LMFDB - Embedded newform 117.3.n.a.38.19

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			38.19
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04133 - 1.80365i) q^{2} +(-2.79053 + 1.10134i) q^{3} +(-0.168757 - 0.292296i) q^{4} +(2.59043 + 4.48676i) q^{5} +(-0.919442 + 6.17999i) q^{6} +(1.68126 + 0.970675i) q^{7} +7.62775 q^{8} +(6.57409 - 6.14666i) q^{9} +10.7900 q^{10} +(-5.82235 + 10.0846i) q^{11} +(0.792839 + 0.629800i) q^{12} +(11.5696 + 5.92831i) q^{13} +(3.50151 - 2.02160i) q^{14} +(-12.1701 - 9.66746i) q^{15} +(8.61807 - 14.9269i) q^{16} -23.0350i q^{17} +(-4.24056 - 18.2580i) q^{18} +15.9539i q^{19} +(0.874306 - 1.51434i) q^{20} +(-5.76065 - 0.857053i) q^{21} +(12.1260 + 21.0029i) q^{22} +(-19.8531 + 11.4622i) q^{23} +(-21.2854 + 8.40077i) q^{24} +(-0.920650 + 1.59461i) q^{25} +(22.7404 - 14.6941i) q^{26} +(-11.5756 + 24.3927i) q^{27} -0.655233i q^{28} +(-38.5384 - 22.2501i) q^{29} +(-30.1098 + 11.8835i) q^{30} +(29.2383 - 16.8807i) q^{31} +(-2.69310 - 4.66458i) q^{32} +(5.14081 - 34.5537i) q^{33} +(-41.5470 - 23.9872i) q^{34} +10.0579i q^{35} +(-2.90607 - 0.884287i) q^{36} +36.7677i q^{37} +(28.7752 + 16.6134i) q^{38} +(-38.8143 - 3.80102i) q^{39} +(19.7591 + 34.2238i) q^{40} +(-1.66104 - 2.87701i) q^{41} +(-7.54458 + 9.49768i) q^{42} +(4.62927 - 8.01814i) q^{43} +3.93025 q^{44} +(44.6083 + 13.5738i) q^{45} +47.7438i q^{46} +(35.1299 - 60.8468i) q^{47} +(-7.60929 + 51.1455i) q^{48} +(-22.6156 - 39.1713i) q^{49} +(1.91741 + 3.32105i) q^{50} +(25.3694 + 64.2798i) q^{51} +(-0.219630 - 4.38218i) q^{52} -36.5504i q^{53} +(31.9418 + 46.2793i) q^{54} -60.3295 q^{55} +(12.8242 + 7.40407i) q^{56} +(-17.5707 - 44.5199i) q^{57} +(-80.2627 + 46.3397i) q^{58} +(-42.5128 - 73.6344i) q^{59} +(-0.771965 + 5.18873i) q^{60} +(16.2346 - 28.1192i) q^{61} -70.3140i q^{62} +(17.0192 - 3.95282i) q^{63} +57.7269 q^{64} +(3.37133 + 67.2667i) q^{65} +(-56.9694 - 45.2542i) q^{66} +(-21.7493 + 12.5570i) q^{67} +(-6.73303 + 3.88732i) q^{68} +(42.7767 - 53.8505i) q^{69} +(18.1408 + 10.4736i) q^{70} -16.8087 q^{71} +(50.1455 - 46.8851i) q^{72} -82.1471i q^{73} +(66.3160 + 38.2875i) q^{74} +(0.812884 - 5.46376i) q^{75} +(4.66327 - 2.69234i) q^{76} +(-19.5777 + 11.3032i) q^{77} +(-47.2744 + 66.0491i) q^{78} +(6.27189 - 10.8632i) q^{79} +89.2980 q^{80} +(5.43725 - 80.8173i) q^{81} -6.91882 q^{82} +(-62.7678 + 108.717i) q^{83} +(0.721637 + 1.82845i) q^{84} +(103.352 - 59.6706i) q^{85} +(-9.64125 - 16.6991i) q^{86} +(132.047 + 19.6457i) q^{87} +(-44.4114 + 76.9228i) q^{88} +13.3476 q^{89} +(70.9345 - 66.3225i) q^{90} +(13.6970 + 21.1973i) q^{91} +(6.70068 + 3.86864i) q^{92} +(-62.9988 + 79.3075i) q^{93} +(-73.1641 - 126.724i) q^{94} +(-71.5814 + 41.3275i) q^{95} +(12.6525 + 10.0506i) q^{96} +(142.130 + 82.0586i) q^{97} -94.2016 q^{98} +(23.7099 + 102.085i) 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 $

$2$	1.04133	−	1.80365i	0.520667	−	0.901823i	−0.479044	−	0.877791i	$-0.659016\pi$
$2$	1.04133	−	1.80365i	0.520667	−	0.901823i	0.999711	−	0.0240315i	$-0.00765020\pi$
$3$	−2.79053	+	1.10134i	−0.930176	+	0.367114i
$3$	−2.79053	+	1.10134i	−0.930176	+	0.367114i
$4$	−0.168757	−	0.292296i	−0.0421893	−	0.0730739i
$5$	2.59043	+	4.48676i	0.518086	+	0.897351i	0.999779	+	0.0210112i	$0.00668858\pi$
$5$	2.59043	+	4.48676i	0.518086	+	0.897351i	−0.481693	+	0.876340i	$0.659978\pi$
$6$	−0.919442	+	6.17999i	−0.153240	+	1.03000i
$7$	1.68126	+	0.970675i	0.240180	+	0.138668i	0.615259	−	0.788325i	$-0.289051\pi$
$7$	1.68126	+	0.970675i	0.240180	+	0.138668i	−0.375080	+	0.926993i	$0.622385\pi$
$8$	7.62775			0.953469
$9$	6.57409	−	6.14666i	0.730454	−	0.682962i
$10$	10.7900			1.07900
$11$	−5.82235	+	10.0846i	−0.529304	+	0.916782i	0.470112	+	0.882607i	$0.344214\pi$
$11$	−5.82235	+	10.0846i	−0.529304	+	0.916782i	−0.999416	+	0.0341747i	$0.989120\pi$
$12$	0.792839	+	0.629800i	0.0660699	+	0.0524833i
$13$	11.5696	+	5.92831i	0.889968	+	0.456023i
$13$	11.5696	+	5.92831i	0.889968	+	0.456023i
$14$	3.50151	−	2.02160i	0.250108	−	0.144400i
$15$	−12.1701	−	9.66746i	−0.811341	−	0.644498i
$16$	8.61807	−	14.9269i	0.538629	−	0.932933i
$17$		−	23.0350i		−	1.35500i	−0.735523	−	0.677500i	$-0.763063\pi$
$17$		−	23.0350i		−	1.35500i	0.735523	−	0.677500i	$-0.236937\pi$
$18$	−4.24056	−	18.2580i	−0.235587	−	1.01434i
$19$			15.9539i			0.839680i	0.907598	+	0.419840i	$0.137914\pi$
$19$			15.9539i			0.839680i	−0.907598	+	0.419840i	$0.862086\pi$
$20$	0.874306	−	1.51434i	0.0437153	−	0.0757172i
$21$	−5.76065	−	0.857053i	−0.274316	−	0.0408121i
$22$	12.1260	+	21.0029i	0.551183	+	0.954677i
$23$	−19.8531	+	11.4622i	−0.863176	+	0.498355i	−0.865075	−	0.501643i	$-0.832729\pi$
$23$	−19.8531	+	11.4622i	−0.863176	+	0.498355i	0.00189847	+	0.999998i	$0.499396\pi$
$24$	−21.2854	+	8.40077i	−0.886894	+	0.350032i
$25$	−0.920650	+	1.59461i	−0.0368260	+	0.0637845i
$26$	22.7404	−	14.6941i	0.874630	−	0.565156i
$27$	−11.5756	+	24.3927i	−0.428726	+	0.903435i
$28$		−	0.655233i		−	0.0234012i
$29$	−38.5384	−	22.2501i	−1.32891	−	0.767246i	−0.343778	−	0.939051i	$-0.611707\pi$
$29$	−38.5384	−	22.2501i	−1.32891	−	0.767246i	−0.985131	+	0.171805i	$0.945040\pi$
$30$	−30.1098	+	11.8835i	−1.00366	+	0.396117i
$31$	29.2383	−	16.8807i	0.943170	−	0.544540i	0.0522177	−	0.998636i	$-0.483371\pi$
$31$	29.2383	−	16.8807i	0.943170	−	0.544540i	0.890953	+	0.454096i	$0.150038\pi$
$32$	−2.69310	−	4.66458i	−0.0841593	−	0.145768i
$33$	5.14081	−	34.5537i	0.155782	−	1.04708i
$34$	−41.5470	−	23.9872i	−1.22197	−	0.705505i
$35$			10.0579i			0.287368i
$36$	−2.90607	−	0.884287i	−0.0807240	−	0.0245635i
$37$			36.7677i			0.993723i	0.867830	+	0.496861i	$0.165514\pi$
$37$			36.7677i			0.993723i	−0.867830	+	0.496861i	$0.834486\pi$
$38$	28.7752	+	16.6134i	0.757243	+	0.437194i
$39$	−38.8143	−	3.80102i	−0.995239	−	0.0974621i
$40$	19.7591	+	34.2238i	0.493979	+	0.855596i
$41$	−1.66104	−	2.87701i	−0.0405133	−	0.0701711i	0.845058	−	0.534675i	$-0.179566\pi$
$41$	−1.66104	−	2.87701i	−0.0405133	−	0.0701711i	−0.885571	+	0.464504i	$0.846233\pi$
$42$	−7.54458	+	9.49768i	−0.179633	+	0.226135i
$43$	4.62927	−	8.01814i	0.107658	−	0.186468i	−0.807163	−	0.590328i	$-0.798998\pi$
$43$	4.62927	−	8.01814i	0.107658	−	0.186468i	0.914821	+	0.403860i	$0.132332\pi$
$44$	3.93025			0.0893238
$45$	44.6083	+	13.5738i	0.991294	+	0.301641i
$46$			47.7438i			1.03791i
$47$	35.1299	−	60.8468i	0.747445	−	1.29461i	−0.201598	−	0.979468i	$-0.564614\pi$
$47$	35.1299	−	60.8468i	0.747445	−	1.29461i	0.949044	−	0.315145i	$-0.102053\pi$
$48$	−7.60929	+	51.1455i	−0.158527	+	1.06553i
$49$	−22.6156	−	39.1713i	−0.461542	−	0.799415i
$50$	1.91741	+	3.32105i	0.0383482	+	0.0664210i
$51$	25.3694	+	64.2798i	0.497440	+	1.26039i
$52$	−0.219630	−	4.38218i	−0.00422365	−	0.0842727i
$53$		−	36.5504i		−	0.689630i	−0.938671	−	0.344815i	$-0.887942\pi$
$53$		−	36.5504i		−	0.689630i	0.938671	−	0.344815i	$-0.112058\pi$
$54$	31.9418	+	46.2793i	0.591514	+	0.857024i
$55$	−60.3295			−1.09690
$56$	12.8242	+	7.40407i	0.229004	+	0.132216i
$57$	−17.5707	−	44.5199i	−0.308259	−	0.781050i
$58$	−80.2627	+	46.3397i	−1.38384	+	0.798960i
$59$	−42.5128	−	73.6344i	−0.720557	−	1.24804i	−0.960777	−	0.277322i	$-0.910553\pi$
$59$	−42.5128	−	73.6344i	−0.720557	−	1.24804i	0.240220	−	0.970718i	$-0.422780\pi$
$60$	−0.771965	+	5.18873i	−0.0128661	+	0.0864788i
$61$	16.2346	−	28.1192i	0.266141	−	0.460970i	−0.701721	−	0.712452i	$-0.747585\pi$
$61$	16.2346	−	28.1192i	0.266141	−	0.460970i	0.967862	+	0.251482i	$0.0809179\pi$
$62$		−	70.3140i		−	1.13410i
$63$	17.0192	−	3.95282i	0.270145	−	0.0627431i
$64$	57.7269			0.901983
$65$	3.37133	+	67.2667i	0.0518666	+	1.03487i
$66$	−56.9694	−	45.2542i	−0.863173	−	0.685670i
$67$	−21.7493	+	12.5570i	−0.324617	+	0.187418i	−0.653448	−	0.756971i	$-0.726678\pi$
$67$	−21.7493	+	12.5570i	−0.324617	+	0.187418i	0.328832	+	0.944388i	$0.393345\pi$
$68$	−6.73303	+	3.88732i	−0.0990152	+	0.0571665i
$69$	42.7767	−	53.8505i	0.619952	−	0.780442i
$70$	18.1408	+	10.4736i	0.259155	+	0.149623i
$71$	−16.8087			−0.236742			−0.118371	−	0.992969i	$-0.537767\pi$
$71$	−16.8087			−0.236742			−0.118371	+	0.992969i	$0.537767\pi$
$72$	50.1455	−	46.8851i	0.696465	−	0.651183i
$73$		−	82.1471i		−	1.12530i	−0.826694	−	0.562651i	$-0.809781\pi$
$73$		−	82.1471i		−	1.12530i	0.826694	−	0.562651i	$-0.190219\pi$
$74$	66.3160	+	38.2875i	0.896162	+	0.517399i
$75$	0.812884	−	5.46376i	0.0108384	−	0.0728501i
$76$	4.66327	−	2.69234i	0.0613588	−	0.0354255i
$77$	−19.5777	+	11.3032i	−0.254256	+	0.146795i
$78$	−47.2744	+	66.0491i	−0.606082	+	0.846784i
$79$	6.27189	−	10.8632i	0.0793910	−	0.137509i	−0.823596	−	0.567176i	$-0.808036\pi$
$79$	6.27189	−	10.8632i	0.0793910	−	0.137509i	0.902987	+	0.429667i	$0.141369\pi$
$80$	89.2980			1.11623
