LMFDB - Embedded newform 117.3.n.a.38.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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, 3]))

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

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (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			38.1
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.92341 + 3.33144i) q^{2} +(-2.97788 - 0.363638i) q^{3} +(-5.39901 - 9.35136i) q^{4} +(0.506509 + 0.877299i) q^{5} +(6.93912 - 9.22121i) q^{6} +(-3.89680 - 2.24982i) q^{7} +26.1508 q^{8} +(8.73553 + 2.16574i) q^{9} -3.89690 q^{10} +(-3.37167 + 5.83991i) q^{11} +(12.6771 + 29.8105i) q^{12} +(7.71724 - 10.4616i) q^{13} +(14.9903 - 8.65465i) q^{14} +(-1.18930 - 2.79668i) q^{15} +(-28.7026 + 49.7144i) q^{16} -18.4481i q^{17} +(-24.0171 + 24.9363i) q^{18} +14.8495i q^{19} +(5.46929 - 9.47309i) q^{20} +(10.7861 + 8.11671i) q^{21} +(-12.9702 - 22.4651i) q^{22} +(24.0204 - 13.8682i) q^{23} +(-77.8739 - 9.50942i) q^{24} +(11.9869 - 20.7619i) q^{25} +(20.0087 + 45.8314i) q^{26} +(-25.2258 - 9.62589i) q^{27} +48.5872i q^{28} +(34.1695 + 19.7278i) q^{29} +(11.6045 + 1.41706i) q^{30} +(11.4179 - 6.59210i) q^{31} +(-58.1123 - 100.653i) q^{32} +(12.1641 - 16.1645i) q^{33} +(61.4590 + 35.4833i) q^{34} -4.55821i q^{35} +(-26.9106 - 93.3820i) q^{36} -73.8784i q^{37} +(-49.4702 - 28.5616i) q^{38} +(-26.7852 + 28.3470i) q^{39} +(13.2456 + 22.9420i) q^{40} +(-19.9812 - 34.6085i) q^{41} +(-47.7864 + 20.3215i) q^{42} +(19.0890 - 33.0631i) q^{43} +72.8148 q^{44} +(2.52462 + 8.76064i) q^{45} +106.697i q^{46} +(-24.2966 + 42.0829i) q^{47} +(103.551 - 137.606i) q^{48} +(-14.3766 - 24.9011i) q^{49} +(46.1114 + 79.8674i) q^{50} +(-6.70845 + 54.9364i) q^{51} +(-139.495 - 15.6846i) q^{52} +37.8047i q^{53} +(80.5877 - 65.5239i) q^{54} -6.83113 q^{55} +(-101.904 - 58.8345i) q^{56} +(5.39983 - 44.2199i) q^{57} +(-131.444 + 75.8892i) q^{58} +(1.97579 + 3.42217i) q^{59} +(-19.7317 + 26.2209i) q^{60} +(-23.6710 + 40.9993i) q^{61} +50.7172i q^{62} +(-29.1681 - 28.0928i) q^{63} +217.474 q^{64} +(13.0868 + 1.47145i) q^{65} +(30.4546 + 71.6148i) q^{66} +(25.4206 - 14.6766i) q^{67} +(-172.515 + 99.6018i) q^{68} +(-76.5729 + 32.5631i) q^{69} +(15.1854 + 8.76731i) q^{70} -103.246 q^{71} +(228.441 + 56.6358i) q^{72} -11.8258i q^{73} +(246.122 + 142.098i) q^{74} +(-43.2454 + 57.4676i) q^{75} +(138.863 - 80.1725i) q^{76} +(26.2775 - 15.1713i) q^{77} +(-42.9174 - 143.756i) q^{78} +(41.1555 - 71.2835i) q^{79} -58.1525 q^{80} +(71.6191 + 37.8378i) q^{81} +153.728 q^{82} +(32.9652 - 57.0974i) q^{83} +(17.6682 - 144.687i) q^{84} +(16.1845 - 9.34415i) q^{85} +(73.4320 + 127.188i) q^{86} +(-94.5789 - 71.1723i) q^{87} +(-88.1719 + 152.718i) q^{88} -30.6014 q^{89} +(-34.0415 - 8.43967i) q^{90} +(-53.6091 + 23.4042i) q^{91} +(-259.373 - 149.749i) q^{92} +(-36.3981 + 15.4785i) q^{93} +(-93.4645 - 161.885i) q^{94} +(-13.0274 + 7.52138i) q^{95} +(136.450 + 320.865i) q^{96} +(104.555 + 60.3648i) q^{97} +110.609 q^{98} +(-42.1011 + 43.7126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

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

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

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 $

$2$	−1.92341	+	3.33144i	−0.961705	+	1.66572i	−0.243487	+	0.969904i	$0.578291\pi$
$2$	−1.92341	+	3.33144i	−0.961705	+	1.66572i	−0.718218	+	0.695818i	$0.755042\pi$
$3$	−2.97788	−	0.363638i	−0.992627	−	0.121213i
$3$	−2.97788	−	0.363638i	−0.992627	−	0.121213i
$4$	−5.39901	−	9.35136i	−1.34975	−	2.33784i
$5$	0.506509	+	0.877299i	0.101302	+	0.175460i	0.912221	−	0.409698i	$-0.134366\pi$
$5$	0.506509	+	0.877299i	0.101302	+	0.175460i	−0.810919	+	0.585158i	$0.801033\pi$
$6$	6.93912	−	9.22121i	1.15652	−	1.53687i
$7$	−3.89680	−	2.24982i	−0.556686	−	0.321403i	0.195128	−	0.980778i	$-0.437488\pi$
$7$	−3.89680	−	2.24982i	−0.556686	−	0.321403i	−0.751814	+	0.659375i	$0.770821\pi$
$8$	26.1508			3.26885
$9$	8.73553	+	2.16574i	0.970615	+	0.240638i
$10$	−3.89690			−0.389690
$11$	−3.37167	+	5.83991i	−0.306516	+	0.530901i	−0.977598	−	0.210482i	$-0.932497\pi$
$11$	−3.37167	+	5.83991i	−0.306516	+	0.530901i	0.671082	+	0.741383i	$0.265830\pi$
$12$	12.6771	+	29.8105i	1.05642	+	2.48421i
$13$	7.71724	−	10.4616i	0.593634	−	0.804735i
$13$	7.71724	−	10.4616i	0.593634	−	0.804735i
$14$	14.9903	−	8.65465i	1.07073	−	0.618189i
$15$	−1.18930	−	2.79668i	−0.0792868	−	0.186445i
$16$	−28.7026	+	49.7144i	−1.79391	+	3.10715i
$17$		−	18.4481i		−	1.08519i	−0.839996	−	0.542593i	$-0.817443\pi$
$17$		−	18.4481i		−	1.08519i	0.839996	−	0.542593i	$-0.182557\pi$
$18$	−24.0171	+	24.9363i	−1.33428	+	1.38535i
$19$			14.8495i			0.781551i	0.920486	+	0.390775i	$0.127793\pi$
$19$			14.8495i			0.781551i	−0.920486	+	0.390775i	$0.872207\pi$
$20$	5.46929	−	9.47309i	0.273465	−	0.473655i
$21$	10.7861	+	8.11671i	0.513623	+	0.386510i
$22$	−12.9702	−	22.4651i	−0.589556	−	1.02114i
$23$	24.0204	−	13.8682i	1.04437	−	0.602965i	0.123299	−	0.992370i	$-0.460652\pi$
$23$	24.0204	−	13.8682i	1.04437	−	0.602965i	0.921067	+	0.389404i	$0.127319\pi$
$24$	−77.8739	−	9.50942i	−3.24474	−	0.396226i
$25$	11.9869	−	20.7619i	0.479476	−	0.830477i
$26$	20.0087	+	45.8314i	0.769565	+	1.76275i
$27$	−25.2258	−	9.62589i	−0.934290	−	0.356515i
$28$			48.5872i			1.73526i
$29$	34.1695	+	19.7278i	1.17826	+	0.680268i	0.955611	−	0.294631i	$-0.0951966\pi$
$29$	34.1695	+	19.7278i	1.17826	+	0.680268i	0.222648	+	0.974899i	$0.428530\pi$
$30$	11.6045	+	1.41706i	0.386816	+	0.0472353i
$31$	11.4179	−	6.59210i	0.368318	−	0.212648i	−0.304406	−	0.952543i	$-0.598458\pi$
$31$	11.4179	−	6.59210i	0.368318	−	0.212648i	0.672723	+	0.739894i	$0.265124\pi$
$32$	−58.1123	−	100.653i	−1.81601	−	3.14542i
$33$	12.1641	−	16.1645i	0.368608	−	0.489833i
$34$	61.4590	+	35.4833i	1.80762	+	1.04363i
$35$		−	4.55821i		−	0.130235i
$36$	−26.9106	−	93.3820i	−0.747517	−	2.59395i
$37$		−	73.8784i		−	1.99671i	−0.0573005	−	0.998357i	$-0.518249\pi$
$37$		−	73.8784i		−	1.99671i	0.0573005	−	0.998357i	$-0.481751\pi$
$38$	−49.4702	−	28.5616i	−1.30185	−	0.751622i
$39$	−26.7852	+	28.3470i	−0.686801	+	0.726846i
$40$	13.2456	+	22.9420i	0.331140	+	0.573551i
$41$	−19.9812	−	34.6085i	−0.487346	−	0.844109i	0.512548	−	0.858659i	$-0.328702\pi$
$41$	−19.9812	−	34.6085i	−0.487346	−	0.844109i	−0.999894	+	0.0145501i	$0.995368\pi$
$42$	−47.7864	+	20.3215i	−1.13777	+	0.483844i
$43$	19.0890	−	33.0631i	0.443930	−	0.768910i	−0.554047	−	0.832486i	$-0.686917\pi$
$43$	19.0890	−	33.0631i	0.443930	−	0.768910i	0.997977	+	0.0635757i	$0.0202504\pi$
$44$	72.8148			1.65488
$45$	2.52462	+	8.76064i	0.0561027	+	0.194681i
$46$			106.697i			2.31950i
$47$	−24.2966	+	42.0829i	−0.516948	+	0.895381i	0.482858	+	0.875699i	$0.339599\pi$
$47$	−24.2966	+	42.0829i	−0.516948	+	0.895381i	−0.999806	+	0.0196821i	$0.993735\pi$
$48$	103.551	−	137.606i	2.15731	−	2.86679i
