LMFDB - Embedded newform 117.3.k.a.29.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.11
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.630376i q^{2} +(2.39963 + 1.80049i) q^{3} +3.60263 q^{4} +(1.96357 - 1.13367i) q^{5} +(1.13499 - 1.51267i) q^{6} +(-4.09731 - 7.09675i) q^{7} -4.79251i q^{8} +(2.51645 + 8.64103i) q^{9} +(-0.714636 - 1.23779i) q^{10} +19.9709i q^{11} +(8.64497 + 6.48650i) q^{12} +(-6.85862 - 11.0435i) q^{13} +(-4.47362 + 2.58285i) q^{14} +(6.75299 + 0.815008i) q^{15} +11.3894 q^{16} +(-5.86667 - 3.38712i) q^{17} +(5.44710 - 1.58631i) q^{18} +(6.12594 - 10.6104i) q^{19} +(7.07400 - 4.08417i) q^{20} +(2.94561 - 24.4067i) q^{21} +12.5892 q^{22} +(-11.7730 - 6.79717i) q^{23} +(8.62889 - 11.5003i) q^{24} +(-9.92960 + 17.1986i) q^{25} +(-6.96157 + 4.32351i) q^{26} +(-9.51956 + 25.2661i) q^{27} +(-14.7611 - 25.5669i) q^{28} +35.8609i q^{29} +(0.513762 - 4.25693i) q^{30} +(1.22045 + 2.11388i) q^{31} -26.3497i q^{32} +(-35.9575 + 47.9228i) q^{33} +(-2.13516 + 3.69821i) q^{34} +(-16.0907 - 9.28996i) q^{35} +(9.06584 + 31.1304i) q^{36} +(-30.7914 - 53.3322i) q^{37} +(-6.68857 - 3.86165i) q^{38} +(3.42562 - 38.8493i) q^{39} +(-5.43311 - 9.41042i) q^{40} +(-8.34931 - 4.82048i) q^{41} +(-15.3854 - 1.85684i) q^{42} +(26.2518 + 45.4694i) q^{43} +71.9477i q^{44} +(14.7373 + 14.1144i) q^{45} +(-4.28478 + 7.42145i) q^{46} +(-70.0665 - 40.4529i) q^{47} +(27.3304 + 20.5066i) q^{48} +(-9.07586 + 15.7199i) q^{49} +(10.8416 + 6.25939i) q^{50} +(-7.97935 - 18.6907i) q^{51} +(-24.7090 - 39.7857i) q^{52} +16.7330i q^{53} +(15.9272 + 6.00091i) q^{54} +(22.6403 + 39.2142i) q^{55} +(-34.0113 + 19.6364i) q^{56} +(33.8040 - 14.4314i) q^{57} +22.6059 q^{58} -6.77988i q^{59} +(24.3285 + 2.93617i) q^{60} +(-43.7577 - 75.7905i) q^{61} +(1.33254 - 0.769341i) q^{62} +(51.0125 - 53.2636i) q^{63} +28.9475 q^{64} +(-25.9870 - 13.9093i) q^{65} +(30.2094 + 22.6667i) q^{66} +(-4.07107 + 7.05130i) q^{67} +(-21.1354 - 12.2025i) q^{68} +(-16.0127 - 37.5080i) q^{69} +(-5.85617 + 10.1432i) q^{70} +(61.6181 + 35.5752i) q^{71} +(41.4123 - 12.0601i) q^{72} +49.6082 q^{73} +(-33.6194 + 19.4101i) q^{74} +(-54.7933 + 23.3921i) q^{75} +(22.0695 - 38.2254i) q^{76} +(141.728 - 81.8269i) q^{77} +(-24.4897 - 2.15943i) q^{78} +(10.9038 - 18.8860i) q^{79} +(22.3639 - 12.9118i) q^{80} +(-68.3349 + 43.4895i) q^{81} +(-3.03871 + 5.26321i) q^{82} +(83.1927 + 48.0313i) q^{83} +(10.6119 - 87.9283i) q^{84} -15.3595 q^{85} +(28.6629 - 16.5485i) q^{86} +(-64.5673 + 86.0529i) q^{87} +95.7108 q^{88} +(13.0504 - 7.53467i) q^{89} +(8.89740 - 9.29002i) q^{90} +(-50.2712 + 93.9226i) q^{91} +(-42.4139 - 24.4877i) q^{92} +(-0.877397 + 7.26993i) q^{93} +(-25.5006 + 44.1683i) q^{94} -27.7791i q^{95} +(47.4424 - 63.2295i) q^{96} +(59.9243 + 103.792i) q^{97} +(9.90942 + 5.72121i) q^{98} +(-172.569 + 50.2558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	0.630376i		−	0.315188i	−0.987504	−	0.157594i	$-0.949626\pi$
$2$		−	0.630376i		−	0.315188i	0.987504	−	0.157594i	$-0.0503737\pi$
$3$	2.39963	+	1.80049i	0.799877	+	0.600164i
$3$	2.39963	+	1.80049i	0.799877	+	0.600164i
$4$	3.60263			0.900656
$5$	1.96357	−	1.13367i	0.392713	−	0.226733i	−0.290622	−	0.956838i	$-0.593862\pi$
$5$	1.96357	−	1.13367i	0.392713	−	0.226733i	0.683335	+	0.730105i	$0.260529\pi$
$6$	1.13499	−	1.51267i	0.189165	−	0.252112i
$7$	−4.09731	−	7.09675i	−0.585330	−	1.01382i	−0.994834	−	0.101513i	$-0.967632\pi$
$7$	−4.09731	−	7.09675i	−0.585330	−	1.01382i	0.409505	−	0.912308i	$-0.365702\pi$
$8$		−	4.79251i		−	0.599064i
$9$	2.51645	+	8.64103i	0.279606	+	0.960115i
$10$	−0.714636	−	1.23779i	−0.0714636	−	0.123779i
$11$			19.9709i			1.81554i	0.419472	+	0.907768i	$0.362215\pi$
$11$			19.9709i			1.81554i	−0.419472	+	0.907768i	$0.637785\pi$
$12$	8.64497	+	6.48650i	0.720414	+	0.540542i
$13$	−6.85862	−	11.0435i	−0.527586	−	0.849501i
$13$	−6.85862	−	11.0435i	−0.527586	−	0.849501i
$14$	−4.47362	+	2.58285i	−0.319544	+	0.184489i
$15$	6.75299	+	0.815008i	0.450199	+	0.0543339i
$16$	11.3894			0.711838
$17$	−5.86667	−	3.38712i	−0.345098	−	0.199243i	0.317426	−	0.948283i	$-0.397182\pi$
$17$	−5.86667	−	3.38712i	−0.345098	−	0.199243i	−0.662524	+	0.749040i	$0.730515\pi$
$18$	5.44710	−	1.58631i	0.302617	−	0.0881284i
$19$	6.12594	−	10.6104i	0.322418	−	0.558444i	−0.658569	−	0.752521i	$-0.728838\pi$
$19$	6.12594	−	10.6104i	0.322418	−	0.558444i	0.980986	+	0.194077i	$0.0621711\pi$
$20$	7.07400	−	4.08417i	0.353700	−	0.204209i
$21$	2.94561	−	24.4067i	0.140267	−	1.16223i
$22$	12.5892			0.572236
$23$	−11.7730	−	6.79717i	−0.511872	−	0.295529i	0.221731	−	0.975108i	$-0.428829\pi$
$23$	−11.7730	−	6.79717i	−0.511872	−	0.295529i	−0.733603	+	0.679579i	$0.762163\pi$
$24$	8.62889	−	11.5003i	0.359537	−	0.479178i
$25$	−9.92960	+	17.1986i	−0.397184	+	0.687943i
$26$	−6.96157	+	4.32351i	−0.267753	+	0.166289i
$27$	−9.51956	+	25.2661i	−0.352576	+	0.935783i
$28$	−14.7611	−	25.5669i	−0.527181	−	0.913104i
$29$			35.8609i			1.23658i	0.785949	+	0.618292i	$0.212175\pi$
$29$			35.8609i			1.23658i	−0.785949	+	0.618292i	$0.787825\pi$
$30$	0.513762	−	4.25693i	0.0171254	−	0.141898i
$31$	1.22045	+	2.11388i	0.0393693	+	0.0681896i	0.885039	−	0.465518i	$-0.154132\pi$
$31$	1.22045	+	2.11388i	0.0393693	+	0.0681896i	−0.845669	+	0.533707i	$0.820798\pi$
$32$		−	26.3497i		−	0.823427i
$33$	−35.9575	+	47.9228i	−1.08962	+	1.45221i
$34$	−2.13516	+	3.69821i	−0.0627989	+	0.108771i
$35$	−16.0907	−	9.28996i	−0.459734	−	0.265427i
$36$	9.06584	+	31.1304i	0.251829	+	0.864734i
$37$	−30.7914	−	53.3322i	−0.832199	−	1.44141i	−0.896291	−	0.443467i	$-0.853748\pi$
$37$	−30.7914	−	53.3322i	−0.832199	−	1.44141i	0.0640919	−	0.997944i	$-0.479585\pi$
$38$	−6.68857	−	3.86165i	−0.176015	−	0.101622i
$39$	3.42562	−	38.8493i	0.0878364	−	0.996135i
$40$	−5.43311	−	9.41042i	−0.135828	−	0.235261i
$41$	−8.34931	−	4.82048i	−0.203642	−	0.117573i	0.394711	−	0.918805i	$-0.370845\pi$
$41$	−8.34931	−	4.82048i	−0.203642	−	0.117573i	−0.598353	+	0.801233i	$0.704178\pi$
$42$	−15.3854	−	1.85684i	−0.366320	−	0.0442106i
$43$	26.2518	+	45.4694i	0.610507	+	1.05743i	0.991155	+	0.132709i	$0.0423676\pi$
$43$	26.2518	+	45.4694i	0.610507	+	1.05743i	−0.380648	+	0.924720i	$0.624299\pi$
$44$			71.9477i			1.63517i
$45$	14.7373	+	14.1144i	0.327495	+	0.313654i
$46$	−4.28478	+	7.42145i	−0.0931473	+	0.161336i
$47$	−70.0665	−	40.4529i	−1.49078	−	0.860701i	−0.490833	−	0.871254i	$-0.663307\pi$
$47$	−70.0665	−	40.4529i	−1.49078	−	0.860701i	−0.999944	+	0.0105532i	$0.996641\pi$
$48$	27.3304	+	20.5066i	0.569383	+	0.427220i
$49$	−9.07586	+	15.7199i	−0.185222	+	0.320813i
$50$	10.8416	+	6.25939i	0.216832	+	0.125188i
$51$	−7.97935	−	18.6907i	−0.156458	−	0.366485i
$52$	−24.7090	−	39.7857i	−0.475174	−	0.765109i
$53$			16.7330i			0.315716i	0.987462	+	0.157858i	$0.0504589\pi$
$53$			16.7330i			0.315716i	−0.987462	+	0.157858i	$0.949541\pi$
$54$	15.9272	+	6.00091i	0.294948	+	0.111128i
