LMFDB - Embedded newform 39.4.j.b.4.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 289 $ x^4 - 17*x^2 + 289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$-3.57071 - 2.06155i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.57071 - 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} -13.4424i q^{5} +(-10.7121 + 6.18466i) q^{6} +(-27.2121 + 15.7109i) q^{7} -4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-3.57071 - 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} -13.4424i q^{5} +(-10.7121 + 6.18466i) q^{6} +(-27.2121 + 15.7109i) q^{7} -4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-27.7121 + 47.9988i) q^{10} +(-35.0707 - 20.2481i) q^{11} +27.0000 q^{12} +(42.1364 - 20.5310i) q^{13} +129.556 q^{14} +(-34.9243 - 20.1635i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-21.5707 - 37.3616i) q^{17} +37.1080i q^{18} +(23.3636 - 13.4890i) q^{19} +(104.773 - 60.4906i) q^{20} +94.2656i q^{21} +(83.4850 + 144.600i) q^{22} +(-9.50500 + 16.4631i) q^{23} +(-10.7121 - 6.18466i) q^{24} -55.6971 q^{25} +(-192.783 - 13.5562i) q^{26} -27.0000 q^{27} +(-244.909 - 141.398i) q^{28} +(77.0557 - 133.464i) q^{29} +(83.1364 + 143.997i) q^{30} -308.270i q^{31} +(-224.955 + 129.878i) q^{32} +(-105.212 + 60.7443i) q^{33} +177.877i q^{34} +(211.192 + 365.796i) q^{35} +(40.5000 - 70.1481i) q^{36} +(-37.6821 - 21.7558i) q^{37} -111.233 q^{38} +(9.86357 - 140.270i) q^{39} -55.4243 q^{40} +(41.4293 + 23.9192i) q^{41} +(194.334 - 336.596i) q^{42} +(171.061 + 296.286i) q^{43} -364.466i q^{44} +(-104.773 + 60.4906i) q^{45} +(67.8793 - 39.1901i) q^{46} +133.468i q^{47} +(-82.5000 - 142.894i) q^{48} +(322.167 - 558.010i) q^{49} +(198.879 + 114.823i) q^{50} -129.424 q^{51} +(349.637 + 236.032i) q^{52} -438.454 q^{53} +(96.4093 + 55.6619i) q^{54} +(-272.182 + 471.433i) q^{55} +(64.7779 + 112.199i) q^{56} -80.9338i q^{57} +(-550.288 + 317.709i) q^{58} +(511.434 - 295.277i) q^{59} -362.944i q^{60} +(270.652 + 468.783i) q^{61} +(-635.516 + 1100.75i) q^{62} +(244.909 + 141.398i) q^{63} +631.000 q^{64} +(-275.985 - 566.413i) q^{65} +500.910 q^{66} +(-199.485 - 115.173i) q^{67} +(194.136 - 336.254i) q^{68} +(28.5150 + 49.3894i) q^{69} -1741.54i q^{70} +(-389.202 + 224.706i) q^{71} +(-32.1364 + 18.5540i) q^{72} -389.711i q^{73} +(89.7014 + 155.367i) q^{74} +(-83.5457 + 144.705i) q^{75} +(210.272 + 121.401i) q^{76} +1272.47 q^{77} +(-324.394 + 480.530i) q^{78} -897.820 q^{79} +(-640.279 - 369.665i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-98.6214 - 170.817i) q^{82} +1300.24i q^{83} +(-734.728 + 424.195i) q^{84} +(-502.228 + 289.961i) q^{85} -1410.60i q^{86} +(-231.167 - 400.393i) q^{87} +(-83.4850 + 144.600i) q^{88} +(801.113 + 462.523i) q^{89} +498.819 q^{90} +(-824.061 + 1220.69i) q^{91} -171.090 q^{92} +(-800.910 - 462.406i) q^{93} +(275.151 - 476.575i) q^{94} +(-181.324 - 314.062i) q^{95} +779.267i q^{96} +(1351.43 - 780.247i) q^{97} +(-2300.73 + 1328.33i) q^{98} +364.466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9	$ 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9} - 68 q^{10} - 126 q^{11} + 108 q^{12} + 40 q^{13} + 204 q^{14} - 54 q^{15} + 110 q^{16} - 72 q^{17} + 222 q^{19} + 162 q^{20} + 34 q^{22} - 138 q^{23} + 120 q^{25} - 714 q^{26} - 108 q^{27} - 594 q^{28} - 6 q^{29} + 204 q^{30} - 378 q^{33} + 402 q^{35} + 162 q^{36} + 492 q^{37} + 612 q^{38} + 168 q^{39} - 136 q^{40} + 180 q^{41} + 306 q^{42} + 470 q^{43} - 162 q^{45} - 714 q^{46} - 330 q^{48} + 346 q^{49} + 1224 q^{50} - 432 q^{51} - 144 q^{52} - 2268 q^{53} - 446 q^{55} + 102 q^{56} - 2244 q^{58} + 2160 q^{59} - 160 q^{61} - 1428 q^{62} + 594 q^{63} + 2524 q^{64} - 804 q^{65} + 204 q^{66} - 498 q^{67} + 648 q^{68} + 414 q^{69} - 1314 q^{71} + 1530 q^{74} + 180 q^{75} + 1998 q^{76} + 2976 q^{77} - 612 q^{78} + 8 q^{79} - 990 q^{80} - 162 q^{81} + 34 q^{82} - 1782 q^{84} - 852 q^{85} + 18 q^{87} - 34 q^{88} - 252 q^{89} + 1224 q^{90} - 1668 q^{91} - 2484 q^{92} - 1404 q^{93} + 2686 q^{94} - 54 q^{95} - 336 q^{97} - 6732 q^{98}+O(q^{100}) $ 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9 - 68 * q^10 - 126 * q^11 + 108 * q^12 + 40 * q^13 + 204 * q^14 - 54 * q^15 + 110 * q^16 - 72 * q^17 + 222 * q^19 + 162 * q^20 + 34 * q^22 - 138 * q^23 + 120 * q^25 - 714 * q^26 - 108 * q^27 - 594 * q^28 - 6 * q^29 + 204 * q^30 - 378 * q^33 + 402 * q^35 + 162 * q^36 + 492 * q^37 + 612 * q^38 + 168 * q^39 - 136 * q^40 + 180 * q^41 + 306 * q^42 + 470 * q^43 - 162 * q^45 - 714 * q^46 - 330 * q^48 + 346 * q^49 + 1224 * q^50 - 432 * q^51 - 144 * q^52 - 2268 * q^53 - 446 * q^55 + 102 * q^56 - 2244 * q^58 + 2160 * q^59 - 160 * q^61 - 1428 * q^62 + 594 * q^63 + 2524 * q^64 - 804 * q^65 + 204 * q^66 - 498 * q^67 + 648 * q^68 + 414 * q^69 - 1314 * q^71 + 1530 * q^74 + 180 * q^75 + 1998 * q^76 + 2976 * q^77 - 612 * q^78 + 8 * q^79 - 990 * q^80 - 162 * q^81 + 34 * q^82 - 1782 * q^84 - 852 * q^85 + 18 * q^87 - 34 * q^88 - 252 * q^89 + 1224 * q^90 - 1668 * q^91 - 2484 * q^92 - 1404 * q^93 + 2686 * q^94 - 54 * q^95 - 336 * q^97 - 6732 * 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 $

$2$	−3.57071	−	2.06155i	−1.26244	−	0.728869i	−0.288892	−	0.957362i	$-0.593287\pi$
$2$	−3.57071	−	2.06155i	−1.26244	−	0.728869i	−0.973546	+	0.228493i	$0.926620\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	4.50000	+	7.79423i	0.562500	+	0.974279i
$5$		−	13.4424i		−	1.20232i	−0.799128	−	0.601161i	$-0.794705\pi$
$5$		−	13.4424i		−	1.20232i	0.799128	−	0.601161i	$-0.205295\pi$
$6$	−10.7121	+	6.18466i	−0.728869	+	0.420813i
$7$	−27.2121	+	15.7109i	−1.46932	+	0.848311i	−0.999408	−	0.0344037i	$-0.989047\pi$
$7$	−27.2121	+	15.7109i	−1.46932	+	0.848311i	−0.469910	+	0.882715i	$0.655713\pi$
$8$		−	4.12311i		−	0.182217i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−27.7121	+	47.9988i	−0.876335	+	1.51786i
$11$	−35.0707	−	20.2481i	−0.961293	−	0.555003i	−0.0647219	−	0.997903i	$-0.520616\pi$
$11$	−35.0707	−	20.2481i	−0.961293	−	0.555003i	−0.896571	+	0.442901i	$0.853949\pi$
$12$	27.0000			0.649519
$13$	42.1364	−	20.5310i	0.898965	−	0.438021i
$13$	42.1364	−	20.5310i	0.898965	−	0.438021i
$14$	129.556			2.47323
$15$	−34.9243	−	20.1635i	−0.601161	−	0.347080i
$16$	27.5000	−	47.6314i	0.429688	−	0.744241i
$17$	−21.5707	−	37.3616i	−0.307745	−	0.533030i	0.670124	−	0.742249i	$-0.266241\pi$
$17$	−21.5707	−	37.3616i	−0.307745	−	0.533030i	−0.977869	+	0.209219i	$0.932908\pi$
$18$			37.1080i			0.485913i
$19$	23.3636	−	13.4890i	0.282104	−	0.162873i	−0.352272	−	0.935898i	$-0.614591\pi$
$19$	23.3636	−	13.4890i	0.282104	−	0.162873i	0.634375	+	0.773025i	$0.281257\pi$
$20$	104.773	−	60.4906i	1.17140	−	0.676306i
$21$			94.2656i			0.979545i
$22$	83.4850	+	144.600i	0.809048	+	1.40131i
$23$	−9.50500	+	16.4631i	−0.0861709	+	0.149252i	−0.905890	−	0.423514i	$-0.860796\pi$
$23$	−9.50500	+	16.4631i	−0.0861709	+	0.149252i	0.819719	+	0.572766i	$0.194130\pi$
$24$	−10.7121	−	6.18466i	−0.0911086	−	0.0526016i
$25$	−55.6971			−0.445577
$26$	−192.783	−	13.5562i	−1.45415	−	0.102253i
$27$	−27.0000			−0.192450
$28$	−244.909	−	141.398i	−1.65298	−	0.954350i
$29$	77.0557	−	133.464i	0.493410	−	0.854611i	−0.506561	−	0.862204i	$-0.669084\pi$
$29$	77.0557	−	133.464i	0.493410	−	0.854611i	0.999971	+	0.00759297i	$0.00241694\pi$
$30$	83.1364	+	143.997i	0.505952	+	0.876335i
$31$		−	308.270i		−	1.78603i	−0.450025	−	0.893016i	$-0.648585\pi$
$31$		−	308.270i		−	1.78603i	0.450025	−	0.893016i	$-0.351415\pi$
$32$	−224.955	+	129.878i	−1.24271	+	0.717480i
$33$	−105.212	+	60.7443i	−0.555003	+	0.320431i
$34$			177.877i			0.897223i
$35$	211.192	+	365.796i	1.01994	+	1.76659i
$36$	40.5000	−	70.1481i	0.187500	−	0.324760i
$37$	−37.6821	−	21.7558i	−0.167430	−	0.0966657i	0.413944	−	0.910303i	$-0.364151\pi$
$37$	−37.6821	−	21.7558i	−0.167430	−	0.0966657i	−0.581373	+	0.813637i	$0.697484\pi$
$38$	−111.233			−0.474851
$39$	9.86357	−	140.270i	0.0404983	−	0.575928i
$40$	−55.4243			−0.219084
$41$	41.4293	+	23.9192i	0.157809	+	0.0911110i	0.576825	−	0.816868i	$-0.304292\pi$
$41$	41.4293	+	23.9192i	0.157809	+	0.0911110i	−0.419016	+	0.907979i	$0.637625\pi$
$42$	194.334	−	336.596i	0.713960	−	1.23662i
$43$	171.061	+	296.286i	0.606663	+	1.05077i	0.991786	+	0.127906i	$0.0408256\pi$
$43$	171.061	+	296.286i	0.606663	+	1.05077i	−0.385123	+	0.922865i	$0.625841\pi$
$44$		−	364.466i		−	1.24876i
$45$	−104.773	+	60.4906i	−0.347080	+	0.200387i
$46$	67.8793	−	39.1901i	0.217571	−	0.125615i
$47$			133.468i			0.414218i	0.978318	+	0.207109i	$0.0664055\pi$
$47$			133.468i			0.414218i	−0.978318	+	0.207109i	$0.933594\pi$
$48$	−82.5000	−	142.894i	−0.248080	−	0.429688i
$49$	322.167	−	558.010i	0.939263	−	1.62685i
$50$	198.879	+	114.823i	0.562514	+	0.324767i
$51$	−129.424			−0.355353
$52$	349.637	+	236.032i	0.932422	+	0.629455i
$53$	−438.454			−1.13635			−0.568173	−	0.822909i	$-0.692350\pi$
$53$	−438.454			−1.13635			−0.568173	+	0.822909i	$0.692350\pi$
$54$	96.4093	+	55.6619i	0.242956	+	0.140271i
$55$	−272.182	+	471.433i	−0.667291	+	1.15578i
