LMFDB - Embedded newform 117.3.k.a.29.5

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			29.5
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.75995i q^{2} +(-1.69762 - 2.47347i) q^{3} -3.61733 q^{4} +(7.95372 - 4.59208i) q^{5} +(-6.82666 + 4.68536i) q^{6} +(-2.71987 - 4.71096i) q^{7} -1.05616i q^{8} +(-3.23614 + 8.39806i) q^{9} +(-12.6739 - 21.9519i) q^{10} +18.2997i q^{11} +(6.14086 + 8.94736i) q^{12} +(12.7394 + 2.59000i) q^{13} +(-13.0020 + 7.50672i) q^{14} +(-24.8608 - 11.8777i) q^{15} -17.3843 q^{16} +(3.53920 + 2.04336i) q^{17} +(23.1782 + 8.93159i) q^{18} +(-4.68429 + 8.11343i) q^{19} +(-28.7712 + 16.6111i) q^{20} +(-7.03511 + 14.7250i) q^{21} +50.5062 q^{22} +(-2.18290 - 1.26030i) q^{23} +(-2.61238 + 1.79296i) q^{24} +(29.6745 - 51.3977i) q^{25} +(7.14827 - 35.1601i) q^{26} +(26.2661 - 6.25224i) q^{27} +(9.83868 + 17.0411i) q^{28} -10.3753i q^{29} +(-32.7818 + 68.6147i) q^{30} +(7.76905 + 13.4564i) q^{31} +43.7550i q^{32} +(45.2637 - 31.0660i) q^{33} +(5.63957 - 9.76803i) q^{34} +(-43.2663 - 24.9798i) q^{35} +(11.7062 - 30.3785i) q^{36} +(-23.6723 - 41.0016i) q^{37} +(22.3927 + 12.9284i) q^{38} +(-15.2204 - 35.9074i) q^{39} +(-4.84996 - 8.40038i) q^{40} +(34.8153 + 20.1006i) q^{41} +(40.6402 + 19.4166i) q^{42} +(-22.9833 - 39.8082i) q^{43} -66.1959i q^{44} +(12.8252 + 81.6565i) q^{45} +(-3.47837 + 6.02471i) q^{46} +(19.2835 + 11.1333i) q^{47} +(29.5119 + 42.9995i) q^{48} +(9.70457 - 16.8088i) q^{49} +(-141.855 - 81.9001i) q^{50} +(-0.954042 - 12.2230i) q^{51} +(-46.0825 - 9.36888i) q^{52} +73.5428i q^{53} +(-17.2559 - 72.4932i) q^{54} +(84.0336 + 145.550i) q^{55} +(-4.97552 + 2.87262i) q^{56} +(28.0205 - 2.18709i) q^{57} -28.6354 q^{58} -3.38499i q^{59} +(89.9298 + 42.9655i) q^{60} +(17.2929 + 29.9521i) q^{61} +(37.1390 - 21.4422i) q^{62} +(48.3648 - 7.59633i) q^{63} +51.2248 q^{64} +(113.219 - 37.9002i) q^{65} +(-85.7405 - 124.926i) q^{66} +(-37.9400 + 65.7140i) q^{67} +(-12.8025 - 7.39150i) q^{68} +(0.588432 + 7.53887i) q^{69} +(-68.9430 + 119.413i) q^{70} +(8.47547 + 4.89331i) q^{71} +(8.86967 + 3.41787i) q^{72} -90.9357 q^{73} +(-113.162 + 65.3343i) q^{74} +(-177.507 + 13.8550i) q^{75} +(16.9446 - 29.3489i) q^{76} +(86.2090 - 49.7728i) q^{77} +(-99.1026 + 42.0075i) q^{78} +(-7.46446 + 12.9288i) q^{79} +(-138.270 + 79.8300i) q^{80} +(-60.0548 - 54.3546i) q^{81} +(55.4767 - 96.0885i) q^{82} +(-37.6357 - 21.7290i) q^{83} +(25.4483 - 53.2651i) q^{84} +37.5331 q^{85} +(-109.869 + 63.4327i) q^{86} +(-25.6631 + 17.6134i) q^{87} +19.3273 q^{88} +(71.5607 - 41.3156i) q^{89} +(225.368 - 35.3970i) q^{90} +(-22.4481 - 67.0592i) q^{91} +(7.89628 + 4.55892i) q^{92} +(20.0951 - 42.0604i) q^{93} +(30.7274 - 53.2214i) q^{94} +86.0427i q^{95} +(108.227 - 74.2796i) q^{96} +(-46.4699 - 80.4881i) q^{97} +(-46.3915 - 26.7841i) q^{98} +(-153.682 - 59.2203i) 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 $

$2$		−	2.75995i		−	1.37998i	−0.723821	−	0.689988i	$-0.757616\pi$
$2$		−	2.75995i		−	1.37998i	0.723821	−	0.689988i	$-0.242384\pi$
$3$	−1.69762	−	2.47347i	−0.565875	−	0.824491i
$3$	−1.69762	−	2.47347i	−0.565875	−	0.824491i
$4$	−3.61733			−0.904332
$5$	7.95372	−	4.59208i	1.59074	−	0.918417i	0.597565	−	0.801820i	$-0.296135\pi$
$5$	7.95372	−	4.59208i	1.59074	−	0.918417i	0.993179	−	0.116597i	$-0.0371985\pi$
$6$	−6.82666	+	4.68536i	−1.13778	+	0.780893i
$7$	−2.71987	−	4.71096i	−0.388554	−	0.672994i	0.603702	−	0.797210i	$-0.293692\pi$
$7$	−2.71987	−	4.71096i	−0.388554	−	0.672994i	−0.992255	+	0.124216i	$0.960358\pi$
$8$		−	1.05616i		−	0.132020i
$9$	−3.23614	+	8.39806i	−0.359571	+	0.933118i
$10$	−12.6739	−	21.9519i	−1.26739	−	2.19519i
$11$			18.2997i			1.66361i	0.555071	+	0.831803i	$0.312691\pi$
$11$			18.2997i			1.66361i	−0.555071	+	0.831803i	$0.687309\pi$
$12$	6.14086	+	8.94736i	0.511739	+	0.745614i
$13$	12.7394	+	2.59000i	0.979953	+	0.199231i
$13$	12.7394	+	2.59000i	0.979953	+	0.199231i
$14$	−13.0020	+	7.50672i	−0.928716	+	0.536194i
$15$	−24.8608	−	11.8777i	−1.65739	−	0.791846i
$16$	−17.3843			−1.08652
$17$	3.53920	+	2.04336i	0.208188	+	0.120198i	0.600469	−	0.799648i	$-0.294981\pi$
$17$	3.53920	+	2.04336i	0.208188	+	0.120198i	−0.392281	+	0.919846i	$0.628314\pi$
$18$	23.1782	+	8.93159i	1.28768	+	0.496200i
$19$	−4.68429	+	8.11343i	−0.246542	+	0.427023i	−0.962564	−	0.271055i	$-0.912628\pi$
$19$	−4.68429	+	8.11343i	−0.246542	+	0.427023i	0.716022	+	0.698078i	$0.245961\pi$
$20$	−28.7712	+	16.6111i	−1.43856	+	0.830554i
$21$	−7.03511	+	14.7250i	−0.335005	+	0.701190i
$22$	50.5062			2.29574
$23$	−2.18290	−	1.26030i	−0.0949089	−	0.0547957i	0.451794	−	0.892122i	$-0.350784\pi$
$23$	−2.18290	−	1.26030i	−0.0949089	−	0.0547957i	−0.546703	+	0.837326i	$0.684117\pi$
$24$	−2.61238	+	1.79296i	−0.108849	+	0.0747066i
$25$	29.6745	−	51.3977i	1.18698	−	2.05591i
$26$	7.14827	−	35.1601i	0.274934	−	1.35231i
$27$	26.2661	−	6.25224i	0.972820	−	0.231564i
$28$	9.83868	+	17.0411i	0.351381	+	0.608610i
$29$		−	10.3753i		−	0.357770i	−0.983870	−	0.178885i	$-0.942751\pi$
$29$		−	10.3753i		−	0.357770i	0.983870	−	0.178885i	$-0.0572491\pi$
$30$	−32.7818	+	68.6147i	−1.09273	+	2.28716i
$31$	7.76905	+	13.4564i	0.250615	+	0.434077i	0.963695	−	0.267005i	$-0.0860340\pi$
$31$	7.76905	+	13.4564i	0.250615	+	0.434077i	−0.713081	+	0.701082i	$0.752701\pi$
$32$			43.7550i			1.36735i
$33$	45.2637	−	31.0660i	1.37163	−	0.941393i
$34$	5.63957	−	9.76803i	0.165870	−	0.287295i
$35$	−43.2663	−	24.9798i	−1.23618	−	0.713708i
$36$	11.7062	−	30.3785i	0.325172	−	0.843848i
$37$	−23.6723	−	41.0016i	−0.639791	−	1.10815i	−0.985478	−	0.169801i	$-0.945687\pi$
$37$	−23.6723	−	41.0016i	−0.639791	−	1.10815i	0.345687	−	0.938350i	$-0.387646\pi$
$38$	22.3927	+	12.9284i	0.589281	+	0.340222i
$39$	−15.2204	−	35.9074i	−0.390266	−	0.920702i
$40$	−4.84996	−	8.40038i	−0.121249	−	0.210010i
$41$	34.8153	+	20.1006i	0.849154	+	0.490259i	0.860365	−	0.509678i	$-0.170235\pi$
$41$	34.8153	+	20.1006i	0.849154	+	0.490259i	−0.0112114	+	0.999937i	$0.503569\pi$
$42$	40.6402	+	19.4166i	0.967624	+	0.462299i
$43$	−22.9833	−	39.8082i	−0.534495	−	0.925772i	−0.999188	−	0.0403000i	$-0.987169\pi$
$43$	−22.9833	−	39.8082i	−0.534495	−	0.925772i	0.464693	−	0.885472i	$-0.346165\pi$
$44$		−	66.1959i		−	1.50445i
$45$	12.8252	+	81.6565i	0.285005	+	1.81459i
$46$	−3.47837	+	6.02471i	−0.0756167	+	0.130972i
$47$	19.2835	+	11.1333i	0.410287	+	0.236879i	0.690913	−	0.722938i	$-0.257209\pi$
$47$	19.2835	+	11.1333i	0.410287	+	0.236879i	−0.280626	+	0.959817i	$0.590542\pi$
$48$	29.5119	+	42.9995i	0.614832	+	0.895823i
$49$	9.70457	−	16.8088i	0.198052	−	0.343037i
$50$	−141.855	−	81.9001i	−2.83710	−	1.63800i
$51$	−0.954042	−	12.2230i	−0.0187067	−	0.239666i
$52$	−46.0825	−	9.36888i	−0.886202	−	0.180171i
$53$			73.5428i			1.38760i	0.720168	+	0.693800i	$0.244065\pi$
$53$			73.5428i			1.38760i	−0.720168	+	0.693800i	$0.755935\pi$