$55$	22.6403	+	39.2142i	0.411642	+	0.712985i
$56$	−34.0113	+	19.6364i	−0.607344	+	0.350650i
$57$	33.8040	−	14.4314i	0.593053	−	0.253183i
$58$	22.6059			0.389756
$59$		−	6.77988i		−	0.114913i	−0.998348	−	0.0574566i	$-0.981701\pi$
$59$		−	6.77988i		−	0.114913i	0.998348	−	0.0574566i	$-0.0182991\pi$
$60$	24.3285	+	2.93617i	0.405475	+	0.0489362i
$61$	−43.7577	−	75.7905i	−0.717339	−	1.24247i	−0.962050	−	0.272872i	$-0.912027\pi$
$61$	−43.7577	−	75.7905i	−0.717339	−	1.24247i	0.244711	−	0.969596i	$-0.421307\pi$
$62$	1.33254	−	0.769341i	0.0214926	−	0.0124087i
$63$	51.0125	−	53.2636i	0.809723	−	0.845454i
$64$	28.9475			0.452304
$65$	−25.9870	−	13.9093i	−0.399800	−	0.213989i
$66$	30.2094	+	22.6667i	0.457718	+	0.343435i
$67$	−4.07107	+	7.05130i	−0.0607622	+	0.105243i	−0.894806	−	0.446455i	$-0.852686\pi$
$67$	−4.07107	+	7.05130i	−0.0607622	+	0.105243i	0.834044	+	0.551698i	$0.186020\pi$
$68$	−21.1354	−	12.2025i	−0.310815	−	0.179449i
$69$	−16.0127	−	37.5080i	−0.232068	−	0.543594i
$70$	−5.85617	+	10.1432i	−0.0836595	+	0.144903i
$71$	61.6181	+	35.5752i	0.867860	+	0.501059i	0.866636	−	0.498940i	$-0.166277\pi$
$71$	61.6181	+	35.5752i	0.867860	+	0.501059i	0.00122342	+	0.999999i	$0.499611\pi$
$72$	41.4123	−	12.0601i	0.575171	−	0.167502i
$73$	49.6082			0.679565			0.339782	−	0.940504i	$-0.389647\pi$
$73$	49.6082			0.679565			0.339782	+	0.940504i	$0.389647\pi$
$74$	−33.6194	+	19.4101i	−0.454316	+	0.262299i
$75$	−54.7933	+	23.3921i	−0.730577	+	0.311894i
$76$	22.0695	−	38.2254i	0.290388	−	0.502966i
$77$	141.728	−	81.8269i	1.84063	−	1.06269i
$78$	−24.4897	−	2.15943i	−0.313970	−	0.0276850i
$79$	10.9038	−	18.8860i	0.138023	−	0.239063i	−0.788725	−	0.614746i	$-0.789259\pi$
$79$	10.9038	−	18.8860i	0.138023	−	0.239063i	0.926748	+	0.375683i	$0.122592\pi$
$80$	22.3639	−	12.9118i	0.279548	−	0.161397i
$81$	−68.3349	+	43.4895i	−0.843641	+	0.536907i
$82$	−3.03871	+	5.26321i	−0.0370575	+	0.0641855i
$83$	83.1927	+	48.0313i	1.00232	+	0.578691i	0.908934	−	0.416939i	$-0.136897\pi$
$83$	83.1927	+	48.0313i	1.00232	+	0.578691i	0.0933871	+	0.995630i	$0.470231\pi$
$84$	10.6119	−	87.9283i	0.126333	−	1.04677i
$85$	−15.3595			−0.180700
$86$	28.6629	−	16.5485i	0.333289	−	0.192425i
$87$	−64.5673	+	86.0529i	−0.742153	+	0.989114i
$88$	95.7108			1.08762
$89$	13.0504	−	7.53467i	0.146634	−	0.0846592i	−0.424888	−	0.905246i	$-0.639687\pi$
$89$	13.0504	−	7.53467i	0.146634	−	0.0846592i	0.571522	+	0.820587i	$0.306353\pi$
$90$	8.89740	−	9.29002i	0.0988600	−	0.103222i
$91$	−50.2712	+	93.9226i	−0.552430	+	1.03212i
$92$	−42.4139	−	24.4877i	−0.461020	−	0.266170i
$93$	−0.877397	+	7.26993i	−0.00943438	+	0.0781713i
$94$	−25.5006	+	44.1683i	−0.271283	+	0.469875i
$95$		−	27.7791i		−	0.292411i
$96$	47.4424	−	63.2295i	0.494192	−	0.658640i
$97$	59.9243	+	103.792i	0.617776	+	1.07002i	0.989891	+	0.141833i	$0.0452996\pi$
$97$	59.9243	+	103.792i	0.617776	+	1.07002i	−0.372114	+	0.928187i	$0.621367\pi$
$98$	9.90942	+	5.72121i	0.101117	+	0.0583797i
$99$	−172.569	+	50.2558i	−1.74312	+	0.507635i
$100$	−35.7726	+	61.9600i	−0.357726	+	0.619600i
$101$		−	112.914i		−	1.11796i	−0.829182	−	0.558978i	$-0.811193\pi$
$101$		−	112.914i		−	1.11796i	0.829182	−	0.558978i	$-0.188807\pi$
$102$	−11.7822	+	5.02999i	−0.115512	+	0.0493137i
$103$	93.9620	+	162.747i	0.912253	+	1.58007i	0.810875	+	0.585220i	$0.198992\pi$
$103$	93.9620	+	162.747i	0.912253	+	1.58007i	0.101378	+	0.994848i	$0.467675\pi$
$104$	−52.9262	+	32.8700i	−0.508906	+	0.316058i
$105$	−21.8852	−	51.2636i	−0.208430	−	0.488225i
$106$	10.5481			0.0995100
$107$	163.384	−	94.3298i	1.52695	−	0.881587i	0.527466	−	0.849576i	$-0.323142\pi$
$107$	163.384	−	94.3298i	1.52695	−	0.881587i	0.999488	−	0.0320112i	$-0.0101912\pi$
$108$	−34.2954	+	91.0245i	−0.317550	+	0.842819i
$109$	34.1963			0.313728			0.156864	−	0.987620i	$-0.449862\pi$
$109$	34.1963			0.313728			0.156864	+	0.987620i	$0.449862\pi$
$110$	24.7197	−	14.2719i	0.224725	−	0.129745i
$111$	22.1363	−	183.417i	0.199427	−	1.65241i
$112$	−46.6659	−	80.8278i	−0.416660	−	0.721677i
$113$		−	6.07283i		−	0.0537418i	−0.999639	−	0.0268709i	$-0.991446\pi$
$113$		−	6.07283i		−	0.0537418i	0.999639	−	0.0268709i	$-0.00855431\pi$
$114$	−9.09723	−	21.3092i	−0.0798002	−	0.186923i
$115$	−30.8229			−0.268025
$116$			129.193i			1.11374i
$117$	78.1680	−	87.0561i	0.668103	−	0.744069i
$118$	−4.27387			−0.0362193
$119$			55.5124i			0.466490i
$120$	3.90594	−	32.3638i	0.0325495	−	0.269698i
$121$	−277.837			−2.29617
$122$	−47.7766	+	27.5838i	−0.391611	+	0.226097i
$123$	−11.3560	−	26.6002i	−0.0923254	−	0.216262i
$124$	4.39682	+	7.61551i	0.0354582	+	0.0614154i
$125$			101.711i			0.813686i
$126$	−33.5761	−	32.1571i	−0.266477	−	0.255215i
$127$	−27.5578	−	47.7314i	−0.216990	−	0.375838i	0.736896	−	0.676006i	$-0.236291\pi$
$127$	−27.5578	−	47.7314i	−0.216990	−	0.375838i	−0.953886	+	0.300168i	$0.902957\pi$
$128$		−	123.646i		−	0.965988i
$129$	−18.8728	+	156.376i	−0.146301	+	1.21222i
$130$	−8.76809	+	16.3816i	−0.0674469	+	0.126012i
$131$	119.916	−	69.2335i	0.915388	−	0.528500i	0.0332275	−	0.999448i	$-0.489421\pi$
$131$	119.916	−	69.2335i	0.915388	−	0.528500i	0.882161	+	0.470948i	$0.156088\pi$
$132$	−129.541	+	172.648i	−0.981373	+	1.30794i
$133$	−100.399			−0.754883
$134$	4.44497	+	2.56630i	0.0331714	+	0.0191515i
$135$	9.95107	+	60.4038i	0.0737116	+	0.447435i
$136$	−16.2328	+	28.1161i	−0.119359	+	0.206736i
$137$	−123.437	+	71.2664i	−0.901000	+	0.520193i	−0.877525	−	0.479532i	$-0.840807\pi$
$137$	−123.437	+	71.2664i	−0.901000	+	0.520193i	−0.0234756	+	0.999724i	$0.507473\pi$
$138$	−23.6441	+	10.0940i	−0.171334	+	0.0731451i
$139$	148.174			1.06600			0.533001	−	0.846115i	$-0.321064\pi$
$139$	148.174			1.06600			0.533001	+	0.846115i	$0.321064\pi$
$140$	−57.9687	−	33.4682i	−0.414062	−	0.239059i
$141$	−95.2986	−	223.226i	−0.675876	−	1.58317i
$142$	22.4258	−	38.8426i	0.157928	−	0.273539i
$143$	220.549	−	136.973i	1.54230	−	0.957852i
$144$	28.6609	+	98.4163i	0.199034	+	0.683447i
$145$	40.6543	+	70.4153i	0.280374	+	0.485623i
$146$		−	31.2718i		−	0.214191i
$147$	−50.0822	+	21.3808i	−0.340695	+	0.145448i
$148$	−110.930	−	192.136i	−0.749525	−	1.29822i
$149$		−	14.6756i		−	0.0984941i	−0.998787	−	0.0492471i	$-0.984318\pi$
$149$		−	14.6756i		−	0.0984941i	0.998787	−	0.0492471i	$-0.0156822\pi$
$150$	14.7458	+	34.5404i	0.0983053	+	0.230269i
$151$	−8.71204	+	15.0897i	−0.0576956	+	0.0999318i	−0.893431	−	0.449201i	$-0.851709\pi$
$151$	−8.71204	+	15.0897i	−0.0576956	+	0.0999318i	0.835735	+	0.549133i	$0.185042\pi$
$152$	−50.8507	−	29.3587i	−0.334544	−	0.193149i
$153$	14.5051	−	59.2176i	0.0948043	−	0.387043i
$154$	−51.5818	−	89.3422i	−0.334946	−	0.580144i
$155$	4.79286	+	2.76716i	0.0309217	+	0.0178526i
$156$	12.3412	−	139.959i	0.0791104	−	0.897175i
$157$	54.8498	+	95.0026i	0.349362	+	0.605112i	0.986136	−	0.165938i	$-0.0530651\pi$
$157$	54.8498	+	95.0026i	0.349362	+	0.605112i	−0.636775	+	0.771050i	$0.719732\pi$