$56$	64.7779	+	112.199i	0.154577	+	0.267735i
$57$		−	80.9338i		−	0.188069i
$58$	−550.288	+	317.709i	−1.24580	+	0.719262i
$59$	511.434	−	295.277i	1.12853	−	0.651555i	0.184963	−	0.982746i	$-0.440784\pi$
$59$	511.434	−	295.277i	1.12853	−	0.651555i	0.943564	+	0.331190i	$0.107450\pi$
$60$		−	362.944i		−	0.780931i
$61$	270.652	+	468.783i	0.568089	+	0.983960i	0.996755	+	0.0804965i	$0.0256506\pi$
$61$	270.652	+	468.783i	0.568089	+	0.983960i	−0.428665	+	0.903463i	$0.641016\pi$
$62$	−635.516	+	1100.75i	−1.30178	+	2.25476i
$63$	244.909	+	141.398i	0.489773	+	0.282770i
$64$	631.000			1.23242
$65$	−275.985	−	566.413i	−0.526642	−	1.08084i
$66$	500.910			0.934208
$67$	−199.485	−	115.173i	−0.363746	−	0.210009i	0.306977	−	0.951717i	$-0.400683\pi$
$67$	−199.485	−	115.173i	−0.363746	−	0.210009i	−0.670723	+	0.741708i	$0.734016\pi$
$68$	194.136	−	336.254i	0.346213	−	0.599659i
$69$	28.5150	+	49.3894i	0.0497508	+	0.0861709i
$70$		−	1741.54i		−	2.97362i
$71$	−389.202	+	224.706i	−0.650561	+	0.375601i	−0.788671	−	0.614816i	$-0.789230\pi$
$71$	−389.202	+	224.706i	−0.650561	+	0.375601i	0.138110	+	0.990417i	$0.455897\pi$
$72$	−32.1364	+	18.5540i	−0.0526016	+	0.0303695i
$73$		−	389.711i		−	0.624826i	−0.949946	−	0.312413i	$-0.898863\pi$
$73$		−	389.711i		−	0.624826i	0.949946	−	0.312413i	$-0.101137\pi$
$74$	89.7014	+	155.367i	0.140913	+	0.244069i
$75$	−83.5457	+	144.705i	−0.128627	+	0.222789i
$76$	210.272	+	121.401i	0.317367	+	0.183232i
$77$	1272.47			1.88326
$78$	−324.394	+	480.530i	−0.470903	+	0.697556i
$79$	−897.820			−1.27864			−0.639321	−	0.768940i	$-0.720784\pi$
$79$	−897.820			−1.27864			−0.639321	+	0.768940i	$0.720784\pi$
$80$	−640.279	−	369.665i	−0.894816	−	0.516623i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−98.6214	−	170.817i	−0.132816	−	0.230044i
$83$			1300.24i			1.71952i	0.510700	+	0.859759i	$0.329386\pi$
$83$			1300.24i			1.71952i	−0.510700	+	0.859759i	$0.670614\pi$
$84$	−734.728	+	424.195i	−0.954350	+	0.550994i
$85$	−502.228	+	289.961i	−0.640874	+	0.370009i
$86$		−	1410.60i		−	1.76871i
$87$	−231.167	−	400.393i	−0.284870	−	0.493410i
$88$	−83.4850	+	144.600i	−0.101131	+	0.175164i
$89$	801.113	+	462.523i	0.954132	+	0.550869i	0.894362	−	0.447344i	$-0.147630\pi$
$89$	801.113	+	462.523i	0.954132	+	0.550869i	0.0597703	+	0.998212i	$0.480963\pi$
$90$	498.819			0.584223
$91$	−824.061	+	1220.69i	−0.949287	+	1.40619i
$92$	−171.090			−0.193884
$93$	−800.910	−	462.406i	−0.893016	−	0.515583i
$94$	275.151	−	476.575i	0.301911	−	0.522925i
$95$	−181.324	−	314.062i	−0.195825	−	0.339179i
$96$			779.267i			0.828475i
$97$	1351.43	−	780.247i	1.41460	−	0.816722i	0.418787	−	0.908085i	$-0.362455\pi$
$97$	1351.43	−	780.247i	1.41460	−	0.816722i	0.995818	+	0.0913623i	$0.0291221\pi$
$98$	−2300.73	+	1328.33i	−2.37152	+	1.36920i
$99$			364.466i			0.370002i
$100$	−250.637	−	434.116i	−0.250637	−	0.434116i
$101$	479.420	−	830.380i	0.472318	−	0.818078i	−0.527181	−	0.849753i	$-0.676751\pi$
$101$	479.420	−	830.380i	0.472318	−	0.818078i	0.999498	+	0.0316752i	$0.0100842\pi$
$102$	462.137	+	266.815i	0.448612	+	0.259006i
$103$	−635.153			−0.607606			−0.303803	−	0.952735i	$-0.598257\pi$
$103$	−635.153			−0.607606			−0.303803	+	0.952735i	$0.598257\pi$
$104$	−84.6514	−	173.733i	−0.0798150	−	0.163807i
$105$	1267.15			1.17773
$106$	1565.59	+	903.897i	1.43457	+	0.828247i
$107$	724.162	−	1254.29i	0.654275	−	1.13324i	−0.327800	−	0.944747i	$-0.606307\pi$
$107$	724.162	−	1254.29i	0.654275	−	1.13324i	0.982075	−	0.188490i	$-0.0603593\pi$
$108$	−121.500	−	210.444i	−0.108253	−	0.187500i
$109$			331.084i			0.290937i	0.989363	+	0.145468i	$0.0464689\pi$
$109$			331.084i			0.290937i	−0.989363	+	0.145468i	$0.953531\pi$
$110$	1943.77	−	1122.24i	1.68483	−	0.972736i
$111$	−113.046	+	65.2674i	−0.0966657	+	0.0558100i
$112$			1728.20i			1.45803i
$113$	−347.602	−	602.065i	−0.289378	−	0.501217i	0.684284	−	0.729216i	$-0.260115\pi$
$113$	−347.602	−	602.065i	−0.289378	−	0.501217i	−0.973661	+	0.227999i	$0.926782\pi$
$114$	−166.849	+	288.991i	−0.137078	+	0.237426i
$115$	221.304	+	127.770i	0.179449	+	0.103605i
$116$	1387.00			1.11017
$117$	−349.637	−	236.032i	−0.276273	−	0.186505i
$118$	−2434.91			−1.89959
$119$	1173.97	+	677.792i	0.904351	+	0.522127i
$120$	−83.1364	+	143.997i	−0.0632440	+	0.109542i
$121$	154.470	+	267.550i	0.116056	+	0.201014i
$122$		−	2231.85i		−	1.65625i
$123$	124.288	−	71.7576i	0.0911110	−	0.0526030i
$124$	2402.73	−	1387.22i	1.74009	−	1.00464i
$125$		−	931.594i		−	0.666595i
$126$	−583.001	−	1009.79i	−0.412205	−	0.713960i
$127$	123.577	−	214.042i	0.0863441	−	0.149552i	−0.819619	−	0.572909i	$-0.805815\pi$
$127$	123.577	−	214.042i	0.0863441	−	0.149552i	0.905963	+	0.423357i	$0.139148\pi$
$128$	−453.481	−	261.817i	−0.313144	−	0.180794i
$129$	1026.36			0.700514
$130$	−182.227	+	2591.46i	−0.122941	+	1.74835i
$131$	472.243			0.314962			0.157481	−	0.987522i	$-0.449663\pi$
$131$	472.243			0.314962			0.157481	+	0.987522i	$0.449663\pi$
$132$	−946.909	−	546.698i	−0.624378	−	0.360485i
$133$	−423.849	+	734.127i	−0.276333	+	0.478623i
$134$	474.869	+	822.498i	0.306138	+	0.530246i
$135$			362.944i			0.231387i
$136$	−154.046	+	88.9383i	−0.0971273	+	0.0560765i
$137$	−1585.43	+	915.349i	−0.988704	+	0.570829i	−0.904887	−	0.425652i	$-0.860045\pi$
$137$	−1585.43	+	915.349i	−0.988704	+	0.570829i	−0.0838175	+	0.996481i	$0.526711\pi$
$138$		−	235.141i		−	0.145047i
$139$	50.0000	+	86.6025i	0.0305104	+	0.0528456i	0.880877	−	0.473344i	$-0.156953\pi$
$139$	50.0000	+	86.6025i	0.0305104	+	0.0528456i	−0.850367	+	0.526190i	$0.823620\pi$
$140$	−1900.73	+	3292.16i	−1.14744	+	1.98742i
$141$	346.759	+	200.202i	0.207109	+	0.119575i
$142$	1852.97			1.09506
$143$	−1893.47	−	133.146i	−1.10727	−	0.0778615i
$144$	−495.000			−0.286458
$145$	−1794.08	−	1035.81i	−1.02752	−	0.593237i
$146$	−803.411	+	1391.55i	−0.455416	+	0.788804i
$147$	−966.501	−	1674.03i	−0.542284	−	0.939263i
$148$		−	391.604i		−	0.217498i
$149$	−129.520	+	74.7784i	−0.0712127	+	0.0411147i	−0.535184	−	0.844736i	$-0.679758\pi$
$149$	−129.520	+	74.7784i	−0.0712127	+	0.0411147i	0.463971	+	0.885850i	$0.346424\pi$
$150$	596.636	−	344.468i	0.324767	−	0.187505i
$151$		−	800.032i		−	0.431163i	−0.976486	−	0.215582i	$-0.930835\pi$
$151$		−	800.032i		−	0.431163i	0.976486	−	0.215582i	$-0.0691647\pi$
$152$	−55.6164	−	96.3305i	−0.0296782	−	0.0514042i
$153$	−194.136	+	336.254i	−0.102582	+	0.177677i
$154$	−4543.61	−	2623.26i	−2.37750	−	1.37265i
$155$	−4143.88			−2.14739
$156$	1137.68	−	554.337i	0.583895	−	0.284503i
$157$	−2706.16			−1.37564			−0.687818	−	0.725884i	$-0.741431\pi$
$157$	−2706.16			−1.37564			−0.687818	+	0.725884i	$0.741431\pi$
$158$	3205.86	+	1850.90i	1.61421	+	0.931962i
$159$	−657.681	+	1139.14i	−0.328035	+	0.568173i
$160$	1745.86	+	3023.93i	0.862642	+	1.49414i
$161$		−	597.330i		−	0.292399i
$162$	289.228	−	166.986i	0.140271	−	0.0809854i
$163$	3185.46	−	1839.12i	1.53070	−	0.883750i	0.531371	−	0.847139i	$-0.321677\pi$
$163$	3185.46	−	1839.12i	1.53070	−	0.883750i	0.999330	−	0.0366108i	$-0.0116562\pi$
$164$			430.546i			0.205000i
$165$	816.546	+	1414.30i	0.385261	+	0.667291i
$166$	2680.52	−	4642.79i	1.25330	−	2.17079i
$167$	2791.30	+	1611.56i	1.29339	+	0.746742i	0.979254	−	0.202635i	$-0.0649504\pi$
$167$	2791.30	+	1611.56i	1.29339	+	0.746742i	0.314140	+	0.949377i	$0.398284\pi$
$168$	388.667			0.178490
$169$	1353.96	−	1730.20i	0.616275	−	0.787531i
$170$	2391.08			1.07875
$171$	−210.272	−	121.401i	−0.0940346	−	0.0542909i
$172$	−1539.55	+	2666.57i	−0.682496	+	1.18212i
$173$	−1344.77	−	2329.21i	−0.590988	−	1.02362i	−0.994100	−	0.108471i	$-0.965405\pi$
$173$	−1344.77	−	2329.21i	−0.590988	−	1.02362i	0.403111	−	0.915151i	$-0.367929\pi$
$174$			1906.25i			0.830533i
$175$	1515.64	−	875.054i	0.654694	−	0.377988i
$176$	−1928.89	+	1113.64i	−0.826111	+	0.476955i
$177$		−	1771.66i		−	0.752351i
$178$	−1907.03	−	3303.07i	−0.803022	−	1.39088i
$179$	−762.021	+	1319.86i	−0.318191	+	0.551122i	−0.980111	−	0.198452i	$-0.936409\pi$
$179$	−762.021	+	1319.86i	−0.318191	+	0.551122i	0.661920	+	0.749574i	$0.269742\pi$
$180$	−942.956	−	544.416i	−0.390465	−	0.225435i
$181$	−476.881			−0.195836			−0.0979180	−	0.995194i	$-0.531218\pi$
$181$	−476.881			−0.195836			−0.0979180	+	0.995194i	$0.531218\pi$
$182$	5459.01	−	2659.91i	2.22335	−	1.08333i
$183$	1623.91			0.655973
$184$	67.8793	+	39.1901i	0.0271963	+	0.0157018i
$185$	−292.449	+	506.537i	−0.116223	+	0.201305i
$186$	1906.55	+	3302.24i	0.751585	+	1.30178i
$187$			1747.06i			0.683197i
$188$	−1040.28	+	600.605i	−0.403564	+	0.232998i
$189$	734.728	−	424.195i	0.282770	−	0.163258i
$190$			1495.23i			0.570924i
$191$	684.871	+	1186.23i	0.259453	+	0.449386i	0.966096	−	0.258185i	$-0.0831243\pi$
$191$	684.871	+	1186.23i	0.259453	+	0.449386i	−0.706642	+	0.707571i	$0.749791\pi$
$192$	946.500	−	1639.39i	0.355770	−	0.616211i
$193$	1857.38	+	1072.36i	0.692732	+	0.399949i	0.804635	−	0.593770i	$-0.202361\pi$
$193$	1857.38	+	1072.36i	0.692732	+	0.399949i	−0.111903	+	0.993719i	$0.535695\pi$
