LMFDB - Embedded newform 13.5.f.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,5,Mod(2,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("13.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, 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:	$1.34380952009$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.3
Root			$-0.816521i$ of defining polynomial
Character	$\chi$	$=$	13.7
Dual form			13.5.f.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38644 - 0.639444i) q^{2} +(4.25709 - 7.37349i) q^{3} +(-8.57021 + 4.94801i) q^{4} +(16.9748 + 16.9748i) q^{5} +(5.44434 - 20.3185i) q^{6} +(-50.2192 - 13.4562i) q^{7} +(-45.2402 + 45.2402i) q^{8} +(4.25442 + 7.36887i) q^{9} +O(q^{10})$	\(q+(2.38644 - 0.639444i) q^{2} +(4.25709 - 7.37349i) q^{3} +(-8.57021 + 4.94801i) q^{4} +(16.9748 + 16.9748i) q^{5} +(5.44434 - 20.3185i) q^{6} +(-50.2192 - 13.4562i) q^{7} +(-45.2402 + 45.2402i) q^{8} +(4.25442 + 7.36887i) q^{9} +(51.3637 + 29.6548i) q^{10} +(-23.3915 - 87.2983i) q^{11} +84.2565i q^{12} +(136.315 - 99.8960i) q^{13} -128.449 q^{14} +(197.426 - 52.9003i) q^{15} +(0.133943 - 0.231996i) q^{16} +(218.366 - 126.074i) q^{17} +(14.8649 + 14.8649i) q^{18} +(-91.9552 + 343.182i) q^{19} +(-229.469 - 61.4860i) q^{20} +(-313.007 + 313.007i) q^{21} +(-111.645 - 193.374i) q^{22} +(-735.005 - 424.355i) q^{23} +(140.987 + 526.170i) q^{24} -48.7139i q^{25} +(261.429 - 325.561i) q^{26} +762.094 q^{27} +(496.971 - 133.163i) q^{28} +(-443.792 + 768.670i) q^{29} +(437.319 - 252.486i) q^{30} +(407.191 + 407.191i) q^{31} +(265.116 - 989.427i) q^{32} +(-743.273 - 199.159i) q^{33} +(440.500 - 440.500i) q^{34} +(-624.044 - 1080.88i) q^{35} +(-72.9226 - 42.1019i) q^{36} +(687.857 + 2567.12i) q^{37} +877.782i q^{38} +(-156.277 - 1430.38i) q^{39} -1535.88 q^{40} +(-750.275 + 201.036i) q^{41} +(-546.820 + 947.121i) q^{42} +(2100.14 - 1212.52i) q^{43} +(632.424 + 632.424i) q^{44} +(-52.8671 + 197.303i) q^{45} +(-2025.39 - 542.703i) q^{46} +(-858.063 + 858.063i) q^{47} +(-1.14041 - 1.97525i) q^{48} +(261.571 + 151.018i) q^{49} +(-31.1498 - 116.253i) q^{50} -2146.83i q^{51} +(-673.962 + 1530.62i) q^{52} +39.2320 q^{53} +(1818.69 - 487.316i) q^{54} +(1084.80 - 1878.93i) q^{55} +(2880.69 - 1663.16i) q^{56} +(2138.99 + 2138.99i) q^{57} +(-567.560 + 2118.16i) q^{58} +(1144.84 + 306.759i) q^{59} +(-1430.24 + 1430.24i) q^{60} +(-2410.92 - 4175.84i) q^{61} +(1232.11 + 711.360i) q^{62} +(-114.497 - 427.307i) q^{63} -2526.45i q^{64} +(4009.63 + 618.206i) q^{65} -1901.13 q^{66} +(-3519.36 + 943.010i) q^{67} +(-1247.63 + 2160.96i) q^{68} +(-6257.96 + 3613.04i) q^{69} +(-2180.40 - 2180.40i) q^{70} +(-165.207 + 616.559i) q^{71} +(-525.840 - 140.898i) q^{72} +(1000.63 - 1000.63i) q^{73} +(3283.06 + 5686.42i) q^{74} +(-359.192 - 207.379i) q^{75} +(-909.992 - 3396.14i) q^{76} +4698.81i q^{77} +(-1287.60 - 3313.59i) q^{78} +3698.19 q^{79} +(6.21173 - 1.66443i) q^{80} +(2899.69 - 5022.41i) q^{81} +(-1661.93 + 959.518i) q^{82} +(-3629.57 - 3629.57i) q^{83} +(1133.77 - 4231.29i) q^{84} +(5846.79 + 1566.64i) q^{85} +(4236.52 - 4236.52i) q^{86} +(3778.52 + 6544.59i) q^{87} +(5007.63 + 2891.16i) q^{88} +(-770.586 - 2875.87i) q^{89} +504.656i q^{90} +(-8189.85 + 3182.41i) q^{91} +8398.87 q^{92} +(4735.87 - 1268.97i) q^{93} +(-1499.03 + 2596.40i) q^{94} +(-7386.35 + 4264.51i) q^{95} +(-6166.91 - 6166.91i) q^{96} +(28.3179 - 105.684i) q^{97} +(720.790 + 193.135i) q^{98} +(543.773 - 543.773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9 - 486 * q^10 - 100 * q^11 + 294 * q^13 + 808 * q^14 + 346 * q^15 + 230 * q^16 + 984 * q^17 + 2434 * q^18 - 1498 * q^19 - 3962 * q^20 - 1076 * q^21 - 1524 * q^22 - 1014 * q^23 - 2142 * q^24 + 614 * q^26 + 3352 * q^27 + 5764 * q^28 + 814 * q^29 + 9162 * q^30 + 4060 * q^31 - 4996 * q^32 - 5636 * q^33 - 2502 * q^34 - 4892 * q^35 - 15750 * q^36 - 1790 * q^37 + 6982 * q^39 + 18816 * q^40 + 4280 * q^41 - 1204 * q^42 - 1368 * q^43 + 10736 * q^44 - 6806 * q^45 - 15246 * q^46 + 1484 * q^47 - 3002 * q^48 - 11820 * q^49 - 13574 * q^50 + 1432 * q^52 + 7204 * q^53 + 13240 * q^54 + 6936 * q^55 + 8124 * q^56 + 12736 * q^57 + 3030 * q^58 - 2380 * q^59 - 6472 * q^60 - 162 * q^61 + 19614 * q^62 + 12004 * q^63 - 5248 * q^65 - 23872 * q^66 - 14854 * q^67 - 6444 * q^68 + 2412 * q^69 - 34524 * q^70 - 8050 * q^71 + 15420 * q^72 - 15448 * q^73 - 2882 * q^74 + 8280 * q^75 + 10622 * q^76 - 11672 * q^78 - 17064 * q^79 + 2564 * q^80 + 2128 * q^81 - 5346 * q^82 + 12788 * q^83 + 25948 * q^84 + 35382 * q^85 + 67260 * q^86 + 29342 * q^87 + 40836 * q^88 + 20492 * q^89 + 8996 * q^91 - 49884 * q^92 - 78920 * q^93 - 30606 * q^94 - 98574 * q^95 - 94664 * q^96 + 50944 * q^97 + 61484 * q^98 - 21632 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	2.38644	−	0.639444i	0.596609	−	0.159861i	0.0521372	−	0.998640i	$-0.483397\pi$
$2$	2.38644	−	0.639444i	0.596609	−	0.159861i	0.544472	+	0.838779i	$0.316730\pi$
$3$	4.25709	−	7.37349i	0.473010	−	0.819277i	−0.526513	−	0.850167i	$-0.676501\pi$
$3$	4.25709	−	7.37349i	0.473010	−	0.819277i	0.999523	+	0.0308902i	$0.00983423\pi$
$4$	−8.57021	+	4.94801i	−0.535638	+	0.309251i
$5$	16.9748	+	16.9748i	0.678991	+	0.678991i	0.959772	−	0.280781i	$-0.0905934\pi$
$5$	16.9748	+	16.9748i	0.678991	+	0.678991i	−0.280781	+	0.959772i	$0.590593\pi$
$6$	5.44434	−	20.3185i	0.151232	−	0.564404i
$7$	−50.2192	−	13.4562i	−1.02488	−	0.274616i	−0.293047	−	0.956098i	$-0.594669\pi$
$7$	−50.2192	−	13.4562i	−1.02488	−	0.274616i	−0.731835	+	0.681482i	$0.761336\pi$
$8$	−45.2402	+	45.2402i	−0.706878	+	0.706878i
$9$	4.25442	+	7.36887i	0.0525237	+	0.0909738i
$10$	51.3637	+	29.6548i	0.513637	+	0.296548i
$11$	−23.3915	−	87.2983i	−0.193318	−	0.721474i	−0.992696	−	0.120644i	$-0.961504\pi$
$11$	−23.3915	−	87.2983i	−0.193318	−	0.721474i	0.799378	−	0.600829i	$-0.205163\pi$
$12$			84.2565i			0.585115i
$13$	136.315	−	99.8960i	0.806598	−	0.591100i
$13$	136.315	−	99.8960i	0.806598	−	0.591100i
$14$	−128.449			−0.655354
$15$	197.426	−	52.9003i	0.877451	−	0.235112i
$16$	0.133943	−	0.231996i	0.000523214	−	0.000906234i
$17$	218.366	−	126.074i	0.755592	−	0.436241i	−0.0721191	−	0.997396i	$-0.522976\pi$
$17$	218.366	−	126.074i	0.755592	−	0.436241i	0.827711	+	0.561155i	$0.189643\pi$
$18$	14.8649	+	14.8649i	0.0458793	+	0.0458793i
$19$	−91.9552	+	343.182i	−0.254724	+	0.950642i	0.713520	+	0.700635i	$0.247100\pi$
$19$	−91.9552	+	343.182i	−0.254724	+	0.950642i	−0.968244	+	0.250007i	$0.919567\pi$
$20$	−229.469	−	61.4860i	−0.573672	−	0.153715i
$21$	−313.007	+	313.007i	−0.709765	+	0.709765i
$22$	−111.645	−	193.374i	−0.230671	−	0.399534i
$23$	−735.005	−	424.355i	−1.38942	−	0.802184i	−0.396173	−	0.918176i	$-0.629662\pi$
$23$	−735.005	−	424.355i	−1.38942	−	0.802184i	−0.993250	+	0.115992i	$0.962995\pi$
$24$	140.987	+	526.170i	0.244769	+	0.913489i
$25$		−	48.7139i		−	0.0779423i
$26$	261.429	−	325.561i	0.386730	−	0.481600i
$27$	762.094			1.04540
$28$	496.971	−	133.163i	0.633891	−	0.169851i
$29$	−443.792	+	768.670i	−0.527695	+	0.913995i	0.471784	+	0.881714i	$0.343610\pi$
$29$	−443.792	+	768.670i	−0.527695	+	0.913995i	−0.999479	+	0.0322805i	$0.989723\pi$
$30$	437.319	−	252.486i	0.485910	−	0.280540i
$31$	407.191	+	407.191i	0.423716	+	0.423716i	0.886481	−	0.462765i	$-0.153143\pi$
$31$	407.191	+	407.191i	0.423716	+	0.423716i	−0.462765	+	0.886481i	$0.653143\pi$
$32$	265.116	−	989.427i	0.258903	−	0.966238i
$33$	−743.273	−	199.159i	−0.682528	−	0.182883i
$34$	440.500	−	440.500i	0.381055	−	0.381055i
$35$	−624.044	−	1080.88i	−0.509423	−	0.882347i
$36$	−72.9226	−	42.1019i	−0.0562674	−	0.0324860i
$37$	687.857	+	2567.12i	0.502452	+	1.87518i	0.483476	+	0.875358i	$0.339374\pi$
$37$	687.857	+	2567.12i	0.502452	+	1.87518i	0.0189767	+	0.999820i	$0.493959\pi$
$38$			877.782i			0.607882i
$39$	−156.277	−	1430.38i	−0.102746	−	0.940423i
$40$	−1535.88			−0.959928
$41$	−750.275	+	201.036i	−0.446327	+	0.119593i	−0.474980	−	0.879997i	$-0.657545\pi$
$41$	−750.275	+	201.036i	−0.446327	+	0.119593i	0.0286534	+	0.999589i	$0.490878\pi$
$42$	−546.820	+	947.121i	−0.309989	+	0.536916i
$43$	2100.14	−	1212.52i	1.13583	−	0.655769i	0.190432	−	0.981700i	$-0.439011\pi$
$43$	2100.14	−	1212.52i	1.13583	−	0.655769i	0.945394	+	0.325931i	$0.105678\pi$
$44$	632.424	+	632.424i	0.326665	+	0.326665i
$45$	−52.8671	+	197.303i	−0.0261072	+	0.0974335i
$46$	−2025.39	−	542.703i	−0.957181	−	0.256476i
$47$	−858.063	+	858.063i	−0.388440	+	0.388440i	−0.874131	−	0.485691i	$-0.838568\pi$
$47$	−858.063	+	858.063i	−0.388440	+	0.388440i	0.485691	+	0.874131i	$0.338568\pi$
$48$	−1.14041	−	1.97525i	−0.000494971	−	0.000857315i
$49$	261.571	+	151.018i	0.108942	+	0.0628979i
$50$	−31.1498	−	116.253i	−0.0124599	−	0.0465011i
$51$		−	2146.83i		−	0.825385i
$52$	−673.962	+	1530.62i	−0.249246	+	0.566057i
$53$	39.2320			0.0139665			0.00698326	−	0.999976i	$-0.497777\pi$
$53$	39.2320			0.0139665			0.00698326	+	0.999976i	$0.497777\pi$
$54$	1818.69	−	487.316i	0.623693	−	0.167118i
$55$	1084.80	−	1878.93i	0.358613	−	0.621135i
$56$	2880.69	−	1663.16i	0.918586	−	0.530346i
$57$	2138.99	+	2138.99i	0.658352	+	0.658352i
$58$	−567.560	+	2118.16i	−0.168716	+	0.629656i
$59$	1144.84	+	306.759i	0.328883	+	0.0881238i	0.419482	−	0.907764i	$-0.362212\pi$
$59$	1144.84	+	306.759i	0.328883	+	0.0881238i	−0.0905996	+	0.995887i	$0.528878\pi$
$60$	−1430.24	+	1430.24i	−0.397288	+	0.397288i
