LMFDB - Embedded newform 38.5.f.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(3,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92805859719$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	38.13
Dual form			38.5.f.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81808 + 2.16670i) q^{2} +(-0.486419 + 1.33642i) q^{3} +(-1.38919 + 7.87846i) q^{4} +(3.87248 + 21.9619i) q^{5} +(-3.77998 + 1.37580i) q^{6} +(-12.4808 + 21.6173i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(60.5002 + 50.7657i) q^{9} +O(q^{10})$	\(q+(1.81808 + 2.16670i) q^{2} +(-0.486419 + 1.33642i) q^{3} +(-1.38919 + 7.87846i) q^{4} +(3.87248 + 21.9619i) q^{5} +(-3.77998 + 1.37580i) q^{6} +(-12.4808 + 21.6173i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(60.5002 + 50.7657i) q^{9} +(-40.5444 + 48.3190i) q^{10} +(-23.8209 - 41.2590i) q^{11} +(-9.85324 - 5.68877i) q^{12} +(-16.3525 - 44.9280i) q^{13} +(-69.5294 + 12.2599i) q^{14} +(-31.2341 - 5.50741i) q^{15} +(-60.1403 - 21.8893i) q^{16} +(200.647 - 168.363i) q^{17} +223.382i q^{18} +(357.128 - 52.7313i) q^{19} -178.406 q^{20} +(-22.8191 - 27.1947i) q^{21} +(46.0877 - 126.625i) q^{22} +(108.960 - 617.944i) q^{23} +(-5.58809 - 31.6917i) q^{24} +(119.978 - 43.6684i) q^{25} +(67.6155 - 117.113i) q^{26} +(-197.037 + 113.759i) q^{27} +(-152.973 - 128.360i) q^{28} +(-115.667 + 137.846i) q^{29} +(-44.8531 - 77.6878i) q^{30} +(-307.796 - 177.706i) q^{31} +(-61.9123 - 170.103i) q^{32} +(66.7265 - 11.7657i) q^{33} +(729.585 + 128.646i) q^{34} +(-523.090 - 190.389i) q^{35} +(-484.001 + 406.125i) q^{36} +596.017i q^{37} +(763.540 + 677.920i) q^{38} +67.9970 q^{39} +(-324.356 - 386.552i) q^{40} +(-862.537 + 2369.80i) q^{41} +(17.4359 - 98.8841i) q^{42} +(103.512 + 587.044i) q^{43} +(358.150 - 130.356i) q^{44} +(-880.626 + 1525.29i) q^{45} +(1537.00 - 887.386i) q^{46} +(-627.241 - 526.318i) q^{47} +(58.5067 - 69.7256i) q^{48} +(888.960 + 1539.72i) q^{49} +(312.746 + 180.564i) q^{50} +(127.406 + 350.045i) q^{51} +(376.680 - 66.4189i) q^{52} +(468.924 + 82.6839i) q^{53} +(-604.711 - 220.097i) q^{54} +(813.882 - 682.928i) q^{55} -564.816i q^{56} +(-103.242 + 502.924i) q^{57} -508.963 q^{58} +(-3815.25 - 4546.84i) q^{59} +(86.7799 - 238.426i) q^{60} +(876.326 - 4969.89i) q^{61} +(-174.561 - 989.986i) q^{62} +(-1852.51 + 674.258i) q^{63} +(256.000 - 443.405i) q^{64} +(923.381 - 533.114i) q^{65} +(146.807 + 123.185i) q^{66} +(3686.52 - 4393.43i) q^{67} +(1047.71 + 1814.68i) q^{68} +(772.835 + 446.197i) q^{69} +(-538.502 - 1479.52i) q^{70} +(-4614.85 + 813.722i) q^{71} +(-1759.90 - 310.319i) q^{72} +(5012.16 + 1824.28i) q^{73} +(-1291.39 + 1083.61i) q^{74} +181.583i q^{75} +(-80.6753 + 2886.87i) q^{76} +1189.21 q^{77} +(123.624 + 147.329i) q^{78} +(2867.68 - 7878.88i) q^{79} +(247.839 - 1405.56i) q^{80} +(1054.67 + 5981.32i) q^{81} +(-6702.81 + 2439.62i) q^{82} +(-1945.55 + 3369.79i) q^{83} +(245.952 - 142.001i) q^{84} +(4474.58 + 3754.62i) q^{85} +(-1083.76 + 1291.57i) q^{86} +(-127.959 - 221.631i) q^{87} +(933.586 + 539.006i) q^{88} +(2772.17 + 7616.47i) q^{89} +(-4905.89 + 865.041i) q^{90} +(1175.32 + 207.240i) q^{91} +(4717.08 + 1716.88i) q^{92} +(387.209 - 324.907i) q^{93} -2315.93i q^{94} +(2541.05 + 7639.02i) q^{95} +257.444 q^{96} +(-5994.88 - 7144.41i) q^{97} +(-1719.92 + 4725.45i) q^{98} +(653.373 - 3705.46i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9}+O(q^{10}) $ 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9} + 90 q^{11} - 432 q^{12} - 330 q^{13} + 576 q^{14} + 2658 q^{15} - 522 q^{17} - 1236 q^{19} - 864 q^{20} - 1998 q^{21} - 1344 q^{22} - 1440 q^{23} - 384 q^{24} - 3276 q^{25} + 576 q^{26} + 1692 q^{27} + 1056 q^{28} + 4050 q^{29} + 2808 q^{31} + 2910 q^{33} + 1536 q^{34} + 1422 q^{35} + 672 q^{36} + 1872 q^{38} - 9024 q^{39} - 3060 q^{41} - 3456 q^{42} - 1218 q^{43} - 5760 q^{44} - 2592 q^{45} - 2880 q^{46} + 990 q^{47} + 1536 q^{48} - 9696 q^{49} + 27648 q^{50} + 35784 q^{51} - 1488 q^{52} + 17082 q^{53} + 2160 q^{54} + 4290 q^{55} + 204 q^{57} - 5376 q^{58} - 11142 q^{59} - 11856 q^{60} - 35928 q^{61} - 7200 q^{62} - 58254 q^{63} + 9216 q^{64} - 34290 q^{65} - 32928 q^{66} + 44322 q^{67} - 4752 q^{68} + 21762 q^{69} + 12864 q^{70} + 40428 q^{71} + 10752 q^{72} + 6936 q^{73} - 4032 q^{74} - 576 q^{76} - 36648 q^{77} - 11040 q^{78} - 29298 q^{79} + 24324 q^{81} - 14592 q^{82} + 23958 q^{83} + 36720 q^{84} + 2772 q^{85} + 30816 q^{86} + 14256 q^{87} + 26064 q^{89} + 14784 q^{90} + 100044 q^{91} + 9360 q^{92} + 26400 q^{93} - 38646 q^{95} - 55746 q^{97} - 64512 q^{98} - 69846 q^{99}+O(q^{100}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9 + 90 * q^11 - 432 * q^12 - 330 * q^13 + 576 * q^14 + 2658 * q^15 - 522 * q^17 - 1236 * q^19 - 864 * q^20 - 1998 * q^21 - 1344 * q^22 - 1440 * q^23 - 384 * q^24 - 3276 * q^25 + 576 * q^26 + 1692 * q^27 + 1056 * q^28 + 4050 * q^29 + 2808 * q^31 + 2910 * q^33 + 1536 * q^34 + 1422 * q^35 + 672 * q^36 + 1872 * q^38 - 9024 * q^39 - 3060 * q^41 - 3456 * q^42 - 1218 * q^43 - 5760 * q^44 - 2592 * q^45 - 2880 * q^46 + 990 * q^47 + 1536 * q^48 - 9696 * q^49 + 27648 * q^50 + 35784 * q^51 - 1488 * q^52 + 17082 * q^53 + 2160 * q^54 + 4290 * q^55 + 204 * q^57 - 5376 * q^58 - 11142 * q^59 - 11856 * q^60 - 35928 * q^61 - 7200 * q^62 - 58254 * q^63 + 9216 * q^64 - 34290 * q^65 - 32928 * q^66 + 44322 * q^67 - 4752 * q^68 + 21762 * q^69 + 12864 * q^70 + 40428 * q^71 + 10752 * q^72 + 6936 * q^73 - 4032 * q^74 - 576 * q^76 - 36648 * q^77 - 11040 * q^78 - 29298 * q^79 + 24324 * q^81 - 14592 * q^82 + 23958 * q^83 + 36720 * q^84 + 2772 * q^85 + 30816 * q^86 + 14256 * q^87 + 26064 * q^89 + 14784 * q^90 + 100044 * q^91 + 9360 * q^92 + 26400 * q^93 - 38646 * q^95 - 55746 * q^97 - 64512 * q^98 - 69846 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.81808	+	2.16670i	0.454519	+	0.541675i
$2$	1.81808	+	2.16670i	0.454519	+	0.541675i
$3$	−0.486419	+	1.33642i	−0.0540465	+	0.148492i	−0.963778	−	0.266705i	$-0.914065\pi$
$3$	−0.486419	+	1.33642i	−0.0540465	+	0.148492i	0.909732	+	0.415197i	$0.136287\pi$
$4$	−1.38919	+	7.87846i	−0.0868241	+	0.492404i
$5$	3.87248	+	21.9619i	0.154899	+	0.878477i	0.958878	+	0.283819i	$0.0916014\pi$
$5$	3.87248	+	21.9619i	0.154899	+	0.878477i	−0.803979	+	0.594658i	$0.797287\pi$
$6$	−3.77998	+	1.37580i	−0.104999	+	0.0382167i
$7$	−12.4808	+	21.6173i	−0.254710	+	0.441170i	−0.964817	−	0.262924i	$-0.915313\pi$
$7$	−12.4808	+	21.6173i	−0.254710	+	0.441170i	0.710107	+	0.704094i	$0.248647\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$	60.5002	+	50.7657i	0.746916	+	0.626737i
$10$	−40.5444	+	48.3190i	−0.405444	+	0.483190i
$11$	−23.8209	−	41.2590i	−0.196867	−	0.340984i	0.750644	−	0.660707i	$-0.229743\pi$
$11$	−23.8209	−	41.2590i	−0.196867	−	0.340984i	−0.947511	+	0.319723i	$0.896410\pi$
$12$	−9.85324	−	5.68877i	−0.0684253	−	0.0395054i
$13$	−16.3525	−	44.9280i	−0.0967601	−	0.265846i	0.881864	−	0.471504i	$-0.156289\pi$
$13$	−16.3525	−	44.9280i	−0.0967601	−	0.265846i	−0.978624	+	0.205658i	$0.934067\pi$
$14$	−69.5294	+	12.2599i	−0.354742	+	0.0625505i
$15$	−31.2341	−	5.50741i	−0.138818	−	0.0244774i
$16$	−60.1403	−	21.8893i	−0.234923	−	0.0855050i
$17$	200.647	−	168.363i	0.694282	−	0.582572i	−0.225859	−	0.974160i	$-0.572519\pi$
$17$	200.647	−	168.363i	0.694282	−	0.582572i	0.920140	+	0.391589i	$0.128074\pi$
$18$			223.382i			0.689450i
$19$	357.128	−	52.7313i	0.989274	−	0.146070i
$19$	357.128	−	52.7313i	0.989274	−	0.146070i
$20$	−178.406			−0.446014
$21$	−22.8191	−	27.1947i	−0.0517439	−	0.0616660i
$22$	46.0877	−	126.625i	0.0952226	−	0.261622i
$23$	108.960	−	617.944i	0.205974	−	1.16814i	−0.689926	−	0.723880i	$-0.742357\pi$
$23$	108.960	−	617.944i	0.205974	−	1.16814i	0.895900	−	0.444256i	$-0.146532\pi$
$24$	−5.58809	−	31.6917i	−0.00970155	−	0.0550202i
$25$	119.978	−	43.6684i	0.191965	−	0.0698695i
$26$	67.6155	−	117.113i	0.100023	−	0.173245i
$27$	−197.037	+	113.759i	−0.270284	+	0.156048i
$28$	−152.973	−	128.360i	−0.195119	−	0.163724i
$29$	−115.667	+	137.846i	−0.137535	+	0.163907i	−0.830415	−	0.557145i	$-0.811897\pi$
$29$	−115.667	+	137.846i	−0.137535	+	0.163907i	0.692881	+	0.721052i	$0.256341\pi$
$30$	−44.8531	−	77.6878i	−0.0498368	−	0.0863198i
$31$	−307.796	−	177.706i	−0.320287	−	0.184918i	0.331233	−	0.943549i	$-0.392535\pi$
$31$	−307.796	−	177.706i	−0.320287	−	0.184918i	−0.651521	+	0.758631i	$0.725869\pi$
$32$	−61.9123	−	170.103i	−0.0604612	−	0.166116i
$33$	66.7265	−	11.7657i	0.0612732	−	0.0108041i
$34$	729.585	+	128.646i	0.631129	+	0.111285i
$35$	−523.090	−	190.389i	−0.427012	−	0.155420i
$36$	−484.001	+	406.125i	−0.373458	+	0.313368i
$37$			596.017i			0.435367i	0.976019	+	0.217683i	$0.0698501\pi$
$37$			596.017i			0.435367i	−0.976019	+	0.217683i	$0.930150\pi$
$38$	763.540	+	677.920i	0.528767	+	0.469474i
$39$	67.9970			0.0447055
$40$	−324.356	−	386.552i	−0.202722	−	0.241595i
$41$	−862.537	+	2369.80i	−0.513109	+	1.40976i	0.364870	+	0.931058i	$0.381113\pi$
$41$	−862.537	+	2369.80i	−0.513109	+	1.40976i	−0.877980	+	0.478698i	$0.841109\pi$
$42$	17.4359	−	98.8841i	0.00988432	−	0.0560568i
$43$	103.512	+	587.044i	0.0559825	+	0.317493i	0.999920	−	0.0126310i	$-0.00402067\pi$
$43$	103.512	+	587.044i	0.0559825	+	0.317493i	−0.943938	+	0.330124i	$0.892910\pi$
$44$	358.150	−	130.356i	0.184995	−	0.0673325i
$45$	−880.626	+	1525.29i	−0.434877	+	0.753229i
$46$	1537.00	−	887.386i	0.726370	−	0.419370i
$47$	−627.241	−	526.318i	−0.283948	−	0.238261i	0.489678	−	0.871904i	$-0.337114\pi$
$47$	−627.241	−	526.318i	−0.283948	−	0.238261i	−0.773626	+	0.633643i	$0.781559\pi$
$48$	58.5067	−	69.7256i	0.0253936	−	0.0302629i
$49$	888.960	+	1539.72i	0.370246	+	0.641285i
$50$	312.746	+	180.564i	0.125098	+	0.0722255i
$51$	127.406	+	350.045i	0.0489835	+	0.134581i
