LMFDB - Embedded newform 39.4.j.c.4.3

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			4.3
Root			$-0.917374i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.c.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.794469 - 0.458687i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-3.57921 - 6.19938i) q^{4} -15.4704i q^{5} +(2.38341 - 1.37606i) q^{6} +(17.8257 - 10.2917i) q^{7} +13.9059i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-0.794469 - 0.458687i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-3.57921 - 6.19938i) q^{4} -15.4704i q^{5} +(2.38341 - 1.37606i) q^{6} +(17.8257 - 10.2917i) q^{7} +13.9059i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-7.09608 + 12.2908i) q^{10} +(-57.0209 - 32.9210i) q^{11} +21.4753 q^{12} +(19.2429 + 42.7400i) q^{13} -18.8826 q^{14} +(40.1933 + 23.2056i) q^{15} +(-22.2552 + 38.5472i) q^{16} +(22.1478 + 38.3611i) q^{17} +8.25636i q^{18} +(127.352 - 73.5266i) q^{19} +(-95.9069 + 55.3719i) q^{20} +61.7500i q^{21} +(30.2009 + 52.3094i) q^{22} +(26.5793 - 46.0367i) q^{23} +(-36.1287 - 20.8589i) q^{24} -114.334 q^{25} +(4.31639 - 42.7821i) q^{26} +27.0000 q^{27} +(-127.604 - 73.6721i) q^{28} +(19.3128 - 33.4508i) q^{29} +(-21.2882 - 36.8723i) q^{30} +88.3894i q^{31} +(131.705 - 76.0401i) q^{32} +(171.063 - 98.7630i) q^{33} -40.6357i q^{34} +(-159.216 - 275.771i) q^{35} +(-32.2129 + 55.7944i) q^{36} +(68.3803 + 39.4794i) q^{37} -134.903 q^{38} +(-139.906 - 14.1155i) q^{39} +215.131 q^{40} +(307.410 + 177.483i) q^{41} +(28.3239 - 49.0585i) q^{42} +(-203.923 - 353.205i) q^{43} +471.325i q^{44} +(-120.580 + 69.6169i) q^{45} +(-42.2329 + 24.3832i) q^{46} +67.9674i q^{47} +(-66.7657 - 115.642i) q^{48} +(40.3369 - 69.8656i) q^{49} +(90.8345 + 52.4433i) q^{50} -132.887 q^{51} +(196.087 - 272.270i) q^{52} +226.572 q^{53} +(-21.4507 - 12.3845i) q^{54} +(-509.302 + 882.136i) q^{55} +(143.115 + 247.883i) q^{56} +441.160i q^{57} +(-30.6869 + 17.7171i) q^{58} +(-123.002 + 71.0154i) q^{59} -332.231i q^{60} +(-133.416 - 231.083i) q^{61} +(40.5431 - 70.2227i) q^{62} +(-160.431 - 92.6250i) q^{63} +216.569 q^{64} +(661.206 - 297.696i) q^{65} -181.205 q^{66} +(356.098 + 205.593i) q^{67} +(158.543 - 274.605i) q^{68} +(79.7379 + 138.110i) q^{69} +292.122i q^{70} +(-79.2458 + 45.7526i) q^{71} +(108.386 - 62.5767i) q^{72} -63.1328i q^{73} +(-36.2173 - 62.7303i) q^{74} +(171.500 - 297.047i) q^{75} +(-911.638 - 526.335i) q^{76} -1355.25 q^{77} +(104.677 + 75.3875i) q^{78} -287.115 q^{79} +(596.341 + 344.298i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-162.818 - 282.010i) q^{82} -373.812i q^{83} +(382.812 - 221.016i) q^{84} +(593.463 - 342.636i) q^{85} +374.147i q^{86} +(57.9385 + 100.352i) q^{87} +(457.798 - 792.929i) q^{88} +(103.406 + 59.7013i) q^{89} +127.729 q^{90} +(782.885 + 563.829i) q^{91} -380.532 q^{92} +(-229.643 - 132.584i) q^{93} +(31.1758 - 53.9980i) q^{94} +(-1137.49 - 1970.18i) q^{95} +456.241i q^{96} +(480.341 - 277.325i) q^{97} +(-64.0928 + 37.0040i) q^{98} +592.578i 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 $

$2$	−0.794469	−	0.458687i	−0.280887	−	0.162170i	0.352938	−	0.935647i	$-0.385183\pi$
$2$	−0.794469	−	0.458687i	−0.280887	−	0.162170i	−0.633825	+	0.773476i	$0.718516\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−3.57921	−	6.19938i	−0.447402	−	0.774922i
$5$		−	15.4704i		−	1.38372i	−0.722034	−	0.691858i	$-0.756792\pi$
$5$		−	15.4704i		−	1.38372i	0.722034	−	0.691858i	$-0.243208\pi$
$6$	2.38341	−	1.37606i	0.162170	−	0.0936291i
$7$	17.8257	−	10.2917i	0.962497	−	0.555698i	0.0655563	−	0.997849i	$-0.479118\pi$
$7$	17.8257	−	10.2917i	0.962497	−	0.555698i	0.896941	+	0.442151i	$0.145784\pi$
$8$			13.9059i			0.614562i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−7.09608	+	12.2908i	−0.224398	+	0.388668i
$11$	−57.0209	−	32.9210i	−1.56295	−	0.902369i	−0.996957	−	0.0779583i	$-0.975160\pi$
$11$	−57.0209	−	32.9210i	−1.56295	−	0.902369i	−0.565992	−	0.824411i	$-0.691507\pi$
$12$	21.4753			0.516615
$13$	19.2429	+	42.7400i	0.410540	+	0.911842i
$13$	19.2429	+	42.7400i	0.410540	+	0.911842i
$14$	−18.8826			−0.360471
$15$	40.1933	+	23.2056i	0.691858	+	0.399444i
$16$	−22.2552	+	38.5472i	−0.347738	+	0.602300i
$17$	22.1478	+	38.3611i	0.315979	+	0.547291i	0.979645	−	0.200738i	$-0.0643339\pi$
$17$	22.1478	+	38.3611i	0.315979	+	0.547291i	−0.663666	+	0.748029i	$0.731001\pi$
$18$			8.25636i			0.108114i
$19$	127.352	−	73.5266i	1.53771	−	0.887798i	0.538738	−	0.842473i	$-0.318901\pi$
$19$	127.352	−	73.5266i	1.53771	−	0.887798i	0.998972	−	0.0453247i	$-0.0144322\pi$
$20$	−95.9069	+	55.3719i	−1.07227	+	0.619077i
$21$			61.7500i			0.641665i
$22$	30.2009	+	52.3094i	0.292675	+	0.506928i
$23$	26.5793	−	46.0367i	0.240964	−	0.417362i	−0.720025	−	0.693948i	$-0.755870\pi$
$23$	26.5793	−	46.0367i	0.240964	−	0.417362i	0.960989	+	0.276586i	$0.0892031\pi$
$24$	−36.1287	−	20.8589i	−0.307281	−	0.177409i
$25$	−114.334			−0.914669
$26$	4.31639	−	42.7821i	0.0325582	−	0.322702i
$27$	27.0000			0.192450
$28$	−127.604	−	73.6721i	−0.861245	−	0.497240i
$29$	19.3128	−	33.4508i	0.123666	−	0.214195i	−0.797545	−	0.603260i	$-0.793868\pi$
$29$	19.3128	−	33.4508i	0.123666	−	0.214195i	0.921211	+	0.389064i	$0.127202\pi$
$30$	−21.2882	−	36.8723i	−0.129556	−	0.224398i
$31$			88.3894i			0.512104i	0.966663	+	0.256052i	$0.0824218\pi$
$31$			88.3894i			0.512104i	−0.966663	+	0.256052i	$0.917578\pi$
$32$	131.705	−	76.0401i	0.727576	−	0.420066i
$33$	171.063	−	98.7630i	0.902369	−	0.520983i
$34$		−	40.6357i		−	0.204969i
$35$	−159.216	−	275.771i	−0.768928	−	1.33182i
$36$	−32.2129	+	55.7944i	−0.149134	+	0.258307i
$37$	68.3803	+	39.4794i	0.303828	+	0.175415i	0.644161	−	0.764890i	$-0.277206\pi$
$37$	68.3803	+	39.4794i	0.303828	+	0.175415i	−0.340333	+	0.940305i	$0.610540\pi$
$38$	−134.903			−0.575898
$39$	−139.906	−	14.1155i	−0.574434	−	0.0579561i
$40$	215.131			0.850379
$41$	307.410	+	177.483i	1.17096	+	0.676054i	0.953906	−	0.300106i	$-0.0970221\pi$
$41$	307.410	+	177.483i	1.17096	+	0.676054i	0.217053	+	0.976160i	$0.430355\pi$
$42$	28.3239	−	49.0585i	0.104059	−	0.180235i
$43$	−203.923	−	353.205i	−0.723208	−	1.25263i	−0.959707	−	0.281002i	$-0.909333\pi$
$43$	−203.923	−	353.205i	−0.723208	−	1.25263i	0.236499	−	0.971632i	$-0.424000\pi$
$44$			471.325i			1.61489i
$45$	−120.580	+	69.6169i	−0.399444	+	0.230619i
$46$	−42.2329	+	24.3832i	−0.135367	+	0.0781544i
$47$			67.9674i			0.210938i	0.994423	+	0.105469i	$0.0336343\pi$
$47$			67.9674i			0.210938i	−0.994423	+	0.105469i	$0.966366\pi$
$48$	−66.7657	−	115.642i	−0.200767	−	0.347738i
$49$	40.3369	−	69.8656i	0.117600	−	0.203690i
$50$	90.8345	+	52.4433i	0.256919	+	0.148332i
$51$	−132.887			−0.364861
$52$	196.087	−	272.270i	0.522931	−	0.726097i
$53$	226.572			0.587209			0.293604	−	0.955927i	$-0.405145\pi$
$53$	226.572			0.587209			0.293604	+	0.955927i	$0.405145\pi$
$54$	−21.4507	−	12.3845i	−0.0540568	−	0.0312097i
$55$	−509.302	+	882.136i	−1.24862	+	2.16268i
$56$	143.115	+	247.883i	0.341511	+	0.591514i
$57$			441.160i			1.02514i
$58$	−30.6869	+	17.7171i	−0.0694722	+	0.0401098i
$59$	−123.002	+	71.0154i	−0.271416	+	0.156702i	−0.629531	−	0.776976i	$-0.716753\pi$
$59$	−123.002	+	71.0154i	−0.271416	+	0.156702i	0.358115	+	0.933677i	$0.383420\pi$
$60$		−	332.231i		−	0.714848i
$61$	−133.416	−	231.083i	−0.280035	−	0.485034i	0.691358	−	0.722512i	$-0.257013\pi$
$61$	−133.416	−	231.083i	−0.280035	−	0.485034i	−0.971393	+	0.237478i	$0.923679\pi$
$62$	40.5431	−	70.2227i	0.0830480	−	0.143843i
$63$	−160.431	−	92.6250i	−0.320832	−	0.185233i
$64$	216.569			0.422987
$65$	661.206	−	297.696i	1.26173	−	0.568071i
$66$	−181.205			−0.337952
$67$	356.098	+	205.593i	0.649318	+	0.374884i	0.788195	−	0.615426i	$-0.211016\pi$
$67$	356.098	+	205.593i	0.649318	+	0.374884i	−0.138877	+	0.990310i	$0.544349\pi$
$68$	158.543	−	274.605i	0.282739	−	0.489718i
$69$	79.7379	+	138.110i	0.139121	+	0.240964i
$70$			292.122i			0.498789i
$71$	−79.2458	+	45.7526i	−0.132461	+	0.0764765i	−0.564766	−	0.825251i	$-0.691034\pi$
$71$	−79.2458	+	45.7526i	−0.132461	+	0.0764765i	0.432305	+	0.901727i	$0.357700\pi$
$72$	108.386	−	62.5767i	0.177409	−	0.102427i
$73$		−	63.1328i		−	0.101221i	−0.998718	−	0.0506105i	$-0.983883\pi$
$73$		−	63.1328i		−	0.101221i	0.998718	−	0.0506105i	$-0.0161167\pi$
$74$	−36.2173	−	62.7303i	−0.0568943	−	0.0985439i
$75$	171.500	−	297.047i	0.264042	−	0.457335i
$76$	−911.638	−	526.335i	−1.37595	−	0.794404i
$77$	−1355.25			−2.00578
$78$	104.677	+	75.3875i	0.151952	+	0.109435i