$81$	5.43725	−	80.8173i	0.0671265	−	0.997744i
$82$	−6.91882			−0.0843758
$83$	−62.7678	+	108.717i	−0.756238	+	1.30984i	0.188518	+	0.982070i	$0.439632\pi$
$83$	−62.7678	+	108.717i	−0.756238	+	1.30984i	−0.944756	+	0.327773i	$0.893702\pi$
$84$	0.721637	+	1.82845i	0.00859091	+	0.0217672i
$85$	103.352	−	59.6706i	1.21591	−	0.702006i
$86$	−9.64125	−	16.6991i	−0.112108	−	0.194176i
$87$	132.047	+	19.6457i	1.51779	+	0.225812i
$88$	−44.4114	+	76.9228i	−0.504675	+	0.874123i
$89$	13.3476			0.149973			0.0749864	−	0.997185i	$-0.476109\pi$
$89$	13.3476			0.149973			0.0749864	+	0.997185i	$0.476109\pi$
$90$	70.9345	−	66.3225i	0.788161	−	0.736917i
$91$	13.6970	+	21.1973i	0.150517	+	0.232938i
$92$	6.70068	+	3.86864i	0.0728335	+	0.0420505i
$93$	−62.9988	+	79.3075i	−0.677406	+	0.852769i
$94$	−73.1641	−	126.724i	−0.778341	−	1.34813i
$95$	−71.5814	+	41.3275i	−0.753488	+	0.435027i
$96$	12.6525	+	10.0506i	0.131797	+	0.104694i
$97$	142.130	+	82.0586i	1.46526	+	0.845965i	0.999246	−	0.0388148i	$-0.0123582\pi$
$97$	142.130	+	82.0586i	1.46526	+	0.845965i	0.466009	+	0.884780i	$0.345692\pi$
$98$	−94.2016			−0.961241
$99$	23.7099	+	102.085i	0.239494	+	1.03116i
$100$	0.621465			0.00621465
$101$	89.4806	+	51.6617i	0.885947	+	0.511502i	0.872615	−	0.488409i	$-0.162423\pi$
$101$	89.4806	+	51.6617i	0.885947	+	0.511502i	0.0133324	+	0.999911i	$0.495756\pi$
$102$	142.356	+	21.1793i	1.39565	+	0.207641i
$103$	50.2550	+	87.0442i	0.487913	+	0.845090i	0.999903	−	0.0139014i	$-0.00442509\pi$
$103$	50.2550	+	87.0442i	0.487913	+	0.845090i	−0.511991	+	0.858991i	$0.671092\pi$
$104$	88.2499	+	45.2196i	0.848556	+	0.434804i
$105$	−11.0772	−	28.0667i	−0.105497	−	0.267302i
$106$	−65.9239	−	38.0612i	−0.621924	−	0.359068i
$107$			67.7199i			0.632896i	0.948610	+	0.316448i	$0.102490\pi$
$107$			67.7199i			0.632896i	−0.948610	+	0.316448i	$0.897510\pi$
$108$	9.08336	−	0.732949i	0.0841052	−	0.00678656i
$109$		−	46.9949i		−	0.431146i	−0.976488	−	0.215573i	$-0.930838\pi$
$109$		−	46.9949i		−	0.431146i	0.976488	−	0.215573i	$-0.0691619\pi$
$110$	−62.8232	+	108.813i	−0.571120	+	0.989209i
$111$	−40.4939	−	102.601i	−0.364810	−	0.924337i
$112$	28.9784	−	16.7307i	0.258736	−	0.149381i
$113$	−98.1089	+	56.6432i	−0.868220	+	0.501267i	−0.866756	−	0.498732i	$-0.833799\pi$
$113$	−98.1089	+	56.6432i	−0.868220	+	0.501267i	−0.00146367	+	0.999999i	$0.500466\pi$
$114$	−98.5951	−	14.6687i	−0.864869	−	0.128673i
$115$	−102.856	−	59.3839i	−0.894399	−	0.516381i
$116$			15.0195i			0.129478i
$117$	112.499	−	32.1410i	0.961527	−	0.274710i
$118$	−177.080			−1.50068
$119$	22.3595	−	38.7278i	0.187895	−	0.325444i
$120$	−92.8306	−	73.7410i	−0.773589	−	0.614508i
$121$	−7.29941	−	12.6430i	−0.0603257	−	0.104487i
$122$	−33.8114	−	58.5630i	−0.277142	−	0.480025i
$123$	7.80377	+	6.19901i	0.0634453	+	0.0503984i
$124$	−9.86833	−	5.69748i	−0.0795833	−	0.0459475i
$125$	119.982			0.959856
$126$	10.5932	−	34.8127i	0.0840727	−	0.276291i
$127$	−10.8278			−0.0852584			−0.0426292	−	0.999091i	$-0.513573\pi$
$127$	−10.8278			−0.0852584			−0.0426292	+	0.999091i	$0.513573\pi$
$128$	70.8854	−	122.777i	0.553792	−	0.959197i
$129$	−4.08740	+	27.4732i	−0.0316852	+	0.212971i
$130$	124.836	+	63.9665i	0.960277	+	0.492050i
$131$	−99.4918	+	57.4416i	−0.759479	+	0.438486i	−0.829109	−	0.559087i	$-0.811152\pi$
$131$	−99.4918	+	57.4416i	−0.759479	+	0.438486i	0.0696294	+	0.997573i	$0.477818\pi$
$132$	−10.9675	+	4.32855i	−0.0830868	+	0.0327920i
$133$	−15.4861	+	26.8227i	−0.116437	+	0.201674i
$134$			52.3041i			0.390329i
$135$	−139.430	+	11.2508i	−1.03281	+	0.0833393i
$136$		−	175.705i		−	1.29195i
$137$	−83.3478	+	144.363i	−0.608378	+	1.05374i	0.383129	+	0.923695i	$0.374846\pi$
$137$	−83.3478	+	144.363i	−0.608378	+	1.05374i	−0.991508	+	0.130048i	$0.958487\pi$
$138$	−52.5823	−	133.230i	−0.381031	−	0.965438i
$139$	−86.4287	−	149.699i	−0.621789	−	1.07697i	−0.989152	−	0.146893i	$-0.953073\pi$
$139$	−86.4287	−	149.699i	−0.621789	−	1.07697i	0.367363	−	0.930078i	$-0.380261\pi$
$140$	2.93987	−	1.69734i	0.0209991	−	0.0121238i
$141$	−31.0178	+	208.485i	−0.219985	+	1.47862i
$142$	−17.5035	+	30.3169i	−0.123264	+	0.213499i
$143$	−127.147	+	82.1579i	−0.889138	+	0.574531i
$144$	−35.0948	−	151.103i	−0.243714	−	1.04933i
$145$		−	230.550i		−	1.59000i
$146$	−148.164	−	85.5426i	−1.01482	−	0.585908i
$147$	106.250	+	84.4012i	0.722792	+	0.574158i
$148$	10.7471	−	6.20482i	0.0726152	−	0.0419244i
$149$	9.64608	+	16.7075i	0.0647388	+	0.112131i	0.896578	−	0.442886i	$-0.146045\pi$
$149$	9.64608	+	16.7075i	0.0647388	+	0.112131i	−0.831839	+	0.555017i	$0.812712\pi$
$150$	−9.00820	−	7.15576i	−0.0600547	−	0.0477051i
$151$	−116.373	−	67.1882i	−0.770685	−	0.444955i	0.0624342	−	0.998049i	$-0.480114\pi$
$151$	−116.373	−	67.1882i	−0.770685	−	0.444955i	−0.833119	+	0.553094i	$0.813447\pi$
$152$			121.693i			0.800609i
$153$	−141.588	−	151.434i	−0.925413	−	0.989765i
$154$			47.0817i			0.305726i
$155$	151.479	+	87.4567i	0.977287	+	0.564237i
$156$	5.43917	+	11.9867i	0.0348665	+	0.0768379i
$157$	−91.7089	−	158.844i	−0.584133	−	1.01175i	−0.994983	−	0.100045i	$-0.968101\pi$
$157$	−91.7089	−	158.844i	−0.584133	−	1.01175i	0.410850	−	0.911703i	$-0.365232\pi$
$158$	−13.0623	−	22.6245i	−0.0826726	−	0.143193i
$159$	40.2545	+	101.995i	0.253173	+	0.641477i
$160$	13.9526	−	24.1665i	0.0872035	−	0.151041i
$161$	−44.5042			−0.276423
$162$	−140.104	−	93.9647i	−0.864838	−	0.580029i
$163$			220.136i			1.35053i	0.737576	+	0.675264i	$0.235970\pi$
$163$			220.136i			1.35053i	−0.737576	+	0.675264i	$0.764030\pi$
$164$	−0.560626	+	0.971033i	−0.00341845	+	0.00592093i
$165$	168.351	−	66.4435i	1.02031	−	0.402688i
$166$	130.725	+	226.422i	0.787497	+	1.36399i
$167$	−99.2266	−	171.865i	−0.594171	−	1.02913i	−0.993663	−	0.112398i	$-0.964147\pi$
$167$	−99.2266	−	171.865i	−0.594171	−	1.02913i	0.399492	−	0.916737i	$-0.369186\pi$
$168$	−43.9408	−	6.53739i	−0.261552	−	0.0389130i
$169$	98.7104	+	137.176i	0.584085	+	0.811692i
$170$		−	248.548i		−	1.46205i
$171$	98.0633	+	104.883i	0.573470	+	0.613348i
$172$	−3.12489			−0.0181680
$173$	126.719	+	73.1612i	0.732479	+	0.422897i	0.819328	−	0.573325i	$-0.194347\pi$
$173$	126.719	+	73.1612i	0.732479	+	0.422897i	−0.0868495	+	0.996221i	$0.527680\pi$
$174$	172.939	−	217.709i	0.993905	−	1.25120i
$175$	−3.09570	+	1.78730i	−0.0176897	+	0.0102132i
$176$	100.355	+	173.820i	0.570198	+	0.987611i
$177$	199.730	+	158.658i	1.12842	+	0.896371i
$178$	13.8993	−	24.0743i	0.0780860	−	0.135249i
$179$		−	300.882i		−	1.68090i	−0.541887	−	0.840451i	$-0.682290\pi$
$179$		−	300.882i		−	1.68090i	0.541887	−	0.840451i	$-0.317710\pi$
$180$	−3.56038	−	15.3295i	−0.0197799	−	0.0851638i
$181$	72.4358			0.400198			0.200099	−	0.979776i	$-0.435874\pi$
$181$	72.4358			0.400198			0.200099	+	0.979776i	$0.435874\pi$
$182$	52.4956	−	2.63102i	0.288437	−	0.0144561i
$183$	−14.3343	+	96.3473i	−0.0783294	+	0.526488i
$184$	−151.434	+	87.4305i	−0.823011	+	0.475166i
$185$	−164.968	+	95.2442i	−0.891718	+	0.514834i
$186$	77.4398	+	196.213i	0.416343	+	1.05491i
$187$	232.299	+	134.118i	1.24224	+	0.717207i
$188$	−23.7137			−0.126137
$189$	−43.1390	+	29.7744i	−0.228249	+	0.157536i
$190$			172.143i			0.906017i
$191$	−5.56688	−	3.21404i	−0.0291459	−	0.0168274i	0.485356	−	0.874316i	$-0.338690\pi$
$191$	−5.56688	−	3.21404i	−0.0291459	−	0.0168274i	−0.514502	+	0.857489i	$0.672023\pi$
$192$	−161.088	+	63.5771i	−0.839003	+	0.331131i
$193$	−292.029	+	168.603i	−1.51310	+	0.873591i	−0.513222	+	0.858256i	$0.671548\pi$
$193$	−292.029	+	168.603i	−1.51310	+	0.873591i	−0.999882	+	0.0153357i	$0.995118\pi$
$194$	296.009	−	170.901i	1.52582	−	0.880933i
$195$	−83.4915	−	183.997i	−0.428162	−	0.943573i
$196$	−7.63308	+	13.2209i	−0.0389443	+	0.0674535i
$197$	68.8698			0.349593			0.174796	−	0.984605i	$-0.444073\pi$
$197$	68.8698			0.349593			0.174796	+	0.984605i	$0.444073\pi$
$198$	208.815	+	63.5403i	1.05462	+	0.320911i
$199$	32.1256			0.161435			0.0807175	−	0.996737i	$-0.474279\pi$
$199$	32.1256			0.161435			0.0807175	+	0.996737i	$0.474279\pi$
$200$	−7.02249	+	12.1633i	−0.0351124	+	0.0608165i
$201$	46.8625	−	58.9940i	0.233147	−	0.293503i
$202$	186.359	−	107.594i	0.922568	−	0.532645i
$203$	−43.1953	−	74.8165i	−0.212785	−	0.368554i
$204$	14.5074	−	18.2631i	0.0711149	−	0.0895248i
$205$	8.60564	−	14.9054i	0.0419787	−	0.0727093i
$206$	209.329			1.01616
$207$	−60.0617	+	197.383i	−0.290153	+	0.953542i
$208$	188.199	−	121.608i	0.904802	−	0.584653i
$209$	−160.889	−	92.8893i	−0.769804	−	0.444446i
$210$	−62.1575	−	9.24762i	−0.295988	−	0.0440363i
$211$	−122.283	−	211.800i	−0.579540	−	1.00379i	−0.995532	−	0.0944247i	$-0.969899\pi$
$211$	−122.283	−	211.800i	−0.579540	−	1.00379i	0.415992	−	0.909368i	$-0.363434\pi$
$212$	−10.6835	+	6.16814i	−0.0503940	+	0.0290950i