$61$	−2410.92	−	4175.84i	−0.647923	−	1.12224i	−0.983618	−	0.180265i	$-0.942304\pi$
$61$	−2410.92	−	4175.84i	−0.647923	−	1.12224i	0.335695	−	0.941971i	$-0.391029\pi$
$62$	1232.11	+	711.360i	0.320529	+	0.185057i
$63$	−114.497	−	427.307i	−0.0288477	−	0.107661i
$64$		−	2526.45i		−	0.616808i
$65$	4009.63	+	618.206i	0.949025	+	0.146321i
$66$	−1901.13			−0.436438
$67$	−3519.36	+	943.010i	−0.783997	+	0.210071i	−0.628546	−	0.777772i	$-0.716350\pi$
$67$	−3519.36	+	943.010i	−0.783997	+	0.210071i	−0.155451	+	0.987844i	$0.549683\pi$
$68$	−1247.63	+	2160.96i	−0.269816	+	0.467335i
$69$	−6257.96	+	3613.04i	−1.31442	+	0.758882i
$70$	−2180.40	−	2180.40i	−0.444980	−	0.444980i
$71$	−165.207	+	616.559i	−0.0327726	+	0.122309i	−0.980374	−	0.197145i	$-0.936833\pi$
$71$	−165.207	+	616.559i	−0.0327726	+	0.122309i	0.947602	+	0.319454i	$0.103500\pi$
$72$	−525.840	−	140.898i	−0.101435	−	0.0271795i
$73$	1000.63	−	1000.63i	0.187771	−	0.187771i	−0.606961	−	0.794732i	$-0.707612\pi$
$73$	1000.63	−	1000.63i	0.187771	−	0.187771i	0.794732	+	0.606961i	$0.207612\pi$
$74$	3283.06	+	5686.42i	0.599535	+	1.03843i
$75$	−359.192	−	207.379i	−0.0638563	−	0.0368674i
$76$	−909.992	−	3396.14i	−0.157547	−	0.587974i
$77$			4698.81i			0.792513i
$78$	−1287.60	−	3313.59i	−0.211636	−	0.544640i
$79$	3698.19			0.592564			0.296282	−	0.955100i	$-0.404253\pi$
$79$	3698.19			0.592564			0.296282	+	0.955100i	$0.404253\pi$
$80$	6.21173	−	1.66443i	0.000970582	−	0.000260067i
$81$	2899.69	−	5022.41i	0.441959	−	0.765495i
$82$	−1661.93	+	959.518i	−0.247164	+	0.142700i
$83$	−3629.57	−	3629.57i	−0.526865	−	0.526865i	0.392771	−	0.919636i	$-0.371516\pi$
$83$	−3629.57	−	3629.57i	−0.526865	−	0.526865i	−0.919636	+	0.392771i	$0.871516\pi$
$84$	1133.77	−	4231.29i	0.160682	−	0.599673i
$85$	5846.79	+	1566.64i	0.809244	+	0.216836i
$86$	4236.52	−	4236.52i	0.572812	−	0.572812i
$87$	3778.52	+	6544.59i	0.499210	+	0.864657i
$88$	5007.63	+	2891.16i	0.646646	+	0.373341i
$89$	−770.586	−	2875.87i	−0.0972840	−	0.363069i	0.900072	−	0.435741i	$-0.143514\pi$
$89$	−770.586	−	2875.87i	−0.0972840	−	0.363069i	−0.997356	+	0.0726728i	$0.976847\pi$
$90$			504.656i			0.0623033i
$91$	−8189.85	+	3182.41i	−0.988993	+	0.384303i
$92$	8398.87			0.992305
$93$	4735.87	−	1268.97i	0.547562	−	0.146719i
$94$	−1499.03	+	2596.40i	−0.169650	+	0.293843i
$95$	−7386.35	+	4264.51i	−0.818432	+	0.472522i
$96$	−6166.91	−	6166.91i	−0.669153	−	0.669153i
$97$	28.3179	−	105.684i	0.00300966	−	0.0112322i	−0.964405	−	0.264431i	$-0.914816\pi$
$97$	28.3179	−	105.684i	0.00300966	−	0.0112322i	0.967414	+	0.253199i	$0.0814826\pi$
$98$	720.790	+	193.135i	0.0750510	+	0.0201098i
$99$	543.773	−	543.773i	0.0554814	−	0.0554814i
$100$	241.037	+	417.489i	0.0241037	+	0.0417489i
$101$	−15761.9	−	9100.14i	−1.54513	−	0.892083i	−0.998502	−	0.0547102i	$-0.982577\pi$
$101$	−15761.9	−	9100.14i	−1.54513	−	0.892083i	−0.546632	−	0.837373i	$-0.684090\pi$
$102$	−1372.77	−	5123.27i	−0.131947	−	0.492432i
$103$			12486.6i			1.17698i	0.808505	+	0.588489i	$0.200277\pi$
$103$			12486.6i			1.17698i	−0.808505	+	0.588489i	$0.799723\pi$
$104$	−1647.61	+	10686.2i	−0.152330	+	0.988002i
$105$	−10626.4			−0.963849
$106$	93.6247	−	25.0867i	0.00833256	−	0.00223270i
$107$	4682.65	−	8110.58i	0.409001	−	0.708410i	−0.585777	−	0.810472i	$-0.699211\pi$
$107$	4682.65	−	8110.58i	0.409001	−	0.708410i	0.994778	+	0.102062i	$0.0325441\pi$
$108$	−6531.31	+	3770.85i	−0.559954	+	0.323290i
$109$	5548.06	+	5548.06i	0.466969	+	0.466969i	0.900931	−	0.433962i	$-0.142885\pi$
$109$	5548.06	+	5548.06i	0.466969	+	0.466969i	−0.433962	+	0.900931i	$0.642885\pi$
$110$	1387.34	−	5177.63i	0.114656	−	0.427903i
$111$	21856.9	+	5856.54i	1.77395	+	0.475330i
$112$	−9.84828	+	9.84828i	−0.000785099	+	0.000785099i
$113$	3975.69	+	6886.09i	0.311355	+	0.539282i	0.978656	−	0.205506i	$-0.0658840\pi$
$113$	3975.69	+	6886.09i	0.311355	+	0.539282i	−0.667301	+	0.744788i	$0.732551\pi$
$114$	6472.31	+	3736.79i	0.498024	+	0.287534i
$115$	−5273.21	−	19679.9i	−0.398730	−	1.48808i
$116$		−	8783.55i		−	0.652761i
$117$	1316.06	+	579.489i	0.0961402	+	0.0423325i
$118$	2928.24			0.210302
$119$	−12662.6	+	3392.94i	−0.894191	+	0.239598i
$120$	−6538.39	+	11324.8i	−0.454055	+	0.786446i
$121$	5605.65	−	3236.42i	0.382873	−	0.221052i
$122$	−8423.73	−	8423.73i	−0.565959	−	0.565959i
$123$	−1711.65	+	6387.97i	−0.113137	+	0.422234i
$124$	−5504.50	−	1474.93i	−0.357993	−	0.0959240i
$125$	11436.1	−	11436.1i	0.731913	−	0.731913i
$126$	−546.478	−	946.528i	−0.0344216	−	0.0596200i
$127$	16381.1	+	9457.66i	1.01563	+	0.586376i	0.912836	−	0.408327i	$-0.133888\pi$
$127$	16381.1	+	9457.66i	1.01563	+	0.586376i	0.102797	+	0.994702i	$0.467221\pi$
$128$	2626.34	+	9801.63i	0.160299	+	0.598244i
$129$		−	20647.2i		−	1.24074i
$130$	9964.04	−	1088.62i	0.589588	−	0.0644156i
$131$	−3296.47			−0.192091			−0.0960454	−	0.995377i	$-0.530619\pi$
$131$	−3296.47			−0.192091			−0.0960454	+	0.995377i	$0.530619\pi$
$132$	7355.45	−	1970.89i	0.422145	−	0.113113i
$133$	9235.84	−	15996.9i	0.522123	−	0.904344i
$134$	−7795.74	+	4500.87i	−0.434158	+	0.250661i
$135$	12936.4	+	12936.4i	0.709815	+	0.709815i
$136$	−4175.32	+	15582.5i	−0.225742	+	0.842480i
$137$	−23571.3	−	6315.91i	−1.25586	−	0.336507i	−0.431264	−	0.902226i	$-0.641932\pi$
$137$	−23571.3	−	6315.91i	−1.25586	−	0.336507i	−0.824599	+	0.565718i	$0.808599\pi$
$138$	−12623.9	+	12623.9i	−0.662881	+	0.662881i
$139$	−788.063	−	1364.97i	−0.0407879	−	0.0706467i	0.844911	−	0.534907i	$-0.179653\pi$
$139$	−788.063	−	1364.97i	−0.0407879	−	0.0706467i	−0.885699	+	0.464261i	$0.846320\pi$
$140$	10696.4	+	6175.55i	0.545733	+	0.315079i
$141$	2674.07	+	9979.77i	0.134504	+	0.501975i
$142$			1577.02i			0.0782097i
$143$	−11909.4	−	9563.36i	−0.582393	−	0.467669i
$144$	2.27940			0.000109925
$145$	−20581.3	+	5514.73i	−0.978895	+	0.262294i
$146$	1748.09	−	3027.79i	0.0820085	−	0.142043i
$147$	2227.06	−	1285.79i	0.103062	−	0.0595027i
$148$	−18597.2	−	18597.2i	−0.849033	−	0.849033i
$149$	2034.98	−	7594.65i	0.0916616	−	0.342086i	−0.904831	−	0.425772i	$-0.860003\pi$
$149$	2034.98	−	7594.65i	0.0916616	−	0.342086i	0.996492	+	0.0836860i	$0.0266693\pi$
$150$	−989.796	−	265.215i	−0.0439909	−	0.0117873i
$151$	−13112.6	+	13112.6i	−0.575089	+	0.575089i	−0.933546	−	0.358457i	$-0.883303\pi$
$151$	−13112.6	+	13112.6i	−0.575089	+	0.575089i	0.358457	+	0.933546i	$0.383303\pi$
$152$	−11365.5	−	19685.7i	−0.491929	−	0.852046i
$153$	1858.04	+	1072.74i	0.0793730	+	0.0458260i
$154$	3004.63	+	11213.4i	0.126692	+	0.472821i
$155$			13824.0i			0.575399i
$156$	8416.89	+	11485.4i	0.345862	+	0.471952i
$157$	212.325			0.00861394			0.00430697	−	0.999991i	$-0.498629\pi$
$157$	212.325			0.00861394			0.00430697	+	0.999991i	$0.498629\pi$
$158$	8825.51	−	2364.79i	0.353529	−	0.0947279i
$159$	167.014	−	289.277i	0.00660630	−	0.0114425i
$160$	21295.6	−	12295.0i	0.831859	−	0.480274i
$161$	31201.2	+	31201.2i	1.20370	+	1.20370i
$162$	3708.38	−	13839.9i	0.141304	−	0.527353i
$163$	5260.75	+	1409.61i	0.198003	+	0.0530548i	0.356458	−	0.934311i	$-0.383984\pi$
$163$	5260.75	+	1409.61i	0.198003	+	0.0530548i	−0.158454	+	0.987366i	$0.550651\pi$
$164$	5435.29	−	5435.29i	0.202086	−	0.202086i
$165$	−9236.21	−	15997.6i	−0.339255	−	0.587606i
$166$	−10982.7	−	6340.84i	−0.398558	−	0.230107i
$167$	5927.10	+	22120.3i	0.212525	+	0.793153i	0.987023	+	0.160578i	$0.0513357\pi$
$167$	5927.10	+	22120.3i	0.212525	+	0.793153i	−0.774498	+	0.632576i	$0.781998\pi$
$168$		−	28320.9i		−	1.00343i
$169$	8602.59	−	27234.7i	0.301201	−	0.953561i
$170$	14954.8			0.517466
$171$	−2920.08	+	782.433i	−0.0998625	+	0.0267581i
$172$	−11999.1	+	20783.1i	−0.405595	+	0.702510i
$173$	30723.4	−	17738.1i	1.02654	−	0.592674i	0.110549	−	0.993871i	$-0.464739\pi$
$173$	30723.4	−	17738.1i	1.02654	−	0.592674i	0.915992	+	0.401197i	$0.131406\pi$
$174$	13202.1	+	13202.1i	0.436058	+	0.436058i
$175$	−655.504	+	2446.37i	−0.0214042	+	0.0798816i
$176$	−23.3860	−	6.26625i	−0.000754971	−	0.000202294i
$177$	7135.57	−	7135.57i	0.227762	−	0.227762i
$178$	−3677.91	−	6370.33i	−0.116081	−	0.201058i
$179$	−42635.6	−	24615.7i	−1.33066	−	0.768256i	−0.345258	−	0.938508i	$-0.612209\pi$
$179$	−42635.6	−	24615.7i	−1.33066	−	0.768256i	−0.985401	+	0.170251i	$0.945542\pi$
$180$	−523.175	−	1952.52i	−0.0161474	−	0.0602628i
$181$			45485.8i			1.38841i	0.719775	+	0.694207i	$0.244245\pi$
$181$			45485.8i			1.38841i	−0.719775	+	0.694207i	$0.755755\pi$
$182$	−17509.6	+	12831.6i	−0.528607	+	0.387380i
$183$	−41054.0			−1.22590
$184$	52449.7	−	14053.9i	1.54920	−	0.415107i
$185$	−31900.0	+	55252.5i	−0.932068	+	1.61439i
$186$	10490.4	−	6056.64i	0.303226	−	0.175068i
$187$	−16113.9	−	16113.9i	−0.460806	−	0.460806i
$188$	3108.08	−	11599.5i	0.0879378	−	0.328188i
$189$	−38271.7	−	10254.9i	−1.07141	−	0.287083i
$190$	−14900.1	+	14900.1i	−0.412746	+	0.412746i
$191$	9534.06	+	16513.5i	0.261343	+	0.452660i	0.966599	−	0.256293i	$-0.0825012\pi$
$191$	9534.06	+	16513.5i	0.261343	+	0.452660i	−0.705256	+	0.708953i	$0.749168\pi$
$192$	−18628.7	−	10755.3i	−0.505337	−	0.291756i
$193$	6694.00	+	24982.4i	0.179710	+	0.670685i	0.995701	+	0.0926219i	$0.0295248\pi$
$193$	6694.00	+	24982.4i	0.179710	+	0.670685i	−0.815992	+	0.578064i	$0.803809\pi$
$194$		−	270.316i		−	0.00718237i
$195$	21627.7	−	26933.2i	0.568775	−	0.708303i
$196$	−2988.96			−0.0778050
$197$	17334.0	−	4644.62i	0.446648	−	0.119679i	−0.0284825	−	0.999594i	$-0.509067\pi$