$79$	−287.115			−0.408899			−0.204449	−	0.978877i	$-0.565540\pi$
$79$	−287.115			−0.408899			−0.204449	+	0.978877i	$0.565540\pi$
$80$	596.341	+	344.298i	0.833412	+	0.481170i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−162.818	−	282.010i	−0.219272	−	0.379790i
$83$		−	373.812i		−	0.494352i	−0.968971	−	0.247176i	$-0.920497\pi$
$83$		−	373.812i		−	0.494352i	0.968971	−	0.247176i	$-0.0795026\pi$
$84$	382.812	−	221.016i	0.497240	−	0.287082i
$85$	593.463	−	342.636i	0.757295	−	0.437224i
$86$			374.147i			0.469132i
$87$	57.9385	+	100.352i	0.0713984	+	0.123666i
$88$	457.798	−	792.929i	0.554561	−	0.960528i
$89$	103.406	+	59.7013i	0.123157	+	0.0711047i	0.560313	−	0.828281i	$-0.310681\pi$
$89$	103.406	+	59.7013i	0.123157	+	0.0711047i	−0.437156	+	0.899386i	$0.644014\pi$
$90$	127.729			0.149598
$91$	782.885	+	563.829i	0.901853	+	0.649509i
$92$	−380.532			−0.431231
$93$	−229.643	−	132.584i	−0.256052	−	0.147832i
$94$	31.1758	−	53.9980i	0.0342078	−	0.0592497i
$95$	−1137.49	−	1970.18i	−1.22846	−	2.12775i
$96$			456.241i			0.485051i
$97$	480.341	−	277.325i	0.502796	−	0.290290i	−0.227071	−	0.973878i	$-0.572915\pi$
$97$	480.341	−	277.325i	0.502796	−	0.290290i	0.729868	+	0.683589i	$0.239582\pi$
$98$	−64.0928	+	37.0040i	−0.0660648	+	0.0381426i
$99$			592.578i			0.601579i
$100$	409.224	+	708.797i	0.409224	+	0.708797i
$101$	−231.282	+	400.593i	−0.227856	+	0.394658i	−0.957172	−	0.289518i	$-0.906505\pi$
$101$	−231.282	+	400.593i	−0.227856	+	0.394658i	0.729317	+	0.684176i	$0.239838\pi$
$102$	105.575	+	60.9535i	0.102485	+	0.0591696i
$103$	−1122.07			−1.07341			−0.536704	−	0.843771i	$-0.680331\pi$
$103$	−1122.07			−1.07341			−0.536704	+	0.843771i	$0.680331\pi$
$104$	−594.340	+	267.591i	−0.560383	+	0.252302i
$105$	955.298			0.887881
$106$	−180.005	−	103.926i	−0.164939	−	0.0952279i
$107$	−301.378	+	522.002i	−0.272293	+	0.471625i	−0.969449	−	0.245295i	$-0.921115\pi$
$107$	−301.378	+	522.002i	−0.272293	+	0.471625i	0.697156	+	0.716920i	$0.254449\pi$
$108$	−96.6387	−	167.383i	−0.0861025	−	0.149134i
$109$			1421.89i			1.24947i	0.780837	+	0.624735i	$0.214793\pi$
$109$			1421.89i			1.24947i	−0.780837	+	0.624735i	$0.785207\pi$
$110$	809.249	−	467.220i	0.701444	−	0.404979i
$111$	−205.141	+	118.438i	−0.175415	+	0.101276i
$112$			916.174i			0.772949i
$113$	198.359	+	343.569i	0.165134	+	0.286020i	0.936703	−	0.350126i	$-0.113861\pi$
$113$	198.359	+	343.569i	0.165134	+	0.286020i	−0.771569	+	0.636145i	$0.780528\pi$
$114$	202.354	−	350.488i	0.166247	−	0.287949i
$115$	−712.207	−	411.193i	−0.577510	−	0.333426i
$116$	−276.499			−0.221313
$117$	246.532	−	342.314i	0.194803	−	0.270487i
$118$	130.295			0.101650
$119$	789.600	+	455.876i	0.608257	+	0.351177i
$120$	−322.696	+	558.926i	−0.245483	+	0.425189i
$121$	1502.09	+	2601.69i	1.12854	+	1.95469i
$122$			244.784i			0.181653i
$123$	−922.229	+	532.449i	−0.676054	+	0.390320i
$124$	547.960	−	316.365i	0.396841	−	0.229116i
$125$		−	165.013i		−	0.118074i
$126$	84.9718	+	147.175i	0.0600785	+	0.104059i
$127$	218.934	−	379.205i	0.152970	−	0.264952i	−0.779348	−	0.626592i	$-0.784449\pi$
$127$	218.934	−	379.205i	0.152970	−	0.264952i	0.932318	+	0.361639i	$0.117783\pi$
$128$	−1225.70	−	707.659i	−0.846388	−	0.488662i
$129$	1223.54			0.835089
$130$	−661.857	−	66.7764i	−0.446528	−	0.0450514i
$131$	1657.44			1.10543			0.552715	−	0.833370i	$-0.313592\pi$
$131$	1657.44			1.10543			0.552715	+	0.833370i	$0.313592\pi$
$132$	−1224.54	−	706.988i	−0.807443	−	0.466177i
$133$	1513.42	−	2621.33i	0.986695	−	1.70901i
$134$	−188.606	−	326.675i	−0.121590	−	0.210600i
$135$		−	417.701i		−	0.266296i
$136$	−533.448	+	307.986i	−0.336344	+	0.194188i
$137$	−1703.84	+	983.711i	−1.06254	+	0.613460i	−0.926135	−	0.377192i	$-0.876890\pi$
$137$	−1703.84	+	983.711i	−1.06254	+	0.613460i	−0.136410	+	0.990653i	$0.543556\pi$
$138$		−	146.299i		−	0.0902449i
$139$	−1412.57	−	2446.64i	−0.861960	−	1.49296i	−0.870035	−	0.492990i	$-0.835904\pi$
$139$	−1412.57	−	2446.64i	−0.861960	−	1.49296i	0.00807518	−	0.999967i	$-0.497430\pi$
$140$	−1139.74	+	1974.08i	−0.688039	+	1.19172i
$141$	−176.585	−	101.951i	−0.105469	−	0.0608925i
$142$	83.9445			0.0496089
$143$	309.797	−	3070.57i	0.181165	−	1.79562i
$144$	400.594			0.231825
$145$	−517.498	−	298.777i	−0.296385	−	0.171118i
$146$	−28.9582	+	50.1571i	−0.0164150	+	0.0284317i
$147$	121.011	+	209.597i	0.0678966	+	0.117600i
$148$		−	565.220i		−	0.313924i
$149$	690.792	−	398.829i	0.379811	−	0.219284i	−0.297925	−	0.954589i	$-0.596294\pi$
$149$	690.792	−	398.829i	0.379811	−	0.219284i	0.677736	+	0.735305i	$0.262961\pi$
$150$	−272.504	+	157.330i	−0.148332	+	0.0856396i
$151$			161.987i			0.0873003i	0.999047	+	0.0436501i	$0.0138987\pi$
$151$			161.987i			0.0873003i	−0.999047	+	0.0436501i	$0.986101\pi$
$152$	1022.46	+	1770.95i	0.545606	+	0.945018i
$153$	199.330	−	345.250i	0.105326	−	0.182430i
$154$	1076.70	+	621.635i	0.563397	+	0.325278i
$155$	1367.42			0.708606
$156$	413.247	+	917.854i	0.212091	+	0.471071i
$157$	−342.000			−0.173851			−0.0869255	−	0.996215i	$-0.527704\pi$
$157$	−342.000			−0.173851			−0.0869255	+	0.996215i	$0.527704\pi$
$158$	228.104	+	131.696i	0.114854	+	0.0663112i
$159$	−339.858	+	588.652i	−0.169513	+	0.293604i
$160$	−1176.37	−	2037.54i	−0.581252	−	1.00676i
$161$		−	1094.18i		−	0.535613i
$162$	64.3520	−	37.1536i	0.0312097	−	0.0180189i
$163$	482.027	−	278.299i	0.231628	−	0.133730i	−0.379695	−	0.925112i	$-0.623971\pi$
$163$	482.027	−	278.299i	0.231628	−	0.133730i	0.611323	+	0.791381i	$0.290638\pi$
$164$		−	2541.00i		−	1.20987i
$165$	−1527.90	−	2646.41i	−0.720892	−	1.24862i
$166$	−171.463	+	296.982i	−0.0801693	+	0.138857i
$167$	2716.22	+	1568.21i	1.25861	+	0.726658i	0.972804	−	0.231630i	$-0.0744058\pi$
$167$	2716.22	+	1568.21i	1.25861	+	0.726658i	0.285805	+	0.958288i	$0.407739\pi$
$168$	−858.692			−0.394342
$169$	−1456.42	+	1644.89i	−0.662913	+	0.748696i
$170$	−628.650			−0.283619
$171$	−1146.17	−	661.739i	−0.512570	−	0.295933i
$172$	−1459.77	+	2528.39i	−0.647129	+	1.12086i
$173$	1662.10	+	2878.84i	0.730444	+	1.26517i	0.956693	+	0.291097i	$0.0940204\pi$
$173$	1662.10	+	2878.84i	0.730444	+	1.26517i	−0.226249	+	0.974070i	$0.572646\pi$
$174$		−	106.303i		−	0.0463148i
$175$	−2038.08	+	1176.68i	−0.880366	+	0.508280i
$176$	2538.02	−	1465.33i	1.08699	−	0.627576i
$177$		−	426.092i		−	0.180944i
$178$	−54.7684	−	94.8616i	−0.0230622	−	0.0399448i
$179$	−1656.62	+	2869.36i	−0.691743	+	1.19813i	0.279524	+	0.960139i	$0.409823\pi$
$179$	−1656.62	+	2869.36i	−0.691743	+	1.19813i	−0.971266	+	0.237995i	$0.923510\pi$
$180$	863.162	+	498.347i	0.357424	+	0.206359i
$181$	−76.0118			−0.0312150			−0.0156075	−	0.999878i	$-0.504968\pi$
$181$	−76.0118			−0.0312150			−0.0156075	+	0.999878i	$0.504968\pi$
$182$	−363.357	−	807.044i	−0.147988	−	0.328693i
$183$	800.494			0.323356
$184$	640.184	+	369.610i	0.256494	+	0.148087i
$185$	610.762	−	1057.87i	0.242725	−	0.420412i
$186$	121.629	+	210.668i	0.0479478	+	0.0830480i
$187$		−	2916.51i		−	1.14052i
$188$	421.356	−	243.270i	0.163460	−	0.0943738i
$189$	481.294	−	277.875i	0.185233	−	0.106944i
$190$			2087.00i			0.796879i
$191$	2036.70	+	3527.66i	0.771572	+	1.33640i	0.936701	+	0.350130i	$0.113862\pi$
$191$	2036.70	+	3527.66i	0.771572	+	1.33640i	−0.165129	+	0.986272i	$0.552804\pi$
$192$	−324.854	+	562.663i	−0.122106	+	0.211493i
$193$	751.347	+	433.791i	0.280224	+	0.161787i	0.633525	−	0.773723i	$-0.281608\pi$
$193$	751.347	+	433.791i	0.280224	+	0.161787i	−0.353301	+	0.935510i	$0.614941\pi$
$194$	−508.821			−0.188305
$195$	−218.372	+	2164.41i	−0.0801947	+	0.794853i
$196$	−577.497			−0.210458
$197$	1634.79	+	943.846i	0.591238	+	0.341352i	0.765587	−	0.643332i	$-0.222449\pi$
$197$	1634.79	+	943.846i	0.591238	+	0.341352i	−0.174349	+	0.984684i	$0.555782\pi$
$198$	271.808	−	470.785i	0.0975583	−	0.168976i
$199$	1393.11	+	2412.94i	0.496256	+	0.859540i	0.999991	−	0.00431832i	$-0.00137457\pi$
$199$	1393.11	+	2412.94i	0.496256	+	0.859540i	−0.503735	+	0.863858i	$0.668041\pi$
$200$		−	1589.92i		−	0.562120i
$201$	−1068.29	+	616.780i	−0.374884	+	0.216439i
$202$	367.493	−	212.172i	0.128004	−	0.0739029i
$203$		−	795.045i		−	0.274883i
$204$	475.630	+	823.816i	0.163239	+	0.282739i
$205$	2745.74	−	4755.75i	0.935466	−	1.62027i
$206$	891.451	+	514.680i	0.301507	+	0.174075i
$207$	−478.428			−0.160643
$208$	−2075.76	−	209.429i	−0.691963	−	0.0698139i
$209$	−9682.28			−3.20448
$210$	−758.955	−	438.183i	−0.249395	−	0.143988i
$211$	−354.395	+	613.830i	−0.115628	+	0.200274i	−0.918031	−	0.396509i	$-0.870221\pi$
$211$	−354.395	+	613.830i	−0.115628	+	0.200274i	0.802403	+	0.596783i	$0.203555\pi$