$213$	46.9051	−	18.5121i	0.220212	−	0.0869114i
$214$	122.143	+	70.5191i	0.570760	+	0.329528i
$215$	47.9672			0.223103
$216$	−88.2957	+	186.062i	−0.408777	+	0.861397i
$217$	65.5428			0.302041
$218$	−84.7621	−	48.9374i	−0.388817	−	0.224484i
$219$	90.4721	+	229.234i	0.413115	+	1.04673i
$220$	10.1810	+	17.6341i	0.0462774	+	0.0801548i
$221$	136.559	−	266.505i	0.617912	−	1.20591i
$222$	−227.224	−	33.8058i	−1.02353	−	0.152278i
$223$	206.126	+	119.007i	0.924332	+	0.533663i	0.885014	−	0.465563i	$-0.154148\pi$
$223$	206.126	+	119.007i	0.924332	+	0.533663i	0.0393174	+	0.999227i	$0.487482\pi$
$224$		−	10.4565i		−	0.0466808i
$225$	3.74910	+	16.1420i	0.0166627	+	0.0717424i
$226$			235.938i			1.04397i
$227$	146.916	−	254.466i	0.647206	−	1.12099i	−0.336581	−	0.941654i	$-0.609271\pi$
$227$	146.916	−	254.466i	0.647206	−	1.12099i	0.983787	−	0.179339i	$-0.0573960\pi$
$228$	−10.0478	+	12.6489i	−0.0440692	+	0.0554776i
$229$	−360.919	+	208.377i	−1.57606	+	0.909941i	−0.580663	+	0.814144i	$0.697207\pi$
$229$	−360.919	+	208.377i	−1.57606	+	0.909941i	−0.995401	+	0.0957972i	$0.969460\pi$
$230$	−214.215	+	123.677i	−0.931369	+	0.537726i
$231$	42.1835	−	53.1037i	0.182613	−	0.229886i
$232$	−293.961	−	169.719i	−1.26707	−	0.731545i
$233$			45.8581i			0.196816i	0.995146	+	0.0984079i	$0.0313750\pi$
$233$			45.8581i			0.196816i	−0.995146	+	0.0984079i	$0.968625\pi$
$234$	59.1778	−	236.377i	0.252897	−	1.01016i
$235$	364.006			1.54896
$236$	−14.3487	+	24.8526i	−0.0607995	+	0.105308i
$237$	−5.53774	+	37.2217i	−0.0233660	+	0.157053i
$238$	−46.5675	−	80.6572i	−0.195662	−	0.338896i
$239$	124.482	+	215.609i	0.520845	+	0.902129i	0.999706	+	0.0242389i	$0.00771623\pi$
$239$	124.482	+	215.609i	0.520845	+	0.902129i	−0.478862	+	0.877890i	$0.658950\pi$
$240$	−249.189	+	98.3477i	−1.03829	+	0.409782i
$241$	−132.042	−	76.2342i	−0.547890	−	0.316325i	0.200380	−	0.979718i	$-0.435782\pi$
$241$	−132.042	−	76.2342i	−0.547890	−	0.316325i	−0.748271	+	0.663394i	$0.769116\pi$
$242$	−30.4045			−0.125639
$243$	73.8348	+	231.511i	0.303847	+	0.952721i
$244$	−10.9588			−0.0449132
$245$	117.168	−	202.941i	0.478237	−	0.828331i
$246$	19.3071	−	7.61999i	0.0784843	−	0.0309756i
$247$	−94.5798	+	184.580i	−0.382914	+	0.747289i
$248$	223.022	−	128.762i	0.899283	−	0.519202i
$249$	55.4205	−	372.507i	0.222572	−	1.49601i
$250$	124.941	−	216.405i	0.499766	−	0.865619i
$251$			86.6764i			0.345324i	0.984981	+	0.172662i	$0.0552369\pi$
$251$			86.6764i			0.345324i	−0.984981	+	0.172662i	$0.944763\pi$
$252$	−4.02749	−	4.30756i	−0.0159821	−	0.0170935i
$253$		−	266.947i		−	1.05513i
$254$	−11.2754	+	19.5295i	−0.0443913	+	0.0768880i
$255$	−222.690	+	280.339i	−0.873294	+	1.09937i
$256$	−32.1772	−	55.7325i	−0.125692	−	0.217705i
$257$	343.940	−	198.574i	1.33829	−	0.772661i	0.351735	−	0.936100i	$-0.385592\pi$
$257$	343.940	−	198.574i	1.33829	−	0.772661i	0.986554	+	0.163438i	$0.0522584\pi$
$258$	45.2956	+	35.9811i	0.175565	+	0.139462i
$259$	−35.6895	+	61.8161i	−0.137797	+	0.238672i
$260$	19.0928	−	12.3372i	0.0734340	−	0.0474506i
$261$	−390.119	+	90.6078i	−1.49471	+	0.347156i
$262$			239.264i			0.913221i
$263$	−0.0947841	−	0.0547236i	−0.000360396	−	0.000208075i	0.499820	−	0.866129i	$-0.333400\pi$
$263$	−0.0947841	−	0.0547236i	−0.000360396	−	0.000208075i	−0.500180	+	0.865921i	$0.666733\pi$
$264$	39.2128	−	263.567i	0.148533	−	0.998361i
$265$	163.993	−	94.6812i	0.618840	−	0.357288i
$266$	32.2524	+	55.8628i	0.121250	+	0.210011i
$267$	−37.2468	+	14.7003i	−0.139501	+	0.0550572i
$268$	7.34070	+	4.23816i	0.0273907	+	0.0158140i
$269$		−	54.3787i		−	0.202151i	−0.994879	−	0.101076i	$-0.967772\pi$
$269$		−	54.3787i		−	0.202151i	0.994879	−	0.101076i	$-0.0322284\pi$
$270$	−124.901	+	263.198i	−0.462596	+	0.974808i
$271$		−	316.336i		−	1.16729i	−0.812009	−	0.583645i	$-0.801626\pi$
$271$		−	316.336i		−	1.16729i	0.812009	−	0.583645i	$-0.198374\pi$
$272$	−343.842	−	198.517i	−1.26413	−	0.729843i
$273$	−61.5674	−	44.0666i	−0.225522	−	0.161416i
$274$	173.586	+	300.660i	0.633526	+	1.09730i
$275$	−10.7207	−	18.5688i	−0.0389843	−	0.0675228i
$276$	−22.9591	−	3.41580i	−0.0831853	−	0.0123761i
$277$	19.9323	−	34.5238i	0.0719578	−	0.124635i	−0.827802	−	0.561021i	$-0.810409\pi$
$277$	19.9323	−	34.5238i	0.0719578	−	0.124635i	0.899759	+	0.436387i	$0.143742\pi$
$278$	−360.005			−1.29498
$279$	88.4550	−	290.693i	0.317043	−	1.04191i
$280$			76.7189i			0.273996i
$281$	125.592	−	217.532i	0.446947	−	0.774136i	−0.551238	−	0.834348i	$-0.685844\pi$
$281$	125.592	−	217.532i	0.446947	−	0.774136i	0.998186	+	0.0602124i	$0.0191778\pi$
$282$	343.733	+	273.048i	1.21891	+	0.968254i
$283$	136.772	+	236.897i	0.483295	+	0.837091i	0.999816	−	0.0191830i	$-0.00610652\pi$
$283$	136.772	+	236.897i	0.483295	+	0.837091i	−0.516521	+	0.856275i	$0.672773\pi$
$284$	2.83659	+	4.91311i	0.00998798	+	0.0172997i
$285$	154.234	−	194.161i	0.541172	−	0.681268i
$286$	15.7815	+	314.881i	0.0551800	+	1.10098i
$287$		−	6.44934i		−	0.0224716i
$288$	−46.3762	−	14.1118i	−0.161029	−	0.0489994i
$289$	−241.611			−0.836025
$290$	−415.830	−	240.079i	−1.43390	−	0.827860i
$291$	−486.992	−	72.4533i	−1.67351	−	0.248980i
$292$	−24.0112	+	13.8629i	−0.0822303	+	0.0474757i
$293$	106.619	+	184.670i	0.363888	+	0.630273i	0.988597	−	0.150585i	$-0.0481156\pi$
$293$	106.619	+	184.670i	0.363888	+	0.630273i	−0.624709	+	0.780858i	$0.714782\pi$
$294$	262.872	−	103.748i	0.894123	−	0.352885i
$295$	220.253	−	381.489i	0.746621	−	1.29318i
$296$			280.455i			0.947484i
$297$	−178.594	−	258.758i	−0.601326	−	0.871240i
$298$	40.1792			0.134830
$299$	−297.643	+	14.9175i	−0.995460	+	0.0498913i
$300$	−1.73421	+	0.684446i	−0.00578071	+	0.00228149i
$301$	15.5660	−	8.98704i	0.0517143	−	0.0298573i
$302$	−242.367	+	139.931i	−0.802541	+	0.463347i
$303$	−306.595	−	45.6144i	−1.01187	−	0.150543i
$304$	238.143	+	137.492i	0.783366	+	0.452277i
$305$	168.219			0.551536
$306$	−420.574	+	97.6813i	−1.37443	+	0.319220i
$307$			185.168i			0.603152i	0.953442	+	0.301576i	$0.0975128\pi$
$307$			185.168i			0.603152i	−0.953442	+	0.301576i	$0.902487\pi$
$308$	6.60776	+	3.81499i	0.0214538	+	0.0123863i
$309$	−236.104	−	187.551i	−0.764089	−	0.606962i
$310$	315.482	−	182.143i	1.01768	−	0.587559i
$311$	−467.154	+	269.712i	−1.50210	+	0.867240i	−0.502107	+	0.864806i	$0.667442\pi$
$311$	−467.154	+	269.712i	−1.50210	+	0.867240i	−0.999997	+	0.00243426i	$0.999225\pi$
$312$	−296.066	−	28.9932i	−0.948929	−	0.0929271i
$313$	−303.999	+	526.541i	−0.971242	+	1.68224i	−0.279424	+	0.960168i	$0.590144\pi$
$313$	−303.999	+	526.541i	−0.971242	+	1.68224i	−0.691817	+	0.722073i	$0.743190\pi$
$314$	−381.999			−1.21656
$315$	61.8222	+	66.1213i	0.196261	+	0.209909i
$316$	−4.23370			−0.0133978
$317$	−168.124	+	291.200i	−0.530360	+	0.918611i	0.469012	+	0.883192i	$0.344610\pi$
$317$	−168.124	+	291.200i	−0.530360	+	0.918611i	−0.999373	+	0.0354194i	$0.988723\pi$
$318$	225.881	+	33.6060i	0.710318	+	0.105679i
$319$	448.767	−	259.096i	1.40679	−	0.812213i
$320$	149.537	+	259.006i	0.467305	+	0.809395i
$321$	−74.5828	−	188.974i	−0.232345	−	0.588705i
$322$	−46.3437	+	80.2697i	−0.143925	+	0.249285i
$323$	367.499			1.13777
$324$	−24.5401	+	12.0492i	−0.0757411	+	0.0371889i
$325$	−20.1049	+	12.9911i	−0.0618612	+	0.0399726i
$326$	397.047	+	229.235i	1.21794	+	0.703176i
$327$	51.7575	+	131.141i	0.158280	+	0.401042i
$328$	−12.6700	−	21.9451i	−0.0386281	−	0.0669059i
$329$	118.125	−	68.1995i	0.359043	−	0.207293i
$330$	55.4695	−	372.836i	0.168089	−	1.12980i
$331$	−420.968	−	243.046i	−1.27181	−	0.734278i	−0.296479	−	0.955039i	$-0.595812\pi$
$331$	−420.968	−	243.046i	−1.27181	−	0.734278i	−0.975328	+	0.220762i	$0.929146\pi$
$332$	42.3700			0.127621
$333$	225.999	+	241.714i	0.678675	+	0.725869i
$334$	−413.312			−1.23746
$335$	−112.680	−	65.0559i	−0.336359	−	0.194197i
$336$	−62.4388	+	78.6027i	−0.185830	+	0.233936i
$337$	86.1155	+	149.156i	0.255536	+	0.442601i	0.965041	−	0.262099i	$-0.0844148\pi$
$337$	86.1155	+	149.156i	0.255536	+	0.442601i	−0.709505	+	0.704700i	$0.751082\pi$
$338$	350.207	−	35.1923i	1.03612	−	0.104119i
$339$	211.392	−	266.116i	0.623575	−	0.785002i
$340$	−34.8829	−	20.1397i	−0.102597	−	0.0592343i
$341$			393.142i			1.15291i
$342$	291.288	−	67.6536i	0.851718	−	0.197817i
$343$		−	182.936i		−	0.533340i
$344$	35.3109	−	61.1603i	0.102648	−	0.177792i
$345$	352.424	+	52.4327i	1.02152	+	0.151979i
$346$	263.914	−	152.371i	0.762756	−	0.440377i
$347$	−336.454	+	194.252i	−0.969607	+	0.559803i	−0.899116	−	0.437710i	$-0.855790\pi$
$347$	−336.454	+	194.252i	−0.969607	+	0.559803i	−0.0704905	+	0.997512i	$0.522456\pi$
$348$	−16.5416	−	41.9123i	−0.0475333	−	0.120438i
$349$	−43.5073	−	25.1189i	−0.124663	−	0.0719740i	0.436372	−	0.899766i	$-0.356263\pi$
$349$	−43.5073	−	25.1189i	−0.124663	−	0.0719740i	−0.561035	+	0.827792i	$0.689597\pi$
