LMFDB - Embedded newform 25.5.f.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,5,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

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("25.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, 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:	$2.58424907710$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	25.2
Dual form			25.5.f.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.62994 - 0.891695i) q^{2} +(2.94614 + 5.78212i) q^{3} +(15.6842 + 5.09611i) q^{4} +(0.584324 - 24.9932i) q^{5} +(-11.4307 - 35.1800i) q^{6} +(-65.0193 - 65.0193i) q^{7} +(-2.49547 - 1.27151i) q^{8} +(22.8574 - 31.4606i) q^{9} +O(q^{10})$	\(q+(-5.62994 - 0.891695i) q^{2} +(2.94614 + 5.78212i) q^{3} +(15.6842 + 5.09611i) q^{4} +(0.584324 - 24.9932i) q^{5} +(-11.4307 - 35.1800i) q^{6} +(-65.0193 - 65.0193i) q^{7} +(-2.49547 - 1.27151i) q^{8} +(22.8574 - 31.4606i) q^{9} +(-25.5760 + 140.189i) q^{10} +(94.4647 - 68.6326i) q^{11} +(16.7415 + 105.702i) q^{12} +(-136.994 + 21.6976i) q^{13} +(308.077 + 424.032i) q^{14} +(146.235 - 70.2547i) q^{15} +(-200.553 - 145.710i) q^{16} +(-93.9518 + 184.391i) q^{17} +(-156.739 + 156.739i) q^{18} +(57.1905 - 18.5823i) q^{19} +(136.533 - 389.020i) q^{20} +(184.393 - 567.505i) q^{21} +(-593.030 + 302.164i) q^{22} +(51.5154 - 325.255i) q^{23} -18.1751i q^{24} +(-624.317 - 29.2082i) q^{25} +790.613 q^{26} +(768.422 + 121.706i) q^{27} +(-688.430 - 1351.12i) q^{28} +(-120.175 - 39.0473i) q^{29} +(-885.940 + 265.133i) q^{30} +(285.993 + 880.196i) q^{31} +(1030.86 + 1030.86i) q^{32} +(675.148 + 344.005i) q^{33} +(693.363 - 954.333i) q^{34} +(-1663.03 + 1587.05i) q^{35} +(518.827 - 376.950i) q^{36} +(-225.824 - 1425.80i) q^{37} +(-338.549 + 53.6208i) q^{38} +(-529.060 - 728.188i) q^{39} +(-33.2371 + 61.6268i) q^{40} +(-626.274 - 455.015i) q^{41} +(-1544.17 + 3030.60i) q^{42} +(998.916 - 998.916i) q^{43} +(1831.36 - 595.046i) q^{44} +(-772.943 - 589.663i) q^{45} +(-580.057 + 1785.23i) q^{46} +(3161.59 - 1610.91i) q^{47} +(251.657 - 1588.90i) q^{48} +6054.01i q^{49} +(3488.82 + 721.141i) q^{50} -1342.96 q^{51} +(-2259.21 - 357.823i) q^{52} +(879.784 + 1726.67i) q^{53} +(-4217.64 - 1370.40i) q^{54} +(-1660.15 - 2401.08i) q^{55} +(79.5813 + 244.926i) q^{56} +(275.936 + 275.936i) q^{57} +(641.762 + 326.994i) q^{58} +(1736.23 - 2389.71i) q^{59} +(2651.60 - 356.659i) q^{60} +(1347.46 - 978.990i) q^{61} +(-825.257 - 5210.47i) q^{62} +(-3531.72 + 559.369i) q^{63} +(-2553.10 - 3514.04i) q^{64} +(462.244 + 3436.58i) q^{65} +(-3494.29 - 2538.75i) q^{66} +(591.414 - 1160.72i) q^{67} +(-2413.23 + 2413.23i) q^{68} +(2032.44 - 660.379i) q^{69} +(10777.9 - 7452.05i) q^{70} +(588.836 - 1812.25i) q^{71} +(-97.0423 + 49.4455i) q^{72} +(-1433.88 + 9053.14i) q^{73} +8228.53i q^{74} +(-1670.44 - 3695.93i) q^{75} +991.684 q^{76} +(-10604.5 - 1679.58i) q^{77} +(2329.25 + 4571.42i) q^{78} +(-3804.27 - 1236.08i) q^{79} +(-3758.95 + 4927.31i) q^{80} +(586.790 + 1805.95i) q^{81} +(3120.15 + 3120.15i) q^{82} +(9986.91 + 5088.58i) q^{83} +(5784.13 - 7961.17i) q^{84} +(4553.61 + 2455.90i) q^{85} +(-6514.57 + 4733.11i) q^{86} +(-128.277 - 809.907i) q^{87} +(-323.001 + 51.1583i) q^{88} +(916.231 + 1261.08i) q^{89} +(3825.82 + 4009.00i) q^{90} +(10318.0 + 7496.45i) q^{91} +(2465.51 - 4838.84i) q^{92} +(-4246.82 + 4246.82i) q^{93} +(-19236.0 + 6250.15i) q^{94} +(-431.013 - 1440.23i) q^{95} +(-2923.50 + 8997.60i) q^{96} +(12843.4 - 6544.05i) q^{97} +(5398.33 - 34083.7i) q^{98} -4540.68i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) $ 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−5.62994	−	0.891695i	−1.40749	−	0.222924i	−0.593979	−	0.804480i	$-0.702444\pi$
$2$	−5.62994	−	0.891695i	−1.40749	−	0.222924i	−0.813506	+	0.581557i	$0.802444\pi$
$3$	2.94614	+	5.78212i	0.327348	+	0.642458i	0.994761	−	0.102231i	$-0.0325981\pi$
$3$	2.94614	+	5.78212i	0.327348	+	0.642458i	−0.667412	+	0.744688i	$0.732598\pi$
$4$	15.6842	+	5.09611i	0.980263	+	0.318507i
$5$	0.584324	−	24.9932i	0.0233729	−	0.999727i
$5$	0.584324	−	24.9932i	0.0233729	−	0.999727i
$6$	−11.4307	−	35.1800i	−0.317519	−	0.977223i
$7$	−65.0193	−	65.0193i	−1.32692	−	1.32692i	−0.908040	−	0.418884i	$-0.862421\pi$
$7$	−65.0193	−	65.0193i	−1.32692	−	1.32692i	−0.418884	−	0.908040i	$-0.637579\pi$
$8$	−2.49547	−	1.27151i	−0.0389917	−	0.0198673i
$9$	22.8574	−	31.4606i	0.282191	−	0.388402i
$10$	−25.5760	+	140.189i	−0.255760	+	1.40189i
$11$	94.4647	−	68.6326i	0.780700	−	0.567212i	−0.124489	−	0.992221i	$-0.539729\pi$
$11$	94.4647	−	68.6326i	0.780700	−	0.567212i	0.905189	+	0.425009i	$0.139729\pi$
$12$	16.7415	+	105.702i	0.116260	+	0.734040i
$13$	−136.994	+	21.6976i	−0.810612	+	0.128388i	−0.547963	−	0.836503i	$-0.684596\pi$
$13$	−136.994	+	21.6976i	−0.810612	+	0.128388i	−0.262650	+	0.964891i	$0.584596\pi$
$14$	308.077	+	424.032i	1.57182	+	2.16343i
$15$	146.235	−	70.2547i	0.649933	−	0.312243i
$16$	−200.553	−	145.710i	−0.783410	−	0.569181i
$17$	−93.9518	+	184.391i	−0.325093	+	0.638030i	−0.994485	−	0.104879i	$-0.966555\pi$
$17$	−93.9518	+	184.391i	−0.325093	+	0.638030i	0.669392	+	0.742909i	$0.266555\pi$
$18$	−156.739	+	156.739i	−0.483763	+	0.483763i
$19$	57.1905	−	18.5823i	0.158422	−	0.0514745i	−0.228732	−	0.973489i	$-0.573458\pi$
$19$	57.1905	−	18.5823i	0.158422	−	0.0514745i	0.387154	+	0.922015i	$0.373458\pi$
$20$	136.533	−	389.020i	0.341331	−	0.972550i
$21$	184.393	−	567.505i	0.418126	−	1.28686i
$22$	−593.030	+	302.164i	−1.22527	+	0.624305i
$23$	51.5154	−	325.255i	0.0973826	−	0.614850i	−0.889934	−	0.456089i	$-0.849250\pi$
$23$	51.5154	−	325.255i	0.0973826	−	0.614850i	0.987317	−	0.158761i	$-0.0507500\pi$
$24$		−	18.1751i		−	0.0315541i
$25$	−624.317	−	29.2082i	−0.998907	−	0.0467331i
$26$	790.613			1.16955
$27$	768.422	+	121.706i	1.05408	+	0.166949i
$28$	−688.430	−	1351.12i	−0.878100	−	1.72337i
$29$	−120.175	−	39.0473i	−0.142896	−	0.0464297i	0.236696	−	0.971584i	$-0.423936\pi$
$29$	−120.175	−	39.0473i	−0.142896	−	0.0464297i	−0.379592	+	0.925154i	$0.623936\pi$
$30$	−885.940	+	265.133i	−0.984378	+	0.294592i
$31$	285.993	+	880.196i	0.297599	+	0.915916i	0.982336	+	0.187126i	$0.0599172\pi$
$31$	285.993	+	880.196i	0.297599	+	0.915916i	−0.684737	+	0.728791i	$0.740083\pi$
$32$	1030.86	+	1030.86i	1.00670	+	1.00670i
$33$	675.148	+	344.005i	0.619970	+	0.315891i
$34$	693.363	−	954.333i	0.599795	−	0.825547i
$35$	−1663.03	+	1587.05i	−1.35758	+	1.29555i
$36$	518.827	−	376.950i	0.400329	−	0.290856i
$37$	−225.824	−	1425.80i	−0.164956	−	1.04149i	−0.921735	−	0.387819i	$-0.873228\pi$
$37$	−225.824	−	1425.80i	−0.164956	−	1.04149i	0.756780	−	0.653670i	$-0.226772\pi$
$38$	−338.549	+	53.6208i	−0.234452	+	0.0371335i
$39$	−529.060	−	728.188i	−0.347837	−	0.478756i
$40$	−33.2371	+	61.6268i	−0.0207732	+	0.0385167i
$41$	−626.274	−	455.015i	−0.372560	−	0.270681i	0.385712	−	0.922619i	$-0.373956\pi$
$41$	−626.274	−	455.015i	−0.372560	−	0.270681i	−0.758272	+	0.651939i	$0.773956\pi$
$42$	−1544.17	+	3030.60i	−0.875377	+	1.71802i
$43$	998.916	−	998.916i	0.540247	−	0.540247i	−0.383355	−	0.923601i	$-0.625231\pi$
$43$	998.916	−	998.916i	0.540247	−	0.540247i	0.923601	+	0.383355i	$0.125231\pi$
$44$	1831.36	−	595.046i	0.945952	−	0.307358i
$45$	−772.943	−	589.663i	−0.381700	−	0.291192i
$46$	−580.057	+	1785.23i	−0.274129	+	0.843683i
$47$	3161.59	−	1610.91i	1.43123	−	0.729248i	0.445140	−	0.895461i	$-0.353154\pi$
$47$	3161.59	−	1610.91i	1.43123	−	0.729248i	0.986090	+	0.166213i	$0.0531539\pi$
$48$	251.657	−	1588.90i	0.109226	−	0.689628i
$49$			6054.01i			2.52145i
$50$	3488.82	+	721.141i	1.39553	+	0.288456i
$51$	−1342.96			−0.516326
$52$	−2259.21	−	357.823i	−0.835506	−	0.132331i
$53$	879.784	+	1726.67i	0.313202	+	0.614693i	0.992921	−	0.118780i	$-0.0378982\pi$
$53$	879.784	+	1726.67i	0.313202	+	0.614693i	−0.679719	+	0.733473i	$0.737898\pi$
$54$	−4217.64	−	1370.40i	−1.44638	−	0.469957i
$55$	−1660.15	−	2401.08i	−0.548809	−	0.793744i
$56$	79.5813	+	244.926i	0.0253767	+	0.0781014i
$57$	275.936	+	275.936i	0.0849295	+	0.0849295i
$58$	641.762	+	326.994i	0.190773	+	0.0972039i
$59$	1736.23	−	2389.71i	0.498773	−	0.686502i	−0.483203	−	0.875508i	$-0.660527\pi$
$59$	1736.23	−	2389.71i	0.498773	−	0.686502i	0.981976	+	0.189006i	$0.0605267\pi$
$60$	2651.60	−	356.659i	0.736557	−	0.0990721i
$61$	1347.46	−	978.990i	0.362124	−	0.263099i	−0.391813	−	0.920045i	$-0.628152\pi$
$61$	1347.46	−	978.990i	0.362124	−	0.263099i	0.753938	+	0.656946i	$0.228152\pi$
$62$	−825.257	−	5210.47i	−0.214687	−	1.35548i
$63$	−3531.72	+	559.369i	−0.889825	+	0.140934i
$64$	−2553.10	−	3514.04i	−0.623315	−	0.857919i
$65$	462.244	+	3436.58i	0.109407	+	0.813392i
$66$	−3494.29	−	2538.75i	−0.802179	−	0.582817i
$67$	591.414	−	1160.72i	0.131747	−	0.258569i	−0.815703	−	0.578470i	$-0.803650\pi$
$67$	591.414	−	1160.72i	0.131747	−	0.258569i	0.947451	+	0.319902i	$0.103650\pi$
$68$	−2413.23	+	2413.23i	−0.521893	+	0.521893i
$69$	2032.44	−	660.379i	0.426893	−	0.138706i
$70$	10777.9	−	7452.05i	2.19958	−	1.52083i
$71$	588.836	−	1812.25i	0.116809	−	0.359502i	−0.875511	−	0.483199i	$-0.839475\pi$
$71$	588.836	−	1812.25i	0.116809	−	0.359502i	0.992320	+	0.123696i	$0.0394749\pi$
$72$	−97.0423	+	49.4455i	−0.0187196	+	0.00953811i
