LMFDB - Embedded newform 25.5.f.a.3.4

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			3.4
Character	$\chi$	$=$	25.3
Dual form			25.5.f.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10795 - 2.17447i) q^{2} +(0.976269 + 6.16392i) q^{3} +(5.90379 - 8.12588i) q^{4} +(23.7728 - 7.73659i) q^{5} +(12.3216 - 8.95217i) q^{6} +(23.7798 - 23.7798i) q^{7} +(-62.7773 - 9.94294i) q^{8} +(39.9948 - 12.9951i) q^{9} +O(q^{10})$	\(q+(-1.10795 - 2.17447i) q^{2} +(0.976269 + 6.16392i) q^{3} +(5.90379 - 8.12588i) q^{4} +(23.7728 - 7.73659i) q^{5} +(12.3216 - 8.95217i) q^{6} +(23.7798 - 23.7798i) q^{7} +(-62.7773 - 9.94294i) q^{8} +(39.9948 - 12.9951i) q^{9} +(-43.1620 - 43.1215i) q^{10} +(-14.4780 + 44.5587i) q^{11} +(55.8509 + 28.4575i) q^{12} +(-103.152 + 202.447i) q^{13} +(-78.0553 - 25.3617i) q^{14} +(70.8963 + 138.981i) q^{15} +(-1.72764 - 5.31714i) q^{16} +(-48.4395 + 305.835i) q^{17} +(-72.5696 - 72.5696i) q^{18} +(-339.672 - 467.518i) q^{19} +(77.4831 - 238.850i) q^{20} +(169.792 + 123.361i) q^{21} +(112.932 - 17.8867i) q^{22} +(-194.850 + 99.2809i) q^{23} -396.661i q^{24} +(505.290 - 367.840i) q^{25} +554.501 q^{26} +(348.639 + 684.243i) q^{27} +(-52.8407 - 333.623i) q^{28} +(-482.419 + 663.993i) q^{29} +(223.659 - 308.145i) q^{30} +(673.491 - 489.320i) q^{31} +(-728.745 + 728.745i) q^{32} +(-288.791 - 45.7400i) q^{33} +(718.697 - 233.519i) q^{34} +(381.338 - 749.288i) q^{35} +(130.524 - 401.713i) q^{36} +(-737.228 - 375.636i) q^{37} +(-640.265 + 1256.59i) q^{38} +(-1348.57 - 438.177i) q^{39} +(-1569.31 + 249.310i) q^{40} +(736.696 + 2267.32i) q^{41} +(80.1246 - 505.887i) q^{42} +(-230.697 - 230.697i) q^{43} +(276.603 + 380.712i) q^{44} +(850.250 - 618.353i) q^{45} +(431.767 + 313.697i) q^{46} +(-27.8575 + 4.41219i) q^{47} +(31.0878 - 15.8400i) q^{48} +1270.04i q^{49} +(-1359.69 - 691.191i) q^{50} -1932.43 q^{51} +(1036.07 + 2033.40i) q^{52} +(-252.613 - 1594.93i) q^{53} +(1101.59 - 1516.21i) q^{54} +(0.549873 + 1171.30i) q^{55} +(-1729.27 + 1256.39i) q^{56} +(2550.13 - 2550.13i) q^{57} +(1978.33 + 313.336i) q^{58} +(1080.90 - 351.204i) q^{59} +(1547.90 + 244.418i) q^{60} +(1666.73 - 5129.66i) q^{61} +(-1810.20 - 922.345i) q^{62} +(642.048 - 1260.09i) q^{63} +(2306.97 + 749.580i) q^{64} +(-885.958 + 5610.77i) q^{65} +(220.505 + 678.644i) q^{66} +(710.055 - 4483.11i) q^{67} +(2199.20 + 2199.20i) q^{68} +(-802.185 - 1104.11i) q^{69} +(-2051.81 + 0.963235i) q^{70} +(-5844.13 - 4246.01i) q^{71} +(-2639.97 + 418.131i) q^{72} +(5246.30 - 2673.12i) q^{73} +2019.27i q^{74} +(2760.64 + 2755.46i) q^{75} -5804.34 q^{76} +(715.314 + 1403.88i) q^{77} +(541.342 + 3417.90i) q^{78} +(-4702.50 + 6472.44i) q^{79} +(-82.2074 - 113.037i) q^{80} +(-1121.50 + 814.817i) q^{81} +(4113.99 - 4113.99i) q^{82} +(-8343.32 - 1321.45i) q^{83} +(2004.84 - 651.412i) q^{84} +(1214.58 + 7645.30i) q^{85} +(-246.043 + 757.243i) q^{86} +(-4563.77 - 2325.36i) q^{87} +(1351.93 - 2653.32i) q^{88} +(7834.32 + 2545.52i) q^{89} +(-2286.62 - 1163.74i) q^{90} +(2361.22 + 7267.08i) q^{91} +(-343.609 + 2169.46i) q^{92} +(3673.64 + 3673.64i) q^{93} +(40.4588 + 55.6868i) q^{94} +(-11691.9 - 8486.30i) q^{95} +(-5203.37 - 3780.47i) q^{96} +(-6912.25 + 1094.79i) q^{97} +(2761.66 - 1407.14i) q^{98} +1970.26i 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−1.10795	−	2.17447i	−0.276987	−	0.543617i	0.710042	−	0.704159i	$-0.248676\pi$
$2$	−1.10795	−	2.17447i	−0.276987	−	0.543617i	−0.987029	+	0.160542i	$0.948676\pi$
$3$	0.976269	+	6.16392i	0.108474	+	0.684880i	0.980662	+	0.195709i	$0.0627007\pi$
$3$	0.976269	+	6.16392i	0.108474	+	0.684880i	−0.872188	+	0.489171i	$0.837299\pi$
$4$	5.90379	−	8.12588i	0.368987	−	0.507867i
$5$	23.7728	−	7.73659i	0.950911	−	0.309463i
$5$	23.7728	−	7.73659i	0.950911	−	0.309463i
$6$	12.3216	−	8.95217i	0.342267	−	0.248671i
$7$	23.7798	−	23.7798i	0.485303	−	0.485303i	−0.421518	−	0.906820i	$-0.638502\pi$
$7$	23.7798	−	23.7798i	0.485303	−	0.485303i	0.906820	+	0.421518i	$0.138502\pi$
$8$	−62.7773	−	9.94294i	−0.980895	−	0.155358i
$9$	39.9948	−	12.9951i	0.493763	−	0.160433i
$10$	−43.1620	−	43.1215i	−0.431620	−	0.431215i
$11$	−14.4780	+	44.5587i	−0.119653	+	0.368254i	−0.992889	−	0.119043i	$-0.962017\pi$
$11$	−14.4780	+	44.5587i	−0.119653	+	0.368254i	0.873236	+	0.487297i	$0.162017\pi$
$12$	55.8509	+	28.4575i	0.387854	+	0.197621i
$13$	−103.152	+	202.447i	−0.610366	+	1.19791i	0.354473	+	0.935066i	$0.384660\pi$
$13$	−103.152	+	202.447i	−0.610366	+	1.19791i	−0.964838	+	0.262844i	$0.915340\pi$
$14$	−78.0553	−	25.3617i	−0.398242	−	0.129397i
$15$	70.8963	+	138.981i	0.315095	+	0.617691i
$16$	−1.72764	−	5.31714i	−0.00674861	−	0.0207701i
$17$	−48.4395	+	305.835i	−0.167611	+	1.05825i	0.750193	+	0.661219i	$0.229960\pi$
$17$	−48.4395	+	305.835i	−0.167611	+	1.05825i	−0.917804	+	0.397034i	$0.870040\pi$
$18$	−72.5696	−	72.5696i	−0.223980	−	0.223980i
$19$	−339.672	−	467.518i	−0.940918	−	1.29506i	−0.955445	−	0.295168i	$-0.904624\pi$
$19$	−339.672	−	467.518i	−0.940918	−	1.29506i	0.0145269	−	0.999894i	$-0.495376\pi$
$20$	77.4831	−	238.850i	0.193708	−	0.597125i
$21$	169.792	+	123.361i	0.385017	+	0.279731i
$22$	112.932	−	17.8867i	0.233332	−	0.0369561i
$23$	−194.850	+	99.2809i	−0.368336	+	0.187677i	−0.628355	−	0.777927i	$-0.716271\pi$
$23$	−194.850	+	99.2809i	−0.368336	+	0.187677i	0.260019	+	0.965604i	$0.416271\pi$
$24$		−	396.661i		−	0.688647i
$25$	505.290	−	367.840i	0.808465	−	0.588545i
$26$	554.501			0.820268
$27$	348.639	+	684.243i	0.478243	+	0.938604i
$28$	−52.8407	−	333.623i	−0.0673989	−	0.425540i
$29$	−482.419	+	663.993i	−0.573625	+	0.789528i	−0.992978	−	0.118296i	$-0.962257\pi$
$29$	−482.419	+	663.993i	−0.573625	+	0.789528i	0.419353	+	0.907823i	$0.362257\pi$
$30$	223.659	−	308.145i	0.248511	−	0.342383i
$31$	673.491	−	489.320i	0.700823	−	0.509178i	−0.179377	−	0.983780i	$-0.557408\pi$
$31$	673.491	−	489.320i	0.700823	−	0.509178i	0.880200	+	0.474603i	$0.157408\pi$
$32$	−728.745	+	728.745i	−0.711665	+	0.711665i
$33$	−288.791	−	45.7400i	−0.265189	−	0.0420018i
$34$	718.697	−	233.519i	0.621710	−	0.202006i
$35$	381.338	−	749.288i	0.311296	−	0.611663i
$36$	130.524	−	401.713i	0.100713	−	0.309964i
$37$	−737.228	−	375.636i	−0.538516	−	0.274387i	0.163507	−	0.986542i	$-0.447719\pi$
$37$	−737.228	−	375.636i	−0.538516	−	0.274387i	−0.702022	+	0.712155i	$0.747719\pi$
$38$	−640.265	+	1256.59i	−0.443397	+	0.870215i
$39$	−1348.57	−	438.177i	−0.886633	−	0.288085i
$40$	−1569.31	+	249.310i	−0.980822	+	0.155819i
$41$	736.696	+	2267.32i	0.438249	+	1.34879i	0.889720	+	0.456506i	$0.150899\pi$
$41$	736.696	+	2267.32i	0.438249	+	1.34879i	−0.451472	+	0.892285i	$0.649101\pi$
$42$	80.1246	−	505.887i	0.0454221	−	0.286784i
$43$	−230.697	−	230.697i	−0.124768	−	0.124768i	0.641965	−	0.766734i	$-0.278119\pi$
$43$	−230.697	−	230.697i	−0.124768	−	0.124768i	−0.766734	+	0.641965i	$0.778119\pi$
$44$	276.603	+	380.712i	0.142874	+	0.196649i
$45$	850.250	−	618.353i	0.419876	−	0.305359i
$46$	431.767	+	313.697i	0.204049	+	0.148250i
$47$	−27.8575	+	4.41219i	−0.0126109	+	0.00199737i	−0.162737	−	0.986670i	$-0.552032\pi$
$47$	−27.8575	+	4.41219i	−0.0126109	+	0.00199737i	0.150126	+	0.988667i	$0.452032\pi$
$48$	31.0878	−	15.8400i	0.0134930	−	0.00687501i
$49$			1270.04i			0.528963i
$50$	−1359.69	−	691.191i	−0.543877	−	0.276476i
$51$	−1932.43			−0.742957
$52$	1036.07	+	2033.40i	0.383162	+	0.751998i
$53$	−252.613	−	1594.93i	−0.0899297	−	0.567794i	−0.990973	−	0.134064i	$-0.957197\pi$
$53$	−252.613	−	1594.93i	−0.0899297	−	0.567794i	0.901043	−	0.433730i	$-0.142803\pi$
$54$	1101.59	−	1516.21i	0.377775	−	0.519962i
$55$	0.549873	+	1171.30i	0.000181776	+	0.387205i
$56$	−1729.27	+	1256.39i	−0.551427	+	0.400635i
$57$	2550.13	−	2550.13i	0.784897	−	0.784897i
$58$	1978.33	+	313.336i	0.588088	+	0.0931439i
$59$	1080.90	−	351.204i	0.310513	−	0.100892i	−0.149615	−	0.988744i	$-0.547803\pi$
$59$	1080.90	−	351.204i	0.310513	−	0.100892i	0.460128	+	0.887852i	$0.347803\pi$
$60$	1547.90	+	244.418i	0.429971	+	0.0678938i
$61$	1666.73	−	5129.66i	0.447925	−	1.37857i	−0.431320	−	0.902199i	$-0.641952\pi$
$61$	1666.73	−	5129.66i	0.447925	−	1.37857i	0.879244	−	0.476371i	$-0.158048\pi$
$62$	−1810.20	−	922.345i	−0.470917	−	0.239944i
$63$	642.048	−	1260.09i	0.161766	−	0.317483i
$64$	2306.97	+	749.580i	0.563225	+	0.183003i
$65$	−885.958	+	5610.77i	−0.209694	+	1.32799i
$66$	220.505	+	678.644i	0.0506209	+	0.155795i
$67$	710.055	−	4483.11i	0.158177	−	0.998688i	−0.773076	−	0.634314i	$-0.781283\pi$
$67$	710.055	−	4483.11i	0.158177	−	0.998688i	0.931253	−	0.364374i	$-0.118717\pi$
$68$	2199.20	+	2199.20i	0.475605	+	0.475605i
$69$	−802.185	−	1104.11i	−0.168491	−	0.231908i
$70$	−2051.81	+	0.963235i	−0.418736	+	0.000196579i