$54$	−17.2559	−	72.4932i	−0.319553	−	1.34247i
$55$	84.0336	+	145.550i	1.52788	+	2.64637i
$56$	−4.97552	+	2.87262i	−0.0888485	+	0.0512967i
$57$	28.0205	−	2.18709i	0.491588	−	0.0383700i
$58$	−28.6354			−0.493714
$59$		−	3.38499i		−	0.0573727i	−0.999588	−	0.0286864i	$-0.990868\pi$
$59$		−	3.38499i		−	0.0573727i	0.999588	−	0.0286864i	$-0.00913241\pi$
$60$	89.9298	+	42.9655i	1.49883	+	0.716091i
$61$	17.2929	+	29.9521i	0.283490	+	0.491019i	0.972242	−	0.233978i	$-0.0751745\pi$
$61$	17.2929	+	29.9521i	0.283490	+	0.491019i	−0.688752	+	0.724997i	$0.741841\pi$
$62$	37.1390	−	21.4422i	0.599016	−	0.345842i
$63$	48.3648	−	7.59633i	0.767696	−	0.120577i
$64$	51.2248			0.800387
$65$	113.219	−	37.9002i	1.74183	−	0.583080i
$66$	−85.7405	−	124.926i	−1.29910	−	1.89281i
$67$	−37.9400	+	65.7140i	−0.566268	+	0.980805i	0.430662	+	0.902513i	$0.358280\pi$
$67$	−37.9400	+	65.7140i	−0.566268	+	0.980805i	−0.996930	+	0.0782922i	$0.975053\pi$
$68$	−12.8025	−	7.39150i	−0.188271	−	0.108699i
$69$	0.588432	+	7.53887i	0.00852801	+	0.109259i
$70$	−68.9430	+	119.413i	−0.984900	+	1.70590i
$71$	8.47547	+	4.89331i	0.119373	+	0.0689199i	0.558498	−	0.829506i	$-0.311378\pi$
$71$	8.47547	+	4.89331i	0.119373	+	0.0689199i	−0.439125	+	0.898426i	$0.644711\pi$
$72$	8.86967	+	3.41787i	0.123190	+	0.0474705i
$73$	−90.9357			−1.24569			−0.622847	−	0.782343i	$-0.714024\pi$
$73$	−90.9357			−1.24569			−0.622847	+	0.782343i	$0.714024\pi$
$74$	−113.162	+	65.3343i	−1.52922	+	0.882896i
$75$	−177.507	+	13.8550i	−2.36676	+	0.184733i
$76$	16.9446	−	29.3489i	0.222956	−	0.386170i
$77$	86.2090	−	49.7728i	1.11960	−	0.646400i
$78$	−99.1026	+	42.0075i	−1.27055	+	0.538558i
$79$	−7.46446	+	12.9288i	−0.0944869	+	0.163656i	−0.909394	−	0.415935i	$-0.863454\pi$
$79$	−7.46446	+	12.9288i	−0.0944869	+	0.163656i	0.814907	+	0.579591i	$0.196788\pi$
$80$	−138.270	+	79.8300i	−1.72837	+	0.997874i
$81$	−60.0548	−	54.3546i	−0.741417	−	0.671045i
$82$	55.4767	−	96.0885i	0.676546	−	1.17181i
$83$	−37.6357	−	21.7290i	−0.453442	−	0.261795i	0.255841	−	0.966719i	$-0.417648\pi$
$83$	−37.6357	−	21.7290i	−0.453442	−	0.261795i	−0.709283	+	0.704924i	$0.750981\pi$
$84$	25.4483	−	53.2651i	0.302956	−	0.634108i
$85$	37.5331			0.441566
$86$	−109.869	+	63.4327i	−1.27754	+	0.737589i
$87$	−25.6631	+	17.6134i	−0.294979	+	0.202453i
$88$	19.3273			0.219629
$89$	71.5607	−	41.3156i	0.804053	−	0.464220i	−0.0408334	−	0.999166i	$-0.513001\pi$
$89$	71.5607	−	41.3156i	0.804053	−	0.464220i	0.844886	+	0.534946i	$0.179668\pi$
$90$	225.368	−	35.3970i	2.50409	−	0.393300i
$91$	−22.4481	−	67.0592i	−0.246683	−	0.736914i
$92$	7.89628	+	4.55892i	0.0858291	+	0.0495535i
$93$	20.0951	−	42.0604i	0.216076	−	0.452263i
$94$	30.7274	−	53.2214i	0.326887	−	0.566186i
$95$			86.0427i			0.905712i
$96$	108.227	−	74.2796i	1.12736	−	0.773746i
$97$	−46.4699	−	80.4881i	−0.479071	−	0.829775i	0.520641	−	0.853776i	$-0.325693\pi$
$97$	−46.4699	−	80.4881i	−0.479071	−	0.829775i	−0.999712	+	0.0240008i	$0.992360\pi$
$98$	−46.3915	−	26.7841i	−0.473382	−	0.273307i
$99$	−153.682	−	59.2203i	−1.55234	−	0.598185i
$100$	−107.342	+	185.922i	−1.07342	+	1.85922i
$101$			91.8050i			0.908961i	0.890757	+	0.454480i	$0.150175\pi$
$101$			91.8050i			0.908961i	−0.890757	+	0.454480i	$0.849825\pi$
$102$	−33.7348	+	2.63311i	−0.330734	+	0.0258148i
$103$	−17.4570	−	30.2365i	−0.169486	−	0.293558i	0.768753	−	0.639545i	$-0.220877\pi$
$103$	−17.4570	−	30.2365i	−0.169486	−	0.293558i	−0.938239	+	0.345987i	$0.887544\pi$
$104$	2.73545	−	13.4548i	0.0263024	−	0.129373i
$105$	11.6630	+	149.424i	0.111076	+	1.42309i
$106$	202.974			1.91485
$107$	153.064	−	88.3715i	1.43050	−	0.825902i	0.433345	−	0.901228i	$-0.357333\pi$
$107$	153.064	−	88.3715i	1.43050	−	0.825902i	0.997159	+	0.0753268i	$0.0240000\pi$
$108$	−95.0132	+	22.6164i	−0.879752	+	0.209411i
$109$	−66.5314			−0.610380			−0.305190	−	0.952292i	$-0.598720\pi$
$109$	−66.5314			−0.610380			−0.305190	+	0.952292i	$0.598720\pi$
$110$	401.712	−	231.929i	3.65193	−	2.10844i
$111$	−61.2297	+	128.158i	−0.551619	+	1.15458i
$112$	47.2830	+	81.8965i	0.422169	+	0.731219i
$113$			168.290i			1.48929i	0.667458	+	0.744647i	$0.267382\pi$
$113$			168.290i			1.48929i	−0.667458	+	0.744647i	$0.732618\pi$
$114$	−6.03626	−	77.3353i	−0.0529497	−	0.678380i
$115$	−23.1496			−0.201301
$116$			37.5310i			0.323543i
$117$	−62.9774	+	98.6045i	−0.538269	+	0.842773i
$118$	−9.34241			−0.0791729
$119$		−	22.2307i		−	0.186813i
$120$	−12.5447	+	26.2570i	−0.104539	+	0.218808i
$121$	−213.878			−1.76759
$122$	82.6664	−	47.7275i	0.677593	−	0.391209i
$123$	−9.38495	−	120.238i	−0.0763004	−	0.977545i
$124$	−28.1032	−	48.6762i	−0.226639	−	0.392550i
$125$		−	315.467i		−	2.52373i
$126$	−20.9655	−	133.485i	−0.166393	−	1.05940i
$127$	19.1179	+	33.1132i	0.150535	+	0.260734i	0.931424	−	0.363936i	$-0.118567\pi$
$127$	19.1179	+	33.1132i	0.150535	+	0.260734i	−0.780889	+	0.624669i	$0.785234\pi$
$128$			33.6424i			0.262831i
$129$	−59.4475	+	124.428i	−0.460834	+	0.964557i
$130$	−104.603	−	312.479i	−0.804635	−	2.40368i
$131$	−67.9435	+	39.2272i	−0.518652	+	0.299444i	−0.736383	−	0.676565i	$-0.763468\pi$
$131$	−67.9435	+	39.2272i	−0.518652	+	0.299444i	0.217731	+	0.976009i	$0.430135\pi$
$132$	−163.734	+	112.376i	−1.24041	+	0.851332i
$133$	50.9628			0.383179
$134$	181.367	+	104.712i	1.35349	+	0.781436i
$135$	180.203	−	170.345i	1.33483	−	1.26181i
$136$	2.15811	−	3.73795i	0.0158684	−	0.0274850i
$137$	99.7360	−	57.5826i	0.728000	−	0.420311i	−0.0896899	−	0.995970i	$-0.528588\pi$
$137$	99.7360	−	57.5826i	0.728000	−	0.420311i	0.817690	+	0.575659i	$0.195254\pi$
$138$	20.8069	−	1.62404i	0.150775	−	0.0117684i
$139$	133.227			0.958467			0.479234	−	0.877687i	$-0.340915\pi$
$139$	133.227			0.958467			0.479234	+	0.877687i	$0.340915\pi$
$140$	156.508	+	90.3601i	1.11792	+	0.645429i
$141$	−5.19813	−	66.5974i	−0.0368662	−	0.472322i
$142$	13.5053	−	23.3919i	0.0951078	−	0.164732i
$143$	−47.3962	+	233.126i	−0.331442	+	1.63026i
$144$	56.2579	−	145.994i	0.390680	−	1.01385i
$145$	−47.6445	−	82.5226i	−0.328582	−	0.569121i
$146$			250.978i			1.71903i
$147$	−58.0508	+	4.53105i	−0.394904	+	0.0308235i
$148$	85.6304	+	148.316i	0.578584	+	1.00214i
$149$		−	1.95766i		−	0.0131387i	−0.999978	−	0.00656933i	$-0.997909\pi$
$149$		−	1.95766i		−	0.0131387i	0.999978	−	0.00656933i	$-0.00209110\pi$
$150$	38.2390	+	489.911i	0.254927	+	3.26607i
$151$	−80.3329	+	139.141i	−0.532006	+	0.921461i	0.467296	+	0.884101i	$0.345228\pi$
$151$	−80.3329	+	139.141i	−0.532006	+	0.921461i	−0.999302	+	0.0373605i	$0.988105\pi$
$152$	8.56906	+	4.94735i	0.0563754	+	0.0325484i
$153$	−28.6136	+	23.1098i	−0.187017	+	0.151045i
$154$	−137.370	−	237.933i	−0.892016	−	1.54502i
$155$	123.586	+	71.3523i	0.797328	+	0.460337i
$156$	55.0571	+	129.889i	0.352930	+	0.832620i
$157$	108.787	+	188.425i	0.692911	+	1.20016i	0.970880	+	0.239566i	$0.0770053\pi$
