LMFDB - Embedded newform 13.5.f.a.2.4

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			2.4
Root			$-3.98977i$ of defining polynomial
Character	$\chi$	$=$	13.2
Dual form			13.5.f.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.50893 + 1.47611i) q^{2} +(-4.28079 - 7.41455i) q^{3} +(14.3130 + 8.26362i) q^{4} +(-29.3294 + 29.3294i) q^{5} +(-12.6379 - 47.1652i) q^{6} +(45.8361 - 12.2817i) q^{7} +(2.12627 + 2.12627i) q^{8} +(3.84960 - 6.66770i) q^{9} +O(q^{10})$	\(q+(5.50893 + 1.47611i) q^{2} +(-4.28079 - 7.41455i) q^{3} +(14.3130 + 8.26362i) q^{4} +(-29.3294 + 29.3294i) q^{5} +(-12.6379 - 47.1652i) q^{6} +(45.8361 - 12.2817i) q^{7} +(2.12627 + 2.12627i) q^{8} +(3.84960 - 6.66770i) q^{9} +(-204.867 + 118.280i) q^{10} +(11.4581 - 42.7622i) q^{11} -141.499i q^{12} +(102.310 + 134.513i) q^{13} +270.637 q^{14} +(343.018 + 91.9113i) q^{15} +(-123.643 - 214.156i) q^{16} +(-205.648 - 118.731i) q^{17} +(31.0495 - 31.0495i) q^{18} +(127.702 + 476.590i) q^{19} +(-662.159 + 177.425i) q^{20} +(-287.279 - 287.279i) q^{21} +(126.244 - 218.661i) q^{22} +(-258.218 + 149.082i) q^{23} +(6.66321 - 24.8674i) q^{24} -1095.43i q^{25} +(365.064 + 892.042i) q^{26} -759.406 q^{27} +(757.544 + 202.983i) q^{28} +(185.692 + 321.628i) q^{29} +(1753.99 + 1012.67i) q^{30} +(625.946 - 625.946i) q^{31} +(-377.475 - 1408.76i) q^{32} +(-366.113 + 98.0995i) q^{33} +(-957.641 - 957.641i) q^{34} +(-984.129 + 1704.56i) q^{35} +(110.199 - 63.6233i) q^{36} +(197.689 - 737.784i) q^{37} +2814.01i q^{38} +(559.381 - 1334.41i) q^{39} -124.724 q^{40} +(-671.311 - 179.877i) q^{41} +(-1158.54 - 2006.65i) q^{42} +(975.366 + 563.128i) q^{43} +(517.371 - 517.371i) q^{44} +(82.6533 + 308.466i) q^{45} +(-1642.57 + 440.125i) q^{46} +(609.937 + 609.937i) q^{47} +(-1058.58 + 1833.52i) q^{48} +(-129.221 + 74.6059i) q^{49} +(1616.98 - 6034.64i) q^{50} +2033.05i q^{51} +(352.807 + 2770.73i) q^{52} +897.855 q^{53} +(-4183.52 - 1120.97i) q^{54} +(918.131 + 1590.25i) q^{55} +(123.574 + 71.3455i) q^{56} +(2987.04 - 2987.04i) q^{57} +(548.205 + 2045.93i) q^{58} +(480.526 - 128.756i) q^{59} +(4150.10 + 4150.10i) q^{60} +(-124.214 + 215.146i) q^{61} +(4372.26 - 2524.32i) q^{62} +(94.5596 - 352.901i) q^{63} -4361.35i q^{64} +(-6945.87 - 944.475i) q^{65} -2161.69 q^{66} +(1803.04 + 483.124i) q^{67} +(-1962.30 - 3398.80i) q^{68} +(2210.76 + 1276.38i) q^{69} +(-7937.63 + 7937.63i) q^{70} +(776.613 + 2898.36i) q^{71} +(22.3626 - 5.99204i) q^{72} +(-6818.40 - 6818.40i) q^{73} +(2178.11 - 3772.59i) q^{74} +(-8122.11 + 4689.30i) q^{75} +(-2110.56 + 7876.72i) q^{76} -2100.78i q^{77} +(5051.33 - 6525.44i) q^{78} +2503.91 q^{79} +(9907.45 + 2654.69i) q^{80} +(2939.04 + 5090.57i) q^{81} +(-3432.69 - 1981.86i) q^{82} +(7971.73 - 7971.73i) q^{83} +(-1737.86 - 6485.78i) q^{84} +(9513.85 - 2549.23i) q^{85} +(4541.98 + 4541.98i) q^{86} +(1589.82 - 2753.65i) q^{87} +(115.287 - 66.5609i) q^{88} +(-3752.75 + 14005.5i) q^{89} +1821.33i q^{90} +(6341.55 + 4908.98i) q^{91} -4927.83 q^{92} +(-7320.65 - 1961.56i) q^{93} +(2459.76 + 4260.44i) q^{94} +(-17723.5 - 10232.7i) q^{95} +(-8829.40 + 8829.40i) q^{96} +(-1917.54 - 7156.34i) q^{97} +(-821.997 + 220.254i) q^{98} +(-241.017 - 241.017i) 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	5.50893	+	1.47611i	1.37723	+	0.369028i	0.870115	−	0.492848i	$-0.164044\pi$
$2$	5.50893	+	1.47611i	1.37723	+	0.369028i	0.507118	+	0.861877i	$0.330711\pi$
$3$	−4.28079	−	7.41455i	−0.475644	−	0.823839i	0.523967	−	0.851739i	$-0.324452\pi$
$3$	−4.28079	−	7.41455i	−0.475644	−	0.823839i	−0.999611	+	0.0278994i	$0.991118\pi$
$4$	14.3130	+	8.26362i	0.894563	+	0.516476i
$5$	−29.3294	+	29.3294i	−1.17318	+	1.17318i	−0.191728	+	0.981448i	$0.561409\pi$
$5$	−29.3294	+	29.3294i	−1.17318	+	1.17318i	−0.981448	+	0.191728i	$0.938591\pi$
$6$	−12.6379	−	47.1652i	−0.351052	−	1.31014i
$7$	45.8361	−	12.2817i	0.935430	−	0.250648i	0.241262	−	0.970460i	$-0.422439\pi$
$7$	45.8361	−	12.2817i	0.935430	−	0.250648i	0.694169	+	0.719812i	$0.255772\pi$
$8$	2.12627	+	2.12627i	0.0332229	+	0.0332229i
$9$	3.84960	−	6.66770i	0.0475259	−	0.0823173i
$10$	−204.867	+	118.280i	−2.04867	+	1.18280i
$11$	11.4581	−	42.7622i	0.0946951	−	0.353407i	−0.902278	−	0.431155i	$-0.858106\pi$
$11$	11.4581	−	42.7622i	0.0946951	−	0.353407i	0.996973	+	0.0777480i	$0.0247730\pi$
$12$		−	141.499i		−	0.982635i
$13$	102.310	+	134.513i	0.605386	+	0.795932i
$13$	102.310	+	134.513i	0.605386	+	0.795932i
$14$	270.637			1.38080
$15$	343.018	+	91.9113i	1.52452	+	0.408495i
$16$	−123.643	−	214.156i	−0.482981	−	0.836547i
$17$	−205.648	−	118.731i	−0.711585	−	0.410834i	0.100063	−	0.994981i	$-0.468096\pi$
$17$	−205.648	−	118.731i	−0.711585	−	0.410834i	−0.811648	+	0.584147i	$0.801429\pi$
$18$	31.0495	−	31.0495i	0.0958317	−	0.0958317i
$19$	127.702	+	476.590i	0.353745	+	1.32019i	0.882056	+	0.471144i	$0.156159\pi$
$19$	127.702	+	476.590i	0.353745	+	1.32019i	−0.528311	+	0.849051i	$0.677175\pi$
$20$	−662.159	+	177.425i	−1.65540	+	0.443563i
$21$	−287.279	−	287.279i	−0.651425	−	0.651425i
$22$	126.244	−	218.661i	0.260834	−	0.451778i
$23$	−258.218	+	149.082i	−0.488125	+	0.281819i	−0.723796	−	0.690014i	$-0.757604\pi$
$23$	−258.218	+	149.082i	−0.488125	+	0.281819i	0.235671	+	0.971833i	$0.424271\pi$
$24$	6.66321	−	24.8674i	0.0115681	−	0.0431726i
$25$		−	1095.43i		−	1.75269i
$26$	365.064	+	892.042i	0.540036	+	1.31959i
$27$	−759.406			−1.04171
$28$	757.544	+	202.983i	0.966255	+	0.258907i
$29$	185.692	+	321.628i	0.220799	+	0.382435i	0.955051	−	0.296442i	$-0.0958002\pi$
$29$	185.692	+	321.628i	0.220799	+	0.382435i	−0.734252	+	0.678877i	$0.762467\pi$
$30$	1753.99	+	1012.67i	1.94888	+	1.12518i
$31$	625.946	−	625.946i	0.651348	−	0.651348i	−0.301969	−	0.953318i	$-0.597644\pi$
$31$	625.946	−	625.946i	0.651348	−	0.651348i	0.953318	+	0.301969i	$0.0976441\pi$
$32$	−377.475	−	1408.76i	−0.368628	−	1.37574i
$33$	−366.113	+	98.0995i	−0.336191	+	0.0900822i
$34$	−957.641	−	957.641i	−0.828409	−	0.828409i
$35$	−984.129	+	1704.56i	−0.803371	+	1.39148i
$36$	110.199	−	63.6233i	0.0850299	−	0.0490920i
$37$	197.689	−	737.784i	0.144404	−	0.538922i	−0.855377	−	0.518005i	$-0.826675\pi$
$37$	197.689	−	737.784i	0.144404	−	0.538922i	0.999781	−	0.0209170i	$-0.00665856\pi$
$38$			2814.01i			1.94876i
$39$	559.381	−	1334.41i	0.367772	−	0.877321i
$40$	−124.724			−0.0779527
$41$	−671.311	−	179.877i	−0.399352	−	0.107006i	0.0535525	−	0.998565i	$-0.482946\pi$
$41$	−671.311	−	179.877i	−0.399352	−	0.107006i	−0.452905	+	0.891559i	$0.649612\pi$
$42$	−1158.54	−	2006.65i	−0.656770	−	1.13756i
$43$	975.366	+	563.128i	0.527510	+	0.304558i	0.740002	−	0.672605i	$-0.234825\pi$
$43$	975.366	+	563.128i	0.527510	+	0.304558i	−0.212492	+	0.977163i	$0.568158\pi$
$44$	517.371	−	517.371i	0.267237	−	0.267237i
$45$	82.6533	+	308.466i	0.0408164	+	0.152329i
$46$	−1642.57	+	440.125i	−0.776261	+	0.207998i
$47$	609.937	+	609.937i	0.276114	+	0.276114i	0.831556	−	0.555441i	$-0.187451\pi$
$47$	609.937	+	609.937i	0.276114	+	0.276114i	−0.555441	+	0.831556i	$0.687451\pi$
$48$	−1058.58	+	1833.52i	−0.459454	+	0.795797i
$49$	−129.221	+	74.6059i	−0.0538197	+	0.0310728i
$50$	1616.98	−	6034.64i	0.646791	−	2.41386i
$51$			2033.05i			0.781642i
$52$	352.807	+	2770.73i	0.130476	+	1.02468i
$53$	897.855			0.319635			0.159818	−	0.987147i	$-0.448909\pi$
$53$	897.855			0.319635			0.159818	+	0.987147i	$0.448909\pi$
$54$	−4183.52	−	1120.97i	−1.43468	−	0.384420i
$55$	918.131	+	1590.25i	0.303514	+	0.525702i
$56$	123.574	+	71.3455i	0.0394050	+	0.0227505i
$57$	2987.04	−	2987.04i	0.919371	−	0.919371i
$58$	548.205	+	2045.93i	0.162962	+	0.608183i
$59$	480.526	−	128.756i	0.138042	−	0.0369883i	−0.189136	−	0.981951i	$-0.560569\pi$
$59$	480.526	−	128.756i	0.138042	−	0.0369883i	0.327179	+	0.944963i	$0.393902\pi$
$60$	4150.10	+	4150.10i	1.15280	+	1.15280i
$61$	−124.214	+	215.146i	−0.0333820	+	0.0578193i	−0.882234	−	0.470812i	$-0.843961\pi$
$61$	−124.214	+	215.146i	−0.0333820	+	0.0578193i	0.848852	+	0.528631i	$0.177294\pi$
$62$	4372.26	−	2524.32i	1.13742	−	0.656692i
$63$	94.5596	−	352.901i	0.0238245	−	0.0889144i
$64$		−	4361.35i		−	1.06478i
$65$	−6945.87	−	944.475i	−1.64399	−	0.223544i
$66$	−2161.69			−0.496257
$67$	1803.04	+	483.124i	0.401658	+	0.107624i	0.453992	−	0.891006i	$-0.349999\pi$
$67$	1803.04	+	483.124i	0.401658	+	0.107624i	−0.0523342	+	0.998630i	$0.516666\pi$
$68$	−1962.30	−	3398.80i	−0.424372	−	0.735034i
$69$	2210.76	+	1276.38i	0.464347	+	0.268091i
$70$	−7937.63	+	7937.63i	−1.61992	+	1.61992i
$71$	776.613	+	2898.36i	0.154059	+	0.574957i	0.999184	+	0.0403881i	$0.0128594\pi$
$71$	776.613	+	2898.36i	0.154059	+	0.574957i	−0.845125	+	0.534569i	$0.820474\pi$
$72$	22.3626	−	5.99204i	0.00431377	−	0.00115587i
$73$	−6818.40	−	6818.40i	−1.27949	−	1.27949i	−0.940953	−	0.338536i	$-0.890068\pi$
$73$	−6818.40	−	6818.40i	−1.27949	−	1.27949i	−0.338536	−	0.940953i	$-0.609932\pi$
$74$	2178.11	−	3772.59i	0.397755	−	0.688932i
$75$	−8122.11	+	4689.30i	−1.44393	+	0.833654i
$76$	−2110.56	+	7876.72i	−0.365402	+	1.36370i