$49$	−14.3766	−	24.9011i	−0.293401	−	0.508185i
$50$	46.1114	+	79.8674i	0.922229	+	1.59735i
$51$	−6.70845	+	54.9364i	−0.131538	+	1.07718i
$52$	−139.495	−	15.6846i	−2.68260	−	0.301627i
$53$			37.8047i			0.713297i	0.934239	+	0.356648i	$0.116081\pi$
$53$			37.8047i			0.713297i	−0.934239	+	0.356648i	$0.883919\pi$
$54$	80.5877	−	65.5239i	1.49237	−	1.21341i
$55$	−6.83113			−0.124202
$56$	−101.904	−	58.8345i	−1.81972	−	1.05062i
$57$	5.39983	−	44.2199i	0.0947339	−	0.775788i
$58$	−131.444	+	75.8892i	−2.26628	+	1.30843i
$59$	1.97579	+	3.42217i	0.0334879	+	0.0580028i	0.882284	−	0.470718i	$-0.156005\pi$
$59$	1.97579	+	3.42217i	0.0334879	+	0.0580028i	−0.848796	+	0.528721i	$0.822672\pi$
$60$	−19.7317	+	26.2209i	−0.328861	+	0.437015i
$61$	−23.6710	+	40.9993i	−0.388048	+	0.672120i	−0.992187	−	0.124760i	$-0.960184\pi$
$61$	−23.6710	+	40.9993i	−0.388048	+	0.672120i	0.604139	+	0.796879i	$0.293517\pi$
$62$			50.7172i			0.818020i
$63$	−29.1681	−	28.0928i	−0.462986	−	0.445918i
$64$	217.474			3.39803
$65$	13.0868	+	1.47145i	0.201335	+	0.0226377i
$66$	30.4546	+	71.6148i	0.461433	+	1.08507i
$67$	25.4206	−	14.6766i	0.379412	−	0.219054i	−0.298150	−	0.954519i	$-0.596370\pi$
$67$	25.4206	−	14.6766i	0.379412	−	0.219054i	0.677563	+	0.735465i	$0.263036\pi$
$68$	−172.515	+	99.6018i	−2.53699	+	1.46473i
$69$	−76.5729	+	32.5631i	−1.10975	+	0.471929i
$70$	15.1854	+	8.76731i	0.216935	+	0.125247i
$71$	−103.246			−1.45418			−0.727088	−	0.686545i	$-0.759127\pi$
$71$	−103.246			−1.45418			−0.727088	+	0.686545i	$0.759127\pi$
$72$	228.441	+	56.6358i	3.17279	+	0.786609i
$73$		−	11.8258i		−	0.161998i	−0.996714	−	0.0809989i	$-0.974189\pi$
$73$		−	11.8258i		−	0.161998i	0.996714	−	0.0809989i	$-0.0258110\pi$
$74$	246.122	+	142.098i	3.32597	+	1.92025i
$75$	−43.2454	+	57.4676i	−0.576605	+	0.766235i
$76$	138.863	−	80.1725i	1.82714	−	1.05490i
$77$	26.2775	−	15.1713i	0.341266	−	0.197030i
$78$	−42.9174	−	143.756i	−0.550223	−	1.84303i
$79$	41.1555	−	71.2835i	0.520956	−	0.902323i	−0.478747	−	0.877953i	$-0.658909\pi$
$79$	41.1555	−	71.2835i	0.520956	−	0.902323i	0.999703	−	0.0243696i	$-0.00775787\pi$
$80$	−58.1525			−0.726906
$81$	71.6191	+	37.8378i	0.884187	+	0.467134i
$82$	153.728			1.87473
$83$	32.9652	−	57.0974i	0.397171	−	0.687921i	−0.596204	−	0.802833i	$-0.703325\pi$
$83$	32.9652	−	57.0974i	0.397171	−	0.687921i	0.993376	+	0.114912i	$0.0366585\pi$
$84$	17.6682	−	144.687i	0.210335	−	1.72246i
$85$	16.1845	−	9.34415i	0.190406	−	0.109931i
$86$	73.4320	+	127.188i	0.853860	+	1.47893i
$87$	−94.5789	−	71.1723i	−1.08711	−	0.818072i
$88$	−88.1719	+	152.718i	−1.00195	+	1.73543i
$89$	−30.6014			−0.343836			−0.171918	−	0.985111i	$-0.554996\pi$
$89$	−30.6014			−0.343836			−0.171918	+	0.985111i	$0.554996\pi$
$90$	−34.0415	−	8.43967i	−0.378238	−	0.0937741i
$91$	−53.6091	+	23.4042i	−0.589112	+	0.257189i
$92$	−259.373	−	149.749i	−2.81927	−	1.62771i
$93$	−36.3981	+	15.4785i	−0.391378	+	0.166436i
$94$	−93.4645	−	161.885i	−0.994304	−	1.72218i
$95$	−13.0274	+	7.52138i	−0.137131	+	0.0791725i
$96$	136.450	+	320.865i	1.42135	+	3.34235i
$97$	104.555	+	60.3648i	1.07789	+	0.622317i	0.930325	−	0.366736i	$-0.119525\pi$
$97$	104.555	+	60.3648i	1.07789	+	0.622317i	0.147560	+	0.989053i	$0.452858\pi$
$98$	110.609			1.12866
$99$	−42.1011	+	43.7126i	−0.425264	+	0.441541i
$100$	−258.870			−2.58870
$101$	56.9277	+	32.8672i	0.563641	+	0.325418i	0.754605	−	0.656179i	$-0.227828\pi$
$101$	56.9277	+	32.8672i	0.563641	+	0.325418i	−0.190965	+	0.981597i	$0.561162\pi$
$102$	−170.114	−	128.014i	−1.66779	−	1.25504i
$103$	26.6752	+	46.2028i	0.258983	+	0.448571i	0.965970	−	0.258656i	$-0.0832795\pi$
$103$	26.6752	+	46.2028i	0.258983	+	0.448571i	−0.706987	+	0.707226i	$0.749946\pi$
$104$	201.812	−	273.578i	1.94050	−	2.63056i
$105$	−1.65754	+	13.5738i	−0.0157861	+	0.129274i
$106$	−125.944	−	72.7140i	−1.18815	−	0.685981i
$107$		−	61.8963i		−	0.578470i	−0.957258	−	0.289235i	$-0.906599\pi$
$107$		−	61.8963i		−	0.578470i	0.957258	−	0.289235i	$-0.0934009\pi$
$108$	46.1793	+	287.866i	0.427586	+	2.66543i
$109$		−	119.514i		−	1.09646i	−0.836328	−	0.548229i	$-0.815302\pi$
$109$		−	119.514i		−	1.09646i	0.836328	−	0.548229i	$-0.184698\pi$
$110$	13.1391	−	22.7575i	0.119446	−	0.206887i
$111$	−26.8650	+	220.001i	−0.242027	+	1.98199i
$112$	223.697	−	129.151i	1.99729	−	1.15314i
$113$	3.79467	−	2.19086i	0.0335812	−	0.0193881i	−0.483115	−	0.875557i	$-0.660495\pi$
$113$	3.79467	−	2.19086i	0.0335812	−	0.0193881i	0.516697	+	0.856169i	$0.327162\pi$
$114$	136.930	+	103.042i	1.20114	+	0.903880i
$115$	24.3331	+	14.0487i	0.211592	+	0.122163i
$116$		−	426.042i		−	3.67278i
$117$	90.0712	−	74.6738i	0.769840	−	0.638237i
$118$	−15.2010			−0.128822
$119$	−41.5050	+	71.8887i	−0.348781	+	0.604107i
$120$	−31.1012	−	73.1352i	−0.259177	−	0.609460i
$121$	37.7636	+	65.4085i	0.312096	+	0.540566i
$122$	−91.0579	−	157.717i	−0.746376	−	1.29276i
$123$	46.9167	+	110.326i	0.381436	+	0.896957i
$124$	−123.290	−	71.1817i	−0.994276	−	0.574046i
$125$	49.6113			0.396890
$126$	149.692	−	43.1379i	1.18803	−	0.342364i
$127$	−163.905			−1.29059			−0.645296	−	0.763932i	$-0.723266\pi$
$127$	−163.905			−1.29059			−0.645296	+	0.763932i	$0.723266\pi$
$128$	−185.842	+	321.888i	−1.45189	+	2.51475i
$129$	−68.8678	+	91.5165i	−0.533859	+	0.709430i
$130$	−30.0733	+	40.7676i	−0.231333	+	0.313597i
$131$	55.1719	−	31.8535i	0.421160	−	0.243157i	−0.274414	−	0.961612i	$-0.588484\pi$
$131$	55.1719	−	31.8535i	0.421160	−	0.243157i	0.695573	+	0.718455i	$0.255150\pi$
$132$	−216.834	−	26.4783i	−1.64268	−	0.200593i
$133$	33.4086	−	57.8654i	0.251193	−	0.435078i
$134$			112.917i			0.842661i
$135$	−4.33231	−	27.0062i	−0.0320912	−	0.200046i
$136$		−	482.433i		−	3.54730i
$137$	−6.08455	+	10.5388i	−0.0444128	+	0.0769252i	−0.887377	−	0.461044i	$-0.847475\pi$
$137$	−6.08455	+	10.5388i	−0.0444128	+	0.0769252i	0.842964	+	0.537969i	$0.180808\pi$
$138$	38.7991	−	317.731i	0.281153	−	2.30240i
$139$	0.914332	+	1.58367i	0.00657793	+	0.0113933i	0.869296	−	0.494293i	$-0.164573\pi$
$139$	0.914332	+	1.58367i	0.00657793	+	0.0113933i	−0.862718	+	0.505686i	$0.831239\pi$
$140$	−42.6255	+	24.6098i	−0.304468	+	0.175785i
$141$	87.6552	−	116.483i	0.621668	−	0.826118i
$142$	198.585	−	343.960i	1.39849	−	2.42225i
$143$	35.0746	+	80.3410i	0.245277	+	0.561825i
$144$	−358.401	+	372.119i	−2.48890	+	2.58416i
$145$			39.9692i			0.275649i
$146$	39.3971	+	22.7459i	0.269843	+	0.155794i
$147$	33.7569	+	79.3802i	0.229639	+	0.540002i
$148$	−690.864	+	398.870i	−4.66800	+	2.69507i
$149$	83.6160	+	144.827i	0.561181	+	0.971995i	0.997394	+	0.0721509i	$0.0229863\pi$
$149$	83.6160	+	144.827i	0.561181	+	0.971995i	−0.436212	+	0.899844i	$0.643680\pi$
$150$	−108.271	−	254.603i	−0.721810	−	1.69736i
$151$	121.464	+	70.1270i	0.804395	+	0.464417i	0.845005	−	0.534758i	$-0.179597\pi$
$151$	121.464	+	70.1270i	0.804395	+	0.464417i	−0.0406110	+	0.999175i	$0.512930\pi$
$152$			388.325i			2.55477i