$194$	−6434.08			−2.38113
$195$	−1885.56	−	132.590i	−0.692451	−	0.0486920i
$196$	5799.01			2.11334
$197$	−207.620	−	119.869i	−0.0750879	−	0.0433520i	0.461986	−	0.886887i	$-0.347137\pi$
$197$	−207.620	−	119.869i	−0.0750879	−	0.0433520i	−0.537074	+	0.843535i	$0.680470\pi$
$198$	751.365	−	1301.40i	0.269683	−	0.467104i
$199$	−794.969	−	1376.93i	−0.283185	−	0.490491i	0.688982	−	0.724778i	$-0.258058\pi$
$199$	−794.969	−	1376.93i	−0.283185	−	0.490491i	−0.972167	+	0.234287i	$0.924724\pi$
$200$			229.645i			0.0811918i
$201$	−598.455	+	345.518i	−0.210009	+	0.121249i
$202$	−3423.74	+	1976.70i	−1.19254	+	0.688515i
$203$			4842.47i			1.67426i
$204$	−582.409	−	1008.76i	−0.199886	−	0.346213i
$205$	321.531	−	556.908i	0.109545	−	0.189737i
$206$	2267.95	+	1309.40i	0.767066	+	0.442866i
$207$	171.090			0.0574472
$208$	180.832	−	2571.62i	0.0602810	−	0.857258i
$209$	−1092.50			−0.361579
$210$	−4524.64	−	2612.30i	−1.48681	−	0.858410i
$211$	936.427	−	1621.94i	0.305527	−	0.529189i	−0.671851	−	0.740686i	$-0.734501\pi$
$211$	936.427	−	1621.94i	0.305527	−	0.529189i	0.977379	+	0.211497i	$0.0678339\pi$
$212$	−1973.04	−	3417.41i	−0.639195	−	1.10712i
$213$			1348.24i			0.433707i
$214$	−5171.55	+	2985.80i	−1.65196	+	0.953761i
$215$	3982.78	−	2299.46i	1.26337	−	0.729404i
$216$			111.324i			0.0350677i
$217$	4843.22	+	8388.70i	1.51511	+	2.62425i
$218$	682.547	−	1182.21i	0.212055	−	0.367290i
$219$	−1012.50	−	584.567i	−0.312413	−	0.180372i
$220$	−4899.28			−1.50141
$221$	−1675.98	−	1131.42i	−0.510130	−	0.344377i
$222$	538.209			0.162713
$223$	−48.6085	−	28.0642i	−0.0145967	−	0.00842742i	0.492684	−	0.870208i	$-0.336016\pi$
$223$	−48.6085	−	28.0642i	−0.0145967	−	0.00842742i	−0.507281	+	0.861781i	$0.669349\pi$
$224$	4081.00	−	7068.51i	1.21729	−	2.10841i
$225$	250.637	+	434.116i	0.0742629	+	0.128627i
$226$			2866.40i			0.843673i
$227$	577.976	−	333.695i	0.168994	−	0.0975687i	−0.413117	−	0.910678i	$-0.635560\pi$
$227$	577.976	−	333.695i	0.168994	−	0.0975687i	0.582111	+	0.813109i	$0.302227\pi$
$228$	630.816	−	364.202i	0.183232	−	0.105789i
$229$			723.299i			0.208720i	0.994540	+	0.104360i	$0.0332795\pi$
$229$			723.299i			0.208720i	−0.994540	+	0.104360i	$0.966721\pi$
$230$	−526.808	−	912.458i	−0.151029	−	0.261590i
$231$	1908.70	−	3305.96i	0.543650	−	0.941629i
$232$	−550.288	−	317.709i	−0.155725	−	0.0899078i
$233$	275.451			0.0774482			0.0387241	−	0.999250i	$-0.487671\pi$
$233$	275.451			0.0774482			0.0387241	+	0.999250i	$0.487671\pi$
$234$	761.863	+	1563.60i	0.212840	+	0.436818i
$235$	1794.12			0.498024
$236$	4602.91	+	2657.49i	1.26959	+	0.733000i
$237$	−1346.73	+	2332.60i	−0.369112	+	0.639321i
$238$	−2794.61	−	4840.41i	−0.761124	−	1.31831i
$239$			1529.39i			0.413925i	0.978349	+	0.206963i	$0.0663579\pi$
$239$			1529.39i			0.413925i	−0.978349	+	0.206963i	$0.933642\pi$
$240$	−1920.84	+	1109.00i	−0.516623	+	0.298272i
$241$	844.830	−	487.763i	0.225810	−	0.130372i	−0.382827	−	0.923820i	$-0.625050\pi$
$241$	844.830	−	487.763i	0.225810	−	0.130372i	0.608638	+	0.793448i	$0.291716\pi$
$242$		−	1273.79i		−	0.338357i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−2435.87	+	4219.05i	−0.639101	+	1.10695i
$245$	−7500.97	−	4330.69i	−1.95600	−	1.12930i
$246$	−591.729			−0.153363
$247$	707.516	−	1048.05i	0.182260	−	0.269984i
$248$	−1271.03			−0.325446
$249$	3378.13	+	1950.36i	0.859759	+	0.496382i
$250$	−1920.53	+	3326.46i	−0.485860	+	0.841534i
$251$	−937.070	−	1623.05i	−0.235647	−	0.408152i	0.723814	−	0.689995i	$-0.242387\pi$
$251$	−937.070	−	1623.05i	−0.235647	−	0.408152i	−0.959460	+	0.281843i	$0.909054\pi$
$252$			2545.17i			0.636233i
$253$	666.694	−	384.916i	0.165671	−	0.0956501i
$254$	−882.517	+	509.522i	−0.218008	+	0.125867i
$255$			1739.77i			0.427249i
$256$	−1444.50	−	2501.95i	−0.352661	−	0.610827i
$257$	−909.094	+	1574.60i	−0.220653	+	0.382181i	−0.955006	−	0.296586i	$-0.904152\pi$
$257$	−909.094	+	1574.60i	−0.220653	+	0.382181i	0.734354	+	0.678767i	$0.237485\pi$
$258$	−3664.85	−	2115.90i	−0.884356	−	0.510583i
$259$	1367.22			0.328010
$260$	3172.82	−	4699.95i	0.756808	−	1.12107i
$261$	−1387.00			−0.328940
$262$	−1686.24	−	973.554i	−0.397620	−	0.229566i
$263$	−336.899	+	583.527i	−0.0789890	+	0.136813i	−0.902814	−	0.430031i	$-0.858503\pi$
$263$	−336.899	+	583.527i	−0.0789890	+	0.136813i	0.823825	+	0.566844i	$0.191836\pi$
$264$	250.455	+	433.801i	0.0583880	+	0.101131i
$265$			5893.86i			1.36625i
$266$	3026.88	−	1747.57i	0.697707	−	0.402822i
$267$	2403.34	−	1387.57i	0.550869	−	0.318044i
$268$		−	2073.11i		−	0.472520i
$269$	1678.20	+	2906.73i	0.380378	+	0.658834i	0.991116	−	0.132998i	$-0.0424605\pi$
$269$	1678.20	+	2906.73i	0.380378	+	0.658834i	−0.610738	+	0.791833i	$0.709127\pi$
$270$	748.228	−	1295.97i	0.168651	−	0.292112i
$271$	−7721.09	−	4457.77i	−1.73071	−	0.999227i	−0.885013	−	0.465567i	$-0.845850\pi$
$271$	−7721.09	−	4457.77i	−1.73071	−	0.999227i	−0.845699	−	0.533660i	$-0.820816\pi$
$272$	−2372.78			−0.528937
$273$	1935.37	+	3972.02i	0.429061	+	0.880577i
$274$	7548.16			1.66424
$275$	1953.34	+	1127.76i	0.428330	+	0.247296i
$276$	−256.635	+	444.505i	−0.0559696	+	0.0969422i
$277$	2008.65	+	3479.09i	0.435698	+	0.754651i	0.997352	−	0.0727208i	$-0.0231682\pi$
$277$	2008.65	+	3479.09i	0.435698	+	0.754651i	−0.561654	+	0.827372i	$0.689835\pi$
$278$		−	412.311i		−	0.0889523i
$279$	−2402.73	+	1387.22i	−0.515583	+	0.297672i
$280$	1508.21	−	870.768i	0.321904	−	0.185851i
$281$			1841.12i			0.390860i	0.980718	+	0.195430i	$0.0626103\pi$
$281$			1841.12i			0.390860i	−0.980718	+	0.195430i	$0.937390\pi$
$282$	−825.452	−	1429.73i	−0.174308	−	0.301911i
$283$	2424.70	−	4199.70i	0.509305	−	0.882143i	−0.490637	−	0.871364i	$-0.663236\pi$
$283$	2424.70	−	4199.70i	0.509305	−	0.882143i	0.999942	−	0.0107784i	$-0.00343094\pi$
$284$	−3502.82	−	2022.35i	−0.731881	−	0.422551i
$285$	−1087.94			−0.226120
$286$	6486.55	+	4378.91i	1.34111	+	0.905351i
$287$	−1503.17			−0.309162
$288$	2024.59	+	1168.90i	0.414238	+	0.239160i
$289$	1525.91	−	2642.95i	0.310586	−	0.537951i
$290$	4270.76	+	7397.17i	0.864785	+	1.49785i
$291$		−	4681.48i		−	0.943070i
$292$	3037.50	−	1753.70i	0.608754	−	0.351464i
$293$	−1224.43	+	706.927i	−0.244137	+	0.140953i	−0.617077	−	0.786903i	$-0.711683\pi$
$293$	−1224.43	+	706.927i	−0.244137	+	0.140953i	0.372940	+	0.927856i	$0.378350\pi$
$294$			7969.97i			1.58101i
$295$	−3969.22	−	6874.89i	−0.783379	−	1.35685i
$296$	−89.7014	+	155.367i	−0.0176142	+	0.0305086i
$297$	946.909	+	546.698i	0.185001	+	0.106810i
$298$	616.639			0.119869
$299$	−62.5022	+	888.845i	−0.0120889	+	0.171917i
$300$	−1503.82			−0.289411
$301$	−9309.86	−	5375.05i	−1.78276	−	1.02928i
$302$	−1649.31	+	2856.68i	−0.314262	+	0.544317i
$303$	−1438.26	−	2491.14i	−0.272693	−	0.472318i
$304$		−	1483.79i		−	0.279937i
$305$	6301.55	−	3638.20i	1.18304	−	0.683026i
$306$	1386.41	−	800.445i	0.259006	−	0.149537i
$307$		−	4625.64i		−	0.859932i	−0.902845	−	0.429966i	$-0.858526\pi$
$307$		−	4625.64i		−	0.859932i	0.902845	−	0.429966i	$-0.141474\pi$
$308$	5726.10	+	9917.89i	1.05933	+	1.83482i
$309$	−952.729	+	1650.18i	−0.175401	+	0.303803i
$310$	14796.6	+	8542.83i	2.71094	+	1.56516i
$311$	6060.79			1.10507			0.552534	−	0.833490i	$-0.313661\pi$
$311$	6060.79			1.10507			0.552534	+	0.833490i	$0.313661\pi$
$312$	−578.349	−	40.6685i	−0.104944	−	0.00737950i
$313$	969.946			0.175158			0.0875792	−	0.996158i	$-0.472087\pi$
$313$	969.946			0.175158			0.0875792	+	0.996158i	$0.472087\pi$
$314$	9662.91	+	5578.88i	1.73665	+	1.00266i
$315$	1900.73	−	3292.16i	0.339981	−	0.588864i
$316$	−4040.19	−	6997.81i	−0.719236	−	1.24575i
$317$		−	8741.63i		−	1.54883i	−0.632679	−	0.774414i	$-0.718045\pi$
$317$		−	8741.63i		−	1.54883i	0.632679	−	0.774414i	$-0.281955\pi$
$318$	4696.78	−	2711.69i	0.828247	−	0.478189i
$319$	−5404.80	+	3120.46i	−0.948623	+	0.547687i
$320$		−	8482.13i		−	1.48177i
$321$	−2172.49	−	3762.86i	−0.377746	−	0.654275i
$322$	−1231.43	+	2132.89i	−0.213120	+	0.369135i
$323$	−1007.94	−	581.933i	−0.173632	−	0.100247i
$324$	−729.000			−0.125000
$325$	−2346.88	+	1143.52i	−0.400558	+	0.195172i
$326$	−15165.8			−2.57655
$327$	860.181	+	496.626i	0.145468	+	0.0839862i
$328$	98.6214	−	170.817i	0.0166020	−	0.0287555i
$329$	−2096.90	−	3631.94i	−0.351386	−	0.608618i
$330$		−	6733.41i		−	1.12322i
$331$	−6051.57	+	3493.88i	−1.00491	+	0.580184i	−0.909697	−	0.415273i	$-0.863686\pi$
$331$	−6051.57	+	3493.88i	−1.00491	+	0.580184i	−0.0952114	+	0.995457i	$0.530353\pi$
$332$	−10134.4	+	5851.09i	−1.67529	+	0.967229i
$333$			391.604i			0.0644438i
$334$	−6644.61	−	11508.8i	−1.08855	−	1.88543i
$335$	−1548.19	+	2681.55i	−0.252498	+	0.437339i
$336$	4490.00	+	2592.30i	0.729017	+	0.420898i
$337$	4156.59			0.671881			0.335940	−	0.941883i	$-0.390946\pi$
$337$	4156.59			0.671881			0.335940	+	0.941883i	$0.390946\pi$
$338$	−8401.50	+	3386.81i	−1.35202	+	0.545025i
$339$	−2085.61			−0.334144
$340$	−4520.05	−	2609.65i	−0.720983	−	0.416260i
$341$	−6241.89	+	10811.3i	−0.991252	+	1.71690i
$342$	500.548	+	866.974i	0.0791419	+	0.137078i