$350$			7.44473i			0.0212707i
$351$	−278.532	+	213.590i	−0.793540	+	0.608519i
$352$	62.7206			0.178183
$353$	−56.6496	+	98.1199i	−0.160480	+	0.277960i	−0.935041	−	0.354539i	$-0.884638\pi$
$353$	−56.6496	+	98.1199i	−0.160480	+	0.277960i	0.774561	+	0.632500i	$0.217971\pi$
$354$	494.148	−	195.026i	1.39590	−	0.550922i
$355$	−43.5417	−	75.4165i	−0.122653	−	0.212441i
$356$	−2.25250	−	3.90144i	−0.00632724	−	0.0109591i
$357$	−19.7422	+	132.697i	−0.0553004	+	0.371699i
$358$	−542.684	−	313.318i	−1.51588	−	0.875191i
$359$	−139.525			−0.388649			−0.194324	−	0.980937i	$-0.562251\pi$
$359$	−139.525			−0.388649			−0.194324	+	0.980937i	$0.562251\pi$
$360$	340.261	+	103.538i	0.945168	+	0.287605i
$361$	106.472			0.294937
$362$	75.4299	−	130.649i	0.208370	−	0.360907i
$363$	34.2934	+	27.2414i	0.0944723	+	0.0750450i
$364$	3.88442	−	7.58077i	0.0106715	−	0.0208263i
$365$	368.574	−	212.796i	1.00979	−	0.583003i
$366$	158.849	+	126.184i	0.434015	+	0.344764i
$367$	199.851	−	346.152i	0.544552	−	0.943192i	−0.454083	−	0.890960i	$-0.650033\pi$
$367$	199.851	−	346.152i	0.544552	−	0.943192i	0.998635	−	0.0522328i	$-0.0166338\pi$
$368$			395.127i			1.07371i
$369$	−28.6039	−	8.70387i	−0.0775172	−	0.0235877i
$370$			396.725i			1.07223i
$371$	35.4786	−	61.4507i	0.0956296	−	0.165635i
$372$	33.8127	+	5.03057i	0.0908945	+	0.0135230i
$373$	−292.378	−	506.414i	−0.783855	−	1.35768i	−0.929681	−	0.368367i	$-0.879917\pi$
$373$	−292.378	−	506.414i	−0.783855	−	1.35768i	0.145825	−	0.989310i	$-0.453416\pi$
$374$	483.802	−	279.323i	1.29359	−	0.746853i
$375$	−334.813	+	132.141i	−0.892835	+	0.352377i
$376$	267.962	−	464.124i	0.712666	−	1.23437i
$377$	−313.967	−	485.892i	−0.832804	−	1.28884i
$378$	8.78023	+	108.813i	0.0232281	+	0.287864i
$379$		−	53.8120i		−	0.141984i	−0.997477	−	0.0709921i	$-0.977383\pi$
$379$		−	53.8120i		−	0.141984i	0.997477	−	0.0709921i	$-0.0226165\pi$
$380$	24.1597	+	13.9486i	0.0635782	+	0.0367069i
$381$	30.2153	−	11.9251i	0.0793053	−	0.0312996i
$382$	−11.5940	+	6.69378i	−0.0303507	+	0.0175230i
$383$	−77.8061	−	134.764i	−0.203149	−	0.351865i	0.746392	−	0.665506i	$-0.231784\pi$
$383$	−77.8061	−	134.764i	−0.203149	−	0.351865i	−0.949541	+	0.313642i	$0.898451\pi$
$384$	−62.5880	+	420.682i	−0.162989	+	1.09553i
$385$	−101.430	−	58.5604i	−0.263453	−	0.152105i
$386$			702.289i			1.81940i
$387$	−18.8515	−	81.1665i	−0.0487118	−	0.209733i
$388$		−	55.3919i		−	0.142763i
$389$	562.403	+	324.704i	1.44577	+	0.834714i	0.998225	−	0.0595488i	$-0.0189662\pi$
$389$	562.403	+	324.704i	1.44577	+	0.834714i	0.447542	+	0.894263i	$0.352300\pi$
$390$	−418.807	−	41.0131i	−1.07387	−	0.105162i
$391$	264.031	+	457.315i	0.675271	+	1.16960i
$392$	−172.506	−	298.789i	−0.440066	−	0.762217i
$393$	214.372	−	269.867i	0.545475	−	0.686685i
$394$	71.7165	−	124.217i	0.182022	−	0.315271i
$395$	64.9876			0.164525
$396$	25.8378	−	24.1579i	0.0652469	−	0.0610047i
$397$			708.677i			1.78508i	0.450967	+	0.892541i	$0.351079\pi$
$397$			708.677i			1.78508i	−0.450967	+	0.892541i	$0.648921\pi$
$398$	33.4535	−	57.9431i	0.0840540	−	0.145586i
$399$	13.6734	−	91.9049i	0.0342691	−	0.230338i
$400$	15.8684	+	27.4850i	0.0396711	+	0.0687124i
$401$	205.025	+	355.113i	0.511283	+	0.885569i	0.999914	+	0.0130783i	$0.00416306\pi$
$401$	205.025	+	355.113i	0.511283	+	0.885569i	−0.488631	+	0.872490i	$0.662504\pi$
$402$	−57.6047	−	145.956i	−0.143295	−	0.363074i
$403$	438.349	−	21.9695i	1.08771	−	0.0545149i
$404$		−	34.8731i		−	0.0863195i
$405$	376.692	−	184.956i	0.930104	−	0.456681i
$406$	−179.923			−0.443161
$407$	−370.788	−	214.074i	−0.911027	−	0.525982i
$408$	193.512	+	490.310i	0.474293	+	1.20174i
$409$	251.330	−	145.105i	0.614499	−	0.354781i	−0.160225	−	0.987080i	$-0.551222\pi$
$409$	251.330	−	145.105i	0.614499	−	0.354781i	0.774724	+	0.632299i	$0.217889\pi$
$410$	−17.9227	−	31.0430i	−0.0437139	−	0.0757147i
$411$	73.5916	−	494.643i	0.179055	−	1.20351i
$412$	16.9618	−	29.3787i	0.0411694	−	0.0713074i
$413$		−	165.065i		−	0.399672i
$414$	293.465	+	313.872i	0.708852	+	0.758145i
$415$	−650.382			−1.56719
$416$	−3.50495	−	69.9328i	−0.00842535	−	0.168108i
$417$	406.051	+	322.551i	0.973744	+	0.773504i
$418$	−335.079	+	193.458i	−0.801623	+	0.462817i
$419$	212.816	−	122.869i	0.507913	−	0.293244i	−0.224062	−	0.974575i	$-0.571932\pi$
$419$	212.816	−	122.869i	0.507913	−	0.293244i	0.731976	+	0.681331i	$0.238599\pi$
$420$	−6.33444	+	7.97427i	−0.0150820	+	0.0189864i
$421$	−496.801	−	286.828i	−1.18005	−	0.681302i	−0.224024	−	0.974584i	$-0.571919\pi$
$421$	−496.801	−	286.828i	−1.18005	−	0.681302i	−0.956026	+	0.293281i	$0.905253\pi$
$422$	−509.350			−1.20699
$423$	−143.057	−	615.944i	−0.338197	−	1.45613i
$424$		−	278.797i		−	0.657541i
$425$	36.7319	+	21.2072i	0.0864280	+	0.0498992i
$426$	15.4546	−	103.878i	0.0362784	−	0.243844i
$427$	54.5892	−	31.5171i	0.127844	−	0.0738105i
$428$	19.7942	−	11.4282i	0.0462482	−	0.0267014i
$429$	264.322	−	369.296i	0.616136	−	0.860830i
$430$	49.9500	−	86.5159i	0.116163	−	0.201200i
$431$	193.685			0.449385			0.224693	−	0.974430i	$-0.427862\pi$
$431$	193.685			0.449385			0.224693	+	0.974430i	$0.427862\pi$
$432$	264.350	+	383.006i	0.611920	+	0.886589i
$433$	−418.947			−0.967546			−0.483773	−	0.875194i	$-0.660734\pi$
$433$	−418.947			−0.967546			−0.483773	+	0.875194i	$0.660734\pi$
$434$	68.2521	−	118.216i	0.157263	−	0.272387i
$435$	253.914	+	643.355i	0.583711	+	1.47898i
$436$	−13.7364	+	7.93072i	−0.0315055	+	0.0181897i
$437$	−182.867	−	316.734i	−0.418459	−	0.724792i
$438$	507.668	+	75.5295i	1.15906	+	0.172442i
$439$	−363.965	+	630.405i	−0.829077	+	1.43600i	0.0696865	+	0.997569i	$0.477800\pi$
$439$	−363.965	+	630.405i	−0.829077	+	1.43600i	−0.898763	+	0.438434i	$0.855533\pi$
$440$	−460.178			−1.04586
$441$	−389.449	−	118.506i	−0.883105	−	0.268720i
$442$	−338.478	−	523.824i	−0.765787	−	1.18512i
$443$	399.357	+	230.569i	0.901484	+	0.520472i	0.877681	−	0.479245i	$-0.159089\pi$
$443$	399.357	+	230.569i	0.901484	+	0.520472i	0.0238025	+	0.999717i	$0.492423\pi$
$444$	−23.1563	+	29.1509i	−0.0521539	+	0.0656552i
$445$	34.5760	+	59.8873i	0.0776988	+	0.134578i
$446$	429.292	−	247.852i	0.962539	−	0.555722i
$447$	−45.3184	−	35.9991i	−0.101383	−	0.0805349i
$448$	97.0539	+	56.0341i	0.216638	+	0.125076i
$449$	−308.063			−0.686108			−0.343054	−	0.939316i	$-0.611461\pi$
$449$	−308.063			−0.686108			−0.343054	+	0.939316i	$0.611461\pi$
$450$	33.0186	+	10.0472i	0.0733746	+	0.0223272i
$451$	38.6847			0.0857754
$452$	33.1131	+	19.1179i	0.0732591	+	0.0422962i
$453$	398.740	+	59.3235i	0.880221	+	0.130957i
$454$	−305.977	−	529.968i	−0.673958	−	1.16733i
$455$	−59.6261	+	116.365i	−0.131046	+	0.255748i
$456$	−134.025	−	339.586i	−0.293915	−	0.744707i
$457$	340.050	+	196.328i	0.744091	+	0.429601i	0.823555	−	0.567237i	$-0.191988\pi$
$457$	340.050	+	196.328i	0.744091	+	0.429601i	−0.0794639	+	0.996838i	$0.525321\pi$
$458$			867.959i			1.89511i
$459$	561.887	+	266.644i	1.22415	+	0.580923i
$460$			40.0858i			0.0871430i
$461$	−203.535	+	352.533i	−0.441508	+	0.764713i	−0.997802	−	0.0662721i	$-0.978889\pi$
$461$	−203.535	+	352.533i	−0.441508	+	0.764713i	0.556294	+	0.830985i	$0.312223\pi$
$462$	−51.8531	−	131.383i	−0.112236	−	0.284379i
$463$	33.4769	−	19.3279i	0.0723043	−	0.0417449i	−0.463412	−	0.886143i	$-0.653375\pi$
$463$	33.4769	−	19.3279i	0.0723043	−	0.0417449i	0.535716	+	0.844398i	$0.320042\pi$
$464$	−664.253	+	383.507i	−1.43158	+	0.826523i
$465$	−519.027	−	77.2195i	−1.11619	−	0.166063i
$466$	82.7117	+	47.7536i	0.177493	+	0.102476i
$467$		−	684.721i		−	1.46621i	−0.680115	−	0.733105i	$-0.738070\pi$
$467$		−	684.721i		−	1.46621i	0.680115	−	0.733105i	$-0.261930\pi$
$468$	−28.3796	−	27.4589i	−0.0606402	−	0.0586728i
$469$	−48.7550			−0.103955
$470$	379.053	−	656.538i	0.806495	−	1.39689i
$471$	430.858	+	342.257i	0.914774	+	0.726660i
$472$	−324.277	−	561.665i	−0.687028	−	1.18997i
$473$	53.9065	+	93.3687i	0.113967	+	0.197397i
$474$	61.3680	+	48.7483i	0.129468	+	0.102845i
$475$	−25.4403	−	14.6880i	−0.0535586	−	0.0309221i
$476$	−15.0933			−0.0317086
$477$	−224.663	−	240.285i	−0.470991	−	0.503743i
$478$	518.509			1.08475
$479$	−254.722	+	441.192i	−0.531779	+	0.921068i	0.467533	+	0.883976i	$0.345143\pi$
$479$	−254.722	+	441.192i	−0.531779	+	0.921068i	−0.999312	+	0.0370926i	$0.988190\pi$
$480$	−12.3193	+	82.8039i	−0.0256653	+	0.172508i
$481$	−217.970	+	425.387i	−0.453161	+	0.884381i
$482$	−274.999	+	158.771i	−0.570537	+	0.329400i
$483$	124.190	−	49.0143i	0.257122	−	0.101479i
$484$	−2.46365	+	4.26717i	−0.00509020	+	0.00881648i
$485$			850.269i			1.75313i
$486$	494.451	+	107.909i	1.01739	+	0.222035i
$487$			754.148i			1.54856i	0.632844	+	0.774280i	$0.281888\pi$
$487$			754.148i			1.54856i	−0.632844	+	0.774280i	$0.718112\pi$
