LMFDB - Embedded newform 39.4.j.c.10.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [39,4,Mod(4,39)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("39.4"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.5
Root			$-5.04537i$ of defining polynomial
Character	$\chi$	$=$	39.10
Dual form			39.4.j.c.4.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.36942 - 2.52268i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(8.72787 - 15.1171i) q^{4} +20.1174i q^{5} +(-13.1082 - 7.56805i) q^{6} +(-13.3609 - 7.71395i) q^{7} -47.7076i q^{8} +(-4.50000 + 7.79423i) q^{9} +(50.7498 + 87.9013i) q^{10} +(23.3283 - 13.4686i) q^{11} -52.3672 q^{12} +(-3.96071 + 46.7045i) q^{13} -77.8394 q^{14} +(52.2665 - 30.1761i) q^{15} +(-50.5283 - 87.5177i) q^{16} +(11.6167 - 20.1207i) q^{17} +45.4083i q^{18} +(-39.0399 - 22.5397i) q^{19} +(304.117 + 175.582i) q^{20} +46.2837i q^{21} +(67.9540 - 117.700i) q^{22} +(-71.0050 - 122.984i) q^{23} +(-123.948 + 71.5615i) q^{24} -279.710 q^{25} +(100.515 + 214.063i) q^{26} +27.0000 q^{27} +(-233.225 + 134.653i) q^{28} +(-1.14534 - 1.98379i) q^{29} +(152.249 - 263.704i) q^{30} +37.7740i q^{31} +(-111.031 - 64.1035i) q^{32} +(-69.9849 - 40.4058i) q^{33} -117.221i q^{34} +(155.185 - 268.787i) q^{35} +(78.5508 + 136.054i) q^{36} +(271.793 - 156.920i) q^{37} -227.442 q^{38} +(127.283 - 59.7666i) q^{39} +959.753 q^{40} +(5.08201 - 2.93410i) q^{41} +(116.759 + 202.233i) q^{42} +(-180.449 + 312.547i) q^{43} -470.209i q^{44} +(-156.800 - 90.5283i) q^{45} +(-620.501 - 358.246i) q^{46} -209.748i q^{47} +(-151.585 + 262.553i) q^{48} +(-52.4900 - 90.9154i) q^{49} +(-1222.17 + 705.619i) q^{50} -69.7003 q^{51} +(671.469 + 467.505i) q^{52} +276.886 q^{53} +(117.974 - 68.1125i) q^{54} +(270.953 + 469.305i) q^{55} +(-368.014 + 637.419i) q^{56} +135.238i q^{57} +(-10.0089 - 5.77866i) q^{58} +(470.415 + 271.594i) q^{59} -1053.49i q^{60} +(-102.894 + 178.218i) q^{61} +(95.2917 + 165.050i) q^{62} +(120.249 - 69.4255i) q^{63} +161.602 q^{64} +(-939.573 - 79.6791i) q^{65} -407.724 q^{66} +(-426.585 + 246.289i) q^{67} +(-202.778 - 351.222i) q^{68} +(-213.015 + 368.953i) q^{69} -1565.93i q^{70} +(716.081 + 413.430i) q^{71} +(371.844 + 214.684i) q^{72} +66.1205i q^{73} +(791.718 - 1371.30i) q^{74} +(419.564 + 726.707i) q^{75} +(-681.470 + 393.447i) q^{76} -415.584 q^{77} +(405.380 - 582.240i) q^{78} +317.642 q^{79} +(1760.63 - 1016.50i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(14.8036 - 25.6406i) q^{82} -141.450i q^{83} +(699.675 + 403.958i) q^{84} +(404.777 + 233.698i) q^{85} +1820.86i q^{86} +(-3.43602 + 5.95136i) q^{87} +(-642.555 - 1112.94i) q^{88} +(555.399 - 320.660i) q^{89} -913.497 q^{90} +(413.195 - 593.464i) q^{91} -2478.89 q^{92} +(98.1396 - 56.6609i) q^{93} +(-529.129 - 916.478i) q^{94} +(453.440 - 785.381i) q^{95} +384.621i q^{96} +(-965.551 - 557.461i) q^{97} +(-458.702 - 264.832i) q^{98} +242.435i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25}+ \cdots + 180 q^{98}+O(q^{100}) $ 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9 + 40 * q^10 + 60 * q^11 - 180 * q^12 + 25 * q^13 - 60 * q^14 + 45 * q^15 - 250 * q^16 + 105 * q^17 + 180 * q^19 + 510 * q^20 - 290 * q^22 - 60 * q^23 - 960 * q^25 - 30 * q^26 + 270 * q^27 + 150 * q^28 - 495 * q^29 + 120 * q^30 + 1440 * q^32 - 180 * q^33 + 60 * q^35 + 270 * q^36 - 405 * q^37 - 1380 * q^38 + 345 * q^39 + 2000 * q^40 + 1065 * q^41 + 90 * q^42 - 370 * q^43 - 135 * q^45 - 390 * q^46 - 750 * q^48 + 775 * q^49 - 4320 * q^50 - 630 * q^51 + 2940 * q^52 + 330 * q^53 - 260 * q^55 - 2670 * q^56 + 2040 * q^58 + 780 * q^59 - 1375 * q^61 - 780 * q^62 - 270 * q^63 - 3140 * q^64 + 1605 * q^65 + 1740 * q^66 + 1590 * q^67 - 600 * q^68 - 180 * q^69 + 1620 * q^71 + 2190 * q^74 + 1440 * q^75 - 5190 * q^76 - 4320 * q^77 + 2340 * q^78 + 1100 * q^79 + 8430 * q^80 - 405 * q^81 - 2390 * q^82 - 450 * q^84 + 525 * q^85 - 1485 * q^87 + 3170 * q^88 + 2040 * q^89 - 720 * q^90 + 4770 * q^91 - 1740 * q^92 - 990 * q^93 - 3230 * q^94 - 1380 * q^95 - 3750 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	4.36942	−	2.52268i	1.54482	−	0.891903i	0.546298	−	0.837591i	$-0.316037\pi$
$2$	4.36942	−	2.52268i	1.54482	−	0.891903i	0.998524	−	0.0543124i	$-0.0172967\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	8.72787	−	15.1171i	1.09098	−	1.88964i
$5$			20.1174i			1.79935i	0.436556	+	0.899677i	$0.356198\pi$
$5$			20.1174i			1.79935i	−0.436556	+	0.899677i	$0.643802\pi$
$6$	−13.1082	−	7.56805i	−0.891903	−	0.514941i
$7$	−13.3609	−	7.71395i	−0.721423	−	0.416514i	0.0938530	−	0.995586i	$-0.470082\pi$
$7$	−13.3609	−	7.71395i	−0.721423	−	0.416514i	−0.815276	+	0.579072i	$0.803415\pi$
$8$		−	47.7076i		−	2.10840i
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	50.7498	+	87.9013i	1.60485	+	2.77968i
$11$	23.3283	−	13.4686i	0.639432	−	0.369176i	−0.144964	−	0.989437i	$-0.546307\pi$
$11$	23.3283	−	13.4686i	0.639432	−	0.369176i	0.784396	+	0.620261i	$0.212973\pi$
$12$	−52.3672			−1.25976
$13$	−3.96071	+	46.7045i	−0.0845002	+	0.996423i
$13$	−3.96071	+	46.7045i	−0.0845002	+	0.996423i
$14$	−77.8394			−1.48596
$15$	52.2665	−	30.1761i	0.899677	−	0.519429i
$16$	−50.5283	−	87.5177i	−0.789505	−	1.36746i
$17$	11.6167	−	20.1207i	0.165733	−	0.287059i	−0.771182	−	0.636615i	$-0.780334\pi$
$17$	11.6167	−	20.1207i	0.165733	−	0.287059i	0.936915	+	0.349556i	$0.113668\pi$
$18$			45.4083i			0.594602i
$19$	−39.0399	−	22.5397i	−0.471388	−	0.272156i	0.245433	−	0.969414i	$-0.421070\pi$
$19$	−39.0399	−	22.5397i	−0.471388	−	0.272156i	−0.716821	+	0.697258i	$0.754403\pi$
$20$	304.117	+	175.582i	3.40013	+	1.96307i
$21$			46.2837i			0.480949i
$22$	67.9540	−	117.700i	0.658539	−	1.14062i
$23$	−71.0050	−	122.984i	−0.643720	−	1.11496i	−0.984595	−	0.174848i	$-0.944057\pi$
$23$	−71.0050	−	122.984i	−0.643720	−	1.11496i	0.340875	−	0.940109i	$-0.389277\pi$
$24$	−123.948	+	71.5615i	−1.05420	+	0.608643i
$25$	−279.710			−2.23768
$26$	100.515	+	214.063i	0.758176	+	1.61466i
$27$	27.0000			0.192450
$28$	−233.225	+	134.653i	−1.57412	+	0.908820i
$29$	−1.14534	−	1.98379i	−0.00733394	−	0.0127028i	0.862335	−	0.506338i	$-0.169001\pi$
$29$	−1.14534	−	1.98379i	−0.00733394	−	0.0127028i	−0.869669	+	0.493635i	$0.835668\pi$
$30$	152.249	−	263.704i	0.926561	−	1.60485i
$31$			37.7740i			0.218852i	0.993995	+	0.109426i	$0.0349012\pi$
$31$			37.7740i			0.218852i	−0.993995	+	0.109426i	$0.965099\pi$
$32$	−111.031	−	64.1035i	−0.613363	−	0.354125i
$33$	−69.9849	−	40.4058i	−0.369176	−	0.213144i
$34$		−	117.221i		−	0.591273i
$35$	155.185	−	268.787i	0.749456	−	1.29810i
$36$	78.5508	+	136.054i	0.363661	+	0.629879i
$37$	271.793	−	156.920i	1.20764	−	0.697228i	0.245393	−	0.969424i	$-0.421083\pi$
$37$	271.793	−	156.920i	1.20764	−	0.697228i	0.962242	+	0.272195i	$0.0877497\pi$
$38$	−227.442			−0.970947
$39$	127.283	−	59.7666i	0.522605	−	0.245393i
$40$	959.753			3.79376
$41$	5.08201	−	2.93410i	0.0193580	−	0.0111763i	−0.490290	−	0.871559i	$-0.663109\pi$
$41$	5.08201	−	2.93410i	0.0193580	−	0.0111763i	0.509648	+	0.860383i	$0.329776\pi$
$42$	116.759	+	202.233i	0.428960	+	0.742980i
$43$	−180.449	+	312.547i	−0.639958	+	1.10844i	0.345483	+	0.938425i	$0.387715\pi$
$43$	−180.449	+	312.547i	−0.639958	+	1.10844i	−0.985441	+	0.170015i	$0.945618\pi$
$44$		−	470.209i		−	1.61106i
$45$	−156.800	−	90.5283i	−0.519429	−	0.299892i
$46$	−620.501	−	358.246i	−1.98887	−	1.14827i
$47$		−	209.748i		−	0.650956i	−0.945550	−	0.325478i	$-0.894475\pi$
$47$		−	209.748i		−	0.650956i	0.945550	−	0.325478i	$-0.105525\pi$
$48$	−151.585	+	262.553i	−0.455821	+	0.789505i
$49$	−52.4900	−	90.9154i	−0.153032	−	0.265060i
$50$	−1222.17	+	705.619i	−3.45681	+	1.99579i
$51$	−69.7003			−0.191372
$52$	671.469	+	467.505i	1.79069	+	1.24676i
$53$	276.886			0.717609			0.358804	−	0.933413i	$-0.383185\pi$
$53$	276.886			0.717609			0.358804	+	0.933413i	$0.383185\pi$
$54$	117.974	−	68.1125i	0.297301	−	0.171647i
$55$	270.953	+	469.305i	0.664278	+	1.15056i
$56$	−368.014	+	637.419i	−0.878178	+	1.52105i
$57$			135.238i			0.314259i
$58$	−10.0089	−	5.77866i	−0.0226593	−	0.0130823i
$59$	470.415	+	271.594i	1.03801	+	0.599298i	0.919270	−	0.393627i	$-0.128780\pi$
$59$	470.415	+	271.594i	1.03801	+	0.599298i	0.118744	+	0.992925i	$0.462113\pi$
$60$		−	1053.49i		−	2.26675i
$61$	−102.894	+	178.218i	−0.215971	+	0.374073i	−0.953573	−	0.301163i	$-0.902625\pi$
$61$	−102.894	+	178.218i	−0.215971	+	0.374073i	0.737601	+	0.675236i	$0.235958\pi$
$62$	95.2917	+	165.050i	0.195195	+	0.338087i
$63$	120.249	−	69.4255i	0.240474	−	0.138838i
$64$	161.602			0.315629
$65$	−939.573	−	79.6791i	−1.79292	−	0.152046i
$66$	−407.724			−0.760415
$67$	−426.585	+	246.289i	−0.777846	+	0.449090i	−0.835666	−	0.549237i	$-0.814918\pi$
