LMFDB - Embedded newform 13.5.f.a.6.1

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			6.1
Root			$4.34562i$ of defining polynomial
Character	$\chi$	$=$	13.6
Dual form			13.5.f.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88469 - 7.03375i) q^{2} +(-0.939567 + 1.62738i) q^{3} +(-32.0652 + 18.5128i) q^{4} +(26.6717 - 26.6717i) q^{5} +(13.2174 + 3.54158i) q^{6} +(7.85376 - 29.3106i) q^{7} +(108.263 + 108.263i) q^{8} +(38.7344 + 67.0900i) q^{9} +O(q^{10})$	\(q+(-1.88469 - 7.03375i) q^{2} +(-0.939567 + 1.62738i) q^{3} +(-32.0652 + 18.5128i) q^{4} +(26.6717 - 26.6717i) q^{5} +(13.2174 + 3.54158i) q^{6} +(7.85376 - 29.3106i) q^{7} +(108.263 + 108.263i) q^{8} +(38.7344 + 67.0900i) q^{9} +(-237.870 - 137.334i) q^{10} +(-29.4111 + 7.88068i) q^{11} -69.5762i q^{12} +(130.585 + 107.278i) q^{13} -220.965 q^{14} +(18.3451 + 68.4648i) q^{15} +(261.245 - 452.490i) q^{16} +(-52.1872 + 30.1303i) q^{17} +(398.892 - 398.892i) q^{18} +(-389.684 - 104.416i) q^{19} +(-361.464 + 1349.00i) q^{20} +(40.3203 + 40.3203i) q^{21} +(110.861 + 192.018i) q^{22} +(448.762 + 259.093i) q^{23} +(-277.904 + 74.4642i) q^{24} -797.759i q^{25} +(508.456 - 1120.69i) q^{26} -297.784 q^{27} +(290.791 + 1085.25i) q^{28} +(158.758 - 274.976i) q^{29} +(446.989 - 258.069i) q^{30} +(-324.998 + 324.998i) q^{31} +(-1308.84 - 350.702i) q^{32} +(14.8088 - 55.2674i) q^{33} +(310.286 + 310.286i) q^{34} +(-572.291 - 991.237i) q^{35} +(-2484.05 - 1434.17i) q^{36} +(99.6664 - 26.7055i) q^{37} +2937.73i q^{38} +(-297.275 + 111.716i) q^{39} +5775.10 q^{40} +(176.697 + 659.441i) q^{41} +(207.612 - 359.594i) q^{42} +(-2920.63 + 1686.23i) q^{43} +(797.178 - 797.178i) q^{44} +(2822.52 + 756.291i) q^{45} +(976.619 - 3644.79i) q^{46} +(-468.402 - 468.402i) q^{47} +(490.915 + 850.290i) q^{48} +(1281.90 + 740.103i) q^{49} +(-5611.24 + 1503.53i) q^{50} -113.238i q^{51} +(-6173.25 - 1022.40i) q^{52} +1063.34 q^{53} +(561.230 + 2094.54i) q^{54} +(-574.253 + 994.635i) q^{55} +(4023.51 - 2322.98i) q^{56} +(536.058 - 536.058i) q^{57} +(-2233.32 - 598.417i) q^{58} +(749.836 - 2798.42i) q^{59} +(-1855.72 - 1855.72i) q^{60} +(-1605.56 - 2780.92i) q^{61} +(2898.47 + 1673.43i) q^{62} +(2270.66 - 608.421i) q^{63} +1507.15i q^{64} +(6344.21 - 621.629i) q^{65} -416.647 q^{66} +(1503.93 + 5612.75i) q^{67} +(1115.60 - 1932.27i) q^{68} +(-843.284 + 486.871i) q^{69} +(-5893.52 + 5893.52i) q^{70} +(-1635.03 - 438.105i) q^{71} +(-3069.85 + 11456.8i) q^{72} +(-4911.25 - 4911.25i) q^{73} +(-375.680 - 650.697i) q^{74} +(1298.26 + 749.548i) q^{75} +(14428.3 - 3866.06i) q^{76} +923.950i q^{77} +(1346.05 + 1880.41i) q^{78} -8184.71 q^{79} +(-5100.83 - 19036.5i) q^{80} +(-2857.70 + 4949.68i) q^{81} +(4305.32 - 2485.68i) q^{82} +(5221.16 - 5221.16i) q^{83} +(-2039.32 - 546.435i) q^{84} +(-588.296 + 2195.55i) q^{85} +(17365.0 + 17365.0i) q^{86} +(298.327 + 516.717i) q^{87} +(-4037.30 - 2330.94i) q^{88} +(-10667.8 + 2858.42i) q^{89} -21278.3i q^{90} +(4169.97 - 2984.99i) q^{91} -19186.2 q^{92} +(-223.537 - 834.251i) q^{93} +(-2411.83 + 4177.41i) q^{94} +(-13178.5 + 7608.60i) q^{95} +(1800.47 - 1800.47i) q^{96} +(12518.4 + 3354.29i) q^{97} +(2789.73 - 10411.4i) q^{98} +(-1667.94 - 1667.94i) 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−1.88469	−	7.03375i	−0.471172	−	1.75844i	−0.635570	−	0.772043i	$-0.719235\pi$
$2$	−1.88469	−	7.03375i	−0.471172	−	1.75844i	0.164398	−	0.986394i	$-0.447432\pi$
$3$	−0.939567	+	1.62738i	−0.104396	+	0.180820i	−0.913491	−	0.406858i	$-0.866624\pi$
$3$	−0.939567	+	1.62738i	−0.104396	+	0.180820i	0.809095	+	0.587678i	$0.199958\pi$
$4$	−32.0652	+	18.5128i	−2.00407	+	1.15705i
$5$	26.6717	−	26.6717i	1.06687	−	1.06687i	0.0692701	−	0.997598i	$-0.477933\pi$
$5$	26.6717	−	26.6717i	1.06687	−	1.06687i	0.997598	−	0.0692701i	$-0.0220670\pi$
$6$	13.2174	+	3.54158i	0.367149	+	0.0983772i
$7$	7.85376	−	29.3106i	0.160281	−	0.598176i	−0.838314	−	0.545187i	$-0.816459\pi$
$7$	7.85376	−	29.3106i	0.160281	−	0.598176i	0.998595	−	0.0529887i	$-0.0168747\pi$
$8$	108.263	+	108.263i	1.69160	+	1.69160i
$9$	38.7344	+	67.0900i	0.478203	+	0.828272i
$10$	−237.870	−	137.334i	−2.37870	−	1.37334i
$11$	−29.4111	+	7.88068i	−0.243067	+	0.0651296i	−0.378296	−	0.925685i	$-0.623490\pi$
$11$	−29.4111	+	7.88068i	−0.243067	+	0.0651296i	0.135229	+	0.990814i	$0.456823\pi$
$12$		−	69.5762i		−	0.483168i
$13$	130.585	+	107.278i	0.772691	+	0.634782i
$13$	130.585	+	107.278i	0.772691	+	0.634782i
$14$	−220.965			−1.12737
$15$	18.3451	+	68.4648i	0.0815337	+	0.304288i
$16$	261.245	−	452.490i	1.02049	−	1.76754i
$17$	−52.1872	+	30.1303i	−0.180579	+	0.104257i	−0.587565	−	0.809177i	$-0.699913\pi$
$17$	−52.1872	+	30.1303i	−0.180579	+	0.104257i	0.406986	+	0.913434i	$0.366580\pi$
$18$	398.892	−	398.892i	1.23115	−	1.23115i
$19$	−389.684	−	104.416i	−1.07946	−	0.289240i	−0.325084	−	0.945685i	$-0.605393\pi$
$19$	−389.684	−	104.416i	−1.07946	−	0.289240i	−0.754374	+	0.656445i	$0.772059\pi$
$20$	−361.464	+	1349.00i	−0.903660	+	3.37251i
$21$	40.3203	+	40.3203i	0.0914293	+	0.0914293i
$22$	110.861	+	192.018i	0.229053	+	0.396731i
$23$	448.762	+	259.093i	0.848322	+	0.489779i	0.860084	−	0.510152i	$-0.170411\pi$
$23$	448.762	+	259.093i	0.848322	+	0.489779i	−0.0117622	+	0.999931i	$0.503744\pi$
$24$	−277.904	+	74.4642i	−0.482472	+	0.129278i
$25$		−	797.759i		−	1.27641i
$26$	508.456	−	1120.69i	0.752154	−	1.65782i
$27$	−297.784			−0.408483
$28$	290.791	+	1085.25i	0.370907	+	1.38424i
$29$	158.758	−	274.976i	0.188772	−	0.326964i	−0.756069	−	0.654492i	$-0.772882\pi$
$29$	158.758	−	274.976i	0.188772	−	0.326964i	0.944841	+	0.327529i	$0.106216\pi$
$30$	446.989	−	258.069i	0.496655	−	0.286744i
$31$	−324.998	+	324.998i	−0.338187	+	0.338187i	−0.855685	−	0.517498i	$-0.826864\pi$
$31$	−324.998	+	324.998i	−0.338187	+	0.338187i	0.517498	+	0.855685i	$0.326864\pi$
$32$	−1308.84	−	350.702i	−1.27816	−	0.342482i
$33$	14.8088	−	55.2674i	0.0135986	−	0.0507506i
$34$	310.286	+	310.286i	0.268413	+	0.268413i
$35$	−572.291	−	991.237i	−0.467176	−	0.809173i
$36$	−2484.05	−	1434.17i	−1.91671	−	1.10661i
$37$	99.6664	−	26.7055i	0.0728023	−	0.0195073i	−0.222234	−	0.974993i	$-0.571335\pi$
$37$	99.6664	−	26.7055i	0.0728023	−	0.0195073i	0.295036	+	0.955486i	$0.404668\pi$
$38$			2937.73i			2.03444i
$39$	−297.275	+	111.716i	−0.195447	+	0.0734489i
$40$	5775.10			3.60943
$41$	176.697	+	659.441i	0.105114	+	0.392291i	0.998358	−	0.0572813i	$-0.0182432\pi$
$41$	176.697	+	659.441i	0.105114	+	0.392291i	−0.893244	+	0.449572i	$0.851577\pi$
$42$	207.612	−	359.594i	0.117694	−	0.203852i
$43$	−2920.63	+	1686.23i	−1.57958	+	0.911968i	−0.584657	+	0.811281i	$0.698771\pi$
$43$	−2920.63	+	1686.23i	−1.57958	+	0.911968i	−0.994918	+	0.100687i	$0.967896\pi$
$44$	797.178	−	797.178i	0.411766	−	0.411766i
$45$	2822.52	+	756.291i	1.39384	+	0.373477i
$46$	976.619	−	3644.79i	0.461540	−	1.72249i
$47$	−468.402	−	468.402i	−0.212042	−	0.212042i	0.593092	−	0.805135i	$-0.297907\pi$
$47$	−468.402	−	468.402i	−0.212042	−	0.212042i	−0.805135	+	0.593092i	$0.797907\pi$
$48$	490.915	+	850.290i	0.213071	+	0.369049i
$49$	1281.90	+	740.103i	0.533901	+	0.308248i
$50$	−5611.24	+	1503.53i	−2.24450	+	0.601411i
$51$		−	113.238i		−	0.0435363i
$52$	−6173.25	−	1022.40i	−2.28301	−	0.378105i
$53$	1063.34			0.378549			0.189274	−	0.981924i	$-0.439386\pi$
$53$	1063.34			0.378549			0.189274	+	0.981924i	$0.439386\pi$
$54$	561.230	+	2094.54i	0.192466	+	0.718292i
$55$	−574.253	+	994.635i	−0.189836	+	0.328805i
$56$	4023.51	−	2322.98i	1.28301	−	0.740745i
$57$	536.058	−	536.058i	0.164992	−	0.164992i
$58$	−2233.32	−	598.417i	−0.663889	−	0.177889i
$59$	749.836	−	2798.42i	0.215408	−	0.803914i	−0.770614	−	0.637302i	$-0.780051\pi$
$59$	749.836	−	2798.42i	0.215408	−	0.803914i	0.986022	−	0.166612i	$-0.0532828\pi$
$60$	−1855.72	−	1855.72i	−0.515477	−	0.515477i
$61$	−1605.56	−	2780.92i	−0.431487	−	0.747358i	0.565514	−	0.824738i	$-0.308678\pi$
$61$	−1605.56	−	2780.92i	−0.431487	−	0.747358i	−0.997002	+	0.0773807i	$0.975344\pi$
$62$	2898.47	+	1673.43i	0.754025	+	0.435337i
$63$	2270.66	−	608.421i	0.572099	−	0.153293i
$64$			1507.15i			0.367957i
$65$	6344.21	−	621.629i	1.50159	−	0.147131i
$66$	−416.647			−0.0956490
$67$	1503.93	+	5612.75i	0.335026	+	1.25034i	0.903841	+	0.427869i	$0.140736\pi$
$67$	1503.93	+	5612.75i	0.335026	+	1.25034i	−0.568814	+	0.822466i	$0.692598\pi$
$68$	1115.60	−	1932.27i	0.241262	−	0.417878i
$69$	−843.284	+	486.871i	−0.177123	+	0.102262i
$70$	−5893.52	+	5893.52i	−1.20276	+	1.20276i
$71$	−1635.03	−	438.105i	−0.324347	−	0.0869084i	0.0929718	−	0.995669i	$-0.470363\pi$
$71$	−1635.03	−	438.105i	−0.324347	−	0.0869084i	−0.417318	+	0.908760i	$0.637030\pi$
$72$	−3069.85	+	11456.8i	−0.592177	+	2.21004i
$73$	−4911.25	−	4911.25i	−0.921608	−	0.921608i	0.0755348	−	0.997143i	$-0.475934\pi$
$73$	−4911.25	−	4911.25i	−0.921608	−	0.921608i	−0.997143	+	0.0755348i	$0.975934\pi$
$74$	−375.680	−	650.697i	−0.0686048	−	0.118827i
$75$	1298.26	+	749.548i	0.230801	+	0.133253i
