LMFDB - Embedded newform 117.3.n.a.38.8

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			38.8
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.8

$q$-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} +(-0.650727 + 12.9837i) 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} +(-12.4836 - 36.9481i) 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} +(3.90490 - 2.00089i) 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} +(59.9404 - 30.7137i) 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} +(79.6408 + 15.9593i) 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	$0.340984\pi$
$2$	−1.04133	+	1.80365i	−0.520667	+	0.901823i	−0.999711	+	0.0240315i	$0.992350\pi$
$3$	−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	$-0.993311\pi$
$5$	−2.59043	−	4.48676i	−0.518086	−	0.897351i	0.481693	−	0.876340i	$-0.340022\pi$
$6$	0.919442	−	6.17999i	0.153240	−	1.03000i
$7$	−1.68126	−	0.970675i	−0.240180	−	0.138668i	0.375080	−	0.926993i	$-0.377615\pi$
$7$	−1.68126	−	0.970675i	−0.240180	−	0.138668i	−0.615259	+	0.788325i	$0.710949\pi$
$8$	−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	$-0.655786\pi$
$11$	5.82235	−	10.0846i	0.529304	−	0.916782i	0.999416	−	0.0341747i	$-0.0108803\pi$
$12$	0.792839	+	0.629800i	0.0660699	+	0.0524833i
$13$	−0.650727	+	12.9837i	−0.0500560	+	0.998746i
$13$	−0.650727	+	12.9837i	−0.0500560	+	0.998746i
$14$	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	$-0.862086\pi$
$19$		−	15.9539i		−	0.839680i	0.907598	−	0.419840i	$-0.137914\pi$
$20$	−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	−0.890953	−	0.454096i	$-0.849962\pi$
$31$	−29.2383	+	16.8807i	−0.943170	+	0.544540i	−0.0522177	+	0.998636i	$0.516629\pi$
$32$	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	$-0.834486\pi$
$37$		−	36.7677i		−	0.993723i	0.867830	−	0.496861i	$-0.165514\pi$
$38$	28.7752	+	16.6134i	0.757243	+	0.437194i
$39$	−12.4836	−	36.9481i	−0.320093	−	0.947386i
$40$	19.7591	+	34.2238i	0.493979	+	0.855596i
$41$	1.66104	+	2.87701i	0.0405133	+	0.0701711i	0.885571	−	0.464504i	$-0.153767\pi$
$41$	1.66104	+	2.87701i	0.0405133	+	0.0701711i	−0.845058	+	0.534675i	$0.820434\pi$
$42$	−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	$0.435386\pi$
$47$	−35.1299	+	60.8468i	−0.747445	+	1.29461i	−0.949044	+	0.315145i	$0.897947\pi$
$48$	−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
$52$	3.90490	−	2.00089i	0.0750942	−	0.0384786i
$53$		−	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	$0.0894470\pi$
$59$	42.5128	+	73.6344i	0.720557	+	1.24804i	−0.240220	+	0.970718i	$0.577220\pi$
$60$	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
$65$	59.9404	−	30.7137i	0.922159	−	0.472519i
$66$	−56.9694	−	45.2542i	−0.863173	−	0.685670i
$67$	21.7493	−	12.5570i	0.324617	−	0.187418i	−0.328832	−	0.944388i	$-0.606655\pi$
$67$	21.7493	−	12.5570i	0.324617	−	0.187418i	0.653448	+	0.756971i	$0.273322\pi$
$68$	−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	$-0.462233\pi$
$71$	16.8087			0.236742			0.118371	+	0.992969i	$0.462233\pi$
$72$	−50.1455	+	46.8851i	−0.696465	+	0.651183i
$73$			82.1471i			1.12530i	0.826694	+	0.562651i	$0.190219\pi$
$73$			82.1471i			1.12530i	−0.826694	+	0.562651i	$0.809781\pi$
$74$	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
$78$	79.6408	+	15.9593i	1.02104	+	0.204606i
$79$	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	$-0.560368\pi$
$83$	62.7678	−	108.717i	0.756238	−	1.30984i	0.944756	−	0.327773i	$-0.106298\pi$
$84$	−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	$-0.523891\pi$
$89$	−13.3476			−0.149973			−0.0749864	+	0.997185i	$0.523891\pi$
$90$	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	−0.466009	−	0.884780i	$-0.654308\pi$