$197$	17334.0	−	4644.62i	0.446648	−	0.119679i	0.475131	+	0.879915i	$0.342401\pi$
$198$	949.968	−	1645.39i	0.0242314	−	0.0419700i
$199$	2615.58	−	1510.10i	0.0660483	−	0.0381330i	−0.466612	−	0.884462i	$-0.654526\pi$
$199$	2615.58	−	1510.10i	0.0660483	−	0.0381330i	0.532660	+	0.846329i	$0.321192\pi$
$200$	2203.83	+	2203.83i	0.0550957	+	0.0550957i
$201$	−8028.96	+	29964.5i	−0.198732	+	0.741676i
$202$	−43433.8	−	11638.1i	−1.06445	−	0.285219i
$203$	32630.2	−	32630.2i	0.791823	−	0.791823i
$204$	10622.5	+	18398.8i	0.255251	+	0.442108i
$205$	−16148.3	−	9323.22i	−0.384254	−	0.221849i
$206$	7984.45	+	29798.4i	0.188153	+	0.702196i
$207$		−	7221.55i		−	0.168535i
$208$	−4.91702	−	45.0049i	−0.000113652	−	0.00104024i
$209$	32110.1			0.735106
$210$	−25359.3	+	6795.01i	−0.575041	+	0.154082i
$211$	38192.3	−	66150.9i	0.857848	−	1.48584i	−0.0161294	−	0.999870i	$-0.505134\pi$
$211$	38192.3	−	66150.9i	0.857848	−	1.48584i	0.873977	−	0.485966i	$-0.161532\pi$
$212$	−336.226	+	194.120i	−0.00748101	+	0.00431916i
$213$	3842.90	+	3842.90i	0.0847031	+	0.0847031i
$214$	5988.58	−	22349.7i	0.130766	−	0.488027i
$215$	56231.7	+	15067.2i	1.21648	+	0.325954i
$216$	−34477.3	+	34477.3i	−0.738968	+	0.738968i
$217$	−14969.6	−	25928.0i	−0.317899	−	0.550618i
$218$	16787.8	+	9692.42i	0.353248	+	0.203948i
$219$	−3118.37	−	11637.9i	−0.0650188	−	0.242653i
$220$			21470.5i			0.443605i
$221$	17172.3	−	38999.6i	0.351596	−	0.798502i
$222$	55905.0			1.13434
$223$	18366.3	−	4921.25i	0.369329	−	0.0989613i	−0.0693808	−	0.997590i	$-0.522102\pi$
$223$	18366.3	−	4921.25i	0.369329	−	0.0989613i	0.438710	+	0.898629i	$0.355436\pi$
$224$	−26627.8	+	46120.8i	−0.530689	+	0.919180i
$225$	358.967	−	207.250i	0.00709070	−	0.00409382i
$226$	13891.0	+	13891.0i	0.271967	+	0.271967i
$227$	980.846	−	3660.57i	0.0190348	−	0.0710390i	−0.955755	−	0.294163i	$-0.904959\pi$
$227$	980.846	−	3660.57i	0.0190348	−	0.0710390i	0.974790	+	0.223125i	$0.0716257\pi$
$228$	−28915.3	−	7747.83i	−0.556234	−	0.149043i
$229$	−57344.9	+	57344.9i	−1.09351	+	1.09351i	−0.0983628	+	0.995151i	$0.531361\pi$
$229$	−57344.9	+	57344.9i	−1.09351	+	1.09351i	−0.995151	+	0.0983628i	$0.968639\pi$
$230$	−25168.4	−	43592.9i	−0.475772	−	0.824062i
$231$	34646.6	+	20003.2i	0.649288	+	0.374866i
$232$	−14697.5	−	54852.0i	−0.273067	−	1.01910i
$233$			6475.98i			0.119287i	0.998220	+	0.0596436i	$0.0189964\pi$
$233$			6475.98i			0.119287i	−0.998220	+	0.0596436i	$0.981004\pi$
$234$	3511.25	+	541.366i	0.0641254	+	0.00988688i
$235$	−29130.9			−0.527494
$236$	−11329.4	+	3035.70i	−0.203414	+	0.0545047i
$237$	15743.5	−	27268.6i	0.280289	−	0.485474i
$238$	−28049.0	+	16194.1i	−0.495180	+	0.285892i
$239$	−34428.3	−	34428.3i	−0.602725	−	0.602725i	0.338310	−	0.941035i	$-0.390145\pi$
$239$	−34428.3	−	34428.3i	−0.602725	−	0.602725i	−0.941035	+	0.338310i	$0.890145\pi$
$240$	14.1712	−	52.8877i	0.000246028	−	0.000918190i
$241$	6890.52	+	1846.31i	0.118636	+	0.0317885i	0.317649	−	0.948208i	$-0.397107\pi$
$241$	6890.52	+	1846.31i	0.118636	+	0.0317885i	−0.199012	+	0.979997i	$0.563773\pi$
$242$	11308.0	−	11308.0i	0.193088	−	0.193088i
$243$	6176.32	+	10697.7i	0.104597	+	0.181167i
$244$	41324.2	+	23858.6i	0.694105	+	0.400742i
$245$	1876.61	+	7003.60i	0.0312638	+	0.116678i
$246$			16339.0i			0.269995i
$247$	21747.6	+	55966.8i	0.356465	+	0.917353i
$248$	−36842.8			−0.599031
$249$	−42214.0	+	11311.2i	−0.680861	+	0.182436i
$250$	19978.9	−	34604.4i	0.319662	−	0.553671i
$251$	−74391.1	+	42949.7i	−1.18079	+	0.681731i	−0.956198	−	0.292721i	$-0.905439\pi$
$251$	−74391.1	+	42949.7i	−1.18079	+	0.681731i	−0.224595	+	0.974452i	$0.572106\pi$
$252$	3095.58	+	3095.58i	0.0487463	+	0.0487463i
$253$	−19852.6	+	74091.0i	−0.310154	+	1.15751i
$254$	45140.2	+	12095.3i	0.699674	+	0.187477i
$255$	36441.9	−	36441.9i	0.560429	−	0.560429i
$256$	32746.8	+	56719.0i	0.499676	+	0.865464i
$257$	−22280.9	−	12863.9i	−0.337339	−	0.194763i	0.321756	−	0.946823i	$-0.395727\pi$
$257$	−22280.9	−	12863.9i	−0.337339	−	0.194763i	−0.659095	+	0.752060i	$0.729060\pi$
$258$	−13202.7	−	49273.2i	−0.198346	−	0.740238i
$259$		−	138175.i		−	2.05982i
$260$	−37422.3	+	14541.6i	−0.553584	+	0.215112i
$261$	−7552.31			−0.110866
$262$	−7866.82	+	2107.91i	−0.114603	+	0.0307078i
$263$	−13784.8	+	23875.9i	−0.199291	+	0.345182i	−0.948299	−	0.317379i	$-0.897197\pi$
$263$	−13784.8	+	23875.9i	−0.199291	+	0.345182i	0.749008	+	0.662561i	$0.230531\pi$
$264$	42635.8	−	24615.8i	0.611740	−	0.353188i
$265$	665.954	+	665.954i	0.00948315	+	0.00948315i
$266$	11811.6	−	44081.5i	0.166934	−	0.623007i
$267$	−24485.6	−	6560.90i	−0.343470	−	0.0920325i
$268$	25495.7	−	25495.7i	0.354974	−	0.354974i
$269$	24054.6	+	41663.8i	0.332425	+	0.575776i	0.982987	−	0.183677i	$-0.0588000\pi$
$269$	24054.6	+	41663.8i	0.332425	+	0.575776i	−0.650562	+	0.759453i	$0.725467\pi$
$270$	39143.9	+	22599.8i	0.536954	+	0.310010i
$271$	−6603.79	−	24645.7i	−0.0899196	−	0.335585i	0.906281	−	0.422676i	$-0.138909\pi$
$271$	−6603.79	−	24645.7i	−0.0899196	−	0.335585i	−0.996200	+	0.0870918i	$0.972243\pi$
$272$		−	67.5467i		−	0.000912990i
$273$	−11399.4	+	73935.6i	−0.152953	+	0.992038i
$274$	−60290.1			−0.803054
$275$	−4252.64	+	1139.49i	−0.0562333	+	0.0150677i
$276$	35754.7	−	61929.0i	0.469370	−	0.812972i
$277$	45643.1	−	26352.0i	0.594861	−	0.343443i	−0.172156	−	0.985070i	$-0.555073\pi$
$277$	45643.1	−	26352.0i	0.594861	−	0.343443i	0.767017	+	0.641627i	$0.221740\pi$
$278$	−2753.48	−	2753.48i	−0.0356281	−	0.0356281i
$279$	−1268.18	+	4732.90i	−0.0162919	+	0.0608022i
$280$	77130.9	+	20667.1i	0.983812	+	0.263612i
$281$	88394.7	−	88394.7i	1.11947	−	1.11947i	0.127654	−	0.991819i	$-0.459255\pi$
$281$	88394.7	−	88394.7i	1.11947	−	1.11947i	0.991819	−	0.127654i	$-0.0407448\pi$
$282$	12763.0	+	22106.2i	0.160493	+	0.277981i
$283$	52282.5	+	30185.3i	0.652805	+	0.376897i	0.789530	−	0.613712i	$-0.210324\pi$
$283$	52282.5	+	30185.3i	0.652805	+	0.376897i	−0.136725	+	0.990609i	$0.543658\pi$
$284$	−1634.89	−	6101.49i	−0.0202699	−	0.0756483i
$285$			72617.6i			0.894030i
$286$	−34536.2	−	15207.0i	−0.422223	−	0.185913i
$287$	40383.4			0.490274
$288$	8418.88	−	2255.83i	0.101501	−	0.0271971i
$289$	−9971.36	+	17270.9i	−0.119387	+	0.206785i
$290$	−45589.5	+	26321.1i	−0.542087	+	0.312974i
$291$	−658.708	−	658.708i	−0.00777869	−	0.00777869i
$292$	−3624.48	+	13526.7i	−0.0425089	+	0.158645i
$293$	64752.7	+	17350.4i	0.754263	+	0.202104i	0.615408	−	0.788209i	$-0.288991\pi$
$293$	64752.7	+	17350.4i	0.754263	+	0.202104i	0.138855	+	0.990313i	$0.455658\pi$
$294$	4492.54	−	4492.54i	0.0519754	−	0.0519754i
$295$	14226.2	+	24640.6i	0.163473	+	0.283144i
$296$	−147256.	−	85018.1i	−1.68069	−	0.970349i
$297$	−17826.5	−	66529.5i	−0.202094	−	0.754226i
$298$		−	19425.4i		−	0.218745i
$299$	−142584.	+	15578.0i	−1.59488	+	0.174249i
$300$	4104.46			0.0456052
$301$	−121783.	+	32631.7i	−1.34417	+	0.360170i
$302$	−22907.6	+	39677.2i	−0.251169	+	0.435038i
$303$	−134200.	+	77480.2i	−1.46173	+	0.843928i
$304$	67.3000	+	67.3000i	0.000728228	+	0.000728228i
$305$	29959.1	−	111809.i	0.322054	−	1.20192i
$306$	5120.06	+	1371.92i	0.0546804	+	0.0146516i
$307$	−56466.7	+	56466.7i	−0.599122	+	0.599122i	−0.940079	−	0.340957i	$-0.889249\pi$
$307$	−56466.7	+	56466.7i	−0.599122	+	0.599122i	0.340957	+	0.940079i	$0.389249\pi$
$308$	−23249.8	−	40269.8i	−0.245085	−	0.424500i
$309$	92069.5	+	53156.4i	0.964271	+	0.556722i
$310$	8839.64	+	32990.0i	0.0919838	+	0.343288i
$311$			23649.5i			0.244513i	0.992499	+	0.122256i	$0.0390130\pi$
$311$			23649.5i			0.244513i	−0.992499	+	0.122256i	$0.960987\pi$
$312$	71780.8	+	57640.8i	0.737393	+	0.592135i
$313$	86256.6			0.880447			0.440224	−	0.897888i	$-0.354899\pi$
$313$	86256.6			0.880447			0.440224	+	0.897888i	$0.354899\pi$
$314$	506.700	−	135.770i	0.00513916	−	0.00137703i
$315$	5309.89	−	9197.00i	0.0535136	−	0.0926883i
$316$	−31694.3	+	18298.7i	−0.317400	+	0.183251i
$317$	−108363.	−	108363.i	−1.07836	−	1.07836i	−0.996657	−	0.0817010i	$-0.973965\pi$
$317$	−108363.	−	108363.i	−1.07836	−	1.07836i	−0.0817010	−	0.996657i	$-0.526035\pi$
$318$	213.592	−	797.137i	0.00211218	−	0.00788276i
$319$	77484.5	+	20761.9i	0.761436	+	0.204026i
$320$	42885.9	−	42885.9i	0.418807	−	0.418807i
$321$	−39868.9	−	69054.9i	−0.386922	−	0.670169i
$322$	94411.0	+	54508.2i	0.910564	+	0.525715i
$323$	23186.3	+	86532.3i	0.222242	+	0.829418i
$324$			57390.9i			0.546705i
$325$	−4866.32	−	6640.44i	−0.0460717	−	0.0628681i
$326$	13455.8			0.126612
$327$	64527.2	−	17290.0i	0.603458	−	0.161696i
$328$	24847.7	−	43037.5i	0.230961	−	0.400036i
$329$	54637.5	−	31545.0i	0.504776	−	0.291433i
$330$	−32271.2	−	32271.2i	−0.296338	−	0.296338i
$331$	25443.1	−	94955.1i	0.232228	−	0.866687i	−0.747151	−	0.664655i	$-0.768579\pi$
$331$	25443.1	−	94955.1i	0.232228	−	0.866687i	0.979379	−	0.202032i	$-0.0647546\pi$
$332$	49065.4	+	13147.0i	0.445143	+	0.119276i
$333$	−15990.3	+	15990.3i	−0.144201	+	0.144201i
$334$	28289.3	+	48998.5i	0.253589	+	0.439228i
$335$	−75747.8	−	43733.0i	−0.674964	−	0.389690i
$336$	30.6912	+	114.541i	0.000271854	+	0.00101457i
$337$		−	30291.6i		−	0.266725i	−0.991067	−	0.133362i	$-0.957423\pi$
$337$		−	30291.6i		−	0.266725i	0.991067	−	0.133362i	$-0.0425774\pi$
$338$	3114.51	−	70494.7i	0.0272619	−	0.617053i
$339$	67699.4			0.589095
$340$	−57860.0	+	15503.5i	−0.500519	+	0.134114i
$341$	26022.3	−	45071.9i	0.223788	−	0.387612i
$342$	−6468.26	+	3734.45i	−0.0553013	+	0.0319282i