$488$	123.834	−	214.486i	0.253757	−	0.439521i
$489$	−242.445	−	614.296i	−0.495798	−	1.25623i
$490$	−244.023	−	422.659i	−0.498005	−	0.862570i
$491$	382.789	−	221.003i	0.779612	−	0.450109i	−0.0566811	−	0.998392i	$-0.518052\pi$
$491$	382.789	−	221.003i	0.779612	−	0.450109i	0.836293	+	0.548283i	$0.184718\pi$
$492$	0.495002	−	3.32713i	0.00100610	−	0.00676247i
$493$	−512.532	+	887.732i	−1.03962	+	1.80067i
$494$	234.428	+	362.798i	0.474551	+	0.734409i
$495$	−396.611	+	370.825i	−0.801235	+	0.749141i
$496$		−	581.917i		−	1.17322i
$497$	−28.2598	−	16.3158i	−0.0568607	−	0.0328285i
$498$	−614.158	−	487.863i	−1.23325	−	0.979645i
$499$	12.8035	−	7.39211i	0.0256583	−	0.0148138i	−0.487116	−	0.873337i	$-0.661951\pi$
$499$	12.8035	−	7.39211i	0.0256583	−	0.0148138i	0.512774	+	0.858523i	$0.328618\pi$
$500$	−20.2478	−	35.0702i	−0.0404956	−	0.0701404i
$501$	466.177	+	370.313i	0.930494	+	0.739147i
$502$	156.333	+	90.2592i	0.311421	+	0.179799i
$503$		−	477.344i		−	0.948995i	−0.880257	−	0.474497i	$-0.842630\pi$
$503$		−	477.344i		−	0.948995i	0.880257	−	0.474497i	$-0.157370\pi$
$504$	129.818	−	30.1511i	0.257575	−	0.0598236i
$505$			535.304i			1.06001i
$506$	−481.477	−	277.981i	−0.951536	−	0.549369i
$507$	−426.532	−	274.079i	−0.841286	−	0.540591i
$508$	1.82727	+	3.16493i	0.00359699	+	0.00623017i
$509$	157.294	+	272.442i	0.309027	+	0.535250i	0.978150	−	0.207902i	$-0.0666635\pi$
$509$	157.294	+	272.442i	0.309027	+	0.535250i	−0.669123	+	0.743152i	$0.733330\pi$
$510$	273.737	+	693.580i	0.536739	+	1.35996i
$511$	79.7382	−	138.111i	0.156043	−	0.270275i
$512$	433.055			0.845810
$513$	−389.160	−	184.676i	−0.758596	−	0.359993i
$514$		−	827.128i		−	1.60920i
$515$	−260.364	+	450.964i	−0.505561	+	0.875658i
$516$	8.72009	−	3.44158i	0.0168994	−	0.00666972i
$517$	409.077	+	708.542i	0.791252	+	1.37049i
$518$	74.3295	+	128.743i	0.143493	+	0.248538i
$519$	−434.188	−	64.5973i	−0.836586	−	0.124465i
$520$	25.7156	+	513.094i	0.0494532	+	0.986719i
$521$		−	356.232i		−	0.683747i	−0.939746	−	0.341874i	$-0.888939\pi$
$521$		−	356.232i		−	0.683747i	0.939746	−	0.341874i	$-0.111061\pi$
$522$	−242.820	+	797.989i	−0.465172	+	1.52871i
$523$	787.642			1.50601			0.753004	−	0.658016i	$-0.228604\pi$
$523$	787.642			1.50601			0.753004	+	0.658016i	$0.228604\pi$
$524$	33.5799	+	19.3874i	0.0640838	+	0.0369988i
$525$	6.67021	−	8.39695i	0.0127052	−	0.0159942i
$526$	−0.197404	+	0.113971i	−0.000375293	+	0.000216675i
$527$	−388.848	−	673.504i	−0.737851	−	1.27800i
$528$	−471.478	−	374.523i	−0.892950	−	0.709324i
$529$	−1.73758	+	3.00957i	−0.00328464	+	0.00568917i
$530$		−	394.379i		−	0.744112i
$531$	−732.088	−	222.767i	−1.37870	−	0.419524i
$532$	10.4535			0.0196495
$533$	−2.16177	−	43.1330i	−0.00405586	−	0.0809250i
$534$	−12.2723	+	82.4879i	−0.0229819	+	0.154472i
$535$	−303.842	+	175.424i	−0.567930	+	0.327894i
$536$	−165.898	+	95.7814i	−0.309512	+	0.178697i
$537$	331.374	+	839.618i	0.617083	+	1.56353i
$538$	−98.0798	−	56.6264i	−0.182304	−	0.105254i
$539$	526.703			0.977185
$540$	26.8184	+	38.8562i	0.0496636	+	0.0719558i
$541$		−	689.163i		−	1.27387i	−0.770918	−	0.636934i	$-0.780202\pi$
$541$		−	689.163i		−	1.27387i	0.770918	−	0.636934i	$-0.219798\pi$
$542$	−570.558	−	329.412i	−1.05269	−	0.607770i
$543$	−202.134	+	79.7767i	−0.372254	+	0.146918i
$544$	−107.449	+	62.0355i	−0.197516	+	0.114036i
$545$	210.855	−	121.737i	0.386889	−	0.223371i
$546$	−143.593	+	65.1576i	−0.262991	+	0.119336i
$547$	411.291	−	712.378i	0.751904	−	1.30234i	−0.194995	−	0.980804i	$-0.562469\pi$
$547$	411.291	−	712.378i	0.751904	−	1.30234i	0.946899	−	0.321531i	$-0.104198\pi$
$548$	56.2621			0.102668
$549$	−66.1112	−	284.647i	−0.120421	−	0.518482i
$550$	−44.6553			−0.0811914
$551$	354.977	−	614.838i	0.644242	−	1.11586i
$552$	326.290	−	410.758i	0.591105	−	0.744127i
$553$	21.0893	−	12.1759i	0.0381362	−	0.0220180i
$554$	−41.5124	−	71.9016i	−0.0749321	−	0.129786i
$555$	355.451	−	447.468i	0.640452	−	0.806248i
$556$	−29.1709	+	50.5255i	−0.0524656	+	0.0908732i
$557$	−888.415			−1.59500			−0.797500	−	0.603318i	$-0.793845\pi$
$557$	−888.415			−1.59500			−0.797500	+	0.603318i	$0.793845\pi$
$558$	−432.196	−	462.250i	−0.774544	−	0.828405i
$559$	101.093	−	65.3227i	0.180846	−	0.116856i
$560$	150.133	+	86.6794i	0.268095	+	0.154785i
$561$	−795.946	−	118.419i	−1.41880	−	0.211085i
$562$	−261.567	−	453.048i	−0.465422	−	0.806134i
$563$	−485.105	+	280.076i	−0.861643	+	0.497470i	−0.864562	−	0.502526i	$-0.832404\pi$
$563$	−485.105	+	280.076i	−0.861643	+	0.497470i	0.00291903	+	0.999996i	$0.499071\pi$
$564$	66.1737	−	26.1169i	0.117329	−	0.0463066i
$565$	−508.288	−	293.460i	−0.899625	−	0.519399i
$566$	569.704			1.00654
$567$	87.5888	−	130.597i	0.154478	−	0.230330i
$568$	−128.212			−0.225726
$569$	551.779	+	318.570i	0.969735	+	0.559877i	0.899155	−	0.437629i	$-0.144182\pi$
$569$	551.779	+	318.570i	0.969735	+	0.559877i	0.0705795	+	0.997506i	$0.477515\pi$
$570$	−189.589	−	480.370i	−0.332612	−	0.842755i
$571$	56.5020	+	97.8643i	0.0989527	+	0.171391i	0.911251	−	0.411851i	$-0.135117\pi$
$571$	56.5020	+	97.8643i	0.0989527	+	0.171391i	−0.812299	+	0.583242i	$0.801784\pi$
$572$	45.4713	+	23.2997i	0.0794953	+	0.0407338i
$573$	19.0743	+	2.83782i	0.0332884	+	0.00495256i
$574$	−11.6323	−	6.71592i	−0.0202654	−	0.0117002i
$575$		−	42.2106i		−	0.0734097i
$576$	379.502	−	354.827i	0.658857	−	0.616020i
$577$		−	460.077i		−	0.797361i	−0.917090	−	0.398680i	$-0.869468\pi$
$577$		−	460.077i		−	0.797361i	0.917090	−	0.398680i	$-0.130532\pi$
$578$	−251.598	+	435.781i	−0.435291	+	0.753947i
$579$	629.226	−	792.116i	1.08675	−	1.36808i
$580$	−67.3887	+	38.9069i	−0.116187	+	0.0670808i
$581$	−211.058	+	121.854i	−0.363266	+	0.209732i
$582$	−637.802	+	802.912i	−1.09588	+	1.37957i
$583$	368.596	+	212.809i	0.632240	+	0.365024i
$584$		−	626.597i		−	1.07294i
$585$	435.629	+	421.495i	0.744665	+	0.720504i
$586$	444.106			0.757860
$587$	−272.897	+	472.672i	−0.464902	+	0.805233i	−0.999197	−	0.0400644i	$-0.987244\pi$
$587$	−272.897	+	472.672i	−0.464902	+	0.805233i	0.534295	+	0.845298i	$0.320577\pi$
$588$	6.73959	−	45.2999i	0.0114619	−	0.0770406i
$589$	269.314	+	466.465i	0.457239	+	0.791962i
$590$	−458.714	−	794.517i	−0.777482	−	1.34664i
$591$	−192.183	+	75.8493i	−0.325183	+	0.128341i
$592$	548.830	+	316.867i	0.927077	+	0.535248i
$593$	164.234			0.276954			0.138477	−	0.990366i	$-0.455779\pi$
$593$	164.234			0.276954			0.138477	+	0.990366i	$0.455779\pi$
$594$	−652.684	+	52.6660i	−1.09879	+	0.0886632i
$595$	231.683			0.389383
$596$	3.25569	−	5.63902i	0.00546256	−	0.00946144i
$597$	−89.6473	+	35.3813i	−0.150163	+	0.0592651i
$598$	−283.040	+	552.376i	−0.473311	+	0.923705i
$599$	−375.199	+	216.621i	−0.626375	+	0.361638i	−0.779347	−	0.626593i	$-0.784449\pi$
$599$	−375.199	+	216.621i	−0.626375	+	0.361638i	0.152972	+	0.988231i	$0.451116\pi$
$600$	6.20047	−	41.6762i	0.0103341	−	0.0694603i
$601$	−155.528	+	269.383i	−0.258782	+	0.448224i	−0.965916	−	0.258856i	$-0.916655\pi$
$601$	−155.528	+	269.383i	−0.258782	+	0.448224i	0.707134	+	0.707080i	$0.249988\pi$
$602$		−	37.4341i		−	0.0621829i
$603$	−65.7985	+	216.236i	−0.109119	+	0.358601i
$604$			45.3539i			0.0750893i
$605$	37.8172	−	65.5014i	0.0625078	−	0.108267i
$606$	−401.541	+	505.489i	−0.662609	+	0.834141i
$607$	−347.895	−	602.571i	−0.573138	−	0.992704i	−0.996241	−	0.0866224i	$-0.972393\pi$
$607$	−347.895	−	602.571i	−0.573138	−	0.992704i	0.423103	−	0.906081i	$-0.360941\pi$
$608$	74.4184	−	42.9655i	0.122399	−	0.0706669i
$609$	202.936	+	161.205i	0.333229	+	0.264704i
$610$	175.172	−	303.407i	0.287167	−	0.497388i
$611$	767.157	−	495.711i	1.25558	−	0.811311i
$612$	−20.3695	+	66.9412i	−0.0332836	+	0.109381i
$613$		−	493.944i		−	0.805782i	−0.915248	−	0.402891i	$-0.868005\pi$
$613$		−	493.944i		−	0.805782i	0.915248	−	0.402891i	$-0.131995\pi$
$614$	333.977	+	192.822i	0.543936	+	0.314042i
$615$	−7.59831	+	51.0717i	−0.0123550	+	0.0830434i
$616$	−149.334	+	86.2181i	−0.242426	+	0.139964i
$617$	442.501	+	766.435i	0.717182	+	1.24220i	0.962112	+	0.272655i	$0.0879017\pi$
$617$	442.501	+	766.435i	0.717182	+	1.24220i	−0.244930	+	0.969541i	$0.578765\pi$
$618$	−584.139	+	230.543i	−0.945209	+	0.373047i
$619$	847.493	+	489.300i	1.36913	+	0.790469i	0.990817	−	0.135208i	$-0.0431702\pi$
$619$	847.493	+	489.300i	1.36913	+	0.790469i	0.378315	+	0.925677i	$0.376504\pi$
$620$		−	59.0357i		−	0.0952189i
$621$	−49.7827	−	616.952i	−0.0801653	−	0.993481i
$622$			1123.44i			1.80617i
$623$	22.4407	+	12.9562i	0.0360205	+	0.0207964i
$624$	−391.242	+	546.622i	−0.626991	+	0.875996i
$625$	333.821	+	578.195i	0.534114	+	0.925112i
$626$	633.129	+	1096.61i	1.01139	+	1.75178i
$627$	551.268	+	82.0162i	0.879215	+	0.130807i
$628$	−30.9530	+	53.6122i	−0.0492883	+	0.0853698i