$73$	−1433.88	+	9053.14i	−0.269071	+	1.69884i	0.369459	+	0.929247i	$0.379543\pi$
$73$	−1433.88	+	9053.14i	−0.269071	+	1.69884i	−0.638530	+	0.769597i	$0.720457\pi$
$74$			8228.53i			1.50265i
$75$	−1670.44	−	3695.93i	−0.296967	−	0.657054i
$76$	991.684			0.171690
$77$	−10604.5	−	1679.58i	−1.78858	−	0.283283i
$78$	2329.25	+	4571.42i	0.382849	+	0.751384i
$79$	−3804.27	−	1236.08i	−0.609560	−	0.198058i	−0.0120606	−	0.999927i	$-0.503839\pi$
$79$	−3804.27	−	1236.08i	−0.609560	−	0.198058i	−0.597500	+	0.801869i	$0.703839\pi$
$80$	−3758.95	+	4927.31i	−0.587336	+	0.769892i
$81$	586.790	+	1805.95i	0.0894361	+	0.275256i
$82$	3120.15	+	3120.15i	0.464032	+	0.464032i
$83$	9986.91	+	5088.58i	1.44969	+	0.738654i	0.988862	−	0.148836i	$-0.0475527\pi$
$83$	9986.91	+	5088.58i	1.44969	+	0.738654i	0.460827	+	0.887490i	$0.347553\pi$
$84$	5784.13	−	7961.17i	0.819746	−	1.12828i
$85$	4553.61	+	2455.90i	0.630258	+	0.339917i
$86$	−6514.57	+	4733.11i	−0.880823	+	0.639955i
$87$	−128.277	−	809.907i	−0.0169476	−	0.107003i
$88$	−323.001	+	51.1583i	−0.0417098	+	0.00660618i
$89$	916.231	+	1261.08i	0.115671	+	0.159208i	0.862927	−	0.505329i	$-0.168629\pi$
$89$	916.231	+	1261.08i	0.115671	+	0.159208i	−0.747256	+	0.664537i	$0.768629\pi$
$90$	3825.82	+	4009.00i	0.472324	+	0.494938i
$91$	10318.0	+	7496.45i	1.24598	+	0.905259i
$92$	2465.51	−	4838.84i	0.291294	−	0.571697i
$93$	−4246.82	+	4246.82i	−0.491019	+	0.491019i
$94$	−19236.0	+	6250.15i	−2.17700	+	0.707351i
$95$	−431.013	−	1440.23i	−0.0477577	−	0.159582i
$96$	−2923.50	+	8997.60i	−0.317220	+	0.976302i
$97$	12843.4	−	6544.05i	1.36501	−	0.695509i	0.390661	−	0.920535i	$-0.372247\pi$
$97$	12843.4	−	6544.05i	1.36501	−	0.695509i	0.974353	+	0.225025i	$0.0722465\pi$
$98$	5398.33	−	34083.7i	0.562092	−	3.54891i
$99$		−	4540.68i		−	0.463287i
$100$	−9643.07	−	3639.69i	−0.964307	−	0.363969i
$101$	−13637.8			−1.33691			−0.668456	−	0.743752i	$-0.733044\pi$
$101$	−13637.8			−1.33691			−0.668456	+	0.743752i	$0.733044\pi$
$102$	7560.81	+	1197.51i	0.726721	+	0.115101i
$103$	−6233.21	−	12233.4i	−0.587540	−	1.15311i	−0.973090	−	0.230426i	$-0.925988\pi$
$103$	−6233.21	−	12233.4i	−0.587540	−	1.15311i	0.385550	−	0.922687i	$-0.374012\pi$
$104$	369.452	+	120.042i	0.0341579	+	0.0110986i
$105$	−14076.0	−	4940.18i	−1.27673	−	0.448089i
$106$	−3413.47	−	10505.6i	−0.303797	−	0.934992i
$107$	−4633.45	−	4633.45i	−0.404703	−	0.404703i	0.475184	−	0.879887i	$-0.342382\pi$
$107$	−4633.45	−	4633.45i	−0.404703	−	0.404703i	−0.879887	+	0.475184i	$0.842382\pi$
$108$	11431.9	+	5824.82i	0.980097	+	0.499384i
$109$	6531.38	−	8989.67i	0.549733	−	0.756643i	−0.440243	−	0.897879i	$-0.645108\pi$
$109$	6531.38	−	8989.67i	0.549733	−	0.756643i	0.989976	+	0.141236i	$0.0451076\pi$
$110$	7205.51	+	14998.3i	0.595497	+	1.23953i
$111$	7578.83	−	5506.34i	0.615115	−	0.446907i
$112$	3565.83	+	22513.8i	0.284266	+	1.79478i
$113$	1604.09	−	254.063i	0.125624	−	0.0198969i	−0.0933058	−	0.995637i	$-0.529743\pi$
$113$	1604.09	−	254.063i	0.125624	−	0.0198969i	0.218930	+	0.975741i	$0.429743\pi$
$114$	−1307.45	−	1799.55i	−0.100604	−	0.138470i
$115$	−8099.06	−	1477.59i	−0.612406	−	0.111727i
$116$	−1685.87	−	1224.85i	−0.125287	−	0.0910265i
$117$	−2448.70	+	4805.84i	−0.178881	+	0.351073i
$118$	−11905.8	+	11905.8i	−0.855053	+	0.855053i
$119$	18097.6	−	5880.28i	1.27799	−	0.415244i
$120$	−454.254	−	10.6202i	−0.0315454	−	0.000737511i
$121$	−311.177	+	957.704i	−0.0212538	+	0.0654125i
$122$	−8459.11	+	4310.13i	−0.568336	+	0.289581i
$123$	785.860	−	4961.73i	0.0519440	−	0.327961i
$124$			15262.6i			0.992626i
$125$	−1094.81	+	15586.6i	−0.0700678	+	0.997542i
$126$	20382.1			1.28383
$127$	−22.6291	−	3.58409i	−0.00140301	−	0.000222214i	0.155733	−	0.987799i	$-0.450226\pi$
$127$	−22.6291	−	3.58409i	−0.00140301	−	0.000222214i	−0.157136	+	0.987577i	$0.550226\pi$
$128$	650.704	+	1277.08i	0.0397158	+	0.0779467i
$129$	8718.79	+	2832.91i	0.523935	+	0.170237i
$130$	461.974	−	19759.9i	0.0273357	−	1.16923i
$131$	484.301	+	1490.52i	0.0282210	+	0.0868554i	0.964175	−	0.265267i	$-0.0854601\pi$
$131$	484.301	+	1490.52i	0.0282210	+	0.0868554i	−0.935954	+	0.352122i	$0.885460\pi$
$132$	8836.07	+	8836.07i	0.507120	+	0.507120i
$133$	−4926.69	−	2510.27i	−0.278517	−	0.141912i
$134$	−4364.63	+	6007.40i	−0.243074	+	0.334562i
$135$	3490.83	−	19134.2i	0.191541	−	1.04989i
$136$	468.908	−	340.682i	0.0253519	−	0.0184192i
$137$	−2785.36	−	17586.1i	−0.148402	−	0.936975i	−0.943711	−	0.330771i	$-0.892691\pi$
$137$	−2785.36	−	17586.1i	−0.148402	−	0.936975i	0.795309	−	0.606205i	$-0.207309\pi$
$138$	−12031.4	+	1905.58i	−0.631766	+	0.100062i
$139$	−3568.16	−	4911.15i	−0.184678	−	0.254187i	0.706633	−	0.707581i	$-0.250213\pi$
$139$	−3568.16	−	4911.15i	−0.184678	−	0.254187i	−0.891311	+	0.453393i	$0.850213\pi$
$140$	−34171.0	+	16416.6i	−1.74342	+	0.837580i
$141$	18628.9	+	13534.7i	0.937022	+	0.680786i
$142$	−4931.09	+	9677.80i	−0.244549	+	0.479955i
$143$	−11451.9	+	11451.9i	−0.560022	+	0.560022i
$144$	−9168.25	+	2978.94i	−0.442142	+	0.143661i
$145$	−1046.14	+	2980.75i	−0.0497569	+	0.141772i
$146$	16145.3	−	49690.1i	0.757425	−	2.33112i
$147$	−35005.0	+	17835.9i	−1.61993	+	0.825394i
$148$	3724.15	−	23513.4i	0.170021	−	1.07347i
$149$			3363.90i			0.151520i	0.997126	+	0.0757600i	$0.0241383\pi$
$149$			3363.90i			0.151520i	−0.997126	+	0.0757600i	$0.975862\pi$
$150$	6108.83	+	22297.4i	0.271503	+	0.990994i
$151$	17365.3			0.761605			0.380802	−	0.924656i	$-0.375648\pi$
$151$	17365.3			0.761605			0.380802	+	0.924656i	$0.375648\pi$
$152$	−166.345	−	26.3464i	−0.00719982	−	0.00114034i
$153$	3653.54	+	7170.48i	0.156074	+	0.306313i
$154$	58204.8	+	18911.9i	2.45424	+	0.797432i
$155$	22166.0	−	6633.55i	0.922622	−	0.276110i
$156$	−4586.96	−	14117.2i	−0.188484	−	0.580095i
$157$	7456.79	+	7456.79i	0.302519	+	0.302519i	0.841999	−	0.539480i	$-0.181379\pi$
$157$	7456.79	+	7456.79i	0.302519	+	0.302519i	−0.539480	+	0.841999i	$0.681379\pi$
$158$	20315.6	+	10351.3i	0.813795	+	0.414649i
$159$	−7391.87	+	10174.0i	−0.292388	+	0.402438i
$160$	26366.8	−	25162.1i	1.02995	−	0.982893i
$161$	−24497.4	+	17798.4i	−0.945078	+	0.686639i
$162$	−1693.23	−	10690.7i	−0.0645189	−	0.407356i
$163$	−51436.1	+	8146.67i	−1.93594	+	0.306623i	−0.999073	−	0.0430547i	$-0.986291\pi$
$163$	−51436.1	+	8146.67i	−1.93594	+	0.306623i	−0.936870	+	0.349678i	$0.886291\pi$
$164$	−7503.80	−	10328.1i	−0.278993	−	0.384001i
$165$	8992.28	−	16673.1i	0.330295	−	0.612418i
$166$	−51688.2	−	37553.7i	−1.87575	−	1.36281i
$167$	−3361.03	+	6596.40i	−0.120515	+	0.236523i	−0.943381	−	0.331712i	$-0.892374\pi$
$167$	−3361.03	+	6596.40i	−0.120515	+	0.236523i	0.822866	+	0.568236i	$0.192374\pi$
$168$	−1181.73	+	1181.73i	−0.0418698	+	0.0418698i
$169$	−8866.69	+	2880.96i	−0.310448	+	0.100871i
$170$	−23446.7	−	17887.0i	−0.811303	−	0.618927i
$171$	722.617	−	2223.99i	0.0247125	−	0.0760572i
$172$	20757.8	−	10576.6i	0.701656	−	0.357512i
$173$	2327.79	−	14697.1i	0.0777770	−	0.491065i	−0.917794	−	0.397056i	$-0.870032\pi$
$173$	2327.79	−	14697.1i	0.0777770	−	0.491065i	0.995571	−	0.0940087i	$-0.0299681\pi$
$174$			4674.11i			0.154383i
$175$	38693.5	+	42491.7i	1.26346	+	1.38749i
$176$	−28945.6			−0.934454
$177$	18932.8	+	2998.66i	0.604321	+	0.0957150i
$178$	−4033.82	−	7916.83i	−0.127314	−	0.249868i
$179$	45955.8	+	14932.0i	1.43428	+	0.466027i	0.920110	−	0.391660i	$-0.128099\pi$
$179$	45955.8	+	14932.0i	1.43428	+	0.466027i	0.514173	+	0.857687i	$0.328099\pi$
$180$	−9118.01	−	13187.4i	−0.281420	−	0.407018i
$181$	5294.24	+	16294.0i	0.161602	+	0.497360i	0.998770	−	0.0495862i	$-0.0157903\pi$
$181$	5294.24	+	16294.0i	0.161602	+	0.497360i	−0.837168	+	0.546946i	$0.815790\pi$
$182$	−51405.1	−	51405.1i	−1.55190	−	1.55190i
$183$	9630.45	+	4906.96i	0.287571	+	0.146525i
$184$	−542.119	+	746.163i	−0.0160125	+	0.0220393i
$185$	−35767.2	+	4810.94i	−1.04506	+	0.140568i
$186$	27696.2	−	20122.5i	0.800561	−	0.581642i
$187$	3780.09	+	23866.6i	0.108098	+	0.682507i
$188$	57796.3	−	9154.04i	1.63525	−	0.258998i
$189$	−42049.0	−	57875.4i	−1.17715	−	1.62021i
$190$	1142.33	+	8492.73i	0.0316436	+	0.235256i
$191$	35133.4	+	25525.9i	0.963059	+	0.699703i	0.953859	−	0.300254i	$-0.0970715\pi$
$191$	35133.4	+	25525.9i	0.963059	+	0.699703i	0.00919989	+	0.999958i	$0.497072\pi$
$192$	12796.8	−	25115.1i	0.347135	−	0.681292i
$193$	21325.1	−	21325.1i	0.572502	−	0.572502i	−0.360325	−	0.932827i	$-0.617334\pi$
$193$	21325.1	−	21325.1i	0.572502	−	0.572502i	0.932827	+	0.360325i	$0.117334\pi$
$194$	−78143.0	+	25390.2i	−2.07628	+	0.674625i
$195$	−18508.9	+	12797.4i	−0.486756	+	0.336552i
$196$	−30851.9	+	94952.3i	−0.803100	+	2.47169i
$197$	−1057.67	+	538.909i	−0.0272532	+	0.0138862i	−0.467564	−	0.883959i	$-0.654868\pi$
$197$	−1057.67	+	538.909i	−0.0272532	+	0.0138862i	0.440311	+	0.897845i	$0.354868\pi$
$198$	−4048.90	+	25563.7i	−0.103278	+	0.652070i
$199$		−	40219.9i		−	1.01563i	−0.861467	−	0.507814i	$-0.830454\pi$
$199$		−	40219.9i		−	1.01563i	0.861467	−	0.507814i	$-0.169546\pi$
$200$	1520.83	+	866.711i	0.0380207	+	0.0216678i
$201$	8453.78			0.209247
$202$	76780.2	+	12160.8i	1.88168	+	0.298029i
$203$	5274.88	+	10352.5i	0.128003	+	0.251220i
$204$	−21063.3	−	6843.89i	−0.506135	−	0.164453i
$205$	−11738.2	+	15386.7i	−0.279315	+	0.366132i
$206$	24184.2	+	74431.3i	0.569898	+	1.75397i
$207$	−9055.21	−	9055.21i	−0.211328	−	0.211328i
