.573416	+	0.819264i	$0.694382\pi$
$488$			155.066i			0.317757i
$489$	307.442	−	385.289i	0.628717	−	0.787912i
$490$	2078.97			4.24279
$491$			947.072i			1.92886i	0.264332	+	0.964432i	$0.414848\pi$
$491$			947.072i			1.92886i	−0.264332	+	0.964432i	$0.585152\pi$
$492$	−266.112	−	212.345i	−0.540878	−	0.431595i
$493$	431.183			0.874611
$494$			616.196i			1.24736i
$495$	159.921	+	702.558i	0.323072	+	1.41931i
$496$	−282.924			−0.570412
$497$			472.710i			0.951126i
$498$	0.589354	−	0.738583i	0.00118344	−	0.00148310i
$499$	−454.602			−0.911026			−0.455513	−	0.890229i	$-0.650544\pi$
$499$	−454.602			−0.911026			−0.455513	+	0.890229i	$0.650544\pi$
$500$		−	1270.52i		−	2.54104i
$501$	630.722	+	503.287i	1.25893	+	1.00456i
$502$	254.100			0.506176
$503$		−	818.520i		−	1.62728i	−0.581372	−	0.813638i	$-0.697484\pi$
$503$		−	818.520i		−	1.62728i	0.581372	−	0.813638i	$-0.302516\pi$
$504$	486.234	−	110.680i	0.964750	−	0.219603i
$505$	951.417			1.88399
$506$			70.2237i			0.138782i
$507$	−219.997	+	275.701i	−0.433918	+	0.543789i
$508$	304.057			0.598538
$509$			329.331i			0.647017i	0.946225	+	0.323508i	$0.104862\pi$
$509$			329.331i			0.647017i	−0.946225	+	0.323508i	$0.895138\pi$
$510$	−635.806	−	507.343i	−1.24668	−	0.994791i
$511$	−510.849			−0.999705
$512$			435.238i			0.850074i
$513$	−674.550	−	325.577i	−1.31491	−	0.634654i
$514$	1547.32			3.01036
$515$		−	740.841i		−	1.43853i
$516$	−595.716	+	746.554i	−1.15449	+	1.44681i
$517$	−437.859			−0.846922
$518$			1482.66i			2.86229i
$519$	−363.724	−	290.235i	−0.700818	−	0.559220i
$520$	−308.728			−0.593707
$521$			128.469i			0.246581i	0.992371	+	0.123290i	$0.0393447\pi$
$521$			128.469i			0.246581i	−0.992371	+	0.123290i	$0.960655\pi$
$522$	265.764	+	1167.54i	0.509126	+	2.23667i
$523$	−131.827			−0.252060			−0.126030	−	0.992026i	$-0.540224\pi$
$523$	−131.827			−0.252060			−0.126030	+	0.992026i	$0.540224\pi$
$524$			478.493i			0.913154i
$525$	1072.01	−	1343.45i	2.04193	−	2.55896i
$526$	−130.039			−0.247222
$527$		−	400.896i		−	0.760713i
$528$	152.511	+	121.697i	0.288847	+	0.230487i
$529$	522.901			0.988471
$530$		−	1849.41i		−	3.48945i
$531$	−67.4061	+	15.3434i	−0.126942	+	0.0288953i
$532$	1741.67			3.27382
$533$			145.485i			0.272955i
$534$	−198.720	+	249.037i	−0.372135	+	0.466362i
$535$	−1155.16			−2.15918
$536$		−	85.0325i		−	0.158643i
$537$	476.036	+	379.855i	0.886473	+	0.707364i
$538$	−763.706			−1.41953
$539$		−	706.620i		−	1.31098i
$540$	572.502	−	1186.14i	1.06019	−	2.19656i
$541$	524.830			0.970110			0.485055	−	0.874484i	$-0.338800\pi$
$541$	524.830			0.970110			0.485055	+	0.874484i	$0.338800\pi$
$542$			1408.83i			2.59931i
$543$	401.825	−	503.569i	0.740009	−	0.927383i
$544$	−418.494			−0.769291
$545$		−	373.508i		−	0.685337i
$546$	−584.599	−	466.483i	−1.07069	−	0.854364i
$547$	181.429			0.331680			0.165840	−	0.986153i	$-0.446966\pi$
$547$	181.429			0.331680			0.165840	+	0.986153i	$0.446966\pi$
$548$		−	162.447i		−	0.296436i
$549$	62.7437	+	275.643i	0.114287	+	0.502083i
$550$	−1451.53			−2.63915
$551$			1191.59i			2.16260i
$552$	22.8122	−	28.5884i	0.0413264	−	0.0517906i
$553$	−312.986			−0.565977
$554$		−	1621.06i		−	2.92610i
$555$	872.138	+	695.926i	1.57142	+	1.25392i
$556$	14.0151			0.0252070
$557$			549.889i			0.987234i	0.869680	+	0.493617i	$0.164325\pi$
$557$			549.889i			0.987234i	−0.869680	+	0.493617i	$0.835675\pi$
$558$	1085.53	−	247.095i	1.94540	−	0.442823i
$559$	408.147			0.730137
$560$		−	693.372i		−	1.23816i
$561$	−172.441	+	216.104i	−0.307382	+	0.385212i
