LMFDB - Embedded newform 115.5.h.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(11,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("115.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.h (of order $22$, degree $10$, 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:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	115.11
Dual form			115.5.h.a.21.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.75822 + 1.77260i) q^{2} +(-0.284694 + 1.98009i) q^{3} +(-2.18096 + 4.77564i) q^{4} +(3.14987 + 10.7275i) q^{5} +(-2.72467 - 5.96619i) q^{6} +(52.3980 - 45.4031i) q^{7} +(-9.91547 - 68.9636i) q^{8} +(73.8792 + 21.6929i) q^{9} +O(q^{10})$	\(q+(-2.75822 + 1.77260i) q^{2} +(-0.284694 + 1.98009i) q^{3} +(-2.18096 + 4.77564i) q^{4} +(3.14987 + 10.7275i) q^{5} +(-2.72467 - 5.96619i) q^{6} +(52.3980 - 45.4031i) q^{7} +(-9.91547 - 68.9636i) q^{8} +(73.8792 + 21.6929i) q^{9} +(-27.7036 - 24.0053i) q^{10} +(38.1187 - 59.3138i) q^{11} +(-8.83530 - 5.67810i) q^{12} +(-43.3933 + 50.0786i) q^{13} +(-64.0437 + 218.113i) q^{14} +(-22.1381 + 3.18298i) q^{15} +(94.5851 + 109.157i) q^{16} +(53.8403 - 24.5880i) q^{17} +(-242.228 + 71.1247i) q^{18} +(178.560 + 81.5455i) q^{19} +(-58.1002 - 8.35354i) q^{20} +(74.9850 + 116.679i) q^{21} +231.170i q^{22} +(516.904 + 112.479i) q^{23} +139.377 q^{24} +(-105.157 + 67.5801i) q^{25} +(30.9191 - 215.047i) q^{26} +(-131.300 + 287.506i) q^{27} +(102.551 + 349.256i) q^{28} +(36.4730 + 79.8647i) q^{29} +(55.4197 - 48.0215i) q^{30} +(139.623 + 971.098i) q^{31} +(615.230 + 180.648i) q^{32} +(106.595 + 92.3649i) q^{33} +(-104.919 + 163.257i) q^{34} +(652.106 + 419.083i) q^{35} +(-264.725 + 305.509i) q^{36} +(-173.965 + 592.471i) q^{37} +(-637.056 + 91.5948i) q^{38} +(-86.8064 - 100.180i) q^{39} +(708.572 - 323.594i) q^{40} +(-2413.80 + 708.757i) q^{41} +(-413.651 - 188.908i) q^{42} +(1018.72 + 146.469i) q^{43} +(200.126 + 311.402i) q^{44} +860.866i q^{45} +(-1625.12 + 606.023i) q^{46} +1455.26 q^{47} +(-243.069 + 156.211i) q^{48} +(342.408 - 2381.50i) q^{49} +(170.253 - 372.802i) q^{50} +(33.3586 + 113.609i) q^{51} +(-144.518 - 316.450i) q^{52} +(4105.70 - 3557.61i) q^{53} +(-147.480 - 1025.75i) q^{54} +(756.355 + 222.086i) q^{55} +(-3650.71 - 3163.36i) q^{56} +(-212.303 + 330.350i) q^{57} +(-242.169 - 155.633i) q^{58} +(1458.64 - 1683.36i) q^{59} +(33.0816 - 112.666i) q^{60} +(-2583.58 + 371.462i) q^{61} +(-2106.48 - 2431.01i) q^{62} +(4856.05 - 2217.68i) q^{63} +(-4234.52 + 1243.37i) q^{64} +(-673.899 - 307.759i) q^{65} +(-457.739 - 65.8129i) q^{66} +(-153.603 - 239.011i) q^{67} +310.747i q^{68} +(-369.879 + 991.495i) q^{69} -2541.52 q^{70} +(-2123.71 + 1364.82i) q^{71} +(763.473 - 5310.07i) q^{72} +(116.250 - 254.552i) q^{73} +(-570.381 - 1942.54i) q^{74} +(-103.877 - 227.460i) q^{75} +(-778.864 + 674.889i) q^{76} +(-695.690 - 4838.63i) q^{77} +(417.011 + 122.445i) q^{78} +(-582.546 - 504.779i) q^{79} +(-873.047 + 1358.49i) q^{80} +(4714.87 + 3030.06i) q^{81} +(5401.47 - 6233.63i) q^{82} +(249.388 - 849.337i) q^{83} +(-720.755 + 103.629i) q^{84} +(433.357 + 500.121i) q^{85} +(-3069.48 + 1401.78i) q^{86} +(-168.523 + 49.4829i) q^{87} +(-4468.46 - 2040.68i) q^{88} +(7373.36 + 1060.13i) q^{89} +(-1525.97 - 2374.46i) q^{90} +4594.21i q^{91} +(-1664.51 + 2223.23i) q^{92} -1962.62 q^{93} +(-4013.94 + 2579.60i) q^{94} +(-312.337 + 2172.35i) q^{95} +(-532.852 + 1166.78i) q^{96} +(1839.93 + 6266.21i) q^{97} +(3277.02 + 7175.67i) q^{98} +(4102.87 - 3555.16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 12 q^{2} - 272 q^{4} + 166 q^{6} - 246 q^{8} - 896 q^{9}+O(q^{10}) $ 320 * q - 12 * q^2 - 272 * q^4 + 166 * q^6 - 246 * q^8 - 896 * q^9	\( 320 q - 12 q^{2} - 272 q^{4} + 166 q^{6} - 246 q^{8} - 896 q^{9} + 30 q^{12} - 204 q^{13} - 2264 q^{16} + 990 q^{17} - 50 q^{18} + 1914 q^{19} + 2706 q^{21} + 258 q^{23} - 7260 q^{24} + 4000 q^{25} - 8922 q^{26} - 6642 q^{27} + 888 q^{29} + 3844 q^{31} + 10512 q^{32} - 12826 q^{34} - 5850 q^{35} - 11920 q^{36} + 20790 q^{38} + 5044 q^{39} + 24200 q^{40} + 10530 q^{41} + 14432 q^{43} + 1914 q^{44} - 9812 q^{46} + 10272 q^{47} - 55958 q^{48} - 16022 q^{49} - 6750 q^{50} - 34848 q^{51} + 7966 q^{52} - 14784 q^{53} - 42582 q^{54} - 7000 q^{55} - 14454 q^{56} - 5082 q^{57} + 92648 q^{58} + 12330 q^{59} + 34650 q^{60} + 22484 q^{61} + 70986 q^{62} + 55550 q^{63} + 20882 q^{64} + 22528 q^{66} + 5852 q^{67} + 17060 q^{69} + 4800 q^{70} - 42486 q^{71} - 180818 q^{72} - 11284 q^{73} - 111870 q^{74} - 61952 q^{76} - 72522 q^{77} - 72762 q^{78} - 3124 q^{79} + 12332 q^{81} + 83702 q^{82} + 130218 q^{83} + 349492 q^{84} + 12850 q^{85} + 60192 q^{86} + 146516 q^{87} + 88176 q^{88} + 45936 q^{89} + 5790 q^{92} - 36668 q^{93} - 182364 q^{94} - 10800 q^{95} - 67282 q^{96} - 125136 q^{97} - 67860 q^{98} - 283008 q^{99}+O(q^{100}) \) 320 * q - 12 * q^2 - 272 * q^4 + 166 * q^6 - 246 * q^8 - 896 * q^9 + 30 * q^12 - 204 * q^13 - 2264 * q^16 + 990 * q^17 - 50 * q^18 + 1914 * q^19 + 2706 * q^21 + 258 * q^23 - 7260 * q^24 + 4000 * q^25 - 8922 * q^26 - 6642 * q^27 + 888 * q^29 + 3844 * q^31 + 10512 * q^32 - 12826 * q^34 - 5850 * q^35 - 11920 * q^36 + 20790 * q^38 + 5044 * q^39 + 24200 * q^40 + 10530 * q^41 + 14432 * q^43 + 1914 * q^44 - 9812 * q^46 + 10272 * q^47 - 55958 * q^48 - 16022 * q^49 - 6750 * q^50 - 34848 * q^51 + 7966 * q^52 - 14784 * q^53 - 42582 * q^54 - 7000 * q^55 - 14454 * q^56 - 5082 * q^57 + 92648 * q^58 + 12330 * q^59 + 34650 * q^60 + 22484 * q^61 + 70986 * q^62 + 55550 * q^63 + 20882 * q^64 + 22528 * q^66 + 5852 * q^67 + 17060 * q^69 + 4800 * q^70 - 42486 * q^71 - 180818 * q^72 - 11284 * q^73 - 111870 * q^74 - 61952 * q^76 - 72522 * q^77 - 72762 * q^78 - 3124 * q^79 + 12332 * q^81 + 83702 * q^82 + 130218 * q^83 + 349492 * q^84 + 12850 * q^85 + 60192 * q^86 + 146516 * q^87 + 88176 * q^88 + 45936 * q^89 + 5790 * q^92 - 36668 * q^93 - 182364 * q^94 - 10800 * q^95 - 67282 * q^96 - 125136 * q^97 - 67860 * q^98 - 283008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−2.75822	+	1.77260i	−0.689556	+	0.443151i	−0.837928	−	0.545781i	$-0.816233\pi$
$2$	−2.75822	+	1.77260i	−0.689556	+	0.443151i	0.148372	+	0.988932i	$0.452597\pi$
$3$	−0.284694	+	1.98009i	−0.0316327	+	0.220010i	−0.999506	−	0.0314280i	$-0.989994\pi$
$3$	−0.284694	+	1.98009i	−0.0316327	+	0.220010i	0.967873	+	0.251438i	$0.0809036\pi$
$4$	−2.18096	+	4.77564i	−0.136310	+	0.298477i
$5$	3.14987	+	10.7275i	0.125995	+	0.429098i
$5$	3.14987	+	10.7275i	0.125995	+	0.429098i
$6$	−2.72467	−	5.96619i	−0.0756852	−	0.165728i
$7$	52.3980	−	45.4031i	1.06935	−	0.926594i	0.0718574	−	0.997415i	$-0.477107\pi$
$7$	52.3980	−	45.4031i	1.06935	−	0.926594i	0.997489	+	0.0708209i	$0.0225619\pi$
$8$	−9.91547	−	68.9636i	−0.154929	−	1.07756i
$9$	73.8792	+	21.6929i	0.912089	+	0.267814i
$10$	−27.7036	−	24.0053i	−0.277036	−	0.240053i
$11$	38.1187	−	59.3138i	0.315031	−	0.490197i	−0.647242	−	0.762285i	$-0.724078\pi$
$11$	38.1187	−	59.3138i	0.315031	−	0.490197i	0.962272	+	0.272088i	$0.0877140\pi$
$12$	−8.83530	−	5.67810i	−0.0613562	−	0.0394313i
$13$	−43.3933	+	50.0786i	−0.256765	+	0.296323i	−0.869467	−	0.493992i	$-0.835537\pi$
$13$	−43.3933	+	50.0786i	−0.256765	+	0.296323i	0.612701	+	0.790314i	$0.290083\pi$
$14$	−64.0437	+	218.113i	−0.326754	+	1.11282i
$15$	−22.1381	+	3.18298i	−0.0983916	+	0.0141466i
$16$	94.5851	+	109.157i	0.369473	+	0.426395i
$17$	53.8403	−	24.5880i	0.186299	−	0.0850798i	−0.320082	−	0.947390i	$-0.603710\pi$
$17$	53.8403	−	24.5880i	0.186299	−	0.0850798i	0.506380	+	0.862310i	$0.330983\pi$
$18$	−242.228	+	71.1247i	−0.747618	+	0.219521i
$19$	178.560	+	81.5455i	0.494626	+	0.225888i	0.647079	−	0.762423i	$-0.275990\pi$
$19$	178.560	+	81.5455i	0.494626	+	0.225888i	−0.152454	+	0.988311i	$0.548718\pi$
$20$	−58.1002	−	8.35354i	−0.145250	−	0.0208839i
$21$	74.9850	+	116.679i	0.170034	+	0.264578i
$22$			231.170i			0.477624i
$23$	516.904	+	112.479i	0.977134	+	0.212626i
$23$	516.904	+	112.479i	0.977134	+	0.212626i
$24$	139.377			0.241974
$25$	−105.157	+	67.5801i	−0.168251	+	0.108128i
$26$	30.9191	−	215.047i	0.0457383	−	0.318117i
$27$	−131.300	+	287.506i	−0.180109	+	0.394384i
$28$	102.551	+	349.256i	0.130805	+	0.445480i
$29$	36.4730	+	79.8647i	0.0433686	+	0.0949639i	0.930076	−	0.367367i	$-0.119741\pi$
$29$	36.4730	+	79.8647i	0.0433686	+	0.0949639i	−0.886708	+	0.462331i	$0.847013\pi$
$30$	55.4197	−	48.0215i	0.0615775	−	0.0533572i
$31$	139.623	+	971.098i	0.145289	+	1.01051i	0.923800	+	0.382876i	$0.125066\pi$
$31$	139.623	+	971.098i	0.145289	+	1.01051i	−0.778510	+	0.627632i	$0.784024\pi$
$32$	615.230	+	180.648i	0.600810	+	0.176414i
$33$	106.595	+	92.3649i	0.0978832	+	0.0848162i
$34$	−104.919	+	163.257i	−0.0907602	+	0.141226i
$35$	652.106	+	419.083i	0.532332	+	0.342109i
$36$	−264.725	+	305.509i	−0.204263	+	0.235732i
$37$	−173.965	+	592.471i	−0.127075	+	0.432777i	−0.998312	−	0.0580862i	$-0.981500\pi$
$37$	−173.965	+	592.471i	−0.127075	+	0.432777i	0.871237	+	0.490863i	$0.163318\pi$
$38$	−637.056	+	91.5948i	−0.441174	+	0.0634313i
$39$	−86.8064	−	100.180i	−0.0570719	−	0.0658645i
$40$	708.572	−	323.594i	0.442857	−	0.202246i
$41$	−2413.80	+	708.757i	−1.43593	+	0.421628i	−0.904864	−	0.425700i	$-0.860028\pi$
$41$	−2413.80	+	708.757i	−1.43593	+	0.421628i	−0.531069	+	0.847328i	$0.678210\pi$
$42$	−413.651	−	188.908i	−0.234496	−	0.107091i
$43$	1018.72	+	146.469i	0.550955	+	0.0792154i	0.412170	−	0.911107i	$-0.364771\pi$
$43$	1018.72	+	146.469i	0.550955	+	0.0792154i	0.138785	+	0.990322i	$0.455680\pi$
$44$	200.126	+	311.402i	0.103371	+	0.160848i
$45$			860.866i			0.425119i
$46$	−1625.12	+	606.023i	−0.768014	+	0.286400i
$47$	1455.26			0.658788			0.329394	−	0.944193i	$-0.393156\pi$
$47$	1455.26			0.658788			0.329394	+	0.944193i	$0.393156\pi$
$48$	−243.069	+	156.211i	−0.105499	+	0.0677999i