$343$			9468.49i			1.49053i
$344$	1221.62	−	705.301i	0.191469	−	0.110544i
$345$	663.911	−	383.309i	0.103605	−	0.0598164i
$346$			11089.3i			1.72301i
$347$	156.256	+	270.644i	0.0241737	+	0.0418701i	0.877859	−	0.478919i	$-0.158971\pi$
$347$	156.256	+	270.644i	0.0241737	+	0.0418701i	−0.853685	+	0.520789i	$0.825638\pi$
$348$	2080.50	−	3603.54i	0.320479	−	0.555086i
$349$	3861.39	+	2229.37i	0.592251	+	0.341936i	0.765987	−	0.642856i	$-0.222251\pi$
$349$	3861.39	+	2229.37i	0.592251	+	0.341936i	−0.173736	+	0.984792i	$0.555584\pi$
$350$	−7215.88			−1.10201
$351$	−1137.68	+	554.337i	−0.173006	+	0.0842972i
$352$	10519.1			1.59281
$353$	−1947.84	−	1124.59i	−0.293692	−	0.169563i	0.345914	−	0.938266i	$-0.387569\pi$
$353$	−1947.84	−	1124.59i	−0.293692	−	0.169563i	−0.639605	+	0.768703i	$0.720902\pi$
$354$	−3652.37	+	6326.09i	−0.548365	+	0.949797i
$355$	3020.58	+	5231.80i	0.451594	+	0.782183i
$356$			8325.41i			1.23945i
$357$	3521.91	−	2033.38i	0.522127	−	0.301450i
$358$	5441.92	−	3141.89i	0.803392	−	0.463838i
$359$		−	7842.79i		−	1.15300i	−0.817098	−	0.576499i	$-0.804418\pi$
$359$		−	7842.79i		−	1.15300i	0.817098	−	0.576499i	$-0.195582\pi$
$360$	249.409	+	431.990i	0.0365140	+	0.0632440i
$361$	−3065.60	+	5309.77i	−0.446945	+	0.774131i
$362$	1702.81	+	983.116i	0.247231	+	0.142739i
$363$	926.820			0.134009
$364$	−13222.7	−	929.796i	−1.90400	−	0.133886i
$365$	−5238.64			−0.751241
$366$	−5798.53	−	3347.78i	−0.828126	−	0.478118i
$367$	−3330.12	+	5767.94i	−0.473653	+	0.820392i	−0.999545	−	0.0301597i	$-0.990398\pi$
$367$	−3330.12	+	5767.94i	−0.473653	+	0.820392i	0.525892	+	0.850552i	$0.323732\pi$
$368$	522.775	+	905.473i	0.0740531	+	0.128264i
$369$		−	430.546i		−	0.0607407i
$370$	2088.51	−	1205.80i	0.293449	−	0.169423i
$371$	11931.3	−	6888.53i	1.66965	−	0.963975i
$372$		−	8323.30i		−	1.16006i
$373$	18.4936	+	32.0319i	0.00256720	+	0.00444651i	0.867306	−	0.497775i	$-0.165850\pi$
$373$	18.4936	+	32.0319i	0.00256720	+	0.00444651i	−0.864739	+	0.502222i	$0.832516\pi$
$374$	3601.66	−	6238.26i	0.497961	−	0.862494i
$375$	−2420.35	−	1397.39i	−0.333297	−	0.192429i
$376$	550.301			0.0754777
$377$	506.696	−	7205.74i	0.0692207	−	0.984389i
$378$	−3498.00			−0.475973
$379$	10461.5	+	6039.93i	1.41786	+	0.818603i	0.996111	−	0.0881092i	$-0.0280825\pi$
$379$	10461.5	+	6039.93i	1.41786	+	0.818603i	0.421751	+	0.906712i	$0.361416\pi$
$380$	1631.91	−	2826.55i	0.220303	−	0.381577i
$381$	−370.731	−	642.126i	−0.0498508	−	0.0863441i
$382$		−	5647.59i		−	0.756429i
$383$	9151.63	−	5283.69i	1.22096	−	0.704919i	0.255835	−	0.966721i	$-0.417650\pi$
$383$	9151.63	−	5283.69i	1.22096	−	0.704919i	0.965122	+	0.261801i	$0.0843164\pi$
$384$	−1360.44	+	785.452i	−0.180794	+	0.104381i
$385$		−	17104.9i		−	2.26428i
$386$	−4421.45	−	7658.18i	−0.583021	−	1.00982i
$387$	1539.55	−	2666.57i	0.202221	−	0.350257i
$388$	12162.8	+	7022.22i	1.59143	+	0.918813i
$389$	9757.49			1.27179			0.635893	−	0.771778i	$-0.280632\pi$
$389$	9757.49			1.27179			0.635893	+	0.771778i	$0.280632\pi$
$390$	6459.46	+	4360.63i	0.838686	+	0.566177i
$391$	820.119			0.106075
$392$	−2300.73	−	1328.33i	−0.296440	−	0.171150i
$393$	708.364	−	1226.92i	0.0909218	−	0.157481i
$394$	494.234	+	856.039i	0.0631959	+	0.109458i
$395$			12068.8i			1.53734i
$396$	−2840.73	+	1640.09i	−0.360485	+	0.208126i
$397$	−12298.0	+	7100.26i	−1.55471	+	0.897612i	−0.556962	+	0.830538i	$0.688033\pi$
$397$	−12298.0	+	7100.26i	−1.55471	+	0.897612i	−0.997748	+	0.0670737i	$0.978634\pi$
$398$			6555.48i			0.825620i
$399$	1271.55	+	2202.38i	0.159541	+	0.276333i
$400$	−1531.67	+	2652.93i	−0.191459	+	0.331617i
$401$	10978.1	+	6338.19i	1.36713	+	0.789313i	0.990561	−	0.137076i	$-0.0437705\pi$
$401$	10978.1	+	6338.19i	1.36713	+	0.789313i	0.376569	+	0.926389i	$0.377104\pi$
$402$	2849.22			0.353497
$403$	−6329.10	−	12989.4i	−0.782319	−	1.60558i
$404$	8629.56			1.06271
$405$	942.956	+	544.416i	0.115693	+	0.0667956i
$406$	9983.01	−	17291.1i	1.22032	−	2.11365i
$407$	881.026	+	1525.98i	0.107299	+	0.185848i
$408$			533.630i			0.0647515i
$409$	−1328.20	+	766.838i	−0.160576	+	0.0927083i	−0.578134	−	0.815942i	$-0.696219\pi$
$409$	−1328.20	+	766.838i	−0.160576	+	0.0927083i	0.417559	+	0.908650i	$0.362886\pi$
$410$	−2296.19	+	1325.71i	−0.276587	+	0.159688i
$411$			5492.09i			0.659136i
$412$	−2858.19	−	4950.53i	−0.341779	−	0.591978i
$413$	−9278.15	+	16070.2i	−1.10544	+	1.91468i
$414$	−610.914	−	352.711i	−0.0725236	−	0.0418715i
$415$	17478.3			2.06741
$416$	−6812.28	+	10091.1i	−0.802883	+	1.18932i
$417$	300.000			0.0352304
$418$	3901.02	+	2252.25i	0.456471	+	0.263544i
$419$	1082.95	−	1875.72i	0.126266	−	0.218699i	−0.795961	−	0.605348i	$-0.793034\pi$
$419$	1082.95	−	1875.72i	0.126266	−	0.218699i	0.922227	+	0.386649i	$0.126367\pi$
$420$	5702.19	+	9876.48i	0.662472	+	1.14744i
$421$		−	734.575i		−	0.0850380i	−0.999096	−	0.0425190i	$-0.986462\pi$
$421$		−	734.575i		−	0.0850380i	0.999096	−	0.0425190i	$-0.0135383\pi$
$422$	−6687.43	+	3860.99i	−0.771419	+	0.445379i
$423$	1040.28	−	600.605i	0.119575	−	0.0690364i
$424$			1807.79i			0.207062i
$425$	1201.43	+	2080.93i	0.137124	+	0.237506i
$426$	2779.46	−	4814.16i	0.316116	−	0.547528i
$427$	−14730.0	−	8504.40i	−1.66941	−	0.963833i
$428$	13034.9			1.47212
$429$	−3186.12	+	4719.66i	−0.358572	+	0.531159i
$430$	−18961.8			−2.12656
$431$	−11872.6	−	6854.66i	−1.32688	−	0.766073i	−0.342061	−	0.939678i	$-0.611125\pi$
$431$	−11872.6	−	6854.66i	−1.32688	−	0.766073i	−0.984815	+	0.173605i	$0.944458\pi$
$432$	−742.500	+	1286.05i	−0.0826934	+	0.143229i
$433$	5024.97	+	8703.50i	0.557701	+	0.965967i	0.997688	+	0.0679624i	$0.0216498\pi$
$433$	5024.97	+	8703.50i	0.557701	+	0.965967i	−0.439987	+	0.898004i	$0.645017\pi$
$434$		−	39938.2i		−	4.41727i
$435$	−5382.23	+	3107.43i	−0.593237	+	0.342506i
$436$	−2580.54	+	1489.88i	−0.283453	+	0.163652i
$437$			512.850i			0.0561395i
$438$	2410.23	+	4174.64i	0.262935	+	0.455416i
$439$	−4066.73	+	7043.79i	−0.442129	+	0.765790i	−0.997847	−	0.0655807i	$-0.979110\pi$
$439$	−4066.73	+	7043.79i	−0.442129	+	0.765790i	0.555718	+	0.831371i	$0.312443\pi$
$440$	1943.77	+	1122.24i	0.210604	+	0.121592i
$441$	−5799.01			−0.626175
$442$	3651.98	+	7495.09i	0.393003	+	0.806572i
$443$	−2370.78			−0.254264			−0.127132	−	0.991886i	$-0.540577\pi$
$443$	−2370.78			−0.254264			−0.127132	+	0.991886i	$0.540577\pi$
$444$	−1017.42	−	587.406i	−0.108749	−	0.0627862i
$445$	6217.40	−	10768.9i	0.662321	−	1.14717i
$446$	115.711	+	200.418i	0.0122850	+	0.0212782i
$447$			448.670i			0.0474751i
$448$	−17170.9	+	9913.60i	−1.81082	+	1.04548i
$449$	11191.8	−	6461.60i	1.17634	−	0.679158i	0.221172	−	0.975235i	$-0.429012\pi$
$449$	11191.8	−	6461.60i	1.17634	−	0.679158i	0.955164	+	0.296077i	$0.0956785\pi$
$450$		−	2066.81i		−	0.216512i
$451$	−968.636	−	1677.73i	−0.101134	−	0.175169i
$452$	3128.42	−	5418.58i	0.325550	−	0.563869i
$453$	−2078.54	−	1200.05i	−0.215582	−	0.124466i
$454$	−2751.72			−0.284459
$455$	16409.0	+	11077.3i	1.69070	+	1.14135i
$456$	−333.699			−0.0342694
$457$	7275.71	+	4200.63i	0.744734	+	0.429972i	0.823788	−	0.566898i	$-0.191857\pi$
$457$	7275.71	+	4200.63i	0.744734	+	0.429972i	−0.0790543	+	0.996870i	$0.525190\pi$
$458$	1491.12	−	2582.70i	0.152130	−	0.263497i
$459$	582.409	+	1008.76i	0.0592256	+	0.102582i
$460$			2299.85i			0.233111i
$461$	−15265.7	+	8813.67i	−1.54229	+	0.890441i	−0.543596	+	0.839347i	$0.682937\pi$
$461$	−15265.7	+	8813.67i	−1.54229	+	0.890441i	−0.998694	+	0.0510940i	$0.983729\pi$
$462$	−13630.8	+	7869.77i	−1.37265	+	0.792499i
$463$		−	5461.81i		−	0.548233i	−0.961697	−	0.274116i	$-0.911615\pi$
$463$		−	5461.81i		−	0.548233i	0.961697	−	0.274116i	$-0.0883853\pi$
$464$	−4238.06	−	7340.54i	−0.424024	−	0.734431i
$465$	−6215.82	+	10766.1i	−0.619897	+	1.07369i
$466$	−983.558	−	567.858i	−0.0977735	−	0.0564496i
$467$	−8262.19			−0.818691			−0.409345	−	0.912379i	$-0.634243\pi$
$467$	−8262.19			−0.818691			−0.409345	+	0.912379i	$0.634243\pi$
$468$	266.316	−	3787.29i	0.0263044	−	0.374076i
$469$	7237.89			0.712611
$470$	−6406.29	−	3698.68i	−0.628724	−	0.362994i
$471$	−4059.23	+	7030.80i	−0.397112	+	0.687818i
$472$	−1217.46	−	2108.70i	−0.118725	−	0.205637i
$473$		−	13854.6i		−	1.34680i
$474$	9617.58	−	5552.71i	0.931962	−	0.538068i
$475$	−1301.28	+	751.297i	−0.125699	+	0.0725723i
$476$			12200.3i			1.17479i
$477$	1973.04	+	3417.41i	0.189391	+	0.328035i
$478$	3152.92	−	5461.02i	0.301697	−	0.522555i
$479$	1364.74	+	787.935i	0.130181	+	0.0751601i	0.563676	−	0.825996i	$-0.309387\pi$
$479$	1364.74	+	787.935i	0.130181	+	0.0751601i	−0.433495	+	0.901156i	$0.642720\pi$
$480$	10475.2			0.996093
$481$	−2034.46	−	143.060i	−0.192855	−	0.0135613i
$482$	−4022.20			−0.380095
$483$	−1551.91	−	895.995i	−0.146199	−	0.0844082i
$484$	−1390.23	+	2407.95i	−0.130563	+	0.226141i
$485$	−10488.4	−	18166.4i	−0.981963	−	1.70081i
$486$		−	1001.91i		−	0.0935139i
$487$	10908.2	−	6297.84i	1.01498	−	0.586001i	0.102337	−	0.994750i	$-0.467368\pi$
$487$	10908.2	−	6297.84i	1.01498	−	0.586001i	0.912647	+	0.408749i	$0.134035\pi$