$157$	108.787	+	188.425i	0.692911	+	1.20016i	−0.277969	+	0.960590i	$0.589661\pi$
$158$	35.6829	+	20.6015i	0.225841	+	0.130390i
$159$	181.906	−	124.848i	1.14406	−	0.785208i
$160$	200.927	+	348.016i	1.25579	+	2.17510i
$161$			13.7114i			0.0851642i
$162$	−150.016	+	165.748i	−0.926025	+	1.02314i
$163$	29.4508	−	51.0104i	0.180680	−	0.312947i	−0.761432	−	0.648244i	$-0.775503\pi$
$163$	29.4508	−	51.0104i	0.180680	−	0.312947i	0.942112	+	0.335297i	$0.108837\pi$
$164$	−125.938	−	72.7106i	−0.767917	−	0.443357i
$165$	217.358	−	454.945i	1.31732	−	2.75724i
$166$	−59.9709	+	103.873i	−0.361270	+	0.625739i
$167$	−31.6310	−	18.2622i	−0.189407	−	0.109354i	0.402298	−	0.915509i	$-0.368212\pi$
$167$	−31.6310	−	18.2622i	−0.189407	−	0.109354i	−0.591705	+	0.806155i	$0.701545\pi$
$168$	15.5519	+	7.43018i	0.0925708	+	0.0442273i
$169$	155.584	+	65.9900i	0.920614	+	0.390474i
$170$		−	103.590i		−	0.609350i
$171$	−52.9781	−	65.5952i	−0.309813	−	0.383598i
$172$	83.1380	+	143.999i	0.483360	+	0.837205i
$173$	−154.231	+	89.0451i	−0.891506	+	0.514711i	−0.874435	−	0.485143i	$-0.838768\pi$
$173$	−154.231	+	89.0451i	−0.891506	+	0.514711i	−0.0170713	+	0.999854i	$0.505434\pi$
$174$	48.6122	+	70.8290i	0.279381	+	0.407063i
$175$	−322.843			−1.84482
$176$		−	318.126i		−	1.80753i
$177$	−8.37269	+	5.74644i	−0.0473033	+	0.0324658i
$178$	−114.029	−	197.504i	−0.640612	−	1.10957i
$179$	109.244	−	63.0721i	0.610302	−	0.352358i	−0.162782	−	0.986662i	$-0.552047\pi$
$179$	109.244	−	63.0721i	0.610302	−	0.352358i	0.773084	+	0.634304i	$0.218713\pi$
$180$	−46.3930	−	295.378i	−0.257739	−	1.64099i
$181$	74.8713			0.413654			0.206827	−	0.978378i	$-0.433686\pi$
$181$	74.8713			0.413654			0.206827	+	0.978378i	$0.433686\pi$
$182$	−185.080	+	61.9557i	−1.01692	+	0.340416i
$183$	44.7290	−	93.6209i	0.244421	−	0.511590i
$184$	−1.33108	+	2.30549i	−0.00723410	+	0.0125298i
$185$	−376.566	−	217.410i	−2.03549	−	1.17519i
$186$	−116.085	−	55.4615i	−0.624111	−	0.298180i
$187$	−37.3928	+	64.7662i	−0.199962	+	0.346344i
$188$	−69.7547	−	40.2729i	−0.371035	−	0.214217i
$189$	−100.895	−	106.733i	−0.533834	−	0.564727i
$190$	237.474			1.24986
$191$	−57.5866	+	33.2476i	−0.301501	+	0.174071i	−0.643117	−	0.765768i	$-0.722359\pi$
$191$	−57.5866	+	33.2476i	−0.301501	+	0.174071i	0.341616	+	0.939840i	$0.389026\pi$
$192$	−86.9604	−	126.703i	−0.452919	−	0.659912i
$193$	−118.582	+	205.389i	−0.614413	+	1.06419i	0.376075	+	0.926589i	$0.377274\pi$
$193$	−118.582	+	205.389i	−0.614413	+	1.06419i	−0.990487	+	0.137605i	$0.956060\pi$
$194$	−222.143	+	128.254i	−1.14507	+	0.661106i
$195$	−285.948	−	215.704i	−1.46640	−	1.10617i
$196$	−35.1046	+	60.8029i	−0.179105	+	0.310219i
$197$	58.7778	−	33.9354i	0.298364	−	0.172261i	−0.343344	−	0.939210i	$-0.611560\pi$
$197$	58.7778	−	33.9354i	0.298364	−	0.172261i	0.641708	+	0.766949i	$0.278226\pi$
$198$	−163.445	+	424.154i	−0.825481	+	2.14219i
$199$	37.1197	−	64.2933i	0.186531	−	0.323082i	−0.757560	−	0.652765i	$-0.773609\pi$
$199$	37.1197	−	64.2933i	0.186531	−	0.323082i	0.944091	+	0.329684i	$0.106942\pi$
$200$	−54.2841	−	31.3409i	−0.271420	−	0.156705i
$201$	226.950	−	17.7141i	1.12910	−	0.0881299i
$202$	253.377			1.25434
$203$	−48.8778	+	28.2196i	−0.240778	+	0.139013i
$204$	3.45108	+	44.2145i	0.0169171	+	0.216738i
$205$	369.215			1.80105
$206$	−83.4512	+	48.1806i	−0.405103	+	0.233886i
$207$	17.6483	−	14.2536i	0.0852573	−	0.0688582i
$208$	−221.465	−	45.0252i	−1.06473	−	0.216467i
$209$	−148.473	−	85.7210i	−0.710398	−	0.410148i
$210$	412.404	−	32.1894i	1.96383	−	0.153283i
$211$	−56.6494	+	98.1196i	−0.268480	+	0.465022i	−0.968470	−	0.249132i	$-0.919855\pi$
$211$	−56.6494	+	98.1196i	−0.268480	+	0.465022i	0.699989	+	0.714153i	$0.253188\pi$
$212$		−	266.028i		−	1.25485i
$213$	−2.28468	−	29.2709i	−0.0107262	−	0.137422i
$214$	−243.901	−	422.449i	−1.13972	−	1.97406i
$215$	−365.605	−	211.082i	−1.70049	−	0.981778i
$216$	−6.60335	−	27.7412i	−0.0305711	−	0.128431i
$217$	42.2617	−	73.1994i	0.194754	−	0.337324i
$218$			183.623i			0.842309i
$219$	154.375	+	224.927i	0.704907	+	1.02706i
$220$	−303.977	−	526.504i	−1.38171	−	2.39320i
$221$	39.7950	+	35.1977i	0.180068	+	0.159266i
$222$	353.710	+	168.991i	1.59329	+	0.761221i
$223$	−133.991			−0.600857			−0.300428	−	0.953804i	$-0.597130\pi$
$223$	−133.991			−0.600857			−0.300428	+	0.953804i	$0.597130\pi$
$224$	206.128	−	119.008i	0.920216	−	0.531287i
$225$	335.610	+	415.538i	1.49160	+	1.84684i
$226$	464.473			2.05519
$227$	28.2529	−	16.3118i	0.124462	−	0.0718583i	−0.436476	−	0.899716i	$-0.643774\pi$
$227$	28.2529	−	16.3118i	0.124462	−	0.0718583i	0.560939	+	0.827857i	$0.310440\pi$
$228$	−101.359	+	7.91142i	−0.444559	+	0.0346992i
$229$	−112.099	−	194.161i	−0.489516	−	0.847866i	0.510411	−	0.859930i	$-0.329493\pi$
$229$	−112.099	−	194.161i	−0.489516	−	0.847866i	−0.999927	+	0.0120642i	$0.996160\pi$
$230$			63.8918i			0.277790i
$231$	−269.462	−	128.740i	−1.16650	−	0.557317i
$232$	−10.9580			−0.0472327
$233$			340.251i			1.46030i	0.683285	+	0.730152i	$0.260551\pi$
$233$			340.251i			1.46030i	−0.683285	+	0.730152i	$0.739449\pi$
$234$	272.143	+	173.815i	1.16301	+	0.742797i
$235$	204.501			0.870215
$236$			12.2446i			0.0518840i
$237$	44.6510	−	3.48515i	0.188401	−	0.0147053i
$238$	−61.3557			−0.257797
$239$	−33.6429	+	19.4238i	−0.140765	+	0.0812709i	−0.568729	−	0.822525i	$-0.692565\pi$
$239$	−33.6429	+	19.4238i	−0.140765	+	0.0812709i	0.427963	+	0.903796i	$0.359231\pi$
$240$	432.187	+	206.485i	1.80078	+	0.860353i
$241$	22.4599	+	38.9017i	0.0931947	+	0.161418i	0.908854	−	0.417115i	$-0.136959\pi$
$241$	22.4599	+	38.9017i	0.0931947	+	0.161418i	−0.815659	+	0.578533i	$0.803625\pi$
$242$			590.292i			2.43922i
$243$	−32.4942	+	240.818i	−0.133721	+	0.991019i
$244$	−62.5540	−	108.347i	−0.256369	−	0.444044i
$245$		−	178.257i		−	0.727578i
$246$	−331.851	+	25.9020i	−1.34899	+	0.105293i
$247$	−80.6888	+	91.2278i	−0.326675	+	0.369343i
$248$	14.2121	−	8.20534i	0.0573067	−	0.0330860i
$249$	10.1452	+	129.979i	0.0407439	+	0.522002i
$250$	−870.672			−3.48269
$251$	−420.624	−	242.847i	−1.67579	−	0.967519i	−0.964296	−	0.264828i	$-0.914685\pi$
$251$	−420.624	−	242.847i	−1.67579	−	0.967519i	−0.711496	−	0.702690i	$-0.751982\pi$
$252$	−174.951	+	27.4784i	−0.694252	+	0.109041i
$253$	23.0631	−	39.9464i	0.0911584	−	0.157891i
$254$	91.3907	−	52.7645i	0.359806	−	0.207734i
$255$	−63.7172	−	92.8372i	−0.249871	−	0.364067i
$256$	297.750			1.16309
$257$	−20.6759	−	11.9373i	−0.0804511	−	0.0464485i	0.459235	−	0.888315i	$-0.348124\pi$
$257$	−20.6759	−	11.9373i	−0.0804511	−	0.0464485i	−0.539686	+	0.841866i	$0.681457\pi$
$258$	343.415	+	164.072i	1.33106	+	0.635939i
$259$	−128.771	+	223.038i	−0.497186	+	0.861152i
$260$	−409.550	+	137.097i	−1.57519	+	0.527297i
$261$	87.1327	+	33.5761i	0.333842	+	0.128644i
$262$	108.265	+	187.521i	0.413225	+	0.715727i
$263$		−	473.709i		−	1.80118i	−0.434673	−	0.900588i	$-0.643136\pi$