$343$	77164.2	+	77164.2i	0.655885	+	0.655885i
$344$	−40156.3	+	149865.i	−0.339341	+	1.26644i
$345$	−167558.	−	44897.0i	−1.40775	−	0.377207i
$346$	61976.8	−	61976.8i	0.517699	−	0.517699i
$347$	92972.7	+	161033.i	0.772141	+	1.33739i	0.936388	+	0.350968i	$0.114147\pi$
$347$	92972.7	+	161033.i	0.772141	+	1.33739i	−0.164247	+	0.986419i	$0.552519\pi$
$348$	−64765.4	−	37392.3i	−0.534792	−	0.308762i
$349$	−41695.7	−	155610.i	−0.342326	−	1.27758i	−0.895705	−	0.444649i	$-0.853329\pi$
$349$	−41695.7	−	155610.i	−0.342326	−	1.27758i	0.553379	−	0.832930i	$-0.313338\pi$
$350$			6257.27i			0.0510798i
$351$	103885.	−	76130.1i	0.843214	−	0.617934i
$352$	−92576.8			−0.747165
$353$	185637.	−	49741.3i	1.48976	−	0.399179i	0.580101	−	0.814544i	$-0.303013\pi$
$353$	185637.	−	49741.3i	1.48976	−	0.399179i	0.909655	+	0.415366i	$0.136346\pi$
$354$	12465.8	−	21591.4i	0.0994749	−	0.172295i
$355$	−13270.3	+	7661.61i	−0.105299	+	0.0607944i
$356$	20833.9	+	20833.9i	0.164388	+	0.164388i
$357$	−28888.1	+	107812.i	−0.226664	+	0.845922i
$358$	−117488.	−	31480.7i	−0.916698	−	0.245628i
$359$	−111215.	+	111215.i	−0.862925	+	0.862925i	−0.991677	−	0.128751i	$-0.958903\pi$
$359$	−111215.	+	111215.i	−0.862925	+	0.862925i	0.128751	+	0.991677i	$0.458903\pi$
$360$	−6534.30	−	11317.7i	−0.0504190	−	0.0873282i
$361$	3543.42	+	2045.80i	0.0271900	+	0.0156981i
$362$	29085.6	+	108549.i	0.221953	+	0.828341i
$363$		−	55110.9i		−	0.418239i
$364$	54442.1	−	67797.5i	0.410896	−	0.511694i
$365$	33970.9			0.254989
$366$	−97972.9	+	26251.8i	−0.731381	+	0.195973i
$367$	−112206.	+	194346.i	−0.833072	+	1.44292i	0.0625190	+	0.998044i	$0.480087\pi$
$367$	−112206.	+	194346.i	−0.833072	+	1.44292i	−0.895591	+	0.444879i	$0.853247\pi$
$368$	−196.897	+	113.679i	−0.00145393	+	0.000839428i
$369$	−4673.39	−	4673.39i	−0.0343226	−	0.0343226i
$370$	−40796.6	+	152255.i	−0.298003	+	1.11216i
$371$	−1970.20	−	527.913i	−0.0143140	−	0.00383543i
$372$	−34308.5	+	34308.5i	−0.247922	+	0.247922i
$373$	−100965.	−	174876.i	−0.725693	−	1.25694i	−0.958688	−	0.284459i	$-0.908186\pi$
$373$	−100965.	−	174876.i	−0.725693	−	1.25694i	0.232995	−	0.972478i	$-0.425147\pi$
$374$	−48758.8	−	28150.9i	−0.348586	−	0.201256i
$375$	−35639.6	−	133009.i	−0.253437	−	0.945841i
$376$		−	77637.9i		−	0.549159i
$377$	16291.5	+	149114.i	0.114625	+	1.04915i
$378$	−97890.5			−0.685105
$379$	134055.	−	35919.8i	0.933261	−	0.250067i	0.240017	−	0.970769i	$-0.422847\pi$
$379$	134055.	−	35919.8i	0.933261	−	0.250067i	0.693245	+	0.720702i	$0.256180\pi$
$380$	42201.7	−	73095.6i	0.292256	−	0.506202i
$381$	139472.	−	80524.1i	0.960808	−	0.554723i
$382$	33311.9	+	33311.9i	0.228282	+	0.228282i
$383$	45484.2	−	169749.i	0.310073	−	1.15721i	−0.618418	−	0.785850i	$-0.712226\pi$
$383$	45484.2	−	169749.i	0.310073	−	1.15721i	0.928490	−	0.371357i	$-0.121107\pi$
$384$	83452.8	+	22361.1i	0.565950	+	0.151646i
$385$	−79761.3	+	79761.3i	−0.538109	+	0.538109i
$386$	31949.6	+	55338.4i	0.214433	+	0.371409i
$387$	17869.8	+	10317.1i	0.119316	+	0.0688869i
$388$	280.235	+	1045.85i	0.00186148	+	0.00694715i
$389$			172903.i			1.14262i	0.820733	+	0.571312i	$0.193565\pi$
$389$			172903.i			1.14262i	−0.820733	+	0.571312i	$0.806435\pi$
$390$	34390.8	−	78104.1i	0.226107	−	0.513505i
$391$	−214000.			−1.39978
$392$	−18665.6	+	5001.43i	−0.121470	+	0.0325478i
$393$	−14033.4	+	24306.5i	−0.0908608	+	0.157376i
$394$	38396.4	−	22168.2i	0.247342	−	0.142803i
$395$	62776.0	+	62776.0i	0.402346	+	0.402346i
$396$	−1969.65	+	7350.85i	−0.0125603	+	0.0468756i
$397$	−157745.	−	42267.7i	−1.00086	−	0.268181i	−0.279056	−	0.960275i	$-0.590022\pi$
$397$	−157745.	−	42267.7i	−1.00086	−	0.268181i	−0.721807	+	0.692094i	$0.756688\pi$
$398$	5276.28	−	5276.28i	0.0333090	−	0.0333090i
$399$	−78635.5	−	136201.i	−0.493939	−	0.855527i
$400$	−11.3014	−	6.52488i	−7.06339e−5	−	4.07805e-5i
$401$	54978.8	+	205184.i	0.341906	+	1.27601i	0.896185	+	0.443680i	$0.146327\pi$
$401$	54978.8	+	205184.i	0.341906	+	1.27601i	−0.554279	+	0.832331i	$0.687006\pi$
$402$			76642.4i			0.474260i
$403$	96183.0	+	14829.5i	0.592227	+	0.0913098i
$404$	180111.			1.10351
$405$	134476.	−	36032.7i	0.819850	−	0.219678i
$406$	57004.8	−	98735.2i	0.345827	−	0.598990i
$407$	208015.	−	120098.i	1.25576	−	0.725012i
$408$	97122.8	+	97122.8i	0.583446	+	0.583446i
$409$	31769.2	−	118564.i	0.189915	−	0.708772i	−0.803610	−	0.595157i	$-0.797090\pi$
$409$	31769.2	−	118564.i	0.189915	−	0.708772i	0.993525	−	0.113616i	$-0.0362433\pi$
$410$	−44498.6	−	11923.4i	−0.264715	−	0.0709301i
$411$	−146915.	+	146915.i	−0.869728	+	0.869728i
$412$	−61783.7	−	107012.i	−0.363981	−	0.630434i
$413$	−53365.1	−	30810.4i	−0.312865	−	0.180633i
$414$	−4617.77	−	17233.8i	−0.0269421	−	0.100549i
$415$		−	123222.i		−	0.715474i
$416$	−62700.5	−	161358.i	−0.362313	−	0.932403i
$417$	−13419.4			−0.0771723
$418$	76628.8	−	20532.6i	0.438571	−	0.117515i
$419$	−114159.	+	197730.i	−0.650254	+	1.12627i	0.332807	+	0.942995i	$0.392004\pi$
$419$	−114159.	+	197730.i	−0.650254	+	1.12627i	−0.983061	+	0.183278i	$0.941329\pi$
$420$	91070.8	−	52579.7i	0.516274	−	0.298071i
$421$	29630.8	+	29630.8i	0.167178	+	0.167178i	0.785738	−	0.618560i	$-0.212284\pi$
$421$	29630.8	+	29630.8i	0.167178	+	0.167178i	−0.618560	+	0.785738i	$0.712284\pi$
$422$	48843.6	−	182287.i	0.274273	−	1.02360i
$423$	−9973.52	−	2672.40i	−0.0557401	−	0.0149355i
$424$	−1774.86	+	1774.86i	−0.00987263	+	0.00987263i
$425$	−6141.54	−	10637.5i	−0.0340016	−	0.0588925i
$426$	11628.1	+	6713.51i	0.0640754	+	0.0369939i
$427$	64883.7	+	242149.i	0.355860	+	1.32809i
$428$			92679.2i			0.505935i
$429$	−121215.	+	47101.5i	−0.658628	+	0.255930i
$430$	143828.			0.777869
$431$	−138387.	+	37080.7i	−0.744973	+	0.199615i	−0.611287	−	0.791409i	$-0.709348\pi$
$431$	−138387.	+	37080.7i	−0.744973	+	0.199615i	−0.133686	+	0.991024i	$0.542681\pi$
$432$	102.077	−	176.803i	0.000546966	−	0.000947373i
$433$	−175596.	+	101381.i	−0.936568	+	0.540728i	−0.888883	−	0.458134i	$-0.848518\pi$
$433$	−175596.	+	101381.i	−0.936568	+	0.540728i	−0.0476854	+	0.998862i	$0.515185\pi$
$434$	−52303.5	−	52303.5i	−0.277684	−	0.277684i
$435$	−46953.4	+	175232.i	−0.248135	+	0.926053i
$436$	−75000.0	−	20096.2i	−0.394537	−	0.105716i
$437$	213219.	−	213219.i	1.11651	−	1.11651i
$438$	−14883.6	−	25779.1i	−0.0775816	−	0.134375i
$439$	5156.12	+	2976.88i	0.0267543	+	0.0154466i	0.513317	−	0.858199i	$-0.328416\pi$
$439$	5156.12	+	2976.88i	0.0267543	+	0.0154466i	−0.486563	+	0.873645i	$0.661750\pi$
$440$	35926.6	+	134080.i	0.185572	+	0.692562i
$441$			2569.98i			0.0132145i
$442$	16042.6	−	104051.i	0.0821164	−	0.532600i
$443$	−25178.3			−0.128298			−0.0641489	−	0.997940i	$-0.520433\pi$
$443$	−25178.3			−0.128298			−0.0641489	+	0.997940i	$0.520433\pi$
$444$	−216296.	+	57956.5i	−1.09719	+	0.293992i
$445$	35736.7	−	61897.7i	0.180465	−	0.312575i
$446$	40683.3	−	23488.5i	0.204525	−	0.118082i
$447$	−47336.0	−	47336.0i	−0.236906	−	0.236906i
$448$	−33996.3	+	126876.i	−0.169385	+	0.632155i
$449$	−195615.	−	52414.9i	−0.970309	−	0.259993i	−0.261351	−	0.965244i	$-0.584168\pi$
$449$	−195615.	−	52414.9i	−0.970309	−	0.259993i	−0.708958	+	0.705250i	$0.750835\pi$
$450$	724.127	−	724.127i	0.00357594	−	0.00357594i
$451$	35100.1	+	60795.2i	0.172566	+	0.298893i
$452$	−68145.0	−	39343.5i	−0.333547	−	0.192573i
$453$	40864.2	+	152507.i	0.199134	+	0.743180i
$454$		−	9362.91i		−	0.0454254i
$455$	−193042.	−	85000.1i	−0.932456	−	0.410579i
$456$	−193536.			−0.930749
$457$	−30190.8	+	8089.60i	−0.144558	+	0.0387342i	−0.330372	−	0.943851i	$-0.607174\pi$
$457$	−30190.8	+	8089.60i	−0.144558	+	0.0387342i	0.185814	+	0.982585i	$0.440508\pi$
$458$	−100181.	+	173519.i	−0.477590	+	0.827210i
$459$	166415.	−	96080.0i	0.789893	−	0.456045i
$460$	142569.	+	142569.i	0.673766	+	0.673766i
$461$	13650.4	−	50943.9i	0.0642308	−	0.239713i	−0.926345	−	0.376675i	$-0.877067\pi$
$461$	13650.4	−	50943.9i	0.0642308	−	0.239713i	0.990576	+	0.136963i	$0.0437340\pi$
$462$	95473.0	+	25581.9i	0.447297	+	0.119853i
$463$	81704.7	−	81704.7i	0.381140	−	0.381140i	−0.490372	−	0.871513i	$-0.663139\pi$
$463$	81704.7	−	81704.7i	0.381140	−	0.381140i	0.871513	+	0.490372i	$0.163139\pi$
$464$	118.885	+	205.916i	0.000552195	+	0.000956430i
$465$	101931.	+	58849.8i	0.471411	+	0.272169i
$466$	4141.03	+	15454.5i	0.0190694	+	0.0711678i
$467$		−	267324.i		−	1.22576i	−0.790177	−	0.612878i	$-0.790012\pi$
$467$		−	267324.i		−	1.22576i	0.790177	−	0.612878i	$-0.209988\pi$
$468$	−14146.3	+	1545.55i	−0.0645877	+	0.00705655i
$469$	189429.			0.861193
$470$	−69519.0	+	18627.6i	−0.314708	+	0.0843257i
$471$	903.886	−	1565.58i	0.00407448	−	0.00705720i
$472$	−65670.6	+	37915.0i	−0.294773	+	0.170187i
$473$	−154976.	−	154976.i	−0.692696	−	0.692696i
$474$	20134.2	−	75141.9i	0.0896145	−	0.334446i
$475$	16717.7	+	4479.50i	0.0740952	+	0.0198537i
$476$	91733.1	−	91733.1i	0.404867	−	0.404867i
$477$	166.909	+	289.096i	0.000733574	+	0.00127059i
$478$	−104176.	−	60145.9i	−0.455944	−	0.263239i
$479$	27192.8	+	101485.i	0.118518	+	0.442313i	0.999526	−	0.0307872i	$-0.00980140\pi$
$479$	27192.8	+	101485.i	0.118518	+	0.442313i	−0.881008	+	0.473101i	$0.843135\pi$
$480$		−	209364.i		−	0.908697i
$481$	350210.	+	281223.i	1.51370	+	1.21551i
$482$	17624.4			0.0758613
$483$	362887.	−	97235.4i	1.55553	−	0.416802i
$484$	−32027.7	+	55473.7i	−0.136721	+	0.236808i
$485$	2274.65	−	1313.27i	0.00967011	−	0.00558304i