$562$	−1013.24			−1.80292
$563$		−	374.249i		−	0.664741i	−0.943149	−	0.332370i	$-0.892152\pi$
$563$		−	374.249i		−	0.664741i	0.943149	−	0.332370i	$-0.107848\pi$
$564$	625.612	+	499.209i	1.10924	+	0.885123i
$565$	−119.497			−0.211499
$566$			1349.55i			2.38436i
$567$	819.542	−	393.487i	1.44540	−	0.693980i
$568$	−207.924			−0.366063
$569$			812.694i			1.42828i	0.700000	+	0.714142i	$0.253183\pi$
$569$			812.694i			1.42828i	−0.700000	+	0.714142i	$0.746817\pi$
$570$	1402.07	−	1757.08i	2.45976	−	3.08259i
$571$	537.470			0.941278			0.470639	−	0.882326i	$-0.344023\pi$
$571$	537.470			0.941278			0.470639	+	0.882326i	$0.344023\pi$
$572$			368.281i			0.643848i
$573$	210.541	+	168.001i	0.367435	+	0.293196i
$574$	705.259			1.22867
$575$		−	126.059i		−	0.219233i
$576$	−201.338	−	884.509i	−0.349545	−	1.53561i
$577$	115.099			0.199479			0.0997395	−	0.995014i	$-0.468199\pi$
$577$	115.099			0.199479			0.0997395	+	0.995014i	$0.468199\pi$
$578$			583.032i			1.00871i
$579$	86.1358	−	107.946i	0.148766	−	0.186435i
$580$	−2095.32			−3.61262
$581$			1.14130i			0.00196438i
$582$	429.850	+	343.000i	0.738574	+	0.589347i
$583$	−628.597			−1.07821
$584$		−	224.700i		−	0.384760i
$585$	−548.792	+	124.920i	−0.938106	+	0.213538i
$586$	−707.638			−1.20757
$587$			280.527i			0.477899i	0.971032	+	0.238950i	$0.0768031\pi$
$587$			280.527i			0.477899i	−0.971032	+	0.238950i	$0.923197\pi$
$588$	−805.627	+	1009.62i	−1.37011	+	1.71704i
$589$	1107.89			1.88097
$590$		−	207.472i		−	0.351647i
$591$	475.935	+	379.774i	0.805305	+	0.642596i
$592$	302.143			0.510377
$593$		−	189.070i		−	0.318837i	−0.987211	−	0.159418i	$-0.949038\pi$
$593$		−	189.070i		−	0.318837i	0.987211	−	0.159418i	$-0.0509619\pi$
$594$	−691.445	−	333.732i	−1.16405	−	0.561838i
$595$	982.487			1.65124
$596$		−	745.114i		−	1.25019i
$597$	−151.090	+	189.347i	−0.253082	+	0.317165i
$598$	−54.8542			−0.0917294
$599$		−	305.707i		−	0.510363i	−0.966893	−	0.255182i	$-0.917865\pi$
$599$		−	305.707i		−	0.510363i	0.966893	−	0.255182i	$-0.0821352\pi$
$600$	590.925	+	471.530i	0.984874	+	0.785884i
$601$	1136.72			1.89138			0.945688	−	0.325076i	$-0.105390\pi$
$601$	1136.72			1.89138			0.945688	+	0.325076i	$0.105390\pi$
$602$		−	1978.55i		−	3.28662i
$603$	−34.4065	−	151.153i	−0.0570588	−	0.250669i
$604$	193.991			0.321177
$605$		−	320.181i		−	0.529225i
$606$	−632.325	+	792.434i	−1.04344	+	1.30765i
$607$	−677.066			−1.11543			−0.557715	−	0.830033i	$-0.688322\pi$
$607$	−677.066			−1.11543			−0.557715	+	0.830033i	$0.688322\pi$
$608$		−	1156.53i		−	1.90218i
$609$	−1130.49	−	902.079i	−1.85631	−	1.48125i
$610$	−848.414			−1.39084
$611$		−	342.027i		−	0.559782i
$612$	492.767	−	112.167i	0.805175	−	0.183279i
$613$	−747.057			−1.21869			−0.609345	−	0.792905i	$-0.708567\pi$
$613$	−747.057			−1.21869			−0.609345	+	0.792905i	$0.708567\pi$
$614$		−	1160.23i		−	1.88962i
$615$	331.031	−	414.850i	0.538262	−	0.674553i
$616$	508.679			0.825778
$617$		−	19.4217i		−	0.0314777i	−0.999876	−	0.0157388i	$-0.994990\pi$
$617$		−	19.4217i		−	0.0314777i	0.999876	−	0.0157388i	$-0.00501003\pi$
$618$	617.045	+	492.373i	0.998455	+	0.796720i
$619$	477.200			0.770921			0.385460	−	0.922724i	$-0.374043\pi$
$619$	477.200			0.770921			0.385460	+	0.922724i	$0.374043\pi$
$620$			1948.14i			3.14216i
$621$	28.9831	−	60.0489i	0.0466717	−	0.0966971i
$622$	582.145			0.935925
$623$		−	384.828i		−	0.617701i
$624$	−95.0617	+	119.132i	−0.152342	+	0.190917i
$625$	704.513			1.12722
$626$			1923.56i			3.07277i