$212$	−810.950	−	1404.61i	−0.262718	−	0.455041i
$213$		−	274.516i		−	0.0883075i
$214$	478.871	−	276.476i	0.152967	−	0.0883156i
$215$	−5464.22	+	3154.77i	−1.73329	+	1.00071i
$216$			375.460i			0.118272i
$217$	909.675	+	1575.60i	0.284575	+	0.492898i
$218$	652.202	−	1129.65i	0.202627	−	0.350960i
$219$	164.024	+	94.6992i	0.0506105	+	0.0292200i
$220$	7291.59			2.23454
$221$	−1213.37	+	1684.78i	−0.369321	+	0.512808i
$222$	217.304			0.0656959
$223$	−4673.62	−	2698.32i	−1.40345	−	0.810281i	−0.408703	−	0.912667i	$-0.634019\pi$
$223$	−4673.62	−	2698.32i	−1.40345	−	0.810281i	−0.994745	+	0.102386i	$0.967352\pi$
$224$	1565.16	−	2710.94i	0.466860	−	0.808625i
$225$	514.501	+	891.142i	0.152445	+	0.264042i
$226$		−	363.940i		−	0.107119i
$227$	2755.51	−	1590.90i	0.805682	−	0.465160i	−0.0397724	−	0.999209i	$-0.512663\pi$
$227$	2755.51	−	1590.90i	0.805682	−	0.465160i	0.845454	+	0.534048i	$0.179330\pi$
$228$	2734.91	−	1579.00i	0.794404	−	0.458649i
$229$		−	2034.00i		−	0.586945i	−0.955967	−	0.293473i	$-0.905189\pi$
$229$		−	2034.00i		−	0.586945i	0.955967	−	0.293473i	$-0.0948110\pi$
$230$	377.218	+	653.360i	0.108143	+	0.187310i
$231$	2032.87	−	3521.04i	0.579018	−	1.00289i
$232$	465.165	+	268.563i	0.131636	+	0.0760001i
$233$	2794.22			0.785645			0.392823	−	0.919614i	$-0.371499\pi$
$233$	2794.22			0.785645			0.392823	+	0.919614i	$0.371499\pi$
$234$	−352.877	+	158.877i	−0.0985825	+	0.0443850i
$235$	1051.48			0.291878
$236$	880.502	+	508.358i	0.242864	+	0.140217i
$237$	430.673	−	745.948i	0.118039	−	0.204449i
$238$	−418.209	−	724.359i	−0.113901	−	0.197282i
$239$		−	5493.81i		−	1.48688i	−0.668800	−	0.743442i	$-0.733192\pi$
$239$		−	5493.81i		−	1.48688i	0.668800	−	0.743442i	$-0.266808\pi$
$240$	−1789.02	+	1032.89i	−0.481170	+	0.277804i
$241$	−3517.16	+	2030.63i	−0.940084	+	0.542758i	−0.889987	−	0.455986i	$-0.849287\pi$
$241$	−3517.16	+	2030.63i	−0.940084	+	0.542758i	−0.0500976	+	0.998744i	$0.515953\pi$
$242$		−	2755.95i		−	0.732062i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	−955.046	+	1654.19i	−0.250576	+	0.434010i
$245$	−1080.85	−	624.028i	−0.281849	−	0.162725i
$246$	976.910			0.253193
$247$	5593.15	+	4028.15i	1.44082	+	1.03767i
$248$	−1229.14			−0.314719
$249$	971.193	+	560.719i	0.247176	+	0.142707i
$250$	−75.6894	+	131.098i	−0.0191481	+	0.0331654i
$251$	−1785.44	−	3092.47i	−0.448988	−	0.777670i	0.549332	−	0.835604i	$-0.314882\pi$
$251$	−1785.44	−	3092.47i	−0.448988	−	0.777670i	−0.998320	+	0.0579336i	$0.981549\pi$
$252$			1326.10i			0.331493i
$253$	−3031.15	+	1750.04i	−0.753228	+	0.434877i
$254$	−347.872	+	200.844i	−0.0859348	+	0.0496145i
$255$			2055.82i			0.504863i
$256$	−217.089	−	376.010i	−0.0530003	−	0.0917993i
$257$	−3759.13	+	6511.01i	−0.912405	+	1.58033i	−0.101749	+	0.994810i	$0.532444\pi$
$257$	−3759.13	+	6511.01i	−0.912405	+	1.58033i	−0.810656	+	0.585522i	$0.800889\pi$
$258$	−972.063	−	561.221i	−0.234566	−	0.135427i
$259$	1625.23			0.389912
$260$	−4212.13	−	3033.55i	−1.00471	−	0.723587i
$261$	−347.631			−0.0824437
$262$	−1316.79	−	760.246i	−0.310501	−	0.179268i
$263$	2330.09	−	4035.84i	0.546310	−	0.946237i	−0.452213	−	0.891910i	$-0.649365\pi$
$263$	2330.09	−	4035.84i	0.546310	−	0.946237i	0.998523	−	0.0543273i	$-0.0173014\pi$
$264$	1373.39	+	2378.79i	0.320176	+	0.554561i
$265$		−	3505.16i		−	0.812530i
$266$	−2404.73	+	1388.37i	−0.554300	+	0.320025i
$267$	−310.217	+	179.104i	−0.0711047	+	0.0410523i
$268$		−	2943.45i		−	0.670895i
$269$	−2673.72	−	4631.02i	−0.606021	−	1.04966i	−0.991889	−	0.127105i	$-0.959432\pi$
$269$	−2673.72	−	4631.02i	−0.606021	−	1.04966i	0.385869	−	0.922554i	$-0.373902\pi$
$270$	−191.594	+	331.851i	−0.0431853	+	0.0747992i
$271$	2574.76	+	1486.54i	0.577143	+	0.333214i	0.759997	−	0.649926i	$-0.225200\pi$
$271$	2574.76	+	1486.54i	0.577143	+	0.333214i	−0.182854	+	0.983140i	$0.558534\pi$
$272$	−1971.62			−0.439511
$273$	−2639.20	+	1188.25i	−0.585097	+	0.263429i
$274$	1804.86			0.397940
$275$	6519.40	+	3763.98i	1.42958	+	0.825369i
$276$	570.798	−	988.651i	0.124486	−	0.215615i
$277$	−382.076	−	661.776i	−0.0828764	−	0.143546i	0.821608	−	0.570053i	$-0.193077\pi$
$277$	−382.076	−	661.776i	−0.0828764	−	0.143546i	−0.904484	+	0.426507i	$0.859744\pi$
$278$			2591.70i			0.559137i
$279$	688.928	−	397.752i	0.147832	−	0.0853506i
$280$	3834.85	−	2214.05i	0.818487	−	0.472554i
$281$			7040.34i			1.49463i	0.664469	+	0.747316i	$0.268658\pi$
$281$			7040.34i			1.49463i	−0.664469	+	0.747316i	$0.731342\pi$
$282$	93.5273	+	161.994i	0.0197499	+	0.0342078i
$283$	−4517.58	+	7824.68i	−0.948913	+	1.64357i	−0.201194	+	0.979551i	$0.564482\pi$
$283$	−4517.58	+	7824.68i	−0.948913	+	1.64357i	−0.747720	+	0.664015i	$0.768851\pi$
$284$	567.275	+	327.517i	0.118527	+	0.0684314i
$285$	6824.92			1.41850
$286$	−1654.55	+	2297.37i	−0.342083	+	0.474988i
$287$	7306.39			1.50273
$288$	−1185.35	−	684.361i	−0.242525	−	0.140022i
$289$	1475.45	−	2555.55i	0.300315	−	0.520161i
$290$	274.091	+	474.739i	0.0555005	+	0.0961297i
$291$			1663.95i			0.335197i
$292$	−391.384	+	225.966i	−0.0784384	+	0.0452865i
$293$	−1546.06	+	892.617i	−0.308265	+	0.177977i	−0.646150	−	0.763211i	$-0.723622\pi$
$293$	−1546.06	+	892.617i	−0.308265	+	0.177977i	0.337885	+	0.941188i	$0.390289\pi$
$294$		−	222.024i		−	0.0440432i
$295$	1098.64	+	1902.89i	0.216831	+	0.375562i
$296$	−548.998	+	950.892i	−0.107804	+	0.186721i
$297$	−1539.56	−	888.867i	−0.300790	−	0.173661i
$298$	−731.751			−0.142246
$299$	2479.07	+	250.120i	0.479494	+	0.0483773i
$300$	−2455.35			−0.472532
$301$	−7270.13	−	4197.41i	−1.39217	−	0.803771i
$302$	74.3015	−	128.694i	0.0141575	−	0.0245215i
$303$	−693.847	−	1201.78i	−0.131553	−	0.227856i
$304$			6545.40i			1.23488i
$305$	−3574.94	+	2063.99i	−0.671150	+	0.387488i
$306$	−316.724	+	182.860i	−0.0591696	+	0.0341616i
$307$		−	5323.13i		−	0.989600i	−0.869007	−	0.494800i	$-0.835241\pi$
$307$		−	5323.13i		−	0.989600i	0.869007	−	0.494800i	$-0.164759\pi$
$308$	4850.72	+	8401.70i	0.897388	+	1.55432i
$309$	1683.11	−	2915.23i	0.309866	−	0.536704i
$310$	−1086.37	−	627.218i	−0.199038	−	0.114915i
$311$	−6265.64			−1.14242			−0.571209	−	0.820805i	$-0.693525\pi$
$311$	−6265.64			−1.14242			−0.571209	+	0.820805i	$0.693525\pi$
$312$	196.289	−	1945.53i	0.0356176	−	0.353025i
$313$	7193.77			1.29909			0.649547	−	0.760322i	$-0.274959\pi$
$313$	7193.77			1.29909			0.649547	+	0.760322i	$0.274959\pi$
$314$	271.709	+	156.871i	0.0488325	+	0.0281935i
$315$	−1432.95	+	2481.94i	−0.256309	+	0.443941i
$316$	1027.65	+	1779.94i	0.182942	+	0.316865i
$317$		−	9576.87i		−	1.69682i	−0.529343	−	0.848408i	$-0.677561\pi$
$317$		−	9576.87i		−	1.69682i	0.529343	−	0.848408i	$-0.322439\pi$
$318$	540.014	−	311.777i	0.0952279	−	0.0549798i
$319$	−2202.47	+	1271.60i	−0.386566	+	0.223184i
$320$		−	3350.41i		−	0.585293i
$321$	−904.134	−	1566.01i	−0.157208	−	0.272293i
$322$	−501.887	+	869.294i	−0.0868604	+	0.150447i
$323$	5641.13	+	3256.91i	0.971767	+	0.561050i
$324$	579.832			0.0994226
$325$	−2200.11	−	4886.62i	−0.375509	−	0.834034i
$326$	−510.608			−0.0867483
$327$	−3694.18	−	2132.83i	−0.624735	−	0.360691i
$328$	−2468.07	+	4274.82i	−0.415477	+	0.719627i
$329$	699.498	+	1211.57i	0.117218	+	0.203027i
$330$			2803.32i			0.467629i
$331$	4999.68	−	2886.56i	0.830233	−	0.479335i	−0.0236996	−	0.999719i	$-0.507545\pi$
$331$	4999.68	−	2886.56i	0.830233	−	0.479335i	0.853932	+	0.520384i	$0.174211\pi$
$332$	−2317.40	+	1337.95i	−0.383085	+	0.221174i
$333$		−	710.629i		−	0.116944i
$334$	−1438.64	−	2491.79i	−0.235685	−	0.408218i
$335$	3180.61	−	5508.98i	0.518733	−	0.898471i
$336$	−2380.29	−	1374.26i	−0.386474	−	0.223131i
$337$	−1238.09			−0.200127			−0.100063	−	0.994981i	$-0.531905\pi$
$337$	−1238.09			−0.200127			−0.100063	+	0.994981i	$0.531905\pi$
$338$	1911.57	−	638.770i	0.307620	−	0.102794i
$339$	−1190.16			−0.190680
$340$	−4248.26	−	2452.73i	−0.677630	−	0.391230i
$341$	2909.87	−	5040.04i	0.462106	−	0.800392i
$342$	607.062	+	1051.46i	0.0959830	+	0.166247i
$343$			5399.55i			0.849995i
$344$	4911.65	−	2835.74i	0.769820	−	0.444456i
$345$	2136.62	−	1233.58i	0.333426	−	0.192503i
$346$		−	3049.53i		−	0.473826i
$347$	−2724.98	−	4719.81i	−0.421570	−	0.730181i	0.574523	−	0.818488i	$-0.305187\pi$
$347$	−2724.98	−	4719.81i	−0.421570	−	0.730181i	−0.996093	+	0.0883076i	$0.971854\pi$
$348$	414.748	−	718.365i	0.0638875	−	0.110656i
$349$	−1189.95	−	687.016i	−0.182511	−	0.105373i	0.405961	−	0.913890i	$-0.366937\pi$
$349$	−1189.95	−	687.016i	−0.182511	−	0.105373i	−0.588472	+	0.808518i	$0.700270\pi$
$350$	2158.92			0.329711