$629$	846.945			1.34649
$630$	183.637	−	42.6510i	0.291487	−	0.0676999i
$631$			729.035i			1.15536i	0.816262	+	0.577682i	$0.196043\pi$
$631$			729.035i			1.15536i	−0.816262	+	0.577682i	$0.803957\pi$
$632$	47.8404	−	82.8620i	0.0756968	−	0.131111i
$633$	574.499	+	456.359i	0.907581	+	0.720947i
$634$	350.147	+	606.473i	0.552283	+	0.956582i
$635$	−28.0487	−	48.5818i	−0.0441712	−	0.0765068i
$636$	23.0194	−	28.9786i	0.0361941	−	0.0455638i
$637$	−29.4332	−	587.268i	−0.0462059	−	0.921928i
$638$		−	1079.22i		−	1.69157i
$639$	−110.502	+	103.317i	−0.172929	+	0.161686i
$640$	734.495			1.14765
$641$	−523.380	−	302.173i	−0.816505	−	0.471409i	0.0327047	−	0.999465i	$-0.489588\pi$
$641$	−523.380	−	302.173i	−0.816505	−	0.471409i	−0.849210	+	0.528056i	$0.822921\pi$
$642$	−418.508	−	62.2645i	−0.651882	−	0.0969852i
$643$	578.620	−	334.067i	0.899876	−	0.519544i	0.0227162	−	0.999742i	$-0.492769\pi$
$643$	578.620	−	334.067i	0.899876	−	0.519544i	0.877160	+	0.480198i	$0.159435\pi$
$644$	7.51039	+	13.0084i	0.0116621	+	0.0201993i
$645$	−133.854	+	52.8284i	−0.207525	+	0.0819044i
$646$	382.689	−	662.837i	0.592398	−	1.02606i
$647$		−	473.645i		−	0.732064i	−0.930602	−	0.366032i	$-0.880716\pi$
$647$		−	473.645i		−	0.732064i	0.930602	−	0.366032i	$-0.119284\pi$
$648$	41.4740	−	616.454i	0.0640030	−	0.951318i
$649$	990.098			1.52557
$650$	2.49542	+	49.7902i	0.00383911	+	0.0766002i
$651$	−182.899	+	72.1851i	−0.280951	+	0.110883i
$652$	64.3448	−	37.1495i	0.0986884	−	0.0569778i
$653$	83.5283	−	48.2251i	0.127915	−	0.0738516i	−0.434677	−	0.900586i	$-0.643138\pi$
$653$	83.5283	−	48.2251i	0.127915	−	0.0738516i	0.562592	+	0.826735i	$0.309804\pi$
$654$	290.428	+	43.2091i	0.444079	+	0.0660689i
$655$	−515.453	−	297.597i	−0.786951	−	0.454346i
$656$	−57.2600			−0.0872866
$657$	−504.930	−	540.042i	−0.768539	−	0.821982i
$658$		−	284.074i		−	0.431724i
$659$	78.0724	+	45.0751i	0.118471	+	0.0683993i	0.558065	−	0.829798i	$-0.311544\pi$
$659$	78.0724	+	45.0751i	0.118471	+	0.0683993i	−0.439593	+	0.898197i	$0.644877\pi$
$660$	−47.8316	−	37.9955i	−0.0724721	−	0.0575690i
$661$	572.582	−	330.581i	0.866236	−	0.500122i	0.000140662	−	1.00000i	$-0.499955\pi$
$661$	572.582	−	330.581i	0.866236	−	0.500122i	0.866096	+	0.499878i	$0.166622\pi$
$662$	−876.737	+	506.185i	−1.32438	+	0.764629i
$663$	−87.5566	+	894.088i	−0.132061	+	1.34855i
$664$	−478.777	+	829.266i	−0.721049	+	1.24889i
$665$	−160.462			−0.241297
$666$	671.307	−	155.916i	1.00797	−	0.234108i
$667$	1020.14			1.52944
$668$	−33.4904	+	58.0070i	−0.0501353	+	0.0868369i
$669$	−706.268	−	105.077i	−1.05571	−	0.157065i
$670$	−234.676	+	135.490i	−0.350262	+	0.202224i
$671$	189.047	+	327.439i	0.281739	+	0.487987i
$672$	11.5162	+	29.1791i	0.0171372	+	0.0434213i
$673$	4.74549	−	8.21943i	0.00705125	−	0.0122131i	−0.862478	−	0.506094i	$-0.831089\pi$
$673$	4.74549	−	8.21943i	0.00705125	−	0.0122131i	0.869529	+	0.493881i	$0.164422\pi$
$674$	358.700			0.532196
$675$	−28.2399	−	40.9158i	−0.0418369	−	0.0606159i
$676$	23.4379	−	52.0021i	0.0346714	−	0.0769261i
$677$	428.695	+	247.507i	0.633227	+	0.365594i	0.782001	−	0.623278i	$-0.214199\pi$
$677$	428.695	+	247.507i	0.633227	+	0.365594i	−0.148774	+	0.988871i	$0.547533\pi$
$678$	−259.849	−	658.392i	−0.383258	−	0.971079i
$679$	159.305	+	275.924i	0.234617	+	0.406368i
$680$	788.346	−	455.152i	1.15933	−	0.669341i
$681$	−129.719	+	871.898i	−0.190483	+	1.28032i
$682$	709.088	+	409.392i	1.03972	+	0.600282i
$683$	−206.319			−0.302077			−0.151038	−	0.988528i	$-0.548262\pi$
$683$	−206.319			−0.302077			−0.151038	+	0.988528i	$0.548262\pi$
$684$	14.1078	−	46.3632i	0.0206255	−	0.0677824i
$685$	−863.627			−1.26077
$686$	−329.951	−	190.497i	−0.480978	−	0.277693i
$687$	777.660	−	978.976i	1.13196	−	1.42500i
$688$	−79.7908	−	138.202i	−0.115975	−	0.200875i
$689$	216.682	−	422.873i	0.314487	−	0.613748i
$690$	461.562	−	581.048i	0.668930	−	0.842098i
$691$	824.447	+	475.995i	1.19312	+	0.688849i	0.959013	−	0.283361i	$-0.0914496\pi$
$691$	824.447	+	475.995i	1.19312	+	0.688849i	0.234108	+	0.972210i	$0.424783\pi$
$692$		−	49.3858i		−	0.0713668i
$693$	−59.2288	+	194.646i	−0.0854673	+	0.280874i
$694$			809.124i			1.16588i
$695$	447.775	−	775.569i	0.644280	−	1.11593i
$696$	1007.22	+	149.852i	1.44716	+	0.215305i
$697$	−66.2720	+	38.2622i	−0.0950818	+	0.0548955i
$698$	−90.6113	+	52.3145i	−0.129816	+	0.0749491i
$699$	−50.5055	−	127.968i	−0.0722539	−	0.183073i
$700$	1.04484	+	0.603240i	0.00149263	+	0.000861772i
$701$			536.246i			0.764974i	0.923961	+	0.382487i	$0.124932\pi$
$701$			536.246i			0.764974i	−0.923961	+	0.382487i	$0.875068\pi$
$702$	95.1952	+	724.792i	0.135606	+	1.03247i
$703$	−586.590			−0.834410
$704$	−336.106	+	582.153i	−0.477423	+	0.826921i
$705$	−1015.77	+	400.896i	−1.44081	+	0.568647i
$706$	117.982	+	204.351i	0.167114	+	0.289450i
$707$	100.293	+	173.713i	0.141858	+	0.245705i
$708$	12.6691	−	85.1548i	0.0178942	−	0.120275i
$709$	−896.526	−	517.609i	−1.26449	−	0.730056i	−0.290553	−	0.956859i	$-0.593839\pi$
$709$	−896.526	−	517.609i	−1.26449	−	0.730056i	−0.973941	+	0.226803i	$0.927173\pi$
$710$	−181.366			−0.255445
$711$	−25.5406	−	109.967i	−0.0359221	−	0.154665i
$712$	101.812			0.142994
$713$	−386.979	+	670.268i	−0.542748	+	0.940067i
$714$	218.779	+	173.789i	0.306413	+	0.243403i
$715$	−697.987	−	357.652i	−0.976206	−	0.500212i
$716$	−87.9464	+	50.7759i	−0.122830	+	0.0709160i
$717$	−584.829	−	464.565i	−0.815662	−	0.647929i
$718$	−145.292	+	251.653i	−0.202357	+	0.350492i
$719$			137.113i			0.190699i	0.995444	+	0.0953497i	$0.0303969\pi$
$719$			137.113i			0.190699i	−0.995444	+	0.0953497i	$0.969603\pi$
$720$	587.053	−	548.884i	0.815351	−	0.762339i
$721$			195.125i			0.270631i
$722$	110.873	−	192.038i	0.153564	−	0.265981i
$723$	452.425	+	67.3106i	0.625761	+	0.0930991i
$724$	−12.2241	−	21.1727i	−0.0168841	−	0.0292440i
$725$	70.9607	−	40.9692i	0.0978768	−	0.0565092i
$726$	84.8447	−	33.4858i	0.116866	−	0.0461237i
$727$	90.2928	−	156.392i	0.124199	−	0.215119i	−0.797220	−	0.603688i	$-0.793697\pi$
$727$	90.2928	−	156.392i	0.124199	−	0.215119i	0.921420	+	0.388569i	$0.127030\pi$
$728$	104.477	+	161.688i	0.143513	+	0.222099i
$729$	−461.011	−	564.721i	−0.632388	−	0.774651i
$730$		−	886.369i		−	1.21420i
$731$	−184.698	−	106.635i	−0.252665	−	0.145876i
$732$	30.5809	−	12.0694i	0.0417772	−	0.0164883i
$733$	−949.602	+	548.253i	−1.29550	+	0.747957i	−0.979623	−	0.200843i	$-0.935632\pi$
$733$	−949.602	+	548.253i	−1.29550	+	0.747957i	−0.315877	+	0.948800i	$0.602299\pi$
$734$	−416.223	−	720.920i	−0.567061	−	0.982179i
$735$	−103.453	+	695.355i	−0.140752	+	0.946061i
$736$	106.932	+	61.7374i	0.145289	+	0.0838824i
$737$		−	292.444i		−	0.396803i
$738$	−45.4849	+	42.5276i	−0.0616327	+	0.0576254i
$739$			275.835i			0.373254i	0.982431	+	0.186627i	$0.0597556\pi$
$739$			275.835i			0.373254i	−0.982431	+	0.186627i	$0.940244\pi$
$740$	55.6790	+	32.1463i	0.0752419	+	0.0434409i
$741$	60.6412	−	619.241i	0.0818370	−	0.835683i
$742$	−73.8901	−	127.981i	−0.0995824	−	0.172482i
$743$	−566.081	−	980.480i	−0.761885	−	1.31962i	−0.941878	−	0.335956i	$-0.890941\pi$
$743$	−566.081	−	980.480i	−0.761885	−	1.31962i	0.179993	−	0.983668i	$-0.442393\pi$
$744$	−480.539	+	604.938i	−0.645885	+	0.813089i
$745$	−49.9750	+	86.5592i	−0.0670805	+	0.116187i
$746$	−1217.85			−1.63251
$747$	255.605	+	1100.53i	0.342175	+	1.47326i
$748$		−	90.5333i		−	0.121034i
$749$	−65.7340	+	113.855i	−0.0877624	+	0.152009i
$750$	−110.316	+	741.487i	−0.147089	+	0.988649i
$751$	−666.191	−	1153.88i	−0.887073	−	1.53645i	−0.843320	−	0.537412i	$-0.819402\pi$
$751$	−666.191	−	1153.88i	−0.887073	−	1.53645i	−0.0437529	−	0.999042i	$-0.513931\pi$
$752$	−605.504	−	1048.76i	−0.805192	−	1.39463i
$753$	−95.4604	−	241.873i	−0.126774	−	0.321212i
$754$	−1203.32	+	60.3090i	−1.59592	+	0.0799855i
$755$		−	696.185i		−	0.922099i
$756$	15.9829	+	7.58472i	0.0211414	+	0.0100327i
$757$	−1211.24			−1.60006			−0.800028	−	0.599962i	$-0.795182\pi$
$757$	−1211.24			−1.60006			−0.800028	+	0.599962i	$0.795182\pi$
$758$	−97.0578	−	56.0364i	−0.128045	−	0.0739266i
$759$	294.000	+	744.922i	0.387352	+	0.981452i
$760$	−546.005	+	315.236i	−0.718427	+	0.414784i
$761$	−247.045	−	427.894i	−0.324632	−	0.562279i	0.656806	−	0.754060i	$-0.271907\pi$
$761$	−247.045	−	427.894i	−0.324632	−	0.562279i	−0.981438	+	0.191781i	$0.938574\pi$
$762$	9.95555	−	66.9158i	0.0130650	−	0.0878160i
$763$	45.6168	−	79.0106i	0.0597861	−	0.103553i
$764$			2.16957i			0.00283975i
$765$	312.674	−	1027.55i	0.408724	−	1.34320i
$766$	−324.089			−0.423092
$767$	−55.3286	−	1103.95i	−0.0721363	−	1.43931i
$768$	151.172	+	120.085i	0.196838	+	0.156361i
$769$	−301.621	+	174.141i	−0.392225	+	0.226451i	−0.683124	−	0.730302i	$-0.739379\pi$
$769$	−301.621	+	174.141i	−0.392225	+	0.226451i	0.290898	+	0.956754i	$0.406046\pi$