$49$	342.408	−	2381.50i	0.142611	−	0.991878i
$50$	170.253	−	372.802i	0.0681012	−	0.149121i
$51$	33.3586	+	113.609i	0.0128253	+	0.0436789i
$52$	−144.518	−	316.450i	−0.0534460	−	0.117030i
$53$	4105.70	−	3557.61i	1.46162	−	1.26650i	0.563971	−	0.825795i	$-0.309273\pi$
$53$	4105.70	−	3557.61i	1.46162	−	1.26650i	0.897651	−	0.440708i	$-0.145273\pi$
$54$	−147.480	−	1025.75i	−0.0505762	−	0.351765i
$55$	756.355	+	222.086i	0.250035	+	0.0734169i
$56$	−3650.71	−	3163.36i	−1.16413	−	1.00872i
$57$	−212.303	+	330.350i	−0.0653440	+	0.101677i
$58$	−242.169	−	155.633i	−0.0719884	−	0.0462641i
$59$	1458.64	−	1683.36i	0.419029	−	0.483586i	−0.506512	−	0.862233i	$-0.669065\pi$
$59$	1458.64	−	1683.36i	0.419029	−	0.483586i	0.925541	+	0.378648i	$0.123611\pi$
$60$	33.0816	−	112.666i	0.00918933	−	0.0312960i
$61$	−2583.58	+	371.462i	−0.694323	+	0.0998286i	−0.480436	−	0.877030i	$-0.659522\pi$
$61$	−2583.58	+	371.462i	−0.694323	+	0.0998286i	−0.213887	+	0.976858i	$0.568613\pi$
$62$	−2106.48	−	2431.01i	−0.547992	−	0.632417i
$63$	4856.05	−	2217.68i	1.22349	−	0.558751i
$64$	−4234.52	+	1243.37i	−1.03382	+	0.303556i
$65$	−673.899	−	307.759i	−0.159503	−	0.0728424i
$66$	−457.739	−	65.8129i	−0.105082	−	0.0151086i
$67$	−153.603	−	239.011i	−0.0342176	−	0.0532437i	0.823723	−	0.566992i	$-0.191893\pi$
$67$	−153.603	−	239.011i	−0.0342176	−	0.0532437i	−0.857941	+	0.513748i	$0.828257\pi$
$68$			310.747i			0.0672031i
$69$	−369.879	+	991.495i	−0.0776893	+	0.208254i
$70$	−2541.52			−0.518678
$71$	−2123.71	+	1364.82i	−0.421287	+	0.270744i	−0.734062	−	0.679083i	$-0.762378\pi$
$71$	−2123.71	+	1364.82i	−0.421287	+	0.270744i	0.312775	+	0.949827i	$0.398741\pi$
$72$	763.473	−	5310.07i	0.147275	−	1.02432i
$73$	116.250	−	254.552i	0.0218146	−	0.0477674i	−0.898411	−	0.439155i	$-0.855278\pi$
$73$	116.250	−	254.552i	0.0218146	−	0.0477674i	0.920226	+	0.391388i	$0.128005\pi$
$74$	−570.381	−	1942.54i	−0.104160	−	0.354737i
$75$	−103.877	−	227.460i	−0.0184671	−	0.0404373i
$76$	−778.864	+	674.889i	−0.134845	+	0.116844i
$77$	−695.690	−	4838.63i	−0.117337	−	0.816096i
$78$	417.011	+	122.445i	0.0685422	+	0.0201258i
$79$	−582.546	−	504.779i	−0.0933417	−	0.0808810i	0.606940	−	0.794748i	$-0.292397\pi$
$79$	−582.546	−	504.779i	−0.0933417	−	0.0808810i	−0.700282	+	0.713867i	$0.746942\pi$
$80$	−873.047	+	1358.49i	−0.136414	+	0.212264i
$81$	4714.87	+	3030.06i	0.718620	+	0.461829i
$82$	5401.47	−	6233.63i	0.803312	−	0.927071i
$83$	249.388	−	849.337i	0.0362009	−	0.123289i	−0.939410	−	0.342795i	$-0.888626\pi$
$83$	249.388	−	849.337i	0.0362009	−	0.123289i	0.975611	+	0.219506i	$0.0704446\pi$
$84$	−720.755	+	103.629i	−0.102148	+	0.0146866i
$85$	433.357	+	500.121i	0.0599802	+	0.0692208i
$86$	−3069.48	+	1401.78i	−0.415019	+	0.189533i
$87$	−168.523	+	49.4829i	−0.0222649	+	0.00653757i
$88$	−4468.46	−	2040.68i	−0.577022	−	0.263517i
$89$	7373.36	+	1060.13i	0.930862	+	0.133838i	0.591031	−	0.806649i	$-0.298721\pi$
$89$	7373.36	+	1060.13i	0.930862	+	0.133838i	0.339831	+	0.940487i	$0.389630\pi$
$90$	−1525.97	−	2374.46i	−0.188392	−	0.293143i
$91$			4594.21i			0.554789i
$92$	−1664.51	+	2223.23i	−0.196657	+	0.262669i
$93$	−1962.62			−0.226918
$94$	−4013.94	+	2579.60i	−0.454271	+	0.291943i
$95$	−312.337	+	2172.35i	−0.0346080	+	0.240704i
$96$	−532.852	+	1166.78i	−0.0578181	+	0.126604i
$97$	1839.93	+	6266.21i	0.195549	+	0.665980i	0.997633	+	0.0687681i	$0.0219068\pi$
$97$	1839.93	+	6266.21i	0.195549	+	0.665980i	−0.802083	+	0.597212i	$0.796275\pi$
$98$	3277.02	+	7175.67i	0.341214	+	0.747154i
$99$	4102.87	−	3555.16i	0.418617	−	0.362734i
$100$	−93.3955	−	649.580i	−0.00933955	−	0.0649580i
$101$	−9534.50	−	2799.58i	−0.934664	−	0.274442i	−0.221276	−	0.975211i	$-0.571022\pi$
$101$	−9534.50	−	2799.58i	−0.934664	−	0.274442i	−0.713388	+	0.700769i	$0.752840\pi$
$102$	−293.394	−	254.227i	−0.0282001	−	0.0244355i
$103$	−1318.82	+	2052.12i	−0.124311	+	0.193432i	−0.897831	−	0.440340i	$-0.854858\pi$
$103$	−1318.82	+	2052.12i	−0.124311	+	0.193432i	0.773520	+	0.633772i	$0.218494\pi$
$104$	3883.86	+	2496.01i	0.359085	+	0.230770i
$105$	−1015.48	+	1171.92i	−0.0921066	+	0.106297i
$106$	−5018.21	+	17090.4i	−0.446619	+	1.52104i
$107$	5432.54	−	781.082i	0.474499	−	0.0682227i	0.0990833	−	0.995079i	$-0.468409\pi$
$107$	5432.54	−	781.082i	0.474499	−	0.0682227i	0.375416	+	0.926856i	$0.377500\pi$
$108$	−1086.66	−	1254.08i	−0.0931640	−	0.107517i
$109$	11202.6	−	5116.05i	0.942899	−	0.430608i	0.116184	−	0.993228i	$-0.462934\pi$
$109$	11202.6	−	5116.05i	0.942899	−	0.430608i	0.826716	+	0.562620i	$0.190207\pi$
$110$	−2479.87	+	728.155i	−0.204948	+	0.0601781i
$111$	−1123.62	−	513.141i	−0.0911956	−	0.0416477i
$112$	9912.14	+	1425.15i	0.790190	+	0.113612i
$113$	3486.57	+	5425.21i	0.273050	+	0.424873i	0.950514	−	0.310682i	$-0.100558\pi$
$113$	3486.57	+	5425.21i	0.273050	+	0.424873i	−0.677464	+	0.735556i	$0.736921\pi$
$114$		−	1287.51i		−	0.0990695i
$115$	421.563	+	5899.36i	0.0318762	+	0.446076i
$116$	−460.951			−0.0342561
$117$	−4292.21	+	2758.44i	−0.313552	+	0.201508i
$118$	−1039.33	+	7228.68i	−0.0746429	+	0.519153i
$119$	1704.75	−	3732.88i	0.120383	−	0.263603i
$120$	439.020	+	1495.16i	0.0304875	+	0.103831i
$121$	4016.99	+	8795.99i	0.274366	+	0.600778i
$122$	6467.63	−	5604.23i	0.434536	−	0.376527i
$123$	−716.208	−	4981.34i	−0.0473401	−	0.329258i
$124$	−4942.12	−	1451.14i	−0.321418	−	0.0943769i
$125$	−1056.19	−	915.196i	−0.0675963	−	0.0585725i
$126$	−9462.99	+	14724.7i	−0.596057	+	0.927482i
$127$	17639.8	+	11336.4i	1.09367	+	0.702859i	0.957675	−	0.287851i	$-0.0929406\pi$
$127$	17639.8	+	11336.4i	1.09367	+	0.702859i	0.135995	+	0.990710i	$0.456577\pi$
$128$	2757.37	−	3182.18i	0.168297	−	0.194225i
$129$	−580.046	+	1975.45i	−0.0348564	+	0.118710i
$130$	2404.30	−	345.686i	0.142266	−	0.0204548i
$131$	−12005.4	−	13855.0i	−0.699574	−	0.807352i	0.289121	−	0.957293i	$-0.406637\pi$
$131$	−12005.4	−	13855.0i	−0.699574	−	0.807352i	−0.988695	+	0.149941i	$0.952092\pi$
$132$	−673.580	+	307.614i	−0.0386582	+	0.0176546i
$133$	13058.6	−	3834.35i	0.738232	−	0.216765i
$134$	847.343	+	386.969i	0.0471900	+	0.0215509i
$135$	−3497.78	−	502.905i	−0.191922	−	0.0275942i
$136$	−2229.53	−	3469.22i	−0.120541	−	0.187566i
$137$		−	22301.6i		−	1.18821i	−0.804386	−	0.594107i	$-0.797506\pi$
$137$		−	22301.6i		−	1.18821i	0.804386	−	0.594107i	$-0.202494\pi$
$138$	−737.320	−	3390.42i	−0.0387166	−	0.178031i
$139$	−14565.6			−0.753875			−0.376937	−	0.926239i	$-0.623023\pi$
$139$	−14565.6			−0.753875			−0.376937	+	0.926239i	$0.623023\pi$
$140$	−3423.61	+	2200.22i	−0.174674	+	0.112256i
$141$	−414.305	+	2881.56i	−0.0208393	+	0.144940i
$142$	3438.37	−	7528.97i	0.170520	−	0.373387i
$143$	1316.26	+	4482.75i	0.0643677	+	0.219216i
$144$	4619.94	+	10116.3i	0.222798	+	0.487860i
$145$	−741.860	+	642.825i	−0.0352846	+	0.0305743i
$146$	130.576	+	908.178i	0.00612574	+	0.0426054i
$147$	4618.11	+	1356.00i	0.213712	+	0.0627516i
$148$	−2450.02	−	2122.95i	−0.111852	−	0.0969207i
$149$	13948.7	−	21704.6i	0.628293	−	0.977643i	−0.370515	−	0.928826i	$-0.620819\pi$
$149$	13948.7	−	21704.6i	0.628293	−	0.977643i	0.998808	−	0.0488161i	$-0.0155448\pi$
$150$	689.713	+	443.252i	0.0306539	+	0.0197001i
$151$	−27849.3	+	32139.8i	−1.22141	+	1.40958i	−0.337887	+	0.941187i	$0.609712\pi$
$151$	−27849.3	+	32139.8i	−1.22141	+	1.40958i	−0.883521	+	0.468392i	$0.844833\pi$
$152$	3853.17	−	13122.7i	0.166775	−	0.567984i
$153$	4511.07	−	648.593i	0.192706	−	0.0277070i
$154$	10495.8	+	12112.9i	0.442564	+	0.510746i
$155$	−9977.62	+	4556.63i	−0.415302	+	0.189662i
$156$	667.744	−	196.067i	0.0274385	−	0.00805668i
$157$	30173.6	+	13779.8i	1.22413	+	0.559041i	0.919372	−	0.393389i	$-0.128697\pi$
$157$	30173.6	+	13779.8i	1.22413	+	0.559041i	0.304758	+	0.952430i	$0.401425\pi$
$158$	2501.56	+	359.671i	0.100207	+	0.0144076i
$159$	5875.52	+	9142.49i	0.232409	+	0.361635i
$160$			7168.87i			0.280034i
$161$	32191.6	−	17575.4i	1.24191	−	0.678035i
$162$	−18375.8			−0.700189
$163$	−10392.8	+	6679.06i	−0.391163	+	0.251385i	−0.721408	−	0.692510i	$-0.756505\pi$
$163$	−10392.8	+	6679.06i	−0.391163	+	0.251385i	0.330245	+	0.943895i	$0.392869\pi$
$164$	1879.65	−	13073.2i	0.0698857	−	0.486066i
$165$	−655.081	+	1434.43i	−0.0240618	+	0.0526879i
$166$	817.670	+	2784.73i	0.0296730	+	0.101057i
$167$	−20167.2	−	44160.0i	−0.723124	−	1.58342i	−0.809473	−	0.587157i	$-0.800247\pi$
$167$	−20167.2	−	44160.0i	−0.723124	−	1.58342i	0.0863488	−	0.996265i	$-0.472480\pi$
$168$	7303.09	−	6328.16i	0.258755	−	0.224212i
$169$	3439.77	+	23924.1i	0.120436	+	0.837651i
$170$	−2081.81	−	611.275i	−0.0720350	−	0.0211514i
$171$	11422.9	+	9898.00i	0.390647	+	0.338497i
$172$	−2921.26	+	4545.57i	−0.0987447	+	0.153650i
$173$	−38408.1	−	24683.4i	−1.28331	−	0.824733i	−0.292017	−	0.956413i	$-0.594326\pi$
$173$	−38408.1	−	24683.4i	−1.28331	−	0.824733i	−0.991292	+	0.131681i	$0.957963\pi$
$174$	377.111	−	435.209i	0.0124558	−	0.0143747i
$175$	−2441.65	+	8315.50i	−0.0797274	+	0.271527i
$176$	10080.0	−	1449.28i	0.325413	−	0.0467873i
$177$	2917.95	+	3367.49i	0.0931388	+	0.107488i
$178$	−22216.6	+	10146.0i	−0.701192	+	0.320224i
$179$	27009.7	−	7930.75i	0.842972	−	0.247519i	0.168391	−	0.985720i	$-0.446143\pi$
$179$	27009.7	−	7930.75i	0.842972	−	0.247519i	0.674580	+	0.738201i	$0.264325\pi$
$180$	−4111.18	−	1877.51i	−0.126888	−	0.0579480i
$181$	−27355.3	−	3933.10i	−0.834997	−	0.120054i	−0.288463	−	0.957491i	$-0.593144\pi$
$181$	−27355.3	−	3933.10i	−0.834997	−	0.120054i	−0.546534	+	0.837437i	$0.684053\pi$
$182$	−8143.71	−	12671.9i	−0.245855	−	0.382558i
$183$		−	5221.48i		−	0.155916i
$184$	2631.62	−	36762.8i	0.0777298	−	1.08586i
$185$	−6903.68			−0.201714
$186$	5413.33	−	3478.94i	0.156473	−	0.100559i
$187$	593.911	−	4130.74i	0.0169839	−	0.118126i
$188$	−3173.87	+	6949.81i	−0.0897994	+	0.196633i
$189$	6173.83	+	21026.1i	0.172835	+	0.588621i
$190$	−2989.22	−	6545.48i	−0.0828039	−	0.181315i