$488$	1932.84	−	1115.93i	0.179294	−	0.103516i
$489$		−	11034.7i		−	1.02047i
$490$	17855.9	+	30927.3i	1.64622	+	2.85133i
$491$	−535.606	+	927.697i	−0.0492293	+	0.0852676i	−0.889590	−	0.456760i	$-0.849010\pi$
$491$	−535.606	+	927.697i	−0.0492293	+	0.0852676i	0.840361	+	0.542028i	$0.182343\pi$
$492$	1118.59	+	645.819i	0.102500	+	0.0591784i
$493$	−6648.59			−0.607378
$494$	−4686.96	+	2283.72i	−0.426875	+	0.207995i
$495$	4899.28			0.444861
$496$	−14683.3	−	8477.44i	−1.32924	−	0.767436i
$497$	7060.68	−	12229.5i	0.637253	−	1.10376i
$498$	−8041.55	−	13928.4i	−0.723595	−	1.25330i
$499$			1422.30i			0.127597i	0.997963	+	0.0637985i	$0.0203215\pi$
$499$			1422.30i			0.127597i	−0.997963	+	0.0637985i	$0.979678\pi$
$500$	7261.06	−	4192.17i	0.649449	−	0.374959i
$501$	8373.89	−	4834.67i	0.746742	−	0.431132i
$502$			7727.28i			0.687022i
$503$	4674.67	+	8096.76i	0.414380	+	0.717727i	0.995363	−	0.0961884i	$-0.0306651\pi$
$503$	4674.67	+	8096.76i	0.414380	+	0.717727i	−0.580983	+	0.813916i	$0.697332\pi$
$504$	583.001	−	1009.79i	0.0515256	−	0.0892450i
$505$	−11162.3	−	6444.54i	−0.983593	−	0.567878i
$506$	−3174.10			−0.278866
$507$	−2464.27	−	6112.99i	−0.215862	−	0.535478i
$508$	2224.39			0.194274
$509$	11896.0	+	6868.15i	1.03591	+	0.598086i	0.918673	−	0.395018i	$-0.129262\pi$
$509$	11896.0	+	6868.15i	1.03591	+	0.598086i	0.117241	+	0.993103i	$0.462595\pi$
$510$	3586.62	−	6212.22i	0.311409	−	0.539376i
$511$	6122.73	+	10604.9i	0.530046	+	0.918067i
$512$			16100.7i			1.38976i
$513$	−630.816	+	364.202i	−0.0542909	+	0.0313449i
$514$	6492.23	−	3748.29i	0.557120	−	0.321654i
$515$			8537.96i			0.730538i
$516$	4618.64	+	7999.72i	0.394039	+	0.682496i
$517$	2702.47	−	4680.81i	0.229892	−	0.398185i
$518$	−4881.94	−	2818.59i	−0.414093	−	0.239076i
$519$	−8068.62			−0.682414
$520$	−2335.38	+	1137.92i	−0.196949	+	0.0959632i
$521$	11052.3			0.929386			0.464693	−	0.885472i	$-0.346165\pi$
$521$	11052.3			0.929386			0.464693	+	0.885472i	$0.346165\pi$
$522$	4952.59	+	2859.38i	0.415266	+	0.239754i
$523$	−3238.52	+	5609.28i	−0.270766	+	0.468980i	−0.969058	−	0.246832i	$-0.920610\pi$
$523$	−3238.52	+	5609.28i	−0.270766	+	0.468980i	0.698292	+	0.715813i	$0.253944\pi$
$524$	2125.09	+	3680.77i	0.177166	+	0.306861i
$525$		−	5250.33i		−	0.436463i
$526$	2405.94	−	1389.07i	0.199437	−	0.115145i
$527$	−11517.5	+	6649.61i	−0.952009	+	0.549643i
$528$			6681.87i			0.550741i
$529$	5902.81	+	10224.0i	0.485149	+	0.840303i
$530$	12150.5	−	21045.3i	0.995819	−	1.72481i
$531$	−4602.91	−	2657.49i	−0.376176	−	0.217185i
$532$	−7629.27			−0.621750
$533$	2236.77	+	157.286i	0.181773	+	0.0127820i
$534$	−11442.2			−0.927250
$535$	−16860.6	−	9734.45i	−1.36252	−	0.786649i
$536$	−474.869	+	822.498i	−0.0382672	+	0.0662808i
$537$	2286.06	+	3959.58i	0.183707	+	0.318191i
$538$		−	13838.8i		−	1.10898i
$539$	−22597.3	+	13046.5i	−1.80581	+	1.04259i
$540$	−2828.87	+	1633.25i	−0.225435	+	0.130155i
$541$			18341.5i			1.45761i	0.684723	+	0.728803i	$0.259923\pi$
$541$			18341.5i			1.45761i	−0.684723	+	0.728803i	$0.740077\pi$
$542$	18379.9	+	31834.9i	1.45661	+	2.52292i
$543$	−715.322	+	1238.97i	−0.0565330	+	0.0979180i
$544$	9704.88	+	5603.11i	0.764877	+	0.441602i
$545$	4450.55			0.349799
$546$	1277.88	−	18172.8i	0.100162	−	1.42440i
$547$	−18943.1			−1.48071			−0.740356	−	0.672215i	$-0.765343\pi$
$547$	−18943.1			−1.48071			−0.740356	+	0.672215i	$0.765343\pi$
$548$	−14268.9	−	8238.14i	−1.11229	−	0.642182i
$549$	2435.87	−	4219.05i	0.189363	−	0.327987i
$550$	−4649.88	−	8053.82i	−0.360493	−	0.624393i
$551$		−	4157.61i		−	0.321452i
$552$	203.638	−	117.570i	0.0157018	−	0.00906545i
$553$	24431.6	−	14105.6i	1.87873	−	1.08469i
$554$		−	16563.8i		−	1.27027i
$555$	877.348	+	1519.61i	0.0671015	+	0.116223i
$556$	−450.000	+	779.423i	−0.0343242	+	0.0594512i
$557$	−359.861	−	207.766i	−0.0273749	−	0.0158049i	0.486250	−	0.873820i	$-0.338364\pi$
$557$	−359.861	−	207.766i	−0.0273749	−	0.0158049i	−0.513625	+	0.858015i	$0.671698\pi$
$558$	11439.3			0.867856
$559$	13290.9	+	8972.38i	1.00563	+	0.678875i
$560$	23231.1			1.75303
$561$	4539.00	+	2620.59i	0.341599	+	0.197222i
$562$	3795.56	−	6574.10i	0.284886	−	0.493437i
$563$	9145.90	+	15841.2i	0.684643	+	1.18584i	0.973549	+	0.228478i	$0.0733750\pi$
$563$	9145.90	+	15841.2i	0.684643	+	1.18584i	−0.288907	+	0.957357i	$0.593292\pi$
$564$			3603.63i			0.269043i
$565$	−8093.17	+	4672.59i	−0.602623	+	0.347925i
$566$	−17315.8	+	9997.29i	−1.28593	+	0.742434i
$567$		−	2545.17i		−	0.188514i
$568$	926.486	+	1604.72i	0.0684410	+	0.118543i
$569$	2173.73	−	3765.02i	0.160154	−	0.277395i	−0.774770	−	0.632244i	$-0.782134\pi$
$569$	2173.73	−	3765.02i	0.160154	−	0.277395i	0.934924	+	0.354848i	$0.115468\pi$
$570$	3884.73	+	2242.85i	0.285462	+	0.164812i
$571$	16756.0			1.22805			0.614024	−	0.789288i	$-0.289550\pi$
$571$	16756.0			1.22805			0.614024	+	0.789288i	$0.289550\pi$
$572$	−7482.84	−	15357.3i	−0.546981	−	1.12259i
$573$	4109.23			0.299591
$574$	5367.40	+	3098.87i	0.390298	+	0.225339i
$575$	529.401	−	916.950i	0.0383958	−	0.0665034i
$576$	−2839.50	−	4918.16i	−0.205404	−	0.355770i
$577$		−	19974.7i		−	1.44117i	−0.693364	−	0.720587i	$-0.743872\pi$
$577$		−	19974.7i		−	1.44117i	0.693364	−	0.720587i	$-0.256128\pi$
$578$	−10897.2	+	6291.48i	−0.784191	+	0.452753i
$579$	5572.14	−	3217.08i	0.399949	−	0.230911i
$580$		−	18644.6i		−	1.33478i
$581$	−20428.0	−	35382.4i	−1.45869	−	2.52652i
$582$	−9651.12	+	16716.2i	−0.687374	+	1.19057i
$583$	15376.9	+	8877.86i	1.09236	+	0.630675i
$584$	−1606.82			−0.113854
$585$	−3172.82	+	4699.95i	−0.224239	+	0.332169i
$586$	5829.47			0.410944
$587$	−13638.7	−	7874.33i	−0.958996	−	0.553677i	−0.0631321	−	0.998005i	$-0.520109\pi$
$587$	−13638.7	−	7874.33i	−0.958996	−	0.553677i	−0.895864	+	0.444329i	$0.853442\pi$
$588$	8698.51	−	15066.3i	0.610069	−	1.05667i
$589$	−4158.25	−	7202.30i	−0.290896	−	0.503846i
$590$			32731.0i			2.28392i
$591$	−622.860	+	359.608i	−0.0433520	+	0.0250293i
$592$	−2072.52	+	1196.57i	−0.143885	+	0.0830721i
$593$			13318.4i			0.922297i	0.887323	+	0.461148i	$0.152562\pi$
$593$			13318.4i			0.922297i	−0.887323	+	0.461148i	$0.847438\pi$
$594$	−2254.09	−	3904.21i	−0.155701	−	0.269683i
$595$	9111.13	−	15780.9i	0.627765	−	1.08732i
$596$	−1165.68	−	673.006i	−0.0801143	−	0.0462540i
$597$	−4769.82			−0.326994
$598$	2055.58	−	3044.96i	0.140567	−	0.208224i
$599$	2970.80			0.202644			0.101322	−	0.994854i	$-0.467693\pi$
$599$	2970.80			0.202644			0.101322	+	0.994854i	$0.467693\pi$
$600$	596.636	+	344.468i	0.0405959	+	0.0234381i
$601$	−5316.31	+	9208.13i	−0.360827	+	0.624971i	−0.988097	−	0.153831i	$-0.950839\pi$
$601$	−5316.31	+	9208.13i	−0.360827	+	0.624971i	0.627270	+	0.778802i	$0.284172\pi$
$602$	22161.9	+	38385.5i	1.50042	+	2.59880i
$603$			2073.11i			0.140006i
$604$	6235.63	−	3600.14i	0.420073	−	0.242529i
$605$	3596.50	−	2076.44i	0.241684	−	0.139536i
$606$			11860.2i			0.795029i
$607$	−5793.94	−	10035.4i	−0.387428	−	0.671045i	0.604675	−	0.796472i	$-0.293303\pi$
$607$	−5793.94	−	10035.4i	−0.387428	−	0.671045i	−0.992103	+	0.125428i	$0.959970\pi$
$608$	−3503.83	+	6068.82i	−0.233716	+	0.404808i
$609$	12581.1	+	7263.71i	0.837130	+	0.483317i
$610$	−30001.4			−1.99135
$611$	2740.22	+	5623.85i	0.181436	+	0.372368i
$612$	−3494.46			−0.230809
$613$	18006.7	+	10396.2i	1.18643	+	0.684988i	0.957494	−	0.288453i	$-0.0931409\pi$
$613$	18006.7	+	10396.2i	1.18643	+	0.684988i	0.228939	+	0.973441i	$0.426474\pi$
$614$	−9536.00	+	16516.8i	−0.626778	+	1.08561i
$615$	−964.592	−	1670.72i	−0.0632457	−	0.109545i
$616$		−	5246.51i		−	0.343162i
$617$	1353.40	−	781.388i	0.0883079	−	0.0509846i	−0.455196	−	0.890391i	$-0.650431\pi$
$617$	1353.40	−	781.388i	0.0883079	−	0.0509846i	0.543504	+	0.839407i	$0.317097\pi$
$618$	6803.85	−	3928.20i	0.442866	−	0.255689i
$619$			758.406i			0.0492454i	0.999697	+	0.0246227i	$0.00783844\pi$
$619$			758.406i			0.0492454i	−0.999697	+	0.0246227i	$0.992162\pi$
$620$	−18647.5	−	32298.4i	−1.20790	−	2.09215i
$621$	256.635	−	444.505i	0.0165836	−	0.0287236i
$622$	−21641.4	−	12494.6i	−1.39508	−	0.805450i
$623$	−29066.7			−1.86923
$624$	−6410.01	−	4327.24i	−0.411227	−	0.277610i
$625$	−19485.0			−1.24704
$626$	−3463.40	−	1999.59i	−0.221127	−	0.127668i
$627$	−1638.75	+	2838.41i	−0.104379	+	0.180789i
$628$	−12177.7	−	21092.4i	−0.773795	−	1.34025i
$629$			1877.15i			0.118994i
$630$	−13573.9	+	7836.91i	−0.858410	+	0.495603i
$631$	−12354.0	+	7132.59i	−0.779406	+	0.449990i	−0.836220	−	0.548394i	$-0.815239\pi$
$631$	−12354.0	+	7132.59i	−0.779406	+	0.449990i	0.0568136	+	0.998385i	$0.481906\pi$
$632$			3701.81i			0.232990i
$633$	−2809.28	−	4865.82i	−0.176396	−	0.305527i
$634$	−18021.3	+	31213.9i	−1.12889	+	1.95530i
$635$	−2877.23	−	1661.17i	−0.179810	−	0.103813i
$636$	−11838.3			−0.738078
$637$	2118.48	−	30127.0i	0.131770	−	1.87390i
$638$	25732.0			1.59677
$639$	3502.82	+	2022.35i	0.216854	+	0.125200i
$640$	−3519.44	+	6095.85i	−0.217372	+	0.376500i
$641$	1992.82	+	3451.67i	0.122795	+	0.212688i	0.920869	−	0.389872i	$-0.127481\pi$