$52$	376.680	−	66.4189i	0.139305	−	0.0245632i
$53$	468.924	+	82.6839i	0.166936	+	0.0294354i	0.256491	−	0.966547i	$-0.417433\pi$
$53$	468.924	+	82.6839i	0.166936	+	0.0294354i	−0.0895553	+	0.995982i	$0.528545\pi$
$54$	−604.711	−	220.097i	−0.207377	−	0.0754790i
$55$	813.882	−	682.928i	0.269052	−	0.225761i
$56$		−	564.816i		−	0.180107i
$57$	−103.242	+	502.924i	−0.0317766	+	0.154793i
$58$	−508.963			−0.151297
$59$	−3815.25	−	4546.84i	−1.09602	−	1.30619i	−0.948376	−	0.317147i	$-0.897275\pi$
$59$	−3815.25	−	4546.84i	−1.09602	−	1.30619i	−0.147645	−	0.989040i	$-0.547169\pi$
$60$	86.7799	−	238.426i	0.0241055	−	0.0662294i
$61$	876.326	−	4969.89i	0.235508	−	1.33563i	−0.606033	−	0.795440i	$-0.707240\pi$
$61$	876.326	−	4969.89i	0.235508	−	1.33563i	0.841541	−	0.540193i	$-0.181649\pi$
$62$	−174.561	−	989.986i	−0.0454113	−	0.257541i
$63$	−1852.51	+	674.258i	−0.466744	+	0.169881i
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	923.381	−	533.114i	0.218552	−	0.126181i
$66$	146.807	+	123.185i	0.0337022	+	0.0282795i
$67$	3686.52	−	4393.43i	0.821235	−	0.978710i	−0.178752	−	0.983894i	$-0.557206\pi$
$67$	3686.52	−	4393.43i	0.821235	−	0.978710i	0.999987	+	0.00518456i	$0.00165031\pi$
$68$	1047.71	+	1814.68i	0.226580	+	0.392448i
$69$	772.835	+	446.197i	0.162326	+	0.0937191i
$70$	−538.502	−	1479.52i	−0.109898	−	0.301943i
$71$	−4614.85	+	813.722i	−0.915462	+	0.161421i	−0.611483	−	0.791258i	$-0.709427\pi$
$71$	−4614.85	+	813.722i	−0.915462	+	0.161421i	−0.303980	+	0.952679i	$0.598315\pi$
$72$	−1759.90	−	310.319i	−0.339488	−	0.0598608i
$73$	5012.16	+	1824.28i	0.940545	+	0.342330i	0.766381	−	0.642386i	$-0.222056\pi$
$73$	5012.16	+	1824.28i	0.940545	+	0.342330i	0.174164	+	0.984717i	$0.444278\pi$
$74$	−1291.39	+	1083.61i	−0.235828	+	0.197883i
$75$			181.583i			0.0322814i
$76$	−80.6753	+	2886.87i	−0.0139673	+	0.499805i
$77$	1189.21			0.200576
$78$	123.624	+	147.329i	0.0203195	+	0.0242158i
$79$	2867.68	−	7878.88i	0.459490	−	1.26244i	−0.466375	−	0.884587i	$-0.654440\pi$
$79$	2867.68	−	7878.88i	0.459490	−	1.26244i	0.925866	−	0.377852i	$-0.123337\pi$
$80$	247.839	−	1405.56i	0.0387248	−	0.219619i
$81$	1054.67	+	5981.32i	0.160748	+	0.911648i
$82$	−6702.81	+	2439.62i	−0.996848	+	0.362823i
$83$	−1945.55	+	3369.79i	−0.282414	+	0.489155i	−0.971979	−	0.235069i	$-0.924468\pi$
$83$	−1945.55	+	3369.79i	−0.282414	+	0.489155i	0.689565	+	0.724224i	$0.257802\pi$
$84$	245.952	−	142.001i	0.0348572	−	0.0201248i
$85$	4474.58	+	3754.62i	0.619319	+	0.519671i
$86$	−1083.76	+	1291.57i	−0.146533	+	0.174631i
$87$	−127.959	−	221.631i	−0.0169056	−	0.0292814i
$88$	933.586	+	539.006i	0.120556	+	0.0696030i
$89$	2772.17	+	7616.47i	0.349977	+	0.961554i	0.982377	+	0.186912i	$0.0598478\pi$
$89$	2772.17	+	7616.47i	0.349977	+	0.961554i	−0.632400	+	0.774642i	$0.717930\pi$
$90$	−4905.89	+	865.041i	−0.605666	+	0.106795i
$91$	1175.32	+	207.240i	0.141929	+	0.0250259i
$92$	4717.08	+	1716.88i	0.557311	+	0.202845i
$93$	387.209	−	324.907i	0.0447692	−	0.0375658i
$94$		−	2315.93i		−	0.262102i
$95$	2541.05	+	7639.02i	0.281557	+	0.846428i
$96$	257.444			0.0279345
$97$	−5994.88	−	7144.41i	−0.637143	−	0.759317i	0.346773	−	0.937949i	$-0.387277\pi$
$97$	−5994.88	−	7144.41i	−0.637143	−	0.759317i	−0.983916	+	0.178632i	$0.942833\pi$
$98$	−1719.92	+	4725.45i	−0.179084	+	0.492029i
$99$	653.373	−	3705.46i	0.0666640	−	0.378070i
$100$	177.368	+	1005.91i	0.0177368	+	0.100591i
$101$	−10390.2	+	3781.74i	−1.01855	+	0.370722i	−0.796711	−	0.604361i	$-0.793429\pi$
$101$	−10390.2	+	3781.74i	−1.01855	+	0.370722i	−0.221840	+	0.975083i	$0.571206\pi$
$102$	−526.809	+	912.460i	−0.0506352	+	0.0877028i
$103$	8660.98	−	5000.42i	0.816381	−	0.471338i	−0.0327861	−	0.999462i	$-0.510438\pi$
$103$	8660.98	−	5000.42i	0.816381	−	0.471338i	0.849167	+	0.528125i	$0.177105\pi$
$104$	828.744	+	695.398i	0.0766220	+	0.0642935i
$105$	508.881	−	606.461i	0.0461570	−	0.0550078i
$106$	673.389	+	1166.34i	0.0599313	+	0.103804i
$107$	−11832.3	−	6831.40i	−1.03348	−	0.596681i	−0.115501	−	0.993307i	$-0.536847\pi$
$107$	−11832.3	−	6831.40i	−1.03348	−	0.596681i	−0.917980	+	0.396627i	$0.870181\pi$
$108$	−622.528	−	1710.38i	−0.0533717	−	0.146638i
$109$	−12833.6	+	2262.91i	−1.08018	+	0.190464i	−0.685294	−	0.728267i	$-0.740326\pi$
$109$	−12833.6	+	2262.91i	−1.08018	+	0.190464i	−0.394884	+	0.918731i	$0.629215\pi$
$110$	2959.40	+	521.822i	0.244579	+	0.0431258i
$111$	−796.532	−	289.914i	−0.0646483	−	0.0235301i
$112$	1223.79	−	1026.88i	0.0975595	−	0.0818621i
$113$			1170.23i			0.0916458i	0.998950	+	0.0458229i	$0.0145910\pi$
$113$			1170.23i			0.0916458i	−0.998950	+	0.0458229i	$0.985409\pi$
$114$	−1277.39	+	690.660i	−0.0982909	+	0.0531440i
$115$	13993.2			1.05809
$116$	−925.334	−	1102.77i	−0.0687674	−	0.0819537i
$117$	1291.47	−	3548.30i	0.0943439	−	0.259208i
$118$	2915.22	−	16533.0i	0.209366	−	1.18738i
$119$	1135.33	+	6438.77i	0.0801729	+	0.454683i
$120$	674.370	−	245.451i	0.0468312	−	0.0170452i
$121$	6185.63	−	10713.8i	0.422487	−	0.731768i
$122$	12361.5	−	7136.91i	0.830522	−	0.479502i
$123$	−2747.50	−	2305.43i	−0.181605	−	0.152385i
$124$	1827.64	−	2178.09i	0.118863	−	0.141655i
$125$	8392.63	+	14536.5i	0.537128	+	0.930333i
$126$	−4828.92	−	2787.98i	−0.304165	−	0.175610i
$127$	−968.690	−	2661.46i	−0.0600589	−	0.165011i	0.906034	−	0.423205i	$-0.139095\pi$
$127$	−968.690	−	2661.46i	−0.0600589	−	0.165011i	−0.966093	+	0.258194i	$0.916873\pi$
$128$	1426.15	−	251.469i	0.0870455	−	0.0153485i
$129$	−834.890	−	147.214i	−0.0501706	−	0.00884644i
$130$	2833.88	+	1031.45i	0.167685	+	0.0610324i
$131$	−8200.42	+	6880.97i	−0.477852	+	0.400966i	−0.849649	−	0.527348i	$-0.823186\pi$
$131$	−8200.42	+	6880.97i	−0.477852	+	0.400966i	0.371797	+	0.928314i	$0.378742\pi$
$132$			542.047i			0.0311092i
$133$	−3317.32	+	8378.29i	−0.187536	+	0.473644i
$134$	16221.6			0.903410
$135$	−3261.40	−	3886.78i	−0.178952	−	0.213266i
$136$	−2027.06	+	5569.30i	−0.109594	+	0.301108i
$137$	5924.62	−	33600.2i	0.315660	−	1.79020i	−0.252835	−	0.967509i	$-0.581363\pi$
$137$	5924.62	−	33600.2i	0.315660	−	1.79020i	0.568495	−	0.822687i	$-0.307526\pi$
$138$	438.300	+	2485.72i	0.0230151	+	0.130525i
$139$	−15481.2	+	5634.70i	−0.801264	+	0.291636i	−0.710010	−	0.704192i	$-0.751310\pi$
$139$	−15481.2	+	5634.70i	−0.801264	+	0.291636i	−0.0912536	+	0.995828i	$0.529087\pi$
$140$	2226.64	−	3856.66i	0.113604	−	0.196768i
$141$	1008.49	−	582.250i	0.0507261	−	0.0292867i
$142$	−10153.2	−	8519.58i	−0.503533	−	0.422514i
$143$	−1464.16	+	1744.91i	−0.0716004	+	0.0853300i
$144$	−2527.28	−	4377.37i	−0.121879	−	0.211100i
$145$	−3475.28	−	2006.46i	−0.165293	−	0.0954319i
$146$	5159.84	+	14176.5i	0.242064	+	0.665065i
$147$	−2490.13	+	439.077i	−0.115236	+	0.0203192i
$148$	−4695.70	−	827.979i	−0.214376	−	0.0378003i
$149$	−34533.3	−	12569.1i	−1.55548	−	0.566150i	−0.585788	−	0.810464i	$-0.699215\pi$
$149$	−34533.3	−	12569.1i	−1.55548	−	0.566150i	−0.969696	+	0.244314i	$0.921437\pi$
$150$	−393.435	+	330.131i	−0.0174860	+	0.0146725i
$151$			27582.8i			1.20972i	0.796333	+	0.604859i	$0.206770\pi$
$151$			27582.8i			1.20972i	−0.796333	+	0.604859i	$0.793230\pi$
$152$	−6401.66	+	5073.76i	−0.277080	+	0.219605i
$153$	20686.3			0.883689
$154$	2162.09	+	2576.67i	0.0911657	+	0.108647i
$155$	2710.83	−	7447.96i	0.112834	−	0.310009i
$156$	−94.4604	+	535.712i	−0.00388151	+	0.0220131i
$157$	2416.57	+	13705.0i	0.0980392	+	0.556008i	0.993774	+	0.111418i	$0.0355394\pi$
$157$	2416.57	+	13705.0i	0.0980392	+	0.556008i	−0.895734	+	0.444590i	$0.853350\pi$
$158$	22284.8	−	8111.02i	0.892679	−	0.324909i
$159$	−338.594	+	586.462i	−0.0133932	+	0.0231977i
$160$	3496.02	−	2018.43i	0.136563	−	0.0788449i
$161$	11998.4	+	10067.9i	0.462884	+	0.388405i
$162$	−11042.3	+	13159.7i	−0.420754	+	0.501435i
$163$	24779.5	+	42919.3i	0.932645	+	1.61539i	0.778780	+	0.627297i	$0.215839\pi$
$163$	24779.5	+	42919.3i	0.932645	+	1.61539i	0.153865	+	0.988092i	$0.450828\pi$
$164$	−17472.2	−	10087.6i	−0.649619	−	0.375058i
$165$	516.794	+	1419.88i	0.0189823	+	0.0521535i
$166$	−10838.5	+	1911.12i	−0.393325	+	0.0693539i
$167$	−29654.9	−	5228.96i	−1.06332	−	0.187492i	−0.385490	−	0.922712i	$-0.625968\pi$
$167$	−29654.9	−	5228.96i	−1.06332	−	0.187492i	−0.677829	+	0.735220i	$0.737079\pi$
$168$	754.833	+	274.737i	0.0267444	+	0.00973416i
$169$	20127.9	−	16889.3i	0.704733	−	0.591341i
$170$			16521.3i			0.571670i
$171$	24283.2	+	14939.6i	0.830452	+	0.510912i
$172$	−4768.80			−0.161195
$173$	−22138.0	−	26383.0i	−0.739683	−	0.881520i	0.256700	−	0.966491i	$-0.417365\pi$
$173$	−22138.0	−	26383.0i	−0.739683	−	0.881520i	−0.996383	+	0.0849707i	$0.972920\pi$
$174$	247.569	−	680.190i	0.00817707	−	0.0224663i
$175$	−553.424	+	3138.62i	−0.0180710	+	0.102486i
$176$	529.467	+	3002.76i	0.0170928	+	0.0969381i
$177$	7932.32	−	2887.13i	0.253194	−	0.0921551i
$178$	−11462.6	+	19853.8i	−0.361778	+	0.626619i
$179$	22568.8	−	13030.1i	0.704374	−	0.406671i	−0.104600	−	0.994514i	$-0.533356\pi$
$179$	22568.8	−	13030.1i	0.704374	−	0.406671i	0.808974	+	0.587844i	$0.200023\pi$
$180$	−10793.6	−	9056.89i	−0.333135	−	0.279534i
$181$	−31858.1	+	37967.0i	−0.972441	+	1.15891i	0.0148349	+	0.999890i	$0.495278\pi$
$181$	−31858.1	+	37967.0i	−0.972441	+	1.15891i	−0.987275	+	0.159020i	$0.949167\pi$
$182$	1687.79	+	2923.34i	0.0509536	+	0.0882543i
$183$	6215.62	+	3588.59i	0.185602	+	0.107157i
$184$	4856.06	+	13341.9i	0.143433	+	0.394079i
$185$	−13089.7	+	2308.07i	−0.382460	+	0.0674380i
$186$	1407.95	+	248.260i	0.0406969	+	0.00717597i
$187$	−11726.1	−	4267.96i	−0.335329	−	0.122050i
$188$	5017.93	−	4210.54i	0.141974	−	0.119130i
$189$		−	5679.22i		−	0.158988i
$190$	−11931.6	+	19394.0i	−0.330516	+	0.537231i
$191$	50596.7			1.38693			0.693466	−	0.720489i	$-0.256083\pi$
$191$	50596.7			1.38693			0.693466	+	0.720489i	$0.256083\pi$