$153$	39.9539	−	161.154i	0.261137	−	1.05330i
$154$			116.723i			0.757939i
$155$	11.5665	+	6.67791i	0.0746225	+	0.0430833i
$156$	409.697	+	97.4327i	2.62626	+	0.624569i
$157$	89.8514	+	155.627i	0.572302	+	0.991256i	0.996329	+	0.0856062i	$0.0272827\pi$
$157$	89.8514	+	155.627i	0.572302	+	0.991256i	−0.424027	+	0.905649i	$0.639384\pi$
$158$	158.318	+	274.215i	1.00201	+	1.73554i
$159$	13.7472	−	112.578i	0.0864606	−	0.708037i
$160$	58.8687	−	101.964i	0.367929	−	0.637273i
$161$	−124.804			−0.775179
$162$	−263.808	+	165.817i	−1.62844	+	1.02356i
$163$		−	37.9287i		−	0.232691i	−0.993209	−	0.116346i	$-0.962882\pi$
$163$		−	37.9287i		−	0.232691i	0.993209	−	0.116346i	$-0.0371181\pi$
$164$	−215.757	+	373.703i	−1.31559	+	2.27868i
$165$	20.3423	+	2.48406i	0.123287	+	0.0150549i
$166$	126.811	+	219.644i	0.763923	+	1.32315i
$167$	−78.7293	−	136.363i	−0.471433	−	0.816546i	0.528033	−	0.849224i	$-0.322930\pi$
$167$	−78.7293	−	136.363i	−0.471433	−	0.816546i	−0.999466	+	0.0326778i	$0.989596\pi$
$168$	282.064	+	212.258i	1.67895	+	1.26344i
$169$	−49.8885	−	161.469i	−0.295198	−	0.955436i
$170$			71.8905i			0.422885i
$171$	−32.1601	+	129.718i	−0.188071	+	0.758585i
$172$	−412.247			−2.39679
$173$	−195.153	−	112.672i	−1.12805	−	0.651281i	−0.184608	−	0.982812i	$-0.559102\pi$
$173$	−195.153	−	112.672i	−1.12805	−	0.651281i	−0.943444	+	0.331531i	$0.892435\pi$
$174$	419.021	−	178.191i	2.40816	−	1.02409i
$175$	−93.4211	+	53.9367i	−0.533835	+	0.308210i
$176$	−193.552	−	335.241i	−1.09973	−	1.90478i
$177$	−4.63923	−	10.9093i	−0.0262103	−	0.0616343i
$178$	58.8590	−	101.947i	0.330669	−	0.572735i
$179$		−	195.080i		−	1.08983i	−0.838490	−	0.544917i	$-0.816561\pi$
$179$		−	195.080i		−	1.08983i	0.838490	−	0.544917i	$-0.183439\pi$
$180$	68.2935	−	70.9075i	0.379408	−	0.393930i
$181$	75.0474			0.414626			0.207313	−	0.978275i	$-0.433528\pi$
$181$	75.0474			0.414626			0.207313	+	0.978275i	$0.433528\pi$
$182$	25.1425	−	223.612i	0.138146	−	1.22864i
$183$	85.3982	−	113.483i	0.466657	−	0.620127i
$184$	628.153	−	362.664i	3.41387	−	1.97100i
$185$	64.8134	−	37.4201i	0.350343	−	0.202271i
$186$	18.4427	−	151.030i	0.0991545	−	0.811988i
$187$	107.736	+	62.2011i	0.576126	+	0.332626i
$188$	524.710			2.79101
$189$	76.6435	+	94.2637i	0.405521	+	0.498750i
$190$		−	57.8668i		−	0.304562i
$191$	−137.295	−	79.2672i	−0.718821	−	0.415011i	0.0954978	−	0.995430i	$-0.469556\pi$
$191$	−137.295	−	79.2672i	−0.718821	−	0.415011i	−0.814318	+	0.580418i	$0.802889\pi$
$192$	−647.611	−	79.0818i	−3.37297	−	0.411884i
$193$	81.3837	−	46.9869i	0.421677	−	0.243455i	−0.274118	−	0.961696i	$-0.588386\pi$
$193$	81.3837	−	46.9869i	0.421677	−	0.243455i	0.695795	+	0.718241i	$0.255052\pi$
$194$	−402.204	+	232.212i	−2.07322	+	1.19697i
$195$	−38.4357	−	9.14066i	−0.197106	−	0.0468752i
$196$	−155.239	+	268.882i	−0.792037	+	1.37185i
$197$	220.300			1.11827			0.559136	−	0.829076i	$-0.311133\pi$
$197$	220.300			1.11827			0.559136	+	0.829076i	$0.311133\pi$
$198$	−64.6483	−	224.335i	−0.326506	−	1.13300i
$199$	18.9035			0.0949926			0.0474963	−	0.998871i	$-0.484876\pi$
$199$	18.9035			0.0949926			0.0474963	+	0.998871i	$0.484876\pi$
$200$	313.467	−	542.940i	1.56733	−	2.71470i
$201$	−81.0366	+	34.4613i	−0.403167	+	0.171449i
$202$	−218.991	+	126.434i	−1.08411	+	0.625912i
$203$	−88.7679	−	153.750i	−0.437280	−	0.757391i
$204$	549.949	−	233.869i	2.69583	−	1.14642i
$205$	20.2413	−	35.0590i	0.0987381	−	0.171019i
$206$	−205.229			−0.996259
$207$	239.866	−	69.1241i	1.15877	−	0.333933i
$208$	298.585	+	683.932i	1.43551	+	3.28813i
$209$	−86.7196	−	50.0676i	−0.414926	−	0.239558i
$210$	−42.0322	−	31.6300i	−0.200153	−	0.150619i
$211$	191.816	+	332.234i	0.909079	+	1.57457i	0.815346	+	0.578974i	$0.196547\pi$
$211$	191.816	+	332.234i	0.909079	+	1.57457i	0.0937328	+	0.995597i	$0.470120\pi$
$212$	353.526	−	204.108i	1.66757	−	0.962774i
$213$	307.455	+	37.5444i	1.44345	+	0.176265i
$214$	206.204	+	119.052i	0.963570	+	0.556317i
$215$	38.6750			0.179884
$216$	−659.675	−	251.725i	−3.05405	−	1.16539i
$217$	−59.3241			−0.273383
$218$	398.154	+	229.874i	1.82639	+	1.05447i
$219$	−4.30033	+	35.2159i	−0.0196362	+	0.160803i
$220$	36.8813	+	63.8804i	0.167642	+	0.290365i
$221$	−192.996	−	142.369i	−0.873287	−	0.644202i
$222$	−681.249	−	512.651i	−3.06869	−	2.30924i
$223$	−13.7903	−	7.96182i	−0.0618398	−	0.0357032i	0.468761	−	0.883325i	$-0.344700\pi$
$223$	−13.7903	−	7.96182i	−0.0618398	−	0.0357032i	−0.530601	+	0.847622i	$0.678034\pi$
$224$			522.968i			2.33468i
$225$	149.677	−	155.406i	0.665231	−	0.690693i
$226$			16.8557i			0.0745825i
$227$	−174.324	+	301.939i	−0.767949	+	1.33013i	0.170724	+	0.985319i	$0.445389\pi$
$227$	−174.324	+	301.939i	−0.767949	+	1.33013i	−0.938673	+	0.344808i	$0.887944\pi$
$228$	−442.670	+	188.248i	−1.94154	+	0.825650i
$229$	−60.9366	+	35.1817i	−0.266098	+	0.153632i	−0.627113	−	0.778928i	$-0.715764\pi$
$229$	−60.9366	+	35.1817i	−0.266098	+	0.153632i	0.361015	+	0.932560i	$0.382430\pi$
$230$	−93.6051	+	54.0429i	−0.406979	+	0.234969i
$231$	−83.7680	+	35.6228i	−0.362632	+	0.154211i
$232$	893.559	+	515.897i	3.85155	+	2.22369i
$233$			38.5444i			0.165427i	0.996573	+	0.0827134i	$0.0263586\pi$
$233$			38.5444i			0.165427i	−0.996573	+	0.0827134i	$0.973641\pi$
$234$	75.5275	+	443.696i	0.322767	+	1.89613i
$235$	−49.2257			−0.209471
$236$	21.3346	−	36.9526i	0.0904009	−	0.156579i
$237$	−148.478	+	197.308i	−0.626488	+	0.832523i
$238$	−159.662	−	276.543i	−0.670850	−	1.16195i
$239$	−148.895	−	257.893i	−0.622990	−	1.07905i	−0.988926	−	0.148411i	$-0.952584\pi$
$239$	−148.895	−	257.893i	−0.622990	−	1.07905i	0.365936	−	0.930640i	$-0.380749\pi$
$240$	173.171	+	21.1465i	0.721546	+	0.0881103i
$241$	−325.592	−	187.980i	−1.35100	−	0.780001i	−0.362612	−	0.931940i	$-0.618115\pi$
$241$	−325.592	−	187.980i	−1.35100	−	0.780001i	−0.988390	+	0.151939i	$0.951448\pi$
$242$	−290.540			−1.20058
$243$	−199.514	−	138.720i	−0.821045	−	0.570864i
$244$	511.199			2.09508
$245$	14.5638	−	25.2252i	0.0594440	−	0.102960i
$246$	−457.784	−	55.9014i	−1.86091	−	0.227242i
$247$	155.349	+	114.597i	0.628942	+	0.463955i
$248$	298.586	−	172.389i	1.20397	−	0.695115i
$249$	−118.929	+	158.042i	−0.477628	+	0.634706i
$250$	−95.4229	+	165.277i	−0.381692	+	0.661109i
$251$			236.810i			0.943465i	0.881742	+	0.471733i	$0.156371\pi$
$251$			236.810i			0.943465i	−0.881742	+	0.471733i	$0.843629\pi$
$252$	−105.227	+	424.435i	−0.417569	+	1.68427i
$253$			187.036i			0.739274i
$254$	315.257	−	546.041i	1.24117	−	2.14977i
$255$	−51.5935	+	21.9404i	−0.202327	+	0.0860409i
$256$	−279.954	−	484.895i	−1.09357	−	1.89412i
$257$	−400.840	+	231.425i	−1.55969	+	0.900486i	−0.562402	+	0.826864i	$0.690123\pi$
$257$	−400.840	+	231.425i	−1.55969	+	0.900486i	−0.997286	+	0.0736221i	$0.976544\pi$
$258$	−172.421	−	405.453i	−0.668299	−	1.57152i
$259$	−166.213	+	287.889i	−0.641749	+	1.11154i
$260$	−56.8955	−	130.323i	−0.218829	−	0.501244i