$351$	519.559	+	1153.98i	0.0790085	+	0.175484i
$352$	−10013.3			−1.51622
$353$	5170.55	+	2985.22i	0.779606	+	0.450106i	0.836291	−	0.548287i	$-0.184720\pi$
$353$	5170.55	+	2985.22i	0.779606	+	0.450106i	−0.0566848	+	0.998392i	$0.518053\pi$
$354$	−195.443	+	338.517i	−0.0293437	+	0.0508248i
$355$	707.811	+	1225.97i	0.105822	+	0.183289i
$356$		−	854.734i		−	0.127249i
$357$	−2368.80	+	1367.63i	−0.351177	+	0.202752i
$358$	2632.27	−	1519.74i	0.388603	−	0.224360i
$359$			7813.71i			1.14872i	0.818602	+	0.574362i	$0.194750\pi$
$359$			7813.71i			1.14872i	−0.818602	+	0.574362i	$0.805250\pi$
$360$	−968.088	−	1676.78i	−0.141730	−	0.245483i
$361$	7382.82	−	12787.4i	1.07637	−	1.86433i
$362$	60.3891	+	34.8656i	0.00876790	+	0.00506215i
$363$	−9012.52			−1.30312
$364$	693.279	−	6871.46i	0.0998288	−	0.989457i
$365$	−976.690			−0.140061
$366$	−635.967	−	367.176i	−0.0908266	−	0.0524388i
$367$	−844.195	+	1462.19i	−0.120073	+	0.207972i	−0.919796	−	0.392397i	$-0.871646\pi$
$367$	−844.195	+	1462.19i	−0.120073	+	0.207972i	0.799724	+	0.600368i	$0.204979\pi$
$368$	1183.06	+	2049.12i	0.167585	+	0.290265i
$369$		−	3194.69i		−	0.450702i
$370$	−970.463	+	560.297i	−0.136357	+	0.0787256i
$371$	4038.80	−	2331.81i	0.565187	−	0.326311i
$372$			1898.19i			0.264560i
$373$	−935.307	−	1620.00i	−0.129835	−	0.224880i	0.793778	−	0.608208i	$-0.208111\pi$
$373$	−935.307	−	1620.00i	−0.129835	−	0.224880i	−0.923612	+	0.383328i	$0.874778\pi$
$374$	−1337.77	+	2317.08i	−0.184958	+	0.320357i
$375$	428.717	+	247.520i	0.0590369	+	0.0340850i
$376$	−945.151			−0.129634
$377$	1801.32	+	181.740i	0.246082	+	0.0248278i
$378$	−509.831			−0.0693726
$379$	10103.9	+	5833.52i	1.36941	+	0.790627i	0.990852	−	0.134952i	$-0.0430882\pi$
$379$	10103.9	+	5833.52i	1.36941	+	0.790627i	0.378554	+	0.925579i	$0.376421\pi$
$380$	−8142.61	+	14103.4i	−1.09923	+	1.90392i
$381$	656.801	+	1137.61i	0.0883175	+	0.152970i
$382$		−	3736.82i		−	0.500504i
$383$	5782.11	−	3338.30i	0.771415	−	0.445376i	−0.0619643	−	0.998078i	$-0.519737\pi$
$383$	5782.11	−	3338.30i	0.771415	−	0.445376i	0.833379	+	0.552702i	$0.186403\pi$
$384$	3677.10	−	2122.98i	0.488662	−	0.282129i
$385$			20966.3i			2.77543i
$386$	−397.948	−	689.266i	−0.0524742	−	0.0908879i
$387$	−1835.31	+	3178.84i	−0.241069	+	0.417544i
$388$	−3438.48	−	1985.21i	−0.449904	−	0.259752i
$389$	−14285.3			−1.86194			−0.930969	−	0.365099i	$-0.881035\pi$
$389$	−14285.3			−1.86194			−0.930969	+	0.365099i	$0.881035\pi$
$390$	1166.28	−	1619.39i	0.151427	−	0.210259i
$391$	2354.69			0.304558
$392$	971.547	+	560.923i	0.125180	+	0.0722726i
$393$	−2486.16	+	4306.16i	−0.319110	+	0.552715i
$394$	−865.860	−	1499.71i	−0.110714	−	0.191763i
$395$			4441.79i			0.565800i
$396$	3673.62	−	2120.96i	0.466177	−	0.269148i
$397$	3091.09	−	1784.64i	0.390774	−	0.225614i	−0.291721	−	0.956503i	$-0.594228\pi$
$397$	3091.09	−	1784.64i	0.390774	−	0.225614i	0.682496	+	0.730890i	$0.260895\pi$
$398$		−	2556.00i		−	0.321912i
$399$	4540.27	+	7863.98i	0.569668	+	0.986695i
$400$	2544.52	−	4407.24i	0.318065	−	0.550905i
$401$	−432.448	−	249.674i	−0.0538540	−	0.0310926i	0.472831	−	0.881153i	$-0.343232\pi$
$401$	−432.448	−	249.674i	−0.0538540	−	0.0310926i	−0.526685	+	0.850060i	$0.676565\pi$
$402$	1131.64			0.140400
$403$	−3777.77	+	1700.87i	−0.466958	+	0.210239i
$404$	3311.23			0.407772
$405$	1085.22	+	626.552i	0.133148	+	0.0768731i
$406$	−364.677	+	631.639i	−0.0445778	+	0.0772111i
$407$	−2599.40	−	4502.30i	−0.316579	−	0.548331i
$408$		−	1847.92i		−	0.224229i
$409$	−9056.46	+	5228.75i	−1.09490	+	0.632140i	−0.934876	−	0.354974i	$-0.884490\pi$
$409$	−9056.46	+	5228.75i	−1.09490	+	0.632140i	−0.160022	+	0.987114i	$0.551156\pi$
$410$	−4362.80	+	2518.87i	−0.525521	+	0.303410i
$411$		−	5902.26i		−	0.708363i
$412$	4016.13	+	6956.15i	0.480245	+	0.831808i
$413$	−1461.73	+	2531.80i	−0.174158	+	0.301650i
$414$	380.096	+	219.448i	0.0451225	+	0.0260515i
$415$	−5783.03			−0.684043
$416$	5784.35	+	4165.86i	0.681734	+	0.490981i
$417$	8475.40			0.995305
$418$	7692.27	+	4441.13i	0.900099	+	0.519672i
$419$	852.710	−	1476.94i	0.0994215	−	0.172203i	−0.812024	−	0.583624i	$-0.801634\pi$
$419$	852.710	−	1476.94i	0.0994215	−	0.172203i	0.911445	+	0.411421i	$0.134967\pi$
$420$	−3419.22	−	5922.25i	−0.397240	−	0.688039i
$421$			8765.57i			1.01475i	0.861727	+	0.507373i	$0.169383\pi$
$421$			8765.57i			1.01475i	−0.861727	+	0.507373i	$0.830617\pi$
$422$	563.111	−	325.112i	0.0649569	−	0.0375029i
$423$	529.754	−	305.853i	0.0608925	−	0.0351563i
$424$			3150.70i			0.360876i
$425$	−2532.24	−	4385.97i	−0.289016	−	0.500590i
$426$	−125.917	+	218.094i	−0.0143209	+	0.0248044i
$427$	−4756.45	−	2746.14i	−0.539065	−	0.311229i
$428$	4314.79			0.487297
$429$	7512.88	+	5410.73i	0.845513	+	0.608934i
$430$	5788.21			0.649145
$431$	−6997.81	−	4040.18i	−0.782071	−	0.451529i	0.0550930	−	0.998481i	$-0.482454\pi$
$431$	−6997.81	−	4040.18i	−0.782071	−	0.451529i	−0.837164	+	0.546953i	$0.815788\pi$
$432$	−600.891	+	1040.77i	−0.0669222	+	0.115913i
$433$	−2062.24	−	3571.91i	−0.228880	−	0.396432i	0.728596	−	0.684943i	$-0.240173\pi$
$433$	−2062.24	−	3571.91i	−0.228880	−	0.396432i	−0.957476	+	0.288511i	$0.906840\pi$
$434$		−	1669.02i		−	0.184598i
$435$	1552.49	−	896.332i	0.171118	−	0.0987950i
$436$	8814.83	−	5089.24i	0.968242	−	0.559015i
$437$		−	7817.14i		−	0.855709i
$438$	−86.8746	−	150.471i	−0.00947723	−	0.0164150i
$439$	−3057.76	+	5296.19i	−0.332435	+	0.575794i	−0.982989	−	0.183666i	$-0.941203\pi$
$439$	−3057.76	+	5296.19i	−0.332435	+	0.575794i	0.650554	+	0.759460i	$0.274537\pi$
$440$	−12266.9	−	7082.32i	−1.32910	−	0.767355i
$441$	−726.064			−0.0784002
$442$	1736.77	−	781.948i	0.186900	−	0.0841482i
$443$	−11058.8			−1.18605			−0.593025	−	0.805184i	$-0.702067\pi$
$443$	−11058.8			−1.18605			−0.593025	+	0.805184i	$0.702067\pi$
$444$	1468.49	+	847.830i	0.156962	+	0.0906222i
$445$	923.603	−	1599.73i	0.0983887	−	0.170414i
$446$	2475.37	+	4287.46i	0.262807	+	0.455195i
$447$			2392.97i			0.253208i
$448$	3860.50	−	2228.86i	0.407123	−	0.235053i
$449$	209.588	−	121.006i	0.0220291	−	0.0127185i	−0.488945	−	0.872315i	$-0.662618\pi$
$449$	209.588	−	121.006i	0.0220291	−	0.0127185i	0.510974	+	0.859596i	$0.329285\pi$
$450$		−	943.980i		−	0.0988881i
$451$	−11685.8	−	20240.5i	−1.22010	−	2.11327i
$452$	1419.94	−	2459.41i	0.147762	−	0.255931i
$453$	−420.855	−	242.981i	−0.0436501	−	0.0252014i
$454$	−2918.89			−0.301741
$455$	8722.67	−	12111.5i	0.898736	−	1.24791i
$456$	−6134.74			−0.630012
$457$	9571.46	+	5526.08i	0.979724	+	0.565644i	0.902187	−	0.431346i	$-0.141961\pi$
$457$	9571.46	+	5526.08i	0.979724	+	0.565644i	0.0775372	+	0.996989i	$0.475294\pi$
$458$	−932.969	+	1615.95i	−0.0951851	+	0.164865i
$459$	597.991	+	1035.75i	0.0608101	+	0.105326i
$460$			5886.99i			0.596700i
$461$	237.086	−	136.882i	0.0239527	−	0.0138291i	−0.487976	−	0.872857i	$-0.662265\pi$
$461$	237.086	−	136.882i	0.0239527	−	0.0138291i	0.511929	+	0.859028i	$0.328931\pi$
$462$	−3230.11	+	1864.90i	−0.325278	+	0.187799i
$463$		−	11579.2i		−	1.16227i	−0.813808	−	0.581134i	$-0.802609\pi$
$463$		−	11579.2i		−	1.16227i	0.813808	−	0.581134i	$-0.197391\pi$
$464$	859.623	+	1488.91i	0.0860064	+	0.148968i
$465$	−2051.13	+	3552.66i	−0.204557	+	0.354303i
$466$	−2219.92	−	1281.67i	−0.220678	−	0.127408i
$467$	−902.915			−0.0894688			−0.0447344	−	0.998999i	$-0.514244\pi$
$467$	−902.915			−0.0894688			−0.0447344	+	0.998999i	$0.514244\pi$
$468$	−3004.52	−	303.134i	−0.296761	−	0.0299410i
$469$	8463.59			0.833289
$470$	−835.372	−	482.302i	−0.0819847	−	0.0473339i
$471$	513.001	−	888.543i	0.0501865	−	0.0869255i
$472$	−987.535	−	1710.46i	−0.0963030	−	0.166802i
$473$			26853.4i			2.61040i
$474$	−684.313	+	395.088i	−0.0663112	+	0.0382848i
$475$	−14560.6	+	8406.56i	−1.40650	+	0.812041i
$476$		−	6526.71i		−	0.628469i
$477$	−1019.57	−	1765.95i	−0.0978682	−	0.169513i
$478$	−2519.94	+	4364.67i	−0.241128	+	0.417647i
$479$	−10451.9	−	6034.38i	−0.996988	−	0.575611i	−0.0896324	−	0.995975i	$-0.528569\pi$
$479$	−10451.9	−	6034.38i	−0.996988	−	0.575611i	−0.907356	+	0.420364i	$0.861903\pi$
$480$	7058.23			0.671172
$481$	−371.514	+	3682.27i	−0.0352174	+	0.349059i
$482$	3725.70			0.352077
$483$	2842.77	+	1641.27i	0.267806	+	0.154618i
$484$	10752.6	−	18624.0i	1.00982	−	1.74906i
$485$	−4290.33	−	7431.07i	−0.401678	−	0.695727i
$486$			222.922i			0.0208065i
$487$	9952.82	−	5746.26i	0.926089	−	0.534678i	0.0405163	−	0.999179i	$-0.487100\pi$
$487$	9952.82	−	5746.26i	0.926089	−	0.534678i	0.885572	+	0.464501i	$0.153766\pi$
$488$	3213.42	−	1855.27i	0.298084	−	0.172099i