$192$	468.054	+	557.805i	0.0126968	+	0.0151314i
$193$	19028.9	−	52281.4i	0.510856	−	1.40356i	−0.369491	−	0.929234i	$-0.620468\pi$
$193$	19028.9	−	52281.4i	0.510856	−	1.40356i	0.880347	−	0.474330i	$-0.157310\pi$
$194$	4580.66	−	25978.2i	0.121709	−	0.690249i
$195$	263.317	+	1493.34i	0.00692484	+	0.0392727i
$196$	−13365.6	+	4864.68i	−0.347917	+	0.126632i
$197$	31572.6	−	54685.4i	0.813539	−	1.40909i	−0.0968331	−	0.995301i	$-0.530871\pi$
$197$	31572.6	−	54685.4i	0.813539	−	1.40909i	0.910372	−	0.413790i	$-0.135795\pi$
$198$	9216.52	−	5321.16i	0.235091	−	0.135730i
$199$	3391.01	+	2845.39i	0.0856294	+	0.0718516i	0.684598	−	0.728921i	$-0.259978\pi$
$199$	3391.01	+	2845.39i	0.0856294	+	0.0718516i	−0.598968	+	0.800773i	$0.704422\pi$
$200$	−1857.03	+	2213.12i	−0.0464257	+	0.0553280i
$201$	4078.29	+	7063.80i	0.100945	+	0.174842i
$202$	−27084.2	−	15637.0i	−0.663762	−	0.383223i
$203$	−1536.26	−	4220.84i	−0.0372797	−	0.102425i
$204$	−2934.81	+	517.486i	−0.0705211	+	0.0124348i
$205$	−55385.5	−	9765.96i	−1.31792	−	0.232385i
$206$	26580.8	+	9674.60i	0.626373	+	0.227981i
$207$	37962.5	−	31854.3i	0.885959	−	0.743408i
$208$			3059.93i			0.0707269i
$209$	−10682.8	−	13478.7i	−0.244563	−	0.308570i
$210$	2239.21			0.0507757
$211$	−287.462	−	342.584i	−0.00645677	−	0.00769488i	0.762806	−	0.646627i	$-0.223821\pi$
$211$	−287.462	−	342.584i	−0.00645677	−	0.00769488i	−0.769263	+	0.638932i	$0.779376\pi$
$212$	−1302.84	+	3579.53i	−0.0289882	+	0.0796443i
$213$	1157.27	−	6563.20i	0.0255079	−	0.144663i
$214$	−6710.50	−	38057.1i	−0.146530	−	0.831014i
$215$	−12491.8	+	4546.63i	−0.270238	+	0.0983587i
$216$	2574.08	−	4458.44i	0.0551715	−	0.0955598i
$217$	7683.07	−	4435.82i	0.163161	−	0.0942008i
$218$	−28235.5	−	23692.4i	−0.594132	−	0.498536i
$219$	−4876.02	+	5811.01i	−0.101666	+	0.121161i
$220$	4249.79	+	7360.85i	0.0878056	+	0.152084i
$221$	−10845.3	−	6261.54i	−0.222053	−	0.128202i
$222$	−820.000	−	2252.93i	−0.0166383	−	0.0457133i
$223$	−62927.8	+	11095.9i	−1.26541	+	0.223127i	−0.765776	−	0.643108i	$-0.777645\pi$
$223$	−62927.8	+	11095.9i	−1.26541	+	0.223127i	−0.499638	+	0.866234i	$0.666534\pi$
$224$	4449.88	+	784.634i	0.0886854	+	0.0156376i
$225$	9475.55	+	3448.82i	0.187171	+	0.0681248i
$226$	−2535.53	+	2127.56i	−0.0496423	+	0.0416548i
$227$			5420.01i			0.105184i	0.998616	+	0.0525919i	$0.0167482\pi$
$227$			5420.01i			0.105184i	−0.998616	+	0.0525919i	$0.983252\pi$
$228$	−3818.84	−	1512.05i	−0.0734619	−	0.0290867i
$229$	−8890.80			−0.169539			−0.0847696	−	0.996401i	$-0.527015\pi$
$229$	−8890.80			−0.169539			−0.0847696	+	0.996401i	$0.527015\pi$
$230$	25440.7	+	30319.1i	0.480921	+	0.573139i
$231$	−578.456	+	1589.30i	−0.0108404	+	0.0297838i
$232$	707.043	−	4009.84i	0.0131362	−	0.0744991i
$233$	3420.46	+	19398.4i	0.0630047	+	0.357317i	0.999969	+	0.00789187i	$0.00251209\pi$
$233$	3420.46	+	19398.4i	0.0630047	+	0.357317i	−0.936964	+	0.349425i	$0.886377\pi$
$234$	10036.1	−	3652.84i	0.183288	−	0.0667112i
$235$	9129.97	−	15813.6i	0.165323	−	0.286348i
$236$	41122.2	−	23741.9i	0.738333	−	0.426277i
$237$	9134.64	+	7664.87i	0.162628	+	0.136461i
$238$	−11886.8	+	14166.1i	−0.209850	+	0.250090i
$239$	34459.6	+	59685.8i	0.603274	+	1.04490i	0.992322	+	0.123684i	$0.0394709\pi$
$239$	34459.6	+	59685.8i	0.603274	+	1.04490i	−0.389047	+	0.921218i	$0.627196\pi$
$240$	1757.87	+	1014.91i	0.0305187	+	0.0176200i
$241$	35213.1	+	96747.1i	0.606275	+	1.66573i	0.738293	+	0.674480i	$0.235632\pi$
$241$	35213.1	+	96747.1i	0.606275	+	1.66573i	−0.132018	+	0.991247i	$0.542146\pi$
$242$	34459.6	−	6076.16i	0.588409	−	0.103752i
$243$	−26655.6	−	4700.11i	−0.451415	−	0.0795967i
$244$	37937.7	+	13808.2i	0.637223	+	0.231930i
$245$	−30372.8	+	25485.8i	−0.506003	+	0.424587i
$246$		−	10144.5i		−	0.167633i
$247$	−8209.03	−	15182.8i	−0.134554	−	0.248861i
$248$	8042.06			0.130757
$249$	−3557.11	−	4239.20i	−0.0573719	−	0.0683731i
$250$	−16237.7	+	44612.7i	−0.259803	+	0.713804i
$251$	−15075.6	+	85498.2i	−0.239292	+	1.35709i	0.594091	+	0.804398i	$0.297512\pi$
$251$	−15075.6	+	85498.2i	−0.239292	+	1.35709i	−0.833383	+	0.552695i	$0.813599\pi$
$252$	−2738.64	−	15531.6i	−0.0431254	−	0.244577i
$253$	−28091.3	+	10224.4i	−0.438865	+	0.159734i
$254$	4005.42	−	6937.59i	0.0620842	−	0.107533i
$255$	−7194.28	+	4153.62i	−0.110639	+	0.0638773i
$256$	3137.72	+	2632.86i	0.0478778	+	0.0401742i
$257$	22703.8	−	27057.4i	0.343742	−	0.409656i	−0.566282	−	0.824212i	$-0.691619\pi$
$257$	22703.8	−	27057.4i	0.343742	−	0.409656i	0.910024	+	0.414556i	$0.136063\pi$
$258$	−1198.93	−	2076.60i	−0.0180116	−	0.0311971i
$259$	−12884.3	−	7438.76i	−0.192071	−	0.110892i
$260$	2917.37	+	8015.41i	0.0431564	+	0.118571i
$261$	−13995.7	+	2467.82i	−0.205454	+	0.0362270i
$262$	−29818.0	−	5257.72i	−0.434386	−	0.0765940i
$263$	−68122.5	−	24794.5i	−0.984870	−	0.358463i	−0.201138	−	0.979563i	$-0.564464\pi$
$263$	−68122.5	−	24794.5i	−0.984870	−	0.358463i	−0.783732	+	0.621100i	$0.786686\pi$
$264$	−1174.45	+	985.484i	−0.0168511	+	0.0141397i
$265$			10618.7i			0.151209i
$266$	−24184.4	+	8044.73i	−0.341800	+	0.113697i
$267$	−11527.3			−0.161698
$268$	29492.2	+	35147.4i	0.410617	+	0.489355i
$269$	4743.16	−	13031.7i	0.0655486	−	0.180093i	−0.902594	−	0.430493i	$-0.858340\pi$
$269$	4743.16	−	13031.7i	0.0655486	−	0.180093i	0.968143	+	0.250400i	$0.0805620\pi$
$270$	2492.02	−	14132.9i	0.0341841	−	0.193867i
$271$	8246.93	+	46770.7i	0.112293	+	0.636847i	0.988055	+	0.154103i	$0.0492488\pi$
$271$	8246.93	+	46770.7i	0.112293	+	0.636847i	−0.875761	+	0.482744i	$0.839640\pi$
$272$	−15752.4	+	5733.39i	−0.212916	+	0.0774950i
$273$	−848.656	+	1469.91i	−0.0113869	+	0.0197227i
$274$	83573.0	−	48250.9i	1.11318	−	0.642694i
$275$	−4659.70	−	3909.96i	−0.0616159	−	0.0517019i
$276$	−4588.95	+	5468.90i	−0.0602415	+	0.0717930i
$277$	−13470.1	−	23330.9i	−0.175554	−	0.304069i	0.764799	−	0.644269i	$-0.222838\pi$
$277$	−13470.1	−	23330.9i	−0.175554	−	0.304069i	−0.940353	+	0.340200i	$0.889505\pi$
$278$	−40354.8	−	23298.8i	−0.522162	−	0.301470i
$279$	−9600.35	−	26376.7i	−0.123333	−	0.338854i
$280$	12404.4	−	2187.24i	0.158220	−	0.0278984i
$281$	79271.4	+	13977.7i	1.00393	+	0.177020i	0.651363	−	0.758766i	$-0.274197\pi$
$281$	79271.4	+	13977.7i	1.00393	+	0.177020i	0.352568	+	0.935786i	$0.385309\pi$
$282$	3095.07	+	1126.51i	0.0389199	+	0.0141657i
$283$	39136.9	−	32839.8i	0.488668	−	0.410041i	−0.364881	−	0.931054i	$-0.618890\pi$
$283$	39136.9	−	32839.8i	0.488668	−	0.410041i	0.853549	+	0.521013i	$0.174446\pi$
$284$		−	37488.3i		−	0.464792i
$285$	−11445.0	−	319.837i	−0.140905	−	0.00393766i
$286$	−6442.65			−0.0787649
$287$	−40463.7	−	48222.7i	−0.491249	−	0.585447i
$288$	4889.67	−	13434.3i	0.0589514	−	0.161968i
$289$	−2590.04	+	14688.9i	−0.0310107	+	0.175870i
$290$	−1970.95	−	11177.8i	−0.0234358	−	0.132911i
$291$	12464.0	−	4536.52i	0.147188	−	0.0535719i
$292$	−21335.3	+	36953.9i	−0.250227	+	0.433405i
$293$	−93634.5	+	54059.9i	−1.09069	+	0.629709i	−0.933760	−	0.357901i	$-0.883493\pi$
$293$	−93634.5	+	54059.9i	−1.09069	+	0.629709i	−0.156929	+	0.987610i	$0.550159\pi$
$294$	−5478.60	−	4597.09i	−0.0633833	−	0.0531849i
$295$	85082.9	−	101398.i	0.977683	−	1.16516i
$296$	−6743.17	−	11679.5i	−0.0769627	−	0.133303i
$297$	9387.20	+	5419.70i	0.106420	+	0.0614416i
$298$	−35550.8	−	97675.0i	−0.400329	−	1.09989i
$299$	−29544.8	+	5209.54i	−0.330475	+	0.0582716i
$300$	−1430.59	−	252.252i	−0.0158955	−	0.00280280i
$301$	−13982.2	−	5089.12i	−0.154328	−	0.0561707i
$302$	−59763.6	+	50147.6i	−0.655274	+	0.549840i
$303$		−	15725.3i		−	0.171283i
$304$	−22632.0	−	4646.00i	−0.244893	−	0.0502727i
$305$	112542.			1.20980
$306$	37609.3	+	44821.0i	0.401654	+	0.478672i
$307$	51431.7	−	141308.i	0.545701	−	1.49930i	−0.293760	−	0.955879i	$-0.594907\pi$
$307$	51431.7	−	141308.i	0.545701	−	1.49930i	0.839460	−	0.543421i	$-0.182871\pi$
$308$	−1652.04	+	9369.18i	−0.0174148	+	0.0987644i
$309$	2469.82	+	14007.0i	0.0258671	+	0.146700i
$310$	21066.0	−	7667.40i	0.219209	−	0.0797856i
$311$	16542.4	−	28652.3i	0.171032	−	0.296236i	−0.767749	−	0.640751i	$-0.778623\pi$
$311$	16542.4	−	28652.3i	0.171032	−	0.296236i	0.938781	+	0.344515i	$0.111956\pi$
$312$	−1332.46	+	769.298i	−0.0136882	+	0.00790288i
$313$	42872.8	+	35974.6i	0.437616	+	0.367203i	0.834816	−	0.550528i	$-0.185574\pi$
$313$	42872.8	+	35974.6i	0.437616	+	0.367203i	−0.397200	+	0.917732i	$0.630018\pi$
$314$	−25301.2	+	30152.8i	−0.256615	+	0.305822i
$315$	−21981.8	−	38073.6i	−0.221535	−	0.383710i
$316$	58089.7	+	33538.1i	0.581735	+	0.335865i
$317$	−12497.3	−	34335.9i	−0.124364	−	0.341688i	0.861849	−	0.507164i	$-0.169306\pi$
$317$	−12497.3	−	34335.9i	−0.124364	−	0.341688i	−0.986214	+	0.165476i	$0.947084\pi$
$318$	−1886.28	+	332.602i	−0.0186531	+	0.00328905i
$319$	8442.69	+	1488.67i	0.0829659	+	0.0146291i
$320$	10729.4	+	3905.18i	0.104779	+	0.0381365i
$321$	14885.1	−	12490.1i	0.144458	−	0.121215i
$322$			44301.1i			0.427270i
$323$	62778.8	−	70707.6i	0.601739	−	0.677737i
$324$	−48588.7			−0.462856
$325$	−3923.87	−	4676.29i	−0.0371491	−	0.0442725i
$326$	−47942.2	+	131720.i	−0.451111	+	1.23942i
$327$	3218.29	−	18251.8i	0.0300975	−	0.170691i
$328$	−9909.03	−	56196.9i	−0.0921051	−	0.522354i
$329$	19206.1	−	6990.43i	0.177438	−	0.0645821i
$330$	−2136.88	+	3701.19i	−0.0196224	+	0.0339871i
$331$	−152310.	+	87936.0i	−1.39018	+	0.802621i	−0.993335	−	0.115264i	$-0.963229\pi$
$331$	−152310.	+	87936.0i	−1.39018	+	0.802621i	−0.396846	+	0.917885i	$0.629895\pi$
$332$	−23846.0	−	20009.2i	−0.216341	−	0.181532i
$333$	−30257.2	+	36059.2i	−0.272860	+	0.325182i
$334$	−42585.3	−	73760.0i	−0.381740	−	0.661192i
$335$	110764.	+	63949.7i	0.986982	+	0.569835i
$336$	777.073	+	2134.99i	0.00688309	+	0.0189111i
$337$	179120.	−	31583.6i	1.57719	−	0.278101i	0.684581	−	0.728936i	$-0.259985\pi$