$71$	−5844.13	−	4246.01i	−1.15932	−	0.842295i	−0.169628	−	0.985508i	$-0.554257\pi$
$71$	−5844.13	−	4246.01i	−1.15932	−	0.842295i	−0.989692	+	0.143213i	$0.954257\pi$
$72$	−2639.97	+	418.131i	−0.509254	+	0.0806579i
$73$	5246.30	−	2673.12i	0.984480	−	0.501618i	0.113819	−	0.993501i	$-0.463691\pi$
$73$	5246.30	−	2673.12i	0.984480	−	0.501618i	0.870661	+	0.491884i	$0.163691\pi$
$74$			2019.27i			0.368748i
$75$	2760.64	+	2755.46i	0.490780	+	0.489859i
$76$	−5804.34			−1.00491
$77$	715.314	+	1403.88i	0.120647	+	0.236783i
$78$	541.342	+	3417.90i	0.0889780	+	0.561785i
$79$	−4702.50	+	6472.44i	−0.753485	+	1.03708i	0.244243	+	0.969714i	$0.421461\pi$
$79$	−4702.50	+	6472.44i	−0.753485	+	1.03708i	−0.997728	+	0.0673694i	$0.978539\pi$
$80$	−82.2074	−	113.037i	−0.0128449	−	0.0176621i
$81$	−1121.50	+	814.817i	−0.170934	+	0.124191i
$82$	4113.99	−	4113.99i	0.611837	−	0.611837i
$83$	−8343.32	−	1321.45i	−1.21111	−	0.191821i	−0.481970	−	0.876188i	$-0.660079\pi$
$83$	−8343.32	−	1321.45i	−1.21111	−	0.191821i	−0.729138	+	0.684367i	$0.760079\pi$
$84$	2004.84	−	651.412i	0.284133	−	0.0923203i
$85$	1214.58	+	7645.30i	0.168107	+	1.05817i
$86$	−246.043	+	757.243i	−0.0332670	+	0.102385i
$87$	−4563.77	−	2325.36i	−0.602955	−	0.307221i
$88$	1351.93	−	2653.32i	0.174578	−	0.342629i
$89$	7834.32	+	2545.52i	0.989057	+	0.321364i	0.758484	−	0.651691i	$-0.225940\pi$
$89$	7834.32	+	2545.52i	0.989057	+	0.321364i	0.230572	+	0.973055i	$0.425940\pi$
$90$	−2286.62	−	1163.74i	−0.282299	−	0.143672i
$91$	2361.22	+	7267.08i	0.285137	+	0.877561i
$92$	−343.609	+	2169.46i	−0.0405965	+	0.256316i
$93$	3673.64	+	3673.64i	0.424747	+	0.424747i
$94$	40.4588	+	55.6868i	0.00457886	+	0.00630226i
$95$	−11691.9	−	8486.30i	−1.29550	−	0.940310i
$96$	−5203.37	−	3780.47i	−0.564602	−	0.410207i
$97$	−6912.25	+	1094.79i	−0.734643	+	0.116356i	−0.512535	−	0.858666i	$-0.671294\pi$
$97$	−6912.25	+	1094.79i	−0.734643	+	0.116356i	−0.222107	+	0.975022i	$0.571294\pi$
$98$	2761.66	−	1407.14i	0.287553	−	0.146516i
$99$			1970.26i			0.201026i
$100$	−5.89411	−	6277.58i	−0.000589411	−	0.627758i
$101$	17534.1			1.71886			0.859429	−	0.511255i	$-0.170819\pi$
$101$	17534.1			1.71886			0.859429	+	0.511255i	$0.170819\pi$
$102$	2141.03	+	4202.01i	0.205789	+	0.403884i
$103$	−1645.28	−	10387.9i	−0.155084	−	0.979161i	−0.935353	−	0.353717i	$-0.884918\pi$
$103$	−1645.28	−	10387.9i	−0.155084	−	0.979161i	0.780269	−	0.625444i	$-0.215082\pi$
$104$	8488.50	−	11683.4i	0.784810	−	1.08020i
$105$	4990.84	+	1619.03i	0.452684	+	0.146851i
$106$	−3188.25	+	2316.40i	−0.283753	+	0.206159i
$107$	12289.4	−	12289.4i	1.07340	−	1.07340i	0.0763202	−	0.997083i	$-0.475683\pi$
$107$	12289.4	−	12289.4i	1.07340	−	1.07340i	0.997083	−	0.0763202i	$-0.0243171\pi$
$108$	7618.36	+	1206.63i	0.653152	+	0.103449i
$109$	−11650.6	+	3785.49i	−0.980604	+	0.318617i	−0.755089	−	0.655622i	$-0.772406\pi$
$109$	−11650.6	+	3785.49i	−0.980604	+	0.318617i	−0.225515	+	0.974240i	$0.572406\pi$
$110$	2546.34	−	1298.93i	0.210441	−	0.107350i
$111$	1595.66	−	4910.93i	0.129507	−	0.398582i
$112$	−167.524	−	85.3576i	−0.0133549	−	0.00680466i
$113$	−1922.01	+	3772.17i	−0.150522	+	0.295416i	−0.953939	−	0.300001i	$-0.903013\pi$
$113$	−1922.01	+	3772.17i	−0.150522	+	0.295416i	0.803417	+	0.595417i	$0.203013\pi$
$114$	−8370.59	−	2719.77i	−0.644090	−	0.209277i
$115$	−3864.03	+	3867.66i	−0.292176	+	0.292450i
$116$	2547.42	+	7840.15i	0.189315	+	0.582651i
$117$	−1494.72	+	9437.28i	−0.109191	+	0.689406i
$118$	−1961.26	−	1961.26i	−0.140855	−	0.140855i
$119$	6120.82	+	8424.59i	0.432231	+	0.594915i
$120$	−3068.80	−	9429.73i	−0.213111	−	0.654843i
$121$	10069.0	+	7315.52i	0.687723	+	0.499660i
$122$	−13000.9	+	2059.15i	−0.873484	+	0.138346i
$123$	−13256.3	+	6754.45i	−0.876221	+	0.446457i
$124$		−	8361.55i		−	0.543805i
$125$	9166.33	−	12653.8i	0.586645	−	0.809844i
$126$	−3451.38			−0.217396
$127$	9911.19	+	19451.8i	0.614495	+	1.20601i	0.963201	+	0.268782i	$0.0866211\pi$
$127$	9911.19	+	19451.8i	0.614495	+	1.20601i	−0.348706	+	0.937232i	$0.613379\pi$
$128$	1653.48	+	10439.7i	0.100920	+	0.637186i
$129$	1196.77	−	1647.22i	0.0719172	−	0.0989855i
$130$	13182.0	−	4289.95i	0.780002	−	0.253843i
$131$	−1660.37	+	1206.33i	−0.0967527	+	0.0702949i	−0.635110	−	0.772422i	$-0.719045\pi$
$131$	−1660.37	+	1206.33i	−0.0967527	+	0.0702949i	0.538357	+	0.842717i	$0.319045\pi$
$132$	−2076.64	+	2076.64i	−0.119183	+	0.119183i
$133$	−19194.8	−	3040.16i	−1.08513	−	0.171867i
$134$	−10535.1	+	3423.06i	−0.586717	+	0.190636i
$135$	13581.8	+	13569.1i	0.745230	+	0.744531i
$136$	6081.80	−	18717.8i	0.328817	−	1.01199i
$137$	−12065.4	−	6147.60i	−0.642834	−	0.327540i	0.102006	−	0.994784i	$-0.467474\pi$
$137$	−12065.4	−	6147.60i	−0.642834	−	0.327540i	−0.744840	+	0.667244i	$0.767474\pi$
$138$	−1512.08	+	2967.63i	−0.0793994	+	0.155830i
$139$	−24513.3	−	7964.84i	−1.26874	−	0.412238i	−0.404137	−	0.914698i	$-0.632428\pi$
$139$	−24513.3	−	7964.84i	−1.26874	−	0.412238i	−0.864600	+	0.502461i	$0.832428\pi$
$140$	−3837.28	−	7522.35i	−0.195779	−	0.383793i
$141$	−54.3928	−	167.404i	−0.00273592	−	0.00842029i
$142$	−2757.83	+	17412.2i	−0.136770	+	0.863531i
$143$	−7527.34	−	7527.34i	−0.368103	−	0.368103i
$144$	−138.194	−	190.207i	−0.00666442	−	0.00917279i
$145$	−6331.41	+	19517.2i	−0.301137	+	0.928287i
$146$	−11625.2	−	8446.23i	−0.545376	−	0.396239i
$147$	−7828.42	+	1239.90i	−0.362276	+	0.0573788i
$148$	−7404.82	+	3772.94i	−0.338058	+	0.172249i
$149$		−	27797.8i		−	1.25210i	−0.779785	−	0.626048i	$-0.784672\pi$
$149$		−	27797.8i		−	1.25210i	0.779785	−	0.626048i	$-0.215328\pi$
$150$	2933.02	−	9055.83i	0.130356	−	0.402481i
$151$	36528.4			1.60205			0.801026	−	0.598630i	$-0.204288\pi$
$151$	36528.4			1.60205			0.801026	+	0.598630i	$0.204288\pi$
$152$	16675.1	+	32726.8i	0.721743	+	1.41650i
$153$	2037.03	+	12861.3i	0.0870189	+	0.549416i
$154$	2260.17	−	3110.86i	0.0953015	−	0.131171i
$155$	12225.1	−	16843.0i	0.508849	−	0.701062i
$156$	−11522.2	+	8371.40i	−0.473465	+	0.343992i
$157$	24862.2	−	24862.2i	1.00865	−	1.00865i	0.00868696	−	0.999962i	$-0.497235\pi$
$157$	24862.2	−	24862.2i	1.00865	−	1.00865i	0.999962	−	0.00868696i	$-0.00276518\pi$
$158$	19284.2	+	3054.32i	0.772482	+	0.122349i
$159$	9584.42	−	3114.17i	0.379116	−	0.123182i
$160$	−11686.3	+	22962.3i	−0.456496	+	0.896964i
$161$	−2272.61	+	6994.38i	−0.0876745	+	0.269834i
$162$	3014.36	+	1535.89i	0.114859	+	0.0585236i
$163$	−2482.04	+	4871.27i	−0.0934186	+	0.183344i	−0.932987	−	0.359909i	$-0.882808\pi$
$163$	−2482.04	+	4871.27i	−0.0934186	+	0.183344i	0.839569	+	0.543253i	$0.182808\pi$
$164$	22773.2	+	7399.48i	0.846715	+	0.275114i
$165$	−7219.23	+	1146.89i	−0.265169	+	0.0421263i
$166$	6370.50	+	19606.4i	0.231184	+	0.711511i
$167$	5989.18	−	37814.2i	0.214751	−	1.35588i	−0.610903	−	0.791705i	$-0.709194\pi$
$167$	5989.18	−	37814.2i	0.214751	−	1.35588i	0.825654	−	0.564177i	$-0.190806\pi$
$168$	−9432.53	−	9432.53i	−0.334202	−	0.334202i
$169$	−13556.7	−	18659.2i	−0.474657	−	0.653309i
$170$	15278.8	−	11111.7i	0.528678	−	0.384486i
$171$	−19660.5	−	14284.2i	−0.672362	−	0.488499i
$172$	−3236.60	+	512.627i	−0.109404	+	0.0173278i
$173$	−3298.04	+	1680.44i	−0.110196	+	0.0561475i	−0.508219	−	0.861228i	$-0.669696\pi$
$173$	−3298.04	+	1680.44i	−0.110196	+	0.0561475i	0.398024	+	0.917375i	$0.369696\pi$
$174$			12500.1i			0.412873i
$175$	3268.54	−	20762.9i	0.106728	−	0.677972i
$176$	261.938			0.00845615
$177$	3220.04	+	6319.69i	0.102781	+	0.201720i
$178$	−3144.85	−	19855.8i	−0.0992567	−	0.626682i
$179$	−11292.2	+	15542.4i	−0.352429	+	0.485077i	−0.948020	−	0.318211i	$-0.896918\pi$
$179$	−11292.2	+	15542.4i	−0.352429	+	0.485077i	0.595591	+	0.803288i	$0.296918\pi$
$180$	−4.95730	−	10559.7i	−0.000153003	−	0.325915i
$181$	−23123.1	+	16799.9i	−0.705811	+	0.512802i	−0.881820	−	0.471587i	$-0.843681\pi$
$181$	−23123.1	+	16799.9i	−0.705811	+	0.512802i	0.176008	+	0.984389i	$0.443681\pi$
$182$	13185.9	−	13185.9i	0.398078	−	0.398078i
$183$	33246.0	+	5265.64i	0.992743	+	0.157235i
$184$	13219.3	−	4295.20i	0.390456	−	0.126867i
$185$	−20432.1	−	3226.30i	−0.596994	−	0.0942672i
$186$	3918.01	−	12058.4i	0.113250	−	0.348549i
$187$	−12926.3	−	6586.28i	−0.369650	−	0.188346i
$188$	−128.612	+	252.415i	−0.00363886	+	0.00714167i
$189$	24561.8	+	7980.60i	0.687600	+	0.223415i
$190$	−5499.16	+	34826.1i	−0.152331	+	0.964712i
$191$	−4522.04	−	13917.4i	−0.123956	−	0.381497i	0.869753	−	0.493486i	$-0.164278\pi$
$191$	−4522.04	−	13917.4i	−0.123956	−	0.381497i	−0.993709	+	0.111989i	$0.964278\pi$
$192$	−2368.13	+	14951.8i	−0.0642395	+	0.405593i
$193$	−11967.7	−	11967.7i	−0.321290	−	0.321290i	0.527972	−	0.849262i	$-0.322953\pi$
$193$	−11967.7	−	11967.7i	−0.321290	−	0.321290i	−0.849262	+	0.527972i	$0.822953\pi$
$194$	10039.0	+	13817.5i	0.266739	+	0.367135i