$77$		−	2100.78i		−	0.354323i
$78$	5051.33	−	6525.44i	0.830264	−	1.07256i
$79$	2503.91			0.401204			0.200602	−	0.979673i	$-0.435710\pi$
$79$	2503.91			0.401204			0.200602	+	0.979673i	$0.435710\pi$
$80$	9907.45	+	2654.69i	1.54804	+	0.414796i
$81$	2939.04	+	5090.57i	0.447957	+	0.775884i
$82$	−3432.69	−	1981.86i	−0.510513	−	0.294745i
$83$	7971.73	−	7971.73i	1.15717	−	1.15717i	0.172086	−	0.985082i	$-0.444949\pi$
$83$	7971.73	−	7971.73i	1.15717	−	1.15717i	0.985082	−	0.172086i	$-0.0550506\pi$
$84$	−1737.86	−	6485.78i	−0.246295	−	0.919187i
$85$	9513.85	−	2549.23i	1.31680	−	0.352834i
$86$	4541.98	+	4541.98i	0.614113	+	0.614113i
$87$	1589.82	−	2753.65i	0.210043	−	0.363806i
$88$	115.287	−	66.5609i	0.0148872	−	0.00859515i
$89$	−3752.75	+	14005.5i	−0.473772	+	1.76814i	0.152255	+	0.988341i	$0.451346\pi$
$89$	−3752.75	+	14005.5i	−0.473772	+	1.76814i	−0.626028	+	0.779801i	$0.715320\pi$
$90$			1821.33i			0.224855i
$91$	6341.55	+	4908.98i	0.765795	+	0.592800i
$92$	−4927.83			−0.582211
$93$	−7320.65	−	1961.56i	−0.846416	−	0.226796i
$94$	2459.76	+	4260.44i	0.278380	+	0.482168i
$95$	−17723.5	−	10232.7i	−1.96383	−	1.13382i
$96$	−8829.40	+	8829.40i	−0.958051	+	0.958051i
$97$	−1917.54	−	7156.34i	−0.203798	−	0.760585i	−0.989813	−	0.142377i	$-0.954526\pi$
$97$	−1917.54	−	7156.34i	−0.203798	−	0.760585i	0.786015	−	0.618208i	$-0.212141\pi$
$98$	−821.997	+	220.254i	−0.0855891	+	0.0229335i
$99$	−241.017	−	241.017i	−0.0245910	−	0.0245910i
$100$	9052.21	−	15678.9i	0.905221	−	1.56789i
$101$	213.602	−	123.323i	0.0209393	−	0.0120893i	−0.489494	−	0.872007i	$-0.662818\pi$
$101$	213.602	−	123.323i	0.0209393	−	0.0120893i	0.510433	+	0.859917i	$0.329485\pi$
$102$	−3001.02	+	11199.9i	−0.288448	+	1.07650i
$103$		−	6944.63i		−	0.654598i	−0.944921	−	0.327299i	$-0.893862\pi$
$103$		−	6944.63i		−	0.654598i	0.944921	−	0.327299i	$-0.106138\pi$
$104$	−68.4707	+	503.548i	−0.00633050	+	0.0465559i
$105$	16851.4			1.52847
$106$	4946.22	+	1325.34i	0.440212	+	0.117954i
$107$	744.542	+	1289.58i	0.0650311	+	0.112637i	0.896708	−	0.442623i	$-0.145952\pi$
$107$	744.542	+	1289.58i	0.0650311	+	0.112637i	−0.831677	+	0.555260i	$0.812619\pi$
$108$	−10869.4	−	6275.44i	−0.931875	−	0.538018i
$109$	−12063.2	+	12063.2i	−1.01534	+	1.01534i	−0.0154553	+	0.999881i	$0.504920\pi$
$109$	−12063.2	+	12063.2i	−1.01534	+	1.01534i	−0.999881	+	0.0154553i	$0.995080\pi$
$110$	2710.53	+	10115.8i	0.224011	+	0.836020i
$111$	−6316.61	+	1692.53i	−0.512670	+	0.137370i
$112$	−8297.53	−	8297.53i	−0.661474	−	0.661474i
$113$	−4538.54	+	7860.98i	−0.355434	+	0.615630i	−0.987192	−	0.159535i	$-0.949000\pi$
$113$	−4538.54	+	7860.98i	−0.355434	+	0.615630i	0.631758	+	0.775166i	$0.282334\pi$
$114$	20864.6	−	12046.2i	1.60546	−	0.926914i
$115$	3200.89	−	11945.9i	0.242033	−	0.903280i
$116$			6137.95i			0.456150i
$117$	1290.74	−	164.355i	0.0942905	−	0.0120063i
$118$	2837.24			0.203766
$119$	−10884.3	−	2916.45i	−0.768613	−	0.205949i
$120$	533.919	+	924.775i	0.0370777	+	0.0642205i
$121$	10982.2	+	6340.55i	0.750096	+	0.433068i
$122$	−1001.87	+	1001.87i	−0.0673118	+	0.0673118i
$123$	1540.03	+	5747.49i	0.101794	+	0.379899i
$124$	14131.7	−	3786.59i	0.919078	−	0.246266i
$125$	13797.4	+	13797.4i	0.883033	+	0.883033i
$126$	1041.84	−	1804.53i	0.0656239	−	0.113664i
$127$	−223.651	+	129.125i	−0.0138664	+	0.00800577i	−0.506917	−	0.861995i	$-0.669215\pi$
$127$	−223.651	+	129.125i	−0.0138664	+	0.00800577i	0.493051	+	0.870001i	$0.335882\pi$
$128$	398.257	−	1486.31i	0.0243077	−	0.0907174i
$129$		−	9642.53i		−	0.579444i
$130$	−36870.2	−	15455.9i	−2.18167	−	0.914553i
$131$	−19031.9			−1.10902			−0.554511	−	0.832177i	$-0.687095\pi$
$131$	−19031.9			−1.10902			−0.554511	+	0.832177i	$0.687095\pi$
$132$	−6050.83	−	1621.31i	−0.347270	−	0.0930507i
$133$	11706.7	+	20276.6i	0.661808	+	1.14628i
$134$	9219.69	+	5322.99i	0.513460	+	0.296446i
$135$	22272.9	−	22272.9i	1.22211	−	1.22211i
$136$	−184.809	−	689.716i	−0.00999183	−	0.0372900i
$137$	31642.9	−	8478.70i	1.68591	−	0.451740i	0.716584	−	0.697500i	$-0.245704\pi$
$137$	31642.9	−	8478.70i	1.68591	−	0.451740i	0.969330	+	0.245761i	$0.0790378\pi$
$138$	10294.8	+	10294.8i	0.540581	+	0.540581i
$139$	−9102.92	+	15766.7i	−0.471141	+	0.816041i	−0.999455	−	0.0330086i	$-0.989491\pi$
$139$	−9102.92	+	15766.7i	−0.471141	+	0.816041i	0.528314	+	0.849049i	$0.322824\pi$
$140$	−28171.7	+	16264.9i	−1.43733	+	0.829844i
$141$	1911.40	−	7133.42i	0.0961418	−	0.358806i
$142$			17113.2i			0.848702i
$143$	6924.33	−	2833.75i	0.338615	−	0.138577i
$144$	−1903.91			−0.0918164
$145$	−14879.4	−	3986.92i	−0.707700	−	0.189628i
$146$	−27497.4	−	47626.8i	−1.28999	−	2.23432i
$147$	1106.34	+	638.745i	0.0511980	+	0.0295592i
$148$	8926.29	−	8926.29i	0.407519	−	0.407519i
$149$	−2763.08	−	10311.9i	−0.124457	−	0.464481i	0.875362	−	0.483467i	$-0.160623\pi$
$149$	−2763.08	−	10311.9i	−0.124457	−	0.464481i	−0.999820	+	0.0189862i	$0.993956\pi$
$150$	−51666.1	+	13843.9i	−2.29627	+	0.615284i
$151$	6497.73	+	6497.73i	0.284976	+	0.284976i	0.835090	−	0.550114i	$-0.185416\pi$
$151$	6497.73	+	6497.73i	0.284976	+	0.284976i	−0.550114	+	0.835090i	$0.685416\pi$
$152$	−741.829	+	1284.89i	−0.0321083	+	0.0556131i
$153$	−1583.33	+	914.133i	−0.0676375	+	0.0390505i
$154$	3100.99	−	11573.0i	0.130755	−	0.487985i
$155$			36717.2i			1.52829i
$156$	19033.4	−	14476.8i	0.782111	−	0.594873i
$157$	−41173.9			−1.67041			−0.835203	−	0.549941i	$-0.814650\pi$
$157$	−41173.9			−1.67041			−0.835203	+	0.549941i	$0.814650\pi$
$158$	13793.9	+	3696.06i	0.552551	+	0.148056i
$159$	−3843.53	−	6657.19i	−0.152032	−	0.263328i
$160$	52389.1	+	30246.8i	2.04645	+	1.18152i
$161$	−10004.7	+	10004.7i	−0.385969	+	0.385969i
$162$	8676.73	+	32382.0i	0.330618	+	1.23388i
$163$	251.446	−	67.3748i	0.00946389	−	0.00253584i	−0.254084	−	0.967182i	$-0.581774\pi$
$163$	251.446	−	67.3748i	0.00946389	−	0.00253584i	0.263548	+	0.964646i	$0.415107\pi$
$164$	−8122.04	−	8122.04i	−0.301980	−	0.301980i
$165$	7860.66	−	13615.1i	0.288730	−	0.500094i
$166$	55682.9	−	32148.5i	2.02072	−	1.16666i
$167$	11267.0	−	42049.0i	0.403994	−	1.50773i	−0.401909	−	0.915680i	$-0.631653\pi$
$167$	11267.0	−	42049.0i	0.403994	−	1.50773i	0.805903	−	0.592048i	$-0.201680\pi$
$168$		−	1221.66i		−	0.0432845i
$169$	−7626.24	+	27524.0i	−0.267016	+	0.963692i
$170$	56174.1			1.94374
$171$	3669.36	+	983.203i	0.125487	+	0.0336241i
$172$	9306.94	+	16120.1i	0.314594	+	0.544893i
$173$	−22529.2	−	13007.2i	−0.752755	−	0.434603i	0.0739337	−	0.997263i	$-0.476445\pi$
$173$	−22529.2	−	13007.2i	−0.752755	−	0.434603i	−0.826688	+	0.562660i	$0.809778\pi$
$174$	12822.9	−	12822.9i	0.423533	−	0.423533i
$175$	−13453.8	−	50210.2i	−0.439307	−	1.63952i
$176$	−10574.5	+	2833.43i	−0.341377	+	0.0914718i
$177$	−3011.70	−	3011.70i	−0.0961315	−	0.0961315i
$178$	−41347.3	+	71615.6i	−1.30499	+	2.26031i
$179$	−30219.6	+	17447.3i	−0.943153	+	0.544530i	−0.890947	−	0.454107i	$-0.849959\pi$
$179$	−30219.6	+	17447.3i	−0.943153	+	0.544530i	−0.0522058	+	0.998636i	$0.516625\pi$
$180$	−1366.03	+	5098.10i	−0.0421614	+	0.157349i
$181$		−	38784.9i		−	1.18387i	−0.805984	−	0.591937i	$-0.798363\pi$
$181$		−	38784.9i		−	1.18387i	0.805984	−	0.591937i	$-0.201637\pi$
$182$	27688.9	+	36404.1i	0.835918	+	1.09902i
$183$	2126.95			0.0635118
$184$	−866.029	−	232.052i	−0.0255798	−	0.00685408i
$185$	15840.7	+	27436.9i	0.462840	+	0.801662i
$186$	−37433.5	−	21612.2i	−1.08202	−	0.624703i
$187$	−7433.54	+	7433.54i	−0.212575	+	0.212575i
$188$	3689.75	+	13770.3i	0.104395	+	0.389608i
$189$	−34808.2	+	9326.83i	−0.974447	+	0.261102i
$190$	−82533.1	−	82533.1i	−2.28624	−	2.28624i
$191$	23632.1	−	40931.9i	0.647791	−	1.12201i	−0.335858	−	0.941912i	$-0.609026\pi$
$191$	23632.1	−	40931.9i	0.647791	−	1.12201i	0.983649	−	0.180094i	$-0.0576403\pi$
$192$	−32337.5	+	18670.1i	−0.877210	+	0.506458i
$193$	−5754.26	+	21475.2i	−0.154481	+	0.576530i	0.844668	+	0.535290i	$0.179798\pi$
$193$	−5754.26	+	21475.2i	−0.154481	+	0.576530i	−0.999149	+	0.0412404i	$0.986869\pi$
$194$		−	42254.3i		−	1.12271i
$195$	22731.0	+	55543.6i	0.597791	+	1.46071i
$196$	−2466.06			−0.0641935
$197$	4551.21	+	1219.49i	0.117272	+	0.0314230i	0.316978	−	0.948433i	$-0.397332\pi$
$197$	4551.21	+	1219.49i	0.117272	+	0.0314230i	−0.199706	+	0.979856i	$0.563999\pi$
$198$	−971.976	−	1683.51i	−0.0247928	−	0.0429424i
$199$	58431.5	+	33735.4i	1.47550	+	0.851883i	0.999618	−	0.0276241i	$-0.00879414\pi$
$199$	58431.5	+	33735.4i	1.47550	+	0.851883i	0.475886	+	0.879507i	$0.342127\pi$
$200$	2329.17	−	2329.17i	0.0582293	−	0.0582293i
$201$	−4136.31	−	15436.9i	−0.102381	−	0.382092i
$202$	1358.76	−	364.078i	0.0332996	−	0.00892260i
$203$	12461.5	+	12461.5i	0.302399	+	0.302399i
$204$	−16800.4	+	29099.1i	−0.403700	+	0.699228i
$205$	24964.8	−	14413.5i	0.594048	−	0.342974i
$206$	10251.1	−	38257.5i	0.241565	−	0.901534i
$207$			2295.63i			0.0535748i
$208$	16156.7	−	38541.9i	0.373445	−	0.890854i
$209$	21843.3			0.500063
$210$	92833.3	+	24874.6i	2.10506	+	0.564050i
$211$	−17393.5	−	30126.5i	−0.390681	−	0.676680i	0.601858	−	0.798603i	$-0.294427\pi$