$67$	−426.585	+	246.289i	−0.777846	+	0.449090i	0.0578203	+	0.998327i	$0.481585\pi$
$68$	−202.778	−	351.222i	−0.361625	−	0.626352i
$69$	−213.015	+	368.953i	−0.371652	+	0.643720i
$70$		−	1565.93i		−	2.67377i
$71$	716.081	+	413.430i	1.19695	+	0.691057i	0.959873	−	0.280435i	$-0.0904786\pi$
$71$	716.081	+	413.430i	1.19695	+	0.691057i	0.237073	+	0.971492i	$0.423812\pi$
$72$	371.844	+	214.684i	0.608643	+	0.351400i
$73$			66.1205i			0.106011i	0.998594	+	0.0530056i	$0.0168801\pi$
$73$			66.1205i			0.106011i	−0.998594	+	0.0530056i	$0.983120\pi$
$74$	791.718	−	1371.30i	1.24372	−	2.15419i
$75$	419.564	+	726.707i	0.645962	+	1.11884i
$76$	−681.470	+	393.447i	−1.02855	+	0.593835i
$77$	−415.584			−0.615068
$78$	405.380	−	582.240i	0.588465	−	0.845201i
$79$	317.642			0.452374			0.226187	−	0.974084i	$-0.427374\pi$
$79$	317.642			0.452374			0.226187	+	0.974084i	$0.427374\pi$
$80$	1760.63	−	1016.50i	2.46055	−	1.42060i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	14.8036	−	25.6406i	0.0199364	−	0.0345309i
$83$		−	141.450i		−	0.187063i	−0.995616	−	0.0935313i	$-0.970184\pi$
$83$		−	141.450i		−	0.187063i	0.995616	−	0.0935313i	$-0.0298155\pi$
$84$	699.675	+	403.958i	0.908820	+	0.524707i
$85$	404.777	+	233.698i	0.516520	+	0.298213i
$86$			1820.86i			2.28312i
$87$	−3.43602	+	5.95136i	−0.00423425	+	0.00733394i
$88$	−642.555	−	1112.94i	−0.778371	−	1.34818i
$89$	555.399	−	320.660i	0.661486	−	0.381909i	−0.131357	−	0.991335i	$-0.541933\pi$
$89$	555.399	−	320.660i	0.661486	−	0.381909i	0.792843	+	0.609426i	$0.208600\pi$
$90$	−913.497			−1.06990
$91$	413.195	−	593.464i	0.475985	−	0.683648i
$92$	−2478.89			−2.80915
$93$	98.1396	−	56.6609i	0.109426	−	0.0631771i
$94$	−529.129	−	916.478i	−0.580590	−	1.00561i
$95$	453.440	−	785.381i	0.489705	−	0.848194i
$96$			384.621i			0.408909i
$97$	−965.551	−	557.461i	−1.01069	−	0.583522i	−0.0992962	−	0.995058i	$-0.531659\pi$
$97$	−965.551	−	557.461i	−1.01069	−	0.583522i	−0.911394	+	0.411536i	$0.864992\pi$
$98$	−458.702	−	264.832i	−0.472815	−	0.272980i
$99$			242.435i			0.246117i
$100$	−2441.27	+	4228.40i	−2.44127	+	4.22840i
$101$	794.953	+	1376.90i	0.783177	+	1.35650i	0.930082	+	0.367351i	$0.119735\pi$
$101$	794.953	+	1376.90i	0.783177	+	1.35650i	−0.146906	+	0.989150i	$0.546931\pi$
$102$	−304.550	+	175.832i	−0.295636	+	0.170686i
$103$	−527.502			−0.504625			−0.252312	−	0.967646i	$-0.581191\pi$
$103$	−527.502			−0.504625			−0.252312	+	0.967646i	$0.581191\pi$
$104$	2228.16	+	188.956i	2.10086	+	0.178160i
$105$	−931.107			−0.865398
$106$	1209.83	−	698.497i	1.10858	−	0.640038i
$107$	−875.982	−	1517.25i	−0.791443	−	1.37082i	−0.925073	−	0.379788i	$-0.875997\pi$
$107$	−875.982	−	1517.25i	−0.791443	−	1.37082i	0.133630	−	0.991031i	$-0.457337\pi$
$108$	235.652	−	408.162i	0.209960	−	0.363661i
$109$		−	967.122i		−	0.849848i	−0.905229	−	0.424924i	$-0.860301\pi$
$109$		−	967.122i		−	0.849848i	0.905229	−	0.424924i	$-0.139699\pi$
$110$	2367.81	+	1367.06i	2.05238	+	1.18494i
$111$	−815.379	−	470.759i	−0.697228	−	0.402545i
$112$			1559.09i			1.31536i
$113$	−955.487	+	1654.95i	−0.795439	+	1.37774i	0.127120	+	0.991887i	$0.459427\pi$
$113$	−955.487	+	1654.95i	−0.795439	+	1.37774i	−0.922560	+	0.385854i	$0.873907\pi$
$114$	341.163	+	590.912i	0.280288	+	0.485474i
$115$	2474.12	−	1428.44i	2.00620	−	1.15828i
$116$	−39.9855			−0.0320048
$117$	−346.203	−	241.041i	−0.273559	−	0.190464i
$118$	2740.59			2.13806
$119$	−310.421	+	179.221i	−0.239128	+	0.138061i
$120$	−1439.63	−	2493.51i	−1.09516	−	1.89688i
$121$	−302.694	+	524.281i	−0.227418	+	0.393900i
$122$			1038.28i			0.770501i
$123$	−15.2460	−	8.80230i	−0.0111763	−	0.00645266i
$124$	571.033	+	329.686i	0.413551	+	0.238764i
$125$		−	3112.35i		−	2.22702i
$126$	350.277	−	606.698i	0.247660	−	0.428960i
$127$	616.557	+	1067.91i	0.430792	+	0.746154i	0.996942	−	0.0781488i	$-0.0249009\pi$
$127$	616.557	+	1067.91i	0.430792	+	0.746154i	−0.566150	+	0.824302i	$0.691568\pi$
$128$	1594.35	−	920.499i	1.10095	−	0.635636i
$129$	1082.69			0.738960
$130$	−4306.39	+	2022.10i	−2.90535	+	1.36423i
$131$	−1274.90			−0.850292			−0.425146	−	0.905125i	$-0.639777\pi$
$131$	−1274.90			−0.850292			−0.425146	+	0.905125i	$0.639777\pi$
$132$	−1221.64	+	705.313i	−0.805530	+	0.465073i
$133$	347.740	+	602.304i	0.226713	+	0.392679i
$134$	−1242.62	+	2152.28i	−0.801089	+	1.38753i
$135$			543.170i			0.346286i
$136$	−959.913	−	554.206i	−0.605234	−	0.349432i
$137$	−1759.18	−	1015.66i	−1.09706	−	0.633385i	−0.161609	−	0.986855i	$-0.551668\pi$
$137$	−1759.18	−	1015.66i	−1.09706	−	0.633385i	−0.935446	+	0.353470i	$0.885002\pi$
$138$			2149.48i			1.32591i
$139$	722.832	−	1251.98i	0.441078	−	0.763969i	−0.556692	−	0.830719i	$-0.687930\pi$
$139$	722.832	−	1251.98i	0.441078	−	0.763969i	0.997770	+	0.0667498i	$0.0212629\pi$
$140$	−2708.86	−	4691.88i	−1.63529	−	2.83240i
$141$	−544.942	+	314.623i	−0.325478	+	0.187915i
$142$	4171.81			2.46542
$143$	536.648	+	1142.88i	0.313824	+	0.668340i
$144$	909.510			0.526337
$145$	39.9086	−	23.0413i	0.0228568	−	0.0131964i
$146$	166.801	+	288.908i	0.0945517	+	0.163768i
$147$	−157.470	+	272.746i	−0.0883532	+	0.153032i
$148$		−	5478.30i		−	3.04266i
$149$	836.856	+	483.159i	0.460120	+	0.265650i	0.712095	−	0.702083i	$-0.247747\pi$
$149$	836.856	+	483.159i	0.460120	+	0.265650i	−0.251975	+	0.967734i	$0.581080\pi$
$150$	3666.50	+	2116.86i	1.99579	+	1.15227i
$151$			1463.09i			0.788505i	0.919002	+	0.394252i	$0.128996\pi$
$151$			1463.09i			0.788505i	−0.919002	+	0.394252i	$0.871004\pi$
$152$	−1075.32	+	1862.50i	−0.573813	+	0.993874i
$153$	104.550	+	181.087i	0.0552445	+	0.0956862i
$154$	−1815.86	+	1048.39i	−0.950170	+	0.548581i
$155$	−759.914			−0.393792
$156$	207.411	−	2445.78i	0.106450	−	1.25525i
$157$	−66.0424			−0.0335717			−0.0167859	−	0.999859i	$-0.505343\pi$
$157$	−66.0424			−0.0335717			−0.0167859	+	0.999859i	$0.505343\pi$
$158$	1387.91	−	801.311i	0.698838	−	0.403474i
$159$	−415.330	−	719.372i	−0.207156	−	0.358804i
$160$	1289.60	−	2233.65i	0.637197	−	1.10366i
$161$			2190.92i			1.07247i
$162$	−353.923	−	204.337i	−0.171647	−	0.0991004i
$163$	−3052.95	−	1762.62i	−1.46703	−	0.846988i	−0.467707	−	0.883883i	$-0.654920\pi$
$163$	−3052.95	−	1762.62i	−1.46703	−	0.846988i	−0.999319	+	0.0368953i	$0.988253\pi$
$164$		−	102.434i		−	0.0487728i
$165$	812.859	−	1407.91i	0.383521	−	0.664278i
$166$	−356.834	−	618.055i	−0.166842	−	0.288978i
$167$	225.731	−	130.326i	0.104596	−	0.0603887i	−0.446789	−	0.894639i	$-0.647433\pi$
$167$	225.731	−	130.326i	0.104596	−	0.0603887i	0.551386	+	0.834250i	$0.314099\pi$
$168$	2208.08			1.01403
$169$	−2165.63	−	369.966i	−0.985719	−	0.168396i
$170$	2358.19			1.06391
$171$	351.359	−	202.857i	0.157129	−	0.0907186i
$172$	3149.87	+	5455.73i	1.39637	+	2.41858i
$173$	455.876	−	789.601i	0.200345	−	0.347007i	−0.748295	−	0.663366i	$-0.769127\pi$
$173$	455.876	−	789.601i	0.200345	−	0.347007i	0.948640	+	0.316359i	$0.102460\pi$
$174$			34.6720i			0.0151062i
$175$	3737.18	+	2157.66i	1.61431	+	0.932023i
$176$	−2357.48	−	1361.09i	−1.00967	−	0.582933i
$177$		−	1629.57i		−	0.692009i
$178$	1617.85	−	2802.19i	0.681252	−	1.17996i
$179$	1345.24	+	2330.03i	0.561721	+	0.972930i	0.997346	+	0.0728016i	$0.0231940\pi$
$179$	1345.24	+	2330.03i	0.561721	+	0.972930i	−0.435625	+	0.900128i	$0.643473\pi$
$180$	−2737.05	+	1580.24i	−1.13338	+	0.654355i
$181$	−4773.85			−1.96043			−0.980213	−	0.197944i	$-0.936573\pi$
$181$	−4773.85			−1.96043			−0.980213	+	0.197944i	$0.936573\pi$
$182$	308.299	−	3635.45i	0.125564	−	1.48065i
$183$	617.364			0.249382
$184$	−5867.29	+	3387.48i	−2.35077	+	1.35722i
$185$	3156.82	+	5467.77i	1.25456	+	2.17296i
$186$	285.875	−	495.150i	0.112696	−	0.195195i
$187$		−	625.844i		−	0.244739i
$188$	−3170.79	−	1830.66i	−1.23007	−	0.710182i
$189$	−360.746	−	208.277i	−0.138838	−	0.0801582i
$190$		−	4575.54i		−	1.74708i
$191$	1028.74	−	1781.82i	0.389721	−	0.675017i	−0.602691	−	0.797975i	$-0.705905\pi$
$191$	1028.74	−	1781.82i	0.389721	−	0.675017i	0.992412	+	0.122958i	$0.0392380\pi$
$192$	−242.403	−	419.854i	−0.0911142	−	0.157814i
$193$	632.089	−	364.937i	0.235745	−	0.136107i	−0.377475	−	0.926020i	$-0.623207\pi$
$193$	632.089	−	364.937i	0.235745	−	0.136107i	0.613219	+	0.789913i	$0.289874\pi$
$194$	−5625.20			−2.08178
$195$	1202.35	+	2560.60i	0.441548	+	0.940351i
$196$	−1832.50			−0.667822
$197$	1473.21	−	850.557i	0.532801	−	0.307613i	−0.209355	−	0.977840i	$-0.567137\pi$
$197$	1473.21	−	850.557i	0.532801	−	0.307613i	0.742156	+	0.670227i	$0.233803\pi$
$198$	611.586	+	1059.30i	0.219513	+	0.380207i
$199$	−920.440	+	1594.25i	−0.327881	+	0.567906i	−0.982091	−	0.188407i	$-0.939668\pi$
$199$	−920.440	+	1594.25i	−0.327881	+	0.567906i	0.654211	+	0.756312i	$0.273001\pi$