$158$	−11.9053	−	6.87350i	−0.0753497	−	0.0435032i
$159$	−30.1276	+	40.1529i	−0.189482	+	0.252534i
$160$	−29.8717	−	51.7393i	−0.186698	−	0.323371i
$161$			111.400i			0.691928i
$162$	27.4148	+	43.0767i	0.169227	+	0.265906i
$163$	18.7035	−	32.3955i	0.114746	−	0.198745i	−0.802932	−	0.596070i	$-0.796728\pi$
$163$	18.7035	−	32.3955i	0.114746	−	0.198745i	0.917678	+	0.397325i	$0.130061\pi$
$164$	−30.0794	−	17.3664i	−0.183411	−	0.105893i
$165$	−16.2765	+	134.863i	−0.0986452	+	0.817353i
$166$	30.2778	−	52.4427i	0.182396	−	0.315920i
$167$	−83.2591	−	48.0697i	−0.498557	−	0.287842i	0.229560	−	0.973294i	$-0.426271\pi$
$167$	−83.2591	−	48.0697i	−0.498557	−	0.287842i	−0.728118	+	0.685452i	$0.759605\pi$
$168$	−116.970	−	14.1169i	−0.696248	−	0.0840291i
$169$	−74.9186	+	151.487i	−0.443306	+	0.896371i
$170$			9.68224i			0.0569544i
$171$	107.101	+	26.2338i	0.626320	+	0.153414i
$172$	94.5754	+	163.809i	0.549857	+	0.952380i
$173$	−201.919	+	116.578i	−1.16716	+	0.673860i	−0.953009	−	0.302940i	$-0.902032\pi$
$173$	−201.919	+	116.578i	−1.16716	+	0.673860i	−0.214151	+	0.976801i	$0.568698\pi$
$174$	54.2457	+	40.7017i	0.311757	+	0.233918i
$175$	162.739			0.929935
$176$			227.457i			1.29237i
$177$	12.2071	−	16.2692i	0.0689668	−	0.0919164i
$178$	−4.74967	−	8.22668i	−0.0266836	−	0.0462173i
$179$	−3.13811	+	1.81179i	−0.0175313	+	0.0101217i	−0.508740	−	0.860920i	$-0.669889\pi$
$179$	−3.13811	+	1.81179i	−0.0175313	+	0.0101217i	0.491209	+	0.871042i	$0.336555\pi$
$180$	53.0929	+	50.8490i	0.294960	+	0.282495i
$181$	163.374			0.902617			0.451308	−	0.892368i	$-0.350957\pi$
$181$	163.374			0.902617			0.451308	+	0.892368i	$0.350957\pi$
$182$	59.2066	+	31.6897i	0.325311	+	0.174119i
$183$	31.4580	−	260.655i	0.171902	−	1.42434i
$184$	−32.5755	+	56.4225i	−0.177041	+	0.306644i
$185$	−120.922	−	69.8142i	−0.653631	−	0.377374i
$186$	4.58279	+	0.553090i	0.0246387	+	0.00297360i
$187$	67.6439	−	117.163i	0.361732	−	0.626539i
$188$	−252.423	−	145.737i	−1.34268	−	0.775196i
$189$	218.312	−	35.9653i	1.15509	−	0.190292i
$190$	−17.5113			−0.0921646
$191$	43.0690	−	24.8659i	0.225492	−	0.130188i	−0.382998	−	0.923749i	$-0.625109\pi$
$191$	43.0690	−	24.8659i	0.225492	−	0.130188i	0.608491	+	0.793561i	$0.291775\pi$
$192$	69.4632	+	52.1197i	0.361787	+	0.271457i
$193$	−4.12467	+	7.14413i	−0.0213713	+	0.0370162i	−0.876513	−	0.481378i	$-0.840137\pi$
$193$	−4.12467	+	7.14413i	−0.0213713	+	0.0370162i	0.855142	+	0.518394i	$0.173470\pi$
$194$	65.4280	−	37.7749i	0.337258	−	0.194716i
$195$	−37.3156	−	80.1666i	−0.191362	−	0.411111i
$196$	−32.6969	+	56.6327i	−0.166821	+	0.288943i
$197$	−204.178	+	117.882i	−1.03644	+	0.598387i	−0.918822	−	0.394672i	$-0.870858\pi$
$197$	−204.178	+	117.882i	−1.03644	+	0.598387i	−0.117615	+	0.993059i	$0.537525\pi$
$198$	31.6801	+	108.784i	0.160000	+	0.549412i
$199$	−8.25862	+	14.3044i	−0.0415006	+	0.0718812i	−0.886030	−	0.463629i	$-0.846547\pi$
$199$	−8.25862	+	14.3044i	−0.0415006	+	0.0718812i	0.844529	+	0.535510i	$0.179881\pi$
$200$	82.4244	+	47.5878i	0.412122	+	0.237939i
$201$	−22.4649	+	9.59058i	−0.111766	+	0.0477143i
$202$	−71.1781			−0.352367
$203$	254.496	−	146.933i	1.25367	−	0.723809i
$204$	−28.7466	−	67.3358i	−0.140915	−	0.330077i
$205$	−21.8592			−0.106630
$206$	102.592	−	59.2314i	0.498019	−	0.287531i
$207$	29.1083	−	118.836i	0.140620	−	0.574087i
$208$	−78.1157	−	125.779i	−0.375556	−	0.604708i
$209$	211.900	+	122.341i	1.01388	+	0.585361i
$210$	−32.3154	+	13.7959i	−0.153883	+	0.0656947i
$211$	155.654	−	269.601i	0.737698	−	1.27773i	−0.215831	−	0.976431i	$-0.569246\pi$
$211$	155.654	−	269.601i	0.737698	−	1.27773i	0.953529	−	0.301300i	$-0.0974207\pi$
$212$			60.2826i			0.284352i
$213$	83.8077	+	196.310i	0.393463	+	0.921644i
$214$	−59.4633	−	102.993i	−0.277866	−	0.481278i
$215$	103.094	+	59.5215i	0.479508	+	0.276844i
$216$	121.088	+	45.6226i	0.560594	+	0.211216i
$217$	10.0011	−	17.3224i	0.0460880	−	0.0798268i
$218$		−	21.5566i		−	0.0988833i
$219$	119.041	+	89.3192i	0.543568	+	0.407850i
$220$	81.5646	+	141.274i	0.370748	+	0.642155i
$221$	2.83150	+	88.0197i	0.0128122	+	0.398279i
$222$	−115.622	−	13.9542i	−0.520819	−	0.0628569i
$223$	168.523			0.755710			0.377855	−	0.925865i	$-0.376662\pi$
$223$	168.523			0.755710			0.377855	+	0.925865i	$0.376662\pi$
$224$	−186.997	+	107.963i	−0.834808	+	0.481976i
$225$	−173.601	−	42.5226i	−0.771559	−	0.188989i
$226$	−3.82817			−0.0169388
$227$	149.522	−	86.3268i	0.658689	−	0.380294i	−0.133088	−	0.991104i	$-0.542489\pi$
$227$	149.522	−	86.3268i	0.658689	−	0.380294i	0.791777	+	0.610810i	$0.209156\pi$
$228$	121.783	−	51.9910i	0.534137	−	0.228031i
$229$	56.2790	+	97.4781i	0.245760	+	0.425668i	0.962345	−	0.271831i	$-0.0876292\pi$
$229$	56.2790	+	97.4781i	0.245760	+	0.425668i	−0.716585	+	0.697500i	$0.754296\pi$
$230$			19.4300i			0.0844783i
$231$	487.425	+	58.8265i	2.11006	+	0.254660i
$232$	171.864			0.740793
$233$		−	372.616i		−	1.59921i	−0.600527	−	0.799604i	$-0.705043\pi$
$233$		−	372.616i		−	1.59921i	0.600527	−	0.799604i	$-0.294957\pi$
$234$	−54.8781	−	49.2753i	−0.234522	−	0.210578i
$235$	−183.440			−0.780597
$236$		−	24.4254i		−	0.103497i
$237$	60.1691	−	25.6871i	0.253878	−	0.108384i
$238$	34.9937			0.147032
$239$	−227.429	+	131.306i	−0.951584	+	0.549398i	−0.893573	−	0.448918i	$-0.851809\pi$
$239$	−227.429	+	131.306i	−0.951584	+	0.549398i	−0.0580116	+	0.998316i	$0.518476\pi$
$240$	76.9126	+	9.28247i	0.320469	+	0.0386770i
$241$	−183.277	−	317.446i	−0.760487	−	1.31720i	−0.942600	−	0.333924i	$-0.891627\pi$
$241$	−183.277	−	317.446i	−0.760487	−	1.31720i	0.182114	−	0.983278i	$-0.441706\pi$
$242$			175.142i			0.723726i
$243$	−242.281	−	18.6778i	−0.997042	−	0.0768633i
$244$	−157.643	−	273.045i	−0.646076	−	1.11904i
$245$			41.1560i			0.167984i
$246$	−16.7682	+	7.15857i	−0.0681632	+	0.0290999i
$247$	−159.192	+	5.12104i	−0.644502	+	0.0207330i
$248$	10.1308	−	5.84901i	0.0408500	−	0.0235847i
$249$	113.152	+	265.045i	0.454424	+	1.06444i
$250$	64.1160			0.256464
$251$	−12.4484	−	7.18709i	−0.0495953	−	0.0286338i	0.474997	−	0.879987i	$-0.342449\pi$
$251$	−12.4484	−	7.18709i	−0.0495953	−	0.0286338i	−0.524593	+	0.851353i	$0.675782\pi$
$252$	183.779	−	191.889i	0.729282	−	0.761464i
$253$	135.746	−	235.118i	0.536544	−	0.929321i
$254$	−30.0888	+	17.3718i	−0.118460	+	0.0683928i
$255$	−36.8570	−	27.6546i	−0.144537	−	0.108449i
$256$	37.8460			0.147836
$257$	−172.226	−	99.4347i	−0.670140	−	0.386906i	0.125990	−	0.992032i	$-0.459789\pi$
$257$	−172.226	−	99.4347i	−0.670140	−	0.386906i	−0.796130	+	0.605126i	$0.793123\pi$
$258$	98.5757	+	11.8970i	0.382076	+	0.0461122i
$259$	−252.323	+	437.037i	−0.974221	+	1.68740i
$260$	−93.6215	−	50.1100i	−0.360083	−	0.192731i
$261$	−309.875	+	90.2423i	−1.18726	+	0.345756i
$262$	−43.6431	−	75.5921i	−0.166577	−	0.288520i
$263$			478.356i			1.81884i	0.415874	+	0.909422i	$0.363476\pi$
$263$			478.356i			1.81884i	−0.415874	+	0.909422i	$0.636524\pi$
$264$	229.671	+	172.327i	0.869965	+	0.652752i
