LMFDB - Embedded newform 39.4.j.c.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(4,39)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			4.4
Root			$3.27897i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.c.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.83967 + 1.63949i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.37583 + 2.38302i) q^{4} +17.5414i q^{5} +(-8.51902 + 4.91846i) q^{6} +(23.1228 - 13.3499i) q^{7} -17.2091i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(2.83967 + 1.63949i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.37583 + 2.38302i) q^{4} +17.5414i q^{5} +(-8.51902 + 4.91846i) q^{6} +(23.1228 - 13.3499i) q^{7} -17.2091i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-28.7589 + 49.8119i) q^{10} +(-18.5352 - 10.7013i) q^{11} -8.25501 q^{12} +(-8.67555 - 46.0623i) q^{13} +87.5483 q^{14} +(-45.5739 - 26.3121i) q^{15} +(39.2208 - 67.9325i) q^{16} +(41.9815 + 72.7141i) q^{17} -29.5108i q^{18} +(-66.7828 + 38.5571i) q^{19} +(-41.8015 + 24.1341i) q^{20} +80.0997i q^{21} +(-35.0892 - 60.7763i) q^{22} +(71.0597 - 123.079i) q^{23} +(44.7107 + 25.8137i) q^{24} -182.701 q^{25} +(50.8828 - 145.025i) q^{26} +27.0000 q^{27} +(63.6263 + 36.7346i) q^{28} +(-67.1115 + 116.241i) q^{29} +(-86.2767 - 149.436i) q^{30} +122.559i q^{31} +(103.520 - 59.7675i) q^{32} +(55.6055 - 32.1039i) q^{33} +275.312i q^{34} +(234.177 + 405.606i) q^{35} +(12.3825 - 21.4471i) q^{36} +(-192.766 - 111.294i) q^{37} -252.855 q^{38} +(132.687 + 46.5537i) q^{39} +301.873 q^{40} +(-171.751 - 99.1604i) q^{41} +(-131.322 + 227.457i) q^{42} +(77.3279 + 133.936i) q^{43} -58.8928i q^{44} +(136.722 - 78.9363i) q^{45} +(403.573 - 233.003i) q^{46} +78.7956i q^{47} +(117.663 + 203.797i) q^{48} +(184.942 - 320.329i) q^{49} +(-518.811 - 299.536i) q^{50} -251.889 q^{51} +(97.8310 - 84.0481i) q^{52} -477.088 q^{53} +(76.6712 + 44.2661i) q^{54} +(187.716 - 325.133i) q^{55} +(-229.741 - 397.923i) q^{56} -231.342i q^{57} +(-381.150 + 220.057i) q^{58} +(37.1769 - 21.4641i) q^{59} -144.804i q^{60} +(-248.269 - 430.015i) q^{61} +(-200.934 + 348.028i) q^{62} +(-208.105 - 120.150i) q^{63} -235.581 q^{64} +(807.998 - 152.181i) q^{65} +210.535 q^{66} +(419.727 + 242.329i) q^{67} +(-115.519 + 200.085i) q^{68} +(213.179 + 369.237i) q^{69} +1535.72i q^{70} +(331.196 - 191.216i) q^{71} +(-134.132 + 77.4411i) q^{72} -193.622i q^{73} +(-364.929 - 632.076i) q^{74} +(274.052 - 474.671i) q^{75} +(-183.764 - 106.096i) q^{76} -571.447 q^{77} +(300.463 + 349.735i) q^{78} +1049.60 q^{79} +(1191.63 + 687.989i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-325.144 - 563.166i) q^{82} +861.900i q^{83} +(-190.879 + 110.204i) q^{84} +(-1275.51 + 736.414i) q^{85} +507.112i q^{86} +(-201.335 - 348.722i) q^{87} +(-184.160 + 318.974i) q^{88} +(838.005 + 483.823i) q^{89} +517.660 q^{90} +(-815.532 - 949.271i) q^{91} +391.065 q^{92} +(-318.418 - 183.839i) q^{93} +(-129.184 + 223.754i) q^{94} +(-676.345 - 1171.46i) q^{95} +358.605i q^{96} +(512.228 - 295.735i) q^{97} +(1050.35 - 606.421i) q^{98} +192.623i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.83967	+	1.63949i	1.00398	+	0.579646i	0.909422	−	0.415874i	$-0.136524\pi$
$2$	2.83967	+	1.63949i	1.00398	+	0.579646i	0.0945542	+	0.995520i	$0.469857\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	1.37583	+	2.38302i	0.171979	+	0.297877i
$5$			17.5414i			1.56895i	0.620160	+	0.784476i	$0.287068\pi$
$5$			17.5414i			1.56895i	−0.620160	+	0.784476i	$0.712932\pi$
$6$	−8.51902	+	4.91846i	−0.579646	+	0.334659i
$7$	23.1228	−	13.3499i	1.24851	−	0.720829i	0.277700	−	0.960668i	$-0.410428\pi$
$7$	23.1228	−	13.3499i	1.24851	−	0.720829i	0.970813	+	0.239838i	$0.0770944\pi$
$8$		−	17.2091i		−	0.760544i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−28.7589	+	49.8119i	−0.909437	+	1.57519i
$11$	−18.5352	−	10.7013i	−0.508051	−	0.293324i	0.223981	−	0.974594i	$-0.428095\pi$
$11$	−18.5352	−	10.7013i	−0.508051	−	0.293324i	−0.732032	+	0.681270i	$0.761428\pi$
$12$	−8.25501			−0.198585
$13$	−8.67555	−	46.0623i	−0.185090	−	0.982722i
$13$	−8.67555	−	46.0623i	−0.185090	−	0.982722i
$14$	87.5483			1.67130
$15$	−45.5739	−	26.3121i	−0.784476	−	0.452917i
$16$	39.2208	−	67.9325i	0.612826	−	1.06144i
$17$	41.9815	+	72.7141i	0.598942	+	1.03740i	0.992978	+	0.118302i	$0.0377452\pi$
$17$	41.9815	+	72.7141i	0.598942	+	1.03740i	−0.394036	+	0.919095i	$0.628922\pi$
$18$		−	29.5108i		−	0.386431i
$19$	−66.7828	+	38.5571i	−0.806370	+	0.465558i	−0.845694	−	0.533669i	$-0.820813\pi$
$19$	−66.7828	+	38.5571i	−0.806370	+	0.465558i	0.0393237	+	0.999227i	$0.487480\pi$
$20$	−41.8015	+	24.1341i	−0.467354	+	0.269827i
$21$			80.0997i			0.832342i
$22$	−35.0892	−	60.7763i	−0.340048	−	0.588980i
$23$	71.0597	−	123.079i	0.644216	−	1.11581i	−0.340266	−	0.940329i	$-0.610517\pi$
$23$	71.0597	−	123.079i	0.644216	−	1.11581i	0.984482	−	0.175486i	$-0.0561495\pi$
$24$	44.7107	+	25.8137i	0.380272	+	0.219550i
$25$	−182.701			−1.46161
$26$	50.8828	−	145.025i	0.383805	−	1.09392i
$27$	27.0000			0.192450
$28$	63.6263	+	36.7346i	0.429437	+	0.247936i
$29$	−67.1115	+	116.241i	−0.429734	+	0.744322i	−0.996849	−	0.0793167i	$-0.974726\pi$
$29$	−67.1115	+	116.241i	−0.429734	+	0.744322i	0.567115	+	0.823639i	$0.308059\pi$
$30$	−86.2767	−	149.436i	−0.525063	−	0.909437i
$31$			122.559i			0.710074i	0.934852	+	0.355037i	$0.115532\pi$
$31$			122.559i			0.710074i	−0.934852	+	0.355037i	$0.884468\pi$
$32$	103.520	−	59.7675i	0.571875	−	0.330172i
$33$	55.6055	−	32.1039i	0.293324	−	0.169350i
$34$			275.312i			1.38870i
$35$	234.177	+	405.606i	1.13095	+	1.95886i
$36$	12.3825	−	21.4471i	0.0573264	−	0.0992923i
$37$	−192.766	−	111.294i	−0.856502	−	0.494502i	0.00633725	−	0.999980i	$-0.497983\pi$
$37$	−192.766	−	111.294i	−0.856502	−	0.494502i	−0.862839	+	0.505478i	$0.831316\pi$
$38$	−252.855			−1.07944
$39$	132.687	+	46.5537i	0.544792	+	0.191143i
$40$	301.873			1.19326
$41$	−171.751	−	99.1604i	−0.654219	−	0.377713i	0.135852	−	0.990729i	$-0.456623\pi$
$41$	−171.751	−	99.1604i	−0.654219	−	0.377713i	−0.790071	+	0.613016i	$0.789956\pi$
$42$	−131.322	+	227.457i	−0.482464	+	0.835652i
$43$	77.3279	+	133.936i	0.274242	+	0.475000i	0.969944	−	0.243330i	$-0.0782398\pi$
$43$	77.3279	+	133.936i	0.274242	+	0.475000i	−0.695702	+	0.718331i	$0.744907\pi$
$44$		−	58.8928i		−	0.201782i
$45$	136.722	−	78.9363i	0.452917	−	0.261492i
$46$	403.573	−	233.003i	1.29356	−	0.746835i
$47$			78.7956i			0.244543i	0.992497	+	0.122271i	$0.0390178\pi$
$47$			78.7956i			0.244543i	−0.992497	+	0.122271i	$0.960982\pi$
$48$	117.663	+	203.797i	0.353815	+	0.612826i
$49$	184.942	−	320.329i	0.539190	−	0.933905i
$50$	−518.811	−	299.536i	−1.46742	−	0.847216i
$51$	−251.889			−0.691598
$52$	97.8310	−	84.0481i	0.260899	−	0.224142i
$53$	−477.088			−1.23647			−0.618237	−	0.785992i	$-0.712153\pi$
$53$	−477.088			−1.23647			−0.618237	+	0.785992i	$0.712153\pi$
$54$	76.6712	+	44.2661i	0.193215	+	0.111553i
$55$	187.716	−	325.133i	0.460210	−	0.797108i
$56$	−229.741	−	397.923i	−0.548222	−	0.949549i
$57$		−	231.342i		−	0.537580i
$58$	−381.150	+	220.057i	−0.862887	+	0.498188i
$59$	37.1769	−	21.4641i	0.0820342	−	0.0473625i	−0.458422	−	0.888735i	$-0.651585\pi$
$59$	37.1769	−	21.4641i	0.0820342	−	0.0473625i	0.540456	+	0.841372i	$0.318252\pi$
$60$		−	144.804i		−	0.311570i
$61$	−248.269	−	430.015i	−0.521109	−	0.902587i	−0.999699	−	0.0245485i	$-0.992185\pi$
$61$	−248.269	−	430.015i	−0.521109	−	0.902587i	0.478590	−	0.878039i	$-0.341148\pi$
$62$	−200.934	+	348.028i	−0.411592	+	0.712897i
$63$	−208.105	−	120.150i	−0.416171	−	0.240276i
$64$	−235.581			−0.460119
$65$	807.998	−	152.181i	1.54184	−	0.290396i
$66$	210.535			0.392653
$67$	419.727	+	242.329i	0.765340	+	0.441869i	0.831210	−	0.555959i	$-0.187649\pi$
$67$	419.727	+	242.329i	0.765340	+	0.441869i	−0.0658696	+	0.997828i	$0.520982\pi$
$68$	−115.519	+	200.085i	−0.206011	+	0.356822i
$69$	213.179	+	369.237i	0.371938	+	0.644216i
$70$			1535.72i			2.62219i
$71$	331.196	−	191.216i	0.553602	−	0.319622i	−0.196971	−	0.980409i	$-0.563111\pi$
$71$	331.196	−	191.216i	0.553602	−	0.319622i	0.750574	+	0.660787i	$0.229777\pi$
$72$	−134.132	+	77.4411i	−0.219550	+	0.126757i
$73$		−	193.622i		−	0.310435i	−0.987880	−	0.155217i	$-0.950392\pi$
$73$		−	193.622i		−	0.310435i	0.987880	−	0.155217i	$-0.0496078\pi$
$74$	−364.929	−	632.076i	−0.573272	−	0.992936i
$75$	274.052	−	474.671i	0.421930	−	0.730804i
$76$	−183.764	−	106.096i	−0.277358	−	0.160133i
$77$	−571.447			−0.845745