$486$	21580.0	+	21580.0i	0.0913647	+	0.0913647i
$487$	44118.2	−	164651.i	0.186020	−	0.694237i	−0.808390	−	0.588648i	$-0.799661\pi$
$487$	44118.2	−	164651.i	0.186020	−	0.694237i	0.994410	−	0.105589i	$-0.0336728\pi$
$488$	297986.	+	79845.2i	1.25129	+	0.335281i
$489$	32789.2	−	32789.2i	0.137124	−	0.137124i
$490$	8956.82	+	15513.7i	0.0373045	+	0.0646133i
$491$	−28245.7	−	16307.7i	−0.117163	−	0.0676439i	0.440273	−	0.897864i	$-0.354882\pi$
$491$	−28245.7	−	16307.7i	−0.117163	−	0.0676439i	−0.557436	+	0.830220i	$0.688215\pi$
$492$	−16938.6	−	63215.6i	−0.0699756	−	0.261152i
$493$			223802.i			0.920809i
$494$	87686.8	+	119655.i	0.359319	+	0.490316i
$495$	18460.8			0.0753427
$496$	149.007	−	39.9263i	0.000605680	−	0.000162291i
$497$	16593.1	−	28740.1i	0.0671760	−	0.116352i
$498$	−93508.3	+	53987.0i	−0.377043	+	0.217686i
$499$	−39397.8	−	39397.8i	−0.158223	−	0.158223i	0.623556	−	0.781779i	$-0.285687\pi$
$499$	−39397.8	−	39397.8i	−0.158223	−	0.158223i	−0.781779	+	0.623556i	$0.785687\pi$
$500$	−41424.0	+	154596.i	−0.165696	+	0.618386i
$501$	188336.	+	50464.4i	0.750338	+	0.201053i
$502$	−150066.	+	150066.i	−0.595490	+	0.595490i
$503$	−195215.	−	338122.i	−0.771573	−	1.33640i	−0.936701	−	0.350131i	$-0.886137\pi$
$503$	−195215.	−	338122.i	−0.771573	−	1.33640i	0.165128	−	0.986272i	$-0.447196\pi$
$504$	24511.3	+	14151.6i	0.0964951	+	0.0557115i
$505$	−113082.	−	422028.i	−0.443415	−	1.65485i
$506$			189508.i			0.740162i
$507$	−164192.	−	179371.i	−0.638759	−	0.697810i
$508$	−187186.			−0.725349
$509$	−449990.	+	120575.i	−1.73687	+	0.465393i	−0.981748	−	0.190189i	$-0.939090\pi$
$509$	−449990.	+	120575.i	−1.73687	+	0.465393i	−0.755124	+	0.655582i	$0.772423\pi$
$510$	63663.7	−	110269.i	0.244766	−	0.423948i
$511$	−63715.5	+	36786.1i	−0.244007	+	0.140878i
$512$	−387.940	−	387.940i	−0.00147987	−	0.00147987i
$513$	−70078.5	+	261537.i	−0.266287	+	0.993797i
$514$	−61397.7	−	16451.5i	−0.232395	−	0.0622699i
$515$	−211957.	+	211957.i	−0.799157	+	0.799157i
$516$	102163.	+	176951.i	0.383700	+	0.664588i
$517$	94978.8	+	54836.1i	0.355341	+	0.205156i
$518$	−88354.9	−	329745.i	−0.329284	−	1.22891i
$519$		−	302051.i		−	1.12136i
$520$	−209364.	+	153429.i	−0.774276	+	0.567414i
$521$	66489.1			0.244949			0.122474	−	0.992472i	$-0.460917\pi$
$521$	66489.1			0.244949			0.122474	+	0.992472i	$0.460917\pi$
$522$	−18023.1	+	4829.28i	−0.0661437	+	0.0177232i
$523$	99709.6	−	172702.i	0.364530	−	0.631385i	−0.624170	−	0.781288i	$-0.714563\pi$
$523$	99709.6	−	172702.i	0.364530	−	0.631385i	0.988701	+	0.149903i	$0.0478962\pi$
$524$	28251.5	−	16311.0i	0.102891	−	0.0594043i
$525$	15247.8	+	15247.8i	0.0553207	+	0.0553207i
$526$	−17629.2	+	65792.9i	−0.0637177	+	0.237798i
$527$	140253.	+	37580.6i	0.504999	+	0.135314i
$528$	−145.760	+	145.760i	−0.000522843	+	0.000522843i
$529$	220234.	+	381457.i	0.786999	+	1.36312i
$530$	2015.10	+	1163.42i	0.00717372	+	0.00414175i
$531$	2610.16	+	9741.27i	0.00925718	+	0.0345483i
$532$			182796.i			0.645868i
$533$	−82191.2	+	102354.i	−0.289315	+	0.360287i
$534$	−62628.7			−0.219630
$535$	217162.	−	58188.5i	0.758712	−	0.203296i
$536$	116555.	−	201879.i	0.405695	−	0.702685i
$537$	−363007.	+	209582.i	−1.25883	+	0.726785i
$538$	84046.4	+	84046.4i	0.290372	+	0.290372i
$539$	7065.07	−	26367.2i	0.0243186	−	0.0907584i
$540$	−174877.	−	46858.1i	−0.599715	−	0.160693i
$541$	142965.	−	142965.i	0.488467	−	0.488467i	−0.419355	−	0.907822i	$-0.637744\pi$
$541$	142965.	−	142965.i	0.488467	−	0.488467i	0.907822	+	0.419355i	$0.137744\pi$
$542$	−31519.1	−	54592.6i	−0.107294	−	0.185838i
$543$	335389.	+	193637.i	1.13750	+	0.656733i
$544$	−66848.3	−	249481.i	−0.225888	−	0.843025i
$545$			188354.i			0.634136i
$546$	20073.7	+	183732.i	0.0673352	+	0.616310i
$547$	−34633.5			−0.115750			−0.0578750	−	0.998324i	$-0.518432\pi$
$547$	−34633.5			−0.115750			−0.0578750	+	0.998324i	$0.518432\pi$
$548$	233262.	−	62502.4i	0.776753	−	0.208130i
$549$	20514.2	−	35531.6i	0.0680627	−	0.117888i
$550$	−9420.02	+	5438.65i	−0.0311406	+	0.0179790i
$551$	−222984.	−	222984.i	−0.734465	−	0.734465i
$552$	119657.	−	446566.i	0.392699	−	1.46557i
$553$	−185720.	−	49763.6i	−0.607308	−	0.162728i
$554$	92073.7	−	92073.7i	0.299996	−	0.299996i
$555$	271602.	+	470429.i	0.881755	+	1.52724i
$556$	13507.7	+	7798.70i	0.0436951	+	0.0252274i
$557$	−104092.	−	388477.i	−0.335512	−	1.25215i	−0.903313	−	0.428981i	$-0.858873\pi$
$557$	−104092.	−	388477.i	−0.335512	−	1.25215i	0.567802	−	0.823165i	$-0.307794\pi$
$558$			12105.7i			0.0388796i
$559$	165155.	−	375080.i	0.528529	−	1.20033i
$560$	−334.345			−0.00106615
$561$	−187414.	+	50217.5i	−0.595493	+	0.159562i
$562$	154425.	−	267472.i	0.488928	−	0.846848i
$563$	−244737.	+	141299.i	−0.772115	+	0.445781i	−0.833629	−	0.552325i	$-0.813741\pi$
$563$	−244737.	+	141299.i	−0.772115	+	0.445781i	0.0615135	+	0.998106i	$0.480407\pi$
$564$	−72297.4	−	72297.4i	−0.227282	−	0.227282i
$565$	−49403.5	+	184376.i	−0.154761	+	0.577575i
$566$	144071.	+	38603.6i	0.449721	+	0.120502i
$567$	−213203.	+	213203.i	−0.663173	+	0.663173i
$568$	−20419.3	−	35367.2i	−0.0632913	−	0.109624i
$569$	99962.8	+	57713.6i	0.308755	+	0.178260i	0.646369	−	0.763025i	$-0.276287\pi$
$569$	99962.8	+	57713.6i	0.308755	+	0.178260i	−0.337614	+	0.941285i	$0.609620\pi$
$570$	46434.9	+	173297.i	0.142921	+	0.533387i
$571$			75184.3i			0.230598i	0.993331	+	0.115299i	$0.0367826\pi$
$571$			75184.3i			0.230598i	−0.993331	+	0.115299i	$0.963217\pi$
$572$	149385.	+	23032.3i	0.456579	+	0.0703955i
$573$	162349.			0.494471
$574$	96372.4	−	25822.9i	0.292502	−	0.0783757i
$575$	−20672.0	+	35805.0i	−0.0625240	+	0.108295i
$576$	18617.1	−	10748.6i	0.0561134	−	0.0323971i
$577$	−198197.	−	198197.i	−0.595313	−	0.595313i	0.343749	−	0.939062i	$-0.388303\pi$
$577$	−198197.	−	198197.i	−0.595313	−	0.595313i	−0.939062	+	0.343749i	$0.888303\pi$
$578$	−12752.3	+	47592.1i	−0.0381708	+	0.142455i
$579$	212704.	+	56993.9i	0.634481	+	0.170009i
$580$	149099.	−	149099.i	0.443219	−	0.443219i
$581$	133434.	+	231115.i	0.395289	+	0.684660i
$582$	−1993.17	−	1150.76i	−0.00588435	−	0.00339733i
$583$	−917.695	−	3424.89i	−0.00269999	−	0.0100765i
$584$			90537.4i			0.265462i
$585$	12503.2	+	32176.6i	0.0365350	+	0.0940217i
$586$	165623.			0.482309
$587$	−25218.8	+	6757.36i	−0.0731894	+	0.0196110i	−0.295228	−	0.955427i	$-0.595396\pi$
$587$	−25218.8	+	6757.36i	−0.0731894	+	0.0196110i	0.222039	+	0.975038i	$0.428729\pi$
$588$	−12724.2	+	22039.0i	−0.0368025	+	0.0637438i
$589$	−177184.	+	102297.i	−0.510733	+	0.294872i
$590$	49706.3	+	49706.3i	0.142793	+	0.142793i
$591$	39545.1	−	147584.i	0.113219	−	0.422538i
$592$	687.694	+	184.267i	0.00196224	+	0.000525780i
$593$	444924.	−	444924.i	1.26525	−	1.26525i	0.316736	−	0.948514i	$-0.397413\pi$
$593$	444924.	−	444924.i	1.26525	−	1.26525i	0.948514	−	0.316736i	$-0.102587\pi$
$594$	−85083.8	−	147369.i	−0.241143	−	0.417671i
$595$	−272540.	−	157351.i	−0.769832	−	0.444463i
$596$	20138.2	+	75156.9i	0.0566929	+	0.211581i
$597$		−	25714.6i		−	0.0721491i
$598$	−330306.	+	128350.i	−0.923663	+	0.358917i
$599$	−174476.			−0.486275			−0.243138	−	0.969992i	$-0.578177\pi$
$599$	−174476.			−0.486275			−0.243138	+	0.969992i	$0.578177\pi$
$600$	25631.8	−	6868.01i	0.0711994	−	0.0190778i
$601$	−251731.	+	436011.i	−0.696929	+	1.20712i	0.272598	+	0.962128i	$0.412117\pi$
$601$	−251731.	+	436011.i	−0.696929	+	1.20712i	−0.969526	+	0.244988i	$0.921216\pi$
$602$	−269762.	+	155747.i	−0.744368	+	0.429761i
$603$	−21921.8	−	21921.8i	−0.0602894	−	0.0602894i
$604$	47496.5	−	177259.i	0.130193	−	0.485887i
$605$	150092.	+	40217.1i	0.410060	+	0.109875i
$606$	−270715.	+	270715.i	−0.737168	+	0.737168i
$607$	27350.5	+	47372.5i	0.0742316	+	0.128573i	0.900752	−	0.434334i	$-0.143016\pi$
$607$	27350.5	+	47372.5i	0.0742316	+	0.128573i	−0.826520	+	0.562907i	$0.809683\pi$
$608$	315174.	+	181966.i	0.852597	+	0.492247i
$609$	−101689.	−	379508.i	−0.274182	−	1.02326i
$610$		−	285982.i		−	0.768562i
$611$	−31249.9	+	202684.i	−0.0837078	+	0.542921i
$612$	−21231.8			−0.0566869
$613$	−538540.	+	144301.i	−1.43317	+	0.384016i	−0.890135	−	0.455697i	$-0.849390\pi$
$613$	−538540.	+	144301.i	−1.43317	+	0.384016i	−0.543031	+	0.839712i	$0.682724\pi$
$614$	−98646.9	+	170861.i	−0.261666	+	0.453218i
$615$	−137489.	+	79379.5i	−0.363512	+	0.209874i
$616$	−212575.	−	212575.i	−0.560210	−	0.560210i
$617$	−46985.1	+	175351.i	−0.123421	+	0.460615i	−0.999778	−	0.0210472i	$-0.993300\pi$
$617$	−46985.1	+	175351.i	−0.123421	+	0.460615i	0.876357	+	0.481662i	$0.159967\pi$
$618$	253709.	+	67981.0i	0.664291	+	0.177996i
$619$	44147.8	−	44147.8i	0.115220	−	0.115220i	−0.647146	−	0.762366i	$-0.724038\pi$
$619$	44147.8	−	44147.8i	0.115220	−	0.115220i	0.762366	+	0.647146i	$0.224038\pi$
$620$	−68401.1	−	118474.i	−0.177943	−	0.308206i
$621$	−560143.	−	323399.i	−1.45250	−	0.838600i
$622$	15122.5	+	56438.1i	0.0390880	+	0.145879i
$623$			154793.i			0.398818i
$624$	−352.775	−	155.334i	−0.000906001	−	0.000398931i
$625$	357806.			0.915983
$626$	205846.	−	55156.2i	0.525283	−	0.140749i
$627$	136696.	−	236764.i	0.347712	−	0.602255i
$628$	−1819.67	+	1050.59i	−0.00461396	+	0.00266387i
$629$	473851.	+	473851.i	1.19768	+	1.19768i
$630$	6790.75	−	25343.4i	0.0171095	−	0.0638535i
$631$	514526.	+	137867.i	1.29226	+	0.346259i	0.838517	−	0.544875i	$-0.183423\pi$
$631$	514526.	+	137867.i	1.29226	+	0.346259i	0.453740	+	0.891134i	$0.350090\pi$
