LMFDB - Embedded newform 117.3.n.a.38.4

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			38.4
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55290 + 2.68970i) q^{2} +(0.846137 - 2.87820i) q^{3} +(-2.82298 - 4.88955i) q^{4} +(0.611466 + 1.05909i) q^{5} +(6.42753 + 6.74541i) q^{6} +(-8.52943 - 4.92447i) q^{7} +5.11202 q^{8} +(-7.56810 - 4.87071i) q^{9} -3.79817 q^{10} +(10.3377 - 17.9053i) q^{11} +(-16.4617 + 3.98788i) q^{12} +(-12.0892 - 4.78034i) q^{13} +(26.4906 - 15.2944i) q^{14} +(3.56566 - 0.863787i) q^{15} +(3.35349 - 5.80841i) q^{16} +25.2931i q^{17} +(24.8532 - 12.7922i) q^{18} -3.49326i q^{19} +(3.45231 - 5.97958i) q^{20} +(-21.3907 + 20.3826i) q^{21} +(32.1066 + 55.6103i) q^{22} +(15.7163 - 9.07382i) q^{23} +(4.32547 - 14.7134i) q^{24} +(11.7522 - 20.3554i) q^{25} +(31.6309 - 25.0929i) q^{26} +(-20.4225 + 17.6612i) q^{27} +55.6067i q^{28} +(-27.9043 - 16.1105i) q^{29} +(-3.21378 + 10.9319i) q^{30} +(-10.7252 + 6.19219i) q^{31} +(20.6393 + 35.7483i) q^{32} +(-42.7881 - 44.9042i) q^{33} +(-68.0308 - 39.2776i) q^{34} -12.0446i q^{35} +(-2.45095 + 50.7545i) q^{36} -19.4885i q^{37} +(9.39582 + 5.42468i) q^{38} +(-23.9879 + 30.7503i) q^{39} +(3.12582 + 5.41408i) q^{40} +(2.02532 + 3.50796i) q^{41} +(-21.6056 - 89.1866i) q^{42} +(-11.9271 + 20.6584i) q^{43} -116.732 q^{44} +(0.530883 - 10.9936i) q^{45} +56.3628i q^{46} +(-6.24342 + 10.8139i) q^{47} +(-13.8803 - 14.5667i) q^{48} +(24.0008 + 41.5705i) q^{49} +(36.5000 + 63.2198i) q^{50} +(72.7987 + 21.4014i) q^{51} +(10.7538 + 72.6054i) q^{52} +58.3168i q^{53} +(-15.7893 - 82.3566i) q^{54} +25.2845 q^{55} +(-43.6026 - 25.1740i) q^{56} +(-10.0543 - 2.95578i) q^{57} +(86.6649 - 50.0360i) q^{58} +(-6.13856 - 10.6323i) q^{59} +(-14.2893 - 14.9960i) q^{60} +(-12.0421 + 20.8574i) q^{61} -38.4634i q^{62} +(40.5659 + 78.8132i) q^{63} -101.375 q^{64} +(-2.32931 - 15.7265i) q^{65} +(187.224 - 45.3554i) q^{66} +(68.5623 - 39.5845i) q^{67} +(123.672 - 71.4019i) q^{68} +(-12.8181 - 52.9124i) q^{69} +(32.3962 + 18.7040i) q^{70} +8.61851 q^{71} +(-38.6883 - 24.8991i) q^{72} -95.4852i q^{73} +(52.4181 + 30.2636i) q^{74} +(-48.6431 - 51.0488i) q^{75} +(-17.0805 + 9.86142i) q^{76} +(-176.349 + 101.815i) q^{77} +(-45.4582 - 112.272i) q^{78} +(64.4313 - 111.598i) q^{79} +8.20216 q^{80} +(33.5524 + 73.7241i) q^{81} -12.5805 q^{82} +(-13.0262 + 22.5620i) q^{83} +(160.047 + 47.0509i) q^{84} +(-26.7877 + 15.4659i) q^{85} +(-37.0433 - 64.1608i) q^{86} +(-69.9802 + 66.6824i) q^{87} +(52.8463 - 91.5324i) q^{88} +146.747 q^{89} +(28.7450 + 18.4998i) q^{90} +(79.5732 + 100.306i) q^{91} +(-88.7337 - 51.2304i) q^{92} +(8.74740 + 36.1087i) q^{93} +(-19.3908 - 33.5858i) q^{94} +(3.69968 - 2.13601i) q^{95} +(120.354 - 29.1561i) q^{96} +(36.9733 + 21.3465i) q^{97} -149.083 q^{98} +(-165.448 + 85.1578i) 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 $

$2$	−1.55290	+	2.68970i	−0.776449	+	1.34485i	0.157528	+	0.987515i	$0.449648\pi$
$2$	−1.55290	+	2.68970i	−0.776449	+	1.34485i	−0.933977	+	0.357334i	$0.883686\pi$
$3$	0.846137	−	2.87820i	0.282046	−	0.959401i
$3$	0.846137	−	2.87820i	0.282046	−	0.959401i
$4$	−2.82298	−	4.88955i	−0.705745	−	1.22239i
$5$	0.611466	+	1.05909i	0.122293	+	0.211818i	0.920672	−	0.390338i	$-0.127642\pi$
$5$	0.611466	+	1.05909i	0.122293	+	0.211818i	−0.798378	+	0.602156i	$0.794309\pi$
$6$	6.42753	+	6.74541i	1.07125	+	1.12423i
$7$	−8.52943	−	4.92447i	−1.21849	−	0.703495i	−0.253895	−	0.967232i	$-0.581712\pi$
$7$	−8.52943	−	4.92447i	−1.21849	−	0.703495i	−0.964595	+	0.263737i	$0.915045\pi$
$8$	5.11202			0.639002
$9$	−7.56810	−	4.87071i	−0.840900	−	0.541190i
$10$	−3.79817			−0.379817
$11$	10.3377	−	17.9053i	0.939787	−	1.62776i	0.173919	−	0.984760i	$-0.444357\pi$
$11$	10.3377	−	17.9053i	0.939787	−	1.62776i	0.765867	−	0.642998i	$-0.222310\pi$
$12$	−16.4617	+	3.98788i	−1.37181	+	0.332324i
$13$	−12.0892	−	4.78034i	−0.929937	−	0.367719i
$13$	−12.0892	−	4.78034i	−0.929937	−	0.367719i
$14$	26.4906	−	15.2944i	1.89219	−	1.09246i
$15$	3.56566	−	0.863787i	0.237711	−	0.0575858i
$16$	3.35349	−	5.80841i	0.209593	−	0.363025i
$17$			25.2931i			1.48783i	0.668274	+	0.743915i	$0.267033\pi$
$17$			25.2931i			1.48783i	−0.668274	+	0.743915i	$0.732967\pi$
$18$	24.8532	−	12.7922i	1.38073	−	0.710677i
$19$		−	3.49326i		−	0.183856i	−0.995766	−	0.0919280i	$-0.970697\pi$
$19$		−	3.49326i		−	0.183856i	0.995766	−	0.0919280i	$-0.0293030\pi$
$20$	3.45231	−	5.97958i	0.172616	−	0.298979i
$21$	−21.3907	+	20.3826i	−1.01860	+	0.970602i
$22$	32.1066	+	55.6103i	1.45939	+	2.52774i
$23$	15.7163	−	9.07382i	0.683318	−	0.394514i	−0.117786	−	0.993039i	$-0.537580\pi$
$23$	15.7163	−	9.07382i	0.683318	−	0.394514i	0.801104	+	0.598525i	$0.204246\pi$
$24$	4.32547	−	14.7134i	0.180228	−	0.613059i
$25$	11.7522	−	20.3554i	0.470089	−	0.814218i
$26$	31.6309	−	25.0929i	1.21657	−	0.965110i
$27$	−20.4225	+	17.6612i	−0.756391	+	0.654120i
$28$			55.6067i			1.98595i
$29$	−27.9043	−	16.1105i	−0.962216	−	0.555536i	−0.0653616	−	0.997862i	$-0.520820\pi$
$29$	−27.9043	−	16.1105i	−0.962216	−	0.555536i	−0.896854	+	0.442326i	$0.854153\pi$
$30$	−3.21378	+	10.9319i	−0.107126	+	0.364397i
$31$	−10.7252	+	6.19219i	−0.345974	+	0.199748i	−0.662911	−	0.748699i	$-0.730679\pi$
$31$	−10.7252	+	6.19219i	−0.345974	+	0.199748i	0.316937	+	0.948447i	$0.397346\pi$
$32$	20.6393	+	35.7483i	0.644977	+	1.11713i
$33$	−42.7881	−	44.9042i	−1.29661	−	1.36073i
$34$	−68.0308	−	39.2776i	−2.00091	−	1.15522i
$35$		−	12.0446i		−	0.344131i
$36$	−2.45095	+	50.7545i	−0.0680820	+	1.40985i
$37$		−	19.4885i		−	0.526715i	−0.964698	−	0.263358i	$-0.915170\pi$
$37$		−	19.4885i		−	0.526715i	0.964698	−	0.263358i	$-0.0848299\pi$
$38$	9.39582	+	5.42468i	0.247259	+	0.142755i
$39$	−23.9879	+	30.7503i	−0.615074	+	0.788469i
$40$	3.12582	+	5.41408i	0.0781456	+	0.135352i
$41$	2.02532	+	3.50796i	0.0493981	+	0.0855601i	0.889667	−	0.456610i	$-0.150936\pi$
$41$	2.02532	+	3.50796i	0.0493981	+	0.0855601i	−0.840269	+	0.542170i	$0.817603\pi$
$42$	−21.6056	−	89.1866i	−0.514419	−	2.12349i
$43$	−11.9271	+	20.6584i	−0.277375	+	0.480428i	−0.970732	−	0.240167i	$-0.922798\pi$
$43$	−11.9271	+	20.6584i	−0.277375	+	0.480428i	0.693356	+	0.720595i	$0.256131\pi$
$44$	−116.732			−2.65300
$45$	0.530883	−	10.9936i	0.0117974	−	0.244302i
$46$			56.3628i			1.22528i
$47$	−6.24342	+	10.8139i	−0.132839	+	0.230084i	−0.924770	−	0.380527i	$-0.875743\pi$
$47$	−6.24342	+	10.8139i	−0.132839	+	0.230084i	0.791931	+	0.610611i	$0.209076\pi$
$48$	−13.8803	−	14.5667i	−0.289172	−	0.303473i
$49$	24.0008	+	41.5705i	0.489811	+	0.848378i
$50$	36.5000	+	63.2198i	0.730000	+	1.26440i
$51$	72.7987	+	21.4014i	1.42743	+	0.419636i
$52$	10.7538	+	72.6054i	0.206804	+	1.39626i
$53$			58.3168i			1.10032i	0.835060	+	0.550159i	$0.185433\pi$
$53$			58.3168i			1.10032i	−0.835060	+	0.550159i	$0.814567\pi$
$54$	−15.7893	−	82.3566i	−0.292394	−	1.52512i