$97$	−142.130	−	82.0586i	−1.46526	−	0.845965i	−0.999246	+	0.0388148i	$0.987642\pi$
$98$	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	$0.671092\pi$
$104$	4.96359	−	99.0364i	0.0477268	−	0.952273i
$105$	−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	$0.0691619\pi$
$109$			46.9949i			0.431146i	−0.976488	+	0.215573i	$0.930838\pi$
$110$	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
$117$	75.5284	+	89.3558i	0.645542	+	0.763725i
$118$	−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
$130$	−7.02136	+	140.094i	−0.0540105	+	1.07765i
$131$	−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	$-0.625154\pi$
$137$	83.3478	−	144.363i	0.608378	−	1.05374i	0.991508	−	0.130048i	$-0.0415130\pi$
$138$	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	0.831839	−	0.555017i	$-0.187288\pi$
$149$	−9.64608	−	16.7075i	−0.0647388	−	0.112131i	−0.896578	+	0.442886i	$0.853955\pi$
$150$	9.00820	+	7.15576i	0.0600547	+	0.0477051i
$151$	116.373	+	67.1882i	0.770685	+	0.444955i	0.833119	−	0.553094i	$-0.186553\pi$
$151$	116.373	+	67.1882i	0.770685	+	0.444955i	−0.0624342	+	0.998049i	$0.519886\pi$
$152$			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
$156$	−8.69306	+	9.88416i	−0.0557247	+	0.0633600i
$157$	−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	$-0.764030\pi$
$163$		−	220.136i		−	1.35053i	0.737576	−	0.675264i	$-0.235970\pi$
$164$	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	$0.0358531\pi$
$167$	99.2266	+	171.865i	0.594171	+	1.02913i	−0.399492	+	0.916737i	$0.630814\pi$
$168$	−43.9408	−	6.53739i	−0.261552	−	0.0389130i
$169$	−168.153	−	16.8977i	−0.994989	−	0.0999864i
$170$		−	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	$0.435874\pi$
$182$	23.9693	+	46.7780i	0.131699	+	0.257022i
$183$	−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	$-0.328452\pi$
$193$	292.029	−	168.603i	1.51310	−	0.873591i	0.999882	−	0.0153357i	$-0.00488170\pi$
$194$	296.009	−	170.901i	1.52582	−	0.880933i
$195$	−133.439	+	151.722i	−0.684302	+	0.778063i
$196$	−7.63308	+	13.2209i	−0.0389443	+	0.0674535i
$197$	−68.8698			−0.349593			−0.174796	−	0.984605i	$-0.555927\pi$
$197$	−68.8698			−0.349593			−0.174796	+	0.984605i	$0.555927\pi$
$198$	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
$221$	299.080	+	14.9895i	1.35330	+	0.0678258i
$222$	−227.224	−	33.8058i	−1.02353	−	0.152278i
$223$	−206.126	−	119.007i	−0.924332	−	0.533663i	−0.0393174	−	0.999227i	$-0.512518\pi$
$223$	−206.126	−	119.007i	−0.924332	−	0.533663i	−0.885014	+	0.465563i	$0.845852\pi$
$224$		−	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	$0.390729\pi$
$227$	−146.916	+	254.466i	−0.647206	+	1.12099i	−0.983787	+	0.179339i	$0.942604\pi$
$228$	10.0478	−	12.6489i	0.0440692	−	0.0554776i
$229$	360.919	−	208.377i	1.57606	−	0.909941i	0.580663	−	0.814144i	$-0.302793\pi$
$229$	360.919	−	208.377i	1.57606	−	0.909941i	0.995401	−	0.0957972i	$-0.0305400\pi$
$230$	−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	$0.968625\pi$
$234$	−239.817	+	43.1771i	−1.02486	+	0.184518i
$235$	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	$-0.992284\pi$
$239$	−124.482	−	215.609i	−0.520845	−	0.902129i	0.478862	−	0.877890i	$-0.341050\pi$
$240$	249.189	−	98.3477i	1.03829	−	0.409782i
$241$	132.042	+	76.2342i	0.547890	+	0.316325i	0.748271	−	0.663394i	$-0.230884\pi$
$241$	132.042	+	76.2342i	0.547890	+	0.316325i	−0.200380	+	0.979718i	$0.564218\pi$
$242$	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
$247$	207.141	+	10.3817i	0.838628	+	0.0420310i
$248$	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	$0.198374\pi$
$271$			316.336i			1.16729i	−0.812009	+	0.583645i	$0.801626\pi$
$272$	−343.842	−	198.517i	−1.26413	−	0.729843i