$200$			13344.3i			4.71792i
$201$	1279.76	+	738.867i	0.449090	+	0.259282i
$202$	6946.97	+	4010.83i	2.41974	+	1.39704i
$203$			35.3404i			0.0122188i
$204$	−608.335	+	1053.67i	−0.208784	+	0.361625i
$205$	59.0265	+	102.237i	0.0201102	+	0.0348319i
$206$	−2304.88	+	1330.72i	−0.779555	+	0.450077i
$207$	1278.09			0.429147
$208$	4287.60	−	2013.27i	1.42929	−	0.671131i
$209$	−1214.31			−0.401894
$210$	−4068.39	+	2348.89i	−1.33689	+	0.771851i
$211$	−71.4850	−	123.816i	−0.0233234	−	0.0403972i	0.854128	−	0.520063i	$-0.174091\pi$
$211$	−71.4850	−	123.816i	−0.0233234	−	0.0403972i	−0.877452	+	0.479665i	$0.840758\pi$
$212$	2416.63	−	4185.72i	0.782899	−	1.35602i
$213$		−	2480.58i		−	0.797964i
$214$	−7655.06	−	4419.65i	−2.44528	−	1.41178i
$215$	−6287.63	−	3630.16i	−1.99448	−	1.15151i
$216$		−	1288.11i		−	0.405762i
$217$	291.386	−	504.696i	0.0911548	−	0.157885i
$218$	−2439.74	−	4225.76i	−0.757983	−	1.31286i
$219$	171.786	−	99.1807i	0.0530056	−	0.0306028i
$220$	9459.37			2.89887
$221$	893.719	+	622.246i	0.272027	+	0.189397i
$222$	−4750.31			−1.43613
$223$	−2025.39	+	1169.36i	−0.608205	+	0.351148i	−0.772263	−	0.635303i	$-0.780875\pi$
$223$	−2025.39	+	1169.36i	−0.608205	+	0.351148i	0.164057	+	0.986451i	$0.447542\pi$
$224$	988.982	+	1712.97i	0.294996	+	0.510949i
$225$	1258.69	−	2180.12i	0.372946	−	0.645962i
$226$			9641.57i			2.83782i
$227$	−2840.01	−	1639.68i	−0.830388	−	0.479425i	0.0235973	−	0.999722i	$-0.492488\pi$
$227$	−2840.01	−	1639.68i	−0.830388	−	0.479425i	−0.853986	+	0.520297i	$0.825821\pi$
$228$	2044.41	+	1180.34i	0.593835	+	0.342851i
$229$		−	1143.72i		−	0.330041i	−0.986290	−	0.165021i	$-0.947231\pi$
$229$		−	1143.72i		−	0.330041i	0.986290	−	0.165021i	$-0.0527690\pi$
$230$	7206.98	−	12482.9i	2.06615	−	3.57868i
$231$	623.376	+	1079.72i	0.177555	+	0.307534i
$232$	−94.6418	+	54.6415i	−0.0267825	+	0.0154629i
$233$	4238.17			1.19164			0.595819	−	0.803118i	$-0.296827\pi$
$233$	4238.17			1.19164			0.595819	+	0.803118i	$0.296827\pi$
$234$	−2120.77	−	179.849i	−0.592476	−	0.0502440i
$235$	4219.59			1.17130
$236$	8211.44	−	4740.88i	2.26491	−	1.30765i
$237$	−476.464	−	825.259i	−0.130589	−	0.226187i
$238$	−904.238	+	1566.19i	−0.246273	+	0.426558i
$239$		−	3310.03i		−	0.895849i	−0.894072	−	0.447924i	$-0.852163\pi$
$239$		−	3310.03i		−	0.895849i	0.894072	−	0.447924i	$-0.147837\pi$
$240$	−5281.88	−	3049.50i	−1.42060	−	0.820184i
$241$	4938.82	+	2851.43i	1.32007	+	0.762145i	0.983740	−	0.179598i	$-0.0574798\pi$
$241$	4938.82	+	2851.43i	1.32007	+	0.762145i	0.336333	+	0.941743i	$0.390813\pi$
$242$			3054.40i			0.811340i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	1796.09	+	3110.92i	0.471242	+	0.816214i
$245$	1828.98	−	1055.96i	0.476936	−	0.275359i
$246$	−88.8217			−0.0230206
$247$	1207.33	−	1734.07i	0.311015	−	0.446705i
$248$	1802.11			0.461427
$249$	−367.499	+	212.175i	−0.0935313	+	0.0540003i
$250$	−7851.48	−	13599.2i	−1.98629	−	3.44035i
$251$	−1955.12	+	3386.36i	−0.491657	+	0.851574i	−0.999954	−	0.00960748i	$-0.996942\pi$
$251$	−1955.12	+	3386.36i	−0.491657	+	0.851574i	0.508297	+	0.861182i	$0.330275\pi$
$252$		−	2423.75i		−	0.605880i
$253$	−3312.85	−	1912.68i	−0.823230	−	0.475292i
$254$	5387.99	+	3110.76i	1.33099	+	0.768450i
$255$		−	1402.19i		−	0.344347i
$256$	3997.85	−	6924.47i	0.976037	−	1.69055i
$257$	3486.40	+	6038.63i	0.846209	+	1.46568i	0.884567	+	0.466413i	$0.154454\pi$
$257$	3486.40	+	6038.63i	0.846209	+	1.46568i	−0.0383576	+	0.999264i	$0.512213\pi$
$258$	4730.74	−	2731.29i	1.14156	−	0.659081i
$259$	−4841.88			−1.16162
$260$	−9404.99	+	13508.2i	−2.24336	+	3.22209i
$261$	20.6161			0.00488930
$262$	−5570.56	+	3216.16i	−1.31355	+	0.758378i
$263$	−140.845	−	243.951i	−0.0330224	−	0.0571965i	0.849042	−	0.528326i	$-0.177180\pi$
$263$	−140.845	−	243.951i	−0.0330224	−	0.0571965i	−0.882064	+	0.471129i	$0.843847\pi$
$264$	−1927.67	+	3338.81i	−0.449392	+	0.778371i
$265$			5570.23i			1.29123i
$266$	3038.84	+	1754.48i	0.700464	+	0.404413i
$267$	−1666.20	−	961.980i	−0.381909	−	0.220495i
$268$			8598.31i			1.95980i
$269$	−2166.56	+	3752.60i	−0.491070	+	0.850558i	−0.999947	−	0.0102813i	$-0.996727\pi$
$269$	−2166.56	+	3752.60i	−0.491070	+	0.850558i	0.508877	+	0.860839i	$0.330061\pi$
$270$	1370.25	+	2373.33i	0.308854	+	0.534950i
$271$	371.175	−	214.298i	0.0832003	−	0.0480357i	−0.457823	−	0.889044i	$-0.651371\pi$
$271$	371.175	−	214.298i	0.0832003	−	0.0480357i	0.541023	+	0.841008i	$0.318037\pi$
$272$	−2347.89			−0.523390
$273$	−2161.66	−	183.316i	−0.479229	−	0.0406403i
$274$	−10248.8			−2.25967
$275$	−6525.15	+	3767.30i	−1.43084	+	0.826096i
$276$	3718.33	+	6440.34i	0.810933	+	1.40458i
$277$	4469.37	−	7741.18i	0.969454	−	1.67914i	0.272313	−	0.962209i	$-0.412211\pi$
$277$	4469.37	−	7741.18i	0.969454	−	1.67914i	0.697140	−	0.716935i	$-0.254455\pi$
$278$		−	7293.91i		−	1.57360i
$279$	−294.419	−	169.983i	−0.0631771	−	0.0364753i
$280$	−12823.2	−	7403.49i	−2.73691	−	1.58015i
$281$			775.819i			0.164703i	0.996603	+	0.0823514i	$0.0262430\pi$
$281$			775.819i			0.164703i	−0.996603	+	0.0823514i	$0.973757\pi$
$282$	−1587.39	+	2749.43i	−0.335204	+	0.580590i
$283$	−2007.27	−	3476.69i	−0.421624	−	0.730274i	0.574475	−	0.818522i	$-0.305206\pi$
$283$	−2007.27	−	3476.69i	−0.421624	−	0.730274i	−0.996098	+	0.0882484i	$0.971873\pi$
$284$	12499.7	−	7216.71i	2.61170	−	1.50786i
$285$	−2720.64			−0.565463
$286$	5227.97	+	3639.94i	1.08090	+	0.752566i
$287$	−90.5340			−0.0186204
$288$	999.275	−	576.932i	0.204454	−	0.118042i
$289$	2186.60	+	3787.31i	0.445065	+	0.770875i
$290$	116.252	−	201.354i	0.0235398	−	0.0407721i
$291$			3344.77i			0.673793i
$292$	999.550	+	577.091i	0.200323	+	0.115656i
$293$	4292.21	+	2478.11i	0.855814	+	0.494104i	0.862608	−	0.505873i	$-0.168829\pi$
$293$	4292.21	+	2478.11i	0.855814	+	0.494104i	−0.00679458	+	0.999977i	$0.502163\pi$
$294$			1588.99i			0.315210i
$295$	−5463.77	+	9463.53i	−1.07835	+	1.86776i
$296$	−7486.27	−	12966.6i	−1.47004	−	2.54618i
$297$	629.864	−	363.652i	0.123059	−	0.0710480i
$298$	4875.43			0.947738
$299$	6025.15	−	2829.15i	1.16536	−	0.547204i
$300$	14647.6			2.81893
$301$	4821.94	−	2783.95i	0.923362	−	0.533103i
$302$	3690.90	+	6392.83i	0.703270	+	1.21810i
$303$	2384.86	−	4130.70i	0.452167	−	0.783177i
$304$			4555.58i			0.859474i
$305$	−3585.28	−	2069.96i	−0.673090	−	0.388608i
$306$	913.649	+	527.495i	0.170686	+	0.0985454i
$307$		−	3894.90i		−	0.724084i	−0.932162	−	0.362042i	$-0.882080\pi$
$307$		−	3894.90i		−	0.724084i	0.932162	−	0.362042i	$-0.117920\pi$
$308$	−3627.16	+	6282.43i	−0.671029	+	1.16226i
$309$	791.254	+	1370.49i	0.145673	+	0.252312i
$310$	−3320.38	+	1917.02i	−0.608338	+	0.351224i
$311$	−3097.44			−0.564758			−0.282379	−	0.959303i	$-0.591124\pi$
$311$	−3097.44			−0.564758			−0.282379	+	0.959303i	$0.591124\pi$
$312$	−2851.32	−	6072.37i	−0.517386	−	1.10186i
$313$	4487.36			0.810353			0.405177	−	0.914238i	$-0.367210\pi$
$313$	4487.36			0.810353			0.405177	+	0.914238i	$0.367210\pi$
$314$	−288.567	+	166.604i	−0.0518623	+	0.0299427i
$315$	1396.66	+	2419.09i	0.249819	+	0.432699i
$316$	2772.34	−	4801.83i	0.493533	−	0.854824i
$317$		−	6820.62i		−	1.20847i	−0.796807	−	0.604233i	$-0.793479\pi$
$317$		−	6820.62i		−	1.20847i	0.796807	−	0.604233i	$-0.206521\pi$
$318$	−3629.50	−	2095.49i	−0.640038	−	0.369526i
$319$	−53.4377	−	30.8523i	−0.00937911	−	0.00541503i
$320$			3251.01i			0.567928i
$321$	−2627.95	+	4551.74i	−0.456940	+	0.791443i
$322$	5526.99	+	9573.02i	0.956543	+	1.65678i
$323$	−907.031	+	523.675i	−0.156249	+	0.0902106i
$324$	−1413.91			−0.242441
$325$	1107.85	−	13063.7i	0.189084	−	2.22967i
$326$	−17786.1			−3.02173
$327$	−2512.66	+	1450.68i	−0.424924	+	0.245330i
$328$	−139.979	−	242.451i	−0.0235642	−	0.0408143i
$329$	−1617.99	+	2802.44i	−0.271132	+	0.469615i
$330$		−	8202.35i		−	1.36826i
$331$	4341.35	+	2506.48i	0.720913	+	0.416219i	0.815088	−	0.579337i	$-0.196688\pi$
$331$	4341.35	+	2506.48i	0.720913	+	0.416219i	−0.0941759	+	0.995556i	$0.530022\pi$
$332$	−2138.32	−	1234.56i	−0.353481	−	0.204082i
$333$			2824.56i			0.464819i
$334$	657.542	−	1138.90i	0.107722	−	0.186580i
$335$	−4954.70	−	8581.78i	−0.808071	−	1.39962i
$336$	4050.64	−	2338.64i	0.657680	−	0.379712i
$337$	−3220.79			−0.520616			−0.260308	−	0.965526i	$-0.583824\pi$
$337$	−3220.79			−0.520616			−0.260308	+	0.965526i	$0.583824\pi$
$338$	−10395.8	+	3846.65i	−1.67295	+	0.619025i
$339$	5732.92			0.918494
$340$	7065.68	−	4079.37i	1.12703	−	0.650691i
$341$	508.762	+	881.202i	0.0807948	+	0.139941i
$342$	1023.49	−	1772.74i	0.161825	−	0.280288i
$343$			6911.39i			1.08799i
$344$	14910.9	+	8608.79i	2.33703	+	1.34929i
$345$	−7422.37	−	4285.31i	−1.15828	−	0.668734i
$346$		−	4600.13i		−	0.714753i
$347$	1680.36	−	2910.46i	0.259960	−	0.450265i	−0.706271	−	0.707942i	$-0.749624\pi$