$265$	18.9696	+	32.8563i	0.0715834	+	0.123986i
$266$			63.2894i			0.237930i
$267$	44.8823	+	5.41678i	0.168099	+	0.0202876i
$268$	−14.6665	+	25.4032i	−0.0547259	+	0.0947880i
$269$	−236.137	−	136.334i	−0.877835	−	0.506818i	−0.00789072	−	0.999969i	$-0.502512\pi$
$269$	−236.137	−	136.334i	−0.877835	−	0.506818i	−0.869944	+	0.493151i	$0.835845\pi$
$270$	38.0771	−	6.27292i	0.141026	−	0.0232330i
$271$	142.178	+	246.260i	0.524643	+	0.908708i	0.999588	+	0.0286930i	$0.00913453\pi$
$271$	142.178	+	246.260i	0.524643	+	0.908708i	−0.474945	+	0.880015i	$0.657532\pi$
$272$	−66.8180	−	38.5774i	−0.245654	−	0.141829i
$273$	−289.739	+	134.867i	−1.06132	+	0.494017i
$274$	44.9246	+	77.8118i	0.163959	+	0.283985i
$275$	−343.471	−	198.303i	−1.24899	−	0.721102i
$276$	−57.6878	−	135.127i	−0.209014	−	0.489591i
$277$	−16.2272	−	28.1064i	−0.0585821	−	0.101467i	0.835247	−	0.549875i	$-0.185325\pi$
$277$	−16.2272	−	28.1064i	−0.0585821	−	0.101467i	−0.893829	+	0.448408i	$0.851991\pi$
$278$		−	93.4056i		−	0.335991i
$279$	−15.1949	+	15.8654i	−0.0544620	+	0.0568652i
$280$	−44.5222	+	77.1148i	−0.159008	+	0.275410i
$281$	−270.886	−	156.396i	−0.964008	−	0.556570i	−0.0666036	−	0.997780i	$-0.521216\pi$
$281$	−270.886	−	156.396i	−0.964008	−	0.556570i	−0.897404	+	0.441209i	$0.854550\pi$
$282$	−140.717	+	60.0740i	−0.498995	+	0.213028i
$283$	101.016	−	174.964i	0.356946	−	0.618249i	−0.630503	−	0.776187i	$-0.717151\pi$
$283$	101.016	−	174.964i	0.356946	−	0.618249i	0.987449	+	0.157938i	$0.0504846\pi$
$284$	221.987	+	128.164i	0.781644	+	0.451282i
$285$	50.0160	−	66.6595i	0.175495	−	0.233893i
$286$	−86.3444	−	139.029i	−0.301904	−	0.486115i
$287$			79.0039i			0.275275i
$288$	227.688	−	66.3077i	0.790585	−	0.230235i
$289$	−121.555	−	210.539i	−0.420605	−	0.728509i
$290$	44.3881	−	25.6275i	0.153063	−	0.0883707i
$291$	−43.0804	+	356.956i	−0.148043	+	1.22665i
$292$	178.720			0.612054
$293$			186.485i			0.636466i	0.948012	+	0.318233i	$0.103090\pi$
$293$			186.485i			0.636466i	−0.948012	+	0.318233i	$0.896910\pi$
$294$	13.4780	+	31.5706i	0.0458434	+	0.107383i
$295$	−7.68612	−	13.3127i	−0.0260546	−	0.0451279i
$296$	−255.595	+	147.568i	−0.863498	+	0.498541i
$297$	−504.588	−	190.114i	−1.69895	−	0.640115i
$298$	−9.25117			−0.0310442
$299$	5.68217	+	176.635i	0.0190039	+	0.590753i
$300$	−197.400	+	84.2728i	−0.657999	+	0.280909i
$301$	215.123	−	372.605i	0.714696	−	1.23789i
$302$	9.51219	+	5.49186i	0.0314973	+	0.0181850i
$303$	203.300	−	270.951i	0.670958	−	0.894228i
$304$	69.7709	−	120.847i	0.229509	−	0.397522i
$305$	−171.842	−	99.2132i	−0.563417	−	0.325289i
$306$	−37.3294	−	9.14364i	−0.121991	−	0.0298812i
$307$	−338.325			−1.10204			−0.551018	−	0.834493i	$-0.685761\pi$
$307$	−338.325			−1.10204			−0.551018	+	0.834493i	$0.685761\pi$
$308$	510.594	−	294.792i	1.65777	−	0.957116i
$309$	−67.5506	+	559.711i	−0.218610	+	1.81136i
$310$	1.74435	−	3.02131i	0.00562694	−	0.00974615i
$311$	86.5958	−	49.9961i	0.278443	−	0.160759i	−0.354275	−	0.935141i	$-0.615272\pi$
$311$	86.5958	−	49.9961i	0.278443	−	0.160759i	0.632718	+	0.774382i	$0.281939\pi$
$312$	−186.186	−	16.4173i	−0.596749	−	0.0526196i
$313$	32.9877	−	57.1364i	0.105392	−	0.182544i	−0.808506	−	0.588488i	$-0.799724\pi$
$313$	32.9877	−	57.1364i	0.105392	−	0.182544i	0.913898	+	0.405943i	$0.133057\pi$
$314$	59.8874	−	34.5760i	0.190724	−	0.110115i
$315$	39.7834	−	162.418i	0.126296	−	0.515612i
$316$	39.2823	−	68.0390i	0.124311	−	0.215313i
$317$	−225.292	−	130.073i	−0.710702	−	0.410324i	0.100619	−	0.994925i	$-0.467918\pi$
$317$	−225.292	−	130.073i	−0.710702	−	0.410324i	−0.811321	+	0.584601i	$0.801251\pi$
$318$	25.3115	+	18.9917i	0.0795958	+	0.0597224i
$319$	−716.175			−2.24506
$320$	56.8403	−	32.8167i	0.177626	−	0.102552i
$321$	561.902	+	67.8151i	1.75047	+	0.211262i
$322$	70.2242			0.218087
$323$	−71.8777	+	41.4986i	−0.222532	+	0.128479i
$324$	−246.185	+	156.676i	−0.759831	+	0.483569i
$325$	258.036	−	8.30076i	0.793958	−	0.0255408i
$326$	−20.4214	−	11.7903i	−0.0626422	−	0.0361665i
$327$	82.0586	+	61.5703i	0.250944	+	0.188288i
$328$	−23.1022	+	40.0142i	−0.0704336	+	0.121995i
$329$			662.992i			2.01517i
$330$	85.0146	+	10.2603i	0.257620	+	0.0310918i
$331$	176.573	+	305.833i	0.533453	+	0.923967i	0.999237	+	0.0390685i	$0.0124391\pi$
$331$	176.573	+	305.833i	0.533453	+	0.923967i	−0.465784	+	0.884898i	$0.654228\pi$
$332$	299.712	+	173.039i	0.902747	+	0.521201i
$333$	383.360	−	400.277i	1.15123	−	1.20203i
$334$	−30.3020	+	52.4846i	−0.0907245	+	0.157139i
$335$			18.4609i			0.0551072i
$336$	33.5488	−	277.978i	0.0998476	−	0.827317i
$337$	−37.6251	−	65.1685i	−0.111647	−	0.193378i	0.804787	−	0.593563i	$-0.202279\pi$
$337$	−37.6251	−	65.1685i	−0.111647	−	0.193378i	−0.916434	+	0.400185i	$0.868946\pi$
$338$	95.4936	+	47.2269i	0.282525	+	0.139725i
$339$	10.9341	−	14.5725i	0.0322539	−	0.0429868i
$340$	−55.3344			−0.162748
$341$	−42.2160	+	24.3734i	−0.123801	+	0.0714764i
$342$	16.5372	−	67.5138i	0.0483542	−	0.197409i
$343$	−252.790			−0.736996
$344$	217.913	−	125.812i	0.633468	−	0.365733i
$345$	−73.9635	−	55.4964i	−0.214387	−	0.160859i
$346$	73.4879	+	127.285i	0.212393	+	0.367875i
$347$			77.9409i			0.224614i	0.993674	+	0.112307i	$0.0358239\pi$
$347$			77.9409i			0.224614i	−0.993674	+	0.112307i	$0.964176\pi$
$348$	−232.612	+	310.017i	−0.668425	+	0.890852i
$349$	−395.200			−1.13238			−0.566188	−	0.824276i	$-0.691583\pi$
$349$	−395.200			−1.13238			−0.566188	+	0.824276i	$0.691583\pi$
$350$		−	102.587i		−	0.293104i
$351$	344.318	−	68.1614i	0.980964	−	0.194192i
$352$	526.227			1.49496
$353$		−	194.953i		−	0.552274i	−0.961118	−	0.276137i	$-0.910946\pi$
$353$		−	194.953i		−	0.552274i	0.961118	−	0.276137i	$-0.0890544\pi$
$354$	−10.2557	−	7.69508i	−0.0289710	−	0.0217375i
$355$	161.322			0.454427
$356$	47.0158	−	27.1446i	0.132067	−	0.0762488i
$357$	−99.9496	+	133.209i	−0.279971	+	0.373135i
$358$	1.14211	+	1.97819i	0.00319025	+	0.00552567i
$359$		−	31.0244i		−	0.0864189i	−0.999066	−	0.0432094i	$-0.986242\pi$
$359$		−	31.0244i		−	0.0864189i	0.999066	−	0.0432094i	$-0.0137583\pi$
$360$	67.6436	−	70.6286i	0.187899	−	0.196190i
$361$	105.446	+	182.637i	0.292093	+	0.505921i
$362$		−	102.987i		−	0.284494i
$363$	−666.706	−	500.243i	−1.83666	−	1.37808i
$364$	−181.108	+	338.368i	−0.497550	+	0.929582i
$365$	97.4090	−	56.2391i	0.266874	−	0.154080i
$366$	−164.311	−	19.8304i	−0.448936	−	0.0541814i
$367$	448.084			1.22094			0.610468	−	0.792041i	$-0.290981\pi$
$367$	448.084			1.22094			0.610468	+	0.792041i	$0.290981\pi$
$368$	−134.088	−	77.4158i	−0.364370	−	0.210369i
$369$	20.6433	−	84.2772i	0.0559438	−	0.228393i
$370$	−44.0092	+	76.2262i	−0.118944	+	0.206017i
$371$	118.750	−	68.5601i	0.320080	−	0.184798i
$372$	−3.16093	+	26.1908i	−0.00849713	+	0.0704055i
$373$	−349.753			−0.937674			−0.468837	−	0.883285i	$-0.655327\pi$
$373$	−349.753			−0.937674			−0.468837	+	0.883285i	$0.655327\pi$
$374$	−73.8566	−	42.6411i	−0.197478	−	0.114014i
