LMFDB - Embedded newform 177.3.b.a.119.6

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

$q$-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	$-0.718078\pi$
$2$		−	3.09739i		−	1.54870i	0.632760	−	0.774348i	$-0.281922\pi$
$3$	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	$0.337204\pi$
$5$			8.72041i			1.74408i	−0.489432	+	0.872041i	$0.662796\pi$
$6$	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	$0.137024\pi$
$11$			9.18062i			0.834601i	−0.908768	+	0.417301i	$0.862976\pi$
$12$	−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	$0.0954006\pi$
$17$			10.0383i			0.590486i	−0.955422	+	0.295243i	$0.904599\pi$
$18$	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	$-0.982903\pi$
$23$		−	2.46954i		−	0.107371i	0.998558	−	0.0536856i	$-0.0170969\pi$
$24$	−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	$-0.734548\pi$
$29$		−	42.9540i		−	1.48117i	0.671962	−	0.740586i	$-0.265452\pi$
$30$	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	$-0.920422\pi$
$41$		−	20.2872i		−	0.494809i	0.968912	−	0.247404i	$-0.0795776\pi$
$42$	−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	$0.169386\pi$
$47$			47.6938i			1.01476i	−0.861722	+	0.507381i	$0.830614\pi$
$48$	−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	$0.223536\pi$
$53$			68.4700i			1.29189i	−0.763386	+	0.645943i	$0.776464\pi$
$54$	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	$0.0958536\pi$
$71$			42.1176i			0.593205i	−0.955001	+	0.296603i	$0.904146\pi$
$72$	−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	$0.000194990\pi$
$83$			0.101688i			0.00122516i	−1.00000		0.000612579i	$0.999805\pi$
$84$	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	$-0.938300\pi$
$89$		−	34.2875i		−	0.385252i	0.981272	−	0.192626i	$-0.0617005\pi$
$90$	−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	$-0.818383\pi$
$101$		−	109.102i		−	1.08022i	0.841594	−	0.540110i	$-0.181617\pi$
$102$	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	$0.212463\pi$
$107$			132.466i			1.23800i	−0.785389	+	0.619002i	$0.787537\pi$
$108$	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	$0.0193121\pi$
$113$			13.7032i			0.121267i	−0.998160	+	0.0606334i	$0.980688\pi$
$114$	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	$0.105864\pi$
$131$			85.5392i			0.652971i	−0.945202	+	0.326485i	$0.894136\pi$
$132$	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	$-0.966200\pi$
$137$		−	29.0403i		−	0.211973i	0.994368	−	0.105986i	$-0.0338000\pi$
$138$	−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	$-0.852496\pi$
$149$		−	133.203i		−	0.893978i	0.894540	−	0.446989i	$-0.147504\pi$
$150$	−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	$-0.702003\pi$
$167$		−	268.971i		−	1.61060i	0.592864	−	0.805302i	$-0.297997\pi$
$168$	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	$0.147968\pi$
$173$			155.110i			0.896589i	−0.893886	+	0.448295i	$0.852032\pi$
$174$	−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	$-0.808083\pi$
$179$		−	203.005i		−	1.13411i	0.823681	−	0.567053i	$-0.191917\pi$
$180$	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	$-0.924478\pi$
$191$		−	89.7848i		−	0.470078i	0.971986	−	0.235039i	$-0.0755217\pi$
$192$	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	$-0.827743\pi$
$197$		−	202.962i		−	1.03026i	0.857111	−	0.515132i	$-0.172257\pi$
$198$	−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	$0.122134\pi$
$227$			169.954i			0.748696i	−0.927288	+	0.374348i	$0.877866\pi$
$228$	−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	$0.262840\pi$
$233$			342.532i			1.47010i	−0.678015	+	0.735048i	$0.737160\pi$
$234$	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	$-0.959053\pi$
$239$		−	61.3192i		−	0.256566i	0.991738	−	0.128283i	$-0.0409466\pi$
$240$	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	$0.0522525\pi$
$251$			82.0368i			0.326840i	−0.986557	+	0.163420i	$0.947747\pi$
$252$	−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	$0.424363\pi$
$257$			499.557i			1.94380i	−0.235391	+	0.971901i	$0.575637\pi$
$258$	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	$-0.974567\pi$
$263$		−	41.9833i		−	0.159632i	0.996810	−	0.0798161i	$-0.0254333\pi$
$264$	−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	$-0.848459\pi$