$261$	255.764	+	246.335i	0.979938	+	0.943812i
$262$			245.070i			0.935380i
$263$	−109.455	−	63.1941i	−0.416180	−	0.240282i	0.277262	−	0.960794i	$-0.410573\pi$
$263$	−109.455	−	63.1941i	−0.416180	−	0.240282i	−0.693442	+	0.720513i	$0.743906\pi$
$264$	318.099	−	422.714i	1.20492	−	1.60119i
$265$	−33.1660	+	19.1484i	−0.125155	+	0.0722582i
$266$	128.517	+	222.598i	0.483146	+	0.836834i
$267$	91.1273	+	11.1278i	0.341301	+	0.0416773i
$268$	−274.493	−	158.478i	−1.02423	−	0.591337i
$269$		−	101.216i		−	0.376268i	−0.982143	−	0.188134i	$-0.939756\pi$
$269$		−	101.216i		−	0.376268i	0.982143	−	0.188134i	$-0.0602439\pi$
$270$	98.3024	+	37.5111i	0.364083	+	0.138930i
$271$		−	333.903i		−	1.23212i	−0.787701	−	0.616058i	$-0.788729\pi$
$271$		−	333.903i		−	1.23212i	0.787701	−	0.616058i	$-0.211271\pi$
$272$	917.138	+	529.510i	3.37183	+	1.94673i
$273$	168.152	−	50.2006i	0.615942	−	0.183885i
$274$	−23.4062	−	40.5407i	−0.0854240	−	0.147959i
$275$	80.8318	+	140.005i	0.293934	+	0.509108i
$276$	717.928	+	540.253i	2.60119	+	1.95744i
$277$	5.18781	−	8.98555i	0.0187286	−	0.0324388i	−0.856509	−	0.516132i	$-0.827372\pi$
$277$	5.18781	−	8.98555i	0.0187286	−	0.0324388i	0.875238	+	0.483693i	$0.160705\pi$
$278$	−7.03454			−0.0253041
$279$	114.018	−	32.8574i	0.408666	−	0.117768i
$280$		−	119.201i		−	0.425717i
$281$	52.6242	−	91.1478i	0.187275	−	0.324369i	−0.757066	−	0.653338i	$-0.773368\pi$
$281$	52.6242	−	91.1478i	0.187275	−	0.324369i	0.944341	+	0.328969i	$0.106701\pi$
$282$	219.458	+	516.062i	0.778221	+	1.83001i
$283$	−42.7502	−	74.0455i	−0.151061	−	0.261645i	0.780557	−	0.625085i	$-0.214936\pi$
$283$	−42.7502	−	74.0455i	−0.151061	−	0.261645i	−0.931618	+	0.363440i	$0.881602\pi$
$284$	557.429	+	965.495i	1.96278	+	3.39963i
$285$	41.5292	−	17.6605i	0.145716	−	0.0619667i
$286$	−335.114	−	37.6797i	−1.17173	−	0.131747i
$287$			179.816i			0.626538i
$288$	−289.652	−	1005.12i	−1.00574	−	3.48999i
$289$	−51.3341			−0.177627
$290$	−133.155	−	76.8771i	−0.459155	−	0.265093i
$291$	−289.401	−	217.779i	−0.994505	−	0.748382i
$292$	−110.588	+	63.8479i	−0.378725	+	0.218657i
$293$	83.1176	+	143.964i	0.283678	+	0.491344i	0.972288	−	0.233788i	$-0.0751121\pi$
$293$	83.1176	+	143.964i	0.283678	+	0.491344i	−0.688610	+	0.725132i	$0.741779\pi$
$294$	−329.379	−	40.2215i	−1.12034	−	0.136808i
$295$	−2.00151	+	3.46671i	−0.00678477	+	0.0117516i
$296$		−	1931.98i		−	6.52695i
$297$	141.268	−	114.861i	0.475649	−	0.386738i
$298$	−643.312			−2.15876
$299$	40.2884	−	358.315i	0.134744	−	1.19838i
$300$	770.883	+	94.1349i	2.56961	+	0.313783i
$301$	−148.772	+	85.8936i	−0.494259	+	0.285361i
$302$	−467.249	+	269.766i	−1.54718	+	0.893265i
$303$	−157.572	−	118.576i	−0.520040	−	0.391339i
$304$	−738.232	−	426.219i	−2.42840	−	1.40203i
$305$	−47.9582			−0.157240
$306$	460.029	+	443.070i	1.50336	+	1.44794i
$307$		−	193.828i		−	0.631362i	−0.948865	−	0.315681i	$-0.897767\pi$
$307$		−	193.828i		−	0.631362i	0.948865	−	0.315681i	$-0.102233\pi$
$308$	−283.745	−	163.820i	−0.921250	−	0.531884i
$309$	−62.6344	−	147.286i	−0.202700	−	0.476655i
$310$	−44.4942	+	25.6887i	−0.143530	+	0.0828668i
$311$	179.327	−	103.535i	0.576615	−	0.332909i	−0.183172	−	0.983081i	$-0.558636\pi$
$311$	179.327	−	103.535i	0.576615	−	0.332909i	0.759787	+	0.650172i	$0.225303\pi$
$312$	−700.455	+	741.296i	−2.24505	+	2.37595i
$313$	17.6298	−	30.5356i	0.0563251	−	0.0975579i	−0.836488	−	0.547985i	$-0.815395\pi$
$313$	17.6298	−	30.5356i	0.0563251	−	0.0975579i	0.892813	+	0.450427i	$0.148728\pi$
$314$	−691.284			−2.20154
$315$	9.87191	−	39.8184i	0.0313394	−	0.126408i
$316$	−888.797			−2.81265
$317$	−109.332	+	189.368i	−0.344895	+	0.597376i	−0.985335	−	0.170633i	$-0.945419\pi$
$317$	−109.332	+	189.368i	−0.344895	+	0.597376i	0.640440	+	0.768009i	$0.278752\pi$
$318$	348.605	+	262.332i	1.09624	+	0.824942i
$319$	−230.417	+	133.031i	−0.722310	+	0.417026i
$320$	110.152	+	190.790i	0.344226	+	0.596217i
$321$	−22.5079	+	184.320i	−0.0701179	+	0.574205i
$322$	240.049	−	415.777i	0.745493	−	1.29123i
$323$	273.945			0.848127
$324$	−32.8373	−	874.023i	−0.101350	−	2.69760i
$325$	−124.696	−	285.626i	−0.383681	−	0.878850i
$326$	126.357	+	72.9525i	0.387599	+	0.223781i
$327$	−43.4598	+	355.898i	−0.132905	+	1.08837i
$328$	−522.524	−	905.038i	−1.59306	−	2.75926i
$329$	189.358	−	109.326i	0.575556	−	0.332297i
$330$	−47.4020	+	62.9913i	−0.143643	+	0.190883i
$331$	309.900	+	178.921i	0.936255	+	0.540547i	0.888784	−	0.458325i	$-0.151551\pi$
$331$	309.900	+	178.921i	0.936255	+	0.540547i	0.0474708	+	0.998873i	$0.484884\pi$
$332$	−711.919			−2.14433
$333$	160.002	−	645.367i	0.480485	−	1.93804i
$334$	605.715			1.81352
$335$	25.7515	+	14.8677i	0.0768703	+	0.0443811i
$336$	−713.106	+	303.253i	−2.12234	+	0.902537i
$337$	102.667	+	177.825i	0.304650	+	0.527669i	0.977183	−	0.212398i	$-0.0681272\pi$
$337$	102.667	+	177.825i	0.304650	+	0.527669i	−0.672533	+	0.740067i	$0.734794\pi$
$338$	633.880	+	144.370i	1.87538	+	0.427130i
$339$	−12.0968	+	5.14422i	−0.0356836	+	0.0151747i
$340$	−174.761	−	100.898i	−0.514003	−	0.296760i
$341$			88.9056i			0.260720i
$342$	−370.291	−	356.641i	−1.08272	−	1.04281i
$343$			349.861i			1.02000i
$344$	499.192	−	864.626i	1.45114	−	2.51345i
$345$	−67.3524	−	50.6839i	−0.195224	−	0.146910i
$346$	750.719	−	433.428i	2.16971	−	1.25268i
$347$	192.948	−	111.398i	0.556045	−	0.321033i	−0.195511	−	0.980701i	$-0.562637\pi$
$347$	192.948	−	111.398i	0.556045	−	0.321033i	0.751557	+	0.659668i	$0.229303\pi$
$348$	−154.925	+	1268.70i	−0.445187	+	3.64570i
$349$	−104.761	−	60.4841i	−0.300176	−	0.173307i	0.342346	−	0.939574i	$-0.388779\pi$
$349$	−104.761	−	60.4841i	−0.300176	−	0.173307i	−0.642522	+	0.766267i	$0.722112\pi$
$350$		−	414.970i		−	1.18563i
$351$	−295.376	+	189.616i	−0.841526	+	0.540217i
$352$	783.742			2.22654
$353$	−131.082	+	227.040i	−0.371336	+	0.643173i	−0.989771	−	0.142663i	$-0.954434\pi$
$353$	−131.082	+	227.040i	−0.371336	+	0.643173i	0.618435	+	0.785836i	$0.287767\pi$
$354$	45.2668	+	5.52767i	0.127872	+	0.0156149i
$355$	−52.2952	−	90.5780i	−0.147310	−	0.255149i
$356$	165.217	+	286.165i	0.464094	+	0.803834i
$357$	149.738	−	198.983i	0.419435	−	0.557376i
$358$	649.899	+	375.219i	1.81536	+	1.04810i
$359$	−244.629			−0.681418			−0.340709	−	0.940169i	$-0.610667\pi$
$359$	−244.629			−0.681418			−0.340709	+	0.940169i	$0.610667\pi$
$360$	66.0208	+	229.098i	0.183391	+	0.636382i
$361$	140.493			0.389178
$362$	−144.347	+	250.016i	−0.398748	+	0.690652i
$363$	−88.6705	−	208.511i	−0.244271	−	0.574411i
$364$	508.298	+	374.959i	1.39642	+	1.03011i
$365$	10.3748	−	5.98989i	0.0284241	−	0.0164107i
$366$	213.808	+	502.774i	0.584174	+	1.37370i
$367$	212.731	−	368.461i	0.579648	−	1.00398i	−0.415871	−	0.909423i	$-0.636523\pi$
$367$	212.731	−	368.461i	0.579648	−	1.00398i	0.995519	−	0.0945566i	$-0.0301433\pi$
$368$			1592.21i			4.32667i
$369$	−99.5935	−	345.597i	−0.269901	−	0.936578i
$370$			287.896i			0.778099i