$55$	25.2845			0.459718
$56$	−43.6026	−	25.1740i	−0.778617	−	0.449535i
$57$	−10.0543	−	2.95578i	−0.176392	−	0.0518558i
$58$	86.6649	−	50.0360i	1.49422	−	0.862690i
$59$	−6.13856	−	10.6323i	−0.104043	−	0.180208i	0.809304	−	0.587391i	$-0.199845\pi$
$59$	−6.13856	−	10.6323i	−0.104043	−	0.180208i	−0.913347	+	0.407182i	$0.866511\pi$
$60$	−14.2893	−	14.9960i	−0.238155	−	0.249933i
$61$	−12.0421	+	20.8574i	−0.197411	+	0.341925i	−0.947688	−	0.319198i	$-0.896587\pi$
$61$	−12.0421	+	20.8574i	−0.197411	+	0.341925i	0.750277	+	0.661123i	$0.229920\pi$
$62$		−	38.4634i		−	0.620377i
$63$	40.5659	+	78.8132i	0.643904	+	1.25100i
$64$	−101.375			−1.58398
$65$	−2.32931	−	15.7265i	−0.0358355	−	0.241947i
$66$	187.224	−	45.3554i	2.83673	−	0.687203i
$67$	68.5623	−	39.5845i	1.02332	−	0.590813i	0.108255	−	0.994123i	$-0.465474\pi$
$67$	68.5623	−	39.5845i	1.02332	−	0.590813i	0.915063	+	0.403310i	$0.132140\pi$
$68$	123.672	−	71.4019i	1.81870	−	1.05003i
$69$	−12.8181	−	52.9124i	−0.185770	−	0.766847i
$70$	32.3962	+	18.7040i	0.462803	+	0.267200i
$71$	8.61851			0.121387			0.0606937	−	0.998156i	$-0.480669\pi$
$71$	8.61851			0.121387			0.0606937	+	0.998156i	$0.480669\pi$
$72$	−38.6883	−	24.8991i	−0.537337	−	0.345821i
$73$		−	95.4852i		−	1.30802i	−0.756487	−	0.654008i	$-0.773086\pi$
$73$		−	95.4852i		−	1.30802i	0.756487	−	0.654008i	$-0.226914\pi$
$74$	52.4181	+	30.2636i	0.708352	+	0.408967i
$75$	−48.6431	−	51.0488i	−0.648575	−	0.680650i
$76$	−17.0805	+	9.86142i	−0.224743	+	0.129756i
$77$	−176.349	+	101.815i	−2.29024	+	1.32227i
$78$	−45.4582	−	112.272i	−0.582798	−	1.43939i
$79$	64.4313	−	111.598i	0.815586	−	1.41264i	−0.0933196	−	0.995636i	$-0.529748\pi$
$79$	64.4313	−	111.598i	0.815586	−	1.41264i	0.908906	−	0.417001i	$-0.136919\pi$
$80$	8.20216			0.102527
$81$	33.5524	+	73.7241i	0.414227	+	0.910174i
$82$	−12.5805			−0.153420
$83$	−13.0262	+	22.5620i	−0.156942	+	0.271831i	−0.933764	−	0.357888i	$-0.883497\pi$
$83$	−13.0262	+	22.5620i	−0.156942	+	0.271831i	0.776823	+	0.629719i	$0.216830\pi$
$84$	160.047	+	47.0509i	1.90533	+	0.560130i
$85$	−26.7877	+	15.4659i	−0.315149	+	0.181951i
$86$	−37.0433	−	64.1608i	−0.430736	−	0.746056i
$87$	−69.9802	+	66.6824i	−0.804370	+	0.766464i
$88$	52.8463	−	91.5324i	0.600526	−	1.04014i
$89$	146.747			1.64884			0.824420	−	0.565979i	$-0.191502\pi$
$89$	146.747			1.64884			0.824420	+	0.565979i	$0.191502\pi$
$90$	28.7450	+	18.4998i	0.319389	+	0.205553i
$91$	79.5732	+	100.306i	0.874430	+	1.10227i
$92$	−88.7337	−	51.2304i	−0.964497	−	0.556852i
$93$	8.74740	+	36.1087i	0.0940581	+	0.388266i
$94$	−19.3908	−	33.5858i	−0.206285	−	0.357296i
$95$	3.69968	−	2.13601i	0.0389440	−	0.0224843i
$96$	120.354	−	29.1561i	1.25369	−	0.303709i
$97$	36.9733	+	21.3465i	0.381168	+	0.220067i	0.678326	−	0.734761i	$-0.262706\pi$
$97$	36.9733	+	21.3465i	0.381168	+	0.220067i	−0.297158	+	0.954828i	$0.596039\pi$
$98$	−149.083			−1.52125
$99$	−165.448	+	85.1578i	−1.67119	+	0.860179i
$100$	−132.705			−1.32705
$101$	−42.4795	−	24.5256i	−0.420589	−	0.242827i	0.274740	−	0.961519i	$-0.411408\pi$
$101$	−42.4795	−	24.5256i	−0.420589	−	0.242827i	−0.695329	+	0.718691i	$0.744742\pi$
$102$	−170.612	+	162.572i	−1.67267	+	1.59384i
$103$	−19.1318	−	33.1372i	−0.185745	−	0.321721i	0.758082	−	0.652159i	$-0.226137\pi$
$103$	−19.1318	−	33.1372i	−0.185745	−	0.321721i	−0.943827	+	0.330439i	$0.892803\pi$
$104$	−61.8001	−	24.4372i	−0.594232	−	0.234973i
$105$	−34.6667	−	10.1914i	−0.330159	−	0.0970606i
$106$	−156.855	−	90.5601i	−1.47976	−	0.854340i
$107$		−	5.36035i		−	0.0500967i	−0.999686	−	0.0250484i	$-0.992026\pi$
$107$		−	5.36035i		−	0.0500967i	0.999686	−	0.0250484i	$-0.00797397\pi$
$108$	144.008	+	49.9996i	1.33341	+	0.462959i
$109$		−	23.6340i		−	0.216825i	−0.994106	−	0.108413i	$-0.965423\pi$
$109$		−	23.6340i		−	0.216825i	0.994106	−	0.108413i	$-0.0345768\pi$
$110$	−39.2642	+	68.0076i	−0.356947	+	0.618251i
$111$	−56.0918	−	16.4899i	−0.505331	−	0.148558i
$112$	−57.2066	+	33.0283i	−0.510773	+	0.294895i
$113$	169.505	−	97.8635i	1.50004	−	0.866049i	0.500040	−	0.866002i	$-0.333319\pi$
$113$	169.505	−	97.8635i	1.50004	−	0.866049i	1.00000		4.62698e-5i	$-1.47281e-5\pi$
$114$	23.5635	−	22.4531i	0.206697	−	0.196957i
$115$	19.2200	+	11.0967i	0.167130	+	0.0964927i
$116$			181.919i			1.56827i
$117$	68.2085	+	95.0610i	0.582979	+	0.812487i
$118$	38.1302			0.323137
$119$	124.555	−	215.736i	1.04668	−	1.81291i
$120$	18.2277	−	4.41569i	0.151898	−	0.0367974i
$121$	−153.234	−	265.409i	−1.26640	−	2.19347i
$122$	−37.4001	−	64.7789i	−0.306558	−	0.530975i
$123$	11.8103	−	2.86107i	0.0960189	−	0.0232607i
$124$	60.5540	+	34.9609i	0.488339	+	0.281943i
$125$	59.3176			0.474541
$126$	−274.978	−	13.2788i	−2.18237	−	0.105387i
$127$	129.792			1.02198			0.510992	−	0.859585i	$-0.329278\pi$
$127$	129.792			1.02198			0.510992	+	0.859585i	$0.329278\pi$
$128$	74.8676	−	129.674i	0.584903	−	1.01308i
$129$	49.3671	+	51.8086i	0.382691	+	0.401617i
$130$	45.9168	+	18.1566i	0.353206	+	0.139666i
$131$	5.56829	−	3.21485i	0.0425060	−	0.0245409i	−0.478596	−	0.878035i	$-0.658854\pi$
$131$	5.56829	−	3.21485i	0.0425060	−	0.0245409i	0.521102	+	0.853494i	$0.325521\pi$
$132$	−98.7713	+	335.978i	−0.748267	+	2.54529i
$133$	−17.2025	+	29.7955i	−0.129342	+	0.224027i
$134$			245.882i			1.83494i
$135$	−31.1925	−	10.8301i	−0.231056	−	0.0802227i
$136$			129.299i			0.950726i
$137$	−19.8959	+	34.4606i	−0.145225	+	0.251538i	−0.929457	−	0.368931i	$-0.879724\pi$
$137$	−19.8959	+	34.4606i	−0.145225	+	0.251538i	0.784232	+	0.620468i	$0.213057\pi$
$138$	162.224	+	47.6907i	1.17553	+	0.345585i
$139$	52.6632	+	91.2153i	0.378872	+	0.656225i	0.990898	−	0.134612i	$-0.0429788\pi$
$139$	52.6632	+	91.2153i	0.378872	+	0.656225i	−0.612027	+	0.790837i	$0.709645\pi$
$140$	−58.8925	+	34.0016i	−0.420660	+	0.242868i
$141$	25.8419	+	27.1199i	0.183276	+	0.192340i
$142$	−13.3837	+	23.1812i	−0.0942511	+	0.163248i
$143$	−210.567	+	167.043i	−1.47250	+	1.16814i
$144$	−53.6706	+	27.6248i	−0.372712	+	0.191839i
$145$		−	39.4041i		−	0.271753i
$146$	256.826	+	148.279i	1.75908	+	1.01561i
$147$	139.956	−	33.9047i	0.952084	−	0.230644i
$148$	−95.2897	+	55.0156i	−0.643850	+	0.371727i
$149$	−94.8152	−	164.225i	−0.636344	−	1.10218i	−0.986229	−	0.165387i	$-0.947113\pi$
$149$	−94.8152	−	164.225i	−0.636344	−	1.10218i	0.349885	−	0.936793i	$-0.386221\pi$
$150$	212.843	−	51.5617i	1.41896	−	0.343745i
$151$	−17.8196	−	10.2881i	−0.118010	−	0.0681333i	0.439833	−	0.898080i	$-0.355038\pi$
$151$	−17.8196	−	10.2881i	−0.118010	−	0.0681333i	−0.557843	+	0.829946i	$0.688371\pi$
$152$		−	17.8576i		−	0.117484i
$153$	123.195	−	191.421i	0.805199	−	1.25112i
$154$		−	632.432i		−	4.10670i
$155$	−13.1162	−	7.57263i	−0.0846205	−	0.0488557i
$156$	218.072	+	30.4825i	1.39790	+	0.195401i
$157$	−60.4201	−	104.651i	−0.384841	−	0.666564i	0.606906	−	0.794774i	$-0.292410\pi$
$157$	−60.4201	−	104.651i	−0.384841	−	0.666564i	−0.991747	+	0.128209i	$0.959077\pi$