$347$	1680.36	−	2910.46i	0.259960	−	0.450265i	0.966231	+	0.257677i	$0.0829571\pi$
$348$	59.9783	+	103.885i	0.00923900	+	0.0160024i
$349$	3976.20	−	2295.66i	0.609859	−	0.352102i	−0.163051	−	0.986618i	$-0.552134\pi$
$349$	3976.20	−	2295.66i	0.609859	−	0.352102i	0.772910	+	0.634515i	$0.218800\pi$
$350$	21772.4			3.32510
$351$	−106.939	+	1261.02i	−0.0162621	+	0.191762i
$352$	−3453.54			−0.522938
$353$	1506.96	−	870.044i	0.227216	−	0.131183i	−0.382071	−	0.924133i	$-0.624789\pi$
$353$	1506.96	−	870.044i	0.227216	−	0.131183i	0.609287	+	0.792950i	$0.291456\pi$
$354$	−4110.88	−	7120.25i	−0.617205	−	1.06903i
$355$	−8317.12	+	14405.7i	−1.24346	+	2.15373i
$356$		−	11194.7i		−	1.66662i
$357$	931.262	+	537.664i	0.138061	+	0.0797093i
$358$	11755.8	+	6787.24i	1.73552	+	1.00200i
$359$		−	1425.49i		−	0.209567i	−0.994495	−	0.104784i	$-0.966585\pi$
$359$		−	1425.49i		−	0.209567i	0.994495	−	0.104784i	$-0.0334150\pi$
$360$	−4318.89	+	7480.54i	−0.632293	+	1.09516i
$361$	−2413.42	−	4180.17i	−0.351862	−	0.609443i
$362$	−20858.9	+	12042.9i	−3.02851	+	1.74851i
$363$	1816.16			0.262600
$364$	−5365.15	−	11426.0i	−0.772555	−	1.64529i
$365$	−1330.17			−0.190752
$366$	2697.52	−	1557.42i	0.385251	−	0.222425i
$367$	−5424.61	−	9395.69i	−0.771559	−	1.33638i	−0.936708	−	0.350111i	$-0.886144\pi$
$367$	−5424.61	−	9395.69i	−0.771559	−	1.33638i	0.165149	−	0.986269i	$-0.447189\pi$
$368$	−7175.53	+	12428.4i	−1.01644	+	1.76053i
$369$			52.8138i			0.00745089i
$370$	27586.9	+	15927.3i	3.87615	+	2.23789i
$371$	−3699.46	−	2135.89i	−0.517700	−	0.298894i
$372$		−	1978.12i		−	0.275700i
$373$	247.374	−	428.465i	0.0343393	−	0.0594774i	−0.848345	−	0.529444i	$-0.822401\pi$
$373$	247.374	−	428.465i	0.0343393	−	0.0594774i	0.882684	+	0.469966i	$0.155734\pi$
$374$	−1578.81	−	2734.57i	−0.218284	−	0.378078i
$375$	−8086.13	+	4668.53i	−1.11351	+	0.642885i
$376$	−10006.6			−1.37248
$377$	97.1882	−	45.6354i	0.0132770	−	0.00623433i
$378$	−2101.66			−0.285973
$379$	10949.4	−	6321.66i	1.48400	−	0.856786i	0.484163	−	0.874978i	$-0.339124\pi$
$379$	10949.4	−	6321.66i	1.48400	−	0.856786i	0.999835	+	0.0181912i	$0.00579076\pi$
$380$	−7915.13	−	13709.4i	−1.06852	−	1.85073i
$381$	1849.67	−	3203.72i	0.248718	−	0.430792i
$382$		−	10380.7i		−	1.39037i
$383$	2010.48	+	1160.75i	0.268227	+	0.154861i	0.628082	−	0.778147i	$-0.283840\pi$
$383$	2010.48	+	1160.75i	0.268227	+	0.154861i	−0.359855	+	0.933008i	$0.617174\pi$
$384$	−4783.05	−	2761.50i	−0.635636	−	0.366984i
$385$		−	8360.47i		−	1.10673i
$386$	1841.24	−	3189.12i	0.242789	−	0.420523i
$387$	−1624.04	−	2812.92i	−0.213319	−	0.369480i
$388$	−16854.4	+	9730.90i	−2.20529	+	1.27323i
$389$	10477.6			1.36564			0.682821	−	0.730586i	$-0.260753\pi$
$389$	10477.6			1.36564			0.682821	+	0.730586i	$0.260753\pi$
$390$	11713.1	+	8155.19i	1.52082	+	1.05886i
$391$	−3299.38			−0.426744
$392$	−4337.36	+	2504.18i	−0.558851	+	0.322653i
$393$	1912.35	+	3312.28i	0.245458	+	0.425146i
$394$	4291.37	−	7432.88i	0.548722	−	0.950414i
$395$			6390.14i			0.813982i
$396$	3664.91	+	2115.94i	0.465073	+	0.268510i
$397$	1530.14	+	883.424i	0.193439	+	0.111682i	0.593592	−	0.804766i	$-0.297709\pi$
$397$	1530.14	+	883.424i	0.193439	+	0.111682i	−0.400152	+	0.916449i	$0.631043\pi$
$398$			9287.91i			1.16975i
$399$	1043.22	−	1806.91i	0.130893	−	0.226713i
$400$	14133.3	+	24479.5i	1.76666	+	3.05994i
$401$	−4331.55	+	2500.82i	−0.539420	+	0.311434i	−0.744844	−	0.667239i	$-0.767476\pi$
$401$	−4331.55	+	2500.82i	−0.539420	+	0.311434i	0.205424	+	0.978673i	$0.434143\pi$
$402$	7455.71			0.925018
$403$	−1764.21	−	149.612i	−0.218069	−	0.0184930i
$404$	27753.0			3.41773
$405$	1411.20	−	814.754i	0.173143	−	0.0999641i
$406$	89.1526	+	154.417i	0.0108980	+	0.0188758i
$407$	4226.98	−	7321.34i	0.514800	−	0.891660i
$408$			3325.24i			0.403490i
$409$	−9706.92	−	5604.29i	−1.17354	−	0.677541i	−0.219025	−	0.975719i	$-0.570288\pi$
$409$	−9706.92	−	5604.29i	−1.17354	−	0.677541i	−0.954510	+	0.298178i	$0.903621\pi$
$410$	515.822	+	297.810i	0.0621333	+	0.0358727i
$411$			6093.96i			0.731370i
$412$	−4603.97	+	7974.31i	−0.550537	+	0.953558i
$413$	−4190.13	−	7257.51i	−0.499232	−	0.864695i
$414$	5584.51	−	3224.22i	0.662956	−	0.382758i
$415$	2845.61			0.336592
$416$	3433.68	−	4931.73i	0.404688	−	0.581246i
$417$	−4336.99			−0.509313
$418$	−5305.84	+	3063.33i	−0.620854	+	0.358450i
$419$	−1642.59	−	2845.06i	−0.191518	−	0.331719i	0.754236	−	0.656604i	$-0.228008\pi$
$419$	−1642.59	−	2845.06i	−0.191518	−	0.331719i	−0.945753	+	0.324885i	$0.894674\pi$
$420$	−8126.58	+	14075.6i	−0.944134	+	1.63529i
$421$			13289.9i			1.53850i	0.638948	+	0.769250i	$0.279370\pi$
$421$			13289.9i			1.53850i	−0.638948	+	0.769250i	$0.720630\pi$
$422$	−624.695	−	360.668i	−0.0720609	−	0.0416044i
$423$	1634.83	+	943.868i	0.187915	+	0.108493i
$424$		−	13209.6i		−	1.51301i
$425$	−3249.31	+	5627.96i	−0.370858	+	0.642344i
$426$	−6257.71	−	10838.7i	−0.711707	−	1.23271i
$427$	2749.52	−	1587.44i	0.311613	−	0.179910i
$428$	−30581.8			−3.45380
$429$	2164.32	−	3108.58i	0.243577	−	0.349845i
$430$	−36631.0			−4.10815
$431$	11857.8	−	6846.13i	1.32523	−	0.765119i	0.340668	−	0.940184i	$-0.389347\pi$
$431$	11857.8	−	6846.13i	1.32523	−	0.765119i	0.984557	+	0.175064i	$0.0560134\pi$
$432$	−1364.27	−	2362.98i	−0.151940	−	0.263168i
$433$	−5001.26	+	8662.43i	−0.555070	+	0.961409i	0.442829	+	0.896606i	$0.353975\pi$
$433$	−5001.26	+	8662.43i	−0.555070	+	0.961409i	−0.997898	+	0.0648023i	$0.979358\pi$
$434$		−	2940.30i		−	0.325205i
$435$	−119.726	−	69.1238i	−0.0131964	−	0.00761892i
$436$	−14620.1	−	8440.91i	−1.60591	−	0.927170i
$437$			6401.73i			0.700769i
$438$	500.403	−	866.724i	0.0545895	−	0.0945517i
$439$	2243.60	+	3886.04i	0.243921	+	0.422484i	0.961828	−	0.273656i	$-0.0882329\pi$
$439$	2243.60	+	3886.04i	0.243921	+	0.422484i	−0.717907	+	0.696139i	$0.754900\pi$
$440$	22389.4	−	12926.5i	2.42585	−	1.40056i
$441$	944.821			0.102021
$442$	5474.76	+	464.279i	0.589158	+	0.0499627i
$443$	2035.35			0.218290			0.109145	−	0.994026i	$-0.465189\pi$
$443$	2035.35			0.218290			0.109145	+	0.994026i	$0.465189\pi$
$444$	−14233.0	+	8217.45i	−1.52133	+	0.878340i
$445$	6450.84	+	11173.2i	0.687190	+	1.19025i
$446$	−5899.83	+	10218.8i	−0.626379	+	1.08492i
$447$		−	2898.95i		−	0.306747i
$448$	−2159.15	−	1246.59i	−0.227702	−	0.131464i
$449$	−3096.55	−	1787.79i	−0.325468	−	0.187909i	0.328359	−	0.944553i	$-0.393504\pi$
$449$	−3096.55	−	1787.79i	−0.325468	−	0.187909i	−0.653827	+	0.756644i	$0.726838\pi$
$450$		−	12701.1i		−	1.33053i
$451$	79.0365	−	136.895i	0.00825207	−	0.0142930i
$452$	16678.7	+	28888.4i	1.73562	+	3.00619i
$453$	3801.21	−	2194.63i	0.394252	−	0.227622i
$454$	−16545.6			−1.71040
$455$	11939.0	+	8312.41i	1.23012	+	0.856465i
$456$	6451.90			0.662583
$457$	−6978.95	+	4029.30i	−0.714358	+	0.412435i	−0.812672	−	0.582721i	$-0.801988\pi$
$457$	−6978.95	+	4029.30i	−0.714358	+	0.412435i	0.0983147	+	0.995155i	$0.468655\pi$
$458$	−2885.25	−	4997.41i	−0.294365	−	0.509855i
$459$	313.651	−	543.260i	0.0318954	−	0.0552445i
$460$		−	49868.8i		−	5.05466i
$461$	10125.7	+	5846.07i	1.02300	+	0.590626i	0.914970	−	0.403522i	$-0.132214\pi$
$461$	10125.7	+	5846.07i	1.02300	+	0.590626i	0.108025	+	0.994148i	$0.465547\pi$
$462$	5447.58	+	3145.16i	0.548581	+	0.316723i
$463$			1732.40i			0.173891i	0.996213	+	0.0869455i	$0.0277106\pi$
$463$			1732.40i			0.173891i	−0.996213	+	0.0869455i	$0.972289\pi$
$464$	−115.744	+	200.475i	−0.0115804	+	0.0200578i
$465$	1139.87	+	1974.31i	0.113678	+	0.196896i
$466$	18518.3	−	10691.6i	1.84087	−	1.06283i
$467$	−10769.9			−1.06718			−0.533588	−	0.845745i	$-0.679157\pi$
$467$	−10769.9			−1.06718			−0.533588	+	0.845745i	$0.679157\pi$
$468$	−6665.45	+	3129.81i	−0.658356	+	0.309135i
$469$	7599.44			0.748208
$470$	18437.1	−	10644.7i	1.80945	−	1.04469i
$471$	99.0636	+	171.583i	0.00969132	+	0.0167859i
$472$	12957.1	−	22442.4i	1.26356	−	2.18855i
$473$			9721.58i			0.945029i
$474$	−4163.74	−	2403.93i	−0.403474	−	0.232946i
$475$	10919.8	+	6304.57i	1.05481	+	0.608997i
$476$			6256.88i			0.602487i
$477$	−1245.99	+	2158.12i	−0.119601	+	0.207156i
$478$	−8350.15	−	14462.9i	−0.799010	−	1.38393i
$479$	6851.68	−	3955.82i	0.653572	−	0.377340i	−0.136251	−	0.990674i	$-0.543505\pi$
$479$	6851.68	−	3955.82i	0.653572	−	0.377340i	0.789824	+	0.613334i	$0.210172\pi$
$480$	−7737.57			−0.735772
$481$	6252.37	+	13315.5i	0.592689	+	1.26223i
$482$	28773.0			2.71904
$483$	5692.17	−	3286.37i	0.536237	−	0.309597i
$484$	5283.74	+	9151.70i	0.496219	+	0.859476i
$485$	11214.7	−	19424.4i	1.04996	−	1.81859i
$486$			1226.02i			0.114431i
$487$	−9495.78	−	5482.39i	−0.883562	−	0.510125i	−0.0117307	−	0.999931i	$-0.503734\pi$