$78$	300.463	+	349.735i	0.436163	+	0.507689i
$79$	1049.60			1.49480			0.747399	−	0.664375i	$-0.231302\pi$
$79$	1049.60			1.49480			0.747399	+	0.664375i	$0.231302\pi$
$80$	1191.63	+	687.989i	1.66536	+	0.961493i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−325.144	−	563.166i	−0.437880	−	0.758431i
$83$			861.900i			1.13983i	0.821704	+	0.569914i	$0.193024\pi$
$83$			861.900i			1.13983i	−0.821704	+	0.569914i	$0.806976\pi$
$84$	−190.879	+	110.204i	−0.247936	+	0.143146i
$85$	−1275.51	+	736.414i	−1.62763	+	0.939710i
$86$			507.112i			0.635853i
$87$	−201.335	−	348.722i	−0.248107	−	0.429734i
$88$	−184.160	+	318.974i	−0.223085	+	0.386395i
$89$	838.005	+	483.823i	0.998072	+	0.576237i	0.907677	−	0.419669i	$-0.137854\pi$
$89$	838.005	+	483.823i	0.998072	+	0.576237i	0.0903946	+	0.995906i	$0.471187\pi$
$90$	517.660			0.606291
$91$	−815.532	−	949.271i	−0.939461	−	1.09352i
$92$	391.065			0.443167
$93$	−318.418	−	183.839i	−0.355037	−	0.204981i
$94$	−129.184	+	223.754i	−0.141748	+	0.245515i
$95$	−676.345	−	1171.46i	−0.730438	−	1.26516i
$96$			358.605i			0.381250i
$97$	512.228	−	295.735i	0.536174	−	0.309560i	−0.207353	−	0.978266i	$-0.566485\pi$
$97$	512.228	−	295.735i	0.536174	−	0.309560i	0.743527	+	0.668706i	$0.233152\pi$
$98$	1050.35	−	606.421i	1.08267	−	0.625079i
$99$			192.623i			0.195549i
$100$	−251.366	−	435.379i	−0.251366	−	0.435379i
$101$	127.555	−	220.932i	0.125665	−	0.217659i	−0.796328	−	0.604866i	$-0.793227\pi$
$101$	127.555	−	220.932i	0.125665	−	0.217659i	0.921993	+	0.387207i	$0.126560\pi$
$102$	−715.283	−	412.969i	−0.694348	−	0.400882i
$103$	247.355			0.236627			0.118313	−	0.992976i	$-0.462251\pi$
$103$	247.355			0.236627			0.118313	+	0.992976i	$0.462251\pi$
$104$	−792.692	+	149.299i	−0.747403	+	0.140769i
$105$	−1405.06			−1.30590
$106$	−1354.77	−	782.180i	−1.24139	−	0.716717i
$107$	−341.742	+	591.914i	−0.308761	+	0.534790i	−0.978092	−	0.208175i	$-0.933248\pi$
$107$	−341.742	+	591.914i	−0.308761	+	0.534790i	0.669331	+	0.742965i	$0.266581\pi$
$108$	37.1475	+	64.3414i	0.0330974	+	0.0573264i
$109$			1697.76i			1.49189i	0.666006	+	0.745946i	$0.268002\pi$
$109$			1697.76i			1.49189i	−0.666006	+	0.745946i	$0.731998\pi$
$110$	1066.10	−	615.515i	0.924081	−	0.533518i
$111$	578.299	−	333.881i	0.494502	−	0.285501i
$112$		−	2094.38i		−	1.76697i
$113$	190.354	+	329.703i	0.158469	+	0.274477i	0.934317	−	0.356443i	$-0.116011\pi$
$113$	190.354	+	329.703i	0.158469	+	0.274477i	−0.775848	+	0.630920i	$0.782677\pi$
$114$	379.283	−	656.937i	0.311606	−	0.539718i
$115$	2158.98	+	1246.49i	1.75066	+	1.01074i
$116$	−369.337			−0.295622
$117$	−319.980	+	274.900i	−0.252839	+	0.217218i
$118$	140.760			0.109814
$119$	1941.46	+	1120.90i	1.49557	+	0.863469i
$120$	−452.809	+	784.288i	−0.344463	+	0.596628i
$121$	−436.465	−	755.979i	−0.327923	−	0.567979i
$122$		−	1628.14i		−	1.20824i
$123$	515.252	−	297.481i	0.377713	−	0.218073i
$124$	−292.061	+	168.621i	−0.211515	+	0.122118i
$125$		−	1012.16i		−	0.724241i
$126$	−393.967	−	682.371i	−0.278551	−	0.482464i
$127$	61.6157	−	106.722i	0.0430513	−	0.0745670i	−0.843697	−	0.536820i	$-0.819625\pi$
$127$	61.6157	−	106.722i	0.0430513	−	0.0745670i	0.886748	+	0.462253i	$0.152959\pi$
$128$	−1497.14	−	864.372i	−1.03382	−	0.596878i
$129$	−463.967			−0.316667
$130$	2543.95	+	892.556i	1.71630	+	0.602172i
$131$	−1218.41			−0.812616			−0.406308	−	0.913736i	$-0.633184\pi$
$131$	−1218.41			−0.812616			−0.406308	+	0.913736i	$0.633184\pi$
$132$	153.008	+	88.3392i	0.100891	+	0.0582496i
$133$	−1029.47	+	1783.09i	−0.671176	+	1.16251i
$134$	794.592	+	1376.27i	0.512256	+	0.887253i
$135$			473.618i			0.301945i
$136$	1251.35	−	722.465i	0.788986	−	0.455521i
$137$	−2363.24	+	1364.41i	−1.47376	+	0.850875i	−0.999563	−	0.0295456i	$-0.990594\pi$
$137$	−2363.24	+	1364.41i	−1.47376	+	0.850875i	−0.474194	+	0.880420i	$0.657261\pi$
$138$			1398.02i			0.862370i
$139$	−1556.39	−	2695.75i	−0.949722	−	1.64497i	−0.746009	−	0.665936i	$-0.768032\pi$
$139$	−1556.39	−	2695.75i	−0.949722	−	1.64497i	−0.203713	−	0.979031i	$-0.565301\pi$
$140$	−644.377	+	1116.09i	−0.388999	+	0.673766i
$141$	−204.717	−	118.193i	−0.122271	−	0.0705934i
$142$	1253.99			0.741071
$143$	−332.123	+	946.612i	−0.194220	+	0.553564i
$144$	−705.975			−0.408550
$145$	−2039.02	−	1177.23i	−1.16780	−	0.674232i
$146$	317.441	−	549.823i	0.179942	−	0.311669i
$147$	554.827	+	960.988i	0.311302	+	0.539190i
$148$		−	612.487i		−	0.340176i
$149$	1186.95	−	685.286i	0.652609	−	0.376784i	−0.136846	−	0.990592i	$-0.543697\pi$
$149$	1186.95	−	685.286i	0.652609	−	0.376784i	0.789455	+	0.613809i	$0.210363\pi$
$150$	1556.43	−	898.608i	0.847216	−	0.489140i
$151$			2847.56i			1.53464i	0.641263	+	0.767321i	$0.278411\pi$
$151$			2847.56i			1.53464i	−0.641263	+	0.767321i	$0.721589\pi$
$152$	663.534	+	1149.27i	0.354077	+	0.613280i
$153$	377.833	−	654.427i	0.199647	−	0.345799i
$154$	−1622.72	−	936.879i	−0.849108	−	0.490233i
$155$	−2149.86			−1.11407
$156$	71.6167	+	380.245i	0.0367559	+	0.195153i
$157$	3354.00			1.70496			0.852479	−	0.522761i	$-0.175098\pi$
$157$	3354.00			1.70496			0.852479	+	0.522761i	$0.175098\pi$
$158$	2980.52	+	1720.80i	1.50074	+	0.866454i
$159$	715.632	−	1239.51i	0.356939	−	0.618237i
$160$	1048.41	+	1815.89i	0.518024	+	0.897244i
$161$		−	3794.57i		−	1.85748i
$162$	−230.014	+	132.798i	−0.111553	+	0.0644051i
$163$	1901.95	−	1098.09i	0.913941	−	0.527664i	0.0322438	−	0.999480i	$-0.489735\pi$
$163$	1901.95	−	1098.09i	0.913941	−	0.527664i	0.881697	+	0.471816i	$0.156401\pi$
$164$		−	545.713i		−	0.259836i
$165$	563.147	+	975.399i	0.265703	+	0.460210i
$166$	−1413.07	+	2447.51i	−0.660697	+	1.14436i
$167$	790.279	+	456.268i	0.366189	+	0.211419i	0.671792	−	0.740740i	$-0.265525\pi$
$167$	790.279	+	456.268i	0.366189	+	0.211419i	−0.305603	+	0.952159i	$0.598858\pi$
$168$	1378.45			0.633033
$169$	−2046.47	+	799.231i	−0.931484	+	0.363783i
$170$	−4829.37			−2.17880
$171$	601.045	+	347.014i	0.268790	+	0.155186i
$172$	−212.781	+	368.547i	−0.0943278	+	0.163381i
$173$	449.818	+	779.108i	0.197682	+	0.342396i	0.947777	−	0.318935i	$-0.103325\pi$
$173$	449.818	+	779.108i	0.197682	+	0.342396i	−0.750094	+	0.661331i	$0.769992\pi$
$174$		−	1320.34i		−	0.575258i
$175$	−4224.56	+	2439.05i	−1.82484	+	1.05357i
$176$	−1453.93	+	839.427i	−0.622694	+	0.359512i
$177$			128.784i			0.0546895i
$178$	1586.44	+	2747.80i	0.668027	+	1.15706i
$179$	156.639	−	271.307i	0.0654064	−	0.113287i	−0.831468	−	0.555573i	$-0.812499\pi$
$179$	156.639	−	271.307i	0.0654064	−	0.113287i	0.896874	+	0.442286i	$0.145832\pi$
$180$	376.213	+	217.207i	0.155785	+	0.0899424i
$181$	2745.06			1.12728			0.563642	−	0.826019i	$-0.309400\pi$
$181$	2745.06			1.12728			0.563642	+	0.826019i	$0.309400\pi$
$182$	−759.529	−	4032.67i	−0.309341	−	1.64243i
$183$	1489.62			0.601725
$184$	−2118.08	−	1222.88i	−0.848626	−	0.489954i
$185$	1952.25	−	3381.39i	0.775849	−	1.34381i
$186$	−602.803	−	1044.09i	−0.237632	−	0.411592i
$187$		−	1797.02i		−	0.702735i
$188$	−187.771	+	108.410i	−0.0728437	+	0.0420563i
$189$	624.315	−	360.449i	0.240276	−	0.138724i
$190$		−	4435.44i		−	1.69358i
$191$	−44.9340	−	77.8279i	−0.0170226	−	0.0294839i	0.857389	−	0.514670i	$-0.172085\pi$
$191$	−44.9340	−	77.8279i	−0.0170226	−	0.0294839i	−0.874411	+	0.485186i	$0.838752\pi$
$192$	353.371	−	612.057i	0.132825	−	0.230060i
$193$	735.215	+	424.477i	0.274207	+	0.158314i	0.630798	−	0.775947i	$-0.282728\pi$
$193$	735.215	+	424.477i	0.274207	+	0.158314i	−0.356591	+	0.934261i	$0.616061\pi$
$194$	1939.41			0.717741
$195$	−816.618	+	2327.51i	−0.299893	+	0.854751i
$196$	1017.80			0.370918
$197$	−3761.90	−	2171.93i	−1.36053	−	0.785501i	−0.370834	−	0.928699i	$-0.620928\pi$
$197$	−3761.90	−	2171.93i	−1.36053	−	0.785501i	−0.989694	+	0.143198i	$0.954261\pi$
$198$	−315.803	+	546.987i	−0.113349	+	0.196327i
$199$	−1664.20	−	2882.48i	−0.592825	−	1.02680i	−0.993850	−	0.110736i	$-0.964679\pi$
$199$	−1664.20	−	2882.48i	−0.592825	−	1.02680i	0.401024	−	0.916067i	$-0.368654\pi$
$200$			3144.13i			1.11162i
$201$	−1259.18	+	726.988i	−0.441869	+	0.255113i
$202$	724.429	−	418.249i	0.252330	−	0.145683i
$203$			3583.74i			1.23906i
$204$	−346.558	−	600.255i	−0.118941	−	0.206011i
$205$	1739.41	−	3012.75i	0.592614	−	1.02644i
$206$	702.406	+	405.535i	0.237568	+	0.137160i
$207$	−1279.07			−0.429477
$208$	−3469.39	−	1217.25i	−1.15653	−	0.405775i
$209$	1650.44			0.546236
$210$	−3989.92	−	2303.58i	−1.31110	−	0.756962i
$211$	2299.94	−	3983.62i	0.750401	−	1.29973i	−0.197228	−	0.980358i	$-0.563194\pi$