$489$			1669.79i			0.154418i
$490$	572.467	+	991.543i	0.0527785	+	0.0914150i
$491$	7852.08	−	13600.2i	0.721710	−	1.25004i	−0.238605	−	0.971117i	$-0.576690\pi$
$491$	7852.08	−	13600.2i	0.721710	−	1.25004i	0.960314	−	0.278921i	$-0.0899767\pi$
$492$	6601.71	+	3811.50i	0.604935	+	0.349259i
$493$	1710.95			0.156303
$494$	−2595.92	−	5765.75i	−0.236429	−	0.525128i
$495$	9167.43			0.832415
$496$	−3407.16	−	1967.13i	−0.308440	−	0.178078i
$497$	−941.741	+	1631.14i	−0.0849957	+	0.147217i
$498$	−514.389	−	890.947i	−0.0462857	−	0.0801693i
$499$			9019.80i			0.809181i	0.914498	+	0.404591i	$0.132586\pi$
$499$			9019.80i			0.809181i	−0.914498	+	0.404591i	$0.867414\pi$
$500$	−1022.98	+	590.617i	−0.0914980	+	0.0528264i
$501$	−8148.67	+	4704.64i	−0.726658	+	0.419536i
$502$			3275.83i			0.291250i
$503$	3016.92	+	5225.46i	0.267431	+	0.463204i	0.968198	−	0.250186i	$-0.0804919\pi$
$503$	3016.92	+	5225.46i	0.267431	+	0.463204i	−0.700767	+	0.713391i	$0.747159\pi$
$504$	1288.04	−	2230.95i	0.113837	−	0.197171i
$505$	6197.33	+	3578.03i	0.546094	+	0.315288i
$506$	3210.87			0.282096
$507$	−2088.91	−	6251.22i	−0.182981	−	0.547587i
$508$	−3134.44			−0.273757
$509$	−19443.6	−	11225.8i	−1.69317	−	0.977551i	−0.951934	−	0.306304i	$-0.900907\pi$
$509$	−19443.6	−	11225.8i	−1.69317	−	0.977551i	−0.741234	−	0.671246i	$-0.765759\pi$
$510$	942.975	−	1633.28i	0.0818738	−	0.141810i
$511$	−649.742	−	1125.39i	−0.0562483	−	0.0974249i
$512$			11720.8i			1.01170i
$513$	3438.50	−	1985.22i	0.295933	−	0.170857i
$514$	5973.03	−	3448.53i	0.512566	−	0.295930i
$515$			17358.9i			1.48529i
$516$	−4379.30	−	7585.17i	−0.373620	−	0.647129i
$517$	2237.56	−	3875.56i	0.190344	−	0.329685i
$518$	−1291.20	−	745.474i	−0.109521	−	0.0632321i
$519$	−9972.58			−0.843445
$520$	4139.74	+	9194.69i	0.349115	+	0.775411i
$521$	15674.7			1.31808			0.659040	−	0.752108i	$-0.270963\pi$
$521$	15674.7			1.31808			0.659040	+	0.752108i	$0.270963\pi$
$522$	276.182	+	159.454i	0.0231574	+	0.0133699i
$523$	−6755.39	+	11700.7i	−0.564804	+	0.978270i	0.432264	+	0.901747i	$0.357715\pi$
$523$	−6755.39	+	11700.7i	−0.564804	+	0.978270i	−0.997068	+	0.0765223i	$0.975618\pi$
$524$	−5932.33	−	10275.1i	−0.494571	−	0.856622i
$525$		−	7060.10i		−	0.586911i
$526$	−3702.37	+	2137.57i	−0.306903	+	0.177191i
$527$	−3390.72	+	1957.63i	−0.280270	+	0.161814i
$528$			8791.97i			0.724662i
$529$	4670.58	+	8089.68i	0.383873	+	0.664887i
$530$	−1607.77	+	2784.74i	−0.131768	+	0.228229i
$531$	1107.02	+	639.138i	0.0904719	+	0.0522340i
$532$	−21667.4			−1.76580
$533$	−1670.17	+	16554.0i	−0.135728	+	1.34528i
$534$	328.610			0.0266299
$535$	8075.59	+	4662.44i	0.652595	+	0.376776i
$536$	−2858.97	+	4951.88i	−0.230389	+	0.399046i
$537$	−4969.87	−	8608.07i	−0.399378	−	0.691743i
$538$			4905.60i			0.393114i
$539$	−4600.09	+	2655.86i	−0.367607	+	0.212238i
$540$	−2589.49	+	1495.04i	−0.206359	+	0.119141i
$541$		−	12103.6i		−	0.961875i	−0.876755	−	0.480937i	$-0.840296\pi$
$541$		−	12103.6i		−	0.961875i	0.876755	−	0.480937i	$-0.159704\pi$
$542$	−1363.71	−	2362.02i	−0.108075	−	0.187191i
$543$	114.018	−	197.485i	0.00901100	−	0.0156075i
$544$	5833.97	+	3368.25i	0.459797	+	0.265464i
$545$	21997.2			1.72891
$546$	2641.80	+	266.537i	0.207067	+	0.0208915i
$547$	−15228.6			−1.19036			−0.595181	−	0.803592i	$-0.702920\pi$
$547$	−15228.6			−1.19036			−0.595181	+	0.803592i	$0.702920\pi$
$548$	12196.8	+	7041.82i	0.950768	+	0.548926i
$549$	−1200.74	+	2079.74i	−0.0933449	+	0.161678i
$550$	−3452.98	−	5980.73i	−0.267701	−	0.463671i
$551$		−	5680.03i		−	0.439160i
$552$	−1920.55	+	1108.83i	−0.148087	+	0.0854982i
$553$	−5118.03	+	2954.90i	−0.393564	+	0.227224i
$554$			701.014i			0.0537603i
$555$	1832.29	+	3173.61i	0.140137	+	0.242725i
$556$	−10111.8	+	17514.1i	−0.771284	+	1.33590i
$557$	20435.5	+	11798.5i	1.55454	+	0.897516i	0.997763	+	0.0668564i	$0.0212969\pi$
$557$	20435.5	+	11798.5i	1.55454	+	0.897516i	0.556781	+	0.830660i	$0.312036\pi$
$558$	−729.775			−0.0553653
$559$	11171.9	−	15512.4i	0.845298	−	1.17371i
$560$	14173.6			1.06954
$561$	7577.33	+	4374.77i	0.570258	+	0.329239i
$562$	3229.31	−	5593.33i	0.242385	−	0.419823i
$563$	3970.81	+	6877.64i	0.297246	+	0.514846i	0.975505	−	0.219978i	$-0.0705984\pi$
$563$	3970.81	+	6877.64i	0.297246	+	0.514846i	−0.678259	+	0.734823i	$0.737265\pi$
$564$			1459.62i			0.108974i
$565$	5315.15	−	3068.70i	0.395770	−	0.228498i
$566$	7178.16	−	4144.31i	0.533075	−	0.307771i
$567$			1667.25i			0.123488i
$568$	−636.233	−	1101.99i	−0.0469995	−	0.0814056i
$569$	1137.33	−	1969.91i	0.0837948	−	0.145137i	−0.821082	−	0.570810i	$-0.806629\pi$
$569$	1137.33	−	1969.91i	0.0837948	−	0.145137i	0.904877	+	0.425673i	$0.139963\pi$
$570$	−5422.19	−	3130.50i	−0.398439	−	0.230039i
$571$	4499.84			0.329794			0.164897	−	0.986311i	$-0.447271\pi$
$571$	4499.84			0.329794			0.164897	+	0.986311i	$0.447271\pi$
$572$	−20144.5	+	9069.67i	−1.47252	+	0.662975i
$573$	−12220.2			−0.890934
$574$	−5804.70	−	3351.34i	−0.422097	−	0.243698i
$575$	−3038.91	+	5263.55i	−0.220402	+	0.381748i
$576$	−974.561	−	1687.99i	−0.0704978	−	0.122106i
$577$		−	25253.3i		−	1.82202i	−0.412381	−	0.911011i	$-0.635303\pi$
$577$		−	25253.3i		−	1.82202i	0.412381	−	0.911011i	$-0.364697\pi$
$578$	−2344.40	+	1353.54i	−0.168709	+	0.0974044i
$579$	−2254.04	+	1301.37i	−0.161787	+	0.0934079i
$580$			4277.55i			0.306234i
$581$	−3847.15	−	6663.47i	−0.274711	−	0.475813i
$582$	763.232	−	1321.96i	0.0543591	−	0.0941527i
$583$	−12919.3	−	7458.98i	−0.917777	−	0.529879i
$584$	877.921			0.0622066
$585$	−5295.74	−	3813.96i	−0.374276	−	0.269552i
$586$	1637.73			0.115450
$587$	9773.25	+	5642.59i	0.687198	+	0.396754i	0.802562	−	0.596569i	$-0.203470\pi$
$587$	9773.25	+	5642.59i	0.687198	+	0.396754i	−0.115363	+	0.993323i	$0.536803\pi$
$588$	866.246	−	1500.38i	0.0607541	−	0.105229i
$589$	6498.97	+	11256.6i	0.454644	+	0.787467i
$590$		−	2015.72i		−	0.140654i
$591$	−4904.37	+	2831.54i	−0.341352	+	0.197079i
$592$	−3043.64	+	1757.24i	−0.211305	+	0.121997i
$593$		−	12824.5i		−	0.888090i	−0.896005	−	0.444045i	$-0.853543\pi$
$593$		−	12824.5i		−	0.888090i	0.896005	−	0.444045i	$-0.146457\pi$
$594$	815.424	+	1412.36i	0.0563253	+	0.0975583i
$595$	7052.59	−	12215.4i	0.485929	−	0.841654i
$596$	−4944.99	−	2854.99i	−0.339857	−	0.196216i
$597$	−8358.65			−0.573027
$598$	−1854.82	−	1335.83i	−0.126838	−	0.0913482i
$599$	−26180.3			−1.78581			−0.892905	−	0.450245i	$-0.851336\pi$
$599$	−26180.3			−1.78581			−0.892905	+	0.450245i	$0.851336\pi$
$600$	4130.73	+	2384.88i	0.281060	+	0.162270i
$601$	−8006.28	+	13867.3i	−0.543399	+	0.941195i	0.455307	+	0.890335i	$0.349530\pi$
$601$	−8006.28	+	13867.3i	−0.543399	+	0.941195i	−0.998706	+	0.0508602i	$0.983804\pi$
$602$	3850.60	+	6669.43i	0.260695	+	0.451538i
$603$		−	3700.68i		−	0.249923i
$604$	1004.22	−	579.787i	0.0676509	−	0.0390583i
$605$	40249.2	−	23237.9i	2.70473	−	1.56158i
$606$			1273.03i			0.0853357i
$607$	4765.74	+	8254.50i	0.318674	+	0.551960i	0.980212	−	0.197952i	$-0.0634290\pi$
$607$	4765.74	+	8254.50i	0.318674	+	0.551960i	−0.661537	+	0.749912i	$0.730096\pi$
$608$	11181.9	−	19367.7i	0.745868	−	1.29188i
$609$	2065.59	+	1192.57i	0.137441	+	0.0793519i
$610$	3786.91			0.251356
$611$	−2904.93	+	1307.89i	−0.192342	+	0.0865984i
$612$	−2853.78			−0.188492
$613$	−8822.27	−	5093.54i	−0.581286	−	0.335605i	0.180359	−	0.983601i	$-0.442274\pi$
$613$	−8822.27	−	5093.54i	−0.581286	−	0.335605i	−0.761644	+	0.647996i	$0.775608\pi$
$614$	−2441.65	+	4229.06i	−0.160484	+	0.277966i
$615$	8237.21	+	14267.3i	0.540091	+	0.935466i
$616$		−	18846.0i		−	1.23267i
$617$	6939.13	−	4006.31i	0.452770	−	0.261407i	−0.256230	−	0.966616i	$-0.582480\pi$
$617$	6939.13	−	4006.31i	0.452770	−	0.261407i	0.708999	+	0.705209i	$0.249147\pi$
$618$	−2674.35	+	1544.04i	−0.174075	+	0.100502i
$619$		−	1886.59i		−	0.122501i	−0.998122	−	0.0612506i	$-0.980491\pi$
$619$		−	1886.59i		−	0.122501i	0.998122	−	0.0612506i	$-0.0195089\pi$
$620$	−4894.29	−	8477.16i	−0.317031	−	0.549114i
$621$	717.641	−	1242.99i	0.0463735	−	0.0803213i
$622$	4977.86	+	2873.97i	0.320891	+	0.185266i
$623$	2457.70			0.158051
$624$	3657.76	−	5078.85i	0.234659	−	0.325828i
$625$	−16844.5			−1.07805
$626$	−5715.23	−	3299.69i	−0.364899	−	0.210674i
$627$	14523.4	−	25155.3i	0.925055	−	1.60224i
$628$	1224.09	+	2120.19i	0.0777812	+	0.134721i
$629$			3497.53i			0.221710i
$630$	2276.86	−	1314.55i	0.143988	−	0.0831315i
$631$	−12952.3	+	7478.04i	−0.817154	+	0.471784i	−0.849434	−	0.527695i	$-0.823057\pi$
$631$	−12952.3	+	7478.04i	−0.817154	+	0.471784i	0.0322798	+	0.999479i	$0.489723\pi$