$337$	179120.	−	31583.6i	1.57719	−	0.278101i	0.892607	+	0.450836i	$0.148874\pi$
$338$	73188.1	+	12905.0i	0.640630	+	0.112960i
$339$	−1563.92	−	569.219i	−0.0136086	−	0.00495314i
$340$	−35796.7	+	30037.0i	−0.309660	+	0.259835i
$341$			16932.5i			0.145617i
$342$	11779.2	+	79775.9i	0.100708	+	0.682055i
$343$	−104312.			−0.886641
$344$	−8670.05	−	10332.6i	−0.0732664	−	0.0873155i
$345$	−6806.55	+	18700.8i	−0.0571859	+	0.157117i
$346$	16915.5	−	95932.8i	0.141297	−	0.801336i
$347$	6870.63	+	38965.3i	0.0570608	+	0.323608i	0.999955	−	0.00948446i	$-0.00301904\pi$
$347$	6870.63	+	38965.3i	0.0570608	+	0.323608i	−0.942894	+	0.333092i	$0.891908\pi$
$348$	1923.87	−	700.230i	0.0158861	−	0.00578206i
$349$	−80075.7	+	138695.i	−0.657431	+	1.13870i	0.323847	+	0.946109i	$0.395024\pi$
$349$	−80075.7	+	138695.i	−0.657431	+	1.13870i	−0.981278	+	0.192595i	$0.938310\pi$
$350$	−7806.62	+	4507.15i	−0.0637275	+	0.0367931i
$351$	8333.02	+	6992.23i	0.0676376	+	0.0567547i
$352$	−5543.46	+	6606.44i	−0.0447400	+	0.0533190i
$353$	−27449.0	−	47543.1i	−0.220281	−	0.381538i	0.734612	−	0.678487i	$-0.237364\pi$
$353$	−27449.0	−	47543.1i	−0.220281	−	0.381538i	−0.954893	+	0.296949i	$0.904031\pi$
$354$	20677.1	+	11937.9i	0.165000	+	0.0952626i
$355$	−35741.8	−	98199.7i	−0.283609	−	0.779208i
$356$	−63857.1	+	11259.7i	−0.503859	+	0.0888440i
$357$	−9157.17	−	1614.66i	−0.0718497	−	0.0126690i
$358$	69264.3	+	25210.1i	0.540435	+	0.196702i
$359$	−32368.4	+	27160.3i	−0.251149	+	0.210739i	−0.759667	−	0.650312i	$-0.774638\pi$
$359$	−32368.4	+	27160.3i	−0.251149	+	0.210739i	0.508518	+	0.861052i	$0.330194\pi$
$360$		−	39852.6i		−	0.307505i
$361$	124760.	−	37663.7i	0.957327	−	0.289007i
$362$	−140184.			−1.06975
$363$	11309.4	+	13478.0i	0.0858275	+	0.102285i
$364$	−3265.46	+	8971.78i	−0.0246457	+	0.0677136i
$365$	−20655.2	+	117141.i	−0.155040	+	0.879273i
$366$	3525.08	+	19991.7i	0.0263152	+	0.149241i
$367$	70386.2	−	25618.5i	0.522583	−	0.190205i	−0.0672407	−	0.997737i	$-0.521420\pi$
$367$	70386.2	−	25618.5i	0.522583	−	0.190205i	0.589824	+	0.807532i	$0.299197\pi$
$368$	−20079.3	+	34778.3i	−0.148270	+	0.256810i
$369$	−172488.	+	99586.1i	−1.26680	+	0.731385i
$370$	−28799.0	−	24165.2i	−0.210365	−	0.176517i
$371$	−7639.94	+	9104.93i	−0.0555063	+	0.0661498i
$372$	2021.86	+	3501.96i	0.0146105	+	0.0253061i
$373$	34380.6	+	19849.7i	0.247113	+	0.142671i	0.618442	−	0.785831i	$-0.287764\pi$
$373$	34380.6	+	19849.7i	0.247113	+	0.142671i	−0.371328	+	0.928502i	$0.621098\pi$
$374$	−12071.6	−	33166.4i	−0.0863022	−	0.237113i
$375$	−23509.2	+	4145.31i	−0.167177	+	0.0294777i
$376$	18246.0	+	3217.26i	0.129060	+	0.0227567i
$377$	8084.59	+	2942.55i	0.0568820	+	0.0207034i
$378$	12305.2	−	10325.3i	0.0861200	−	0.0722633i
$379$		−	104843.i		−	0.729894i	−0.931028	−	0.364947i	$-0.881087\pi$
$379$		−	104843.i		−	0.729894i	0.931028	−	0.364947i	$-0.118913\pi$
$380$	−63713.7	+	9407.57i	−0.441231	+	0.0651494i
$381$	4028.02			0.0277487
$382$	91988.7	+	109628.i	0.630388	+	0.751267i
$383$	−69723.6	+	191564.i	−0.475316	+	1.30592i	0.438112	+	0.898920i	$0.355647\pi$
$383$	−69723.6	+	191564.i	−0.475316	+	1.30592i	−0.913428	+	0.407000i	$0.866575\pi$
$384$	−357.638	+	2028.27i	−0.00242539	+	0.0137551i
$385$	4605.21	+	26117.4i	0.0310690	+	0.176201i
$386$	147874.	−	53821.8i	0.992470	−	0.361230i
$387$	−23539.2	+	40771.1i	−0.157170	+	0.272227i
$388$	64615.0	−	37305.5i	0.429210	−	0.247805i
$389$	86188.8	+	72321.0i	0.569576	+	0.477931i	0.881505	−	0.472174i	$-0.156531\pi$
$389$	86188.8	+	72321.0i	0.569576	+	0.477931i	−0.311929	+	0.950105i	$0.600975\pi$
$390$	−2756.90	+	3285.55i	−0.0181256	+	0.0216012i
$391$	−82176.5	−	142334.i	−0.537519	−	0.931010i
$392$	−34840.0	−	20114.9i	−0.226728	−	0.130902i
$393$	−5207.06	−	14306.3i	−0.0337138	−	0.0926278i
$394$	175888.	−	31013.9i	1.13304	−	0.199785i
$395$	184140.	+	32468.9i	1.18020	+	0.208101i
$396$	28285.7	+	10295.2i	0.180375	+	0.0656512i
$397$	−58462.0	+	49055.4i	−0.370931	+	0.311248i	−0.809130	−	0.587630i	$-0.800061\pi$
$397$	−58462.0	+	49055.4i	−0.370931	+	0.311248i	0.438199	+	0.898878i	$0.355617\pi$
$398$			12520.5i			0.0790413i
$399$	−9583.34	−	8508.71i	−0.0601965	−	0.0534463i
$400$	−8171.39			−0.0510712
$401$	−128349.	−	152961.i	−0.798188	−	0.951243i	0.201413	−	0.979506i	$-0.435447\pi$
$401$	−128349.	−	152961.i	−0.798188	−	0.951243i	−0.999601	+	0.0282636i	$0.991002\pi$
$402$	−7890.50	+	21679.0i	−0.0488262	+	0.134149i
$403$	−2950.76	+	16734.6i	−0.0181687	+	0.103040i
$404$	−15360.3	−	87112.6i	−0.0941103	−	0.533726i
$405$	−127277.	+	46325.1i	−0.775962	+	0.282427i
$406$	6352.25	−	11002.4i	0.0385368	−	0.0667477i
$407$	24591.1	−	14197.7i	0.148453	−	0.0857094i
$408$	−6456.94	−	5418.02i	−0.0387888	−	0.0325477i
$409$	117801.	−	140390.i	0.704210	−	0.839245i	−0.288786	−	0.957394i	$-0.593251\pi$
$409$	117801.	−	140390.i	0.704210	−	0.839245i	0.992996	+	0.118149i	$0.0376959\pi$
$410$	−79535.3	−	137759.i	−0.473143	−	0.819507i
$411$	42022.3	+	24261.6i	0.248769	+	0.143627i
$412$	27363.9	+	75181.7i	0.161207	+	0.442912i
$413$	145908.	−	25727.5i	0.855419	−	0.150833i
$414$	138037.	+	24339.7i	0.805371	+	0.142009i
$415$	−81541.1	−	29678.5i	−0.473457	−	0.172324i
$416$	−6629.95	+	5563.19i	−0.0383110	+	0.0321468i
$417$		−	23430.3i		−	0.134743i
$418$	9782.11	−	47651.6i	0.0559861	−	0.272725i
$419$	−309078.			−1.76052			−0.880259	−	0.474493i	$-0.842631\pi$
$419$	−309078.			−1.76052			−0.880259	+	0.474493i	$0.842631\pi$
$420$	4071.05	+	4851.69i	0.0230785	+	0.0275039i
$421$	8000.37	−	21980.8i	0.0451384	−	0.124017i	−0.915075	−	0.403283i	$-0.867869\pi$
$421$	8000.37	−	21980.8i	0.0451384	−	0.124017i	0.960214	+	0.279266i	$0.0900912\pi$
$422$	219.648	−	1245.69i	0.00123340	−	0.00699495i
$423$	−11229.3	−	63684.6i	−0.0627585	−	0.355921i
$424$	−10124.5	+	3685.00i	−0.0563170	+	0.0204977i
$425$	16721.1	−	28961.8i	0.0925737	−	0.160342i
$426$	16324.5	−	9424.95i	0.0899540	−	0.0519350i
$427$	96498.6	+	80971.9i	0.529255	+	0.444098i
$428$	70258.2	−	83730.4i	0.383539	−	0.457084i
$429$	−1619.75	−	2805.49i	−0.00880104	−	0.0152438i
$430$	−32562.2	−	18799.8i	−0.176107	−	0.101675i
$431$	−38307.3	−	105248.i	−0.206218	−	0.566580i	0.792865	−	0.609398i	$-0.208589\pi$
$431$	−38307.3	−	105248.i	−0.206218	−	0.566580i	−0.999083	+	0.0428180i	$0.986366\pi$
$432$	14340.0	−	2528.52i	0.0768389	−	0.0135488i
$433$	58600.0	+	10332.8i	0.312552	+	0.0551113i	0.327724	−	0.944774i	$-0.393718\pi$
$433$	58600.0	+	10332.8i	0.312552	+	0.0551113i	−0.0151719	+	0.999885i	$0.504830\pi$
$434$	23579.5	+	8582.25i	0.125186	+	0.0455640i
$435$	4371.92	−	3668.48i	0.0231043	−	0.0193868i
$436$		−	104253.i		−	0.548420i
$437$	6327.74	−	226431.i	0.0331349	−	1.18569i
$438$	−21455.7			−0.111839
$439$	5538.24	+	6600.22i	0.0287371	+	0.0342475i	0.780222	−	0.625503i	$-0.215106\pi$
$439$	5538.24	+	6600.22i	0.0287371	+	0.0342475i	−0.751484	+	0.659751i	$0.770662\pi$
$440$	−8222.31	+	22590.6i	−0.0424706	+	0.116687i
$441$	−24382.9	+	138282.i	−0.125374	+	0.711032i
$442$	−6150.72	−	34882.5i	−0.0314834	−	0.178551i
$443$	−28101.3	+	10228.0i	−0.143192	+	0.0521176i	−0.412622	−	0.910902i	$-0.635387\pi$
$443$	−28101.3	+	10228.0i	−0.143192	+	0.0521176i	0.269430	+	0.963020i	$0.413165\pi$
$444$	3390.61	−	5872.70i	0.0171993	−	0.0297901i
$445$	−156537.	+	90376.7i	−0.790492	+	0.456391i
$446$	−138449.	−	116172.i	−0.696017	−	0.584028i
$447$	33595.3	−	40037.3i	0.168137	−	0.200378i
$448$	6390.16	+	11068.1i	0.0318387	+	0.0551463i
$449$	148552.	+	85766.5i	0.736861	+	0.425427i	0.820927	−	0.571033i	$-0.193457\pi$
$449$	148552.	+	85766.5i	0.736861	+	0.425427i	−0.0840661	+	0.996460i	$0.526791\pi$
$450$	9754.73	+	26800.9i	0.0481715	+	0.132350i
$451$	118322.	−	20863.4i	0.581719	−	0.102573i
$452$	−9219.58	−	1625.66i	−0.0451268	−	0.00795706i
$453$	−36862.3	−	13416.8i	−0.179633	−	0.0653810i
$454$	−11743.6	+	9854.01i	−0.0569754	+	0.0478081i
$455$			26614.7i			0.128558i
$456$	−3666.81	−	11023.3i	−0.0176343	−	0.0530130i
$457$	−319391.			−1.52929			−0.764646	−	0.644451i	$-0.777086\pi$
$457$	−319391.			−1.52929			−0.764646	+	0.644451i	$0.777086\pi$
$458$	−16164.2	−	19263.7i	−0.0770588	−	0.0918351i
$459$	−20382.1	+	55999.3i	−0.0967438	+	0.265801i
$460$	−19439.1	+	110245.i	−0.0918674	+	0.521006i
$461$	−43674.2	−	247689.i	−0.205505	−	1.16548i	−0.896643	−	0.442755i	$-0.854001\pi$
$461$	−43674.2	−	247689.i	−0.205505	−	1.16548i	0.691137	−	0.722724i	$-0.257110\pi$
$462$	−4495.21	+	1636.12i	−0.0210604	+	0.00766534i
$463$	48982.9	−	84840.9i	0.228498	−	0.395770i	−0.728865	−	0.684657i	$-0.759952\pi$
$463$	48982.9	−	84840.9i	0.228498	−	0.395770i	0.957363	+	0.288887i	$0.0932852\pi$
$464$	9973.59	−	5758.25i	0.0463250	−	0.0267458i
$465$	8635.03	+	7245.65i	0.0399354	+	0.0335098i
$466$	−35811.9	+	42678.9i	−0.164913	+	0.196536i
$467$	43645.7	+	75596.6i	0.200128	+	0.346632i	0.948570	−	0.316569i	$-0.102531\pi$
$467$	43645.7	+	75596.6i	0.200128	+	0.346632i	−0.748441	+	0.663201i	$0.769198\pi$
$468$	26161.0	+	15104.1i	0.119444	+	0.0689608i
$469$	48963.6	+	134526.i	0.222601	+	0.611591i
$470$	50862.3	−	8968.39i	0.230250	−	0.0405993i
$471$	−19491.2	−	3436.83i	−0.0878612	−	0.0154923i
$472$	126205.	+	45934.9i	0.566490	+	0.206186i
$473$	21755.1	−	18254.7i	0.0972388	−	0.0815930i
$474$			33727.4i			0.150116i
$475$	40544.8	−	21921.8i	0.179700	−	0.0971604i
$476$	−52304.8			−0.230849
$477$	24172.5	+	28807.6i	0.106239	+	0.126611i
$478$	−66671.0	+	183177.i	−0.291797	+	0.801707i
$479$	−64952.2	+	368362.i	−0.283089	+	1.60548i	0.428944	+	0.903331i	$0.358886\pi$
$479$	−64952.2	+	368362.i	−0.283089	+	1.60548i	−0.712033	+	0.702146i	$0.752225\pi$
$480$	996.948	+	5653.97i	0.00432703	+	0.0245398i
$481$	26777.9	−	9746.35i	0.115741	−	0.0421261i
$482$	−145602.	+	252190.i	−0.626719	+	1.08551i
$483$	−19291.2	+	11137.8i	−0.0826922	+	0.0477423i