$273$	−14.8763	+	74.2368i	−0.0544921	+	0.271930i
$274$	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	−0.998186	−	0.0602124i	$-0.980822\pi$
$281$	−125.592	+	217.532i	−0.446947	+	0.774136i	0.551238	+	0.834348i	$0.314156\pi$
$282$	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
$286$	−280.586	+	143.774i	−0.981070	+	0.502705i
$287$		−	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	0.624709	−	0.780858i	$-0.285218\pi$
$293$	−106.619	−	184.670i	−0.363888	−	0.630273i	−0.988597	+	0.150585i	$0.951884\pi$
$294$	−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
$299$	−135.902	−	265.225i	−0.454523	−	0.887040i
$300$	−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	$-0.902487\pi$
$307$		−	185.168i		−	0.603152i	0.953442	−	0.301576i	$-0.0975128\pi$
$308$	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	$0.999225\pi$
$312$	95.2221	+	281.831i	0.305199	+	0.903303i
$313$	−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	$-0.655390\pi$
$317$	168.124	−	291.200i	0.530360	−	0.918611i	0.999373	−	0.0354194i	$-0.0112767\pi$
$318$	−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	0.975328	−	0.220762i	$-0.0708543\pi$
$331$	420.968	+	243.046i	1.27181	+	0.734278i	0.296479	+	0.955039i	$0.404188\pi$
$332$	−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	$0.751082\pi$
$338$	205.581	−	285.692i	0.608228	−	0.845244i
$339$	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	0.561035	−	0.827792i	$-0.310403\pi$
$349$	43.5073	+	25.1189i	0.124663	+	0.0719740i	−0.436372	+	0.899766i	$0.643737\pi$
$350$			7.44473i			0.0212707i
$351$	−309.175	−	166.167i	−0.880842	−	0.473411i
$352$	62.7206			0.178183
$353$	56.6496	−	98.1199i	0.160480	−	0.277960i	−0.774561	−	0.632500i	$-0.782029\pi$
$353$	56.6496	−	98.1199i	0.160480	−	0.277960i	0.935041	+	0.354539i	$0.115362\pi$
$354$	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	$-0.437749\pi$
$359$	139.525			0.388649			0.194324	+	0.980937i	$0.437749\pi$
$360$	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
$364$	−8.50735	−	0.426378i	−0.0233719	−	0.00117137i
$365$	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	$0.0226165\pi$
$379$			53.8120i			0.141984i	−0.997477	+	0.0709921i	$0.977383\pi$
$380$	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	0.949541	−	0.313642i	$-0.101549\pi$
$383$	77.8061	+	134.764i	0.203149	+	0.351865i	−0.746392	+	0.665506i	$0.768216\pi$
$384$	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	$0.352300\pi$
$390$	−134.699	−	398.670i	−0.345381	−	1.02223i
$391$	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	$-0.648921\pi$
$397$		−	708.677i		−	1.78508i	0.450967	−	0.892541i	$-0.351079\pi$
$398$	−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	$-0.995837\pi$
$401$	−205.025	−	355.113i	−0.511283	−	0.885569i	0.488631	−	0.872490i	$-0.337496\pi$
$402$	−57.6047	−	145.956i	−0.143295	−	0.363074i
$403$	−200.148	−	390.606i	−0.496646	−	0.969246i
$404$		−	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	−0.774724	−	0.632299i	$-0.782111\pi$
$409$	−251.330	+	145.105i	−0.614499	+	0.354781i	0.160225	+	0.987080i	$0.448778\pi$
$410$	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
$416$	−62.3160	+	31.9310i	−0.149798	+	0.0767572i
$417$	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	0.956026	−	0.293281i	$-0.0947472\pi$
$421$	496.801	+	286.828i	1.18005	+	0.681302i	0.224024	+	0.974584i	$0.428081\pi$
$422$	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
$429$	−445.290	−	89.2319i	−1.03797	−	0.208000i
$430$	49.9500	−	86.5159i	0.116163	−	0.201200i
$431$	−193.685			−0.449385			−0.224693	−	0.974430i	$-0.572138\pi$
$431$	−193.685			−0.449385			−0.224693	+	0.974430i	$0.572138\pi$
$432$	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	$-0.388539\pi$