$371$	85.0538	−	147.317i	0.229255	−	0.397082i
$372$	341.259	+	256.803i	0.917363	+	0.690332i
$373$	−132.778	−	229.978i	−0.355973	−	0.616564i	0.631311	−	0.775530i	$-0.282517\pi$
$373$	−132.778	−	229.978i	−0.355973	−	0.616564i	−0.987284	+	0.158966i	$0.949184\pi$
$374$	−414.439	+	239.277i	−1.10813	+	0.639777i
$375$	−147.736	−	18.0406i	−0.393964	−	0.0481082i
$376$	−635.374	+	1100.50i	−1.68983	+	2.92686i
$377$	470.078	−	205.222i	1.24689	−	0.544357i
$378$	−461.451	+	74.0257i	−1.22077	+	0.195835i
$379$			565.992i			1.49338i	0.665171	+	0.746691i	$0.268359\pi$
$379$			565.992i			1.49338i	−0.665171	+	0.746691i	$0.731641\pi$
$380$	140.670	+	81.2161i	0.370185	+	0.213727i
$381$	488.090	+	59.6022i	1.28108	+	0.156436i
$382$	528.148	−	304.927i	1.38259	−	0.798237i
$383$	−299.091	−	518.041i	−0.780917	−	1.35259i	−0.931408	−	0.363976i	$-0.881419\pi$
$383$	−299.091	−	518.041i	−0.780917	−	1.35259i	0.150492	−	0.988611i	$-0.451914\pi$
$384$	670.467	−	890.965i	1.74601	−	2.32022i
$385$	26.6195	+	15.3688i	0.0691417	+	0.0399190i
$386$			361.500i			0.936529i
$387$	238.359	−	247.482i	0.615914	−	0.639489i
$388$		−	1303.64i		−	3.35990i
$389$	470.852	+	271.847i	1.21042	+	0.698834i	0.962850	−	0.270037i	$-0.0870358\pi$
$389$	470.852	+	271.847i	1.21042	+	0.698834i	0.247566	+	0.968871i	$0.420369\pi$
$390$	104.379	−	110.465i	0.267639	−	0.283244i
$391$	−255.843	−	443.132i	−0.654329	−	1.13333i
$392$	−375.960	−	651.182i	−0.959082	−	1.66118i
$393$	−175.879	+	74.7934i	−0.447528	+	0.190314i
$394$	−423.727	+	733.916i	−1.07545	+	1.86273i
$395$	83.3826			0.211095
$396$	636.077	+	157.698i	1.60625	+	0.398228i
$397$		−	255.071i		−	0.642497i	−0.946995	−	0.321249i	$-0.895897\pi$
$397$		−	255.071i		−	0.642497i	0.946995	−	0.321249i	$-0.104103\pi$
$398$	−36.3592	+	62.9760i	−0.0913548	+	0.158231i
$399$	−120.529	+	160.168i	−0.302077	+	0.401423i
$400$	688.111	+	1191.84i	1.72028	+	2.97961i
$401$	−43.4551	−	75.2664i	−0.108367	−	0.187697i	0.806742	−	0.590904i	$-0.201229\pi$
$401$	−43.4551	−	75.2664i	−0.108367	−	0.187697i	−0.915109	+	0.403207i	$0.867895\pi$
$402$	41.0608	−	336.252i	0.102141	−	0.836448i
$403$	19.1506	−	170.321i	0.0475202	−	0.422634i
$404$		−	709.802i		−	1.75694i
$405$	3.08063	+	81.9966i	0.00760650	+	0.202461i
$406$	682.948			1.68214
$407$	431.443	+	249.094i	1.06006	+	0.612024i
$408$	−175.431	+	1436.63i	−0.429978	+	3.52115i
$409$	−222.597	+	128.516i	−0.544246	+	0.314220i	−0.746798	−	0.665051i	$-0.768410\pi$
$409$	−222.597	+	128.516i	−0.544246	+	0.314220i	0.202552	+	0.979271i	$0.435076\pi$
$410$	77.8646	+	134.866i	0.189914	+	0.328940i
$411$	21.9514	−	29.1706i	0.0534096	−	0.0709746i
$412$	288.039	−	498.899i	0.699125	−	1.21092i
$413$		−	17.7807i		−	0.0430525i
$414$	−231.078	+	932.055i	−0.558159	+	2.25134i
$415$	66.7887			0.160937
$416$	−1501.46	−	168.821i	−3.60927	−	0.405820i
$417$	−2.14689	−	5.04846i	−0.00514841	−	0.0121066i
$418$	333.595	−	192.601i	0.798073	−	0.460768i
$419$	149.833	−	86.5064i	0.357598	−	0.206459i	−0.310429	−	0.950597i	$-0.600473\pi$
$419$	149.833	−	86.5064i	0.357598	−	0.206459i	0.668026	+	0.744138i	$0.267139\pi$
$420$	135.883	−	57.7849i	0.323530	−	0.137583i
$421$	98.2256	+	56.7106i	0.233315	+	0.134704i	0.612100	−	0.790780i	$-0.290325\pi$
$421$	98.2256	+	56.7106i	0.233315	+	0.134704i	−0.378785	+	0.925485i	$0.623658\pi$
$422$	−1475.76			−3.49706
$423$	−303.384	+	314.996i	−0.717220	+	0.744673i
$424$			988.623i			2.33166i
$425$	−383.019	−	221.136i	−0.901221	−	0.520320i
$426$	−716.440	+	952.058i	−1.68178	+	2.23488i
$427$	184.482	−	106.511i	0.432042	−	0.249440i
$428$	−578.815	+	334.179i	−1.35237	+	0.780791i
$429$	−75.2328	−	252.000i	−0.175368	−	0.587413i
$430$	−74.3879	+	128.844i	−0.172995	+	0.299636i
$431$	336.595			0.780964			0.390482	−	0.920611i	$-0.372308\pi$
$431$	336.595			0.780964			0.390482	+	0.920611i	$0.372308\pi$
$432$	1202.59	−	977.798i	2.78378	−	2.26342i
$433$	−9.37880			−0.0216600			−0.0108300	−	0.999941i	$-0.503447\pi$
$433$	−9.37880			−0.0216600			−0.0108300	+	0.999941i	$0.503447\pi$
$434$	114.105	−	197.635i	0.262914	−	0.455380i
$435$	14.5343	−	119.023i	0.0334122	−	0.273617i
$436$	−1117.62	+	645.257i	−2.56334	+	1.47995i
$437$	205.935	+	356.691i	0.471248	+	0.816226i
$438$	−109.049	−	82.0610i	−0.248969	−	0.187354i
$439$	−211.280	+	365.948i	−0.481276	+	0.833595i	−0.999769	−	0.0214868i	$-0.993160\pi$
$439$	−211.280	+	365.948i	−0.481276	+	0.833595i	0.518493	+	0.855082i	$0.326493\pi$
$440$	−178.639			−0.405998
$441$	−71.6583	−	248.660i	−0.162490	−	0.563855i
$442$	845.505	−	369.123i	1.91291	−	0.835120i
$443$	1.71237	+	0.988636i	0.00386539	+	0.00223168i	0.501931	−	0.864907i	$-0.332623\pi$
$443$	1.71237	+	0.988636i	0.00386539	+	0.00223168i	−0.498066	+	0.867139i	$0.665956\pi$
$444$	2202.35	−	936.564i	4.96026	−	2.10938i
$445$	−15.4999	−	26.8466i	−0.0348312	−	0.0603294i
$446$	53.0487	−	30.6277i	0.118943	−	0.0686719i
$447$	−196.334	−	461.684i	−0.439225	−	1.03285i
$448$	−847.452	−	489.277i	−1.89163	−	1.09214i
$449$	710.683			1.58281			0.791407	−	0.611290i	$-0.209349\pi$
$449$	710.683			1.58281			0.791407	+	0.611290i	$0.209349\pi$
$450$	229.836	+	797.550i	0.510747	+	1.77233i
$451$	269.480			0.597517
$452$	−40.9750	−	23.6569i	−0.0906526	−	0.0523383i
$453$	−336.203	−	252.999i	−0.742170	−	0.558496i
$454$	−670.595	−	1161.50i	−1.47708	−	2.55838i
$455$	−47.6860	−	35.1768i	−0.104804	−	0.0773116i
$456$	141.210	−	1156.39i	0.309671	−	2.53593i
$457$	−392.661	−	226.703i	−0.859214	−	0.496068i	0.00453490	−	0.999990i	$-0.498556\pi$
$457$	−392.661	−	226.703i	−0.859214	−	0.496068i	−0.863749	+	0.503922i	$0.831890\pi$
$458$		−	270.676i		−	0.590995i
$459$	−177.580	+	465.370i	−0.386884	+	1.01388i
$460$		−	303.397i		−	0.659559i
$461$	−352.115	+	609.881i	−0.763807	+	1.32295i	0.177068	+	0.984199i	$0.443339\pi$
$461$	−352.115	+	609.881i	−0.763807	+	1.32295i	−0.940875	+	0.338754i	$0.889995\pi$
$462$	42.4448	−	347.586i	0.0918719	−	0.752350i
$463$	102.370	−	59.1035i	0.221102	−	0.127653i	−0.385358	−	0.922767i	$-0.625922\pi$
$463$	102.370	−	59.1035i	0.221102	−	0.127653i	0.606460	+	0.795114i	$0.292589\pi$
$464$	−1961.51	+	1132.48i	−4.22739	+	2.44069i
$465$	−32.0152	−	24.0920i	−0.0688500	−	0.0518108i
$466$	−128.409	−	74.1368i	−0.275555	−	0.159092i
$467$			650.881i			1.39375i	0.717193	+	0.696875i	$0.245427\pi$
$467$			650.881i			1.39375i	−0.717193	+	0.696875i	$0.754573\pi$
$468$	−1184.60	−	439.124i	−2.53119	−	0.938300i
$469$	−132.079			−0.281618
$470$	94.6812	−	163.993i	0.201449	−	0.348921i
$471$	−210.975	−	496.112i	−0.447929	−	1.05332i
$472$	51.6684	+	89.4923i	0.109467	+	0.189602i
$473$	128.724	+	222.956i	0.272143	+	0.471366i
$474$	−371.737	−	874.149i	−0.784255	−	1.84420i
$475$	308.303	+	177.999i	0.649060	+	0.374735i
$476$	896.344			1.88307
$477$	−81.8753	+	330.244i	−0.171646	+	0.692336i
$478$	1145.54			2.39653
$479$	−36.1529	+	62.6187i	−0.0754758	+	0.130728i	−0.901293	−	0.433210i	$-0.857381\pi$