$158$	200.110	+	346.602i	1.26652	+	2.19368i
$159$	167.848	+	49.3441i	1.05565	+	0.310340i
$160$	−25.2404	+	43.7177i	−0.157753	+	0.273235i
$161$	−178.735			−1.11015
$162$	−250.399	−	24.2402i	−1.54567	−	0.149631i
$163$			41.6323i			0.255413i	0.991812	+	0.127707i	$0.0407616\pi$
$163$			41.6323i			0.255413i	−0.991812	+	0.127707i	$0.959238\pi$
$164$	11.4349	−	19.8058i	0.0697250	−	0.120767i
$165$	21.3941	−	72.7739i	0.129661	−	0.441054i
$166$	−40.4566	−	70.0729i	−0.243714	−	0.422126i
$167$	92.0192	+	159.382i	0.551013	+	0.954383i	0.998202	+	0.0599433i	$0.0190920\pi$
$167$	92.0192	+	159.382i	0.551013	+	0.954383i	−0.447189	+	0.894440i	$0.647575\pi$
$168$	−109.350	+	104.196i	−0.650890	+	0.620217i
$169$	123.297	+	115.581i	0.729566	+	0.683910i
$170$		−	96.0676i		−	0.565104i
$171$	−17.0147	+	26.4374i	−0.0995011	+	0.154605i
$172$	134.680			0.783025
$173$	−61.9707	−	35.7788i	−0.358212	−	0.206814i	0.310084	−	0.950709i	$-0.399643\pi$
$173$	−61.9707	−	35.7788i	−0.358212	−	0.206814i	−0.668296	+	0.743895i	$0.732976\pi$
$174$	−70.6834	−	291.777i	−0.406226	−	1.67688i
$175$	−200.479	+	115.747i	−1.14560	+	0.661410i
$176$	−69.3343	−	120.091i	−0.393945	−	0.682333i
$177$	−35.7960	+	8.67163i	−0.202237	+	0.0489923i
$178$	−227.883	+	394.704i	−1.28024	+	2.21744i
$179$		−	234.641i		−	1.31084i	−0.755263	−	0.655422i	$-0.772491\pi$
$179$		−	234.641i		−	1.31084i	0.755263	−	0.655422i	$-0.227509\pi$
$180$	−55.2522	+	28.4389i	−0.306957	+	0.157994i
$181$	−114.420			−0.632154			−0.316077	−	0.948734i	$-0.602366\pi$
$181$	−114.420			−0.632154			−0.316077	+	0.948734i	$0.602366\pi$
$182$	−393.363	+	58.2622i	−2.16133	+	0.320122i
$183$	49.8427	+	52.3077i	0.272365	+	0.285835i
$184$	80.3421	−	46.3855i	0.436642	−	0.252095i
$185$	20.6400	−	11.9165i	0.111568	−	0.0644137i
$186$	−110.705	−	32.5453i	−0.595190	−	0.174975i
$187$	452.882	+	261.471i	2.42183	+	1.39824i
$188$	70.5003			0.375001
$189$	261.165	−	50.0702i	1.38182	−	0.264921i
$190$			13.2680i			0.0698317i
$191$	−171.230	−	98.8599i	−0.896494	−	0.517591i	−0.0204332	−	0.999791i	$-0.506505\pi$
$191$	−171.230	−	98.8599i	−0.896494	−	0.517591i	−0.876061	+	0.482200i	$0.839838\pi$
$192$	−85.7770	+	291.777i	−0.446755	+	1.51967i
$193$	−255.158	+	147.316i	−1.32206	+	0.763293i	−0.984058	−	0.177851i	$-0.943086\pi$
$193$	−255.158	+	147.316i	−1.32206	+	0.763293i	−0.338006	+	0.941144i	$0.609752\pi$
$194$	−114.831	+	66.2980i	−0.591915	+	0.341742i
$195$	−47.2351	−	6.60259i	−0.242231	−	0.0338594i
$196$	135.507	−	234.706i	0.691364	−	1.19748i
$197$	−195.256			−0.991146			−0.495573	−	0.868566i	$-0.665042\pi$
$197$	−195.256			−0.991146			−0.495573	+	0.868566i	$0.665042\pi$
$198$	27.8754	−	577.247i	0.140785	−	2.91539i
$199$	144.081			0.724027			0.362014	−	0.932173i	$-0.382089\pi$
$199$	144.081			0.724027			0.362014	+	0.932173i	$0.382089\pi$
$200$	60.0775	−	104.057i	0.300388	−	0.520287i
$201$	−55.9190	−	230.830i	−0.278204	−	1.14841i
$202$	131.933	−	76.1714i	0.653132	−	0.377086i
$203$	158.672	+	274.827i	0.781633	+	1.35383i
$204$	−100.866	−	416.368i	−0.494441	−	2.04102i
$205$	−2.47683	+	4.29000i	−0.0120821	+	0.0209268i
$206$	118.839			0.576887
$207$	−163.139	−	7.87802i	−0.788109	−	0.0380581i
$208$	−68.3071	+	54.1881i	−0.328399	+	0.260520i
$209$	−62.5481	−	36.1122i	−0.299273	−	0.172785i
$210$	81.2455	−	77.4168i	0.386883	−	0.368652i
$211$	94.8655	+	164.312i	0.449599	+	0.778729i	0.998360	−	0.0572508i	$-0.0182335\pi$
$211$	94.8655	+	164.312i	0.449599	+	0.778729i	−0.548761	+	0.835980i	$0.684900\pi$
$212$	285.143	−	164.627i	1.34501	−	0.776544i
$213$	7.29244	−	24.8058i	0.0342368	−	0.116459i
$214$	14.4177	+	8.32407i	0.0673725	+	0.0388975i
$215$	−29.1721			−0.135684
$216$	−104.400	+	90.2846i	−0.483335	+	0.417984i
$217$	121.973			0.562088
$218$	63.5682	+	36.7011i	0.291597	+	0.168354i
$219$	−274.826	−	80.7936i	−1.25491	−	0.368921i
$220$	−71.3776	−	123.630i	−0.324444	−	0.561953i
$221$	120.910	−	305.773i	0.547103	−	1.38359i
$222$	131.458	−	125.263i	0.592152	−	0.564246i
$223$	−277.799	−	160.388i	−1.24574	−	0.719227i	−0.275481	−	0.961306i	$-0.588837\pi$
$223$	−277.799	−	160.388i	−1.24574	−	0.719227i	−0.970256	+	0.242080i	$0.922170\pi$
$224$		−	406.550i		−	1.81495i
$225$	−188.087	+	96.8104i	−0.835944	+	0.430269i
$226$			607.888i			2.68977i
$227$	47.0775	−	81.5406i	0.207390	−	0.359210i	−0.743502	−	0.668734i	$-0.766837\pi$
$227$	47.0775	−	81.5406i	0.207390	−	0.359210i	0.950892	+	0.309524i	$0.100170\pi$
$228$	13.9307	+	57.5052i	0.0610997	+	0.252216i
$229$	342.485	−	197.734i	1.49557	−	0.863467i	0.495582	−	0.868561i	$-0.334955\pi$
$229$	342.485	−	197.734i	1.49557	−	0.863467i	0.999987	+	0.00509440i	$0.00162161\pi$
$230$	−59.6933	+	34.4639i	−0.259536	+	0.149843i
$231$	143.829	+	593.716i	0.622635	+	2.57020i
$232$	−142.647	−	82.3573i	−0.614858	−	0.354988i
$233$		−	310.274i		−	1.33165i	−0.746110	−	0.665823i	$-0.768080\pi$
$233$		−	310.274i		−	1.33165i	0.746110	−	0.665823i	$-0.231920\pi$
$234$	−361.606	+	35.8402i	−1.54533	+	0.153163i
$235$	−15.2706			−0.0649811
$236$	−34.6580	+	60.0295i	−0.146856	+	0.254362i
$237$	−266.685	−	279.874i	−1.12525	−	1.18090i
$238$	386.842	+	670.031i	1.62539	+	2.81526i
$239$	130.497	+	226.027i	0.546012	+	0.945721i	0.998542	+	0.0539721i	$0.0171882\pi$
$239$	130.497	+	226.027i	0.546012	+	0.945721i	−0.452530	+	0.891749i	$0.649478\pi$
$240$	6.94016	−	23.6075i	0.0289173	−	0.0983645i
$241$	284.068	+	164.007i	1.17870	+	0.680525i	0.955715	−	0.294295i	$-0.0950849\pi$
$241$	284.068	+	164.007i	1.17870	+	0.680525i	0.222990	+	0.974821i	$0.428418\pi$
$242$	951.828			3.93317
$243$	240.583	−	34.1898i	0.990052	−	0.140699i
$244$	135.978			0.557286
$245$	−29.3513	+	50.8379i	−0.119801	+	0.207502i
$246$	−10.6448	+	36.2092i	−0.0432716	+	0.147192i
$247$	−16.6990	+	42.2307i	−0.0676073	+	0.170975i
$248$	−54.8274	+	31.6546i	−0.221078	+	0.127639i
$249$	53.9160	+	56.5825i	0.216530	+	0.227239i
$250$	−92.1141	+	159.546i	−0.368457	+	0.638185i
$251$		−	10.1232i		−	0.0403315i	−0.999797	−	0.0201657i	$-0.993581\pi$
$251$		−	10.1232i		−	0.0403315i	0.999797	−	0.0201657i	$-0.00641939\pi$
$252$	270.844	−	420.837i	1.07478	−	1.66999i
$253$		−	375.208i		−	1.48304i
$254$	−201.554	+	349.101i	−0.793519	+	1.37441i
$255$	21.8479	+	90.1866i	0.0856779	+	0.353673i
$256$	29.7737	+	51.5695i	0.116303	+	0.201444i
$257$	−278.454	+	160.766i	−1.08348	+	0.625548i	−0.931833	−	0.362887i	$-0.881791\pi$
$257$	−278.454	+	160.766i	−1.08348	+	0.625548i	−0.151647	+	0.988435i	$0.548458\pi$
$258$	−216.011	+	52.3291i	−0.837254	+	0.202826i
$259$	−95.9703	+	166.225i	−0.370542	+	0.641797i
$260$	−70.3200	+	55.7850i	−0.270462	+	0.214558i
$261$	132.713	+	257.840i	0.508477	+	0.987892i
$262$			19.9693i			0.0762189i
$263$	187.874	+	108.469i	0.714351	+	0.412430i	0.812670	−	0.582724i	$-0.198013\pi$
$263$	187.874	+	108.469i	0.714351	+	0.412430i	−0.0983193	+	0.995155i	$0.531347\pi$