$263$		−	473.709i		−	1.80118i	0.434673	−	0.900588i	$-0.356864\pi$
$264$	−32.8105	−	47.8056i	−0.124282	−	0.181082i
$265$	337.715	+	584.939i	1.27439	+	2.20732i
$266$		−	140.655i		−	0.528777i
$267$	−223.676	−	106.865i	−0.837739	−	0.400244i
$268$	137.241	−	237.709i	0.512094	−	0.886974i
$269$	77.5036	+	44.7467i	0.288117	+	0.166345i	0.637093	−	0.770787i	$-0.280137\pi$
$269$	77.5036	+	44.7467i	0.288117	+	0.166345i	−0.348975	+	0.937132i	$0.613470\pi$
$270$	−470.143	−	497.351i	−1.74127	−	1.84204i
$271$	37.7478	+	65.3811i	0.139291	+	0.241259i	0.927228	−	0.374496i	$-0.122184\pi$
$271$	37.7478	+	65.3811i	0.139291	+	0.241259i	−0.787938	+	0.615755i	$0.788851\pi$
$272$	−61.5264	−	35.5223i	−0.226200	−	0.130597i
$273$	−127.761	+	169.366i	−0.467988	+	0.620389i
$274$	−158.925	−	275.267i	−0.580019	−	1.00462i
$275$	940.561	+	543.033i	3.42022	+	1.97467i
$276$	−2.12855	−	27.2706i	−0.00771215	−	0.0988064i
$277$	155.217	+	268.844i	0.560350	+	0.970554i	0.997466	+	0.0711492i	$0.0226667\pi$
$277$	155.217	+	268.844i	0.560350	+	0.970554i	−0.437116	+	0.899405i	$0.644000\pi$
$278$		−	367.700i		−	1.32266i
$279$	−138.149	+	21.6982i	−0.495159	+	0.0777712i
$280$	−26.3826	+	45.6960i	−0.0942235	+	0.163200i
$281$	100.496	+	58.0212i	0.357636	+	0.206481i	0.668043	−	0.744122i	$-0.267132\pi$
$281$	100.496	+	58.0212i	0.357636	+	0.206481i	−0.310407	+	0.950604i	$0.600465\pi$
$282$	−183.805	+	14.3466i	−0.651792	+	0.0508744i
$283$	209.421	−	362.728i	0.740005	−	1.28173i	−0.212488	−	0.977164i	$-0.568157\pi$
$283$	209.421	−	362.728i	0.740005	−	1.28173i	0.952492	−	0.304562i	$-0.0985102\pi$
$284$	−30.6586	−	17.7007i	−0.107953	−	0.0623265i
$285$	212.824	−	146.068i	0.746752	−	0.512520i
$286$	643.418	+	130.811i	2.24971	+	0.457381i
$287$		−	218.685i		−	0.761968i
$288$	−367.457	−	141.598i	−1.27589	−	0.491658i
$289$	−136.149	−	235.818i	−0.471105	−	0.815978i
$290$	−227.758	+	131.496i	−0.785374	+	0.453436i
$291$	−120.197	+	251.581i	−0.413048	+	0.864538i
$292$	328.944			1.12652
$293$			520.151i			1.77526i	0.460559	+	0.887629i	$0.347649\pi$
$293$			520.151i			1.77526i	−0.460559	+	0.887629i	$0.652351\pi$
$294$	12.5055	+	160.217i	0.0425356	+	0.544957i
$295$	−15.5442	−	26.9233i	−0.0526921	−	0.0912654i
$296$	−43.3041	+	25.0017i	−0.146298	+	0.0844650i
$297$	114.414	+	480.661i	0.385232	+	1.61839i
$298$	−5.40305			−0.0181310
$299$	−24.5447	−	21.7092i	−0.0820892	−	0.0726059i
$300$	642.101	−	50.1180i	2.14034	−	0.167060i
$301$	−125.023	+	216.547i	−0.415359	+	0.719424i
$302$	384.021	+	221.715i	1.27159	+	0.734155i
$303$	227.077	−	155.850i	0.749430	−	0.514358i
$304$	81.4329	−	141.046i	0.267871	−	0.463967i
$305$	275.085	+	158.821i	0.901919	+	0.520723i
$306$	63.7820	+	78.9722i	0.208438	+	0.258079i
$307$	−544.605			−1.77396			−0.886979	−	0.461810i	$-0.847200\pi$
$307$	−544.605			−1.77396			−0.886979	+	0.461810i	$0.847200\pi$
$308$	−311.846	+	180.045i	−1.01249	+	0.584560i
$309$	−45.1536	+	94.5098i	−0.146128	+	0.305857i
$310$	196.929	−	341.091i	0.635254	−	1.10029i
$311$	205.911	−	118.883i	0.662092	−	0.382259i	−0.130982	−	0.991385i	$-0.541813\pi$
$311$	205.911	−	118.883i	0.662092	−	0.382259i	0.793074	+	0.609126i	$0.208480\pi$
$312$	−37.9238	+	16.0751i	−0.121551	+	0.0515228i
$313$	93.2954	−	161.592i	0.298068	−	0.516270i	−0.677626	−	0.735407i	$-0.736991\pi$
$313$	93.2954	−	161.592i	0.298068	−	0.516270i	0.975694	+	0.219137i	$0.0703243\pi$
$314$	520.042	−	300.247i	1.65619	−	0.956200i
$315$	349.797	−	282.514i	1.11047	−	0.896871i
$316$	27.0014	−	46.7678i	0.0854475	−	0.147999i
$317$	−194.516	−	112.304i	−0.613616	−	0.354271i	0.160763	−	0.986993i	$-0.448604\pi$
$317$	−194.516	−	112.304i	−0.613616	−	0.354271i	−0.774379	+	0.632722i	$0.781938\pi$
$318$	−344.574	−	502.052i	−1.08357	−	1.57878i
$319$	189.865			0.595189
$320$	407.428	−	235.228i	1.27321	−	0.735089i
$321$	−478.429	−	228.578i	−1.49043	−	0.712080i
$322$	37.8429			0.117524
$323$	−33.1573	+	19.1434i	−0.102654	+	0.0592675i
$324$	217.238	+	196.618i	0.670487	+	0.606847i
$325$	511.155	−	577.918i	1.57278	−	1.77821i
$326$	−140.786	−	81.2829i	−0.431859	−	0.249334i
$327$	112.945	+	164.564i	0.345398	+	0.503253i
$328$	21.2294	−	36.7704i	0.0647239	−	0.112105i
$329$		−	121.125i		−	0.368161i
$330$	−1255.63	−	599.897i	−3.80493	−	1.81787i
$331$	−45.6994	−	79.1537i	−0.138065	−	0.239135i	0.788699	−	0.614779i	$-0.210755\pi$
$331$	−45.6994	−	79.1537i	−0.138065	−	0.239135i	−0.926764	+	0.375644i	$0.877422\pi$
$332$	136.141	+	78.6008i	0.410062	+	0.236749i
$333$	420.941	−	66.1142i	1.26409	−	0.198541i
$334$	−50.4027	+	87.3001i	−0.150906	+	0.261377i
$335$			696.894i			2.08028i
$336$	122.300	−	255.983i	0.363988	−	0.761853i
$337$	−302.402	−	523.776i	−0.897336	−	1.55423i	−0.830887	−	0.556441i	$-0.812166\pi$
$337$	−302.402	−	523.776i	−0.897336	−	1.55423i	−0.0664486	−	0.997790i	$-0.521167\pi$
$338$	182.129	−	429.404i	0.538844	−	1.27042i
$339$	416.262	−	285.694i	1.22791	−	0.842754i
$340$	−135.770			−0.399322
$341$	−246.247	+	142.171i	−0.722133	+	0.416924i
$342$	−181.039	+	146.217i	−0.529355	+	0.427535i
$343$	−372.129			−1.08492
$344$	−42.0437	+	24.2739i	−0.122220	+	0.0705638i
$345$	39.2994	+	57.2600i	0.113911	+	0.165971i
$346$	245.760	+	425.669i	0.710289	+	1.23026i
$347$		−	512.214i		−	1.47612i	−0.674735	−	0.738060i	$-0.735742\pi$
$347$		−	512.214i		−	1.47612i	0.674735	−	0.738060i	$-0.264258\pi$
$348$	92.8320	−	63.7136i	0.266759	−	0.183085i
$349$	−118.621			−0.339888			−0.169944	−	0.985454i	$-0.554359\pi$
$349$	−118.621			−0.339888			−0.169944	+	0.985454i	$0.554359\pi$
$350$			891.032i			2.54581i
$351$	350.808	−	11.6204i	0.999452	−	0.0331065i
$352$	−800.703			−2.27472
$353$		−	362.350i		−	1.02649i	−0.858243	−	0.513244i	$-0.828444\pi$
$353$		−	362.350i		−	1.02649i	0.858243	−	0.513244i	$-0.171556\pi$
$354$	15.8599	+	23.1082i	0.0448020	+	0.0652774i
$355$	89.8821			0.253189
$356$	−258.859	+	149.452i	−0.727131	+	0.419809i
$357$	−54.9871	+	37.7394i	−0.154026	+	0.105713i
$358$	−174.076	−	301.508i	−0.486246	−	0.842202i
$359$			238.002i			0.662958i	0.943463	+	0.331479i	$0.107548\pi$
$359$			238.002i			0.662958i	−0.943463	+	0.331479i	$0.892452\pi$
$360$	86.2421	−	13.5454i	0.239561	−	0.0376262i
$361$	136.615	+	236.624i	0.378434	+	0.655467i
$362$		−	206.641i		−	0.570832i
$363$	363.084	+	529.021i	1.00023	+	1.45736i
$364$	81.2022	+	242.575i	0.223083	+	0.666415i
$365$	−723.278	+	417.584i	−1.98158	+	1.14407i
$366$	−258.389	−	123.450i	−0.705981	−	0.337295i
$367$	−314.924			−0.858103			−0.429051	−	0.903280i	$-0.641152\pi$
$367$	−314.924			−0.858103			−0.429051	+	0.903280i	$0.641152\pi$
$368$	37.9482	+	21.9094i	0.103120	+	0.0595363i
$369$	−281.474	+	227.333i	−0.762801	+	0.616077i
$370$	−600.042	+	1039.30i	−1.62173	+	2.80893i
$371$	346.457	−	200.027i	0.933847	−	0.539157i
$372$	−72.6905	+	152.146i	−0.195405	+	0.408996i
$373$	54.9890			0.147424			0.0737118	−	0.997280i	$-0.476516\pi$
$373$	54.9890			0.147424			0.0737118	+	0.997280i	$0.476516\pi$