$211$	2299.94	−	3983.62i	0.750401	−	1.29973i	0.947629	−	0.319375i	$-0.103473\pi$
$212$	−656.394	−	1136.91i	−0.212648	−	0.368317i
$213$			1147.30i			0.369068i
$214$	−1940.87	+	1120.56i	−0.619978	+	0.357944i
$215$	−2349.42	+	1356.44i	−0.745253	+	0.430272i
$216$		−	464.647i		−	0.146367i
$217$	1636.16	+	2833.91i	0.511842	+	0.886537i
$218$	−2783.46	+	4821.09i	−0.864769	+	1.49782i
$219$	503.045	+	290.433i	0.155217	+	0.0896148i
$220$	1033.06			0.316587
$221$	2985.16	−	2564.60i	0.908615	−	0.780604i
$222$	2189.57			0.661958
$223$	2190.68	+	1264.79i	0.657842	+	0.379806i	0.791454	−	0.611228i	$-0.209324\pi$
$223$	2190.68	+	1264.79i	0.657842	+	0.379806i	−0.133612	+	0.991034i	$0.542658\pi$
$224$	1595.79	−	2763.98i	0.475996	−	0.824449i
$225$	822.155	+	1424.01i	0.243601	+	0.421930i
$226$			1248.33i			0.367425i
$227$	32.2742	−	18.6335i	0.00943661	−	0.00544823i	−0.495274	−	0.868737i	$-0.664932\pi$
$227$	32.2742	−	18.6335i	0.00943661	−	0.00544823i	0.504711	+	0.863288i	$0.331599\pi$
$228$	551.293	−	318.289i	0.160133	−	0.0924527i
$229$			4094.45i			1.18152i	0.806846	+	0.590762i	$0.201173\pi$
$229$			4094.45i			1.18152i	−0.806846	+	0.590762i	$0.798827\pi$
$230$	4087.20	+	7079.23i	1.17175	+	2.02953i
$231$	857.170	−	1484.66i	0.244146	−	0.422873i
$232$	2000.40	+	1154.93i	0.566089	+	0.326832i
$233$	−1466.04			−0.412205			−0.206103	−	0.978530i	$-0.566078\pi$
$233$	−1466.04			−0.412205			−0.206103	+	0.978530i	$0.566078\pi$
$234$	−1359.33	+	256.022i	−0.379754	+	0.0715243i
$235$	−1382.19			−0.383676
$236$	102.298	+	59.0621i	0.0282164	+	0.0162907i
$237$	−1574.40	+	2726.94i	−0.431511	+	0.747399i
$238$	3675.41	+	6365.99i	1.00101	+	1.73381i
$239$		−	5520.53i		−	1.49412i	−0.664759	−	0.747058i	$-0.731466\pi$
$239$		−	5520.53i		−	1.49412i	0.664759	−	0.747058i	$-0.268534\pi$
$240$	−3574.89	+	2063.97i	−0.961493	+	0.555119i
$241$	−2308.50	+	1332.81i	−0.617028	+	0.356241i	−0.775711	−	0.631088i	$-0.782609\pi$
$241$	−2308.50	+	1332.81i	−0.617028	+	0.356241i	0.158683	+	0.987330i	$0.449275\pi$
$242$		−	2862.31i		−	0.760316i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	683.155	−	1183.26i	0.179240	−	0.310453i
$245$	5619.03	+	3244.15i	1.46525	+	0.845963i
$246$	1950.87			0.505621
$247$	2355.40	+	2741.67i	0.606764	+	0.706267i
$248$	2109.14			0.540042
$249$	−2239.28	−	1292.85i	−0.569914	−	0.329040i
$250$	1659.42	−	2874.20i	0.419803	−	0.727121i
$251$	789.605	+	1367.64i	0.198564	+	0.343922i	0.948063	−	0.318083i	$-0.103039\pi$
$251$	789.605	+	1367.64i	0.198564	+	0.343922i	−0.749499	+	0.662005i	$0.769706\pi$
$252$		−	661.224i		−	0.165290i
$253$	−2634.21	+	1520.86i	−0.654590	+	0.377927i
$254$	349.937	−	202.036i	0.0864449	−	0.0499090i
$255$		−	4418.49i		−	1.08508i
$256$	−1891.93	−	3276.92i	−0.461897	−	0.800029i
$257$	−1331.96	+	2307.01i	−0.323288	+	0.559952i	−0.981164	−	0.193174i	$-0.938122\pi$
$257$	−1331.96	+	2307.01i	−0.323288	+	0.559952i	0.657876	+	0.753126i	$0.271455\pi$
$258$	−1317.52	−	760.668i	−0.317926	−	0.183555i
$259$	−5943.06			−1.42581
$260$	1474.32	+	1716.09i	0.351667	+	0.409337i
$261$	1208.01			0.286490
$262$	−3459.88	−	1997.56i	−0.815847	−	0.471030i
$263$	1218.47	−	2110.45i	0.285680	−	0.494812i	−0.687094	−	0.726569i	$-0.741114\pi$
$263$	1218.47	−	2110.45i	0.285680	−	0.494812i	0.972774	+	0.231756i	$0.0744472\pi$
$264$	−552.480	−	956.923i	−0.128798	−	0.223085i
$265$		−	8368.80i		−	1.93997i
$266$	−5846.72	+	3375.61i	−1.34769	+	0.778089i
$267$	−2514.02	+	1451.47i	−0.576237	+	0.332691i
$268$			1333.62i			0.303970i
$269$	1341.59	+	2323.70i	0.304083	+	0.526687i	0.977057	−	0.212980i	$-0.0683168\pi$
$269$	1341.59	+	2323.70i	0.304083	+	0.526687i	−0.672974	+	0.739666i	$0.734983\pi$
$270$	−776.491	+	1344.92i	−0.175021	+	0.303146i
$271$	−3340.38	−	1928.57i	−0.748759	−	0.432296i	0.0764866	−	0.997071i	$-0.475630\pi$
$271$	−3340.38	−	1928.57i	−0.748759	−	0.432296i	−0.825245	+	0.564775i	$0.808963\pi$
$272$	6586.20			1.46819
$273$	3689.58	−	694.909i	0.817961	−	0.154058i
$274$	−8947.76			−1.97282
$275$	3386.40	+	1955.14i	0.742572	+	0.428724i
$276$	−586.598	+	1016.02i	−0.127931	+	0.221584i
$277$	552.453	+	956.877i	0.119833	+	0.207557i	0.919701	−	0.392619i	$-0.128431\pi$
$277$	552.453	+	956.877i	0.119833	+	0.207557i	−0.799868	+	0.600175i	$0.795097\pi$
$278$		−	10206.7i		−	2.20201i
$279$	955.255	−	551.517i	0.204981	−	0.118346i
$280$	6980.14	−	4029.98i	1.48980	−	0.860134i
$281$		−	4982.58i		−	1.05778i	−0.848691	−	0.528890i	$-0.822609\pi$
$281$		−	4982.58i		−	1.05778i	0.848691	−	0.528890i	$-0.177391\pi$
$282$	−387.553	−	671.261i	−0.0818384	−	0.141748i
$283$	1292.43	−	2238.55i	0.271473	−	0.470205i	−0.697766	−	0.716326i	$-0.745822\pi$
$283$	1292.43	−	2238.55i	0.271473	−	0.470205i	0.969239	+	0.246120i	$0.0791558\pi$
$284$	911.342	+	526.164i	0.190416	+	0.109937i
$285$	4058.07			0.843437
$286$	−2495.08	+	2143.56i	−0.515864	+	0.443186i
$287$	−5295.14			−1.08907
$288$	−931.684	−	537.908i	−0.190625	−	0.110057i
$289$	−1068.39	+	1850.51i	−0.217462	+	0.376655i
$290$	−3860.11	−	6685.90i	−0.781632	−	1.35383i
$291$			1774.41i			0.357449i
$292$	461.404	−	266.392i	0.0924714	−	0.0533884i
$293$	80.1491	−	46.2741i	0.0159807	−	0.00922649i	−0.491988	−	0.870602i	$-0.663730\pi$
$293$	80.1491	−	46.2741i	0.0159807	−	0.00922649i	0.507969	+	0.861375i	$0.330396\pi$
$294$			3638.52i			0.721779i
$295$	376.510	+	652.135i	0.0743094	+	0.128708i
$296$	−1915.27	+	3317.34i	−0.376090	+	0.651407i
$297$	−500.450	−	288.935i	−0.0977745	−	0.0564502i
$298$	4494.07			0.873605
$299$	−6285.78	−	2205.39i	−1.21577	−	0.426559i
$300$	1508.20			0.290253
$301$	3576.07	+	2064.65i	0.684789	+	0.395363i
$302$	−4668.53	+	8086.14i	−0.889549	+	1.54074i
$303$	382.665	+	662.795i	0.0725529	+	0.125665i
$304$			6048.96i			1.14122i
$305$	7543.07	−	4355.00i	1.41612	−	0.817595i
$306$	2145.85	−	1238.91i	0.400882	−	0.231449i
$307$			3979.46i			0.739803i	0.929071	+	0.369901i	$0.120609\pi$
$307$			3979.46i			0.739803i	−0.929071	+	0.369901i	$0.879391\pi$
$308$	−786.216	−	1361.77i	−0.145451	−	0.251928i
$309$	−371.032	+	642.646i	−0.0683083	+	0.118313i
$310$	−6104.91	−	3524.67i	−1.11850	−	0.645767i
$311$	−3450.91			−0.629207			−0.314604	−	0.949223i	$-0.601872\pi$
$311$	−3450.91			−0.629207			−0.314604	+	0.949223i	$0.601872\pi$
$312$	801.149	−	2283.42i	0.145372	−	0.414338i
$313$	−6189.03			−1.11765			−0.558825	−	0.829285i	$-0.688748\pi$
$313$	−6189.03			−1.11765			−0.558825	+	0.829285i	$0.688748\pi$
$314$	9524.27	+	5498.84i	1.71174	+	0.988272i
$315$	2107.59	−	3650.46i	0.376982	−	0.652952i
$316$	1444.07	+	2501.21i	0.257075	+	0.445266i
$317$			5437.78i			0.963459i	0.876320	+	0.481729i	$0.159991\pi$
$317$			5437.78i			0.963459i	−0.876320	+	0.481729i	$0.840009\pi$
$318$	4064.32	−	2346.54i	0.716717	−	0.413797i
$319$	2487.85	−	1436.36i	0.436654	−	0.252102i
$320$		−	4132.42i		−	0.721904i
$321$	−1025.23	−	1775.74i	−0.178263	−	0.308761i
$322$	6221.15	−	10775.3i	1.07668	−	1.86487i
$323$	−5607.28	−	3237.37i	−0.965937	−	0.557684i
$324$	−222.885			−0.0382176
$325$	1585.03	+	8415.63i	0.270528	+	1.43635i
$326$	7201.23			1.22343
$327$	−4410.92	−	2546.64i	−0.745946	−	0.430672i
$328$	−1706.46	+	2955.68i	−0.287268	+	0.497562i
$329$	1051.92	+	1821.97i	0.176274	+	0.305315i
$330$			3693.09i			0.616054i
$331$	5738.84	−	3313.32i	0.952976	−	0.550201i	0.0589722	−	0.998260i	$-0.481218\pi$
$331$	5738.84	−	3313.32i	0.952976	−	0.550201i	0.894004	+	0.448058i	$0.147884\pi$
$332$	−2053.92	+	1185.83i	−0.339529	+	0.196027i
$333$			2003.29i			0.329668i
$334$	1496.09	+	2591.30i	0.245097	+	0.424520i
$335$	−4250.80	+	7362.60i	−0.693271	+	1.20078i
$336$	5441.37	+	3141.58i	0.883485	+	0.510081i
$337$	5538.63			0.895277			0.447638	−	0.894215i	$-0.352265\pi$
$337$	5538.63			0.895277			0.447638	+	0.894215i	$0.352265\pi$
$338$	−7121.64	−	1085.60i	−1.14605	−	0.174701i
$339$	−1142.13			−0.182985
$340$	−3509.77	−	2026.37i	−0.559836	−	0.323221i
$341$	1311.54	−	2271.66i	0.208281	−	0.360754i
$342$	1137.85	+	1970.81i	0.179906	+	0.311606i
$343$		−	717.813i		−	0.112998i
$344$	2304.92	−	1330.75i	0.361259	−	0.208573i
$345$	−6476.94	+	3739.46i	−1.01074	+	0.583553i
$346$			2949.88i			0.458343i
$347$	−4699.47	−	8139.72i	−0.727034	−	1.25926i	−0.958131	−	0.286329i	$-0.907565\pi$
$347$	−4699.47	−	8139.72i	−0.727034	−	1.25926i	0.231098	−	0.972931i	$-0.425768\pi$
$348$	554.006	−	959.567i	0.0853387	−	0.147811i
$349$	4985.99	+	2878.66i	0.764739	+	0.441522i	0.830995	−	0.556280i	$-0.187772\pi$
$349$	4985.99	+	2878.66i	0.764739	+	0.441522i	−0.0662555	+	0.997803i	$0.521105\pi$
$350$	−15995.2			−2.44279