$211$	−17393.5	−	30126.5i	−0.390681	−	0.676680i	−0.992540	+	0.121923i	$0.961094\pi$
$212$	12851.0	+	7419.53i	0.285934	+	0.165084i
$213$	18165.5	−	18165.5i	0.400395	−	0.400395i
$214$	2198.06	+	8203.26i	0.0479967	+	0.179126i
$215$	−45123.1	+	12090.7i	−0.976162	+	0.261562i
$216$	−1614.70	−	1614.70i	−0.0346086	−	0.0346086i
$217$	21003.2	−	36378.6i	0.446032	−	0.772550i
$218$	−84262.0	+	48648.7i	−1.77304	+	1.02367i
$219$	−21367.2	+	79743.5i	−0.445512	+	1.66267i
$220$			30348.4i			0.627032i
$221$	−5069.10	−	39809.6i	−0.103788	−	0.815086i
$222$	−37296.1			−0.756759
$223$	30988.2	+	8303.26i	0.623142	+	0.166970i	0.556556	−	0.830810i	$-0.312123\pi$
$223$	30988.2	+	8303.26i	0.623142	+	0.166970i	0.0665860	+	0.997781i	$0.478789\pi$
$224$	−34603.9	−	59935.8i	−0.689651	−	1.19451i
$225$	−7303.99	−	4216.96i	−0.144276	−	0.0832980i
$226$	−36606.2	+	36606.2i	−0.716701	+	0.716701i
$227$	16767.8	+	62578.1i	0.325404	+	1.21443i	0.913905	+	0.405928i	$0.133052\pi$
$227$	16767.8	+	62578.1i	0.325404	+	1.21443i	−0.588501	+	0.808497i	$0.700282\pi$
$228$	67437.2	−	18069.8i	1.29727	−	0.347602i
$229$	54161.9	+	54161.9i	1.03282	+	1.03282i	0.999443	+	0.0333737i	$0.0106252\pi$
$229$	54161.9	+	54161.9i	1.03282	+	1.03282i	0.0333737	+	0.999443i	$0.489375\pi$
$230$	35266.9	−	61084.1i	0.666672	−	1.15471i
$231$	−15576.3	+	8993.00i	−0.291905	+	0.168531i
$232$	−289.036	+	1078.70i	−0.00537002	+	0.0200412i
$233$		−	61901.5i		−	1.14022i	−0.821568	−	0.570111i	$-0.806900\pi$
$233$		−	61901.5i		−	1.14022i	0.821568	−	0.570111i	$-0.193100\pi$
$234$	7353.22	+	999.864i	0.134291	+	0.0182604i
$235$	−35778.2			−0.647862
$236$	7941.76	+	2127.99i	0.142591	+	0.0382072i
$237$	−10718.7	−	18565.4i	−0.190830	−	0.330528i
$238$	−55656.0	−	32133.0i	−0.982558	−	0.567280i
$239$	34967.7	−	34967.7i	0.612169	−	0.612169i	−0.331342	−	0.943511i	$-0.607501\pi$
$239$	34967.7	−	34967.7i	0.612169	−	0.612169i	0.943511	+	0.331342i	$0.107501\pi$
$240$	−22728.4	−	84823.5i	−0.394590	−	1.47263i
$241$	−1631.90	+	437.266i	−0.0280970	+	0.00752856i	−0.272840	−	0.962059i	$-0.587963\pi$
$241$	−1631.90	+	437.266i	−0.0280970	+	0.00752856i	0.244743	+	0.969588i	$0.421296\pi$
$242$	51140.6	+	51140.6i	0.873243	+	0.873243i
$243$	−5593.06	+	9687.47i	−0.0947190	+	0.164058i
$244$	−3555.76	+	2052.92i	−0.0597246	+	0.0344820i
$245$	1601.83	−	5978.13i	0.0266861	−	0.0995940i
$246$			33935.8i			0.560774i
$247$	−51042.1	+	65937.6i	−0.836633	+	1.08078i
$248$	2661.85			0.0432794
$249$	−93232.1	−	24981.5i	−1.50372	−	0.402920i
$250$	55642.4	+	96375.4i	0.890278	+	1.54201i
$251$	39494.7	+	22802.3i	0.626890	+	0.361935i	0.779546	−	0.626344i	$-0.215450\pi$
$251$	39494.7	+	22802.3i	0.626890	+	0.361935i	−0.152657	+	0.988279i	$0.548783\pi$
$252$	4269.67	−	4269.67i	0.0672347	−	0.0672347i
$253$	3416.40	+	12750.2i	0.0533737	+	0.199193i
$254$	−1422.68	+	381.207i	−0.0220516	+	0.00590872i
$255$	−59628.2	−	59628.2i	−0.917004	−	0.917004i
$256$	−30502.9	+	52832.6i	−0.465437	+	0.806161i
$257$	11270.0	−	6506.71i	0.170630	−	0.0985134i	−0.412253	−	0.911070i	$-0.635258\pi$
$257$	11270.0	−	6506.71i	0.170630	−	0.0985134i	0.582883	+	0.812556i	$0.301925\pi$
$258$	14233.5	−	53120.1i	0.213831	−	0.798030i
$259$		−	36245.1i		−	0.540319i
$260$	−91611.5	−	70916.3i	−1.35520	−	1.04906i
$261$	2859.36			0.0419747
$262$	−104846.	−	28093.3i	−1.52738	−	0.409260i
$263$	9694.16	+	16790.8i	0.140152	+	0.242750i	0.927554	−	0.373690i	$-0.121908\pi$
$263$	9694.16	+	16790.8i	0.140152	+	0.242750i	−0.787402	+	0.616440i	$0.788574\pi$
$264$	−987.038	−	569.867i	−0.0141621	−	0.00817646i
$265$	−26333.6	+	26333.6i	−0.374988	+	0.374988i
$266$	34560.9	+	128983.i	0.488452	+	1.82293i
$267$	119909.	−	32129.5i	1.68201	−	0.450694i
$268$	21814.6	+	21814.6i	0.303723	+	0.303723i
$269$	−10955.6	+	18975.6i	−0.151402	+	0.262236i	−0.931743	−	0.363118i	$-0.881712\pi$
$269$	−10955.6	+	18975.6i	−0.151402	+	0.262236i	0.780341	+	0.625354i	$0.215045\pi$
$270$	155577.	−	89822.7i	2.13412	−	1.23214i
$271$	11073.9	−	41328.3i	0.150786	−	0.562742i	−0.848643	−	0.528966i	$-0.822580\pi$
$271$	11073.9	−	41328.3i	0.150786	−	0.562742i	0.999429	−	0.0337763i	$-0.0107534\pi$
$272$			58721.0i			0.793699i
$273$	9251.03	−	68034.1i	0.124127	−	0.912854i
$274$	186834.			2.48860
$275$	−46843.0	−	12551.5i	−0.619411	−	0.165971i
$276$	21095.0	+	36537.7i	0.276925	+	0.479648i
$277$	−83627.0	−	48282.1i	−1.08990	−	0.629255i	−0.156351	−	0.987702i	$-0.549973\pi$
$277$	−83627.0	−	48282.1i	−1.08990	−	0.629255i	−0.933550	+	0.358447i	$0.883306\pi$
$278$	−73420.8	+	73420.8i	−0.950013	+	0.950013i
$279$	−1763.98	−	6583.26i	−0.0226613	−	0.0845731i
$280$	−5716.87	+	1531.83i	−0.0729193	+	0.0195387i
$281$	50030.4	+	50030.4i	0.633609	+	0.633609i	0.948971	−	0.315362i	$-0.102126\pi$
$281$	50030.4	+	50030.4i	0.633609	+	0.633609i	−0.315362	+	0.948971i	$0.602126\pi$
$282$	21059.5	−	36476.1i	0.264819	−	0.458681i
$283$	127894.	−	73839.8i	1.59690	−	0.921972i	0.604824	−	0.796359i	$-0.293244\pi$
$283$	127894.	−	73839.8i	1.59690	−	0.921972i	0.992079	−	0.125613i	$-0.0400897\pi$
$284$	−12835.3	+	47901.9i	−0.159136	+	0.593904i
$285$			175216.i			2.15717i
$286$	42328.6	−	5389.85i	0.517490	−	0.0658938i
$287$	−32979.5			−0.400387
$288$	−10846.3	−	2906.25i	−0.130766	−	0.0350387i
$289$	−13566.4	−	23497.7i	−0.162431	−	0.281339i
$290$	−76084.4	−	43927.4i	−0.904690	−	0.522323i
$291$	−44852.5	+	44852.5i	−0.529664	+	0.529664i
$292$	−41247.2	−	153936.i	−0.483758	−	1.80541i
$293$	−9633.69	+	2581.34i	−0.112217	+	0.0300684i	−0.314490	−	0.949261i	$-0.601834\pi$
$293$	−9633.69	+	2581.34i	−0.112217	+	0.0300684i	0.202274	+	0.979329i	$0.435167\pi$
$294$	5151.88	+	5151.88i	0.0596034	+	0.0596034i
$295$	−10317.2	+	17869.9i	−0.118554	+	0.205342i
$296$	1989.07	−	1148.39i	0.0227021	−	0.0131070i
$297$	−8701.35	+	32473.9i	−0.0986447	+	0.368147i
$298$		−	60886.4i		−	0.685627i
$299$	−46471.8	−	19480.9i	−0.519813	−	0.217905i
$300$	−155003.			−1.72225
$301$	51623.1	+	13832.4i	0.569785	+	0.152674i
$302$	26204.2	+	45386.9i	0.287314	+	0.497642i
$303$	−1828.77	−	1055.84i	−0.0199193	−	0.0115004i
$304$	86275.2	−	86275.2i	0.933553	−	0.933553i
$305$	−2666.96	−	9953.23i	−0.0286693	−	0.106995i
$306$	−10071.8	+	2698.73i	−0.107563	+	0.0288215i
$307$	−58686.7	−	58686.7i	−0.622677	−	0.622677i	0.323538	−	0.946215i	$-0.395128\pi$
$307$	−58686.7	−	58686.7i	−0.622677	−	0.622677i	−0.946215	+	0.323538i	$0.895128\pi$
$308$	17360.0	−	30068.5i	0.182999	−	0.316964i
$309$	−51491.3	+	29728.5i	−0.539283	+	0.311355i
$310$	−54198.8	+	202273.i	−0.563983	+	2.10481i
$311$			38813.8i			0.401296i	0.979663	+	0.200648i	$0.0643048\pi$
$311$			38813.8i			0.401296i	−0.979663	+	0.200648i	$0.935695\pi$
$312$	4026.69	−	1647.91i	0.0413656	−	0.0169287i
$313$	−98727.3			−1.00774			−0.503870	−	0.863779i	$-0.668091\pi$
$313$	−98727.3			−1.00774			−0.503870	+	0.863779i	$0.668091\pi$
$314$	−226824.	−	60777.3i	−2.30054	−	0.616428i
$315$	7577.01	+	13123.8i	0.0763619	+	0.132263i
$316$	35838.5	+	20691.4i	0.358902	+	0.207212i
$317$	49531.4	−	49531.4i	0.492904	−	0.492904i	−0.416316	−	0.909220i	$-0.636679\pi$
$317$	49531.4	−	49531.4i	0.492904	−	0.492904i	0.909220	+	0.416316i	$0.136679\pi$
$318$	−11347.0	−	42347.5i	−0.112209	−	0.418768i
$319$	15881.2	−	4255.35i	0.156064	−	0.0418171i
$320$	127916.	+	127916.i	1.24918	+	1.24918i
$321$	6374.46	−	11040.9i	0.0618633	−	0.107150i
$322$	−69883.4	+	40347.2i	−0.674003	+	0.389136i
$323$	30324.4	−	113172.i	0.290661	−	1.08476i
$324$			97148.6i			0.925436i
$325$	147349.	−	112074.i	1.39502	−	1.06105i
$326$	1484.65			0.0139698
$327$	141083.	+	37803.2i	1.31941	+	0.353535i
$328$	−1044.92	−	1809.85i	−0.00971259	−	0.0168227i
$329$	35448.2	+	20466.0i	0.327493	+	0.189078i
$330$	63401.2	−	63401.2i	0.582197	−	0.582197i
$331$	17404.7	+	64955.1i	0.158858	+	0.592867i	0.998744	+	0.0501038i	$0.0159552\pi$
$331$	17404.7	+	64955.1i	0.158858	+	0.592867i	−0.839886	+	0.542763i	$0.817378\pi$
$332$	179975.	−	48224.1i	1.63281	−	0.437510i
$333$	−4158.30	−	4158.30i	−0.0374997	−	0.0374997i
$334$	124138.	−	215014.i	1.11279	−	1.92741i
$335$	−67051.9	+	38712.4i	−0.597477	+	0.344954i
$336$	−26002.4	+	97042.4i	−0.230322	+	0.859574i
$337$		−	104833.i		−	0.923075i	−0.887121	−	0.461538i	$-0.847298\pi$
$337$		−	104833.i		−	0.923075i	0.887121	−	0.461538i	$-0.152702\pi$
$338$	−82641.0	+	140371.i	−0.723373	+	1.22869i
$339$	77714.3			0.676241
$340$	157238.	+	42131.7i	1.36019	+	0.364461i
$341$	−19594.7	−	33939.0i	−0.168511	−	0.291870i
$342$	18762.9	+	10832.8i	0.160416	+	0.0926165i
$343$	−85570.7	+	85570.7i	−0.727339	+	0.727339i
$344$	876.528	+	3271.25i	0.00740711	+	0.0276437i
$345$	−102276.	+	27404.7i	−0.859279	+	0.230243i
$346$	−104912.	−	104912.i	−0.876338	−	0.876338i
$347$	−76200.4	+	131983.i	−0.632846	+	1.09612i	0.354121	+	0.935200i	$0.384780\pi$
$347$	−76200.4	+	131983.i	−0.632846	+	1.09612i	−0.986967	+	0.160922i	$0.948553\pi$
$348$	45510.2	−	26275.3i	0.375794	−	0.216965i
$349$	−55177.5	+	205925.i	−0.453014	+	1.69067i	0.240849	+	0.970562i	$0.422574\pi$