$191$	−6555.72	+	5680.57i	−0.179702	+	0.155713i	−0.740067	−	0.672533i	$-0.765206\pi$
$191$	−6555.72	+	5680.57i	−0.179702	+	0.155713i	0.560365	+	0.828246i	$0.310661\pi$
$192$	−1256.44	−	8738.72i	−0.0340831	−	0.237053i
$193$	−58401.1	−	17148.1i	−1.56786	−	0.460364i	−0.621481	−	0.783430i	$-0.713469\pi$
$193$	−58401.1	−	17148.1i	−1.56786	−	0.460364i	−0.946377	+	0.323065i	$0.895287\pi$
$194$	−16182.4	−	14022.2i	−0.429972	−	0.372573i
$195$	801.247	−	1246.77i	0.0210716	−	0.0327880i
$196$	10626.4	+	6829.17i	0.276614	+	0.177769i
$197$	17434.3	−	20120.3i	0.449234	−	0.518443i	−0.485286	−	0.874356i	$-0.661284\pi$
$197$	17434.3	−	20120.3i	0.449234	−	0.518443i	0.934519	+	0.355912i	$0.115830\pi$
$198$	−5014.75	+	17078.7i	−0.127914	+	0.435636i
$199$	−51948.3	+	7469.04i	−1.31179	+	0.188607i	−0.762481	−	0.647010i	$-0.776019\pi$
$199$	−51948.3	+	7469.04i	−1.31179	+	0.188607i	−0.549311	+	0.835618i	$0.685110\pi$
$200$	5703.25	+	6581.90i	0.142581	+	0.164547i
$201$	516.994	−	236.103i	0.0127966	−	0.00584399i
$202$	31260.9	−	9179.01i	0.766122	−	0.224954i
$203$	5537.21	+	2528.76i	0.134369	+	0.0613643i
$204$	−615.309	−	88.4680i	−0.0147854	−	0.00212582i
$205$	−15206.3	−	23661.5i	−0.361840	−	0.563034i
$206$		−	7997.94i		−	0.188471i
$207$	35748.4	+	19523.0i	0.834289	+	0.455623i
$208$	−9570.79			−0.221218
$209$	11643.2	−	7482.66i	0.266552	−	0.171302i
$210$	723.558	−	5032.46i	0.0164072	−	0.114115i
$211$	12056.8	−	26400.6i	0.270811	−	0.592993i	−0.724548	−	0.689224i	$-0.757952\pi$
$211$	12056.8	−	26400.6i	0.270811	−	0.592993i	0.995359	+	0.0962314i	$0.0306789\pi$
$212$	8035.47	+	27366.3i	0.178789	+	0.608898i
$213$	−2097.87	−	4593.69i	−0.0462401	−	0.101252i
$214$	−13599.6	+	11784.1i	−0.296961	+	0.257318i
$215$	1637.58	+	11389.6i	0.0354262	+	0.246395i
$216$	21129.3	+	6204.13i	0.452875	+	0.132976i
$217$	51406.8	+	44544.3i	1.09170	+	0.945959i
$218$	−21830.5	+	33969.0i	−0.459358	+	0.714775i
$219$	470.942	+	302.656i	0.00981926	+	0.00631046i
$220$	−2710.18	+	3127.72i	−0.0559955	+	0.0646223i
$221$	−1104.98	+	3763.20i	−0.0226239	+	0.0770501i
$222$	4008.79	−	576.378i	0.0813407	−	0.0116950i
$223$	18830.8	+	21732.0i	0.378669	+	0.437008i	0.912808	−	0.408389i	$-0.133909\pi$
$223$	18830.8	+	21732.0i	0.378669	+	0.437008i	−0.534139	+	0.845397i	$0.679364\pi$
$224$	40438.8	−	18467.8i	0.805938	−	0.368060i
$225$	−9234.90	+	2711.61i	−0.182418	+	0.0535627i
$226$	−19233.5	−	8783.64i	−0.376566	−	0.171972i
$227$	−92252.7	−	13263.9i	−1.79031	−	0.257407i	−0.834417	−	0.551133i	$-0.814196\pi$
$227$	−92252.7	−	13263.9i	−1.79031	−	0.257407i	−0.955890	+	0.293726i	$0.905105\pi$
$228$	−1114.61	−	1734.36i	−0.0214413	−	0.0333633i
$229$		−	68161.4i		−	1.29977i	−0.760031	−	0.649886i	$-0.774816\pi$
$229$		−	68161.4i		−	1.29977i	0.760031	−	0.649886i	$-0.225184\pi$
$230$	−11620.0	−	15524.5i	−0.219659	−	0.293469i
$231$	9779.00			0.183261
$232$	5146.11	−	3307.20i	0.0956099	−	0.0614448i
$233$	12844.8	−	89337.4i	0.236600	−	1.64559i	−0.431932	−	0.901906i	$-0.642168\pi$
$233$	12844.8	−	89337.4i	0.236600	−	1.64559i	0.668532	−	0.743683i	$-0.266923\pi$
$234$	6949.27	−	15216.8i	0.126913	−	0.277902i
$235$	4583.88	+	15611.3i	0.0830038	+	0.282685i
$236$	4857.88	+	10637.3i	0.0872214	+	0.190988i
$237$	1165.36	−	1009.79i	0.0207473	−	0.0179777i
$238$	1914.83	+	13318.0i	0.0338047	+	0.235117i
$239$	−69820.1	−	20501.0i	−1.22232	−	0.358905i	−0.393973	−	0.919122i	$-0.628900\pi$
$239$	−69820.1	−	20501.0i	−1.22232	−	0.358905i	−0.828346	+	0.560217i	$0.810718\pi$
$240$	−2441.38	−	2115.47i	−0.0423851	−	0.0367269i
$241$	−1218.65	+	1896.25i	−0.0209819	+	0.0326484i	−0.851586	−	0.524215i	$-0.824359\pi$
$241$	−1218.65	+	1896.25i	−0.0209819	+	0.0326484i	0.830604	+	0.556863i	$0.187995\pi$
$242$	−26671.6	−	17140.8i	−0.455426	−	0.292685i
$243$	−24107.5	+	27821.6i	−0.408263	+	0.471161i
$244$	3860.71	−	13148.4i	0.0648466	−	0.220847i
$245$	26626.0	−	3828.24i	0.443582	−	0.0637774i
$246$	10805.4	+	12470.1i	0.178554	+	0.206063i
$247$	−11832.0	+	5403.49i	−0.193938	+	0.0885687i
$248$	65586.0	−	19257.8i	1.06637	−	0.313114i
$249$	1610.77	+	735.613i	0.0259797	+	0.0118645i
$250$	4535.49	+	652.106i	0.0725679	+	0.0104337i
$251$	−24652.5	−	38360.1i	−0.391304	−	0.608881i	0.588582	−	0.808437i	$-0.299686\pi$
$251$	−24652.5	−	38360.1i	−0.391304	−	0.608881i	−0.979886	+	0.199556i	$0.936050\pi$
$252$			28027.4i			0.441348i
$253$	26375.3	−	26372.0i	0.412055	−	0.412004i
$254$	−68749.5			−1.06562
$255$	−1113.66	+	715.706i	−0.0171266	+	0.0110066i
$256$	8084.50	−	56228.9i	0.123360	−	0.857985i
$257$	−7742.53	+	16953.8i	−0.117224	+	0.256685i	−0.959144	−	0.282917i	$-0.908698\pi$
$257$	−7742.53	+	16953.8i	−0.117224	+	0.256685i	0.841920	+	0.539602i	$0.181425\pi$
$258$	−1901.80	−	6476.94i	−0.0285710	−	0.0973039i
$259$	17784.6	+	38942.9i	0.265121	+	0.580535i
$260$	2939.49	−	2547.09i	0.0434836	−	0.0376788i
$261$	962.098	+	6691.54i	0.0141234	+	0.0982302i
$262$	57672.9	+	16934.3i	0.840174	+	0.246697i
$263$	93282.9	+	80830.1i	1.34862	+	1.16859i	0.970019	+	0.243029i	$0.0781411\pi$
$263$	93282.9	+	80830.1i	1.34862	+	1.16859i	0.378604	+	0.925559i	$0.376404\pi$
$264$	5312.88	−	8267.00i	0.0762293	−	0.118615i
$265$	51096.4	+	32837.7i	0.727610	+	0.467607i
$266$	−29221.8	+	33723.7i	−0.412993	+	0.476620i
$267$	−4198.31	+	14298.1i	−0.0588914	+	0.200566i
$268$	1476.43	−	212.279i	0.0205562	−	0.00295554i
$269$	63516.5	+	73301.9i	0.877772	+	1.01300i	0.999790	+	0.0204752i	$0.00651791\pi$
$269$	63516.5	+	73301.9i	0.877772	+	1.01300i	−0.122018	+	0.992528i	$0.538937\pi$
$270$	10539.1	−	4813.05i	0.144570	−	0.0660227i
$271$	9859.68	−	2895.06i	0.134253	−	0.0394203i	−0.213916	−	0.976852i	$-0.568622\pi$
$271$	9859.68	−	2895.06i	0.134253	−	0.0394203i	0.348169	+	0.937432i	$0.386804\pi$
$272$	7776.45	+	3551.39i	0.105110	+	0.0480021i
$273$	−9096.96	−	1307.95i	−0.122059	−	0.0175495i
$274$	39531.9	+	61512.8i	0.526558	+	0.819340i
$275$			8813.31i			0.116540i
$276$	−3928.33	−	3928.82i	−0.0515692	−	0.0515755i
$277$	−120002.			−1.56397			−0.781986	−	0.623296i	$-0.785793\pi$
$277$	−120002.			−1.56397			−0.781986	+	0.623296i	$0.785793\pi$
$278$	40175.2	−	25819.0i	0.519839	−	0.334080i
$279$	−10750.7	+	74772.8i	−0.138111	+	0.960584i
$280$	22435.6	−	49127.0i	0.286168	−	0.626620i
$281$	1019.77	+	3473.03i	0.0129149	+	0.0439841i	0.965698	−	0.259666i	$-0.0836126\pi$
$281$	1019.77	+	3473.03i	0.0129149	+	0.0439841i	−0.952783	+	0.303651i	$0.901794\pi$
$282$	−3965.11	−	8682.38i	−0.0498605	−	0.109179i
$283$	93437.5	−	80964.0i	1.16667	−	1.01093i	0.166982	−	0.985960i	$-0.446598\pi$
$283$	93437.5	−	80964.0i	1.16667	−	1.01093i	0.999688	−	0.0249656i	$-0.00794762\pi$
$284$	−1886.18	−	13118.7i	−0.0233855	−	0.162650i
$285$	−4212.54	−	1236.91i	−0.0518626	−	0.0152282i
$286$	−11576.7	−	10031.2i	−0.141531	−	0.122637i
$287$	−94298.7	+	146732.i	−1.14483	+	1.78139i
$288$	41533.9	+	26692.2i	0.500746	+	0.321810i
$289$	−52400.4	+	60473.3i	−0.627392	+	0.724049i
$290$	906.742	−	3088.08i	0.0107817	−	0.0367191i
$291$	−12931.5	+	1859.27i	−0.152708	+	0.0219561i
$292$	962.112	+	1110.34i	0.0112839	+	0.0130223i
$293$	−75356.2	+	34414.0i	−0.877776	+	0.400867i	−0.802751	−	0.596315i	$-0.796631\pi$
$293$	−75356.2	+	34414.0i	−0.877776	+	0.400867i	−0.0750253	+	0.997182i	$0.523904\pi$
$294$	−15141.4	+	4445.93i	−0.175175	+	0.0514361i
$295$	22652.7	+	10345.1i	0.260301	+	0.118876i
$296$	42583.9	+	6122.64i	0.486029	+	0.0698804i
$297$	12048.1	+	18747.2i	0.136586	+	0.212532i
$298$			84591.8i			0.952568i
$299$	−28063.0	+	21005.0i	−0.313900	+	0.234952i
$300$	1312.82			0.0145869
$301$	60028.8	−	38578.2i	0.662562	−	0.425803i
$302$	19843.5	−	138015.i	0.217573	−	1.51325i
$303$	8257.86	−	18082.2i	0.0899460	−	0.196954i
$304$	7987.83	+	27204.1i	0.0864334	+	0.294365i
$305$	−12122.8	−	26545.2i	−0.130317	−	0.285355i
$306$	−11292.8	+	9785.30i	−0.120604	+	0.104504i
$307$	−4814.81	−	33487.7i	−0.0510860	−	0.355311i	−0.999291	−	0.0376517i	$-0.988012\pi$
$307$	−4814.81	−	33487.7i	−0.0510860	−	0.355311i	0.948205	−	0.317659i	$-0.102897\pi$
$308$	24624.8	+	7230.50i	0.259580	+	0.0762196i
$309$	−3687.93	−	3195.61i	−0.0386247	−	0.0334685i
$310$	19443.4	−	30254.6i	0.202325	−	0.314824i
$311$	64354.4	+	41358.1i	0.665362	+	0.427602i	0.829251	−	0.558877i	$-0.188768\pi$
$311$	64354.4	+	41358.1i	0.665362	+	0.427602i	−0.163889	+	0.986479i	$0.552404\pi$
$312$	−6048.04	+	6979.81i	−0.0621306	+	0.0717026i
$313$	−4747.85	+	16169.7i	−0.0484628	+	0.165049i	−0.980169	−	0.198164i	$-0.936502\pi$
$313$	−4747.85	+	16169.7i	−0.0484628	+	0.165049i	0.931706	+	0.363213i	$0.118320\pi$
$314$	−107652.	+	15478.0i	−1.09185	+	0.156984i
$315$	39086.0	+	45107.6i	0.393913	+	0.454599i
$316$	3681.15	−	1681.12i	0.0368646	−	0.0168355i
$317$	−51302.5	+	15063.8i	−0.510528	+	0.149905i	−0.526844	−	0.849962i	$-0.676625\pi$
$317$	−51302.5	+	15063.8i	−0.510528	+	0.149905i	0.0163152	+	0.999867i	$0.494806\pi$
$318$	−32412.0	−	14802.1i	−0.320518	−	0.146375i
$319$	6127.38	+	880.984i	0.0602134	+	0.00865739i
$320$	−26676.3	−	41509.1i	−0.260511	−	0.405363i
$321$			10979.3i			0.106553i
$322$	−57637.5	+	105540.i	−0.555896	+	1.01790i
$323$	11618.8			0.111367
$324$	−24753.4	+	15908.0i	−0.235801	+	0.151540i
$325$	1178.78	−	8198.62i	0.0111601	−	0.0776201i
$326$	16826.4	−	36844.7i	0.158327	−	0.346689i
$327$	6940.94	+	23638.7i	0.0649117	+	0.221069i
$328$	72812.5	+	159437.i	0.676796	+	1.48198i
$329$	76252.8	−	66073.5i	0.704473	−	0.610429i
$330$	−735.810	−	5117.67i	−0.00675675	−	0.0469942i
$331$	−122663.	−	36017.1i	−1.11959	−	0.328740i	−0.330979	−	0.943638i	$-0.607379\pi$
$331$	−122663.	−	36017.1i	−1.11959	−	0.328740i	−0.788607	+	0.614898i	$0.789197\pi$
$332$	3512.22	+	3043.36i	0.0318644	+	0.0276107i
$333$	−25704.8	+	39997.5i	−0.231807	+	0.360699i
$334$	133904.	+	86054.8i	1.20033	+	0.771405i
$335$	2080.15	−	2400.62i	0.0185355	−	0.0213912i
$336$	−5643.86	+	19221.2i	−0.0499917	+	0.170256i