$375$	−183.129	+	244.068i	−0.488345	+	0.650848i
$376$	−193.871	+	335.795i	−0.515615	+	0.893071i
$377$	396.031	−	245.956i	1.05048	−	0.652404i
$378$	−22.6716	−	137.619i	−0.0599779	−	0.364071i
$379$	−19.0545	−	33.0034i	−0.0502758	−	0.0870802i	0.839792	−	0.542908i	$-0.182677\pi$
$379$	−19.0545	−	33.0034i	−0.0502758	−	0.0870802i	−0.890068	+	0.455828i	$0.849343\pi$
$380$		−	100.078i		−	0.263362i
$381$	19.8117	−	164.155i	0.0519991	−	0.430854i
$382$	−15.6749	−	27.1497i	−0.0410337	−	0.0710725i
$383$		−	97.7578i		−	0.255242i	−0.991823	−	0.127621i	$-0.959266\pi$
$383$		−	97.7578i		−	0.255242i	0.991823	−	0.127621i	$-0.0407342\pi$
$384$	222.625	−	296.706i	0.579752	−	0.772672i
$385$	185.529	−	321.345i	0.481893	−	0.834663i
$386$	4.50349	+	2.60009i	0.0116671	+	0.00673599i
$387$	−326.842	+	341.264i	−0.844552	+	0.881820i
$388$	215.885	+	373.924i	0.556404	+	0.963720i
$389$	236.515	+	136.552i	0.608008	+	0.351033i	0.772185	−	0.635397i	$-0.219164\pi$
$389$	236.515	+	136.552i	0.608008	+	0.351033i	−0.164178	+	0.986431i	$0.552497\pi$
$390$	−50.5351	+	23.5229i	−0.129577	+	0.0603151i
$391$	46.0457	+	79.7535i	0.117764	+	0.203973i
$392$	75.3376	+	43.4962i	0.192188	+	0.110960i
$393$	412.408	+	49.7729i	1.04938	+	0.126649i
$394$	74.3102	+	128.709i	0.188605	+	0.326673i
$395$		−	49.4451i		−	0.125177i
$396$	−621.702	+	181.053i	−1.56996	+	0.457204i
$397$	−243.539	+	421.823i	−0.613449	+	1.06253i	0.377205	+	0.926130i	$0.376885\pi$
$397$	−243.539	+	421.823i	−0.613449	+	1.06253i	−0.990654	+	0.136396i	$0.956448\pi$
$398$	9.01712	+	5.20604i	0.0226561	+	0.0130805i
$399$	−240.922	−	180.768i	−0.603813	−	0.453054i
$400$	−113.092	+	195.882i	−0.282731	+	0.489704i
$401$	419.770	+	242.354i	1.04681	+	0.604375i	0.921754	−	0.387775i	$-0.126756\pi$
$401$	419.770	+	242.354i	1.04681	+	0.604375i	0.125054	+	0.992150i	$0.460090\pi$
$402$	6.04567	+	14.1613i	0.0150390	+	0.0352272i
$403$	14.9741	−	27.9763i	0.0371565	−	0.0694202i
$404$		−	406.786i		−	1.00690i
$405$	−84.8776	+	162.864i	−0.209574	+	0.402132i
$406$	−92.6232	−	160.428i	−0.228136	−	0.395143i
$407$	1065.09	−	614.931i	2.61693	−	1.51089i
$408$	−89.5757	+	38.2412i	−0.219548	+	0.0937283i
$409$	167.330			0.409120			0.204560	−	0.978854i	$-0.434424\pi$
$409$	167.330			0.409120			0.204560	+	0.978854i	$0.434424\pi$
$410$			13.7795i			0.0336087i
$411$	−424.518	−	51.2344i	−1.03289	−	0.124658i
$412$	338.510	+	586.316i	0.821626	+	1.42310i
$413$	−48.1151	+	27.7792i	−0.116501	+	0.0672621i
$414$	−74.9114	−	18.3492i	−0.180945	−	0.0443217i
$415$	217.806			0.524833
$416$	−290.993	+	180.722i	−0.699503	+	0.434429i
$417$	355.564	+	266.787i	0.852670	+	0.639776i
$418$	77.1206	−	133.577i	0.184499	−	0.319562i
$419$	−449.540	−	259.542i	−1.07289	−	0.619431i	−0.143918	−	0.989590i	$-0.545970\pi$
$419$	−449.540	−	259.542i	−1.07289	−	0.619431i	−0.928969	+	0.370158i	$0.879303\pi$
$420$	−78.8441	−	184.684i	−0.187724	−	0.439723i
$421$	298.881	−	517.677i	0.709931	−	1.22964i	−0.254951	−	0.966954i	$-0.582060\pi$
$421$	298.881	−	517.677i	0.709931	−	1.22964i	0.964882	−	0.262682i	$-0.0846072\pi$
$422$	−169.950	−	98.1208i	−0.402726	−	0.232514i
$423$	173.236	−	707.245i	0.409541	−	1.67197i
$424$	80.1930			0.189134
$425$	116.507	−	67.2656i	0.274135	−	0.158272i
$426$	123.749	−	52.8304i	0.290491	−	0.124015i
$427$	−358.577	+	621.074i	−0.839760	+	1.45451i
$428$	588.612	−	339.835i	1.37526	−	0.794007i
$429$	775.855	+	68.4127i	1.80852	+	0.159470i
$430$	37.5210	−	64.9882i	0.0872580	−	0.151135i
$431$	15.9982	−	9.23657i	0.0371188	−	0.0214306i	−0.481326	−	0.876542i	$-0.659845\pi$
$431$	15.9982	−	9.23657i	0.0371188	−	0.0214306i	0.518445	+	0.855111i	$0.326511\pi$
$432$	−108.422	+	287.767i	−0.250977	+	0.666126i
$433$	89.1122	−	154.347i	0.205802	−	0.356459i	−0.744586	−	0.667526i	$-0.767353\pi$
$433$	89.1122	−	154.347i	0.205802	−	0.356459i	0.950388	+	0.311067i	$0.100686\pi$
$434$	−10.9196	−	6.30446i	−0.0251605	−	0.0145264i
$435$	−29.2269	+	242.168i	−0.0671884	+	0.556709i
$436$	123.197			0.282561
$437$	−144.242	+	83.2781i	−0.330073	+	0.190568i
$438$	56.3047	−	75.0409i	0.128550	−	0.171326i
$439$	192.714			0.438984			0.219492	−	0.975614i	$-0.429560\pi$
$439$	192.714			0.438984			0.219492	+	0.975614i	$0.429560\pi$
$440$	187.935	−	108.504i	0.427124	−	0.246600i
$441$	−158.675	−	38.8666i	−0.359807	−	0.0881328i
$442$	55.4855	−	1.78491i	0.125533	−	0.00403826i
$443$	−275.781	−	159.222i	−0.622531	−	0.359419i	0.155323	−	0.987864i	$-0.450358\pi$
$443$	−275.781	−	159.222i	−0.622531	−	0.359419i	−0.777854	+	0.628445i	$0.783692\pi$
$444$	79.7490	−	660.783i	0.179615	−	1.48825i
$445$	17.0836	−	29.5896i	0.0383901	−	0.0664936i
$446$		−	106.233i		−	0.238191i
$447$	26.4234	−	35.2161i	0.0591127	−	0.0787832i
$448$	−118.607	−	205.433i	−0.264747	−	0.458555i
$449$	592.947	+	342.338i	1.32059	+	0.762446i	0.983823	−	0.179141i	$-0.0573317\pi$
$449$	592.947	+	342.338i	1.32059	+	0.762446i	0.336771	+	0.941586i	$0.390665\pi$
$450$	−26.8053	+	109.434i	−0.0595672	+	0.243186i
$451$	96.2693	−	166.743i	0.213457	−	0.369719i
$452$		−	21.8781i		−	0.0484029i
$453$	−48.0746	+	20.5237i	−0.106125	+	0.0453062i
$454$	−54.4184	−	94.2554i	−0.119864	−	0.207611i
$455$	7.76604	+	241.414i	0.0170682	+	0.530580i
$456$	−69.1628	−	162.006i	−0.151673	−	0.355277i
$457$	248.829			0.544485			0.272242	−	0.962229i	$-0.412235\pi$
$457$	248.829			0.544485			0.272242	+	0.962229i	$0.412235\pi$
$458$	61.4479	−	35.4769i	0.134166	−	0.0774606i
$459$	141.428	−	115.984i	0.308121	−	0.252689i
$460$	−111.043			−0.241399
$461$	−506.226	+	292.269i	−1.09810	+	0.633990i	−0.935722	−	0.352738i	$-0.885251\pi$
$461$	−506.226	+	292.269i	−1.09810	+	0.633990i	−0.162381	+	0.986728i	$0.551917\pi$
$462$	37.0829	−	307.261i	0.0802659	−	0.665067i
$463$	30.9599	+	53.6242i	0.0668681	+	0.115819i	0.897521	−	0.440971i	$-0.145366\pi$
$463$	30.9599	+	53.6242i	0.0668681	+	0.115819i	−0.830653	+	0.556790i	$0.812033\pi$
$464$			408.435i			0.880247i
$465$	6.51885	+	15.2697i	0.0140190	+	0.0328380i
$466$	−234.888			−0.504052
$467$		−	214.626i		−	0.459585i	−0.973240	−	0.229793i	$-0.926195\pi$
$467$		−	214.626i		−	0.459585i	0.973240	−	0.229793i	$-0.0738048\pi$
$468$	281.610	−	313.630i	0.601731	−	0.670151i
$469$	66.7217			0.142264
$470$			115.636i			0.246035i
$471$	−39.4323	+	326.728i	−0.0837204	+	0.693690i
$472$	−32.4927			−0.0688404
$473$	−908.066	+	524.272i	−1.91980	+	1.10840i
$474$	−16.1925	−	37.9292i	−0.0341614	−	0.0800194i
$475$	121.656	+	210.715i	0.256119	+	0.443610i
$476$			199.990i			0.420148i
$477$	−144.590	+	42.1077i	−0.303124	+	0.0882761i
$478$	82.7722	+	143.366i	0.173164	+	0.299928i
$479$			571.983i			1.19412i	0.802197	+	0.597059i	$0.203664\pi$
$479$			571.983i			1.19412i	−0.802197	+	0.597059i	$0.796336\pi$
$480$	21.4752	−	177.939i	0.0447400	−	0.370707i
$481$	−377.789	+	705.830i	−0.785424	+	1.46742i
$482$	−200.110	+	115.534i	−0.415166	+	0.239696i
$483$	−200.576	+	267.320i	−0.415270	+	0.553457i