$76$	14428.3	−	3866.06i	2.49798	−	0.669332i
$77$			923.950i			0.155836i
$78$	1346.05	+	1880.41i	0.221245	+	0.309075i
$79$	−8184.71			−1.31144			−0.655721	−	0.755003i	$-0.727635\pi$
$79$	−8184.71			−1.31144			−0.655721	+	0.755003i	$0.727635\pi$
$80$	−5100.83	−	19036.5i	−0.797004	−	2.97446i
$81$	−2857.70	+	4949.68i	−0.435559	+	0.754410i
$82$	4305.32	−	2485.68i	0.640292	−	0.369673i
$83$	5221.16	−	5221.16i	0.757898	−	0.757898i	−0.218042	−	0.975939i	$-0.569967\pi$
$83$	5221.16	−	5221.16i	0.757898	−	0.757898i	0.975939	+	0.218042i	$0.0699668\pi$
$84$	−2039.32	−	546.435i	−0.289020	−	0.0774425i
$85$	−588.296	+	2195.55i	−0.0814250	+	0.303882i
$86$	17365.0	+	17365.0i	2.34789	+	2.34789i
$87$	298.327	+	516.717i	0.0394143	+	0.0682676i
$88$	−4037.30	−	2330.94i	−0.521346	−	0.300999i
$89$	−10667.8	+	2858.42i	−1.34677	+	0.360866i	−0.858942	−	0.512072i	$-0.828878\pi$
$89$	−10667.8	+	2858.42i	−1.34677	+	0.360866i	−0.487830	+	0.872939i	$0.662211\pi$
$90$		−	21278.3i		−	2.62695i
$91$	4169.97	−	2984.99i	0.503559	−	0.360462i
$92$	−19186.2			−2.26680
$93$	−223.537	−	834.251i	−0.0258454	−	0.0964564i
$94$	−2411.83	+	4177.41i	−0.272955	+	0.472772i
$95$	−13178.5	+	7608.60i	−1.46022	+	0.843058i
$96$	1800.47	−	1800.47i	0.195363	−	0.195363i
$97$	12518.4	+	3354.29i	1.33047	+	0.356498i	0.852889	−	0.522092i	$-0.174848\pi$
$97$	12518.4	+	3354.29i	1.33047	+	0.356498i	0.477578	+	0.878590i	$0.341515\pi$
$98$	2789.73	−	10411.4i	0.290476	−	1.08407i
$99$	−1667.94	−	1667.94i	−0.170180	−	0.170180i
$100$	14768.8	+	25580.3i	1.47688	+	2.55803i
$101$	−3620.95	−	2090.55i	−0.354960	−	0.204936i	0.311908	−	0.950112i	$-0.399032\pi$
$101$	−3620.95	−	2090.55i	−0.354960	−	0.204936i	−0.666868	+	0.745176i	$0.732365\pi$
$102$	−796.486	+	213.418i	−0.0765558	+	0.0205131i
$103$			4123.11i			0.388643i	0.980938	+	0.194322i	$0.0622505\pi$
$103$			4123.11i			0.388643i	−0.980938	+	0.194322i	$0.937749\pi$
$104$	2523.24	+	25751.7i	0.233288	+	2.38089i
$105$	2150.82			0.195086
$106$	−2004.07	−	7479.29i	−0.178362	−	0.665654i
$107$	9923.64	−	17188.3i	0.866769	−	1.50129i	0.00148989	−	0.999999i	$-0.499526\pi$
$107$	9923.64	−	17188.3i	0.866769	−	1.50129i	0.865279	−	0.501290i	$-0.167141\pi$
$108$	9548.50	−	5512.83i	0.818630	−	0.472636i
$109$	5173.19	−	5173.19i	0.435417	−	0.435417i	−0.455049	−	0.890466i	$-0.650378\pi$
$109$	5173.19	−	5173.19i	0.435417	−	0.435417i	0.890466	+	0.455049i	$0.150378\pi$
$110$	8078.30	+	2164.57i	0.667628	+	0.178890i
$111$	−50.1832	+	187.286i	−0.00407298	+	0.0152006i
$112$	−11211.0	−	11211.0i	−0.893735	−	0.893735i
$113$	−7281.22	−	12611.5i	−0.570227	−	0.987662i	−0.996542	−	0.0830871i	$-0.973522\pi$
$113$	−7281.22	−	12611.5i	−0.570227	−	0.987662i	0.426316	−	0.904574i	$-0.359811\pi$
$114$	−4780.80	−	2760.20i	−0.367867	−	0.212388i
$115$	18879.7	−	5058.80i	1.42758	−	0.382518i
$116$			11756.2i			0.873679i
$117$	−2139.16	+	12916.3i	−0.156269	+	0.943553i
$118$	−21096.6			−1.51513
$119$	473.272	+	1766.28i	0.0334208	+	0.124728i
$120$	−5426.09	+	9398.26i	−0.376812	+	0.652657i
$121$	−11876.6	+	6856.94i	−0.811186	+	0.468338i
$122$	−16534.3	+	16534.3i	−1.11088	+	1.11088i
$123$	−1239.18	−	332.037i	−0.0819074	−	0.0219470i
$124$	4404.48	−	16437.8i	0.286452	−	1.06905i
$125$	−4607.78	−	4607.78i	−0.294898	−	0.294898i
$126$	−8558.97	−	14824.6i	−0.539114	−	0.933772i
$127$	17537.5	+	10125.3i	1.08733	+	0.627769i	0.932864	−	0.360229i	$-0.117301\pi$
$127$	17537.5	+	10125.3i	1.08733	+	0.627769i	0.154465	+	0.987998i	$0.450635\pi$
$128$	−10340.5	+	2770.72i	−0.631133	+	0.169112i
$129$		−	6337.30i		−	0.380824i
$130$	−16329.2	−	43452.0i	−0.966227	−	2.57113i
$131$	24061.4			1.40210			0.701050	−	0.713112i	$-0.252715\pi$
$131$	24061.4			1.40210			0.701050	+	0.713112i	$0.252715\pi$
$132$	548.308	+	2046.31i	0.0314685	+	0.117442i
$133$	−6120.97	+	10601.8i	−0.346033	+	0.599346i
$134$	36644.3	−	21156.6i	2.04078	−	1.17825i
$135$	−7942.41	+	7942.41i	−0.435797	+	0.435797i
$136$	−8911.91	−	2387.94i	−0.481829	−	0.129106i
$137$	−4224.61	+	15766.5i	−0.225085	+	0.840027i	0.757286	+	0.653083i	$0.226525\pi$
$137$	−4224.61	+	15766.5i	−0.225085	+	0.840027i	−0.982371	+	0.186944i	$0.940142\pi$
$138$	5013.85	+	5013.85i	0.263277	+	0.263277i
$139$	6794.45	+	11768.3i	0.351662	+	0.609096i	0.986541	−	0.163516i	$-0.0522835\pi$
$139$	6794.45	+	11768.3i	0.351662	+	0.609096i	−0.634879	+	0.772611i	$0.718950\pi$
$140$	36701.2	+	21189.5i	1.87251	+	1.08110i
$141$	1202.36	−	322.172i	0.0604779	−	0.0162050i
$142$			12326.1i			0.611292i
$143$	−4686.07	−	2126.07i	−0.229159	−	0.103969i
$144$	40476.8			1.95200
$145$	−3099.75	−	11568.4i	−0.147432	−	0.550222i
$146$	−25288.3	+	43800.7i	−1.18635	+	2.05483i
$147$	−2408.85	+	1390.75i	−0.111475	+	0.0643599i
$148$	−2701.43	+	2701.43i	−0.123330	+	0.123330i
$149$	−28767.2	−	7708.15i	−1.29576	−	0.347198i	−0.455915	−	0.890023i	$-0.650688\pi$
$149$	−28767.2	−	7708.15i	−1.29576	−	0.347198i	−0.839846	+	0.542825i	$0.817355\pi$
$150$	2825.33	−	10544.3i	0.125570	−	0.468634i
$151$	−10632.6	−	10632.6i	−0.466321	−	0.466321i	0.434399	−	0.900720i	$-0.356961\pi$
$151$	−10632.6	−	10632.6i	−0.466321	−	0.466321i	−0.900720	+	0.434399i	$0.856961\pi$
$152$	−30883.9	−	53492.5i	−1.33674	−	2.31529i
$153$	−4042.89	−	2334.16i	−0.172707	−	0.0997121i
$154$	6498.83	−	1741.36i	0.274027	−	0.0734254i
$155$			17336.5i			0.721602i
$156$	7464.01	−	9085.60i	0.306706	−	0.373340i
$157$	11569.3			0.469363			0.234681	−	0.972072i	$-0.424595\pi$
$157$	11569.3			0.469363			0.234681	+	0.972072i	$0.424595\pi$
$158$	15425.6	+	57569.2i	0.617915	+	2.30609i
$159$	−999.082	+	1730.46i	−0.0395191	+	0.0684491i
$160$	−44262.8	+	25555.1i	−1.72901	+	0.998247i
$161$	11118.6	−	11118.6i	0.428944	−	0.428944i
$162$	40200.7	+	10771.7i	1.53181	+	0.410446i
$163$	5820.04	−	21720.7i	0.219054	−	0.817519i	−0.765646	−	0.643262i	$-0.777581\pi$
$163$	5820.04	−	21720.7i	0.219054	−	0.817519i	0.984700	−	0.174258i	$-0.0557526\pi$
$164$	−17873.9	−	17873.9i	−0.664557	−	0.664557i
$165$	−1079.10	−	1869.05i	−0.0396363	−	0.0686520i
$166$	−46564.6	−	26884.1i	−1.68982	−	0.975616i
$167$	7231.89	−	1937.78i	0.259310	−	0.0694819i	−0.126822	−	0.991926i	$-0.540478\pi$
$167$	7231.89	−	1937.78i	0.259310	−	0.0694819i	0.386132	+	0.922444i	$0.373811\pi$
$168$			8730.36i			0.309324i
$169$	5543.80	+	28017.8i	0.194104	+	0.980981i
$170$	16551.7			0.572723
$171$	−8088.96	−	30188.4i	−0.276631	−	1.03240i
$172$	62433.8	−	108139.i	2.11039	−	3.65530i
$173$	23442.8	−	13534.7i	0.783281	−	0.452227i	−0.0543110	−	0.998524i	$-0.517296\pi$
$173$	23442.8	−	13534.7i	0.783281	−	0.452227i	0.837592	+	0.546297i	$0.183963\pi$
$174$	3072.21	−	3072.21i	0.101473	−	0.101473i
$175$	−23382.8	−	6265.41i	−0.763520	−	0.204585i
$176$	−4117.58	+	15367.0i	−0.132928	+	0.496094i
$177$	3849.57	+	3849.57i	0.122876	+	0.122876i
$178$	40210.9	+	69647.3i	1.26912	+	2.19818i
$179$	−41557.2	−	23993.0i	−1.29700	−	0.748823i	−0.317115	−	0.948387i	$-0.602714\pi$
$179$	−41557.2	−	23993.0i	−1.29700	−	0.748823i	−0.979885	+	0.199564i	$0.936047\pi$
$180$	−104506.	+	28002.2i	−3.22548	+	0.864266i
$181$			18315.0i			0.559048i	0.960139	+	0.279524i	$0.0901767\pi$
$181$			18315.0i			0.559048i	−0.960139	+	0.279524i	$0.909823\pi$
$182$	−28854.7	−	23704.8i	−0.871113	−	0.715637i
$183$	6034.14			0.180183
$184$	20534.1	+	76634.3i	0.606513	+	2.26354i
$185$	1945.99	−	3370.55i	0.0568587	−	0.0984822i
$186$	−5446.62	+	3144.61i	−0.157435	+	0.0908951i
$187$	1297.44	−	1297.44i	0.0371025	−	0.0371025i
$188$	23690.8	+	6347.94i	0.670293	+	0.179605i
$189$	−2338.72	+	8728.24i	−0.0654720	+	0.244345i
$190$	78354.3	+	78354.3i	2.17048	+	2.17048i
$191$	10819.2	+	18739.4i	0.296571	+	0.513676i	0.975349	−	0.220667i	$-0.0708235\pi$
$191$	10819.2	+	18739.4i	0.296571	+	0.513676i	−0.678778	+	0.734343i	$0.737490\pi$
$192$	−2452.70	−	1416.07i	−0.0665339	−	0.0384133i
$193$	15038.8	−	4029.64i	0.403737	−	0.108181i	−0.0512352	−	0.998687i	$-0.516316\pi$
$193$	15038.8	−	4029.64i	0.403737	−	0.108181i	0.454972	+	0.890506i	$0.349649\pi$
$194$		−	94372.8i		−	2.50751i
$195$	−4949.18	+	10908.5i	−0.130156	+	0.286877i
$196$	−54805.7			−1.42664
$197$	−9050.39	−	33776.5i	−0.233203	−	0.870327i	−0.978951	−	0.204098i	$-0.934574\pi$
$197$	−9050.39	−	33776.5i	−0.233203	−	0.870327i	0.745747	−	0.666229i	$-0.232093\pi$
$198$	−8588.31	+	14875.4i	−0.219067	+	0.379435i
$199$	−24096.8	+	13912.3i	−0.608490	+	0.351312i	−0.772374	−	0.635168i	$-0.780931\pi$
$199$	−24096.8	+	13912.3i	−0.608490	+	0.351312i	0.163884	+	0.986480i	$0.447598\pi$
$200$	86367.5	−	86367.5i	2.15919	−	2.15919i
$201$	−10547.1	−	2826.09i	−0.261061	−	0.0699510i
$202$	−7880.08	+	29408.9i	−0.193120	+	0.720735i
$203$	−6812.88	−	6812.88i	−0.165325	−	0.165325i
$204$	2096.35	+	3630.99i	0.0503737	+	0.0872499i
$205$	22301.2	+	12875.6i	0.530665	+	0.306380i
$206$	29001.0	−	7770.78i	0.683404	−	0.183118i
$207$			40143.3i			0.936855i
$208$	82657.0	−	31062.4i	1.91053	−	0.717974i
$209$	12283.9			0.281219
$210$	−4053.63	−	15128.3i	−0.0919190	−	0.343046i