$337$	−99106.9	+	14249.4i	−0.872658	+	0.125469i	−0.564070	−	0.825727i	$-0.690765\pi$
$337$	−99106.9	+	14249.4i	−0.872658	+	0.125469i	−0.308587	+	0.951196i	$0.599856\pi$
$338$	−51895.7	−	59890.8i	−0.454253	−	0.524236i
$339$	−11735.0	+	5359.21i	−0.102114	+	0.0466338i
$340$	−3333.53	+	978.812i	−0.0288368	+	0.00846724i
$341$	62921.8	+	28735.4i	0.541119	+	0.247121i
$342$	−49052.2	−	7052.63i	−0.419378	−	0.0602975i
$343$	−187.035	−	291.033i	−0.00158978	−	0.00247374i
$344$		−	71706.7i		−	0.605958i
$345$	−11801.3	−	844.780i	−0.0991497	−	0.00709750i
$346$	149692.			1.25039
$347$	−104299.	+	67028.9i	−0.866207	+	0.556677i	−0.896590	−	0.442861i	$-0.853963\pi$
$347$	−104299.	+	67028.9i	−0.866207	+	0.556677i	0.0303836	+	0.999538i	$0.490327\pi$
$348$	131.230	−	912.725i	0.00108361	−	0.00753671i
$349$	78660.2	−	172242.i	0.645809	−	1.41412i	−0.249366	−	0.968409i	$-0.580222\pi$
$349$	78660.2	−	172242.i	0.645809	−	1.41412i	0.895175	−	0.445715i	$-0.147050\pi$
$350$	−8005.46	−	27264.1i	−0.0653507	−	0.222564i
$351$	−8700.36	−	19051.1i	−0.0706192	−	0.154634i
$352$	34166.7	−	29605.6i	0.275751	−	0.238940i
$353$	−28517.9	−	198346.i	−0.228859	−	1.59175i	−0.702927	−	0.711262i	$-0.748124\pi$
$353$	−28517.9	−	198346.i	−0.228859	−	1.59175i	0.474068	−	0.880488i	$-0.342785\pi$
$354$	−14017.6	−	4115.93i	−0.111858	−	0.0328444i
$355$	−21330.5	−	18483.0i	−0.169256	−	0.146661i
$356$	−21143.8	+	32900.4i	−0.166833	+	0.259598i
$357$	6906.12	+	4438.29i	0.0541873	+	0.0348241i
$358$	−60440.6	+	69752.2i	−0.471588	+	0.544242i
$359$	−15927.2	+	54243.2i	−0.123581	+	0.420878i	−0.997922	−	0.0644340i	$-0.979476\pi$
$359$	−15927.2	+	54243.2i	−0.123581	+	0.420878i	0.874341	+	0.485312i	$0.161294\pi$
$360$	59368.4	−	8535.89i	0.458090	−	0.0658634i
$361$	−60108.2	−	69368.5i	−0.461232	−	0.532290i
$362$	82424.0	−	37641.8i	0.628979	−	0.287245i
$363$	−18560.5	+	5449.85i	−0.140856	+	0.0413592i
$364$	−21940.3	−	10019.8i	−0.165592	−	0.0756233i
$365$	3096.87	+	445.263i	0.0232454	+	0.00334219i
$366$	9255.61	+	14402.0i	0.0690944	+	0.107513i
$367$		−	46495.5i		−	0.345207i	−0.984991	−	0.172603i	$-0.944782\pi$
$367$		−	46495.5i		−	0.345207i	0.984991	−	0.172603i	$-0.0552179\pi$
$368$	36613.5	+	67062.5i	0.270362	+	0.495204i
$369$	−193705.			−1.42262
$370$	19041.9	−	12237.5i	0.139093	−	0.0893899i
$371$	53603.8	−	372823.i	0.389446	−	2.70866i
$372$	4280.39	−	9372.74i	0.0309312	−	0.0677299i
$373$	−54212.7	−	184631.i	−0.389658	−	1.32705i	−0.887909	−	0.460019i	$-0.847842\pi$
$373$	−54212.7	−	184631.i	−0.389658	−	1.32705i	0.498251	−	0.867033i	$-0.333976\pi$
$374$	5684.02	+	12446.3i	0.0406362	+	0.0889808i
$375$	2112.86	−	1830.81i	0.0150248	−	0.0130191i
$376$	−14429.6	−	100360.i	−0.102066	−	0.709881i
$377$	−5582.19	−	1639.08i	−0.0392755	−	0.0115323i
$378$	−54299.8	−	47051.0i	−0.380027	−	0.329295i
$379$	76730.8	−	119396.i	0.534185	−	0.831208i	−0.464331	−	0.885661i	$-0.653705\pi$
$379$	76730.8	−	119396.i	0.534185	−	0.831208i	0.998516	+	0.0544537i	$0.0173417\pi$
$380$	−9693.16	−	6229.42i	−0.0671272	−	0.0431400i
$381$	−27469.1	+	31701.0i	−0.189232	+	0.218385i
$382$	8012.77	−	27289.0i	0.0549105	−	0.187008i
$383$	−159036.	+	22866.0i	−1.08417	+	0.155881i	−0.661162	−	0.750243i	$-0.729936\pi$
$383$	−159036.	+	22866.0i	−1.08417	+	0.155881i	−0.423012	+	0.906124i	$0.639027\pi$
$384$	5516.00	+	6365.80i	0.0374078	+	0.0431709i
$385$	49714.9	−	22704.0i	0.335402	−	0.153173i
$386$	191480.	−	56223.7i	1.28514	−	0.377350i
$387$	72084.6	+	32919.9i	0.481305	+	0.219805i
$388$	−33937.9	−	4879.54i	−0.225435	−	0.0324127i
$389$	−7582.57	−	11798.7i	−0.0501092	−	0.0779714i	0.815295	−	0.579046i	$-0.196575\pi$
$389$	−7582.57	−	11798.7i	−0.0501092	−	0.0779714i	−0.865404	+	0.501074i	$0.832938\pi$
$390$			4859.15i			0.0319471i
$391$	30595.9	−	6653.74i	0.200129	−	0.0435224i
$392$	−167632.			−1.09090
$393$	30852.0	−	19827.4i	0.199755	−	0.128375i
$394$	−12422.5	+	86400.3i	−0.0800233	+	0.556574i
$395$	3580.05	−	7839.22i	0.0229454	−	0.0502433i
$396$	8029.94	+	27347.5i	0.0512061	+	0.174392i
$397$	18016.0	+	39449.6i	0.114308	+	0.250301i	0.958136	−	0.286314i	$-0.0924301\pi$
$397$	18016.0	+	39449.6i	0.114308	+	0.250301i	−0.843827	+	0.536615i	$0.819703\pi$
$398$	130045.	−	112685.i	0.820973	−	0.711377i
$399$	3874.66	+	26948.9i	0.0243382	+	0.169276i
$400$	−17323.1	−	5086.52i	−0.108269	−	0.0317908i
$401$	−50707.0	−	43937.9i	−0.315340	−	0.273244i	0.482780	−	0.875741i	$-0.339627\pi$
$401$	−50707.0	−	43937.9i	−0.315340	−	0.273244i	−0.798121	+	0.602497i	$0.794172\pi$
$402$	−1007.47	+	1567.65i	−0.00623418	+	0.00970057i
$403$	−54689.9	−	35147.1i	−0.336742	−	0.216411i
$404$	34164.2	−	39427.6i	0.209319	−	0.241567i
$405$	−17653.6	+	60122.8i	−0.107628	+	0.366547i
$406$	−19755.4	+	2840.39i	−0.119849	+	0.0172316i
$407$	28510.4	+	32902.8i	0.172113	+	0.198629i
$408$	7504.12	−	3427.02i	0.0450795	−	0.0205871i
$409$	81227.2	−	23850.5i	0.485573	−	0.142577i	−0.0297773	−	0.999557i	$-0.509480\pi$
$409$	81227.2	−	23850.5i	0.485573	−	0.142577i	0.515351	+	0.856979i	$0.327662\pi$
$410$	83884.9	+	38308.9i	0.499018	+	0.227894i
$411$	44159.2	+	6349.14i	0.261419	+	0.0375864i
$412$	−6923.89	−	10773.8i	−0.0407902	−	0.0634707i
$413$		−	154432.i		−	0.905390i
$414$	−133209.	+	9518.98i	−0.777199	+	0.0555379i
$415$	9896.77			0.0574642
$416$	−35743.4	+	22970.9i	−0.206543	+	0.132737i
$417$	4146.75	−	28841.3i	0.0238471	−	0.165860i
$418$	−18850.9	+	41277.7i	−0.107890	+	0.236245i
$419$	80801.1	+	275183.i	0.460245	+	1.56745i	0.783658	+	0.621192i	$0.213351\pi$
$419$	80801.1	+	275183.i	0.460245	+	1.56745i	−0.323413	+	0.946258i	$0.604830\pi$
$420$	−3381.96	−	7405.45i	−0.0191721	−	0.0419810i
$421$	190397.	−	164980.i	1.07423	−	0.930824i	0.0764252	−	0.997075i	$-0.475649\pi$
$421$	190397.	−	164980.i	1.07423	−	0.930824i	0.997803	+	0.0662513i	$0.0211039\pi$
$422$	13542.6	+	94190.7i	0.0760460	+	0.528912i
$423$	107514.	+	31568.9i	0.600873	+	0.176432i
$424$	−286055.	−	247868.i	−1.59118	−	1.37876i
$425$	−4000.01	+	6224.13i	−0.0221454	+	0.0344589i
$426$	13929.2	+	8951.75i	0.0767550	+	0.0493274i
$427$	−118509.	+	136766.i	−0.649972	+	0.750107i
$428$	−8118.00	+	27647.4i	−0.0443161	+	0.150927i
$429$	−9251.00	+	1330.09i	−0.0502660	+	0.00722716i
$430$	−24706.0	−	28512.3i	−0.133618	−	0.154204i
$431$	−286084.	+	130650.i	−1.54006	+	0.703324i	−0.991174	−	0.132570i	$-0.957677\pi$
$431$	−286084.	+	130650.i	−1.54006	+	0.703324i	−0.548891	+	0.835894i	$0.684950\pi$
$432$	−43802.3	+	12861.5i	−0.234709	+	0.0689167i
$433$	49181.1	+	22460.3i	0.262315	+	0.119795i	0.542232	−	0.840229i	$-0.317580\pi$
$433$	49181.1	+	22460.3i	0.262315	+	0.119795i	−0.279917	+	0.960024i	$0.590307\pi$
$434$	−220751.	−	31739.2i	−1.17199	−	0.168506i
$435$	−1061.65	−	1651.96i	−0.00561052	−	0.00873014i
$436$			64657.4i			0.340130i
$437$	83126.1	+	62235.4i	0.435286	+	0.325893i
$438$	−1835.45			−0.00956741
$439$	−234860.	+	150935.i	−1.21865	+	0.783181i	−0.982086	−	0.188434i	$-0.939659\pi$
$439$	−234860.	+	150935.i	−1.21865	+	0.783181i	−0.236567	+	0.971615i	$0.576022\pi$
$440$	7816.23	−	54363.1i	0.0403731	−	0.280801i
$441$	76958.5	−	168516.i	0.395712	−	0.866488i
$442$	−3622.89	−	12338.4i	−0.0185443	−	0.0631562i
$443$	87351.6	+	191273.i	0.445106	+	0.974646i	0.990633	+	0.136553i	$0.0436023\pi$
$443$	87351.6	+	191273.i	0.445106	+	0.974646i	−0.545527	+	0.838093i	$0.683670\pi$
$444$	4901.15	−	4246.87i	0.0248618	−	0.0215428i
$445$	11852.6	+	82436.7i	0.0598541	+	0.416294i
$446$	−90461.8	−	26562.0i	−0.454774	−	0.133534i
$447$	39006.1	+	33799.0i	0.195217	+	0.169156i
$448$	−165427.	+	257410.i	−0.824236	+	1.28254i
$449$	182219.	+	117105.i	0.903860	+	0.580875i	0.907933	−	0.419116i	$-0.137660\pi$
$449$	182219.	+	117105.i	0.903860	+	0.580875i	−0.00407282	+	0.999992i	$0.501296\pi$
$450$	20665.3	−	23849.0i	0.102051	−	0.117773i
$451$	−49972.0	+	170189.i	−0.245682	+	0.836716i
$452$	−33512.9	+	4818.43i	−0.164034	+	0.0235846i
$453$	−55711.3	−	64294.3i	−0.271486	−	0.313311i
$454$	277965.	−	126943.i	1.34859	−	0.615879i
$455$	−49284.2	+	14471.1i	−0.238059	+	0.0699004i
$456$	24887.2	+	11365.6i	0.119687	+	0.0546591i
$457$	−138816.	−	19958.7i	−0.664672	−	0.0955653i	−0.198282	−	0.980145i	$-0.563536\pi$
$457$	−138816.	−	19958.7i	−0.664672	−	0.0955653i	−0.466389	+	0.884580i	$0.654445\pi$
$458$	120823.	+	188004.i	0.575995	+	0.896266i
$459$			18707.8i			0.0887968i
$460$	−29092.6	−	10853.0i	−0.137489	−	0.0512903i
$461$	276557.			1.30132			0.650658	−	0.759371i	$-0.274493\pi$
$461$	276557.			1.30132			0.650658	+	0.759371i	$0.274493\pi$
$462$	−26972.7	+	17334.3i	−0.126369	+	0.0812124i
$463$	5419.02	−	37690.1i	0.0252789	−	0.175819i	−0.973270	−	0.229662i	$-0.926238\pi$
$463$	5419.02	−	37690.1i	0.0252789	−	0.175819i	0.998549	+	0.0538431i	$0.0171471\pi$
$464$	−5267.99	+	11535.3i	−0.0244686	+	0.0535787i
$465$	−6181.97	−	21053.9i	−0.0285905	−	0.0973702i
$466$	122931.	+	269181.i	0.566095	+	1.23958i
$467$	109344.	−	94747.3i	0.501374	−	0.434443i	−0.367097	−	0.930183i	$-0.619648\pi$
$467$	109344.	−	94747.3i	0.501374	−	0.434443i	0.868471	+	0.495739i	$0.165103\pi$
$468$	−3812.15	−	26514.1i	−0.0174052	−	0.121056i
$469$	−18900.3	−	5549.64i	−0.0859258	−	0.0252301i
$470$	−40316.0	−	34934.0i	−0.182508	−	0.158144i
$471$	−35875.6	+	55823.5i	−0.161717	+	0.251637i
$472$	−130554.	−	83901.8i	−0.586011	−	0.376606i
$473$	47519.8	−	54840.7i	0.212399	−	0.245121i
$474$	−1424.36	+	4850.93i	−0.00633963	+	0.0215908i
$475$	−24287.6	+	3492.03i	−0.107646	+	0.0154772i
$476$	14108.9	+	16282.5i	0.0622700	+	0.0718634i
$477$	380500.	−	173769.i	1.67232	−	0.763721i
$478$	228920.	−	67216.9i	1.00191	−	0.294186i
$479$	228080.	+	104160.i	0.994066	+	0.453975i	0.844950	−	0.534845i	$-0.179630\pi$
$479$	228080.	+	104160.i	0.994066	+	0.453975i	0.149116	+	0.988820i	$0.452357\pi$
$480$	−14195.0	−	2040.94i	−0.0616103	−	0.00885823i
$481$	−22121.2	−	34421.2i	−0.0956133	−	0.148777i