$641$	1992.82	+	3451.67i	0.122795	+	0.212688i	−0.798074	+	0.602560i	$0.794147\pi$
$642$			17914.8i			1.10131i
$643$	7063.78	−	4078.28i	0.433232	−	0.250127i	−0.267490	−	0.963561i	$-0.586194\pi$
$643$	7063.78	−	4078.28i	0.433232	−	0.250127i	0.700723	+	0.713434i	$0.252861\pi$
$644$	4655.73	−	2687.98i	0.284878	−	0.164474i
$645$		−	13796.8i		−	0.842243i
$646$	2399.37	+	4155.83i	0.146133	+	0.253110i
$647$	5639.62	−	9768.11i	0.342684	−	0.593546i	−0.642246	−	0.766498i	$-0.721997\pi$
$647$	5639.62	−	9768.11i	0.342684	−	0.593546i	0.984930	+	0.172953i	$0.0553307\pi$
$648$	289.228	+	166.986i	0.0175339	+	0.0101232i
$649$	−23915.2			−1.44646
$650$	10737.5	+	755.041i	0.647935	+	0.0455617i
$651$	29059.3			1.74950
$652$	28669.1	+	16552.1i	1.72204	+	0.994219i
$653$	−3282.88	+	5686.11i	−0.196736	+	0.340757i	−0.947468	−	0.319850i	$-0.896368\pi$
$653$	−3282.88	+	5686.11i	−0.196736	+	0.340757i	0.750732	+	0.660607i	$0.229701\pi$
$654$	−2047.64	−	3546.62i	−0.122430	−	0.212055i
$655$		−	6348.06i		−	0.378686i
$656$	2278.61	−	1315.56i	0.135617	−	0.0782986i
$657$	−3037.50	+	1753.70i	−0.180372	+	0.104138i
$658$			17291.5i			1.02446i
$659$	−2399.67	−	4156.36i	−0.141848	−	0.245688i	0.786344	−	0.617788i	$-0.211971\pi$
$659$	−2399.67	−	4156.36i	−0.141848	−	0.245688i	−0.928193	+	0.372100i	$0.878638\pi$
$660$	−7348.92	+	12728.7i	−0.433419	+	0.750703i
$661$	−13504.5	−	7796.80i	−0.794648	−	0.458790i	0.0469482	−	0.998897i	$-0.485050\pi$
$661$	−13504.5	−	7796.80i	−0.794648	−	0.458790i	−0.841596	+	0.540107i	$0.818384\pi$
$662$	28811.3			1.69151
$663$	−5453.48	+	2657.21i	−0.319450	+	0.155652i
$664$	5361.03			0.313326
$665$	9868.41	+	5697.53i	0.575459	+	0.332242i
$666$	807.313	−	1398.31i	0.0469711	−	0.0813563i
$667$	1464.83	+	2537.16i	0.0850351	+	0.147285i
$668$			29008.0i			1.68017i
$669$	−145.826	+	84.1925i	−0.00842742	+	0.00486557i
$670$	11056.3	−	6383.37i	0.637526	−	0.368076i
$671$		−	21920.8i		−	1.26116i
$672$	−12243.0	−	21205.5i	−0.702804	−	1.21729i
$673$	−1102.77	+	1910.06i	−0.0631630	+	0.109402i	−0.895878	−	0.444301i	$-0.853452\pi$
$673$	−1102.77	+	1910.06i	−0.0631630	+	0.109402i	0.832715	+	0.553702i	$0.186785\pi$
$674$	−14842.0	−	8569.03i	−0.848208	−	0.489713i
$675$	1503.82			0.0857514
$676$	19578.4	+	2767.13i	1.11393	+	0.157438i
$677$	−15046.4			−0.854182			−0.427091	−	0.904209i	$-0.640462\pi$
$677$	−15046.4			−0.854182			−0.427091	+	0.904209i	$0.640462\pi$
$678$	7447.13	+	4299.60i	0.421837	+	0.243547i
$679$	−24516.8	+	42464.4i	−1.38567	+	2.40005i
$680$	1195.54	+	2070.74i	0.0674219	+	0.116778i
$681$		−	2002.17i		−	0.112663i
$682$	44576.0	−	25736.0i	2.50279	−	1.44499i
$683$	26528.5	−	15316.3i	1.48622	−	0.858068i	0.486340	−	0.873770i	$-0.338332\pi$
$683$	26528.5	−	15316.3i	1.48622	−	0.858068i	0.999877	+	0.0157020i	$0.00499830\pi$
$684$		−	2185.21i		−	0.122155i
$685$	12304.5	+	21311.9i	0.686320	+	1.18874i
$686$	19519.8	−	33809.3i	1.08640	−	1.88170i
$687$	1879.19	+	1084.95i	0.104360	+	0.0602524i
$688$	18816.7			1.04270
$689$	−18474.9	+	9001.90i	−1.02153	+	0.497743i
$690$	−3160.85			−0.174393
$691$	1884.22	+	1087.86i	0.103733	+	0.0598901i	0.550969	−	0.834526i	$-0.314258\pi$
$691$	1884.22	+	1087.86i	0.103733	+	0.0598901i	−0.447236	+	0.894416i	$0.647592\pi$
$692$	12102.9	−	20962.9i	0.664862	−	1.15157i
$693$	−5726.10	−	9917.89i	−0.313876	−	0.543650i
$694$		−	1288.52i		−	0.0704780i
$695$	1164.14	−	672.118i	0.0635373	−	0.0366833i
$696$	−1650.86	+	953.127i	−0.0899078	+	0.0519083i
$697$		−	2063.82i		−	0.112156i
$698$	−9191.95	−	15920.9i	−0.498453	−	0.863346i
$699$	413.177	−	715.644i	0.0223574	−	0.0387241i
$700$	13640.7	+	7875.49i	0.736531	+	0.425236i
$701$	32718.2			1.76284			0.881419	−	0.472335i	$-0.156589\pi$
$701$	32718.2			1.76284			0.881419	+	0.472335i	$0.156589\pi$
$702$	5205.14	+	366.017i	0.279851	+	0.0196787i
$703$	−1173.85			−0.0629768
$704$	−22129.6	−	12776.5i	−1.18472	−	0.683997i
$705$	2691.18	−	4661.26i	0.143767	−	0.249012i
$706$	4636.79	+	8031.15i	0.247178	+	0.428125i
$707$			30128.6i			1.60269i
$708$	13808.7	−	7972.47i	0.733000	−	0.423197i
$709$	−21840.9	+	12609.8i	−1.15691	+	0.667945i	−0.950563	−	0.310533i	$-0.899492\pi$
$709$	−21840.9	+	12609.8i	−1.15691	+	0.667945i	−0.206352	+	0.978478i	$0.566159\pi$
$710$		−	24908.3i		−	1.31661i
$711$	4040.19	+	6997.81i	0.213107	+	0.369112i
$712$	1907.03	−	3303.07i	0.100378	−	0.173859i
$713$	5075.10	+	2930.11i	0.266569	+	0.153904i
$714$	−16767.7			−0.878871
$715$	−1789.79	+	25452.7i	−0.0936146	+	1.33130i
$716$	−13716.4			−0.715929
$717$	3973.48	+	2294.09i	0.206963	+	0.119490i
$718$	−16168.3	+	28004.4i	−0.840385	+	1.45559i
$719$	−17733.1	−	30714.6i	−0.919796	−	1.59313i	−0.799724	−	0.600368i	$-0.795021\pi$
$719$	−17733.1	−	30714.6i	−0.919796	−	1.59313i	−0.120071	−	0.992765i	$-0.538312\pi$
$720$			6653.97i			0.344415i
$721$	17283.9	−	9978.85i	0.892767	−	0.515439i
$722$	21892.7	−	12639.8i	1.12848	−	0.651529i
$723$		−	2926.58i		−	0.150540i
$724$	−2145.97	−	3716.92i	−0.110158	−	0.190799i
$725$	−4291.78	+	7433.59i	−0.219852	+	0.380795i
$726$	−3309.41	−	1910.69i	−0.169179	−	0.0976753i
$727$	14262.2			0.727588			0.363794	−	0.931479i	$-0.381481\pi$
$727$	14262.2			0.727588			0.363794	+	0.931479i	$0.381481\pi$
$728$	5033.05	+	3397.69i	0.256233	+	0.172976i
$729$	729.000			0.0370370
$730$	18705.7	+	10799.7i	0.948396	+	0.547557i
$731$	7379.80	−	12782.2i	0.373395	−	0.646739i
$732$	7307.61	+	12657.1i	0.368985	+	0.639101i
$733$		−	16022.5i		−	0.807371i	−0.914898	−	0.403685i	$-0.867729\pi$
$733$		−	16022.5i		−	0.807371i	0.914898	−	0.403685i	$-0.132271\pi$
$734$	23781.8	−	13730.4i	1.19592	−	0.690463i
$735$	−22502.9	+	12992.1i	−1.12930	+	0.651999i
$736$		−	4937.96i		−	0.247304i
$737$	4664.05	+	8078.38i	0.233111	+	0.403760i
$738$	−887.593	+	1537.36i	−0.0442720	+	0.0766814i
$739$	−3287.61	−	1898.11i	−0.163649	−	0.0944830i	0.415939	−	0.909393i	$-0.363453\pi$
$739$	−3287.61	−	1898.11i	−0.163649	−	0.0944830i	−0.579588	+	0.814910i	$0.696786\pi$
$740$	−5264.09			−0.261502
$741$	−1661.65	−	3410.26i	−0.0823782	−	0.169068i
$742$	−56804.3			−2.81044
$743$	−26266.0	−	15164.7i	−1.29691	−	0.748772i	−0.317042	−	0.948412i	$-0.602690\pi$
$743$	−26266.0	−	15164.7i	−1.29691	−	0.748772i	−0.979869	+	0.199639i	$0.936023\pi$
$744$	−1906.55	+	3302.24i	−0.0939481	+	0.162723i
$745$	1005.20	+	1741.05i	0.0494331	+	0.0856206i
$746$		−	152.502i		−	0.00748460i
$747$	10134.4	−	5851.09i	0.496382	−	0.286586i
$748$	−13617.0	+	7861.78i	−0.665624	+	0.384298i
$749$			45509.1i			2.22011i
$750$	5761.59	+	9979.37i	0.280511	+	0.485860i
$751$	10775.9	−	18664.5i	0.523595	−	0.906893i	−0.476028	−	0.879430i	$-0.657924\pi$
$751$	10775.9	−	18664.5i	0.523595	−	0.906893i	0.999623	−	0.0274629i	$-0.00874280\pi$
$752$	6357.25	+	3670.36i	0.308278	+	0.177984i
$753$	−5622.42			−0.272101
$754$	−16664.3	+	24685.1i	−0.804877	+	1.19228i
$755$	−10754.3			−0.518397
$756$	6612.55	+	3817.76i	0.318117	+	0.183665i
$757$	10208.8	−	17682.2i	0.490153	−	0.848970i	−0.509783	−	0.860303i	$-0.670274\pi$
$757$	10208.8	−	17682.2i	0.490153	−	0.848970i	0.999936	+	0.0113335i	$0.00360764\pi$
$758$	−24903.3	−	43133.7i	−1.19331	−	2.06687i
$759$		−	2309.50i		−	0.110447i
$760$	−1294.91	+	747.616i	−0.0618043	+	0.0356828i
$761$	−27171.9	+	15687.7i	−1.29432	+	0.747278i	−0.979417	−	0.201845i	$-0.935306\pi$
$761$	−27171.9	+	15687.7i	−1.29432	+	0.747278i	−0.314906	+	0.949123i	$0.601973\pi$
$762$			3057.13i			0.145339i
$763$	−5201.64	−	9009.50i	−0.246805	−	0.427478i
$764$	−6163.84	+	10676.1i	−0.291885	+	0.505559i
$765$	4520.05	+	2609.65i	0.213625	+	0.123336i
$766$	−43570.5			−2.05518
$767$	15487.7	−	22942.2i	0.729111	−	1.08004i
$768$	−8667.00			−0.407218
$769$	10784.3	+	6226.33i	0.505712	+	0.291973i	0.731069	−	0.682303i	$-0.239022\pi$
$769$	10784.3	+	6226.33i	0.505712	+	0.291973i	−0.225357	+	0.974276i	$0.572355\pi$
$770$	−35262.8	+	61076.9i	−1.65037	+	2.85852i
$771$	2727.28	+	4723.79i	0.127394	+	0.220653i
$772$			19302.5i			0.899885i
$773$	32432.4	−	18724.9i	1.50907	−	0.871264i	0.509129	−	0.860690i	$-0.329967\pi$
$773$	32432.4	−	18724.9i	1.50907	−	0.871264i	0.999944	−	0.0105740i	$-0.00336588\pi$
$774$	−10994.6	+	6347.71i	−0.510583	+	0.294785i
$775$			17169.8i			0.795815i
$776$	−3217.04	−	5572.08i	−0.148821	−	0.257765i
$777$	2050.82	−	3552.13i	0.0946884	−	0.164005i
$778$	−34841.2	−	20115.6i	−1.60555	−	0.926965i
$779$	1290.58			0.0593580
$780$	−7451.59	−	15293.2i	−0.342064	−	0.702029i
$781$	18199.5			0.833839
$782$	−2928.41	−	1690.72i	−0.133913	−	0.0773145i
$783$	−2080.50	+	3603.54i	−0.0949568	+	0.164470i
$784$	−17719.2	−	30690.5i	−0.807179	−	1.39807i
$785$			36377.1i			1.65396i
$786$	−5058.73	+	2920.66i	−0.229566	+	0.132540i
$787$	−22915.2	+	13230.1i	−1.03791	+	0.599240i	−0.919242	−	0.393694i	$-0.871197\pi$
$787$	−22915.2	+	13230.1i	−1.03791	+	0.599240i	−0.118672	+	0.992934i	$0.537864\pi$
$788$		−	2157.65i		−	0.0975420i
$789$	1010.70	+	1750.58i	0.0456043	+	0.0789890i
$790$	24880.5	−	43094.3i	1.12052	−	1.94079i
$791$	18918.0	+	10922.3i	0.850375	+	0.490964i
$792$	1502.73			0.0674207