$208$	30636.0	+	15609.8i	0.708118	+	0.360804i
$209$	4127.13	−	5680.50i	0.0944833	−	0.130045i
$210$	74841.9	+	40364.4i	1.69709	+	0.915293i
$211$	−33190.7	+	24114.4i	−0.745506	+	0.541642i	−0.894431	−	0.447207i	$-0.852419\pi$
$211$	−33190.7	+	24114.4i	−0.745506	+	0.541642i	0.148925	+	0.988849i	$0.452419\pi$
$212$	4999.40	+	31565.0i	0.111236	+	0.702318i
$213$	12213.4	−	1934.42i	0.269202	−	0.0426375i
$214$	21954.4	+	30217.6i	0.479396	+	0.659832i
$215$	−24382.4	−	25549.8i	−0.527472	−	0.552726i
$216$	−1762.82	−	1280.77i	−0.0377834	−	0.0274513i
$217$	38634.6	−	75824.7i	0.820460	−	1.61024i
$218$	−44787.3	+	44787.3i	−0.942415	+	0.942415i
$219$	−56570.7	+	18380.9i	−1.17952	+	0.383248i
$220$	−13802.0	−	46119.2i	−0.285165	−	0.952877i
$221$	8869.94	−	27298.9i	0.181609	−	0.558934i
$222$	−47578.3	+	24242.4i	−0.965391	+	0.491891i
$223$	1931.95	−	12197.8i	0.0388495	−	0.245286i	−0.960620	−	0.277867i	$-0.910373\pi$
$223$	1931.95	−	12197.8i	0.0388495	−	0.245286i	0.999469	+	0.0325808i	$0.0103726\pi$
$224$		−	134051.i		−	2.67162i
$225$	−15189.2	+	18973.7i	−0.300033	+	0.374790i
$226$	−9257.50			−0.181249
$227$	−111.616	−	17.6782i	−0.00216608	−	0.000343073i	0.155351	−	0.987859i	$-0.450349\pi$
$227$	−111.616	−	17.6782i	−0.00216608	−	0.000343073i	−0.157517	+	0.987516i	$0.550349\pi$
$228$	2921.64	+	5734.03i	0.0562026	+	0.110304i
$229$	−29187.4	−	9483.57i	−0.556577	−	0.180843i	0.0172036	−	0.999852i	$-0.494524\pi$
$229$	−29187.4	−	9483.57i	−0.556577	−	0.180843i	−0.573780	+	0.819009i	$0.694524\pi$
$230$	44279.7	+	15540.6i	0.837045	+	0.293774i
$231$	−21530.7	−	66264.6i	−0.403491	−	1.24182i
$232$	250.245	+	250.245i	0.00464932	+	0.00464932i
$233$	53184.4	+	27098.8i	0.979652	+	0.499158i	0.869059	−	0.494708i	$-0.164725\pi$
$233$	53184.4	+	27098.8i	0.979652	+	0.499158i	0.110593	+	0.993866i	$0.464725\pi$
$234$	18071.4	−	24873.1i	0.330035	−	0.454254i
$235$	−38414.3	−	79959.4i	−0.695597	−	1.44788i
$236$	39409.6	−	28632.7i	0.707584	−	0.514090i
$237$	−4060.72	−	25638.4i	−0.0722947	−	0.456451i
$238$	−107132.	+	16968.0i	−1.89132	+	0.299556i
$239$	31062.3	+	42753.6i	0.543798	+	0.748474i	0.989154	−	0.146880i	$-0.0469230\pi$
$239$	31062.3	+	42753.6i	0.543798	+	0.748474i	−0.445356	+	0.895353i	$0.646923\pi$
$240$	−39564.7	−	7218.15i	−0.686887	−	0.125315i
$241$	−61662.1	−	44800.2i	−1.06166	−	0.771339i	−0.0872633	−	0.996185i	$-0.527812\pi$
$241$	−61662.1	−	44800.2i	−1.06166	−	0.771339i	−0.974394	+	0.224846i	$0.927812\pi$
$242$	2605.89	−	5114.34i	0.0444964	−	0.0873291i
$243$	35847.0	−	35847.0i	0.607072	−	0.607072i
$244$	26122.9	−	8487.86i	0.438776	−	0.142567i
$245$	151309.	+	3537.50i	2.52076	+	0.0589338i
$246$	−8848.69	+	27233.5i	−0.146221	+	0.450021i
$247$	−7431.53	+	3786.55i	−0.121810	+	0.0620655i
$248$	405.487	−	2560.14i	0.00659286	−	0.0416257i
$249$			72737.2i			1.17316i
$250$	20062.2	−	86775.4i	0.320995	−	1.38841i
$251$	−32664.7			−0.518479			−0.259240	−	0.965813i	$-0.583472\pi$
$251$	−32664.7			−0.518479			−0.259240	+	0.965813i	$0.583472\pi$
$252$	−58242.7	−	9224.75i	−0.917151	−	0.145262i
$253$	−17456.7	−	34260.8i	−0.272723	−	0.535250i
$254$	124.204	+	40.3565i	0.00192517	+	0.000625527i
$255$	−784.726	+	33564.9i	−0.0120681	+	0.516185i
$256$	18951.2	+	58325.9i	0.289173	+	0.889982i
$257$	63804.2	+	63804.2i	0.966013	+	0.966013i	0.999441	−	0.0334279i	$-0.0106424\pi$
$257$	63804.2	+	63804.2i	0.966013	+	0.966013i	−0.0334279	+	0.999441i	$0.510642\pi$
$258$	−46560.2	−	23723.6i	−0.699480	−	0.356403i
$259$	−78021.5	+	107387.i	−1.16309	+	1.60086i
$260$	−10263.2	+	56255.7i	−0.151823	+	0.832184i
$261$	−3975.35	+	2888.26i	−0.0583572	+	0.0423990i
$262$	−1397.49	−	8823.41i	−0.0203585	−	0.128539i
$263$	36585.1	−	5794.52i	0.528924	−	0.0837733i	0.113740	−	0.993511i	$-0.463717\pi$
$263$	36585.1	−	5794.52i	0.528924	−	0.0837733i	0.415184	+	0.909737i	$0.363717\pi$
$264$	−1247.41	−	1716.91i	−0.0178978	−	0.0246342i
$265$	43669.1	−	20979.7i	0.621846	−	0.298749i
$266$	25498.6	+	18525.8i	0.360373	+	0.261826i
$267$	−4592.40	+	9013.08i	−0.0644194	+	0.126430i
$268$	15191.0	−	15191.0i	0.211503	−	0.211503i
$269$	89990.7	−	29239.7i	1.24363	−	0.404081i	0.387999	−	0.921660i	$-0.373166\pi$
$269$	89990.7	−	29239.7i	1.24363	−	0.404081i	0.855636	+	0.517578i	$0.173166\pi$
$270$	−36715.0	+	104612.i	−0.503635	+	1.43500i
$271$	16957.8	−	52190.6i	0.230903	−	0.710647i	−0.766735	−	0.641963i	$-0.778120\pi$
$271$	16957.8	−	52190.6i	0.230903	−	0.710647i	0.997638	−	0.0686836i	$-0.0218799\pi$
$272$	45709.9	−	23290.4i	0.617835	−	0.314803i
$273$	−12947.2	+	81745.4i	−0.173720	+	1.09683i
$274$			101492.i			1.35186i
$275$	−60980.6	+	40089.4i	−0.806354	+	0.530107i
$276$	35242.5			0.462646
$277$	−125403.	−	19861.8i	−1.63436	−	0.258857i	−0.729316	−	0.684177i	$-0.760162\pi$
$277$	−125403.	−	19861.8i	−1.63436	−	0.258857i	−0.905043	+	0.425320i	$0.860162\pi$
$278$	15709.3	+	30831.2i	0.203267	+	0.398934i
$279$	34228.5	+	11121.5i	0.439723	+	0.142875i
$280$	6167.98	−	1845.87i	0.0786732	−	0.0235443i
$281$	−41862.6	−	128840.i	−0.530168	−	1.63169i	−0.753863	−	0.657031i	$-0.771812\pi$
$281$	−41862.6	−	128840.i	−0.530168	−	1.63169i	0.223695	−	0.974659i	$-0.428188\pi$
$282$	−92811.0	−	92811.0i	−1.16708	−	1.16708i
$283$	−10441.8	−	5320.35i	−0.130377	−	0.0664305i	0.387585	−	0.921834i	$-0.373309\pi$
$283$	−10441.8	−	5320.35i	−0.130377	−	0.0664305i	−0.517962	+	0.855403i	$0.673309\pi$
$284$	18470.8	−	25422.9i	0.229008	−	0.315202i
$285$	7057.75	−	6735.28i	0.0868914	−	0.0829213i
$286$	74685.0	−	54261.8i	0.913064	−	0.663380i
$287$	11135.2	+	70304.6i	0.135186	+	0.853532i
$288$	55994.2	−	8868.60i	0.675084	−	0.106923i
$289$	23919.4	+	32922.2i	0.286388	+	0.394179i
$290$	8547.61	−	15848.6i	0.101636	−	0.188449i
$291$	75676.9	+	54982.5i	0.893670	+	0.649290i
$292$	−68625.0	+	134684.i	−0.804853	+	1.57961i
$293$	−68155.7	+	68155.7i	−0.793903	+	0.793903i	−0.982126	−	0.188224i	$-0.939727\pi$
$293$	−68155.7	+	68155.7i	−0.793903	+	0.793903i	0.188224	+	0.982126i	$0.439727\pi$
$294$	212980.	−	69201.5i	2.46402	−	0.800610i
$295$	−58712.0	−	44790.2i	−0.674657	−	0.514682i
$296$	−1249.37	+	3845.18i	−0.0142597	+	0.0438867i
$297$	80941.7	−	41241.9i	0.917613	−	0.467547i
$298$	2999.57	−	18938.5i	0.0337774	−	0.213262i
$299$			45675.6i			0.510908i
$300$	−7364.66	−	66480.4i	−0.0818295	−	0.738671i
$301$	−129898.			−1.43373
$302$	−97765.9	−	15484.6i	−1.07195	−	0.169780i
$303$	−40178.9	−	78855.6i	−0.437636	−	0.858909i
$304$	−14177.3	−	4606.50i	−0.153408	−	0.0498452i
$305$	−23680.7	−	34249.5i	−0.254563	−	0.368175i
$306$	−14175.3	−	43627.2i	−0.151388	−	0.465923i
$307$	90740.0	+	90740.0i	0.962769	+	0.962769i	0.999331	−	0.0365623i	$-0.0116407\pi$
$307$	90740.0	+	90740.0i	0.962769	+	0.962769i	−0.0365623	+	0.999331i	$0.511641\pi$
$308$	−157763.	−	80384.4i	−1.66305	−	0.847365i
$309$	52370.9	−	72082.4i	0.548496	−	0.754939i
$310$	−130708.	+	17581.2i	−1.36013	+	0.182947i
$311$	43056.2	−	31282.2i	0.445159	−	0.323427i	−0.342522	−	0.939510i	$-0.611281\pi$
$311$	43056.2	−	31282.2i	0.445159	−	0.323427i	0.787682	+	0.616083i	$0.211281\pi$
$312$	394.358	+	2489.88i	0.00405118	+	0.0255781i
$313$	48791.8	−	7727.86i	0.498033	−	0.0788806i	0.0976354	−	0.995222i	$-0.468872\pi$
$313$	48791.8	−	7727.86i	0.498033	−	0.0788806i	0.400397	+	0.916342i	$0.368872\pi$
$314$	−35332.1	−	48630.4i	−0.358352	−	0.493229i
$315$	11916.7	+	88595.6i	0.120098	+	0.892876i
$316$	−53367.7	−	38773.9i	−0.534446	−	0.388298i
$317$	−33652.0	+	66045.7i	−0.334882	+	0.657243i	−0.995632	−	0.0933628i	$-0.970238\pi$
$317$	−33652.0	+	66045.7i	−0.334882	+	0.657243i	0.660750	+	0.750606i	$0.270238\pi$
$318$	50687.9	−	50687.9i	0.501245	−	0.501245i
$319$	−14032.2	+	4559.35i	−0.137894	+	0.0448045i
$320$	−89318.7	+	61756.7i	−0.872253	+	0.603092i
$321$	13140.4	−	40441.9i	0.127526	−	0.392484i
$322$	153789.	−	78359.6i	1.48325	−	0.755754i
$323$	−1946.74	+	12291.2i	−0.0186596	+	0.117812i
$324$			31315.3i			0.298309i
$325$	86161.1	−	9544.88i	0.815727	−	0.0903657i
$326$	296846.			2.79316
$327$	71221.7	+	11280.4i	0.666065	+	0.105494i
$328$	984.294	+	1931.79i	0.00914908	+	0.0179561i
$329$	−310304.	−	100824.i	−2.86679	−	0.931477i
$330$	−65493.3	+	85850.0i	−0.601408	+	0.788338i
$331$	37592.2	+	115697.i	0.343117	+	1.05600i	0.962584	+	0.270982i	$0.0873484\pi$
$331$	37592.2	+	115697.i	0.343117	+	1.05600i	−0.619468	+	0.785022i	$0.712652\pi$
$332$	130705.	+	130705.i	1.18581	+	1.18581i
$333$	−50018.2	−	25485.5i	−0.451066	−	0.229829i
$334$	24804.4	−	34140.3i	0.222349	−	0.306038i
$335$	−28664.4	−	15459.5i	−0.255419	−	0.137755i
$336$	−119672.	+	86946.7i	−1.06002	+	0.770149i
$337$	−16085.2	−	101558.i	−0.141634	−	0.894239i	−0.951505	−	0.307632i	$-0.900463\pi$
$337$	−16085.2	−	101558.i	−0.141634	−	0.894239i	0.809872	−	0.586607i	$-0.199537\pi$
$338$	52487.9	−	8313.26i	0.459437	−	0.0727676i
$339$	6194.90	+	8526.55i	0.0539058	+	0.0741949i
$340$	58904.3	+	61724.5i	0.509552	+	0.533949i
$341$	87426.4	+	63519.0i	0.751854	+	0.546254i
$342$	−6051.41	+	11876.6i	−0.0517374	+	0.101540i
$343$	237516.	−	237516.i	2.01885	−	2.01885i
$344$	−3762.89	+	1222.64i	−0.0317984	+	0.0103319i
$345$	−15317.4	−	51182.9i	−0.128690	−	0.430018i
$346$	−26210.6	+	80668.0i	−0.218940	+	0.673828i
$347$	−193855.	+	98774.1i	−1.60997	+	0.820322i	−0.610370	+	0.792117i	$0.708979\pi$