$351$	−234.240	−	1243.68i	−0.0356205	−	0.189125i
$352$	−2558.36			−0.387389
$353$	−2994.56	−	1728.91i	−0.451514	−	0.260682i	0.256955	−	0.966423i	$-0.417281\pi$
$353$	−2994.56	−	1728.91i	−0.451514	−	0.260682i	−0.708470	+	0.705741i	$0.750614\pi$
$354$	−211.140	+	365.706i	−0.0317005	+	0.0549069i
$355$	3354.20	+	5809.65i	0.501472	+	0.868575i
$356$			2662.64i			0.396403i
$357$	−5824.37	+	3362.70i	−0.863469	+	0.498524i
$358$	889.607	−	513.615i	0.131333	−	0.0758251i
$359$			7168.96i			1.05394i	0.849885	+	0.526968i	$0.176671\pi$
$359$			7168.96i			1.05394i	−0.849885	+	0.526968i	$0.823329\pi$
$360$	−1358.43	−	2352.86i	−0.198876	−	0.344463i
$361$	−456.203	+	790.167i	−0.0665116	+	0.115202i
$362$	7795.07	+	4500.49i	1.13177	+	0.653426i
$363$	2618.79			0.378652
$364$	1140.09	−	3249.47i	0.164167	−	0.467907i
$365$	3396.40			0.487057
$366$	4230.03	+	2442.21i	0.604118	+	0.348787i
$367$	−1955.05	+	3386.25i	−0.278073	+	0.481637i	−0.970906	−	0.239461i	$-0.923029\pi$
$367$	−1955.05	+	3386.25i	−0.278073	+	0.481637i	0.692832	+	0.721099i	$0.256363\pi$
$368$	−5574.04	−	9654.52i	−0.789584	−	1.36760i
$369$			1784.89i			0.251809i
$370$	11087.5	−	6401.37i	1.55787	−	0.899436i
$371$	−11031.6	+	6369.10i	−1.54375	+	0.891286i
$372$		−	1011.73i		−	0.141010i
$373$	−5688.80	−	9853.28i	−0.789691	−	1.36778i	−0.926156	−	0.377140i	$-0.876908\pi$
$373$	−5688.80	−	9853.28i	−0.789691	−	1.36778i	0.136466	−	0.990645i	$-0.456426\pi$
$374$	2946.20	−	5102.96i	0.407337	−	0.705529i
$375$	2629.66	+	1518.24i	0.362120	+	0.209070i
$376$	1356.00			0.185986
$377$	5936.54	+	2082.86i	0.811001	+	0.284543i
$378$	2363.80			0.321643
$379$	3492.00	+	2016.11i	0.473278	+	0.273247i	0.717611	−	0.696444i	$-0.245236\pi$
$379$	3492.00	+	2016.11i	0.473278	+	0.273247i	−0.244333	+	0.969691i	$0.578569\pi$
$380$	1861.08	−	3223.48i	0.251240	−	0.435161i
$381$	184.847	+	320.165i	0.0248557	+	0.0430513i
$382$		−	294.675i		−	0.0394682i
$383$	−1724.22	+	995.480i	−0.230035	+	0.132811i	−0.610588	−	0.791948i	$-0.709067\pi$
$383$	−1724.22	+	995.480i	−0.230035	+	0.132811i	0.380553	+	0.924759i	$0.375734\pi$
$384$	4491.41	−	2593.12i	0.596878	−	0.344608i
$385$		−	10024.0i		−	1.32693i
$386$	1391.85	+	2410.75i	0.183532	+	0.317886i
$387$	695.951	−	1205.42i	0.0914139	−	0.158333i
$388$	1409.48	+	813.765i	0.184422	+	0.106476i
$389$	11122.4			1.44969			0.724846	−	0.688911i	$-0.241911\pi$
$389$	11122.4			1.44969			0.724846	+	0.688911i	$0.241911\pi$
$390$	−6134.85	+	5270.54i	−0.796539	+	0.684318i
$391$	11932.8			1.54339
$392$	−5512.59	−	3182.70i	−0.710275	−	0.410078i
$393$	1827.61	−	3165.51i	0.234582	−	0.406308i
$394$	−7121.71	−	12335.2i	−0.910625	−	1.57725i
$395$			18411.4i			2.34527i
$396$	−459.024	+	265.018i	−0.0582496	+	0.0336304i
$397$	−9334.12	+	5389.06i	−1.18002	+	0.681282i	−0.956018	−	0.293308i	$-0.905244\pi$
$397$	−9334.12	+	5389.06i	−1.18002	+	0.681282i	−0.223997	+	0.974590i	$0.571911\pi$
$398$		−	10913.8i		−	1.37452i
$399$	−3088.41	−	5349.28i	−0.387503	−	0.671176i
$400$	−7165.69	+	12411.3i	−0.895711	+	1.55142i
$401$	−4080.35	−	2355.79i	−0.508137	−	0.293373i	0.223931	−	0.974605i	$-0.428111\pi$
$401$	−4080.35	−	2355.79i	−0.508137	−	0.293373i	−0.732067	+	0.681232i	$0.761444\pi$
$402$	−4767.55			−0.591502
$403$	5645.36	−	1063.27i	0.697805	−	0.131427i
$404$	701.978			0.0864473
$405$	−1230.50	−	710.427i	−0.150972	−	0.0871640i
$406$	−5875.50	+	10176.7i	−0.718217	+	1.24399i
$407$	2381.97	+	4125.69i	0.290098	+	0.502465i
$408$			4334.79i			0.525991i
$409$	1026.05	−	592.388i	0.124046	−	0.0716179i	−0.436693	−	0.899611i	$-0.643850\pi$
$409$	1026.05	−	592.388i	0.124046	−	0.0716179i	0.560739	+	0.827993i	$0.310517\pi$
$410$	9878.73	−	5703.49i	1.18994	−	0.687013i
$411$		−	8186.49i		−	0.982505i
$412$	340.319	+	589.450i	0.0406949	+	0.0704857i
$413$	573.089	−	992.619i	0.0682805	−	0.118265i
$414$	−3632.15	−	2097.03i	−0.431185	−	0.248945i
$415$	−15118.9			−1.78834
$416$	−3651.13	−	4249.87i	−0.430315	−	0.500882i
$417$	9338.35			1.09664
$418$	4686.72	+	2705.88i	0.548409	+	0.316624i
$419$	3084.15	−	5341.91i	0.359596	−	0.622838i	−0.628298	−	0.777973i	$-0.716248\pi$
$419$	3084.15	−	5341.91i	0.359596	−	0.622838i	0.987893	+	0.155135i	$0.0495813\pi$
$420$	−1933.13	−	3348.28i	−0.224589	−	0.388999i
$421$		−	10328.8i		−	1.19571i	−0.801603	−	0.597857i	$-0.796019\pi$
$421$		−	10328.8i		−	1.19571i	0.801603	−	0.597857i	$-0.203981\pi$
$422$	13062.2	−	7541.45i	1.50677	−	0.869934i
$423$	614.151	−	354.580i	0.0705934	−	0.0407571i
$424$			8210.27i			0.940392i
$425$	−7670.06	−	13284.9i	−0.875418	−	1.51627i
$426$	−1880.98	+	3257.95i	−0.213929	+	0.370536i
$427$	−11481.4	−	6628.77i	−1.30122	−	0.751261i
$428$	−1880.72			−0.212402
$429$	−1961.19	−	2282.80i	−0.220715	−	0.256910i
$430$	−8895.46			−0.997622
$431$	9796.87	+	5656.23i	1.09489	+	0.632137i	0.934875	−	0.354977i	$-0.115511\pi$
$431$	9796.87	+	5656.23i	1.09489	+	0.632137i	0.160018	+	0.987114i	$0.448845\pi$
$432$	1058.96	−	1834.18i	0.117938	−	0.204275i
$433$	−5237.87	−	9072.27i	−0.581331	−	1.00689i	−0.995322	−	0.0966135i	$-0.969199\pi$
$433$	−5237.87	−	9072.27i	−0.581331	−	1.00689i	0.413991	−	0.910281i	$-0.364134\pi$
$434$			10729.8i			1.18675i
$435$	6117.07	−	3531.69i	0.674232	−	0.389268i
$436$	−4045.80	+	2335.84i	−0.444400	+	0.256575i
$437$			10959.4i			1.19968i
$438$	952.322	+	1649.47i	0.103890	+	0.179942i
$439$	−1020.31	+	1767.23i	−0.110926	+	0.192130i	−0.916144	−	0.400849i	$-0.868715\pi$
$439$	−1020.31	+	1767.23i	−0.110926	+	0.192130i	0.805218	+	0.592979i	$0.202048\pi$
$440$	−5595.26	−	3230.42i	−0.606235	−	0.350010i
$441$	−3328.96			−0.359460
$442$	12681.5	−	2388.49i	1.36470	−	0.257033i
$443$	−4089.28			−0.438572			−0.219286	−	0.975661i	$-0.570373\pi$
$443$	−4089.28			−0.438572			−0.219286	+	0.975661i	$0.570373\pi$
$444$	1591.29	+	918.730i	0.170088	+	0.0982004i
$445$	−8486.93	+	14699.8i	−0.904088	+	1.56593i
$446$	4147.21	+	7183.19i	0.440306	+	0.762632i
$447$			4111.71i			0.435072i
$448$	−5447.29	+	3144.99i	−0.574465	+	0.331667i
$449$	13179.1	−	7608.96i	1.38521	−	0.799753i	0.392441	−	0.919777i	$-0.371631\pi$
$449$	13179.1	−	7608.96i	1.38521	−	0.799753i	0.992771	+	0.120025i	$0.0382973\pi$
$450$			5391.65i			0.564810i
$451$	2122.29	+	3675.91i	0.221585	+	0.383796i
$452$	−523.792	+	907.235i	−0.0545069	+	0.0944087i
$453$	−7398.17	−	4271.34i	−0.767321	−	0.443013i
$454$	122.197			0.0126322
$455$	16651.5	−	14305.6i	1.71568	−	1.47397i
$456$	−3981.20			−0.408853
$457$	−758.912	−	438.158i	−0.0776814	−	0.0448494i	0.460656	−	0.887579i	$-0.347614\pi$
$457$	−758.912	−	438.158i	−0.0776814	−	0.0448494i	−0.538338	+	0.842729i	$0.680947\pi$
$458$	−6712.80	+	11626.9i	−0.684865	+	1.18622i
$459$	1133.50	+	1963.28i	0.115266	+	0.199647i
$460$			6859.84i			0.695308i
$461$	−14110.5	+	8146.69i	−1.42558	+	0.823057i	−0.996768	−	0.0803390i	$-0.974400\pi$
$461$	−14110.5	+	8146.69i	−1.42558	+	0.823057i	−0.428808	+	0.903396i	$0.641066\pi$
$462$	4868.17	−	2810.64i	0.490233	−	0.283036i
$463$		−	11704.8i		−	1.17488i	−0.809269	−	0.587438i	$-0.800137\pi$
$463$		−	11704.8i		−	1.17488i	0.809269	−	0.587438i	$-0.199863\pi$
$464$	5264.34	+	9118.11i	0.526704	+	0.912279i
$465$	3224.79	−	5585.50i	0.321605	−	0.557036i
$466$	−4163.09	−	2403.56i	−0.413844	−	0.238933i
$467$	15616.1			1.54738			0.773688	−	0.633567i	$-0.218410\pi$
$467$	15616.1			1.54738			0.773688	+	0.633567i	$0.218410\pi$
$468$	−1095.33	−	384.301i	−0.108187	−	0.0379580i
$469$	12940.3			1.27405
$470$	−3924.96	−	2266.07i	−0.385202	−	0.222396i
$471$	−5031.00	+	8713.95i	−0.492179	+	0.852479i
$472$	−369.378	−	639.782i	−0.0360212	−	0.0623906i
$473$		−	3310.03i		−	0.321766i
$474$	−8941.56	+	5162.41i	−0.866454	+	0.500248i
$475$	12201.3	−	7044.42i	1.17860	−	0.680463i
$476$			6168.70i			0.593996i
$477$	2146.90	+	3718.53i	0.206079	+	0.356939i
$478$	9050.84	−	15676.5i	0.866058	−	1.50006i
$479$	8985.90	+	5188.01i	0.857153	+	0.494877i	0.863058	−	0.505105i	$-0.168546\pi$
$479$	8985.90	+	5188.01i	0.857153	+	0.494877i	−0.00590498	+	0.999983i	$0.501880\pi$
$480$	−6290.44			−0.598163
$481$	−3454.09	+	9844.79i	−0.327428	+	0.933230i
$482$	−8740.53			−0.825976
$483$	9858.59	+	5691.86i	0.928740	+	0.536208i
$484$	1201.01	−	2080.21i	0.112792	−	0.195361i
$485$	5187.61	+	8985.20i	0.485685	+	0.841231i
$486$		−	796.791i		−	0.0743686i
$487$	−3459.14	+	1997.13i	−0.321865	+	0.185829i	−0.652224	−	0.758027i	$-0.726164\pi$
$487$	−3459.14	+	1997.13i	−0.321865	+	0.185829i	0.330358	+	0.943856i	$0.392830\pi$
$488$	−7400.19	+	4272.50i	−0.686457	+	0.396326i