$479$	−36.1529	+	62.6187i	−0.0754758	+	0.130728i	0.825817	+	0.563938i	$0.190714\pi$
$480$	−212.382	+	282.228i	−0.442462	+	0.587976i
$481$	−772.883	−	570.137i	−1.60683	−	1.18532i
$482$	1252.49	−	723.127i	2.59853	−	1.50026i
$483$	371.651	+	45.3834i	0.769463	+	0.0939615i
$484$	407.773	−	706.283i	0.842505	−	1.45926i
$485$			122.301i			0.252167i
$486$	845.885	−	397.854i	1.74050	−	0.818629i
$487$			618.023i			1.26904i	0.772906	+	0.634521i	$0.218803\pi$
$487$			618.023i			1.26904i	−0.772906	+	0.634521i	$0.781197\pi$
$488$	−619.014	+	1072.16i	−1.26847	+	2.19706i
$489$	−13.7923	+	112.947i	−0.0282052	+	0.230976i
$490$	56.0242	+	97.0368i	0.114335	+	0.198034i
$491$	232.442	−	134.201i	0.473406	−	0.273321i	−0.244259	−	0.969710i	$-0.578545\pi$
$491$	232.442	−	134.201i	0.473406	−	0.273321i	0.717664	+	0.696389i	$0.245211\pi$
$492$	778.393	−	1034.38i	1.58210	−	2.10241i
$493$	363.941	−	630.364i	0.738217	−	1.27863i
$494$	−680.572	+	297.118i	−1.37768	+	0.601454i
$495$	−59.6736	−	14.7945i	−0.120553	−	0.0298878i
$496$			756.842i			1.52589i
$497$	402.331	+	232.286i	0.809519	+	0.467376i
$498$	−297.758	−	700.186i	−0.597907	−	1.40600i
$499$	736.750	−	425.363i	1.47645	−	0.852430i	0.476806	−	0.879009i	$-0.341795\pi$
$499$	736.750	−	425.363i	1.47645	−	0.852430i	0.999647	+	0.0265784i	$0.00846117\pi$
$500$	−267.852	−	463.933i	−0.535704	−	0.927867i
$501$	184.860	+	434.702i	0.368981	+	0.867669i
$502$	−788.918	−	455.482i	−1.57155	−	0.907335i
$503$		−	313.134i		−	0.622533i	−0.950323	−	0.311267i	$-0.899247\pi$
$503$		−	313.134i		−	0.622533i	0.950323	−	0.311267i	$-0.100753\pi$
$504$	−762.769	−	734.649i	−1.51343	−	1.45764i
$505$			66.5901i			0.131862i
$506$	−623.101	−	359.747i	−1.23142	−	0.710963i
$507$	89.8456	+	498.976i	0.177210	+	0.984173i
$508$	884.927	+	1532.74i	1.74198	+	3.01720i
$509$	210.022	+	363.769i	0.412618	+	0.714675i	0.995175	−	0.0981149i	$-0.0312813\pi$
$509$	210.022	+	363.769i	0.412618	+	0.714675i	−0.582558	+	0.812789i	$0.697948\pi$
$510$	26.1421	−	214.081i	0.0512591	−	0.419767i
$511$	−26.6060	+	46.0829i	−0.0520665	+	0.0901819i
$512$	667.129			1.30299
$513$	142.939	−	374.590i	0.278634	−	0.730195i
$514$		−	1780.50i		−	3.46401i
$515$	−27.0224	+	46.8042i	−0.0524708	+	0.0908820i
$516$	1227.62	+	149.909i	2.37911	+	0.290521i
$517$	−163.840	−	283.780i	−0.316906	−	0.548897i
$518$	−639.392	−	1107.46i	−1.23435	−	2.13795i
$519$	540.171	+	406.488i	1.04079	+	0.783213i
$520$	342.229	+	38.4796i	0.658133	+	0.0739993i
$521$			598.910i			1.14954i	0.818315	+	0.574770i	$0.194909\pi$
$521$			598.910i			1.14954i	−0.818315	+	0.574770i	$0.805091\pi$
$522$	−1312.59	+	378.259i	−2.51454	+	0.724634i
$523$	−627.654			−1.20010			−0.600051	−	0.799961i	$-0.704853\pi$
$523$	−627.654			−1.20010			−0.600051	+	0.799961i	$0.704853\pi$
$524$	−595.748	−	343.955i	−1.13692	−	0.656403i
$525$	297.810	−	126.645i	0.567258	−	0.241230i
$526$	421.055	−	243.096i	0.800485	−	0.462160i
$527$	−121.612	−	210.638i	−0.230763	−	0.399693i
$528$	454.467	+	1068.69i	0.860733	+	2.02404i
$529$	120.154	−	208.113i	0.227134	−	0.393408i
$530$		−	147.321i		−	0.277964i
$531$	9.84804	+	34.1735i	0.0185462	+	0.0643569i
$532$	−721.494			−1.35619
$533$	−516.258	−	58.0472i	−0.968589	−	0.108907i
$534$	−212.347	+	282.182i	−0.397653	+	0.528431i
$535$	54.3015	−	31.3510i	0.101498	−	0.0586000i
$536$	664.769	−	383.805i	1.24024	−	0.716054i
$537$	−70.9387	+	580.926i	−0.132102	+	1.08180i
$538$	337.195	+	194.680i	0.626757	+	0.361858i
$539$	193.893			0.359728
$540$	−229.154	+	186.320i	−0.424360	+	0.345037i
$541$			706.783i			1.30644i	0.757169	+	0.653219i	$0.226582\pi$
$541$			706.783i			1.30644i	−0.757169	+	0.653219i	$0.773418\pi$
$542$	1112.38	+	642.233i	2.05236	+	1.18493i
$543$	−223.482	−	27.2901i	−0.411569	−	0.0502580i
$544$	−1856.87	+	1072.06i	−3.41336	+	1.97070i
$545$	104.849	−	60.5348i	0.192384	−	0.111073i
$546$	−156.185	+	656.746i	−0.286054	+	1.20283i
$547$	−114.106	+	197.638i	−0.208604	+	0.361312i	−0.951275	−	0.308344i	$-0.900225\pi$
$547$	−114.106	+	197.638i	−0.208604	+	0.361312i	0.742671	+	0.669656i	$0.233559\pi$
$548$	131.402			0.239785
$549$	−295.572	+	306.886i	−0.538383	+	0.558990i
$550$	−621.891			−1.13071
$551$	−292.947	+	507.399i	−0.531664	+	0.920870i
$552$	−2002.44	+	851.550i	−3.62761	+	1.54266i
$553$	−320.750	+	185.185i	−0.580018	+	0.334873i
$554$	19.9566	+	34.5658i	0.0360227	+	0.0623931i
$555$	−206.614	+	87.8638i	−0.372277	+	0.158313i
$556$	9.87298	−	17.1005i	0.0177572	−	0.0307563i
$557$	290.193			0.520993			0.260497	−	0.965475i	$-0.416114\pi$
$557$	290.193			0.520993			0.260497	+	0.965475i	$0.416114\pi$
$558$	−109.840	+	443.042i	−0.196847	+	0.793982i
$559$	−198.577	−	454.857i	−0.355237	−	0.813697i
$560$	226.609	+	130.833i	0.404658	+	0.233630i
$561$	−298.205	−	224.404i	−0.531559	−	0.400008i
$562$	202.436	+	350.629i	0.360206	+	0.623895i
$563$	66.0457	−	38.1315i	0.117310	−	0.0677291i	−0.440197	−	0.897901i	$-0.645091\pi$
$563$	66.0457	−	38.1315i	0.117310	−	0.0677291i	0.557507	+	0.830172i	$0.311758\pi$
$564$	−1562.52	−	190.805i	−2.77043	−	0.338306i
$565$	3.84407	+	2.21937i	0.00680366	+	0.00392810i
$566$	328.905			0.581103
$567$	−193.957	−	308.576i	−0.342076	−	0.544227i
$568$	−2699.97			−4.75348
$569$	155.132	+	89.5656i	0.272640	+	0.157409i	0.630087	−	0.776525i	$-0.283019\pi$
$569$	155.132	+	89.5656i	0.272640	+	0.157409i	−0.357447	+	0.933934i	$0.616353\pi$
$570$	−21.0426	+	172.320i	−0.0369168	+	0.302317i
$571$	275.839	+	477.767i	0.483080	+	0.836719i	0.999811	−	0.0194284i	$-0.00618463\pi$
$571$	275.839	+	477.767i	0.483080	+	0.836719i	−0.516731	+	0.856148i	$0.672851\pi$
$572$	561.929	−	761.757i	0.982394	−	1.33174i
$573$	380.023	+	285.974i	0.663216	+	0.499082i
$574$	−599.048	−	345.860i	−1.04364	−	0.602544i
$575$		−	664.947i		−	1.15643i
$576$	1899.75	+	470.992i	3.29818	+	0.817695i
$577$			1040.32i			1.80297i	0.432806	+	0.901487i	$0.357524\pi$
$577$			1040.32i			1.80297i	−0.432806	+	0.901487i	$0.642476\pi$
$578$	98.7364	−	171.017i	0.170824	−	0.295876i
$579$	−259.437	+	110.327i	−0.448078	+	0.190548i
$580$	373.766	−	215.794i	0.644424	−	0.372059i
$581$	−256.918	+	148.332i	−0.442199	+	0.255304i
$582$	1282.16	−	545.244i	2.20302	−	0.936845i
$583$	−220.776	−	127.465i	−0.378690	−	0.218637i
$584$		−	309.255i		−	0.529546i
$585$	111.133	+	41.1965i	0.189971	+	0.0704213i
$586$	−639.477			−1.09126
$587$	498.764	−	863.885i	0.849684	−	1.47170i	−0.0318070	−	0.999494i	$-0.510126\pi$
$587$	498.764	−	863.885i	0.849684	−	1.47170i	0.881491	−	0.472201i	$-0.156540\pi$
$588$	560.060	−	744.248i	0.952482	−	1.26573i
$589$	97.8892	+	169.549i	0.166196	+	0.287859i
$590$	−7.69944	−	13.3358i	−0.0130499	−	0.0226031i
$591$	−656.026	−	80.1094i	−1.11003	−	0.135549i
$592$	3672.82	+	2120.50i	6.20409	+	3.58193i
$593$	−475.811			−0.802379			−0.401189	−	0.915995i	$-0.631403\pi$
$593$	−475.811			−0.802379			−0.401189	+	0.915995i	$0.631403\pi$
$594$	110.938	+	691.550i	0.186764	+	1.16423i