$374$	178.752	+	103.202i	0.477946	+	0.275942i
$375$	−780.298	+	535.544i	−2.08080	+	1.42812i
$376$	11.7585	−	20.3664i	0.0312727	−	0.0541659i
$377$	26.8721	−	132.175i	0.0712789	−	0.350598i
$378$	−294.579	+	278.464i	−0.779309	+	0.736678i
$379$	129.326	+	224.000i	0.341231	+	0.591029i	0.984662	−	0.174475i	$-0.0558229\pi$
$379$	129.326	+	224.000i	0.341231	+	0.591029i	−0.643431	+	0.765504i	$0.722490\pi$
$380$		−	311.245i		−	0.819065i
$381$	49.4495	−	103.501i	0.129789	−	0.271657i
$382$	91.7618	+	158.936i	0.240214	+	0.416063i
$383$		−	293.822i		−	0.767158i	−0.923508	−	0.383579i	$-0.874691\pi$
$383$		−	293.822i		−	0.767158i	0.923508	−	0.383579i	$-0.125309\pi$
$384$	83.2135	−	57.1121i	0.216702	−	0.148729i
$385$	457.122	−	791.758i	1.18733	−	2.05651i
$386$	566.865	+	327.280i	1.46856	+	0.847874i
$387$	408.689	−	64.1899i	1.05604	−	0.165865i
$388$	168.097	+	291.152i	0.433239	+	0.750392i
$389$	−70.6008	−	40.7614i	−0.181493	−	0.104785i	0.406501	−	0.913650i	$-0.366749\pi$
$389$	−70.6008	−	40.7614i	−0.181493	−	0.104785i	−0.587994	+	0.808865i	$0.700082\pi$
$390$	−595.332	+	789.204i	−1.52649	+	2.02360i
$391$	−5.15049	−	8.92092i	−0.0131726	−	0.0228156i
$392$	−17.7527	−	10.2495i	−0.0452876	−	0.0261468i
$393$	212.370	+	101.463i	0.540381	+	0.258176i
$394$	−93.6599	−	162.224i	−0.237716	−	0.411735i
$395$			137.110i			0.347113i
$396$	555.917	+	214.219i	1.40383	+	0.540958i
$397$	155.489	−	269.314i	0.391659	−	0.678373i	−0.601010	−	0.799242i	$-0.705235\pi$
$397$	155.489	−	269.314i	0.391659	−	0.678373i	0.992669	+	0.120869i	$0.0385680\pi$
$398$	−177.446	−	102.449i	−0.445845	−	0.257409i
$399$	−86.5156	−	126.055i	−0.216831	−	0.315927i
$400$	−515.869	+	893.511i	−1.28967	+	2.23378i
$401$	−354.860	−	204.879i	−0.884939	−	0.510920i	−0.0126552	−	0.999920i	$-0.504028\pi$
$401$	−354.860	−	204.879i	−0.884939	−	0.510920i	−0.872284	+	0.489000i	$0.837362\pi$
$402$	−48.8901	−	626.370i	−0.121617	−	1.55813i
$403$	64.1209	+	191.548i	0.159109	+	0.475305i
$404$		−	332.089i		−	0.822002i
$405$	−727.260	−	156.545i	−1.79570	−	0.386531i
$406$	77.8848	+	134.900i	0.191834	+	0.332267i
$407$	750.316	−	433.195i	1.84353	−	1.06436i
$408$	−12.9094	+	1.00762i	−0.0316407	+	0.00246965i
$409$	−122.817			−0.300286			−0.150143	−	0.988664i	$-0.547973\pi$
$409$	−122.817			−0.300286			−0.150143	+	0.988664i	$0.547973\pi$
$410$		−	1019.02i		−	2.48540i
$411$	−311.743	−	148.941i	−0.758500	−	0.362386i
$412$	63.1479	+	109.375i	0.153272	+	0.265474i
$413$	−15.9466	+	9.20675i	−0.0386115	+	0.0222924i
$414$	−39.3394	−	48.7083i	−0.0950226	−	0.117653i
$415$	−399.125			−0.961747
$416$	−113.326	+	557.412i	−0.272417	+	1.33993i
$417$	−226.169	−	329.533i	−0.542372	−	0.790248i
$418$	−236.586	+	409.779i	−0.565995	+	0.980331i
$419$	459.582	+	265.340i	1.09685	+	0.633269i	0.935393	−	0.353610i	$-0.115046\pi$
$419$	459.582	+	265.340i	1.09685	+	0.633269i	0.161461	+	0.986879i	$0.448379\pi$
$420$	−42.1890	−	540.516i	−0.100450	−	1.28694i
$421$	299.520	−	518.784i	0.711450	−	1.23227i	−0.252863	−	0.967502i	$-0.581372\pi$
$421$	299.520	−	518.784i	0.711450	−	1.23227i	0.964313	−	0.264765i	$-0.0852943\pi$
$422$	270.805	+	156.349i	0.641718	+	0.370496i
$423$	−155.902	+	125.915i	−0.368563	+	0.297671i
$424$	77.6727			0.183190
$425$	210.048	−	121.271i	0.494231	−	0.285344i
$426$	−80.7861	+	6.30561i	−0.189639	+	0.0148019i
$427$	94.0689	−	162.932i	0.220302	−	0.381574i
$428$	−553.682	+	319.669i	−1.29365	+	0.746889i
$429$	657.093	−	278.528i	1.53169	−	0.649250i
$430$	−582.576	+	1009.05i	−1.35483	+	2.34663i
$431$	−644.922	+	372.346i	−1.49634	+	0.863912i	−0.999991	−	0.00421181i	$-0.998659\pi$
$431$	−644.922	+	372.346i	−1.49634	+	0.863912i	−0.496348	+	0.868124i	$0.665326\pi$
$432$	−456.617	+	108.691i	−1.05698	+	0.251598i
$433$	−250.282	+	433.502i	−0.578019	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$433$	−250.282	+	433.502i	−0.578019	+	1.00116i	−0.995706	+	0.0925678i	$0.970493\pi$
$434$	−202.027	−	116.640i	−0.465499	−	0.268756i
$435$	−123.235	+	257.940i	−0.283299	+	0.592965i
$436$	240.666			0.551986
$437$	20.4507	−	11.8072i	0.0467980	−	0.0270188i
$438$	620.788	−	426.067i	1.41732	−	0.972755i
$439$	−265.192			−0.604082			−0.302041	−	0.953295i	$-0.597668\pi$
$439$	−265.192			−0.604082			−0.302041	+	0.953295i	$0.597668\pi$
$440$	153.724	−	88.7527i	0.349373	−	0.201711i
$441$	109.756	+	135.895i	0.248880	+	0.308152i
$442$	97.1439	−	109.832i	0.219783	−	0.248489i
$443$	580.726	+	335.282i	1.31089	+	0.756845i	0.982244	−	0.187607i	$-0.0600733\pi$
$443$	580.726	+	335.282i	1.31089	+	0.756845i	0.328649	+	0.944452i	$0.393407\pi$
$444$	221.488	−	463.590i	0.498847	−	1.04412i
$445$	379.449	−	657.226i	0.852695	−	1.47691i
$446$			369.809i			0.829168i
$447$	−4.84222	+	3.32337i	−0.0108327	+	0.00743484i
$448$	−139.325	−	241.318i	−0.310993	−	0.538656i
$449$	25.9817	+	15.0005i	0.0578657	+	0.0334088i	0.528654	−	0.848838i	$-0.322697\pi$
$449$	25.9817	+	15.0005i	0.0578657	+	0.0334088i	−0.470788	+	0.882246i	$0.656030\pi$
$450$	1146.87	−	926.267i	2.54859	−	2.05837i
$451$	−367.835	+	637.109i	−0.815598	+	1.41266i
$452$		−	608.761i		−	1.34682i
$453$	480.536	−	37.5073i	1.06079	−	0.0827976i
$454$	−45.0199	−	77.9767i	−0.0991627	−	0.171755i
$455$	−486.488	−	430.287i	−1.06920	−	0.945685i
$456$	−2.30991	−	29.5941i	−0.00506559	−	0.0648993i
$457$	−548.269			−1.19971			−0.599856	−	0.800108i	$-0.704776\pi$
$457$	−548.269			−1.19971			−0.599856	+	0.800108i	$0.704776\pi$
$458$	−535.876	+	309.388i	−1.17003	+	0.675520i
$459$	105.737	+	31.5432i	0.230363	+	0.0687216i
$460$	83.7398			0.182043
$461$	−708.821	+	409.238i	−1.53757	+	0.887718i	−0.538593	+	0.842566i	$0.681044\pi$
$461$	−708.821	+	409.238i	−1.53757	+	0.887718i	−0.998980	+	0.0451524i	$0.985623\pi$
$462$	−355.317	+	743.703i	−0.769083	+	1.60975i
$463$	133.168	+	230.654i	0.287620	+	0.498172i	0.973241	−	0.229786i	$-0.0738028\pi$
$463$	133.168	+	230.654i	0.287620	+	0.498172i	−0.685621	+	0.727958i	$0.740469\pi$
$464$			180.368i			0.388723i
$465$	−33.3143	−	426.815i	−0.0716436	−	0.917883i
$466$	939.076			2.01518
$467$		−	558.383i		−	1.19568i	−0.801615	−	0.597840i	$-0.796026\pi$
$467$		−	558.383i		−	1.19568i	0.801615	−	0.597840i	$-0.203974\pi$
$468$	227.810	−	356.685i	0.486773	−	0.762147i
$469$	412.768			0.880102
$470$		−	564.412i		−	1.20088i
$471$	281.384	−	588.956i	0.597418	−	1.25044i
$472$	−3.57508			−0.00757433
$473$	728.477	−	420.586i	1.54012	−	0.889189i
$474$	−9.61883	−	123.234i	−0.0202929	−	0.259988i
$475$	278.008	+	481.524i	0.585280	+	1.01373i
$476$			80.4158i			0.168941i
$477$	−617.616	−	237.995i	−1.29479	−	0.498941i
$478$	53.6086	+	92.8528i	0.112152	+	0.194253i
$479$			631.510i			1.31839i	0.751971	+	0.659196i	$0.229103\pi$
$479$			631.510i			1.31839i	−0.751971	+	0.659196i	$0.770897\pi$
$480$	519.709	−	1087.79i	1.08273	−	2.26622i
$481$	−195.376	−	583.646i	−0.406187	−	1.21340i