$770$	−211.244	+	121.962i	−0.274343	+	0.158392i
$771$	−741.077	+	932.922i	−0.961189	+	1.21002i
$772$	98.5640	+	56.9059i	0.127674	+	0.0737124i
$773$	−34.2676			−0.0443306			−0.0221653	−	0.999754i	$-0.507056\pi$
$773$	−34.2676			−0.0443306			−0.0221653	+	0.999754i	$0.507056\pi$
$774$	−166.026	−	50.5201i	−0.214504	−	0.0652715i
$775$			62.1650i			0.0802129i
$776$	1084.13	+	625.923i	1.39707	+	0.806602i
$777$	31.5119	−	211.806i	0.0405559	−	0.272595i
$778$	1171.30	−	676.251i	1.50553	−	0.869217i
$779$	45.8997	−	26.5002i	0.0589213	−	0.0340182i
$780$	−39.6917	+	55.4550i	−0.0508868	+	0.0710961i
$781$	97.8660	−	169.509i	0.125309	−	0.217041i
$782$	1099.78			1.40637
$783$	988.846	−	682.498i	1.26289	−	0.871645i
$784$	−779.611			−0.994401
$785$	475.131	−	822.951i	0.605262	−	1.04834i
$786$	−263.512	−	667.672i	−0.335256	−	0.849456i
$787$	−177.850	+	102.682i	−0.225985	+	0.130473i	−0.608719	−	0.793386i	$-0.708316\pi$
$787$	−177.850	+	102.682i	−0.225985	+	0.130473i	0.382733	+	0.923859i	$0.374983\pi$
$788$	−11.6223	−	20.1304i	−0.0147491	−	0.0255461i
$789$	0.324767	+	0.0483180i	0.000411619	+	6.12395e-5i
$790$	67.6738	−	117.214i	0.0856631	−	0.148373i
$791$	−219.929			−0.278039
$792$	180.854	+	778.679i	0.228350	+	0.983180i
$793$	354.527	−	229.083i	0.447071	−	0.288882i
$794$	1278.20	+	737.970i	1.60983	+	0.929434i
$795$	−353.350	+	444.823i	−0.444465	+	0.559525i
$796$	−5.42142	−	9.39017i	−0.00681082	−	0.0117967i
$797$	−379.026	+	218.831i	−0.475566	+	0.274568i	−0.718567	−	0.695458i	$-0.755202\pi$
$797$	−379.026	+	218.831i	−0.475566	+	0.274568i	0.243001	+	0.970026i	$0.421868\pi$
$798$	−151.525	−	120.366i	−0.189881	−	0.150834i
$799$	−1401.61	−	809.218i	−1.75420	−	1.01279i
$800$	9.91760			0.0123970
$801$	87.7482	−	82.0430i	0.109548	−	0.102426i
$802$	853.997			1.06483
$803$	828.420	+	478.289i	1.03166	+	0.595627i
$804$	−25.1521	−	3.74206i	−0.0312837	−	0.00465430i
$805$	−115.285	−	199.679i	−0.143211	−	0.248049i
$806$	416.843	−	813.503i	0.517175	−	1.00931i
$807$	59.8895	+	151.745i	0.0742126	+	0.188036i
$808$	682.536	+	394.062i	0.844723	+	0.487701i
$809$			679.073i			0.839397i	0.907663	+	0.419699i	$0.137864\pi$
$809$			679.073i			0.839397i	−0.907663	+	0.419699i	$0.862136\pi$
$810$	58.6680	−	872.020i	0.0724296	−	1.07657i
$811$		−	555.671i		−	0.685168i	−0.939487	−	0.342584i	$-0.888698\pi$
$811$		−	555.671i		−	0.685168i	0.939487	−	0.342584i	$-0.111302\pi$
$812$	−14.5790	+	25.2516i	−0.0179545	+	0.0310981i
$813$	348.394	+	882.744i	0.428529	+	1.08579i
$814$	−772.229	+	445.847i	−0.948684	+	0.547723i
$815$	−987.697	+	570.247i	−1.21190	+	0.699690i
$816$	1178.14	+	175.280i	1.44379	+	0.214804i
$817$	127.921	+	73.8551i	0.156574	+	0.0903979i
$818$		−	604.414i		−	0.738892i
$819$	220.338	+	55.1623i	0.269033	+	0.0673532i
$820$	−5.80905			−0.00708421
$821$	−115.616	+	200.252i	−0.140823	+	0.243913i	−0.927807	−	0.373061i	$-0.878308\pi$
$821$	−115.616	+	200.252i	−0.140823	+	0.243913i	0.786984	+	0.616974i	$0.211642\pi$
$822$	−815.526	−	647.822i	−0.992124	−	0.788104i
$823$	−205.560	−	356.040i	−0.249769	−	0.432613i	0.713693	−	0.700459i	$-0.247021\pi$
$823$	−205.560	−	356.040i	−0.249769	−	0.432613i	−0.963462	+	0.267846i	$0.913688\pi$
$824$	383.333	+	663.952i	0.465210	+	0.805767i
$825$	50.3669	+	40.0095i	0.0610508	+	0.0484964i
$826$	−297.718	−	171.888i	−0.360434	−	0.208096i
$827$	697.850			0.843833			0.421916	−	0.906635i	$-0.361358\pi$
$827$	697.850			0.843833			0.421916	+	0.906635i	$0.361358\pi$
$828$	67.8301	−	15.7540i	0.0819204	−	0.0190266i
$829$	−1181.61			−1.42534			−0.712671	−	0.701498i	$-0.752515\pi$
$829$	−1181.61			−1.42534			−0.712671	+	0.701498i	$0.752515\pi$
$830$	−677.265	+	1173.06i	−0.815982	+	1.41332i
$831$	−17.5991	+	118.292i	−0.0211783	+	0.142349i
$832$	667.876	+	342.223i	0.802736	+	0.411325i
$833$	−902.312	+	520.950i	−1.08321	+	0.625390i
$834$	1004.60	−	396.489i	1.20456	−	0.475406i
$835$	514.079	−	890.411i	0.615663	−	1.06636i
$836$			62.7029i			0.0750034i
$837$	73.3167	+	908.606i	0.0875946	+	1.08555i
$838$		−	511.792i		−	0.610730i
$839$	−323.924	+	561.053i	−0.386083	+	0.668716i	−0.991919	−	0.126874i	$-0.959506\pi$
$839$	−323.924	+	561.053i	−0.386083	+	0.668716i	0.605835	+	0.795590i	$0.292839\pi$
$840$	−84.4938	−	214.086i	−0.100588	−	0.254864i
$841$	569.638	+	986.641i	0.677334	+	1.17318i
$842$	−1034.67	+	597.369i	−1.22883	+	0.709464i
$843$	−110.891	+	745.349i	−0.131543	+	0.884163i
$844$	−41.2722	+	71.4856i	−0.0489007	+	0.0846986i
$845$	−359.773	+	798.234i	−0.425767	+	0.944656i
$846$	−1259.91	−	383.379i	−1.48926	−	0.453167i
$847$		−	28.3414i		−	0.0334610i
$848$	−545.585	−	314.994i	−0.643379	−	0.371455i
$849$	−642.572	−	510.434i	−0.756858	−	0.601218i
$850$	76.5004	−	44.1675i	0.0900005	−	0.0519618i
$851$	−421.438	−	729.952i	−0.495227	−	0.857758i
$852$	−13.3266	−	10.5861i	−0.0156415	−	0.0124250i
$853$	545.504	+	314.947i	0.639512	+	0.369222i	0.784427	−	0.620222i	$-0.212957\pi$
$853$	545.504	+	314.947i	0.639512	+	0.369222i	−0.144914	+	0.989444i	$0.546291\pi$
$854$		−	131.279i		−	0.153723i
$855$	−216.556	+	711.677i	−0.253282	+	0.832371i
$856$			516.550i			0.603446i
$857$	372.338	+	214.969i	0.434466	+	0.250839i	0.701248	−	0.712918i	$-0.252627\pi$
$857$	372.338	+	214.969i	0.434466	+	0.250839i	−0.266781	+	0.963757i	$0.585960\pi$
$858$	−390.831	−	861.304i	−0.455514	−	1.00385i
$859$	−149.568	−	259.060i	−0.174119	−	0.301583i	0.765737	−	0.643154i	$-0.222374\pi$
$859$	−149.568	−	259.060i	−0.174119	−	0.301583i	−0.939856	+	0.341571i	$0.889041\pi$
$860$	−8.09481	−	14.0206i	−0.00941257	−	0.0163030i
$861$	7.10294	+	17.9971i	0.00824964	+	0.0209025i
$862$	201.691	−	349.339i	0.233980	−	0.405266i
$863$	760.723			0.881487			0.440743	−	0.897633i	$-0.354715\pi$
$863$	760.723			0.881487			0.440743	+	0.897633i	$0.354715\pi$
$864$	144.956	−	11.6967i	0.167773	−	0.0135379i
$865$			758.075i			0.876388i
$866$	−436.265	+	755.632i	−0.503770	+	0.872555i
$867$	674.223	−	266.097i	0.777651	−	0.306917i
$868$	−11.0608	−	19.1579i	−0.0127429	−	0.0220713i
$869$	73.0342	+	126.499i	0.0840440	+	0.145568i
$870$	1424.79	+	211.977i	1.63769	+	0.243652i
$871$	−326.072	+	16.3423i	−0.374365	+	0.0187627i
$872$		−	358.465i		−	0.411084i
$873$	1438.76	−	334.162i	1.64806	−	0.382774i
$874$	−761.701			−0.871512
$875$	201.721	+	116.464i	0.230538	+	0.133101i
$876$	51.7362	−	65.1294i	0.0590596	−	0.0743486i
$877$	1171.56	−	676.402i	1.33587	−	0.771267i	0.349682	−	0.936869i	$-0.386290\pi$
$877$	1171.56	−	676.402i	1.33587	−	0.771267i	0.986193	+	0.165601i	$0.0529564\pi$
$878$	758.018	+	1312.93i	0.863347	+	1.49536i
$879$	−500.909	−	397.902i	−0.569863	−	0.452676i
$880$	−519.924	+	900.535i	−0.590823	+	1.02333i
$881$			485.906i			0.551539i	0.961224	+	0.275770i	$0.0889327\pi$
$881$			485.906i			0.551539i	−0.961224	+	0.275770i	$0.911067\pi$
$882$	−619.289	+	579.025i	−0.702142	+	0.656491i
$883$	−1031.60			−1.16829			−0.584145	−	0.811649i	$-0.698570\pi$
$883$	−1031.60			−1.16829			−0.584145	+	0.811649i	$0.698570\pi$
$884$	−100.944	+	5.05917i	−0.114190	+	0.00572304i
$885$	−194.471	+	1307.13i	−0.219742	+	1.47698i
$886$	831.729	−	480.199i	0.938747	−	0.541986i
$887$	683.226	−	394.461i	0.770266	−	0.444713i	−0.0627037	−	0.998032i	$-0.519972\pi$
$887$	683.226	−	394.461i	0.770266	−	0.444713i	0.832969	+	0.553319i	$0.186639\pi$
$888$	−308.877	−	782.618i	−0.347835	−	0.881326i
$889$	−18.2044	−	10.5103i	−0.0204774	−	0.0118226i
$890$	144.021			0.161821
$891$	783.352	+	525.379i	0.879183	+	0.589651i
$892$		−	80.3330i		−	0.0900594i
$893$	970.746	+	560.460i	1.08706	+	0.627615i
$894$	−112.121	+	44.2511i	−0.125415	+	0.0494979i
$895$	1349.98	−	779.412i	1.50836	−	0.870852i
$896$	238.354	−	137.613i	0.266020	−	0.153586i
$897$	814.151	−	369.434i	0.907637	−	0.411855i
$898$	−320.796	+	555.636i	−0.357234	+	0.618748i
$899$	−1502.39			−1.67118
$900$	4.08556	−	3.81993i	0.00453951	−	0.00424437i
$901$	−841.938			−0.934449
$902$	40.2837	−	69.7735i	0.0446605	−	0.0773542i
$903$	−33.5396	+	42.2221i	−0.0371424	+	0.0467576i
$904$	−748.350	+	432.060i	−0.827821	+	0.477942i
$905$	187.640	+	325.002i	0.207337	+	0.359118i
$906$	522.221	−	657.410i	0.576403	−	0.725618i
$907$	9.11880	−	15.7942i	0.0100538	−	0.0174137i	−0.860955	−	0.508682i	$-0.830133\pi$
$907$	9.11880	−	15.7942i	0.0100538	−	0.0174137i	0.871009	+	0.491268i	$0.163466\pi$
$908$	−99.1723			−0.109221
$909$	905.800	−	210.378i	0.996480	−	0.231439i
$910$	147.791	+	228.720i	0.162408	+	0.251340i
$911$	−240.907	−	139.088i	−0.264442	−	0.152676i	0.361917	−	0.932210i	$-0.382122\pi$
$911$	−240.907	−	139.088i	−0.264442	−	0.152676i	−0.626359	+	0.779534i	$0.715456\pi$
$912$	−815.971	−	121.398i	−0.894705	−	0.133112i
$913$	−730.911	−	1265.98i	−0.800560	−	1.38661i
$914$	708.211	−	408.886i	0.774848	−	0.447359i