$595$	−84.0905			−0.141329
$596$	902.888	−	1563.85i	1.51491	−	2.62391i
$597$	−56.2924	−	6.87404i	−0.0942921	−	0.0115143i
$598$	1116.22	+	823.406i	1.86658	+	1.37693i
$599$	−152.842	+	88.2435i	−0.255162	+	0.147318i	−0.622126	−	0.782917i	$-0.713731\pi$
$599$	−152.842	+	88.2435i	−0.255162	+	0.147318i	0.366964	+	0.930235i	$0.380397\pi$
$600$	−1130.90	+	1502.82i	−1.88483	+	2.50470i
$601$	−564.099	+	977.047i	−0.938600	+	1.62570i	−0.170515	+	0.985355i	$0.554543\pi$
$601$	−564.099	+	977.047i	−0.938600	+	1.62570i	−0.768085	+	0.640347i	$0.778790\pi$
$602$		−	660.834i		−	1.09773i
$603$	253.849	−	73.1535i	0.420976	−	0.121316i
$604$		−	1514.47i		−	2.50740i
$605$	−38.2552	+	66.2600i	−0.0632318	+	0.109521i
$606$	698.104	−	296.873i	1.15199	−	0.489889i
$607$	−124.328	−	215.342i	−0.204824	−	0.354765i	0.745253	−	0.666782i	$-0.232329\pi$
$607$	−124.328	−	215.342i	−0.204824	−	0.354765i	−0.950077	+	0.312017i	$0.898995\pi$
$608$	1494.65	−	862.936i	2.45830	−	1.41930i
$609$	208.430	+	490.130i	0.342250	+	0.804811i
$610$	92.2432	−	159.770i	0.151218	−	0.261918i
$611$	252.750	+	578.944i	0.413667	+	0.947535i
$612$	−1722.73	+	496.451i	−2.81491	+	0.811194i
$613$		−	990.181i		−	1.61530i	−0.589660	−	0.807652i	$-0.700738\pi$
$613$		−	990.181i		−	1.61530i	0.589660	−	0.807652i	$-0.299262\pi$
$614$	645.727	+	372.811i	1.05167	+	0.607184i
$615$	−73.0249	+	97.0409i	−0.118740	+	0.157790i
$616$	687.177	−	396.742i	1.11555	−	0.644061i
$617$	398.195	+	689.693i	0.645372	+	1.11782i	0.984215	+	0.176975i	$0.0566311\pi$
$617$	398.195	+	689.693i	0.645372	+	1.11782i	−0.338843	+	0.940843i	$0.610036\pi$
$618$	611.148	+	74.6292i	0.988913	+	0.120759i
$619$	761.806	+	439.829i	1.23070	+	0.710548i	0.967177	−	0.254104i	$-0.0817805\pi$
$619$	761.806	+	439.829i	1.23070	+	0.710548i	0.263528	+	0.964652i	$0.415114\pi$
$620$		−	144.216i		−	0.232607i
$621$	−739.429	+	118.619i	−1.19071	+	0.191012i
$622$			796.559i			1.28064i
$623$	119.248	+	68.8476i	0.191409	+	0.110510i
$624$	−640.447	−	2145.24i	−1.02636	−	3.43789i
$625$	−274.544	−	475.524i	−0.439270	−	0.760838i
$626$	67.8185	+	117.465i	0.108336	+	0.187644i
$627$	240.034	+	180.630i	0.382829	+	0.288086i
$628$	970.217	−	1680.47i	1.54493	−	2.67590i
$629$	−1362.92			−2.16680
$630$	113.665	+	109.475i	0.180421	+	0.173770i
$631$		−	621.433i		−	0.984839i	−0.870358	−	0.492420i	$-0.836113\pi$
$631$		−	621.433i		−	0.984839i	0.870358	−	0.492420i	$-0.163887\pi$
$632$	1076.25	−	1864.12i	1.70293	−	2.94955i
$633$	−450.391	−	1059.11i	−0.711518	−	1.67315i
$634$	−420.580	−	728.465i	−0.663375	−	1.14900i
$635$	−83.0194	−	143.794i	−0.130739	−	0.226447i
$636$	−1126.98	+	479.254i	−1.77198	+	0.753544i
$637$	−371.452	−	41.7654i	−0.583127	−	0.0655658i
$638$		−	1023.49i		−	1.60422i
$639$	−901.913	−	223.605i	−1.41144	−	0.349930i
$640$	−376.523			−0.588317
$641$	320.482	+	185.031i	0.499972	+	0.288659i	0.728702	−	0.684831i	$-0.240124\pi$
$641$	320.482	+	185.031i	0.499972	+	0.288659i	−0.228730	+	0.973490i	$0.573457\pi$
$642$	−570.759	−	429.506i	−0.889032	−	0.669012i
$643$	708.559	−	409.087i	1.10196	−	0.636215i	0.165223	−	0.986256i	$-0.447166\pi$
$643$	708.559	−	409.087i	1.10196	−	0.636215i	0.936734	+	0.350041i	$0.113832\pi$
$644$	673.817	+	1167.09i	1.04630	+	1.81224i
$645$	−115.169	−	14.0637i	−0.178557	−	0.0218042i
$646$	−526.909	+	912.633i	−0.815648	+	1.41274i
$647$			546.797i			0.845127i	0.906333	+	0.422564i	$0.138870\pi$
$647$			546.797i			0.845127i	−0.906333	+	0.422564i	$0.861130\pi$
$648$	1872.90	+	989.489i	2.89027	+	1.52699i
$649$	−26.6469			−0.0410583
$650$	1191.39	+	133.958i	1.83291	+	0.206089i
$651$	176.660	+	21.5725i	0.271367	+	0.0331375i
$652$	−354.685	+	204.778i	−0.543996	+	0.314076i
$653$	−832.609	+	480.707i	−1.27505	+	0.736152i	−0.975934	−	0.218065i	$-0.930026\pi$
$653$	−832.609	+	480.707i	−1.27505	+	0.736152i	−0.299118	+	0.954216i	$0.596692\pi$
$654$	−1102.06	−	829.321i	−1.68511	−	1.26808i
$655$	55.8901	+	32.2682i	0.0853285	+	0.0492644i
$656$	2294.05			3.49703
$657$	25.6117	−	103.305i	0.0389828	−	0.157238i
$658$			841.113i			1.27829i
$659$	169.034	+	97.5918i	0.256501	+	0.148091i	0.622737	−	0.782431i	$-0.286021\pi$
$659$	169.034	+	97.5918i	0.256501	+	0.148091i	−0.366237	+	0.930522i	$0.619354\pi$
$660$	−86.5989	−	203.640i	−0.131210	−	0.308545i
$661$	−1064.02	+	614.310i	−1.60971	+	0.929364i	−0.620271	+	0.784387i	$0.712977\pi$
$661$	−1064.02	+	614.310i	−1.60971	+	0.929364i	−0.989435	+	0.144977i	$0.953689\pi$
$662$	−1192.13	+	688.277i	−1.80080	+	1.03969i
$663$	522.949	+	494.138i	0.788762	+	0.745306i
$664$	862.066	−	1493.14i	1.29829	−	2.24871i
$665$	67.6870			0.101785
$666$	1842.26	+	1774.34i	2.76615	+	2.66418i
$667$	1094.36			1.64071
$668$	−850.121	+	1472.45i	−1.27264	+	2.20427i
$669$	38.1706	+	28.7240i	0.0570561	+	0.0429357i
$670$	−99.0615	+	57.1932i	−0.147853	+	0.0853630i
$671$	−159.621	−	276.473i	−0.237886	−	0.412031i
$672$	190.171	−	1557.34i	0.282993	−	2.31746i
$673$	−42.4937	+	73.6012i	−0.0631407	+	0.109363i	−0.895868	−	0.444321i	$-0.853445\pi$
$673$	−42.4937	+	73.6012i	−0.0631407	+	0.109363i	0.832727	+	0.553684i	$0.186778\pi$
$674$	−789.883			−1.17193
$675$	−502.231	+	408.352i	−0.744046	+	0.604966i
$676$	−1240.60	+	1338.30i	−1.83521	+	1.97973i
$677$	−662.600	−	382.552i	−0.978729	−	0.565069i	−0.0768428	−	0.997043i	$-0.524484\pi$
$677$	−662.600	−	382.552i	−0.978729	−	0.565069i	−0.901886	+	0.431974i	$0.857817\pi$
$678$	6.12936	−	50.1941i	0.00904035	−	0.0740326i
$679$	−271.620	−	470.459i	−0.400029	−	0.692870i
$680$	423.238	−	244.357i	0.622409	−	0.359348i
$681$	628.914	−	835.746i	0.923515	−	1.22723i
$682$	−296.184	−	171.002i	−0.434288	−	0.250736i
$683$	902.968			1.32206			0.661031	−	0.750359i	$-0.270119\pi$
$683$	902.968			1.32206			0.661031	+	0.750359i	$0.270119\pi$
$684$	1386.67	−	399.608i	2.02730	−	0.584223i
$685$	−12.3275			−0.0179964
$686$	−1165.54	−	672.927i	−1.69904	−	0.980943i
$687$	194.255	−	82.6081i	0.282759	−	0.120245i
$688$	1095.81	+	1898.00i	1.59275	+	2.75872i
$689$	395.496	+	291.748i	0.574015	+	0.423437i
$690$	298.397	−	126.895i	0.432459	−	0.183906i
$691$	−743.858	−	429.466i	−1.07649	−	0.621514i	−0.146546	−	0.989204i	$-0.546816\pi$
$691$	−743.858	−	429.466i	−1.07649	−	0.621514i	−0.929949	+	0.367690i	$0.880149\pi$
$692$			2433.26i			3.51628i
$693$	262.405	−	75.6193i	0.378651	−	0.109119i
$694$			857.060i			1.23496i
$695$	−0.926234	+	1.60428i	−0.00133271	+	0.00230832i
$696$	−2473.31	−	1861.21i	−3.55361	−	2.67415i
$697$	−638.462	+	368.616i	−0.916014	+	0.528861i
$698$	402.999	−	232.671i	0.577362	−	0.333340i
$699$	14.0162	−	114.781i	0.0200518	−	0.164207i
$700$	1008.76	+	582.410i	1.44109	+	0.832014i
$701$		−	786.070i		−	1.12136i	−0.828034	−	0.560678i	$-0.810541\pi$
$701$		−	786.070i		−	1.12136i	0.828034	−	0.560678i	$-0.189459\pi$
$702$	−63.5672	−	1348.74i	−0.0905516	−	1.92128i
$703$	1097.06			1.56053
$704$	−733.251	+	1270.03i	−1.04155	+	1.80402i
$705$	146.588	+	17.9003i	0.207927	+	0.0253906i