$487$	−9495.78	−	5482.39i	−0.883562	−	0.510125i	−0.871831	+	0.489806i	$0.837067\pi$
$488$	8502.35	+	4908.83i	0.788695	+	0.455353i
$489$			10575.7i			0.978018i
$490$	5327.72	−	9227.88i	0.491188	−	0.850762i
$491$	−4569.69	−	7914.93i	−0.420014	−	0.727486i	0.575926	−	0.817502i	$-0.304642\pi$
$491$	−4569.69	−	7914.93i	−0.420014	−	0.727486i	−0.995940	+	0.0900157i	$0.971308\pi$
$492$	−266.131	+	153.651i	−0.0243864	+	0.0140795i
$493$	−53.2204			−0.00486192
$494$	900.832	−	10622.6i	0.0820452	−	0.967474i
$495$	−4877.16			−0.442852
$496$	3305.89	−	1908.66i	0.299272	−	0.172785i
$497$	−6378.35	−	11047.6i	−0.575670	−	0.997090i
$498$	−1070.50	+	1854.17i	−0.0963261	+	0.166842i
$499$			12577.5i			1.12835i	0.825655	+	0.564175i	$0.190806\pi$
$499$			12577.5i			1.12835i	−0.825655	+	0.564175i	$0.809194\pi$
$500$	−47049.8	−	27164.2i	−4.20826	−	2.42964i
$501$	−677.193	−	390.978i	−0.0603887	−	0.0348655i
$502$			19728.6i			1.75404i
$503$	−6607.30	+	11444.2i	−0.585696	+	1.01446i	0.409092	+	0.912493i	$0.365845\pi$
$503$	−6607.30	+	11444.2i	−0.585696	+	1.01446i	−0.994788	+	0.101962i	$0.967488\pi$
$504$	−3312.13	−	5736.77i	−0.292726	−	0.507016i
$505$	−27699.6	+	15992.4i	−2.44083	+	1.40921i
$506$	−19300.3			−1.69566
$507$	2287.24	+	6181.41i	0.200355	+	0.541471i
$508$	21524.9			1.87995
$509$	−18809.9	+	10859.9i	−1.63798	+	0.945689i	−0.656454	+	0.754366i	$0.727945\pi$
$509$	−18809.9	+	10859.9i	−1.63798	+	0.945689i	−0.981527	+	0.191323i	$0.938722\pi$
$510$	−3537.28	−	6126.74i	−0.307124	−	0.531955i
$511$	510.050	−	883.432i	0.0441551	−	0.0764789i
$512$		−	25613.2i		−	2.21085i
$513$	−1054.08	−	608.572i	−0.0907186	−	0.0523764i
$514$	30467.1	+	17590.2i	2.61449	+	1.50947i
$515$		−	10612.0i		−	0.907999i
$516$	9449.60	−	16367.2i	0.806193	−	1.39637i
$517$	−2825.02	−	4893.07i	−0.240317	−	0.416242i
$518$	−21156.2	+	12214.5i	−1.79450	+	1.03605i
$519$	−2735.26			−0.231338
$520$	−3801.30	+	44824.8i	−0.320573	+	3.78019i
$521$	−4627.05			−0.389088			−0.194544	−	0.980894i	$-0.562323\pi$
$521$	−4627.05			−0.389088			−0.194544	+	0.980894i	$0.562323\pi$
$522$	90.0804	−	52.0080i	0.00755309	−	0.00436078i
$523$	−6891.98	−	11937.3i	−0.576224	−	0.998049i	−0.995907	−	0.0903788i	$-0.971192\pi$
$523$	−6891.98	−	11937.3i	−0.576224	−	0.998049i	0.419683	−	0.907671i	$-0.362141\pi$
$524$	−11127.1	+	19272.8i	−0.927654	+	1.60674i
$525$		−	12946.0i		−	1.07621i
$526$	−1230.82	−	710.617i	−0.102028	−	0.0589056i
$527$	760.040	+	438.809i	0.0628233	+	0.0362710i
$528$			8166.55i			0.673113i
$529$	−3999.93	+	6928.07i	−0.328752	+	0.569415i
$530$	14051.9	+	24338.7i	1.15165	+	1.99472i
$531$	−4233.74	+	2444.35i	−0.346005	+	0.199766i
$532$	12140.1			0.989362
$533$	116.907	+	248.974i	0.00950061	+	0.0202331i
$534$	−9707.09			−0.786642
$535$	30523.0	−	17622.5i	2.46659	−	1.42409i
$536$	11749.9	+	20351.4i	0.946860	+	1.64001i
$537$	4035.73	−	6990.08i	0.324310	−	0.561721i
$538$			21862.2i			1.75195i
$539$	−2449.01	−	1413.93i	−0.195707	−	0.112992i
$540$	8211.15	+	4740.71i	0.654355	+	0.377792i
$541$			454.638i			0.0361302i	0.999837	+	0.0180651i	$0.00575061\pi$
$541$			454.638i			0.0361302i	−0.999837	+	0.0180651i	$0.994249\pi$
$542$	1081.21	−	1872.72i	0.0856865	−	0.148413i
$543$	7160.77	+	12402.8i	0.565926	+	0.980213i
$544$	−2579.62	+	1489.34i	−0.203309	+	0.117381i
$545$	19456.0			1.52918
$546$	−9907.63	+	4652.19i	−0.776570	+	0.364644i
$547$	11611.4			0.907621			0.453810	−	0.891098i	$-0.350064\pi$
$547$	11611.4			0.907621			0.453810	+	0.891098i	$0.350064\pi$
$548$	−30707.7	+	17729.1i	−2.39374	+	1.38202i
$549$	−926.047	−	1603.96i	−0.0719904	−	0.124691i
$550$	−19007.4	+	32921.8i	−1.47360	+	2.55234i
$551$			103.263i			0.00798390i
$552$	17601.9	+	10162.4i	1.35722	+	0.783591i
$553$	−4244.00	−	2450.28i	−0.326353	−	0.188420i
$554$		−	45099.3i		−	3.45864i
$555$	9470.45	−	16403.3i	0.724321	−	1.25456i
$556$	−12617.6	−	21854.3i	−0.962417	−	1.66696i
$557$	4229.61	−	2441.97i	0.321749	−	0.185762i	−0.330423	−	0.943833i	$-0.607191\pi$
$557$	4229.61	−	2441.97i	0.321749	−	0.185762i	0.652172	+	0.758071i	$0.273858\pi$
$558$	−1715.25			−0.130130
$559$	−13882.6	−	9665.69i	−1.05040	−	0.731333i
$560$	−31364.9			−2.36680
$561$	−1625.99	+	938.766i	−0.122370	+	0.0706501i
$562$	1957.14	+	3389.87i	0.146899	+	0.254436i
$563$	9808.67	−	16989.1i	0.734256	−	1.27177i	−0.220793	−	0.975321i	$-0.570864\pi$
$563$	9808.67	−	16989.1i	0.734256	−	1.27177i	0.955049	−	0.296448i	$-0.0958022\pi$
$564$			10983.9i			0.820048i
$565$	−33293.3	−	19221.9i	−2.47905	−	1.43128i
$566$	−17541.2	−	10127.4i	−1.30267	−	0.752095i
$567$			1249.66i			0.0925587i
$568$	19723.7	−	34162.5i	1.45702	−	2.52364i
$569$	3737.59	+	6473.70i	0.275374	+	0.476963i	0.970230	−	0.242187i	$-0.0778648\pi$
$569$	3737.59	+	6473.70i	0.275374	+	0.476963i	−0.694855	+	0.719150i	$0.744531\pi$
$570$	−11887.6	+	6863.31i	−0.873539	+	0.504338i
$571$	7799.56			0.571631			0.285816	−	0.958285i	$-0.407735\pi$
$571$	7799.56			0.571631			0.285816	+	0.958285i	$0.407735\pi$
$572$	21960.9	+	1862.36i	1.60530	+	0.136135i
$573$	−6172.42			−0.450011
$574$	−395.581	+	228.389i	−0.0287652	+	0.0166076i
$575$	19860.8	+	34399.9i	1.44044	+	2.49491i
$576$	−727.209	+	1259.56i	−0.0526048	+	0.0911142i
$577$		−	13136.1i		−	0.947771i	−0.880587	−	0.473885i	$-0.842851\pi$
$577$		−	13136.1i		−	0.947771i	0.880587	−	0.473885i	$-0.157149\pi$
$578$	19108.4	+	11032.2i	1.37509	+	0.793910i
$579$	−1896.27	−	1094.81i	−0.136107	−	0.0785816i
$580$		−	804.404i		−	0.0575880i
$581$	−1091.14	+	1889.91i	−0.0779142	+	0.134951i
$582$	8437.79	+	14614.7i	0.600958	+	1.04089i
$583$	6459.29	−	3729.27i	0.458862	−	0.264924i
$584$	3154.45			0.223514
$585$	4849.12	−	6964.69i	0.342712	−	0.492230i
$586$	25005.9			1.76277
$587$	−19183.1	+	11075.3i	−1.34884	+	0.778754i	−0.988085	−	0.153907i	$-0.950814\pi$
$587$	−19183.1	+	11075.3i	−1.34884	+	0.778754i	−0.360756	+	0.932660i	$0.617481\pi$
$588$	2748.76	+	4760.99i	0.192784	+	0.333911i
$589$	851.414	−	1474.69i	0.0595618	−	0.103164i
$590$			55133.4i			3.84713i
$591$	−4419.63	−	2551.67i	−0.307613	−	0.177600i
$592$	−27466.5	−	15857.8i	−1.90687	−	1.10093i
$593$		−	22770.3i		−	1.57684i	−0.615138	−	0.788419i	$-0.710900\pi$
$593$		−	22770.3i		−	1.57684i	0.615138	−	0.788419i	$-0.289100\pi$
$594$	1834.76	−	3177.90i	0.126736	−	0.219513i
$595$	−3605.47	−	6244.86i	−0.248420	−	0.430276i
$596$	14607.9	−	8433.89i	1.00397	−	0.579640i
$597$	5522.64			0.378604
$598$	19189.4	−	27561.3i	1.31223	−	1.88472i
$599$	−7214.11			−0.492088			−0.246044	−	0.969259i	$-0.579131\pi$
$599$	−7214.11			−0.492088			−0.246044	+	0.969259i	$0.579131\pi$
$600$	34669.5	−	20016.4i	2.35896	−	1.36194i
$601$	−13638.4	−	23622.4i	−0.925658	−	1.60329i	−0.790499	−	0.612464i	$-0.790179\pi$
$601$	−13638.4	−	23622.4i	−0.925658	−	1.60329i	−0.135160	−	0.990824i	$-0.543155\pi$
$602$	14046.0	−	24328.4i	0.950953	−	1.64710i
$603$		−	4433.20i		−	0.299393i
$604$	22117.6	+	12769.6i	1.48999	+	0.860245i
$605$	−10547.2	−	6089.41i	−0.708765	−	0.409206i
$606$		−	24065.0i		−	1.61316i
$607$	−5783.08	+	10016.6i	−0.386701	+	0.669787i	−0.992004	−	0.126209i	$-0.959719\pi$
$607$	−5783.08	+	10016.6i	−0.386701	+	0.669787i	0.605302	+	0.795996i	$0.293052\pi$
$608$	2889.75	+	5005.19i	0.192755	+	0.333861i
$609$	91.8170	−	53.0106i	0.00610938	−	0.00352725i
$610$	−20887.4			−1.38640
$611$	9796.20	+	830.752i	0.648628	+	0.0550059i
$612$	3650.01			0.241083
$613$	−21197.3	+	12238.3i	−1.39666	+	0.806362i	−0.994041	−	0.109006i	$-0.965233\pi$
$613$	−21197.3	+	12238.3i	−1.39666	+	0.806362i	−0.402619	+	0.915368i	$0.631900\pi$
$614$	−9825.61	−	17018.5i	−0.645813	−	1.11858i
$615$	177.079	−	306.711i	0.0116106	−	0.0201102i
$616$			19826.5i			1.29681i
$617$	2098.62	+	1211.64i	0.136933	+	0.0790581i	0.566901	−	0.823786i	$-0.308142\pi$
$617$	2098.62	+	1211.64i	0.136933	+	0.0790581i	−0.429969	+	0.902844i	$0.641475\pi$
$618$	6914.63	+	3992.17i	0.450077	+	0.259852i
$619$			17223.4i			1.11836i	0.829045	+	0.559182i	$0.188885\pi$
$619$			17223.4i			1.11836i	−0.829045	+	0.559182i	$0.811115\pi$
$620$	−6632.42	+	11487.7i	−0.429620	+	0.744124i
$621$	−1917.14	−	3320.58i	−0.123884	−	0.214573i
$622$	−13534.0	+	7813.86i	−0.872450	+	0.503709i
$623$	−9894.22			−0.636282
$624$	−11662.0	−	8119.60i	−0.748165	−	0.520904i
$625$	27648.7			1.76952
$626$	19607.1	−	11320.2i	1.25185	−	0.722757i
$627$	1821.47	+	3154.88i	0.116017	+	0.200947i
$628$	−576.409	+	998.370i	−0.0366262	+	0.0634384i
$629$		−	7291.57i		−	0.462216i
$630$	12205.2	+	7046.67i	0.771851	+	0.445628i
$631$	−8004.31	−	4621.29i	−0.504987	−	0.291554i	0.225784	−	0.974177i	$-0.427506\pi$
$631$	−8004.31	−	4621.29i	−0.504987	−	0.291554i	−0.730771	+	0.682623i	$0.760839\pi$
$632$		−	15154.0i		−	0.953786i
$633$	−214.455	+	371.447i	−0.0134657	+	0.0233234i