$482$	107.367	−	61.9883i	0.222753	−	0.128606i
$483$	33.9149	−	23.2769i	0.0702171	−	0.0481923i
$484$	773.666			1.59848
$485$	−739.217	−	426.787i	−1.52416	−	0.879973i
$486$	664.645	+	89.6825i	1.36758	+	0.184532i
$487$	323.946	−	561.091i	0.665187	−	1.15214i	−0.314047	−	0.949407i	$-0.601685\pi$
$487$	323.946	−	561.091i	0.665187	−	1.15214i	0.979235	−	0.202731i	$-0.0649816\pi$
$488$	31.6342	−	18.2640i	0.0648241	−	0.0374262i
$489$	−176.169	+	13.7506i	−0.360264	+	0.0281197i
$490$	−491.980			−1.00404
$491$	150.400	+	86.8333i	0.306313	+	0.176850i	0.645275	−	0.763950i	$-0.276743\pi$
$491$	150.400	+	86.8333i	0.306313	+	0.176850i	−0.338962	+	0.940800i	$0.610076\pi$
$492$	33.9485	+	434.940i	0.0690009	+	0.884025i
$493$	21.2006	−	36.7204i	0.0430032	−	0.0744837i
$494$	251.784	+	222.697i	0.509685	+	0.450804i
$495$	−1494.29	+	234.697i	−3.01876	+	0.474136i
$496$	−135.059	−	233.929i	−0.272297	−	0.471632i
$497$		−	53.2368i		−	0.107116i
$498$	358.734	−	28.0003i	0.720350	−	0.0562256i
$499$	350.517	+	607.113i	0.702438	+	1.21666i	0.967608	+	0.252457i	$0.0812387\pi$
$499$	350.517	+	607.113i	0.702438	+	1.21666i	−0.265170	+	0.964202i	$0.585428\pi$
$500$			1141.15i			2.28229i
$501$	8.52659	+	109.241i	0.0170191	+	0.218046i
$502$	−670.246	+	1160.90i	−1.33515	+	2.31255i
$503$	507.409	+	292.953i	1.00876	+	0.582411i	0.910830	−	0.412782i	$-0.135443\pi$
$503$	507.409	+	292.953i	1.00876	+	0.582411i	0.0979351	+	0.995193i	$0.468776\pi$
$504$	−8.02292	−	51.0809i	−0.0159185	−	0.101351i
$505$	421.576	+	730.192i	0.834805	+	1.44592i
$506$	−110.250	−	63.6529i	−0.217886	−	0.125796i
$507$	−100.898	−	496.859i	−0.199010	−	0.979997i
$508$	−69.1557	−	119.781i	−0.136133	−	0.235790i
$509$	−853.491	−	492.763i	−1.67680	−	0.968100i	−0.963681	−	0.267057i	$-0.913949\pi$
$509$	−853.491	−	492.763i	−1.67680	−	0.968100i	−0.713118	−	0.701044i	$-0.752718\pi$
$510$	−256.226	+	175.856i	−0.502404	+	0.344816i
$511$	247.334	+	428.395i	0.484019	+	0.838346i
$512$		−	687.207i		−	1.34220i
$513$	−72.3111	+	242.396i	−0.140957	+	0.472506i
$514$	−32.9462	+	57.0645i	−0.0640977	+	0.111021i
$515$	−277.697	−	160.328i	−0.539218	−	0.311317i
$516$	215.041	−	450.096i	0.416747	−	0.872280i
$517$	−203.736	+	352.881i	−0.394074	+	0.682556i
$518$	615.575	+	355.402i	1.18837	+	0.686105i
$519$	482.076	+	230.320i	0.928856	+	0.443777i
$520$	−40.0285	−	119.577i	−0.0769780	−	0.229956i
$521$			483.726i			0.928456i	0.885716	+	0.464228i	$0.153668\pi$
$521$			483.726i			0.928456i	−0.885716	+	0.464228i	$0.846332\pi$
$522$	92.6683	−	240.482i	0.177526	−	0.460694i
$523$	328.154	+	568.379i	0.627445	+	1.08677i	0.988063	+	0.154053i	$0.0492326\pi$
$523$	328.154	+	568.379i	0.627445	+	1.08677i	−0.360618	+	0.932714i	$0.617434\pi$
$524$	245.774	−	141.898i	0.469034	−	0.270797i
$525$	548.067	+	798.545i	1.04394	+	1.52104i
$526$	−1307.41			−2.48558
$527$			63.4999i			0.120493i
$528$	−786.876	+	540.059i	−1.49030	+	1.02284i
$529$	−261.323	−	452.625i	−0.493995	−	0.855624i
$530$	1614.40	−	932.076i	3.04604	−	1.75863i
$531$	28.4274	+	10.9543i	0.0535355	+	0.0206296i
$532$	−184.349			−0.346521
$533$	391.465	+	346.241i	0.734456	+	0.649608i
$534$	−294.943	+	617.335i	−0.552327	+	1.15606i
$535$	811.618	−	1405.76i	1.51704	−	2.62760i
$536$	69.4043	+	40.0706i	0.129486	+	0.0747585i
$537$	−341.463	−	163.140i	−0.635871	−	0.303798i
$538$	123.499	−	213.906i	0.229552	−	0.397595i
$539$	307.595	+	177.590i	0.570678	+	0.329481i
$540$	−651.852	+	616.193i	−1.20713	+	1.14110i
$541$	−438.431			−0.810408			−0.405204	−	0.914226i	$-0.632800\pi$
$541$	−438.431			−0.810408			−0.405204	+	0.914226i	$0.632800\pi$
$542$	180.449	−	104.182i	0.332931	−	0.192218i
$543$	−127.103	−	185.192i	−0.234076	−	0.341054i
$544$	−89.4073	+	154.858i	−0.164352	+	0.284665i
$545$	−529.172	+	305.518i	−0.970958	+	0.560583i
$546$	467.442	+	352.613i	0.856122	+	0.645812i
$547$	447.046	−	774.307i	0.817270	−	1.41555i	−0.0904170	−	0.995904i	$-0.528820\pi$
$547$	447.046	−	774.307i	0.817270	−	1.41555i	0.907687	−	0.419649i	$-0.137847\pi$
$548$	−360.778	+	208.295i	−0.658354	+	0.380101i
$549$	−307.502	+	48.2972i	−0.560113	+	0.0879730i
$550$	1498.74	−	2595.90i	2.72499	−	4.71982i
$551$	84.1797	+	48.6011i	0.152776	+	0.0882054i
$552$	7.96223	−	0.621477i	0.0144243	−	0.00112586i
$553$	81.2096			0.146853
$554$	741.995	−	428.391i	1.33934	−	0.773269i
$555$	101.509	+	1300.51i	0.182898	+	2.34325i
$556$	−481.925			−0.866772
$557$	−182.429	+	105.325i	−0.327520	+	0.189094i	−0.654739	−	0.755855i	$-0.727222\pi$
$557$	−182.429	+	105.325i	−0.327520	+	0.189094i	0.327220	+	0.944948i	$0.393888\pi$
$558$	59.8858	+	381.285i	0.107322	+	0.683307i
$559$	−189.689	−	566.658i	−0.339337	−	1.01370i
$560$	752.152	+	434.255i	1.34313	+	0.775455i
$561$	223.677	−	17.4586i	0.398710	−	0.0311206i
$562$	160.136	−	277.363i	0.284939	−	0.493529i
$563$			190.847i			0.338982i	0.985532	+	0.169491i	$0.0542124\pi$
$563$			190.847i			0.338982i	−0.985532	+	0.169491i	$0.945788\pi$
$564$	18.8033	+	240.904i	0.0333393	+	0.427136i
$565$	772.803	+	1338.53i	1.36779	+	2.36909i
$566$	−1001.11	−	577.993i	−1.76875	−	1.02119i
$567$	−92.7210	+	430.753i	−0.163529	+	0.759706i
$568$	5.16811	−	8.95143i	0.00909878	−	0.0157596i
$569$		−	136.551i		−	0.239984i	−0.992775	−	0.119992i	$-0.961713\pi$
$569$		−	136.551i		−	0.239984i	0.992775	−	0.119992i	$-0.0382869\pi$
$570$	−403.141	−	587.385i	−0.707265	−	1.03050i
$571$	−117.557	−	203.615i	−0.205879	−	0.356593i	0.744533	−	0.667585i	$-0.232672\pi$
$571$	−117.557	−	203.615i	−0.205879	−	0.356593i	−0.950413	+	0.310992i	$0.899339\pi$
$572$	171.447	−	843.295i	0.299733	−	1.47429i
$573$	179.998	+	85.9969i	0.314132	+	0.150082i
$574$	−603.559			−1.05150
$575$	−129.553	+	74.7975i	−0.225310	+	0.130083i
$576$	−165.771	+	430.189i	−0.287796	+	0.746855i
$577$	−873.524			−1.51391			−0.756953	−	0.653469i	$-0.773313\pi$
$577$	−873.524			−1.51391			−0.756953	+	0.653469i	$0.773313\pi$
$578$	−650.845	+	375.766i	−1.12603	+	0.650113i
$579$	709.332	−	55.3656i	1.22510	−	0.0956228i
$580$	172.346	+	298.511i	0.297148	+	0.514675i
$581$			236.400i			0.406885i
$582$	694.350	+	331.738i	1.19304	+	0.569996i
$583$	−1345.81			−2.30842
$584$			96.0424i			0.164456i
$585$	−48.1049	+	1073.47i	−0.0822307	+	1.83499i
$586$	1435.59			2.44981
$587$		−	243.480i		−	0.414788i	−0.978258	−	0.207394i	$-0.933502\pi$
$587$		−	243.480i		−	0.414788i	0.978258	−	0.207394i	$-0.0664982\pi$
$588$	209.989	−	16.3903i	0.357124	−	0.0278746i
$589$	−145.570			−0.247148
$590$	−74.3069	+	42.9011i	−0.125944	+	0.0727138i
$591$	−183.721	−	87.7757i	−0.310864	−	0.148521i
$592$	411.525	+	712.782i	0.695143	+	1.20402i
$593$		−	80.7878i		−	0.136236i	−0.997677	−	0.0681179i	$-0.978301\pi$
$593$		−	80.7878i		−	0.136236i	0.997677	−	0.0681179i	$-0.0216994\pi$
$594$	1326.60	−	315.777i	2.23334	−	0.531611i
$595$	−102.085	−	176.817i	−0.171572	−	0.297172i
$596$			7.08150i			0.0118817i
$597$	−222.043	+	17.3312i	−0.371932	+	0.0290304i