$489$			6588.55i			0.609294i
$490$	10637.5	+	18424.6i	0.980719	+	1.69865i
$491$	6133.65	−	10623.8i	0.563763	−	0.976467i	−0.433400	−	0.901202i	$-0.642686\pi$
$491$	6133.65	−	10623.8i	0.563763	−	0.976467i	0.997164	−	0.0752653i	$-0.0239804\pi$
$492$	1417.80	+	818.570i	0.129918	+	0.0750081i
$493$	−11269.8			−1.02954
$494$	2193.66	+	11647.1i	0.199792	+	1.06078i
$495$	−3378.88			−0.306807
$496$	8325.75	+	4806.88i	0.753704	+	0.435151i
$497$	5105.45	−	8842.90i	0.460786	−	0.798105i
$498$	−4239.22	−	7342.54i	−0.381454	−	0.660697i
$499$		−	3578.76i		−	0.321056i	−0.987031	−	0.160528i	$-0.948680\pi$
$499$		−	3578.76i		−	0.321056i	0.987031	−	0.160528i	$-0.0513198\pi$
$500$	2411.99	−	1392.56i	0.215735	−	0.124554i
$501$	−2370.84	+	1368.80i	−0.211419	+	0.122063i
$502$			5178.19i			0.460386i
$503$	648.409	+	1123.08i	0.0574774	+	0.0995537i	0.893332	−	0.449397i	$-0.148361\pi$
$503$	648.409	+	1123.08i	0.0574774	+	0.0995537i	−0.835855	+	0.548950i	$0.815028\pi$
$504$	−2067.67	+	3581.31i	−0.182741	+	0.316516i
$505$	3875.45	+	2237.49i	0.341496	+	0.197163i
$506$	−9973.72			−0.876257
$507$	993.241	−	6515.73i	0.0870047	−	0.570757i
$508$	339.092			0.0296157
$509$	−4095.09	−	2364.30i	−0.356604	−	0.205886i	0.310986	−	0.950415i	$-0.399341\pi$
$509$	−4095.09	−	2364.30i	−0.356604	−	0.205886i	−0.667590	+	0.744529i	$0.732674\pi$
$510$	7244.05	−	12547.1i	0.628965	−	1.08940i
$511$	−2584.84	−	4477.08i	−0.223771	−	0.387582i
$512$			1422.78i			0.122810i
$513$	−1803.14	+	1041.04i	−0.155186	+	0.0895967i
$514$	−7564.64	+	4367.45i	−0.649148	+	0.374786i
$515$			4338.95i			0.371256i
$516$	−638.342	−	1105.64i	−0.0544602	−	0.0943278i
$517$	843.214	−	1460.49i	0.0717302	−	0.124240i
$518$	−16876.4	−	9743.57i	−1.43148	−	0.826463i
$519$	−2698.91			−0.228264
$520$	−2618.91	−	13904.9i	−0.220859	−	1.17264i
$521$	−9220.74			−0.775370			−0.387685	−	0.921792i	$-0.626725\pi$
$521$	−9220.74			−0.775370			−0.387685	+	0.921792i	$0.626725\pi$
$522$	3430.35	+	1980.51i	0.287629	+	0.166063i
$523$	6051.33	−	10481.2i	0.505939	−	0.876313i	−0.494037	−	0.869441i	$-0.664479\pi$
$523$	6051.33	−	10481.2i	0.505939	−	0.876313i	0.999976	−	0.00687187i	$-0.00218740\pi$
$524$	−1676.33	−	2903.48i	−0.139753	−	0.242059i
$525$		−	14634.3i		−	1.21656i
$526$	6920.10	−	3995.32i	0.573632	−	0.331187i
$527$	−8911.78	+	5145.22i	−0.736629	+	0.425293i
$528$		−	5036.56i		−	0.415129i
$529$	−4015.45	−	6954.97i	−0.330028	−	0.571626i
$530$	13720.5	−	23764.7i	1.12449	−	1.94768i
$531$	−334.592	−	193.177i	−0.0273447	−	0.0157875i
$532$	−5665.52			−0.461713
$533$	−3077.52	+	8771.51i	−0.250098	+	0.712826i
$534$	−9518.65			−0.771371
$535$	−10383.0	−	5994.63i	−0.839059	−	0.484431i
$536$	4170.28	−	7223.14i	0.336061	−	0.582075i
$537$	469.917	+	813.920i	0.0377624	+	0.0654064i
$538$			8798.08i			0.705041i
$539$	−6855.87	+	3958.24i	−0.547873	+	0.316314i
$540$	−1128.64	+	651.620i	−0.0899424	+	0.0519283i
$541$			12801.3i			1.01732i	0.860968	+	0.508659i	$0.169859\pi$
$541$			12801.3i			1.01732i	−0.860968	+	0.508659i	$0.830141\pi$
$542$	−6323.73	−	10953.0i	−0.501157	−	0.868030i
$543$	−4117.59	+	7131.87i	−0.325419	+	0.563642i
$544$	8691.88	+	5018.26i	0.685039	+	0.395508i
$545$	−29781.2			−2.34071
$546$	11616.5	+	4075.70i	0.910512	+	0.319457i
$547$	400.693			0.0313207			0.0156603	−	0.999877i	$-0.495015\pi$
$547$	400.693			0.0313207			0.0156603	+	0.999877i	$0.495015\pi$
$548$	−6502.84	−	3754.42i	−0.506912	−	0.292666i
$549$	−2234.43	+	3870.14i	−0.173703	+	0.300862i
$550$	6410.84	+	11103.9i	0.497017	+	0.860858i
$551$		−	10350.5i		−	0.800265i
$552$	6354.25	−	3668.63i	0.489954	−	0.282875i
$553$	24269.7	−	14012.1i	1.86628	−	1.07750i
$554$			3622.96i			0.277843i
$555$	5856.74	+	10144.2i	0.447937	+	0.775849i
$556$	4282.67	−	7417.81i	0.326665	−	0.565801i
$557$	−12536.2	−	7237.77i	−0.953636	−	0.550582i	−0.0594277	−	0.998233i	$-0.518928\pi$
$557$	−12536.2	−	7237.77i	−0.953636	−	0.550582i	−0.894209	+	0.447650i	$0.852261\pi$
$558$	3616.82			0.274394
$559$	5498.53	−	4723.87i	0.416034	−	0.357421i
$560$	36738.5			2.77229
$561$	4668.80	+	2695.54i	0.351367	+	0.202862i
$562$	8168.88	−	14148.9i	0.613138	−	1.06199i
$563$	−7388.18	−	12796.7i	−0.553063	−	0.957934i	−0.998051	−	0.0623972i	$-0.980125\pi$
$563$	−7388.18	−	12796.7i	−0.553063	−	0.957934i	0.444988	−	0.895536i	$-0.353208\pi$
$564$		−	650.458i		−	0.0485625i
$565$	−5783.46	+	3339.08i	−0.430641	+	0.248631i
$566$	7340.16	−	4237.84i	0.545106	−	0.314717i
$567$			2162.69i			0.160184i
$568$	−3290.67	−	5699.60i	−0.243087	−	0.421039i
$569$	−3434.44	+	5948.63i	−0.253039	+	0.438277i	−0.964361	−	0.264590i	$-0.914763\pi$
$569$	−3434.44	+	5948.63i	−0.253039	+	0.438277i	0.711322	+	0.702866i	$0.248097\pi$
$570$	11523.6	+	6653.16i	0.846791	+	0.488895i
$571$	−3011.00			−0.220677			−0.110338	−	0.993894i	$-0.535193\pi$
$571$	−3011.00			−0.220677			−0.110338	+	0.993894i	$0.535193\pi$
$572$	−2712.74	+	510.927i	−0.198296	+	0.0373478i
$573$	269.604			0.0196559
$574$	−15036.5	−	8681.32i	−1.09340	−	0.631274i
$575$	−12982.7	+	22486.7i	−0.941591	+	1.63088i
$576$	1060.11	+	1836.17i	0.0766865	+	0.132825i
$577$			23106.6i			1.66714i	0.552411	+	0.833572i	$0.313708\pi$
$577$			23106.6i			1.66714i	−0.552411	+	0.833572i	$0.686292\pi$
$578$	−6067.76	+	3503.22i	−0.436653	+	0.252102i
$579$	−2205.65	+	1273.43i	−0.158314	+	0.0914023i
$580$		−	6478.70i		−	0.463816i
$581$	11506.3	+	19929.5i	0.821622	+	1.42309i
$582$	−2909.12	+	5038.74i	−0.207194	+	0.358871i
$583$	8842.91	+	5105.46i	0.628192	+	0.362687i
$584$	−3332.07			−0.236099
$585$	−4822.12	−	5612.90i	−0.340804	−	0.396692i
$586$	303.463			0.0213924
$587$	2619.56	+	1512.40i	0.184192	+	0.106343i	0.589261	−	0.807943i	$-0.299419\pi$
$587$	2619.56	+	1512.40i	0.184192	+	0.106343i	−0.405069	+	0.914286i	$0.632752\pi$
$588$	−1526.70	+	2644.32i	−0.107075	+	0.185459i
$589$	−4725.53	−	8184.85i	−0.330580	−	0.572582i
$590$			2469.13i			0.172293i
$591$	11285.7	−	6515.80i	0.785501	−	0.453509i
$592$	−15120.9	+	8730.06i	−1.04977	+	0.606087i
$593$		−	6396.07i		−	0.442926i	−0.975169	−	0.221463i	$-0.928917\pi$
$593$		−	6396.07i		−	0.442926i	0.975169	−	0.221463i	$-0.0710832\pi$
$594$	−947.410	−	1640.96i	−0.0654422	−	0.113349i
$595$	−19662.2	+	34055.9i	−1.35474	+	2.34648i
$596$	3266.09	+	1885.68i	0.224470	+	0.129598i
$597$	9985.22			0.684536
$598$	−14233.9	−	16568.1i	−0.973354	−	1.13297i
$599$	12095.9			0.825084			0.412542	−	0.910939i	$-0.364641\pi$
$599$	12095.9			0.825084			0.412542	+	0.910939i	$0.364641\pi$
$600$	−8168.68	−	4716.19i	−0.555808	−	0.320896i
$601$	5908.25	−	10233.4i	0.401003	−	0.694557i	−0.592845	−	0.805317i	$-0.701995\pi$
$601$	5908.25	−	10233.4i	0.401003	−	0.694557i	0.993847	+	0.110760i	$0.0353285\pi$
$602$	6769.92	+	11725.8i	0.458341	+	0.793870i
$603$		−	4361.93i		−	0.294580i
$604$	−6785.77	+	3917.77i	−0.457134	+	0.263927i
$605$	13260.9	−	7656.21i	0.891131	−	0.514495i
$606$			2509.50i			0.168220i
$607$	12582.0	+	21792.6i	0.841329	+	1.45722i	0.888771	+	0.458351i	$0.151560\pi$
$607$	12582.0	+	21792.6i	0.841329	+	1.45722i	−0.0474421	+	0.998874i	$0.515107\pi$
$608$	−4608.92	+	7982.89i	−0.307428	+	0.532482i
$609$	−9310.83	−	5375.61i	−0.619530	−	0.357686i
$610$	28559.8			1.89566
$611$	3629.50	−	683.595i	0.240318	−	0.0452623i
$612$	2079.35			0.137341
$613$	16959.4	+	9791.51i	1.11743	+	0.645148i	0.940743	−	0.339120i	$-0.110129\pi$
$613$	16959.4	+	9791.51i	1.11743	+	0.645148i	0.176685	+	0.984267i	$0.443462\pi$
$614$	−6524.26	+	11300.4i	−0.428824	+	0.742745i
$615$	5218.24	+	9038.25i	0.342146	+	0.592614i
$616$			9834.10i			0.643226i
$617$	−17040.8	+	9838.54i	−1.11189	+	0.641952i	−0.939319	−	0.343044i	$-0.888542\pi$
$617$	−17040.8	+	9838.54i	−1.11189	+	0.641952i	−0.172575	+	0.984996i	$0.555209\pi$
$618$	−2107.22	+	1216.60i	−0.137160	+	0.0791893i
$619$		−	4394.05i		−	0.285318i	−0.989772	−	0.142659i	$-0.954435\pi$
$619$		−	4394.05i		−	0.285318i	0.989772	−	0.142659i	$-0.0455652\pi$
$620$	−2957.85	−	5123.15i	−0.191597	−	0.331856i
$621$	1918.61	−	3323.13i	0.123979	−	0.214739i
$622$	−9799.47	−	5657.73i	−0.631709	−	0.364717i
$623$	25836.0			1.66147
$624$	8366.59	−	7187.86i	0.536750	−	0.461129i
$625$	−5082.96			−0.325310
$626$	−17574.8	−	10146.8i	−1.12210	−	0.647842i
$627$	−2475.66	+	4287.97i	−0.157685	+	0.273118i
$628$	4614.55	+	7992.64i	0.293218	+	0.507868i
$629$		−	18689.1i		−	1.18471i
$630$	11969.8	−	6910.74i	0.756962	−	0.437032i
$631$	−20687.3	+	11943.8i	−1.30515	+	0.753529i	−0.981282	−	0.192574i	$-0.938316\pi$
$631$	−20687.3	+	11943.8i	−1.30515	+	0.753529i	−0.323867	+	0.946102i	$0.604983\pi$