$632$		−	3992.61i		−	0.251293i
$633$	−1063.18	−	1841.49i	−0.0667579	−	0.115628i
$634$	−4392.79	+	7608.53i	−0.275173	+	0.476614i
$635$	−5866.45	−	3387.00i	−0.366619	−	0.211667i
$636$	4865.70			0.303361
$637$	3762.26	+	379.583i	0.234013	+	0.0236101i
$638$	2333.06			0.144775
$639$	713.212	+	411.773i	0.0441537	+	0.0254922i
$640$	−10947.8	+	18962.1i	−0.676170	+	1.17116i
$641$	11845.9	+	20517.6i	0.729927	+	1.26427i	0.956913	+	0.290373i	$0.0937794\pi$
$641$	11845.9	+	20517.6i	0.729927	+	1.26427i	−0.226986	+	0.973898i	$0.572887\pi$
$642$			1658.86i			0.101978i
$643$	11822.4	−	6825.65i	0.725083	−	0.418627i	−0.0915374	−	0.995802i	$-0.529178\pi$
$643$	11822.4	−	6825.65i	0.725083	−	0.418627i	0.816621	+	0.577175i	$0.195845\pi$
$644$	−6783.25	+	3916.31i	−0.415058	+	0.239634i
$645$		−	18928.6i		−	1.15553i
$646$	−2987.80	−	5175.02i	−0.181971	−	0.315184i
$647$	−9066.14	+	15703.0i	−0.550892	+	0.954172i	0.447319	+	0.894375i	$0.352379\pi$
$647$	−9066.14	+	15703.0i	−0.550892	+	0.954172i	−0.998211	+	0.0597977i	$0.980954\pi$
$648$	−975.475	−	563.191i	−0.0591362	−	0.0341423i
$649$	9351.59			0.565612
$650$	−493.509	+	4891.43i	−0.0297800	+	0.295166i
$651$	−5458.05			−0.328599
$652$	−3450.56	−	1992.18i	−0.207261	−	0.119662i
$653$	−3181.74	+	5510.93i	−0.190675	+	0.330259i	−0.945474	−	0.325697i	$-0.894401\pi$
$653$	−3181.74	+	5510.93i	−0.190675	+	0.330259i	0.754799	+	0.655956i	$0.227734\pi$
$654$	1956.61	+	3388.94i	0.116987	+	0.202627i
$655$		−	25641.3i		−	1.52960i
$656$	−13682.9	+	7899.85i	−0.814374	+	0.470179i
$657$	−492.071	+	284.098i	−0.0292200	+	0.0168702i
$658$		−	1283.40i		−	0.0760369i
$659$	525.717	+	910.568i	0.0310759	+	0.0538250i	0.881145	−	0.472846i	$-0.156773\pi$
$659$	525.717	+	910.568i	0.0310759	+	0.0538250i	−0.850069	+	0.526671i	$0.823440\pi$
$660$	−10937.4	+	18944.1i	−0.645057	+	1.11727i
$661$	7031.91	+	4059.87i	0.413781	+	0.238897i	0.692413	−	0.721501i	$-0.256548\pi$
$661$	7031.91	+	4059.87i	0.413781	+	0.238897i	−0.278632	+	0.960398i	$0.589881\pi$
$662$	−5296.12			−0.310936
$663$	−2557.13	−	5679.59i	−0.149790	−	0.332695i
$664$	5198.21			0.303810
$665$	−40553.0	−	23413.3i	−2.36478	−	1.36530i
$666$	−325.956	+	564.573i	−0.0189648	+	0.0328480i
$667$	−1026.64	−	1778.20i	−0.0595979	−	0.103227i
$668$		−	22451.9i		−	1.30043i
$669$	14020.9	−	8094.95i	0.810281	−	0.467816i
$670$	−5053.80	+	2917.81i	−0.291411	+	0.168246i
$671$			17568.7i			1.01078i
$672$	4695.48	+	8132.81i	0.269542	+	0.466860i
$673$	−95.1322	+	164.774i	−0.00544885	+	0.00943769i	−0.868737	−	0.495274i	$-0.835068\pi$
$673$	−95.1322	+	164.774i	−0.00544885	+	0.00943769i	0.863288	+	0.504711i	$0.168401\pi$
$674$	983.620	+	567.893i	0.0562131	+	0.0324547i
$675$	−3087.01			−0.176028
$676$	15410.1	+	3141.51i	0.876770	+	0.178738i
$677$	4861.93			0.276010			0.138005	−	0.990431i	$-0.455931\pi$
$677$	4861.93			0.276010			0.138005	+	0.990431i	$0.455931\pi$
$678$	945.543	+	545.909i	0.0535595	+	0.0309226i
$679$	5708.27	−	9887.02i	0.322627	−	0.558806i
$680$	4764.67	+	8252.66i	0.268701	+	0.465404i
$681$			9545.37i			0.537121i
$682$	−4623.60	+	2669.44i	−0.259600	+	0.149880i
$683$	12591.7	−	7269.80i	0.705426	−	0.407278i	−0.103939	−	0.994584i	$-0.533145\pi$
$683$	12591.7	−	7269.80i	0.705426	−	0.407278i	0.809365	+	0.587306i	$0.199811\pi$
$684$			9474.02i			0.529603i
$685$	15218.4	+	26359.1i	0.848855	+	1.47026i
$686$	2476.70	−	4289.77i	0.137844	−	0.238753i
$687$	5284.49	+	3051.00i	0.293473	+	0.169436i
$688$	18153.4			1.00595
$689$	4359.91	+	9683.70i	0.241073	+	0.535442i
$690$	−2263.31			−0.124873
$691$	19144.8	+	11053.2i	1.05398	+	0.608517i	0.923762	−	0.382968i	$-0.125098\pi$
$691$	19144.8	+	11053.2i	1.05398	+	0.608517i	0.130221	+	0.991485i	$0.458431\pi$
$692$	11898.0	−	20607.9i	0.653604	−	1.13208i
$693$	6098.62	+	10563.1i	0.334296	+	0.579018i
$694$			4999.66i			0.273465i
$695$	−37850.5	+	21853.0i	−2.06583	+	1.19271i
$696$	−1395.49	+	805.689i	−0.0760001	+	0.0438787i
$697$			15723.4i			0.854474i
$698$	630.251	+	1091.63i	0.0341767	+	0.0591958i
$699$	−4191.33	+	7259.59i	−0.226796	+	0.392823i
$700$	14589.4	+	8423.20i	0.787754	+	0.454810i
$701$	−229.971			−0.0123907			−0.00619535	−	0.999981i	$-0.501972\pi$
$701$	−229.971			−0.0123907			−0.00619535	+	0.999981i	$0.501972\pi$
$702$	116.543	−	1155.12i	0.00626584	−	0.0621041i
$703$	11611.1			0.622934
$704$	−12349.0	−	7129.68i	−0.661107	−	0.381690i
$705$	−1577.23	+	2731.84i	−0.0842578	+	0.145939i
$706$	−2738.56	−	4743.33i	−0.145988	−	0.252858i
$707$			9521.12i			0.506476i
$708$	−2641.51	+	1525.07i	−0.140217	+	0.0809545i
$709$	4158.85	−	2401.11i	0.220294	−	0.127187i	−0.385792	−	0.922586i	$-0.626072\pi$
$709$	4158.85	−	2401.11i	0.220294	−	0.127187i	0.606087	+	0.795399i	$0.292738\pi$
$710$		−	1298.66i		−	0.0686446i
$711$	1292.02	+	2237.84i	0.0681498	+	0.118039i
$712$	−830.202	+	1437.95i	−0.0436982	+	0.0756876i
$713$	4069.16	+	2349.33i	0.213732	+	0.123398i
$714$	2509.25			0.131522
$715$	−47503.0	−	4792.69i	−2.48463	−	0.250681i
$716$	23717.6			1.23795
$717$	14273.3	+	8240.72i	0.743442	+	0.429227i
$718$	3584.05	−	6207.75i	0.186289	−	0.322662i
$719$	−5508.46	−	9540.94i	−0.285718	−	0.494878i	0.687065	−	0.726596i	$-0.258899\pi$
$719$	−5508.46	−	9540.94i	−0.285718	−	0.494878i	−0.972783	+	0.231718i	$0.925565\pi$
$720$		−	6197.36i		−	0.320780i
$721$	−20001.7	+	11548.0i	−1.03315	+	0.596491i
$722$	−11730.8	+	6772.81i	−0.604677	+	0.349110i
$723$		−	12183.8i		−	0.626723i
$724$	272.063	+	471.226i	0.0139656	+	0.0241892i
$725$	−2208.11	+	3824.55i	−0.113113	+	0.195918i
$726$	7160.16	+	4133.92i	0.366031	+	0.211328i
$727$	13498.2			0.688612			0.344306	−	0.938857i	$-0.388114\pi$
$727$	13498.2			0.688612			0.344306	+	0.938857i	$0.388114\pi$
$728$	−7840.57	+	10886.7i	−0.399163	+	0.554244i
$729$	729.000			0.0370370
$730$	775.950	+	447.995i	0.0393414	+	0.0227138i
$731$	9032.89	−	15645.4i	0.457037	−	0.791610i
$732$	−2865.14	−	4962.56i	−0.144670	−	0.250576i
$733$		−	17014.7i		−	0.857368i	−0.903455	−	0.428684i	$-0.858977\pi$
$733$		−	17014.7i		−	0.857368i	0.903455	−	0.428684i	$-0.141023\pi$
$734$	1341.37	−	774.442i	0.0674537	−	0.0389444i
$735$	3242.55	−	1872.09i	0.162725	−	0.0939495i
$736$		−	8084.38i		−	0.404883i
$737$	−13536.7	−	23446.2i	−0.676567	−	1.17185i
$738$	−1465.36	+	2538.09i	−0.0730905	+	0.126597i
$739$	11598.3	+	6696.31i	0.577337	+	0.333326i	0.760074	−	0.649836i	$-0.225162\pi$
$739$	11598.3	+	6696.31i	0.577337	+	0.333326i	−0.182737	+	0.983162i	$0.558496\pi$
$740$	−8744.19			−0.434382
$741$	−18855.2	+	8489.20i	−0.934767	+	0.420862i
$742$	−4278.27			−0.211672
$743$	−10216.1	−	5898.26i	−0.504431	−	0.291233i	0.226111	−	0.974102i	$-0.427399\pi$
$743$	−10216.1	−	5898.26i	−0.504431	−	0.291233i	−0.730541	+	0.682868i	$0.760732\pi$
$744$	1843.71	−	3193.40i	0.0908516	−	0.157360i
$745$	−6170.05	−	10686.8i	−0.303427	−	0.525551i
$746$			1716.05i			0.0842214i
$747$	−2913.58	+	1682.16i	−0.142707	+	0.0823921i
$748$	−18080.6	+	10438.8i	−0.883812	+	0.510269i
$749$			12406.7i			0.605250i
$750$	−227.068	−	393.294i	−0.0110551	−	0.0191481i
$751$	−6225.26	+	10782.5i	−0.302480	+	0.523911i	−0.976697	−	0.214622i	$-0.931148\pi$
$751$	−6225.26	+	10782.5i	−0.302480	+	0.523911i	0.674217	+	0.738534i	$0.264481\pi$
$752$	−2619.95	−	1512.63i	−0.127048	−	0.0733510i
$753$	10712.6			0.518447
$754$	−1347.73	−	970.630i	−0.0650949	−	0.0468810i
$755$	2506.01			0.120799
$756$	−3445.31	−	1989.15i	−0.165747	−	0.0956939i
$757$	3514.92	−	6088.02i	0.168761	−	0.292302i	−0.769224	−	0.638980i	$-0.779357\pi$
$757$	3514.92	−	6088.02i	0.168761	−	0.292302i	0.937984	+	0.346677i	$0.112690\pi$
$758$	−5351.51	−	9269.10i	−0.256432	−	0.444154i
$759$		−	10500.2i		−	0.502152i
$760$	27397.3	−	15817.8i	1.30764	−	0.754964i
$761$	−15363.8	+	8870.29i	−0.731849	+	0.422533i	−0.819098	−	0.573653i	$-0.805526\pi$
$761$	−15363.8	+	8870.29i	−0.731849	+	0.422533i	0.0872491	+	0.996187i	$0.472192\pi$
$762$		−	1205.06i		−	0.0572899i
$763$	14633.6	+	25346.2i	0.694328	+	1.20261i
$764$	14579.5	−	25252.5i	0.690405	−	1.19582i
$765$	−5341.16	−	3083.72i	−0.252432	−	0.145741i
$766$	−6124.94			−0.288907
$767$	−5402.12	−	3890.58i	−0.254314	−	0.183156i
$768$	1302.54			0.0611995
$769$	−27692.4	−	15988.2i	−1.29859	−	0.749741i	−0.318429	−	0.947947i	$-0.603155\pi$
$769$	−27692.4	−	15988.2i	−1.29859	−	0.749741i	−0.980160	+	0.198206i	$0.936489\pi$
$770$	9616.95	−	16657.0i	0.450092	−	0.779582i
$771$	−11277.4	−	19533.0i	−0.526777	−	0.912405i
$772$		−	6210.51i		−	0.289535i
$773$	−1849.06	+	1067.56i	−0.0860364	+	0.0496732i	−0.542401	−	0.840120i	$-0.682485\pi$