$349$	−55177.5	+	205925.i	−0.453014	+	1.69067i	−0.693863	+	0.720107i	$0.744093\pi$
$350$		−	296464.i		−	2.42011i
$351$	−77695.0	−	102150.i	−0.630636	−	0.829130i
$352$	−64566.6			−0.521102
$353$	199880.	+	53557.7i	1.60406	+	0.429806i	0.946265	−	0.323393i	$-0.104824\pi$
$353$	199880.	+	53557.7i	1.60406	+	0.429806i	0.657793	+	0.753199i	$0.271490\pi$
$354$	−12145.6	−	21036.9i	−0.0969202	−	0.167871i
$355$	−107785.	−	62229.6i	−0.855265	−	0.493788i
$356$	−169449.	+	169449.i	−1.33702	+	1.33702i
$357$	24969.4	+	93187.1i	0.195917	+	0.731172i
$358$	−192232.	+	51508.3i	−1.49989	+	0.401894i
$359$	−100758.	−	100758.i	−0.781795	−	0.781795i	0.198339	−	0.980134i	$-0.436445\pi$
$359$	−100758.	−	100758.i	−0.781795	−	0.781795i	−0.980134	+	0.198339i	$0.936445\pi$
$360$	−480.138	+	831.624i	−0.00370477	+	0.00641685i
$361$	−97969.1	+	56562.5i	−0.751752	+	0.434024i
$362$	57250.9	−	213663.i	0.436883	−	1.63047i
$363$		−	108570.i		−	0.823945i
$364$	50200.7	+	122666.i	0.378885	+	0.925812i
$365$	399959.			3.00213
$366$	11717.2	+	3139.61i	0.0874705	+	0.0234376i
$367$	50429.7	+	87346.8i	0.374416	+	0.648507i	0.990239	−	0.139377i	$-0.0445099\pi$
$367$	50429.7	+	87346.8i	0.374416	+	0.648507i	−0.615824	+	0.787884i	$0.711177\pi$
$368$	63853.7	+	36866.0i	0.471510	+	0.272226i
$369$	−3783.65	+	3783.65i	−0.0277880	+	0.0277880i
$370$	46765.3	+	174531.i	0.341602	+	1.27488i
$371$	41154.2	−	11027.2i	0.298996	−	0.0801158i
$372$	−88571.0	−	88571.0i	−0.640038	−	0.640038i
$373$	−41170.6	+	71309.6i	−0.295917	+	0.512543i	−0.975198	−	0.221335i	$-0.928958\pi$
$373$	−41170.6	+	71309.6i	−0.295917	+	0.512543i	0.679281	+	0.733878i	$0.262292\pi$
$374$	−51923.6	+	29978.1i	−0.371212	+	0.214319i
$375$	43237.7	−	161365.i	0.307468	−	1.14749i
$376$			2593.78i			0.0183467i
$377$	−24264.8	+	57883.7i	−0.170724	+	0.407262i
$378$	−205523.			−1.43839
$379$	−35058.7	−	9393.95i	−0.244072	−	0.0653988i	0.134709	−	0.990885i	$-0.456990\pi$
$379$	−35058.7	−	9393.95i	−0.244072	−	0.0653988i	−0.378781	+	0.925486i	$0.623657\pi$
$380$	−169118.	−	292921.i	−1.17118	−	2.02854i
$381$	1914.81	+	1105.52i	0.0131909	+	0.00761579i
$382$	190608.	−	190608.i	1.30621	−	1.30621i
$383$	−39784.2	−	148477.i	−0.271215	−	1.01219i	−0.958336	−	0.285644i	$-0.907793\pi$
$383$	−39784.2	−	148477.i	−0.271215	−	1.01219i	0.687121	−	0.726543i	$-0.258874\pi$
$384$	−12725.2	+	3409.71i	−0.0862983	+	0.0231236i
$385$	61614.6	+	61614.6i	0.415683	+	0.415683i
$386$	−63399.6	+	109811.i	−0.425512	+	0.737009i
$387$	7509.53	−	4335.63i	0.0501408	−	0.0289488i
$388$	31691.6	−	118275.i	0.210514	−	0.785648i
$389$		−	15749.1i		−	0.104077i	−0.998645	−	0.0520387i	$-0.983428\pi$
$389$		−	15749.1i		−	0.104077i	0.998645	−	0.0520387i	$-0.0165719\pi$
$390$	43234.7	+	339540.i	0.284252	+	2.23234i
$391$	70802.7			0.463123
$392$	−433.391	−	116.127i	−0.00282038	−	0.000755718i
$393$	81471.7	+	141113.i	0.527499	+	0.913655i
$394$	23272.2	+	13436.2i	0.149915	+	0.0865535i
$395$	−73438.3	+	73438.3i	−0.470683	+	0.470683i
$396$	−1458.00	−	5441.34i	−0.00929754	−	0.0346989i
$397$	−197343.	+	52877.9i	−1.25211	+	0.335501i	−0.823149	−	0.567825i	$-0.807785\pi$
$397$	−197343.	+	52877.9i	−1.25211	+	0.335501i	−0.428956	+	0.903325i	$0.641118\pi$
$398$	272098.	+	272098.i	1.71774	+	1.71774i
$399$	100228.	−	173600.i	0.629569	−	1.09045i
$400$	−234593.	+	135442.i	−1.46620	+	0.846514i
$401$	30468.8	−	113711.i	0.189481	−	0.707153i	−0.804146	−	0.594432i	$-0.797377\pi$
$401$	30468.8	−	113711.i	0.189481	−	0.707153i	0.993627	−	0.112721i	$-0.0359565\pi$
$402$		−	91146.5i		−	0.564011i
$403$	148238.	+	20156.9i	0.912746	+	0.124112i
$404$	4076.38			0.0249754
$405$	−235504.	−	63103.1i	−1.43578	−	0.384716i
$406$	50255.1	+	87044.5i	0.304880	+	0.528067i
$407$	−29284.2	−	16907.2i	−0.176784	−	0.102067i
$408$	−4322.81	+	4322.81i	−0.0259684	+	0.0259684i
$409$	−15720.6	−	58670.2i	−0.0939774	−	0.350728i	0.902885	−	0.429882i	$-0.141445\pi$
$409$	−15720.6	−	58670.2i	−0.0939774	−	0.350728i	−0.996862	+	0.0791538i	$0.974778\pi$
$410$	158806.	−	42551.8i	0.944709	−	0.253134i
$411$	−198323.	−	198323.i	−1.17406	−	1.17406i
$412$	57387.8	−	99398.5i	0.338084	−	0.585579i
$413$	20444.1	−	11803.4i	0.119858	−	0.0692001i
$414$	−3388.61	+	12646.5i	−0.0197706	+	0.0737850i
$415$			467612.i			2.71512i
$416$	150876.	−	194905.i	0.871832	−	1.12625i
$417$	155871.			0.896382
$418$	120333.	+	32243.2i	0.688704	+	0.184538i
$419$	−162880.	−	282117.i	−0.927770	−	1.60695i	−0.787044	−	0.616897i	$-0.788390\pi$
$419$	−162880.	−	282117.i	−0.927770	−	1.60695i	−0.140726	−	0.990049i	$-0.544944\pi$
$420$	241195.	+	139254.i	1.36732	+	0.789420i
$421$	84760.5	−	84760.5i	0.478222	−	0.478222i	−0.426341	−	0.904563i	$-0.640198\pi$
$421$	84760.5	−	84760.5i	0.478222	−	0.478222i	0.904563	+	0.426341i	$0.140198\pi$
$422$	−51349.6	−	191639.i	−0.288345	−	1.07612i
$423$	6414.89	−	1718.86i	0.0358516	−	0.00960641i
$424$	1909.08	+	1909.08i	0.0106192	+	0.0106192i
$425$	−130061.	+	225273.i	−0.720063	+	1.24718i
$426$	126887.	−	73258.2i	0.699194	−	0.403680i
$427$	−3051.14	+	11387.0i	−0.0167343	+	0.0624531i
$428$			24610.4i			0.134348i
$429$	−50652.7	−	39210.1i	−0.275225	−	0.213051i
$430$	−266427.			−1.44093
$431$	300893.	+	80623.9i	1.61978	+	0.434020i	0.950938	−	0.309382i	$-0.100122\pi$
$431$	300893.	+	80623.9i	1.61978	+	0.434020i	0.668846	+	0.743401i	$0.266789\pi$
$432$	93895.3	+	162631.i	0.503126	+	0.871439i
$433$	57127.4	+	32982.5i	0.304697	+	0.175917i	0.644551	−	0.764561i	$-0.277044\pi$
$433$	57127.4	+	32982.5i	0.304697	+	0.175917i	−0.339854	+	0.940478i	$0.610378\pi$
$434$	169404.	−	169404.i	0.899383	−	0.899383i
$435$	34134.4	+	127391.i	0.180390	+	0.673226i
$436$	−272347.	+	72975.0i	−1.43268	+	0.383885i
$437$	−104026.	−	104026.i	−0.544727	−	0.544727i
$438$	−235421.	+	407761.i	−1.22715	+	2.12548i
$439$	138158.	−	79765.7i	0.716882	−	0.413892i	−0.0967219	−	0.995311i	$-0.530836\pi$
$439$	138158.	−	79765.7i	0.716882	−	0.413892i	0.813604	+	0.581419i	$0.197502\pi$
$440$	−1429.10	+	5333.49i	−0.00738173	+	0.0275490i
$441$			1148.81i			0.00590706i
$442$	30838.2	−	226791.i	0.157850	−	1.16086i
$443$	−372577.			−1.89849			−0.949246	−	0.314535i	$-0.898151\pi$
$443$	−372577.			−1.89849			−0.949246	+	0.314535i	$0.898151\pi$
$444$	−104396.	−	27972.8i	−0.529564	−	0.141896i
$445$	−300706.	−	520838.i	−1.51852	−	2.63016i
$446$	158455.	+	91484.2i	0.796594	+	0.459914i
$447$	−64630.3	+	64630.3i	−0.323460	+	0.323460i
$448$	−53565.0	−	199907.i	−0.266886	−	0.996031i
$449$	−70951.0	+	19011.3i	−0.351938	+	0.0943014i	−0.430457	−	0.902611i	$-0.641648\pi$
$449$	−70951.0	+	19011.3i	−0.351938	+	0.0943014i	0.0785191	+	0.996913i	$0.474981\pi$
$450$	−34012.5	−	34012.5i	−0.167963	−	0.167963i
$451$	−15383.9	+	26645.7i	−0.0756333	+	0.131001i
$452$	−129920.	+	75009.6i	−0.635917	+	0.367147i
$453$	20362.3	−	75993.2i	0.0992272	−	0.370321i
$454$			369490.i			1.79263i
$455$	−329971.	+	42016.4i	−1.59387	+	0.202953i
$456$	12702.5			0.0610884
$457$	−311394.	−	83437.8i	−1.49100	−	0.399512i	−0.580926	−	0.813957i	$-0.697309\pi$
$457$	−311394.	−	83437.8i	−1.49100	−	0.399512i	−0.910075	+	0.414444i	$0.863976\pi$
$458$	218425.	+	378324.i	1.04129	+	1.80357i
$459$	156170.	+	90165.0i	0.741265	+	0.427969i
$460$	144530.	−	144530.i	0.683036	−	0.683036i
$461$	44899.4	+	167567.i	0.211271	+	0.788473i	0.987446	+	0.157956i	$0.0504903\pi$
$461$	44899.4	+	167567.i	0.211271	+	0.788473i	−0.776176	+	0.630517i	$0.782843\pi$
$462$	−99083.6	+	26549.4i	−0.464214	+	0.124386i
$463$	88275.9	+	88275.9i	0.411794	+	0.411794i	0.882363	−	0.470569i	$-0.155951\pi$
$463$	88275.9	+	88275.9i	0.411794	+	0.411794i	−0.470569	+	0.882363i	$0.655951\pi$
$464$	45919.1	−	79534.1i	0.213283	−	0.369418i
$465$	272242.	−	157179.i	1.25907	−	0.726923i
$466$	91373.6	−	341011.i	0.420774	−	1.57035i
$467$		−	2610.83i		−	0.0119714i	−0.999982	−	0.00598570i	$-0.998095\pi$
$467$		−	2610.83i		−	0.0119714i	0.999982	−	0.00598570i	$-0.00190532\pi$
$468$	19832.6	+	8313.80i	0.0905498	+	0.0379584i
$469$	88578.0			0.402699
$470$	−197100.	−	52812.7i	−0.892257	−	0.239080i
$471$	176257.	+	305286.i	0.794519	+	1.37615i
$472$	1295.50	+	747.955i	0.00581503	+	0.00335731i
$473$	35256.4	−	35256.4i	0.157585	−	0.157585i
$474$	−31644.2	−	118098.i	−0.140844	−	0.525635i
$475$	522070.	−	139888.i	2.31389	−	0.620004i
$476$	−131687.	−	131687.i	−0.581205	−	0.581205i
$477$	3456.38	−	5986.63i	0.0151910	−	0.0263115i
$478$	244251.	−	141018.i	1.06901	−	0.617191i
$479$	−89374.4	+	333550.i	−0.389531	+	1.45375i	0.441367	+	0.897326i	$0.354494\pi$
$479$	−89374.4	+	333550.i	−0.389531	+	1.45375i	−0.830899	+	0.556424i	$0.812173\pi$
$480$		−	517922.i		−	2.24793i
$481$	119467.	−	48891.3i	0.516365	−	0.211320i
$482$	−9635.48			−0.0414743
$483$	117009.	+	31352.4i	0.501561	+	0.134393i
$484$	104792.	+	181505.i	0.447339	+	0.774814i
$485$	266131.	+	153651.i	1.13139	+	0.653209i
$486$	−45111.6	+	45111.6i	−0.190992	+	0.190992i
$487$	80455.8	+	300265.i	0.339234	+	1.26604i	0.899205	+	0.437527i	$0.144145\pi$