$347$	−193855.	+	98774.1i	−1.60997	+	0.820322i	−0.999602	+	0.0282050i	$0.991021\pi$
$348$	2115.45	−	13356.5i	0.0174681	−	0.110289i
$349$			62745.2i			0.515145i	0.966259	+	0.257573i	$0.0829227\pi$
$349$			62745.2i			0.515145i	−0.966259	+	0.257573i	$0.917077\pi$
$350$	−179953.	−	273729.i	−1.46900	−	2.23452i
$351$	−107909.			−0.875882
$352$	168130.	+	26629.2i	1.35694	+	0.214918i
$353$	−1465.85	−	2876.90i	−0.0117636	−	0.0230874i	0.885050	−	0.465496i	$-0.154124\pi$
$353$	−1465.85	−	2876.90i	−0.0117636	−	0.0230874i	−0.896814	+	0.442409i	$0.854124\pi$
$354$	−103916.	−	33764.5i	−0.829236	−	0.269435i
$355$	−44949.8	−	15775.8i	−0.356674	−	0.125180i
$356$	7943.74	+	24448.3i	0.0626794	+	0.192907i
$357$	87318.6	+	87318.6i	0.685125	+	0.685125i
$358$	−245414.	−	125045.i	−1.91484	−	0.975661i
$359$	6002.31	−	8261.48i	0.0465725	−	0.0641016i	−0.785096	−	0.619375i	$-0.787386\pi$
$359$	6002.31	−	8261.48i	0.0465725	−	0.0641016i	0.831668	+	0.555273i	$0.187386\pi$
$360$	1179.10	+	2454.29i	0.00909797	+	0.0189374i
$361$	−102506.	+	74475.3i	−0.786569	+	0.571476i
$362$	−15277.0	−	96455.1i	−0.116579	−	0.736051i
$363$	−6454.33	+	1022.27i	−0.0489821	+	0.00775801i
$364$	123627.	+	170157.i	0.933059	+	1.28425i
$365$	225429.	+	41127.1i	1.69209	+	0.308704i
$366$	−49843.4	−	36213.3i	−0.372088	−	0.270337i
$367$	22039.2	−	43254.3i	0.163630	−	0.321142i	−0.794604	−	0.607129i	$-0.792321\pi$
$367$	22039.2	−	43254.3i	0.163630	−	0.321142i	0.958234	+	0.285986i	$0.0923212\pi$
$368$	−57724.6	+	57724.6i	−0.426251	+	0.426251i
$369$	−28630.0	+	9302.46i	−0.210266	+	0.0683196i
$370$	205657.	+	4808.12i	1.50224	+	0.0351214i
$371$	55064.1	−	169470.i	0.400056	−	1.23125i
$372$	−88250.3	+	44965.8i	−0.637720	+	0.324935i
$373$	−31548.3	+	199188.i	−0.226756	+	1.43168i	0.567137	+	0.823624i	$0.308051\pi$
$373$	−31548.3	+	199188.i	−0.226756	+	1.43168i	−0.793893	+	0.608058i	$0.791949\pi$
$374$		−	137738.i		−	0.984716i
$375$	−93349.0	+	39589.9i	−0.663815	+	0.281528i
$376$	−9937.93			−0.0702943
$377$	17310.5	+	2741.71i	0.121794	+	0.0192903i
$378$	185126.	+	363330.i	1.29564	+	2.54283i
$379$	121054.	+	39332.8i	0.842754	+	0.273827i	0.698408	−	0.715700i	$-0.253892\pi$
$379$	121054.	+	39332.8i	0.842754	+	0.273827i	0.144346	+	0.989527i	$0.453892\pi$
$380$	579.464	−	24785.3i	0.00401291	−	0.171644i
$381$	−45.9447	−	141.403i	−0.000316509	−	0.000974113i
$382$	−175037.	−	175037.i	−1.19951	−	1.19951i
$383$	52697.7	+	26850.8i	0.359248	+	0.183046i	0.624293	−	0.781190i	$-0.285387\pi$
$383$	52697.7	+	26850.8i	0.359248	+	0.183046i	−0.265046	+	0.964236i	$0.585387\pi$
$384$	−5467.16	+	7524.90i	−0.0370765	+	0.0510315i
$385$	−48174.5	+	264058.i	−0.325009	+	1.78147i
$386$	−139075.	+	101044.i	−0.933412	+	0.678164i
$387$	−8593.80	−	54259.1i	−0.0573804	−	0.362285i
$388$	234788.	−	37186.7i	1.55960	−	0.247016i
$389$	29846.2	+	41079.8i	0.197238	+	0.271474i	0.896168	−	0.443716i	$-0.146340\pi$
$389$	29846.2	+	41079.8i	0.197238	+	0.271474i	−0.698930	+	0.715190i	$0.746340\pi$
$390$	115615.	−	55544.2i	0.760127	−	0.365182i
$391$	55134.1	+	40057.3i	0.360634	+	0.262016i
$392$	7697.71	−	15107.6i	0.0500944	−	0.0983158i
$393$	−7191.57	+	7191.57i	−0.0465628	+	0.0465628i
$394$	6435.15	−	2090.91i	0.0414540	−	0.0134692i
$395$	−33116.5	+	94358.4i	−0.212251	+	0.604765i
$396$	23139.8	−	71216.9i	0.147560	−	0.454143i
$397$	14808.5	−	7545.30i	0.0939571	−	0.0478735i	−0.406380	−	0.913704i	$-0.633209\pi$
$397$	14808.5	−	7545.30i	0.0939571	−	0.0478735i	0.500338	+	0.865830i	$0.333209\pi$
$398$	−35863.9	+	226436.i	−0.226408	+	1.42948i
$399$		−	35882.3i		−	0.225390i
$400$	120953.	+	96827.2i	0.755954	+	0.605170i
$401$	−43746.4			−0.272053			−0.136027	−	0.990705i	$-0.543433\pi$
$401$	−43746.4			−0.272053			−0.136027	+	0.990705i	$0.543433\pi$
$402$	−47594.3	−	7538.19i	−0.294512	−	0.0466461i
$403$	−58277.3	−	114376.i	−0.358831	−	0.704245i
$404$	−213899.	−	69499.9i	−1.31052	−	0.425815i
$405$	45479.4	−	13610.5i	0.277271	−	0.0829781i
$406$	−20466.0	−	62987.8i	−0.124160	−	0.382124i
$407$	−119189.	−	119189.i	−0.719526	−	0.719526i
$408$	3351.33	+	1707.59i	0.0201324	+	0.0102580i
$409$	97023.6	−	133542.i	0.580004	−	0.798307i	−0.413692	−	0.910417i	$-0.635761\pi$
$409$	97023.6	−	133542.i	0.580004	−	0.798307i	0.993696	+	0.112110i	$0.0357609\pi$
$410$	79805.6	−	76159.3i	0.474751	−	0.453059i
$411$	93478.8	−	67916.3i	0.553388	−	0.402060i
$412$	−35420.4	−	223636.i	−0.208670	−	1.31749i
$413$	−268266.	+	42489.1i	−1.57277	+	0.249102i
$414$	42905.8	+	59054.8i	0.250331	+	0.344552i
$415$	133015.	−	246631.i	0.772335	−	1.43203i
$416$	−163588.	−	118854.i	−0.945290	−	0.686793i
$417$	17884.6	−	35100.5i	0.102851	−	0.201856i
$418$	−28300.7	+	28300.7i	−0.161974	+	0.161974i
$419$	44593.4	−	14489.3i	0.254005	−	0.0825312i	−0.179247	−	0.983804i	$-0.557366\pi$
$419$	44593.4	−	14489.3i	0.254005	−	0.0825312i	0.433252	+	0.901273i	$0.357366\pi$
$420$	−195595.	−	149216.i	−1.10882	−	0.845894i
$421$	−66298.8	+	204047.i	−0.374060	+	1.15124i	0.570051	+	0.821610i	$0.306924\pi$
$421$	−66298.8	+	204047.i	−0.374060	+	1.15124i	−0.944111	+	0.329629i	$0.893076\pi$
$422$	208364.	−	106167.i	1.17003	−	0.596162i
$423$	21585.7	−	136287.i	0.120638	−	0.761679i
$424$		−	5427.51i		−	0.0301904i
$425$	64041.4	−	112374.i	0.354555	−	0.622141i
$426$	−70485.9			−0.388403
$427$	−151264.	−	23957.9i	−0.829623	−	0.131399i
$428$	−49059.4	−	96284.5i	−0.267815	−	0.525616i
$429$	−99954.9	−	32477.3i	−0.543112	−	0.176468i
$430$	114489.	+	165585.i	0.619193	+	0.895540i
$431$	−13747.8	−	42311.4i	−0.0740080	−	0.227773i	0.907209	−	0.420680i	$-0.138208\pi$
$431$	−13747.8	−	42311.4i	−0.0740080	−	0.227773i	−0.981217	+	0.192907i	$0.938208\pi$
$432$	−136375.	−	136375.i	−0.730749	−	0.730749i
$433$	24826.4	+	12649.7i	0.132415	+	0.0674690i	0.518943	−	0.854809i	$-0.326326\pi$
$433$	24826.4	+	12649.7i	0.132415	+	0.0674690i	−0.386528	+	0.922278i	$0.626326\pi$
$434$	−285123.	+	392438.i	−1.51375	+	2.08349i
$435$	−20317.1	+	2732.79i	−0.107370	+	0.0144420i
$436$	148252.	−	107711.i	0.779879	−	0.566615i
$437$	−3097.81	−	19558.8i	−0.0162215	−	0.102419i
$438$	334880.	−	53039.8i	1.74559	−	0.276474i
$439$	−17760.5	−	24445.3i	−0.0921567	−	0.126843i	0.760449	−	0.649398i	$-0.224979\pi$
$439$	−17760.5	−	24445.3i	−0.0921567	−	0.126843i	−0.852606	+	0.522555i	$0.824979\pi$
$440$	1089.87	+	8102.70i	0.00562950	+	0.0418528i
$441$	190463.	+	138379.i	0.979337	+	0.711530i
$442$	−74279.5	+	145782.i	−0.380211	+	0.746206i
$443$	−65192.3	+	65192.3i	−0.332192	+	0.332192i	−0.853418	−	0.521227i	$-0.825475\pi$
$443$	−65192.3	+	65192.3i	−0.332192	+	0.332192i	0.521227	+	0.853418i	$0.325475\pi$
$444$	146929.	−	47740.1i	0.745317	−	0.242168i
$445$	32053.9	−	22162.6i	0.161868	−	0.111918i
$446$	−21753.5	+	66950.3i	−0.109360	+	0.336576i
$447$	−19450.4	+	9910.50i	−0.0973452	+	0.0495999i
$448$	−62479.6	+	394481.i	−0.311302	+	1.96548i
$449$		−	265460.i		−	1.31676i	−0.752687	−	0.658379i	$-0.771242\pi$
$449$		−	265460.i		−	1.31676i	0.752687	−	0.658379i	$-0.228758\pi$
$450$	102433.	−	93276.9i	0.505842	−	0.460627i
$451$	−90389.6			−0.444391
$452$	26453.7	+	4189.85i	0.129482	+	0.0205079i
$453$	51160.7	+	100408.i	0.249310	+	0.489299i
$454$	612.627	+	199.054i	0.00297224	+	0.000965740i
$455$	193389.	−	253499.i	0.934134	−	1.22448i
$456$	−337.736	−	1039.44i	−0.00162423	−	0.00499887i
$457$	96808.0	+	96808.0i	0.463531	+	0.463531i	0.899811	−	0.436280i	$-0.143704\pi$
$457$	96808.0	+	96808.0i	0.463531	+	0.463531i	−0.436280	+	0.899811i	$0.643704\pi$
$458$	155867.	+	79418.2i	0.743059	+	0.378608i
$459$	−94636.1	+	130255.i	−0.449191	+	0.618259i
$460$	−119497.	−	64448.5i	−0.564733	−	0.304577i
$461$	−91860.3	+	66740.4i	−0.432241	+	0.314042i	−0.782544	−	0.622595i	$-0.786079\pi$
$461$	−91860.3	+	66740.4i	−0.432241	+	0.314042i	0.350303	+	0.936636i	$0.386079\pi$
$462$	62128.6	+	392264.i	0.291077	+	1.83779i
$463$	−103545.	+	16399.9i	−0.483021	+	0.0765030i	−0.393196	−	0.919455i	$-0.628631\pi$
$463$	−103545.	+	16399.9i	−0.483021	+	0.0765030i	−0.0898246	+	0.995958i	$0.528631\pi$
$464$	18411.9	+	25341.8i	0.0855191	+	0.117707i
$465$	103660.	+	108623.i	0.479408	+	0.502361i
$466$	−275261.	−	199989.i	−1.26757	−	0.920945i
$467$	74576.2	−	146364.i	0.341953	−	0.671121i	−0.654428	−	0.756125i	$-0.727090\pi$
$467$	74576.2	−	146364.i	0.341953	−	0.671121i	0.996381	+	0.0850040i	$0.0270903\pi$
$468$	−62897.0	+	62897.0i	−0.287169	+	0.287169i
$469$	−113922.	+	37015.6i	−0.517920	+	0.168282i
$470$	144971.	+	484420.i	0.656275	+	2.19294i
$471$	−21147.3	+	65084.7i	−0.0953264	+	0.293385i
$472$	−7371.24	+	3755.84i	−0.0330869	+	0.0168586i
$473$	25804.1	−	162921.i	0.115336	−	0.728205i
$474$			147963.i			0.658564i
$475$	−36247.7	+	9930.82i	−0.160655	+	0.0440147i
$476$	313813.			1.38503
$477$	74431.7	+	11788.8i	0.327131	+	0.0518124i
$478$	−136756.	−	268398.i	−0.598535	−	1.17469i
$479$	346857.	+	112701.i	1.51175	+	0.491197i	0.943419	−	0.331603i	$-0.107589\pi$
$479$	346857.	+	112701.i	1.51175	+	0.491197i	0.568331	+	0.822800i	$0.307589\pi$
$480$	223170.	+	78324.9i	0.968621	+	0.339952i
$481$	61873.0	+	190425.i	0.267430	+	0.823066i
$482$	307206.	+	307206.i	1.32232	+	1.32232i
$483$	−175085.	−	89210.2i	−0.750506	−	0.382402i
$484$	−9761.12	+	13435.0i	−0.0416686	+	0.0573519i
$485$	−156052.	−	324821.i	−0.663415	−	1.38090i