$482$		−	7390.47i		−	0.0318110i
$483$	25636.1	+	68746.0i	0.109890	+	0.294682i
$484$	−50767.4			−0.216717
$485$	−61425.0	+	39475.4i	−0.261133	+	0.167820i
$486$	17177.4	−	119471.i	0.0727251	−	0.505814i
$487$	58848.5	−	128860.i	0.248129	−	0.543327i	−0.744054	−	0.668120i	$-0.767099\pi$
$487$	58848.5	−	128860.i	0.248129	−	0.543327i	0.992183	+	0.124793i	$0.0398267\pi$
$488$	51234.8	+	174490.i	0.215142	+	0.732706i
$489$	−10266.4	−	22480.2i	−0.0429338	−	0.0940120i
$490$	−66654.5	+	57756.4i	−0.277611	+	0.240552i
$491$	35955.4	+	250075.i	0.149142	+	1.03731i	0.917628	+	0.397441i	$0.130102\pi$
$491$	35955.4	+	250075.i	0.149142	+	1.03731i	−0.768485	+	0.639867i	$0.778989\pi$
$492$	25351.1	+	7443.75i	0.104729	+	0.0307512i
$493$	3927.43	+	3403.14i	0.0161590	+	0.0140019i
$494$	23057.0	−	35877.5i	0.0944821	−	0.147017i
$495$	51061.3	+	32815.1i	0.208392	+	0.133925i
$496$	−92796.0	+	107092.i	−0.377195	+	0.435306i
$497$	−49310.7	+	167937.i	−0.199631	+	0.679881i
$498$	−5746.81	+	826.267i	−0.0231722	+	0.00333167i
$499$	306600.	+	353836.i	1.23132	+	1.42102i	0.873211	+	0.487343i	$0.162034\pi$
$499$	306600.	+	353836.i	1.23132	+	1.42102i	0.358111	+	0.933679i	$0.383421\pi$
$500$	6674.16	−	3047.98i	0.0266966	−	0.0121919i
$501$	93182.5	−	27360.9i	0.371244	−	0.109007i
$502$	135994.	+	62106.6i	0.539652	+	0.246451i
$503$	−325079.	−	46739.4i	−1.28485	−	0.184734i	−0.534159	−	0.845384i	$-0.679372\pi$
$503$	−325079.	−	46739.4i	−1.28485	−	0.184734i	−0.750694	+	0.660650i	$0.770281\pi$
$504$	−201089.	−	312901.i	−0.791640	−	1.23182i
$505$		−	111099.i		−	0.435641i
$506$	−26001.8	+	119493.i	−0.101555	+	0.466703i
$507$	−48351.3			−0.188102
$508$	−92610.3	+	59517.0i	−0.358866	+	0.230629i
$509$	−19814.4	+	137812.i	−0.0764796	+	0.531927i	0.915180	+	0.403045i	$0.132048\pi$
$509$	−19814.4	+	137812.i	−0.0764796	+	0.531927i	−0.991660	+	0.128883i	$0.958861\pi$
$510$	1803.06	−	3948.15i	0.00693219	−	0.0151794i
$511$	−5466.19	−	18616.1i	−0.0209336	−	0.0712932i
$512$	105359.	+	230705.i	0.401914	+	0.880068i
$513$	−46889.6	+	40630.1i	−0.178173	+	0.154388i
$514$	−8696.69	−	60486.8i	−0.0329176	−	0.228947i
$515$	−26168.1	−	7683.65i	−0.0986638	−	0.0289703i
$516$	−8168.99	−	7078.47i	−0.0306810	−	0.0265852i
$517$	55472.7	−	86317.2i	0.207538	−	0.322936i
$518$	−118084.	−	75888.1i	−0.440081	−	0.282823i
$519$	59810.1	−	69024.5i	0.222044	−	0.256253i
$520$	−14542.2	+	49526.1i	−0.0537802	+	0.183159i
$521$	301359.	−	43328.8i	1.11022	−	0.159625i	0.437281	−	0.899325i	$-0.355942\pi$
$521$	301359.	−	43328.8i	1.11022	−	0.159625i	0.672937	+	0.739700i	$0.265033\pi$
$522$	−14515.1	−	16751.4i	−0.0532697	−	0.0614765i
$523$	−369859.	+	168909.i	−1.35218	+	0.617518i	−0.954004	−	0.299792i	$-0.903083\pi$
$523$	−369859.	+	168909.i	−1.35218	+	0.617518i	−0.398172	+	0.917311i	$0.630355\pi$
$524$	92349.6	−	27116.3i	0.336335	−	0.0987569i
$525$	−15770.3	−	7202.07i	−0.0572167	−	0.0261300i
$526$	−400575.	−	57594.0i	−1.44781	−	0.208164i
$527$	31394.7	+	48851.2i	0.113041	+	0.175895i
$528$			20371.9i			0.0730742i
$529$	254538.	+	116282.i	0.909581	+	0.415528i
$530$	−199144.			−0.708949
$531$	144280.	−	92723.3i	0.511703	−	0.328851i
$532$	−10168.8	+	70725.7i	−0.0359292	+	0.249893i
$533$	69249.5	−	151635.i	0.243760	−	0.533759i
$534$	−13765.0	−	46879.4i	−0.0482719	−	0.164399i
$535$	25490.8	+	55817.1i	0.0890586	+	0.195011i
$536$	−14960.0	+	12962.9i	−0.0520718	+	0.0451205i
$537$	8014.13	+	55739.5i	0.0277912	+	0.193292i
$538$	−305128.	−	89593.6i	−1.05419	−	0.309537i
$539$	−128204.	−	111089.i	−0.441289	−	0.382379i
$540$	10030.2	−	15607.3i	0.0343972	−	0.0535231i
$541$	40545.4	+	26057.0i	0.138531	+	0.0890286i	0.608071	−	0.793883i	$-0.291944\pi$
$541$	40545.4	+	26057.0i	0.138531	+	0.0890286i	−0.469540	+	0.882911i	$0.655580\pi$
$542$	−22063.4	+	25462.5i	−0.0751059	+	0.0866769i
$543$	15575.8	−	53046.4i	0.0528264	−	0.179910i
$544$	37565.9	−	5401.17i	0.126939	−	0.0182511i
$545$	90168.8	+	104060.i	0.303573	+	0.350342i
$546$	27409.9	−	12517.7i	0.0919438	−	0.0419893i
$547$	386456.	−	113474.i	1.29159	−	0.379245i	0.437429	−	0.899253i	$-0.355889\pi$
$547$	386456.	−	113474.i	1.29159	−	0.379245i	0.854162	+	0.520007i	$0.174071\pi$
$548$	106504.	+	48638.9i	0.354655	+	0.161965i
$549$	−198931.	−	28601.9i	−0.660020	−	0.0948966i
$550$	−15622.5	−	24309.1i	−0.0516446	−	0.0803606i
$551$			17234.8i			0.0567680i
$552$	72044.6	+	15677.0i	0.236441	+	0.0514500i
$553$	−53442.7			−0.174759
$554$	330993.	−	212716.i	1.07845	−	0.693076i
$555$	1965.44	−	13669.9i	0.00638078	−	0.0443793i
$556$	31767.0	−	69560.1i	0.102761	−	0.225014i
$557$	−142491.	−	485280.i	−0.459280	−	1.56416i	−0.785495	−	0.618868i	$-0.787591\pi$
$557$	−142491.	−	485280.i	−0.459280	−	1.56416i	0.326215	−	0.945296i	$-0.394227\pi$
$558$	−102890.	−	225297.i	−0.330448	−	0.723580i
$559$	−51540.4	+	44660.1i	−0.164939	+	0.142921i
$560$	15933.7	+	110821.i	0.0508089	+	0.353384i
$561$	8010.17	+	2352.00i	0.0254516	+	0.00747328i
$562$	−8969.06	−	7771.74i	−0.0283971	−	0.0246063i
$563$	−200057.	+	311296.i	−0.631158	+	0.982101i	0.367485	+	0.930029i	$0.380219\pi$
$563$	−200057.	+	311296.i	−0.631158	+	0.982101i	−0.998643	+	0.0520716i	$0.983418\pi$
$564$	−12857.7	−	8263.13i	−0.0404208	−	0.0259769i
$565$	−47216.5	+	54490.7i	−0.147910	+	0.170697i
$566$	−114204.	+	388944.i	−0.356492	+	1.21410i
$567$	384624.	−	55300.5i	1.19638	−	0.172014i
$568$	115181.	+	132926.i	0.357012	+	0.412014i
$569$	−129965.	+	59352.9i	−0.401422	+	0.183323i	−0.605887	−	0.795551i	$-0.707182\pi$
$569$	−129965.	+	59352.9i	−0.401422	+	0.183323i	0.204465	+	0.978874i	$0.434454\pi$
$570$	13811.7	−	4055.47i	0.0425105	−	0.0124822i
$571$	−27196.0	−	12420.0i	−0.0834129	−	0.0380934i	0.373272	−	0.927722i	$-0.378236\pi$
$571$	−27196.0	−	12420.0i	−0.0834129	−	0.0380934i	−0.456685	+	0.889629i	$0.650963\pi$
$572$	−24278.7	−	3490.75i	−0.0742051	−	0.0106691i
$573$	−9381.67	−	14598.2i	−0.0285740	−	0.0444620i
$574$		−	571873.i		−	1.73570i
$575$	−61957.2	+	23104.5i	−0.187394	+	0.0698812i
$576$	−339815.			−1.02423
$577$	456001.	−	293054.i	1.36966	−	0.880229i	0.370839	−	0.928697i	$-0.379070\pi$
$577$	456001.	−	293054.i	1.36966	−	0.880229i	0.998825	+	0.0484679i	$0.0154339\pi$
$578$	37336.9	−	259684.i	0.111759	−	0.777302i
$579$	50581.3	−	110758.i	0.150881	−	0.330382i
$580$	−1451.93	−	4944.83i	−0.00431609	−	0.0146993i
$581$	−25495.1	−	55826.6i	−0.0755275	−	0.165382i
$582$	32372.2	−	28050.7i	0.0955711	−	0.0828128i
$583$	−54511.5	−	379136.i	−0.160380	−	1.11547i
$584$	−18707.5	−	5493.02i	−0.0548518	−	0.0161059i
$585$	−43110.9	−	37355.8i	−0.125972	−	0.109156i
$586$	146847.	−	228498.i	0.427631	−	0.665407i
$587$	−225565.	−	144962.i	−0.654630	−	0.420705i	0.170726	−	0.985319i	$-0.445389\pi$
$587$	−225565.	−	144962.i	−0.654630	−	0.420705i	−0.825355	+	0.564614i	$0.809025\pi$
$588$	−16547.7	+	19097.0i	−0.0478611	+	0.0552346i
$589$	−54257.7	+	184785.i	−0.156398	+	0.532642i
$590$	−80819.1	+	11620.0i	−0.232172	+	0.0333813i
$591$	34876.6	+	40249.7i	0.0998524	+	0.115236i
$592$	−81126.9	+	37049.4i	−0.231484	+	0.105715i
$593$	213640.	−	62730.5i	0.607539	−	0.178390i	0.0365289	−	0.999333i	$-0.488370\pi$
$593$	213640.	−	62730.5i	0.607539	−	0.178390i	0.571010	+	0.820943i	$0.306552\pi$
$594$	−66462.8	−	30352.5i	−0.188367	−	0.0860245i
$595$	45414.1	+	6529.56i	0.128279	+	0.0184438i
$596$	73231.9	+	113951.i	0.206162	+	0.320794i
$597$		−	104989.i		−	0.294574i
$598$	40170.5	−	107681.i	0.112332	−	0.301118i
$599$	−262493.			−0.731584			−0.365792	−	0.930697i	$-0.619202\pi$
$599$	−262493.			−0.731584			−0.365792	+	0.930697i	$0.619202\pi$
$600$	−14656.5	+	9419.13i	−0.0407124	+	0.0261643i
$601$	−38642.5	+	268765.i	−0.106983	+	0.744086i	0.863749	+	0.503922i	$0.168110\pi$
$601$	−38642.5	+	268765.i	−0.106983	+	0.744086i	−0.970732	+	0.240164i	$0.922799\pi$
$602$	−97189.2	+	212815.i	−0.268179	+	0.587230i
$603$	−6163.23	−	20990.0i	−0.0169502	−	0.0577269i
$604$	−92749.8	−	203094.i	−0.254237	−	0.556702i
$605$	−81705.6	+	70798.3i	−0.223224	+	0.193425i
$606$	9275.52	+	64512.6i	0.0252576	+	0.175671i
$607$	−90763.5	−	26650.6i	−0.246339	−	0.0723318i	0.156232	−	0.987720i	$-0.450065\pi$
$607$	−90763.5	−	26650.6i	−0.246339	−	0.0723318i	−0.402571	+	0.915389i	$0.631883\pi$
$608$	95124.3	+	82425.7i	0.257326	+	0.222975i
$609$	−6583.60	+	10244.3i	−0.0177512	+	0.0276215i
$610$	80491.3	+	51728.6i	0.216316	+	0.139018i
$611$	−63148.7	+	72877.5i	−0.169154	+	0.195214i
$612$	−6741.01	+	22957.8i	−0.0179979	+	0.0612953i
$613$	90453.6	−	13005.3i	0.240716	−	0.0346097i	−0.0209008	−	0.999782i	$-0.506653\pi$
$613$	90453.6	−	13005.3i	0.240716	−	0.0346097i	0.261617	+	0.965172i	$0.415744\pi$
$614$	72640.8	+	83831.9i	0.192683	+	0.222368i
$615$	51181.1	−	23373.6i	0.135319	−	0.0617982i
$616$	−326791.	+	95954.6i	−0.861210	+	0.252874i
$617$	−144855.	−	66152.9i	−0.380507	−	0.173772i	0.215974	−	0.976399i	$-0.430707\pi$
$617$	−144855.	−	66152.9i	−0.380507	−	0.173772i	−0.596480	+	0.802628i	$0.703435\pi$
$618$	15836.7	+	2276.97i	0.0414655	+	0.00596184i
$619$	278997.	+	434128.i	0.728146	+	1.13302i	0.985986	+	0.166829i	$0.0533529\pi$
$619$	278997.	+	434128.i	0.728146	+	1.13302i	−0.257840	+	0.966188i	$0.583011\pi$
$620$		−	57587.3i		−	0.149811i
$621$	−100208.	+	133844.i	−0.259847	+	0.347070i
$622$	−250815.			−0.648296
$623$	434482.	−	279225.i	1.11943	−	0.719412i
$624$	2724.75	−	18951.1i	0.00699774	−	0.0486703i
$625$	6490.86	−	14213.0i	0.0166166	−	0.0363853i
$626$	−15566.8	−	53015.7i	−0.0397238	−	0.135287i
$627$	11501.6	+	25185.0i	0.0292565	+	0.0640629i
$628$	−131615.	+	114045.i	−0.333722	+	0.289172i
$629$	5201.37	+	36176.3i	0.0131467	+	0.0914372i
$630$	−187766.	−	55133.0i	−0.473081	−	0.138909i
$631$	−219879.	−	190526.i	−0.552235	−	0.478515i	0.333471	−	0.942760i	$-0.391780\pi$
$631$	−219879.	−	190526.i	−0.552235	−	0.478515i	−0.885706	+	0.464246i	$0.846325\pi$
$632$	−29035.1	+	45179.6i	−0.0726925	+	0.113112i