$269$		−	246.564i		−	0.916596i	0.888799	−	0.458298i	$-0.151541\pi$
$270$	−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	$-0.802240\pi$
$281$		−	327.127i		−	1.16415i	0.813134	−	0.582077i	$-0.197760\pi$
$282$	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	$-0.872521\pi$
$293$		−	228.463i		−	0.779736i	0.920871	−	0.389868i	$-0.127479\pi$
$294$	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	$0.0977095\pi$
$311$			187.947i			0.604331i	−0.953256	+	0.302165i	$0.902291\pi$
$312$	−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	$-0.835405\pi$
$317$		−	313.420i		−	0.988706i	0.869261	−	0.494353i	$-0.164595\pi$
$318$	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	$0.134861\pi$
$347$			285.316i			0.822235i	−0.911582	+	0.411118i	$0.865139\pi$
$348$	−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	$-0.822882\pi$
$353$		−	372.881i		−	1.05632i	0.849145	−	0.528160i	$-0.177118\pi$
$354$	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	$-0.966893\pi$
$359$		−	74.5446i		−	0.207645i	0.994596	−	0.103823i	$-0.0331074\pi$
$360$	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	$-0.873151\pi$
$383$		−	297.241i		−	0.776086i	0.921641	−	0.388043i	$-0.126849\pi$
$384$	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	$0.0606721\pi$
$389$			147.396i			0.378910i	−0.981889	+	0.189455i	$0.939328\pi$
$390$	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	$0.175589\pi$
$401$			420.309i			1.04815i	−0.851671	+	0.524076i	$0.824411\pi$
$402$	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	$0.347975\pi$
$419$			744.229i			1.77620i	−0.459648	+	0.888101i	$0.652025\pi$
$420$	−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	$0.0237864\pi$
$431$			64.3549i			0.149315i	−0.997209	+	0.0746576i	$0.976214\pi$
$432$	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	$-0.851831\pi$
$443$		−	397.689i		−	0.897717i	0.893603	−	0.448859i	$-0.148169\pi$
$444$	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	$0.0786934\pi$
$449$			219.751i			0.489424i	−0.969596	+	0.244712i	$0.921307\pi$
$450$	−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	$-0.861933\pi$
$461$		−	387.495i		−	0.840554i	0.907396	−	0.420277i	$-0.138067\pi$
$462$	−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	$-0.669251\pi$
$467$		−	805.049i		−	1.72387i	0.507016	−	0.861937i	$-0.330749\pi$
$468$	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	$0.0666931\pi$
$479$			199.257i			0.415986i	−0.978130	+	0.207993i	$0.933307\pi$
$480$	−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	$-0.585152\pi$
$491$		−	947.072i		−	1.92886i	0.264332	−	0.964432i	$-0.414848\pi$
$492$	−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	$0.302516\pi$
$503$			818.520i			1.62728i	−0.581372	+	0.813638i	$0.697484\pi$
$504$	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	$-0.895138\pi$
$509$		−	329.331i		−	0.647017i	0.946225	−	0.323508i	$-0.104862\pi$
$510$	−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	$-0.960655\pi$
$521$		−	128.469i		−	0.246581i	0.992371	−	0.123290i	$-0.0393447\pi$
$522$	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	$-0.835675\pi$
$557$		−	549.889i		−	0.987234i	0.869680	−	0.493617i	$-0.164325\pi$
$558$	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	$0.107848\pi$
$563$			374.249i			0.664741i	−0.943149	+	0.332370i	$0.892152\pi$
$564$	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	$-0.746817\pi$
$569$		−	812.694i		−	1.42828i	0.700000	−	0.714142i	$-0.253183\pi$
$570$	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	$-0.923197\pi$
$587$		−	280.527i		−	0.477899i	0.971032	−	0.238950i	$-0.0768031\pi$
$588$	−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	$0.0509619\pi$
$593$			189.070i			0.318837i	−0.987211	+	0.159418i	$0.949038\pi$
$594$	−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	$0.0821352\pi$
$599$			305.707i			0.510363i	−0.966893	+	0.255182i	$0.917865\pi$
$600$	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	$0.00501003\pi$
$617$			19.4217i			0.0314777i	−0.999876	+	0.0157388i	$0.994990\pi$
$618$	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	$-0.940266\pi$
$641$		−	239.172i		−	0.373123i	0.982443	−	0.186562i	$-0.0597344\pi$
$642$	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	$0.307918\pi$