$486$	−233781.	+	169852.i	−0.989775	+	0.719114i
$487$	45535.9	+	287502.i	0.191998	+	1.21222i	0.875842	+	0.482597i	$0.160307\pi$
$487$	45535.9	+	287502.i	0.191998	+	1.21222i	−0.683845	+	0.729627i	$0.739693\pi$
$488$	−4607.35	+	729.733i	−0.0193469	+	0.00306425i
$489$	−198643.	−	273408.i	−0.830720	−	1.14339i
$490$	−848706.	−	154837.i	−3.53480	−	0.644887i
$491$	64476.5	+	46844.9i	0.267448	+	0.194312i	0.713424	−	0.700733i	$-0.247143\pi$
$491$	64476.5	+	46844.9i	0.267448	+	0.194312i	−0.445976	+	0.895045i	$0.647143\pi$
$492$	37611.1	−	73815.9i	0.155377	−	0.304944i
$493$	18490.7	−	18490.7i	0.0760779	−	0.0760779i
$494$	45215.5	−	14691.4i	0.185282	−	0.0602018i
$495$	−113486.	−	2653.22i	−0.463161	−	0.0108284i
$496$	70896.8	−	218198.i	0.288180	−	0.886926i
$497$	−156117.	+	79545.5i	−0.632029	+	0.322035i
$498$	64859.4	−	409506.i	0.261525	−	1.65121i
$499$		−	269090.i		−	1.08068i	−0.841448	−	0.540339i	$-0.818296\pi$
$499$		−	269090.i		−	1.08068i	0.841448	−	0.540339i	$-0.181704\pi$
$500$	−96602.2	+	238884.i	−0.386409	+	0.955536i
$501$	−48043.2			−0.191407
$502$	183900.	+	29126.9i	0.729751	+	0.115581i
$503$	−11902.8	−	23360.5i	−0.0470449	−	0.0923309i	0.866287	−	0.499546i	$-0.166500\pi$
$503$	−11902.8	−	23360.5i	−0.0470449	−	0.0923309i	−0.913332	+	0.407215i	$0.866500\pi$
$504$	9524.53	+	3094.71i	0.0374958	+	0.0121831i
$505$	−7968.91	+	340853.i	−0.0312476	+	1.33655i
$506$	67730.3	+	208452.i	0.264534	+	0.814152i
$507$	−42780.5	−	42780.5i	−0.166430	−	0.166430i
$508$	−336.654	−	171.534i	−0.00130454	−	0.000664695i
$509$	51369.8	−	70704.5i	0.198277	−	0.272905i	−0.698288	−	0.715817i	$-0.746055\pi$
$509$	51369.8	−	70704.5i	0.198277	−	0.272905i	0.896565	+	0.442912i	$0.146055\pi$
$510$	34347.6	−	188269.i	0.132056	−	0.723833i
$511$	681858.	−	495399.i	2.61127	−	1.89720i
$512$	−58272.8	−	367920.i	−0.222293	−	1.40350i
$513$	46208.0	−	7318.62i	0.175583	−	0.0278096i
$514$	−302320.	−	416108.i	−1.14430	−	1.57500i
$515$	−309393.	+	148640.i	−1.16653	+	0.560428i
$516$	122311.	+	88863.8i	0.459372	+	0.333753i
$517$	188097.	−	369162.i	0.703723	−	1.38113i
$518$	535013.	−	535013.i	1.99391	−	1.99391i
$519$	91838.2	−	29840.0i	0.340948	−	0.110781i
$520$	3216.12	−	9163.63i	0.0118939	−	0.0338892i
$521$	−142022.	+	437098.i	−0.523214	+	1.61029i	0.244606	+	0.969623i	$0.421341\pi$
$521$	−142022.	+	437098.i	−0.523214	+	1.61029i	−0.767820	+	0.640665i	$0.778659\pi$
$522$	24956.4	−	12715.9i	0.0915886	−	0.0466667i
$523$	−38170.2	+	240997.i	−0.139547	+	0.881066i	0.814228	+	0.580545i	$0.197160\pi$
$523$	−38170.2	+	240997.i	−0.139547	+	0.881066i	−0.953775	+	0.300521i	$0.902840\pi$
$524$			25845.7i			0.0941296i
$525$	−131696.	+	348917.i	−0.477808	+	1.26591i
$526$	−211139.			−0.763128
$527$	−189170.	−	29961.5i	−0.681130	−	0.107880i
$528$	−85277.8	−	167367.i	−0.305892	−	0.600347i
$529$	163007.	+	52964.3i	0.582500	+	0.189266i
$530$	−264562.	+	79174.7i	−0.941837	+	0.281861i
$531$	−35496.0	−	109245.i	−0.125890	−	0.387449i
$532$	−64478.6	−	64478.6i	−0.227820	−	0.227820i
$533$	95668.2	+	48745.4i	0.336754	+	0.171585i
$534$	33891.8	−	46648.1i	0.118854	−	0.163588i
$535$	−118512.	+	113097.i	−0.414052	+	0.395134i
$536$	−2951.71	+	2144.55i	−0.0102741	+	0.00746458i
$537$	49053.8	+	309714.i	0.170108	+	1.07402i
$538$	−532715.	+	84373.8i	−1.84048	+	0.291503i
$539$	415503.	+	571890.i	1.43020	+	1.96850i
$540$	152261.	−	282315.i	0.522156	−	0.968157i
$541$	−31333.1	−	22764.9i	−0.107056	−	0.0777805i	0.532969	−	0.846134i	$-0.321076\pi$
$541$	−31333.1	−	22764.9i	−0.107056	−	0.0777805i	−0.640025	+	0.768354i	$0.721076\pi$
$542$	−142009.	+	278709.i	−0.483413	+	0.948751i
$543$	−78616.3	+	78616.3i	−0.266632	+	0.266632i
$544$	−286932.	+	93229.8i	−0.969574	+	0.315034i
$545$	−220864.	−	168493.i	−0.743587	−	0.567268i
$546$	145784.	−	448677.i	0.489017	−	1.50504i
$547$	−155335.	+	79147.3i	−0.519153	+	0.264522i	−0.693874	−	0.720096i	$-0.744098\pi$
$547$	−155335.	+	79147.3i	−0.519153	+	0.264522i	0.174721	+	0.984618i	$0.444098\pi$
$548$	45934.4	−	290018.i	0.152960	−	0.965749i
$549$		−	64769.2i		−	0.214894i
$550$	379064.	−	171325.i	1.25311	−	0.566363i
$551$	−7598.47			−0.0250278
$552$	−5911.56	−	936.299i	−0.0194010	−	0.00307282i
$553$	166981.	+	327720.i	0.546032	+	1.07165i
$554$	688299.	+	223642.i	2.24263	+	0.728675i
$555$	−133192.	−	192636.i	−0.432408	−	0.625392i
$556$	−30936.0	−	95211.3i	−0.100073	−	0.307992i
$557$	−217154.	−	217154.i	−0.699935	−	0.699935i	0.264462	−	0.964396i	$-0.414806\pi$
$557$	−217154.	−	217154.i	−0.699935	−	0.699935i	−0.964396	+	0.264462i	$0.914806\pi$
$558$	−182787.	−	93134.9i	−0.587054	−	0.299119i
$559$	−115171.	+	158519.i	−0.368569	+	0.507292i
$560$	564774.	−	75966.1i	1.80094	−	0.242239i
$561$	−126863.	+	92171.1i	−0.403096	+	0.292866i
$562$	120798.	+	762690.i	0.382461	+	2.41477i
$563$	318857.	−	50501.9i	1.00596	−	0.159328i	0.368347	−	0.929688i	$-0.379924\pi$
$563$	318857.	−	50501.9i	1.00596	−	0.159328i	0.637608	+	0.770361i	$0.279924\pi$
$564$	223206.	+	307216.i	0.701693	+	0.965797i
$565$	−5412.54	−	40239.8i	−0.0169553	−	0.126055i
$566$	54042.4	+	39264.1i	0.168695	+	0.122564i
$567$	79269.2	−	155575.i	0.246569	−	0.483919i
$568$	−3773.71	+	3773.71i	−0.0116969	+	0.0116969i
$569$	−37780.2	+	12275.5i	−0.116692	+	0.0379154i	−0.366781	−	0.930307i	$-0.619540\pi$
$569$	−37780.2	+	12275.5i	−0.116692	+	0.0379154i	0.250089	+	0.968223i	$0.419540\pi$
$570$	−45740.5	+	31625.9i	−0.140783	+	0.0973403i
$571$	−60281.6	+	185528.i	−0.184890	+	0.569032i	−0.999946	−	0.0103492i	$-0.996706\pi$
$571$	−60281.6	+	185528.i	−0.184890	+	0.569032i	0.815057	+	0.579381i	$0.196706\pi$
$572$	−237974.	+	121254.i	−0.727339	+	0.370598i
$573$	−44086.0	+	278348.i	−0.134274	+	0.847771i
$574$		−	405740.i		−	1.23147i
$575$	−41662.1	+	201558.i	−0.126010	+	0.609627i
$576$	−168911.			−0.509111
$577$	−71465.0	−	11318.9i	−0.214655	−	0.0339981i	0.0481804	−	0.998839i	$-0.484658\pi$
$577$	−71465.0	−	11318.9i	−0.214655	−	0.0339981i	−0.262836	+	0.964841i	$0.584658\pi$
$578$	−105308.	−	206679.i	−0.315215	−	0.618643i
$579$	186131.	+	60477.7i	0.555216	+	0.180401i
$580$	−31598.0	+	41419.4i	−0.0939300	+	0.123125i
$581$	−318485.	−	980198.i	−0.943490	−	2.90376i
$582$	−377029.	−	377029.i	−1.11309	−	1.11309i
$583$	201615.	+	102728.i	0.593178	+	0.302239i
$584$	15089.3	−	20768.7i	0.0442429	−	0.0608952i
$585$	118682.	+	64008.9i	0.346797	+	0.187038i
$586$	444487.	−	322939.i	1.29439	−	0.940426i
$587$	−10210.8	−	64468.3i	−0.0296335	−	0.187098i	0.968431	−	0.249280i	$-0.0801941\pi$
$587$	−10210.8	−	64468.3i	−0.0296335	−	0.187098i	−0.998065	+	0.0621821i	$0.980194\pi$
$588$	−639919.	+	101353.i	−1.85085	+	0.293145i
$589$	32712.1	+	45024.4i	0.0942927	+	0.129783i
$590$	290606.	+	304519.i	0.834834	+	0.874804i
$591$	−6232.07	−	4527.86i	−0.0178426	−	0.0129634i
$592$	−162464.	+	318853.i	−0.463568	+	0.909803i
$593$	−407271.	+	407271.i	−1.15818	+	1.15818i	−0.173308	+	0.984868i	$0.555446\pi$
$593$	−407271.	+	407271.i	−1.15818	+	1.15818i	−0.984868	+	0.173308i	$0.944554\pi$
$594$	−492472.	+	160014.i	−1.39575	+	0.453508i
$595$	−136392.	−	455753.i	−0.385261	−	1.28735i
$596$	−17142.8	+	52760.0i	−0.0482601	+	0.148529i
$597$	232556.	−	118493.i	0.652498	−	0.332464i
$598$	40728.7	−	257151.i	0.113893	−	0.719095i
$599$			369137.i			1.02881i	0.857548	+	0.514404i	$0.171987\pi$
$599$			369137.i			1.02881i	−0.857548	+	0.514404i	$0.828013\pi$
$600$	−530.863	+	11347.0i	−0.00147462	+	0.0315196i
$601$	414496.			1.14755			0.573774	−	0.819013i	$-0.305479\pi$
$601$	414496.			1.14755			0.573774	+	0.819013i	$0.305479\pi$
$602$	731316.	+	115829.i	2.01796	+	0.319613i
$603$	−22998.6	−	45137.2i	−0.0632508	−	0.124137i
$604$	272362.	+	88495.6i	0.746573	+	0.242576i
$605$	23754.2	+	8336.91i	0.0648978	+	0.0227769i
$606$	155890.	+	479780.i	0.424495	+	1.30646i
$607$	134379.	+	134379.i	0.364716	+	0.364716i	0.865546	−	0.500830i	$-0.166972\pi$
$607$	134379.	+	134379.i	0.364716	+	0.364716i	−0.500830	+	0.865546i	$0.666972\pi$
$608$	78111.0	+	39799.5i	0.211303	+	0.107664i
$609$	−44319.1	+	61000.0i	−0.119497	+	0.164473i
$610$	102781.	+	213938.i	0.276219	+	0.574949i
$611$	−398164.	+	289283.i	−1.06655	+	0.774891i
$612$	20761.4	+	131082.i	0.0554310	+	0.349978i
$613$	261856.	−	41473.9i	0.696853	−	0.110371i	0.202049	−	0.979375i	$-0.435240\pi$
$613$	261856.	−	41473.9i	0.696853	−	0.110371i	0.494804	+	0.869005i	$0.335240\pi$
$614$	−429948.	−	591773.i	−1.14046	−	1.56971i
$615$	−123550.	−	22540.4i	−0.326658	−	0.0595952i
$616$	24327.5	+	17675.0i	0.0641116	+	0.0465798i
$617$	277401.	−	544430.i	0.728681	−	1.43012i	−0.167246	−	0.985915i	$-0.553487\pi$
$617$	277401.	−	544430.i	0.728681	−	1.43012i	0.895927	−	0.444202i	$-0.146513\pi$
$618$	−359121.	+	359121.i	−0.940293	+	0.940293i
$619$	−319102.	+	103682.i	−0.832814	+	0.270598i	−0.694230	−	0.719753i	$-0.744255\pi$
$619$	−319102.	+	103682.i	−0.832814	+	0.270598i	−0.138584	+	0.990351i	$0.544255\pi$
$620$	381461.	+	8918.31i	0.992355	+	0.0232006i
$621$	79171.1	−	243664.i	0.205297	−	0.631840i
$622$	−270298.	+	137724.i	−0.698655	+	0.355982i
$623$	22422.1	−	141567.i	0.0577697	−	0.364743i
$624$			223130.i			0.573044i
$625$	388919.	+	36470.4i	0.995632	+	0.0933641i
$626$	−281586.			−0.718558
$627$	45004.4	+	7128.00i	0.114477	+	0.0181314i
$628$	78953.2	+	154954.i	0.200194	+	0.392902i