$633$	48843.2	+	31389.6i	0.121898	+	0.0783391i
$634$	114802.	−	132488.i	0.285608	−	0.329609i
$635$	−66047.9	+	224938.i	−0.163799	+	0.557848i
$636$	−56475.5	+	8119.95i	−0.139619	+	0.0200742i
$637$	104404.	+	120489.i	0.257299	+	0.296939i
$638$	−18462.3	+	8431.46i	−0.0453571	+	0.0207139i
$639$	−186505.	+	54762.7i	−0.456760	+	0.134117i
$640$	42822.0	+	19556.2i	0.104546	+	0.0477445i
$641$	−678949.	−	97618.1i	−1.65242	−	0.237582i	−0.747839	−	0.663880i	$-0.768909\pi$
$641$	−678949.	−	97618.1i	−1.65242	−	0.237582i	−0.904583	+	0.426297i	$0.859818\pi$
$642$	−19462.0	−	30283.4i	−0.0472190	−	0.0734742i
$643$		−	309005.i		−	0.747385i	−0.927553	−	0.373692i	$-0.878092\pi$
$643$		−	309005.i		−	0.747385i	0.927553	−	0.373692i	$-0.121908\pi$
$644$	13724.9	+	192067.i	0.0330931	+	0.463106i
$645$	−23018.7			−0.0553300
$646$	−32047.2	+	20595.5i	−0.0767935	+	0.0493522i
$647$	82757.2	−	575589.i	0.197696	−	1.37500i	−0.613253	−	0.789886i	$-0.710139\pi$
$647$	82757.2	−	575589.i	0.197696	−	1.37500i	0.810949	−	0.585117i	$-0.198951\pi$
$648$	162214.	−	355199.i	0.386312	−	0.845905i
$649$	−44245.1	−	150685.i	−0.105045	−	0.357751i
$650$	11281.6	+	24703.2i	0.0267019	+	0.0584690i
$651$	−102837.	+	89108.8i	−0.242654	+	0.210261i
$652$	−9230.43	−	64199.1i	−0.0217134	−	0.151020i
$653$	738338.	+	216796.i	1.73153	+	0.508422i	0.987213	−	0.159409i	$-0.0509588\pi$
$653$	738338.	+	216796.i	1.73153	+	0.508422i	0.744313	+	0.667831i	$0.232777\pi$
$654$	−61046.7	−	52897.2i	−0.142727	−	0.123674i
$655$	110813.	−	172429.i	0.258291	−	0.401908i
$656$	−305676.	−	196446.i	−0.710319	−	0.456494i
$657$	14110.4	−	16284.3i	0.0326896	−	0.0377258i
$658$	−93200.4	+	317411.i	−0.215261	+	0.733113i
$659$	554282.	−	79693.8i	1.27632	−	0.183507i	0.529373	−	0.848389i	$-0.322427\pi$
$659$	554282.	−	79693.8i	1.27632	−	0.183507i	0.746949	+	0.664882i	$0.231518\pi$
$660$	−5421.60	−	6256.86i	−0.0124463	−	0.0143638i
$661$	−647434.	+	295673.i	−1.48181	+	0.676720i	−0.981907	−	0.189362i	$-0.939358\pi$
$661$	−647434.	+	295673.i	−1.48181	+	0.676720i	−0.499903	+	0.866082i	$0.666631\pi$
$662$	402176.	−	118089.i	0.917699	−	0.269461i
$663$	−7136.91	−	3259.32i	−0.0162362	−	0.00741481i
$664$	−61046.2	−	8777.12i	−0.138459	−	0.0199075i
$665$	82265.6	+	128008.i	0.186027	+	0.289463i
$666$		−	155887.i		−	0.351447i
$667$	9869.91	+	45384.8i	0.0221851	+	0.102014i
$668$	254876.			0.571185
$669$	−48392.3	+	31099.9i	−0.108125	+	0.0694874i
$670$	−1482.17	+	10308.7i	−0.00330179	+	0.0229644i
$671$	−76449.7	+	167402.i	−0.169797	+	0.371804i
$672$	25055.2	+	85330.2i	0.0554829	+	0.188957i
$673$	106303.	+	232772.i	0.234702	+	0.513926i	0.989934	−	0.141532i	$-0.0452028\pi$
$673$	106303.	+	232772.i	0.234702	+	0.513926i	−0.755231	+	0.655458i	$0.772476\pi$
$674$	248100.	−	214980.i	0.546145	−	0.473237i
$675$	−5622.65	−	39106.4i	−0.0123405	−	0.0858302i
$676$	−121755.	−	35750.5i	−0.266436	−	0.0782328i
$677$	−498055.	−	431567.i	−1.08668	−	0.941610i	−0.0881618	−	0.996106i	$-0.528099\pi$
$677$	−498055.	−	431567.i	−1.08668	−	0.941610i	−0.998514	+	0.0544963i	$0.982645\pi$
$678$	22868.1	−	35583.4i	0.0497474	−	0.0774085i
$679$	380914.	+	244798.i	0.826204	+	0.530969i
$680$	30193.2	−	34844.8i	0.0652967	−	0.0753564i
$681$	52527.7	−	178893.i	0.113265	−	0.385744i
$682$	−224489.	+	32276.6i	−0.482643	+	0.0693936i
$683$	−139224.	−	160673.i	−0.298450	−	0.344430i	0.586641	−	0.809847i	$-0.300450\pi$
$683$	−139224.	−	160673.i	−0.298450	−	0.344430i	−0.885092	+	0.465417i	$0.845904\pi$
$684$	−72182.1	+	32964.5i	−0.154283	+	0.0704586i
$685$	239239.	−	70247.0i	0.509861	−	0.149709i
$686$	1031.77	+	471.194i	0.00219248	+	0.00100127i
$687$	134966.	+	19405.2i	0.285964	+	0.0411154i
$688$	80367.2	+	125054.i	0.169786	+	0.264192i
$689$			359984.i			0.758306i
$690$	34048.1	−	18588.9i	0.0715145	−	0.0390441i
$691$	−601050.			−1.25879			−0.629397	−	0.777084i	$-0.716698\pi$
$691$	−601050.			−1.25879			−0.629397	+	0.777084i	$0.716698\pi$
$692$	201646.	−	129590.i	0.421092	−	0.270619i
$693$	53566.9	−	372566.i	0.111540	−	0.775776i
$694$	168865.	−	369762.i	0.350606	−	0.767720i
$695$	−45879.7	−	156252.i	−0.0949841	−	0.323486i
$696$	5083.50	+	11131.3i	0.0104941	+	0.0229788i
$697$	−112533.	+	97510.4i	−0.231641	+	0.200718i
$698$	88353.9	+	614515.i	0.181349	+	1.26131i
$699$	173240.	+	50867.7i	0.354562	+	0.104109i
$700$	−34386.7	−	29796.2i	−0.0701769	−	0.0608086i
$701$	−236142.	+	367445.i	−0.480549	+	0.747749i	−0.993883	−	0.110440i	$-0.964774\pi$
$701$	−236142.	+	367445.i	−0.480549	+	0.747749i	0.513334	+	0.858189i	$0.328410\pi$
$702$	57767.6	+	37125.0i	0.117222	+	0.0753342i
$703$	−79376.6	+	91605.5i	−0.160613	+	0.185358i
$704$	−87665.4	+	298561.i	−0.176882	+	0.602404i
$705$	−32216.8	+	4632.07i	−0.0648192	+	0.00931960i
$706$	430248.	+	496533.i	0.863196	+	0.996182i
$707$	−626699.	+	286204.i	−1.25378	+	0.572580i
$708$	−22445.8	+	6590.69i	−0.0447785	+	0.0131481i
$709$	−554100.	−	253049.i	−1.10229	−	0.503399i	−0.220665	−	0.975350i	$-0.570823\pi$
$709$	−554100.	−	253049.i	−1.10229	−	0.503399i	−0.881625	+	0.471951i	$0.843550\pi$
$710$	91597.1	+	13169.7i	0.181704	+	0.0261251i
$711$	−32087.9	−	49929.7i	−0.0634749	−	0.0987689i
$712$		−	519005.i		−	1.02379i
$713$	−37056.7	+	517669.i	−0.0728932	+	1.01829i
$714$	−26916.0			−0.0527975
$715$	−43942.5	+	28240.1i	−0.0859554	+	0.0552402i
$716$	−21032.6	+	146285.i	−0.0410267	+	0.285347i
$717$	60471.3	−	132414.i	0.117628	−	0.257570i
$718$	−52220.7	−	177848.i	−0.101296	−	0.344984i
$719$	21483.4	+	47042.0i	0.0415570	+	0.0909972i	0.929272	−	0.369396i	$-0.120436\pi$
$719$	21483.4	+	47042.0i	0.0415570	+	0.0909972i	−0.887715	+	0.460394i	$0.847708\pi$
$720$	−93969.6	+	81425.1i	−0.181268	+	0.157070i
$721$	24069.2	+	167405.i	0.0463012	+	0.322032i
$722$	288755.	+	84786.0i	0.553930	+	0.162648i
$723$	−3407.81	−	2952.89i	−0.00651927	−	0.00564898i
$724$	78444.0	−	122061.i	0.149652	−	0.232863i
$725$	−9232.64	−	5933.46i	−0.0175651	−	0.0112884i
$726$	41533.6	−	47932.3i	0.0788000	−	0.0909401i
$727$	187218.	−	637607.i	0.354225	−	1.20638i	−0.569070	−	0.822289i	$-0.692697\pi$
$727$	187218.	−	637607.i	0.354225	−	1.20638i	0.923295	−	0.384091i	$-0.125485\pi$
$728$	316833.	−	45553.7i	0.597816	−	0.0859530i
$729$	249061.	+	287432.i	0.468653	+	0.540854i
$730$	−9331.14	+	4261.39i	−0.0175101	+	0.00799660i
$731$	58449.4	−	17162.3i	0.109382	−	0.0321174i
$732$	24935.9	+	11387.8i	0.0465374	+	0.0212529i
$733$	−675627.	−	97140.5i	−1.25747	−	0.180797i	−0.518821	−	0.854883i	$-0.673629\pi$
$733$	−675627.	−	97140.5i	−1.25747	−	0.180797i	−0.738653	+	0.674086i	$0.764538\pi$
$734$	82418.1	+	128245.i	0.152979	+	0.238039i
$735$			53811.8i			0.0996100i
$736$	297695.	+	162578.i	0.549562	+	0.300128i
$737$	−20031.8			−0.0368795
$738$	534282.	−	343362.i	0.980974	−	0.630434i
$739$	81537.5	−	567106.i	0.149303	−	1.03842i	−0.768061	−	0.640376i	$-0.778778\pi$
$739$	81537.5	−	567106.i	0.149303	−	1.03842i	0.917364	−	0.398049i	$-0.130312\pi$
$740$	15056.6	−	32969.5i	0.0274957	−	0.0602072i
$741$	−7330.91	−	24966.8i	−0.0133512	−	0.0454701i
$742$	513015.	+	1.12335e6i	0.931799	+	2.04036i
$743$	−172802.	+	149734.i	−0.313020	+	0.271233i	−0.797174	−	0.603749i	$-0.793673\pi$
$743$	−172802.	+	149734.i	−0.313020	+	0.271233i	0.484154	+	0.874983i	$0.339127\pi$
$744$	19460.3	+	135349.i	0.0351563	+	0.244517i
$745$	276772.	+	81267.7i	0.498666	+	0.146422i
$746$	476809.	+	413157.i	0.856775	+	0.742400i
$747$	36849.2	−	57338.4i	0.0660369	−	0.102755i
$748$	18431.6	+	11845.3i	0.0329428	+	0.0211710i
$749$	249191.	−	287581.i	0.444189	−	0.512622i
$750$	−2582.46	+	8795.05i	−0.00459104	+	0.0156356i
$751$	−796827.	+	114566.i	−1.41281	+	0.203132i	−0.806095	−	0.591787i	$-0.798423\pi$
$751$	−796827.	+	114566.i	−1.41281	+	0.203132i	−0.606717	+	0.794918i	$0.707514\pi$
$752$	137646.	+	158852.i	0.243405	+	0.280904i
$753$	82975.0	−	37893.4i	0.146338	−	0.0668304i
$754$	18302.4	−	5374.06i	0.0321932	−	0.00945279i
$755$	−432500.	−	197516.i	−0.758739	−	0.346504i
$756$	−113878.	−	16373.2i	−0.199249	−	0.0286477i
$757$	137546.	+	214025.i	0.240024	+	0.373485i	0.940277	−	0.340410i	$-0.110566\pi$
$757$	137546.	+	214025.i	0.240024	+	0.373485i	−0.700253	+	0.713895i	$0.746929\pi$
$758$			465333.i			0.809889i
$759$	44710.1	+	59733.4i	0.0776108	+	0.103689i
$760$	152910.			0.264734
$761$	388265.	−	249523.i	0.670438	−	0.430864i	−0.160645	−	0.987012i	$-0.551358\pi$
$761$	388265.	−	249523.i	0.670438	−	0.430864i	0.831083	+	0.556148i	$0.187721\pi$
$762$	19572.6	−	136130.i	0.0337084	−	0.234447i
$763$	354708.	−	776703.i	0.609288	−	1.33415i
$764$	−12830.6	−	43696.8i	−0.0219816	−	0.0748623i
$765$	21167.0	+	46349.3i	0.0361690	+	0.0791991i
$766$	398126.	−	344978.i	0.678520	−	0.587941i
$767$	21005.0	+	146093.i	0.0357053	+	0.248336i
$768$	109037.	+	32016.1i	0.184863	+	0.0542808i
$769$	−806527.	−	698859.i	−1.36385	−	1.18178i	−0.964220	−	0.265104i	$-0.914594\pi$
$769$	−806527.	−	698859.i	−1.36385	−	1.18178i	−0.399628	−	0.916677i	$-0.630861\pi$
$770$	−96879.6	+	150748.i	−0.163400	+	0.254255i
$771$	−31365.8	−	20157.6i	−0.0527652	−	0.0339102i
$772$	209264.	−	241503.i	0.351123	−	0.405218i
$773$	12255.3	−	41737.7i	0.0205100	−	0.0698506i	−0.948602	−	0.316471i	$-0.897502\pi$
$773$	12255.3	−	41737.7i	0.0205100	−	0.0698506i	0.969112	+	0.246621i	$0.0793201\pi$
$774$	−257179.	+	36976.8i	−0.429294	+	0.0617231i
$775$	−80309.2	−	92681.8i	−0.133709	−	0.154309i
$776$	413897.	−	189020.i	0.687335	−	0.313895i
$777$	−82173.7	+	24128.4i	−0.136110	+	0.0399656i
$778$	41828.9	+	19102.6i	0.0691062	+	0.0315597i
$779$	−488804.	−	70279.5i	−0.805490	−	0.115812i
$780$	4206.61	+	6545.61i	0.00691422	+	0.0107587i
$781$			177990.i			0.291806i
$782$	−72595.9	+	72586.9i	−0.118713	+	0.118698i
$783$	−27750.4			−0.0452633
$784$	292344.	−	187878.i	0.475623	−	0.305664i
$785$	−52779.6	+	367090.i	−0.0856499	+	0.595708i
$786$	−49950.7	+	109377.i	−0.0808530	+	0.177043i