$773$	−1849.06	+	1067.56i	−0.0860364	+	0.0496732i	0.456365	+	0.889793i	$0.349151\pi$
$774$	2916.19	−	1683.66i	0.135427	−	0.0781886i
$775$		−	10105.9i		−	0.468405i
$776$	3856.47	+	6679.59i	0.178401	+	0.308999i
$777$	−2437.85	+	4222.48i	−0.112558	+	0.194956i
$778$	11349.2	+	6552.48i	0.522994	+	0.301951i
$779$	52198.9			2.40080
$780$	14199.6	−	6393.10i	0.651829	−	0.293474i
$781$	6024.89			0.276040
$782$	−1870.73	−	1080.07i	−0.0855464	−	0.0493902i
$783$	521.446	−	903.172i	0.0237995	−	0.0412219i
$784$	1795.41	+	3109.75i	0.0817882	+	0.141661i
$785$			5290.89i			0.240560i
$786$	3950.36	−	2280.74i	0.179268	−	0.103500i
$787$	10136.3	−	5852.18i	0.459109	−	0.265067i	−0.252560	−	0.967581i	$-0.581273\pi$
$787$	10136.3	−	5852.18i	0.459109	−	0.265067i	0.711670	+	0.702514i	$0.247939\pi$
$788$		−	13512.9i		−	0.610885i
$789$	6990.28	+	12107.5i	0.315412	+	0.546310i
$790$	2037.39	−	3528.87i	0.0917559	−	0.158926i
$791$	7071.79	+	4082.90i	0.317881	+	0.183529i
$792$	−8240.36			−0.369708
$793$	7309.17	−	10148.9i	0.327309	−	0.454474i
$794$	−3274.37			−0.146351
$795$	9106.68	+	5257.75i	0.406265	+	0.234557i
$796$	9972.46	−	17272.8i	0.444051	−	0.769119i
$797$	−74.8667	−	129.673i	−0.00332737	−	0.00576317i	0.864357	−	0.502879i	$-0.167726\pi$
$797$	−74.8667	−	129.673i	−0.00332737	−	0.00576317i	−0.867684	+	0.497116i	$0.834392\pi$
$798$		−	8330.25i		−	0.369533i
$799$	−2607.31	+	1505.33i	−0.115444	+	0.0666518i
$800$	−15058.4	+	8693.94i	−0.665491	+	0.384222i
$801$		−	1074.62i		−	0.0474032i
$802$	229.045	+	396.717i	0.0100846	+	0.0174670i
$803$	−2078.40	+	3599.89i	−0.0913387	+	0.158203i
$804$	7647.30	+	4415.17i	0.335447	+	0.193671i
$805$	−16927.4			−0.741135
$806$	3781.49	+	381.524i	0.165257	+	0.0166732i
$807$	16042.3			0.699772
$808$	−5570.62	−	3216.20i	−0.242542	−	0.140031i
$809$	−11760.4	+	20369.6i	−0.511093	+	0.885239i	0.488825	+	0.872382i	$0.337426\pi$
$809$	−11760.4	+	20369.6i	−0.511093	+	0.885239i	−0.999917	+	0.0128565i	$0.995908\pi$
$810$	−574.782	−	995.552i	−0.0249331	−	0.0431853i
$811$			29604.8i			1.28183i	0.767612	+	0.640915i	$0.221445\pi$
$811$			29604.8i			1.28183i	−0.767612	+	0.640915i	$0.778555\pi$
$812$	−4928.79	+	2845.64i	−0.213013	+	0.122983i
$813$	−7724.29	+	4459.62i	−0.333214	+	0.192381i
$814$			4769.25i			0.205359i
$815$	−4305.39	−	7457.16i	−0.185045	−	0.320507i
$816$	2957.43	−	5122.42i	0.126876	−	0.219755i
$817$	−51939.9	−	29987.5i	−2.22417	−	1.28413i
$818$	9593.44			0.410057
$819$	871.632	−	8639.21i	0.0371884	−	0.368594i
$820$	−39310.3			−1.67412
$821$	−37269.2	−	21517.4i	−1.58429	−	0.914691i	−0.994223	−	0.107338i	$-0.965767\pi$
$821$	−37269.2	−	21517.4i	−1.58429	−	0.914691i	−0.590068	−	0.807353i	$-0.700899\pi$
$822$	−2707.29	+	4689.17i	−0.114875	+	0.198970i
$823$	2792.47	+	4836.71i	0.118274	+	0.204857i	0.919084	−	0.394062i	$-0.128931\pi$
$823$	2792.47	+	4836.71i	0.118274	+	0.204857i	−0.800810	+	0.598919i	$0.795597\pi$
$824$		−	15603.5i		−	0.659675i
$825$	−19558.2	+	11291.9i	−0.825369	+	0.476527i
$826$	2322.60	−	1340.96i	0.0978374	−	0.0564865i
$827$			4788.13i			0.201330i	0.994920	+	0.100665i	$0.0320970\pi$
$827$			4788.13i			0.201330i	−0.994920	+	0.100665i	$0.967903\pi$
$828$	1712.39	+	2965.95i	0.0718718	+	0.124486i
$829$	−16196.1	+	28052.5i	−0.678546	+	1.17528i	0.296873	+	0.954917i	$0.404056\pi$
$829$	−16196.1	+	28052.5i	−0.678546	+	1.17528i	−0.975419	+	0.220359i	$0.929277\pi$
$830$	4594.44	+	2652.60i	0.192139	+	0.110931i
$831$	2292.46			0.0956974
$832$	4167.42	+	9256.17i	0.173653	+	0.385697i
$833$	3573.50			0.148637
$834$	−6733.45	−	3887.56i	−0.279569	−	0.161409i
$835$	24260.9	−	42021.1i	1.00549	−	1.74156i
$836$	34654.9	+	60024.1i	1.43369	+	2.48323i
$837$			2386.51i			0.0985544i
$838$	−1354.90	+	782.254i	−0.0558525	+	0.0322464i
$839$	−11777.0	+	6799.43i	−0.484607	+	0.279788i	−0.722335	−	0.691544i	$-0.756931\pi$
$839$	−11777.0	+	6799.43i	−0.484607	+	0.279788i	0.237727	+	0.971332i	$0.423598\pi$
$840$			13284.3i			0.545658i
$841$	11448.5	+	19829.4i	0.469414	+	0.813048i
$842$	4020.65	−	6963.97i	0.164562	−	0.285029i
$843$	−18291.3	−	10560.5i	−0.747316	−	0.431463i
$844$	5073.82			0.206929
$845$	25447.1	+	22531.4i	1.03598	+	0.917284i
$846$	−561.164			−0.0228052
$847$	53551.4	+	30917.9i	2.17243	+	1.25425i
$848$	−5042.41	+	8733.72i	−0.204195	+	0.353676i
$849$	−13552.8	−	23474.1i	−0.547855	−	0.948913i
$850$			4646.02i			0.187479i
$851$	3635.00	−	2098.67i	0.146423	−	0.0845375i
$852$	−1701.83	+	982.550i	−0.0684314	+	0.0395089i
$853$		−	41037.0i		−	1.64722i	−0.567155	−	0.823611i	$-0.691956\pi$
$853$		−	41037.0i		−	1.64722i	0.567155	−	0.823611i	$-0.308044\pi$
$854$	2519.24	+	4363.44i	0.100944	+	0.174841i
$855$	−10237.4	+	17731.7i	−0.409487	+	0.709252i
$856$	−7258.93	−	4190.95i	−0.289843	−	0.167341i
$857$	39959.3			1.59275			0.796374	−	0.604804i	$-0.206749\pi$
$857$	39959.3			1.59275			0.796374	+	0.604804i	$0.206749\pi$
$858$	−3486.92	−	7744.72i	−0.138743	−	0.308159i
$859$	−32570.5			−1.29371			−0.646853	−	0.762615i	$-0.723915\pi$
$859$	−32570.5			−1.29371			−0.646853	+	0.762615i	$0.723915\pi$
$860$	39115.2	+	22583.2i	1.55095	+	0.895442i
$861$	−10959.6	+	18982.6i	−0.433800	+	0.751363i
$862$	3706.36	+	6419.60i	0.146449	+	0.253657i
$863$		−	16951.8i		−	0.668652i	−0.942457	−	0.334326i	$-0.891491\pi$
$863$		−	16951.8i		−	0.668652i	0.942457	−	0.334326i	$-0.108509\pi$
$864$	3556.05	−	2053.08i	0.140022	−	0.0808418i
$865$	44536.8	−	25713.3i	1.75063	−	1.01073i
$866$			3783.69i			0.148470i
$867$	4426.35	+	7666.65i	0.173387	+	0.300315i
$868$	6511.84	−	11278.8i	0.254639	−	0.441047i
$869$	16371.6	+	9452.13i	0.639088	+	0.368978i
$870$	−1644.54			−0.0640865
$871$	−1934.70	+	19175.9i	−0.0752639	+	0.745981i
$872$	−19772.7			−0.767876
$873$	−4323.07	−	2495.92i	−0.167599	−	0.0967632i
$874$	−3585.62	+	6210.48i	−0.138771	+	0.240358i
$875$	−1698.26	−	2941.47i	−0.0656134	−	0.113646i
$876$		−	1355.79i		−	0.0522923i
$877$	−39784.5	+	22969.6i	−1.53184	+	0.884411i	−0.532568	+	0.846388i	$0.678773\pi$
$877$	−39784.5	+	22969.6i	−1.53184	+	0.884411i	−0.999277	+	0.0380232i	$0.987894\pi$
$878$	4858.59	−	2805.11i	0.186753	−	0.107822i
$879$		−	5355.70i		−	0.205510i
$880$	−22669.2	−	39264.3i	−0.868386	−	1.50409i
$881$	18980.3	−	32874.8i	0.725836	−	1.25718i	−0.232793	−	0.972526i	$-0.574787\pi$
$881$	18980.3	−	32874.8i	0.725836	−	1.25718i	0.958629	−	0.284658i	$-0.0918801\pi$
$882$	576.836	+	333.036i	0.0220216	+	0.0127142i
$883$	−43172.9			−1.64539			−0.822697	−	0.568480i	$-0.807532\pi$
$883$	−43172.9			−1.64539			−0.822697	+	0.568480i	$0.807532\pi$
$884$	14787.5	+	1491.95i	0.562621	+	0.0567642i
$885$	−6591.82			−0.250375
$886$	8785.89	+	5072.54i	0.333146	+	0.192342i
$887$	−14353.1	+	24860.4i	−0.543327	+	0.941071i	0.455383	+	0.890296i	$0.349502\pi$
$887$	−14353.1	+	24860.4i	−0.543327	+	0.941071i	−0.998710	+	0.0507749i	$0.983831\pi$
$888$	−1646.99	−	2852.68i	−0.0622404	−	0.107804i
$889$		−	9012.78i		−	0.340021i
$890$	−1467.55	+	847.289i	−0.0552723	+	0.0319115i
$891$	4618.69	−	2666.60i	0.173661	−	0.100263i
$892$			38631.4i			1.45008i
$893$	4997.41	+	8655.78i	0.187270	+	0.324361i
$894$	1097.63	−	1901.14i	0.0410628	−	0.0711228i
$895$	44390.1	+	25628.7i	1.65788	+	0.957175i
$896$	−29131.9			−1.08619
$897$	−4368.44	+	6065.64i	−0.162607	+	0.225781i
$898$	−222.015			−0.00825027
$899$	2956.70	+	1707.05i	0.109690	+	0.0633296i
$900$	3683.02	−	6379.18i	0.136408	−	0.236266i
$901$	5018.08	+	8691.57i	0.185545	+	0.321374i
$902$			21440.6i			0.791456i
$903$	21810.4	−	12592.2i	0.803771	−	0.464057i
$904$	−4777.65	+	2758.38i	−0.175777	+	0.101485i
$905$			1175.93i			0.0431927i
$906$	222.904	+	386.082i	0.00817384	+	0.0141575i
$907$	−11178.0	+	19360.9i	−0.409218	+	0.708786i	−0.994802	−	0.101826i	$-0.967532\pi$
$907$	−11178.0	+	19360.9i	−0.409218	+	0.708786i	0.585585	+	0.810611i	$0.300865\pi$
$908$	−19725.1	−	11388.3i	−0.720926	−	0.416227i
$909$	4163.08			0.151904
$910$	−12485.3	+	5621.28i	−0.454817	+	0.204773i
$911$	6953.80			0.252897			0.126449	−	0.991973i	$-0.459642\pi$
$911$	6953.80			0.252897			0.126449	+	0.991973i	$0.459642\pi$
$912$	−17005.5	−	9818.11i	−0.617442	−	0.356480i
$913$	−12306.3	+	21315.1i	−0.446088	+	0.772647i
$914$	−5069.48	−	8780.60i	−0.183461	−	0.317764i
$915$		−	12384.0i		−	0.447433i
$916$	−12609.5	+	7280.12i	−0.454837	+	0.262600i
$917$	29545.0	−	17057.8i	1.06397	−	0.614285i
$918$		−	1097.16i		−	0.0394464i
$919$	−20312.6	−	35182.4i	−0.729108	−	1.26285i	−0.957261	−	0.289227i	$-0.906602\pi$
$919$	−20312.6	−	35182.4i	−0.729108	−	1.26285i	0.228153	−	0.973625i	$-0.426731\pi$