$598$	−59.9162	+	67.7421i	−0.100194	+	0.113281i
$599$	−119.798	+	69.1655i	−0.199997	+	0.115468i	−0.596654	−	0.802499i	$-0.703504\pi$
$599$	−119.798	+	69.1655i	−0.199997	+	0.115468i	0.396657	+	0.917967i	$0.370170\pi$
$600$	14.6330	+	187.475i	0.0243884	+	0.312459i
$601$	−196.015			−0.326149			−0.163074	−	0.986614i	$-0.552141\pi$
$601$	−196.015			−0.326149			−0.163074	+	0.986614i	$0.552141\pi$
$602$	597.658	+	345.058i	0.992787	+	0.573186i
$603$	−429.091	−	531.282i	−0.711593	−	0.881064i
$604$	290.590	−	503.317i	0.481110	−	0.833307i
$605$	−1701.13	+	982.145i	−2.81178	+	1.62338i
$606$	−430.140	−	626.722i	−0.709801	−	1.03420i
$607$	−599.524			−0.987684			−0.493842	−	0.869552i	$-0.664408\pi$
$607$	−599.524			−0.987684			−0.493842	+	0.869552i	$0.664408\pi$
$608$	−355.004	−	204.961i	−0.583888	−	0.337108i
$609$	152.777	+	72.9917i	0.250865	+	0.119855i
$610$	438.337	−	759.222i	0.718585	−	1.24463i
$611$	216.824	+	191.776i	0.354868	+	0.313872i
$612$	103.505	−	83.5958i	0.169126	−	0.136594i
$613$	−65.0110	−	112.602i	−0.106054	−	0.183691i	0.808114	−	0.589026i	$-0.200488\pi$
$613$	−65.0110	−	112.602i	−0.106054	−	0.183691i	−0.914168	+	0.405335i	$0.867155\pi$
$614$			1503.08i			2.44802i
$615$	−626.789	−	913.244i	−1.01917	−	1.48495i
$616$	−52.5679	−	91.0503i	−0.0853375	−	0.147809i
$617$			471.972i			0.764946i	0.923967	+	0.382473i	$0.124928\pi$
$617$			471.972i			0.764946i	−0.923967	+	0.382473i	$0.875072\pi$
$618$	260.842	+	124.622i	0.422075	+	0.201653i
$619$	518.078	−	897.338i	0.836960	−	1.44966i	−0.0554648	−	0.998461i	$-0.517664\pi$
$619$	518.078	−	897.338i	0.836960	−	1.44966i	0.892425	−	0.451196i	$-0.149003\pi$
$620$	−447.050	−	258.105i	−0.721049	−	0.416298i
$621$	−65.2161	−	19.4552i	−0.105018	−	0.0313288i
$622$	−328.110	−	568.303i	−0.527508	−	0.913671i
$623$	−389.272	−	224.746i	−0.624835	−	0.360749i
$624$	264.595	+	624.223i	0.424031	+	1.00036i
$625$	−706.787	−	1224.19i	−1.13086	−	1.95871i
$626$	−445.987	−	257.491i	−0.712439	−	0.411327i
$627$	40.0230	+	512.766i	0.0638326	+	0.817809i
$628$	−393.518	−	681.593i	−0.626621	−	1.08534i
$629$		−	193.484i		−	0.307606i
$630$	−779.726	−	965.424i	−1.23766	−	1.53242i
$631$	50.5861	−	87.6176i	0.0801681	−	0.138855i	−0.823154	−	0.567818i	$-0.807788\pi$
$631$	50.5861	−	87.6176i	0.0801681	−	0.138855i	0.903322	+	0.428963i	$0.141121\pi$
$632$	13.6549	+	7.88365i	0.0216058	+	0.0124741i
$633$	338.866	−	26.4495i	0.535333	−	0.0417844i
$634$	−309.953	+	536.855i	−0.488886	+	0.846775i
$635$	304.117	+	175.582i	0.478924	+	0.276507i
$636$	−658.014	+	451.616i	−1.03461	+	0.710088i
$637$	167.165	−	188.999i	0.262425	−	0.296702i
$638$		−	524.019i		−	0.821346i
$639$	−68.5222	+	55.3420i	−0.107233	+	0.0866072i
$640$	154.489	+	267.582i	0.241388	+	0.418097i
$641$	760.261	−	438.937i	1.18605	−	0.684769i	0.228647	−	0.973509i	$-0.426570\pi$
$641$	760.261	−	438.937i	1.18605	−	0.684769i	0.957407	+	0.288741i	$0.0932366\pi$
$642$	−630.864	+	1320.44i	−0.982654	+	2.05676i
$643$	988.379			1.53714			0.768568	−	0.639768i	$-0.220969\pi$
$643$	988.379			1.53714			0.768568	+	0.639768i	$0.220969\pi$
$644$		−	49.5987i		−	0.0770167i
$645$	98.5540	+	1262.65i	0.152797	+	1.95760i
$646$	52.8348	+	91.5126i	0.0817876	+	0.141660i
$647$	292.366	−	168.797i	0.451879	−	0.260892i	−0.256744	−	0.966479i	$-0.582650\pi$
$647$	292.366	−	168.797i	0.451879	−	0.260892i	0.708623	+	0.705587i	$0.249317\pi$
$648$	−57.4070	+	63.4273i	−0.0885911	+	0.0978816i
$649$	61.9442			0.0954456
$650$	−1595.03	−	1410.76i	−2.45389	−	2.17040i
$651$	−252.801	+	19.7319i	−0.388328	+	0.0303102i
$652$	−106.533	+	184.521i	−0.163395	+	0.283008i
$653$	399.414	+	230.602i	0.611660	+	0.353142i	0.773615	−	0.633656i	$-0.218447\pi$
$653$	399.414	+	230.602i	0.611660	+	0.353142i	−0.161955	+	0.986798i	$0.551780\pi$
$654$	454.187	−	311.723i	0.694476	−	0.476641i
$655$	−360.269	+	624.004i	−0.550029	+	0.952678i
$656$	−605.238	−	349.434i	−0.922619	−	0.532674i
$657$	294.281	−	763.683i	0.447916	−	1.16238i
$658$	−334.299			−0.508053
$659$	642.759	−	371.097i	0.975355	−	0.563122i	0.0744906	−	0.997222i	$-0.476267\pi$
$659$	642.759	−	371.097i	0.975355	−	0.563122i	0.900865	+	0.434100i	$0.142934\pi$
$660$	−786.254	+	1645.69i	−1.19129	+	2.49346i
$661$	290.932	−	503.908i	0.440139	−	0.762342i	−0.557561	−	0.830136i	$-0.688263\pi$
$661$	290.932	−	503.908i	0.440139	−	0.762342i	0.997699	+	0.0677937i	$0.0215960\pi$
$662$	−218.460	+	126.128i	−0.330001	+	0.190526i
$663$	19.5036	−	158.184i	0.0294172	−	0.238589i
$664$	−22.9492	+	39.7492i	−0.0345621	+	0.0598633i
$665$	405.344	−	234.025i	0.609539	−	0.351918i
$666$	−182.472	−	1161.78i	−0.273982	−	1.74441i
$667$	−13.0760	+	22.6484i	−0.0196043	+	0.0339556i
$668$	114.420	+	66.0603i	0.171287	+	0.0988927i
$669$	227.467	+	331.423i	0.340010	+	0.495401i
$670$	1923.39			2.87074
$671$	−548.114	+	316.454i	−0.816861	+	0.471615i
$672$	−644.292	−	307.822i	−0.958768	−	0.458068i
$673$	−678.859			−1.00871			−0.504353	−	0.863498i	$-0.668269\pi$
$673$	−678.859			−1.00871			−0.504353	+	0.863498i	$0.668269\pi$
$674$	−1445.60	+	834.615i	−2.14480	+	1.23830i
$675$	458.083	−	1535.55i	0.678641	−	2.27489i
$676$	−562.798	−	238.708i	−0.832541	−	0.353118i
$677$	332.591	+	192.021i	0.491271	+	0.283636i	0.725102	−	0.688642i	$-0.241793\pi$
$677$	332.591	+	192.021i	0.491271	+	0.283636i	−0.233830	+	0.972277i	$0.575126\pi$
$678$	−788.501	−	1148.86i	−1.16298	−	1.69449i
$679$	−252.784	+	437.835i	−0.372289	+	0.644824i
$680$		−	39.6409i		−	0.0582954i
$681$	−88.3098	−	42.1915i	−0.129677	−	0.0619552i
$682$	392.385	+	679.631i	0.575345	+	0.996526i
$683$	−793.380	−	458.058i	−1.16161	−	0.670656i	−0.209921	−	0.977718i	$-0.567321\pi$
$683$	−793.380	−	458.058i	−1.16161	−	0.670656i	−0.951689	+	0.307062i	$0.900654\pi$
$684$	191.639	+	237.279i	0.280174	+	0.346900i
$685$	528.849	−	915.993i	0.772042	−	1.33722i
$686$			1027.06i			1.49717i
$687$	−289.951	+	606.887i	−0.422053	+	0.883388i
$688$	399.547	+	692.036i	0.580737	+	1.00587i
$689$	−190.476	+	936.890i	−0.276453	+	1.35978i
$690$	158.035	−	108.464i	0.229036	−	0.157195i
$691$	90.8448			0.131469			0.0657343	−	0.997837i	$-0.479061\pi$
$691$	90.8448			0.131469			0.0657343	+	0.997837i	$0.479061\pi$
$692$	557.902	−	322.105i	0.806217	−	0.465470i
$693$	139.010	+	885.060i	0.200592	+	1.27714i
$694$	−1413.68			−2.03701
$695$	1059.65	−	611.789i	1.52468	−	0.880272i
$696$	18.6026	+	27.1043i	0.0267278	+	0.0389430i
$697$	82.1456	+	142.280i	0.117856	+	0.204133i
$698$			327.388i			0.469037i
$699$	841.601	−	577.618i	1.20401	−	0.826349i
$700$	1167.83			1.66833
$701$		−	905.030i		−	1.29106i	−0.763737	−	0.645528i	$-0.776638\pi$
$701$		−	905.030i		−	1.29106i	0.763737	−	0.645528i	$-0.223362\pi$
$702$	−32.0717	−	968.212i	−0.0456862	−	1.37922i
$703$	443.552			0.630941
$704$			937.396i			1.33153i
$705$	−347.165	−	505.827i	−0.492433	−	0.717485i
$706$	−1000.07			−1.41653
$707$	432.490	−	249.698i	0.611725	−	0.353180i