$787$	186410.	+	634855.i	0.300968	+	1.02500i	0.961637	+	0.274326i	$0.0884546\pi$
$787$	186410.	+	634855.i	0.300968	+	1.02500i	−0.660669	+	0.750677i	$0.729727\pi$
$788$	58063.6	+	127141.i	0.0935085	+	0.204755i
$789$	−186608.	+	161697.i	−0.299762	+	0.259745i
$790$	4021.24	+	27968.3i	0.00644326	+	0.0448139i
$791$	429011.	+	125969.i	0.685670	+	0.201331i
$792$	−285858.	−	247698.i	−0.455722	−	0.394886i
$793$	93507.7	−	145501.i	0.148697	−	0.231376i
$794$	−119621.	−	76875.6i	−0.189743	−	0.121940i
$795$	−79568.6	+	91827.0i	−0.125895	+	0.145290i
$796$	77627.8	−	264376.i	0.122515	−	0.417249i
$797$	−268774.	+	38643.9i	−0.423127	+	0.0608365i	−0.350590	−	0.936529i	$-0.614019\pi$
$797$	−268774.	+	38643.9i	−0.423127	+	0.0608365i	−0.0725377	+	0.997366i	$0.523110\pi$
$798$	−58456.8	−	67462.8i	−0.0917972	−	0.105940i
$799$	78351.8	−	35782.1i	0.122731	−	0.0560495i
$800$	−76903.7	+	22581.0i	−0.120162	+	0.0352828i
$801$	521741.	+	238271.i	0.813186	+	0.371369i
$802$	217746.	+	31307.1i	0.338533	+	0.0486737i
$803$	−10667.2	−	16598.4i	−0.0165431	−	0.0257416i
$804$			2983.91i			0.00461608i
$805$	289938.	+	289974.i	0.447418	+	0.447474i
$806$	213149.			0.328105
$807$	−163227.	+	104900.i	−0.250637	+	0.161075i
$808$	−98530.3	+	685293.i	−0.150920	+	1.04967i
$809$	−406636.	+	890409.i	−0.621311	+	1.36048i	0.293252	+	0.956035i	$0.405263\pi$
$809$	−406636.	+	890409.i	−0.621311	+	1.36048i	−0.914562	+	0.404445i	$0.867465\pi$
$810$	−57881.2	−	197125.i	−0.0882200	−	0.300450i
$811$	294706.	+	645316.i	0.448071	+	0.981139i	0.990046	+	0.140744i	$0.0449496\pi$
$811$	294706.	+	645316.i	0.448071	+	0.981139i	−0.541975	+	0.840395i	$0.682323\pi$
$812$	−24152.9	+	20928.6i	−0.0366317	+	0.0317415i
$813$	2925.50	+	20347.3i	0.00442608	+	0.0307841i
$814$	−136962.	−	40215.6i	−0.206705	−	0.0606940i
$815$	−104385.	−	90450.3i	−0.157153	−	0.136174i
$816$	−9245.99	+	14387.0i	−0.0138859	+	0.0216068i
$817$	169958.	+	109225.i	0.254623	+	0.163636i
$818$	−181765.	+	209769.i	−0.271647	+	0.313497i
$819$	−99661.6	+	339416.i	−0.148580	+	0.506017i
$820$	146163.	−	21015.1i	0.217375	−	0.0312538i
$821$	−781546.	−	901952.i	−1.15949	−	1.33813i	−0.931189	−	0.364536i	$-0.881228\pi$
$821$	−781546.	−	901952.i	−1.15949	−	1.33813i	−0.228303	−	0.973590i	$-0.573318\pi$
$822$	−133056.	+	60764.4i	−0.196920	+	0.0899303i
$823$	−342195.	+	100478.i	−0.505213	+	0.148344i	−0.524400	−	0.851472i	$-0.675710\pi$
$823$	−342195.	+	100478.i	−0.505213	+	0.148344i	0.0191873	+	0.999816i	$0.493892\pi$
$824$	154598.	+	70602.6i	0.227693	+	0.103984i
$825$	−17451.2	−	2509.10i	−0.0256399	−	0.00368647i
$826$	273746.	+	425957.i	0.401225	+	0.624318i
$827$			779970.i			1.14043i	0.821497	+	0.570213i	$0.193139\pi$
$827$			779970.i			1.14043i	−0.821497	+	0.570213i	$0.806861\pi$
$828$	−171201.	+	128143.i	−0.249715	+	0.186910i
$829$	469288.			0.682859			0.341429	−	0.939907i	$-0.389089\pi$
$829$	469288.			0.682859			0.341429	+	0.939907i	$0.389089\pi$
$830$	−27297.5	+	17543.0i	−0.0396248	+	0.0254653i
$831$	34163.9	−	237615.i	0.0494727	−	0.344090i
$832$	121484.	−	266012.i	0.175498	−	0.384286i
$833$	−40121.1	−	136640.i	−0.0578206	−	0.196919i
$834$	39686.5	+	86901.2i	0.0570572	+	0.124938i
$835$	410201.	−	355441.i	0.588334	−	0.509794i
$836$	10341.0	+	71923.3i	0.0147962	+	0.102910i
$837$	−297529.	−	87362.3i	−0.424696	−	0.124702i
$838$	−710658.	−	615789.i	−1.01198	−	0.876887i
$839$	−590077.	+	918178.i	−0.838272	+	1.30438i	0.112238	+	0.993681i	$0.464198\pi$
$839$	−590077.	+	918178.i	−0.838272	+	1.30438i	−0.950510	+	0.310695i	$0.899438\pi$
$840$	90888.8	+	58410.7i	0.128811	+	0.0827816i
$841$	458122.	−	528702.i	0.647723	−	0.747513i
$842$	−232714.	+	792551.i	−0.328245	+	1.11790i
$843$	−7167.24	+	1030.49i	−0.0100855	+	0.00145007i
$844$	99784.5	+	115157.i	0.140081	+	0.161662i
$845$	−245810.	+	112258.i	−0.344260	+	0.157218i
$846$	−352506.	+	103505.i	−0.492522	+	0.144618i
$847$	609848.	+	278508.i	0.850070	+	0.388214i
$848$	776675.	+	111669.i	1.08006	+	0.155289i
$849$	133715.	+	208065.i	0.185509	+	0.288658i
$850$		−	24258.0i		−	0.0335751i
$851$	−156564.	+	286683.i	−0.216188	+	0.395861i
$852$	26513.2			0.0365244
$853$	−217921.	+	140049.i	−0.299502	+	0.192478i	−0.681757	−	0.731578i	$-0.738784\pi$
$853$	−217921.	+	140049.i	−0.299502	+	0.192478i	0.382255	+	0.924057i	$0.375148\pi$
$854$	84441.1	−	587301.i	0.115781	−	0.805276i
$855$	−70199.8	+	153716.i	−0.0960292	+	0.210275i
$856$	−107732.	−	366903.i	−0.147028	−	0.500730i
$857$	134438.	+	294378.i	0.183046	+	0.400814i	0.978804	−	0.204801i	$-0.0656546\pi$
$857$	134438.	+	294378.i	0.183046	+	0.400814i	−0.795758	+	0.605615i	$0.792927\pi$
$858$	23158.6	−	20067.1i	0.0314585	−	0.0272589i
$859$	7992.32	+	55587.8i	0.0108315	+	0.0753344i	0.994520	−	0.104545i	$-0.0333385\pi$
$859$	7992.32	+	55587.8i	0.0108315	+	0.0753344i	−0.983689	+	0.179879i	$0.942429\pi$
$860$	−57964.0	−	17019.8i	−0.0783722	−	0.0230121i
$861$	−263696.	−	228494.i	−0.355711	−	0.308225i
$862$	557493.	−	867476.i	0.750282	−	1.16746i
$863$	−470061.	−	302090.i	−0.631150	−	0.405616i	0.185585	−	0.982628i	$-0.440582\pi$
$863$	−470061.	−	302090.i	−0.631150	−	0.405616i	−0.816735	+	0.577013i	$0.804218\pi$
$864$	−132717.	+	153163.i	−0.177786	+	0.205176i
$865$	143810.	−	489771.i	0.192201	−	0.654578i
$866$	−175466.	+	25228.2i	−0.233968	+	0.0336395i
$867$	−104825.	−	120974.i	−0.139452	−	0.160936i
$868$	−324844.	+	148351.i	−0.431156	+	0.196902i
$869$	−52146.2	+	15311.5i	−0.0690531	+	0.0202758i
$870$	5856.54	+	2674.59i	0.00773753	+	0.00353361i
$871$	18634.7	+	2679.26i	0.0245632	+	0.00353166i
$872$	−463900.	−	721843.i	−0.610087	−	0.949314i
$873$			502856.i			0.659804i
$874$	−339599.	−	24309.8i	−0.444574	−	0.0318242i
$875$	−96895.1			−0.126557
$876$	−2472.48	+	1588.97i	−0.00322199	+	0.00207065i
$877$	−49028.4	+	341000.i	−0.0637454	+	0.443359i	0.932806	+	0.360379i	$0.117353\pi$
$877$	−49028.4	+	341000.i	−0.0637454	+	0.443359i	−0.996551	+	0.0829795i	$0.973556\pi$
$878$	380248.	−	832627.i	0.493263	−	1.08009i
$879$	−46689.5	−	159010.i	−0.0604284	−	0.205800i
$880$	47297.7	+	103568.i	0.0610766	+	0.133739i
$881$	676513.	−	586202.i	0.871615	−	0.755258i	−0.0992055	−	0.995067i	$-0.531630\pi$
$881$	676513.	−	586202.i	0.871615	−	0.755258i	0.970820	+	0.239809i	$0.0770847\pi$
$882$	86442.5	+	601221.i	0.111119	+	0.772852i
$883$	35325.2	+	10372.4i	0.0453068	+	0.0133033i	0.304307	−	0.952574i	$-0.401575\pi$
$883$	35325.2	+	10372.4i	0.0453068	+	0.0133033i	−0.259001	+	0.965877i	$0.583393\pi$
$884$	−15561.8	−	13484.4i	−0.0199138	−	0.0172554i
$885$	−26933.5	+	41909.3i	−0.0343879	+	0.0535086i
$886$	−579987.	−	372735.i	−0.738841	−	0.474824i
$887$	59936.9	−	69170.8i	0.0761810	−	0.0879176i	−0.716380	−	0.697711i	$-0.754202\pi$
$887$	59936.9	−	69170.8i	0.0761810	−	0.0879176i	0.792561	+	0.609793i	$0.208748\pi$
$888$	−24246.8	+	82577.0i	−0.0307488	+	0.104721i
$889$	1.43900e6	−	206897.i	1.82078	−	0.261788i
$890$	−178820.	−	206369.i	−0.225754	−	0.260534i
$891$	359449.	−	164155.i	0.452774	−	0.206775i
$892$	−144853.	+	42532.8i	−0.182053	+	0.0534557i
$893$	259852.	+	118670.i	0.325853	+	0.148812i
$894$	−167500.	−	24082.8i	−0.209575	−	0.0301323i
$895$	170154.	+	264764.i	0.212420	+	0.330532i
$896$		−	291933.i		−	0.363636i
$897$	−33602.4	−	61547.3i	−0.0417624	−	0.0764934i
$898$	−710182.			−0.880677
$899$	−72464.0	+	46569.8i	−0.0896608	+	0.0576215i
$900$	7191.28	−	50016.5i	0.00887812	−	0.0617487i
$901$	133577.	−	292494.i	0.164544	−	0.360302i
$902$	−163843.	−	558000.i	−0.201380	−	0.685837i
$903$	59298.5	+	129846.i	0.0727224	+	0.159240i
$904$	339571.	−	294240.i	0.415522	−	0.360052i
$905$	−43973.4	−	305842.i	−0.0536900	−	0.373422i
$906$	267632.	+	78584.0i	0.326049	+	0.0957365i
$907$	−839418.	−	727360.i	−1.02038	−	0.884168i	−0.0270732	−	0.999633i	$-0.508619\pi$
$907$	−839418.	−	727360.i	−1.02038	−	0.884168i	−0.993312	+	0.115465i	$0.963164\pi$
$908$	264543.	−	411637.i	0.320867	−	0.499279i
$909$	−643671.	−	413662.i	−0.778997	−	0.500631i
$910$	110285.	−	127276.i	0.133179	−	0.153696i
$911$	290014.	−	987698.i	0.349448	−	1.19011i	−0.577962	−	0.816064i	$-0.696152\pi$
$911$	290014.	−	987698.i	0.349448	−	1.19011i	0.927410	−	0.374047i	$-0.122030\pi$
$912$	−56140.7	+	8071.81i	−0.0674975	+	0.00970468i
$913$	−40871.1	−	47167.8i	−0.0490315	−	0.0565853i
$914$	418265.	−	191015.i	0.500678	−	0.228652i
$915$	56013.2	−	16447.0i	0.0669034	−	0.0196446i
$916$	325514.	+	148657.i	0.387953	+	0.177172i
$917$	−1.25812e6	−	180890.i	−1.49617	−	0.215117i
$918$	−33161.5	−	51600.3i	−0.0393504	−	0.0612304i
$919$		−	387408.i		−	0.458709i	−0.973343	−	0.229355i	$-0.926338\pi$
$919$		−	387408.i		−	0.458709i	0.973343	−	0.229355i	$-0.0736616\pi$
$920$	402661.	−	87567.4i	0.475734	−	0.103459i
$921$	67679.6			0.0797881
$922$	−762807.	+	490226.i	−0.897331	+	0.576679i
$923$	23806.3	−	165576.i	0.0279440	−	0.194355i
$924$	−21327.6	+	46701.0i	−0.0249803	+	0.0546993i
$925$	−21745.7	−	74058.9i	−0.0254149	−	0.0865553i
$926$	51862.7	+	113563.i	0.0604830	+	0.132439i
$927$	−141950.	+	123000.i	−0.165186	+	0.143135i
$928$	8011.88	+	55723.9i	0.00930333	+	0.0647061i
$929$	−178281.	−	52348.1i	−0.206573	−	0.0606554i	0.176809	−	0.984245i	$-0.443423\pi$
$929$	−178281.	−	52348.1i	−0.206573	−	0.0606554i	−0.383382	+	0.923590i	$0.625241\pi$
$930$	54371.4	+	47113.1i	0.0628644	+	0.0544723i
$931$	255341.	−	397318.i	0.294592	−	0.458394i
$932$	398629.	+	256183.i	0.458920	+	0.294930i
$933$	−100214.	+	115653.i	−0.115124	+	0.132860i
$934$	−133647.	+	455158.i	−0.153202	+	0.521758i
$935$	46183.1	−	6640.12i	0.0528275	−	0.00759544i
$936$	232791.	+	268655.i	0.265714	+	0.306651i
$937$	−1.04686e6	+	478085.i	−1.19237	+	0.544536i	−0.909935	−	0.414752i	$-0.863868\pi$
$937$	−1.04686e6	+	478085.i	−1.19237	+	0.544536i	−0.282432	+	0.959287i	$0.591141\pi$
$938$	61968.6	−	18195.6i	0.0704314	−	0.0206805i
$939$	−30665.8	−	14004.6i	−0.0347795	−	0.0158833i