$484$	−1000.94			−2.06806
$485$	235.331	+	135.868i	0.485218	+	0.280141i
$486$	−11.7740	+	152.728i	−0.0242264	+	0.314256i
$487$	−365.627	+	633.284i	−0.750773	+	1.30038i	0.196675	+	0.980469i	$0.436986\pi$
$487$	−365.627	+	633.284i	−0.750773	+	1.30038i	−0.947448	+	0.319909i	$0.896348\pi$
$488$	−363.227	+	209.709i	−0.744318	+	0.429732i
$489$	103.209	−	44.0616i	0.211062	−	0.0901056i
$490$	25.9437			0.0529464
$491$	−745.280	−	430.288i	−1.51788	−	0.876350i	−0.999779	−	0.0210324i	$-0.993305\pi$
$491$	−745.280	−	430.288i	−1.51788	−	0.876350i	−0.518104	−	0.855318i	$-0.673362\pi$
$492$	−40.9115	−	95.8307i	−0.0831535	−	0.194778i
$493$	121.465	−	210.384i	0.246380	−	0.426743i
$494$	3.22818	+	100.351i	0.00653479	+	0.203139i
$495$	−281.878	+	294.317i	−0.569450	+	0.594579i
$496$	13.9002	+	24.0758i	0.0280246	+	0.0485400i
$497$		−	583.050i		−	1.17314i
$498$	167.078	−	71.3281i	0.335498	−	0.143229i
$499$	−79.5360	−	137.760i	−0.159391	−	0.276073i	0.775258	−	0.631644i	$-0.217620\pi$
$499$	−79.5360	−	137.760i	−0.159391	−	0.276073i	−0.934649	+	0.355571i	$0.884286\pi$
$500$			366.426i			0.732851i
$501$	−113.242	−	265.257i	−0.226032	−	0.529455i
$502$	−4.53057	+	7.84718i	−0.00902505	+	0.0156318i
$503$	−166.991	−	96.4125i	−0.331991	−	0.191675i	0.324734	−	0.945805i	$-0.394725\pi$
$503$	−166.991	−	96.4125i	−0.331991	−	0.191675i	−0.656725	+	0.754131i	$0.728059\pi$
$504$	−255.267	−	244.478i	−0.506481	−	0.485076i
$505$	−128.006	−	221.714i	−0.253478	−	0.439037i
$506$	−148.213	−	85.5708i	−0.292911	−	0.169112i
$507$	−452.528	+	228.621i	−0.892559	+	0.450930i
$508$	−99.2803	−	171.959i	−0.195434	−	0.338501i
$509$	−203.445	−	117.459i	−0.399696	−	0.230764i	0.286657	−	0.958033i	$-0.407456\pi$
$509$	−203.445	−	117.459i	−0.399696	−	0.230764i	−0.686353	+	0.727269i	$0.740789\pi$
$510$	−17.4328	+	23.2338i	−0.0341820	+	0.0455565i
$511$	−203.260	−	352.057i	−0.397769	−	0.688957i
$512$		−	518.443i		−	1.01258i
$513$	209.769	+	255.786i	0.408906	+	0.498607i
$514$	−62.6813	+	108.567i	−0.121948	+	0.211220i
$515$	369.001	+	213.043i	0.716508	+	0.413676i
$516$	−67.9916	+	563.364i	−0.131767	+	1.09179i
$517$	807.881	−	1399.29i	1.56263	−	2.70656i
$518$	275.498	+	159.059i	0.531849	+	0.307063i
$519$	−694.428	−	83.8094i	−1.33801	−	0.161483i
$520$	−66.6605	+	124.543i	−0.128193	+	0.239506i
$521$		−	314.451i		−	0.603552i	−0.953379	−	0.301776i	$-0.902420\pi$
$521$		−	314.451i		−	0.603552i	0.953379	−	0.301776i	$-0.0975795\pi$
$522$	56.8866	+	195.338i	0.108978	+	0.374211i
$523$	−28.9142	−	50.0808i	−0.0552852	−	0.0957568i	0.837058	−	0.547114i	$-0.184273\pi$
$523$	−28.9142	−	50.0808i	−0.0552852	−	0.0957568i	−0.892344	+	0.451357i	$0.850940\pi$
$524$	432.012	−	249.422i	0.824451	−	0.475997i
$525$	390.512	+	293.010i	0.743833	+	0.558113i
$526$	301.544			0.573278
$527$		−	16.5352i		−	0.0313762i
$528$	−409.534	+	545.812i	−0.775633	+	1.03374i
$529$	−172.097	−	298.081i	−0.325325	−	0.563479i
$530$	20.7118	−	11.9580i	0.0390789	−	0.0225622i
$531$	58.5852	−	17.0612i	0.110330	−	0.0321304i
$532$	−361.702			−0.679890
$533$	4.02973	+	125.268i	0.00756047	+	0.235024i
$534$	3.41461	−	28.2927i	0.00639440	−	0.0529827i
$535$	213.877	−	370.446i	0.399770	−	0.692422i
$536$	33.7934	+	19.5107i	0.0630475	+	0.0364005i
$537$	−10.7924	−	1.30252i	−0.0200976	−	0.00242555i
$538$	−85.9417	+	148.855i	−0.159743	+	0.276683i
$539$	−313.940	−	181.253i	−0.582448	−	0.336277i
$540$	35.8500	+	217.612i	0.0663888	+	0.402985i
$541$	23.5926			0.0436092			0.0218046	−	0.999762i	$-0.493059\pi$
$541$	23.5926			0.0436092			0.0218046	+	0.999762i	$0.493059\pi$
$542$	155.236	−	89.6258i	0.286414	−	0.165361i
$543$	392.036	+	294.153i	0.721982	+	0.541718i
$544$	−89.2496	+	154.585i	−0.164062	+	0.284163i
$545$	67.1468	−	38.7672i	0.123205	−	0.0711325i
$546$	85.0167	+	182.645i	0.155708	+	0.334514i
$547$	−442.013	+	765.588i	−0.808067	+	1.39961i	0.106134	+	0.994352i	$0.466153\pi$
$547$	−442.013	+	765.588i	−0.808067	+	1.39961i	−0.914201	+	0.405261i	$0.867181\pi$
$548$	−444.697	+	256.746i	−0.811492	+	0.468515i
$549$	544.794	−	568.835i	0.992340	−	1.03613i
$550$	−125.006	+	216.516i	−0.227283	+	0.393665i
$551$	380.500	+	219.682i	0.690563	+	0.398696i
$552$	−179.758	+	76.7411i	−0.325648	+	0.139024i
$553$	−178.705			−0.323156
$554$	−17.7176	+	10.2293i	−0.0319812	+	0.0184644i
$555$	−164.468	−	385.247i	−0.296338	−	0.694139i
$556$	533.817			0.960102
$557$	−300.210	+	173.327i	−0.538977	+	0.311179i	−0.744664	−	0.667439i	$-0.767390\pi$
$557$	−300.210	+	173.327i	−0.538977	+	0.311179i	0.205687	+	0.978618i	$0.434057\pi$
$558$	10.0012	+	9.57850i	0.0179233	+	0.0171658i
$559$	322.092	−	601.770i	0.576192	−	1.07651i
$560$	−183.263	−	105.807i	−0.327256	−	0.188941i
$561$	373.271	−	159.355i	0.665367	−	0.284055i
$562$	−98.5885	+	170.760i	−0.175424	+	0.303844i
$563$		−	18.1202i		−	0.0321850i	−0.999871	−	0.0160925i	$-0.994877\pi$
$563$		−	18.1202i		−	0.0321850i	0.999871	−	0.0160925i	$-0.00512262\pi$
$564$	−343.325	−	804.201i	−0.608732	−	1.42589i
$565$	−6.88456	−	11.9244i	−0.0121851	−	0.0211051i
$566$	−110.293	−	63.6780i	−0.194865	−	0.112505i
$567$	588.623	+	306.766i	1.03814	+	0.541033i
$568$	170.495	−	295.305i	0.300167	−	0.519904i
$569$			851.409i			1.49633i	0.663516	+	0.748163i	$0.269064\pi$
$569$			851.409i			1.49633i	−0.663516	+	0.748163i	$0.730936\pi$
$570$	−42.0206	−	31.5289i	−0.0737203	−	0.0553139i
$571$	242.204	+	419.510i	0.424176	+	0.734694i	0.996343	−	0.0854429i	$-0.0272305\pi$
$571$	242.204	+	419.510i	0.424176	+	0.734694i	−0.572167	+	0.820137i	$0.693897\pi$
$572$	794.556	−	493.462i	1.38908	−	0.862696i
$573$	148.121	+	17.8765i	0.258500	+	0.0311980i
$574$	49.8022			0.0867634
$575$	233.803	−	134.986i	0.406615	−	0.234759i
$576$	72.8449	+	250.136i	0.126467	+	0.434264i
$577$	−245.489			−0.425458			−0.212729	−	0.977111i	$-0.568235\pi$
$577$	−245.489			−0.425458			−0.212729	+	0.977111i	$0.568235\pi$
$578$	−132.719	+	76.6252i	−0.229617	+	0.132570i
$579$	−22.7606	+	9.71684i	−0.0393102	+	0.0167821i
$580$	146.462	+	253.680i	0.252521	+	0.437379i
$581$		−	787.196i		−	1.35490i
$582$	225.016	+	27.1569i	0.386626	+	0.0466613i
$583$	−334.172			−0.573195
$584$		−	237.748i		−	0.407103i
$585$	54.7957	−	259.557i	0.0936678	−	0.443687i
$586$	117.556			0.200607
$587$		−	727.399i		−	1.23918i	−0.784925	−	0.619590i	$-0.787299\pi$
$587$		−	727.399i		−	1.23918i	0.784925	−	0.619590i	$-0.212701\pi$
$588$	−180.427	+	77.0271i	−0.306849	+	0.130998i
$589$	29.9056			0.0507734
$590$	−8.39204	+	4.84515i	−0.0142238	+	0.00821211i
$591$	−702.198	−	84.7472i	−1.18815	−	0.143396i
$592$	−350.696	−	607.423i	−0.592391	−	1.02605i
$593$			839.449i			1.41560i	0.706414	+	0.707799i	$0.250312\pi$
$593$			839.449i			1.41560i	−0.706414	+	0.707799i	$0.749688\pi$
$594$	−119.843	+	318.080i	−0.201757	+	0.535488i
$595$	62.9325	+	109.002i	0.105769	+	0.183197i
$596$		−	52.8708i		−	0.0887094i
$597$	−45.5725	+	19.4556i	−0.0763359	+	0.0325889i
$598$	111.347	−	3.58190i	0.186198	−	0.00598981i