$634$	−17206.3	−	29802.1i	−1.07784	−	1.86687i
$635$	−21483.5	+	12403.5i	−1.34259	+	0.775147i
$636$	−14499.8			−0.904014
$637$	4454.06	−	2091.43i	0.277043	−	0.130087i
$638$	−311.322			−0.0193187
$639$	−6444.73	+	3720.87i	−0.398982	+	0.230352i
$640$	18518.0	+	32074.2i	1.14373	+	1.98100i
$641$	−5799.42	+	10044.9i	−0.357353	+	0.618953i	−0.987518	−	0.157508i	$-0.949654\pi$
$641$	−5799.42	+	10044.9i	−0.357353	+	0.618953i	0.630165	+	0.776461i	$0.282987\pi$
$642$			26517.9i			1.63018i
$643$	21965.8	+	12682.0i	1.34720	+	0.777804i	0.987852	−	0.155401i	$-0.0496669\pi$
$643$	21965.8	+	12682.0i	1.34720	+	0.777804i	0.359345	+	0.933205i	$0.383000\pi$
$644$	33120.3	+	19122.0i	2.02659	+	1.17005i
$645$			21781.0i			1.32965i
$646$	−2642.13	+	4576.31i	−0.160918	+	0.278719i
$647$	−3295.05	−	5707.19i	−0.200219	−	0.346789i	0.748380	−	0.663270i	$-0.230832\pi$
$647$	−3295.05	−	5707.19i	−0.200219	−	0.346789i	−0.948599	+	0.316481i	$0.897499\pi$
$648$	−3346.60	+	1932.16i	−0.202881	+	0.117133i
$649$	14632.0			0.884985
$650$	−28114.9	−	59875.5i	−1.69655	−	3.61309i
$651$	−1748.32			−0.105257
$652$	−53291.4	+	30767.8i	−3.20100	+	1.84810i
$653$	−7849.12	−	13595.1i	−0.470382	−	0.814726i	0.529044	−	0.848594i	$-0.322551\pi$
$653$	−7849.12	−	13595.1i	−0.470382	−	0.814726i	−0.999426	+	0.0338683i	$0.989217\pi$
$654$	−7319.23	+	12677.3i	−0.437621	+	0.757983i
$655$		−	25647.6i		−	1.52998i
$656$	−513.571	−	296.511i	−0.0305664	−	0.0176475i
$657$	−515.358	−	297.542i	−0.0306028	−	0.0176685i
$658$			16326.7i			0.967295i
$659$	−1420.41	+	2460.22i	−0.0839624	+	0.145427i	−0.904949	−	0.425521i	$-0.860091\pi$
$659$	−1420.41	+	2460.22i	−0.0839624	+	0.145427i	0.820986	+	0.570948i	$0.193424\pi$
$660$	−14189.1	−	24576.2i	−0.836831	−	1.44943i
$661$	18029.9	−	10409.5i	1.06094	−	0.612533i	0.135247	−	0.990812i	$-0.456817\pi$
$661$	18029.9	−	10409.5i	1.06094	−	0.612533i	0.925692	+	0.378279i	$0.123484\pi$
$662$	25292.2			1.48491
$663$	276.063	−	3255.32i	0.0161710	−	0.190688i
$664$	−6748.26			−0.394403
$665$	−12116.8	+	6995.63i	−0.706569	+	0.407938i
$666$	7125.46	+	12341.7i	0.414574	+	0.718063i
$667$	−162.650	+	281.718i	−0.00944202	+	0.0163541i
$668$		−	4549.87i		−	0.263532i
$669$	6076.16	+	3508.07i	0.351148	+	0.202735i
$670$	−43298.3	−	24998.3i	−2.49665	−	1.44144i
$671$			5543.36i			0.318925i
$672$	2966.95	−	5138.90i	0.170316	−	0.294996i
$673$	15632.3	+	27075.9i	0.895364	+	1.55082i	0.833354	+	0.552740i	$0.186418\pi$
$673$	15632.3	+	27075.9i	0.895364	+	1.55082i	0.0620102	+	0.998076i	$0.480249\pi$
$674$	−14073.0	+	8125.04i	−0.804260	+	0.464340i
$675$	−7552.16			−0.430641
$676$	−24494.1	+	29509.0i	−1.39361	+	1.67894i
$677$	−27953.2			−1.58689			−0.793447	−	0.608639i	$-0.791716\pi$
$677$	−27953.2			−1.58689			−0.793447	+	0.608639i	$0.791716\pi$
$678$	25049.5	−	14462.3i	1.41891	−	0.819208i
$679$	8600.46	+	14896.4i	0.486090	+	0.841933i
$680$	11149.2	−	19310.9i	0.628752	−	1.08903i
$681$			9838.09i			0.553592i
$682$	4445.99	+	2566.89i	0.249627	+	0.144122i
$683$	30059.7	+	17354.9i	1.68404	+	0.972282i	0.958926	+	0.283655i	$0.0915470\pi$
$683$	30059.7	+	17354.9i	1.68404	+	0.972282i	0.725116	+	0.688627i	$0.241786\pi$
$684$		−	7082.05i		−	0.395890i
$685$	20432.4	−	35390.0i	1.13968	−	1.97399i
$686$	17435.2	+	30198.7i	0.970380	+	1.68075i
$687$	−2971.48	+	1715.59i	−0.165021	+	0.0952747i
$688$	36471.1			2.02100
$689$	−1096.67	+	12931.8i	−0.0606381	+	0.715042i
$690$	−43241.9			−2.38578
$691$	10271.7	−	5930.39i	0.565492	−	0.326487i	−0.189855	−	0.981812i	$-0.560802\pi$
$691$	10271.7	−	5930.39i	0.565492	−	0.326487i	0.755347	+	0.655325i	$0.227468\pi$
$692$	−7957.66	−	13783.1i	−0.437146	−	0.757158i
$693$	1870.13	−	3239.16i	0.102511	−	0.177555i
$694$		−	16956.0i		−	0.927438i
$695$	25186.6	+	14541.5i	1.37465	+	0.793655i
$696$	283.925	+	163.924i	0.0154629	+	0.00892750i
$697$		−	136.338i		−	0.00740916i
$698$	11582.4	−	20061.4i	0.628083	−	1.08787i
$699$	−6357.26	−	11011.1i	−0.343996	−	0.595819i
$700$	65235.3	−	37663.6i	3.52237	−	2.03364i
$701$	−16100.5			−0.867486			−0.433743	−	0.901037i	$-0.642807\pi$
$701$	−16100.5			−0.867486			−0.433743	+	0.901037i	$0.642807\pi$
$702$	2713.90	+	5779.70i	0.145911	+	0.310742i
$703$	−14147.7			−0.759019
$704$	3769.90	−	2176.55i	0.201823	−	0.116523i
$705$	−6329.39	−	10962.8i	−0.338125	−	0.585650i
$706$	4389.69	−	7603.17i	0.234006	−	0.405310i
$707$		−	24528.9i		−	1.30482i
$708$	−24634.3	−	14222.6i	−1.30765	−	0.754971i
$709$	24651.8	+	14232.7i	1.30581	+	0.753910i	0.981394	−	0.192005i	$-0.0614990\pi$
$709$	24651.8	+	14232.7i	1.30581	+	0.753910i	0.324416	+	0.945915i	$0.394832\pi$
$710$			83925.9i			4.43617i
$711$	−1429.39	+	2475.78i	−0.0753957	+	0.130589i
$712$	−15297.9	−	26496.8i	−0.805217	−	1.39468i
$713$	4645.60	−	2682.14i	0.244010	−	0.140879i
$714$	5425.43			0.284372
$715$	−22991.8	+	10796.0i	−1.20258	+	0.564680i
$716$	46964.4			2.45131
$717$	−8599.70	+	4965.04i	−0.447924	+	0.258609i
$718$	−3596.07	−	6228.57i	−0.186914	−	0.323744i
$719$	−13911.0	+	24094.6i	−0.721550	+	1.24976i	0.238829	+	0.971062i	$0.423237\pi$
$719$	−13911.0	+	24094.6i	−0.721550	+	1.24976i	−0.960378	+	0.278699i	$0.910097\pi$
$720$			18297.0i			0.947067i
$721$	7047.93	+	4069.13i	0.364048	+	0.210183i
$722$	−21090.5	−	12176.6i	−1.08713	−	0.627654i
$723$		−	17108.6i		−	0.880049i
$724$	−41665.5	+	72166.7i	−2.13879	+	3.70450i
$725$	320.363	+	554.884i	0.0164110	+	0.0284247i
$726$	7935.57	−	4581.60i	0.405670	−	0.234214i
$727$	−866.153			−0.0441869			−0.0220934	−	0.999756i	$-0.507033\pi$
$727$	−866.153			−0.0441869			−0.0220934	+	0.999756i	$0.507033\pi$
$728$	−28312.8	−	19712.6i	−1.44140	−	1.00357i
$729$	729.000			0.0370370
$730$	−5812.07	+	3355.60i	−0.294677	+	0.170132i
$731$	4192.45	+	7261.53i	0.212125	+	0.367411i
$732$	5388.27	−	9332.76i	0.272071	−	0.471242i
$733$			23120.1i			1.16502i	0.812823	+	0.582511i	$0.197930\pi$
$733$			23120.1i			1.16502i	−0.812823	+	0.582511i	$0.802070\pi$
$734$	−47404.7	−	27369.1i	−2.38384	−	1.37631i
$735$	−5486.94	−	3167.89i	−0.275359	−	0.158979i
$736$			18206.7i			0.911831i
$737$	−6634.34	+	11491.0i	−0.331586	+	0.574324i
$738$	133.233	+	230.766i	0.00664547	+	0.0115103i
$739$	17983.1	−	10382.6i	0.895156	−	0.516819i	0.0195308	−	0.999809i	$-0.493783\pi$
$739$	17983.1	−	10382.6i	0.895156	−	0.516819i	0.875626	+	0.482990i	$0.160449\pi$
$740$	110209.			5.47482
$741$	−6316.24	−	535.639i	−0.313135	−	0.0265549i
$742$	−21552.7			−1.06634
$743$	32039.3	−	18497.9i	1.58198	−	0.913354i	0.587405	−	0.809293i	$-0.300150\pi$
$743$	32039.3	−	18497.9i	1.58198	−	0.913354i	0.994571	−	0.104061i	$-0.0331838\pi$
$744$	−2703.16	−	4682.01i	−0.133202	−	0.230713i
$745$	−9719.90	+	16835.4i	−0.477999	+	0.827919i
$746$		−	2496.19i		−	0.122509i
$747$	1102.50	+	636.526i	0.0540003	+	0.0311771i
$748$	−9460.95	−	5462.28i	−0.462468	−	0.267006i
$749$			27029.1i			1.31859i
$750$	−23554.4	+	40797.5i	−1.14678	+	1.98629i
$751$	−17214.6	−	29816.5i	−0.836443	−	1.44876i	−0.892851	−	0.450353i	$-0.851298\pi$
$751$	−17214.6	−	29816.5i	−0.836443	−	1.44876i	0.0564080	−	0.998408i	$-0.482035\pi$
$752$	−18356.7	+	10598.2i	−0.890159	+	0.513933i
$753$	11730.7			0.567716
$754$	309.532	−	444.575i	0.0149503	−	0.0214728i
$755$	−29433.5			−1.41880
$756$	−6297.08	+	3635.62i	−0.302940	+	0.174902i
$757$	−2134.44	−	3696.96i	−0.102480	−	0.177501i	0.810226	−	0.586118i	$-0.199345\pi$
$757$	−2134.44	−	3696.96i	−0.102480	−	0.177501i	−0.912706	+	0.408617i	$0.866011\pi$
$758$	31895.1	−	55244.0i	1.52834	−	2.64717i
$759$			11476.1i			0.548820i
$760$	−37468.7	−	21632.6i	−1.78833	−	1.03249i
$761$	6358.45	+	3671.05i	0.302883	+	0.174869i	0.643737	−	0.765247i	$-0.277383\pi$
$761$	6358.45	+	3671.05i	0.302883	+	0.174869i	−0.340854	+	0.940116i	$0.610716\pi$
$762$		−	18664.5i		−	0.887329i
$763$	−7460.33	+	12921.7i	−0.353974	+	0.613100i
$764$	−17957.3	−	31103.0i	−0.850359	−	1.47286i
$765$	−3642.99	+	2103.28i	−0.172173	+	0.0994044i
$766$	11712.9			0.552484
$767$	−14547.9	+	20894.8i	−0.684867	+	0.983661i
$768$	−23987.1			−1.12703
$769$	12755.2	−	7364.23i	0.598134	−	0.345333i	−0.170173	−	0.985414i	$-0.554433\pi$
$769$	12755.2	−	7364.23i	0.598134	−	0.345333i	0.768307	+	0.640081i	$0.221099\pi$
$770$	−21090.8	−	36530.4i	−0.987092	−	1.70969i
$771$	10459.2	−	18115.9i	0.488559	−	0.846209i
$772$		−	12740.5i		−	0.593963i
$773$	8606.05	+	4968.71i	0.400437	+	0.231193i	0.686673	−	0.726967i	$-0.259071\pi$
$773$	8606.05	+	4968.71i	0.400437	+	0.231193i	−0.286235	+	0.958159i	$0.592404\pi$
$774$	−14192.2	−	8193.88i	−0.659081	−	0.380521i
$775$		−	10565.7i		−	0.489719i
$776$	−26595.2	+	46064.2i	−1.23030	+	2.13094i
$777$	7262.83	+	12579.6i	0.335331	+	0.580811i
$778$	45780.9	−	26431.6i	2.10967	−	1.21802i
$779$	−264.535			−0.0121668
$780$	49202.8	+	4172.57i	2.25865	+	0.191541i