$940$	−84551.0	−	12156.6i	−0.0956893	−	0.0137580i
$941$	−273075.	−	424913.i	−0.308391	−	0.479866i	0.652117	−	0.758119i	$-0.273881\pi$
$941$	−273075.	−	424913.i	−0.308391	−	0.479866i	−0.960508	+	0.278252i	$0.910245\pi$
$942$		−	217567.i		−	0.245183i
$943$	−1.32742e6	+	94856.6i	−1.49275	+	0.106670i
$944$	321717.			0.361018
$945$	−206110.	+	132459.i	−0.230800	+	0.148326i
$946$	−33859.3	+	235497.i	−0.0378352	+	0.263150i
$947$	182762.	−	400192.i	0.203791	−	0.446240i	−0.779948	−	0.625844i	$-0.784755\pi$
$947$	182762.	−	400192.i	0.203791	−	0.446240i	0.983739	+	0.179604i	$0.0574818\pi$
$948$	2280.78	+	7767.62i	0.00253785	+	0.00864314i
$949$	7703.13	+	16867.5i	0.00855333	+	0.0187292i
$950$	60800.7	−	52684.1i	0.0673692	−	0.0583758i
$951$	−15222.1	−	105872.i	−0.0168312	−	0.117063i
$952$	−274336.	−	80552.4i	−0.302698	−	0.0888802i
$953$	694245.	+	601567.i	0.764411	+	0.662366i	0.947148	−	0.320796i	$-0.103950\pi$
$953$	694245.	+	601567.i	0.764411	+	0.662366i	−0.182737	+	0.983162i	$0.558496\pi$
$954$	−741482.	+	1.15377e6i	−0.814712	+	1.26772i
$955$	−81587.7	−	52433.2i	−0.0894577	−	0.0574910i
$956$	250180.	−	288723.i	0.273739	−	0.315912i
$957$	−3488.86	+	11882.0i	−0.00380943	+	0.0129737i
$958$	−813730.	+	116997.i	−0.886644	+	0.127480i
$959$	−1.01256e6	−	1.16856e6i	−1.10099	−	1.27061i
$960$	89786.6	−	41004.2i	0.0974247	−	0.0444924i
$961$	−37425.3	+	10989.1i	−0.0405246	+	0.0118991i
$962$	122030.	+	55729.4i	0.131861	+	0.0602191i
$963$	418296.	+	60141.9i	0.451057	+	0.0648521i
$964$	−6397.99	−	9955.47i	−0.00688477	−	0.0107129i
$965$		−	680510.i		−	0.730768i
$966$	−192569.	−	144174.i	−0.206364	−	0.154502i
$967$	1.39069e6			1.48722			0.743612	−	0.668612i	$-0.233111\pi$
$967$	1.39069e6			1.48722			0.743612	+	0.668612i	$0.233111\pi$
$968$	566773.	−	364243.i	0.604865	−	0.388723i
$969$	−3307.80	+	23006.2i	−0.00352283	+	0.0245018i
$970$	99449.6	−	217764.i	0.105696	−	0.231442i
$971$	80388.7	+	273779.i	0.0852622	+	0.290376i	0.991076	−	0.133300i	$-0.0425575\pi$
$971$	80388.7	+	273779.i	0.0852622	+	0.290376i	−0.905813	+	0.423677i	$0.860739\pi$
$972$	−80288.2	−	175807.i	−0.0849805	−	0.186081i
$973$	−763208.	+	661324.i	−0.806153	+	0.698536i
$974$	66100.7	+	459740.i	0.0696768	+	0.484613i
$975$	15898.4	+	4668.20i	0.0167242	+	0.00491067i
$976$	−284916.	−	246881.i	−0.299100	−	0.259172i
$977$	−275166.	+	428167.i	−0.288274	+	0.448563i	−0.954942	−	0.296791i	$-0.904083\pi$
$977$	−275166.	+	428167.i	−0.288274	+	0.448563i	0.666668	+	0.745355i	$0.267720\pi$
$978$	68165.5	+	43807.3i	0.0712668	+	0.0458004i
$979$	343943.	−	396931.i	0.358857	−	0.414143i
$980$	−39787.9	+	135505.i	−0.0414285	+	0.141093i
$981$	938620.	−	134953.i	0.975331	−	0.140231i
$982$	−542457.	−	626029.i	−0.562526	−	0.649190i
$983$	692644.	−	316320.i	0.716808	−	0.327355i	−0.0234066	−	0.999726i	$-0.507451\pi$
$983$	692644.	−	316320.i	0.716808	−	0.327355i	0.740214	+	0.672371i	$0.234724\pi$
$984$	−336430.	+	98784.6i	−0.347459	+	0.102023i
$985$	270755.	+	123650.i	0.279064	+	0.127444i
$986$	−16865.2	−	2424.84i	−0.0173475	−	0.00249419i
$987$	109123.	+	169798.i	0.112016	+	0.174301i
$988$		−	68290.1i		−	0.0699590i
$989$	510103.	+	190295.i	0.521514	+	0.194551i
$990$	−199007.			−0.203047
$991$	790318.	−	507907.i	0.804739	−	0.517174i	−0.0724204	−	0.997374i	$-0.523072\pi$
$991$	790318.	−	507907.i	0.804739	−	0.517174i	0.877159	+	0.480200i	$0.159436\pi$
$992$	−89526.6	+	622671.i	−0.0909764	+	0.632755i
$993$	106239.	−	232630.i	0.107742	−	0.235922i
$994$	−161675.	−	550616.i	−0.163633	−	0.557283i
$995$	−243754.	−	533747.i	−0.246210	−	0.539124i
$996$	−7026.04	+	6088.10i	−0.00708259	+	0.00613710i
$997$	−183889.	−	1.27898e6i	−0.184997	−	1.28668i	−0.844734	−	0.535187i	$-0.820241\pi$
$997$	−183889.	−	1.27898e6i	−0.184997	−	1.28668i	0.659737	−	0.751497i	$-0.270668\pi$
$998$	−1.47288e6	−	432478.i	−1.47879	−	0.434213i
$999$	−147497.	−	127807.i	−0.147793	−	0.128063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.h.a.11.10	✓	320
23.21	odd	22	inner	115.5.h.a.21.10	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.h.a.11.10	✓	320	1.1	even	1	trivial
115.5.h.a.21.10	yes	320	23.21	odd	22	inner

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75822 + 1.77260i) q^{2} +(-0.284694 + 1.98009i) q^{3} +(-2.18096 + 4.77564i) q^{4} +(3.14987 + 10.7275i) q^{5} +(-2.72467 - 5.96619i) q^{6} +(52.3980 - 45.4031i) q^{7} +(-9.91547 - 68.9636i) q^{8} +(73.8792 + 21.6929i) q^{9} +O(q^{10})\)	\(q+(-2.75822 + 1.77260i) q^{2} +(-0.284694 + 1.98009i) q^{3} +(-2.18096 + 4.77564i) q^{4} +(3.14987 + 10.7275i) q^{5} +(-2.72467 - 5.96619i) q^{6} +(52.3980 - 45.4031i) q^{7} +(-9.91547 - 68.9636i) q^{8} +(73.8792 + 21.6929i) q^{9} +(-27.7036 - 24.0053i) q^{10} +(38.1187 - 59.3138i) q^{11} +(-8.83530 - 5.67810i) q^{12} +(-43.3933 + 50.0786i) q^{13} +(-64.0437 + 218.113i) q^{14} +(-22.1381 + 3.18298i) q^{15} +(94.5851 + 109.157i) q^{16} +(53.8403 - 24.5880i) q^{17} +(-242.228 + 71.1247i) q^{18} +(178.560 + 81.5455i) q^{19} +(-58.1002 - 8.35354i) q^{20} +(74.9850 + 116.679i) q^{21} +231.170i q^{22} +(516.904 + 112.479i) q^{23} +139.377 q^{24} +(-105.157 + 67.5801i) q^{25} +(30.9191 - 215.047i) q^{26} +(-131.300 + 287.506i) q^{27} +(102.551 + 349.256i) q^{28} +(36.4730 + 79.8647i) q^{29} +(55.4197 - 48.0215i) q^{30} +(139.623 + 971.098i) q^{31} +(615.230 + 180.648i) q^{32} +(106.595 + 92.3649i) q^{33} +(-104.919 + 163.257i) q^{34} +(652.106 + 419.083i) q^{35} +(-264.725 + 305.509i) q^{36} +(-173.965 + 592.471i) q^{37} +(-637.056 + 91.5948i) q^{38} +(-86.8064 - 100.180i) q^{39} +(708.572 - 323.594i) q^{40} +(-2413.80 + 708.757i) q^{41} +(-413.651 - 188.908i) q^{42} +(1018.72 + 146.469i) q^{43} +(200.126 + 311.402i) q^{44} +860.866i q^{45} +(-1625.12 + 606.023i) q^{46} +1455.26 q^{47} +(-243.069 + 156.211i) q^{48} +(342.408 - 2381.50i) q^{49} +(170.253 - 372.802i) q^{50} +(33.3586 + 113.609i) q^{51} +(-144.518 - 316.450i) q^{52} +(4105.70 - 3557.61i) q^{53} +(-147.480 - 1025.75i) q^{54} +(756.355 + 222.086i) q^{55} +(-3650.71 - 3163.36i) q^{56} +(-212.303 + 330.350i) q^{57} +(-242.169 - 155.633i) q^{58} +(1458.64 - 1683.36i) q^{59} +(33.0816 - 112.666i) q^{60} +(-2583.58 + 371.462i) q^{61} +(-2106.48 - 2431.01i) q^{62} +(4856.05 - 2217.68i) q^{63} +(-4234.52 + 1243.37i) q^{64} +(-673.899 - 307.759i) q^{65} +(-457.739 - 65.8129i) q^{66} +(-153.603 - 239.011i) q^{67} +310.747i q^{68} +(-369.879 + 991.495i) q^{69} -2541.52 q^{70} +(-2123.71 + 1364.82i) q^{71} +(763.473 - 5310.07i) q^{72} +(116.250 - 254.552i) q^{73} +(-570.381 - 1942.54i) q^{74} +(-103.877 - 227.460i) q^{75} +(-778.864 + 674.889i) q^{76} +(-695.690 - 4838.63i) q^{77} +(417.011 + 122.445i) q^{78} +(-582.546 - 504.779i) q^{79} +(-873.047 + 1358.49i) q^{80} +(4714.87 + 3030.06i) q^{81} +(5401.47 - 6233.63i) q^{82} +(249.388 - 849.337i) q^{83} +(-720.755 + 103.629i) q^{84} +(433.357 + 500.121i) q^{85} +(-3069.48 + 1401.78i) q^{86} +(-168.523 + 49.4829i) q^{87} +(-4468.46 - 2040.68i) q^{88} +(7373.36 + 1060.13i) q^{89} +(-1525.97 - 2374.46i) q^{90} +4594.21i q^{91} +(-1664.51 + 2223.23i) q^{92} -1962.62 q^{93} +(-4013.94 + 2579.60i) q^{94} +(-312.337 + 2172.35i) q^{95} +(-532.852 + 1166.78i) q^{96} +(1839.93 + 6266.21i) q^{97} +(3277.02 + 7175.67i) q^{98} +(4102.87 - 3555.16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 12 q^{2} - 272 q^{4} + 166 q^{6} - 246 q^{8} - 896 q^{9}+O(q^{10}) \) 320 * q - 12 * q^2 - 272 * q^4 + 166 * q^6 - 246 * q^8 - 896 * q^9	\( 320 q - 12 q^{2} - 272 q^{4} + 166 q^{6} - 246 q^{8} - 896 q^{9} + 30 q^{12} - 204 q^{13} - 2264 q^{16} + 990 q^{17} - 50 q^{18} + 1914 q^{19} + 2706 q^{21} + 258 q^{23} - 7260 q^{24} + 4000 q^{25} - 8922 q^{26} - 6642 q^{27} + 888 q^{29} + 3844 q^{31} + 10512 q^{32} - 12826 q^{34} - 5850 q^{35} - 11920 q^{36} + 20790 q^{38} + 5044 q^{39} + 24200 q^{40} + 10530 q^{41} + 14432 q^{43} + 1914 q^{44} - 9812 q^{46} + 10272 q^{47} - 55958 q^{48} - 16022 q^{49} - 6750 q^{50} - 34848 q^{51} + 7966 q^{52} - 14784 q^{53} - 42582 q^{54} - 7000 q^{55} - 14454 q^{56} - 5082 q^{57} + 92648 q^{58} + 12330 q^{59} + 34650 q^{60} + 22484 q^{61} + 70986 q^{62} + 55550 q^{63} + 20882 q^{64} + 22528 q^{66} + 5852 q^{67} + 17060 q^{69} + 4800 q^{70} - 42486 q^{71} - 180818 q^{72} - 11284 q^{73} - 111870 q^{74} - 61952 q^{76} - 72522 q^{77} - 72762 q^{78} - 3124 q^{79} + 12332 q^{81} + 83702 q^{82} + 130218 q^{83} + 349492 q^{84} + 12850 q^{85} + 60192 q^{86} + 146516 q^{87} + 88176 q^{88} + 45936 q^{89} + 5790 q^{92} - 36668 q^{93} - 182364 q^{94} - 10800 q^{95} - 67282 q^{96} - 125136 q^{97} - 67860 q^{98} - 283008 q^{99}+O(q^{100}) \) 320 * q - 12 * q^2 - 272 * q^4 + 166 * q^6 - 246 * q^8 - 896 * q^9 + 30 * q^12 - 204 * q^13 - 2264 * q^16 + 990 * q^17 - 50 * q^18 + 1914 * q^19 + 2706 * q^21 + 258 * q^23 - 7260 * q^24 + 4000 * q^25 - 8922 * q^26 - 6642 * q^27 + 888 * q^29 + 3844 * q^31 + 10512 * q^32 - 12826 * q^34 - 5850 * q^35 - 11920 * q^36 + 20790 * q^38 + 5044 * q^39 + 24200 * q^40 + 10530 * q^41 + 14432 * q^43 + 1914 * q^44 - 9812 * q^46 + 10272 * q^47 - 55958 * q^48 - 16022 * q^49 - 6750 * q^50 - 34848 * q^51 + 7966 * q^52 - 14784 * q^53 - 42582 * q^54 - 7000 * q^55 - 14454 * q^56 - 5082 * q^57 + 92648 * q^58 + 12330 * q^59 + 34650 * q^60 + 22484 * q^61 + 70986 * q^62 + 55550 * q^63 + 20882 * q^64 + 22528 * q^66 + 5852 * q^67 + 17060 * q^69 + 4800 * q^70 - 42486 * q^71 - 180818 * q^72 - 11284 * q^73 - 111870 * q^74 - 61952 * q^76 - 72522 * q^77 - 72762 * q^78 - 3124 * q^79 + 12332 * q^81 + 83702 * q^82 + 130218 * q^83 + 349492 * q^84 + 12850 * q^85 + 60192 * q^86 + 146516 * q^87 + 88176 * q^88 + 45936 * q^89 + 5790 * q^92 - 36668 * q^93 - 182364 * q^94 - 10800 * q^95 - 67282 * q^96 - 125136 * q^97 - 67860 * q^98 - 283008 * q^99

Introduction

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