$449$	308.063			0.686108			0.343054	+	0.939316i	$0.388539\pi$
$450$	−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
$455$	−130.588	−	6.54493i	−0.287007	−	0.0143845i
$456$	−134.025	−	339.586i	−0.293915	−	0.744707i
$457$	−340.050	−	196.328i	−0.744091	−	0.429601i	0.0794639	−	0.996838i	$-0.474679\pi$
$457$	−340.050	−	196.328i	−0.744091	−	0.429601i	−0.823555	+	0.567237i	$0.808012\pi$
$458$			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	−0.556294	−	0.830985i	$-0.687777\pi$
$461$	203.535	−	352.533i	0.441508	−	0.764713i	0.997802	+	0.0662721i	$0.0211105\pi$
$462$	51.8531	+	131.383i	0.112236	+	0.284379i
$463$	−33.4769	+	19.3279i	−0.0723043	+	0.0417449i	−0.535716	−	0.844398i	$-0.679958\pi$
$463$	−33.4769	+	19.3279i	−0.0723043	+	0.0417449i	0.463412	+	0.886143i	$0.346625\pi$
$464$	−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	$-0.261930\pi$
$468$	13.3724	−	37.1561i	0.0285734	−	0.0793933i
$469$	−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	$-0.654857\pi$
$479$	254.722	−	441.192i	0.531779	−	0.921068i	0.999312	−	0.0370926i	$-0.0118097\pi$
$480$	−12.3193	+	82.8039i	−0.0256653	+	0.172508i
$481$	477.381	+	23.9258i	0.992477	+	0.0497417i
$482$	−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	$-0.718112\pi$
$487$		−	754.148i		−	1.54856i	0.632844	−	0.774280i	$-0.281888\pi$
$488$	−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	−0.512774	−	0.858523i	$-0.671382\pi$
$499$	−12.8035	+	7.39211i	−0.0256583	+	0.0148138i	0.487116	+	0.873337i	$0.338049\pi$
$500$	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
$507$	487.846	−	138.041i	0.962221	−	0.272270i
$508$	1.82727	+	3.16493i	0.00359699	+	0.00623017i
$509$	−157.294	−	272.442i	−0.309027	−	0.535250i	0.669123	−	0.743152i	$-0.266670\pi$
$509$	−157.294	−	272.442i	−0.309027	−	0.535250i	−0.978150	+	0.207902i	$0.933337\pi$
$510$	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
$520$	−457.210	+	234.277i	−0.879250	+	0.450532i
$521$		−	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
$533$	−38.4352	+	19.6944i	−0.0721110	+	0.0369500i
$534$	−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	$0.219798\pi$
$541$			689.163i			1.27387i	−0.770918	+	0.636934i	$0.780202\pi$
$542$	−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
$546$	−118.406	−	104.137i	−0.216860	−	0.190727i
$547$	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	$-0.206155\pi$
$557$	888.415			1.59500			0.797500	+	0.603318i	$0.206155\pi$
$558$	−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	$0.801784\pi$
$572$	2.55752	−	51.0292i	0.00447119	−	0.0892118i
$573$	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	$0.130532\pi$
$577$			460.077i			0.797361i	−0.917090	+	0.398680i	$0.869468\pi$
$578$	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
$585$	205.267	−	570.347i	0.350883	−	0.974953i
$586$	444.106			0.757860
$587$	272.897	−	472.672i	0.464902	−	0.805233i	−0.534295	−	0.845298i	$-0.679423\pi$
$587$	272.897	−	472.672i	0.464902	−	0.805233i	0.999197	+	0.0400644i	$0.0127563\pi$
$588$	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	$-0.544221\pi$
$593$	−164.234			−0.276954			−0.138477	+	0.990366i	$0.544221\pi$
$594$	−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
$598$	619.891	+	31.0682i	1.03661	+	0.0519535i
$599$	−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	$0.131995\pi$
$613$			493.944i			0.805782i	−0.915248	+	0.402891i	$0.868005\pi$
$614$	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	$-0.912098\pi$
$617$	−442.501	−	766.435i	−0.717182	−	1.24220i	0.244930	−	0.969541i	$-0.421235\pi$
$618$	584.139	−	230.543i	0.945209	−	0.373047i
$619$	−847.493	−	489.300i	−1.36913	−	0.790469i	−0.378315	−	0.925677i	$-0.623496\pi$