$195$	−35449.2	+	16.6419i	−0.932261	+	0.000437657i
$196$	10320.2	+	7498.05i	0.268643	+	0.195180i
$197$	−39649.3	+	6279.83i	−1.02165	+	0.161814i	−0.644713	−	0.764424i	$-0.723023\pi$
$197$	−39649.3	+	6279.83i	−1.02165	+	0.161814i	−0.376939	+	0.926238i	$0.623023\pi$
$198$	4284.27	−	2182.94i	0.109281	−	0.0556817i
$199$			42317.5i			1.06860i	0.845296	+	0.534298i	$0.179424\pi$
$199$			42317.5i			1.06860i	−0.845296	+	0.534298i	$0.820576\pi$
$200$	−35378.2	+	18067.9i	−0.884454	+	0.451698i
$201$	28326.7			0.701139
$202$	−19426.8	−	38127.3i	−0.476101	−	0.934401i
$203$	4317.79	+	27261.5i	0.104778	+	0.661542i
$204$	−11408.7	+	15702.7i	−0.274142	+	0.377323i
$205$	35054.6	+	48200.9i	0.834137	+	1.14696i
$206$	−20765.3	+	15086.9i	−0.489333	+	0.355521i
$207$	−6502.81	+	6502.81i	−0.151761	+	0.151761i
$208$	1254.65	+	198.717i	0.0289998	+	0.00459312i
$209$	25749.8	−	8366.60i	0.589496	−	0.191539i
$210$	−2009.05	−	12646.2i	−0.0455567	−	0.286762i
$211$	−8223.01	+	25307.8i	−0.184700	+	0.568447i	−0.999943	−	0.0106715i	$-0.996603\pi$
$211$	−8223.01	+	25307.8i	−0.184700	+	0.568447i	0.815243	+	0.579118i	$0.196603\pi$
$212$	−14451.6	−	7363.46i	−0.321547	−	0.163836i
$213$	20466.6	−	40168.0i	0.451115	−	0.885362i
$214$	−40338.9	−	13106.9i	−0.880840	−	0.286202i
$215$	−7269.11	−	3699.50i	−0.157255	−	0.0800324i
$216$	−15083.2	−	46421.4i	−0.323286	−	0.994971i
$217$	4379.56	−	27651.4i	0.0930060	−	0.587217i
$218$	21139.6	+	21139.6i	0.444820	+	0.444820i
$219$	21598.7	+	29728.1i	0.450339	+	0.619838i
$220$	9521.04	+	6910.62i	0.196716	+	0.142781i
$221$	−56918.7	−	41353.8i	−1.16539	−	0.846703i
$222$	−12446.6	+	1971.35i	−0.252548	+	0.0399997i
$223$	63280.6	−	32243.1i	1.27251	−	0.648376i	0.318435	−	0.947945i	$-0.396843\pi$
$223$	63280.6	−	32243.1i	1.27251	−	0.648376i	0.954075	+	0.299569i	$0.0968428\pi$
$224$			34658.9i			0.690746i
$225$	15428.9	−	21278.0i	0.304768	−	0.420306i
$226$	10332.0			0.202286
$227$	23087.3	+	45311.3i	0.448044	+	0.879336i	0.998996	+	0.0447990i	$0.0142648\pi$
$227$	23087.3	+	45311.3i	0.448044	+	0.879336i	−0.550952	+	0.834537i	$0.685735\pi$
$228$	−5666.60	−	35777.5i	−0.109007	−	0.688240i
$229$	−15307.8	+	21069.4i	−0.291905	+	0.401773i	−0.929632	−	0.368490i	$-0.879875\pi$
$229$	−15307.8	+	21069.4i	−0.291905	+	0.401773i	0.637726	+	0.770263i	$0.279875\pi$
$230$	12691.2	+	4117.05i	0.239910	+	0.0778270i
$231$	−7955.08	+	5779.71i	−0.149080	+	0.108313i
$232$	36887.0	−	36887.0i	0.685326	−	0.685326i
$233$	3253.24	+	515.262i	0.0599244	+	0.00949109i	0.186325	−	0.982488i	$-0.440342\pi$
$233$	3253.24	+	515.262i	0.0599244	+	0.00949109i	−0.126400	+	0.991979i	$0.540342\pi$
$234$	22177.2	−	7205.79i	0.405018	−	0.131598i
$235$	−628.115	+	320.412i	−0.0113737	+	0.00580194i
$236$	3527.54	−	10856.7i	0.0633357	−	0.194927i
$237$	−44486.5	−	22667.0i	−0.792011	−	0.403550i
$238$	11537.5	−	22643.5i	0.203684	−	0.399752i
$239$	33851.9	+	10999.1i	0.592635	+	0.192559i	0.589953	−	0.807438i	$-0.299146\pi$
$239$	33851.9	+	10999.1i	0.592635	+	0.192559i	0.00268189	+	0.999996i	$0.499146\pi$
$240$	616.495	−	617.074i	0.0107030	−	0.0107131i
$241$	−989.443	−	3045.19i	−0.0170356	−	0.0524301i	0.942177	−	0.335115i	$-0.108775\pi$
$241$	−989.443	−	3045.19i	−0.0170356	−	0.0524301i	−0.959213	+	0.282685i	$0.908775\pi$
$242$	4751.51	−	29999.8i	0.0811336	−	0.512257i
$243$	37867.1	+	37867.1i	0.641283	+	0.641283i
$244$	−31843.0	−	43828.1i	−0.534852	−	0.736161i
$245$	9825.77	+	30192.4i	0.163695	+	0.502996i
$246$	29374.7	+	21342.0i	0.485404	+	0.352666i
$247$	129685.	−	20540.1i	2.12567	−	0.336673i
$248$	−47145.2	+	24021.7i	−0.766539	+	0.390571i
$249$		−	52717.6i		−	0.850271i
$250$	−37671.1	−	5912.15i	−0.602738	−	0.0945944i
$251$	−65062.3			−1.03272			−0.516359	−	0.856372i	$-0.672713\pi$
$251$	−65062.3			−1.03272			−0.516359	+	0.856372i	$0.672713\pi$
$252$	−6448.82	−	12656.5i	−0.101550	−	0.199303i
$253$	−1602.79	−	10119.6i	−0.0250401	−	0.158097i
$254$	31316.3	−	43103.1i	0.485403	−	0.668100i
$255$	−45939.3	+	14950.4i	−0.706486	+	0.229918i
$256$	52267.6	−	37974.6i	0.797540	−	0.579447i
$257$	−81617.2	+	81617.2i	−1.23571	+	1.23571i	−0.273968	+	0.961739i	$0.588336\pi$
$257$	−81617.2	+	81617.2i	−1.23571	+	1.23571i	−0.961739	+	0.273968i	$0.911664\pi$
$258$	−4907.79	−	777.317i	−0.0737303	−	0.0116777i
$259$	−26463.7	+	8598.59i	−0.394504	+	0.128182i
$260$	40361.9	+	40324.0i	0.597069	+	0.596509i
$261$	−10665.6	+	32825.3i	−0.156568	+	0.481868i
$262$	4462.74	+	2273.88i	0.0650128	+	0.0331257i
$263$	−17273.5	+	33901.1i	−0.249729	+	0.490120i	−0.981508	−	0.191422i	$-0.938690\pi$
$263$	−17273.5	+	33901.1i	−0.249729	+	0.490120i	0.731779	+	0.681542i	$0.238690\pi$
$264$	17674.7	+	5742.86i	0.253597	+	0.0823987i
$265$	−18344.6	−	35961.6i	−0.261227	−	0.512092i
$266$	14656.1	+	45106.9i	0.207136	+	0.637499i
$267$	−8042.00	+	50775.2i	−0.112808	+	0.712245i
$268$	−32237.2	−	32237.2i	−0.448836	−	0.448836i
$269$	−25624.8	−	35269.6i	−0.354125	−	0.487411i	0.594375	−	0.804188i	$-0.297399\pi$
$269$	−25624.8	−	35269.6i	−0.354125	−	0.487411i	−0.948500	+	0.316777i	$0.897399\pi$
$270$	14457.6	−	44567.1i	0.198321	−	0.611345i
$271$	32730.1	+	23779.8i	0.445666	+	0.323795i	0.787882	−	0.615826i	$-0.211178\pi$
$271$	32730.1	+	23779.8i	0.445666	+	0.323795i	−0.342217	+	0.939621i	$0.611178\pi$
$272$	1709.85	−	270.814i	0.0231111	−	0.00366044i
$273$	−42488.5	+	21649.0i	−0.570094	+	0.290477i
$274$			33047.0i			0.440180i
$275$	9074.90	+	27840.7i	0.119999	+	0.368141i
$276$	−13707.8			−0.179949
$277$	7198.20	+	14127.3i	0.0938132	+	0.184119i	0.933145	−	0.359501i	$-0.117053\pi$
$277$	7198.20	+	14127.3i	0.0938132	+	0.184119i	−0.839331	+	0.543620i	$0.817053\pi$
$278$	9840.11	+	62128.0i	0.127324	+	0.803892i
$279$	20577.4	−	28322.3i	0.264351	−	0.363848i
$280$	−31389.5	+	43246.6i	−0.400376	+	0.551615i
$281$	1491.53	−	1083.66i	0.0188895	−	0.0137240i	−0.578300	−	0.815824i	$-0.696284\pi$
$281$	1491.53	−	1083.66i	0.0188895	−	0.0137240i	0.597190	+	0.802100i	$0.296284\pi$
$282$	−303.750	+	303.750i	−0.00381960	+	0.00381960i
$283$	−115129.	−	18234.6i	−1.43751	−	0.227680i	−0.611461	−	0.791275i	$-0.709418\pi$
$283$	−115129.	−	18234.6i	−1.43751	−	0.227680i	−0.826051	+	0.563595i	$0.809418\pi$
$284$	−69005.1	+	22421.1i	−0.855548	+	0.277984i
$285$	40894.4	−	80353.0i	0.503471	−	0.989264i
$286$	−8028.07	+	24707.9i	−0.0981475	+	0.302067i
$287$	71435.0	+	36397.9i	0.867255	+	0.441889i
$288$	−19675.9	+	38616.1i	−0.237219	+	0.465568i
$289$	−11755.4	−	3819.56i	−0.140748	−	0.0457318i
$290$	49454.5	−	7856.62i	0.588044	−	0.0934200i
$291$	−13496.4	−	41537.7i	−0.159380	−	0.490520i
$292$	9251.60	−	58412.3i	0.108505	−	0.685076i
$293$	−21067.7	−	21067.7i	−0.245405	−	0.245405i	0.573677	−	0.819082i	$-0.305516\pi$
$293$	−21067.7	−	21067.7i	−0.245405	−	0.245405i	−0.819082	+	0.573677i	$0.805516\pi$
$294$	11369.6	+	15648.9i	0.131538	+	0.181046i
$295$	22978.8	−	16711.6i	0.264048	−	0.192032i
$296$	42546.2	+	30911.6i	0.485599	+	0.352808i
$297$	−35536.6	+	5628.44i	−0.402868	+	0.0638080i
$298$	−60445.4	+	30798.5i	−0.680661	+	0.346814i
$299$		−	49687.7i		−	0.555785i
$300$	38688.7	−	6164.94i	0.429875	−	0.0684993i
$301$	−10971.9			−0.121101
$302$	−40471.5	−	79429.8i	−0.443747	−	0.870903i
$303$	17118.0	+	108079.i	0.186452	+	1.17721i
$304$	−1899.03	+	2613.79i	−0.0205487	+	0.0282828i
$305$	−63.3021	−	134841.i	−0.000680485	−	1.44951i
$306$	25709.5	−	18679.1i	0.274569	−	0.199486i
$307$	−38872.7	+	38872.7i	−0.412447	+	0.412447i	−0.882590	−	0.470143i	$-0.844202\pi$
$307$	−38872.7	+	38872.7i	−0.412447	+	0.412447i	0.470143	+	0.882590i	$0.344202\pi$
$308$	15630.9	+	2475.68i	0.164771	+	0.0260972i
$309$	62424.1	−	20282.8i	0.653785	−	0.212428i
$310$	−50169.4	−	7921.91i	−0.522054	−	0.0824340i
$311$	37458.8	−	115286.i	0.387287	−	1.19195i	−0.547521	−	0.836792i	$-0.684428\pi$
$311$	37458.8	−	115286.i	0.387287	−	1.19195i	0.934808	−	0.355154i	$-0.115572\pi$
$312$	80302.7	+	40916.3i	0.824937	+	0.420327i
$313$	23610.2	−	46337.6i	0.240996	−	0.472982i	−0.738550	−	0.674198i	$-0.764489\pi$
$313$	23610.2	−	46337.6i	0.240996	−	0.472982i	0.979547	+	0.201216i	$0.0644894\pi$
$314$	−81608.1	−	26516.1i	−0.827702	−	0.268937i
$315$	5514.47	−	34923.1i	0.0555755	−	0.351959i
$316$	24831.6	+	76423.9i	0.248674	+	0.765341i
$317$	−27229.1	+	171918.i	−0.270966	+	1.71081i	0.358284	+	0.933613i	$0.383362\pi$
$317$	−27229.1	+	171918.i	−0.270966	+	1.71081i	−0.629251	+	0.777202i	$0.716638\pi$
$318$	−17390.7	−	17390.7i	−0.171974	−	0.171974i
$319$	−22602.2	−	31109.3i	−0.222111	−	0.305709i
$320$	60642.3	−	28.4690i	0.592210	−	0.000278017i
$321$	87748.6	+	63753.1i	0.851589	+	0.618716i
$322$	17727.0	−	2807.68i	0.170971	−	0.0270792i
$323$	159437.	−	81237.1i	1.52821	−	0.778662i
$324$			13923.7i			0.132637i