$487$	80455.8	+	300265.i	0.339234	+	1.26604i	−0.559971	+	0.828512i	$0.689188\pi$
$488$	−721.570	+	193.344i	−0.00302997	+	0.000811879i
$489$	−1575.94	−	1575.94i	−0.00659057	−	0.00659057i
$490$	17648.8	−	30568.6i	0.0735060	−	0.127316i
$491$	−14230.2	+	8215.83i	−0.0590268	+	0.0340791i	−0.529223	−	0.848483i	$-0.677516\pi$
$491$	−14230.2	+	8215.83i	−0.0590268	+	0.0340791i	0.470196	+	0.882562i	$0.344183\pi$
$492$	−25452.5	+	94990.1i	−0.105148	+	0.392417i
$493$		−	88189.5i		−	0.362847i
$494$	−378519.	+	287901.i	−1.55108	+	1.17975i
$495$	14137.7			0.0576992
$496$	−211444.	−	56656.2i	−0.859472	−	0.230295i
$497$	71193.8	+	123311.i	0.288224	+	0.499218i
$498$	−476734.	−	275242.i	−1.92228	−	1.10983i
$499$	165805.	−	165805.i	0.665883	−	0.665883i	−0.290877	−	0.956760i	$-0.593947\pi$
$499$	165805.	−	165805.i	0.665883	−	0.665883i	0.956760	+	0.290877i	$0.0939472\pi$
$500$	83465.8	+	311499.i	0.333863	+	1.24599i
$501$	−360006.	+	96463.4i	−1.43428	+	0.384315i
$502$	183915.	+	183915.i	0.729809	+	0.729809i
$503$	152830.	−	264710.i	0.604050	−	1.04625i	−0.388150	−	0.921596i	$-0.626886\pi$
$503$	152830.	−	264710.i	0.604050	−	1.04625i	0.992201	−	0.124650i	$-0.0397807\pi$
$504$	951.421	−	549.303i	0.00374551	−	0.00216247i
$505$	−2647.82	+	9881.81i	−0.0103826	+	0.0387484i
$506$			75282.8i			0.294032i
$507$	236725.	−	61279.5i	0.920932	−	0.238396i
$508$	−4268.16			−0.0165392
$509$	134054.	+	35919.6i	0.517421	+	0.138642i	0.508073	−	0.861314i	$-0.330358\pi$
$509$	134054.	+	35919.6i	0.517421	+	0.138642i	0.00934737	+	0.999956i	$0.497025\pi$
$510$	−240470.	−	416506.i	−0.924528	−	1.60133i
$511$	−396271.	−	228787.i	−1.51757	−	0.876172i
$512$	−263434.	+	263434.i	−1.00492	+	1.00492i
$513$	−96977.6	−	361925.i	−0.368499	−	1.37526i
$514$	71690.1	−	19209.3i	0.271352	−	0.0727085i
$515$	203682.	+	203682.i	0.767959	+	0.767959i
$516$	79682.2	−	138014.i	0.299269	−	0.518350i
$517$	33071.0	−	19093.5i	0.123727	−	0.0714340i
$518$	53501.9	−	199672.i	0.199393	−	0.744145i
$519$			222725.i			0.826865i
$520$	−12760.6	−	16777.0i	−0.0471914	−	0.0620450i
$521$	−82330.3			−0.303308			−0.151654	−	0.988434i	$-0.548460\pi$
$521$	−82330.3			−0.303308			−0.151654	+	0.988434i	$0.548460\pi$
$522$	15752.0	+	4220.74i	0.0578089	+	0.0154899i
$523$	−176253.	−	305279.i	−0.644367	−	1.11608i	−0.984447	−	0.175680i	$-0.943788\pi$
$523$	−176253.	−	305279.i	−0.644367	−	1.11608i	0.340081	−	0.940396i	$-0.389546\pi$
$524$	−272404.	−	157273.i	−0.992090	−	0.572783i
$525$	−314693.	+	314693.i	−1.14174	+	1.14174i
$526$	28619.4	+	106809.i	0.103440	+	0.386043i
$527$	−203044.	+	54405.4i	−0.731085	+	0.195894i
$528$	66275.9	+	66275.9i	0.237732	+	0.237732i
$529$	−95469.5	+	165358.i	−0.341156	+	0.590900i
$530$	−183941.	+	106198.i	−0.654828	+	0.378065i
$531$	991.321	−	3699.66i	0.00351581	−	0.0131212i
$532$			386959.i			1.36723i
$533$	−44486.2	−	108703.i	−0.156593	−	0.382637i
$534$	707997.			2.48284
$535$	−59659.7	−	15985.8i	−0.208436	−	0.0558504i
$536$	2806.50	+	4861.00i	0.00976866	+	0.0169198i
$537$	258728.	+	149376.i	0.897210	+	0.518004i
$538$	−88363.7	+	88363.7i	−0.305288	+	0.305288i
$539$	1709.68	+	6380.63i	0.00588489	+	0.0219627i
$540$	502848.	−	134738.i	1.72444	−	0.462063i
$541$	148284.	+	148284.i	0.506642	+	0.506642i	0.913494	−	0.406852i	$-0.133374\pi$
$541$	148284.	+	148284.i	0.506642	+	0.506642i	−0.406852	+	0.913494i	$0.633374\pi$
$542$	122011.	−	211329.i	0.415336	−	0.719383i
$543$	−287573.	+	166030.i	−0.975322	+	0.563102i
$544$	−89635.9	+	334526.i	−0.302889	+	1.13040i
$545$		−	707613.i		−	2.38234i
$546$	151389.	−	361140.i	0.507820	−	1.21141i
$547$	−103249.			−0.345075			−0.172537	−	0.985003i	$-0.555197\pi$
$547$	−103249.			−0.345075			−0.172537	+	0.985003i	$0.555197\pi$
$548$	522970.	+	140129.i	1.74147	+	0.466625i
$549$	956.351	+	1656.45i	0.00317302	+	0.00549583i
$550$	−239527.	−	138291.i	−0.791825	−	0.457161i
$551$	−129571.	+	129571.i	−0.426782	+	0.426782i
$552$	1986.73	+	7414.58i	0.00652020	+	0.0243337i
$553$	114770.	−	30752.4i	0.375298	−	0.100561i
$554$	−389426.	−	389426.i	−1.26883	−	1.26883i
$555$	135621.	−	234903.i	0.440294	−	0.762611i
$556$	−260580.	+	150446.i	−0.842931	+	0.486667i
$557$	−39436.9	+	147180.i	−0.127114	+	0.474395i	−0.999906	−	0.0136967i	$-0.995640\pi$
$557$	−39436.9	+	147180.i	−0.127114	+	0.474395i	0.872793	+	0.488091i	$0.162307\pi$
$558$		−	38870.6i		−	0.124840i
$559$	24042.2	+	188813.i	0.0769396	+	0.604237i
$560$	486723.			1.55205
$561$	86937.8	+	23294.9i	0.276238	+	0.0740176i
$562$	201764.	+	349465.i	0.638808	+	1.10645i
$563$	−452857.	−	261457.i	−1.42871	−	0.824866i	−0.431691	−	0.902022i	$-0.642083\pi$
$563$	−452857.	−	261457.i	−1.42871	−	0.824866i	−0.997019	+	0.0771554i	$0.975416\pi$
$564$	86305.7	−	86305.7i	0.271320	−	0.271320i
$565$	−97445.3	−	363671.i	−0.305256	−	1.13923i
$566$	813557.	−	217992.i	2.53954	−	0.680468i
$567$	197235.	+	197235.i	0.613506	+	0.613506i
$568$	−4511.40	+	7813.97i	−0.0139835	+	0.0242201i
$569$	−273094.	+	157671.i	−0.843504	+	0.486997i	−0.858454	−	0.512891i	$-0.828574\pi$
$569$	−273094.	+	157671.i	−0.843504	+	0.486997i	0.0149499	+	0.999888i	$0.495241\pi$
$570$	−258639.	+	965253.i	−0.796057	+	2.97092i
$571$		−	6380.52i		−	0.0195697i	−0.999952	−	0.00978484i	$-0.996885\pi$
$571$		−	6380.52i		−	0.0195697i	0.999952	−	0.00978484i	$-0.00311466\pi$
$572$	122525.	+	16660.5i	0.374484	+	0.0509210i
$573$	−404656.			−1.23247
$574$	−181682.	−	48681.5i	−0.551426	−	0.147754i
$575$	163309.	+	282859.i	0.493940	+	0.855529i
$576$	−29080.2	−	16789.5i	−0.0876501	−	0.0506048i
$577$	−78575.8	+	78575.8i	−0.236014	+	0.236014i	−0.815197	−	0.579184i	$-0.803371\pi$
$577$	−78575.8	+	78575.8i	−0.236014	+	0.236014i	0.579184	+	0.815197i	$0.303371\pi$
$578$	−40051.1	−	149473.i	−0.119883	−	0.447411i
$579$	183862.	−	49265.6i	0.548446	−	0.146956i
$580$	−180022.	−	180022.i	−0.535144	−	0.535144i
$581$	267486.	−	463300.i	0.792408	−	1.37249i
$582$	−313297.	+	180882.i	−0.924932	+	0.534010i
$583$	10287.7	−	38394.3i	0.0302679	−	0.112961i
$584$		−	28995.5i		−	0.0850167i
$585$	−33036.3	+	42677.1i	−0.0965338	+	0.124705i
$586$	−56881.7			−0.165645
$587$	−115671.	−	30993.9i	−0.335698	−	0.0899499i	0.0870327	−	0.996205i	$-0.472262\pi$
$587$	−115671.	−	30993.9i	−0.335698	−	0.0899499i	−0.422730	+	0.906256i	$0.638928\pi$
$588$	10556.7	+	18284.7i	0.0305333	+	0.0528851i
$589$	378254.	+	218385.i	1.09032	+	0.629495i
$590$	−83214.6	+	83214.6i	−0.239054	+	0.239054i
$591$	−10440.8	−	38965.6i	−0.0298923	−	0.111560i
$592$	−182444.	+	48885.7i	−0.520578	+	0.139488i
$593$	86441.2	+	86441.2i	0.245817	+	0.245817i	0.819251	−	0.573435i	$-0.194389\pi$
$593$	86441.2	+	86441.2i	0.245817	+	0.245817i	−0.573435	+	0.819251i	$0.694389\pi$
$594$	−95870.3	+	166052.i	−0.271713	+	0.470622i
$595$	404769.	−	233693.i	1.14333	−	0.660104i
$596$	45666.0	−	170428.i	0.128559	−	0.479787i
$597$		−	577657.i		−	1.62077i
$598$	−227254.	−	175917.i	−0.635490	−	0.491931i
$599$	−256983.			−0.716228			−0.358114	−	0.933678i	$-0.616580\pi$
$599$	−256983.			−0.716228			−0.358114	+	0.933678i	$0.616580\pi$
$600$	−27240.5	−	7299.07i	−0.0756680	−	0.0202752i
$601$	172073.	+	298039.i	0.476391	+	0.825133i	0.999634	−	0.0270505i	$-0.00861150\pi$
$601$	172073.	+	298039.i	0.476391	+	0.825133i	−0.523243	+	0.852183i	$0.675278\pi$
$602$	263970.	+	152403.i	0.728386	+	0.420534i
$603$	10162.3	−	10162.3i	0.0279485	−	0.0279485i
$604$	39307.3	+	146697.i	0.107746	+	0.402112i
$605$	−508065.	+	136136.i	−1.38806	+	0.371930i
$606$	−8516.03	−	8516.03i	−0.0231895	−	0.0231895i
$607$	79343.2	−	137426.i	0.215344	−	0.372986i	−0.738035	−	0.674762i	$-0.764246\pi$
$607$	79343.2	−	137426.i	0.215344	−	0.372986i	0.953379	+	0.301776i	$0.0975795\pi$
$608$	623195.	−	359802.i	1.68584	−	0.973321i
$609$	39051.5	−	145742.i	0.105294	−	0.392962i
$610$		−	58768.4i		−	0.157937i
$611$	−19641.4	+	144447.i	−0.0526126	+	0.386924i
$612$	−30216.2			−0.0806746
$613$	635084.	+	170170.i	1.69009	+	0.452859i	0.970413	−	0.241450i	$-0.0776229\pi$
$613$	635084.	+	170170.i	1.69009	+	0.452859i	0.719678	+	0.694308i	$0.244290\pi$
$614$	−236673.	−	409929.i	−0.627786	−	1.08736i
$615$	−213739.	−	123402.i	−0.565110	−	0.326266i
$616$	4466.81	−	4466.81i	0.0117716	−	0.0117716i
$617$	30045.8	+	112133.i	0.0789248	+	0.294552i	0.994095	−	0.108517i	$-0.0346102\pi$
$617$	30045.8	+	112133.i	0.0789248	+	0.294552i	−0.915170	+	0.403069i	$0.867944\pi$
$618$	−327545.	+	87765.4i	−0.857618	+	0.229798i
$619$	−349306.	−	349306.i	−0.911644	−	0.911644i	0.0847577	−	0.996402i	$-0.472988\pi$
$619$	−349306.	−	349306.i	−0.911644	−	0.911644i	−0.996402	+	0.0847577i	$0.972988\pi$
$620$	−303417.	+	525534.i	−0.789327	+	1.36715i
$621$	196092.	−	113214.i	0.508484	−	0.293573i
$622$	−57293.6	+	213823.i	−0.148090	+	0.552679i
$623$			688046.i			1.77272i
$624$	−354935.	+	45195.0i	−0.911547	+	0.116070i
$625$	−124696.			−0.319221
$626$	−543882.	−	145733.i	−1.38789	−	0.371885i
$627$	−93506.6	−	161958.i	−0.237852	−	0.411972i
$628$	−589322.	−	340245.i	−1.49428	−	0.862726i
$629$	−128252.	+	128252.i	−0.324163	+	0.324163i