$484$	75815.4	+	63616.7i	0.323644	+	0.271569i
$485$	133690.	−	159326.i	0.568350	−	0.677333i
$486$	−38278.3	−	66299.9i	−0.162062	−	0.280699i
$487$	329977.	+	190512.i	1.39132	+	0.803276i	0.993461	−	0.114172i	$-0.0364215\pi$
$487$	329977.	+	190512.i	1.39132	+	0.803276i	0.397855	+	0.917448i	$0.369755\pi$
$488$	39055.5	+	107304.i	0.163999	+	0.450585i
$489$	−69411.5	+	12239.1i	−0.290278	+	0.0511838i
$490$	−110440.	−	19473.6i	−0.459976	−	0.0811062i
$491$	92211.1	+	33562.1i	0.382490	+	0.139215i	0.526107	−	0.850418i	$-0.323651\pi$
$491$	92211.1	+	33562.1i	0.382490	+	0.139215i	−0.143617	+	0.989633i	$0.545873\pi$
$492$	21980.0	−	18443.4i	0.0908026	−	0.0761924i
$493$			47132.5i			0.193922i
$494$	17971.8	−	45390.0i	0.0736442	−	0.185997i
$495$	83909.3			0.342452
$496$	14621.1	+	17424.7i	0.0594315	+	0.0708277i
$497$	40006.4	−	109917.i	0.161963	−	0.444990i
$498$	2717.97	−	15414.4i	0.0109594	−	0.0621538i
$499$	19094.8	+	108292.i	0.0766857	+	0.434906i	0.998843	+	0.0480910i	$0.0153138\pi$
$499$	19094.8	+	108292.i	0.0766857	+	0.434906i	−0.922157	+	0.386815i	$0.873575\pi$
$500$	−126184.	+	45927.2i	−0.504735	+	0.183709i
$501$	21412.8	−	37088.1i	0.0853096	−	0.147761i
$502$	−212658.	+	122778.i	−0.843867	+	0.487207i
$503$	235935.	+	197973.i	0.932515	+	0.782473i	0.976267	−	0.216570i	$-0.0694868\pi$
$503$	235935.	+	197973.i	0.932515	+	0.782473i	−0.0437523	+	0.999042i	$0.513931\pi$
$504$	28673.2	−	34171.4i	0.112880	−	0.134525i
$505$	−123290.	−	213545.i	−0.483444	−	0.837349i
$506$	−73225.4	−	42276.7i	−0.285997	−	0.165120i
$507$	12780.7	+	35114.6i	0.0497208	+	0.136607i
$508$	22313.9	−	3934.54i	0.0864664	−	0.0152464i
$509$	−92527.4	−	16315.1i	−0.357137	−	0.0629729i	−0.00779885	−	0.999970i	$-0.502482\pi$
$509$	−92527.4	−	16315.1i	−0.357137	−	0.0629729i	−0.349338	+	0.936997i	$0.613594\pi$
$510$	−22079.4	−	8036.25i	−0.0848882	−	0.0308968i
$511$	−101992.	+	85581.2i	−0.390592	+	0.327745i
$512$			11585.2i			0.0441942i
$513$	−64368.7	+	51016.7i	−0.244591	+	0.193855i
$514$	99902.6			0.378138
$515$	143358.	+	170848.i	0.540516	+	0.644162i
$516$	2319.63	−	6373.14i	0.00871204	−	0.0239361i
$517$	−6773.91	+	38416.8i	−0.0253430	+	0.143727i
$518$	−7307.11	−	41440.7i	−0.0272324	−	0.154443i
$519$	46027.2	−	16752.5i	0.170876	−	0.0621937i
$520$	−12063.0	+	20893.7i	−0.0446117	+	0.0772697i
$521$	31306.8	−	18075.0i	0.115336	−	0.0665890i	−0.441222	−	0.897398i	$-0.645455\pi$
$521$	31306.8	−	18075.0i	0.115336	−	0.0665890i	0.556558	+	0.830809i	$0.312122\pi$
$522$	−30792.3	−	25837.8i	−0.113006	−	0.0948233i
$523$	−156413.	+	186405.i	−0.571832	+	0.681483i	−0.972006	−	0.234956i	$-0.924505\pi$
$523$	−156413.	+	186405.i	−0.571832	+	0.681483i	0.400174	+	0.916439i	$0.368950\pi$
$524$	−42819.6	−	74165.7i	−0.155948	−	0.270110i
$525$	−3925.33	−	2266.29i	−0.0142416	−	0.00822238i
$526$	−70129.6	−	192679.i	−0.253472	−	0.696408i
$527$	−91677.7	+	16165.2i	−0.330098	+	0.0582051i
$528$	−4270.50	−	753.004i	−0.0153183	−	0.00270103i
$529$	−107018.	−	38951.4i	−0.382425	−	0.139191i
$530$	−23007.5	+	19305.5i	−0.0819062	+	0.0687275i
$531$		−	468768.i		−	1.66253i
$532$	−61399.6	−	37774.4i	−0.216941	−	0.133467i
$533$	120575.			0.424427
$534$	−20957.5	−	24976.1i	−0.0734947	−	0.0875876i
$535$	104210.	−	286315.i	0.364085	−	1.00031i
$536$	−22534.9	+	127802.i	−0.0784378	+	0.444843i
$537$	6435.87	+	36499.7i	0.0223182	+	0.126573i
$538$	36859.3	−	13415.7i	0.127345	−	0.0463498i
$539$	42351.7	−	73355.3i	0.145778	−	0.252496i
$540$	35152.5	−	20295.3i	0.120551	−	0.0695999i
$541$	−376155.	−	315632.i	−1.28521	−	1.07842i	−0.992504	−	0.122211i	$-0.961001\pi$
$541$	−376155.	−	315632.i	−1.28521	−	1.07842i	−0.292701	−	0.956204i	$-0.594554\pi$
$542$	−86344.5	+	102901.i	−0.293925	+	0.350286i
$543$	−35243.7	−	61043.8i	−0.119531	−	0.207034i
$544$	−41061.5	−	23706.9i	−0.138751	−	0.0801082i
$545$	−99395.6	−	273087.i	−0.334637	−	0.919408i
$546$	−4727.79	+	833.636i	−0.0158589	+	0.00279635i
$547$	−34525.9	−	6087.85i	−0.115391	−	0.0203465i	0.115655	−	0.993289i	$-0.463103\pi$
$547$	−34525.9	−	6087.85i	−0.115391	−	0.0203465i	−0.231045	+	0.972943i	$0.574215\pi$
$548$	256487.	+	93353.8i	0.854093	+	0.310864i
$549$	305318.	−	256192.i	1.01299	−	0.850004i
$550$		−	17204.8i		−	0.0568753i
$551$	−34039.0	+	55328.0i	−0.112118	+	0.182239i
$552$	−20192.6			−0.0662694
$553$	134530.	+	160326.i	0.439914	+	0.524269i
$554$	26061.4	−	71603.1i	0.0849138	−	0.233299i
$555$	3282.51	−	18616.1i	0.0106566	−	0.0604368i
$556$	−22886.5	−	129796.i	−0.0740338	−	0.419866i
$557$	456979.	−	166327.i	1.47294	−	0.536108i	0.524046	−	0.851690i	$-0.324422\pi$
$557$	456979.	−	166327.i	1.47294	−	0.536108i	0.948898	+	0.315583i	$0.102200\pi$
$558$	39696.3	−	68756.0i	0.127492	−	0.220822i
$559$	24682.0	−	14250.2i	0.0789873	−	0.0456034i
$560$	27291.3	+	22900.1i	0.0870259	+	0.0730234i
$561$	11407.6	−	13595.0i	0.0362467	−	0.0431971i
$562$	113836.	+	197170.i	0.360419	+	0.624264i
$563$	−107187.	−	61884.4i	−0.338162	−	0.195238i	0.321297	−	0.946979i	$-0.395881\pi$
$563$	−107187.	−	61884.4i	−0.338162	−	0.195238i	−0.659459	+	0.751740i	$0.729215\pi$
$564$	3186.26	+	8754.17i	0.0100167	+	0.0275205i
$565$	−25700.4	+	4531.67i	−0.0805087	+	0.0141959i
$566$	142308.	+	25092.7i	0.444218	+	0.0783277i
$567$	−142463.	−	51852.4i	−0.443136	−	0.161288i
$568$	81225.9	−	68156.6i	0.251767	−	0.211257i
$569$			127326.i			0.393271i	0.980477	+	0.196636i	$0.0630016\pi$
$569$			127326.i			0.393271i	−0.980477	+	0.196636i	$0.936998\pi$
$570$	−20114.9	−	25379.3i	−0.0619110	−	0.0781143i
$571$	−155133.			−0.475807			−0.237904	−	0.971289i	$-0.576460\pi$
$571$	−155133.			−0.475807			−0.237904	+	0.971289i	$0.576460\pi$
$572$	−11713.2	−	13959.3i	−0.0358002	−	0.0426650i
$573$	−24611.2	+	67618.7i	−0.0749589	+	0.205948i
$574$	30918.1	−	175345.i	0.0938403	−	0.532195i
$575$	−13911.8	−	78897.8i	−0.0420773	−	0.238632i
$576$	37997.8	−	13830.1i	0.114528	−	0.0416850i
$577$	−108437.	+	187818.i	−0.325705	+	0.564138i	−0.981655	−	0.190667i	$-0.938935\pi$
$577$	−108437.	+	187818.i	−0.325705	+	0.564138i	0.655950	+	0.754805i	$0.272268\pi$
$578$	−36535.3	+	21093.6i	−0.109360	+	0.0631387i
$579$	60614.1	+	50861.3i	0.180808	+	0.151716i
$580$	20635.6	−	24592.6i	0.0613425	−	0.0731051i
$581$	−48563.9	−	84115.1i	−0.143867	−	0.249185i
$582$	32489.8	+	18758.0i	0.0959182	+	0.0553784i
$583$	−7758.74	−	21317.0i	−0.0228273	−	0.0627174i
$584$	−118857.	+	20957.7i	−0.348498	+	0.0614496i
$585$	82928.6	+	14622.5i	0.242322	+	0.0427279i
$586$	−287366.	−	104593.i	−0.836837	−	0.304584i
$587$	−244834.	+	205441.i	−0.710553	+	0.596225i	−0.924754	−	0.380565i	$-0.875730\pi$
$587$	−244834.	+	205441.i	−0.710553	+	0.596225i	0.214201	+	0.976790i	$0.431285\pi$
$588$		−	20228.4i		−	0.0585068i
$589$	−119293.	−	47233.4i	−0.343863	−	0.136150i
$590$	374386.			1.07551
$591$	57725.4	+	68794.4i	0.165269	+	0.196960i
$592$	13046.4	−	35844.7i	0.0372261	−	0.102278i
$593$	9882.03	−	56043.8i	0.0281020	−	0.159374i	−0.967527	−	0.252766i	$-0.918660\pi$
$593$	9882.03	−	56043.8i	0.0281020	−	0.159374i	0.995629	+	0.0933917i	$0.0297709\pi$
$594$	5323.79	+	30192.7i	0.0150886	+	0.0855715i
$595$	−137011.	+	49868.0i	−0.387010	+	0.140860i
$596$	146998.	−	254609.i	0.413828	−	0.716771i
$597$	−5452.10	+	3147.77i	−0.0152973	+	0.00883192i
$598$	−65002.2	−	54543.3i	−0.181771	−	0.152524i
$599$	−287143.	+	342204.i	−0.800285	+	0.953743i	−0.999657	−	0.0261810i	$-0.991665\pi$
$599$	−287143.	+	342204.i	−0.800285	+	0.953743i	0.199372	+	0.979924i	$0.436110\pi$
$600$	−2054.37	−	3558.28i	−0.00570659	−	0.00988411i
$601$	−276748.	−	159780.i	−0.766188	−	0.442359i	0.0653251	−	0.997864i	$-0.479192\pi$
$601$	−276748.	−	159780.i	−0.766188	−	0.442359i	−0.831513	+	0.555505i	$0.812525\pi$
$602$	−14394.2	−	39547.7i	−0.0397187	−	0.109126i
$603$	446071.	−	78654.3i	1.22679	−	0.216316i
$604$	−217310.	−	38317.6i	−0.595670	−	0.105033i
$605$	259250.	+	94359.2i	0.708284	+	0.257794i
$606$	34072.0	−	28589.8i	0.0927795	−	0.0778512i
$607$			540515.i			1.46700i	0.679688	+	0.733501i	$0.262115\pi$
$607$			540515.i			1.46700i	−0.679688	+	0.733501i	$0.737885\pi$
$608$	−31080.3	−	57483.7i	−0.0840772	−	0.155502i
$609$	6388.09			0.0172241
$610$	204610.	+	243845.i	0.549879	+	0.655320i
$611$	−13389.5	+	36787.3i	−0.0358659	+	0.0985406i
$612$	−28737.1	+	162976.i	−0.0767255	+	0.435132i
$613$	62375.7	+	353750.i	0.165995	+	0.941403i	0.948033	+	0.318172i	$0.103069\pi$
$613$	62375.7	+	353750.i	0.165995	+	0.941403i	−0.782038	+	0.623231i	$0.785820\pi$
$614$	399678.	−	145471.i	1.06017	−	0.385869i
$615$	39992.0	−	69268.2i	0.105736	−	0.183140i
$616$	−23303.8	+	13454.4i	−0.0614136	+	0.0354572i
$617$	−144392.	−	121159.i	−0.379290	−	0.318262i	0.433134	−	0.901330i	$-0.357408\pi$
$617$	−144392.	−	121159.i	−0.379290	−	0.318262i	−0.812424	+	0.583068i	$0.801852\pi$
$618$	−25858.8	+	30817.3i	−0.0677065	+	0.0806895i
$619$	223783.	+	387603.i	0.584044	+	1.01159i	0.994994	+	0.0999360i	$0.0318638\pi$
$619$	223783.	+	387603.i	0.584044	+	1.01159i	−0.410950	+	0.911658i	$0.634803\pi$
$620$	54912.6	+	31703.8i	0.142853	+	0.0824761i
$621$	48827.7	+	134153.i	0.126614	+	0.347870i
$622$	92156.3	−	16249.6i	0.238201	−	0.0420013i
$623$	−199247.	−	35132.6i	−0.513351	−	0.0905177i
$624$	−4089.36	−	1488.41i	−0.0105023	−	0.00382254i
$625$	−225619.	+	189317.i	−0.577585	+	0.484651i
$626$			158297.i			0.403947i
$627$	23209.5	−	7720.43i	0.0590378	−	0.0196384i
$628$	−111332.			−0.282293
$629$	100347.	+	119589.i	0.253632	+	0.302267i
$630$	42529.5	−	116849.i	0.107154	−	0.294403i
$631$	33131.4	−	187897.i	0.0832110	−	0.471913i	−0.914517	−	0.404547i	$-0.867429\pi$
$631$	33131.4	−	187897.i	0.0832110	−	0.471913i	0.997728	−	0.0673662i	$-0.0214596\pi$
$632$	32944.6	+	186838.i	0.0824802	+	0.467769i
$633$	597.664	−	217.532i	0.00149159	−	0.000542895i
$634$	51674.7	−	89503.2i	0.128558	−	0.222669i