$325$	22346.5	+	140238.i	0.211564	+	1.32770i
$326$	13342.4			0.125545
$327$	−34707.5	−	68117.4i	−0.324585	−	0.637034i
$328$	−23704.0	−	149661.i	−0.220330	−	1.39111i
$329$	−557.525	+	767.367i	−0.00515078	+	0.00708943i
$330$	10492.4	+	14427.3i	0.0963490	+	0.132482i
$331$	122786.	−	89209.2i	1.12071	−	0.814242i	0.136392	−	0.990655i	$-0.456449\pi$
$331$	122786.	−	89209.2i	1.12071	−	0.814242i	0.984316	+	0.176413i	$0.0564493\pi$
$332$	−59995.2	+	59995.2i	−0.544302	+	0.544302i
$333$	−34366.7	−	5443.15i	−0.309920	−	0.0490865i
$334$	−88861.5	+	28872.9i	−0.796564	+	0.258819i
$335$	−17804.0	−	112069.i	−0.158645	−	0.998614i
$336$	362.589	−	1115.94i	0.00321171	−	0.00988463i
$337$	70468.6	+	35905.5i	0.620492	+	0.316156i	0.735826	−	0.677170i	$-0.236794\pi$
$337$	70468.6	+	35905.5i	0.620492	+	0.316156i	−0.115335	+	0.993327i	$0.536794\pi$
$338$	−25553.7	+	50151.9i	−0.223676	+	0.438990i
$339$	−25127.7	−	8164.49i	−0.218652	−	0.0710444i
$340$	69295.4	+	35266.8i	0.599441	+	0.305076i
$341$	12052.7	+	37094.3i	0.103651	+	0.319005i
$342$	−9277.75	+	58577.4i	−0.0793214	+	0.500815i
$343$	87296.7	+	87296.7i	0.742010	+	0.742010i
$344$	12188.7	+	16776.3i	0.103001	+	0.141768i
$345$	−27612.2	−	20041.7i	−0.231987	−	0.168382i
$346$	7308.12	+	5309.66i	0.0610455	+	0.0443521i
$347$	−58274.8	+	9229.82i	−0.483974	+	0.0766539i	−0.393654	−	0.919259i	$-0.628789\pi$
$347$	−58274.8	+	9229.82i	−0.483974	+	0.0766539i	−0.0903201	+	0.995913i	$0.528789\pi$
$348$	−45839.1	+	23356.2i	−0.378510	+	0.192861i
$349$		−	81432.0i		−	0.668566i	−0.942473	−	0.334283i	$-0.891506\pi$
$349$		−	81432.0i		−	0.668566i	0.942473	−	0.334283i	$-0.108494\pi$
$350$	−48769.7	+	15896.9i	−0.398120	+	0.129770i
$351$	−174485.			−1.41627
$352$	−21921.2	−	43022.7i	−0.176921	−	0.347226i
$353$	−20270.1	−	127980.i	−0.162669	−	1.02705i	−0.925028	−	0.379899i	$-0.875959\pi$
$353$	−20270.1	−	127980.i	−0.162669	−	1.02705i	0.762359	−	0.647155i	$-0.224041\pi$
$354$	10174.3	−	14003.8i	0.0811894	−	0.111748i
$355$	−171781.	−	55725.8i	−1.36307	−	0.442181i
$356$	66936.8	−	48632.4i	0.528159	−	0.383730i
$357$	−45952.9	+	45952.9i	−0.360559	+	0.360559i
$358$	46307.5	+	7334.39i	0.361314	+	0.0572266i
$359$	11180.3	−	3632.71i	0.0867493	−	0.0281866i	−0.265321	−	0.964160i	$-0.585478\pi$
$359$	11180.3	−	3632.71i	0.0867493	−	0.0281866i	0.352070	+	0.935974i	$0.385478\pi$
$360$	−59524.6	+	30364.5i	−0.459295	+	0.234294i
$361$	−62924.7	+	193662.i	−0.482844	+	1.48604i
$362$	62150.0	+	31667.0i	0.474269	+	0.241652i
$363$	−35262.3	+	69206.1i	−0.267607	+	0.525208i
$364$	72991.5	+	23716.4i	0.550896	+	0.178997i
$365$	104038.	−	104136.i	0.780921	−	0.781655i
$366$	−25384.8	−	78126.4i	−0.189501	−	0.583224i
$367$	17311.9	−	109303.i	0.128532	−	0.811520i	−0.836226	−	0.548384i	$-0.815243\pi$
$367$	17311.9	−	109303.i	0.128532	−	0.811520i	0.964759	−	0.263136i	$-0.0847569\pi$
$368$	864.522	+	864.522i	0.00638381	+	0.00638381i
$369$	58928.0	+	81107.5i	0.432782	+	0.595673i
$370$	15622.2	+	48003.6i	0.114114	+	0.350647i
$371$	−43934.3	−	31920.2i	−0.319195	−	0.231909i
$372$	51539.9	−	8163.12i	0.372441	−	0.0589889i
$373$	−17769.4	+	9053.99i	−0.127719	+	0.0650762i	−0.516683	−	0.856177i	$-0.672833\pi$
$373$	−17769.4	+	9053.99i	−0.127719	+	0.0650762i	0.388963	+	0.921253i	$0.372833\pi$
$374$			35405.1i			0.253118i
$375$	86945.9	+	44147.0i	0.618282	+	0.313934i
$376$	1792.69			0.0126803
$377$	−84660.8	−	166156.i	−0.595662	−	1.16905i
$378$	−9859.57	−	62250.9i	−0.0690040	−	0.435674i
$379$	−127218.	+	175100.i	−0.885664	+	1.21901i	0.0891554	+	0.996018i	$0.471583\pi$
$379$	−127218.	+	175100.i	−0.885664	+	1.21901i	−0.974820	+	0.222995i	$0.928417\pi$
$380$	−137985.	+	44905.8i	−0.955577	+	0.310982i
$381$	−110223.	+	80081.9i	−0.759318	+	0.551677i
$382$	−25252.8	+	25252.8i	−0.173054	+	0.173054i
$383$	49125.0	+	7780.64i	0.334892	+	0.0530417i	0.321616	−	0.946870i	$-0.395774\pi$
$383$	49125.0	+	7780.64i	0.334892	+	0.0530417i	0.0132761	+	0.999912i	$0.495774\pi$
$384$	−62735.0	+	20383.8i	−0.425449	+	0.138237i
$385$	27866.3	+	27840.1i	0.188000	+	0.187823i
$386$	−12763.9	+	39283.1i	−0.0856657	+	0.263652i
$387$	−12224.6	−	6228.74i	−0.0816230	−	0.0415890i
$388$	−31912.4	+	62631.5i	−0.211980	+	0.416035i
$389$	80370.7	+	26114.0i	0.531127	+	0.172574i	0.562289	−	0.826941i	$-0.309921\pi$
$389$	80370.7	+	26114.0i	0.531127	+	0.172574i	−0.0311620	+	0.999514i	$0.509921\pi$
$390$	39312.1	+	77064.8i	0.258462	+	0.506672i
$391$	−20925.1	−	64401.0i	−0.136872	−	0.421249i
$392$	12627.9	−	79729.6i	0.0821788	−	0.518856i
$393$	−9056.70	−	9056.70i	−0.0586388	−	0.0586388i
$394$	57584.6	+	79258.5i	0.370949	+	0.510568i
$395$	−61717.0	+	190249.i	−0.395558	+	1.21935i
$396$	16010.1	+	11632.0i	0.102095	+	0.0741762i
$397$	189997.	−	30092.6i	1.20550	−	0.190932i	0.478821	−	0.877913i	$-0.341064\pi$
$397$	189997.	−	30092.6i	1.20550	−	0.190932i	0.726676	+	0.686981i	$0.241064\pi$
$398$	92018.1	−	46885.6i	0.580908	−	0.295987i
$399$		−	121283.i		−	0.761825i
$400$	−2828.82	−	2051.20i	−0.0176801	−	0.0128200i
$401$	−115550.			−0.718590			−0.359295	−	0.933224i	$-0.616983\pi$
$401$	−115550.			−0.718590			−0.359295	+	0.933224i	$0.616983\pi$
$402$	−31384.5	−	61595.6i	−0.194206	−	0.381152i
$403$	29589.4	+	186820.i	0.182191	+	1.15031i
$404$	103518.	−	142480.i	0.634237	−	0.872952i
$405$	−20357.3	+	28047.1i	−0.124111	+	0.170993i
$406$	54495.4	−	39593.2i	0.330604	−	0.240198i
$407$	27411.5	−	27411.5i	0.165479	−	0.165479i
$408$	121313.	+	19214.0i	0.728763	+	0.115425i
$409$	243436.	−	79097.2i	1.45525	−	0.472841i	0.528637	−	0.848848i	$-0.322703\pi$
$409$	243436.	−	79097.2i	1.45525	−	0.472841i	0.926617	+	0.376008i	$0.122703\pi$
$410$	65972.8	−	129629.i	0.392462	−	0.771144i
$411$	26114.3	−	80371.6i	0.154595	−	0.475794i
$412$	−94124.4	−	47958.8i	−0.554508	−	0.282536i
$413$	17351.9	−	34055.1i	0.101730	−	0.199656i
$414$	21344.9	+	6935.39i	0.124536	+	0.0404641i
$415$	−208567.	+	33134.2i	−1.21102	+	0.192389i
$416$	−72360.7	−	222703.i	−0.418135	−	1.28689i
$417$	25163.1	−	158874.i	0.144708	−	0.913650i
$418$	−46722.3	−	46722.3i	−0.267406	−	0.267406i
$419$	109580.	+	150825.i	0.624173	+	0.859100i	0.997648	−	0.0685397i	$-0.0218340\pi$
$419$	109580.	+	150825.i	0.624173	+	0.859100i	−0.373475	+	0.927640i	$0.621834\pi$
$420$	42620.9	−	30996.5i	0.241615	−	0.175717i
$421$	22829.5	+	16586.6i	0.128805	+	0.0935823i	0.650322	−	0.759658i	$-0.274634\pi$
$421$	22829.5	+	16586.6i	0.128805	+	0.0935823i	−0.521517	+	0.853241i	$0.674634\pi$
$422$	64141.8	−	10159.1i	0.360177	−	0.0570464i
$423$	−1056.82	+	538.475i	−0.00590635	+	0.00300944i
$424$			102637.i			0.570917i
$425$	88022.4	+	172353.i	0.487321	+	0.954206i
$426$	−110020.			−0.606251
$427$	−82347.9	−	161617.i	−0.451645	−	0.886403i
$428$	−27308.0	−	172416.i	−0.149074	−	0.941219i
$429$	39049.2	−	53746.6i	0.212177	−	0.292036i
$430$	9.34468	+	19905.3i	5.05391e−5	+	0.107654i
$431$	99581.0	−	72349.9i	0.536071	−	0.389478i	−0.286553	−	0.958064i	$-0.592509\pi$
$431$	99581.0	−	72349.9i	0.536071	−	0.389478i	0.822624	+	0.568586i	$0.192509\pi$
$432$	3035.89	−	3035.89i	0.0162674	−	0.0162674i
$433$	−91064.8	−	14423.3i	−0.485708	−	0.0769285i	−0.0912219	−	0.995831i	$-0.529077\pi$
$433$	−91064.8	−	14423.3i	−0.485708	−	0.0769285i	−0.394486	+	0.918902i	$0.629077\pi$
$434$	−64979.5	+	21113.1i	−0.344983	+	0.112092i
$435$	−126484.	−	19972.2i	−0.668431	−	0.105547i
$436$	−38022.0	+	117020.i	−0.200015	+	0.615582i
$437$	112601.	+	57372.8i	0.589627	+	0.300430i
$438$	40712.5	−	79902.8i	0.212217	−	0.416499i
$439$	−139392.	−	45291.2i	−0.723284	−	0.235009i	−0.0758375	−	0.997120i	$-0.524163\pi$
$439$	−139392.	−	45291.2i	−0.723284	−	0.235009i	−0.647446	+	0.762111i	$0.724163\pi$
$440$	11611.6	−	73536.2i	0.0599773	−	0.379836i
$441$	16504.3	+	50794.9i	0.0848632	+	0.261182i
$442$	−26859.7	+	169586.i	−0.137486	+	0.868050i
$443$	31632.1	+	31632.1i	0.161184	+	0.161184i	0.783091	−	0.621907i	$-0.213642\pi$
$443$	31632.1	+	31632.1i	0.161184	+	0.161184i	−0.621907	+	0.783091i	$0.713642\pi$
$444$	−30485.2	−	41959.3i	−0.154640	−	0.212844i
$445$	205937.	−	96.6787i	1.03996	−	0.000488215i
$446$	−140223.	−	101878.i	−0.704937	−	0.512167i
$447$	171343.	−	27138.1i	0.857535	−	0.135820i
$448$	72684.2	−	37034.5i	0.362146	−	0.184523i
$449$			113831.i			0.564637i	0.959321	+	0.282318i	$0.0911034\pi$
$449$			113831.i			0.564637i	−0.959321	+	0.282318i	$0.908897\pi$
$450$	−63362.7	−	9974.70i	−0.312902	−	0.0492578i
$451$	−111695.			−0.549135
$452$	19305.0	+	37888.1i	0.0944914	+	0.185450i
$453$	35661.5	+	225158.i	0.173781	+	1.09721i
$454$	72948.6	−	100405.i	0.353920	−	0.487129i
$455$	112355.	+	154491.i	0.542713	+	0.746243i
$456$	−185446.	+	134734.i	−0.891842	+	0.647961i
$457$	−228992.	+	228992.i	−1.09645	+	1.09645i	−0.101627	+	0.994823i	$0.532405\pi$