$632$		−	18062.7i		−	1.13686i
$633$	6899.83	+	11950.9i	0.433244	+	0.750401i
$634$	−8915.18	+	15441.5i	−0.558465	+	0.967290i
$635$	1872.05	+	1080.83i	0.116992	+	0.0675453i
$636$	3938.37			0.245545
$637$	−16359.6	−	5739.83i	−1.01757	−	0.357018i
$638$	9419.57			0.584521
$639$	−2980.77	−	1720.95i	−0.184534	−	0.106541i
$640$	15162.3	−	26261.9i	0.936473	−	1.62202i
$641$	−2721.81	−	4714.31i	−0.167714	−	0.290490i	0.769901	−	0.638163i	$-0.220305\pi$
$641$	−2721.81	−	4714.31i	−0.167714	−	0.290490i	−0.937616	+	0.347673i	$0.886972\pi$
$642$		−	6723.38i		−	0.413318i
$643$	−5056.73	+	2919.50i	−0.310137	+	0.179057i	−0.646988	−	0.762501i	$-0.723971\pi$
$643$	−5056.73	+	2919.50i	−0.310137	+	0.179057i	0.336851	+	0.941558i	$0.390638\pi$
$644$	9042.52	−	5220.70i	0.553300	−	0.319448i
$645$		−	8138.64i		−	0.496835i
$646$	−10615.2	−	18386.1i	−0.646519	−	1.11980i
$647$	4354.43	−	7542.09i	0.264591	−	0.458285i	−0.702866	−	0.711323i	$-0.748096\pi$
$647$	4354.43	−	7542.09i	0.264591	−	0.458285i	0.967456	+	0.253038i	$0.0814298\pi$
$648$	1207.19	+	696.970i	0.0731833	+	0.0422524i
$649$	−918.773			−0.0555701
$650$	−9296.34	+	26496.3i	−0.560973	+	1.59888i
$651$	−9816.96			−0.591024
$652$	5233.54	+	3021.59i	0.314358	+	0.181495i
$653$	−1397.47	+	2420.48i	−0.0837475	+	0.145055i	−0.904857	−	0.425716i	$-0.860022\pi$
$653$	−1397.47	+	2420.48i	−0.0837475	+	0.145055i	0.821109	+	0.570771i	$0.193356\pi$
$654$	−8350.38	−	14463.3i	−0.499275	−	0.864769i
$655$		−	21372.6i		−	1.27495i
$656$	−13472.4	+	7778.31i	−0.801844	+	0.462945i
$657$	−1509.13	+	871.299i	−0.0896148	+	0.0517391i
$658$			6898.41i			0.408705i
$659$	−15695.0	−	27184.5i	−0.927752	−	1.60691i	−0.787074	−	0.616859i	$-0.788405\pi$
$659$	−15695.0	−	27184.5i	−0.927752	−	1.60691i	−0.140678	−	0.990055i	$-0.544928\pi$
$660$	−1549.59	+	2683.98i	−0.0913907	+	0.158293i
$661$	17837.7	+	10298.6i	1.04963	+	0.606005i	0.922546	−	0.385887i	$-0.126104\pi$
$661$	17837.7	+	10298.6i	1.04963	+	0.606005i	0.127085	+	0.991892i	$0.459438\pi$
$662$	21728.6			1.27569
$663$	2185.27	+	11602.6i	0.128008	+	0.679648i
$664$	14832.5			0.866889
$665$	−31278.0	−	18058.4i	−1.82392	−	1.05304i
$666$	−3284.36	+	5688.68i	−0.191091	+	0.330979i
$667$	9537.85	+	16520.0i	0.553684	+	0.959008i
$668$			2511.00i			0.145439i
$669$	−6572.04	+	3794.37i	−0.379806	+	0.219281i
$670$	−24141.8	+	13938.3i	−1.39206	+	0.803704i
$671$			10627.2i			0.611414i
$672$	4787.36	+	8291.95i	0.274816	+	0.475996i
$673$	−8967.89	+	15532.8i	−0.513651	+	0.889669i	0.486224	+	0.873834i	$0.338374\pi$
$673$	−8967.89	+	15532.8i	−0.513651	+	0.889669i	−0.999875	+	0.0158347i	$0.994959\pi$
$674$	15727.9	+	9080.51i	0.898837	+	0.518944i
$675$	−4932.93			−0.281287
$676$	−4720.18	−	3777.16i	−0.268559	−	0.214904i
$677$	−24104.0			−1.36838			−0.684188	−	0.729305i	$-0.739843\pi$
$677$	−24104.0			−1.36838			−0.684188	+	0.729305i	$0.739843\pi$
$678$	−3243.27	−	1872.50i	−0.183712	−	0.106066i
$679$	7896.09	−	13676.4i	0.446280	−	0.772980i
$680$	12673.1	+	21950.4i	0.714691	+	1.23788i
$681$			111.801i			0.00629107i
$682$	7448.70	−	4300.51i	0.418219	−	0.241459i
$683$	5840.69	−	3372.12i	0.327215	−	0.188918i	−0.327389	−	0.944890i	$-0.606169\pi$
$683$	5840.69	−	3372.12i	0.327215	−	0.188918i	0.654604	+	0.755972i	$0.272835\pi$
$684$			1909.73i			0.106755i
$685$	−23933.8	−	41454.5i	−1.33498	−	2.31225i
$686$	1176.85	−	2038.36i	0.0654988	−	0.113447i
$687$	−10637.7	−	6141.67i	−0.590762	−	0.341076i
$688$	12131.5			0.672249
$689$	4139.00	+	21975.8i	0.228858	+	1.21511i
$690$	−24523.2			−1.35302
$691$	26712.1	+	15422.2i	1.47059	+	0.849043i	0.999455	−	0.0330199i	$-0.0105125\pi$
$691$	26712.1	+	15422.2i	1.47059	+	0.849043i	0.471131	+	0.882063i	$0.343846\pi$
$692$	−1237.75	+	2143.85i	−0.0679945	+	0.117770i
$693$	2571.51	+	4453.98i	0.140958	+	0.244146i
$694$		−	30818.9i		−	1.68569i
$695$	47287.2	−	27301.3i	2.58087	−	1.49007i
$696$	−6001.20	+	3464.79i	−0.326832	+	0.188696i
$697$		−	16651.6i		−	0.904913i
$698$	9439.06	+	16348.9i	0.511853	+	0.886556i
$699$	2199.07	−	3808.90i	0.118993	−	0.206103i
$700$	−11624.6	−	6711.46i	−0.627669	−	0.362385i
$701$	21007.6			1.13188			0.565940	−	0.824447i	$-0.308514\pi$
$701$	21007.6			1.13188			0.565940	+	0.824447i	$0.308514\pi$
$702$	1373.84	−	3915.69i	0.0738634	−	0.210524i
$703$	17164.6			0.920877
$704$	4366.53	+	2521.02i	0.233764	+	0.134964i
$705$	2073.28	−	3591.02i	0.110758	−	0.191838i
$706$	−5669.06	−	9819.10i	−0.302207	−	0.523437i
$707$		−	6811.41i		−	0.362333i
$708$	−306.895	+	177.186i	−0.0162907	+	0.00940546i
$709$	12785.5	−	7381.68i	0.677246	−	0.391008i	−0.121570	−	0.992583i	$-0.538793\pi$
$709$	12785.5	−	7381.68i	0.677246	−	0.391008i	0.798817	+	0.601574i	$0.205460\pi$
$710$			21996.7i			1.16271i
$711$	−4723.20	−	8180.81i	−0.249133	−	0.431511i
$712$	8326.17	−	14421.4i	0.438253	−	0.759077i
$713$	15084.5	+	8709.02i	0.792311	+	0.457441i
$714$	−22052.4			−1.15587
$715$	−16604.9	−	5825.91i	−0.868515	−	0.304722i
$716$	862.037			0.0449942
$717$	14342.8	+	8280.80i	0.747058	+	0.431314i
$718$	−11753.4	+	20357.5i	−0.610910	+	1.05813i
$719$	−13093.1	−	22678.0i	−0.679126	−	1.17628i	−0.975245	−	0.221129i	$-0.929026\pi$
$719$	−13093.1	−	22678.0i	−0.679126	−	1.17628i	0.296119	−	0.955151i	$-0.404308\pi$
$720$		−	12383.8i		−	0.640996i
$721$	5719.53	−	3302.17i	0.295432	−	0.170568i
$722$	−2590.94	+	1495.88i	−0.133552	+	0.0771064i
$723$		−	7996.89i		−	0.411352i
$724$	3776.75	+	6541.52i	0.193870	+	0.335792i
$725$	12261.3	−	21237.3i	0.628103	−	1.08791i
$726$	7436.51	+	4293.47i	0.380158	+	0.219484i
$727$	−20044.0			−1.02254			−0.511272	−	0.859419i	$-0.670825\pi$
$727$	−20044.0			−1.02254			−0.511272	+	0.859419i	$0.670825\pi$
$728$	−16336.1	+	14034.6i	−0.831672	+	0.714501i
$729$	729.000			0.0370370
$730$	9644.68	+	5568.36i	0.488994	+	0.282321i
$731$	−6492.68	+	11245.6i	−0.328509	+	0.568995i
$732$	2049.47	+	3549.78i	0.103484	+	0.179240i
$733$			25555.5i			1.28774i	0.765134	+	0.643871i	$0.222673\pi$
$733$			25555.5i			1.28774i	−0.765134	+	0.643871i	$0.777327\pi$
$734$	−11103.4	+	6410.57i	−0.558358	+	0.322368i
$735$	−16857.1	+	9732.44i	−0.845963	+	0.488417i
$736$		−	16988.2i		−	0.850809i
$737$	−5186.47	−	8983.23i	−0.259221	−	0.448985i
$738$	−2926.30	+	5068.50i	−0.145960	+	0.252810i
$739$	9620.24	+	5554.25i	0.478872	+	0.276477i	0.719946	−	0.694030i	$-0.244166\pi$
$739$	9620.24	+	5554.25i	0.478872	+	0.276477i	−0.241074	+	0.970507i	$0.577500\pi$
$740$	10743.9			0.533720
$741$	−10656.2	+	2007.02i	−0.528291	+	0.0995004i
$742$	−41768.2			−2.06652
$743$	−24411.7	−	14094.1i	−1.20535	−	0.695911i	−0.243612	−	0.969873i	$-0.578333\pi$
$743$	−24411.7	−	14094.1i	−1.20535	−	0.695911i	−0.961741	+	0.273962i	$0.911666\pi$
$744$	−3163.71	+	5479.70i	−0.155897	+	0.270021i
$745$	12020.9	+	20820.8i	0.591155	+	1.02391i
$746$		−	37306.8i		−	1.83096i
$747$	6717.84	−	3878.55i	0.329040	−	0.189971i
$748$	4282.34	−	2472.41i	0.209328	−	0.120856i
$749$			18248.9i			0.890256i
$750$	4978.26	+	8622.59i	0.242374	+	0.419803i
$751$	8588.28	−	14875.3i	0.417298	−	0.722782i	−0.578369	−	0.815776i	$-0.696310\pi$
$751$	8588.28	−	14875.3i	0.417298	−	0.722782i	0.995667	+	0.0929941i	$0.0296438\pi$
$752$	5352.78	+	3090.43i	0.259569	+	0.149862i
$753$	−4737.63			−0.229281
$754$	13443.0	+	15647.5i	0.649291	+	0.755768i
$755$	−49950.2			−2.40778
$756$	1717.91	+	991.835i	0.0826452	+	0.0477152i
$757$	2204.98	−	3819.14i	0.105867	−	0.183367i	−0.808225	−	0.588874i	$-0.799572\pi$
$757$	2204.98	−	3819.14i	0.105867	−	0.183367i	0.914092	+	0.405507i	$0.132905\pi$
$758$	6610.77	+	11450.2i	0.316773	+	0.548667i
$759$		−	9125.16i		−	0.436393i
$760$	−20159.9	+	11639.3i	−0.962206	+	0.555530i
$761$	28097.0	−	16221.8i	1.33839	−	0.772721i	0.351823	−	0.936067i	$-0.385562\pi$
$761$	28097.0	−	16221.8i	1.33839	−	0.772721i	0.986569	+	0.163346i	$0.0522286\pi$
$762$			1212.22i			0.0576300i
$763$	22665.1	+	39257.0i	1.07540	+	1.86265i
$764$	123.643	−	214.157i	0.00585505	−	0.0101413i
$765$	11479.6	+	6627.73i	0.542542	+	0.313237i
$766$	−6528.30			−0.307934
$767$	−1311.21	−	1526.24i	−0.0617278	−	0.0718505i
$768$	11351.6			0.533353
$769$	−27707.7	−	15997.1i	−1.29931	−	0.750155i	−0.319022	−	0.947747i	$-0.603354\pi$
$769$	−27707.7	−	15997.1i	−1.29931	−	0.750155i	−0.980284	+	0.197593i	$0.936688\pi$
$770$	16434.2	−	28464.8i	0.769152	−	1.33221i
$771$	−3995.87	−	6921.04i	−0.186651	−	0.323288i
$772$			2336.04i			0.108907i
$773$	7776.38	−	4489.70i	0.361833	−	0.208904i	−0.308051	−	0.951370i	$-0.599677\pi$