$264$	−218.734	−	229.551i	−0.828536	−	0.869512i
$265$	−61.7627	+	35.6587i	−0.233067	+	0.134561i
$266$	−53.4273	−	92.5389i	−0.200855	−	0.347890i
$267$	124.168	−	422.367i	0.465048	−	1.58190i
$268$	−387.100	−	223.492i	−1.44440	−	0.833927i
$269$			379.276i			1.40995i	0.709233	+	0.704975i	$0.249042\pi$
$269$			379.276i			1.40995i	−0.709233	+	0.704975i	$0.750958\pi$
$270$	77.5684	−	67.0805i	0.287290	−	0.248446i
$271$			157.928i			0.582761i	0.956607	+	0.291380i	$0.0941145\pi$
$271$			157.928i			0.582761i	−0.956607	+	0.291380i	$0.905886\pi$
$272$	146.913	+	84.8201i	0.540120	+	0.311838i
$273$	356.032	−	144.155i	1.30415	−	0.528039i
$274$	−61.7925	−	107.028i	−0.225520	−	0.390612i
$275$	−242.981	−	420.855i	−0.883566	−	1.53038i
$276$	−222.532	+	212.046i	−0.806277	+	0.768281i
$277$	−100.007	+	173.217i	−0.361035	+	0.625332i	−0.988132	−	0.153610i	$-0.950910\pi$
$277$	−100.007	+	173.217i	−0.361035	+	0.625332i	0.627096	+	0.778942i	$0.284243\pi$
$278$	−327.122			−1.17670
$279$	111.330	+	5.37615i	0.399031	+	0.0192694i
$280$		−	61.5720i		−	0.219900i
$281$	94.9870	−	164.522i	0.338032	−	0.585489i	−0.646030	−	0.763312i	$-0.723572\pi$
$281$	94.9870	−	164.522i	0.338032	−	0.585489i	0.984062	+	0.177823i	$0.0569054\pi$
$282$	−113.074	+	27.3924i	−0.400972	+	0.0971362i
$283$	−189.618	−	328.429i	−0.670030	−	1.16053i	−0.977895	−	0.209095i	$-0.932948\pi$
$283$	−189.618	−	328.429i	−0.670030	−	1.16053i	0.307866	−	0.951430i	$-0.400385\pi$
$284$	−24.3299	−	42.1406i	−0.0856686	−	0.148382i
$285$	−3.01744	−	12.4558i	−0.0105875	−	0.0437045i
$286$	−122.307	−	825.764i	−0.427645	−	2.88729i
$287$		−	39.8945i		−	0.139005i
$288$	17.9193	−	371.074i	0.0622198	−	1.28845i
$289$	−350.741			−1.21364
$290$	105.985	+	61.1906i	0.365466	+	0.211002i
$291$	92.7242	−	88.3545i	0.318640	−	0.303624i
$292$	−466.879	+	269.553i	−1.59890	+	0.923126i
$293$	8.42558	+	14.5935i	0.0287563	+	0.0498073i	0.880045	−	0.474890i	$-0.157512\pi$
$293$	8.42558	+	14.5935i	0.0287563	+	0.0498073i	−0.851289	+	0.524697i	$0.824179\pi$
$294$	−126.145	+	429.091i	−0.429063	+	1.45949i
$295$	7.50703	−	13.0026i	0.0254476	−	0.0440765i
$296$		−	99.6254i		−	0.336572i
$297$	105.109	+	548.249i	0.353904	+	1.84595i
$298$	588.953			1.97635
$299$	−233.373	+	34.5657i	−0.780513	+	0.115604i
$300$	−112.287	+	381.952i	−0.374289	+	1.27317i
$301$	203.463	−	117.470i	0.675958	−	0.390265i
$302$	55.3439	−	31.9528i	0.183258	−	0.105804i
$303$	−106.533	+	101.513i	−0.351594	+	0.335025i
$304$	−20.2903	−	11.7146i	−0.0667444	−	0.0385349i
$305$	−29.4532			−0.0965679
$306$	323.554	+	628.615i	1.05737	+	2.05430i
$307$		−	57.0349i		−	0.185782i	−0.995676	−	0.0928908i	$-0.970389\pi$
$307$		−	57.0349i		−	0.185782i	0.995676	−	0.0928908i	$-0.0296107\pi$
$308$	995.657	+	574.843i	3.23265	+	1.86637i
$309$	−111.564	+	27.0265i	−0.361048	+	0.0874644i
$310$	40.7361	−	23.5190i	0.131407	−	0.0758678i
$311$	35.6272	−	20.5694i	0.114557	−	0.0661395i	−0.441627	−	0.897199i	$-0.645598\pi$
$311$	35.6272	−	20.5694i	0.114557	−	0.0661395i	0.556184	+	0.831059i	$0.312265\pi$
$312$	−122.627	+	157.196i	−0.393034	+	0.503833i
$313$	−166.556	+	288.483i	−0.532127	+	0.921672i	0.467169	+	0.884168i	$0.345274\pi$
$313$	−166.556	+	288.483i	−0.532127	+	0.921672i	−0.999296	+	0.0375036i	$0.988059\pi$
$314$	375.305			1.19524
$315$	−58.6656	+	91.1545i	−0.186240	+	0.289379i
$316$	−727.553			−2.30238
$317$	−88.9725	+	154.105i	−0.280670	+	0.486135i	−0.971550	−	0.236834i	$-0.923890\pi$
$317$	−88.9725	+	154.105i	−0.280670	+	0.486135i	0.690880	+	0.722970i	$0.257223\pi$
$318$	−393.371	+	374.833i	−1.23701	+	1.17872i
$319$	−576.929	+	333.090i	−1.80856	+	1.04417i
$320$	−61.9872	−	107.365i	−0.193710	−	0.335516i
$321$	−15.4282	−	4.53559i	−0.0480628	−	0.0141296i
$322$	277.557	−	480.743i	0.861978	−	1.49299i
$323$	88.3555			0.273547
$324$	265.760	−	372.177i	0.820245	−	1.14870i
$325$	−239.381	+	189.901i	−0.736556	+	0.584311i
$326$	−111.978	−	64.6508i	−0.343492	−	0.198315i
$327$	−68.0234	−	19.9976i	−0.208023	−	0.0611547i
$328$	10.3535	+	17.9328i	0.0315655	+	0.0546730i
$329$	106.506	−	61.4911i	0.323725	−	0.186903i
$330$	162.517	+	170.554i	0.492475	+	0.516831i
$331$	−20.6670	−	11.9321i	−0.0624382	−	0.0360487i	0.468456	−	0.883487i	$-0.344810\pi$
$331$	−20.6670	−	11.9321i	−0.0624382	−	0.0360487i	−0.530894	+	0.847438i	$0.678144\pi$
$332$	147.090			0.443043
$333$	−94.9227	+	147.491i	−0.285053	+	0.442915i
$334$	−571.586			−1.71133
$335$	83.8470	+	48.4091i	0.250290	+	0.144505i
$336$	46.6574	+	192.599i	0.138861	+	0.573210i
$337$	176.891	+	306.385i	0.524900	+	0.909153i	0.999580	+	0.0289946i	$0.00923055\pi$
$337$	176.891	+	306.385i	0.524900	+	0.909153i	−0.474680	+	0.880159i	$0.657436\pi$
$338$	−502.345	+	152.145i	−1.48623	+	0.450134i
$339$	−138.247	−	570.674i	−0.407808	−	1.68341i
$340$	151.242	+	87.3197i	0.444830	+	0.256823i
$341$			256.051i			0.750883i
$342$	−44.6865	−	86.8189i	−0.130662	−	0.253856i
$343$			9.83416i			0.0286710i
$344$	−60.9717	+	105.606i	−0.177243	+	0.306995i
$345$	48.2012	−	45.9297i	0.139714	−	0.133130i
$346$	192.468	−	111.122i	0.556267	−	0.321161i
$347$	113.652	−	65.6170i	0.327527	−	0.189098i	−0.327216	−	0.944950i	$-0.606110\pi$
$347$	113.652	−	65.6170i	0.327527	−	0.189098i	0.654743	+	0.755852i	$0.272777\pi$
$348$	523.599	+	153.928i	1.50460	+	0.442323i
$349$	−428.731	−	247.528i	−1.22846	−	0.709250i	−0.261750	−	0.965136i	$-0.584299\pi$
$349$	−428.731	−	247.528i	−1.22846	−	0.709250i	−0.966707	+	0.255886i	$0.917633\pi$
$350$		−	718.972i		−	2.05421i
$351$	331.319	−	115.883i	0.943928	−	0.330152i
$352$	853.446			2.42456
$353$	−149.196	+	258.416i	−0.422652	+	0.732055i	−0.996198	−	0.0871182i	$-0.972234\pi$
$353$	−149.196	+	258.416i	−0.422652	+	0.732055i	0.573546	+	0.819174i	$0.305568\pi$
$354$	32.2634	−	109.746i	0.0911395	−	0.310018i
$355$	5.26992	+	9.12777i	0.0148449	+	0.0257120i
$356$	−414.263	−	717.525i	−1.16366	−	2.01552i
$357$	−515.540	−	541.037i	−1.44409	−	1.51551i
$358$	631.113	+	364.373i	1.76289	+	1.01780i
$359$	−112.423			−0.313157			−0.156579	−	0.987665i	$-0.550046\pi$
$359$	−112.423			−0.313157			−0.156579	+	0.987665i	$0.550046\pi$
$360$	2.71388	−	56.1993i	0.00753856	−	0.156109i
$361$	348.797			0.966197
$362$	177.682	−	307.755i	0.490835	−	0.850151i
$363$	−893.559	+	216.466i	−2.46160	+	0.596326i
$364$	265.819	−	672.239i	0.730272	−	1.84681i
$365$	101.127	−	58.3859i	0.277061	−	0.159961i
$366$	−218.093	+	52.8333i	−0.595881	+	0.144353i
$367$	88.8097	−	153.823i	0.241988	−	0.419136i	−0.719292	−	0.694708i	$-0.755534\pi$
$367$	88.8097	−	153.823i	0.241988	−	0.419136i	0.961281	+	0.275572i	$0.0888671\pi$
$368$		−	121.716i		−	0.330749i
$369$	1.75841	−	36.4134i	0.00476535	−	0.0986812i
$370$			74.0206i			0.200056i
$371$	287.179	−	497.409i	0.774068	−	1.34073i
$372$	151.862	−	144.705i	0.408230	−	0.388992i
$373$	−181.640	−	314.610i	−0.486972	−	0.843460i	0.512916	−	0.858439i	$-0.328565\pi$