$630$	22369.0	+	83482.4i	0.0563594	+	0.210336i
$631$	−40085.9	+	10741.0i	−0.100678	+	0.0269765i	−0.308806	−	0.951125i	$-0.599929\pi$
$631$	−40085.9	+	10741.0i	−0.100678	+	0.0269765i	0.208129	+	0.978101i	$0.433263\pi$
$632$	5323.99	+	5323.99i	0.0133292	+	0.0133292i
$633$	−148916.	+	257930.i	−0.371650	+	0.643717i
$634$	345979.	−	199751.i	0.860739	−	0.496948i
$635$	2772.40	−	10346.7i	0.00687556	−	0.0256599i
$636$		−	127046.i		−	0.314085i
$637$	−23256.1	−	9748.92i	−0.0573136	−	0.0240258i
$638$	93769.8			0.230368
$639$	22315.0	+	5979.30i	0.0546507	+	0.0146436i
$640$	31912.1	+	55273.3i	0.0779103	+	0.134945i
$641$	64704.3	+	37357.1i	0.157477	+	0.0909194i	0.576668	−	0.816979i	$-0.304353\pi$
$641$	64704.3	+	37357.1i	0.157477	+	0.0909194i	−0.419191	+	0.907898i	$0.637686\pi$
$642$	51414.1	−	51414.1i	0.124742	−	0.124742i
$643$	170013.	+	634497.i	0.411206	+	1.53464i	0.792315	+	0.610113i	$0.208876\pi$
$643$	170013.	+	634497.i	0.411206	+	1.53464i	−0.381108	+	0.924530i	$0.624457\pi$
$644$	−225873.	+	60522.4i	−0.544618	+	0.145930i
$645$	282810.	+	282810.i	0.679790	+	0.679790i
$646$	334110.	−	578695.i	0.800615	−	1.38671i
$647$	373958.	−	215905.i	0.893335	−	0.515767i	0.0183032	−	0.999832i	$-0.494174\pi$
$647$	373958.	−	215905.i	0.893335	−	0.515767i	0.875032	+	0.484065i	$0.160840\pi$
$648$	−4574.72	+	17073.1i	−0.0108947	+	0.0406595i
$649$		−	22023.6i		−	0.0522877i
$650$	977168.	−	399902.i	2.31282	−	0.946513i
$651$	−359641.			−0.848609
$652$	4155.71	+	1113.52i	0.00977575	+	0.00261940i
$653$	281002.	+	486709.i	0.658995	+	1.14141i	0.980876	+	0.194633i	$0.0623516\pi$
$653$	281002.	+	486709.i	0.658995	+	1.14141i	−0.321881	+	0.946780i	$0.604315\pi$
$654$	721417.	+	416510.i	1.68667	+	0.973801i
$655$	558195.	−	558195.i	1.30108	−	1.30108i
$656$	44481.2	+	166006.i	0.103364	+	0.385759i
$657$	−71711.2	+	19214.9i	−0.166133	+	0.0445152i
$658$	165072.	+	165072.i	0.381259	+	0.381259i
$659$	382964.	−	663314.i	0.881835	−	1.52738i	0.0325370	−	0.999471i	$-0.489641\pi$
$659$	382964.	−	663314.i	0.881835	−	1.52738i	0.849298	−	0.527913i	$-0.177025\pi$
$660$	225019.	−	129915.i	0.516574	−	0.298244i
$661$	58036.5	−	216595.i	0.132831	−	0.495731i	−0.867167	−	0.498018i	$-0.834061\pi$
$661$	58036.5	−	216595.i	0.132831	−	0.495731i	0.999997	+	0.00228712i	$0.000728014\pi$
$662$			383524.i			0.875139i
$663$	−273471.	+	208002.i	−0.622134	+	0.473195i
$664$	33900.0			0.0768889
$665$	−938053.	−	251350.i	−2.12121	−	0.568377i
$666$	−16769.7	−	29045.9i	−0.0378074	−	0.0654843i
$667$	−95898.0	−	55366.7i	−0.215555	−	0.124451i
$668$	508742.	−	508742.i	1.14010	−	1.14010i
$669$	−71089.1	−	265308.i	−0.158837	−	0.592787i
$670$	−426528.	+	114288.i	−0.950163	+	0.254595i
$671$	7776.84	+	7776.84i	0.0172726	+	0.0172726i
$672$	−296265.	+	513145.i	−0.656057	+	1.13632i
$673$	−460732.	+	266004.i	−1.01723	+	0.587297i	−0.913300	−	0.407288i	$-0.866475\pi$
$673$	−460732.	+	266004.i	−1.01723	+	0.587297i	−0.103928	+	0.994585i	$0.533141\pi$
$674$	154745.	−	577516.i	0.340641	−	1.27129i
$675$			831875.i			1.82579i
$676$	−336602.	+	330931.i	−0.736587	+	0.724176i
$677$	538896.			1.17578			0.587892	−	0.808940i	$-0.299958\pi$
$677$	538896.			1.17578			0.587892	+	0.808940i	$0.299958\pi$
$678$	428123.	+	114715.i	0.931341	+	0.249552i
$679$	−175785.	−	304468.i	−0.381278	−	0.660392i
$680$	25649.3	+	14808.6i	0.0554699	+	0.0320256i
$681$	392209.	−	392209.i	0.845715	−	0.845715i
$682$	−57847.9	−	215891.i	−0.124371	−	0.464159i
$683$	749210.	−	200750.i	1.60606	−	0.430343i	0.659196	−	0.751971i	$-0.270897\pi$
$683$	749210.	−	200750.i	1.60606	−	0.430343i	0.946866	+	0.321628i	$0.104230\pi$
$684$	44394.8	+	44394.8i	0.0948899	+	0.0948899i
$685$	−679393.	+	1.17674e6i	−1.44791	+	2.50785i
$686$	−597715.	+	345091.i	−1.27012	+	0.733306i
$687$	169730.	−	633443.i	0.359622	−	1.34213i
$688$		−	278507.i		−	0.588382i
$689$	91859.7	+	120773.i	0.193503	+	0.254408i
$690$	−603882.			−1.26839
$691$	−639643.	−	171392.i	−1.33962	−	0.358950i	−0.483326	−	0.875440i	$-0.660572\pi$
$691$	−639643.	−	171392.i	−1.33962	−	0.358950i	−0.856293	+	0.516490i	$0.827238\pi$
$692$	−214974.	−	372345.i	−0.448924	−	0.777560i
$693$	−14007.4	−	8087.15i	−0.0291669	−	0.0168395i
$694$	−614605.	+	614605.i	−1.27608	+	1.27608i
$695$	−195445.	−	729412.i	−0.404628	−	1.51009i
$696$	9235.36	−	2474.61i	0.0190649	−	0.00510843i
$697$	116697.	+	116697.i	0.240211	+	0.240211i
$698$	−607938.	+	1.05298e6i	−1.24781	+	2.16127i
$699$	−458972.	+	264987.i	−0.939359	+	0.542339i
$700$	222354.	−	829835.i	0.453783	−	1.69354i
$701$			263737.i			0.536705i	0.963321	+	0.268352i	$0.0864791\pi$
$701$			263737.i			0.536705i	−0.963321	+	0.268352i	$0.913521\pi$
$702$	−277232.	−	677422.i	−0.562560	−	1.37463i
$703$	376866.			0.762564
$704$	−186501.	−	49972.8i	−0.376302	−	0.100830i
$705$	153159.	+	265279.i	0.308152	+	0.533734i
$706$	1.02207e6	+	590091.i	2.05055	+	1.18389i
$707$	8276.05	−	8276.05i	0.0165571	−	0.0165571i
$708$	−18219.0	−	67994.1i	−0.0363460	−	0.135645i
$709$	467638.	−	125303.i	0.930287	−	0.249270i	0.238310	−	0.971189i	$-0.423407\pi$
$709$	467638.	−	125303.i	0.930287	−	0.249270i	0.691977	+	0.721919i	$0.256740\pi$
$710$	−501921.	−	501921.i	−0.995678	−	0.995678i
$711$	9639.07	−	16695.4i	0.0190676	−	0.0330260i
$712$	−37758.7	+	21800.0i	−0.0744829	+	0.0430027i
$713$	−68313.0	+	254948.i	−0.134377	+	0.501501i
$714$			550219.i			1.07929i
$715$	−119974.	+	286199.i	−0.234680	+	0.559830i
$716$	−576711.			−1.12495
$717$	−408959.	−	109580.i	−0.795503	−	0.213154i
$718$	−406341.	−	703803.i	−0.788209	−	1.36522i
$719$	413140.	+	238526.i	0.799170	+	0.461401i	0.843181	−	0.537630i	$-0.180680\pi$
$719$	413140.	+	238526.i	0.799170	+	0.461401i	−0.0440110	+	0.999031i	$0.514014\pi$
$720$	55840.4	−	55840.4i	0.107717	−	0.107717i
$721$	−85292.1	−	318315.i	−0.164074	−	0.612331i
$722$	−623198.	+	166985.i	−1.19551	+	0.320335i
$723$	10228.0	+	10228.0i	0.0195665	+	0.0195665i
$724$	320504.	−	555129.i	0.611443	−	1.05905i
$725$	352320.	−	203412.i	0.670289	−	0.386991i
$726$	160262.	−	598107.i	0.304059	−	1.13476i
$727$		−	1.00958e6i		−	1.91017i	−0.296330	−	0.955086i	$-0.595763\pi$
$727$		−	1.00958e6i		−	1.91017i	0.296330	−	0.955086i	$-0.404237\pi$
$728$	3046.02	+	23921.6i	0.00574738	+	0.0451365i
$729$	571896.			1.07612
$730$	2.20335e6	+	590385.i	4.13464	+	1.10787i
$731$	−133721.	−	231612.i	−0.250245	−	0.433438i
$732$	30443.0	+	17576.3i	0.0568153	+	0.0328023i
$733$	−438348.	+	438348.i	−0.815851	+	0.815851i	−0.985504	−	0.169653i	$-0.945735\pi$
$733$	−438348.	+	438348.i	−0.815851	+	0.815851i	0.169653	+	0.985504i	$0.445735\pi$
$734$	148880.	+	555628.i	0.276340	+	1.03132i
$735$	−51182.3	+	13714.2i	−0.0947425	+	0.0253862i
$736$	307491.	+	307491.i	0.567645	+	0.567645i
$737$	41318.9	−	71566.4i	0.0760700	−	0.131757i
$738$	−26428.9	+	15258.8i	−0.0485252	+	0.0280160i
$739$	−145021.	+	541227.i	−0.265548	+	0.991039i	0.696366	+	0.717687i	$0.254799\pi$
$739$	−145021.	+	541227.i	−0.265548	+	0.991039i	−0.961914	+	0.273352i	$0.911868\pi$
$740$			523606.i			0.956183i
$741$	707398.	+	96189.5i	1.28833	+	0.175183i
$742$	242993.			0.441353
$743$	442353.	+	118528.i	0.801293	+	0.214706i	0.636152	−	0.771564i	$-0.280525\pi$
$743$	442353.	+	118528.i	0.801293	+	0.214706i	0.165142	+	0.986270i	$0.447192\pi$
$744$	−11394.8	−	19736.5i	−0.0205856	−	0.0356552i
$745$	383483.	+	221404.i	0.690929	+	0.398908i
$746$	−332067.	+	332067.i	−0.596689	+	0.596689i
$747$	−22465.1	−	83841.1i	−0.0402595	−	0.150250i
$748$	−167824.	+	44968.4i	−0.299952	+	0.0803718i
$749$	49965.2	+	49965.2i	0.0890644	+	0.0890644i
$750$	476387.	−	825127.i	0.846910	−	1.46689i
$751$	−721955.	+	416821.i	−1.28006	+	0.739043i	−0.976859	−	0.213884i	$-0.931389\pi$
$751$	−721955.	+	416821.i	−1.28006	+	0.739043i	−0.303201	+	0.952927i	$0.598055\pi$
$752$	55207.2	−	206036.i	0.0976248	−	0.364341i
$753$		−	390447.i		−	0.688608i
$754$	−219116.	+	283060.i	−0.385418	+	0.497892i
$755$	−381149.			−0.668653
$756$	−575284.	−	154147.i	−1.00656	−	0.269706i
$757$	−149580.	−	259080.i	−0.261025	−	0.452108i	0.705490	−	0.708720i	$-0.250727\pi$
$757$	−149580.	−	259080.i	−0.261025	−	0.452108i	−0.966515	+	0.256612i	$0.917394\pi$
$758$	−179269.	−	103501.i	−0.312009	−	0.180139i
$759$	79911.9	−	79911.9i	0.138716	−	0.138716i
$760$	−15927.5	−	59442.4i	−0.0275754	−	0.102913i
$761$	−453793.	+	121593.i	−0.783589	+	0.209962i	−0.628366	−	0.777918i	$-0.716276\pi$
$761$	−453793.	+	121593.i	−0.783589	+	0.209962i	−0.155223	+	0.987880i	$0.549609\pi$
$762$	8916.69	+	8916.69i	0.0153566	+	0.0153566i
$763$	−404773.	+	701087.i	−0.695284	+	1.20427i
$764$	676492.	−	390573.i	1.15898	−	0.669137i
$765$	19627.0	−	73249.0i	0.0335375	−	0.125164i
$766$		−	876674.i		−	1.49410i
$767$	66482.0	+	51463.6i	0.113009	+	0.0874801i
$768$	522306.			0.885529
$769$	−684828.	−	183499.i	−1.15805	−	0.310300i	−0.371866	−	0.928287i	$-0.621282\pi$
$769$	−684828.	−	183499.i	−1.15805	−	0.310300i	−0.786188	+	0.617987i	$0.787948\pi$
$770$	248480.	+	430381.i	0.419093	+	0.725891i
$771$	−96488.7	−	55707.8i	−0.162318	−	0.0937146i