$635$	54699.4	−	31580.7i	0.135655	−	0.0783204i
$636$	−4150.05	−	3482.30i	−0.0102598	−	0.00860900i
$637$	54640.1	−	65117.5i	0.134658	−	0.160479i
$638$	12124.0	+	20999.3i	0.0297854	+	0.0515898i
$639$	−320508.	−	185045.i	−0.784941	−	0.453186i
$640$	11045.5	+	30347.3i	0.0269666	+	0.0740900i
$641$	−558127.	+	98412.8i	−1.35837	+	0.239516i	−0.804927	−	0.593374i	$-0.797796\pi$
$641$	−558127.	+	98412.8i	−1.35837	+	0.239516i	−0.553438	+	0.832890i	$0.686685\pi$
$642$	54124.6	+	9543.62i	0.131318	+	0.0231549i
$643$	−351525.	−	127945.i	−0.850225	−	0.309457i	−0.120093	−	0.992763i	$-0.538319\pi$
$643$	−351525.	−	127945.i	−0.850225	−	0.309457i	−0.730132	+	0.683306i	$0.760542\pi$
$644$	−95987.2	+	80542.8i	−0.231442	+	0.194203i
$645$		−	18905.9i		−	0.0454441i
$646$	267339.	+	7470.94i	0.640615	+	0.0179024i
$647$	661706.			1.58073			0.790363	−	0.612638i	$-0.209892\pi$
$647$	661706.			1.58073			0.790363	+	0.612638i	$0.209892\pi$
$648$	−88338.1	−	105277.i	−0.210377	−	0.250717i
$649$	−96715.5	+	265724.i	−0.229618	+	0.630871i
$650$	2998.21	−	17003.7i	0.00709636	−	0.0402454i
$651$	2190.95	+	12425.5i	0.00516977	+	0.0293192i
$652$	−372561.	+	135601.i	−0.876400	+	0.318983i
$653$	−19790.1	+	34277.5i	−0.0464111	+	0.0803864i	−0.888298	−	0.459268i	$-0.848112\pi$
$653$	−19790.1	+	34277.5i	−0.0464111	+	0.0803864i	0.841887	+	0.539654i	$0.181445\pi$
$654$	45397.4	−	26210.2i	0.106139	−	0.0612794i
$655$	−182875.	−	153451.i	−0.426258	−	0.357673i
$656$	103747.	−	123640.i	0.241083	−	0.287311i
$657$	210626.	+	364815.i	0.487957	+	0.845166i
$658$	50064.3	+	28904.6i	0.115632	+	0.0667599i
$659$	−95761.9	−	263104.i	−0.220507	−	0.605837i	0.779276	−	0.626681i	$-0.215587\pi$
$659$	−95761.9	−	263104.i	−0.220507	−	0.605837i	−0.999783	+	0.0208435i	$0.993365\pi$
$660$	−11904.4	+	2099.07i	−0.0273287	+	0.00481879i
$661$	−169246.	−	29842.7i	−0.387362	−	0.0683023i	−0.0234240	−	0.999726i	$-0.507457\pi$
$661$	−169246.	−	29842.7i	−0.387362	−	0.0683023i	−0.363938	+	0.931423i	$0.618568\pi$
$662$	−467442.	−	170135.i	−1.06662	−	0.388220i
$663$	13643.4	−	11448.2i	0.0310382	−	0.0260441i
$664$		−	88045.4i		−	0.199697i
$665$	−196850.	−	40410.1i	−0.445134	−	0.0913790i
$666$	−133139.			−0.300164
$667$	72578.2	+	86495.3i	0.163138	+	0.194420i
$668$	82392.3	−	226371.i	0.184643	−	0.507304i
$669$	15780.5	−	89495.4i	0.0352588	−	0.199962i
$670$	62817.9	+	356258.i	0.139937	+	0.793625i
$671$	−225928.	+	82231.0i	−0.501793	+	0.182638i
$672$	−3213.11	+	5565.26i	−0.00711519	+	0.0123239i
$673$	97049.1	−	56031.3i	0.214270	−	0.123709i	−0.389024	−	0.921228i	$-0.627188\pi$
$673$	97049.1	−	56031.3i	0.214270	−	0.123709i	0.603294	+	0.797519i	$0.293854\pi$
$674$	394086.	+	330677.i	0.867503	+	0.727922i
$675$	−18672.4	+	22252.9i	−0.0409820	+	0.0488404i
$676$	105100.	+	182039.i	0.229991	+	0.398356i
$677$	−444316.	−	256526.i	−0.969426	−	0.559698i	−0.0703649	−	0.997521i	$-0.522416\pi$
$677$	−444316.	−	256526.i	−0.969426	−	0.559698i	−0.899061	+	0.437823i	$0.855750\pi$
$678$	−1610.00	−	4423.43i	−0.00350240	−	0.00962276i
$679$	229264.	−	40425.4i	0.497275	−	0.0876829i
$680$	−130162.	−	22951.1i	−0.281493	−	0.0496348i
$681$	−7243.44	−	2636.40i	−0.0156189	−	0.00568482i
$682$	−36687.7	+	30784.6i	−0.0788772	+	0.0661858i
$683$		−	41053.6i		−	0.0880054i	−0.999031	−	0.0440027i	$-0.985989\pi$
$683$		−	41053.6i		−	0.0880054i	0.999031	−	0.0440027i	$-0.0140110\pi$
$684$	−151435.	+	170561.i	−0.323678	+	0.364558i
$685$	760868.			1.62154
$686$	−189648.	−	226014.i	−0.402995	−	0.480271i
$687$	4324.65	−	11881.9i	0.00916300	−	0.0251751i
$688$	6624.75	−	37570.8i	0.0139956	−	0.0793732i
$689$	−3953.23	−	22419.9i	−0.00832748	−	0.0472275i
$690$	−52893.9	+	19251.8i	−0.111098	+	0.0404365i
$691$	342282.	−	592851.i	0.716850	−	1.24162i	−0.245391	−	0.969424i	$-0.578916\pi$
$691$	342282.	−	592851.i	0.716850	−	1.24162i	0.962242	−	0.272197i	$-0.0877503\pi$
$692$	238611.	−	137762.i	0.498286	−	0.287686i
$693$	71947.7	+	60371.3i	0.149813	+	0.125708i
$694$	−71934.8	+	85728.5i	−0.149355	+	0.177994i
$695$	−183700.	−	318177.i	−0.380311	−	0.658717i
$696$	5014.93	+	2895.37i	0.0103525	+	0.00597704i
$697$	225921.	+	620714.i	0.465042	+	1.27769i
$698$	−446095.	+	78658.6i	−0.915623	+	0.161449i
$699$	−27588.3	−	4864.56i	−0.0564638	−	0.00995609i
$700$	−23958.7	−	8720.25i	−0.0488953	−	0.0177964i
$701$	711469.	−	596993.i	1.44784	−	1.21488i	0.513698	−	0.857971i	$-0.328275\pi$
$701$	711469.	−	596993.i	1.44784	−	1.21488i	0.934139	−	0.356909i	$-0.116169\pi$
$702$			30767.6i			0.0624337i
$703$	31428.8	+	212854.i	0.0635941	+	0.430697i
$704$	−24392.6			−0.0492168
$705$	16692.7	+	19893.5i	0.0335851	+	0.0400252i
$706$	53107.2	−	145911.i	0.106548	−	0.292737i
$707$	47927.2	−	271808.i	0.0958833	−	0.543781i
$708$	11726.7	+	66505.2i	0.0233942	+	0.132675i
$709$	203138.	−	73936.3i	0.404110	−	0.147084i	−0.131965	−	0.991254i	$-0.542129\pi$
$709$	203138.	−	73936.3i	0.404110	−	0.147084i	0.536075	+	0.844170i	$0.319906\pi$
$710$	147788.	−	255977.i	0.293172	−	0.507789i
$711$	573472.	−	331094.i	1.13442	−	0.654956i
$712$	−140494.	−	117888.i	−0.277138	−	0.232547i
$713$	−143350.	+	170838.i	−0.281980	+	0.336051i
$714$	−13150.0	−	22776.4i	−0.0257946	−	0.0446775i
$715$	−43991.6	−	25398.5i	−0.0860513	−	0.0496817i
$716$	71305.1	+	195909.i	0.139090	+	0.382145i
$717$	−96527.4	+	17020.4i	−0.187764	+	0.0331078i
$718$	−117696.	−	20753.1i	−0.228304	−	0.0402562i
$719$	386073.	+	140519.i	0.746812	+	0.271817i	0.687264	−	0.726408i	$-0.258812\pi$
$719$	386073.	+	140519.i	0.746812	+	0.271817i	0.0595485	+	0.998225i	$0.481034\pi$
$720$	86348.6	−	72455.1i	0.166568	−	0.139767i
$721$			249637.i			0.480217i
$722$	308429.	+	201842.i	0.591672	+	0.387201i
$723$	−146423.			−0.280114
$724$	−254865.	−	303736.i	−0.486220	−	0.579455i
$725$	−7857.93	+	21589.5i	−0.0149497	+	0.0410739i
$726$	−8641.47	+	49008.2i	−0.0163951	+	0.0929813i
$727$	−170009.	−	964170.i	−0.321665	−	1.82425i	−0.532143	−	0.846654i	$-0.678613\pi$
$727$	−170009.	−	964170.i	−0.321665	−	1.82425i	0.210478	−	0.977599i	$-0.432498\pi$
$728$	−25376.0	+	9236.12i	−0.0478808	+	0.0174272i
$729$	−226733.	+	392714.i	−0.426639	+	0.738960i
$730$	−291363.	+	168218.i	−0.546749	+	0.315666i
$731$	119606.	+	100361.i	0.223830	+	0.187816i
$732$	−36907.2	+	43984.3i	−0.0688794	+	0.0820872i
$733$	194690.	+	337213.i	0.362356	+	0.627619i	0.988348	−	0.152210i	$-0.0486391\pi$
$733$	194690.	+	337213.i	0.362356	+	0.627619i	−0.625992	+	0.779829i	$0.715306\pi$
$734$	183475.	+	105929.i	0.340553	+	0.196618i
$735$	−19286.0	−	52987.8i	−0.0356999	−	0.0980846i
$736$	−111860.	+	19723.9i	−0.206499	+	0.0364114i
$737$	−269085.	−	47447.0i	−0.495398	−	0.0873521i
$738$	−529370.	−	192675.i	−0.971956	−	0.353763i
$739$	109972.	−	92277.2i	0.201369	−	0.168968i	−0.536527	−	0.843883i	$-0.680264\pi$
$739$	109972.	−	92277.2i	0.201369	−	0.168968i	0.737896	+	0.674915i	$0.235820\pi$
$740$		−	106333.i		−	0.194180i
$741$	24283.6	−	3585.57i	0.0442260	−	0.00653013i
$742$	−33617.7			−0.0610604
$743$	−589610.	−	702669.i	−1.06804	−	1.27284i	−0.960393	−	0.278649i	$-0.910113\pi$
$743$	−589610.	−	702669.i	−1.06804	−	1.27284i	−0.107646	−	0.994189i	$-0.534331\pi$
$744$	−3911.81	+	10747.6i	−0.00706695	+	0.0194163i
$745$	142312.	−	807092.i	0.256406	−	1.45415i
$746$	19498.4	+	110581.i	0.0350365	+	0.198702i
$747$	−288775.	+	105106.i	−0.517510	+	0.188358i
$748$	49914.7	−	86454.7i	0.0892123	−	0.154520i
$749$	295353.	−	170522.i	0.526476	−	0.303961i
$750$	−51723.2	−	43400.9i	−0.0919524	−	0.0771572i
$751$	−8288.76	+	9878.16i	−0.0146964	+	0.0175144i	−0.773343	−	0.633988i	$-0.781417\pi$
$751$	−8288.76	+	9878.16i	−0.0146964	+	0.0175144i	0.758646	+	0.651503i	$0.225861\pi$
$752$	26201.8	+	45382.8i	0.0463335	+	0.0802519i
$753$	−106929.	−	61735.4i	−0.188584	−	0.108879i
$754$	8322.79	+	22866.7i	0.0146395	+	0.0402217i
$755$	−605771.	+	106814.i	−1.06271	+	0.187384i
$756$	44743.5	+	7889.49i	0.0782865	+	0.0138040i
$757$	972607.	+	354000.i	1.69725	+	0.617748i	0.995507	−	0.0946837i	$-0.0301840\pi$
$757$	972607.	+	354000.i	1.69725	+	0.617748i	0.701741	+	0.712432i	$0.252406\pi$
$758$	227163.	−	190612.i	0.395365	−	0.331751i
$759$		−	42515.3i		−	0.0738008i
$760$	−136220.	−	120945.i	−0.235838	−	0.209392i
$761$	41268.8			0.0712610			0.0356305	−	0.999365i	$-0.488656\pi$
$761$	41268.8			0.0712610			0.0356305	+	0.999365i	$0.488656\pi$
$762$	7323.26	+	8727.52i	0.0126123	+	0.0150308i
$763$	111255.	−	305671.i	0.191105	−	0.525055i
$764$	−70288.2	+	398624.i	−0.120419	+	0.682931i
$765$	80107.2	+	454310.i	0.136883	+	0.776300i
$766$	−541825.	+	197208.i	−0.923425	+	0.336099i
$767$	−141892.	+	245764.i	−0.241194	+	0.417760i
$768$	−5044.86	+	2912.65i	−0.00855316	+	0.00493817i
$769$	−659966.	−	553777.i	−1.11601	−	0.936446i	−0.117616	−	0.993059i	$-0.537525\pi$
$769$	−659966.	−	553777.i	−1.11601	−	0.936446i	−0.998396	+	0.0566134i	$0.981970\pi$
$770$	−48216.1	+	57461.7i	−0.0813224	+	0.0969163i
$771$	25116.6	+	43503.2i	0.0422524	+	0.0731833i
$772$	385462.	+	222547.i	0.646766	+	0.373411i
$773$	148503.	+	408009.i	0.248529	+	0.682827i	0.999741	+	0.0227658i	$0.00724722\pi$
$773$	148503.	+	408009.i	0.248529	+	0.682827i	−0.751212	+	0.660061i	$0.770531\pi$
$774$	−131135.	+	23122.6i	−0.218895	+	0.0385971i
$775$	−44688.9	−	7879.86i	−0.0744040	−	0.0131194i
$776$	198305.	+	72177.1i	0.329314	+	0.119860i
$777$	16208.5	−	13600.6i	0.0268473	−	0.0225276i
$778$			318231.i			0.525754i
$779$	−183073.	+	891805.i	−0.301683	+	1.46959i
$780$	−12131.1			−0.0199393
$781$	143503.	+	171021.i	0.235266	+	0.280379i
$782$	158992.	−	436826.i	0.259992	−	0.714323i
$783$	7109.32	−	40319.0i	0.0115959	−	0.0657636i
$784$	−19758.9	−	112058.i	−0.0321463	−	0.182310i
$785$	−291631.	+	106145.i	−0.473254	+	0.172250i
$786$	21530.6	−	37292.1i	0.0348506	−	0.0603631i