$781$	22273.3			1.02049
$782$	−14416.4	+	8323.29i	−0.659243	+	0.380614i
$783$	−30.9242	−	53.5623i	−0.00141142	−	0.00244465i
$784$	−5304.47	+	9187.61i	−0.241639	+	0.418532i
$785$		−	1328.60i		−	0.0604074i
$786$	16711.7	+	9648.49i	0.758378	+	0.437850i
$787$	−31441.1	−	18152.5i	−1.42408	−	0.822194i	−0.427437	−	0.904045i	$-0.640584\pi$
$787$	−31441.1	−	18152.5i	−1.42408	−	0.822194i	−0.996645	+	0.0818508i	$0.973917\pi$
$788$		−	29694.2i		−	1.34240i
$789$	−422.536	+	731.854i	−0.0190655	+	0.0330224i
$790$	16120.3	+	27921.2i	0.725993	+	1.25746i
$791$	25532.4	−	14741.2i	1.14770	−	0.662623i
$792$	11566.0			0.518914
$793$	−7916.04	−	5511.49i	−0.354485	−	0.246808i
$794$	8914.40			0.398439
$795$	14471.9	−	8355.35i	0.645616	−	0.372747i
$796$	16066.9	+	27828.8i	0.715424	+	1.23915i
$797$	−4575.37	+	7924.77i	−0.203347	+	0.352208i	−0.949605	−	0.313449i	$-0.898515\pi$
$797$	−4575.37	+	7924.77i	−0.203347	+	0.352208i	0.746258	+	0.665657i	$0.231849\pi$
$798$		−	10526.9i		−	0.466976i
$799$	−4220.29	−	2436.59i	−0.186863	−	0.107885i
$800$	31056.3	+	17930.4i	1.37251	+	0.792418i
$801$			5771.88i			0.254606i
$802$	−12617.6	+	21854.3i	−0.555539	+	0.962221i
$803$	890.550	+	1542.48i	0.0391368	+	0.0677869i
$804$	22339.1	−	12897.5i	0.979898	−	0.565745i
$805$	−44075.5			−1.92976
$806$	−8086.01	+	3796.84i	−0.353372	+	0.165928i
$807$	12999.4			0.567038
$808$	65688.6	−	37925.4i	2.86005	−	1.65125i
$809$	−15174.9	−	26283.8i	−0.659484	−	1.14226i	−0.980749	−	0.195271i	$-0.937441\pi$
$809$	−15174.9	−	26283.8i	−0.659484	−	1.14226i	0.321265	−	0.946989i	$-0.395892\pi$
$810$	4110.74	−	7120.00i	0.178317	−	0.308854i
$811$			4238.72i			0.183529i	0.995781	+	0.0917643i	$0.0292506\pi$
$811$			4238.72i			0.183529i	−0.995781	+	0.0917643i	$0.970749\pi$
$812$	534.244	+	308.446i	0.0230890	+	0.0133305i
$813$	−1113.53	−	642.894i	−0.0480357	−	0.0277334i
$814$		−	42653.3i		−	1.83661i
$815$	35459.3	−	61417.3i	1.52403	−	2.63970i
$816$	3521.84	+	6100.01i	0.151090	+	0.261695i
$817$	14089.4	−	8134.53i	0.603337	−	0.348337i
$818$	−56551.4			−2.41721
$819$	2766.22	+	5891.13i	0.118021	+	0.251346i
$820$	2060.70			0.0877595
$821$	−5139.41	+	2967.24i	−0.218473	+	0.126136i	−0.605243	−	0.796041i	$-0.706924\pi$
$821$	−5139.41	+	2967.24i	−0.218473	+	0.126136i	0.386770	+	0.922176i	$0.373591\pi$
$822$	15373.1	+	26627.1i	0.652311	+	1.12984i
$823$	−11229.8	+	19450.6i	−0.475633	+	0.823820i	−0.999610	−	0.0279120i	$-0.991114\pi$
$823$	−11229.8	+	19450.6i	−0.475633	+	0.823820i	0.523978	+	0.851732i	$0.324448\pi$
$824$			25165.9i			1.06395i
$825$	19575.4	+	11301.9i	0.826096	+	0.476947i
$826$	−36616.8	−	21140.7i	−1.54245	−	0.890533i
$827$			20138.4i			0.846772i	0.905949	+	0.423386i	$0.139159\pi$
$827$			20138.4i			0.846772i	−0.905949	+	0.423386i	$0.860841\pi$
$828$	11155.0	−	19321.0i	0.468192	−	0.810933i
$829$	2922.85	+	5062.53i	0.122455	+	0.212098i	0.920735	−	0.390188i	$-0.127590\pi$
$829$	2922.85	+	5062.53i	0.122455	+	0.212098i	−0.798281	+	0.602286i	$0.794257\pi$
$830$	12433.7	−	7178.58i	0.519974	−	0.300207i
$831$	−26816.2			−1.11943
$832$	−640.058	+	7547.54i	−0.0266707	+	0.314500i
$833$	−2439.05			−0.101450
$834$	−18950.1	+	10940.9i	−0.786798	+	0.454258i
$835$	2621.82	+	4541.12i	0.108661	+	0.188206i
$836$	−10598.4	+	18356.9i	−0.438459	+	0.759434i
$837$			1019.90i			0.0421180i
$838$	−14354.4	−	8287.49i	−0.591722	−	0.341631i
$839$	24058.1	+	13889.9i	0.989961	+	0.571554i	0.905263	−	0.424852i	$-0.139674\pi$
$839$	24058.1	+	13889.9i	0.989961	+	0.571554i	0.0846986	+	0.996407i	$0.473007\pi$
$840$			44420.9i			1.82460i
$841$	12191.9	−	21116.9i	0.499892	−	0.865839i
$842$	33526.1	+	58069.0i	1.37219	+	2.37671i
$843$	2015.64	−	1163.73i	0.0823514	−	0.0475456i
$844$	−2495.65			−0.101782
$845$	7442.75	−	43566.7i	0.303004	−	1.77366i
$846$	9524.32			0.387060
$847$	8088.55	−	4669.92i	0.328130	−	0.189446i
$848$	−13990.6	−	24232.4i	−0.566556	−	0.981304i
$849$	−6021.80	+	10430.1i	−0.243425	+	0.421624i
$850$			32787.9i			1.32308i
$851$	−38597.3	−	22284.2i	−1.55476	−	0.897640i
$852$	−37499.1	−	21650.1i	−1.50786	−	0.870565i
$853$			16480.5i			0.661526i	0.943714	+	0.330763i	$0.107306\pi$
$853$			16480.5i			0.661526i	−0.943714	+	0.330763i	$0.892694\pi$
$854$	8009.21	−	13872.4i	0.320925	−	0.555858i
$855$	4080.96	+	7068.43i	0.163235	+	0.282731i
$856$	−72384.2	+	41791.0i	−2.89024	+	1.66868i
$857$	45445.2			1.81141			0.905704	−	0.423910i	$-0.139343\pi$
$857$	45445.2			1.81141			0.905704	+	0.423910i	$0.139343\pi$
$858$	1614.88	−	19042.6i	0.0642552	−	0.757695i
$859$	−28243.1			−1.12182			−0.560909	−	0.827877i	$-0.689548\pi$
$859$	−28243.1			−1.12182			−0.560909	+	0.827877i	$0.689548\pi$
$860$	−109755.	+	63367.1i	−4.35188	+	2.51256i
$861$	135.801	+	235.214i	0.00537524	+	0.00931020i
$862$	34541.2	−	59827.2i	1.36482	−	2.36395i
$863$			328.319i			0.0129503i	0.999979	+	0.00647514i	$0.00206112\pi$
$863$			328.319i			0.0129503i	−0.999979	+	0.00647514i	$0.997939\pi$
$864$	−2997.83	−	1730.80i	−0.118042	−	0.0681514i
$865$	15884.7	+	9171.05i	0.624389	+	0.360491i
$866$			50466.4i			1.98027i
$867$	6559.81	−	11361.9i	0.256958	−	0.445065i
$868$	−5086.36	−	8809.84i	−0.198897	−	0.344499i
$869$	7410.06	−	4278.20i	0.289262	−	0.167006i
$870$	−697.510			−0.0271814
$871$	−9813.24	−	20898.9i	−0.381755	−	0.813012i
$872$	−46139.1			−1.79182
$873$	8689.96	−	5017.15i	0.336897	−	0.194507i
$874$	16149.5	+	27971.8i	0.625018	+	1.08256i
$875$	−24008.5	+	41584.0i	−0.927584	+	1.60662i
$876$		−	3462.54i		−	0.133549i
$877$	36788.7	+	21240.0i	1.41650	+	0.817815i	0.995989	−	0.0894746i	$-0.0285188\pi$
$877$	36788.7	+	21240.0i	1.41650	+	0.817815i	0.420507	+	0.907289i	$0.361852\pi$
$878$	19606.5	+	11319.8i	0.753629	+	0.435108i
$879$		−	14868.6i		−	0.570542i
$880$	27381.6	−	47426.4i	1.04890	−	1.81675i
$881$	−2610.47	−	4521.47i	−0.0998287	−	0.172908i	0.811785	−	0.583956i	$-0.198496\pi$
$881$	−2610.47	−	4521.47i	−0.0998287	−	0.172908i	−0.911614	+	0.411048i	$0.865163\pi$
$882$	4128.32	−	2383.48i	0.157605	−	0.0909933i
$883$	−11790.3			−0.449349			−0.224674	−	0.974434i	$-0.572132\pi$
$883$	−11790.3			−0.449349			−0.224674	+	0.974434i	$0.572132\pi$
$884$	17206.8	−	8079.57i	0.654670	−	0.307404i
$885$	32782.6			1.24517
$886$	8893.30	−	5134.55i	0.337219	−	0.194694i
$887$	24676.2	+	42740.4i	0.934097	+	1.61790i	0.776236	+	0.630443i	$0.217127\pi$
$887$	24676.2	+	42740.4i	0.934097	+	1.61790i	0.157861	+	0.987461i	$0.449540\pi$
$888$	−22458.8	+	38899.8i	−0.848726	+	1.47004i
$889$		−	19024.4i		−	0.717724i
$890$	56372.8	+	32546.9i	2.12317	+	1.22581i
$891$	−1889.59	−	1090.96i	−0.0710480	−	0.0410196i
$892$			40823.9i			1.53238i
$893$	−4727.67	+	8188.56i	−0.177162	+	0.306853i
$894$	−7313.14	−	12666.7i	−0.273588	−	0.473869i
$895$	−46874.1	+	27062.8i	−1.75065	+	1.01074i
$896$	−28402.7			−1.05900
$897$	−16388.1	−	11410.1i	−0.610013	−	0.424717i
$898$	−18040.1			−0.670386
$899$	74.9355	−	43.2640i	0.00278002	−	0.00160505i
$900$	−21971.4	−	38055.6i	−0.813756	−	1.40947i
$901$	3216.51	−	5571.16i	0.118932	−	0.205996i
$902$		−	797.536i		−	0.0294402i
$903$	−14465.8	−	8351.84i	−0.533103	−	0.307787i
$904$	78953.9	+	45584.0i	2.90483	+	1.67710i
$905$		−	96037.3i		−	3.52750i
$906$	11072.7	−	19178.5i	0.406033	−	0.703270i
$907$	3044.47	+	5273.17i	0.111455	+	0.193046i	0.916357	−	0.400362i	$-0.131116\pi$
$907$	3044.47	+	5273.17i	0.111455	+	0.193046i	−0.804902	+	0.593408i	$0.797782\pi$
$908$	−49574.5	+	28621.8i	−1.81188	+	1.04609i
$909$	−14309.2			−0.522118
$910$	73135.8	+	6202.17i	2.66421	+	0.225934i
$911$	−30301.7			−1.10202			−0.551010	−	0.834499i	$-0.685757\pi$
$911$	−30301.7			−1.10202			−0.551010	+	0.834499i	$0.685757\pi$
$912$	11835.7	−	6833.36i	0.429737	−	0.248109i
$913$	−1905.14	−	3299.80i	−0.0690590	−	0.119614i
$914$	−20329.3	+	35211.4i	−0.735704	+	1.27428i
$915$			12419.8i			0.448726i
$916$	−17289.8	−	9982.27i	−0.623658	−	0.360069i
$917$	17033.8	+	9834.49i	0.613421	+	0.354159i
$918$		−	3164.97i		−	0.113790i
$919$	−17347.9	+	30047.4i	−0.622692	+	1.07853i	0.366290	+	0.930501i	$0.380628\pi$
$919$	−17347.9	+	30047.4i	−0.622692	+	1.07853i	−0.988982	+	0.148034i	$0.952705\pi$
$920$	−68147.3	−	118035.i	−2.44212	−	4.22988i
$921$	−10119.3	+	5842.36i	−0.362042	+	0.209025i
$922$	58991.2			2.10713
$923$	−22145.2	+	31806.7i	−0.789728	+	1.13427i
$924$	21763.0			0.774837
$925$	−76023.1	+	43892.0i	−2.70230	+	1.56017i
$926$	4370.30	+	7569.59i	0.155094	+	0.268631i
$927$	2373.76	−	4111.47i	0.0841041	−	0.145673i
$928$			293.681i			0.0103885i
$929$	−14714.5	−	8495.40i	−0.519662	−	0.300027i	0.217134	−	0.976142i	$-0.430329\pi$
$929$	−14714.5	−	8495.40i	−0.519662	−	0.300027i	−0.736796	+	0.676115i	$0.763662\pi$
$930$	9961.14	+	5751.06i	0.351224	+	0.202779i
$931$			4732.44i			0.166594i