$632$	−167307.	+	167307.i	−0.418871	+	0.418871i
$633$	−325175.	−	563220.i	−0.811541	−	1.40563i
$634$	−327894.	−	189310.i	−0.815746	−	0.470971i
$635$	117525.	+	438608.i	0.291462	+	1.08775i
$636$			3305.55i			0.00817202i
$637$	50742.1	−	5543.84i	0.125052	−	0.0136626i
$638$	198188.			0.486896
$639$	−5246.21	+	1405.72i	−0.0128482	+	0.00344268i
$640$	−121799.	+	210962.i	−0.297361	+	0.515044i
$641$	684128.	−	394982.i	1.66503	−	0.961304i	0.694769	−	0.719233i	$-0.255507\pi$
$641$	684128.	−	394982.i	1.66503	−	0.961304i	0.970259	−	0.242071i	$-0.0778266\pi$
$642$	−139301.	−	139301.i	−0.337975	−	0.337975i
$643$	−113621.	+	424039.i	−0.274812	+	1.02561i	0.681155	+	0.732140i	$0.261478\pi$
$643$	−113621.	+	424039.i	−0.274812	+	1.02561i	−0.955967	+	0.293474i	$0.905189\pi$
$644$	−421784.	−	113017.i	−1.01699	−	0.272503i
$645$	350481.	−	350481.i	0.842452	−	0.842452i
$646$	110665.	+	191678.i	0.265183	+	0.459311i
$647$	−149216.	−	86150.0i	−0.356457	−	0.205801i	0.311068	−	0.950388i	$-0.399313\pi$
$647$	−149216.	−	86150.0i	−0.356457	−	0.205801i	−0.667526	+	0.744587i	$0.732646\pi$
$648$	96032.3	+	358398.i	0.228701	+	0.853522i
$649$		−	107118.i		−	0.254316i
$650$	−15859.4	−	12735.3i	−0.0375370	−	0.0301426i
$651$	−254907.			−0.601478
$652$	−52060.5	+	13949.6i	−0.122465	+	0.0328145i
$653$	219480.	−	380151.i	0.514718	−	0.891518i	−0.485136	−	0.874439i	$-0.661230\pi$
$653$	219480.	−	380151.i	0.514718	−	0.891518i	0.999854	−	0.0170793i	$-0.00543676\pi$
$654$	142934.	−	82523.0i	0.334180	−	0.192939i
$655$	−55956.8	−	55956.8i	−0.130428	−	0.130428i
$656$	−53.8546	+	200.988i	−0.000125145	+	0.000467049i
$657$	11630.6	+	3116.41i	0.0269446	+	0.00721979i
$658$	110218.	−	110218.i	0.254566	−	0.254566i
$659$	21131.3	+	36600.5i	0.0486581	+	0.0842784i	0.889329	−	0.457269i	$-0.151172\pi$
$659$	21131.3	+	36600.5i	0.0486581	+	0.0842784i	−0.840671	+	0.541547i	$0.817839\pi$
$660$	158313.	+	91401.8i	0.363435	+	0.209830i
$661$	50011.7	+	186646.i	0.114464	+	0.427185i	0.999246	−	0.0388193i	$-0.0123597\pi$
$661$	50011.7	+	186646.i	0.114464	+	0.427185i	−0.884782	+	0.466005i	$0.845693\pi$
$662$		−	242874.i		−	0.554198i
$663$	−214459.	−	292645.i	−0.487885	−	0.665754i
$664$	328405.			0.744859
$665$	428321.	−	114768.i	0.968558	−	0.259524i
$666$	−27935.0	+	48384.9i	−0.0629797	+	0.109084i
$667$	652378.	−	376651.i	1.46638	−	0.846617i
$668$	−160248.	−	160248.i	−0.359120	−	0.359120i
$669$	41900.4	−	156374.i	0.0936193	−	0.349392i
$670$	−208732.	−	55929.6i	−0.464986	−	0.124593i
$671$	−308149.	+	308149.i	−0.684408	+	0.684408i
$672$	226714.	+	392680.i	0.502042	+	0.869562i
$673$	475305.	+	274417.i	1.04940	+	0.605873i	0.922482	−	0.386040i	$-0.126157\pi$
$673$	475305.	+	274417.i	1.04940	+	0.605873i	0.126920	+	0.991913i	$0.459491\pi$
$674$	−19369.8	−	72289.1i	−0.0426388	−	0.159130i
$675$		−	37124.6i		−	0.0814805i
$676$	61031.4	+	275973.i	0.133555	+	0.603910i
$677$	−427627.			−0.933014			−0.466507	−	0.884518i	$-0.654488\pi$
$677$	−427627.			−0.933014			−0.466507	+	0.884518i	$0.654488\pi$
$678$	161560.	−	43290.0i	0.351460	−	0.0941733i
$679$	−2844.21	+	4926.31i	−0.00616910	+	0.0106852i
$680$	−335385.	+	193635.i	−0.725313	+	0.418760i
$681$	−22815.6	−	22815.6i	−0.0491969	−	0.0491969i
$682$	33279.6	−	124201.i	0.0715499	−	0.267028i
$683$	−476441.	−	127662.i	−1.02133	−	0.273666i	−0.290976	−	0.956730i	$-0.593980\pi$
$683$	−476441.	−	127662.i	−1.02133	−	0.273666i	−0.730358	+	0.683065i	$0.760647\pi$
$684$	21154.2	−	21154.2i	0.0452152	−	0.0452152i
$685$	−292906.	−	507328.i	−0.624234	−	1.08120i
$686$	233490.	+	134805.i	0.496157	+	0.286457i
$687$	178710.	+	666955.i	0.378648	+	1.41313i
$688$		−	649.632i		−	0.00137243i
$689$	5347.91	−	3919.12i	0.0112654	−	0.00825562i
$690$	−428576.			−0.900180
$691$	−397657.	+	106552.i	−0.832823	+	0.223154i	−0.649945	−	0.759981i	$-0.725208\pi$
$691$	−397657.	+	106552.i	−0.832823	+	0.223154i	−0.182878	+	0.983136i	$0.558541\pi$
$692$	−175537.	+	304039.i	−0.366570	+	0.634918i
$693$	−34624.9	+	19990.7i	−0.0720979	+	0.0416257i
$694$	324845.	+	324845.i	0.674462	+	0.674462i
$695$	9792.79	−	36547.2i	0.0202739	−	0.0756631i
$696$	−467019.	−	125137.i	−0.964087	−	0.258326i
$697$	−138489.	+	138489.i	−0.285069	+	0.285069i
$698$	−199008.	−	344692.i	−0.408470	−	0.707490i
$699$	47750.6	+	27568.8i	0.0977292	+	0.0564240i
$700$	−6486.88	−	24209.4i	−0.0132385	−	0.0494069i
$701$		−	44529.2i		−	0.0906169i	−0.998973	−	0.0453085i	$-0.985573\pi$
$701$		−	44529.2i		−	0.0906169i	0.998973	−	0.0453085i	$-0.0144271\pi$
$702$	199234.	−	248108.i	0.404286	−	0.503462i
$703$	−944240.			−1.91061
$704$	−220554.	+	59097.4i	−0.445011	+	0.119240i
$705$	−124013.	+	214796.i	−0.249510	+	0.432164i
$706$	411204.	−	237409.i	0.824989	−	0.476308i
$707$	669097.	+	669097.i	1.33860	+	1.33860i
$708$	−25846.4	+	96460.3i	−0.0515625	+	0.192434i
$709$	−381648.	−	102262.i	−0.759224	−	0.203434i	−0.141618	−	0.989921i	$-0.545231\pi$
$709$	−381648.	−	102262.i	−0.759224	−	0.203434i	−0.617606	+	0.786488i	$0.711897\pi$
$710$	−26769.6	+	26769.6i	−0.0531037	+	0.0531037i
$711$	15733.7	+	27251.5i	0.0311237	+	0.0539078i
$712$	164966.	+	95243.3i	0.325413	+	0.187877i
$713$	−126494.	−	472081.i	−0.248823	−	0.928619i
$714$			275759.i			0.540919i
$715$	−39823.0	−	364495.i	−0.0778971	−	0.712983i
$716$	487195.			0.950336
$717$	−400421.	+	107292.i	−0.778893	+	0.208704i
$718$	−194291.	+	336522.i	−0.376881	+	0.652777i
$719$	−242496.	+	140005.i	−0.469081	+	0.270824i	−0.715855	−	0.698249i	$-0.753963\pi$
$719$	−242496.	+	140005.i	−0.469081	+	0.270824i	0.246774	+	0.969073i	$0.420629\pi$
$720$	38.6923	+	38.6923i	7.46379e−5	+	7.46379e-5i
$721$	168021.	−	627065.i	0.323217	−	1.20626i
$722$	9764.33	+	2616.34i	0.0187313	+	0.00501904i
$723$	42947.3	−	42947.3i	0.0821597	−	0.0821597i
$724$	−225065.	−	389823.i	−0.429368	−	0.743688i
$725$	37444.9	+	21618.8i	0.0712388	+	0.0411298i
$726$	−35240.3	−	131519.i	−0.0668601	−	0.249525i
$727$			133105.i			0.251840i	0.992040	+	0.125920i	$0.0401882\pi$
$727$			133105.i			0.251840i	−0.992040	+	0.125920i	$0.959812\pi$
$728$	226537.	−	514483.i	0.427442	−	0.970753i
$729$	574923.			1.08182
$730$	81069.5	−	21722.5i	0.152129	−	0.0407628i
$731$	305733.	−	529545.i	0.572147	−	0.990988i
$732$	351842.	−	203136.i	0.656637	−	0.379110i
$733$	313844.	+	313844.i	0.584125	+	0.584125i	0.936034	−	0.351909i	$-0.114467\pi$
$733$	313844.	+	313844.i	0.584125	+	0.584125i	−0.351909	+	0.936034i	$0.614467\pi$
$734$	−143498.	+	535543.i	−0.266351	+	0.994037i
$735$	59629.9	+	15977.8i	0.110380	+	0.0295762i
$736$	−614731.	+	614731.i	−1.13483	+	1.13483i
$737$	164646.	+	285176.i	0.303122	+	0.525023i
$738$	−14141.1	−	8164.39i	−0.0259640	−	0.0149903i
$739$	169959.	+	634297.i	0.311212	+	1.16146i	0.927465	+	0.373911i	$0.121983\pi$
$739$	169959.	+	634297.i	0.311212	+	1.16146i	−0.616253	+	0.787549i	$0.711350\pi$
$740$		−	631367.i		−	1.15297i
$741$	505252.	+	77899.9i	0.920177	+	0.141873i
$742$	−5039.32			−0.00915302
$743$	1.00260e6	−	268647.i	1.81615	−	0.486636i	0.819851	−	0.572577i	$-0.194056\pi$
$743$	1.00260e6	−	268647.i	1.81615	−	0.486636i	0.996300	+	0.0859410i	$0.0273896\pi$
$744$	−156843.	+	271660.i	−0.283347	+	0.490772i
$745$	163461.	−	94374.1i	0.294511	−	0.170036i
$746$	−352770.	−	352770.i	−0.633890	−	0.633890i
$747$	11304.1	−	42187.6i	0.0202580	−	0.0756038i
$748$	217832.	+	58367.8i	0.389330	+	0.104321i
$749$	−344296.	+	344296.i	−0.613718	+	0.613718i
$750$	−170104.	−	294628.i	−0.302406	−	0.523783i
$751$	−202178.	−	116728.i	−0.358471	−	0.206964i	0.309939	−	0.950757i	$-0.399692\pi$
$751$	−202178.	−	116728.i	−0.358471	−	0.206964i	−0.668410	+	0.743793i	$0.733025\pi$
$752$	84.1356	+	313.999i	0.000148780	+	0.000555254i
$753$			731363.i			1.28986i
$754$	134229.	+	345434.i	0.236104	+	0.607607i
$755$	−445167.			−0.780961
$756$	378738.	−	101483.i	0.662667	−	0.177561i
$757$	426788.	−	739218.i	0.744767	−	1.28997i	−0.205537	−	0.978649i	$-0.565894\pi$
$757$	426788.	−	739218.i	0.744767	−	1.28997i	0.950304	−	0.311325i	$-0.100773\pi$
$758$	296944.	−	171441.i	0.516817	−	0.298384i
$759$	461795.	+	461795.i	0.801615	+	0.801615i
$760$	141233.	−	527087.i	0.244516	−	0.912547i
$761$	−1.06451e6	−	285235.i	−1.83815	−	0.492531i	−0.839446	−	0.543443i	$-0.817120\pi$
$761$	−1.06451e6	−	285235.i	−1.83815	−	0.492531i	−0.998703	+	0.0509128i	$0.983787\pi$
$762$	281350.	−	281350.i	0.484548	−	0.484548i
$763$	−203963.	−	353275.i	−0.350351	−	0.606825i
$764$	−163418.	−	94349.4i	−0.279971	−	0.161641i
$765$	13330.3	+	49749.4i	0.0227781	+	0.0850090i
$766$		−	434181.i		−	0.739969i
$767$	186703.	−	72549.1i	0.317366	−	0.123322i
$768$	557623.			0.945406
$769$	−54491.5	+	14600.9i	−0.0921459	+	0.0246904i	−0.304597	−	0.952481i	$-0.598522\pi$
$769$	−54491.5	+	14600.9i	−0.0921459	+	0.0246904i	0.212452	+	0.977172i	$0.431855\pi$
$770$	−139342.	+	241348.i	−0.235018	+	0.407064i
$771$	−189703.	+	109525.i	−0.319129	+	0.184249i
$772$	−180982.	−	180982.i	−0.303669	−	0.303669i
$773$	−204530.	+	763318.i	−0.342294	+	1.27746i	0.553449	+	0.832883i	$0.313311\pi$
$773$	−204530.	+	763318.i	−0.342294	+	1.27746i	−0.895742	+	0.444574i	$0.853355\pi$
$774$	49242.3	+	13194.4i	0.0821971	+	0.0220247i
$775$	19835.9	−	19835.9i	0.0330254	−	0.0330254i
$776$	3500.05	+	6062.27i	0.00581234	+	0.0100673i
$777$	−1.01883e6	−	588221.i	−1.68756	−	0.974313i
$778$	110562.	+	412622.i	0.182661	+	0.681700i
$779$		−	275967.i		−	0.454760i
$780$	−52087.9	+	337837.i	−0.0856145	+	0.555288i