$773$	7776.38	−	4489.70i	0.361833	−	0.208904i	0.669885	+	0.742465i	$0.266344\pi$
$774$	3952.55	−	2282.00i	0.183555	−	0.105975i
$775$		−	22391.7i		−	1.03785i
$776$	−5089.34	−	8815.00i	−0.235434	−	0.407784i
$777$	8914.59	−	15440.5i	0.411595	−	0.712903i
$778$	31584.1	+	18235.1i	1.45546	+	0.840308i
$779$	15293.3			0.703390
$780$	−6670.03	+	1256.26i	−0.306186	+	0.0576683i
$781$	−8185.04			−0.375011
$782$	33885.2	+	19563.6i	1.54953	+	0.894620i
$783$	−1812.01	+	3138.50i	−0.0827024	+	0.143245i
$784$	−14507.2	−	25127.2i	−0.660859	−	1.14464i
$785$			58833.9i			2.67500i
$786$	10379.6	−	5992.68i	0.471030	−	0.271949i
$787$	−10886.4	+	6285.27i	−0.493086	+	0.284683i	−0.725854	−	0.687849i	$-0.758555\pi$
$787$	−10886.4	+	6285.27i	−0.493086	+	0.284683i	0.232768	+	0.972532i	$0.425222\pi$
$788$		−	11952.9i		−	0.540360i
$789$	3655.40	+	6331.34i	0.164937	+	0.285680i
$790$	−30185.3	+	52282.5i	−1.35942	+	2.35459i
$791$	8803.05	+	5082.44i	0.395702	+	0.228459i
$792$	3314.88			0.148724
$793$	−17653.6	+	15166.5i	−0.790540	+	0.679165i
$794$	−35341.2			−1.57961
$795$	21742.8	+	12553.2i	0.969983	+	0.560020i
$796$	4579.34	−	7931.65i	0.203907	−	0.353178i
$797$	18931.7	+	32790.6i	0.841398	+	1.45734i	0.888713	+	0.458464i	$0.151600\pi$
$797$	18931.7	+	32790.6i	0.841398	+	1.45734i	−0.0473148	+	0.998880i	$0.515066\pi$
$798$		−	20253.6i		−	0.898460i
$799$	−5729.55	+	3307.96i	−0.253688	+	0.146467i
$800$	−18913.3	+	10919.6i	−0.835857	+	0.482582i
$801$		−	8708.81i		−	0.384158i
$802$	−7724.58	−	13379.4i	−0.340105	−	0.589079i
$803$	−2072.00	+	3588.82i	−0.0910578	+	0.157717i
$804$	−3464.85	−	2000.43i	−0.151985	−	0.0877485i
$805$	66562.1			2.91429
$806$	17774.2	+	6236.16i	0.776761	+	0.272530i
$807$	−8049.54			−0.351124
$808$	−3802.04	−	2195.11i	−0.165539	−	0.0955739i
$809$	−1251.90	+	2168.35i	−0.0544058	+	0.0942336i	−0.891946	−	0.452143i	$-0.850660\pi$
$809$	−1251.90	+	2168.35i	−0.0544058	+	0.0942336i	0.837540	+	0.546376i	$0.183993\pi$
$810$	−2329.47	−	4034.76i	−0.101049	−	0.175021i
$811$			5409.55i			0.234223i	0.993119	+	0.117112i	$0.0373635\pi$
$811$			5409.55i			0.234223i	−0.993119	+	0.117112i	$0.962636\pi$
$812$	−8540.11	+	4930.64i	−0.369088	+	0.213093i
$813$	10021.1	−	5785.71i	0.432296	−	0.249586i
$814$			15620.8i			0.672617i
$815$	19262.1	+	33362.9i	0.827879	+	1.43393i
$816$	−9879.29	+	17111.4i	−0.423829	+	0.734093i
$817$	−10328.3	−	5963.07i	−0.442280	−	0.255351i
$818$	3884.85			0.166052
$819$	−3728.94	+	10628.2i	−0.159096	+	0.453453i
$820$	9572.58			0.407669
$821$	−27177.3	−	15690.8i	−1.15529	−	0.667007i	−0.205119	−	0.978737i	$-0.565758\pi$
$821$	−27177.3	−	15690.8i	−1.15529	−	0.667007i	−0.950171	+	0.311730i	$0.899092\pi$
$822$	13421.6	−	23247.0i	0.569505	−	0.986412i
$823$	−16523.1	−	28618.8i	−0.699827	−	1.21214i	−0.968526	−	0.248912i	$-0.919927\pi$
$823$	−16523.1	−	28618.8i	−0.699827	−	1.21214i	0.268699	−	0.963224i	$-0.413406\pi$
$824$		−	4256.76i		−	0.179965i
$825$	−10159.2	+	5865.41i	−0.428724	+	0.247524i
$826$	3254.77	−	1879.14i	0.137104	−	0.0791571i
$827$		−	33653.7i		−	1.41506i	−0.706684	−	0.707529i	$-0.749810\pi$
$827$		−	33653.7i		−	1.41506i	0.706684	−	0.707529i	$-0.250190\pi$
$828$	−1759.79	−	3048.05i	−0.0738612	−	0.127931i
$829$	6449.25	−	11170.4i	0.270195	−	0.467992i	−0.698716	−	0.715399i	$-0.746245\pi$
$829$	6449.25	−	11170.4i	0.270195	−	0.467992i	0.968912	+	0.247407i	$0.0795784\pi$
$830$	−42932.8	−	24787.3i	−1.79545	−	1.03660i
$831$	−3314.72			−0.138371
$832$	2043.79	+	10851.4i	0.0851632	+	0.452169i
$833$	31056.6			1.29177
$834$	26517.9	+	15310.1i	1.10101	+	0.635666i
$835$	−8003.58	+	13862.6i	−0.331707	+	0.574533i
$836$	2270.73	+	3933.03i	0.0939414	+	0.162711i
$837$			3309.10i			0.136654i
$838$	17516.0	−	10112.8i	0.722051	−	0.416877i
$839$	−342.798	+	197.915i	−0.0141057	+	0.00814395i	−0.507036	−	0.861925i	$-0.669259\pi$
$839$	−342.798	+	197.915i	−0.0141057	+	0.00814395i	0.492931	+	0.870069i	$0.335926\pi$
$840$			24179.9i			0.993197i
$841$	3186.59	+	5519.33i	0.130657	+	0.226304i
$842$	16934.0	−	29330.5i	0.693091	−	1.20047i
$843$	12945.1	+	7473.87i	0.528890	+	0.305355i
$844$	12657.4			0.516214
$845$	−14019.6	−	35898.0i	−0.570758	−	1.46145i
$846$	2325.32			0.0944989
$847$	−20184.6	−	11653.6i	−0.818831	−	0.472752i
$848$	−18711.8	+	32409.8i	−0.757742	+	1.31245i
$849$	3877.29	+	6715.66i	0.156735	+	0.271473i
$850$		−	50299.9i		−	2.02973i
$851$	−27395.8	+	15817.0i	−1.10354	+	0.637132i
$852$	−2734.03	+	1578.49i	−0.109937	+	0.0634721i
$853$		−	21248.9i		−	0.852930i	−0.904504	−	0.426465i	$-0.859759\pi$
$853$		−	21248.9i		−	0.852930i	0.904504	−	0.426465i	$-0.140241\pi$
$854$	−21735.6	−	37647.1i	−0.870932	−	1.50850i
$855$	−6087.11	+	10543.2i	−0.243479	+	0.421718i
$856$	10186.3	+	5881.08i	0.406731	+	0.234826i
$857$	9920.37			0.395418			0.197709	−	0.980261i	$-0.436650\pi$
$857$	9920.37			0.395418			0.197709	+	0.980261i	$0.436650\pi$
$858$	−1826.51	−	9697.75i	−0.0726760	−	0.385869i
$859$	20946.3			0.831990			0.415995	−	0.909367i	$-0.363433\pi$
$859$	20946.3			0.831990			0.415995	+	0.909367i	$0.363433\pi$
$860$	−6464.84	−	3732.47i	−0.256336	−	0.147996i
$861$	7942.72	−	13757.2i	0.314387	−	0.544534i
$862$	18546.6	+	32123.7i	0.732831	+	1.26930i
$863$			11271.4i			0.444594i	0.974979	+	0.222297i	$0.0713554\pi$
$863$			11271.4i			0.444594i	−0.974979	+	0.222297i	$0.928645\pi$
$864$	2795.05	−	1613.72i	0.110057	−	0.0635417i
$865$	−13666.6	+	7890.44i	−0.537202	+	0.310154i
$866$		−	34349.7i		−	1.34786i
$867$	−3205.17	−	5551.52i	−0.125552	−	0.217462i
$868$	−4502.17	+	7797.99i	−0.176053	+	0.304932i
$869$	−19454.5	−	11232.1i	−0.759435	−	0.438460i
$870$	23160.7			0.902551
$871$	7520.89	−	21435.9i	0.292578	−	0.833902i
$872$	29217.0			1.13465
$873$	−4610.05	−	2661.61i	−0.178725	−	0.103187i
$874$	−17967.8	+	31121.2i	−0.695389	+	1.20445i
$875$	−13512.2	−	23403.9i	−0.522054	−	0.904224i
$876$			1598.35i			0.0616476i
$877$	8172.12	−	4718.18i	0.314656	−	0.181667i	−0.334352	−	0.942448i	$-0.608518\pi$
$877$	8172.12	−	4718.18i	0.314656	−	0.181667i	0.649008	+	0.760782i	$0.275184\pi$
$878$	−5794.69	+	3345.57i	−0.222735	+	0.128596i
$879$			277.645i			0.0106538i
$880$	−14724.7	−	25504.0i	−0.564057	−	0.976976i
$881$	−10171.5	+	17617.6i	−0.388974	+	0.673723i	−0.992312	−	0.123763i	$-0.960504\pi$
$881$	−10171.5	+	17617.6i	−0.388974	+	0.673723i	0.603337	+	0.797486i	$0.293837\pi$
$882$	−9453.16	−	5457.79i	−0.360890	−	0.208360i
$883$	−46521.9			−1.77303			−0.886515	−	0.462699i	$-0.846881\pi$
$883$	−46521.9			−1.77303			−0.886515	+	0.462699i	$0.846881\pi$
$884$	10218.6	+	3585.23i	0.388787	+	0.136408i
$885$	−2259.06			−0.0858051
$886$	−11612.2	−	6704.32i	−0.440316	−	0.254217i
$887$	9977.53	−	17281.6i	0.377692	−	0.654181i	−0.613034	−	0.790056i	$-0.710051\pi$
$887$	9977.53	−	17281.6i	0.377692	−	0.654181i	0.990726	+	0.135875i	$0.0433845\pi$
$888$	−5745.80	−	9952.02i	−0.217136	−	0.376090i
$889$		−	3290.27i		−	0.124130i
$890$	−48200.2	+	27828.4i	−1.81537	+	1.04810i
$891$	1501.35	−	866.804i	0.0564502	−	0.0325915i
$892$			6960.57i			0.261275i
$893$	−3038.13	−	5262.19i	−0.113849	−	0.197192i
$894$	−6741.10	+	11675.9i	−0.252188	+	0.436802i
$895$	4759.10	+	2747.67i	0.177742	+	0.102619i
$896$	−46157.3			−1.72099
$897$	15158.5	−	13022.8i	0.564243	−	0.484749i
$898$	49899.1			1.85429
$899$	−14246.4	−	8225.14i	−0.528523	−	0.305143i
$900$	−2262.30	+	3918.41i	−0.0837888	+	0.145126i
$901$	−20028.9	−	34691.0i	−0.740575	−	1.28271i
$902$			13917.9i			0.513762i
$903$	−10728.2	+	6193.94i	−0.395363	+	0.228263i
$904$	5673.91	−	3275.83i	0.208752	−	0.120523i
$905$			48152.2i			1.76866i
$906$	−14005.6	−	24258.4i	−0.513582	−	0.889549i
$907$	−1326.97	+	2298.39i	−0.0485793	+	0.0841419i	−0.889293	−	0.457339i	$-0.848803\pi$
$907$	−1326.97	+	2298.39i	−0.0485793	+	0.0841419i	0.840713	+	0.541481i	$0.182136\pi$
$908$	88.8078	+	51.2732i	0.00324580	+	0.00187397i
$909$	−2295.99			−0.0837769
$910$	70738.8	−	13323.2i	2.57689	−	0.485341i
$911$	1797.50			0.0653720			0.0326860	−	0.999466i	$-0.489594\pi$
$911$	1797.50			0.0653720			0.0326860	+	0.999466i	$0.489594\pi$
$912$	−15715.7	−	9073.45i	−0.570612	−	0.329443i
$913$	9223.43	−	15975.5i	0.334339	−	0.579091i
$914$	−1436.71	−	2488.45i	−0.0519936	−	0.0900555i
$915$			26130.0i			0.944077i
$916$	−9757.14	+	5633.29i	−0.351949	+	0.203198i
$917$	−28173.0	+	16265.7i	−1.01456	+	0.585757i
$918$			7433.43i			0.267255i
$919$	24321.0	+	42125.2i	0.872987	+	1.51206i	0.858891	+	0.512158i	$0.171154\pi$
$919$	24321.0	+	42125.2i	0.872987	+	1.51206i	0.0140961	+	0.999901i	$0.495513\pi$