$647$			1065.46i			1.64677i	−0.567480	+	0.823387i	$0.692082\pi$
$648$	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	$0.0603062\pi$
$653$			245.954i			0.376652i	−0.982107	+	0.188326i	$0.939694\pi$
$654$	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	$-0.944100\pi$
$659$		−	230.272i		−	0.349426i	0.984619	−	0.174713i	$-0.0558997\pi$
$660$	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	$0.0552499\pi$
$677$			233.839i			0.345405i	−0.984974	+	0.172702i	$0.944750\pi$
$678$	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	$0.0334073\pi$
$683$			143.102i			0.209519i	−0.994498	+	0.104760i	$0.966593\pi$
$684$	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	$0.218513\pi$
$701$			888.614i			1.26764i	−0.773482	+	0.633819i	$0.781487\pi$
$702$	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	$-0.994464\pi$
$719$		−	25.0099i		−	0.0347842i	0.999849	−	0.0173921i	$-0.00553636\pi$
$720$	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	$0.0608651\pi$
$743$			282.415i			0.380101i	−0.981774	+	0.190050i	$0.939135\pi$
$744$	−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	$-0.857703\pi$
$761$		−	657.957i		−	0.864595i	0.901731	−	0.432298i	$-0.142297\pi$
$762$	−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	$-0.895382\pi$
$773$		−	499.019i		−	0.645561i	0.946474	−	0.322781i	$-0.104618\pi$
$774$	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	$-0.945408\pi$
$797$		−	272.042i		−	0.341333i	0.985329	−	0.170667i	$-0.0545921\pi$
$798$	−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	$0.0689009\pi$
$809$			347.502i			0.429545i	−0.976664	+	0.214772i	$0.931099\pi$
$810$	−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	$0.168847\pi$
$821$			830.719i			1.01184i	−0.862581	+	0.505919i	$0.831153\pi$
$822$	−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	$-0.804530\pi$
$827$		−	953.056i		−	1.15243i	0.817299	−	0.576213i	$-0.195470\pi$
$828$	−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	$0.228115\pi$
$839$			1102.21i			1.31372i	−0.754014	+	0.656858i	$0.771885\pi$
$840$	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	$-0.951157\pi$
$857$		−	261.975i		−	0.305689i	0.988250	−	0.152844i	$-0.0488433\pi$
$858$	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	$-0.723291\pi$
$863$		−	1318.46i		−	1.52776i	0.645356	−	0.763882i	$-0.276709\pi$
$864$	−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	$-0.651092\pi$
$881$		−	1567.20i		−	1.77889i	0.457044	−	0.889444i	$-0.348908\pi$
$882$	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	$-0.844947\pi$
$887$		−	830.369i		−	0.936155i	0.883687	−	0.468077i	$-0.155053\pi$
$888$	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	$-0.838941\pi$
$911$		−	883.062i		−	0.969333i	0.874699	−	0.484667i	$-0.161059\pi$
$912$	−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	$0.109627\pi$
$929$			627.326i			0.675270i	−0.941277	+	0.337635i	$0.890373\pi$
$930$	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	$-0.910132\pi$
$941$		−	524.314i		−	0.557188i	0.960409	−	0.278594i	$-0.0898684\pi$
$942$	−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	$-0.923010\pi$
$947$		−	453.653i		−	0.479043i	0.970891	−	0.239521i	$-0.0769905\pi$
$948$	−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	$0.203435\pi$
$953$			1136.89i			1.19296i	−0.802627	+	0.596482i	$0.796565\pi$
$954$	−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	$-0.746680\pi$
$971$		−	1387.45i		−	1.42889i	0.699693	−	0.714444i	$-0.253320\pi$
$972$	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	$0.121344\pi$
$977$			726.978i			0.744092i	−0.928214	+	0.372046i	$0.878656\pi$
$978$	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	$-0.709118\pi$
$983$		−	1556.78i		−	1.58370i	0.610715	−	0.791851i	$-0.290882\pi$
$984$	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.119.6	✓	38
3.2	odd	2	inner	177.3.b.a.119.33	yes	38

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.09739i q^{2} +(1.87116 + 2.34495i) q^{3} -5.59384 q^{4} +8.72041i q^{5} +(7.26322 - 5.79571i) q^{6} -11.2236 q^{7} +4.93675i q^{8} +(-1.99754 + 8.77552i) q^{9} +O(q^{10})\)	\(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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