$781$	57689.0			0.0945782
$782$	−510698.	+	136841.i	−0.835123	+	0.223771i
$783$	−338211.	+	585798.i	−0.551651	+	0.955487i
$784$	70.0711	−	40.4555i	0.000114000	−	6.58182e-5i
$785$	3604.17	+	3604.17i	0.00584879	+	0.00584879i
$786$	−17947.1	+	66979.5i	−0.0290502	+	0.108417i
$787$	963567.	+	258187.i	1.55572	+	0.416855i	0.931307	−	0.364236i	$-0.118670\pi$
$787$	963567.	+	258187.i	1.55572	+	0.416855i	0.624417	+	0.781091i	$0.285336\pi$
$788$	−125574.	+	125574.i	−0.202231	+	0.202231i
$789$	117366.	+	203284.i	0.188533	+	0.326549i
$790$	189953.	+	109669.i	0.304363	+	0.175724i
$791$	−106995.	−	399312.i	−0.171006	−	0.638203i
$792$			49200.8i			0.0784371i
$793$	−745795.	−	328389.i	−1.18597	−	0.522206i
$794$	−403477.			−0.639996
$795$	7745.43	−	2075.38i	0.0122549	−	0.00328370i
$796$	−14944.0	+	25883.8i	−0.0235853	+	0.0408510i
$797$	−24778.6	+	14305.9i	−0.0390086	+	0.0225216i	−0.519377	−	0.854545i	$-0.673836\pi$
$797$	−24778.6	+	14305.9i	−0.0390086	+	0.0225216i	0.480369	+	0.877067i	$0.340503\pi$
$798$	−274751.	−	274751.i	−0.431454	−	0.431454i
$799$	−79192.6	+	295551.i	−0.124048	+	0.462955i
$800$	−48198.9	−	12914.8i	−0.0753107	−	0.0201795i
$801$	17913.5	−	17913.5i	0.0279200	−	0.0279200i
$802$	262407.	+	454502.i	0.407969	+	0.706622i
$803$	−110760.	−	63947.0i	−0.171771	−	0.0991721i
$804$	−79454.8	−	296529.i	−0.122916	−	0.458728i
$805$			1.05927e6i			1.63461i
$806$	239017.	−	26113.9i	0.367925	−	0.0401978i
$807$	409610.			0.628960
$808$	1.12476e6	−	301380.i	1.72282	−	0.461627i
$809$	174832.	−	302818.i	0.267131	−	0.462684i	−0.700989	−	0.713172i	$-0.747258\pi$
$809$	174832.	−	302818.i	0.267131	−	0.462684i	0.968120	+	0.250488i	$0.0805911\pi$
$810$	297878.	−	171980.i	0.454012	−	0.262124i
$811$	−765373.	−	765373.i	−1.16367	−	1.16367i	−0.983665	−	0.180009i	$-0.942387\pi$
$811$	−765373.	−	765373.i	−1.16367	−	1.16367i	−0.180009	−	0.983665i	$-0.557613\pi$
$812$	−118193.	+	441103.i	−0.179259	+	0.669003i
$813$	−209838.	−	56225.8i	−0.317470	−	0.0850657i
$814$	419619.	−	419619.i	0.633296	−	0.633296i
$815$	65372.2	+	113228.i	0.0984187	+	0.170466i
$816$	−498.055	−	287.552i	−0.000747992	−	0.000431853i
$817$	222995.	+	832228.i	0.334080	+	1.24680i
$818$		−	303261.i		−	0.453220i
$819$	−58293.9	−	46810.7i	−0.0869071	−	0.0697874i
$820$	184526.			0.274429
$821$	−305102.	+	81751.8i	−0.452646	+	0.121286i	−0.477937	−	0.878394i	$-0.658615\pi$
$821$	−305102.	+	81751.8i	−0.452646	+	0.121286i	0.0252913	+	0.999680i	$0.491949\pi$
$822$	−256660.	+	444548.i	−0.379852	+	0.657923i
$823$	−473653.	+	273464.i	−0.699295	+	0.403738i	−0.807085	−	0.590435i	$-0.798956\pi$
$823$	−473653.	+	273464.i	−0.699295	+	0.403738i	0.107790	+	0.994174i	$0.465623\pi$
$824$	−564894.	−	564894.i	−0.831980	−	0.831980i
$825$	−9701.83	+	36207.7i	−0.0142543	+	0.0531978i
$826$	−147054.	−	39403.0i	−0.215535	−	0.0577523i
$827$	−322764.	+	322764.i	−0.471926	+	0.471926i	−0.902537	−	0.430612i	$-0.858298\pi$
$827$	−322764.	+	322764.i	−0.471926	+	0.471926i	0.430612	+	0.902537i	$0.358298\pi$
$828$	35732.3	+	61890.2i	0.0521195	+	0.0902737i
$829$	−327506.	−	189086.i	−0.476552	−	0.275137i	0.242427	−	0.970170i	$-0.422057\pi$
$829$	−327506.	−	189086.i	−0.476552	−	0.275137i	−0.718978	+	0.695032i	$0.755390\pi$
$830$	−78793.8	−	294063.i	−0.114376	−	0.426858i
$831$		−	448732.i		−	0.649808i
$832$	−252382.	−	344393.i	−0.364596	−	0.497516i
$833$	76157.5			0.109755
$834$	−32024.6	+	8580.96i	−0.0460417	+	0.0123368i
$835$	−274875.	+	476098.i	−0.394242	+	0.682846i
$836$	−275191.	+	158881.i	−0.393751	+	0.227332i
$837$	310318.	+	310318.i	0.442951	+	0.442951i
$838$	−145997.	+	544868.i	−0.207901	+	0.775895i
$839$	968504.	+	259510.i	1.37587	+	0.368663i	0.869619	−	0.493723i	$-0.164364\pi$
$839$	968504.	+	259510.i	1.37587	+	0.368663i	0.506251	+	0.862386i	$0.331031\pi$
$840$	480742.	−	480742.i	0.681323	−	0.681323i
$841$	−40261.6	−	69735.1i	−0.0569244	−	0.0985960i
$842$	89659.3	+	51764.8i	0.126465	+	0.0730148i
$843$	−275474.	−	1.02808e6i	−0.387637	−	1.44668i
$844$			755903.i			1.06116i
$845$	608329.	−	316275.i	0.851972	−	0.442947i
$846$	−25510.0			−0.0356427
$847$	−325061.	+	87099.8i	−0.453104	+	0.121409i
$848$	5.25484	−	9.10166i	7.30749e−6	−	1.26569e-5i
$849$	445142.	−	257003.i	0.617566	−	0.356552i
$850$	−21458.5	−	21458.5i	−0.0297003	−	0.0297003i
$851$	583792.	−	2.17874e6i	0.806119	−	3.00848i
$852$	−51949.1	−	13919.7i	−0.0715647	−	0.0191757i
$853$	743379.	−	743379.i	1.02167	−	1.02167i	0.0219142	−	0.999760i	$-0.493024\pi$
$853$	743379.	−	743379.i	1.02167	−	1.02167i	0.999760	−	0.0219142i	$-0.00697607\pi$
$854$	309682.	+	536384.i	0.424619	+	0.735462i
$855$	−62849.3	−	36286.1i	−0.0859742	−	0.0496372i
$856$	155080.	+	578768.i	0.211646	+	0.789873i
$857$			424271.i			0.577672i	0.957379	+	0.288836i	$0.0932683\pi$
$857$			424271.i			0.577672i	−0.957379	+	0.288836i	$0.906732\pi$
$858$	−259152.	+	189915.i	−0.352030	+	0.257979i
$859$	396196.			0.536938			0.268469	−	0.963288i	$-0.413482\pi$
$859$	396196.			0.536938			0.268469	+	0.963288i	$0.413482\pi$
$860$	−556470.	+	149106.i	−0.752393	+	0.201603i
$861$	171916.	−	297767.i	0.231904	−	0.401670i
$862$	−306541.	+	176981.i	−0.412547	+	0.238184i
$863$	908405.	+	908405.i	1.21971	+	1.21971i	0.967732	+	0.251982i	$0.0810823\pi$
$863$	908405.	+	908405.i	1.21971	+	1.21971i	0.251982	+	0.967732i	$0.418918\pi$
$864$	202043.	−	754036.i	0.270656	−	1.01010i
$865$	822623.	+	220421.i	1.09943	+	0.294592i
$866$	−354222.	+	354222.i	−0.472324	+	0.472324i
$867$	84897.9	+	147048.i	0.112943	+	0.195623i
$868$	256585.	+	148139.i	0.340558	+	0.196621i
$869$	−86506.4	−	322846.i	−0.114554	−	0.427520i
$870$			448205.i			0.592159i
$871$	−385539.	+	480117.i	−0.508197	+	0.632864i
$872$	−501991.			−0.660180
$873$	899.248	−	240.953i	0.00117992	−	0.000316157i
$874$	372491.	−	645174.i	0.487633	−	0.844606i
$875$	−728201.	+	420427.i	−0.951119	+	0.549129i
$876$	84309.6	+	84309.6i	0.109867	+	0.109867i
$877$	−51239.4	+	191228.i	−0.0666200	+	0.248629i	−0.991203	−	0.132352i	$-0.957747\pi$
$877$	−51239.4	+	191228.i	−0.0666200	+	0.248629i	0.924583	+	0.380981i	$0.124414\pi$
$878$	14208.3	+	3807.10i	0.0184312	+	0.00493862i
$879$	403591.	−	403591.i	0.522353	−	0.522353i
$880$	−290.603	−	503.340i	−0.000375263	−	0.000649974i
$881$	1.08767e6	+	627966.i	1.40134	+	0.809066i	0.994531	−	0.104445i	$-0.0333066\pi$
$881$	1.08767e6	+	627966.i	1.40134	+	0.809066i	0.406813	+	0.913511i	$0.366640\pi$
$882$	1643.36	+	6133.09i	0.00211249	+	0.00788391i
$883$		−	781993.i		−	1.00296i	−0.865171	−	0.501478i	$-0.832790\pi$
$883$		−	781993.i		−	1.00296i	0.865171	−	0.501478i	$-0.167210\pi$
$884$	45800.3	+	419204.i	0.0586089	+	0.536440i
$885$	242249.			0.309297
$886$	−60086.4	+	16100.1i	−0.0765436	+	0.0205098i
$887$	451584.	−	782166.i	0.573972	−	0.994149i	−0.422180	−	0.906512i	$-0.638735\pi$
$887$	451584.	−	782166.i	0.573972	−	0.994149i	0.996152	−	0.0876373i	$-0.0279317\pi$
$888$	−1.25376e6	+	723859.i	−1.58997	+	0.917969i
$889$	−695384.	−	695384.i	−0.879875	−	0.879875i
$890$	45703.2	−	170567.i	0.0576988	−	0.215335i
$891$	−506276.	−	135656.i	−0.637723	−	0.170877i
$892$	−133053.	+	133053.i	−0.167223	+	0.167223i
$893$	−215568.	−	373375.i	−0.270322	−	0.468212i
$894$	−143233.	−	82695.6i	−0.179212	−	0.103468i
$895$	−305884.	−	1.14158e6i	−0.381866	−	1.42514i
$896$		−	527570.i		−	0.657150i
$897$	−492127.	+	1.11766e6i	−0.611634	+	1.38907i
$898$	−500340.			−0.620458
$899$	−493703.	+	132287.i	−0.610867	+	0.163681i
$900$	−2050.95	+	3552.35i	−0.00253203	+	0.00438561i
$901$	8566.93	−	4946.12i	0.0105530	−	0.00609277i
$902$	122639.	+	122639.i	0.150736	+	0.150736i
$903$	−277832.	+	1.03688e6i	−0.340728	+	1.27161i
$904$	−491389.	−	131667.i	−0.601296	−	0.161117i
$905$	−772112.	+	772112.i	−0.942721	+	0.942721i
$906$	195040.	+	337819.i	0.237611	+	0.411554i
$907$	−248347.	−	143383.i	−0.301887	−	0.174294i	0.341403	−	0.939917i	$-0.389098\pi$
$907$	−248347.	−	143383.i	−0.301887	−	0.174294i	−0.643290	+	0.765622i	$0.722431\pi$
$908$	9706.48	+	36225.1i	0.0117731	+	0.0439377i
$909$		−	154863.i		−	0.187422i
$910$	−515035.	−	79408.2i	−0.621947	−	0.0958920i
$911$	463939.			0.559016			0.279508	−	0.960143i	$-0.409829\pi$
$911$	463939.			0.559016			0.279508	+	0.960143i	$0.409829\pi$
$912$	782.737	−	209.734i	0.000941080	−	0.000252162i
$913$	−231954.	+	401757.i	−0.278267	+	0.481972i
$914$	−66875.6	+	38610.6i	−0.0800525	+	0.0462183i
$915$	−696883.	−	696883.i	−0.832373	−	0.832373i
$916$	207715.	−	775202.i	0.247558	−	0.923898i
$917$	165546.	+	44357.9i	0.196870	+	0.0527512i
$918$	335702.	−	335702.i	0.398354	−	0.398354i
$919$	413609.	+	716391.i	0.489732	+	0.848241i	0.999930	−	0.0118161i	$-0.00376126\pi$
$919$	413609.	+	716391.i	0.489732	+	0.848241i	−0.510198	+	0.860057i	$0.670428\pi$
$920$	1.12888e6	+	651761.i	1.33375	+	0.770039i
$921$	175973.	+	656740.i	0.207456	+	0.774238i
$922$		−	130303.i		−	0.153283i
$923$	39071.6	+	100550.i	0.0458626	+	0.118026i
$924$	−395905.			−0.463711
$925$	125054.	−	33508.2i	0.146156	−	0.0391623i
$926$	142738.	−	247229.i	0.166462	−	0.288321i
$927$	−92011.9	+	53123.1i	−0.107074	+	0.0618193i
$928$	642886.	+	642886.i	0.746515	+	0.746515i
$929$	−327602.	+	1.22263e6i	−0.379590	+	1.41665i	0.466930	+	0.884294i	$0.345360\pi$
$929$	−327602.	+	1.22263e6i	−0.379590	+	1.41665i	−0.846521	+	0.532356i	$0.821307\pi$
$930$	280883.	+	75262.3i	0.324757	+	0.0870185i
$931$	−75879.4	+	75879.4i	−0.0875436	+	0.0875436i