$627$	−597.213	−	476.548i	−0.952493	−	0.760045i
$628$	1509.39			2.40350
$629$			428.128i			0.680649i
$630$	605.564	+	2660.34i	0.961213	+	4.22277i
$631$	360.411			0.571174			0.285587	−	0.958353i	$-0.407811\pi$
$631$	360.411			0.571174			0.285587	+	0.958353i	$0.407811\pi$
$632$		−	137.668i		−	0.217830i
$633$	−150.281	+	188.333i	−0.237410	+	0.297524i
$634$	−970.784			−1.53121
$635$			474.004i			0.746464i
$636$	898.138	+	716.672i	1.41217	+	1.12684i
$637$	551.965			0.866507
$638$			1221.44i			1.91448i
$639$	−369.604	+	84.1316i	−0.578409	+	0.131661i
$640$	1268.25			1.98165
$641$			239.172i			0.373123i	0.982443	+	0.186562i	$0.0597344\pi$
$641$			239.172i			0.373123i	−0.982443	+	0.186562i	$0.940266\pi$
$642$	767.737	−	962.133i	1.19585	−	1.49865i
$643$	−491.031			−0.763657			−0.381828	−	0.924233i	$-0.624705\pi$
$643$	−491.031			−0.763657			−0.381828	+	0.924233i	$0.624705\pi$
$644$			155.045i			0.240753i
$645$	−1163.83	−	928.680i	−1.80438	−	1.43981i
$646$	862.541			1.33520
$647$		−	1065.46i		−	1.64677i	−0.567480	−	0.823387i	$-0.692082\pi$
$647$		−	1065.46i		−	1.64677i	0.567480	−	0.823387i	$-0.307918\pi$
$648$	173.077	+	360.480i	0.267094	+	0.556296i
$649$	−70.5177			−0.108656
$650$		−	1133.84i		−	1.74437i
$651$	−838.715	+	1051.08i	−1.28835	+	1.61457i
$652$	−919.102			−1.40967
$653$		−	245.954i		−	0.376652i	−0.982107	−	0.188326i	$-0.939694\pi$
$653$		−	245.954i		−	0.376652i	0.982107	−	0.188326i	$-0.0603062\pi$
$654$	311.095	+	248.239i	0.475680	+	0.379570i
$655$	−745.937			−1.13884
$656$		−	143.721i		−	0.219086i
$657$	−90.9195	−	399.424i	−0.138386	−	0.607952i
$658$	−1658.02			−2.51979
$659$			230.272i			0.349426i	0.984619	+	0.174713i	$0.0558997\pi$
$659$			230.272i			0.349426i	−0.984619	+	0.174713i	$0.944100\pi$
$660$	837.971	−	1050.15i	1.26965	−	1.59114i
$661$	703.422			1.06418			0.532089	−	0.846688i	$-0.321407\pi$
$661$	703.422			1.06418			0.532089	+	0.846688i	$0.321407\pi$
$662$			387.239i			0.584953i
$663$	−168.806	−	134.700i	−0.254610	−	0.203167i
$664$	−0.502009			−0.000756037
$665$			2715.14i			4.08292i
$666$	−1159.27	+	263.881i	−1.74065	+	0.396217i
$667$	−106.076			−0.159035
$668$		−	1504.58i		−	2.25237i
$669$	−3.59670	+	4.50741i	−0.00537623	+	0.00673753i
$670$	465.240			0.694389
$671$			288.368i			0.429758i
$672$	1097.22	+	875.533i	1.63277	+	1.30288i
$673$	−590.571			−0.877520			−0.438760	−	0.898604i	$-0.644582\pi$
$673$	−590.571			−0.877520			−0.438760	+	0.898604i	$0.644582\pi$
$674$		−	1309.59i		−	1.94302i
$675$	1241.22	+	599.084i	1.83884	+	0.887532i
$676$	657.682			0.972902
$677$		−	233.839i		−	0.345405i	−0.984974	−	0.172702i	$-0.944750\pi$
$677$		−	233.839i		−	0.345405i	0.984974	−	0.172702i	$-0.0552499\pi$
$678$	79.4195	−	99.5290i	0.117138	−	0.146798i
$679$	−664.231			−0.978249
$680$			432.152i			0.635518i
$681$	−398.533	−	318.011i	−0.585217	−	0.466976i
$682$	1135.64			1.66516
$683$		−	143.102i		−	0.209519i	−0.994498	−	0.104760i	$-0.966593\pi$
$683$		−	143.102i		−	0.209519i	0.994498	−	0.104760i	$-0.0334073\pi$
$684$	309.978	+	1361.78i	0.453184	+	1.99091i
$685$	253.243			0.369698
$686$		−	972.298i		−	1.41734i
$687$	210.272	−	263.514i	0.306072	−	0.383572i
$688$	−403.196			−0.586041
$689$		−	491.018i		−	0.712654i
$690$	156.416	+	124.813i	0.226690	+	0.180888i
$691$	73.3360			0.106130			0.0530651	−	0.998591i	$-0.483101\pi$
$691$	73.3360			0.106130			0.0530651	+	0.998591i	$0.483101\pi$
$692$			867.660i			1.25384i
$693$	904.224	−	205.825i	1.30480	−	0.297006i
$694$	883.734			1.27339
$695$			21.8486i			0.0314368i