$708$	30.2867	−	20.7868i	0.0427779	−	0.0293598i
$709$	−469.965	−	814.004i	−0.662857	−	1.14810i	−0.979862	−	0.199677i	$-0.936011\pi$
$709$	−469.965	−	814.004i	−0.662857	−	1.14810i	0.317005	−	0.948424i	$-0.397323\pi$
$710$		−	248.070i		−	0.349394i
$711$	−84.4210	−	104.527i	−0.118736	−	0.147013i
$712$	−43.6358	−	75.5794i	−0.0612862	−	0.106151i
$713$		−	39.1653i		−	0.0549304i
$714$	104.159	+	151.762i	0.145881	+	0.212551i
$715$	693.561	+	2071.87i	0.970015	+	2.89772i
$716$	−395.172	+	228.152i	−0.551916	+	0.318649i
$717$	105.157	+	50.2406i	0.146663	+	0.0700706i
$718$	656.874			0.914866
$719$	−623.182	−	359.794i	−0.866734	−	0.500409i	−0.000472449	−	1.00000i	$-0.500150\pi$
$719$	−623.182	−	359.794i	−0.866734	−	0.500409i	−0.866262	+	0.499591i	$0.833484\pi$
$720$	−222.957	−	1419.54i	−0.309662	−	1.97158i
$721$	−94.9620	+	164.479i	−0.131709	+	0.228126i
$722$	653.070	−	377.050i	0.904529	−	0.522230i
$723$	58.0939	−	121.595i	0.0803511	−	0.168181i
$724$	−270.834			−0.374080
$725$	−533.269	−	307.883i	−0.735543	−	0.424666i
$726$	1460.07	−	1002.09i	2.01112	−	1.38030i
$727$	−346.337	+	599.874i	−0.476392	+	0.825136i	−0.999634	−	0.0270484i	$-0.991389\pi$
$727$	−346.337	+	599.874i	−0.476392	+	0.825136i	0.523242	+	0.852184i	$0.324723\pi$
$728$	−70.8251	+	23.7088i	−0.0972872	+	0.0325670i
$729$	650.819	−	328.444i	0.892756	−	0.450541i
$730$	1152.51	+	1996.21i	1.57878	+	2.73453i
$731$		−	187.852i		−	0.256980i
$732$	−161.799	+	338.658i	−0.221037	+	0.462647i
$733$	−135.599	−	234.864i	−0.184992	−	0.320415i	0.758582	−	0.651578i	$-0.225893\pi$
$733$	−135.599	−	234.864i	−0.184992	−	0.320415i	−0.943574	+	0.331162i	$0.892559\pi$
$734$			869.174i			1.18416i
$735$	−440.913	+	302.613i	−0.599882	+	0.411718i
$736$	55.1445	−	95.5131i	0.0749246	−	0.129773i
$737$	−1202.54	−	694.289i	−1.63167	−	0.942047i
$738$	627.427	+	776.853i	0.850171	+	1.05265i
$739$	−289.204	−	500.916i	−0.391345	−	0.677830i	0.601282	−	0.799037i	$-0.294657\pi$
$739$	−289.204	−	500.916i	−0.391345	−	0.677830i	−0.992627	+	0.121207i	$0.961323\pi$
$740$	1362.16	+	786.444i	1.84076	+	1.06276i
$741$	362.629	+	44.7110i	0.489378	+	0.0603388i
$742$	−552.065	−	956.204i	−0.744023	−	1.28869i
$743$	1224.51	+	706.972i	1.64806	+	0.951510i	0.977841	+	0.209351i	$0.0671351\pi$
$743$	1224.51	+	706.972i	1.64806	+	0.951510i	0.670223	+	0.742159i	$0.266198\pi$
$744$	−44.4224	−	21.2236i	−0.0597076	−	0.0285263i
$745$	−8.98975	−	15.5707i	−0.0120668	−	0.0209003i
$746$		−	151.767i		−	0.203441i
$747$	304.276	−	245.749i	0.407330	−	0.328981i
$748$	135.262	−	234.281i	0.180832	−	0.313209i
$749$	−832.629	−	480.719i	−1.11165	−	0.641814i
$750$	1478.07	+	2153.58i	1.97077	+	2.87145i
$751$	−339.578	+	588.167i	−0.452168	+	0.783178i	−0.998520	−	0.0543771i	$-0.982683\pi$
$751$	−339.578	+	588.167i	−0.452168	+	0.783178i	0.546352	+	0.837556i	$0.316016\pi$
$752$	−335.229	−	193.544i	−0.445783	−	0.257373i
$753$	113.385	+	1452.66i	0.150578	+	1.92917i
$754$	−364.798	−	74.1658i	−0.483817	−	0.0983631i
$755$			1475.58i			1.95441i
$756$	364.969	+	386.090i	0.482763	+	0.510701i
$757$	−46.7179	−	80.9178i	−0.0617146	−	0.106893i	0.833517	−	0.552493i	$-0.186324\pi$
$757$	−46.7179	−	80.9178i	−0.0617146	−	0.106893i	−0.895232	+	0.445601i	$0.852990\pi$
$758$	618.229	−	356.935i	0.815606	−	0.470890i
$759$	−137.959	+	10.7681i	−0.181764	+	0.0141872i
$760$	90.8746			0.119572
$761$		−	1082.76i		−	1.42281i	−0.702781	−	0.711406i	$-0.748059\pi$
$761$		−	1082.76i		−	1.42281i	0.702781	−	0.711406i	$-0.251941\pi$
$762$	−285.659	−	136.478i	−0.374880	−	0.179105i
$763$	180.957	+	313.427i	0.237165	+	0.410782i
$764$	208.310	−	120.268i	0.272657	−	0.157418i
$765$	−121.463	+	315.205i	−0.158775	+	0.412033i
$766$	−810.933			−1.05866
$767$	8.76713	−	43.1227i	0.0114304	−	0.0562226i
$768$	−505.468	−	736.478i	−0.658162	−	0.958955i
$769$	−693.040	+	1200.38i	−0.901222	+	1.56096i	−0.0753122	+	0.997160i	$0.523995\pi$
$769$	−693.040	+	1200.38i	−0.901222	+	1.56096i	−0.825910	+	0.563802i	$0.809338\pi$

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-2.75995i q^{2} +(-1.69762 - 2.47347i) q^{3} -3.61733 q^{4} +(7.95372 - 4.59208i) q^{5} +(-6.82666 + 4.68536i) q^{6} +(-2.71987 - 4.71096i) q^{7} -1.05616i q^{8} +(-3.23614 + 8.39806i) q^{9} +(-12.6739 - 21.9519i) q^{10} +18.2997i q^{11} +(6.14086 + 8.94736i) q^{12} +(12.7394 + 2.59000i) q^{13} +(-13.0020 + 7.50672i) q^{14} +(-24.8608 - 11.8777i) q^{15} -17.3843 q^{16} +(3.53920 + 2.04336i) q^{17} +(23.1782 + 8.93159i) q^{18} +(-4.68429 + 8.11343i) q^{19} +(-28.7712 + 16.6111i) q^{20} +(-7.03511 + 14.7250i) q^{21} +50.5062 q^{22} +(-2.18290 - 1.26030i) q^{23} +(-2.61238 + 1.79296i) q^{24} +(29.6745 - 51.3977i) q^{25} +(7.14827 - 35.1601i) q^{26} +(26.2661 - 6.25224i) q^{27} +(9.83868 + 17.0411i) q^{28} -10.3753i q^{29} +(-32.7818 + 68.6147i) q^{30} +(7.76905 + 13.4564i) q^{31} +43.7550i q^{32} +(45.2637 - 31.0660i) q^{33} +(5.63957 - 9.76803i) q^{34} +(-43.2663 - 24.9798i) q^{35} +(11.7062 - 30.3785i) q^{36} +(-23.6723 - 41.0016i) q^{37} +(22.3927 + 12.9284i) q^{38} +(-15.2204 - 35.9074i) q^{39} +(-4.84996 - 8.40038i) q^{40} +(34.8153 + 20.1006i) q^{41} +(40.6402 + 19.4166i) q^{42} +(-22.9833 - 39.8082i) q^{43} -66.1959i q^{44} +(12.8252 + 81.6565i) q^{45} +(-3.47837 + 6.02471i) q^{46} +(19.2835 + 11.1333i) q^{47} +(29.5119 + 42.9995i) q^{48} +(9.70457 - 16.8088i) q^{49} +(-141.855 - 81.9001i) q^{50} +(-0.954042 - 12.2230i) q^{51} +(-46.0825 - 9.36888i) q^{52} +73.5428i q^{53} +(-17.2559 - 72.4932i) q^{54} +(84.0336 + 145.550i) q^{55} +(-4.97552 + 2.87262i) q^{56} +(28.0205 - 2.18709i) q^{57} -28.6354 q^{58} -3.38499i q^{59} +(89.9298 + 42.9655i) q^{60} +(17.2929 + 29.9521i) q^{61} +(37.1390 - 21.4422i) q^{62} +(48.3648 - 7.59633i) q^{63} +51.2248 q^{64} +(113.219 - 37.9002i) q^{65} +(-85.7405 - 124.926i) q^{66} +(-37.9400 + 65.7140i) q^{67} +(-12.8025 - 7.39150i) q^{68} +(0.588432 + 7.53887i) q^{69} +(-68.9430 + 119.413i) q^{70} +(8.47547 + 4.89331i) q^{71} +(8.86967 + 3.41787i) q^{72} -90.9357 q^{73} +(-113.162 + 65.3343i) q^{74} +(-177.507 + 13.8550i) q^{75} +(16.9446 - 29.3489i) q^{76} +(86.2090 - 49.7728i) q^{77} +(-99.1026 + 42.0075i) q^{78} +(-7.46446 + 12.9288i) q^{79} +(-138.270 + 79.8300i) q^{80} +(-60.0548 - 54.3546i) q^{81} +(55.4767 - 96.0885i) q^{82} +(-37.6357 - 21.7290i) q^{83} +(25.4483 - 53.2651i) q^{84} +37.5331 q^{85} +(-109.869 + 63.4327i) q^{86} +(-25.6631 + 17.6134i) q^{87} +19.3273 q^{88} +(71.5607 - 41.3156i) q^{89} +(225.368 - 35.3970i) q^{90} +(-22.4481 - 67.0592i) q^{91} +(7.89628 + 4.55892i) q^{92} +(20.0951 - 42.0604i) q^{93} +(30.7274 - 53.2214i) q^{94} +86.0427i q^{95} +(108.227 - 74.2796i) q^{96} +(-46.4699 - 80.4881i) q^{97} +(-46.3915 - 26.7841i) q^{98} +(-153.682 - 59.2203i) 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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