$211$	18708.8	−	32404.6i	0.420224	−	0.727849i	−0.575737	−	0.817635i	$-0.695285\pi$
$211$	18708.8	−	32404.6i	0.420224	−	0.727849i	0.995961	+	0.0897855i	$0.0286182\pi$
$212$	−34096.3	+	19685.5i	−0.758640	+	0.438001i
$213$	2249.18	−	2249.18i	0.0495754	−	0.0495754i
$214$	−139601.	−	37405.9i	−3.04832	−	0.816795i
$215$	−32923.7	+	122873.i	−0.712249	+	2.65815i
$216$	−32238.9	−	32238.9i	−0.690991	−	0.690991i
$217$	6973.43	+	12078.3i	0.148091	+	0.256500i
$218$	−46136.7	−	26637.1i	−0.970809	−	0.560497i
$219$	12606.9	−	3378.01i	0.262857	−	0.0704324i
$220$		−	42524.2i		−	0.878599i
$221$	−10047.2	−	1663.99i	−0.205712	−	0.0340695i
$222$	1411.91			0.0286484
$223$	−11569.1	−	43176.3i	−0.232642	−	0.868232i	−0.979198	−	0.202909i	$-0.934960\pi$
$223$	−11569.1	−	43176.3i	−0.232642	−	0.868232i	0.746556	−	0.665323i	$-0.231706\pi$
$224$	−20558.6	+	35608.5i	−0.409729	+	0.709672i
$225$	53521.7	−	30900.7i	1.05722	−	0.610385i
$226$	−74983.0	+	74983.0i	−1.46807	+	1.46807i
$227$	62149.7	+	16653.0i	1.20611	+	0.323177i	0.805235	−	0.592956i	$-0.202039\pi$
$227$	62149.7	+	16653.0i	1.20611	+	0.323177i	0.400876	+	0.916132i	$0.368706\pi$
$228$	−7264.84	+	27112.8i	−0.139752	+	0.521560i
$229$	−11963.7	−	11963.7i	−0.228137	−	0.228137i	0.583777	−	0.811914i	$-0.301574\pi$
$229$	−11963.7	−	11963.7i	−0.228137	−	0.228137i	−0.811914	+	0.583777i	$0.801574\pi$
$230$	−71164.7	−	123261.i	−1.34527	−	2.33007i
$231$	−1503.62	−	868.113i	−0.0281782	−	0.0162687i
$232$	46957.2	−	12582.1i	0.872421	−	0.233764i
$233$			27976.0i			0.515317i	0.966236	+	0.257659i	$0.0829510\pi$
$233$			27976.0i			0.515317i	−0.966236	+	0.257659i	$0.917049\pi$
$234$	94881.6	−	9296.85i	1.73281	−	0.169787i
$235$	−24986.1			−0.452443
$236$	27763.2	+	103614.i	0.498477	+	1.86034i
$237$	7690.08	−	13319.6i	0.136910	−	0.237135i
$238$	11531.6	−	6657.76i	0.203580	−	0.117537i
$239$	1069.01	−	1069.01i	0.0187148	−	0.0187148i	−0.697687	−	0.716402i	$-0.745788\pi$
$239$	1069.01	−	1069.01i	0.0187148	−	0.0187148i	0.716402	+	0.697687i	$0.245788\pi$
$240$	35772.2	+	9585.13i	0.621045	+	0.166409i
$241$	6716.79	−	25067.4i	0.115645	−	0.431594i	−0.883689	−	0.468074i	$-0.844948\pi$
$241$	6716.79	−	25067.4i	0.115645	−	0.431594i	0.999334	+	0.0364804i	$0.0116146\pi$
$242$	70613.6	+	70613.6i	1.20575	+	1.20575i
$243$	−17430.3	−	30190.1i	−0.295183	−	0.511272i
$244$	102965.	+	59447.1i	1.72946	+	0.998507i
$245$	53930.2	−	14450.5i	0.898462	−	0.240742i
$246$			9341.85i			0.154370i
$247$	−39685.4	−	55439.7i	−0.650484	−	0.908714i
$248$	−70370.2			−1.14416
$249$	3591.17	+	13402.4i	0.0579211	+	0.216165i
$250$	−23725.8	+	41094.2i	−0.379612	+	0.657507i
$251$	50159.7	−	28959.7i	0.796173	−	0.459671i	−0.0459580	−	0.998943i	$-0.514634\pi$
$251$	50159.7	−	28959.7i	0.796173	−	0.459671i	0.842131	+	0.539272i	$0.181301\pi$
$252$	−61545.5	+	61545.5i	−0.969160	+	0.969160i
$253$	−15240.4	−	4083.66i	−0.238098	−	0.0637982i
$254$	38166.0	−	142438.i	0.591575	−	2.20779i
$255$	−3020.24	−	3020.24i	−0.0464474	−	0.0464474i
$256$	51034.4	+	88394.1i	0.778723	+	1.34879i
$257$	−24207.4	−	13976.2i	−0.366507	−	0.211603i	0.305424	−	0.952216i	$-0.401202\pi$
$257$	−24207.4	−	13976.2i	−0.366507	−	0.211603i	−0.671931	+	0.740613i	$0.734535\pi$
$258$	−44575.0	+	11943.8i	−0.669656	+	0.179434i
$259$		−	3131.02i		−	0.0466752i
$260$	−191920.	+	137382.i	−2.83906	+	2.03228i
$261$	24597.5			0.361086
$262$	−45348.3	−	169242.i	−0.660630	−	2.46551i
$263$	−29031.4	+	50283.9i	−0.419717	+	0.726972i	−0.995911	−	0.0903416i	$-0.971204\pi$
$263$	−29031.4	+	50283.9i	−0.419717	+	0.726972i	0.576194	+	0.817313i	$0.304537\pi$
$264$	7586.63	−	4380.14i	0.108853	−	0.0628464i
$265$	28361.2	−	28361.2i	0.403862	−	0.403862i
$266$	86106.8	+	23072.2i	1.21695	+	0.326082i
$267$	5371.36	−	20046.2i	0.0753462	−	0.281196i
$268$	−152132.	−	152132.i	−2.11812	−	2.11812i
$269$	51837.2	+	89784.7i	0.716370	+	1.24079i	0.962429	+	0.271534i	$0.0875310\pi$
$269$	51837.2	+	89784.7i	0.716370	+	1.24079i	−0.246059	+	0.969255i	$0.579136\pi$
$270$	70833.9	+	40896.0i	0.971658	+	0.560987i
$271$	−119089.	+	31909.8i	−1.62156	+	0.434496i	−0.951460	−	0.307772i	$-0.900417\pi$
$271$	−119089.	+	31909.8i	−1.62156	+	0.434496i	−0.670102	+	0.742269i	$0.733750\pi$
$272$			31485.6i			0.425573i
$273$	939.733	+	9590.71i	0.0126090	+	0.128684i
$274$	118859.			1.58319
$275$	6286.88	+	23463.0i	0.0831323	+	0.310254i
$276$	18026.7	−	31223.2i	0.236646	−	0.409882i
$277$	−77143.1	+	44538.6i	−1.00540	+	0.580466i	−0.909841	−	0.414958i	$-0.863796\pi$
$277$	−77143.1	+	44538.6i	−1.00540	+	0.580466i	−0.0955564	+	0.995424i	$0.530463\pi$
$278$	69970.1	−	69970.1i	0.905364	−	0.905364i
$279$	−34392.7	−	9215.50i	−0.441833	−	0.118389i
$280$	45356.2	−	169272.i	0.578523	−	2.15908i
$281$	−27025.0	−	27025.0i	−0.342258	−	0.342258i	0.514958	−	0.857216i	$-0.327808\pi$
$281$	−27025.0	−	27025.0i	−0.342258	−	0.342258i	−0.857216	+	0.514958i	$0.827808\pi$
$282$	−4532.15	−	7849.91i	−0.0569910	−	0.0987113i
$283$	−11023.5	−	6364.41i	−0.137640	−	0.0794668i	0.429599	−	0.903020i	$-0.358655\pi$
$283$	−11023.5	−	6364.41i	−0.137640	−	0.0794668i	−0.567239	+	0.823553i	$0.691988\pi$
$284$	60538.2	−	16221.2i	0.750573	−	0.201115i
$285$		−	28595.2i		−	0.352049i
$286$	−6122.48	+	36967.6i	−0.0748505	+	0.451949i
$287$	20716.3			0.251507
$288$	−27168.5	−	101394.i	−0.327552	−	1.22244i
$289$	−39944.8	+	69186.5i	−0.478261	+	0.828372i
$290$	−75527.3	+	43605.7i	−0.898066	+	0.518499i
$291$	−17220.5	+	17220.5i	−0.203358	+	0.203358i
$292$	248401.	+	66559.0i	2.91332	+	0.780622i
$293$	36357.5	−	135688.i	0.423505	−	1.58054i	−0.343660	−	0.939094i	$-0.611667\pi$
$293$	36357.5	−	135688.i	0.423505	−	1.58054i	0.767166	−	0.641449i	$-0.221666\pi$
$294$	14322.1	+	14322.1i	0.165697	+	0.165697i
$295$	−54639.3	−	94638.1i	−0.627858	−	1.08748i
$296$	13681.3	+	7898.93i	0.156151	+	0.0901540i
$297$	8758.16	−	2346.74i	0.0992887	−	0.0266043i
$298$			216869.i			2.44210i
$299$	30806.5	+	81976.0i	0.344588	+	0.916948i
$300$	−55505.1			−0.616723
$301$	26486.5	+	98848.8i	0.292342	+	1.09103i
$302$	−54747.9	+	94826.1i	−0.600279	+	1.03971i
$303$	6804.24	−	3928.43i	0.0741130	−	0.0427892i
$304$	−149050.	+	149050.i	−1.61282	+	1.61282i
$305$	−116995.	−	31348.7i	−1.25767	−	0.336992i
$306$	−8798.33	+	32835.8i	−0.0939631	+	0.350675i
$307$	67673.8	+	67673.8i	0.718032	+	0.718032i	0.968202	−	0.250170i	$-0.0804866\pi$
$307$	67673.8	+	67673.8i	0.718032	+	0.718032i	−0.250170	+	0.968202i	$0.580487\pi$
$308$	−17104.9	−	29626.6i	−0.180310	−	0.312306i
$309$	−6709.86	−	3873.94i	−0.0702743	−	0.0405729i
$310$	121941.	−	32673.9i	1.26889	−	0.339999i
$311$		−	77336.4i		−	0.799583i	−0.916606	−	0.399791i	$-0.869083\pi$
$311$		−	77336.4i		−	0.799583i	0.916606	−	0.399791i	$-0.130917\pi$
$312$	−44278.4	−	20089.1i	−0.454866	−	0.206373i
$313$	−21984.2			−0.224399			−0.112200	−	0.993686i	$-0.535790\pi$
$313$	−21984.2			−0.224399			−0.112200	+	0.993686i	$0.535790\pi$
$314$	−21804.6	−	81375.7i	−0.221151	−	0.825345i
$315$	44334.7	−	76790.0i	0.446810	−	0.773898i
$316$	262444.	−	151522.i	2.62823	−	1.51741i
$317$	−91443.9	+	91443.9i	−0.909990	+	0.909990i	−0.996271	−	0.0862812i	$-0.972502\pi$
$317$	−91443.9	+	91443.9i	−0.909990	+	0.909990i	0.0862812	+	0.996271i	$0.472502\pi$
$318$	14054.6	+	3765.92i	0.138984	+	0.0372406i
$319$	−2502.24	+	9338.47i	−0.0245893	+	0.0917687i
$320$	40198.3	+	40198.3i	0.392561	+	0.392561i
$321$	18647.8	+	32299.0i	0.180975	+	0.313458i
$322$	−99161.0	−	57250.6i	−0.956377	−	0.552164i
$323$	23482.6	−	6292.15i	0.225082	−	0.0603107i
$324$		−	211617.i		−	2.01586i
$325$	85582.1	−	104175.i	0.810245	−	0.986275i
$326$	−163747.			−1.54077
$327$	3558.17	+	13279.3i	0.0332760	+	0.124188i
$328$	−52263.1	+	90522.4i	−0.485789	+	0.841411i
$329$	−17407.9	+	10050.4i	−0.160825	+	0.0928523i
$330$	−11112.7	+	11112.7i	−0.102045	+	0.102045i
$331$	162966.	+	43666.5i	1.48744	+	0.398559i	0.908873	−	0.417073i	$-0.136944\pi$
$331$	162966.	+	43666.5i	1.48744	+	0.398559i	0.578570	+	0.815633i	$0.303611\pi$
$332$	−70758.9	+	264076.i	−0.641956	+	2.39581i
$333$	5652.19	+	5652.19i	0.0509716	+	0.0509716i
$334$	−27259.7	−	47215.2i	−0.244359	−	0.423242i
$335$	189814.	+	109589.i	1.69137	+	0.976514i
$336$	28778.0	−	7711.05i	0.254907	−	0.0683023i
$337$		−	113257.i		−	0.997254i	−0.866817	−	0.498627i	$-0.833838\pi$
$337$		−	113257.i		−	0.997254i	0.866817	−	0.498627i	$-0.166162\pi$
$338$	186622.	−	91798.5i	1.63354	−	0.803530i
$339$	27364.8			0.238118
$340$	−21782.1	−	81291.7i	−0.188426	−	0.703216i
$341$	6997.34	−	12119.7i	0.0601761	−	0.104228i
$342$	−197093.	+	113791.i	−1.68507	+	0.972875i
$343$	83278.5	−	83278.5i	0.707856	−	0.707856i
$344$	−498751.	−	133640.i	−4.21470	−	1.12933i
$345$	−9506.17	+	35477.5i	−0.0798670	+	0.298068i
$346$	−139382.	−	139382.i	−1.16427	−	1.16427i
$347$	−93265.0	−	161540.i	−0.774568	−	1.34159i	−0.935037	−	0.354551i	$-0.884634\pi$
$347$	−93265.0	−	161540.i	−0.774568	−	1.34159i	0.160468	−	0.987041i	$-0.448700\pi$
$348$	−19131.8	−	11045.8i	−0.157978	−	0.0912089i
$349$	−61242.9	+	16410.0i	−0.502811	+	0.134728i	−0.501304	−	0.865271i	$-0.667146\pi$