$457$	−228992.	+	228992.i	−1.09645	+	1.09645i	−0.994823	+	0.101627i	$0.967595\pi$
$458$	62775.0	+	9942.58i	0.299265	+	0.0473989i
$459$	−226153.	+	73481.6i	−1.07344	+	0.348781i
$460$	8615.67	+	54232.4i	0.0407168	+	0.256297i
$461$	−43749.3	+	134647.i	−0.205859	+	0.633568i	0.793818	+	0.608155i	$0.208090\pi$
$461$	−43749.3	+	134647.i	−0.205859	+	0.633568i	−0.999677	+	0.0254131i	$0.991910\pi$
$462$	21381.6	+	10894.5i	0.100174	+	0.0510414i
$463$	117778.	−	231152.i	0.549415	−	1.07829i	−0.434670	−	0.900590i	$-0.643135\pi$
$463$	117778.	−	231152.i	0.549415	−	1.07829i	0.984085	−	0.177698i	$-0.0568651\pi$
$464$	4363.99	+	1417.95i	0.0202697	+	0.00658603i
$465$	115754.	+	58911.1i	0.535340	+	0.272453i
$466$	−2483.99	−	7644.94i	−0.0114387	−	0.0352049i
$467$	8184.14	−	51672.6i	0.0375266	−	0.236934i	−0.961795	−	0.273772i	$-0.911729\pi$
$467$	8184.14	−	51672.6i	0.0375266	−	0.236934i	0.999321	+	0.0368383i	$0.0117287\pi$
$468$	67861.7	+	67861.7i	0.309837	+	0.309837i
$469$	−89722.6	−	123493.i	−0.407902	−	0.561430i
$470$	1392.64	+	1010.82i	0.00630441	+	0.00457590i
$471$	177521.	+	128976.i	0.800216	+	0.581391i
$472$	−71347.7	+	11300.4i	−0.320255	+	0.0507234i
$473$	13619.6	−	6939.52i	0.0608753	−	0.0310175i
$474$			121848.i			0.542329i
$475$	−343605.	−	111287.i	−1.52290	−	0.493240i
$476$	104593.			0.461625
$477$	−30829.5	−	60506.3i	−0.135497	−	0.265928i
$478$	−13588.8	−	85796.4i	−0.0594738	−	0.375503i
$479$	−105519.	+	145234.i	−0.459896	+	0.632992i	−0.974487	−	0.224443i	$-0.927944\pi$
$479$	−105519.	+	145234.i	−0.459896	+	0.632992i	0.514592	+	0.857435i	$0.327944\pi$
$480$	−152947.	−	49616.0i	−0.663831	−	0.215347i
$481$	152093.	−	110502.i	0.657383	−	0.477617i
$482$	−5525.43	+	5525.43i	−0.0237833	+	0.0237833i
$483$	−45331.5	−	7179.80i	−0.194315	−	0.0307764i
$484$	118890.	−	38629.7i	0.507522	−	0.164904i
$485$	−155854.	+	79503.5i	−0.662572	+	0.337989i
$486$	40386.1	−	124296.i	0.170986	−	0.526239i
$487$	−58732.8	−	29925.8i	−0.247641	−	0.126179i	0.325765	−	0.945451i	$-0.394378\pi$
$487$	−58732.8	−	29925.8i	−0.247641	−	0.126179i	−0.573406	+	0.819271i	$0.694378\pi$
$488$	−155636.	+	305454.i	−0.653539	+	1.28264i
$489$	−32449.3	−	10543.4i	−0.135702	−	0.0440923i
$490$	54765.9	−	54817.4i	0.228096	−	0.228311i
$491$	2138.80	+	6582.55i	0.00887171	+	0.0273043i	0.955394	−	0.295333i	$-0.0954306\pi$
$491$	2138.80	+	6582.55i	0.00887171	+	0.0273043i	−0.946523	+	0.322637i	$0.895431\pi$
$492$	−23377.0	+	147596.i	−0.0965735	+	0.609741i
$493$	−179704.	−	179704.i	−0.739374	−	0.739374i
$494$	−188348.	−	259239.i	−0.771805	−	1.06230i
$495$	15243.1	+	46838.6i	0.0622103	+	0.191158i
$496$	−3765.33	−	2735.68i	−0.0153052	−	0.0111199i
$497$	−239942.	+	38003.1i	−0.971389	+	0.153853i
$498$	−114633.	+	58408.4i	−0.462222	+	0.235514i
$499$		−	571.613i		−	0.00229562i	−0.999999	−	0.00114781i	$-0.999635\pi$
$499$		−	571.613i		−	0.00229562i	0.999999	−	0.00114781i	$-0.000365360\pi$
$500$	−48707.2	−	149190.i	−0.194829	−	0.596760i
$501$	238931.			0.951911
$502$	72085.6	+	141476.i	0.286050	+	0.561404i
$503$	19729.9	+	124570.i	0.0779811	+	0.492353i	0.995508	+	0.0946793i	$0.0301826\pi$
$503$	19729.9	+	124570.i	0.0779811	+	0.492353i	−0.917527	+	0.397674i	$0.869817\pi$
$504$	−52835.0	+	72721.2i	−0.207999	+	0.286286i
$505$	416834.	−	135654.i	1.63448	−	0.531924i
$506$	−20229.1	+	14697.3i	−0.0790086	+	0.0574031i
$507$	101779.	−	101779.i	0.395950	−	0.395950i
$508$	216576.	+	34302.3i	0.839236	+	0.132922i
$509$	170355.	−	55351.8i	0.657537	−	0.213647i	0.0388026	−	0.999247i	$-0.487646\pi$
$509$	170355.	−	55351.8i	0.657537	−	0.213647i	0.618735	+	0.785600i	$0.287646\pi$
$510$	83407.5	+	83329.3i	0.320675	+	0.320374i
$511$	61189.7	−	188322.i	0.234334	−	0.721207i
$512$	10199.7	+	5197.02i	0.0389089	+	0.0198251i
$513$	201473.	−	395413.i	0.765564	−	1.50250i
$514$	267902.	+	87046.5i	1.01403	+	0.329477i
$515$	−119480.	−	234221.i	−0.450486	−	0.883103i
$516$	−6319.58	−	19449.7i	−0.0237350	−	0.0730487i
$517$	206.719	−	1305.17i	0.000773392	−	0.00488300i
$518$	48017.8	+	48017.8i	0.178955	+	0.178955i
$519$	−13577.9	−	18688.3i	−0.0504077	−	0.0693802i
$520$	111406.	−	343419.i	0.412003	−	1.27004i
$521$	273458.	+	198679.i	1.00743	+	0.731942i	0.963669	−	0.267100i	$-0.0860653\pi$
$521$	273458.	+	198679.i	1.00743	+	0.731942i	0.0437632	+	0.999042i	$0.486065\pi$
$522$	83194.6	−	13176.7i	0.305319	−	0.0483578i
$523$	−313166.	+	159566.i	−1.14491	+	0.583360i	−0.920348	−	0.391100i	$-0.872095\pi$
$523$	−313166.	+	159566.i	−1.14491	+	0.583360i	−0.224561	+	0.974460i	$0.572095\pi$
$524$			20613.9i			0.0750754i
$525$	131172.	−	123.159i	0.475907	−	0.000446836i
$526$	92855.0			0.335609
$527$	117028.	+	229679.i	0.421373	+	0.826991i
$528$	255.722	+	1614.56i	0.000917275	+	0.00579145i
$529$	−136377.	+	187706.i	−0.487336	+	0.670761i
$530$	−57872.6	+	79733.5i	−0.206026	+	0.283850i
$531$	38666.3	−	28092.7i	0.137133	−	0.0996333i
$532$	−138026.	+	138026.i	−0.487684	+	0.487684i
$533$	−535003.	−	84736.1i	−1.88322	−	0.298273i
$534$	119319.	−	38769.2i	0.418435	−	0.135958i
$535$	197075.	−	387231.i	0.688532	−	1.35289i
$536$	−89150.6	+	274377.i	−0.310309	+	0.955034i
$537$	−106826.	−	54430.6i	−0.370449	−	0.188753i
$538$	−48301.6	+	94797.3i	−0.166877	+	0.327515i
$539$	−56591.3	−	18387.6i	−0.194793	−	0.0632919i
$540$	190445.	−	30255.2i	0.653103	−	0.103756i
$541$	−11803.3	−	36326.7i	−0.0403280	−	0.124117i	0.928866	−	0.370417i	$-0.120785\pi$
$541$	−11803.3	−	36326.7i	−0.0403280	−	0.124117i	−0.969194	+	0.246300i	$0.920785\pi$
$542$	15445.2	−	97517.5i	0.0525771	−	0.331959i
$543$	−126128.	−	126128.i	−0.427770	−	0.427770i
$544$	−187576.	−	258176.i	−0.633838	−	0.872403i
$545$	−247679.	+	180127.i	−0.833867	+	0.606438i
$546$	94150.1	+	68404.1i	0.315817	+	0.229454i
$547$	94547.4	−	14974.8i	0.315991	−	0.0500481i	0.00357559	−	0.999994i	$-0.498862\pi$
$547$	94547.4	−	14974.8i	0.315991	−	0.0500481i	0.312416	+	0.949946i	$0.398862\pi$
$548$	−121186.	+	61747.4i	−0.403544	+	0.205616i
$549$		−	226819.i		−	0.752549i
$550$	50484.2	−	50579.1i	0.166890	−	0.167204i
$551$	474292.			1.56222
$552$	39380.9	+	77289.3i	0.129243	+	0.253654i
$553$	42088.8	+	265738.i	0.137631	+	0.868968i
$554$	22744.1	−	31304.5i	0.0741052	−	0.101997i
$555$	−60.6029	−	129092.i	−0.000196747	−	0.419094i
$556$	−209443.	+	152169.i	−0.677510	+	0.492240i
$557$	215048.	−	215048.i	0.693145	−	0.693145i	−0.269778	−	0.962923i	$-0.586950\pi$
$557$	215048.	−	215048.i	0.693145	−	0.693145i	0.962923	+	0.269778i	$0.0869502\pi$
$558$	−84384.7	−	13365.2i	−0.271016	−	0.0429247i
$559$	70500.6	−	22907.0i	0.225616	−	0.0733069i
$560$	−4642.88	−	733.126i	−0.0148051	−	0.00233778i
$561$	27977.8	−	86106.7i	0.0888970	−	0.273597i
$562$	−4008.93	−	2042.65i	−0.0126927	−	0.00646728i
$563$	−28158.6	+	55264.4i	−0.0888371	+	0.174353i	−0.931150	−	0.364636i	$-0.881193\pi$
$563$	−28158.6	+	55264.4i	−0.0888371	+	0.174353i	0.842313	+	0.538989i	$0.181193\pi$
$564$	−1681.43	−	546.328i	−0.00528591	−	0.00171750i
$565$	−16508.0	+	104545.i	−0.0517126	+	0.327495i
$566$	87906.1	+	270547.i	0.274401	+	0.844521i
$567$	−7292.86	+	46045.3i	−0.0226846	+	0.143225i
$568$	324661.	+	324661.i	1.00631	+	1.00631i
$569$	−76926.0	−	105880.i	−0.237601	−	0.327030i	0.673520	−	0.739169i	$-0.264782\pi$
$569$	−76926.0	−	105880.i	−0.237601	−	0.327030i	−0.911121	+	0.412139i	$0.864782\pi$
$570$	−220034.	+	103.297i	−0.677236	+	0.000317933i
$571$	−419454.	−	304751.i	−1.28651	−	0.934703i	−0.286779	−	0.957997i	$-0.592585\pi$
$571$	−419454.	−	304751.i	−1.28651	−	0.934703i	−0.999729	+	0.0232938i	$0.992585\pi$
$572$	−105606.	+	16726.4i	−0.322773	+	0.0511222i
$573$	81371.0	−	41460.6i	0.247834	−	0.126278i
$574$		−	195660.i		−	0.593853i
$575$	−61936.2	+	121839.i	−0.187331	+	0.368512i
$576$	102008.			0.307459
$577$	207997.	+	408217.i	0.624748	+	1.22614i	0.958934	+	0.283630i	$0.0915388\pi$
$577$	207997.	+	408217.i	0.624748	+	1.22614i	−0.334186	+	0.942507i	$0.608461\pi$
$578$	4718.85	+	29793.6i	0.0141247	+	0.0891801i
$579$	62084.4	−	85451.9i	0.185193	−	0.254897i
$580$	121215.	+	166674.i	0.360331	+	0.495464i
$581$	−229827.	+	166979.i	−0.680845	+	0.494663i
$582$	−75369.2	+	75369.2i	−0.222509	+	0.222509i
$583$	74725.5	+	11835.4i	0.219853	+	0.0348212i
$584$	−355927.	+	115648.i	−1.04360	+	0.339087i
$585$	37478.7	+	235915.i	0.109515	+	0.689355i
$586$	−22469.2	+	69153.1i	−0.0654324	+	0.201380i
$587$	−15489.9	−	7892.50i	−0.0449544	−	0.0229054i	0.431369	−	0.902176i	$-0.358031\pi$
$587$	−15489.9	−	7892.50i	−0.0449544	−	0.0229054i	−0.476323	+	0.879270i	$0.658031\pi$
$588$	−36142.1	+	70932.8i	−0.104534	+	0.205160i
$589$	−457531.	−	148661.i	−1.31883	−	0.428515i
$590$	−61798.1	−	31451.2i	−0.177530	−	0.0903509i
$591$	−77416.7	−	238264.i	−0.221646	−	0.682156i