$920$	21451.0	−	37154.2i	0.768714	−	1.33145i
$921$	−10338.9	−	5969.18i	−0.369901	−	0.213563i
$922$	−53425.6			−1.90833
$923$	−11681.2	−	13596.7i	−0.416566	−	0.484878i
$924$	4717.30			0.167952
$925$	35218.6	+	20333.5i	1.25187	+	0.722768i
$926$	19189.8	−	33237.8i	0.681012	−	1.17955i
$927$	−1113.10	−	1927.94i	−0.0394378	−	0.0683083i
$928$			16044.4i			0.567545i
$929$	32688.3	−	18872.6i	1.15443	−	0.666513i	0.204471	−	0.978873i	$-0.434453\pi$
$929$	32688.3	−	18872.6i	1.15443	−	0.666513i	0.949964	+	0.312359i	$0.101119\pi$
$930$	18314.7	−	10574.0i	0.645767	−	0.372834i
$931$			28523.3i			1.00410i
$932$	−2017.04	−	3493.61i	−0.0708908	−	0.122786i
$933$	5176.37	−	8965.74i	0.181636	−	0.314604i
$934$	44344.5	+	25602.3i	1.55353	+	0.896931i
$935$	31522.3			1.10256
$936$	4730.78	+	5506.58i	0.165204	+	0.192295i
$937$	2705.50			0.0943273			0.0471637	−	0.998887i	$-0.484982\pi$
$937$	2705.50			0.0943273			0.0471637	+	0.998887i	$0.484982\pi$
$938$	36746.4	+	21215.5i	1.27912	+	0.738498i
$939$	9283.55	−	16079.6i	0.322638	−	0.558825i
$940$	−1901.66	−	3293.77i	−0.0659843	−	0.114288i
$941$			5189.27i			0.179772i	0.995952	+	0.0898860i	$0.0286503\pi$
$941$			5189.27i			0.179772i	−0.995952	+	0.0898860i	$0.971350\pi$
$942$	−28572.8	+	16496.5i	−0.988272	+	0.570579i
$943$	−24409.1	+	14092.6i	−0.842916	+	0.486658i
$944$		−	3367.36i		−	0.116100i
$945$	6322.78	+	10951.4i	0.217651	+	0.376982i
$946$	5426.75	−	9399.41i	0.186511	−	0.323046i
$947$	−62.5886	−	36.1356i	−0.00214768	−	0.00123997i	0.498926	−	0.866645i	$-0.333728\pi$
$947$	−62.5886	−	36.1356i	−0.00214768	−	0.00123997i	−0.501073	+	0.865405i	$0.667061\pi$
$948$	−8664.45			−0.296844
$949$	−8918.67	+	1679.78i	−0.305071	+	0.0574582i
$950$	46196.9			1.57771
$951$	−14127.8	−	8156.68i	−0.481729	−	0.278127i
$952$	19289.7	−	33410.8i	0.656706	−	1.13745i
$953$	22347.5	+	38707.1i	0.759609	+	1.31568i	0.943050	+	0.332651i	$0.107943\pi$
$953$	22347.5	+	38707.1i	0.759609	+	1.31568i	−0.183441	+	0.983031i	$0.558724\pi$
$954$			14079.2i			0.477811i
$955$	1365.21	−	788.205i	0.0462588	−	0.0267076i
$956$	13155.5	−	7595.34i	0.445063	−	0.256957i
$957$			8618.16i			0.291103i
$958$	17011.4	+	29464.5i	0.573708	+	0.993691i
$959$	−36429.7	+	63098.1i	−1.22667	+	2.12466i
$960$	10736.3	+	6198.63i	0.360952	+	0.208396i
$961$	14770.2			0.495795
$962$	−25948.9	+	22293.1i	−0.869673	+	0.747149i
$963$	6151.35			0.205841
$964$	−6352.24	−	3667.47i	−0.212232	−	0.122532i
$965$	−7445.92	+	12896.7i	−0.248386	+	0.430217i
$966$	18663.5	+	32326.0i	0.621622	+	1.07668i
$967$		−	17936.9i		−	0.596496i	−0.954488	−	0.298248i	$-0.903598\pi$
$967$		−	17936.9i		−	0.596496i	0.954488	−	0.298248i	$-0.0964022\pi$
$968$	−13009.8	+	7511.18i	−0.431972	+	0.249399i
$969$	16821.9	−	9712.10i	0.557684	−	0.321979i
$970$			34020.1i			1.12610i
$971$	20457.3	+	35433.1i	0.676113	+	1.17106i	0.976142	+	0.217132i	$0.0696703\pi$
$971$	20457.3	+	35433.1i	0.676113	+	1.17106i	−0.300029	+	0.953930i	$0.596996\pi$
$972$	334.328	−	579.073i	0.0110325	−	0.0191088i
$973$	−71976.2	−	41555.5i	−2.37148	−	1.36918i
$974$	−13097.1			−0.430860
$975$	−24242.0	−	8505.41i	−0.796272	−	0.279376i
$976$	−38949.3			−1.27740
$977$	−20886.8	−	12059.0i	−0.683961	−	0.394885i	0.117385	−	0.993086i	$-0.462549\pi$
$977$	−20886.8	−	12059.0i	−0.683961	−	0.394885i	−0.801346	+	0.598202i	$0.795882\pi$
$978$	−10801.8	+	18709.4i	−0.353175	+	0.611717i
$979$	−10355.1	−	17935.5i	−0.338048	−	0.585516i
$980$			17853.6i			0.581953i
$981$	13232.8	−	7639.93i	0.430672	−	0.248649i
$982$	34835.2	−	20112.1i	1.13201	−	0.653567i
$983$			2928.61i			0.0950235i	0.998871	+	0.0475118i	$0.0151292\pi$
$983$			2928.61i			0.0950235i	−0.998871	+	0.0475118i	$0.984871\pi$
$984$	−5119.39	−	8867.05i	−0.165854	−	0.287268i
$985$	38098.7	−	65989.0i	1.23241	−	2.13460i
$986$	−32002.5	−	18476.6i	−1.03364	−	0.596771i
$987$	−6311.50			−0.203543
$988$	−3292.79	+	9385.05i	−0.106030	+	0.302205i
$989$	21979.6			0.706683
$990$	−9594.93	−	5539.63i	−0.308027	−	0.177839i
$991$	−24904.9	+	43136.6i	−0.798317	+	1.38272i	0.122395	+	0.992481i	$0.460943\pi$
$991$	−24904.9	+	43136.6i	−0.798317	+	1.38272i	−0.920712	+	0.390244i	$0.872391\pi$
$992$	7325.06	+	12687.4i	0.234447	+	0.406073i
$993$			19879.9i			0.635318i
$994$	28995.6	−	16740.6i	0.925238	−	0.534186i
$995$	50562.8	−	29192.5i	1.61100	−	0.930114i
$996$		−	7114.99i		−	0.226352i
$997$	20575.8	+	35638.4i	0.653604	+	1.13208i	0.982242	+	0.187620i	$0.0600772\pi$
$997$	20575.8	+	35638.4i	0.653604	+	1.13208i	−0.328638	+	0.944456i	$0.606589\pi$
$998$	5867.33	−	10162.5i	0.186099	−	0.322333i
$999$	−5204.69	−	3004.93i	−0.164834	−	0.0951669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.c.4.4	✓	10
3.2	odd	2		117.4.q.e.82.2		10
4.3	odd	2		624.4.bv.h.433.5		10
13.4	even	6		507.4.b.i.337.8		10
13.6	odd	12		507.4.a.r.1.3		10
13.7	odd	12		507.4.a.r.1.8		10
13.9	even	3		507.4.b.i.337.3		10
13.10	even	6	inner	39.4.j.c.10.4	yes	10
39.20	even	12		1521.4.a.bk.1.3		10
39.23	odd	6		117.4.q.e.10.2		10
39.32	even	12		1521.4.a.bk.1.8		10
52.23	odd	6		624.4.bv.h.49.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.4	✓	10	1.1	even	1	trivial
39.4.j.c.10.4	yes	10	13.10	even	6	inner
117.4.q.e.10.2		10	39.23	odd	6
117.4.q.e.82.2		10	3.2	odd	2
507.4.a.r.1.3		10	13.6	odd	12
507.4.a.r.1.8		10	13.7	odd	12
507.4.b.i.337.3		10	13.9	even	3
507.4.b.i.337.8		10	13.4	even	6
624.4.bv.h.49.1		10	52.23	odd	6
624.4.bv.h.433.5		10	4.3	odd	2
1521.4.a.bk.1.3		10	39.20	even	12
1521.4.a.bk.1.8		10	39.32	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.83967 + 1.63949i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.37583 + 2.38302i) q^{4} +17.5414i q^{5} +(-8.51902 + 4.91846i) q^{6} +(23.1228 - 13.3499i) q^{7} -17.2091i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(2.83967 + 1.63949i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.37583 + 2.38302i) q^{4} +17.5414i q^{5} +(-8.51902 + 4.91846i) q^{6} +(23.1228 - 13.3499i) q^{7} -17.2091i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-28.7589 + 49.8119i) q^{10} +(-18.5352 - 10.7013i) q^{11} -8.25501 q^{12} +(-8.67555 - 46.0623i) q^{13} +87.5483 q^{14} +(-45.5739 - 26.3121i) q^{15} +(39.2208 - 67.9325i) q^{16} +(41.9815 + 72.7141i) q^{17} -29.5108i q^{18} +(-66.7828 + 38.5571i) q^{19} +(-41.8015 + 24.1341i) q^{20} +80.0997i q^{21} +(-35.0892 - 60.7763i) q^{22} +(71.0597 - 123.079i) q^{23} +(44.7107 + 25.8137i) q^{24} -182.701 q^{25} +(50.8828 - 145.025i) q^{26} +27.0000 q^{27} +(63.6263 + 36.7346i) q^{28} +(-67.1115 + 116.241i) q^{29} +(-86.2767 - 149.436i) q^{30} +122.559i q^{31} +(103.520 - 59.7675i) q^{32} +(55.6055 - 32.1039i) q^{33} +275.312i q^{34} +(234.177 + 405.606i) q^{35} +(12.3825 - 21.4471i) q^{36} +(-192.766 - 111.294i) q^{37} -252.855 q^{38} +(132.687 + 46.5537i) q^{39} +301.873 q^{40} +(-171.751 - 99.1604i) q^{41} +(-131.322 + 227.457i) q^{42} +(77.3279 + 133.936i) q^{43} -58.8928i q^{44} +(136.722 - 78.9363i) q^{45} +(403.573 - 233.003i) q^{46} +78.7956i q^{47} +(117.663 + 203.797i) q^{48} +(184.942 - 320.329i) q^{49} +(-518.811 - 299.536i) q^{50} -251.889 q^{51} +(97.8310 - 84.0481i) q^{52} -477.088 q^{53} +(76.6712 + 44.2661i) q^{54} +(187.716 - 325.133i) q^{55} +(-229.741 - 397.923i) q^{56} -231.342i q^{57} +(-381.150 + 220.057i) q^{58} +(37.1769 - 21.4641i) q^{59} -144.804i q^{60} +(-248.269 - 430.015i) q^{61} +(-200.934 + 348.028i) q^{62} +(-208.105 - 120.150i) q^{63} -235.581 q^{64} +(807.998 - 152.181i) q^{65} +210.535 q^{66} +(419.727 + 242.329i) q^{67} +(-115.519 + 200.085i) q^{68} +(213.179 + 369.237i) q^{69} +1535.72i q^{70} +(331.196 - 191.216i) q^{71} +(-134.132 + 77.4411i) q^{72} -193.622i q^{73} +(-364.929 - 632.076i) q^{74} +(274.052 - 474.671i) q^{75} +(-183.764 - 106.096i) q^{76} -571.447 q^{77} +(300.463 + 349.735i) q^{78} +1049.60 q^{79} +(1191.63 + 687.989i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-325.144 - 563.166i) q^{82} +861.900i q^{83} +(-190.879 + 110.204i) q^{84} +(-1275.51 + 736.414i) q^{85} +507.112i q^{86} +(-201.335 - 348.722i) q^{87} +(-184.160 + 318.974i) q^{88} +(838.005 + 483.823i) q^{89} +517.660 q^{90} +(-815.532 - 949.271i) q^{91} +391.065 q^{92} +(-318.418 - 183.839i) q^{93} +(-129.184 + 223.754i) q^{94} +(-676.345 - 1171.46i) q^{95} +358.605i q^{96} +(512.228 - 295.735i) q^{97} +(1050.35 - 606.421i) q^{98} +192.623i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) 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

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