$373$	−181.640	−	314.610i	−0.486972	−	0.843460i	−0.999888	+	0.0149791i	$0.995232\pi$
$374$	−1406.56	+	812.076i	−3.76085	+	2.17133i
$375$	50.1908	−	170.728i	0.133842	−	0.455275i
$376$	−31.9165	+	55.2810i	−0.0848843	+	0.147024i
$377$	260.326	+	328.155i	0.690519	+	0.870438i
$378$	−270.889	+	780.208i	−0.716637	+	2.06404i
$379$			407.877i			1.07619i	0.842883	+	0.538097i	$0.180856\pi$
$379$			407.877i			1.07619i	−0.842883	+	0.538097i	$0.819144\pi$
$380$	−20.8882	−	12.0598i	−0.0549691	−	0.0317364i
$381$	109.822	−	373.568i	0.288246	−	0.980493i
$382$	531.807	−	307.039i	1.39216	−	0.803766i
$383$	126.399	+	218.929i	0.330023	+	0.571616i	0.982516	−	0.186179i	$-0.0596103\pi$
$383$	126.399	+	218.929i	0.330023	+	0.571616i	−0.652493	+	0.757795i	$0.726277\pi$
$384$	−309.881	−	325.206i	−0.806982	−	0.846892i
$385$	−215.662	−	124.513i	−0.560161	−	0.323409i
$386$		−	915.064i		−	2.37063i
$387$	190.887	−	98.2514i	0.493248	−	0.253880i
$388$		−	241.043i		−	0.621246i
$389$	236.386	+	136.477i	0.607675	+	0.350841i	0.772055	−	0.635556i	$-0.219229\pi$
$389$	236.386	+	136.477i	0.607675	+	0.350841i	−0.164380	+	0.986397i	$0.552562\pi$
$390$	91.1102	−	116.795i	0.233616	−	0.299474i
$391$	229.505	+	397.514i	0.586969	+	1.01666i
$392$	122.692	+	212.509i	0.312990	+	0.542115i
$393$	−4.54146	−	18.7469i	−0.0115559	−	0.0477020i
$394$	303.212	−	525.179i	0.769574	−	1.33294i
$395$	157.590			0.398962
$396$	883.440	+	568.568i	2.23091	+	1.43578i
$397$		−	271.431i		−	0.683705i	−0.939754	−	0.341852i	$-0.888946\pi$
$397$		−	271.431i		−	0.683705i	0.939754	−	0.341852i	$-0.111054\pi$
$398$	−223.744	+	387.535i	−0.562170	+	0.973707i
$399$	71.2020	+	74.7233i	0.178451	+	0.187276i
$400$	−78.8218	−	136.523i	−0.197054	−	0.341308i
$401$	63.1130	+	109.315i	0.157389	+	0.272606i	0.933926	−	0.357465i	$-0.116359\pi$
$401$	63.1130	+	109.315i	0.157389	+	0.272606i	−0.776537	+	0.630071i	$0.783026\pi$
$402$	707.700	+	208.050i	1.76045	+	0.517538i
$403$	159.260	−	23.5885i	0.395185	−	0.0585321i
$404$			276.941i			0.685497i
$405$	−57.5643	+	80.6147i	−0.142134	+	0.199049i
$406$	−985.603			−2.42759
$407$	−348.948	−	201.465i	−0.857365	−	0.495000i
$408$	372.148	+	109.405i	0.912128	+	0.268148i
$409$	677.374	−	391.082i	1.65617	−	0.956191i	0.681715	−	0.731618i	$-0.261235\pi$
$409$	677.374	−	391.082i	1.65617	−	0.956191i	0.974457	−	0.224573i	$-0.0720988\pi$
$410$	−7.69253	−	13.3238i	−0.0187623	−	0.0324972i
$411$	82.3501	+	86.4228i	0.200365	+	0.210274i
$412$	−108.017	+	187.091i	−0.262178	+	0.454105i
$413$			120.916i			0.292776i
$414$	274.527	−	426.560i	0.663109	−	1.03034i
$415$	−31.8602			−0.0767716
$416$	−78.6229	−	530.830i	−0.188997	−	1.27603i
$417$	307.096	−	74.3946i	0.736442	−	0.178404i
$418$	194.262	−	112.157i	0.464741	−	0.268318i
$419$	197.372	−	113.953i	0.471055	−	0.271963i	−0.245626	−	0.969365i	$-0.578994\pi$
$419$	197.372	−	113.953i	0.471055	−	0.271963i	0.716681	+	0.697401i	$0.245660\pi$
$420$	48.0323	+	198.274i	0.114363	+	0.472082i
$421$	−589.735	−	340.484i	−1.40080	−	0.808750i	−0.406322	−	0.913730i	$-0.633189\pi$
$421$	−589.735	−	340.484i	−1.40080	−	0.808750i	−0.994474	+	0.104979i	$0.966522\pi$
$422$	−589.265			−1.39636
$423$	99.9224	−	51.4310i	0.236223	−	0.121586i
$424$			298.117i			0.703105i
$425$	514.852	+	297.250i	1.21142	+	0.699412i
$426$	55.3957	+	58.1354i	0.130037	+	0.136468i
$427$	205.424	−	118.601i	0.481086	−	0.277755i
$428$	−26.2097	+	15.1322i	−0.0612375	+	0.0353555i
$429$	302.616	+	747.398i	0.705398	+	1.74219i
$430$	45.3014	−	78.4642i	0.105352	−	0.182475i
$431$	43.2839			0.100427			0.0502133	−	0.998739i	$-0.484010\pi$
$431$	43.2839			0.100427			0.0502133	+	0.998739i	$0.484010\pi$
$432$	34.0970	+	177.849i	0.0789282	+	0.411688i
$433$	−95.3259			−0.220152			−0.110076	−	0.993923i	$-0.535109\pi$
$433$	−95.3259			−0.220152			−0.110076	+	0.993923i	$0.535109\pi$
$434$	−189.412	+	328.070i	−0.436432	+	0.755923i
$435$	−113.413	−	33.3413i	−0.260720	−	0.0766467i
$436$	−115.559	+	66.7182i	−0.265044	+	0.153023i
$437$	−31.6973	−	54.9012i	−0.0725338	−	0.125632i
$438$	644.087	−	613.734i	1.47052	−	1.40122i
$439$	201.483	−	348.979i	0.458959	−	0.794940i	−0.539947	−	0.841699i	$-0.681556\pi$
$439$	201.483	−	348.979i	0.458959	−	0.794940i	0.998906	+	0.0467588i	$0.0148892\pi$
$440$	129.255			0.293761
$441$	20.8378	−	431.511i	0.0472512	−	0.978482i
$442$	634.676	+	800.045i	1.43592	+	1.81006i
$443$	−478.511	−	276.268i	−1.08016	−	0.623631i	−0.149220	−	0.988804i	$-0.547676\pi$
$443$	−478.511	−	276.268i	−1.08016	−	0.623631i	−0.930940	+	0.365173i	$0.881010\pi$
$444$	77.7177	+	320.814i	0.175040	+	0.722554i
$445$	89.7306	+	155.418i	0.201642	+	0.349254i
$446$	862.788	−	498.131i	1.93450	−	1.11689i
$447$	−552.899	+	133.941i	−1.23691	+	0.299644i
$448$	864.669	+	499.217i	1.93006	+	1.11432i
$449$	−631.702			−1.40691			−0.703454	−	0.710740i	$-0.748360\pi$
$449$	−631.702			−1.40691			−0.703454	+	0.710740i	$0.748360\pi$
$450$	31.6898	−	656.235i	0.0704218	−	1.45830i
$451$	83.7483			0.185695
$452$	−957.016	−	552.533i	−2.11729	−	1.22242i
$453$	−44.6891	+	42.5832i	−0.0986515	+	0.0940026i
$454$	146.213	+	253.248i	0.322055	+	0.557816i
$455$	−57.5772	+	145.609i	−0.126543	+	0.320020i
$456$	−51.3979	−	15.1100i	−0.112715	−	0.0331360i
$457$	−401.315	−	231.700i	−0.878152	−	0.507001i	−0.00810315	−	0.999967i	$-0.502579\pi$
$457$	−401.315	−	231.700i	−0.878152	−	0.507001i	−0.870049	+	0.492966i	$0.835913\pi$
$458$			1228.24i			2.68175i
$459$	−446.708	−	516.550i	−0.973220	−	1.12538i
$460$		−	125.303i		−	0.272397i
$461$	−297.103	+	514.598i	−0.644476	+	1.11627i	0.339946	+	0.940445i	$0.389591\pi$
$461$	−297.103	+	514.598i	−0.644476	+	1.11627i	−0.984422	+	0.175820i	$0.943742\pi$
$462$	−1820.27	−	535.125i	−3.93997	−	1.15828i
$463$	96.7700	−	55.8702i	0.209007	−	0.120670i	−0.391843	−	0.920032i	$-0.628162\pi$
$463$	96.7700	−	55.8702i	0.209007	−	0.120670i	0.600850	+	0.799362i	$0.294829\pi$
$464$	−187.153	+	108.053i	−0.403347	+	0.232873i
$465$	−32.8936	+	31.3435i	−0.0707390	+	0.0674054i
$466$	834.542	+	481.823i	1.79086	+	1.03396i
$467$		−	273.583i		−	0.585831i	−0.956138	−	0.292915i	$-0.905375\pi$
$467$		−	273.583i		−	0.585831i	0.956138	−	0.292915i	$-0.0946255\pi$
$468$	272.254	−	601.864i	0.581739	−	1.28603i
$469$	−779.730			−1.66254
$470$	23.7136	−	41.0732i	0.0504545	−	0.0873897i
$471$	−352.329	+	85.3524i	−0.748045	+	0.181215i
$472$	−31.3804	−	54.3524i	−0.0664839	−	0.115153i
$473$	246.597	+	427.119i	0.521347	+	0.903000i
$474$	1166.91	−	282.686i	2.46184	−	0.596384i
$475$	−71.1070	−	41.0536i	−0.149699	−	0.0864287i
$476$	−1406.47			−2.95476
$477$	284.044	−	441.348i	0.595481	−	0.925257i
$478$	−810.594			−1.69580
$479$	−66.9177	+	115.905i	−0.139703	+	0.241973i	−0.927384	−	0.374110i	$-0.877948\pi$
$479$	−66.9177	+	115.905i	−0.139703	+	0.241973i	0.787681	+	0.616083i	$0.211281\pi$
$480$	104.471	+	109.638i	0.217649	+	0.228413i
$481$	−93.1615	+	235.600i	−0.193683	+	0.489812i