$787$	743414.	−	429210.i	1.20028	−	0.692980i	0.239660	−	0.970857i	$-0.422964\pi$
$787$	743414.	−	429210.i	1.20028	−	0.692980i	0.960617	+	0.277877i	$0.0896307\pi$
$788$	386977.	+	324712.i	0.623207	+	0.522933i
$789$	66272.1	−	78980.0i	0.106458	−	0.126871i
$790$	264431.	+	458008.i	0.423700	+	0.733870i
$791$	−25297.2	−	14605.3i	−0.0404314	−	0.0233431i
$792$	29119.1	+	80004.1i	0.0464224	+	0.127544i
$793$	−237617.	+	41898.3i	−0.377861	+	0.0666270i
$794$	−212577.	−	37483.0i	−0.337190	−	0.0594557i
$795$	−14191.0	−	5165.11i	−0.0224533	−	0.00817232i
$796$	−27128.1	+	22763.2i	−0.0428147	+	0.0359258i
$797$			309649.i			0.487476i	0.969841	+	0.243738i	$0.0783736\pi$
$797$			309649.i			0.487476i	−0.969841	+	0.243738i	$0.921626\pi$
$798$	1012.57	−	36233.7i	0.00159008	−	0.0568993i
$799$	−214467.			−0.335944
$800$	−14856.2	−	17705.0i	−0.0232128	−	0.0276640i
$801$	−218938.	+	601529.i	−0.341238	+	0.937543i
$802$	98071.2	−	556189.i	0.152473	−	0.864717i
$803$	−44126.4	−	250253.i	−0.0684332	−	0.388104i
$804$	−61317.4	+	22317.7i	−0.0948575	+	0.0345253i
$805$	−174646.	+	302496.i	−0.269505	+	0.466796i
$806$	−41623.6	+	24031.4i	−0.0640722	+	0.0369921i
$807$	15108.8	+	12677.7i	0.0231997	+	0.0194668i
$808$	160821.	−	191659.i	0.246331	−	0.293566i
$809$	−2538.06	−	4396.05i	−0.00387797	−	0.00671685i	0.864080	−	0.503355i	$-0.167901\pi$
$809$	−2538.06	−	4396.05i	−0.00387797	−	0.00671685i	−0.867958	+	0.496638i	$0.834568\pi$
$810$	−331772.	−	191549.i	−0.505673	−	0.291951i
$811$	314924.	+	865248.i	0.478812	+	1.31552i	0.910503	+	0.413503i	$0.135695\pi$
$811$	314924.	+	865248.i	0.478812	+	1.31552i	−0.431691	+	0.902021i	$0.642083\pi$
$812$	35387.8	−	6239.83i	0.0536713	−	0.00946369i
$813$	−66516.9	−	11728.7i	−0.100635	−	0.0177448i
$814$	75470.7	+	27469.1i	0.113902	+	0.0414568i
$815$	−846632.	+	710408.i	−1.27462	+	1.06953i
$816$		−	23840.6i		−	0.0358045i
$817$	67922.5	+	204192.i	0.101758	+	0.305910i
$818$	518354.			0.774676
$819$	60586.1	+	72203.7i	0.0903245	+	0.107644i
$820$	153882.	−	422786.i	0.228854	−	0.628772i
$821$	105365.	−	597556.i	0.156319	−	0.886527i	−0.801252	−	0.598328i	$-0.795832\pi$
$821$	105365.	−	597556.i	0.156319	−	0.886527i	0.957570	−	0.288200i	$-0.0930567\pi$
$822$	23832.2	+	135159.i	0.0352712	+	0.200033i
$823$	−290456.	+	105717.i	−0.428825	+	0.156080i	−0.547410	−	0.836864i	$-0.684386\pi$
$823$	−290456.	+	105717.i	−0.428825	+	0.156080i	0.118585	+	0.992944i	$0.462164\pi$
$824$	−113147.	+	195976.i	−0.166643	+	0.288634i
$825$	7491.93	−	4325.47i	0.0110074	−	0.00635514i
$826$	321016.	+	269364.i	0.470507	+	0.394802i
$827$	−570045.	+	679353.i	−0.833486	+	0.993310i	0.166488	+	0.986043i	$0.446757\pi$
$827$	−570045.	+	679353.i	−0.833486	+	0.993310i	−0.999974	+	0.00726603i	$0.997687\pi$
$828$	198226.	+	343337.i	0.289134	+	0.500795i
$829$	−134155.	−	77454.2i	−0.195207	−	0.112703i	0.399211	−	0.916859i	$-0.369284\pi$
$829$	−134155.	−	77454.2i	−0.195207	−	0.112703i	−0.594418	+	0.804156i	$0.702618\pi$
$830$	−83943.5	−	230633.i	−0.121852	−	0.334784i
$831$	37732.1	−	6653.19i	0.0546398	−	0.00963447i
$832$	−24107.5	−	4250.81i	−0.0348262	−	0.00614080i
$833$	437600.	+	159274.i	0.630649	+	0.229537i
$834$	50766.4	−	42598.1i	0.0729868	−	0.0612432i
$835$		−	671528.i		−	0.963144i
$836$	121031.	−	65439.4i	0.173175	−	0.0936325i
$837$	80862.9			0.115425
$838$	−561929.	−	669680.i	−0.800190	−	0.953629i
$839$	−101065.	+	277673.i	−0.143574	+	0.394466i	−0.990548	−	0.137168i	$-0.956200\pi$
$839$	−101065.	+	277673.i	−0.143574	+	0.394466i	0.846974	+	0.531635i	$0.178422\pi$
$840$	−3110.67	+	17641.5i	−0.00440855	+	0.0250021i
$841$	117195.	+	664647.i	0.165698	+	0.939722i
$842$	62171.2	−	22628.5i	0.0876930	−	0.0319176i
$843$	−57239.2	+	99141.2i	−0.0805450	+	0.139508i
$844$	3098.37	−	1788.85i	0.00434959	−	0.00251124i
$845$	448866.	+	376643.i	0.628642	+	0.527493i
$846$	117570.	−	140114.i	0.164269	−	0.195768i
$847$	154403.	+	267434.i	0.215223	+	0.372777i
$848$	−26391.3	−	15237.0i	−0.0367003	−	0.0211889i
$849$	24851.0	+	68277.4i	0.0344769	+	0.0947244i
$850$	93151.9	−	16425.2i	0.128930	−	0.0227338i
$851$	368305.	+	64942.2i	0.508568	+	0.0896743i
$852$	50100.3	+	18235.0i	0.0690177	+	0.0251204i
$853$	−199406.	+	167322.i	−0.274057	+	0.229961i	−0.769449	−	0.638709i	$-0.779469\pi$
$853$	−199406.	+	167322.i	−0.274057	+	0.229961i	0.495392	+	0.868670i	$0.335024\pi$
$854$			356297.i			0.488536i
$855$	−234066.	+	591160.i	−0.320188	+	0.808673i
$856$	309154.			0.421917
$857$	−832271.	−	991862.i	−1.13319	−	1.35048i	−0.928358	−	0.371688i	$-0.878779\pi$
$857$	−832271.	−	991862.i	−1.13319	−	1.35048i	−0.204834	−	0.978797i	$-0.565665\pi$
$858$	3133.83	−	8610.12i	0.00425697	−	0.0116959i
$859$	216916.	−	1.23019e6i	0.293971	−	1.66719i	−0.377382	−	0.926058i	$-0.623176\pi$
$859$	216916.	−	1.23019e6i	0.293971	−	1.66719i	0.671354	−	0.741137i	$-0.265713\pi$
$860$	−18467.1	−	104732.i	−0.0249690	−	0.141606i
$861$	84128.3	−	30620.2i	0.113484	−	0.0413049i
$862$	158396.	−	274350.i	0.213172	−	0.369225i
$863$	1.05271e6	−	607780.i	1.41347	−	0.816065i	0.417752	−	0.908561i	$-0.362818\pi$
$863$	1.05271e6	−	607780.i	1.41347	−	0.816065i	0.995713	+	0.0924964i	$0.0294847\pi$
$864$	31549.8	+	26473.4i	0.0422638	+	0.0354635i
$865$	493693.	−	588360.i	0.659819	−	0.786342i
$866$	84151.4	+	145755.i	0.112208	+	0.194351i
$867$	−18370.7	−	10606.3i	−0.0244392	−	0.0141100i
$868$	24274.3	+	66693.0i	0.0322186	+	0.0885198i
$869$	−393386.	+	69364.6i	−0.520930	+	0.0918540i
$870$	15897.0	+	2803.07i	0.0210028	+	0.00370335i
$871$	−257672.	−	93784.8i	−0.339649	−	0.123622i
$872$	225884.	−	189539.i	0.297066	−	0.249268i
$873$		−	736572.i		−	0.966467i
$874$	502112.	−	397958.i	0.657321	−	0.520973i
$875$	−418986.			−0.547247
$876$	−39008.1	−	46488.1i	−0.0508332	−	0.0605806i
$877$	2266.93	−	6228.33i	0.00294740	−	0.00809790i	−0.938210	−	0.346066i	$-0.887517\pi$
$877$	2266.93	−	6228.33i	0.00294740	−	0.00809790i	0.941158	+	0.337968i	$0.109740\pi$
$878$	−4231.74	+	23999.4i	−0.00548947	+	0.0311323i
$879$	−26701.4	−	151431.i	−0.0345586	−	0.195992i
$880$	−63895.9	+	23256.2i	−0.0825102	+	0.0300313i
$881$	−282639.	+	489546.i	−0.364151	+	0.630727i	−0.988639	−	0.150306i	$-0.951974\pi$
$881$	−282639.	+	489546.i	−0.364151	+	0.630727i	0.624489	+	0.781034i	$0.285307\pi$
$882$	−343946.	+	198577.i	−0.442134	+	0.255266i
$883$	−953024.	−	799682.i	−1.22231	−	1.02564i	−0.998701	−	0.0509636i	$-0.983771\pi$
$883$	−953024.	−	799682.i	−1.22231	−	1.02564i	−0.223612	−	0.974678i	$-0.571785\pi$
$884$	64397.4	−	76745.8i	0.0824069	−	0.0982088i
$885$	94124.6	+	163029.i	0.120176	+	0.208150i
$886$	−73251.4	−	42291.7i	−0.0933144	−	0.0538751i
$887$	−365053.	−	1.00298e6i	−0.463990	−	1.27480i	−0.922460	−	0.386093i	$-0.873825\pi$
$887$	−365053.	−	1.00298e6i	−0.463990	−	1.27480i	0.458470	−	0.888710i	$-0.348398\pi$
$888$	18888.8	−	3330.60i	0.0239540	−	0.00422374i
$889$	69623.6	+	12276.5i	0.0880953	+	0.0155336i
$890$	−480416.	−	174857.i	−0.606509	−	0.220751i
$891$	221660.	−	185995.i	0.279211	−	0.234286i
$892$		−	511188.i		−	0.642467i
$893$	−251759.	−	154888.i	−0.315705	−	0.194229i
$894$	147828.			0.184961
$895$	373564.	+	445196.i	0.466358	+	0.555783i
$896$	−12363.4	+	33968.2i	−0.0154001	+	0.0423113i
$897$	7408.97	−	42018.4i	0.00920816	−	0.0522221i
$898$	84248.6	+	477798.i	0.104474	+	0.592504i
$899$	60097.9	−	21873.8i	0.0743601	−	0.0270649i
$900$	−40334.7	+	69861.7i	−0.0497959	+	0.0862490i
$901$	108009.	−	62359.2i	0.133049	−	0.0768158i
$902$	260324.	+	218437.i	0.319964	+	0.268481i
$903$	13602.4	−	16210.8i	0.0166817	−	0.0198805i
$904$	−13239.6	−	22931.6i	−0.0162008	−	0.0280607i
$905$	−957199.	−	552639.i	−1.16871	−	0.674752i
$906$	−37948.4	−	104262.i	−0.0462314	−	0.127020i
$907$	132669.	−	23393.2i	0.161271	−	0.0284364i	−0.0924297	−	0.995719i	$-0.529463\pi$
$907$	132669.	−	23393.2i	0.161271	−	0.0284364i	0.253700	+	0.967283i	$0.418352\pi$
$908$	−42701.4	−	7529.41i	−0.0517929	−	0.00913249i
$909$	−820594.	−	298672.i	−0.993117	−	0.361465i
$910$	−57666.1	+	48387.6i	−0.0696367	+	0.0584321i
$911$			1.38840e6i			1.67293i	0.548017	+	0.836467i	$0.315383\pi$
$911$			1.38840e6i			1.67293i	−0.548017	+	0.836467i	$0.684617\pi$
$912$	17217.7	−	27986.1i	0.0207007	−	0.0336475i
$913$	185379.			0.222392
$914$	−580678.	−	692025.i	−0.695093	−	0.828380i
$915$	−54742.5	+	150404.i	−0.0653856	+	0.179645i
$916$	12351.0	−	70045.8i	0.0147201	−	0.0834817i
$917$	−46400.7	−	263151.i	−0.0551805	−	0.312944i
$918$	−158390.	+	57649.2i	−0.187950	+	0.0684082i
$919$	721910.	−	1.25038e6i	0.854775	−	1.48051i	−0.0220776	−	0.999756i	$-0.507028\pi$
$919$	721910.	−	1.25038e6i	0.854775	−	1.48051i	0.876853	−	0.480758i	$-0.159639\pi$
$920$	−274209.	+	158315.i	−0.323971	+	0.187045i
$921$	163829.	+	137469.i	0.193140	+	0.162064i
$922$	457264.	−	544946.i	0.537905	−	0.641050i
$923$	112023.	+	194029.i	0.131493	+	0.227753i
$924$	−11717.6	−	6765.17i	−0.0137245	−	0.00792382i
$925$	26027.1	+	71509.0i	0.0304189	+	0.0835751i
$926$	272880.	−	48116.1i	0.318236	−	0.0561136i
$927$	777841.	+	137154.i	0.905172	+	0.159606i
$928$	30609.2	+	11140.8i	0.0355431	+	0.0129366i
$929$	504839.	−	423610.i	0.584954	−	0.490834i	−0.301616	−	0.953429i	$-0.597526\pi$
$929$	504839.	−	423610.i	0.584954	−	0.490834i	0.886570	+	0.462595i	$0.153082\pi$
$930$			31882.7i			0.0368629i
$931$	398664.	+	503003.i	0.459947	+	0.580324i
$932$	−157581.			−0.181415
$933$	30245.1	+	36044.7i	0.0347449	+	0.0414074i
$934$	−84443.9	+	232008.i	−0.0967998	+	0.265955i
$935$	48323.4	−	274055.i	0.0552757	−	0.313484i
$936$	14836.8	+	84143.5i	0.0169351	+	0.0960437i
$937$	−117771.	+	42865.1i	−0.134140	+	0.0488230i	−0.408218	−	0.912885i	$-0.633850\pi$
$937$	−117771.	+	42865.1i	−0.134140	+	0.0488230i	0.274078	+	0.961708i	$0.411627\pi$
$938$	−202459.	+	350669.i	−0.230107	+	0.398558i
$939$	−68931.4	+	39797.6i	−0.0781782	+	0.0451362i