$599$	439.085	−	253.506i	0.733029	−	0.423215i	−0.0865001	−	0.996252i	$-0.527568\pi$
$599$	439.085	−	253.506i	0.733029	−	0.423215i	0.819529	+	0.573037i	$0.194235\pi$
$600$	112.107	+	262.598i	0.186845	+	0.437663i
$601$	733.260			1.22007			0.610033	−	0.792376i	$-0.291156\pi$
$601$	733.260			1.22007			0.610033	+	0.792376i	$0.291156\pi$
$602$	−234.881	−	135.609i	−0.390168	−	0.225264i
$603$	−71.1751	−	17.4340i	−0.118035	−	0.0289121i
$604$	−31.3862	+	54.3625i	−0.0519639	+	0.0900042i
$605$	−545.551	+	314.974i	−0.901738	+	0.520618i
$606$	−170.801	−	128.156i	−0.281850	−	0.211478i
$607$	873.697			1.43937			0.719685	−	0.694301i	$-0.244286\pi$
$607$	873.697			1.43937			0.719685	+	0.694301i	$0.244286\pi$
$608$	−279.582	−	161.417i	−0.459838	−	0.265488i
$609$	875.248	+	105.632i	1.43719	+	0.173452i
$610$	−62.5416	+	108.325i	−0.102527	+	0.177582i
$611$	33.8171	+	1051.23i	0.0553471	+	1.72051i
$612$	52.2563	−	213.339i	0.0853861	−	0.348593i
$613$	−355.448	−	615.654i	−0.579850	−	1.00433i	−0.995496	−	0.0948030i	$-0.969778\pi$
$613$	−355.448	−	615.654i	−0.579850	−	1.00433i	0.415646	−	0.909526i	$-0.363555\pi$
$614$			213.272i			0.347349i
$615$	−52.4541	−	39.3574i	−0.0852912	−	0.0639958i
$616$	−392.157	−	679.235i	−0.636618	−	1.10265i
$617$		−	788.131i		−	1.27736i	−0.769473	−	0.638680i	$-0.779481\pi$
$617$		−	788.131i		−	1.27736i	0.769473	−	0.638680i	$-0.220519\pi$
$618$	352.828	+	42.5823i	0.570919	+	0.0689034i
$619$	−82.0508	+	142.116i	−0.132554	+	0.229590i	−0.924660	−	0.380793i	$-0.875651\pi$
$619$	−82.0508	+	142.116i	−0.132554	+	0.229590i	0.792107	+	0.610383i	$0.208984\pi$
$620$	17.2669	+	9.96904i	0.0278498	+	0.0160791i
$621$	283.813	−	232.753i	0.457025	−	0.374804i
$622$	−31.5163	−	54.5879i	−0.0506694	−	0.0877619i
$623$	−106.943	−	61.7437i	−0.171658	−	0.0991071i
$624$	39.0158	−	442.470i	0.0625253	−	0.709087i
$625$	−132.934	−	230.249i	−0.212695	−	0.368398i
$626$	−36.0174	−	20.7947i	−0.0575358	−	0.0332183i
$627$	288.208	+	675.096i	0.459663	+	1.07671i
$628$	197.603	+	342.259i	0.314655	+	0.544998i
$629$			417.177i			0.663238i
$630$	−102.384	−	25.0785i	−0.162515	−	0.0398072i
$631$	185.255	−	320.871i	0.293590	−	0.508512i	−0.681066	−	0.732222i	$-0.738483\pi$
$631$	185.255	−	320.871i	0.293590	−	0.508512i	0.974656	+	0.223710i	$0.0718168\pi$
$632$	−90.5112	−	52.2567i	−0.143214	−	0.0826846i
$633$	858.928	−	366.689i	1.35692	−	0.579287i
$634$	−81.9947	+	142.019i	−0.129329	+	0.224005i
$635$	−108.223	−	62.4826i	−0.170430	−	0.0983978i
$636$	−108.538	+	144.656i	−0.170658	+	0.227447i
$637$	235.850	−	7.58706i	0.370252	−	0.0119106i
$638$			451.460i			0.707617i
$639$	−152.348	+	621.967i	−0.238416	+	0.973344i
$640$	−140.174	−	242.788i	−0.219022	−	0.379356i
$641$	−875.418	+	505.423i	−1.36571	+	0.788491i	−0.990376	−	0.138400i	$-0.955804\pi$
$641$	−875.418	+	505.423i	−1.36571	+	0.788491i	−0.375330	+	0.926891i	$0.622471\pi$
$642$	42.7490	−	354.209i	0.0665872	−	0.551728i
$643$	−1118.93			−1.74017			−0.870084	−	0.492903i	$-0.835936\pi$
$643$	−1118.93			−1.74017			−0.870084	+	0.492903i	$0.835936\pi$
$644$			401.334i			0.623189i
$645$	140.220	+	328.450i	0.217396	+	0.509225i
$646$	26.1598	+	45.3100i	0.0404950	+	0.0701394i
$647$	433.692	−	250.392i	0.670312	−	0.387005i	−0.125883	−	0.992045i	$-0.540176\pi$
$647$	433.692	−	250.392i	0.670312	−	0.387005i	0.796195	+	0.605041i	$0.206843\pi$
$648$	208.424	+	327.496i	0.321642	+	0.505395i
$649$	135.400			0.208629
$650$	−5.23260	−	162.660i	−0.00805015	−	0.250246i
$651$	55.1878	−	23.5605i	0.0847739	−	0.0361912i
$652$	67.3819	−	116.709i	0.103346	−	0.179001i
$653$	955.134	+	551.447i	1.46269	+	0.844482i	0.999135	−	0.0415882i	$-0.0132417\pi$
$653$	955.134	+	551.447i	1.46269	+	0.844482i	0.463551	+	0.886070i	$0.346575\pi$
$654$	38.8124	−	51.7278i	0.0593462	−	0.0790945i
$655$	156.975	−	271.889i	0.239657	−	0.415098i
$656$	−95.0938	−	54.9024i	−0.144960	−	0.0836927i
$657$	124.837	+	428.666i	0.190010	+	0.652460i
$658$	417.935			0.635159
$659$	−1038.38	+	599.511i	−1.57570	+	0.909728i	−0.580246	+	0.814442i	$0.697043\pi$
$659$	−1038.38	+	599.511i	−1.57570	+	0.909728i	−0.995450	+	0.0952866i	$0.969623\pi$
$660$	−58.6380	+	485.862i	−0.0888454	+	0.736155i
$661$	27.1508	−	47.0266i	0.0410754	−	0.0711446i	−0.844757	−	0.535150i	$-0.820255\pi$
$661$	27.1508	−	47.0266i	0.0410754	−	0.0711446i	0.885832	+	0.464006i	$0.153588\pi$
$662$	192.790	−	111.307i	0.291223	−	0.168138i
$663$	−151.684	+	216.313i	−0.228785	+	0.326264i
$664$	230.191	−	398.702i	0.346673	−	0.600455i
$665$	−197.141	+	113.819i	−0.296453	+	0.171157i
$666$	−252.325	−	241.661i	−0.378867	−	0.362855i
$667$	243.753	−	422.192i	0.365446	−	0.632972i
$668$	−299.951	−	173.177i	−0.449029	−	0.259247i
$669$	404.394	+	303.425i	0.604475	+	0.453550i
$670$	11.6373			0.0173691
$671$	1513.61	−	873.880i	2.25575	−	1.30236i
$672$	−643.110	−	77.6159i	−0.957008	−	0.115500i
$673$	−475.751			−0.706910			−0.353455	−	0.935452i	$-0.614993\pi$
$673$	−475.751			−0.706910			−0.353455	+	0.935452i	$0.614993\pi$
$674$	−41.0807	+	23.7179i	−0.0609506	+	0.0351898i
$675$	−340.016	−	414.606i	−0.503728	−	0.614231i
$676$	−269.904	+	545.750i	−0.399266	+	0.807322i
$677$	32.5663	+	18.8021i	0.0481038	+	0.0277727i	0.523859	−	0.851805i	$-0.324492\pi$
$677$	32.5663	+	18.8021i	0.0481038	+	0.0277727i	−0.475755	+	0.879578i	$0.657825\pi$
$678$	−9.18618	−	6.89258i	−0.0135489	−	0.0101661i
$679$	491.057	−	850.535i	0.723206	−	1.25263i
$680$			73.6105i			0.108251i
$681$	514.229	+	62.0615i	0.755109	+	0.0911330i
$682$	15.3644	+	26.6120i	0.0225285	+	0.0390205i
$683$	904.148	+	522.010i	1.32379	+	0.764290i	0.984331	−	0.176331i	$-0.0564229\pi$
$683$	904.148	+	522.010i	1.32379	+	0.764290i	0.339458	+	0.940621i	$0.389756\pi$
$684$	385.844	+	94.5105i	0.564099	+	0.138173i
$685$	−161.585	+	279.873i	−0.235890	+	0.408573i
$686$			159.353i			0.232293i
$687$	−40.4598	+	335.241i	−0.0588934	+	0.487978i
$688$	298.993	+	517.870i	0.434582	+	0.752719i
$689$	184.791	−	114.765i	0.268202	−	0.166568i
$690$	−34.9836	+	46.6249i	−0.0507009	+	0.0675723i
$691$	−244.608			−0.353991			−0.176996	−	0.984212i	$-0.556638\pi$
$691$	−244.608			−0.353991			−0.176996	+	0.984212i	$0.556638\pi$
$692$	−727.438	+	419.986i	−1.05121	+	0.606917i
$693$	1063.72	+	1018.77i	1.53495	+	1.47008i
$694$	49.1321			0.0707956
$695$	290.950	−	167.980i	0.418633	−	0.241698i
$696$	412.410	+	309.440i	0.592543	+	0.444597i
$697$	32.6551	+	56.5603i	0.0468510	+	0.0811482i
$698$			249.124i			0.356912i
$699$	670.892	−	894.140i	0.959788	−	1.27917i
$700$	586.286			0.837552
$701$			198.920i			0.283766i	0.989883	+	0.141883i	$0.0453157\pi$
$701$			198.920i			0.283766i	−0.989883	+	0.141883i	$0.954684\pi$
$702$	−42.9674	−	217.050i	−0.0612071	−	0.309188i
$703$	−754.504			−1.07326
$704$			578.107i			0.821174i
$705$	−440.189	−	330.283i	−0.624382	−	0.468487i
$706$	−122.894			−0.174070
$707$	−801.319	+	462.642i	−1.13341	+	0.654373i
$708$	43.9777	−	58.6118i	0.0621154	−	0.0827851i