$482$	−882.256	+	509.371i	−1.83041	+	1.05679i
$483$	−151.234	+	514.435i	−0.313114	+	1.06508i
$484$	−865.154	+	1498.49i	−1.78751	+	3.09606i
$485$			52.2107i			0.107651i
$486$	−281.640	+	700.188i	−0.579506	+	1.44072i
$487$		−	777.334i		−	1.59617i	−0.602546	−	0.798084i	$-0.705847\pi$
$487$		−	777.334i		−	1.59617i	0.602546	−	0.798084i	$-0.294153\pi$
$488$	−61.5592	+	106.624i	−0.126146	+	0.218491i
$489$	119.826	+	35.2267i	0.245044	+	0.0720382i
$490$	−91.1590	−	157.892i	−0.186039	−	0.322229i
$491$	495.481	−	286.066i	1.00913	−	0.582620i	0.0981909	−	0.995168i	$-0.468694\pi$
$491$	495.481	−	286.066i	1.00913	−	0.582620i	0.910936	+	0.412548i	$0.135361\pi$
$492$	−47.3297	−	49.6704i	−0.0961985	−	0.100956i
$493$	407.485	−	705.785i	0.826542	−	1.43161i
$494$	−87.6560	−	110.495i	−0.177441	−	0.223675i
$495$	−191.356	−	123.153i	−0.386577	−	0.248795i
$496$			83.0617i			0.167463i
$497$	−73.5110	−	42.4416i	−0.147909	−	0.0853955i
$498$	−235.916	+	57.1510i	−0.473726	+	0.114761i
$499$	382.938	−	221.089i	0.767411	−	0.443065i	−0.0645394	−	0.997915i	$-0.520558\pi$
$499$	382.938	−	221.089i	0.767411	−	0.443065i	0.831950	+	0.554850i	$0.187224\pi$
$500$	−167.452	−	290.036i	−0.334905	−	0.580072i
$501$	536.595	−	129.991i	1.07105	−	0.259463i
$502$	27.2283	+	15.7203i	0.0542397	+	0.0313153i
$503$			374.526i			0.744584i	0.928116	+	0.372292i	$0.121428\pi$
$503$			374.526i			0.744584i	−0.928116	+	0.372292i	$0.878572\pi$
$504$	207.374	+	402.895i	0.411456	+	0.799394i
$505$		−	59.9862i		−	0.118785i
$506$	1009.20	+	582.659i	1.99446	+	1.15150i
$507$	436.991	−	257.075i	0.861915	−	0.507052i
$508$	−366.400	−	634.624i	−0.721261	−	1.24926i
$509$	150.147	+	260.062i	0.294984	+	0.510927i	0.974981	−	0.222287i	$-0.0713523\pi$
$509$	150.147	+	260.062i	0.294984	+	0.510927i	−0.679997	+	0.733215i	$0.738019\pi$
$510$	−276.502	−	81.2864i	−0.542161	−	0.159385i
$511$	−470.214	+	814.434i	−0.920184	+	1.59380i
$512$	413.998			0.808591
$513$	61.6954	+	71.3414i	0.120264	+	0.139067i
$514$		−	998.611i		−	1.94282i
$515$	23.3969	−	40.5245i	0.0454308	−	0.0786884i
$516$	113.958	−	387.637i	0.220849	−	0.751235i
$517$	129.085	+	223.581i	0.249680	+	0.432459i
$518$	−298.064	−	516.262i	−0.575413	−	0.996645i
$519$	−155.414	+	148.091i	−0.299450	+	0.285338i
$520$	−11.9075	−	80.3943i	−0.0228990	−	0.154604i
$521$			609.830i			1.17050i	0.810853	+	0.585249i	$0.199003\pi$
$521$			609.830i			1.17050i	−0.810853	+	0.585249i	$0.800997\pi$
$522$	−899.600	−	43.4420i	−1.72337	−	0.0832222i
$523$	640.706			1.22506			0.612530	−	0.790448i	$-0.290152\pi$
$523$	640.706			1.22506			0.612530	+	0.790448i	$0.290152\pi$
$524$	−31.4383	−	18.1509i	−0.0599968	−	0.0346392i
$525$	163.510	+	674.958i	0.311447	+	1.28563i
$526$	−583.499	+	336.883i	−1.10931	+	0.640462i
$527$	−156.620	−	271.273i	−0.297191	−	0.514750i
$528$	−404.311	+	97.9451i	−0.765741	+	0.185502i
$529$	−99.8316	+	172.913i	−0.188718	+	0.326869i
$530$		−	221.497i		−	0.417920i
$531$	−5.32958	+	110.365i	−0.0100369	+	0.207844i
$532$	194.249			0.365130
$533$	−7.71524	−	52.0901i	−0.0144751	−	0.0977301i
$534$	943.219	+	989.866i	1.76633	+	1.85368i
$535$	5.67709	−	3.27767i	0.0106114	−	0.00612648i
$536$	350.492	−	202.356i	0.653902	−	0.377531i
$537$	−675.344	−	198.539i	−1.25762	−	0.369718i
$538$	−1020.14	−	588.977i	−1.89617	−	1.09475i
$539$	992.446			1.84127
$540$	35.1018	+	183.090i	0.0650034	+	0.339056i
$541$			792.516i			1.46491i	0.680816	+	0.732455i	$0.261625\pi$
$541$			792.516i			1.46491i	−0.680816	+	0.732455i	$0.738375\pi$
$542$	−424.779	−	245.246i	−0.783725	−	0.452484i
$543$	−96.8149	+	329.324i	−0.178296	+	0.606489i
$544$	−904.185	+	522.031i	−1.66210	+	0.959616i
$545$	25.0305	−	14.4514i	0.0459275	−	0.0265163i
$546$	−165.148	+	1181.48i	−0.302470	+	2.16387i
$547$	162.120	−	280.800i	0.296380	−	0.513345i	−0.678925	−	0.734207i	$-0.737554\pi$
$547$	162.120	−	280.800i	0.296380	−	0.513345i	0.975305	+	0.220863i	$0.0708873\pi$
$548$	224.663			0.409968
$549$	192.726	−	99.1979i	0.351049	−	0.180688i
$550$	1509.30			2.74418
$551$	−56.2784	+	97.4770i	−0.102139	+	0.176909i
$552$	−65.5265	−	270.489i	−0.118707	−	0.490017i
$553$	−1099.12	+	634.580i	−1.98757	+	1.14752i
$554$	−310.601	−	537.976i	−0.560651	−	0.971076i
$555$	−16.8339	−	69.4892i	−0.0303313	−	0.125206i
$556$	297.334	−	514.998i	0.534774	−	0.926255i
$557$	262.057			0.470479			0.235239	−	0.971937i	$-0.424413\pi$
$557$	262.057			0.470479			0.235239	+	0.971937i	$0.424413\pi$
$558$	−187.344	+	291.095i	−0.335742	+	0.521675i
$559$	242.944	−	192.728i	0.434604	−	0.344772i
$560$	−69.9598	−	40.3913i	−0.124928	−	0.0721273i
$561$	1135.77	−	1082.24i	2.02454	−	1.92914i
$562$	295.010	+	510.973i	0.524929	+	0.909204i
$563$	105.814	−	61.0915i	0.187946	−	0.108511i	−0.403075	−	0.915167i	$-0.632058\pi$
$563$	105.814	−	61.0915i	0.187946	−	0.108511i	0.591021	+	0.806656i	$0.298725\pi$
$564$	59.6529	−	202.914i	0.105768	−	0.359777i
$565$	207.292	+	119.680i	0.366889	+	0.211824i
$566$	1177.83			2.08097
$567$	76.8693	−	794.052i	0.135572	−	1.40044i
$568$	44.0580			0.0775668
$569$	731.319	+	422.227i	1.28527	+	0.742051i	0.977807	−	0.209509i	$-0.0671865\pi$
$569$	731.319	+	422.227i	1.28527	+	0.742051i	0.307463	+	0.951560i	$0.400520\pi$
$570$	38.1881	+	11.2266i	0.0669966	+	0.0196957i
$571$	−304.502	−	527.413i	−0.533278	−	0.923665i	−0.999245	−	0.0388626i	$-0.987627\pi$
$571$	−304.502	−	527.413i	−0.533278	−	0.923665i	0.465966	−	0.884802i	$-0.345707\pi$
$572$	1411.19	+	558.019i	2.46712	+	0.975557i
$573$	−429.423	+	409.187i	−0.749430	+	0.714113i
$574$	107.304	+	61.9521i	0.186941	+	0.107931i
$575$		−	426.550i		−	0.741826i
$576$	767.215	+	493.767i	1.33197	+	0.857235i
$577$		−	775.270i		−	1.34362i	−0.740722	−	0.671811i	$-0.765517\pi$
$577$		−	775.270i		−	1.34362i	0.740722	−	0.671811i	$-0.234483\pi$
$578$	544.665	−	943.388i	0.942327	−	1.63216i
$579$	208.105	+	859.046i	0.359422	+	1.48367i
$580$	−192.668	+	111.237i	−0.332187	+	0.191788i
$581$	222.211	−	128.294i	0.382464	−	0.220816i
$582$	93.6558	+	386.605i	0.160921	+	0.664270i
$583$	1044.18	+	602.859i	1.79105	+	1.03406i
$584$		−	488.122i		−	0.835825i
$585$	−58.9710	+	130.365i	−0.100805	+	0.222847i
$586$	−52.3363			−0.0893110
$587$	507.863	−	879.645i	0.865184	−	1.49854i	−0.00167957	−	0.999999i	$-0.500535\pi$
$587$	507.863	−	879.645i	0.865184	−	1.49854i	0.866864	−	0.498545i	$-0.166132\pi$
$588$	−560.872	−	588.611i	−0.953864	−	1.00104i
$589$	21.6310	+	37.4659i	0.0367249	+	0.0636094i
$590$	23.3153	+	40.3833i	0.0395175	+	0.0684463i
$591$	−165.213	+	561.985i	−0.279548	+	0.950906i
$592$	−113.197	−	65.3543i	−0.191211	−	0.110396i
$593$	−799.947			−1.34898			−0.674492	−	0.738282i	$-0.735637\pi$
$593$	−799.947			−1.34898			−0.674492	+	0.738282i	$0.735637\pi$
$594$	−1637.85	−	568.661i	−2.75732	−	0.957342i
$595$	304.645			0.512008
$596$	−535.323	+	927.206i	−0.898193	+	1.55572i
$597$	121.913	−	414.696i	0.204209	−	0.694632i