$706$	−504.248	−	873.383i	−0.714232	−	1.23709i
$707$	−147.891	−	256.154i	−0.209180	−	0.362311i
$708$	−76.9693	+	102.282i	−0.108714	+	0.144467i
$709$	−846.314	−	488.619i	−1.19367	−	0.689167i	−0.234535	−	0.972108i	$-0.575357\pi$
$709$	−846.314	−	488.619i	−1.19367	−	0.689167i	−0.959137	+	0.282941i	$0.908690\pi$
$710$	402.341			0.566677
$711$	513.897	−	533.567i	0.722781	−	0.750446i
$712$	−800.250			−1.12395
$713$	182.841	−	316.690i	0.256439	−	0.444166i
$714$	374.893	+	881.571i	0.525060	+	1.23469i
$715$	−52.7174	+	71.4643i	−0.0737307	+	0.0999500i
$716$	−1824.27	+	1053.24i	−2.54786	+	1.47101i
$717$	349.611	+	822.118i	0.487602	+	1.14661i
$718$	470.522	−	814.968i	0.655323	−	1.13505i
$719$		−	1058.76i		−	1.47254i	−0.676686	−	0.736272i	$-0.736584\pi$
$719$		−	1058.76i		−	1.47254i	0.676686	−	0.736272i	$-0.263416\pi$
$720$	−507.993	−	125.943i	−0.705546	−	0.174921i
$721$		−	240.057i		−	0.332951i
$722$	−270.226	+	468.045i	−0.374274	+	0.648262i
$723$	901.215	+	678.180i	1.24649	+	0.938009i
$724$	−405.182	−	701.795i	−0.559643	−	0.969330i
$725$	819.173	−	472.950i	1.12989	−	0.652345i
$726$	865.192	+	105.651i	1.19173	+	0.145525i
$727$	−528.724	+	915.777i	−0.727269	+	1.25967i	0.230765	+	0.973010i	$0.425877\pi$
$727$	−528.724	+	915.777i	−0.727269	+	1.25967i	−0.958033	+	0.286656i	$0.907456\pi$
$728$	−1401.92	+	612.039i	−1.92572	+	0.840712i
$729$	543.684	+	485.642i	0.745795	+	0.666176i
$730$			46.0841i			0.0631289i
$731$	−609.953	−	352.157i	−0.834409	−	0.481747i
$732$	−1522.29	−	185.892i	−2.07963	−	0.253950i
$733$	682.796	−	394.213i	0.931509	−	0.537807i	0.0442205	−	0.999022i	$-0.485920\pi$
$733$	682.796	−	394.213i	0.931509	−	0.537807i	0.887289	+	0.461215i	$0.152586\pi$
$734$	818.337	+	1417.40i	1.11490	+	1.93107i
$735$	−52.5420	+	69.8217i	−0.0714857	+	0.0949955i
$736$	−2791.76	−	1611.82i	−3.79316	−	2.18998i
$737$			197.939i			0.268574i
$738$	1342.90	+	332.936i	1.81964	+	0.451132i
$739$			264.795i			0.358315i	0.983820	+	0.179158i	$0.0573372\pi$
$739$			264.795i			0.358315i	−0.983820	+	0.179158i	$0.942663\pi$
$740$	−699.857	−	404.063i	−0.945753	−	0.546031i
$741$	−420.938	−	397.746i	−0.568067	−	0.536770i
$742$	327.187	+	566.704i	0.440952	+	0.763752i
$743$	−435.727	−	754.702i	−0.586443	−	1.01575i	−0.994694	−	0.102880i	$-0.967194\pi$
$743$	−435.727	−	754.702i	−0.586443	−	1.01575i	0.408250	−	0.912870i	$-0.366139\pi$
$744$	−951.839	+	404.775i	−1.27935	+	0.544053i
$745$	−84.7045	+	146.712i	−0.113697	+	0.196929i
$746$	1021.55			1.36936
$747$	411.627	−	427.382i	0.551040	−	0.572132i
$748$		−	1343.30i		−	1.79585i
$749$	−139.255	+	241.197i	−0.185922	+	0.322026i
$750$	344.259	−	457.476i	0.459012	−	0.609969i
$751$	230.810	+	399.774i	0.307336	+	0.532322i	0.977779	−	0.209639i	$-0.0672290\pi$
$751$	230.810	+	399.774i	0.307336	+	0.532322i	−0.670442	+	0.741962i	$0.733896\pi$
$752$	−1394.75	−	2415.78i	−1.85472	−	3.21247i
$753$	86.1131	−	705.191i	0.114360	−	0.936509i
$754$	−220.465	+	1960.76i	−0.292394	+	2.60048i
$755$			142.080i			0.188185i
$756$	467.695	−	1225.65i	0.618644	−	1.62123i
$757$	1006.60			1.32972			0.664859	−	0.746969i	$-0.268492\pi$
$757$	1006.60			1.32972			0.664859	+	0.746969i	$0.268492\pi$
$758$	−1885.57	−	1088.63i	−2.48756	−	1.43619i
$759$	68.0135	−	556.971i	0.0896094	−	0.733823i
$760$	−340.677	+	196.690i	−0.448259	+	0.258803i
$761$	187.836	+	325.341i	0.246827	+	0.427517i	0.962644	−	0.270771i	$-0.0872786\pi$
$761$	187.836	+	325.341i	0.246827	+	0.427517i	−0.715816	+	0.698288i	$0.753945\pi$
$762$	−1137.36	+	1511.41i	−1.49260	+	1.98347i
$763$	−268.884	+	465.722i	−0.352404	+	0.610382i
$764$			1711.86i			2.24065i
$765$	161.618	−	46.5746i	0.211265	−	0.0608818i
$766$	2301.10			3.00405
$767$	51.0488	+	5.73984i	0.0665565	+	0.00748350i
$768$	657.344	+	1545.76i	0.855916	+	2.01271i
$769$	878.062	−	506.949i	1.14182	−	0.659232i	0.194942	−	0.980815i	$-0.437548\pi$
$769$	878.062	−	506.949i	1.14182	−	0.659232i	0.946881	+	0.321583i	$0.104215\pi$
$770$	−102.401	+	59.1210i	−0.132988	+	0.0767805i
$771$	1277.81	−	543.395i	1.65734	−	0.704792i
$772$

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92341 + 3.33144i) q^{2} +(-2.97788 - 0.363638i) q^{3} +(-5.39901 - 9.35136i) q^{4} +(0.506509 + 0.877299i) q^{5} +(6.93912 - 9.22121i) q^{6} +(-3.89680 - 2.24982i) q^{7} +26.1508 q^{8} +(8.73553 + 2.16574i) q^{9} -3.89690 q^{10} +(-3.37167 + 5.83991i) q^{11} +(12.6771 + 29.8105i) q^{12} +(7.71724 - 10.4616i) q^{13} +(14.9903 - 8.65465i) q^{14} +(-1.18930 - 2.79668i) q^{15} +(-28.7026 + 49.7144i) q^{16} -18.4481i q^{17} +(-24.0171 + 24.9363i) q^{18} +14.8495i q^{19} +(5.46929 - 9.47309i) q^{20} +(10.7861 + 8.11671i) q^{21} +(-12.9702 - 22.4651i) q^{22} +(24.0204 - 13.8682i) q^{23} +(-77.8739 - 9.50942i) q^{24} +(11.9869 - 20.7619i) q^{25} +(20.0087 + 45.8314i) q^{26} +(-25.2258 - 9.62589i) q^{27} +48.5872i q^{28} +(34.1695 + 19.7278i) q^{29} +(11.6045 + 1.41706i) q^{30} +(11.4179 - 6.59210i) q^{31} +(-58.1123 - 100.653i) q^{32} +(12.1641 - 16.1645i) q^{33} +(61.4590 + 35.4833i) q^{34} -4.55821i q^{35} +(-26.9106 - 93.3820i) q^{36} -73.8784i q^{37} +(-49.4702 - 28.5616i) q^{38} +(-26.7852 + 28.3470i) q^{39} +(13.2456 + 22.9420i) q^{40} +(-19.9812 - 34.6085i) q^{41} +(-47.7864 + 20.3215i) q^{42} +(19.0890 - 33.0631i) q^{43} +72.8148 q^{44} +(2.52462 + 8.76064i) q^{45} +106.697i q^{46} +(-24.2966 + 42.0829i) q^{47} +(103.551 - 137.606i) q^{48} +(-14.3766 - 24.9011i) q^{49} +(46.1114 + 79.8674i) q^{50} +(-6.70845 + 54.9364i) q^{51} +(-139.495 - 15.6846i) q^{52} +37.8047i q^{53} +(80.5877 - 65.5239i) q^{54} -6.83113 q^{55} +(-101.904 - 58.8345i) q^{56} +(5.39983 - 44.2199i) q^{57} +(-131.444 + 75.8892i) q^{58} +(1.97579 + 3.42217i) q^{59} +(-19.7317 + 26.2209i) q^{60} +(-23.6710 + 40.9993i) q^{61} +50.7172i q^{62} +(-29.1681 - 28.0928i) q^{63} +217.474 q^{64} +(13.0868 + 1.47145i) q^{65} +(30.4546 + 71.6148i) q^{66} +(25.4206 - 14.6766i) q^{67} +(-172.515 + 99.6018i) q^{68} +(-76.5729 + 32.5631i) q^{69} +(15.1854 + 8.76731i) q^{70} -103.246 q^{71} +(228.441 + 56.6358i) q^{72} -11.8258i q^{73} +(246.122 + 142.098i) q^{74} +(-43.2454 + 57.4676i) q^{75} +(138.863 - 80.1725i) q^{76} +(26.2775 - 15.1713i) q^{77} +(-42.9174 - 143.756i) q^{78} +(41.1555 - 71.2835i) q^{79} -58.1525 q^{80} +(71.6191 + 37.8378i) q^{81} +153.728 q^{82} +(32.9652 - 57.0974i) q^{83} +(17.6682 - 144.687i) q^{84} +(16.1845 - 9.34415i) q^{85} +(73.4320 + 127.188i) q^{86} +(-94.5789 - 71.1723i) q^{87} +(-88.1719 + 152.718i) q^{88} -30.6014 q^{89} +(-34.0415 - 8.43967i) q^{90} +(-53.6091 + 23.4042i) q^{91} +(-259.373 - 149.749i) q^{92} +(-36.3981 + 15.4785i) q^{93} +(-93.4645 - 161.885i) q^{94} +(-13.0274 + 7.52138i) q^{95} +(136.450 + 320.865i) q^{96} +(104.555 + 60.3648i) q^{97} +110.609 q^{98} +(-42.1011 + 43.7126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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