$772$	−259823.	+	259823.i	−0.435957	+	0.435957i
$773$	97632.6	+	364370.i	0.163394	+	0.609794i	0.998240	+	0.0593102i	$0.0188901\pi$
$773$	97632.6	+	364370.i	0.163394	+	0.609794i	−0.834846	+	0.550484i	$0.814443\pi$
$774$	47769.4	−	12799.8i	0.0797384	−	0.0213659i
$775$	−685679.	−	685679.i	−1.14161	−	1.14161i
$776$	11139.1	−	19293.5i	0.0184981	−	0.0320396i
$777$	−268741.	+	155158.i	−0.445136	+	0.256999i
$778$	23247.4	−	86760.6i	0.0384075	−	0.143339i
$779$		−	342911.i		−	0.565075i
$780$	−133643.	+	982837.i	−0.219662	+	1.61545i
$781$	132839.			0.217782
$782$	390047.	+	104513.i	0.637828	+	0.170906i
$783$	−141016.	−	244246.i	−0.230008	−	0.398386i
$784$	31954.6	+	18449.0i	0.0519878	+	0.0300152i
$785$	1.20761e6	−	1.20761e6i	1.95968	−	1.95968i
$786$	240523.	+	897644.i	0.389324	+	1.45298i
$787$	385944.	−	103413.i	0.623124	−	0.166966i	0.0665767	−	0.997781i	$-0.478792\pi$
$787$	385944.	−	103413.i	0.623124	−	0.166966i	0.556548	+	0.830816i	$0.312126\pi$
$788$	55064.1	+	55064.1i	0.0886781	+	0.0886781i
$789$	82997.4	−	143756.i	0.133325	−	0.230925i
$790$	−512970.	+	296163.i	−0.821936	+	0.474545i
$791$	−111482.	+	416058.i	−0.178178	+	0.664968i
$792$		−	1024.93i		−	0.00163397i
$793$	−41648.2	+	5303.21i	−0.0662292	+	0.00843320i
$794$	−1.16520e6			−1.84825
$795$	307980.	+	82523.0i	0.487291	+	0.130569i
$796$	557553.	+	965711.i	0.879955	+	1.52413i
$797$	−499761.	−	288537.i	−0.786766	−	0.454240i	0.0520569	−	0.998644i	$-0.483422\pi$
$797$	−499761.	−	288537.i	−0.786766	−	0.454240i	−0.838823	+	0.544405i	$0.816756\pi$
$798$	808403.	−	808403.i	1.26947	−	1.26947i
$799$	−53013.9	−	197851.i	−0.0830418	−	0.309916i
$800$	−1.54319e6	+	413497.i	−2.41124	+	0.646089i
$801$	78937.6	+	78937.6i	0.123032	+	0.123032i
$802$	335701.	−	581450.i	0.521919	−	0.903991i
$803$	−369696.	+	213444.i	−0.573341	+	0.331019i
$804$	68361.7	−	255129.i	0.105755	−	0.394683i
$805$		−	586865.i		−	0.905620i
$806$	786880.	+	329859.i	1.21126	+	0.507760i
$807$	187594.			0.288053
$808$	716.392	+	191.957i	0.00109731	+	0.000294022i
$809$	44219.0	+	76589.6i	0.0675635	+	0.117023i	0.897828	−	0.440346i	$-0.145144\pi$
$809$	44219.0	+	76589.6i	0.0675635	+	0.117023i	−0.830265	+	0.557369i	$0.811811\pi$
$810$	−1.20423e6	−	695261.i	−1.83543	−	1.05969i
$811$	−342385.	+	342385.i	−0.520562	+	0.520562i	−0.917741	−	0.397179i	$-0.869989\pi$
$811$	−342385.	+	342385.i	−0.520562	+	0.520562i	0.397179	+	0.917741i	$0.369989\pi$
$812$	75384.7	+	281340.i	0.114333	+	0.426696i
$813$	−353836.	+	94810.2i	−0.535330	+	0.143441i
$814$	−136367.	−	136367.i	−0.205808	−	0.205808i
$815$	−5398.70	+	9350.83i	−0.00812782	+	0.0140778i
$816$	435390.	−	251373.i	0.653881	−	0.377518i
$817$	−143825.	+	536762.i	−0.215472	+	0.804151i
$818$		−	346415.i		−	0.517715i
$819$	57144.0	−	23385.9i	0.0851928	−	0.0348648i
$820$	476430.			0.708551
$821$	534427.	+	143199.i	0.792870	+	0.212449i	0.632451	−	0.774600i	$-0.282049\pi$
$821$	534427.	+	143199.i	0.792870	+	0.212449i	0.160419	+	0.987049i	$0.448716\pi$
$822$	−799799.	−	1.38529e6i	−1.18369	−	2.05021i
$823$	−284246.	−	164110.i	−0.419658	−	0.242290i	0.275273	−	0.961366i	$-0.411232\pi$
$823$	−284246.	−	164110.i	−0.419658	−	0.242290i	−0.694931	+	0.719076i	$0.744565\pi$
$824$	14766.1	−	14766.1i	0.0217476	−	0.0217476i
$825$	107461.	+	401050.i	0.157886	+	0.589238i
$826$	130048.	−	34846.3i	0.190609	−	0.0510736i
$827$	−440313.	−	440313.i	−0.643800	−	0.643800i	0.307688	−	0.951487i	$-0.400445\pi$
$827$	−440313.	−	440313.i	−0.643800	−	0.643800i	−0.951487	+	0.307688i	$0.900445\pi$
$828$	−18970.2	+	32857.3i	−0.0276701	+	0.0479260i
$829$	−38845.9	+	22427.7i	−0.0565244	+	0.0326344i	−0.527996	−	0.849247i	$-0.677056\pi$
$829$	−38845.9	+	22427.7i	−0.0565244	+	0.0326344i	0.471471	+	0.881881i	$0.343723\pi$
$830$	−690249.	+	2.57604e6i	−1.00196	+	3.73936i
$831$			826743.i			1.19720i
$832$	586657.	−	446211.i	0.847495	−	0.644605i
$833$	35432.1			0.0510631
$834$	858682.	+	230083.i	1.23453	+	0.330790i
$835$	902818.	+	1.56373e6i	1.29487	+	2.24279i
$836$	312643.	+	180505.i	0.447338	+	0.258271i
$837$	−475347.	+	475347.i	−0.678515	+	0.678515i
$838$	−480860.	−	1.79459e6i	−0.684747	−	2.55551i
$839$	614324.	−	164608.i	0.872718	−	0.233844i	0.205455	−	0.978667i	$-0.434133\pi$
$839$	614324.	−	164608.i	0.872718	−	0.233844i	0.667263	+	0.744823i	$0.267466\pi$
$840$	35830.6	+	35830.6i	0.0507803	+	0.0507803i
$841$	284677.	−	493076.i	0.402496	−	0.697143i
$842$	592056.	−	341824.i	0.835100	−	0.482145i
$843$	156783.	−	585123.i	0.220620	−	0.823364i
$844$		−	574934.i		−	0.807110i
$845$	−583590.	−	1.03094e6i	−0.817324	−	1.44384i
$846$	37876.4			0.0529210
$847$	581252.	+	155746.i	0.810210	+	0.217095i
$848$	−111014.	−	192281.i	−0.154378	−	0.267390i
$849$	−1.09498e6	−	632186.i	−1.51911	−	0.877061i
$850$	−1.04903e6	+	1.04903e6i	−1.45194	+	1.45194i
$851$	58943.7	+	219981.i	0.0813914	+	0.303757i
$852$	410116.	−	109890.i	0.564973	−	0.151384i
$853$	−467145.	−	467145.i	−0.642027	−	0.642027i	0.309026	−	0.951053i	$-0.399997\pi$
$853$	−467145.	−	467145.i	−0.642027	−	0.642027i	−0.951053	+	0.309026i	$0.899997\pi$
$854$	−33617.0	+	58226.4i	−0.0460939	+	0.0798370i
$855$	−136457.	+	78783.5i	−0.186665	+	0.107771i
$856$	−1158.90	+	4325.09i	−0.00158161	+	0.00590266i
$857$			481160.i			0.655131i	0.944829	+	0.327565i	$0.106228\pi$
$857$			481160.i			0.655131i	−0.944829	+	0.327565i	$0.893772\pi$
$858$	−221163.	−	290775.i	−0.300427	−	0.394987i
$859$	480348.			0.650983			0.325491	−	0.945545i	$-0.394470\pi$
$859$	480348.			0.650983			0.325491	+	0.945545i	$0.394470\pi$
$860$	−745760.	−	199826.i	−1.00833	−	0.270181i
$861$	141178.	+	244528.i	0.190442	+	0.329855i
$862$	1.53859e6	+	888304.i	2.07065	+	1.19549i
$863$	415207.	−	415207.i	0.557497	−	0.557497i	−0.371097	−	0.928594i	$-0.621018\pi$
$863$	415207.	−	415207.i	0.557497	−	0.557497i	0.928594	+	0.371097i	$0.121018\pi$
$864$	286657.	+	1.06982e6i	0.384003	+	1.43312i
$865$	1.04226e6	−	279273.i	1.39298	−	0.373248i
$866$	266025.	+	266025.i	0.354721	+	0.354721i
$867$	−116150.	+	201178.i	−0.154519	+	0.267634i
$868$	601238.	−	347125.i	0.798007	−	0.460730i
$869$	28690.1	−	107073.i	0.0379920	−	0.141788i
$870$			752176.i			0.993759i
$871$	119483.	+	291960.i	0.157497	+	0.384846i
$872$	−51299.2			−0.0674648
$873$	−55098.1	−	14763.5i	−0.0722950	−	0.0193714i
$874$	−419518.	−	726627.i	−0.549197	−	0.951236i
$875$	801875.	+	462962.i	1.04735	+	0.604686i
$876$	−964800.	+	964800.i	−1.25727	+	1.25727i
$877$	14359.0	+	53588.5i	0.0186692	+	0.0696743i	0.974632	−	0.223814i	$-0.0718507\pi$
$877$	14359.0	+	53588.5i	0.0186692	+	0.0696743i	−0.955963	+	0.293488i	$0.905184\pi$
$878$	878848.	−	235487.i	1.14005	−	0.305476i
$879$	60379.3	+	60379.3i	0.0781467	+	0.0781467i
$880$	227041.	−	393247.i	0.293183	−	0.507808i
$881$	−403831.	+	233152.i	−0.520293	+	0.300391i	−0.737055	−	0.675833i	$-0.763784\pi$
$881$	−403831.	+	233152.i	−0.520293	+	0.300391i	0.216761	+	0.976225i	$0.430451\pi$
$882$	−1695.78	+	6328.72i	−0.00217987	+	0.00813540i
$883$			280955.i			0.360343i	0.983635	+	0.180171i	$0.0576652\pi$
$883$			280955.i			0.360343i	−0.983635	+	0.180171i	$0.942335\pi$
$884$	256418.	−	611685.i	0.328128	−	0.782750i
$885$	176663.			0.225558
$886$	−2.05250e6	−	549966.i	−2.61467	−	0.700597i
$887$	440784.	+	763461.i	0.560246	+	0.970375i	0.997475	+	0.0710243i	$0.0226268\pi$
$887$	440784.	+	763461.i	0.560246	+	0.970375i	−0.437228	+	0.899350i	$0.644040\pi$
$888$	−17029.6	−	9832.02i	−0.0215962	−	0.0124686i
$889$	−8665.42	+	8665.42i	−0.0109644	+	0.0109644i
$890$	−887752.	−	3.31313e6i	−1.12076	−	4.18272i
$891$	251360.	−	67351.7i	0.316622	−	0.0848386i
$892$	374919.	+	374919.i	0.471203	+	0.471203i
$893$	−212800.	+	368580.i	−0.266851	+	0.462199i
$894$	−451446.	+	260642.i	−0.564846	+	0.326114i
$895$	374604.	−	1.39804e6i	0.467656	−	1.74531i
$896$		−	73018.1i		−	0.0909525i
$897$	54493.8	+	427961.i	0.0677270	+	0.531887i
$898$	−418927.			−0.519500
$899$	317555.	+	85088.5i	0.392915	+	0.105281i
$900$	−69694.7	−	120715.i	−0.0860429	−	0.149031i
$901$	−184642.	−	106603.i	−0.227448	−	0.131317i
$902$	−124081.	+	124081.i	−0.152508	+	0.152508i
$903$	−118427.	−	441976.i	−0.145236	−	0.542030i
$904$	−26364.7	+	7064.40i	−0.0322616	+	0.00864447i
$905$	1.13754e6	+	1.13754e6i	1.38889	+	1.38889i
$906$	224349.	−	388584.i	0.273318	−	0.473401i
$907$	600124.	−	346482.i	0.729502	−	0.421178i	−0.0887382	−	0.996055i	$-0.528283\pi$
$907$	600124.	−	346482.i	0.729502	−	0.421178i	0.818240	+	0.574877i	$0.194950\pi$
$908$	−277125.	+	1.03424e6i	−0.336127	+	1.25444i
$909$		−	1898.98i		−	0.00229822i
$910$	−1.87981e6	−	255610.i	−2.27003	−	0.308670i
$911$	−1.13827e6			−1.37154			−0.685769	−	0.727819i	$-0.740534\pi$
$911$	−1.13827e6			−1.37154			−0.685769	+	0.727819i	$0.740534\pi$
$912$	−1.00902e6	−	270366.i	−1.21314	−	0.325059i
$913$	−249548.	−	432230.i	−0.299373	−	0.518529i
$914$	−1.59228e6	−	919306.i	−1.90602	−	1.10044i
$915$	−62382.1	+	62382.1i	−0.0745105	+	0.0745105i
$916$	327647.	+	1.22279e6i	0.390494	+	1.45735i
$917$	−872349.	+	233745.i	−1.03741	+	0.277974i