$598$	269.434	−	681.381i	0.450558	−	1.13943i
$599$	8.50606	−	4.91098i	0.0142004	−	0.00819862i	−0.492883	−	0.870096i	$-0.664057\pi$
$599$	8.50606	−	4.91098i	0.0142004	−	0.00819862i	0.507083	+	0.861897i	$0.330724\pi$
$600$	−248.664	−	260.962i	−0.414440	−	0.434937i
$601$	17.1826	−	29.7611i	0.0285900	−	0.0495194i	−0.851376	−	0.524555i	$-0.824232\pi$
$601$	17.1826	−	29.7611i	0.0285900	−	0.0495194i	0.879966	+	0.475036i	$0.157565\pi$
$602$			729.673i			1.21208i
$603$	−711.691	−	34.3678i	−1.18025	−	0.0569947i
$604$			116.173i			0.192339i
$605$	187.395	−	324.577i	0.309744	−	0.536492i
$606$	−107.604	−	444.181i	−0.177564	−	0.732971i
$607$	535.271	+	927.117i	0.881830	+	1.52737i	0.849304	+	0.527904i	$0.177022\pi$
$607$	535.271	+	927.117i	0.881830	+	1.52737i	0.0325263	+	0.999471i	$0.489645\pi$
$608$	124.878	−	72.0984i	0.205392	−	0.118583i
$609$	925.266	−	224.147i	1.51932	−	0.368058i
$610$	45.7378	−	79.2202i	0.0749800	−	0.129869i
$611$	127.172	−	100.886i	0.208138	−	0.165116i
$612$	−1283.74	−	61.9922i	−2.09761	−	0.101294i
$613$			587.652i			0.958650i	0.877637	+	0.479325i	$0.159118\pi$
$613$			587.652i			0.958650i	−0.877637	+	0.479325i	$0.840882\pi$
$614$	153.407	+	88.5694i	0.249848	+	0.144250i
$615$	10.2517	+	10.7587i	0.0166695	+	0.0174939i
$616$	−901.497	+	520.479i	−1.46347	+	0.844934i
$617$	496.007	+	859.109i	0.803901	+	1.39240i	0.917030	+	0.398817i	$0.130579\pi$
$617$	496.007	+	859.109i	0.803901	+	1.39240i	−0.113130	+	0.993580i	$0.536088\pi$
$618$	100.554	−	342.042i	0.162709	−	0.553466i
$619$	−533.108	−	307.790i	−0.861240	−	0.497237i	0.00318717	−	0.999995i	$-0.498985\pi$
$619$	−533.108	−	307.790i	−0.861240	−	0.497237i	−0.864427	+	0.502758i	$0.832319\pi$
$620$			85.5095i			0.137919i
$621$	−160.712	+	462.880i	−0.258796	+	0.745379i
$622$			127.769i			0.205416i
$623$	−1251.67	−	722.649i	−2.00909	−	1.15995i
$624$	98.1671	+	242.452i	0.157319	+	0.388545i
$625$	−257.535	−	446.063i	−0.412056	−	0.713701i
$626$	−517.288	−	895.970i	−0.826339	−	1.43126i
$627$	−156.862	+	149.470i	−0.250179	+	0.238390i
$628$	−341.129	+	590.853i	−0.543200	+	0.940849i
$629$	492.924			0.783663
$630$	−154.076	−	299.346i	−0.244566	−	0.475153i
$631$		−	156.910i		−	0.248670i	−0.992240	−	0.124335i	$-0.960320\pi$
$631$		−	156.910i		−	0.248670i	0.992240	−	0.124335i	$-0.0396797\pi$
$632$	329.374	−	570.492i	0.521161	−	0.902678i
$633$	553.192	−	134.012i	0.873921	−	0.211709i
$634$	−276.330	−	478.618i	−0.435852	−	0.754918i
$635$	79.3634	+	137.461i	0.124982	+	0.216475i
$636$	−232.561	−	959.996i	−0.365661	−	1.50943i
$637$	−91.4281	−	617.285i	−0.143529	−	0.969051i
$638$		−	2069.02i		−	3.24298i
$639$	−65.2258	−	41.9783i	−0.102075	−	0.0656937i
$640$	183.116			0.286118
$641$	448.845	+	259.141i	0.700226	+	0.404276i	0.807432	−	0.589961i	$-0.200857\pi$
$641$	448.845	+	259.141i	0.700226	+	0.404276i	−0.107206	+	0.994237i	$0.534190\pi$
$642$	36.1577	−	34.4538i	0.0563204	−	0.0536663i
$643$	−177.835	+	102.673i	−0.276571	+	0.159678i	−0.631870	−	0.775074i	$-0.717712\pi$
$643$	−177.835	+	102.673i	−0.276571	+	0.159678i	0.355299	+	0.934753i	$0.384379\pi$
$644$	504.565	+	873.932i	0.783486	+	1.35704i
$645$	−24.6836	+	83.9634i	−0.0382692	+	0.130176i
$646$	−137.207	+	237.650i	−0.212395	+	0.367879i
$647$		−	244.936i		−	0.378571i	−0.981922	−	0.189286i	$-0.939383\pi$
$647$		−	244.936i		−	0.378571i	0.981922	−	0.189286i	$-0.0606172\pi$
$648$	171.520	+	376.879i	0.264692	+	0.581603i
$649$	−253.833			−0.391114
$650$	−139.043	−	938.758i	−0.213912	−	1.44424i
$651$	103.206	−	351.063i	0.158534	−	0.539267i
$652$	203.563	−	117.527i	0.312214	−	0.180257i
$653$	−230.756	+	133.227i	−0.353378	+	0.204023i	−0.666172	−	0.745798i	$-0.732068\pi$
$653$	−230.756	+	133.227i	−0.353378	+	0.204023i	0.312794	+	0.949821i	$0.398735\pi$
$654$	159.421	−	151.908i	0.243763	−	0.232275i
$655$	6.80963	+	3.93154i	0.0103964	+	0.00600236i
$656$	27.1676			0.0414140
$657$	−465.081	+	722.642i	−0.707886	+	1.09991i
$658$			381.957i			0.580482i
$659$	693.369	+	400.317i	1.05215	+	0.607461i	0.923251	−	0.384197i	$-0.125522\pi$
$659$	693.369	+	400.317i	1.05215	+	0.607461i	0.128901	+	0.991657i	$0.458855\pi$
$660$	−416.226	+	100.832i	−0.630646	+	0.152775i
$661$	109.979	−	63.4963i	0.166382	−	0.0960609i	−0.414497	−	0.910051i	$-0.636042\pi$
$661$	109.979	−	63.4963i	0.166382	−	0.0960609i	0.580879	+	0.813990i	$0.302709\pi$
$662$	64.1875	−	37.0587i	0.0969600	−	0.0559799i
$663$	−777.770	−	606.729i	−1.17311	−	0.915126i
$664$	−66.5900	+	115.337i	−0.100286	+	0.173701i
$665$	−42.0749			−0.0632705
$666$	−249.300	−	484.351i	−0.374325	−	0.727254i
$667$	−584.736			−0.876666
$668$	519.537	−	899.864i	0.777750	−	1.34710i
$669$	−696.685	+	663.853i	−1.04138	+	0.992307i
$670$	−260.412	+	150.349i	−0.388674	+	0.224401i
$671$	248.973	+	431.234i	0.371048	+	0.642674i
$672$	−1170.13	−	343.997i	−1.74127	−	0.511900i
$673$	−456.273	+	790.288i	−0.677969	+	1.17428i	0.297623	+	0.954683i	$0.403806\pi$
$673$	−456.273	+	790.288i	−0.677969	+	1.17428i	−0.975592	+	0.219593i	$0.929527\pi$
$674$	−1098.78			−1.63023
$675$	119.492	+	623.269i	0.177025	+	0.923361i
$676$	217.074	−	929.147i	0.321115	−	1.37448i
$677$	665.602	+	384.286i	0.983164	+	0.567630i	0.903224	−	0.429169i	$-0.141194\pi$
$677$	665.602	+	384.286i	0.983164	+	0.567630i	0.0799403	+	0.996800i	$0.474527\pi$
$678$	1749.62	+	514.357i	2.58057	+	0.758638i
$679$	−210.241	−	364.148i	−0.309633	−	0.536300i
$680$	−136.939	+	79.0617i	−0.201381	+	0.116267i
$681$	−194.856	−	204.493i	−0.286133	−	0.300283i
$682$	−688.700	−	397.621i	−1.00982	−	0.583022i
$683$	−510.032			−0.746752			−0.373376	−	0.927680i	$-0.621800\pi$
$683$	−510.032			−0.746752			−0.373376	+	0.927680i	$0.621800\pi$
$684$	177.299	+	8.56182i	0.259209	+	0.0125173i
$685$	−48.6625			−0.0710402
$686$	−26.4509	−	15.2714i	−0.0385582	−	0.0222616i
$687$	−279.329	−	1153.05i	−0.406592	−	1.67839i
$688$	79.9950	+	138.555i	0.116272	+	0.201389i
$689$	278.774	−	705.003i	0.404607	−	1.02323i
$690$	48.6855	+	200.971i	0.0705587	+	0.291262i
$691$	−429.570	−	248.013i	−0.621665	−	0.358918i	0.155852	−	0.987780i	$-0.450188\pi$
$691$	−429.570	−	248.013i	−0.621665	−	0.358918i	−0.777517	+	0.628862i	$0.783521\pi$
$692$			404.012i			0.583832i
$693$	1830.53	+	88.3971i	2.64146	+	0.127557i
$694$			407.586i			0.587299i
$695$	−64.4034	+	111.550i	−0.0926668	+	0.160504i
$696$	−357.740	+	340.882i	−0.513994	+	0.489772i
$697$	−88.7273	+	51.2267i	−0.127299	+	0.0734960i
$698$	1331.55	−	768.772i	1.90767	−	1.10139i
$699$	−893.030	−	262.534i	−1.27758	−	0.375585i
$700$	1131.90	+	653.502i	1.61700	+	0.933574i
$701$			468.089i			0.667745i	0.942618	+	0.333872i	$0.108355\pi$
$701$			468.089i			0.667745i	−0.942618	+	0.333872i	$0.891645\pi$
$702$	−202.813	+	1071.10i	−0.288908	+	1.52579i
$703$	−68.0784			−0.0968398
$704$	−1047.98	+	1815.15i	−1.48860	+	2.57834i
$705$	−12.9210	+	43.9518i	−0.0183276	+	0.0623429i