$592$	−723.644	+	4568.91i	−0.00206482	+	0.0130367i
$593$	−360231.	−	360231.i	−1.02441	−	1.02441i	−0.999695	−	0.0247113i	$-0.992133\pi$
$593$	−360231.	−	360231.i	−1.02441	−	1.02441i	−0.0247113	−	0.999695i	$-0.507867\pi$
$594$	51611.5	+	71037.2i	0.146276	+	0.201332i
$595$	210686.	+	152922.i	0.595117	+	0.431951i
$596$	−225881.	−	164112.i	−0.635898	−	0.462007i
$597$	−260842.	+	41313.2i	−0.731860	+	0.115915i
$598$	−108044.	+	55051.4i	−0.302134	+	0.153945i
$599$			272492.i			0.759451i	0.925099	+	0.379726i	$0.123982\pi$
$599$			272492.i			0.759451i	−0.925099	+	0.379726i	$0.876018\pi$
$600$	−145908.	−	200429.i	−0.405300	−	0.556747i
$601$	76039.1			0.210517			0.105259	−	0.994445i	$-0.466433\pi$
$601$	76039.1			0.210517			0.105259	+	0.994445i	$0.466433\pi$
$602$	12156.2	+	23858.0i	0.0335433	+	0.0658325i
$603$	−29859.9	−	188528.i	−0.0821210	−	0.518492i
$604$	215656.	−	296825.i	0.591136	−	0.813629i
$605$	295964.	+	96011.0i	0.808590	+	0.262307i
$606$	216048.	−	156968.i	0.588308	−	0.427431i
$607$	215841.	−	215841.i	0.585810	−	0.585810i	−0.350684	−	0.936494i	$-0.614051\pi$
$607$	215841.	−	215841.i	0.585810	−	0.585810i	0.936494	+	0.350684i	$0.114051\pi$
$608$	588235.	+	93167.2i	1.59127	+	0.252032i
$609$	−163822.	+	53229.1i	−0.441711	+	0.143521i
$610$	−293138.	+	149534.i	−0.787793	+	0.401866i
$611$	1980.31	−	6094.78i	0.00530459	−	0.0163258i
$612$	116535.	+	59377.7i	0.311139	+	0.158533i
$613$	−86593.2	+	169949.i	−0.230443	+	0.452269i	−0.977054	−	0.212991i	$-0.931679\pi$
$613$	−86593.2	+	169949.i	−0.230443	+	0.452269i	0.746611	+	0.665260i	$0.231679\pi$
$614$	127596.	+	41458.6i	0.338456	+	0.109971i
$615$	−262884.	+	263131.i	−0.695046	+	0.695699i
$616$	−30946.7	−	95244.3i	−0.0815555	−	0.251002i
$617$	−14133.4	+	89235.0i	−0.0371259	+	0.234404i	−0.999273	−	0.0381272i	$-0.987861\pi$
$617$	−14133.4	+	89235.0i	−0.0371259	+	0.234404i	0.962147	+	0.272531i	$0.0878608\pi$
$618$	−113267.	−	113267.i	−0.296569	−	0.296569i
$619$	398615.	+	548646.i	1.04033	+	1.43190i	0.896899	+	0.442235i	$0.145814\pi$
$619$	398615.	+	548646.i	1.04033	+	1.43190i	0.143433	+	0.989660i	$0.454186\pi$
$620$	−64689.8	−	198777.i	−0.168288	−	0.517110i
$621$	−135864.	−	98711.3i	−0.352308	−	0.255967i
$622$	−292189.	+	46278.1i	−0.755236	+	0.119618i
$623$	246831.	−	125767.i	0.635951	−	0.324033i
$624$			7927.55i			0.0203596i
$625$	120012.	−	371732.i	0.307231	−	0.951635i
$626$	−126918.			−0.323874
$627$	76709.7	+	150551.i	0.195126	+	0.382957i
$628$	−55245.8	−	348808.i	−0.140081	−	0.884438i
$629$	150594.	−	207274.i	0.380632	−	0.523895i
$630$	−82049.0	+	26701.9i	−0.206725	+	0.0672762i
$631$	−284185.	+	206472.i	−0.713744	+	0.518565i	−0.884379	−	0.466769i	$-0.845418\pi$
$631$	−284185.	+	206472.i	−0.713744	+	0.518565i	0.170636	+	0.985334i	$0.445418\pi$
$632$	359565.	−	359565.i	0.900209	−	0.900209i
$633$	−164023.	−	25978.7i	−0.409353	−	0.0648351i
$634$	403999.	−	131267.i	1.00508	−	0.326571i
$635$	386107.	+	385745.i	0.957547	+	0.956649i
$636$	31279.1	−	96267.2i	0.0773286	−	0.237993i
$637$	−257115.	−	131007.i	−0.633649	−	0.322861i
$638$	−42604.1	+	83615.2i	−0.104667	+	0.205421i
$639$	−288912.	−	93873.2i	−0.707561	−	0.229901i
$640$	120075.	+	235388.i	0.293152	+	0.574677i
$641$	115836.	+	356507.i	0.281922	+	0.867666i	0.987304	+	0.158839i	$0.0507751\pi$
$641$	115836.	+	356507.i	0.281922	+	0.867666i	−0.705383	+	0.708827i	$0.749225\pi$
$642$	41408.3	−	261442.i	0.100466	−	0.634315i
$643$	531851.	+	531851.i	1.28638	+	1.28638i	0.936972	+	0.349404i	$0.113616\pi$
$643$	531851.	+	531851.i	1.28638	+	1.28638i	0.349404	+	0.936972i	$0.386384\pi$
$644$	43418.4	+	59760.3i	0.104689	+	0.144092i
$645$	15706.8	−	48417.9i	0.0377545	−	0.116382i
$646$	−353295.	−	256684.i	−0.846589	−	0.615083i
$647$	251564.	−	39843.9i	0.600953	−	0.0951816i	0.151457	−	0.988464i	$-0.451604\pi$
$647$	251564.	−	39843.9i	0.600953	−	0.0951816i	0.449496	+	0.893282i	$0.351604\pi$
$648$	78506.4	−	40001.0i	0.186963	−	0.0952622i
$649$			53248.1i			0.126420i
$650$	280184.	−	203968.i	0.663158	−	0.482764i
$651$	174717.			0.412262
$652$	24929.9	+	48927.7i	0.0586443	+	0.115096i
$653$	984.148	+	6213.67i	0.00230799	+	0.0145721i	0.988815	−	0.149144i	$-0.0476518\pi$
$653$	984.148	+	6213.67i	0.00230799	+	0.0145721i	−0.986507	+	0.163716i	$0.947652\pi$
$654$	−109665.	+	150941.i	−0.256397	+	0.352900i
$655$	−30138.8	+	41523.5i	−0.0702495	+	0.0967857i
$656$	10782.9	−	7834.24i	0.0250569	−	0.0182049i
$657$	175087.	−	175087.i	0.405624	−	0.405624i
$658$	2286.33	+	362.118i	0.00528064	+	0.000836371i
$659$	−347264.	+	112833.i	−0.799631	+	0.259816i	−0.680200	−	0.733027i	$-0.738107\pi$
$659$	−347264.	+	112833.i	−0.799631	+	0.259816i	−0.119431	+	0.992843i	$0.538107\pi$
$660$	−33301.4	+	65433.6i	−0.0764495	+	0.150215i
$661$	183671.	−	565281.i	0.420375	−	1.29378i	−0.486978	−	0.873414i	$-0.661901\pi$
$661$	183671.	−	565281.i	0.420375	−	1.29378i	0.907354	−	0.420368i	$-0.138099\pi$
$662$	−330023.	−	168155.i	−0.753058	−	0.383702i
$663$	199334.	−	391214.i	0.453475	−	0.889995i
$664$	510632.	+	165914.i	1.15817	+	0.376312i
$665$	−479835.	+	76229.3i	−1.08505	+	0.172377i
$666$	26240.5	+	80760.1i	0.0591595	+	0.182074i
$667$	28077.4	−	177274.i	0.0631111	−	0.398468i
$668$	−271915.	−	271915.i	−0.609368	−	0.609368i
$669$	260523.	+	358579.i	0.582094	+	0.801184i
$670$	−223966.	+	162881.i	−0.498921	+	0.362845i
$671$	204440.	+	148534.i	0.454068	+	0.329900i
$672$	−213634.	+	33836.4i	−0.473078	+	0.0749281i
$673$	564178.	−	287463.i	1.24562	−	0.634676i	0.298151	−	0.954519i	$-0.403630\pi$
$673$	564178.	−	287463.i	1.24562	−	0.634676i	0.947471	+	0.319843i	$0.103630\pi$
$674$		−	193013.i		−	0.424881i
$675$	427856.	+	217498.i	0.939053	+	0.477361i
$676$	−231658.			−0.506936
$677$	−297667.	−	584204.i	−0.649461	−	1.27464i	−0.947400	−	0.320053i	$-0.896299\pi$
$677$	−297667.	−	584204.i	−0.649461	−	1.27464i	0.297939	−	0.954585i	$-0.403701\pi$
$678$	10086.8	+	63685.3i	0.0219428	+	0.138541i
$679$	−138338.	+	190406.i	−0.300056	+	0.412992i
$680$	−230.986	−	492028.i	−0.000499537	−	1.06407i
$681$	−256756.	+	186544.i	−0.553638	+	0.402242i
$682$	67306.6	−	67306.6i	0.144707	−	0.144707i
$683$	102547.	+	16241.9i	0.219828	+	0.0348173i	0.265377	−	0.964145i	$-0.414504\pi$
$683$	102547.	+	16241.9i	0.219828	+	0.0348173i	−0.0455489	+	0.998962i	$0.514504\pi$
$684$	−232143.	+	75428.0i	−0.496186	+	0.161220i
$685$	−334388.	−	52801.0i	−0.712640	−	0.112528i
$686$	93103.8	−	286544.i	0.197842	−	0.608896i
$687$	−144815.	−	73786.7i	−0.306831	−	0.156338i
$688$	−828.085	+	1625.21i	−0.00174944	+	0.00343346i
$689$	348947.	+	113380.i	0.735056	+	0.238834i
$690$	−12987.1	+	82247.1i	−0.0272781	+	0.172752i
$691$	29149.2	+	89712.1i	0.0610479	+	0.187886i	0.976929	−	0.213563i	$-0.0685067\pi$
$691$	29149.2	+	89712.1i	0.0610479	+	0.187886i	−0.915881	+	0.401449i	$0.868507\pi$
$692$	−5815.95	+	36720.5i	−0.0121453	+	0.0766824i
$693$	46852.4	+	46852.4i	0.0975587	+	0.0975587i
$694$	84635.4	+	116491.i	0.175725	+	0.241864i
$695$	−644369.	+	302.504i	−1.33403	+	0.000626269i
$696$	263380.	+	191357.i	0.543706	+	0.395026i
$697$	−729110.	+	115480.i	−1.50082	+	0.237706i
$698$	−177071.	+	90222.3i	−0.363444	+	0.185184i
$699$			20555.7i			0.0420705i
$700$	−149420.	−	149140.i	−0.304939	−	0.304367i
$701$	−474733.			−0.966081			−0.483041	−	0.875598i	$-0.660468\pi$
$701$	−474733.			−0.966081			−0.483041	+	0.875598i	$0.660468\pi$
$702$	193321.	+	379413.i	0.392287	+	0.769907i
$703$	74798.7	+	472260.i	0.151350	+	0.955588i
$704$	−66800.6	+	91943.2i	−0.134783	+	0.185513i
$705$	−2588.20	−	3558.84i	−0.00520739	−	0.00716028i
$706$	−255831.	+	185872.i	−0.513267	+	0.372910i
$707$	416957.	−	416957.i	0.834167	−	0.834167i
$708$	70363.4	+	11144.5i	0.140372	+	0.0222327i
$709$	570651.	−	185416.i	1.13522	−	0.368854i	0.319659	−	0.947532i	$-0.396431\pi$
$709$	570651.	−	185416.i	1.13522	−	0.368854i	0.815556	+	0.578679i	$0.196431\pi$
$710$	69150.1	+	435274.i	0.137175	+	0.863467i
$711$	−103966.	+	319973.i	−0.205660	+	0.632957i
$712$	−466507.	−	237697.i	−0.920234	−	0.468883i
$713$	−82649.4	+	162209.i	−0.162578	+	0.319077i
$714$	150837.	+	49009.8i	0.295876	+	0.0961360i
$715$	−237182.	−	120710.i	−0.463948	−	0.236119i
$716$	59628.5	+	183518.i	0.116313	+	0.357974i
$717$	−34749.3	+	219398.i	−0.0675939	+	0.426771i
$718$	−20286.5	−	20286.5i	−0.0393511	−	0.0393511i
$719$	211680.	+	291352.i	0.409469	+	0.563586i	0.963089	−	0.269183i	$-0.0867538\pi$
$719$	211680.	+	291352.i	0.409469	+	0.563586i	−0.553619	+	0.832770i	$0.686754\pi$
$720$	−4756.80	−	3452.60i	−0.00917592	−	0.00666012i
$721$	−286148.	−	207898.i	−0.550452	−	0.399927i
$722$	490830.	−	77739.8i	0.941579	−	0.149131i
$723$	17804.4	−	9071.77i	0.0340604	−	0.0173546i
$724$			287078.i			0.547676i