$932$	36990.2	−	64068.9i	1.30006	−	2.25177i
$933$	4646.16	+	8047.38i	0.163032	+	0.282379i
$934$	−47058.1	+	27169.0i	−1.64860	+	0.951817i
$935$	12590.3			0.440372
$936$	−11499.5	+	16516.5i	−0.401574	+	0.576772i
$937$	9307.86			0.324519			0.162260	−	0.986748i	$-0.448122\pi$
$937$	9307.86			0.324519			0.162260	+	0.986748i	$0.448122\pi$
$938$	33205.1	−	19171.0i	1.15585	−	0.667330i
$939$	−6731.04	−	11658.5i	−0.233929	−	0.405177i
$940$	36828.0	−	63788.0i	1.27787	−	2.21334i
$941$		−	52285.3i		−	1.81132i	−0.424006	−	0.905659i	$-0.639377\pi$
$941$		−	52285.3i		−	1.81132i	0.424006	−	0.905659i	$-0.360623\pi$
$942$	865.700	+	499.812i	0.0299427	+	0.0172874i
$943$	−721.697	−	416.672i	−0.0249222	−	0.0143889i
$944$		−	54892.8i		−	1.89260i
$945$	4189.98	−	7257.26i	0.144233	−	0.249819i
$946$	24524.5	+	42477.6i	0.842874	+	1.45990i
$947$	10694.1	−	6174.26i	0.366962	−	0.211865i	−0.305169	−	0.952298i	$-0.598713\pi$
$947$	10694.1	−	6174.26i	0.366962	−	0.211865i	0.672130	+	0.740433i	$0.265379\pi$
$948$	−16634.0			−0.569882
$949$	−3088.13	−	261.884i	−0.105632	−	0.00895797i
$950$	63617.7			2.17267
$951$	−17720.5	+	10230.9i	−0.604233	+	0.348854i
$952$	8550.23	+	14809.4i	0.291087	+	0.504177i
$953$	−12815.5	+	22197.1i	−0.435609	+	0.754497i	−0.997345	−	0.0728193i	$-0.976800\pi$
$953$	−12815.5	+	22197.1i	−0.435609	+	0.754497i	0.561736	+	0.827317i	$0.310134\pi$
$954$			12572.9i			0.426692i
$955$	35845.7	+	20695.5i	1.21459	+	0.701247i
$956$	−50038.0	−	28889.5i	−1.69283	−	0.977356i
$957$			185.114i			0.00625274i
$958$	19958.6	−	34569.2i	0.673102	−	1.16585i
$959$	15669.5	+	27140.4i	0.527627	+	0.913878i
$960$	8446.37	−	4876.51i	0.283964	−	0.163947i
$961$	28364.1			0.952104
$962$	60909.9	+	42408.1i	2.04139	+	1.42130i
$963$	15767.7			0.527629
$964$	86210.8	−	49773.8i	2.88036	−	1.66297i
$965$	7341.57	+	12716.0i	0.244905	+	0.424188i
$966$	16581.0	−	28719.1i	0.552261	−	0.956543i
$967$			11185.6i			0.371981i	0.982552	+	0.185991i	$0.0595494\pi$
$967$			11185.6i			0.371981i	−0.982552	+	0.185991i	$0.940451\pi$
$968$	25012.2	+	14440.8i	0.830498	+	0.479488i
$969$	2721.09	+	1571.02i	0.0902106	+	0.0520831i
$970$		−	113164.i		−	3.74586i
$971$	11770.6	−	20387.3i	0.389019	−	0.673801i	−0.603299	−	0.797515i	$-0.706147\pi$
$971$	11770.6	−	20387.3i	0.389019	−	0.673801i	0.992318	+	0.123714i	$0.0394806\pi$
$972$	2120.87	+	3673.46i	0.0699866	+	0.121220i
$973$	−19315.4	+	11151.8i	−0.636408	+	0.367430i
$974$	−55321.3			−1.81993
$975$	−35602.3	+	16717.3i	−1.16942	+	0.549109i
$976$	20796.3			0.682041
$977$	−20956.8	+	12099.4i	−0.686251	+	0.396207i	−0.802206	−	0.597047i	$-0.796341\pi$
$977$	−20956.8	+	12099.4i	−0.686251	+	0.396207i	0.115955	+	0.993254i	$0.463007\pi$
$978$	26679.2	+	46209.7i	0.872297	+	1.51086i
$979$	8637.68	−	14960.9i	0.281983	−	0.488409i
$980$		−	36865.2i		−	1.20165i
$981$	7537.97	+	4352.05i	0.245330	+	0.141641i
$982$	−39933.7	−	23055.7i	−1.29769	−	0.749224i
$983$		−	33757.4i		−	1.09532i	−0.836702	−	0.547658i	$-0.815520\pi$
$983$		−	33757.4i		−	1.09532i	0.836702	−	0.547658i	$-0.184480\pi$
$984$	−419.937	+	727.352i	−0.0136048	+	0.0235642i
$985$	17111.0	+	29637.1i	0.553504	+	0.958697i
$986$	−232.542	+	134.258i	−0.00751080	+	0.00433636i
$987$	9707.93			0.313077
$988$	−15676.6	−	33386.1i	−0.504798	−	1.07505i
$989$	51251.1			1.64782
$990$	−21310.3	+	12303.5i	−0.684128	+	0.394981i
$991$	−12649.3	−	21909.2i	−0.405466	−	0.702288i	0.588909	−	0.808199i	$-0.299558\pi$
$991$	−12649.3	−	21909.2i	−0.405466	−	0.702288i	−0.994376	+	0.105911i	$0.966224\pi$
$992$	2421.44	−	4194.06i	0.0775009	−	0.134236i
$993$		−	15038.9i		−	0.480608i
$994$	−55739.3	−	32181.1i	−1.77862	−	1.02688i
$995$	−32072.1	−	18516.8i	−1.02186	−	0.589973i
$996$			7407.36i			0.235654i
$997$	14383.0	−	24912.2i	0.456886	−	0.791350i	−0.541908	−	0.840438i	$-0.682298\pi$
$997$	14383.0	−	24912.2i	0.456886	−	0.791350i	0.998794	+	0.0490874i	$0.0156313\pi$
$998$	31729.1	+	54956.4i	1.00638	+	1.74310i
$999$	7338.41	−	4236.83i	0.232409	−	0.134182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.c.10.5	yes	10
3.2	odd	2		117.4.q.e.10.1		10
4.3	odd	2		624.4.bv.h.49.5		10
13.2	odd	12		507.4.a.r.1.9		10
13.3	even	3		507.4.b.i.337.9		10
13.4	even	6	inner	39.4.j.c.4.5	✓	10
13.10	even	6		507.4.b.i.337.2		10
13.11	odd	12		507.4.a.r.1.2		10
39.2	even	12		1521.4.a.bk.1.2		10
39.11	even	12		1521.4.a.bk.1.9		10
39.17	odd	6		117.4.q.e.82.1		10
52.43	odd	6		624.4.bv.h.433.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.5	✓	10	13.4	even	6	inner
39.4.j.c.10.5	yes	10	1.1	even	1	trivial
117.4.q.e.10.1		10	3.2	odd	2
117.4.q.e.82.1		10	39.17	odd	6
507.4.a.r.1.2		10	13.11	odd	12
507.4.a.r.1.9		10	13.2	odd	12
507.4.b.i.337.2		10	13.10	even	6
507.4.b.i.337.9		10	13.3	even	3
624.4.bv.h.49.5		10	4.3	odd	2
624.4.bv.h.433.1		10	52.43	odd	6
1521.4.a.bk.1.2		10	39.2	even	12
1521.4.a.bk.1.9		10	39.11	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.36942 - 2.52268i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(8.72787 - 15.1171i) q^{4} +20.1174i q^{5} +(-13.1082 - 7.56805i) q^{6} +(-13.3609 - 7.71395i) q^{7} -47.7076i q^{8} +(-4.50000 + 7.79423i) q^{9} +(50.7498 + 87.9013i) q^{10} +(23.3283 - 13.4686i) q^{11} -52.3672 q^{12} +(-3.96071 + 46.7045i) q^{13} -77.8394 q^{14} +(52.2665 - 30.1761i) q^{15} +(-50.5283 - 87.5177i) q^{16} +(11.6167 - 20.1207i) q^{17} +45.4083i q^{18} +(-39.0399 - 22.5397i) q^{19} +(304.117 + 175.582i) q^{20} +46.2837i q^{21} +(67.9540 - 117.700i) q^{22} +(-71.0050 - 122.984i) q^{23} +(-123.948 + 71.5615i) q^{24} -279.710 q^{25} +(100.515 + 214.063i) q^{26} +27.0000 q^{27} +(-233.225 + 134.653i) q^{28} +(-1.14534 - 1.98379i) q^{29} +(152.249 - 263.704i) q^{30} +37.7740i q^{31} +(-111.031 - 64.1035i) q^{32} +(-69.9849 - 40.4058i) q^{33} -117.221i q^{34} +(155.185 - 268.787i) q^{35} +(78.5508 + 136.054i) q^{36} +(271.793 - 156.920i) q^{37} -227.442 q^{38} +(127.283 - 59.7666i) q^{39} +959.753 q^{40} +(5.08201 - 2.93410i) q^{41} +(116.759 + 202.233i) q^{42} +(-180.449 + 312.547i) q^{43} -470.209i q^{44} +(-156.800 - 90.5283i) q^{45} +(-620.501 - 358.246i) q^{46} -209.748i q^{47} +(-151.585 + 262.553i) q^{48} +(-52.4900 - 90.9154i) q^{49} +(-1222.17 + 705.619i) q^{50} -69.7003 q^{51} +(671.469 + 467.505i) q^{52} +276.886 q^{53} +(117.974 - 68.1125i) q^{54} +(270.953 + 469.305i) q^{55} +(-368.014 + 637.419i) q^{56} +135.238i q^{57} +(-10.0089 - 5.77866i) q^{58} +(470.415 + 271.594i) q^{59} -1053.49i q^{60} +(-102.894 + 178.218i) q^{61} +(95.2917 + 165.050i) q^{62} +(120.249 - 69.4255i) q^{63} +161.602 q^{64} +(-939.573 - 79.6791i) q^{65} -407.724 q^{66} +(-426.585 + 246.289i) q^{67} +(-202.778 - 351.222i) q^{68} +(-213.015 + 368.953i) q^{69} -1565.93i q^{70} +(716.081 + 413.430i) q^{71} +(371.844 + 214.684i) q^{72} +66.1205i q^{73} +(791.718 - 1371.30i) q^{74} +(419.564 + 726.707i) q^{75} +(-681.470 + 393.447i) q^{76} -415.584 q^{77} +(405.380 - 582.240i) q^{78} +317.642 q^{79} +(1760.63 - 1016.50i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(14.8036 - 25.6406i) q^{82} -141.450i q^{83} +(699.675 + 403.958i) q^{84} +(404.777 + 233.698i) q^{85} +1820.86i q^{86} +(-3.43602 + 5.95136i) q^{87} +(-642.555 - 1112.94i) q^{88} +(555.399 - 320.660i) q^{89} -913.497 q^{90} +(413.195 - 593.464i) q^{91} -2478.89 q^{92} +(98.1396 - 56.6609i) q^{93} +(-529.129 - 916.478i) q^{94} +(453.440 - 785.381i) q^{95} +384.621i q^{96} +(-965.551 - 557.461i) q^{97} +(-458.702 - 264.832i) q^{98} +242.435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25}+ \cdots + 180 q^{98}+O(q^{100}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9 + 40 * q^10 + 60 * q^11 - 180 * q^12 + 25 * q^13 - 60 * q^14 + 45 * q^15 - 250 * q^16 + 105 * q^17 + 180 * q^19 + 510 * q^20 - 290 * q^22 - 60 * q^23 - 960 * q^25 - 30 * q^26 + 270 * q^27 + 150 * q^28 - 495 * q^29 + 120 * q^30 + 1440 * q^32 - 180 * q^33 + 60 * q^35 + 270 * q^36 - 405 * q^37 - 1380 * q^38 + 345 * q^39 + 2000 * q^40 + 1065 * q^41 + 90 * q^42 - 370 * q^43 - 135 * q^45 - 390 * q^46 - 750 * q^48 + 775 * q^49 - 4320 * q^50 - 630 * q^51 + 2940 * q^52 + 330 * q^53 - 260 * q^55 - 2670 * q^56 + 2040 * q^58 + 780 * q^59 - 1375 * q^61 - 780 * q^62 - 270 * q^63 - 3140 * q^64 + 1605 * q^65 + 1740 * q^66 + 1590 * q^67 - 600 * q^68 - 180 * q^69 + 1620 * q^71 + 2190 * q^74 + 1440 * q^75 - 5190 * q^76 - 4320 * q^77 + 2340 * q^78 + 1100 * q^79 + 8430 * q^80 - 405 * q^81 - 2390 * q^82 - 450 * q^84 + 525 * q^85 - 1485 * q^87 + 3170 * q^88 + 2040 * q^89 - 720 * q^90 + 4770 * q^91 - 1740 * q^92 - 990 * q^93 - 3230 * q^94 - 1380 * q^95 - 3750 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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