$696$	396.784	−	497.253i	0.570092	−	0.714443i
$697$	203.648			0.292178
$698$		−	455.315i		−	0.652314i
$699$	−803.220	−	640.932i	−1.14910	−	0.916927i
$700$	−3204.79			−4.57827
$701$		−	888.614i		−	1.26764i	−0.773482	−	0.633819i	$-0.781487\pi$
$701$		−	888.614i		−	1.26764i	0.773482	−	0.633819i	$-0.218513\pi$
$702$	260.689	−	540.111i	0.371353	−	0.769389i
$703$	−1183.15			−1.68300
$704$		−	925.339i		−	1.31440i
$705$	−778.233	+	975.286i	−1.10388	+	1.38339i
$706$	−1154.96			−1.63592
$707$		−	1224.52i		−	1.73199i
$708$	100.756	+	80.3982i	0.142310	+	0.113557i
$709$	−23.4690			−0.0331015			−0.0165508	−	0.999863i	$-0.505269\pi$
$709$	−23.4690			−0.0331015			−0.0165508	+	0.999863i	$0.505269\pi$
$710$		−	1137.62i		−	1.60228i
$711$	−55.7043	−	244.718i	−0.0783464	−	0.344189i
$712$	169.269			0.237737
$713$			98.6253i			0.138324i
$714$	−652.975	+	818.312i	−0.914530	+	1.14610i
$715$	−574.125			−0.802972
$716$		−	1135.58i		−	1.58600i
$717$	143.790	+	114.738i	0.200544	+	0.160025i
$718$	−230.894			−0.321579
$719$			25.0099i			0.0347842i	0.999849	+	0.0173921i	$0.00553636\pi$
$719$			25.0099i			0.0347842i	−0.999849	+	0.0173921i	$0.994464\pi$
$720$	542.135	−	123.404i	0.752966	−	0.171395i
$721$	−953.496			−1.32246
$722$			1265.51i			1.75278i
$723$	−200.337	+	251.064i	−0.277092	+	0.347253i
$724$	−1201.26			−1.65920
$725$		−	2192.61i		−	3.02429i
$726$	266.678	+	212.797i	0.367326	+	0.293109i
$727$	1393.92			1.91736			0.958680	−	0.284488i	$-0.0918236\pi$
$727$	1393.92			1.91736			0.958680	+	0.284488i	$0.0918236\pi$
$728$			397.347i			0.545806i
$729$	453.520	+	570.754i	0.622113	+	0.782927i
$730$	1229.40			1.68411
$731$		−	571.317i		−	0.781555i
$732$	328.772	−	412.019i	0.449142	−	0.562868i
$733$	235.168			0.320829			0.160415	−	0.987050i	$-0.448717\pi$
$733$	235.168			0.320829			0.160415	+	0.987050i	$0.448717\pi$
$734$			1981.52i			2.69962i
$735$	−1573.92	−	1255.92i	−2.14139	−	1.70873i
$736$	102.955			0.139884
$737$		−	158.131i		−	0.214560i
$738$	125.520	+	551.430i	0.170081	+	0.747195i
$739$	892.737			1.20803			0.604017	−	0.796971i	$-0.293566\pi$
$739$	892.737			1.20803			0.604017	+	0.796971i	$0.293566\pi$
$740$		−	2080.48i		−	2.81145i
$741$	372.248	−	466.504i	0.502359	−	0.629560i
$742$	−2380.28			−3.20792
$743$		−	282.415i		−	0.380101i	−0.981774	−	0.190050i	$-0.939135\pi$
$743$		−	282.415i		−	0.380101i	0.981774	−	0.190050i	$-0.0608651\pi$
$744$	−462.324	−	368.913i	−0.621403	−	0.495851i
$745$	1161.58			1.55917
$746$		−	844.553i		−	1.13211i
$747$	−0.892366	+	0.203126i	−0.00119460	+	0.000271923i
$748$	515.514			0.689190
$749$			1486.75i			1.98498i
$750$	−1316.37	+	1649.68i	−1.75516	+	2.19958i
$751$	583.942			0.777552			0.388776	−	0.921332i	$-0.372898\pi$
$751$	583.942			0.777552			0.388776	+	0.921332i	$0.372898\pi$
$752$			337.878i			0.449306i
$753$	−192.372	−	153.504i	−0.255474	−	0.203856i
$754$	−954.107			−1.26539
$755$			302.418i			0.400554i
$756$	−1526.62	−	736.836i	−2.01934	−	0.974651i
$757$	540.866			0.714486			0.357243	−	0.934011i	$-0.383717\pi$
$757$	540.866			0.714486			0.357243	+	0.934011i	$0.383717\pi$
$758$			1468.12i			1.93683i
$759$	42.4227	−	53.1643i	0.0558928	−	0.0700452i
$760$	−1194.27			−1.57141
$761$			657.957i			0.864595i	0.901731	+	0.432298i	$0.142297\pi$
$761$			657.957i			0.864595i	−0.901731	+	0.432298i	$0.857703\pi$
$762$	−394.798	−	315.030i	−0.518107	−	0.413425i
$763$	−480.723			−0.630043
$764$		−	502.242i		−	0.657385i
$765$	174.860	+	768.190i	0.228576	+	1.00417i
$766$	−920.672			−1.20192
$767$		−	55.0838i		−	0.0718172i