$725$	481.628	+	512962.i	0.000916296	+	0.975910i
$726$	189555.			0.359636
$727$	279741.	+	549023.i	0.529283	+	1.03878i	0.988609	+	0.150508i	$0.0480910\pi$
$727$	279741.	+	549023.i	0.529283	+	1.03878i	−0.459326	+	0.888268i	$0.651909\pi$
$728$	−75974.6	−	479685.i	−0.143353	−	0.905093i
$729$	−262441.	+	361220.i	−0.493830	+	0.679699i
$730$	−341709.	−	110851.i	−0.641226	−	0.208014i
$731$	81729.9	−	59380.3i	0.152949	−	0.111124i
$732$	239065.	−	239065.i	0.446164	−	0.446164i
$733$	161378.	+	25559.7i	0.300355	+	0.0475716i	0.304793	−	0.952419i	$-0.401413\pi$
$733$	161378.	+	25559.7i	0.300355	+	0.0475716i	−0.00443790	+	0.999990i	$0.501413\pi$
$734$	−256856.	+	83457.7i	−0.476758	+	0.154908i
$735$	−176511.	+	90041.1i	−0.326735	+	0.166673i
$736$	69645.3	−	214346.i	0.128569	−	0.395695i
$737$	189481.	+	96545.6i	0.348844	+	0.177745i
$738$	111077.	−	218000.i	0.203943	−	0.400262i
$739$	−210816.	−	68498.2i	−0.386024	−	0.125427i	0.109574	−	0.993979i	$-0.465051\pi$
$739$	−210816.	−	68498.2i	−0.386024	−	0.125427i	−0.495598	+	0.868552i	$0.665051\pi$
$740$	−146843.	+	146981.i	−0.268158	+	0.268410i
$741$	253215.	+	779316.i	0.461162	+	1.41931i
$742$	−20732.5	+	130900.i	−0.0376568	+	0.237756i
$743$	−385318.	−	385318.i	−0.697978	−	0.697978i	0.265996	−	0.963974i	$-0.414299\pi$
$743$	−385318.	−	385318.i	−0.697978	−	0.697978i	−0.963974	+	0.265996i	$0.914299\pi$
$744$	−194094.	−	267147.i	−0.350644	−	0.482620i
$745$	−215060.	−	660830.i	−0.387478	−	1.19063i
$746$	39375.2	+	28607.8i	0.0707531	+	0.0514051i
$747$	−350862.	+	55571.0i	−0.628774	+	0.0995881i
$748$	−129834.	+	66153.5i	−0.232051	+	0.118236i
$749$		−	584480.i		−	1.04185i
$750$	−335.156	−	237974.i	−0.000595832	−	0.423064i
$751$	−434899.			−0.771096			−0.385548	−	0.922688i	$-0.625988\pi$
$751$	−434899.			−0.771096			−0.385548	+	0.922688i	$0.625988\pi$
$752$	71.5880	+	140.499i	0.000126592	+	0.000248450i
$753$	−63518.3	−	401039.i	−0.112023	−	0.707288i
$754$	−267502.	+	368185.i	−0.470527	+	0.647624i
$755$	868381.	−	282605.i	1.52341	−	0.495776i
$756$	209857.	−	152470.i	0.367180	−	0.266772i
$757$	112978.	−	112978.i	0.197153	−	0.197153i	−0.601626	−	0.798778i	$-0.705480\pi$
$757$	112978.	−	112978.i	0.197153	−	0.197153i	0.798778	+	0.601626i	$0.205480\pi$
$758$	521700.	+	82629.2i	0.907994	+	0.143812i
$759$	60811.9	−	19759.0i	0.105561	−	0.0342990i
$760$	649608.	+	648999.i	1.12467	+	1.12361i
$761$	155821.	−	479568.i	0.269065	−	0.828096i	−0.721664	−	0.692243i	$-0.756622\pi$
$761$	155821.	−	479568.i	0.269065	−	0.828096i	0.990729	−	0.135853i	$-0.0433775\pi$
$762$	296257.	+	150951.i	0.510222	+	0.259971i
$763$	−187030.	+	367067.i	−0.321264	+	0.630516i
$764$	−139788.	−	45419.9i	−0.239488	−	0.0778144i
$765$	147928.	+	289989.i	0.252771	+	0.495517i
$766$	−37509.2	−	115441.i	−0.0639263	−	0.196745i
$767$	−40396.2	+	255051.i	−0.0686672	+	0.433548i
$768$	285100.	+	285100.i	0.483364	+	0.483364i
$769$	−487601.	−	671125.i	−0.824540	−	1.13488i	−0.988915	−	0.148484i	$-0.952561\pi$
$769$	−487601.	−	671125.i	−0.824540	−	1.13488i	0.164375	−	0.986398i	$-0.447439\pi$
$770$	29663.1	−	91439.8i	0.0500306	−	0.154225i
$771$	−582762.	−	423401.i	−0.980353	−	0.712268i
$772$	−167903.	+	26593.3i	−0.281725	+	0.0446208i
$773$	219412.	−	111796.i	0.367199	−	0.187097i	−0.260648	−	0.965434i	$-0.583936\pi$
$773$	219412.	−	111796.i	0.367199	−	0.187097i	0.627847	+	0.778337i	$0.283936\pi$
$774$			33483.1i			0.0558913i
$775$	160317.	−	494986.i	0.266917	−	0.824118i
$776$	444818.			0.738684
$777$	−78836.7	−	154726.i	−0.130583	−	0.256283i
$778$	−32262.4	−	203697.i	−0.0533012	−	0.336531i
$779$	809777.	−	1.11456e6i	1.33441	−	1.83666i
$780$	−209150.	+	288154.i	−0.343770	+	0.473626i
$781$	273808.	−	198933.i	0.448894	−	0.326141i
$782$	−116854.	+	116854.i	−0.191087	+	0.191087i
$783$	−622522.	−	98597.8i	−1.01539	−	0.160821i
$784$	6752.98	−	2194.18i	0.0109866	−	0.00356976i
$785$	398695.	−	783392.i	0.646996	−	1.27128i
$786$	−9659.17	+	29727.9i	−0.0156349	+	0.0481192i
$787$	−67080.3	−	34179.1i	−0.108304	−	0.0551838i	0.398999	−	0.916951i	$-0.369358\pi$
$787$	−67080.3	−	34179.1i	−0.108304	−	0.0551838i	−0.507303	+	0.861768i	$0.669358\pi$
$788$	−183052.	+	359260.i	−0.294797	+	0.578571i
$789$	−225827.	−	73375.7i	−0.362762	−	0.117869i
$790$	482070.	−	76584.4i	0.772425	−	0.122712i
$791$	43996.3	+	135407.i	0.0703175	+	0.216415i
$792$	19590.2	−	123687.i	0.0312311	−	0.197186i
$793$	866557.	+	866557.i	1.37800	+	1.37800i
$794$	−275942.	−	379802.i	−0.437701	−	0.602443i
$795$	203755.	−	148183.i	0.322385	−	0.234458i
$796$	343867.	+	249834.i	0.542705	+	0.394298i
$797$	−272286.	+	43125.8i	−0.428655	+	0.0678923i	−0.367034	−	0.930207i	$-0.619627\pi$
$797$	−272286.	+	43125.8i	−0.428655	+	0.0678923i	−0.0616206	+	0.998100i	$0.519627\pi$
$798$	−263727.	+	134376.i	−0.414141	+	0.211016i
$799$		−	8733.51i		−	0.0136803i
$800$	−100166.	+	636289.i	−0.156509	+	0.994202i
$801$	346411.			0.539917
$802$	128023.	+	251260.i	0.199040	+	0.390638i
$803$	43155.0	+	272470.i	0.0669267	+	0.422559i
$804$	167235.	−	230179.i	0.258711	−	0.356086i
$805$	86.3135	+	183858.i	0.000133195	+	0.283721i
$806$	373451.	−	271328.i	0.574863	−	0.417662i
$807$	192382.	−	192382.i	0.295405	−	0.295405i
$808$	−1.10074e6	−	174340.i	−1.68602	−	0.267039i
$809$	−285514.	+	92769.2i	−0.436245	+	0.141745i	−0.518903	−	0.854833i	$-0.673659\pi$
$809$	−285514.	+	92769.2i	−0.436245	+	0.141745i	0.0826574	+	0.996578i	$0.473659\pi$
$810$	83542.3	+	13191.6i	0.127332	+	0.0201061i
$811$	36767.5	−	113159.i	0.0559013	−	0.172047i	−0.919207	−	0.393774i	$-0.871169\pi$
$811$	36767.5	−	113159.i	0.0559013	−	0.172047i	0.975109	+	0.221727i	$0.0711694\pi$
$812$	247015.	+	125860.i	0.374637	+	0.190887i
$813$	−114624.	+	224961.i	−0.173417	+	0.340351i
$814$	−89975.9	−	29234.9i	−0.135793	−	0.0441218i
$815$	−21317.9	+	135006.i	−0.0320944	+	0.203254i
$816$	3338.55	+	10275.0i	0.00501393	+	0.0154313i
$817$	−29493.7	+	186216.i	−0.0441860	+	0.278980i
$818$	−441709.	−	441709.i	−0.660130	−	0.660130i
$819$	188873.	+	259961.i	0.281580	+	0.387562i
$820$	598630.	−	281.031i	0.890289	−	0.000417952i
$821$	−170388.	−	123794.i	−0.252786	−	0.183660i	0.454174	−	0.890913i	$-0.349934\pi$
$821$	−170388.	−	123794.i	−0.252786	−	0.183660i	−0.706961	+	0.707253i	$0.749934\pi$
$822$	−203699.	+	32262.7i	−0.301470	+	0.0477482i
$823$	−452461.	+	230540.i	−0.668008	+	0.340367i	−0.754890	−	0.655852i	$-0.772310\pi$
$823$	−452461.	+	230540.i	−0.668008	+	0.340367i	0.0868820	+	0.996219i	$0.472310\pi$
$824$			668484.i			0.984547i
$825$	−162748.	+	83116.9i	−0.239116	+	0.122119i
$826$	−93276.9			−0.136714
$827$	443244.	+	869916.i	0.648085	+	1.27194i	0.948090	+	0.318002i	$0.103012\pi$
$827$	443244.	+	869916.i	0.648085	+	1.27194i	−0.300005	+	0.953938i	$0.596988\pi$
$828$	14449.8	+	91232.3i	0.0210766	+	0.133072i
$829$	−111499.	+	153465.i	−0.162241	+	0.223305i	−0.882396	−	0.470508i	$-0.844071\pi$
$829$	−111499.	+	153465.i	−0.162241	+	0.223305i	0.720155	+	0.693813i	$0.244071\pi$
$830$	303131.	+	416813.i	0.440022	+	0.605041i
$831$	−80051.9	+	58161.1i	−0.115923	+	0.0842230i
$832$	−389718.	+	389718.i	−0.562994	+	0.562994i
$833$	−388422.	−	61520.0i	−0.559776	−	0.0886598i
$834$	−373345.	+	121307.i	−0.536758	+	0.174403i
$835$	−150173.	−	945285.i	−0.215387	−	1.35578i
$836$	84035.3	−	258634.i	0.120240	−	0.370061i
$837$	569619.	+	290235.i	0.813080	+	0.414285i
$838$	206554.	−	405385.i	0.294134	−	0.577271i
$839$	−251532.	−	81727.6i	−0.357329	−	0.116103i	0.124851	−	0.992176i	$-0.460155\pi$
$839$	−251532.	−	81727.6i	−0.357329	−	0.116103i	−0.482180	+	0.876072i	$0.660155\pi$
$840$	−297213.	−	151262.i	−0.421220	−	0.214373i
$841$	10403.5	+	32018.7i	0.0147091	+	0.0452701i
$842$	10773.2	−	68019.2i	0.0151957	−	0.0959417i
$843$	8135.73	+	8135.73i	0.0114483	+	0.0114483i
$844$	157101.	+	216231.i	0.220544	+	0.303552i
$845$	−466638.	−	338698.i	−0.653531	−	0.474350i
$846$	2341.80	+	1701.41i	0.00327196	+	0.00237722i
$847$	413400.	−	65476.1i	0.576240	−	0.0912675i
$848$	−8044.06	+	4098.65i	−0.0111862	+	0.00569967i
$849$		−	727447.i		−	1.00922i
$850$	277253.	−	382361.i	0.383741	−	0.529219i
$851$	180942.			0.249851
$852$	−205569.	−	403453.i	−0.283191	−	0.555793i
$853$	87974.8	+	555451.i	0.120910	+	0.763393i	0.971408	+	0.237415i	$0.0763003\pi$
$853$	87974.8	+	555451.i	0.120910	+	0.763393i	−0.850499	+	0.525977i	$0.823700\pi$
$854$	−260194.	+	358126.i	−0.356764	+	0.491044i
$855$	−577897.	−	187470.i	−0.790529	−	0.256448i
$856$	−893687.	+	649302.i	−1.21966	+	0.886133i
$857$	−580391.	+	580391.i	−0.790240	+	0.790240i	−0.981533	−	0.191293i	$-0.938732\pi$
$857$	−580391.	+	580391.i	−0.790240	+	0.790240i	0.191293	+	0.981533i	$0.438732\pi$
$858$	−160135.	−	25362.9i	−0.217526	−	0.0344527i
$859$	899402.	−	292233.i	1.21890	−	0.396044i	0.372218	−	0.928146i	$-0.378598\pi$