$793$	21028.9	+	14196.1i	0.941687	+	0.635710i
$794$	58550.3			2.61697
$795$	15312.7	+	8840.79i	0.683127	+	0.394403i
$796$	7154.72	−	12392.3i	0.318583	−	0.551803i
$797$	2374.74	+	4113.17i	0.105543	+	0.182805i	0.913960	−	0.405805i	$-0.133009\pi$
$797$	2374.74	+	4113.17i	0.105543	+	0.182805i	−0.808417	+	0.588610i	$0.799675\pi$
$798$		−	10485.4i		−	0.465138i
$799$	4986.56	−	2878.99i	0.220791	−	0.127474i
$800$	12529.4	−	7233.82i	0.553724	−	0.319693i
$801$		−	8325.41i		−	0.367246i
$802$	−26133.0	−	45263.8i	−1.15061	−	1.99292i
$803$	−7890.91	+	13667.5i	−0.346780	+	0.600640i
$804$	−5386.09	−	3109.66i	−0.236260	−	0.136405i
$805$	−8029.53			−0.351557
$806$	−4178.97	+	59429.2i	−0.182628	+	2.59715i
$807$	10069.2			0.439223
$808$	−3423.74	−	1976.70i	−0.149068	−	0.0860644i
$809$	2232.02	−	3865.98i	0.0970009	−	0.168010i	−0.813441	−	0.581647i	$-0.802408\pi$
$809$	2232.02	−	3865.98i	0.0970009	−	0.168010i	0.910442	+	0.413637i	$0.135742\pi$
$810$	−2244.68	−	3887.91i	−0.0973705	−	0.168651i
$811$			20774.6i			0.899499i	0.893155	+	0.449749i	$0.148487\pi$
$811$			20774.6i			0.899499i	−0.893155	+	0.449749i	$0.851513\pi$
$812$	−37743.3	+	21791.1i	−1.63120	+	0.941771i
$813$	−23163.3	+	13373.3i	−0.999227	+	0.576904i
$814$		−	7265.13i		−	0.312829i
$815$	−24722.2	−	42820.1i	−1.06255	−	1.84039i
$816$	−3559.17	+	6164.66i	−0.152691	+	0.264468i
$817$	7993.18	+	4614.86i	0.342284	+	0.197618i
$818$	6323.51			0.270289
$819$	13222.7	+	929.796i	0.564148	+	0.0396700i
$820$	5787.55			0.246476
$821$	30977.0	+	17884.6i	1.31682	+	0.760264i	0.983215	−	0.182450i	$-0.0584029\pi$
$821$	30977.0	+	17884.6i	1.31682	+	0.760264i	0.333601	+	0.942714i	$0.391736\pi$
$822$	11322.2	−	19610.7i	0.480424	−	0.832119i
$823$	1472.72	+	2550.83i	0.0623764	+	0.108039i	0.895527	−	0.445007i	$-0.146799\pi$
$823$	1472.72	+	2550.83i	0.0623764	+	0.108039i	−0.833151	+	0.553046i	$0.813465\pi$
$824$			2618.80i			0.110716i
$825$	5860.02	−	3383.28i	0.247296	−	0.142777i
$826$	66259.2	−	38254.8i	2.79111	−	1.61145i
$827$			17878.6i			0.751753i	0.926670	+	0.375877i	$0.122658\pi$
$827$			17878.6i			0.751753i	−0.926670	+	0.375877i	$0.877342\pi$
$828$	769.905	+	1333.51i	0.0323141	+	0.0559696i
$829$	6711.90	−	11625.4i	0.281199	−	0.487051i	−0.690481	−	0.723350i	$-0.742601\pi$
$829$	6711.90	−	11625.4i	0.281199	−	0.487051i	0.971680	+	0.236299i	$0.0759345\pi$
$830$	−62410.1	−	36032.5i	−2.60998	−	1.50687i
$831$	12051.9			0.503101
$832$	26588.1	−	12955.1i	1.10790	−	0.539827i
$833$	−27797.5			−1.15621
$834$	−1071.21	−	618.466i	−0.0444762	−	0.0256783i
$835$	21663.1	−	37521.6i	0.897824	−	1.55508i
$836$	−4916.26	−	8515.22i	−0.203388	−	0.352279i
$837$			8323.30i			0.343722i
$838$	−7733.79	+	4465.11i	−0.318806	+	0.184063i
$839$	27316.8	−	15771.3i	1.12405	−	0.648971i	0.181619	−	0.983369i	$-0.441866\pi$
$839$	27316.8	−	15771.3i	1.12405	−	0.648971i	0.942432	+	0.334398i	$0.108533\pi$
$840$		−	5224.61i		−	0.214602i
$841$	319.334	+	553.103i	0.0130934	+	0.0226784i
$842$	−1514.37	+	2622.96i	−0.0619816	+	0.107355i
$843$	4783.36	+	2761.67i	0.195430	+	0.112832i
$844$	16855.7			0.687437
$845$	−23258.0	−	18200.4i	−0.946865	−	0.740961i
$846$	−4952.71			−0.201274
$847$	−8406.92	−	4853.74i	−0.341045	−	0.196902i
$848$	−12057.5	+	20884.2i	−0.488274	+	0.845715i
$849$	−7274.10	−	12599.1i	−0.294048	−	0.509305i
$850$		−	9907.22i		−	0.399782i
$851$	716.338	−	413.578i	0.0288552	−	0.0166595i
$852$	−10508.5	+	6067.06i	−0.422551	+	0.243960i
$853$		−	21810.6i		−	0.875476i	−0.899103	−	0.437738i	$-0.855780\pi$
$853$		−	21810.6i		−	0.875476i	0.899103	−	0.437738i	$-0.144220\pi$
$854$	35064.5	+	60733.5i	1.40502	+	2.43356i
$855$	−1631.91	+	2826.55i	−0.0652751	+	0.113060i
$856$	−5171.55	−	2985.80i	−0.206495	−	0.119220i
$857$	−33234.6			−1.32470			−0.662352	−	0.749193i	$-0.730442\pi$
$857$	−33234.6			−1.32470			−0.662352	+	0.749193i	$0.730442\pi$
$858$	21106.6	−	10284.2i	0.839821	−	0.409203i
$859$	42697.7			1.69596			0.847978	−	0.530032i	$-0.177820\pi$
$859$	42697.7			1.69596			0.847978	+	0.530032i	$0.177820\pi$
$860$	35845.0	+	20695.1i	1.42129	+	0.820580i
$861$	−2254.76	+	3905.36i	−0.0892474	+	0.154581i
$862$	28262.5	+	48952.1i	1.11673	+	1.93424i
$863$		−	27419.2i		−	1.08153i	−0.841174	−	0.540765i	$-0.818135\pi$
$863$		−	27419.2i		−	1.08153i	0.841174	−	0.540765i	$-0.181865\pi$
$864$	6073.78	−	3506.70i	0.239160	−	0.138079i
$865$	−31310.1	+	18076.9i	−1.23072	+	0.710558i
$866$		−	41437.0i		−	1.62596i
$867$	−4577.73	−	7928.85i	−0.179317	−	0.310586i
$868$	−43589.0	+	75498.3i	−1.70450	+	2.95228i
$869$	31487.2	+	18179.1i	1.22915	+	0.709649i
$870$	25624.5			0.998567
$871$	−10770.2	−	757.343i	−0.418983	−	0.0294622i
$872$	1365.09			0.0530137
$873$	−12162.8	−	7022.22i	−0.471535	−	0.272241i
$874$	1057.27	−	1831.24i	0.0409183	−	0.0708727i
$875$	14636.2	+	25350.7i	0.565479	+	0.979439i
$876$		−	10522.2i		−	0.405836i
$877$	−36896.3	+	21302.1i	−1.42064	+	0.820206i	−0.996353	−	0.0853227i	$-0.972808\pi$
$877$	−36896.3	+	21302.1i	−1.42064	+	0.820206i	−0.424285	+	0.905529i	$0.639475\pi$
$878$	29042.3	−	16767.6i	1.11632	−	0.644508i
$879$			4241.56i			0.162758i
$880$	14970.0	+	25928.8i	0.573454	+	0.993251i
$881$	−2349.70	+	4069.80i	−0.0898562	+	0.155636i	−0.907450	−	0.420160i	$-0.861974\pi$
$881$	−2349.70	+	4069.80i	−0.0898562	+	0.155636i	0.817594	+	0.575795i	$0.195307\pi$
$882$	20706.6	+	11955.0i	0.790507	+	0.456400i
$883$	−22233.5			−0.847358			−0.423679	−	0.905812i	$-0.639262\pi$
$883$	−22233.5			−0.847358			−0.423679	+	0.905812i	$0.639262\pi$
$884$	1276.59	−	18154.4i	0.0485704	−	0.690721i
$885$	−23815.3			−0.904568
$886$	8465.38	+	4887.49i	0.320993	+	0.185325i
$887$	4426.23	−	7666.45i	0.167552	−	0.290208i	−0.770007	−	0.638036i	$-0.779747\pi$
$887$	4426.23	−	7666.45i	0.167552	−	0.290208i	0.937558	+	0.347828i	$0.113081\pi$
$888$	269.104	+	466.102i	0.0101695	+	0.0176142i
$889$			7766.05i			0.292986i
$890$	−44401.1	+	25635.0i	−1.67228	+	0.965491i
$891$	2840.73	−	1640.09i	0.106810	−	0.0616669i
$892$		−	505.155i		−	0.0189617i
$893$	1800.34	+	3118.28i	0.0674649	+	0.116853i
$894$	924.958	−	1602.07i	0.0346032	−	0.0599344i
$895$	17742.0	+	10243.4i	0.662626	+	0.382567i
$896$	16453.6			0.613477
$897$	2215.53	+	1495.65i	0.0824688	+	0.0556727i
$898$	−53283.7			−1.98007
$899$	−41143.1	−	23754.0i	−1.52636	−	0.881246i
$900$	−2255.73	+	3907.05i	−0.0835457	+	0.144705i
$901$	9457.77	+	16381.3i	0.349705	+	0.605707i
$902$			7987.58i			0.294853i
$903$	−27929.6	+	16125.1i	−1.02928	+	0.594254i
$904$	−2482.38	+	1433.20i	−0.0913303	+	0.0527296i
$905$			6410.41i			0.235458i
$906$	4947.92	+	8570.05i	0.181439	+	0.314262i
$907$	18586.2	−	32192.3i	0.680424	−	1.17853i	−0.294427	−	0.955674i	$-0.595129\pi$
$907$	18586.2	−	32192.3i	0.680424	−	1.17853i	0.974851	−	0.222856i	$-0.0715378\pi$
$908$	5201.79	+	3003.25i	0.190118	+	0.109765i
$909$	−8629.56			−0.314878
$910$	−35755.4	−	73382.1i	−1.30251	−	2.67318i
$911$	38035.1			1.38327			0.691635	−	0.722247i	$-0.256891\pi$
$911$	38035.1			1.38327			0.691635	+	0.722247i	$0.256891\pi$
$912$	−3854.99	−	2225.68i	−0.139969	−	0.0808110i
$913$	26327.4	−	45600.4i	0.954337	−	1.65296i
$914$	−17319.6	−	29998.5i	−0.626787	−	1.08563i
$915$		−	21829.2i		−	0.788691i
$916$	−5637.56	+	3254.85i	−0.203352	+	0.117405i
$917$	−12850.7	+	7419.38i	−0.462780	+	0.267186i
$918$		−	4802.67i		−	0.172671i
$919$	4176.14	+	7233.28i	0.149900	+	0.259634i	0.931190	−	0.364533i	$-0.118772\pi$
$919$	4176.14	+	7233.28i	0.149900	+	0.259634i	−0.781290	+	0.624168i	$0.785438\pi$
$920$	526.808	−	912.458i	0.0188786	−	0.0326987i
$921$	−12017.8	−	6938.46i	−0.429966	−	0.248241i
$922$	72679.4			2.59606
$923$	−11786.2	+	17459.0i	−0.420310	+	0.622611i
$924$	34356.6			1.22321
$925$	2098.79	+	1211.74i	0.0746029	+	0.0430720i
$926$	−11259.8	+	19502.6i	−0.399590	+	0.692110i
$927$	2858.19	+	4950.53i	0.101268	+	0.175401i
$928$			40031.3i			1.41605i
$929$	−17521.5	+	10116.0i	−0.618796	+	0.357262i	−0.776400	−	0.630240i	$-0.782956\pi$
$929$	−17521.5	+	10116.0i	−0.618796	+	0.357262i	0.157604	+	0.987502i	$0.449623\pi$
$930$	44389.9	−	25628.5i	1.56516	−	0.903647i
$931$		−	17382.8i		−	0.611921i
$932$	1239.53	+	2146.93i	0.0435646	+	0.0754561i
$933$	9091.19	−	15746.4i	0.319006	−	0.552534i
$934$	29501.9	+	17032.9i	1.03355	+	0.596718i
$935$	23484.7			0.821423
$936$	−973.183	+	1441.59i	−0.0339845	+	0.0503417i
$937$	−27766.9			−0.968095			−0.484048	−	0.875042i	$-0.660834\pi$
$937$	−27766.9			−0.968095			−0.484048	+	0.875042i	$0.660834\pi$
$938$	−25844.4	−	14921.3i	−0.899627	−	0.519400i
$939$	1454.92	−	2519.99i	0.0505639	−	0.0875792i
$940$	8073.55	+	13983.8i	0.280138	+	0.485214i
$941$			400.765i			0.0138837i	0.999976	+	0.00694185i	$0.00220968\pi$
$941$			400.765i			0.0138837i	−0.999976	+	0.00694185i	$0.997790\pi$
$942$	28988.7	−	16736.6i	1.00266	−	0.578885i
$943$	−787.571	+	454.704i	−0.0271971	+	0.0157022i
$944$		−	32480.4i		−	1.11986i
$945$	−5702.19	−	9876.48i	−0.196288	−	0.339981i
$946$	−28562.0	+	49470.8i	−0.981639	+	1.70025i