$709$	−399.883	−	692.617i	−0.564009	−	0.976893i	−0.997141	−	0.0755624i	$-0.975925\pi$
$709$	−399.883	−	692.617i	−0.564009	−	0.976893i	0.433132	−	0.901331i	$-0.357409\pi$
$710$		−	101.693i		−	0.143230i
$711$	190.633	+	46.6946i	0.268120	+	0.0656745i
$712$	−36.1100	−	62.5444i	−0.0507163	−	0.0878432i
$713$		−	33.1824i		−	0.0465391i
$714$	83.9719	+	63.0059i	0.117608	+	0.0882435i
$715$	277.781	−	518.984i	0.388505	−	0.725852i
$716$	−11.3054	+	6.52719i	−0.0157897	+	0.00911619i
$717$	−782.160	−	94.3978i	−1.09088	−	0.131657i
$718$	−19.5570			−0.0272382
$719$	−1195.44	−	690.190i	−1.66265	−	0.959930i	−0.971444	−	0.237271i	$-0.923747\pi$
$719$	−1195.44	−	690.190i	−1.66265	−	0.959930i	−0.691204	−	0.722659i	$-0.742920\pi$
$720$	167.849	+	160.755i	0.233123	+	0.223271i
$721$	769.983	−	1333.65i	1.06794	−	1.84972i
$722$	115.130	−	66.4705i	0.159460	−	0.0920644i
$723$	131.761	−	1091.74i	0.182242	−	1.51002i
$724$	588.574			0.812948
$725$	−616.757	−	356.085i	−0.850699	−	0.491151i
$726$	−315.341	+	420.276i	−0.434355	+	0.578892i
$727$	−109.714	+	190.030i	−0.150913	+	0.261389i	−0.931563	−	0.363579i	$-0.881555\pi$
$727$	−109.714	+	190.030i	−0.150913	+	0.261389i	0.780650	+	0.624968i	$0.214888\pi$
$728$	450.125	+	240.925i	0.618304	+	0.330941i
$729$	−547.756	−	481.045i	−0.751380	−	0.659870i
$730$	−35.4518	−	61.4043i	−0.0485641	−	0.0841155i
$731$		−	355.672i		−	0.486556i
$732$	113.331	−	939.041i	0.154824	−	1.28284i
$733$	281.145	+	486.957i	0.383554	+	0.664335i	0.991567	−	0.129592i	$-0.0413668\pi$
$733$	281.145	+	486.957i	0.383554	+	0.664335i	−0.608014	+	0.793927i	$0.708033\pi$
$734$		−	282.461i		−	0.384825i
$735$	−74.1010	+	98.7591i	−0.100818	+	0.134366i
$736$	−179.103	+	310.216i	−0.243347	+	0.421489i
$737$	−140.821	−	81.3029i	−0.191073	−	0.110316i
$738$	−53.1263	−	13.0130i	−0.0719869	−	0.0176328i
$739$	314.180	+	544.176i	0.425142	+	0.736368i	0.996434	−	0.0843791i	$-0.0268907\pi$
$739$	314.180	+	544.176i	0.425142	+	0.736368i	−0.571291	+	0.820747i	$0.693557\pi$
$740$	−435.636	−	251.515i	−0.588697	−	0.339884i
$741$	−391.223	−	274.336i	−0.527966	−	0.370223i
$742$	−43.2187	−	74.8569i	−0.0582462	−	0.100885i
$743$	83.6874	+	48.3169i	0.112634	+	0.0650295i	0.555259	−	0.831678i	$-0.312619\pi$
$743$	83.6874	+	48.3169i	0.112634	+	0.0650295i	−0.442624	+	0.896707i	$0.645953\pi$
$744$	34.8413	+	4.20494i	0.0468296	+	0.00565180i
$745$	−16.6373	−	28.8166i	−0.0223319	−	0.0386800i
$746$			220.476i			0.295544i
$747$	−205.690	+	839.739i	−0.275354	+	1.12415i
$748$	243.696	−	422.093i	0.325796	−	0.564296i
$749$	−1338.87	−	772.997i	−1.78754	−	1.03204i
$750$	153.855	+	115.440i	0.205140	+	0.153921i
$751$	−646.220	+	1119.29i	−0.860479	+	1.49039i	0.0109877	+	0.999940i	$0.496502\pi$
$751$	−646.220	+	1119.29i	−0.860479	+	1.49039i	−0.871467	+	0.490454i	$0.836831\pi$
$752$	−798.017	−	460.735i	−1.06119	−	0.612680i
$753$	−16.9313	−	39.6596i	−0.0224851	−	0.0526689i
$754$	−155.045	−	249.648i	−0.205630	−	0.331099i
$755$			39.5062i			0.0523260i
$756$	786.496	−	129.569i	1.04034	−	0.171388i
$757$	639.573	+	1107.77i	0.844879	+	1.46337i	0.885726	+	0.464208i	$0.153661\pi$
$757$	639.573	+	1107.77i	0.844879	+	1.46337i	−0.0408470	+	0.999165i	$0.513006\pi$
$758$	−20.8046	+	12.0115i	−0.0274466	+	0.0158463i
$759$	749.068	−	319.788i	0.986915	−	0.421328i
$760$	−133.132			−0.175173
$761$		−	1103.93i		−	1.45064i	−0.688414	−	0.725318i	$-0.741693\pi$
$761$		−	1103.93i		−	1.45064i	0.688414	−	0.725318i	$-0.258307\pi$
$762$	−103.480	−	12.4888i	−0.135800	−	0.0163895i
$763$	−140.113	−	242.683i	−0.183634	−	0.318064i
$764$	155.162	−	89.5826i	0.203091	−	0.117255i
$765$	−38.6514	−	132.722i	−0.0505247	−	0.173492i
$766$	−61.6242			−0.0804493
$767$	−74.8737	+	46.5006i	−0.0976189	+	0.0606266i
$768$	90.8164	+	68.1414i	0.118251	+	0.0887258i
$769$	−0.423754	+	0.733964i	−0.000551046	+	0.000954439i	−0.866301	−	0.499523i	$-0.833509\pi$
$769$	−0.423754	+	0.733964i	−0.000551046	+	0.000954439i	0.865750	+	0.500477i

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.630376i q^{2} +(2.39963 + 1.80049i) q^{3} +3.60263 q^{4} +(1.96357 - 1.13367i) q^{5} +(1.13499 - 1.51267i) q^{6} +(-4.09731 - 7.09675i) q^{7} -4.79251i q^{8} +(2.51645 + 8.64103i) q^{9} +(-0.714636 - 1.23779i) q^{10} +19.9709i q^{11} +(8.64497 + 6.48650i) q^{12} +(-6.85862 - 11.0435i) q^{13} +(-4.47362 + 2.58285i) q^{14} +(6.75299 + 0.815008i) q^{15} +11.3894 q^{16} +(-5.86667 - 3.38712i) q^{17} +(5.44710 - 1.58631i) q^{18} +(6.12594 - 10.6104i) q^{19} +(7.07400 - 4.08417i) q^{20} +(2.94561 - 24.4067i) q^{21} +12.5892 q^{22} +(-11.7730 - 6.79717i) q^{23} +(8.62889 - 11.5003i) q^{24} +(-9.92960 + 17.1986i) q^{25} +(-6.96157 + 4.32351i) q^{26} +(-9.51956 + 25.2661i) q^{27} +(-14.7611 - 25.5669i) q^{28} +35.8609i q^{29} +(0.513762 - 4.25693i) q^{30} +(1.22045 + 2.11388i) q^{31} -26.3497i q^{32} +(-35.9575 + 47.9228i) q^{33} +(-2.13516 + 3.69821i) q^{34} +(-16.0907 - 9.28996i) q^{35} +(9.06584 + 31.1304i) q^{36} +(-30.7914 - 53.3322i) q^{37} +(-6.68857 - 3.86165i) q^{38} +(3.42562 - 38.8493i) q^{39} +(-5.43311 - 9.41042i) q^{40} +(-8.34931 - 4.82048i) q^{41} +(-15.3854 - 1.85684i) q^{42} +(26.2518 + 45.4694i) q^{43} +71.9477i q^{44} +(14.7373 + 14.1144i) q^{45} +(-4.28478 + 7.42145i) q^{46} +(-70.0665 - 40.4529i) q^{47} +(27.3304 + 20.5066i) q^{48} +(-9.07586 + 15.7199i) q^{49} +(10.8416 + 6.25939i) q^{50} +(-7.97935 - 18.6907i) q^{51} +(-24.7090 - 39.7857i) q^{52} +16.7330i q^{53} +(15.9272 + 6.00091i) q^{54} +(22.6403 + 39.2142i) q^{55} +(-34.0113 + 19.6364i) q^{56} +(33.8040 - 14.4314i) q^{57} +22.6059 q^{58} -6.77988i q^{59} +(24.3285 + 2.93617i) q^{60} +(-43.7577 - 75.7905i) q^{61} +(1.33254 - 0.769341i) q^{62} +(51.0125 - 53.2636i) q^{63} +28.9475 q^{64} +(-25.9870 - 13.9093i) q^{65} +(30.2094 + 22.6667i) q^{66} +(-4.07107 + 7.05130i) q^{67} +(-21.1354 - 12.2025i) q^{68} +(-16.0127 - 37.5080i) q^{69} +(-5.85617 + 10.1432i) q^{70} +(61.6181 + 35.5752i) q^{71} +(41.4123 - 12.0601i) q^{72} +49.6082 q^{73} +(-33.6194 + 19.4101i) q^{74} +(-54.7933 + 23.3921i) q^{75} +(22.0695 - 38.2254i) q^{76} +(141.728 - 81.8269i) q^{77} +(-24.4897 - 2.15943i) q^{78} +(10.9038 - 18.8860i) q^{79} +(22.3639 - 12.9118i) q^{80} +(-68.3349 + 43.4895i) q^{81} +(-3.03871 + 5.26321i) q^{82} +(83.1927 + 48.0313i) q^{83} +(10.6119 - 87.9283i) q^{84} -15.3595 q^{85} +(28.6629 - 16.5485i) q^{86} +(-64.5673 + 86.0529i) q^{87} +95.7108 q^{88} +(13.0504 - 7.53467i) q^{89} +(8.89740 - 9.29002i) q^{90} +(-50.2712 + 93.9226i) q^{91} +(-42.4139 - 24.4877i) q^{92} +(-0.877397 + 7.26993i) q^{93} +(-25.5006 + 44.1683i) q^{94} -27.7791i q^{95} +(47.4424 - 63.2295i) q^{96} +(59.9243 + 103.792i) q^{97} +(9.90942 + 5.72121i) q^{98} +(-172.569 + 50.2558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

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Database

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