$918$	727238.	+	727238.i	0.862961	+	0.862961i
$919$	−629139.	+	1.08970e6i	−0.744930	+	1.29026i	0.205298	+	0.978700i	$0.434184\pi$
$919$	−629139.	+	1.08970e6i	−0.744930	+	1.29026i	−0.950228	+	0.311557i	$0.899150\pi$
$920$	32206.0	−	18594.2i	0.0380506	−	0.0219685i
$921$	−183910.	+	686361.i	−0.216813	+	0.809158i
$922$			989392.i			1.16388i
$923$	−310410.	+	400996.i	−0.364362	+	0.470692i
$924$	−297259.			−0.348170
$925$	−808190.	−	216554.i	−0.944561	−	0.253094i
$926$	356001.	+	616611.i	0.415173	+	0.719101i
$927$	−46304.7	−	26734.0i	−0.0538847	−	0.0311104i
$928$	383001.	−	383001.i	0.444738	−	0.444738i
$929$	−99542.9	−	371499.i	−0.115340	−	0.430454i	0.883972	−	0.467539i	$-0.154859\pi$
$929$	−99542.9	−	371499.i	−0.115340	−	0.430454i	−0.999312	+	0.0370854i	$0.988193\pi$
$930$	1.73178e6	−	464028.i	2.00228	−	0.536510i
$931$	−52058.2	−	52058.2i	−0.0600606	−	0.0600606i
$932$	511530.	−	885996.i	0.588897	−	1.02000i
$933$	287787.	−	166154.i	0.330604	−	0.190874i
$934$	3853.88	−	14382.9i	0.00441779	−	0.0164874i
$935$		−	436042.i		−	0.498776i
$936$	3093.92	+	2395.00i	0.00353149	+	0.00273372i
$937$	−310991.			−0.354216			−0.177108	−	0.984191i	$-0.556674\pi$
$937$	−310991.			−0.354216			−0.177108	+	0.984191i	$0.556674\pi$
$938$	487970.	+	130751.i	0.554610	+	0.148607i
$939$	422631.	+	732019.i	0.479326	+	0.830216i
$940$	−512093.	−	295657.i	−0.579553	−	0.334605i
$941$	685037.	−	685037.i	0.773633	−	0.773633i	−0.205107	−	0.978740i	$-0.565754\pi$
$941$	685037.	−	685037.i	0.773633	−	0.773633i	0.978740	+	0.205107i	$0.0657541\pi$
$942$	520350.	+	1.94197e6i	0.586400	+	2.18847i
$943$	200161.	−	53633.0i	0.225090	−	0.0603127i
$944$	−86987.6	−	86987.6i	−0.0976143	−	0.0976143i
$945$	747354.	−	1.29445e6i	0.836879	−	1.44952i
$946$	246268.	−	142183.i	0.275185	−	0.158878i
$947$	256413.	−	956945.i	0.285917	−	1.06706i	−0.662250	−	0.749283i	$-0.730398\pi$
$947$	256413.	−	956945.i	0.285917	−	1.06706i	0.948167	−	0.317773i	$-0.102935\pi$
$948$		−	354302.i		−	0.394237i
$949$	219568.	−	1.61475e6i	0.243802	−	1.79297i
$950$	3.08254e6			3.41556
$951$	−579287.	−	155220.i	−0.640520	−	0.171627i
$952$	−16941.8	−	29344.1i	−0.0186933	−	0.0323778i
$953$	−850383.	−	490969.i	−0.936330	−	0.540590i	−0.0475219	−	0.998870i	$-0.515132\pi$
$953$	−850383.	−	490969.i	−0.936330	−	0.540590i	−0.888808	+	0.458280i	$0.848466\pi$
$954$	27877.9	−	27877.9i	0.0306312	−	0.0306312i
$955$	507395.	+	1.89362e6i	0.556339	+	2.07628i
$956$	789452.	−	211533.i	0.863794	−	0.231453i
$957$	−99535.7	−	99535.7i	−0.108681	−	0.108681i
$958$	−984715.	+	1.70558e6i	−1.07295	+	1.85840i
$959$	1.34626e6	−	777261.i	1.46383	−	0.845142i
$960$	400858.	−	1.49602e6i	0.434958	−	1.62329i
$961$			139905.i			0.151491i
$962$	730304.	−	92992.1i	0.789139	−	0.100484i
$963$	11464.7			0.0123627
$964$	−26970.8	−	7226.81i	−0.0290228	−	0.00777665i
$965$	−461085.	−	798623.i	−0.495138	−	0.857605i
$966$	598313.	+	345436.i	0.641171	+	0.370180i
$967$	−751098.	+	751098.i	−0.803237	+	0.803237i	−0.983600	−	0.180363i	$-0.942273\pi$
$967$	−751098.	+	751098.i	−0.803237	+	0.803237i	0.180363	+	0.983600i	$0.442273\pi$
$968$	9869.29	+	36832.7i	0.0105326	+	0.0393082i
$969$	−968932.	+	259625.i	−1.03192	+	0.276502i
$970$	1.23929e6	+	1.23929e6i	1.31714	+	1.31714i
$971$	186818.	−	323579.i	0.198144	−	0.343196i	−0.749783	−	0.661684i	$-0.769842\pi$
$971$	186818.	−	323579.i	0.198144	−	0.343196i	0.947927	+	0.318489i	$0.103175\pi$
$972$	−160107.	+	92437.9i	−0.169464	+	0.0978402i
$973$	−223599.	+	834485.i	−0.236181	+	0.881440i
$974$			1.77290e6i			1.86882i
$975$	−1.46175e6	−	612762.i	−1.53767	−	0.644589i
$976$	61433.0			0.0644915
$977$	−31340.3	−	8397.61i	−0.0328333	−	0.00879764i	0.242365	−	0.970185i	$-0.422077\pi$
$977$	−31340.3	−	8397.61i	−0.0328333	−	0.00879764i	−0.275198	+	0.961387i	$0.588744\pi$
$978$	−6355.49	−	11008.0i	−0.00664464	−	0.0115089i
$979$	555905.	+	320952.i	0.580009	+	0.334869i
$980$	72328.0	−	72328.0i	0.0753103	−	0.0753103i
$981$	33995.3	+	126872.i	0.0353249	+	0.131834i
$982$	−90520.9	+	24255.0i	−0.0938698	+	0.0251523i
$983$	7991.46	+	7991.46i	0.00827026	+	0.00827026i	0.711230	−	0.702960i	$-0.248139\pi$
$983$	7991.46	+	7991.46i	0.00827026	+	0.00827026i	−0.702960	+	0.711230i	$0.748139\pi$
$984$	−8946.17	+	15495.2i	−0.00923946	+	0.0160032i
$985$	−169251.	+	97717.4i	−0.174446	+	0.100716i
$986$	130178.	−	485830.i	0.133901	−	0.499724i
$987$		−	350444.i		−	0.359736i
$988$	−1.27545e6	+	521972.i	−1.30662	+	0.534729i
$989$	−335809.			−0.343321
$990$	77883.9	+	20868.9i	0.0794653	+	0.0212927i
$991$	−654572.	−	1.13375e6i	−0.666515	−	1.15444i	−0.978872	−	0.204473i	$-0.934452\pi$
$991$	−654572.	−	1.13375e6i	−0.666515	−	1.15444i	0.312357	−	0.949965i	$-0.398882\pi$
$992$	−1.11808e6	−	645525.i	−1.13619	−	0.655979i
$993$	407107.	−	407107.i	0.412867	−	0.412867i
$994$	210180.	+	784404.i	0.212725	+	0.793902i
$995$	−2.70320e6	+	724320.i	−2.73044	+	0.731618i
$996$	−1.12799e6	−	1.12799e6i	−1.13707	−	1.13707i
$997$	312077.	−	540533.i	0.313958	−	0.543791i	−0.665257	−	0.746614i	$-0.731678\pi$
$997$	312077.	−	540533.i	0.313958	−	0.543791i	0.979215	+	0.202823i	$0.0650115\pi$
$998$	1.15816e6	−	668663.i	1.16281	−	0.671346i
$999$	−150126.	+	560278.i	−0.150427	+	0.561400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.f.a.2.4	✓	16
3.2	odd	2		117.5.bd.c.28.1		16
13.2	odd	12		169.5.d.c.99.7		16
13.3	even	3		169.5.d.d.70.2		16
13.7	odd	12	inner	13.5.f.a.7.4	yes	16
13.10	even	6		169.5.d.c.70.7		16
13.11	odd	12		169.5.d.d.99.2		16
39.20	even	12		117.5.bd.c.46.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.2.4	✓	16	1.1	even	1	trivial
13.5.f.a.7.4	yes	16	13.7	odd	12	inner
117.5.bd.c.28.1		16	3.2	odd	2
117.5.bd.c.46.1		16	39.20	even	12
169.5.d.c.70.7		16	13.10	even	6
169.5.d.c.99.7		16	13.2	odd	12
169.5.d.d.70.2		16	13.3	even	3
169.5.d.d.99.2		16	13.11	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)

\(f(q)\)	\(=\)	\(q+(5.50893 + 1.47611i) q^{2} +(-4.28079 - 7.41455i) q^{3} +(14.3130 + 8.26362i) q^{4} +(-29.3294 + 29.3294i) q^{5} +(-12.6379 - 47.1652i) q^{6} +(45.8361 - 12.2817i) q^{7} +(2.12627 + 2.12627i) q^{8} +(3.84960 - 6.66770i) q^{9} +O(q^{10})\)	\(q+(5.50893 + 1.47611i) q^{2} +(-4.28079 - 7.41455i) q^{3} +(14.3130 + 8.26362i) q^{4} +(-29.3294 + 29.3294i) q^{5} +(-12.6379 - 47.1652i) q^{6} +(45.8361 - 12.2817i) q^{7} +(2.12627 + 2.12627i) q^{8} +(3.84960 - 6.66770i) q^{9} +(-204.867 + 118.280i) q^{10} +(11.4581 - 42.7622i) q^{11} -141.499i q^{12} +(102.310 + 134.513i) q^{13} +270.637 q^{14} +(343.018 + 91.9113i) q^{15} +(-123.643 - 214.156i) q^{16} +(-205.648 - 118.731i) q^{17} +(31.0495 - 31.0495i) q^{18} +(127.702 + 476.590i) q^{19} +(-662.159 + 177.425i) q^{20} +(-287.279 - 287.279i) q^{21} +(126.244 - 218.661i) q^{22} +(-258.218 + 149.082i) q^{23} +(6.66321 - 24.8674i) q^{24} -1095.43i q^{25} +(365.064 + 892.042i) q^{26} -759.406 q^{27} +(757.544 + 202.983i) q^{28} +(185.692 + 321.628i) q^{29} +(1753.99 + 1012.67i) q^{30} +(625.946 - 625.946i) q^{31} +(-377.475 - 1408.76i) q^{32} +(-366.113 + 98.0995i) q^{33} +(-957.641 - 957.641i) q^{34} +(-984.129 + 1704.56i) q^{35} +(110.199 - 63.6233i) q^{36} +(197.689 - 737.784i) q^{37} +2814.01i q^{38} +(559.381 - 1334.41i) q^{39} -124.724 q^{40} +(-671.311 - 179.877i) q^{41} +(-1158.54 - 2006.65i) q^{42} +(975.366 + 563.128i) q^{43} +(517.371 - 517.371i) q^{44} +(82.6533 + 308.466i) q^{45} +(-1642.57 + 440.125i) q^{46} +(609.937 + 609.937i) q^{47} +(-1058.58 + 1833.52i) q^{48} +(-129.221 + 74.6059i) q^{49} +(1616.98 - 6034.64i) q^{50} +2033.05i q^{51} +(352.807 + 2770.73i) q^{52} +897.855 q^{53} +(-4183.52 - 1120.97i) q^{54} +(918.131 + 1590.25i) q^{55} +(123.574 + 71.3455i) q^{56} +(2987.04 - 2987.04i) q^{57} +(548.205 + 2045.93i) q^{58} +(480.526 - 128.756i) q^{59} +(4150.10 + 4150.10i) q^{60} +(-124.214 + 215.146i) q^{61} +(4372.26 - 2524.32i) q^{62} +(94.5596 - 352.901i) q^{63} -4361.35i q^{64} +(-6945.87 - 944.475i) q^{65} -2161.69 q^{66} +(1803.04 + 483.124i) q^{67} +(-1962.30 - 3398.80i) q^{68} +(2210.76 + 1276.38i) q^{69} +(-7937.63 + 7937.63i) q^{70} +(776.613 + 2898.36i) q^{71} +(22.3626 - 5.99204i) q^{72} +(-6818.40 - 6818.40i) q^{73} +(2178.11 - 3772.59i) q^{74} +(-8122.11 + 4689.30i) q^{75} +(-2110.56 + 7876.72i) q^{76} -2100.78i q^{77} +(5051.33 - 6525.44i) q^{78} +2503.91 q^{79} +(9907.45 + 2654.69i) q^{80} +(2939.04 + 5090.57i) q^{81} +(-3432.69 - 1981.86i) q^{82} +(7971.73 - 7971.73i) q^{83} +(-1737.86 - 6485.78i) q^{84} +(9513.85 - 2549.23i) q^{85} +(4541.98 + 4541.98i) q^{86} +(1589.82 - 2753.65i) q^{87} +(115.287 - 66.5609i) q^{88} +(-3752.75 + 14005.5i) q^{89} +1821.33i q^{90} +(6341.55 + 4908.98i) q^{91} -4927.83 q^{92} +(-7320.65 - 1961.56i) q^{93} +(2459.76 + 4260.44i) q^{94} +(-17723.5 - 10232.7i) q^{95} +(-8829.40 + 8829.40i) q^{96} +(-1917.54 - 7156.34i) q^{97} +(-821.997 + 220.254i) q^{98} +(-241.017 - 241.017i) 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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