$629$	284121.	+	92316.5i	0.718128	+	0.233334i
$630$	11909.8	−	509414.i	0.0300070	−	1.28348i
$631$	178459.	+	549242.i	0.448209	+	1.37945i	0.878925	+	0.476959i	$0.158261\pi$
$631$	178459.	+	549242.i	0.448209	+	1.37945i	−0.430716	+	0.902487i	$0.641739\pi$
$632$	7921.75	+	7921.75i	0.0198329	+	0.0198329i
$633$	−237217.	−	120868.i	−0.592022	−	0.301650i
$634$	248351.	−	341826.i	0.617857	−	0.850407i
$635$	−102.801	+	563.478i	−0.000254946	+	0.00139743i
$636$	−167783.	+	121902.i	−0.414796	+	0.301367i
$637$	−131358.	−	829360.i	−0.323725	−	2.04392i
$638$	83066.3	−	13156.4i	0.204072	−	0.0323218i
$639$	−43555.1	−	59948.5i	−0.106669	−	0.146817i
$640$	32298.5	−	15516.9i	0.0788537	−	0.0378831i
$641$	−522667.	−	379740.i	−1.27207	−	0.924209i	−0.272782	−	0.962076i	$-0.587944\pi$
$641$	−522667.	−	379740.i	−1.27207	−	0.924209i	−0.999283	+	0.0378663i	$0.987944\pi$
$642$	−110041.	+	215968.i	−0.266984	+	0.523986i
$643$	−53788.6	+	53788.6i	−0.130097	+	0.130097i	−0.769157	−	0.639060i	$-0.779324\pi$
$643$	−53788.6	+	53788.6i	−0.130097	+	0.130097i	0.639060	+	0.769157i	$0.279324\pi$
$644$	−474924.	+	154312.i	−1.14512	+	0.372073i
$645$	75898.0	−	216255.i	0.182436	−	0.519812i
$646$	21920.1	−	67463.0i	0.0525263	−	0.161659i
$647$	−570940.	+	290908.i	−1.36390	+	0.694941i	−0.974133	−	0.225974i	$-0.927444\pi$
$647$	−570940.	+	290908.i	−1.36390	+	0.694941i	−0.389764	+	0.920915i	$0.627444\pi$
$648$	831.964	−	5252.81i	0.00198132	−	0.0125096i
$649$		−	344905.i		−	0.818862i
$650$	−493593.	−	23092.4i	−1.16827	−	0.0546565i
$651$	552250.			1.30309
$652$	−848250.	−	134350.i	−1.99539	−	0.316039i
$653$	154024.	+	302290.i	0.361213	+	0.708920i	0.998072	−	0.0620596i	$-0.0197669\pi$
$653$	154024.	+	302290.i	0.361213	+	0.708920i	−0.636860	+	0.770980i	$0.719767\pi$
$654$	−390915.	−	127016.i	−0.913960	−	0.296964i
$655$	37535.9	−	11233.3i	0.0874912	−	0.0261832i
$656$	59300.8	+	182509.i	0.137801	+	0.424108i
$657$	252042.	+	252042.i	0.583905	+	0.583905i
$658$	1.65709e6	+	844330.i	3.82732	+	1.95011i
$659$	506476.	−	697104.i	1.16624	−	1.60519i	0.481391	−	0.876506i	$-0.340132\pi$
$659$	506476.	−	697104.i	1.16624	−	1.60519i	0.684849	−	0.728685i	$-0.259868\pi$
$660$	226004.	−	215678.i	0.518835	−	0.495129i
$661$	175333.	−	127387.i	0.401291	−	0.291555i	−0.368776	−	0.929518i	$-0.620223\pi$
$661$	175333.	−	127387.i	0.401291	−	0.291555i	0.770067	+	0.637963i	$0.220223\pi$
$662$	−108475.	−	684887.i	−0.247523	−	1.56280i
$663$	183977.	−	29139.2i	0.418540	−	0.0662903i
$664$	−18451.9	−	25396.8i	−0.0418509	−	0.0576028i
$665$	−65618.5	+	121667.i	−0.148383	+	0.275124i
$666$	258874.	+	188083.i	0.583634	+	0.424035i
$667$	−18891.2	+	37076.2i	−0.0424628	+	0.0833380i
$668$	−86331.1	+	86331.1i	−0.193470	+	0.193470i
$669$	76221.1	−	24765.7i	0.170303	−	0.0553349i
$670$	147594.	+	112596.i	0.328789	+	0.250827i
$671$	60097.2	−	184960.i	0.133478	−	0.410802i
$672$	775101.	−	394934.i	1.71640	−	0.874552i
$673$	131589.	−	830818.i	0.290528	−	1.83432i	−0.221265	−	0.975214i	$-0.571019\pi$
$673$	131589.	−	830818.i	0.290528	−	1.83432i	0.511793	−	0.859109i	$-0.328981\pi$
$674$			586107.i			1.29020i
$675$	−476184.	−	98427.4i	−1.04512	−	0.216027i
$676$	−153749.			−0.336448
$677$	465677.	+	73755.9i	1.01603	+	0.160924i	0.642171	−	0.766561i	$-0.278034\pi$
$677$	465677.	+	73755.9i	1.01603	+	0.160924i	0.373860	+	0.927485i	$0.378034\pi$
$678$	−27273.9	−	53527.9i	−0.0593317	−	0.116445i
$679$	−1.26056e6	−	409580.i	−2.73416	−	0.888382i
$680$	−8240.72	−	11918.6i	−0.0178216	−	0.0257754i
$681$	−226.618	−	697.458i	−0.000488652	−	0.00150392i
$682$	−435566.	−	435566.i	−0.936451	−	0.936451i
$683$	−395311.	−	201421.i	−0.847418	−	0.431781i	−0.0243360	−	0.999704i	$-0.507747\pi$
$683$	−395311.	−	201421.i	−0.847418	−	0.431781i	−0.823082	+	0.567923i	$0.807747\pi$
$684$	22667.4	−	31198.9i	0.0484494	−	0.0666849i
$685$	−441160.	+	59339.1i	−0.940188	+	0.126462i
$686$	−1.54899e6	+	1.12541e6i	−3.29156	+	2.39146i
$687$	−31155.0	−	196705.i	−0.0660108	−	0.416776i
$688$	−345888.	+	54783.3i	−0.730732	+	0.115737i
$689$	−157989.	−	217454.i	−0.332805	−	0.458067i
$690$	40596.3	+	301815.i	0.0852684	+	0.633932i
$691$	86394.0	+	62768.9i	0.180937	+	0.131458i	0.674567	−	0.738214i	$-0.264330\pi$
$691$	86394.0	+	62768.9i	0.180937	+	0.131458i	−0.493630	+	0.869672i	$0.664330\pi$
$692$	111407.	−	218649.i	0.232649	−	0.456600i
$693$	−295231.	+	295231.i	−0.614747	+	0.614747i
$694$	1.17947e6	−	383233.i	2.44888	−	0.795690i
$695$	−124830.	+	86310.0i	−0.258434	+	0.178686i
$696$	−709.691	+	2184.20i	−0.00146504	+	0.00450894i
$697$	142740.	−	72729.7i	0.293819	−	0.149708i
$698$	55949.6	−	353252.i	0.114838	−	0.725059i
$699$			387355.i			0.792784i
$700$	390335.	+	863635.i	0.796602	+	1.76252i
$701$	−238002.			−0.484334			−0.242167	−	0.970235i	$-0.577858\pi$
$701$	−238002.			−0.484334			−0.242167	+	0.970235i	$0.577858\pi$
$702$	607524.	+	96222.3i	1.23279	+	0.195255i
$703$	−39409.6	−	77345.8i	−0.0797429	−	0.156504i
$704$	−482355.	−	156727.i	−0.973243	−	0.316226i
$705$	349161.	−	457687.i	0.702501	−	0.920854i
$706$	5687.35	+	17503.9i	0.0114104	+	0.0351176i
$707$	886722.	+	886722.i	1.77398	+	1.77398i
$708$	281664.	+	143515.i	0.561907	+	0.286306i
$709$	−406908.	+	560061.i	−0.809476	+	1.11415i	0.181928	+	0.983312i	$0.441766\pi$
$709$	−406908.	+	560061.i	−0.809476	+	1.11415i	−0.991404	+	0.130836i	$0.958234\pi$
$710$	238998.	+	128898.i	0.474108	+	0.255700i
$711$	−125844.	+	91430.7i	−0.248938	+	0.180864i
$712$	−682.952	−	4311.99i	−0.00134720	−	0.00850585i
$713$	301022.	−	47677.1i	0.592132	−	0.0937845i
$714$	−413737.	−	569460.i	−0.811573	−	1.11703i
$715$	279527.	+	292910.i	0.546779	+	0.572958i
$716$	644686.	+	468392.i	1.25754	+	0.913657i
$717$	−155692.	+	305564.i	−0.302851	+	0.594379i
$718$	−41159.4	+	41159.4i	−0.0798399	+	0.0798399i
$719$	126644.	−	41149.2i	0.244978	−	0.0795982i	−0.183954	−	0.982935i	$-0.558890\pi$
$719$	126644.	−	41149.2i	0.244978	−	0.0795982i	0.428932	+	0.903337i	$0.358890\pi$
$720$	69096.1	+	230884.i	0.133287	+	0.445379i
$721$	−390126.	+	1.20068e6i	−0.750472	+	2.30971i
$722$	643514.	−	327887.i	1.23448	−	0.628999i
$723$	77374.8	−	488525.i	0.148021	−	0.934567i
$724$			282538.i			0.539015i
$725$	73887.0	+	27888.0i	0.140570	+	0.0530569i
$726$	37249.0			0.0706711
$727$	−221803.	−	35130.2i	−0.419662	−	0.0664679i	−0.0569673	−	0.998376i	$-0.518143\pi$
$727$	−221803.	−	35130.2i	−0.419662	−	0.0664679i	−0.362694	+	0.931908i	$0.618143\pi$
$728$	−16216.4	−	31826.6i	−0.0305980	−	0.0600519i
$729$	459164.	+	149191.i	0.863998	+	0.280730i
$730$	−1.23248e6	−	432557.i	−2.31278	−	0.811704i
$731$	90341.0	+	278041.i	0.169064	+	0.520324i
$732$	126040.	+	126040.i	0.235226	+	0.235226i
$733$	712382.	+	362977.i	1.32588	+	0.675570i	0.966270	−	0.257532i	$-0.0829092\pi$
$733$	712382.	+	362977.i	1.32588	+	0.675570i	0.359612	+	0.933102i	$0.382909\pi$
$734$	−162649.	+	223867.i	−0.301897	+	0.415526i
$735$	425322.	+	885308.i	0.787306	+	1.63878i
$736$	388397.	−	282187.i	0.717003	−	0.520933i
$737$	−23795.2	−	150237.i	−0.0438081	−	0.276593i
$738$	169480.	−	26843.0i	0.311176	−	0.0492855i
$739$	−383656.	−	528058.i	−0.702512	−	0.966925i	−0.999926	−	0.0121760i	$-0.996124\pi$
$739$	−383656.	−	528058.i	−0.702512	−	0.966925i	0.297414	−	0.954749i	$-0.403876\pi$
$740$	−585497.	−	106818.i	−1.06921	−	0.195065i
$741$	−43788.6	−	31814.3i	−0.0797489	−	0.0579410i
$742$	−461123.	+	905005.i	−0.837547	+	1.64378i
$743$	291918.	−	291918.i	0.528790	−	0.528790i	−0.391422	−	0.920211i	$-0.628017\pi$
$743$	291918.	−	291918.i	0.528790	−	0.528790i	0.920211	+	0.391422i	$0.128017\pi$
$744$	15997.7	−	5197.96i	0.0289009	−	0.00939047i
$745$	84074.4	+	1965.60i	0.151479	+	0.00354147i
$746$	355231.	−	1.09329e6i	0.638312	−	1.96452i
$747$	388365.	−	197882.i	0.695983	−	0.354621i
$748$	−62338.8	+	393592.i	−0.111418	+	0.703466i
$749$			602527.i			1.07402i
$750$	560851.	−	139650.i	0.997069	−	0.248267i
$751$	−417464.			−0.740182			−0.370091	−	0.928995i	$-0.620674\pi$
$751$	−417464.			−0.740182			−0.370091	+	0.928995i	$0.620674\pi$
$752$	−868791.	−	137603.i	−1.53631	−	0.243328i
$753$	−96234.7	−	188871.i	−0.169723	−	0.333101i
$754$	−95012.2	−	30871.3i	−0.167123	−	0.0543016i
$755$	10147.0	−	434015.i	0.0178009	−	0.761397i
$756$	−364565.	−	1.12202e6i	−0.637869	−	1.96316i
$757$	−282010.	−	282010.i	−0.492122	−	0.492122i	0.416852	−	0.908974i	$-0.363133\pi$
$757$	−282010.	−	282010.i	−0.492122	−	0.492122i	−0.908974	+	0.416852i	$0.863133\pi$
$758$	−646454.	−	329385.i	−1.12512	−	0.573278i
$759$	146670.	−	201874.i	0.254600	−	0.350426i
$760$	−755.679	+	4142.08i	−0.00130831	+	0.00717120i
$761$	814649.	−	591877.i	1.40670	−	1.02203i	0.412907	−	0.910773i	$-0.364513\pi$
$761$	814649.	−	591877.i	1.40670	−	1.02203i	0.993792	−	0.111253i	$-0.0354865\pi$
$762$	132.577	+	837.060i	0.000228328	+	0.00144161i
$763$	−1.00917e6	+	159836.i	−1.73346	+	0.274553i
$764$	420956.	+	579396.i	0.721191	+	0.992634i
$765$	181348.	−	87123.7i	0.309877	−	0.148872i
$766$	−272742.	−	198159.i	−0.464831	−	0.337719i
$767$	−186001.	+	365047.i	−0.316173	+	0.620524i
$768$	−281414.	+	281414.i	−0.477115	+	0.477115i
$769$	−173272.	+	56299.3i	−0.293005	+	0.0952030i	−0.451831	−	0.892104i	$-0.649229\pi$
$769$	−173272.	+	56299.3i	−0.293005	+	0.0952030i	0.158826	+	0.987307i	$0.449229\pi$
$770$	506679.	−	1.44367e6i	0.854577	−	2.43493i