$349$	−61242.9	+	16410.0i	−0.502811	+	0.134728i	−0.00150679	+	0.999999i	$0.500480\pi$
$350$			176277.i			1.43900i
$351$	−38886.1	−	31945.7i	−0.315631	−	0.259298i
$352$	41258.1			0.332985
$353$	6800.65	+	25380.4i	0.0545759	+	0.203680i	0.987830	−	0.155537i	$-0.0497106\pi$
$353$	6800.65	+	25380.4i	0.0545759	+	0.203680i	−0.933254	+	0.359216i	$0.883044\pi$
$354$	19821.7	−	34332.2i	0.158174	−	0.273965i
$355$	−55294.1	+	31924.1i	−0.438755	+	0.253315i
$356$	289147.	−	289147.i	2.28149	−	2.28149i
$357$	−3319.07	−	889.342i	−0.0260423	−	0.00697802i
$358$	−90438.8	+	337522.i	−0.705649	+	2.63352i
$359$	129125.	+	129125.i	1.00189	+	1.00189i	0.999998	+	0.00189580i	$0.000603453\pi$
$359$	129125.	+	129125.i	1.00189	+	1.00189i	0.00189580	+	0.999998i	$0.499397\pi$
$360$	223695.	+	387451.i	1.72604	+	2.98959i
$361$	28090.0	+	16217.7i	0.215544	+	0.124445i
$362$	128823.	−	34518.0i	0.983051	−	0.263408i
$363$		−	25770.2i		−	0.195571i
$364$	−78450.3	+	172912.i	−0.592096	+	1.30504i
$365$	−261983.			−1.96647
$366$	−11372.5	−	42442.6i	−0.0848970	−	0.316840i
$367$	17514.3	−	30335.7i	0.130035	−	0.225228i	−0.793655	−	0.608368i	$-0.791824\pi$
$367$	17514.3	−	30335.7i	0.130035	−	0.225228i	0.923690	+	0.383141i	$0.125158\pi$
$368$	234474.	−	135374.i	1.73141	−	0.999629i
$369$	−37397.6	+	37397.6i	−0.274657	+	0.274657i
$370$	−27375.2	−	7335.17i	−0.199965	−	0.0535805i
$371$	8351.24	−	31167.2i	0.0606741	−	0.226439i
$372$	22612.1	+	22612.1i	0.163401	+	0.163401i
$373$	49024.7	+	84913.3i	0.352369	+	0.610321i	0.986664	−	0.162770i	$-0.0520429\pi$
$373$	49024.7	+	84913.3i	0.352369	+	0.610321i	−0.634295	+	0.773091i	$0.718710\pi$
$374$	−11571.1	−	6680.58i	−0.0827240	−	0.0477607i
$375$	11827.9	−	3169.28i	0.0841096	−	0.0225371i
$376$		−	101421.i		−	0.717383i
$377$	50230.3	−	18876.5i	0.353413	−	0.132813i
$378$	65800.0			0.460513
$379$	40042.3	+	149440.i	0.278766	+	1.04037i	0.953275	+	0.302103i	$0.0976887\pi$
$379$	40042.3	+	149440.i	0.278766	+	1.04037i	−0.674509	+	0.738267i	$0.735645\pi$
$380$	281714.	−	487943.i	1.95093	−	3.37910i
$381$	−32955.3	+	19026.8i	−0.227026	+	0.131074i
$382$	111418.	−	111418.i	0.763531	−	0.763531i
$383$	240210.	+	64364.2i	1.63755	+	0.438780i	0.956089	−	0.293076i	$-0.0946788\pi$
$383$	240210.	+	64364.2i	1.63755	+	0.438780i	0.681460	+	0.731856i	$0.261345\pi$
$384$	5206.56	−	19431.1i	0.0353092	−	0.131776i
$385$	24643.3	+	24643.3i	0.166256	+	0.166256i
$386$	−56686.9	−	98184.6i	−0.380459	−	0.658975i
$387$	−226258.	−	130630.i	−1.51071	−	0.872211i
$388$	−463501.	+	124195.i	−3.07884	+	0.824973i
$389$		−	31005.0i		−	0.204896i	−0.994738	−	0.102448i	$-0.967333\pi$
$389$		−	31005.0i		−	0.204896i	0.994738	−	0.102448i	$-0.0326675\pi$
$390$	86055.2	+	14252.2i	0.565781	+	0.0937031i
$391$	−31226.2			−0.204252
$392$	58655.9	+	218907.i	0.381716	+	1.42458i
$393$	−22607.3	+	39157.1i	−0.146374	+	0.253527i
$394$	−220518.	+	127316.i	−1.42054	+	0.820147i
$395$	−218300.	+	218300.i	−1.39914	+	1.39914i
$396$	84361.0	+	22604.4i	0.537961	+	0.144146i
$397$	45004.1	−	167957.i	0.285542	−	1.06566i	−0.662900	−	0.748708i	$-0.730674\pi$
$397$	45004.1	−	167957.i	0.285542	−	1.06566i	0.948442	−	0.316951i	$-0.102659\pi$
$398$	143271.	+	143271.i	0.904463	+	0.904463i
$399$	−11502.1	−	19922.3i	−0.0722490	−	0.125139i
$400$	−360978.	−	208411.i	−2.25611	−	1.30257i
$401$	−103299.	+	27678.8i	−0.642401	+	0.172131i	−0.565291	−	0.824892i	$-0.691236\pi$
$401$	−103299.	+	27678.8i	−0.642401	+	0.172131i	−0.0771101	+	0.997023i	$0.524569\pi$
$402$			79512.1i			0.492018i
$403$	−77305.0	+	7574.62i	−0.475989	+	0.0466392i
$404$	154808.			0.948488
$405$	55796.7	+	208236.i	0.340172	+	1.26954i
$406$	−35080.0	+	60760.3i	−0.212817	+	0.368610i
$407$	−2720.84	+	1570.88i	−0.0164253	+	0.00948317i
$408$	12259.4	−	12259.4i	0.0736461	−	0.0736461i
$409$	−2035.60	−	545.438i	−0.0121688	−	0.00326061i	0.252730	−	0.967537i	$-0.418672\pi$
$409$	−2035.60	−	545.438i	−0.0121688	−	0.00326061i	−0.264898	+	0.964276i	$0.585338\pi$
$410$	48533.0	−	181128.i	0.288715	−	1.07750i
$411$	−21688.7	−	21688.7i	−0.128395	−	0.128395i
$412$	−76330.6	−	132208.i	−0.449680	−	0.778869i
$413$	−76134.5	−	43956.3i	−0.446356	−	0.257704i
$414$	282358.	−	75657.6i	1.64740	−	0.441420i
$415$		−	278514.i		−	1.61715i
$416$	−133292.	−	186206.i	−0.770223	−	1.07599i
$417$	−25535.4			−0.146849
$418$	−23151.3	−	86401.9i	−0.132502	−	0.494505i
$419$	43703.4	−	75696.4i	0.248935	−	0.431169i	−0.714295	−	0.699844i	$-0.753253\pi$
$419$	43703.4	−	75696.4i	0.248935	−	0.431169i	0.963231	+	0.268676i	$0.0865860\pi$
$420$	−68966.5	+	39817.8i	−0.390967	+	0.225725i
$421$	204448.	−	204448.i	1.15350	−	1.15350i	0.167658	−	0.985845i	$-0.446379\pi$
$421$	204448.	−	204448.i	1.15350	−	1.15350i	0.985845	−	0.167658i	$-0.0536206\pi$
$422$	−263186.	−	70520.5i	−1.47788	−	0.395996i
$423$	13281.8	−	49568.3i	0.0742294	−	0.277028i
$424$	115120.	+	115120.i	0.640354	+	0.640354i
$425$	24036.7	+	41632.9i	0.133075	+	0.230493i
$426$	−20059.2	−	11581.2i	−0.110534	−	0.0638167i
$427$	−94120.1	+	25219.4i	−0.516210	+	0.138318i
$428$			734859.i			4.01159i
$429$	7862.79	−	5628.41i	0.0427230	−	0.0305824i
$430$	926308.			5.00978
$431$	−38539.5	−	143831.i	−0.207468	−	0.774282i	−0.988683	−	0.150020i	$-0.952066\pi$
$431$	−38539.5	−	143831.i	−0.207468	−	0.774282i	0.781215	−	0.624263i	$-0.214600\pi$
$432$	−77794.7	+	134744.i	−0.416853	+	0.722010i
$433$	135436.	−	78194.2i	0.722370	−	0.417060i	−0.0932545	−	0.995642i	$-0.529727\pi$
$433$	135436.	−	78194.2i	0.722370	−	0.417060i	0.815624	+	0.578582i	$0.196394\pi$
$434$	71813.3	−	71813.3i	0.381264	−	0.381264i
$435$	21738.6	+	5824.84i	0.114882	+	0.0307826i
$436$	−70108.8	+	261650.i	−0.368807	+	1.37641i
$437$	−147822.	−	147822.i	−0.774064	−	0.774064i
$438$	−47520.2	−	82307.3i	−0.247702	−	0.429033i
$439$	288145.	+	166361.i	1.49514	+	0.863220i	0.999984	−	0.00558348i	$-0.00177728\pi$
$439$	288145.	+	166361.i	1.49514	+	0.863220i	0.495157	+	0.868804i	$0.335111\pi$
$440$	−169852.	+	45511.7i	−0.877334	+	0.235081i
$441$			114670.i			0.589620i
$442$	7231.73	+	73805.5i	0.0370167	+	0.377785i
$443$	−167715.			−0.854605			−0.427302	−	0.904109i	$-0.640536\pi$
$443$	−167715.			−0.854605			−0.427302	+	0.904109i	$0.640536\pi$
$444$	−1858.07	−	6934.41i	−0.00942532	−	0.0351758i
$445$	−208289.	+	360767.i	−1.05183	+	1.82182i
$446$	−281887.	+	162748.i	−1.41712	+	0.818173i
$447$	39572.8	−	39572.8i	0.198053	−	0.198053i
$448$	44175.5	+	11836.8i	0.220103	+	0.0589764i
$449$	59265.1	−	221180.i	0.293972	−	1.09712i	−0.648058	−	0.761591i	$-0.724418\pi$
$449$	59265.1	−	221180.i	0.293972	−	1.09712i	0.942030	−	0.335528i	$-0.108915\pi$
$450$	−318220.	−	318220.i	−1.57146	−	1.57146i
$451$	−10393.7	−	18002.4i	−0.0510995	−	0.0885069i
$452$	466948.	+	269592.i	2.28555	+	1.31956i
$453$	27293.3	−	7313.21i	0.133002	−	0.0356378i
$454$		−	468531.i		−	2.27314i
$455$	31605.5	−	190835.i	0.152665	−	0.921796i
$456$	116070.			0.558201
$457$	9229.09	+	34443.4i	0.0441903	+	0.164920i	0.984495	−	0.175414i	$-0.0561264\pi$
$457$	9229.09	+	34443.4i	0.0441903	+	0.164920i	−0.940304	+	0.340334i	$0.889460\pi$
$458$	−61601.9	+	106698.i	−0.293672	+	0.508655i
$459$	15540.5	−	8972.33i	0.0737633	−	0.0425873i
$460$	−511729.	+	511729.i	−2.41838	+	2.41838i
$461$	−119457.	−	32008.4i	−0.562095	−	0.150613i	−0.0334264	−	0.999441i	$-0.510642\pi$
$461$	−119457.	−	32008.4i	−0.562095	−	0.150613i	−0.528669	+	0.848828i	$0.677309\pi$
$462$	−3272.24	+	12212.2i	−0.0153307	+	0.0572149i
$463$	39759.1	+	39759.1i	0.185470	+	0.185470i	0.793735	−	0.608264i	$-0.208134\pi$
$463$	39759.1	+	39759.1i	0.185470	+	0.185470i	−0.608264	+	0.793735i	$0.708134\pi$
$464$	−82949.4	−	143673.i	−0.385281	−	0.667326i
$465$	−28213.0	−	16288.8i	−0.130480	−	0.0753326i
$466$	196777.	−	52726.1i	0.906153	−	0.242803i
$467$			288154.i			1.32127i	0.750709	+	0.660633i	$0.229712\pi$
$467$			288154.i			1.32127i	−0.750709	+	0.660633i	$0.770288\pi$
$468$	−170525.	−	453765.i	−0.778566	−	2.07176i
$469$	176325.			0.801618
$470$	47091.1	+	175746.i	0.213178	+	0.795592i
$471$	−10870.2	+	18827.7i	−0.0489997	+	0.0848700i
$472$	384144.	−	221786.i	1.72429	−	0.995518i
$473$	72610.4	−	72610.4i	0.324546	−	0.324546i
$474$	−108180.	−	28986.8i	−0.481494	−	0.129016i
$475$	−83298.5	+	310874.i	−0.369190	+	1.37784i
$476$	−47874.4	−	47874.4i	−0.211295	−	0.211295i
$477$	41188.0	+	71339.7i	0.181023	+	0.313541i
$478$	−9533.86	−	5504.38i	−0.0417266	−	0.0240909i
$479$	11558.0	−	3096.94i	0.0503744	−	0.0134978i	−0.233544	−	0.972346i	$-0.575032\pi$
$479$	11558.0	−	3096.94i	0.0503744	−	0.0134978i	0.283918	+	0.958848i	$0.408366\pi$
$480$		−	96042.9i		−	0.416853i
$481$	15879.8	+	7204.69i	0.0686366	+	0.0311405i
$482$	−188977.			−0.813420
$483$	7647.52	+	28540.9i	0.0327813	+	0.122342i
$484$	253883.	−	439738.i	1.08378	−	1.87717i
$485$	423351.	−	244422.i	1.79977	−	1.03910i
$486$	−179499.	+	179499.i	−0.759958	+	0.759958i
$487$	−16202.8	−	4341.53i	−0.0683176	−	0.0183056i	0.224498	−	0.974474i	$-0.427926\pi$