$920$	5718.02	−	9903.91i	0.204911	−	0.354915i
$921$	13829.9	+	7984.70i	0.494800	+	0.285673i
$922$	−251.143			−0.00897068
$923$	−3480.39	−	2506.56i	−0.124115	−	0.0893871i
$924$	−29104.3			−1.03621
$925$	−7818.17	−	4513.82i	−0.277902	−	0.160447i
$926$	−5311.22	+	9199.30i	−0.188485	+	0.326466i
$927$	5049.32	+	8745.69i	0.178901	+	0.309866i
$928$		−	5874.20i		−	0.207791i
$929$	37077.8	−	21406.9i	1.30946	−	0.756014i	0.327450	−	0.944869i	$-0.393811\pi$
$929$	37077.8	−	21406.9i	1.30946	−	0.756014i	0.982005	+	0.188854i	$0.0604774\pi$
$930$	3259.12	−	1881.65i	0.114915	−	0.0663461i
$931$		−	11863.3i		−	0.417621i
$932$	−10001.1	−	17322.4i	−0.351499	−	0.608814i
$933$	9398.46	−	16278.6i	0.329788	−	0.571209i
$934$	717.338	+	414.155i	0.0251306	+	0.0145092i
$935$	−45119.7			−1.57815
$936$	4760.20	+	3428.27i	0.166231	+	0.119718i
$937$	43484.1			1.51608			0.758038	−	0.652210i	$-0.226158\pi$
$937$	43484.1			1.51608			0.758038	+	0.652210i	$0.226158\pi$
$938$	−6724.06	−	3882.14i	−0.234060	−	0.135135i
$939$	−10790.7	+	18690.0i	−0.375016	+	0.649547i
$940$	−3763.49	−	6518.55i	−0.130587	−	0.226183i
$941$		−	7108.58i		−	0.246263i	−0.992390	−	0.123131i	$-0.960706\pi$
$941$		−	7108.58i		−	0.246263i	0.992390	−	0.123131i	$-0.0392936\pi$
$942$	−815.126	+	470.613i	−0.0281935	+	0.0162775i
$943$	16341.5	−	9434.75i	0.564318	−	0.325809i
$944$		−	6321.85i		−	0.217965i
$945$	−4298.84	−	7445.81i	−0.147980	−	0.256309i
$946$	12317.3	−	21334.2i	0.423330	−	0.733229i
$947$	1679.22	+	969.496i	0.0576211	+	0.0332676i	0.528534	−	0.848912i	$-0.322742\pi$
$947$	1679.22	+	969.496i	0.0576211	+	0.0332676i	−0.470913	+	0.882180i	$0.656075\pi$
$948$	−6165.88			−0.211243
$949$	2698.30	−	1214.86i	0.0922976	−	0.0415553i
$950$	15423.9			0.526756
$951$	24881.4	+	14365.3i	0.848408	+	0.489829i
$952$	−6339.39	+	10980.1i	−0.215820	+	0.373811i
$953$	−23903.3	−	41401.8i	−0.812492	−	1.40728i	−0.911115	−	0.412153i	$-0.864777\pi$
$953$	−23903.3	−	41401.8i	−0.812492	−	1.40728i	0.0986228	−	0.995125i	$-0.468556\pi$
$954$			1870.66i			0.0634852i
$955$	54574.4	−	31508.5i	1.84920	−	1.06764i
$956$	−34058.2	+	19663.5i	−1.15222	+	0.665234i
$957$		−	7629.58i		−	0.257711i
$958$	5535.78	+	9588.26i	0.186694	+	0.323364i
$959$	−20248.1	+	35070.7i	−0.681797	+	1.18091i
$960$	8704.63	+	5025.62i	0.292647	+	0.168960i
$961$	21978.3			0.737750
$962$	1984.17	−	2755.04i	0.0664991	−	0.0923349i
$963$	5424.81			0.181528
$964$	25177.3	+	14536.1i	0.841190	+	0.485662i
$965$	6710.92	−	11623.7i	0.223867	−	0.387750i
$966$	−1505.66	−	2607.88i	−0.0501489	−	0.0868604i
$967$		−	2832.71i		−	0.0942025i	−0.998890	−	0.0471013i	$-0.985002\pi$
$967$		−	2832.71i		−	0.0942025i	0.998890	−	0.0471013i	$-0.0149983\pi$
$968$	−36178.9	+	20887.9i	−1.20128	+	0.693557i
$969$	−16923.4	+	9770.72i	−0.561050	+	0.323922i
$970$			7871.68i			0.260561i
$971$	20638.1	+	35746.3i	0.682090	+	1.18142i	0.974342	+	0.225074i	$0.0722623\pi$
$971$	20638.1	+	35746.3i	0.682090	+	1.18142i	−0.292251	+	0.956342i	$0.594404\pi$
$972$	−869.749	+	1506.45i	−0.0287008	+	0.0497113i
$973$	−50360.0	−	29075.3i	−1.65927	−	0.957978i
$974$	−10542.9			−0.346835
$975$	15996.0	+	1613.88i	0.525417	+	0.0530106i
$976$	11876.8			0.389515
$977$	−3705.63	−	2139.45i	−0.121344	−	0.0700583i	0.438099	−	0.898927i	$-0.355652\pi$
$977$	−3705.63	−	2139.45i	−0.121344	−	0.0700583i	−0.559444	+	0.828868i	$0.688985\pi$
$978$	765.912	−	1326.60i	0.0250421	−	0.0433741i
$979$	−3930.85	−	6808.43i	−0.128325	−	0.222266i
$980$			8934.12i			0.291214i
$981$	11082.5	−	6398.50i	0.360691	−	0.208245i
$982$	−12476.5	+	7203.29i	−0.405438	+	0.234080i
$983$		−	22652.9i		−	0.735011i	−0.930021	−	0.367505i	$-0.880212\pi$
$983$		−	22652.9i		−	0.735011i	0.930021	−	0.367505i	$-0.119788\pi$
$984$	−7404.21	−	12824.5i	−0.239876	−	0.415477i
$985$	14601.7	−	25290.9i	0.472333	−	0.818105i
$986$	−1359.30	−	784.790i	−0.0439034	−	0.0253477i
$987$	−4196.99			−0.135351
$988$	4952.98	−	49091.7i	0.159489	−	1.58078i
$989$	−21680.5			−0.697068
$990$	−7283.24	−	4204.98i	−0.233815	−	0.134993i
$991$	−11030.1	+	19104.7i	−0.353565	+	0.612393i	−0.986871	−	0.161508i	$-0.948364\pi$
$991$	−11030.1	+	19104.7i	−0.353565	+	0.612393i	0.633306	+	0.773901i	$0.281697\pi$
$992$	6721.15	+	11641.4i	0.215118	+	0.372594i
$993$			17319.4i			0.553488i
$994$	1496.37	−	863.929i	0.0477484	−	0.0275676i
$995$	37329.1	−	21552.0i	1.18936	−	0.686677i
$996$		−	8027.72i		−	0.255390i
$997$	−17817.8	−	30861.3i	−0.565992	−	0.980327i	−0.996957	−	0.0779583i	$-0.975160\pi$
$997$	−17817.8	−	30861.3i	−0.565992	−	0.980327i	0.430964	−	0.902369i	$-0.358173\pi$
$998$	4137.26	−	7165.95i	0.131225	−	0.227289i
$999$	1846.27	+	1065.94i	0.0584718	+	0.0337587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.c.4.3	✓	10
3.2	odd	2		117.4.q.e.82.3		10
4.3	odd	2		624.4.bv.h.433.2		10
13.4	even	6		507.4.b.i.337.5		10
13.6	odd	12		507.4.a.r.1.6		10
13.7	odd	12		507.4.a.r.1.5		10
13.9	even	3		507.4.b.i.337.6		10
13.10	even	6	inner	39.4.j.c.10.3	yes	10
39.20	even	12		1521.4.a.bk.1.6		10
39.23	odd	6		117.4.q.e.10.3		10
39.32	even	12		1521.4.a.bk.1.5		10
52.23	odd	6		624.4.bv.h.49.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.3	✓	10	1.1	even	1	trivial
39.4.j.c.10.3	yes	10	13.10	even	6	inner
117.4.q.e.10.3		10	39.23	odd	6
117.4.q.e.82.3		10	3.2	odd	2
507.4.a.r.1.5		10	13.7	odd	12
507.4.a.r.1.6		10	13.6	odd	12
507.4.b.i.337.5		10	13.4	even	6
507.4.b.i.337.6		10	13.9	even	3
624.4.bv.h.49.4		10	52.23	odd	6
624.4.bv.h.433.2		10	4.3	odd	2
1521.4.a.bk.1.5		10	39.32	even	12
1521.4.a.bk.1.6		10	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)

\(f(q)\)	\(=\)	\(q+(-0.794469 - 0.458687i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-3.57921 - 6.19938i) q^{4} -15.4704i q^{5} +(2.38341 - 1.37606i) q^{6} +(17.8257 - 10.2917i) q^{7} +13.9059i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-0.794469 - 0.458687i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-3.57921 - 6.19938i) q^{4} -15.4704i q^{5} +(2.38341 - 1.37606i) q^{6} +(17.8257 - 10.2917i) q^{7} +13.9059i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-7.09608 + 12.2908i) q^{10} +(-57.0209 - 32.9210i) q^{11} +21.4753 q^{12} +(19.2429 + 42.7400i) q^{13} -18.8826 q^{14} +(40.1933 + 23.2056i) q^{15} +(-22.2552 + 38.5472i) q^{16} +(22.1478 + 38.3611i) q^{17} +8.25636i q^{18} +(127.352 - 73.5266i) q^{19} +(-95.9069 + 55.3719i) q^{20} +61.7500i q^{21} +(30.2009 + 52.3094i) q^{22} +(26.5793 - 46.0367i) q^{23} +(-36.1287 - 20.8589i) q^{24} -114.334 q^{25} +(4.31639 - 42.7821i) q^{26} +27.0000 q^{27} +(-127.604 - 73.6721i) q^{28} +(19.3128 - 33.4508i) q^{29} +(-21.2882 - 36.8723i) q^{30} +88.3894i q^{31} +(131.705 - 76.0401i) q^{32} +(171.063 - 98.7630i) q^{33} -40.6357i q^{34} +(-159.216 - 275.771i) q^{35} +(-32.2129 + 55.7944i) q^{36} +(68.3803 + 39.4794i) q^{37} -134.903 q^{38} +(-139.906 - 14.1155i) q^{39} +215.131 q^{40} +(307.410 + 177.483i) q^{41} +(28.3239 - 49.0585i) q^{42} +(-203.923 - 353.205i) q^{43} +471.325i q^{44} +(-120.580 + 69.6169i) q^{45} +(-42.2329 + 24.3832i) q^{46} +67.9674i q^{47} +(-66.7657 - 115.642i) q^{48} +(40.3369 - 69.8656i) q^{49} +(90.8345 + 52.4433i) q^{50} -132.887 q^{51} +(196.087 - 272.270i) q^{52} +226.572 q^{53} +(-21.4507 - 12.3845i) q^{54} +(-509.302 + 882.136i) q^{55} +(143.115 + 247.883i) q^{56} +441.160i q^{57} +(-30.6869 + 17.7171i) q^{58} +(-123.002 + 71.0154i) q^{59} -332.231i q^{60} +(-133.416 - 231.083i) q^{61} +(40.5431 - 70.2227i) q^{62} +(-160.431 - 92.6250i) q^{63} +216.569 q^{64} +(661.206 - 297.696i) q^{65} -181.205 q^{66} +(356.098 + 205.593i) q^{67} +(158.543 - 274.605i) q^{68} +(79.7379 + 138.110i) q^{69} +292.122i q^{70} +(-79.2458 + 45.7526i) q^{71} +(108.386 - 62.5767i) q^{72} -63.1328i q^{73} +(-36.2173 - 62.7303i) q^{74} +(171.500 - 297.047i) q^{75} +(-911.638 - 526.335i) q^{76} -1355.25 q^{77} +(104.677 + 75.3875i) q^{78} -287.115 q^{79} +(596.341 + 344.298i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-162.818 - 282.010i) q^{82} -373.812i q^{83} +(382.812 - 221.016i) q^{84} +(593.463 - 342.636i) q^{85} +374.147i q^{86} +(57.9385 + 100.352i) q^{87} +(457.798 - 792.929i) q^{88} +(103.406 + 59.7013i) q^{89} +127.729 q^{90} +(782.885 + 563.829i) q^{91} -380.532 q^{92} +(-229.643 - 132.584i) q^{93} +(31.1758 - 53.9980i) q^{94} +(-1137.49 - 1970.18i) q^{95} +456.241i q^{96} +(480.341 - 277.325i) q^{97} +(-64.0928 + 37.0040i) q^{98} +592.578i 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

Introduction

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