$932$	−32043.2	−	55500.5i	−0.0368897	−	0.0638948i
$933$	174379.	+	100678.i	0.200324	+	0.115657i
$934$	−170939.	−	637952.i	−0.195951	−	0.731298i
$935$		−	547061.i		−	0.625766i
$936$	−85755.1	+	33322.7i	−0.0978832	+	0.0380355i
$937$	−134570.			−0.153275			−0.0766374	−	0.997059i	$-0.524418\pi$
$937$	−134570.			−0.153275			−0.0766374	+	0.997059i	$0.524418\pi$
$938$	452060.	−	121129.i	0.513796	−	0.137671i
$939$	367202.	−	636012.i	0.416460	−	0.721330i
$940$	249658.	−	144140.i	0.282546	−	0.163128i
$941$	211534.	+	211534.i	0.238891	+	0.238891i	0.816391	−	0.577500i	$-0.195972\pi$
$941$	211534.	+	211534.i	0.238891	+	0.238891i	−0.577500	+	0.816391i	$0.695972\pi$
$942$	1155.97	−	4314.13i	0.00130270	−	0.00486174i
$943$	636767.	+	170621.i	0.716072	+	0.191871i
$944$	224.510	−	224.510i	0.000251937	−	0.000251937i
$945$	−475580.	−	823728.i	−0.532549	−	0.922402i
$946$	−468940.	−	270742.i	−0.524004	−	0.302534i
$947$	−410792.	−	1.53310e6i	−0.458060	−	1.70950i	−0.678934	−	0.734199i	$-0.737558\pi$
$947$	−410792.	−	1.53310e6i	−0.458060	−	1.70950i	0.220874	−	0.975302i	$-0.429109\pi$
$948$			311597.i			0.346718i
$949$	36442.0	−	236360.i	0.0404641	−	0.262447i
$950$	42760.2			0.0473797
$951$	−1.26033e6	+	337703.i	−1.39355	+	0.373400i
$952$	419363.	−	726357.i	0.462717	−	0.801450i
$953$	219063.	−	126476.i	0.241203	−	0.139259i	−0.374526	−	0.927216i	$-0.622195\pi$
$953$	219063.	−	126476.i	0.241203	−	0.139259i	0.615730	+	0.787958i	$0.288861\pi$
$954$	583.179	+	583.179i	0.000640775	+	0.000640775i
$955$	−118474.	+	442151.i	−0.129902	+	0.484802i
$956$	465409.	+	124706.i	0.509236	+	0.136449i
$957$	482946.	−	482946.i	0.527321	−	0.527321i
$958$	129788.	+	224799.i	0.141417	+	0.244942i
$959$	1.09874e6	+	634359.i	1.19470	+	0.689760i
$960$	−133650.	−	498787.i	−0.145019	−	0.541219i
$961$		−	591912.i		−	0.640930i
$962$	1.01558e6	+	447181.i	1.09740	+	0.483207i
$963$	79687.8			0.0859289
$964$	−68188.8	+	18271.1i	−0.0733768	+	0.0196613i
$965$	−310441.	+	537699.i	−0.333368	+	0.577411i
$966$	803831.	−	464092.i	0.861412	−	0.497336i
$967$	−422826.	−	422826.i	−0.452177	−	0.452177i	0.443899	−	0.896077i	$-0.353595\pi$
$967$	−422826.	−	422826.i	−0.452177	−	0.452177i	−0.896077	+	0.443899i	$0.853595\pi$
$968$	−107184.	+	400017.i	−0.114388	+	0.426901i
$969$	736751.	+	197412.i	0.784645	+	0.210245i
$970$	4588.55	−	4588.55i	0.00487677	−	0.00487677i
$971$	737641.	+	1.27763e6i	0.782360	+	1.35509i	0.930563	+	0.366131i	$0.119318\pi$
$971$	737641.	+	1.27763e6i	0.782360	+	1.35509i	−0.148203	+	0.988957i	$0.547349\pi$
$972$	−105865.	−	61121.1i	−0.112052	−	0.0646932i
$973$	21208.7	+	79151.8i	0.0224020	+	0.0836055i
$974$		−	421141.i		−	0.443925i
$975$	−69679.6	+	7612.86i	−0.0732987	+	0.00800827i
$976$	−1291.70			−0.00135601
$977$	−303867.	+	81421.0i	−0.318343	+	0.0852997i	−0.414452	−	0.910071i	$-0.636027\pi$
$977$	−303867.	+	81421.0i	−0.318343	+	0.0852997i	0.0961095	+	0.995371i	$0.469360\pi$
$978$	57282.6	−	99216.3i	0.0598887	−	0.103730i
$979$	−233033.	+	134542.i	−0.243138	+	0.140376i
$980$	−50736.9	−	50736.9i	−0.0528289	−	0.0528289i
$981$	−17279.2	+	64486.8i	−0.0179550	+	0.0670089i
$982$	−77834.4	−	20855.7i	−0.0807139	−	0.0216272i
$983$	262323.	−	262323.i	0.271475	−	0.271475i	−0.558219	−	0.829694i	$-0.688515\pi$
$983$	262323.	−	262323.i	0.271475	−	0.271475i	0.829694	+	0.558219i	$0.188515\pi$
$984$	−211558.	−	366429.i	−0.218494	−	0.378442i
$985$	373082.	+	215399.i	0.384531	+	0.222009i
$986$	143109.	+	534089.i	0.147201	+	0.549363i
$987$		−	537159.i		−	0.551402i
$988$	−463306.	−	372040.i	−0.474629	−	0.381132i
$989$	−2.05815e6			−2.10419
$990$	44055.6	−	11804.7i	0.0449502	−	0.0120444i
$991$	−573080.	+	992603.i	−0.583536	+	1.01071i	0.411520	+	0.911401i	$0.364998\pi$
$991$	−573080.	+	992603.i	−0.583536	+	1.01071i	−0.995056	+	0.0993134i	$0.968335\pi$
$992$	510839.	−	294933.i	0.519111	−	0.299709i
$993$	−591837.	−	591837.i	−0.600210	−	0.600210i
$994$	21220.7	−	79196.7i	0.0214776	−	0.0801557i
$995$	70032.5	+	18765.2i	0.0707381	+	0.0189542i
$996$	305815.	−	305815.i	0.308277	−	0.308277i
$997$	−253665.	−	439360.i	−0.255193	−	0.442008i	0.709755	−	0.704449i	$-0.248806\pi$
$997$	−253665.	−	439360.i	−0.255193	−	0.442008i	−0.964948	+	0.262441i	$0.915472\pi$
$998$	−119213.	−	68827.7i	−0.119691	−	0.0691038i
$999$	524212.	+	1.95639e6i	0.525262	+	1.96030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.f.a.7.3	yes	16
3.2	odd	2		117.5.bd.c.46.2		16
13.2	odd	12	inner	13.5.f.a.2.3	✓	16
13.4	even	6		169.5.d.c.99.6		16
13.6	odd	12		169.5.d.d.70.3		16
13.7	odd	12		169.5.d.c.70.6		16
13.9	even	3		169.5.d.d.99.3		16
39.2	even	12		117.5.bd.c.28.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.2.3	✓	16	13.2	odd	12	inner
13.5.f.a.7.3	yes	16	1.1	even	1	trivial
117.5.bd.c.28.2		16	39.2	even	12
117.5.bd.c.46.2		16	3.2	odd	2
169.5.d.c.70.6		16	13.7	odd	12
169.5.d.c.99.6		16	13.4	even	6
169.5.d.d.70.3		16	13.6	odd	12
169.5.d.d.99.3		16	13.9	even	3

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.38644 - 0.639444i) q^{2} +(4.25709 - 7.37349i) q^{3} +(-8.57021 + 4.94801i) q^{4} +(16.9748 + 16.9748i) q^{5} +(5.44434 - 20.3185i) q^{6} +(-50.2192 - 13.4562i) q^{7} +(-45.2402 + 45.2402i) q^{8} +(4.25442 + 7.36887i) q^{9} +O(q^{10})\)	\(q+(2.38644 - 0.639444i) q^{2} +(4.25709 - 7.37349i) q^{3} +(-8.57021 + 4.94801i) q^{4} +(16.9748 + 16.9748i) q^{5} +(5.44434 - 20.3185i) q^{6} +(-50.2192 - 13.4562i) q^{7} +(-45.2402 + 45.2402i) q^{8} +(4.25442 + 7.36887i) q^{9} +(51.3637 + 29.6548i) q^{10} +(-23.3915 - 87.2983i) q^{11} +84.2565i q^{12} +(136.315 - 99.8960i) q^{13} -128.449 q^{14} +(197.426 - 52.9003i) q^{15} +(0.133943 - 0.231996i) q^{16} +(218.366 - 126.074i) q^{17} +(14.8649 + 14.8649i) q^{18} +(-91.9552 + 343.182i) q^{19} +(-229.469 - 61.4860i) q^{20} +(-313.007 + 313.007i) q^{21} +(-111.645 - 193.374i) q^{22} +(-735.005 - 424.355i) q^{23} +(140.987 + 526.170i) q^{24} -48.7139i q^{25} +(261.429 - 325.561i) q^{26} +762.094 q^{27} +(496.971 - 133.163i) q^{28} +(-443.792 + 768.670i) q^{29} +(437.319 - 252.486i) q^{30} +(407.191 + 407.191i) q^{31} +(265.116 - 989.427i) q^{32} +(-743.273 - 199.159i) q^{33} +(440.500 - 440.500i) q^{34} +(-624.044 - 1080.88i) q^{35} +(-72.9226 - 42.1019i) q^{36} +(687.857 + 2567.12i) q^{37} +877.782i q^{38} +(-156.277 - 1430.38i) q^{39} -1535.88 q^{40} +(-750.275 + 201.036i) q^{41} +(-546.820 + 947.121i) q^{42} +(2100.14 - 1212.52i) q^{43} +(632.424 + 632.424i) q^{44} +(-52.8671 + 197.303i) q^{45} +(-2025.39 - 542.703i) q^{46} +(-858.063 + 858.063i) q^{47} +(-1.14041 - 1.97525i) q^{48} +(261.571 + 151.018i) q^{49} +(-31.1498 - 116.253i) q^{50} -2146.83i q^{51} +(-673.962 + 1530.62i) q^{52} +39.2320 q^{53} +(1818.69 - 487.316i) q^{54} +(1084.80 - 1878.93i) q^{55} +(2880.69 - 1663.16i) q^{56} +(2138.99 + 2138.99i) q^{57} +(-567.560 + 2118.16i) q^{58} +(1144.84 + 306.759i) q^{59} +(-1430.24 + 1430.24i) q^{60} +(-2410.92 - 4175.84i) q^{61} +(1232.11 + 711.360i) q^{62} +(-114.497 - 427.307i) q^{63} -2526.45i q^{64} +(4009.63 + 618.206i) q^{65} -1901.13 q^{66} +(-3519.36 + 943.010i) q^{67} +(-1247.63 + 2160.96i) q^{68} +(-6257.96 + 3613.04i) q^{69} +(-2180.40 - 2180.40i) q^{70} +(-165.207 + 616.559i) q^{71} +(-525.840 - 140.898i) q^{72} +(1000.63 - 1000.63i) q^{73} +(3283.06 + 5686.42i) q^{74} +(-359.192 - 207.379i) q^{75} +(-909.992 - 3396.14i) q^{76} +4698.81i q^{77} +(-1287.60 - 3313.59i) q^{78} +3698.19 q^{79} +(6.21173 - 1.66443i) q^{80} +(2899.69 - 5022.41i) q^{81} +(-1661.93 + 959.518i) q^{82} +(-3629.57 - 3629.57i) q^{83} +(1133.77 - 4231.29i) q^{84} +(5846.79 + 1566.64i) q^{85} +(4236.52 - 4236.52i) q^{86} +(3778.52 + 6544.59i) q^{87} +(5007.63 + 2891.16i) q^{88} +(-770.586 - 2875.87i) q^{89} +504.656i q^{90} +(-8189.85 + 3182.41i) q^{91} +8398.87 q^{92} +(4735.87 - 1268.97i) q^{93} +(-1499.03 + 2596.40i) q^{94} +(-7386.35 + 4264.51i) q^{95} +(-6166.91 - 6166.91i) q^{96} +(28.3179 - 105.684i) q^{97} +(720.790 + 193.135i) q^{98} +(543.773 - 543.773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 + 8 * q^5 - 38 * q^6 + 56 * q^7 + 90 * q^8 - 164 * q^9 - 486 * q^10 - 100 * q^11 + 294 * q^13 + 808 * q^14 + 346 * q^15 + 230 * q^16 + 984 * q^17 + 2434 * q^18 - 1498 * q^19 - 3962 * q^20 - 1076 * q^21 - 1524 * q^22 - 1014 * q^23 - 2142 * q^24 + 614 * q^26 + 3352 * q^27 + 5764 * q^28 + 814 * q^29 + 9162 * q^30 + 4060 * q^31 - 4996 * q^32 - 5636 * q^33 - 2502 * q^34 - 4892 * q^35 - 15750 * q^36 - 1790 * q^37 + 6982 * q^39 + 18816 * q^40 + 4280 * q^41 - 1204 * q^42 - 1368 * q^43 + 10736 * q^44 - 6806 * q^45 - 15246 * q^46 + 1484 * q^47 - 3002 * q^48 - 11820 * q^49 - 13574 * q^50 + 1432 * q^52 + 7204 * q^53 + 13240 * q^54 + 6936 * q^55 + 8124 * q^56 + 12736 * q^57 + 3030 * q^58 - 2380 * q^59 - 6472 * q^60 - 162 * q^61 + 19614 * q^62 + 12004 * q^63 - 5248 * q^65 - 23872 * q^66 - 14854 * q^67 - 6444 * q^68 + 2412 * q^69 - 34524 * q^70 - 8050 * q^71 + 15420 * q^72 - 15448 * q^73 - 2882 * q^74 + 8280 * q^75 + 10622 * q^76 - 11672 * q^78 - 17064 * q^79 + 2564 * q^80 + 2128 * q^81 - 5346 * q^82 + 12788 * q^83 + 25948 * q^84 + 35382 * q^85 + 67260 * q^86 + 29342 * q^87 + 40836 * q^88 + 20492 * q^89 + 8996 * q^91 - 49884 * q^92 - 78920 * q^93 - 30606 * q^94 - 98574 * q^95 - 94664 * q^96 + 50944 * q^97 + 61484 * q^98 - 21632 * q^99

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