$768$	−88.5028	+	110.912i	−0.115238	+	0.144417i
$769$	557.505			0.724974			0.362487	−	0.931989i	$-0.381928\pi$
$769$	557.505			0.724974			0.362487	+	0.931989i	$0.381928\pi$
$770$			2783.15i			3.61448i
$771$	−1171.43	−	934.750i	−1.51937	−	1.21239i
$772$	−257.504			−0.333554
$773$			499.019i			0.645561i	0.946474	+	0.322781i	$0.104618\pi$
$773$			499.019i			0.645561i	−0.946474	+	0.322781i	$0.895382\pi$
$774$	1546.99	−	352.136i	1.99870	−	0.454956i
$775$	−2038.60			−2.63045
$776$		−	292.165i		−	0.376502i
$777$	895.689	−	1122.48i	1.15275	−	1.44464i
$778$	456.543			0.586816
$779$			562.789i			0.722451i
$780$	820.309	+	654.568i	1.05168	+	0.839190i
$781$	−386.665			−0.495090
$782$			76.7840i			0.0981892i
$783$	504.119	−	1044.46i	0.643830	−	1.33392i
$784$	−545.270			−0.695498
$785$			2353.04i			2.99751i
$786$	495.760	−	621.290i	0.630738	−	0.790445i
$787$	1476.26			1.87580			0.937901	−	0.346904i	$-0.112767\pi$
$787$	1476.26			1.87580			0.937901	+	0.346904i	$0.112767\pi$
$788$		−	1135.34i		−	1.44078i
$789$	98.4485	+	78.5573i	0.124776	+	0.0995657i
$790$	753.228			0.953453
$791$			153.798i			0.194435i
$792$	90.5334	+	397.728i	0.114310	+	0.502182i
$793$	−225.254			−0.284053
$794$		−	2078.96i		−	2.61834i
$795$	−1117.24	+	1400.14i	−1.40534	+	1.76118i
$796$	451.686			0.567444
$797$			272.042i			0.341333i	0.985329	+	0.170667i	$0.0545921\pi$
$797$			272.042i			0.341333i	−0.985329	+	0.170667i	$0.945408\pi$
$798$	−2261.44	−	1804.52i	−2.83388	−	2.26131i
$799$	−478.763			−0.599203
$800$			2128.09i			2.66011i
$801$	300.890	−	68.4906i	0.375643	−	0.0855064i
$802$	1301.86			1.62327
$803$		−	417.862i		−	0.520376i
$804$	−180.287	+	225.937i	−0.224238	+	0.281016i
$805$	−241.704			−0.300254
$806$			887.088i			1.10061i
$807$	578.180	+	461.361i	0.716456	+	0.571698i
$808$	538.610			0.666597
$809$		−	347.502i		−	0.429545i	−0.976664	−	0.214772i	$-0.931099\pi$
$809$		−	347.502i		−	0.429545i	0.976664	−	0.214772i	$-0.0689009\pi$
$810$	−1972.30	+	946.961i	−2.43494	+	1.16909i
$811$	461.211			0.568695			0.284347	−	0.958721i	$-0.408223\pi$
$811$	461.211			0.568695			0.284347	+	0.958721i	$0.408223\pi$
$812$			2696.77i			3.32115i
$813$	851.084	−	1066.58i	1.04684	−	1.31191i
$814$	−1212.78			−1.48991
$815$		−	1432.82i		−	1.75806i
$816$	166.759	+	133.066i	0.204361	+	0.163071i
$817$	1578.86			1.93251
$818$		−	368.894i		−	0.450970i
$819$	160.777	+	706.321i	0.196309	+	0.862419i
$820$	−989.620			−1.20685
$821$		−	830.719i		−	1.01184i	−0.862581	−	0.505919i	$-0.831153\pi$
$821$		−	830.719i		−	1.01184i	0.862581	−	0.505919i	$-0.168847\pi$
$822$	−168.309	+	210.926i	−0.204756	+	0.256601i
$823$	462.566			0.562048			0.281024	−	0.959701i	$-0.409326\pi$
$823$	462.566			0.562048			0.281024	+	0.959701i	$0.409326\pi$
$824$		−	419.400i		−	0.508981i
$825$	1098.91	+	876.880i	1.33201	+	1.06289i
$826$	−267.026			−0.323276
$827$			953.056i			1.15243i	0.817299	+	0.576213i	$0.195470\pi$
$827$			953.056i			1.15243i	−0.817299	+	0.576213i	$0.804530\pi$
$828$	−121.227	+	27.5944i	−0.146409	+	0.0333266i
$829$	−170.387			−0.205533			−0.102767	−	0.994706i	$-0.532769\pi$
$829$	−170.387			−0.205533			−0.102767	+	0.994706i	$0.532769\pi$
$830$		−	2.74665i		−	0.00330922i
$831$	−979.295	+	1227.26i	−1.17845	+	1.47685i
$832$	722.814			0.868767
$833$		−	772.632i		−	0.927529i
$834$	−18.1977	−	14.5209i	−0.0218197	−	0.0174111i
$835$	2345.54			2.80903
$836$			1424.64i			1.70412i
$837$	−971.096	−	468.708i	−1.16021	−	0.559986i
$838$	2305.17			2.75080