$771$	−180948.	+	556899.i	−0.304400	+	0.936846i
$772$	443143.	−	225793.i	0.743548	−	0.378857i
$773$	17323.2	−	109374.i	0.0289914	−	0.183045i	−0.968943	−	0.247284i	$-0.920462\pi$
$773$	17323.2	−	109374.i	0.0289914	−	0.183045i	0.997935	+	0.0642391i	$0.0204620\pi$
$774$			313139.i			0.522703i
$775$	−152841.	−	557875.i	−0.254471	−	0.928824i
$776$	−40371.2			−0.0670421
$777$	−850788.	−	134752.i	−1.40922	−	0.223199i
$778$	−131402.	−	257890.i	−0.217091	−	0.426065i
$779$	−44272.1	−	14384.9i	−0.0729550	−	0.0237045i
$780$	−355514.	+	106394.i	−0.584342	+	0.174874i
$781$	−68755.3	−	211607.i	−0.112721	−	0.346919i
$782$	−274683.	−	274683.i	−0.449178	−	0.449178i
$783$	−87593.0	−	44630.9i	−0.142872	−	0.0727967i
$784$	882131.	−	1.21415e6i	1.43516	−	1.97533i
$785$	190726.	−	182012.i	0.309507	−	0.295365i
$786$	46900.8	−	34075.4i	0.0759164	−	0.0551565i
$787$	−37473.3	−	236597.i	−0.0605023	−	0.381997i	−0.999296	−	0.0375167i	$-0.988055\pi$
$787$	−37473.3	−	236597.i	−0.0605023	−	0.381997i	0.938794	−	0.344480i	$-0.111945\pi$
$788$	−19335.0	+	3062.37i	−0.0311381	+	0.00493179i
$789$	141289.	+	194468.i	0.226963	+	0.312388i
$790$	270583.	−	501702.i	0.433557	−	0.803881i
$791$	−120816.	−	87778.0i	−0.193095	−	0.140292i
$792$	−5773.50	+	11331.1i	−0.00920425	+	0.0180644i
$793$	−163352.	+	163352.i	−0.259764	+	0.259764i
$794$	−90099.0	+	29274.9i	−0.142915	+	0.0464360i
$795$	249962.	+	190691.i	0.395494	+	0.301715i
$796$	204965.	−	630817.i	0.323484	−	0.995582i
$797$	−990532.	+	504701.i	−1.55938	+	0.794544i	−0.999423	−	0.0339781i	$-0.989182\pi$
$797$	−990532.	+	504701.i	−1.55938	+	0.794544i	−0.559957	+	0.828522i	$0.689182\pi$
$798$	−31996.1	+	202015.i	−0.0502448	+	0.317233i
$799$			734315.i			1.15024i
$800$	−613473.	−	673692.i	−0.958552	−	1.05264i
$801$	60617.1			0.0944779
$802$	246290.	+	39008.5i	0.382911	+	0.0606471i
$803$	485890.	+	953613.i	0.753541	+	1.47891i
$804$	132591.	+	43081.4i	0.205117	+	0.0666465i
$805$	430523.	+	622667.i	0.664362	+	0.960869i
$806$	226110.	+	695894.i	0.348056	+	1.07121i
$807$	434192.	+	434192.i	0.666707	+	0.666707i
$808$	34032.8	+	17340.6i	0.0521285	+	0.0265608i
$809$	438593.	−	603672.i	0.670139	−	0.922367i	−0.329625	−	0.944112i	$-0.606922\pi$
$809$	438593.	−	603672.i	0.670139	−	0.922367i	0.999764	+	0.0217452i	$0.00692224\pi$
$810$	−268183.	+	36072.5i	−0.408753	+	0.0549801i
$811$	815516.	−	592507.i	1.23991	−	0.900849i	0.242319	−	0.970197i	$-0.422092\pi$
$811$	815516.	−	592507.i	1.23991	−	0.900849i	0.997593	+	0.0693480i	$0.0220919\pi$
$812$	29974.7	+	189253.i	0.0454614	+	0.287032i
$813$	351732.	−	55708.9i	0.532146	−	0.0842837i
$814$	564746.	+	777306.i	0.852323	+	1.17312i
$815$	173556.	+	1.29031e6i	0.261291	+	1.94258i
$816$	269335.	+	195684.i	0.404495	+	0.293883i
$817$	38566.3	−	75690.6i	0.0577782	−	0.113396i
$818$	−665316.	+	665316.i	−0.994309	+	0.994309i
$819$	471685.	−	153260.i	0.703209	−	0.228486i
$820$	−262517.	+	181509.i	−0.390417	+	0.269942i
$821$	238935.	−	735367.i	0.354482	−	1.09098i	−0.601828	−	0.798626i	$-0.705561\pi$
$821$	238935.	−	735367.i	0.354482	−	1.09098i	0.956309	−	0.292357i	$-0.0944394\pi$
$822$	−586841.	+	299010.i	−0.868514	+	0.442530i
$823$	−43983.0	+	277698.i	−0.0649360	+	0.409990i	0.933713	+	0.358023i	$0.116549\pi$
$823$	−43983.0	+	277698.i	−0.0649360	+	0.409990i	−0.998649	+	0.0519668i	$0.983451\pi$
$824$			38453.6i			0.0566347i
$825$	−411459.	−	234488.i	−0.604530	−	0.344519i
$826$	1.54821e6			2.26918
$827$	−721870.	−	114333.i	−1.05547	−	0.167171i	−0.395506	−	0.918464i	$-0.629431\pi$
$827$	−721870.	−	114333.i	−1.05547	−	0.167171i	−0.659969	+	0.751293i	$0.729431\pi$
$828$	−95877.4	−	188170.i	−0.139848	−	0.274467i
$829$	264510.	+	85944.6i	0.384887	+	0.125057i	0.495068	−	0.868854i	$-0.335143\pi$
$829$	264510.	+	85944.6i	0.384887	+	0.125057i	−0.110181	+	0.993912i	$0.535143\pi$
$830$	−968789.	+	1.26991e6i	−1.40628	+	1.84339i
$831$	−254610.	−	783609.i	−0.368700	−	1.13474i
$832$	426004.	+	426004.i	0.615414	+	0.615414i
$833$	−1.11630e6	−	568785.i	−1.60876	−	0.819706i
$834$	−131988.	+	181666.i	−0.189759	+	0.261181i
$835$	162901.	+	87857.3i	0.233642	+	0.126010i
$836$	93679.1	−	68061.9i	0.134039	−	0.0973848i
$837$	112638.	+	711168.i	0.160781	+	1.01513i
$838$	−263978.	+	41810.0i	−0.375906	+	0.0595377i
$839$	−204811.	−	281898.i	−0.290957	−	0.400468i	0.638367	−	0.769732i	$-0.279610\pi$
$839$	−204811.	−	281898.i	−0.290957	−	0.400468i	−0.929325	+	0.369263i	$0.879610\pi$
$840$	28844.8	+	30225.8i	0.0408798	+	0.0428370i
$841$	−559285.	−	406344.i	−0.790753	−	0.574516i
$842$	555206.	−	1.08965e6i	0.783122	−	1.53696i
$843$	621635.	−	621635.i	0.874742	−	0.874742i
$844$	−643459.	+	209072.i	−0.903308	+	0.293503i
$845$	66823.4	+	223290.i	0.0935869	+	0.312720i
$846$	−243052.	+	748037.i	−0.339593	+	1.04516i
$847$	82501.7	−	42036.7i	0.115000	−	0.0585952i
$848$	75150.7	−	474483.i	0.104506	−	0.659825i
$849$		−	76050.1i		−	0.105508i
$850$	−460753.	+	575554.i	−0.637720	+	0.796615i
$851$	−475382.			−0.656423
$852$	201416.	+	31901.2i	0.277469	+	0.0439468i
$853$	−434553.	−	852859.i	−0.597235	−	1.17214i	−0.969747	−	0.244112i	$-0.921504\pi$
$853$	−434553.	−	852859.i	−0.597235	−	1.17214i	0.372512	−	0.928027i	$-0.378496\pi$
$854$	830246.	+	269763.i	1.13839	+	0.369886i
$855$	−55162.3	−	19360.0i	−0.0754588	−	0.0264834i
$856$	5671.18	+	17454.1i	0.00773973	+	0.0238204i
$857$	609755.	+	609755.i	0.830221	+	0.830221i	0.987547	−	0.157326i	$-0.0502873\pi$
$857$	609755.	+	609755.i	0.830221	+	0.830221i	−0.157326	+	0.987547i	$0.550287\pi$
$858$	533781.	+	271975.i	0.725084	+	0.369449i
$859$	4794.83	−	6599.52i	0.00649811	−	0.00894388i	−0.805756	−	0.592248i	$-0.798240\pi$
$859$	4794.83	−	6599.52i	0.00649811	−	0.00894388i	0.812254	+	0.583304i	$0.198240\pi$
$860$	−252214.	−	524983.i	−0.341014	−	0.709820i
$861$	−373704.	+	271512.i	−0.504105	+	0.366254i
$862$	39670.5	+	250469.i	0.0533891	+	0.337086i
$863$	−739030.	+	117051.i	−0.992294	+	0.157164i	−0.631412	−	0.775448i	$-0.717524\pi$
$863$	−739030.	+	117051.i	−0.992294	+	0.157164i	−0.360882	+	0.932611i	$0.617524\pi$
$864$	666672.	+	917596.i	0.893069	+	1.22920i
$865$	−365966.	−	66766.6i	−0.489113	−	0.0892334i
$866$	−128492.	−	93354.6i	−0.171332	−	0.124480i
$867$	−119890.	+	235298.i	−0.159495	+	0.313026i
$868$	992364.	−	992364.i	1.31714	−	1.31714i
$869$	−444204.	+	144331.i	−0.588224	+	0.191126i
$870$	116821.	+	2731.19i	0.154341	+	0.00360839i
$871$	−55835.1	+	171843.i	−0.0735989	+	0.226514i
$872$	−27729.3	+	14128.8i	−0.0364675	+	0.0185811i
$873$	87688.1	−	553641.i	0.115057	−	0.726440i
$874$			112877.i			0.147769i
$875$	1.08461e6	−	942245.i	1.41664	−	1.23069i
$876$	−980938.			−1.27830
$877$	732926.	+	116084.i	0.952930	+	0.150929i	0.613494	−	0.789700i	$-0.289764\pi$
$877$	732926.	+	116084.i	0.952930	+	0.150929i	0.339437	+	0.940629i	$0.389764\pi$
$878$	78193.0	+	153462.i	0.101433	+	0.199073i
$879$	−594881.	−	193288.i	−0.769932	−	0.250166i
$880$	−16913.6	+	723443.i	−0.0218409	+	0.934198i
$881$	340441.	+	1.04777e6i	0.438622	+	1.34994i	0.889329	+	0.457268i	$0.151172\pi$
$881$	340441.	+	1.04777e6i	0.438622	+	1.34994i	−0.450707	+	0.892672i	$0.648828\pi$
$882$	−948901.	−	948901.i	−1.21979	−	1.21979i
$883$	194597.	+	99151.9i	0.249582	+	0.127169i	0.574307	−	0.818640i	$-0.305272\pi$
$883$	194597.	+	99151.9i	0.249582	+	0.127169i	−0.324725	+	0.945809i	$0.605272\pi$
$884$	278236.	−	382959.i	0.356048	−	0.490058i
$885$	86008.8	−	471438.i	0.109814	−	0.601919i
$886$	425160.	−	308897.i	0.541608	−	0.393501i
$887$	171191.	+	1.08086e6i	0.217587	+	1.37379i	0.818514	+	0.574487i	$0.194798\pi$
$887$	171191.	+	1.08086e6i	0.217587	+	1.37379i	−0.600927	+	0.799304i	$0.705202\pi$
$888$	−25914.1	+	4104.39i	−0.0328632	+	0.00520502i
$889$	1238.29	+	1704.36i	0.00156682	+	0.00215654i
$890$	−200224.	+	96192.1i	−0.252776	+	0.121439i
$891$	179378.	+	130326.i	0.225951	+	0.164163i
$892$	92462.5	−	181468.i	0.116208	−	0.228071i
$893$	150878.	−	150878.i	0.189201	−	0.189201i
$894$	118342.	−	38451.7i	0.148069	−	0.0481105i
$895$	400050.	−	1.13986e6i	0.499423	−	1.42300i
$896$	40726.4	−	125343.i	0.0507294	−	0.156129i
$897$	−264102.	+	134567.i	−0.328236	+	0.167245i
$898$	−236709.	+	1.49452e6i	−0.293537	+	1.85332i
$899$		−	116945.i		−	0.144698i
$900$	−334923.	+	220182.i	−0.413485	+	0.271830i
$901$	−401040.			−0.494013
$902$	508888.	+	80600.0i	0.625474	+	0.0990653i
$903$	−382696.	−	751083.i	−0.469330	−	0.921112i
$904$	−4326.01	−	1405.61i	−0.00529360	−	0.00171999i
$905$	410332.	−	122799.i	0.501001	−	0.149933i
$906$	−198498.	−	610913.i	−0.241824	−	0.744258i
$907$	−847613.	−	847613.i	−1.03035	−	1.03035i	−0.999525	−	0.0308213i	$-0.990188\pi$
$907$	−847613.	−	847613.i	−1.03035	−	1.03035i	−0.0308213	−	0.999525i	$-0.509812\pi$
$908$	−1660.51	−	846.074i	−0.00201405	−	0.00102621i
$909$	−311726.	+	429054.i	−0.377264	+	0.519259i
$910$	−1.31481e6	+	1.25474e6i	−1.58775	+	1.51520i
$911$	−259451.	+	188503.i	−0.312622	+	0.227133i	−0.733021	−	0.680206i	$-0.761890\pi$
$911$	−259451.	+	188503.i	−0.312622	+	0.227133i	0.420399	+	0.907339i	$0.361890\pi$
$912$	−15133.1	−	95546.5i	−0.0181944	−	0.114875i
$913$	1.29265e6	−	204736.i	1.55075	−	0.245614i
$914$	−458700.	−	631346.i	−0.549081	−	0.755745i
$915$	128268.	−	237828.i	0.153206	−	0.284067i
$916$	−409452.	−	297485.i	−0.487992	−	0.354547i