$487$	−16202.8	−	4341.53i	−0.0683176	−	0.0183056i	−0.292816	+	0.956169i	$0.594592\pi$
$488$	127247.	−	474892.i	0.534328	−	1.99414i
$489$	29879.4	+	29879.4i	0.124955	+	0.124955i
$490$	−203283.	−	352097.i	−0.846660	−	1.46646i
$491$	−166909.	−	96364.8i	−0.692335	−	0.399720i	0.112151	−	0.993691i	$-0.464226\pi$
$491$	−166909.	−	96364.8i	−0.692335	−	0.399720i	−0.804486	+	0.593971i	$0.797559\pi$
$492$	45881.4	−	12293.9i	0.189542	−	0.0507877i
$493$			19133.7i			0.0787235i
$494$	−315155.	+	383623.i	−1.29143	+	1.57200i
$495$	−88973.4			−0.363120
$496$	62154.2	+	231963.i	0.252643	+	0.942876i
$497$	−25682.3	+	44483.0i	−0.103973	+	0.180087i
$498$	87501.1	−	50518.8i	0.352821	−	0.203701i
$499$	−272196.	+	272196.i	−1.09315	+	1.09315i	−0.0979611	+	0.995190i	$0.531232\pi$
$499$	−272196.	+	272196.i	−1.09315	+	1.09315i	−0.995190	+	0.0979611i	$0.968768\pi$
$500$	233052.	+	62446.2i	0.932210	+	0.249785i
$501$	−3641.35	+	13589.7i	−0.0145073	+	0.0541420i
$502$	−298231.	−	298231.i	−1.18344	−	1.18344i
$503$	53835.0	+	93244.9i	0.212779	+	0.368544i	0.952583	−	0.304278i	$-0.0984153\pi$
$503$	53835.0	+	93244.9i	0.212779	+	0.368544i	−0.739804	+	0.672822i	$0.765082\pi$
$504$	311697.	+	179958.i	1.22708	+	0.708452i
$505$	−152335.	+	40818.2i	−0.597335	+	0.160056i
$506$			114894.i			0.448741i
$507$	−50804.3	−	17302.7i	−0.197644	−	0.0673130i
$508$	−749792.			−2.90545
$509$	11545.8	+	43089.4i	0.0445643	+	0.166316i	0.984622	−	0.174700i	$-0.0558955\pi$
$509$	11545.8	+	43089.4i	0.0445643	+	0.166316i	−0.940057	+	0.341016i	$0.889229\pi$
$510$	−15551.4	+	26935.9i	−0.0597902	+	0.103560i
$511$	−182524.	+	105380.i	−0.699000	+	0.403568i
$512$	404442.	−	404442.i	1.54282	−	1.54282i
$513$	116042.	+	31093.3i	0.440940	+	0.118150i
$514$	−52681.4	+	196610.i	−0.199403	+	0.744182i
$515$	109970.	+	109970.i	0.414631	+	0.414631i
$516$	117321.	+	203207.i	0.440634	+	0.763200i
$517$	17467.5	+	10084.9i	0.0653507	+	0.0377303i
$518$	−22022.8	+	5901.00i	−0.0820755	+	0.0219921i
$519$			50867.1i			0.188843i
$520$	754140.	+	619542.i	2.78898	+	2.29120i
$521$	334990.			1.23412			0.617059	−	0.786917i	$-0.288324\pi$
$521$	334990.			1.23412			0.617059	+	0.786917i	$0.288324\pi$
$522$	−46358.7	−	173013.i	−0.170134	−	0.634947i
$523$	174062.	−	301485.i	0.636357	−	1.10220i	−0.349868	−	0.936799i	$-0.613774\pi$
$523$	174062.	−	301485.i	0.636357	−	1.10220i	0.986226	−	0.165404i	$-0.0528929\pi$
$524$	−771535.	+	445446.i	−2.80991	+	1.62230i
$525$	32165.9	−	32165.9i	0.116702	−	0.116702i
$526$	408400.	+	109430.i	1.47609	+	0.395518i
$527$	7168.45	−	26753.0i	0.0258110	−	0.0963278i
$528$	−21139.2	−	21139.2i	−0.0758265	−	0.0758265i
$529$	−5662.03	−	9806.92i	−0.0202330	−	0.0350446i
$530$	−252937.	−	146033.i	−0.900454	−	0.519877i
$531$	216791.	−	58088.9i	0.768868	−	0.206018i
$532$		−	453266.i		−	1.60151i
$533$	−47669.7	+	105069.i	−0.167798	+	0.369844i
$534$	−151123.			−0.529967
$535$	−193760.	−	723120.i	−0.676948	−	2.52641i
$536$	−444832.	+	770471.i	−1.54834	+	2.68180i
$537$	78091.5	−	45086.1i	0.270804	−	0.156349i
$538$	533826.	−	533826.i	1.84432	−	1.84432i
$539$	−43534.5	−	11665.0i	−0.149850	−	0.0401521i
$540$	107638.	−	401711.i	0.369130	−	1.37761i
$541$	343464.	+	343464.i	1.17351	+	1.17351i	0.981367	+	0.192142i	$0.0615435\pi$
$541$	343464.	+	343464.i	1.17351	+	1.17351i	0.192142	+	0.981367i	$0.438457\pi$
$542$	448892.	+	777503.i	1.52807	+	2.64669i
$543$	−29805.4	−	17208.1i	−0.101087	−	0.0583626i
$544$	78871.4	−	21133.5i	0.266515	−	0.0714125i
$545$		−	275955.i		−	0.929064i
$546$	65687.5	−	24685.3i	0.220342	−	0.0828045i
$547$	−83813.5			−0.280117			−0.140058	−	0.990143i	$-0.544729\pi$
$547$	−83813.5			−0.280117			−0.140058	+	0.990143i	$0.544729\pi$
$548$	−156419.	−	583764.i	−0.520869	−	1.94391i
$549$	124381.	−	215435.i	0.412677	−	0.714777i
$550$	153184.	−	88440.7i	0.506393	−	0.292366i
$551$	−90577.2	+	90577.2i	−0.298343	+	0.298343i
$552$	−144006.	−	38586.3i	−0.472610	−	0.126635i
$553$	−64280.7	+	239899.i	−0.210199	+	0.784473i
$554$	458664.	+	458664.i	1.49443	+	1.49443i
$555$	3656.77	+	6333.72i	0.0118717	+	0.0205624i
$556$	−435731.	−	251569.i	−1.40951	−	0.813782i
$557$	107239.	−	28734.5i	0.345654	−	0.0926176i	−0.0818156	−	0.996647i	$-0.526072\pi$
$557$	107239.	−	28734.5i	0.345654	−	0.0926176i	0.427469	+	0.904030i	$0.359405\pi$
$558$			259278.i			0.832717i
$559$	−562286.	−	93124.3i	−1.79942	−	0.298016i
$560$	−598033.			−1.90699
$561$	892.391	+	3330.45i	0.00283550	+	0.0105822i
$562$	−139154.	+	241021.i	−0.440577	+	0.763101i
$563$	−132089.	+	76261.5i	−0.416724	+	0.240596i	−0.693675	−	0.720288i	$-0.744010\pi$
$563$	−132089.	+	76261.5i	−0.416724	+	0.240596i	0.276950	+	0.960884i	$0.410676\pi$
$564$	−32589.6	+	32589.6i	−0.102452	+	0.102452i
$565$	−530571.	−	142166.i	−1.66206	−	0.445348i
$566$	−23989.9	+	89531.4i	−0.0748850	+	0.279475i
$567$	122635.	+	122635.i	0.381458	+	0.381458i
$568$	−129582.	−	224443.i	−0.401651	−	0.695680i
$569$	−189558.	−	109441.i	−0.585487	−	0.338031i	0.177824	−	0.984062i	$-0.443094\pi$
$569$	−189558.	−	109441.i	−0.585487	−	0.338031i	−0.763311	+	0.646031i	$0.776428\pi$
$570$	−201131.	+	53892.9i	−0.619056	+	0.165875i
$571$			80171.1i			0.245893i	0.992413	+	0.122946i	$0.0392343\pi$
$571$			80171.1i			0.245893i	−0.992413	+	0.122946i	$0.960766\pi$
$572$	189619.	−	18579.6i	0.579549	−	0.0567864i
$573$	−40661.5			−0.123844
$574$	−39043.8	−	145714.i	−0.118503	−	0.442259i
$575$	206694.	−	358004.i	0.625161	−	1.08281i
$576$	−101115.	+	58378.7i	−0.304768	+	0.175958i
$577$	190159.	−	190159.i	0.571171	−	0.571171i	−0.361285	−	0.932456i	$-0.617662\pi$
$577$	190159.	−	190159.i	0.571171	−	0.571171i	0.932456	+	0.361285i	$0.117662\pi$
$578$	561924.	+	150567.i	1.68198	+	0.450686i
$579$	−7572.22	+	28259.9i	−0.0225874	+	0.0842973i
$580$	313558.	+	313558.i	0.932100	+	0.932100i
$581$	−112030.	−	194041.i	−0.331880	−	0.574833i
$582$	153580.	+	88669.6i	0.453408	+	0.261775i
$583$	−31274.1	+	8379.87i	−0.0920127	+	0.0246547i
$584$		−	1.06341e6i		−	3.11799i
$585$	287444.	+	401555.i	0.839928	+	1.17336i
$586$	−1.02292e6			−2.97883
$587$	91015.4	+	339674.i	0.264143	+	0.985794i	0.962773	+	0.270311i	$0.0871267\pi$
$587$	91015.4	+	339674.i	0.264143	+	0.985794i	−0.698630	+	0.715483i	$0.746207\pi$
$588$	51493.6	−	89189.5i	0.148936	−	0.257964i
$589$	160581.	−	92711.7i	0.462876	−	0.267242i
$590$	−562683.	+	562683.i	−1.61644	+	1.61644i
$591$	63470.6	+	17006.9i	0.181718	+	0.0486911i
$592$	13953.4	−	52074.8i	0.0398140	−	0.148588i
$593$	−361504.	−	361504.i	−1.02803	−	1.02803i	−0.999596	−	0.0284306i	$-0.990949\pi$
$593$	−361504.	−	361504.i	−1.02803	−	1.02803i	−0.0284306	−	0.999596i	$-0.509051\pi$
$594$	−33012.8	−	57179.8i	−0.0935641	−	0.162058i
$595$	59732.6	+	34486.6i	0.168724	+	0.0974129i
$596$	1.06513e6	−	285399.i	2.99853	−	0.803453i
$597$		−	52286.1i		−	0.146703i
$598$	518538.	−	371185.i	1.45003	−	1.03798i
$599$	276010.			0.769255			0.384628	−	0.923072i	$-0.374330\pi$
$599$	276010.			0.769255			0.384628	+	0.923072i	$0.374330\pi$
$600$	59404.5	+	221700.i	0.165012	+	0.615835i
$601$	−281989.	+	488419.i	−0.780698	+	1.35221i	0.150837	+	0.988559i	$0.451803\pi$
$601$	−281989.	+	488419.i	−0.780698	+	1.35221i	−0.931535	+	0.363651i	$0.881530\pi$
$602$	645359.	−	372598.i	1.78077	−	1.02813i
$603$	−318306.	+	318306.i	−0.875406	+	0.875406i
$604$	537775.	+	144096.i	1.47410	+	0.394984i
$605$	−133882.	+	499655.i	−0.365773	+	1.36508i
$606$	−40455.5	−	40455.5i	−0.110162	−	0.110162i
$607$	299464.	+	518686.i	0.812768	+	1.40776i	0.910920	+	0.412584i	$0.135374\pi$
$607$	299464.	+	518686.i	0.812768	+	1.40776i	−0.0981516	+	0.995171i	$0.531293\pi$
$608$	473415.	+	273326.i	1.28066	+	0.739391i
$609$	17488.3	−	4685.97i	0.0471534	−	0.0126347i
$610$			881996.i			2.37032i
$611$	−10916.9	−	111415.i	−0.0292426	−	0.298444i
$612$	172848.			0.461489
$613$	−111568.	−	416377.i	−0.296905	−	1.10807i	−0.939692	−	0.342021i	$-0.888889\pi$
$613$	−111568.	−	416377.i	−0.296905	−	1.10807i	0.642787	−	0.766045i	$-0.277778\pi$
$614$	348456.	−	603544.i	0.924297	−	1.60093i
$615$	−41906.9	+	24195.0i	−0.110799	+	0.0639698i
$616$	−100029.	+	100029.i	−0.263612	+	0.263612i
$617$	−695844.	−	186451.i	−1.82785	−	0.489772i	−0.830153	−	0.557535i	$-0.811747\pi$
$617$	−695844.	−	186451.i	−1.82785	−	0.489772i	−0.997701	+	0.0677629i	$0.978414\pi$
$618$	−14602.3	+	54496.7i	−0.0382336	+	0.142690i
$619$	−319539.	−	319539.i	−0.833955	−	0.833955i	0.154100	−	0.988055i	$-0.450752\pi$
$619$	−319539.	−	319539.i	−0.833955	−	0.833955i	−0.988055	+	0.154100i	$0.950752\pi$
$620$	−320948.	−	555898.i	−0.834932	−	1.44614i
$621$	−133634.	−	77153.8i	−0.346525	−	0.200066i
$622$	−543965.	+	145755.i	−1.40602	+	0.376741i
$623$			335129.i			0.863446i
$624$	−27111.4	+	163699.i	−0.0696279	+	0.420415i
$625$	252805.			0.647180
$626$	41433.3	+	154631.i	0.105731	+	0.394592i
$627$	−11541.6	+	19990.6i	−0.0293582	+	0.0508499i
$628$	−370973.	+	214181.i	−0.940638	+	0.543077i
$629$	−4396.67	+	4396.67i	−0.0111128	+	0.0111128i
$630$	−623679.	−	167114.i	−1.57137	−	0.421049i