$619$	−847.493	−	489.300i	−1.36913	−	0.790469i	−0.990817	+	0.135208i	$0.956830\pi$
$620$		−	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
$624$	−659.106	−	132.078i	−1.05626	−	0.211664i
$625$	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	$-0.803957\pi$
$631$		−	729.035i		−	1.15536i	0.816262	−	0.577682i	$-0.196043\pi$
$632$	−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
$637$	523.306	−	268.144i	0.821516	−	0.420948i
$638$		−	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	−0.877160	−	0.480198i	$-0.840565\pi$
$643$	−578.620	+	334.067i	−0.899876	+	0.519544i	−0.0227162	+	0.999742i	$0.507231\pi$
$644$	−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
$650$	44.3672	−	22.7340i	0.0682573	−	0.0349754i
$651$	−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	−0.866096	−	0.499878i	$-0.833378\pi$
$661$	−572.582	+	330.581i	−0.866236	+	0.500122i	−0.000140662		1.00000i	$0.500045\pi$
$662$	−876.737	+	506.185i	−1.32438	+	0.764629i
$663$	−851.099	+	287.561i	−1.28371	+	0.433726i
$664$	−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	$-0.451738\pi$
$683$	206.319			0.302077			0.151038	+	0.988528i	$0.451738\pi$
$684$	−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
$689$	474.559	+	23.7843i	0.688766	+	0.0345201i
$690$	461.562	−	581.048i	0.668930	−	0.842098i
$691$	−824.447	−	475.995i	−1.19312	−	0.688849i	−0.234108	−	0.972210i	$-0.575217\pi$
$691$	−824.447	−	475.995i	−1.19312	−	0.688849i	−0.959013	+	0.283361i	$0.908550\pi$
$692$		−	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	$0.875068\pi$
$702$	621.662	−	384.607i	0.885558	−	0.547874i
$703$	−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	0.973941	−	0.226803i	$-0.0728274\pi$
$709$	896.526	+	517.609i	1.26449	+	0.730056i	0.290553	+	0.956859i	$0.406161\pi$
$710$	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
$715$	39.2581	−	783.300i	0.0549064	−	1.09552i
$716$	−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	0.315877	−	0.948800i	$-0.397701\pi$
$733$	949.602	−	548.253i	1.29550	−	0.747957i	0.979623	+	0.200843i	$0.0643681\pi$
$734$	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	$-0.940244\pi$
$739$		−	275.835i		−	0.373254i	0.982431	−	0.186627i	$-0.0597556\pi$
$740$	55.6790	+	32.1463i	0.0752419	+	0.0434409i
$741$	−589.467	+	199.163i	−0.795502	+	0.268776i
$742$	−73.8901	−	127.981i	−0.0995824	−	0.172482i
$743$	566.081	+	980.480i	0.761885	+	1.31962i	0.941878	+	0.335956i	$0.109059\pi$
$743$	566.081	+	980.480i	0.761885	+	1.31962i	−0.179993	+	0.983668i	$0.557607\pi$
$744$	−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
$754$	549.432	+	1072.26i	0.728689	+	1.42210i
$755$		−	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	0.981438	−	0.191781i	$-0.0614263\pi$
$761$	247.045	+	427.894i	0.324632	+	0.562279i	−0.656806	+	0.754060i	$0.728093\pi$
$762$	−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
$767$	−983.712	+	504.058i	−1.28254	+	0.657182i
$768$	151.172	+	120.085i	0.196838	+	0.156361i
$769$	301.621	−	174.141i	0.392225	−	0.226451i	−0.290898	−	0.956754i	$-0.593954\pi$
$769$	301.621	−	174.141i	0.392225	−	0.226451i	0.683124	+	0.730302i	$0.260621\pi$
$770$	−211.244	+	121.962i	−0.274343	+	0.158392i
$771$	−741.077	+	932.922i

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} +(-0.650727 + 12.9837i) 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} +(-12.4836 - 36.9481i) 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} +(3.90490 - 2.00089i) 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} +(59.9404 - 30.7137i) 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} +(79.6408 + 15.9593i) 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

Related objects

Downloads

Learn more