$940$	111903.	+	93898.1i	0.126645	+	0.106268i
$941$	−237742.	+	283329.i	−0.268489	+	0.319972i	−0.883396	−	0.468627i	$-0.844749\pi$
$941$	−237742.	+	283329.i	−0.268489	+	0.319972i	0.614907	+	0.788599i	$0.289193\pi$
$942$	−27990.0	−	48480.1i	−0.0315428	−	0.0546338i
$943$	1.37042e6	+	791214.i	1.54110	+	0.889755i
$944$	129923.	+	356962.i	0.145795	+	0.400569i
$945$	124727.	−	21992.7i	0.139668	−	0.0246272i
$946$	79105.0	+	13948.4i	0.0883938	+	0.0155862i
$947$	−110215.	−	40115.1i	−0.122897	−	0.0447309i	0.279840	−	0.960047i	$-0.409719\pi$
$947$	−110215.	−	40115.1i	−0.122897	−	0.0447309i	−0.402737	+	0.915316i	$0.631941\pi$
$948$	−73077.1	+	61319.0i	−0.0813139	+	0.0682304i
$949$		−	255018.i		−	0.283164i
$950$	121212.	+	47992.9i	0.134307	+	0.0531777i
$951$	51966.2			0.0574593
$952$	−95094.1	−	113329.i	−0.104925	−	0.125045i
$953$	−99971.7	+	274670.i	−0.110076	+	0.302430i	−0.982484	−	0.186348i	$-0.940335\pi$
$953$	−99971.7	+	274670.i	−0.110076	+	0.302430i	0.872408	+	0.488778i	$0.162557\pi$
$954$	−18470.1	+	104749.i	−0.0202942	+	0.115094i
$955$	195935.	+	1.11120e6i	0.214835	+	1.21839i
$956$	−518103.	+	188574.i	−0.566892	+	0.206332i
$957$	−6096.18	+	10558.9i	−0.00665632	+	0.0115291i
$958$	−916219.	+	528979.i	−0.998317	+	0.576379i
$959$	652403.	+	547431.i	0.709380	+	0.595240i
$960$	−10437.9	+	12439.5i	−0.0113259	+	0.0134977i
$961$	−398602.	−	690398.i	−0.431611	−	0.747572i
$962$	69801.7	+	40300.0i	0.0754251	+	0.0435467i
$963$	−369057.	−	1.01398e6i	−0.397962	−	1.09339i
$964$	−811136.	+	143025.i	−0.872850	+	0.153907i
$965$	1.22189e6	+	215452.i	1.31213	+	0.231364i
$966$	−59205.1	−	21548.9i	−0.0634460	−	0.0230925i
$967$	−1.25746e6	+	1.05513e6i	−1.34475	+	1.12838i	−0.364366	+	0.931256i	$0.618714\pi$
$967$	−1.25746e6	+	1.05513e6i	−1.34475	+	1.12838i	−0.980380	+	0.197119i	$0.936841\pi$
$968$			279930.i			0.298743i
$969$	63958.6	+	118293.i	0.0681163	+	0.125982i
$970$	588270.			0.625220
$971$	959837.	+	1.14389e6i	1.01803	+	1.21324i	0.976815	+	0.214086i	$0.0686773\pi$
$971$	959837.	+	1.14389e6i	1.01803	+	1.21324i	0.0412114	+	0.999150i	$0.486878\pi$
$972$	74059.2	−	203476.i	0.0783875	−	0.215368i
$973$	71410.3	−	404988.i	0.0754285	−	0.427776i
$974$	187141.	+	1.06133e6i	0.197265	+	1.11875i
$975$	8158.14	−	2969.32i	0.00858187	−	0.00312355i
$976$	−161490.	+	279709.i	−0.169530	+	0.293634i
$977$	−315495.	+	182151.i	−0.330525	+	0.190828i	−0.656074	−	0.754697i	$-0.727784\pi$
$977$	−315495.	+	182151.i	−0.330525	+	0.190828i	0.325549	+	0.945525i	$0.394451\pi$
$978$	−152714.	−	128142.i	−0.159662	−	0.133972i
$979$	248213.	−	295808.i	0.258975	−	0.308635i
$980$	−158596.	−	274696.i	−0.165135	−	0.286022i
$981$	−891312.	−	514599.i	−0.926173	−	0.534726i
$982$	94927.9	+	260812.i	0.0984399	+	0.270461i
$983$	−590410.	+	104105.i	−0.611008	+	0.107737i	−0.470585	−	0.882354i	$-0.655957\pi$
$983$	−590410.	+	104105.i	−0.611008	+	0.107737i	−0.140423	+	0.990092i	$0.544846\pi$
$984$	79922.9	+	14092.6i	0.0825431	+	0.0145546i
$985$	1.32326e6	+	481628.i	1.36387	+	0.496408i
$986$	−102122.	+	85690.6i	−0.105043	+	0.0881412i
$987$			29067.7i			0.0298385i
$988$	131021.	−	43582.9i	0.134223	−	0.0446480i
$989$	374039.			0.382406
$990$	152554.	+	181806.i	0.155651	+	0.185498i
$991$	−197363.	+	542250.i	−0.200964	+	0.552144i	−0.998706	−	0.0508548i	$-0.983805\pi$
$991$	−197363.	+	542250.i	−0.200964	+	0.552144i	0.797742	+	0.602999i	$0.206028\pi$
$992$	−11171.9	+	63359.1i	−0.0113528	+	0.0643851i
$993$	−43433.6	−	246324.i	−0.0440481	−	0.249809i
$994$	310891.	−	113155.i	0.314656	−	0.114525i
$995$	−49358.7	+	85491.8i	−0.0498560	+	0.0863532i
$996$	38339.9	−	22135.5i	0.0386485	−	0.0223137i
$997$	−1.27375e6	−	1.06880e6i	−1.28142	−	1.07524i	−0.993046	−	0.117725i	$-0.962440\pi$
$997$	−1.27375e6	−	1.06880e6i	−1.28142	−	1.07524i	−0.288378	−	0.957517i	$-0.593116\pi$
$998$	−199921.	+	238256.i	−0.200723	+	0.239212i
$999$	−67802.5	−	117437.i	−0.0679384	−	0.117673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.f.a.13.5	yes	36
19.3	odd	18	inner	38.5.f.a.3.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.f.a.3.5	✓	36	19.3	odd	18	inner
38.5.f.a.13.5	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81808 + 2.16670i) q^{2} +(-0.486419 + 1.33642i) q^{3} +(-1.38919 + 7.87846i) q^{4} +(3.87248 + 21.9619i) q^{5} +(-3.77998 + 1.37580i) q^{6} +(-12.4808 + 21.6173i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(60.5002 + 50.7657i) q^{9} +O(q^{10})\)	\(q+(1.81808 + 2.16670i) q^{2} +(-0.486419 + 1.33642i) q^{3} +(-1.38919 + 7.87846i) q^{4} +(3.87248 + 21.9619i) q^{5} +(-3.77998 + 1.37580i) q^{6} +(-12.4808 + 21.6173i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(60.5002 + 50.7657i) q^{9} +(-40.5444 + 48.3190i) q^{10} +(-23.8209 - 41.2590i) q^{11} +(-9.85324 - 5.68877i) q^{12} +(-16.3525 - 44.9280i) q^{13} +(-69.5294 + 12.2599i) q^{14} +(-31.2341 - 5.50741i) q^{15} +(-60.1403 - 21.8893i) q^{16} +(200.647 - 168.363i) q^{17} +223.382i q^{18} +(357.128 - 52.7313i) q^{19} -178.406 q^{20} +(-22.8191 - 27.1947i) q^{21} +(46.0877 - 126.625i) q^{22} +(108.960 - 617.944i) q^{23} +(-5.58809 - 31.6917i) q^{24} +(119.978 - 43.6684i) q^{25} +(67.6155 - 117.113i) q^{26} +(-197.037 + 113.759i) q^{27} +(-152.973 - 128.360i) q^{28} +(-115.667 + 137.846i) q^{29} +(-44.8531 - 77.6878i) q^{30} +(-307.796 - 177.706i) q^{31} +(-61.9123 - 170.103i) q^{32} +(66.7265 - 11.7657i) q^{33} +(729.585 + 128.646i) q^{34} +(-523.090 - 190.389i) q^{35} +(-484.001 + 406.125i) q^{36} +596.017i q^{37} +(763.540 + 677.920i) q^{38} +67.9970 q^{39} +(-324.356 - 386.552i) q^{40} +(-862.537 + 2369.80i) q^{41} +(17.4359 - 98.8841i) q^{42} +(103.512 + 587.044i) q^{43} +(358.150 - 130.356i) q^{44} +(-880.626 + 1525.29i) q^{45} +(1537.00 - 887.386i) q^{46} +(-627.241 - 526.318i) q^{47} +(58.5067 - 69.7256i) q^{48} +(888.960 + 1539.72i) q^{49} +(312.746 + 180.564i) q^{50} +(127.406 + 350.045i) q^{51} +(376.680 - 66.4189i) q^{52} +(468.924 + 82.6839i) q^{53} +(-604.711 - 220.097i) q^{54} +(813.882 - 682.928i) q^{55} -564.816i q^{56} +(-103.242 + 502.924i) q^{57} -508.963 q^{58} +(-3815.25 - 4546.84i) q^{59} +(86.7799 - 238.426i) q^{60} +(876.326 - 4969.89i) q^{61} +(-174.561 - 989.986i) q^{62} +(-1852.51 + 674.258i) q^{63} +(256.000 - 443.405i) q^{64} +(923.381 - 533.114i) q^{65} +(146.807 + 123.185i) q^{66} +(3686.52 - 4393.43i) q^{67} +(1047.71 + 1814.68i) q^{68} +(772.835 + 446.197i) q^{69} +(-538.502 - 1479.52i) q^{70} +(-4614.85 + 813.722i) q^{71} +(-1759.90 - 310.319i) q^{72} +(5012.16 + 1824.28i) q^{73} +(-1291.39 + 1083.61i) q^{74} +181.583i q^{75} +(-80.6753 + 2886.87i) q^{76} +1189.21 q^{77} +(123.624 + 147.329i) q^{78} +(2867.68 - 7878.88i) q^{79} +(247.839 - 1405.56i) q^{80} +(1054.67 + 5981.32i) q^{81} +(-6702.81 + 2439.62i) q^{82} +(-1945.55 + 3369.79i) q^{83} +(245.952 - 142.001i) q^{84} +(4474.58 + 3754.62i) q^{85} +(-1083.76 + 1291.57i) q^{86} +(-127.959 - 221.631i) q^{87} +(933.586 + 539.006i) q^{88} +(2772.17 + 7616.47i) q^{89} +(-4905.89 + 865.041i) q^{90} +(1175.32 + 207.240i) q^{91} +(4717.08 + 1716.88i) q^{92} +(387.209 - 324.907i) q^{93} -2315.93i q^{94} +(2541.05 + 7639.02i) q^{95} +257.444 q^{96} +(-5994.88 - 7144.41i) q^{97} +(-1719.92 + 4725.45i) q^{98} +(653.373 - 3705.46i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9}+O(q^{10}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9} + 90 q^{11} - 432 q^{12} - 330 q^{13} + 576 q^{14} + 2658 q^{15} - 522 q^{17} - 1236 q^{19} - 864 q^{20} - 1998 q^{21} - 1344 q^{22} - 1440 q^{23} - 384 q^{24} - 3276 q^{25} + 576 q^{26} + 1692 q^{27} + 1056 q^{28} + 4050 q^{29} + 2808 q^{31} + 2910 q^{33} + 1536 q^{34} + 1422 q^{35} + 672 q^{36} + 1872 q^{38} - 9024 q^{39} - 3060 q^{41} - 3456 q^{42} - 1218 q^{43} - 5760 q^{44} - 2592 q^{45} - 2880 q^{46} + 990 q^{47} + 1536 q^{48} - 9696 q^{49} + 27648 q^{50} + 35784 q^{51} - 1488 q^{52} + 17082 q^{53} + 2160 q^{54} + 4290 q^{55} + 204 q^{57} - 5376 q^{58} - 11142 q^{59} - 11856 q^{60} - 35928 q^{61} - 7200 q^{62} - 58254 q^{63} + 9216 q^{64} - 34290 q^{65} - 32928 q^{66} + 44322 q^{67} - 4752 q^{68} + 21762 q^{69} + 12864 q^{70} + 40428 q^{71} + 10752 q^{72} + 6936 q^{73} - 4032 q^{74} - 576 q^{76} - 36648 q^{77} - 11040 q^{78} - 29298 q^{79} + 24324 q^{81} - 14592 q^{82} + 23958 q^{83} + 36720 q^{84} + 2772 q^{85} + 30816 q^{86} + 14256 q^{87} + 26064 q^{89} + 14784 q^{90} + 100044 q^{91} + 9360 q^{92} + 26400 q^{93} - 38646 q^{95} - 55746 q^{97} - 64512 q^{98} - 69846 q^{99}+O(q^{100}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9 + 90 * q^11 - 432 * q^12 - 330 * q^13 + 576 * q^14 + 2658 * q^15 - 522 * q^17 - 1236 * q^19 - 864 * q^20 - 1998 * q^21 - 1344 * q^22 - 1440 * q^23 - 384 * q^24 - 3276 * q^25 + 576 * q^26 + 1692 * q^27 + 1056 * q^28 + 4050 * q^29 + 2808 * q^31 + 2910 * q^33 + 1536 * q^34 + 1422 * q^35 + 672 * q^36 + 1872 * q^38 - 9024 * q^39 - 3060 * q^41 - 3456 * q^42 - 1218 * q^43 - 5760 * q^44 - 2592 * q^45 - 2880 * q^46 + 990 * q^47 + 1536 * q^48 - 9696 * q^49 + 27648 * q^50 + 35784 * q^51 - 1488 * q^52 + 17082 * q^53 + 2160 * q^54 + 4290 * q^55 + 204 * q^57 - 5376 * q^58 - 11142 * q^59 - 11856 * q^60 - 35928 * q^61 - 7200 * q^62 - 58254 * q^63 + 9216 * q^64 - 34290 * q^65 - 32928 * q^66 + 44322 * q^67 - 4752 * q^68 + 21762 * q^69 + 12864 * q^70 + 40428 * q^71 + 10752 * q^72 + 6936 * q^73 - 4032 * q^74 - 576 * q^76 - 36648 * q^77 - 11040 * q^78 - 29298 * q^79 + 24324 * q^81 - 14592 * q^82 + 23958 * q^83 + 36720 * q^84 + 2772 * q^85 + 30816 * q^86 + 14256 * q^87 + 26064 * q^89 + 14784 * q^90 + 100044 * q^91 + 9360 * q^92 + 26400 * q^93 - 38646 * q^95 - 55746 * q^97 - 64512 * q^98 - 69846 * q^99

Introduction

L-functions

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