$839$		−	1102.21i		−	1.31372i	−0.754014	−	0.656858i	$-0.771885\pi$
$839$		−	1102.21i		−	1.31372i	0.754014	−	0.656858i	$-0.228115\pi$
$840$	904.106	−	1133.03i	1.07632	−	1.34885i
$841$	−1004.04			−1.19387
$842$		−	1129.78i		−	1.34178i
$843$	767.096	+	612.107i	0.909959	+	0.726105i
$844$	449.266			0.532305
$845$			1025.28i			1.21335i
$846$	−295.090	−	1296.38i	−0.348806	−	1.53236i
$847$	−412.088			−0.486527
$848$			485.063i			0.572008i
$849$	815.272	−	1021.70i	0.960273	−	1.20342i
$850$	−1587.13			−1.86721
$851$		−	105.325i		−	0.123766i
$852$	552.467	+	440.843i	0.648435	+	0.517421i
$853$	789.108			0.925097			0.462548	−	0.886594i	$-0.346935\pi$
$853$	789.108			0.925097			0.462548	+	0.886594i	$0.346935\pi$
$854$			1091.95i			1.27863i
$855$	−2122.93	+	483.234i	−2.48295	+	0.565186i
$856$	−653.954			−0.763965
$857$			261.975i			0.305689i	0.988250	+	0.152844i	$0.0488433\pi$
$857$			261.975i			0.305689i	−0.988250	+	0.152844i	$0.951157\pi$
$858$	381.572	−	478.188i	0.444722	−	0.557328i
$859$	−442.523			−0.515161			−0.257581	−	0.966257i	$-0.582925\pi$
$859$	−442.523			−0.515161			−0.257581	+	0.966257i	$0.582925\pi$
$860$			2776.30i			3.22825i
$861$	−533.931	−	426.052i	−0.620129	−	0.494834i
$862$	199.332			0.231244
$863$			1318.46i			1.52776i	0.645356	+	0.763882i	$0.276709\pi$
$863$			1318.46i			1.52776i	−0.645356	+	0.763882i	$0.723291\pi$
$864$	−489.283	+	1013.72i	−0.566300	+	1.17329i
$865$	−1352.62			−1.56373
$866$		−	1237.50i		−	1.42898i
$867$	352.214	−	441.397i	0.406245	−	0.509108i
$868$	2507.34			2.88865
$869$		−	256.015i		−	0.294608i
$870$	2720.63	+	2170.93i	3.12716	+	2.49533i
$871$	123.521			0.141815
$872$		−	211.448i		−	0.242487i
$873$	−118.218	−	519.351i	−0.135416	−	0.594904i
$874$	−212.196			−0.242787
$875$		−	2549.19i		−	2.91336i
$876$	−476.411	+	597.041i	−0.543848	+	0.681554i
$877$	−389.648			−0.444296			−0.222148	−	0.975013i	$-0.571307\pi$
$877$	−389.648			−0.444296			−0.222148	+	0.975013i	$0.571307\pi$
$878$		−	2346.99i		−	2.67311i
$879$	535.732	+	427.489i	0.609479	+	0.486336i
$880$	567.161			0.644501
$881$			1567.20i			1.77889i	0.457044	+	0.889444i	$0.348908\pi$
$881$			1567.20i			1.77889i	−0.457044	+	0.889444i	$0.651092\pi$
$882$	2092.10	−	476.218i	2.37200	−	0.539930i
$883$	−788.136			−0.892566			−0.446283	−	0.894892i	$-0.647253\pi$
$883$	−788.136			−0.892566			−0.446283	+	0.894892i	$0.647253\pi$
$884$			402.686i			0.455527i
$885$	−125.335	+	157.071i	−0.141622	+	0.177481i
$886$	−1231.80			−1.39029
$887$			830.369i			0.936155i	0.883687	+	0.468077i	$0.155053\pi$
$887$			830.369i			0.936155i	−0.883687	+	0.468077i	$0.844947\pi$
$888$	493.730	+	393.973i	0.556002	+	0.443664i
$889$	610.066			0.686238
$890$			926.123i			1.04059i
$891$	321.863	+	670.365i	0.361238	+	0.752374i
$892$	10.7524			0.0120542
$893$		−	1323.08i		−	1.48162i
$894$	−772.004	+	967.480i	−0.863539	+	1.08219i
$895$	1770.29			1.97798
$896$		−	1632.30i		−	1.82176i
$897$	41.5285	+	33.1378i	0.0462971	+	0.0369429i
$898$	680.656			0.757969
$899$			1715.44i			1.90817i
$900$	−570.380	−	2505.77i	−0.633755	−	2.78419i
$901$	−687.320			−0.762841
$902$			576.885i			0.639562i
$903$	−1195.25	+	1497.90i	−1.32365	+	1.65880i
$904$	−67.6490			−0.0748330
$905$		−	1872.68i		−	2.06926i
$906$	−251.884	−	200.991i	−0.278017	−	0.221845i
$907$	−561.671			−0.619263			−0.309631	−	0.950857i	$-0.600206\pi$
$907$	−561.671			−0.619263			−0.309631	+	0.950857i	$0.600206\pi$
$908$			950.696i			1.04702i
$909$	957.430	−	217.936i	1.05328	−	0.239754i
$910$	−2174.01			−2.38903