$947$	−18883.1	−	10902.2i	−0.647961	−	0.374101i	0.139713	−	0.990192i	$-0.455382\pi$
$947$	−18883.1	−	10902.2i	−0.647961	−	0.374101i	−0.787675	+	0.616091i	$0.788715\pi$
$948$	−24241.1			−0.830502
$949$	−8001.16	−	16421.0i	−0.273687	−	0.561696i
$950$	6195.35			0.211583
$951$	−22711.4	−	13112.4i	−0.774414	−	0.447108i
$952$	2794.61	−	4840.41i	0.0951406	−	0.164788i
$953$	15240.2	+	26396.8i	0.518026	+	0.897248i	0.999781	+	0.0209414i	$0.00666633\pi$
$953$	15240.2	+	26396.8i	0.518026	+	0.897248i	−0.481755	+	0.876306i	$0.660000\pi$
$954$		−	16270.1i		−	0.552165i
$955$	15945.8	−	9206.29i	0.540307	−	0.311946i
$956$	−11920.4	+	6882.26i	−0.403278	+	0.232833i
$957$			18722.8i			0.632415i
$958$	−3248.74	−	5626.98i	−0.109564	−	0.189770i
$959$	28762.0	−	49817.2i	0.968480	−	1.67746i
$960$	−22037.2	−	12723.2i	−0.740884	−	0.427749i
$961$	−65239.6			−2.18991
$962$	6969.55	+	4704.97i	0.233583	+	0.157686i
$963$	−13034.9			−0.436183
$964$	7603.47	+	4389.87i	0.254037	+	0.146668i
$965$	14415.0	−	24967.6i	0.480867	−	0.832886i
$966$	3694.28	+	6398.68i	0.123045	+	0.213120i
$967$		−	23864.1i		−	0.793608i	−0.917903	−	0.396804i	$-0.870119\pi$
$967$		−	23864.1i		−	0.793608i	0.917903	−	0.396804i	$-0.129881\pi$
$968$	1103.14	−	636.896i	0.0366283	−	0.0211473i
$969$	−3023.81	+	1745.80i	−0.100247	+	0.0578774i
$970$			86489.2i			2.86289i
$971$	7005.15	+	12133.3i	0.231520	+	0.401004i	0.958256	−	0.285913i	$-0.0922968\pi$
$971$	7005.15	+	12133.3i	0.231520	+	0.401004i	−0.726736	+	0.686917i	$0.758963\pi$
$972$	−1093.50	+	1894.00i	−0.0360844	+	0.0625000i
$973$	−2721.21	−	1571.09i	−0.0896589	−	0.0517646i
$974$	−51933.3			−1.70847
$975$	−549.373	+	7812.65i	−0.0180451	+	0.256620i
$976$	29771.7			0.976404
$977$	−22038.8	−	12724.1i	−0.721681	−	0.416663i	0.0936898	−	0.995601i	$-0.470134\pi$
$977$	−22038.8	−	12724.1i	−0.721681	−	0.416663i	−0.815371	+	0.578938i	$0.803467\pi$
$978$	−22748.7	+	39401.9i	−0.743787	+	1.28828i
$979$	−18730.4	−	32442.0i	−0.611467	−	1.05909i
$980$		−	77952.4i		−	2.54092i
$981$	2580.54	−	1489.88i	0.0839862	−	0.0484894i
$982$	3824.99	−	2208.36i	0.124298	−	0.0717634i
$983$			52479.9i			1.70280i	0.524519	+	0.851399i	$0.324245\pi$
$983$			52479.9i			1.70280i	−0.524519	+	0.851399i	$0.675755\pi$
$984$	−295.864	−	512.452i	−0.00958517	−	0.0166020i
$985$	−1611.33	+	2790.90i	−0.0521230	+	0.0902798i
$986$	23740.2	+	13706.4i	0.766777	+	0.442699i
$987$	−12581.4			−0.405746
$988$	11352.6	+	798.296i	0.365561	+	0.0257057i
$989$	−6503.73			−0.209107
$990$	−17493.9	−	10100.1i	−0.561609	−	0.324245i
$991$	−19024.3	+	32951.0i	−0.609814	+	1.05623i	0.381457	+	0.924386i	$0.375422\pi$
$991$	−19024.3	+	32951.0i	−0.609814	+	1.05623i	−0.991271	+	0.131842i	$0.957911\pi$
$992$	40037.5	+	69347.0i	1.28144	+	2.21952i
$993$			20963.3i			0.669939i
$994$	−50423.4	+	29111.9i	−1.60899	+	0.928948i
$995$	−18509.2	+	10686.3i	−0.589728	+	0.340480i
$996$			35106.5i			1.11686i
$997$	15618.3	+	27051.7i	0.496125	+	0.859314i	0.999990	−	0.00446833i	$-0.00142232\pi$
$997$	15618.3	+	27051.7i	0.496125	+	0.859314i	−0.503865	+	0.863783i	$0.668089\pi$
$998$	2932.15	−	5078.63i	0.0930015	−	0.161083i
$999$	1017.42	+	587.406i	0.0322219	+	0.0186033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.b.4.1	✓	4
3.2	odd	2		117.4.q.d.82.2		4
4.3	odd	2		624.4.bv.c.433.1		4
13.4	even	6		507.4.b.e.337.2		4
13.6	odd	12		507.4.a.k.1.3		4
13.7	odd	12		507.4.a.k.1.2		4
13.9	even	3		507.4.b.e.337.3		4
13.10	even	6	inner	39.4.j.b.10.1	yes	4
39.20	even	12		1521.4.a.z.1.3		4
39.23	odd	6		117.4.q.d.10.2		4
39.32	even	12		1521.4.a.z.1.2		4
52.23	odd	6		624.4.bv.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.b.4.1	✓	4	1.1	even	1	trivial
39.4.j.b.10.1	yes	4	13.10	even	6	inner
117.4.q.d.10.2		4	39.23	odd	6
117.4.q.d.82.2		4	3.2	odd	2
507.4.a.k.1.2		4	13.7	odd	12
507.4.a.k.1.3		4	13.6	odd	12
507.4.b.e.337.2		4	13.4	even	6
507.4.b.e.337.3		4	13.9	even	3
624.4.bv.c.49.2		4	52.23	odd	6
624.4.bv.c.433.1		4	4.3	odd	2
1521.4.a.z.1.2		4	39.32	even	12
1521.4.a.z.1.3		4	39.20	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)

\(f(q)\)	\(=\)	\(q+(-3.57071 - 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} -13.4424i q^{5} +(-10.7121 + 6.18466i) q^{6} +(-27.2121 + 15.7109i) q^{7} -4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-3.57071 - 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} -13.4424i q^{5} +(-10.7121 + 6.18466i) q^{6} +(-27.2121 + 15.7109i) q^{7} -4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-27.7121 + 47.9988i) q^{10} +(-35.0707 - 20.2481i) q^{11} +27.0000 q^{12} +(42.1364 - 20.5310i) q^{13} +129.556 q^{14} +(-34.9243 - 20.1635i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-21.5707 - 37.3616i) q^{17} +37.1080i q^{18} +(23.3636 - 13.4890i) q^{19} +(104.773 - 60.4906i) q^{20} +94.2656i q^{21} +(83.4850 + 144.600i) q^{22} +(-9.50500 + 16.4631i) q^{23} +(-10.7121 - 6.18466i) q^{24} -55.6971 q^{25} +(-192.783 - 13.5562i) q^{26} -27.0000 q^{27} +(-244.909 - 141.398i) q^{28} +(77.0557 - 133.464i) q^{29} +(83.1364 + 143.997i) q^{30} -308.270i q^{31} +(-224.955 + 129.878i) q^{32} +(-105.212 + 60.7443i) q^{33} +177.877i q^{34} +(211.192 + 365.796i) q^{35} +(40.5000 - 70.1481i) q^{36} +(-37.6821 - 21.7558i) q^{37} -111.233 q^{38} +(9.86357 - 140.270i) q^{39} -55.4243 q^{40} +(41.4293 + 23.9192i) q^{41} +(194.334 - 336.596i) q^{42} +(171.061 + 296.286i) q^{43} -364.466i q^{44} +(-104.773 + 60.4906i) q^{45} +(67.8793 - 39.1901i) q^{46} +133.468i q^{47} +(-82.5000 - 142.894i) q^{48} +(322.167 - 558.010i) q^{49} +(198.879 + 114.823i) q^{50} -129.424 q^{51} +(349.637 + 236.032i) q^{52} -438.454 q^{53} +(96.4093 + 55.6619i) q^{54} +(-272.182 + 471.433i) q^{55} +(64.7779 + 112.199i) q^{56} -80.9338i q^{57} +(-550.288 + 317.709i) q^{58} +(511.434 - 295.277i) q^{59} -362.944i q^{60} +(270.652 + 468.783i) q^{61} +(-635.516 + 1100.75i) q^{62} +(244.909 + 141.398i) q^{63} +631.000 q^{64} +(-275.985 - 566.413i) q^{65} +500.910 q^{66} +(-199.485 - 115.173i) q^{67} +(194.136 - 336.254i) q^{68} +(28.5150 + 49.3894i) q^{69} -1741.54i q^{70} +(-389.202 + 224.706i) q^{71} +(-32.1364 + 18.5540i) q^{72} -389.711i q^{73} +(89.7014 + 155.367i) q^{74} +(-83.5457 + 144.705i) q^{75} +(210.272 + 121.401i) q^{76} +1272.47 q^{77} +(-324.394 + 480.530i) q^{78} -897.820 q^{79} +(-640.279 - 369.665i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-98.6214 - 170.817i) q^{82} +1300.24i q^{83} +(-734.728 + 424.195i) q^{84} +(-502.228 + 289.961i) q^{85} -1410.60i q^{86} +(-231.167 - 400.393i) q^{87} +(-83.4850 + 144.600i) q^{88} +(801.113 + 462.523i) q^{89} +498.819 q^{90} +(-824.061 + 1220.69i) q^{91} -171.090 q^{92} +(-800.910 - 462.406i) q^{93} +(275.151 - 476.575i) q^{94} +(-181.324 - 314.062i) q^{95} +779.267i q^{96} +(1351.43 - 780.247i) q^{97} +(-2300.73 + 1328.33i) q^{98} +364.466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9	\( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9} - 68 q^{10} - 126 q^{11} + 108 q^{12} + 40 q^{13} + 204 q^{14} - 54 q^{15} + 110 q^{16} - 72 q^{17} + 222 q^{19} + 162 q^{20} + 34 q^{22} - 138 q^{23} + 120 q^{25} - 714 q^{26} - 108 q^{27} - 594 q^{28} - 6 q^{29} + 204 q^{30} - 378 q^{33} + 402 q^{35} + 162 q^{36} + 492 q^{37} + 612 q^{38} + 168 q^{39} - 136 q^{40} + 180 q^{41} + 306 q^{42} + 470 q^{43} - 162 q^{45} - 714 q^{46} - 330 q^{48} + 346 q^{49} + 1224 q^{50} - 432 q^{51} - 144 q^{52} - 2268 q^{53} - 446 q^{55} + 102 q^{56} - 2244 q^{58} + 2160 q^{59} - 160 q^{61} - 1428 q^{62} + 594 q^{63} + 2524 q^{64} - 804 q^{65} + 204 q^{66} - 498 q^{67} + 648 q^{68} + 414 q^{69} - 1314 q^{71} + 1530 q^{74} + 180 q^{75} + 1998 q^{76} + 2976 q^{77} - 612 q^{78} + 8 q^{79} - 990 q^{80} - 162 q^{81} + 34 q^{82} - 1782 q^{84} - 852 q^{85} + 18 q^{87} - 34 q^{88} - 252 q^{89} + 1224 q^{90} - 1668 q^{91} - 2484 q^{92} - 1404 q^{93} + 2686 q^{94} - 54 q^{95} - 336 q^{97} - 6732 q^{98}+O(q^{100}) \) 4 * q + 6 * q^3 + 18 * q^4 - 66 * q^7 - 18 * q^9 - 68 * q^10 - 126 * q^11 + 108 * q^12 + 40 * q^13 + 204 * q^14 - 54 * q^15 + 110 * q^16 - 72 * q^17 + 222 * q^19 + 162 * q^20 + 34 * q^22 - 138 * q^23 + 120 * q^25 - 714 * q^26 - 108 * q^27 - 594 * q^28 - 6 * q^29 + 204 * q^30 - 378 * q^33 + 402 * q^35 + 162 * q^36 + 492 * q^37 + 612 * q^38 + 168 * q^39 - 136 * q^40 + 180 * q^41 + 306 * q^42 + 470 * q^43 - 162 * q^45 - 714 * q^46 - 330 * q^48 + 346 * q^49 + 1224 * q^50 - 432 * q^51 - 144 * q^52 - 2268 * q^53 - 446 * q^55 + 102 * q^56 - 2244 * q^58 + 2160 * q^59 - 160 * q^61 - 1428 * q^62 + 594 * q^63 + 2524 * q^64 - 804 * q^65 + 204 * q^66 - 498 * q^67 + 648 * q^68 + 414 * q^69 - 1314 * q^71 + 1530 * q^74 + 180 * q^75 + 1998 * q^76 + 2976 * q^77 - 612 * q^78 + 8 * q^79 - 990 * q^80 - 162 * q^81 + 34 * q^82 - 1782 * q^84 - 852 * q^85 + 18 * q^87 - 34 * q^88 - 252 * q^89 + 1224 * q^90 - 1668 * q^91 - 2484 * q^92 - 1404 * q^93 + 2686 * q^94 - 54 * q^95 - 336 * q^97 - 6732 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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