$631$	−8880.18	+	33141.3i	−0.0223030	+	0.0832359i	−0.976180	−	0.216961i	$-0.930386\pi$
$631$	−8880.18	+	33141.3i	−0.0223030	+	0.0832359i	0.953877	+	0.300197i	$0.0970523\pi$
$632$	−886098.	−	886098.i	−2.21844	−	2.21844i
$633$	35156.3	+	60892.5i	0.0877397	+	0.151970i
$634$	815537.	+	470851.i	2.02892	+	1.17140i
$635$	737814.	−	197697.i	1.82978	−	0.490289i
$636$		−	73983.4i		−	0.182903i
$637$	87999.3	+	234166.i	0.216870	+	0.577091i
$638$	70400.4			0.172955
$639$	−33939.5	−	126664.i	−0.0831197	−	0.310207i
$640$	−201898.	+	349698.i	−0.492916	+	0.853755i
$641$	257700.	−	148783.i	0.627188	−	0.362107i	−0.152474	−	0.988307i	$-0.548724\pi$
$641$	257700.	−	148783.i	0.627188	−	0.362107i	0.779662	+	0.626200i	$0.215391\pi$
$642$	192038.	−	192038.i	0.465926	−	0.465926i
$643$	181894.	+	48738.3i	0.439943	+	0.117882i	0.471990	−	0.881604i	$-0.343536\pi$
$643$	181894.	+	48738.3i	0.439943	+	0.117882i	−0.0320471	+	0.999486i	$0.510203\pi$
$644$	−150684.	+	562359.i	−0.363324	+	1.35595i
$645$	−169027.	−	169027.i	−0.406289	−	0.406289i
$646$	−88514.8	−	153312.i	−0.212105	−	0.367377i
$647$	207812.	+	119980.i	0.496435	+	0.286617i	0.727240	−	0.686383i	$-0.240803\pi$
$647$	207812.	+	119980.i	0.496435	+	0.286617i	−0.230805	+	0.973000i	$0.574136\pi$
$648$	−845248.	+	226483.i	−2.01295	+	0.539370i
$649$			88213.9i			0.209434i
$650$	−894038.	−	405626.i	−2.11607	−	0.960060i
$651$	−26208.0			−0.0618404
$652$	215491.	+	804223.i	0.506913	+	1.89183i
$653$	−136640.	+	236668.i	−0.320444	+	0.555025i	−0.980580	−	0.196121i	$-0.937165\pi$
$653$	−136640.	+	236668.i	−0.320444	+	0.555025i	0.660136	+	0.751146i	$0.270499\pi$
$654$	86697.1	−	50054.6i	0.202698	−	0.117028i
$655$	641760.	−	641760.i	1.49586	−	1.49586i
$656$	344552.	+	92322.3i	0.800657	+	0.214535i
$657$	139261.	−	519730.i	0.322626	−	1.20406i
$658$	103501.	+	103501.i	0.239051	+	0.239051i
$659$	−221515.	−	383675.i	−0.510072	−	0.883471i	−0.999932	−	0.0116698i	$-0.996285\pi$
$659$	−221515.	−	383675.i	−0.510072	−	0.883471i	0.489860	−	0.871801i	$-0.337048\pi$
$660$	69202.9	+	39954.3i	0.158868	+	0.0917225i
$661$	−504300.	+	135127.i	−1.15421	+	0.309270i	−0.784652	−	0.619936i	$-0.787158\pi$
$661$	−504300.	+	135127.i	−1.15421	+	0.309270i	−0.369560	+	0.929207i	$0.620492\pi$
$662$		−	1.22856e6i		−	2.80337i
$663$	12147.9	−	14787.1i	0.0276360	−	0.0336401i
$664$	1.13051e6			2.56412
$665$	119512.	+	446026.i	0.270252	+	1.00859i
$666$	29103.5	−	50408.7i	0.0656140	−	0.113647i
$667$	142489.	−	82266.0i	0.320280	−	0.184914i
$668$	−196018.	+	196018.i	−0.439282	+	0.439282i
$669$	81134.0	+	21739.8i	0.181280	+	0.0485739i
$670$	413083.	−	1.54165e6i	0.920212	−	3.43428i
$671$	69136.9	+	69136.9i	0.153555	+	0.153555i
$672$	−38632.3	−	66913.2i	−0.0855485	−	0.148174i
$673$	61635.1	+	35585.1i	0.136081	+	0.0785665i	0.566495	−	0.824065i	$-0.308299\pi$
$673$	61635.1	+	35585.1i	0.136081	+	0.0785665i	−0.430414	+	0.902632i	$0.641632\pi$
$674$	−796622.	+	213454.i	−1.75361	+	0.469878i
$675$			237560.i			0.521394i
$676$	−696452.	−	795765.i	−1.52405	−	1.74137i
$677$	425776.			0.928974			0.464487	−	0.885580i	$-0.346239\pi$
$677$	425776.			0.928974			0.464487	+	0.885580i	$0.346239\pi$
$678$	−51574.1	−	192477.i	−0.112195	−	0.418716i
$679$	196632.	−	340577.i	0.426496	−	0.738713i
$680$	−301386.	+	174005.i	−0.651787	+	0.376309i
$681$	−85494.5	+	85494.5i	−0.184350	+	0.184350i
$682$	−98435.1	−	26375.6i	−0.211632	−	0.0567066i
$683$	−69844.2	+	260662.i	−0.149723	+	0.558774i	0.849776	+	0.527143i	$0.176737\pi$
$683$	−69844.2	+	260662.i	−0.149723	+	0.558774i	−0.999500	+	0.0316312i	$0.989930\pi$
$684$	818247.	+	818247.i	1.74893	+	1.74893i
$685$	307841.	+	533196.i	0.656062	+	1.13633i
$686$	−742714.	−	428806.i	−1.57824	−	0.911198i
$687$	30710.2	−	8228.76i	0.0650682	−	0.0174350i
$688$			1.76208e6i			3.72262i
$689$	138857.	+	114074.i	0.292501	+	0.240296i
$690$	267456.			0.561764
$691$	−135958.	−	507402.i	−0.284740	−	1.06266i	−0.949029	−	0.315189i	$-0.897932\pi$
$691$	−135958.	−	507402.i	−0.284740	−	1.06266i	0.664289	−	0.747476i	$-0.268734\pi$
$692$	−501132.	+	867986.i	−1.04650	+	1.81259i
$693$	−61987.8	+	35788.7i	−0.129074	+	0.0745211i
$694$	−960455.	+	960455.i	−1.99415	+	1.99415i
$695$	495101.	+	132662.i	1.02500	+	0.274648i
$696$	−23643.5	+	88238.8i	−0.0488083	+	0.182155i
$697$	−29090.5	−	29090.5i	−0.0598805	−	0.0598805i
$698$	230847.	+	399840.i	0.473821	+	0.820682i
$699$	−45527.6	−	26285.4i	−0.0931795	−	0.0537972i
$700$	865765.	−	231981.i	1.76687	−	0.473431i
$701$			33690.6i			0.0685602i	0.999412	+	0.0342801i	$0.0109138\pi$
$701$			33690.6i			0.0685602i	−0.999412	+	0.0342801i	$0.989086\pi$
$702$	−151410.	+	333723.i	−0.307242	+	0.677192i
$703$	−41626.9			−0.0842293
$704$	−11877.4	−	44327.0i	−0.0239649	−	0.0894381i
$705$	23476.1	−	40661.9i	0.0472333	−	0.0818105i
$706$	165702.	−	95668.1i	0.332444	−	0.191937i
$707$	−89713.5	+	89713.5i	−0.179481	+	0.179481i
$708$	−194704.	−	52170.7i	−0.388426	−	0.104078i
$709$	147910.	−	552009.i	0.294243	−	1.09813i	−0.647574	−	0.762003i	$-0.724216\pi$
$709$	147910.	−	552009.i	0.294243	−	1.09813i	0.941817	−	0.336127i	$-0.109117\pi$
$710$	328758.	+	328758.i	0.652168	+	0.652168i
$711$	−317030.	−	549112.i	−0.627135	−	1.08623i
$712$	−1.46438e6	−	845461.i	−2.88865	−	1.66776i
$713$	−230052.	+	61642.1i	−0.452529	+	0.121255i
$714$			25021.6i			0.0490817i
$715$	−181691.	+	68279.5i	−0.355404	+	0.133560i
$716$	1.77672e6			3.46571
$717$	735.274	+	2744.08i	0.00143025	+	0.00533775i
$718$	664873.	−	1.15159e6i	1.28970	−	2.23383i
$719$	−681878.	+	393683.i	−1.31901	+	0.761533i	−0.983570	−	0.180528i	$-0.942219\pi$
$719$	−681878.	+	393683.i	−1.31901	+	0.761533i	−0.335443	+	0.942060i	$0.608886\pi$
$720$	1.07958e6	−	1.07958e6i	2.08253	−	2.08253i
$721$	120851.	+	32381.9i	0.232477	+	0.0622920i
$722$	61130.8	−	228143.i	0.117270	−	0.437656i
$723$	34483.3	+	34483.3i	0.0659677	+	0.0659677i
$724$	−339062.	−	587273.i	−0.646848	−	1.12037i
$725$	−219365.	−	126650.i	−0.417341	−	0.240952i
$726$	−181261.	+	48568.8i	−0.343900	+	0.0921476i
$727$			564800.i			1.06863i	0.845287	+	0.534313i	$0.179430\pi$
$727$			564800.i			1.06863i	−0.845287	+	0.534313i	$0.820570\pi$
$728$	774614.	+	128289.i	1.46158	+	0.242063i
$729$	−397440.			−0.747853
$730$	493756.	+	1.84272e6i	0.926545	+	3.45791i
$731$	101613.	−	175999.i	0.190158	−	0.329364i
$732$	−193486.	+	111709.i	−0.361099	+	0.208481i
$733$	76656.8	−	76656.8i	0.142673	−	0.142673i	−0.632163	−	0.774836i	$-0.717833\pi$
$733$	76656.8	−	76656.8i	0.142673	−	0.142673i	0.774836	+	0.632163i	$0.217833\pi$
$734$	−246383.	−	66018.0i	−0.457318	−	0.122538i
$735$	−27154.5	+	101342.i	−0.0502652	+	0.187592i
$736$	−496493.	−	496493.i	−0.916552	−	0.916552i
$737$	−88464.6	−	153225.i	−0.162868	−	0.282095i
$738$	333528.	+	192563.i	0.612379	+	0.353557i
$739$	290906.	−	77947.9i	0.532676	−	0.142730i	0.0175523	−	0.999846i	$-0.494413\pi$
$739$	290906.	−	77947.9i	0.532676	−	0.142730i	0.515124	+	0.857116i	$0.327746\pi$
$740$			144103.i			0.263154i
$741$	127508.	−	12493.7i	0.232221	−	0.0227539i
$742$	−234962.			−0.426766
$743$	32553.2	+	121490.i	0.0589679	+	0.220071i	0.989122	−	0.147099i	$-0.0469934\pi$
$743$	32553.2	+	121490.i	0.0589679	+	0.220071i	−0.930154	+	0.367170i	$0.880327\pi$
$744$	66117.5	−	114519.i	0.119446	−	0.206886i
$745$	−972859.	+	561681.i	−1.75282	+	1.01199i
$746$	504863.	−	504863.i	0.907185	−	0.907185i
$747$	552526.	+	148049.i	0.990174	+	0.265316i
$748$	−17583.3	+	65621.8i	−0.0314266	+	0.117286i
$749$	−425860.	−	425860.i	−0.759108	−	0.759108i
$750$	−44583.9	−	77221.5i	−0.0792602	−	0.137283i
$751$	423155.	+	244308.i	0.750273	+	0.433170i	0.825793	−	0.563974i	$-0.190728\pi$
$751$	423155.	+	244308.i	0.750273	+	0.433170i	−0.0755196	+	0.997144i	$0.524062\pi$
$752$	−334315.	+	89579.4i	−0.591181	+	0.158406i
$753$			108838.i			0.191952i
$754$	−227441.	−	317731.i	−0.400061	−	0.558878i
$755$	−567178.			−0.995006
$756$	−86592.9	−	323169.i	−0.151509	−	0.565439i
$757$	−249019.	+	431313.i	−0.434551	+	0.752664i	−0.997259	−	0.0739919i	$-0.976426\pi$
$757$	−249019.	+	431313.i	−0.434551	+	0.752664i	0.562708	+	0.826656i	$0.309759\pi$
$758$	975655.	−	563295.i	1.69808	−	0.980386i
$759$	20965.0	−	20965.0i	0.0363925	−	0.0363925i
$760$	−2.25046e6	−	603010.i	−3.89623	−	1.04399i
$761$	−148259.	+	553310.i	−0.256007	+	0.955430i	0.711521	+	0.702665i	$0.248007\pi$
$761$	−148259.	+	553310.i	−0.256007	+	0.955430i	−0.967528	+	0.252765i	$0.918660\pi$
$762$	195940.	+	195940.i	0.337453	+	0.337453i
$763$	−111000.	−	192258.i	−0.190667	−	0.330245i
$764$	−693840.	−	400589.i	−1.18870	−	0.686297i
$765$	−170087.	+	45574.6i	−0.290635	+	0.0778753i
$766$		−	1.81089e6i		−	3.08627i
$767$	398127.	−	284991.i	0.676754	−	0.484440i
$768$	−191801.			−0.325183
$769$	−142434.	−	531572.i	−0.240859	−	0.898896i	−0.975420	−	0.220354i	$-0.929279\pi$
$769$	−142434.	−	531572.i	−0.240859	−	0.898896i	0.734561	−	0.678542i	$-0.237388\pi$
$770$	126890.	−	219780.i	0.214016	−	0.370686i
$771$	45489.0	−	26263.1i	0.0765240	−	0.0441812i