$911$			883.062i			0.969333i	0.874699	+	0.484667i	$0.161059\pi$
$911$			883.062i			0.969333i	−0.874699	+	0.484667i	$0.838941\pi$
$912$	−367.733	+	460.845i	−0.403216	+	0.505313i
$913$	−0.933559			−0.00102252
$914$			1289.39i			1.41071i
$915$	642.310	+	512.533i	0.701978	+	0.560145i
$916$	−628.609			−0.686255
$917$			960.056i			1.04695i
$918$	−756.039	−	364.909i	−0.823572	−	0.397504i
$919$	−618.189			−0.672675			−0.336338	−	0.941741i	$-0.609188\pi$
$919$	−618.189			−0.672675			−0.336338	+	0.941741i	$0.609188\pi$
$920$		−	106.315i		−	0.115560i
$921$	−700.900	+	878.373i	−0.761021	+	0.953716i
$922$	−1200.23			−1.30176
$923$		−	302.037i		−	0.327235i
$924$	−1351.59	−	1078.51i	−1.46276	−	1.16722i
$925$	2177.08			2.35360
$926$		−	1380.49i		−	1.49082i
$927$	−169.701	−	745.523i	−0.183064	−	0.804232i
$928$	1790.75			1.92968
$929$		−	627.326i		−	0.675270i	−0.941277	−	0.337635i	$-0.890373\pi$
$929$		−	627.326i		−	0.675270i	0.941277	−	0.337635i	$-0.109627\pi$
$930$	2018.44	−	2529.52i	2.17037	−	2.71992i
$931$	2135.20			2.29345
$932$			1916.07i			2.05587i
$933$	−440.725	−	351.678i	−0.472374	−	0.376933i
$934$	−2493.55			−2.66976
$935$			803.651i			0.859520i
$936$	−310.679	+	70.7187i	−0.331922	+	0.0755542i
$937$	−1024.73			−1.09363			−0.546815	−	0.837253i	$-0.684160\pi$
$937$	−1024.73			−1.09363			−0.546815	+	0.837253i	$0.684160\pi$
$938$		−	598.786i		−	0.638365i
$939$	1162.03	−	1456.27i	1.23752	−	1.55087i
$940$	2326.53			2.47504
$941$			524.314i			0.557188i	0.960409	+	0.278594i	$0.0898684\pi$
$941$			524.314i			0.557188i	−0.960409	+	0.278594i	$0.910132\pi$
$942$	−1959.85	−	1563.87i	−2.08052	−	1.66015i
$943$	−50.0999			−0.0531282
$944$			54.4156i			0.0576437i
$945$	1148.68	−	2379.89i	1.21553	−	2.51841i
$946$	1618.40			1.71079
$947$			453.653i			0.479043i	0.970891	+	0.239521i	$0.0769905\pi$
$947$			453.653i			0.479043i	−0.970891	+	0.239521i	$0.923010\pi$
$948$	−291.886	+	365.793i	−0.307897	+	0.385858i
$949$	326.407			0.343948
$950$		−	4386.11i		−	4.61695i
$951$	734.953	+	586.458i	0.772821	+	0.616675i
$952$	556.200			0.584243
$953$		−	1136.89i		−	1.19296i	−0.802627	−	0.596482i	$-0.796565\pi$
$953$		−	1136.89i		−	1.19296i	0.802627	−	0.596482i	$-0.203435\pi$
$954$	−423.635	−	1861.10i	−0.444062	−	1.95084i
$955$	782.961			0.819854
$956$		−	343.010i		−	0.358797i
$957$	737.879	−	924.715i	0.771034	−	0.966264i
$958$	617.177			0.644235
$959$		−	325.936i		−	0.339871i
$960$	−2061.10	−	1644.66i	−2.14698	−	1.71319i
$961$	633.944			0.659671
$962$		−	947.348i		−	0.984769i
$963$	−1162.46	+	264.607i	−1.20713	+	0.274774i
$964$	598.910			0.621276
$965$		−	401.430i		−	0.415990i
$966$	160.640	−	201.315i	0.166294	−	0.208401i
$967$	698.379			0.722212			0.361106	−	0.932525i	$-0.382399\pi$
$967$	698.379			0.722212			0.361106	+	0.932525i	$0.382399\pi$
$968$		−	181.259i		−	0.187251i
$969$	−653.004	−	521.067i	−0.673895	−	0.537737i
$970$	1598.53			1.64797
$971$			1387.45i			1.42889i	0.699693	+	0.714444i	$0.253320\pi$
$971$			1387.45i			1.42889i	−0.699693	+	0.714444i	$0.746680\pi$
$972$	304.416	−	1324.78i	0.313185	−	1.36294i
$973$	28.1202			0.0289005
$974$		−	1729.92i		−	1.77609i
$975$	−684.962	+	858.398i	−0.702525	+	0.880408i
$976$	222.522			0.227994
$977$		−	726.978i		−	0.744092i	−0.928214	−	0.372046i	$-0.878656\pi$
$977$		−	726.978i		−	0.744092i	0.928214	−	0.372046i	$-0.121344\pi$
$978$	1193.39	+	952.270i	1.22024	+	0.973691i
$979$	314.780			0.321532
$980$			3754.58i			3.83120i
$981$	−85.5577	−	375.869i	−0.0872148	−	0.383149i
$982$	−2933.45			−2.98722