$915$	−469.419	+	185.266i	−0.513026	+	0.202477i
$916$	121.815	+	70.3300i	0.132986	+	0.0767795i
$917$	−223.029			−0.243216
$918$	1066.04	−	735.779i	1.16127	−	0.801502i
$919$	209.842			0.228338			0.114169	−	0.993461i	$-0.463580\pi$
$919$	209.842			0.228338			0.114169	+	0.993461i	$0.463580\pi$
$920$	−784.559	−	452.965i	−0.852781	−	0.492353i
$921$	−203.933	−	516.716i	−0.221426	−	0.561038i
$922$	423.896	+	734.210i	0.459757	+	0.796323i
$923$	−194.470	−	99.6470i	−0.210693	−	0.107960i
$924$	−22.6408	−	3.36843i	−0.0245030	−	0.00364549i
$925$	−58.6303	−	33.8502i	−0.0633841	−	0.0365948i
$926$		−	80.5073i		−	0.0869409i
$927$	865.412	+	263.336i	0.933562	+	0.284074i
$928$			239.687i			0.258284i
$929$	−348.198	+	603.097i	−0.374810	+	0.649190i	−0.990299	−	0.138956i	$-0.955625\pi$
$929$	−348.198	+	603.097i	−0.374810	+	0.649190i	0.615489	+	0.788146i	$0.288959\pi$
$930$	−679.758	+	855.730i	−0.730922	+	0.920139i
$931$	624.937	−	360.807i	0.671253	−	0.387548i
$932$	13.4041	−	7.73888i	0.0143821	−	0.00830352i
$933$	1006.56	−	1267.13i	1.07884	−	1.35813i
$934$	−1234.99	−	713.023i	−1.32226	−	0.763408i
$935$			1389.69i			1.48630i
$936$	858.112	−	245.164i	0.916786	−	0.261927i
$937$	1373.57			1.46592			0.732960	−	0.680272i	$-0.238138\pi$
$937$	1373.57			1.46592			0.732960	+	0.680272i	$0.238138\pi$
$938$	−50.7703	+	87.9367i	−0.0541261	+	0.0937491i
$939$	268.414	−	1804.13i	0.285851	−	1.92134i
$940$	−61.4287	−	106.398i	−0.0653496	−	0.113189i
$941$	−306.616	−	531.074i	−0.325841	−	0.564372i	0.655842	−	0.754899i	$-0.272314\pi$
$941$	−306.616	−	531.074i	−0.325841	−	0.564372i	−0.981682	+	0.190526i	$0.938981\pi$
$942$	1065.98	−	420.712i	1.13161	−	0.446615i
$943$	65.9536	+	38.0783i	0.0699402	+	0.0403800i
$944$	−1465.51			−1.55245
$945$	−245.339	−	116.426i	−0.259618	−	0.123202i
$946$	224.539			0.237356
$947$	597.691	−	1035.23i	0.631142	−	1.09317i	−0.356177	−	0.934419i	$-0.615920\pi$
$947$	597.691	−	1035.23i	0.631142	−	1.09317i	0.987319	−	0.158751i	$-0.0507468\pi$
$948$	11.8143	−	4.66276i	0.0124623	−	0.00491852i
$949$	486.993	−	950.407i	0.513164	−	1.00148i
$950$	−52.9838	+	30.5902i	−0.0557724	+	0.0322002i
$951$	148.445	−	997.763i	0.156093	−	1.04917i
$952$	170.553	−	295.406i	0.179152	−	0.310300i
$953$		−	268.873i		−	0.282133i	−0.990000	−	0.141067i	$-0.954947\pi$
$953$		−	268.873i		−	0.282133i	0.990000	−	0.141067i	$-0.0450532\pi$
$954$	−667.339	+	154.994i	−0.699517	+	0.162468i
$955$		−	33.3029i		−	0.0348722i
$956$	42.0144	−	72.7710i	0.0439481	−	0.0761203i
$957$	−966.944	+	1217.26i	−1.01039	+	1.27196i
$958$	530.502	+	918.857i	0.553760	+	0.959141i
$959$	−280.259	+	161.807i	−0.292240	+	0.168725i
$960$	−702.543	−	558.073i	−0.731816	−	0.581326i
$961$	89.4181	−	154.877i	0.0930470	−	0.161162i
$962$	540.268	+	836.112i	0.561609	+	0.869139i
$963$	416.251	+	445.196i	0.432244	+	0.462301i
$964$			51.4602i			0.0533820i
$965$	−1512.96	−	873.509i	−1.56784	−	0.905191i
$966$	40.9190	−	275.035i	0.0423592	−	0.284716i
$967$	412.037	−	237.890i	0.426098	−	0.246008i	−0.271585	−	0.962415i	$-0.587548\pi$
$967$	412.037	−	237.890i	0.426098	−	0.246008i	0.697683	+	0.716407i	$0.254214\pi$
$968$	−55.6781	−	96.4373i	−0.0575187	−	0.0996253i
$969$	−1025.52	+	404.742i	−1.05832	+	0.417691i
$970$	1533.58	+	885.414i	1.58101	+	0.912798i
$971$		−	889.886i		−	0.916464i	−0.888833	−	0.458232i	$-0.848483\pi$
$971$		−	889.886i		−	0.916464i	0.888833	−	0.458232i	$-0.151517\pi$
$972$	55.2096	−	60.6507i	0.0568000	−	0.0623979i
$973$		−	335.577i		−	0.344889i
$974$	1360.22	+	785.321i	1.39653	+	0.806284i
$975$	41.7956	−	58.3944i	0.0428672	−	0.0598917i
$976$	−279.822	−	484.666i	−0.286703	−	0.496584i
$977$	201.956	+	349.799i	0.206711	+	0.358033i	0.950676	−	0.310184i	$-0.100391\pi$
$977$	201.956	+	349.799i	0.206711	+	0.358033i	−0.743966	+	0.668218i	$0.767057\pi$
$978$	−1360.44	−	202.402i	−1.39104	−	0.206955i
$979$	−77.7142	+	134.605i	−0.0793812	+	0.137492i
$980$	−79.0918			−0.0807059
$981$	−288.862	−	308.949i	−0.294456	−	0.314932i
$982$		−	920.555i		−	0.937428i
$983$	−799.183	+	1384.22i	−0.813004	+	1.40816i	0.0977489	+	0.995211i	$0.468836\pi$
$983$	−799.183	+	1384.22i	−0.813004	+	1.40816i	−0.910753	+	0.412953i	$0.864498\pi$
$984$	59.5252	+	47.2845i	0.0604931	+	0.0480533i
$985$	178.402	+	309.002i	0.181119	+	0.313708i
$986$	1067.44	+	1848.85i	1.08259	+	1.87510i
$987$	−254.520	+	320.409i	−0.257872	+	0.324629i
$988$	69.9130	−	3.50396i	0.0707622	−	0.00354651i
$989$			212.246i			0.214607i
$990$	255.831	+	1101.50i	0.258415	+	1.11263i
$991$	−153.998			−0.155397			−0.0776984	−	0.996977i	$-0.524757\pi$
$991$	−153.998			−0.155397			−0.0776984	+	0.996977i	$0.524757\pi$
$992$	−157.483	−	90.9229i	−0.158753	−	0.0916562i
$993$	1442.40	+	214.596i	1.45257	+	0.216109i
$994$	−58.8558	+	33.9804i	−0.0592110	+	0.0341855i
$995$	83.2190	+	144.140i	0.0836372	+	0.144864i
$996$	−118.235	+	46.6639i	−0.118710	+	0.0468513i
$997$	327.240	−	566.797i	0.328225	−	0.568503i	−0.653935	−	0.756551i	$-0.726883\pi$
$997$	327.240	−	566.797i	0.328225	−	0.568503i	0.982160	+	0.188049i	$0.0602162\pi$
$998$		−	30.7906i		−	0.0308524i
$999$	−896.866	−	425.609i	−0.897764	−	0.426035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.n.a.38.19	yes	52
3.2	odd	2		351.3.n.a.116.8		52
9.4	even	3		351.3.n.a.233.19		52
9.5	odd	6	inner	117.3.n.a.77.8	yes	52
13.12	even	2	inner	117.3.n.a.38.8	✓	52
39.38	odd	2		351.3.n.a.116.19		52
117.77	odd	6	inner	117.3.n.a.77.19	yes	52
117.103	even	6		351.3.n.a.233.8		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.n.a.38.8	✓	52	13.12	even	2	inner
117.3.n.a.38.19	yes	52	1.1	even	1	trivial
117.3.n.a.77.8	yes	52	9.5	odd	6	inner
117.3.n.a.77.19	yes	52	117.77	odd	6	inner
351.3.n.a.116.8		52	3.2	odd	2
351.3.n.a.116.19		52	39.38	odd	2
351.3.n.a.233.8		52	117.103	even	6
351.3.n.a.233.19		52	9.4	even	3

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+(1.04133 - 1.80365i) q^{2} +(-2.79053 + 1.10134i) q^{3} +(-0.168757 - 0.292296i) q^{4} +(2.59043 + 4.48676i) q^{5} +(-0.919442 + 6.17999i) q^{6} +(1.68126 + 0.970675i) q^{7} +7.62775 q^{8} +(6.57409 - 6.14666i) q^{9} +10.7900 q^{10} +(-5.82235 + 10.0846i) q^{11} +(0.792839 + 0.629800i) q^{12} +(11.5696 + 5.92831i) q^{13} +(3.50151 - 2.02160i) q^{14} +(-12.1701 - 9.66746i) q^{15} +(8.61807 - 14.9269i) q^{16} -23.0350i q^{17} +(-4.24056 - 18.2580i) q^{18} +15.9539i q^{19} +(0.874306 - 1.51434i) q^{20} +(-5.76065 - 0.857053i) q^{21} +(12.1260 + 21.0029i) q^{22} +(-19.8531 + 11.4622i) q^{23} +(-21.2854 + 8.40077i) q^{24} +(-0.920650 + 1.59461i) q^{25} +(22.7404 - 14.6941i) q^{26} +(-11.5756 + 24.3927i) q^{27} -0.655233i q^{28} +(-38.5384 - 22.2501i) q^{29} +(-30.1098 + 11.8835i) q^{30} +(29.2383 - 16.8807i) q^{31} +(-2.69310 - 4.66458i) q^{32} +(5.14081 - 34.5537i) q^{33} +(-41.5470 - 23.9872i) q^{34} +10.0579i q^{35} +(-2.90607 - 0.884287i) q^{36} +36.7677i q^{37} +(28.7752 + 16.6134i) q^{38} +(-38.8143 - 3.80102i) q^{39} +(19.7591 + 34.2238i) q^{40} +(-1.66104 - 2.87701i) q^{41} +(-7.54458 + 9.49768i) q^{42} +(4.62927 - 8.01814i) q^{43} +3.93025 q^{44} +(44.6083 + 13.5738i) q^{45} +47.7438i q^{46} +(35.1299 - 60.8468i) q^{47} +(-7.60929 + 51.1455i) q^{48} +(-22.6156 - 39.1713i) q^{49} +(1.91741 + 3.32105i) q^{50} +(25.3694 + 64.2798i) q^{51} +(-0.219630 - 4.38218i) q^{52} -36.5504i q^{53} +(31.9418 + 46.2793i) q^{54} -60.3295 q^{55} +(12.8242 + 7.40407i) q^{56} +(-17.5707 - 44.5199i) q^{57} +(-80.2627 + 46.3397i) q^{58} +(-42.5128 - 73.6344i) q^{59} +(-0.771965 + 5.18873i) q^{60} +(16.2346 - 28.1192i) q^{61} -70.3140i q^{62} +(17.0192 - 3.95282i) q^{63} +57.7269 q^{64} +(3.37133 + 67.2667i) q^{65} +(-56.9694 - 45.2542i) q^{66} +(-21.7493 + 12.5570i) q^{67} +(-6.73303 + 3.88732i) q^{68} +(42.7767 - 53.8505i) q^{69} +(18.1408 + 10.4736i) q^{70} -16.8087 q^{71} +(50.1455 - 46.8851i) q^{72} -82.1471i q^{73} +(66.3160 + 38.2875i) q^{74} +(0.812884 - 5.46376i) q^{75} +(4.66327 - 2.69234i) q^{76} +(-19.5777 + 11.3032i) q^{77} +(-47.2744 + 66.0491i) q^{78} +(6.27189 - 10.8632i) q^{79} +89.2980 q^{80} +(5.43725 - 80.8173i) q^{81} -6.91882 q^{82} +(-62.7678 + 108.717i) q^{83} +(0.721637 + 1.82845i) q^{84} +(103.352 - 59.6706i) q^{85} +(-9.64125 - 16.6991i) q^{86} +(132.047 + 19.6457i) q^{87} +(-44.4114 + 76.9228i) q^{88} +13.3476 q^{89} +(70.9345 - 66.3225i) q^{90} +(13.6970 + 21.1973i) q^{91} +(6.70068 + 3.86864i) q^{92} +(-62.9988 + 79.3075i) q^{93} +(-73.1641 - 126.724i) q^{94} +(-71.5814 + 41.3275i) q^{95} +(12.6525 + 10.0506i) q^{96} +(142.130 + 82.0586i) q^{97} -94.2016 q^{98} +(23.7099 + 102.085i) 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

Fields

Representations

Groups

Database

Properties

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