$772$	−407622.	+	407622.i	−0.683948	+	0.683948i
$773$	126731.	+	33957.4i	0.212092	+	0.0568298i	0.363300	−	0.931672i	$-0.381650\pi$
$773$	126731.	+	33957.4i	0.212092	+	0.0568298i	−0.151209	+	0.988502i	$0.548317\pi$
$774$	−492394.	+	1.83764e6i	−0.821923	+	3.06746i
$775$	259270.	+	259270.i	0.431667	+	0.431667i
$776$	992127.	+	1.71841e6i	1.64757	+	2.85367i
$777$	5095.35	+	2941.80i	0.00843980	+	0.00487272i
$778$	−218081.	+	58434.7i	−0.360296	+	0.0965410i
$779$		−	275424.i		−	0.453864i
$780$	−43250.6	−	441406.i	−0.0710891	−	0.725520i
$781$	51540.6			0.0844983
$782$	58851.7	+	219638.i	0.0962378	+	0.359164i
$783$	−47275.5	+	81883.6i	−0.0771104	+	0.133559i
$784$	669779.	−	386697.i	1.08968	−	0.629128i
$785$	308573.	−	308573.i	0.500748	−	0.500748i
$786$	318029.	+	85215.5i	0.514779	+	0.137935i
$787$	−103897.	+	387751.i	−0.167747	+	0.626041i	0.829927	+	0.557873i	$0.188382\pi$
$787$	−103897.	+	387751.i	−0.167747	+	0.626041i	−0.997674	+	0.0681686i	$0.978284\pi$
$788$	915502.	+	915502.i	1.47437	+	1.47437i
$789$	−54553.9	−	94490.2i	−0.0876339	−	0.151786i
$790$	1.94690e6	+	1.12404e6i	3.11953	+	1.80106i
$791$	−426834.	+	114370.i	−0.682192	+	0.182793i
$792$		−	361150.i		−	0.575755i
$793$	88669.5	−	535388.i	0.141003	−	0.851377i
$794$	−1.26619e6			−2.00843
$795$	19507.1	+	72801.6i	0.0308645	+	0.115188i
$796$	515113.	−	892201.i	0.812973	−	1.40811i
$797$	−115291.	+	66563.2i	−0.181501	+	0.104789i	−0.587997	−	0.808863i	$-0.700084\pi$
$797$	−115291.	+	66563.2i	−0.181501	+	0.104789i	0.406497	+	0.913652i	$0.366750\pi$
$798$	−118450.	+	118450.i	−0.186007	+	0.186007i
$799$	38557.7	+	10331.5i	0.0603973	+	0.0161834i
$800$	−279776.	+	1.04414e6i	−0.437150	+	1.63146i
$801$	−604982.	−	604982.i	−0.942925	−	0.942925i
$802$	389371.	+	674411.i	0.605362	+	1.04852i
$803$	183149.	+	105741.i	0.284036	+	0.163989i
$804$	390514.	−	104638.i	0.604122	−	0.161874i
$805$		−	593107.i		−	0.915253i
$806$	198974.	+	529468.i	0.306285	+	0.815023i
$807$	−194818.			−0.299145
$808$	−165684.	−	618342.i	−0.253781	−	0.947122i
$809$	46491.1	−	80525.0i	0.0710351	−	0.123036i	−0.828320	−	0.560255i	$-0.810703\pi$
$809$	46491.1	−	80525.0i	0.0710351	−	0.123036i	0.899355	+	0.437219i	$0.144036\pi$
$810$	1.35952e6	−	784920.i	2.07213	−	1.19634i
$811$	440995.	−	440995.i	0.670489	−	0.670489i	−0.287340	−	0.957829i	$-0.592771\pi$
$811$	440995.	−	440995.i	0.670489	−	0.670489i	0.957829	+	0.287340i	$0.0927709\pi$
$812$	344582.	+	92330.5i	0.522614	+	0.140034i
$813$	59962.9	−	223784.i	0.0907196	−	0.338570i
$814$	16177.1	+	16177.1i	0.0244147	+	0.0244147i
$815$	−424097.	−	734557.i	−0.638484	−	1.10589i
$816$	−51239.0	−	29582.8i	−0.0769521	−	0.0444283i
$817$	1.31419e6	−	352137.i	1.96886	−	0.527555i
$818$			15345.9i			0.0229343i
$819$	361784.	+	164142.i	0.539364	+	0.244709i
$820$	−953456.			−1.41799
$821$	240433.	+	897307.i	0.356703	+	1.33123i	0.878328	+	0.478059i	$0.158660\pi$
$821$	240433.	+	897307.i	0.356703	+	1.33123i	−0.521624	+	0.853175i	$0.674674\pi$
$822$	−111676.	+	193429.i	−0.165279	+	0.286272i
$823$	−702667.	+	405685.i	−1.03741	+	0.598948i	−0.919098	−	0.394029i	$-0.871081\pi$
$823$	−702667.	+	405685.i	−1.03741	+	0.598948i	−0.118310	+	0.992977i	$0.537748\pi$
$824$	−446379.	+	446379.i	−0.657430	+	0.657430i
$825$	−44090.1	−	11813.9i	−0.0647788	−	0.0173574i
$826$	−165688.	+	618355.i	−0.242846	+	0.906312i
$827$	−135180.	−	135180.i	−0.197651	−	0.197651i	0.601341	−	0.798992i	$-0.294633\pi$
$827$	−135180.	−	135180.i	−0.197651	−	0.197651i	−0.798992	+	0.601341i	$0.794633\pi$
$828$	−743167.	−	1.28720e6i	−1.08399	−	1.87753i
$829$	247898.	+	143124.i	0.360714	+	0.208258i	0.669394	−	0.742908i	$-0.266554\pi$
$829$	247898.	+	143124.i	0.360714	+	0.208258i	−0.308680	+	0.951166i	$0.599887\pi$
$830$	−1.95900e6	+	524913.i	−2.84366	+	0.761958i
$831$		−	167388.i		−	0.242394i
$832$	−161684.	+	196811.i	−0.233572	+	0.284317i
$833$	−89198.2			−0.128548
$834$	48126.2	+	179609.i	0.0691910	+	0.258224i
$835$	141203.	−	244571.i	0.202521	−	0.350777i
$836$	−393886.	+	227410.i	−0.563583	+	0.325385i
$837$	96779.2	−	96779.2i	0.138144	−	0.138144i
$838$	−614797.	−	164734.i	−0.875475	−	0.234583i
$839$	−2418.73	+	9026.84i	−0.00343609	+	0.0128237i	−0.967623	−	0.252402i	$-0.918780\pi$
$839$	−2418.73	+	9026.84i	−0.00343609	+	0.0128237i	0.964187	+	0.265225i	$0.0854463\pi$
$840$	232854.	+	232854.i	0.330008	+	0.330008i
$841$	303233.	+	525214.i	0.428730	+	0.742582i
$842$	−1.82336e6	−	1.05272e6i	−2.57186	−	1.48487i
$843$	69371.7	−	18588.1i	0.0976174	−	0.0261565i
$844$			1.38541e6i			1.94489i
$845$	895145.	+	599420.i	1.25366	+	0.839494i
$846$	−373683.			−0.522111
$847$	107705.	+	401962.i	0.150131	+	0.560297i
$848$	277794.	−	481153.i	0.386305	−	0.669100i
$849$	20714.6	−	11959.6i	0.0287383	−	0.0165921i
$850$	247533.	−	247533.i	0.342607	−	0.342607i
$851$	51645.7	+	13838.4i	0.0713141	+	0.0191086i
$852$	−30481.7	+	113759.i	−0.0419914	+	0.156714i
$853$	47982.7	+	47982.7i	0.0659457	+	0.0659457i	0.739310	−	0.673365i	$-0.235152\pi$
$853$	47982.7	+	47982.7i	0.0659457	+	0.0659457i	−0.673365	+	0.739310i	$0.735152\pi$
$854$	354774.	+	614487.i	0.486448	+	0.842552i
$855$	−1.02092e6	−	589430.i	−1.39656	−	0.806306i
$856$	2.93520e6	−	786486.i	4.00581	−	1.07335i
$857$			463715.i			0.631379i	0.948863	+	0.315689i	$0.102236\pi$
$857$			463715.i			0.631379i	−0.948863	+	0.315689i	$0.897764\pi$
$858$	−54407.8	−	44697.1i	−0.0739071	−	0.0607162i
$859$	803560.			1.08901			0.544505	−	0.838757i	$-0.316717\pi$
$859$	803560.			1.08901			0.544505	+	0.838757i	$0.316717\pi$
$860$	−1.21902e6	−	4.54945e6i	−1.64822	−	6.15123i
$861$	−19464.4	+	33713.3i	−0.0262564	+	0.0454773i
$862$	−939040.	+	542155.i	−1.26377	+	0.729640i
$863$	−780782.	+	780782.i	−1.04835	+	1.04835i	−0.0495840	+	0.998770i	$0.515790\pi$
$863$	−780782.	+	780782.i	−1.04835	+	1.04835i	−0.998770	+	0.0495840i	$0.984210\pi$
$864$	389751.	+	104434.i	0.522108	+	0.139898i
$865$	264266.	−	986253.i	0.353190	−	1.31812i
$866$	−805254.	−	805254.i	−1.07373	−	1.07373i
$867$	−75061.7	−	130011.i	−0.0998573	−	0.172958i
$868$	−447209.	−	258196.i	−0.593569	−	0.342697i
$869$	240721.	−	64501.1i	0.318768	−	0.0854137i
$870$		−	163882.i		−	0.216517i
$871$	−405735.	+	894280.i	−0.534818	+	1.17879i
$872$	1.12013e6			1.47310
$873$	259853.	+	969783.i	0.340956	+	1.27247i
$874$	−761146.	+	1.31834e6i	−0.996427	+	1.72586i
$875$	−171245.	+	98868.5i	−0.223667	+	0.129134i
$876$	−341706.	+	341706.i	−0.445292	+	0.445292i
$877$	−545053.	−	146047.i	−0.708663	−	0.189886i	−0.113556	−	0.993532i	$-0.536224\pi$
$877$	−545053.	−	146047.i	−0.708663	−	0.189886i	−0.595108	+	0.803646i	$0.702891\pi$
$878$	627076.	−	2.34028e6i	0.813450	−	3.03584i
$879$	186655.	+	186655.i	0.241581	+	0.241581i
$880$	300042.	+	519688.i	0.387451	+	0.671084i
$881$	962437.	+	555663.i	1.24000	+	0.715912i	0.969093	−	0.246694i	$-0.0793443\pi$
$881$	962437.	+	555663.i	1.24000	+	0.715912i	0.270903	+	0.962607i	$0.412678\pi$
$882$	806559.	−	216117.i	1.03681	−	0.277812i
$883$		−	1.16473e6i		−	1.49384i	−0.664913	−	0.746921i	$-0.731532\pi$
$883$		−	1.16473e6i		−	1.49384i	0.664913	−	0.746921i	$-0.268468\pi$
$884$	352970.	−	132646.i	0.451683	−	0.169742i
$885$	205349.			0.262184
$886$	316091.	+	1.17967e6i	0.402666	+	1.50277i
$887$	−95048.3	+	164628.i	−0.120808	+	0.209246i	−0.920087	−	0.391715i	$-0.871882\pi$
$887$	−95048.3	+	164628.i	−0.120808	+	0.209246i	0.799278	+	0.600961i	$0.205215\pi$
$888$	−25709.1	+	14843.1i	−0.0326032	+	0.0188235i
$889$	434514.	−	434514.i	0.549794	−	0.549794i
$890$	2.93010e6	+	785119.i	3.69916	+	0.991186i
$891$	45041.2	−	168096.i	0.0567355	−	0.211740i
$892$	1.17028e6	+	1.17028e6i	1.47082	+	1.47082i
$893$	133620.	+	231437.i	0.167560	+	0.290222i
$894$	−352927.	−	203763.i	−0.441581	−	0.254947i
$895$	−1.74834e6	+	468465.i	−2.18262	+	0.584832i
$896$			324846.i			0.404634i
$897$	−162351.	−	26888.1i	−0.201776	−	0.0334176i
$898$	−1.66742e6			−2.06773
$899$	37770.8	+	140963.i	0.0467344	+	0.174415i
$900$	−1.14412e6	+	1.98168e6i	−1.41250	+	2.44651i
$901$	−55493.0	+	32038.9i	−0.0683578	+	0.0394664i
$902$	−107035.	+	107035.i	−0.131557	+	0.131557i
$903$	−185750.	−	49771.6i	−0.227800	−	0.0610388i
$904$	577064.	−	2.15363e6i	0.706134	−	2.63533i
$905$	488491.	+	488491.i	0.596430	+	0.596430i
$906$	−102879.	−	178191.i	−0.125334	−	0.217085i
$907$	442938.	+	255730.i	0.538428	+	0.310862i	0.744442	−	0.667687i	$-0.232716\pi$
$907$	442938.	+	255730.i	0.538428	+	0.310862i	−0.206013	+	0.978549i	$0.566049\pi$
$908$	−2.30114e6	+	616587.i	−2.79107	+	0.747865i
$909$		−	323906.i		−	0.392004i
$910$	−1.40185e6	+	137358.i	−1.69285	+	0.165872i
$911$	−96940.9			−0.116807			−0.0584037	−	0.998293i	$-0.518601\pi$
$911$	−96940.9			−0.116807			−0.0584037	+	0.998293i	$0.518601\pi$
$912$	−102518.	−	382604.i	−0.123257	−	0.460002i
$913$	−112414.	+	194706.i	−0.134858	+	0.233581i
$914$	224873.	−	129830.i	0.269181	−	0.155412i
$915$	160941.	−	160941.i	0.192231	−	0.192231i
$916$	605101.	+	162136.i	0.721168	+	0.193237i
$917$	188973.	−	705256.i	0.224730	−	0.838703i