$983$			1556.78i			1.58370i	0.610715	+	0.791851i	$0.290882\pi$
$983$			1556.78i			1.58370i	−0.610715	+	0.791851i	$0.709118\pi$
$984$	187.401	−	234.852i	0.190448	−	0.238671i
$985$	1769.91			1.79687
$986$			1335.54i			1.35451i
$987$	1255.24	+	1001.62i	1.27177	+	1.01481i
$988$	−1112.84			−1.12636
$989$			140.551i			0.142114i
$990$	−2176.10	+	495.337i	−2.19808	+	0.500341i
$991$	−477.090			−0.481423			−0.240711	−	0.970597i	$-0.577381\pi$
$991$	−477.090			−0.481423			−0.240711	+	0.970597i	$0.577381\pi$
$992$		−	1664.96i		−	1.67839i
$993$	233.934	−	293.167i	0.235583	−	0.295234i
$994$	−1464.17			−1.47301
$995$			704.147i			0.707685i
$996$	1.33387	+	1.06436i	0.00133923	+	0.00106864i
$997$	399.358			0.400560			0.200280	−	0.979739i	$-0.435815\pi$
$997$	399.358			0.400560			0.200280	+	0.979739i	$0.435815\pi$
$998$		−	1408.08i		−	1.41090i
$999$	1037.06	+	500.547i	1.03810	+	0.501048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.33	yes	38
3.2	odd	2	inner	177.3.b.a.119.6	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.6	✓	38	3.2	odd	2	inner
177.3.b.a.119.33	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)

\(f(q)\)	\(=\)	\(q+3.09739i q^{2} +(1.87116 - 2.34495i) q^{3} -5.59384 q^{4} -8.72041i q^{5} +(7.26322 + 5.79571i) q^{6} -11.2236 q^{7} -4.93675i q^{8} +(-1.99754 - 8.77552i) q^{9} +O(q^{10})\)	\(q+3.09739i q^{2} +(1.87116 - 2.34495i) q^{3} -5.59384 q^{4} -8.72041i q^{5} +(7.26322 + 5.79571i) q^{6} -11.2236 q^{7} -4.93675i q^{8} +(-1.99754 - 8.77552i) q^{9} +27.0105 q^{10} -9.18062i q^{11} +(-10.4670 + 13.1173i) q^{12} +7.17130 q^{13} -34.7638i q^{14} +(-20.4489 - 16.3173i) q^{15} -7.08431 q^{16} -10.0383i q^{17} +(27.1812 - 6.18717i) q^{18} +27.7412 q^{19} +48.7806i q^{20} +(-21.0011 + 26.3187i) q^{21} +28.4360 q^{22} +2.46954i q^{23} +(-11.5764 - 9.23743i) q^{24} -51.0456 q^{25} +22.2123i q^{26} +(-24.3158 - 11.7363i) q^{27} +62.7829 q^{28} +42.9540i q^{29} +(50.5410 - 63.3383i) q^{30} +39.9367 q^{31} -41.6899i q^{32} +(-21.5280 - 17.1784i) q^{33} +31.0924 q^{34} +97.8742i q^{35} +(11.1739 + 49.0889i) q^{36} -42.6497 q^{37} +85.9253i q^{38} +(13.4186 - 16.8163i) q^{39} -43.0505 q^{40} +20.2872i q^{41} +(-81.5193 - 65.0486i) q^{42} +56.9139 q^{43} +51.3549i q^{44} +(-76.5262 + 17.4194i) q^{45} -7.64913 q^{46} -47.6938i q^{47} +(-13.2559 + 16.6123i) q^{48} +76.9687 q^{49} -158.108i q^{50} +(-23.5392 - 18.7832i) q^{51} -40.1151 q^{52} -68.4700i q^{53} +(36.3518 - 75.3157i) q^{54} -80.0588 q^{55} +55.4080i q^{56} +(51.9081 - 65.0515i) q^{57} -133.045 q^{58} -7.68115i q^{59} +(114.388 + 91.2762i) q^{60} -31.4105 q^{61} +123.700i q^{62} +(22.4196 + 98.4928i) q^{63} +100.793 q^{64} -62.5367i q^{65} +(53.2082 - 66.6808i) q^{66} +17.2244 q^{67} +56.1524i q^{68} +(5.79093 + 4.62089i) q^{69} -303.155 q^{70} -42.1176i q^{71} +(-43.3226 + 9.86136i) q^{72} +45.5157 q^{73} -132.103i q^{74} +(-95.5143 + 119.699i) q^{75} -155.180 q^{76} +103.039i q^{77} +(52.0867 + 41.5627i) q^{78} +27.8864 q^{79} +61.7781i q^{80} +(-73.0197 + 35.0590i) q^{81} -62.8373 q^{82} -0.101688i q^{83} +(117.477 - 147.222i) q^{84} -87.5378 q^{85} +176.285i q^{86} +(100.725 + 80.3736i) q^{87} -45.3224 q^{88} +34.2875i q^{89} +(-53.9547 - 237.032i) q^{90} -80.4876 q^{91} -13.8142i q^{92} +(74.7279 - 93.6495i) q^{93} +147.727 q^{94} -241.914i q^{95} +(-97.7605 - 78.0083i) q^{96} +59.1817 q^{97} +238.402i q^{98} +(-80.5647 + 18.3387i) 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

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