$917$	65423.9	−	128402.i	0.0778033	−	0.152698i
$918$	648943.	−	648943.i	0.770054	−	0.770054i
$919$	930915.	−	302473.i	1.10225	−	0.358142i	0.299280	−	0.954165i	$-0.403253\pi$
$919$	930915.	−	302473.i	1.10225	−	0.358142i	0.802967	+	0.596023i	$0.203253\pi$
$920$	18332.2	+	13985.3i	0.0216590	+	0.0165233i
$921$	−257337.	+	792002.i	−0.303377	+	0.933699i
$922$	576680.	−	293833.i	0.678380	−	0.345652i
$923$	−41345.1	+	261043.i	−0.0485312	+	0.306414i
$924$		−	1.14903e6i		−	1.34582i
$925$	99341.0	+	896747.i	0.116103	+	1.04806i
$926$	597574.			0.696899
$927$	−527344.	−	83523.1i	−0.613669	−	0.0971957i
$928$	−83631.5	−	164136.i	−0.0971122	−	0.190594i
$929$	−813861.	−	264439.i	−0.943015	−	0.306404i	−0.203141	−	0.979149i	$-0.565115\pi$
$929$	−813861.	−	264439.i	−0.943015	−	0.306404i	−0.739874	+	0.672745i	$0.765115\pi$
$930$	−486741.	−	703974.i	−0.562772	−	0.813937i
$931$	112497.	+	346232.i	0.129791	+	0.399455i
$932$	696056.	+	696056.i	0.801332	+	0.801332i
$933$	307727.	+	156795.i	0.353510	+	0.180123i
$934$	−550372.	+	757522.i	−0.630903	+	0.868363i
$935$	598710.	−	80530.7i	0.684847	−	0.0921167i
$936$	12221.3	−	8879.31i	0.0139497	−	0.0101351i
$937$	174473.	+	1.10158e6i	0.198724	+	1.25469i	0.862229	+	0.506520i	$0.169068\pi$
$937$	174473.	+	1.10158e6i	0.198724	+	1.25469i	−0.663505	+	0.748172i	$0.730932\pi$
$938$	674382.	−	106812.i	0.766479	−	0.121398i
$939$	188431.	+	259352.i	0.213708	+	0.294143i
$940$	−195017.	−	1.44986e6i	−0.220707	−	1.64086i
$941$	837612.	+	608561.i	0.945940	+	0.687266i	0.949843	−	0.312727i	$-0.101242\pi$
$941$	837612.	+	608561.i	0.945940	+	0.687266i	−0.00390327	+	0.999992i	$0.501242\pi$
$942$	177094.	−	347566.i	0.199573	−	0.391684i
$943$	−180259.	+	180259.i	−0.202709	+	0.202709i
$944$	−696411.	+	226278.i	−0.781487	+	0.253921i
$945$	−1.47106e6	+	1.01712e6i	−1.64728	+	1.13896i
$946$	−290551.	+	894223.i	−0.324668	+	0.999226i
$947$	1.49490e6	−	761689.i	1.66691	−	0.849332i	0.672936	−	0.739701i	$-0.265033\pi$
$947$	1.49490e6	−	761689.i	1.66691	−	0.849332i	0.993972	−	0.109632i	$-0.0349671\pi$
$948$	66966.7	−	422811.i	0.0745148	−	0.470468i
$949$		−	1.27133e6i		−	1.41165i
$950$	212928.	−	23588.0i	0.235931	−	0.0261363i
$951$	−481028.			−0.531874
$952$	−52638.9	−	8337.19i	−0.0580809	−	0.00919910i
$953$	−173902.	−	341301.i	−0.191478	−	0.375796i	0.775230	−	0.631679i	$-0.217634\pi$
$953$	−173902.	−	341301.i	−0.191478	−	0.375796i	−0.966708	+	0.255883i	$0.917634\pi$
$954$	−408534.	−	132741.i	−0.448881	−	0.145850i
$955$	658502.	−	863179.i	0.722022	−	0.946442i
$956$	269310.	+	828852.i	0.294671	+	0.906904i
$957$	−67703.6	−	67703.6i	−0.0739245	−	0.0739245i
$958$	−1.85229e6	−	943790.i	−2.01827	−	1.02836i
$959$	−962333.	+	1.32454e6i	−1.04638	+	1.44021i
$960$	−620230.	−	334508.i	−0.672992	−	0.362964i
$961$	54191.6	−	39372.5i	0.0586793	−	0.0426330i
$962$	−178540.	−	1.12726e6i	−0.192923	−	1.21807i
$963$	−251680.	+	39862.1i	−0.271391	+	0.0429841i
$964$	−738815.	−	1.01689e6i	−0.795027	−	1.09426i
$965$	−520522.	−	545443.i	−0.558965	−	0.585727i
$966$	906169.	+	658371.i	0.971080	+	0.705531i
$967$	−177522.	+	348406.i	−0.189845	+	0.372592i	−0.966236	−	0.257660i	$-0.917048\pi$
$967$	−177522.	+	348406.i	−0.189845	+	0.372592i	0.776391	+	0.630252i	$0.217048\pi$
$968$	1994.26	−	1994.26i	0.00212829	−	0.00212829i
$969$	−76804.7	+	24955.4i	−0.0817976	+	0.0265776i
$970$	588920.	+	1.96788e6i	0.625912	+	2.09148i
$971$	355254.	−	1.09336e6i	0.376791	−	1.15964i	−0.565471	−	0.824768i	$-0.691306\pi$
$971$	355254.	−	1.09336e6i	0.376791	−	1.15964i	0.942262	−	0.334875i	$-0.108694\pi$
$972$	744911.	−	379551.i	0.788446	−	0.401733i
$973$	−87320.3	+	551319.i	−0.0922337	+	0.582341i
$974$		−	1.65922e6i		−	1.74899i
$975$	309032.	+	470073.i	0.325083	+	0.494489i
$976$	−412887.			−0.433442
$977$	502091.	+	79523.4i	0.526009	+	0.0833116i	0.413791	−	0.910372i	$-0.364204\pi$
$977$	502091.	+	79523.4i	0.526009	+	0.0833116i	0.112218	+	0.993684i	$0.464204\pi$
$978$	874550.	+	1.71640e6i	0.914338	+	1.79449i
$979$	173103.	+	56244.6i	0.180609	+	0.0586834i
$980$	2.35513e6	+	826569.i	2.45224	+	0.860651i
$981$	−133530.	−	410962.i	−0.138752	−	0.427035i
$982$	−321228.	−	321228.i	−0.333112	−	0.333112i
$983$	535292.	+	272745.i	0.553967	+	0.282260i	0.708480	−	0.705731i	$-0.249381\pi$
$983$	535292.	+	272745.i	0.553967	+	0.282260i	−0.154514	+	0.987991i	$0.549381\pi$
$984$	−8269.95	+	11382.6i	−0.00854108	+	0.0117558i
$985$	12851.0	+	26749.4i	0.0132454	+	0.0275703i
$986$	−120589.	+	87613.3i	−0.124038	+	0.0901190i
$987$	−331223.	−	2.09126e6i	−0.340005	−	2.14671i
$988$	−135854.	+	21517.2i	−0.139174	+	0.0220431i
$989$	−273443.	−	376362.i	−0.279560	−	0.384781i
$990$	636553.	+	116132.i	0.649478	+	0.118490i
$991$	−1.51359e6	−	1.09969e6i	−1.54121	−	1.11975i	−0.949574	−	0.313542i	$-0.898484\pi$
$991$	−1.51359e6	−	1.09969e6i	−1.54121	−	1.11975i	−0.591631	−	0.806209i	$-0.701516\pi$
$992$	−612539.	+	1.20218e6i	−0.622459	+	1.22164i
$993$	−558221.	+	558221.i	−0.566119	+	0.566119i
$994$	949859.	−	308628.i	0.961361	−	0.312365i
$995$	−1.00522e6	−	23501.4i	−1.01535	−	0.0237382i
$996$	−370676.	+	1.14082e6i	−0.373660	+	1.15001i
$997$	−155941.	+	79456.1i	−0.156881	+	0.0799350i	−0.530668	−	0.847580i	$-0.678059\pi$
$997$	−155941.	+	79456.1i	−0.156881	+	0.0799350i	0.373787	+	0.927515i	$0.378059\pi$
$998$	−239946.	+	1.51496e6i	−0.240909	+	1.52104i
$999$		−	1.12310e6i		−	1.12535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.2.2	✓	72
5.2	odd	4		125.5.f.a.93.8		72
5.3	odd	4		125.5.f.b.93.2		72
5.4	even	2		125.5.f.c.32.8		72
25.9	even	10		125.5.f.a.82.8		72
25.12	odd	20		125.5.f.c.43.8		72
25.13	odd	20	inner	25.5.f.a.13.2	yes	72
25.16	even	5		125.5.f.b.82.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.2.2	✓	72	1.1	even	1	trivial
25.5.f.a.13.2	yes	72	25.13	odd	20	inner
125.5.f.a.82.8		72	25.9	even	10
125.5.f.a.93.8		72	5.2	odd	4
125.5.f.b.82.2		72	25.16	even	5
125.5.f.b.93.2		72	5.3	odd	4
125.5.f.c.32.8		72	5.4	even	2
125.5.f.c.43.8		72	25.12	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.62994 - 0.891695i) q^{2} +(2.94614 + 5.78212i) q^{3} +(15.6842 + 5.09611i) q^{4} +(0.584324 - 24.9932i) q^{5} +(-11.4307 - 35.1800i) q^{6} +(-65.0193 - 65.0193i) q^{7} +(-2.49547 - 1.27151i) q^{8} +(22.8574 - 31.4606i) q^{9} +O(q^{10})\)	\(q+(-5.62994 - 0.891695i) q^{2} +(2.94614 + 5.78212i) q^{3} +(15.6842 + 5.09611i) q^{4} +(0.584324 - 24.9932i) q^{5} +(-11.4307 - 35.1800i) q^{6} +(-65.0193 - 65.0193i) q^{7} +(-2.49547 - 1.27151i) q^{8} +(22.8574 - 31.4606i) q^{9} +(-25.5760 + 140.189i) q^{10} +(94.4647 - 68.6326i) q^{11} +(16.7415 + 105.702i) q^{12} +(-136.994 + 21.6976i) q^{13} +(308.077 + 424.032i) q^{14} +(146.235 - 70.2547i) q^{15} +(-200.553 - 145.710i) q^{16} +(-93.9518 + 184.391i) q^{17} +(-156.739 + 156.739i) q^{18} +(57.1905 - 18.5823i) q^{19} +(136.533 - 389.020i) q^{20} +(184.393 - 567.505i) q^{21} +(-593.030 + 302.164i) q^{22} +(51.5154 - 325.255i) q^{23} -18.1751i q^{24} +(-624.317 - 29.2082i) q^{25} +790.613 q^{26} +(768.422 + 121.706i) q^{27} +(-688.430 - 1351.12i) q^{28} +(-120.175 - 39.0473i) q^{29} +(-885.940 + 265.133i) q^{30} +(285.993 + 880.196i) q^{31} +(1030.86 + 1030.86i) q^{32} +(675.148 + 344.005i) q^{33} +(693.363 - 954.333i) q^{34} +(-1663.03 + 1587.05i) q^{35} +(518.827 - 376.950i) q^{36} +(-225.824 - 1425.80i) q^{37} +(-338.549 + 53.6208i) q^{38} +(-529.060 - 728.188i) q^{39} +(-33.2371 + 61.6268i) q^{40} +(-626.274 - 455.015i) q^{41} +(-1544.17 + 3030.60i) q^{42} +(998.916 - 998.916i) q^{43} +(1831.36 - 595.046i) q^{44} +(-772.943 - 589.663i) q^{45} +(-580.057 + 1785.23i) q^{46} +(3161.59 - 1610.91i) q^{47} +(251.657 - 1588.90i) q^{48} +6054.01i q^{49} +(3488.82 + 721.141i) q^{50} -1342.96 q^{51} +(-2259.21 - 357.823i) q^{52} +(879.784 + 1726.67i) q^{53} +(-4217.64 - 1370.40i) q^{54} +(-1660.15 - 2401.08i) q^{55} +(79.5813 + 244.926i) q^{56} +(275.936 + 275.936i) q^{57} +(641.762 + 326.994i) q^{58} +(1736.23 - 2389.71i) q^{59} +(2651.60 - 356.659i) q^{60} +(1347.46 - 978.990i) q^{61} +(-825.257 - 5210.47i) q^{62} +(-3531.72 + 559.369i) q^{63} +(-2553.10 - 3514.04i) q^{64} +(462.244 + 3436.58i) q^{65} +(-3494.29 - 2538.75i) q^{66} +(591.414 - 1160.72i) q^{67} +(-2413.23 + 2413.23i) q^{68} +(2032.44 - 660.379i) q^{69} +(10777.9 - 7452.05i) q^{70} +(588.836 - 1812.25i) q^{71} +(-97.0423 + 49.4455i) q^{72} +(-1433.88 + 9053.14i) q^{73} +8228.53i q^{74} +(-1670.44 - 3695.93i) q^{75} +991.684 q^{76} +(-10604.5 - 1679.58i) q^{77} +(2329.25 + 4571.42i) q^{78} +(-3804.27 - 1236.08i) q^{79} +(-3758.95 + 4927.31i) q^{80} +(586.790 + 1805.95i) q^{81} +(3120.15 + 3120.15i) q^{82} +(9986.91 + 5088.58i) q^{83} +(5784.13 - 7961.17i) q^{84} +(4553.61 + 2455.90i) q^{85} +(-6514.57 + 4733.11i) q^{86} +(-128.277 - 809.907i) q^{87} +(-323.001 + 51.1583i) q^{88} +(916.231 + 1261.08i) q^{89} +(3825.82 + 4009.00i) q^{90} +(10318.0 + 7496.45i) q^{91} +(2465.51 - 4838.84i) q^{92} +(-4246.82 + 4246.82i) q^{93} +(-19236.0 + 6250.15i) q^{94} +(-431.013 - 1440.23i) q^{95} +(-2923.50 + 8997.60i) q^{96} +(12843.4 - 6544.05i) q^{97} +(5398.33 - 34083.7i) q^{98} -4540.68i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Introduction

L-functions

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