$918$	−92398.2	−	92398.2i	−0.109642	−	0.109642i
$919$	73114.0	+	126637.i	0.0865704	+	0.149944i	0.906059	−	0.423151i	$-0.139076\pi$
$919$	73114.0	+	126637.i	0.0865704	+	0.149944i	−0.819489	+	0.573095i	$0.805743\pi$
$920$	2.59165e6	+	1.49629e6i	3.06196	+	1.76783i
$921$	−173715.	+	46546.7i	−0.204794	+	0.0548744i
$922$			900557.i			1.05937i
$923$	−166511.	−	232613.i	−0.195452	−	0.273043i
$924$	64285.0			0.0752949
$925$	−21304.6	−	79509.8i	−0.0248994	−	0.0929259i
$926$	204722.	−	354589.i	0.238750	−	0.413527i
$927$	−276620.	+	159706.i	−0.321902	+	0.185850i
$928$	−304223.	+	304223.i	−0.353261	+	0.353261i
$929$	−434933.	−	116540.i	−0.503954	−	0.135034i	−0.00211946	−	0.999998i	$-0.500675\pi$
$929$	−434933.	−	116540.i	−0.503954	−	0.135034i	−0.501834	+	0.864964i	$0.667341\pi$
$930$	−61398.6	+	229143.i	−0.0709892	+	0.264935i
$931$	−422257.	−	422257.i	−0.487166	−	0.487166i
$932$	−517916.	−	897057.i	−0.596249	−	1.03273i
$933$	125856.	+	72662.7i	0.144580	+	0.0834735i
$934$	2.02680e6	−	543080.i	2.32336	−	0.622544i
$935$		−	69209.7i		−	0.0791669i
$936$	−1.62994e6	+	1.16676e6i	−1.86046	+	1.33177i
$937$	−492047.			−0.560438			−0.280219	−	0.959936i	$-0.590407\pi$
$937$	−492047.			−0.560438			−0.280219	+	0.959936i	$0.590407\pi$
$938$	−332317.	−	1.24022e6i	−0.377700	−	1.40960i
$939$	20655.6	−	35776.5i	0.0234264	−	0.0405758i
$940$	801185.	−	462565.i	0.906729	−	0.523500i
$941$	−265942.	+	265942.i	−0.300337	+	0.300337i	−0.841145	−	0.540809i	$-0.818118\pi$
$941$	−265942.	+	265942.i	−0.300337	+	0.300337i	0.540809	+	0.841145i	$0.318118\pi$
$942$	152916.	+	40973.7i	0.172326	+	0.0461746i
$943$	−91561.7	+	341713.i	−0.102965	+	0.384272i
$944$	−1.07037e6	−	1.07037e6i	−1.20113	−	1.20113i
$945$	170419.	+	295175.i	0.190834	+	0.330533i
$946$	−647571.	−	373876.i	−0.723611	−	0.417777i
$947$	385596.	−	103320.i	0.429964	−	0.115209i	−0.0373452	−	0.999302i	$-0.511890\pi$
$947$	385596.	−	103320.i	0.429964	−	0.115209i	0.467309	+	0.884094i	$0.345223\pi$
$948$			569461.i			0.633647i
$949$	−114465.	−	1.16820e6i	−0.127098	−	1.29714i
$950$	2.34360e6			2.59679
$951$	−62896.1	−	234732.i	−0.0695445	−	0.259544i
$952$	−139984.	+	242459.i	−0.154456	+	0.267525i
$953$	738306.	−	426261.i	0.812925	−	0.469342i	−0.0350456	−	0.999386i	$-0.511158\pi$
$953$	738306.	−	426261.i	0.812925	−	0.469342i	0.847971	+	0.530043i	$0.177824\pi$
$954$	424159.	−	424159.i	0.466050	−	0.466050i
$955$	788379.	+	211245.i	0.864427	+	0.231622i
$956$	−14487.5	+	54068.2i	−0.0158518	+	0.0591597i
$957$	−12846.2	−	12846.2i	−0.0140265	−	0.0140265i
$958$	−43566.3	−	75459.0i	−0.0474700	−	0.0822205i
$959$	428946.	+	247652.i	0.466407	+	0.269280i
$960$	−103187.	+	27648.8i	−0.111965	+	0.0300009i
$961$			712274.i			0.771259i
$962$	20747.4	−	125273.i	0.0224189	−	0.135366i
$963$	1.53755e6			1.65797
$964$	248694.	+	928138.i	0.267615	+	0.998754i
$965$	293633.	−	508588.i	0.315319	−	0.546149i
$966$	186337.	−	107582.i	0.199684	−	0.115288i
$967$	−910594.	+	910594.i	−0.973804	+	0.973804i	−0.999666	−	0.0258613i	$-0.991767\pi$
$967$	−910594.	+	910594.i	−0.973804	+	0.973804i	0.0258613	+	0.999666i	$0.491767\pi$
$968$	−2.02814e6	−	543438.i	−2.16445	−	0.579962i
$969$	−11823.8	+	44127.0i	−0.0125924	+	0.0469956i
$970$	−2.51708e6	−	2.51708e6i	−2.67519	−	2.67519i
$971$	−816973.	−	1.41504e6i	−0.866501	−	1.50082i	−0.865549	−	0.500825i	$-0.833030\pi$
$971$	−816973.	−	1.41504e6i	−0.866501	−	1.50082i	−0.000952461	−	1.00000i	$-0.500303\pi$
$972$	1.11781e6	+	645367.i	1.18314	+	0.683085i
$973$	398299.	−	106724.i	0.420711	−	0.112729i
$974$			122149.i			0.128757i
$975$	89122.3	+	237154.i	0.0937513	+	0.249472i
$976$	−1.67778e6			−1.76131
$977$	−254676.	−	950462.i	−0.266808	−	0.995739i	−0.961135	−	0.276080i	$-0.910965\pi$
$977$	−254676.	−	950462.i	−0.266808	−	0.995739i	0.694327	−	0.719660i	$-0.255702\pi$
$978$	153851.	−	266478.i	0.160851	−	0.278601i
$979$	291225.	−	168139.i	0.303853	−	0.175429i
$980$	−1.46176e6	+	1.46176e6i	−1.52203	+	1.52203i
$981$	547449.	+	146689.i	0.568861	+	0.152426i
$982$	−363235.	+	1.35561e6i	−0.376673	+	1.40576i
$983$	−324223.	−	324223.i	−0.335534	−	0.335534i	0.519149	−	0.854683i	$-0.326249\pi$
$983$	−324223.	−	324223.i	−0.335534	−	0.335534i	−0.854683	+	0.519149i	$0.826249\pi$
$984$	−98209.4	−	170104.i	−0.101429	−	0.175680i
$985$	−1.14227e6	−	659488.i	−1.17732	−	0.679726i
$986$	134582.	−	36061.0i	0.138430	−	0.0370923i
$987$		−	37772.2i		−	0.0387738i
$988$	2.29886e6	+	1.04300e6i	2.35505	+	1.06849i
$989$	−1.74756e6			−1.78665
$990$	167687.	+	625817.i	0.171092	+	0.638523i
$991$	159780.	−	276747.i	0.162696	−	0.281797i	−0.773139	−	0.634237i	$-0.781314\pi$
$991$	159780.	−	276747.i	0.162696	−	0.281797i	0.935835	+	0.352440i	$0.114648\pi$
$992$	539347.	−	311392.i	0.548081	−	0.316435i
$993$	−224179.	+	224179.i	−0.227351	+	0.227351i
$994$	361285.	+	96806.1i	0.365660	+	0.0979784i
$995$	−271638.	+	1.01377e6i	−0.274375	+	1.02398i
$996$	−363268.	−	363268.i	−0.366192	−	0.366192i
$997$	−416227.	−	720926.i	−0.418735	−	0.725271i	0.577077	−	0.816690i	$-0.304193\pi$
$997$	−416227.	−	720926.i	−0.418735	−	0.725271i	−0.995813	+	0.0914186i	$0.970860\pi$
$998$	2.42756e6	+	1.40155e6i	2.43730	+	1.40718i
$999$	−29679.1	+	7952.48i	−0.0297385	+	0.00796841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.f.a.6.1	✓	16
3.2	odd	2		117.5.bd.c.19.4		16
13.4	even	6		169.5.d.c.70.8		16
13.6	odd	12		169.5.d.c.99.8		16
13.7	odd	12		169.5.d.d.99.1		16
13.9	even	3		169.5.d.d.70.1		16
13.11	odd	12	inner	13.5.f.a.11.1	yes	16
39.11	even	12		117.5.bd.c.37.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.6.1	✓	16	1.1	even	1	trivial
13.5.f.a.11.1	yes	16	13.11	odd	12	inner
117.5.bd.c.19.4		16	3.2	odd	2
117.5.bd.c.37.4		16	39.11	even	12
169.5.d.c.70.8		16	13.4	even	6
169.5.d.c.99.8		16	13.6	odd	12
169.5.d.d.70.1		16	13.9	even	3
169.5.d.d.99.1		16	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.88469 - 7.03375i) q^{2} +(-0.939567 + 1.62738i) q^{3} +(-32.0652 + 18.5128i) q^{4} +(26.6717 - 26.6717i) q^{5} +(13.2174 + 3.54158i) q^{6} +(7.85376 - 29.3106i) q^{7} +(108.263 + 108.263i) q^{8} +(38.7344 + 67.0900i) q^{9} +O(q^{10})\)	\(q+(-1.88469 - 7.03375i) q^{2} +(-0.939567 + 1.62738i) q^{3} +(-32.0652 + 18.5128i) q^{4} +(26.6717 - 26.6717i) q^{5} +(13.2174 + 3.54158i) q^{6} +(7.85376 - 29.3106i) q^{7} +(108.263 + 108.263i) q^{8} +(38.7344 + 67.0900i) q^{9} +(-237.870 - 137.334i) q^{10} +(-29.4111 + 7.88068i) q^{11} -69.5762i q^{12} +(130.585 + 107.278i) q^{13} -220.965 q^{14} +(18.3451 + 68.4648i) q^{15} +(261.245 - 452.490i) q^{16} +(-52.1872 + 30.1303i) q^{17} +(398.892 - 398.892i) q^{18} +(-389.684 - 104.416i) q^{19} +(-361.464 + 1349.00i) q^{20} +(40.3203 + 40.3203i) q^{21} +(110.861 + 192.018i) q^{22} +(448.762 + 259.093i) q^{23} +(-277.904 + 74.4642i) q^{24} -797.759i q^{25} +(508.456 - 1120.69i) q^{26} -297.784 q^{27} +(290.791 + 1085.25i) q^{28} +(158.758 - 274.976i) q^{29} +(446.989 - 258.069i) q^{30} +(-324.998 + 324.998i) q^{31} +(-1308.84 - 350.702i) q^{32} +(14.8088 - 55.2674i) q^{33} +(310.286 + 310.286i) q^{34} +(-572.291 - 991.237i) q^{35} +(-2484.05 - 1434.17i) q^{36} +(99.6664 - 26.7055i) q^{37} +2937.73i q^{38} +(-297.275 + 111.716i) q^{39} +5775.10 q^{40} +(176.697 + 659.441i) q^{41} +(207.612 - 359.594i) q^{42} +(-2920.63 + 1686.23i) q^{43} +(797.178 - 797.178i) q^{44} +(2822.52 + 756.291i) q^{45} +(976.619 - 3644.79i) q^{46} +(-468.402 - 468.402i) q^{47} +(490.915 + 850.290i) q^{48} +(1281.90 + 740.103i) q^{49} +(-5611.24 + 1503.53i) q^{50} -113.238i q^{51} +(-6173.25 - 1022.40i) q^{52} +1063.34 q^{53} +(561.230 + 2094.54i) q^{54} +(-574.253 + 994.635i) q^{55} +(4023.51 - 2322.98i) q^{56} +(536.058 - 536.058i) q^{57} +(-2233.32 - 598.417i) q^{58} +(749.836 - 2798.42i) q^{59} +(-1855.72 - 1855.72i) q^{60} +(-1605.56 - 2780.92i) q^{61} +(2898.47 + 1673.43i) q^{62} +(2270.66 - 608.421i) q^{63} +1507.15i q^{64} +(6344.21 - 621.629i) q^{65} -416.647 q^{66} +(1503.93 + 5612.75i) q^{67} +(1115.60 - 1932.27i) q^{68} +(-843.284 + 486.871i) q^{69} +(-5893.52 + 5893.52i) q^{70} +(-1635.03 - 438.105i) q^{71} +(-3069.85 + 11456.8i) q^{72} +(-4911.25 - 4911.25i) q^{73} +(-375.680 - 650.697i) q^{74} +(1298.26 + 749.548i) q^{75} +(14428.3 - 3866.06i) q^{76} +923.950i q^{77} +(1346.05 + 1880.41i) q^{78} -8184.71 q^{79} +(-5100.83 - 19036.5i) q^{80} +(-2857.70 + 4949.68i) q^{81} +(4305.32 - 2485.68i) q^{82} +(5221.16 - 5221.16i) q^{83} +(-2039.32 - 546.435i) q^{84} +(-588.296 + 2195.55i) q^{85} +(17365.0 + 17365.0i) q^{86} +(298.327 + 516.717i) q^{87} +(-4037.30 - 2330.94i) q^{88} +(-10667.8 + 2858.42i) q^{89} -21278.3i q^{90} +(4169.97 - 2984.99i) q^{91} -19186.2 q^{92} +(-223.537 - 834.251i) q^{93} +(-2411.83 + 4177.41i) q^{94} +(-13178.5 + 7608.60i) q^{95} +(1800.47 - 1800.47i) q^{96} +(12518.4 + 3354.29i) q^{97} +(2789.73 - 10411.4i) q^{98} +(-1667.94 - 1667.94i) 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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