$706$	−463.373	−	802.586i	−0.656336	−	1.13681i
$707$	241.551	+	418.378i	0.341656	+	0.591765i
$708$	143.452	+	150.546i	0.202615	+	0.212636i
$709$	782.263	+	451.640i	1.10333	+	0.637009i	0.937094	−	0.349076i	$-0.113505\pi$
$709$	782.263	+	451.640i	1.10333	+	0.637009i	0.166238	+	0.986086i	$0.446838\pi$
$710$	−32.7346			−0.0461051
$711$	−1031.19	+	530.761i	−1.45033	+	0.746500i
$712$	750.171			1.05361
$713$	−112.374	+	194.637i	−0.157607	+	0.272983i
$714$	2255.81	−	546.473i	3.15939	−	0.765368i
$715$	−305.669	−	120.868i	−0.427509	−	0.169047i
$716$	−1147.29	+	662.387i	−1.60236	+	0.925121i
$717$	760.971	−	184.347i	1.06133	−	0.257108i
$718$	174.582	−	302.385i	0.243151	−	0.421149i
$719$			1133.38i			1.57632i	0.615468	+	0.788162i	$0.288967\pi$
$719$			1133.38i			1.57632i	−0.615468	+	0.788162i	$0.711033\pi$
$720$	−62.0748	−	39.9504i	−0.0862150	−	0.0554866i
$721$			376.855i			0.522684i
$722$	−541.646	+	938.159i	−0.750202	+	1.29939i
$723$	712.405	−	678.833i	0.985345	−	0.938911i
$724$	323.005	+	559.461i	0.446140	+	0.772736i
$725$	−655.874	+	378.669i	−0.904654	+	0.522302i
$726$	805.377	−	2739.55i	1.10933	−	3.77349i
$727$	5.42709	−	9.40000i	0.00746505	−	0.0129298i	−0.862269	−	0.506451i	$-0.830957\pi$
$727$	5.42709	−	9.40000i	0.00746505	−	0.0129298i	0.869734	+	0.493521i	$0.164290\pi$
$728$	406.779	+	512.768i	0.558763	+	0.704351i
$729$	105.161	−	721.375i	0.144253	−	0.989541i
$730$			362.669i			0.496807i
$731$	−522.516	−	301.674i	−0.714796	−	0.412687i
$732$	115.056	−	391.372i	0.157180	−	0.534661i
$733$	980.042	−	565.827i	1.33703	−	0.771934i	0.350663	−	0.936502i	$-0.385956\pi$
$733$	980.042	−	565.827i	1.33703	−	0.771934i	0.986366	+	0.164568i	$0.0526231\pi$
$734$	275.825	+	477.743i	0.375783	+	0.650875i
$735$	121.487	+	127.495i	0.165288	+	0.173462i
$736$	648.746	+	374.554i	0.881449	+	0.508905i
$737$		−	1636.84i		−	2.22095i
$738$	95.2103	+	61.2758i	0.129011	+	0.0830296i
$739$			408.332i			0.552547i	0.961079	+	0.276273i	$0.0890995\pi$
$739$			408.332i			0.552547i	−0.961079	+	0.276273i	$0.910900\pi$
$740$	−116.533	−	67.2802i	−0.157477	−	0.0909192i
$741$	107.419	+	83.7961i	0.144965	+	0.113085i
$742$	891.920	+	1544.85i	1.20205	+	2.08201i
$743$	−431.107	−	746.698i	−0.580224	−	1.00498i	−0.995452	−	0.0952605i	$-0.969632\pi$
$743$	−431.107	−	746.698i	−0.580224	−	1.00498i	0.415228	−	0.909717i	$-0.363702\pi$
$744$	44.7169	+	184.588i	0.0601033	+	0.248103i
$745$	115.952	−	200.836i	0.155641	−	0.269578i
$746$	1128.28			1.51243
$747$	208.476	−	107.305i	0.279085	−	0.143648i
$748$		−	2952.51i		−	3.94721i
$749$	−26.3969	+	45.7207i	−0.0352428	+	0.0610423i
$750$	381.266	+	400.121i	0.508354	+	0.533495i
$751$	645.450	+	1117.95i	0.859454	+	1.48862i	0.872450	+	0.488703i	$0.162530\pi$
$751$	645.450	+	1117.95i	0.859454	+	1.48862i	−0.0129961	+	0.999916i	$0.504137\pi$
$752$	41.8745	+	72.5287i	0.0556841	+	0.0964477i
$753$	−29.1366	−	8.56562i	−0.0386940	−	0.0113753i
$754$	−1286.90	+	190.606i	−1.70676	+	0.252794i
$755$		−	25.1634i		−	0.0333290i
$756$	−982.084	−	1135.63i	−1.29905	−	1.50216i
$757$	−602.004			−0.795249			−0.397625	−	0.917548i	$-0.630165\pi$
$757$	−602.004			−0.795249			−0.397625	+	0.917548i	$0.630165\pi$
$758$	−1097.07	−	633.392i	−1.44732	−	0.835609i
$759$	−1079.92	−	317.477i	−1.42283	−	0.418284i
$760$	18.9128	−	10.9193i	0.0248853	−	0.0143675i
$761$	−234.682	−	406.482i	−0.308387	−	0.534142i	0.669623	−	0.742701i	$-0.266456\pi$
$761$	−234.682	−	406.482i	−0.308387	−	0.534142i	−0.978010	+	0.208560i	$0.933122\pi$
$762$	834.242	+	875.500i	1.09481	+	1.14895i
$763$	−116.385	+	201.584i	−0.152536	+	0.264200i
$764$			1116.32i			1.46115i
$765$	278.062	+	13.4277i	0.363479	+	0.0175525i
$766$	−785.137			−1.02498
$767$	23.3841	+	157.880i	0.0304878	+	0.205841i
$768$	173.620	−	42.0598i	0.226068	−	0.0547654i
$769$	453.182	−	261.645i	0.589314	−	0.340240i	−0.175512	−	0.984477i	$-0.556158\pi$
$769$	453.182	−	261.645i	0.589314	−	0.340240i	0.764826	+	0.644237i	$0.222825\pi$
$770$	669.802	−	386.711i	0.869873	−	0.502221i
$771$	227.106	+	937.478i	0.294560	+	1.21593i

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+(-1.55290 + 2.68970i) q^{2} +(0.846137 - 2.87820i) q^{3} +(-2.82298 - 4.88955i) q^{4} +(0.611466 + 1.05909i) q^{5} +(6.42753 + 6.74541i) q^{6} +(-8.52943 - 4.92447i) q^{7} +5.11202 q^{8} +(-7.56810 - 4.87071i) q^{9} -3.79817 q^{10} +(10.3377 - 17.9053i) q^{11} +(-16.4617 + 3.98788i) q^{12} +(-12.0892 - 4.78034i) q^{13} +(26.4906 - 15.2944i) q^{14} +(3.56566 - 0.863787i) q^{15} +(3.35349 - 5.80841i) q^{16} +25.2931i q^{17} +(24.8532 - 12.7922i) q^{18} -3.49326i q^{19} +(3.45231 - 5.97958i) q^{20} +(-21.3907 + 20.3826i) q^{21} +(32.1066 + 55.6103i) q^{22} +(15.7163 - 9.07382i) q^{23} +(4.32547 - 14.7134i) q^{24} +(11.7522 - 20.3554i) q^{25} +(31.6309 - 25.0929i) q^{26} +(-20.4225 + 17.6612i) q^{27} +55.6067i q^{28} +(-27.9043 - 16.1105i) q^{29} +(-3.21378 + 10.9319i) q^{30} +(-10.7252 + 6.19219i) q^{31} +(20.6393 + 35.7483i) q^{32} +(-42.7881 - 44.9042i) q^{33} +(-68.0308 - 39.2776i) q^{34} -12.0446i q^{35} +(-2.45095 + 50.7545i) q^{36} -19.4885i q^{37} +(9.39582 + 5.42468i) q^{38} +(-23.9879 + 30.7503i) q^{39} +(3.12582 + 5.41408i) q^{40} +(2.02532 + 3.50796i) q^{41} +(-21.6056 - 89.1866i) q^{42} +(-11.9271 + 20.6584i) q^{43} -116.732 q^{44} +(0.530883 - 10.9936i) q^{45} +56.3628i q^{46} +(-6.24342 + 10.8139i) q^{47} +(-13.8803 - 14.5667i) q^{48} +(24.0008 + 41.5705i) q^{49} +(36.5000 + 63.2198i) q^{50} +(72.7987 + 21.4014i) q^{51} +(10.7538 + 72.6054i) q^{52} +58.3168i q^{53} +(-15.7893 - 82.3566i) q^{54} +25.2845 q^{55} +(-43.6026 - 25.1740i) q^{56} +(-10.0543 - 2.95578i) q^{57} +(86.6649 - 50.0360i) q^{58} +(-6.13856 - 10.6323i) q^{59} +(-14.2893 - 14.9960i) q^{60} +(-12.0421 + 20.8574i) q^{61} -38.4634i q^{62} +(40.5659 + 78.8132i) q^{63} -101.375 q^{64} +(-2.32931 - 15.7265i) q^{65} +(187.224 - 45.3554i) q^{66} +(68.5623 - 39.5845i) q^{67} +(123.672 - 71.4019i) q^{68} +(-12.8181 - 52.9124i) q^{69} +(32.3962 + 18.7040i) q^{70} +8.61851 q^{71} +(-38.6883 - 24.8991i) q^{72} -95.4852i q^{73} +(52.4181 + 30.2636i) q^{74} +(-48.6431 - 51.0488i) q^{75} +(-17.0805 + 9.86142i) q^{76} +(-176.349 + 101.815i) q^{77} +(-45.4582 - 112.272i) q^{78} +(64.4313 - 111.598i) q^{79} +8.20216 q^{80} +(33.5524 + 73.7241i) q^{81} -12.5805 q^{82} +(-13.0262 + 22.5620i) q^{83} +(160.047 + 47.0509i) q^{84} +(-26.7877 + 15.4659i) q^{85} +(-37.0433 - 64.1608i) q^{86} +(-69.9802 + 66.6824i) q^{87} +(52.8463 - 91.5324i) q^{88} +146.747 q^{89} +(28.7450 + 18.4998i) q^{90} +(79.5732 + 100.306i) q^{91} +(-88.7337 - 51.2304i) q^{92} +(8.74740 + 36.1087i) q^{93} +(-19.3908 - 33.5858i) q^{94} +(3.69968 - 2.13601i) q^{95} +(120.354 - 29.1561i) q^{96} +(36.9733 + 21.3465i) q^{97} -149.083 q^{98} +(-165.448 + 85.1578i) 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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