$859$	899402.	−	292233.i	1.21890	−	0.396044i	0.846681	+	0.532102i	$0.178598\pi$
$860$	−72977.0	+	37226.8i	−0.0986708	+	0.0503337i
$861$	−154614.	+	475853.i	−0.208566	+	0.641899i
$862$	−267653.	−	136376.i	−0.360212	−	0.183537i
$863$	67867.5	−	133197.i	0.0911255	−	0.178844i	−0.840945	−	0.541120i	$-0.818000\pi$
$863$	67867.5	−	133197.i	0.0911255	−	0.178844i	0.932071	+	0.362276i	$0.118000\pi$
$864$	−752707.	−	244569.i	−1.00832	−	0.327623i
$865$	−65402.8	+	65464.3i	−0.0874107	+	0.0874928i
$866$	69532.2	+	213998.i	0.0927150	+	0.285347i
$867$	12067.0	−	76188.3i	0.0160532	−	0.101356i
$868$	−198836.	−	198836.i	−0.263910	−	0.263910i
$869$	−220321.	−	303245.i	−0.291753	−	0.401564i
$870$	96708.5	+	297163.i	0.127769	+	0.392606i
$871$	834348.	+	606189.i	1.09979	+	0.799046i
$872$	769029.	−	121802.i	1.01137	−	0.160185i
$873$	−262227.	+	133611.i	−0.344072	+	0.175313i
$874$		−	308412.i		−	0.403747i
$875$	−82931.7	−	518879.i	−0.108319	−	0.677720i
$876$	369081.			0.480965
$877$	148012.	+	290490.i	0.192441	+	0.377687i	0.966985	−	0.254833i	$-0.0820205\pi$
$877$	148012.	+	290490.i	0.192441	+	0.377687i	−0.774544	+	0.632520i	$0.782020\pi$
$878$	55954.7	+	353284.i	0.0725851	+	0.458284i
$879$	109292.	−	150428.i	0.141453	−	0.194693i
$880$	6226.99	−	2026.50i	0.00804105	−	0.00261687i
$881$	182013.	−	132240.i	0.234505	−	0.170378i	−0.464327	−	0.885664i	$-0.653704\pi$
$881$	182013.	−	132240.i	0.234505	−	0.170378i	0.698832	+	0.715286i	$0.253704\pi$
$882$	92166.2	−	92166.2i	0.118477	−	0.118477i
$883$	−569506.	−	90200.9i	−0.730427	−	0.115688i	−0.219866	−	0.975530i	$-0.570562\pi$
$883$	−569506.	−	90200.9i	−0.730427	−	0.115688i	−0.510561	+	0.859842i	$0.670562\pi$
$884$	−672072.	+	218369.i	−0.860026	+	0.279439i
$885$	125442.	+	125324.i	0.160161	+	0.160011i
$886$	33736.4	−	103830.i	0.0429765	−	0.132268i
$887$	−1.14159e6	−	581668.i	−1.45098	−	0.739312i	−0.461935	−	0.886914i	$-0.652845\pi$
$887$	−1.14159e6	−	581668.i	−1.45098	−	0.739312i	−0.989047	+	0.147602i	$0.952845\pi$
$888$	−149000.	+	292429.i	−0.188956	+	0.370847i
$889$	698247.	+	226874.i	0.883498	+	0.287066i
$890$	−228378.	−	447697.i	−0.288320	−	0.565203i
$891$	−20070.1	−	61769.5i	−0.0252810	−	0.0778071i
$892$	111592.	−	704567.i	0.140251	−	0.885508i
$893$	11525.2	+	11525.2i	0.0144525	+	0.0144525i
$894$	−248850.	−	342513.i	−0.311360	−	0.428550i
$895$	−148202.	+	456848.i	−0.185015	+	0.570329i
$896$	287573.	+	208934.i	0.358205	+	0.260251i
$897$	306271.	−	48508.6i	0.380646	−	0.0602884i
$898$	247523.	−	126119.i	0.306946	−	0.156397i
$899$			683250.i			0.845397i
$900$	−81813.5	−	250994.i	−0.101004	−	0.309869i
$901$	500023.			0.615942
$902$	123752.	+	242877.i	0.152103	+	0.298520i
$903$	−10711.5	−	67629.6i	−0.0131363	−	0.0829395i
$904$	158165.	−	217696.i	0.193542	−	0.266387i
$905$	−419726.	+	578274.i	−0.512471	+	0.706052i
$906$	450088.	−	327008.i	0.548329	−	0.398384i
$907$	−844630.	+	844630.i	−1.02672	+	1.02672i	−0.0270873	+	0.999633i	$0.508623\pi$
$907$	−844630.	+	844630.i	−1.02672	+	1.02672i	−0.999633	+	0.0270873i	$0.991377\pi$
$908$	504496.	+	79904.4i	0.611908	+	0.0969168i
$909$	701272.	−	227857.i	0.848708	−	0.275762i
$910$	211452.	−	415481.i	0.255346	−	0.501728i
$911$	−370019.	+	1.13880e6i	−0.445848	+	1.37218i	0.435703	+	0.900091i	$0.356500\pi$
$911$	−370019.	+	1.13880e6i	−0.445848	+	1.37218i	−0.881551	+	0.472089i	$0.843500\pi$
$912$	−17965.1	−	9153.69i	−0.0215993	−	0.0110054i
$913$	179677.	−	352636.i	0.215551	−	0.423043i
$914$	751648.	+	244225.i	0.899751	+	0.292347i
$915$	831087.	−	132031.i	0.992669	−	0.157701i
$916$	80833.1	+	248779.i	0.0963381	+	0.296498i
$917$	−10797.0	+	68169.7i	−0.0128400	+	0.0810687i
$918$	410349.	+	410349.i	0.486932	+	0.486932i
$919$	−495704.	−	682278.i	−0.586937	−	0.807849i	0.407497	−	0.913206i	$-0.366402\pi$
$919$	−495704.	−	682278.i	−0.586937	−	0.807849i	−0.994434	+	0.105357i	$0.966402\pi$
$920$	281029.	−	204381.i	0.332028	−	0.241471i
$921$	−277558.	−	201658.i	−0.327216	−	0.237737i
$922$	341257.	−	54049.8i	0.401439	−	0.0635817i
$923$	1.46242e6	−	745142.i	1.71660	−	0.874653i
$924$			98764.2i			0.115679i
$925$	−510688.	+	81376.7i	−0.596860	+	0.0951079i
$926$	−633123.			−0.738357
$927$	−200795.	−	394082.i	−0.233665	−	0.458593i
$928$	−132321.	−	835441.i	−0.153650	−	0.970108i
$929$	−239597.	+	329777.i	−0.277620	+	0.382111i	−0.924944	−	0.380104i	$-0.875888\pi$
$929$	−239597.	+	329777.i	−0.277620	+	0.382111i	0.647324	+	0.762215i	$0.275888\pi$
$930$	−148.806	−	316974.i	−0.000172050	−	0.366486i
$931$	593766.	−	431396.i	0.685040	−	0.497711i
$932$	23393.4	−	23393.4i	0.0269315	−	0.0269315i
$933$	747185.	+	118342.i	0.858350	+	0.135949i
$934$	−121428.	+	39454.4i	−0.139196	+	0.0452274i
$935$	−358250.	−	56568.8i	−0.409791	−	0.0647073i
$936$	187669.	−	577585.i	0.214210	−	0.659271i
$937$	1.12158e6	+	571475.i	1.27747	+	0.650905i	0.955262	−	0.295762i	$-0.0955735\pi$
$937$	1.12158e6	+	571475.i	1.27747	+	0.650905i	0.322212	+	0.946667i	$0.395574\pi$
$938$	−169123.	+	331922.i	−0.192219	+	0.377252i
$939$	308671.	+	100293.i	0.350078	+	0.113747i
$940$	−1104.63	+	6995.63i	−0.00125015	+	0.00791719i
$941$	−452281.	−	1.39198e6i	−0.510775	−	1.57200i	−0.790840	−	0.612022i	$-0.790356\pi$
$941$	−452281.	−	1.39198e6i	−0.510775	−	1.57200i	0.280066	−	0.959981i	$-0.409644\pi$
$942$	83771.5	−	528912.i	0.0944049	−	0.596049i
$943$	−368647.	−	368647.i	−0.414559	−	0.414559i
$944$	−3734.81	−	5140.52i	−0.00419106	−	0.00576850i
$945$	645644.	−	303.102i	0.722985	−	0.000339411i
$946$	−30179.6	−	21926.7i	−0.0337233	−	0.0245014i
$947$	−672295.	+	106481.i	−0.749653	+	0.118733i	−0.519558	−	0.854435i	$-0.673903\pi$
$947$	−672295.	+	106481.i	−0.749653	+	0.118733i	−0.230094	+	0.973168i	$0.573903\pi$
$948$	−446828.	+	227670.i	−0.497192	+	0.253332i
$949$			1.33783e6i			1.48549i
$950$	138705.	+	870458.i	0.153690	+	0.964497i
$951$	−1.08627e6			−1.20110
$952$	−300483.	−	589731.i	−0.331548	−	0.650699i
$953$	−32562.3	−	205590.i	−0.0358533	−	0.226369i	0.963255	−	0.268588i	$-0.0865571\pi$
$953$	−32562.3	−	205590.i	−0.0358533	−	0.226369i	−0.999108	+	0.0422195i	$0.986557\pi$
$954$	−97411.6	+	134076.i	−0.107032	+	0.147317i
$955$	−215174.	−	295870.i	−0.235930	−	0.324410i
$956$	289232.	−	210140.i	0.316469	−	0.229928i
$957$	169689.	−	169689.i	0.185281	−	0.185281i
$958$	432717.	+	68535.6i	0.471490	+	0.0746768i
$959$	−433101.	+	140723.i	−0.470925	+	0.153013i
$960$	59378.6	+	373766.i	0.0644300	+	0.405562i
$961$	−71227.5	+	219216.i	−0.0771260	+	0.237370i
$962$	−408794.	−	208291.i	−0.441727	−	0.225071i
$963$	331810.	−	651214.i	0.357797	−	0.702216i
$964$	−30586.3	−	9938.10i	−0.0329134	−	0.0106942i
$965$	−377096.	−	191917.i	−0.404946	−	0.206091i
$966$	34612.6	+	106527.i	0.0370920	+	0.114157i
$967$	−69309.5	+	437603.i	−0.0741208	+	0.467980i	0.922511	+	0.385971i	$0.126134\pi$
$967$	−69309.5	+	437603.i	−0.0741208	+	0.467980i	−0.996632	+	0.0820089i	$0.973866\pi$
$968$	−559363.	−	559363.i	−0.596957	−	0.596957i
$969$	656392.	+	903446.i	0.699062	+	0.962176i
$970$	345555.	+	250813.i	0.367261	+	0.266567i
$971$	181515.	+	131878.i	0.192519	+	0.139873i	0.679869	−	0.733333i	$-0.262037\pi$
$971$	181515.	+	131878.i	0.192519	+	0.139873i	−0.487350	+	0.873207i	$0.662037\pi$
$972$	531263.	−	84143.8i	0.562311	−	0.0890614i
$973$	−772324.	+	393519.i	−0.815782	+	0.415662i
$974$			160869.i			0.169572i
$975$	−842598.	+	274652.i	−0.886362	+	0.288917i
$976$	−30154.6			−0.0316559
$977$	−813432.	−	1.59645e6i	−0.852181	−	1.67250i	−0.733628	−	0.679552i	$-0.762174\pi$
$977$	−813432.	−	1.59645e6i	−0.852181	−	1.67250i	−0.118553	−	0.992948i	$-0.537826\pi$
$978$	13025.8	+	82241.5i	0.0136184	+	0.0859831i
$979$	−226851.	+	312233.i	−0.236687	+	0.325772i
$980$	303349.	+	98406.5i	0.315857	+	0.102464i
$981$	−416769.	+	302800.i	−0.433069	+	0.314643i
$982$	11943.9	−	11943.9i	0.0123858	−	0.0123858i
$983$	1.25602e6	+	198933.i	1.29983	+	0.205874i	0.767713	−	0.640794i	$-0.221395\pi$
$983$	1.25602e6	+	198933.i	1.29983	+	0.205874i	0.532122	+	0.846668i	$0.321395\pi$
$984$	899356.	−	292219.i	0.928841	−	0.301799i
$985$	−893990.	+	456039.i	−0.921425	+	0.470035i
$986$	−191658.	+	589864.i	−0.197140	+	0.606733i
$987$	−5274.28	−	2687.38i	−0.00541414	−	0.00275864i
$988$	598728.	−	1.17507e6i	0.613360	−	1.20379i
$989$	67855.0	+	22047.4i	0.0693728	+	0.0225406i
$990$	84960.5	−	85040.3i	0.0866855	−	0.0867670i
$991$	−364348.	−	1.12135e6i	−0.370996	−	1.14181i	−0.946141	−	0.323756i	$-0.895054\pi$
$991$	−364348.	−	1.12135e6i	−0.370996	−	1.14181i	0.575145	−	0.818051i	$-0.304946\pi$
$992$	−134214.	+	847392.i	−0.136387	+	0.861115i
$993$	669750.	+	669750.i	0.679226	+	0.679226i
$994$	348480.	+	479641.i	0.352699	+	0.485449i
$995$	327393.	+	1.00600e6i	0.330692	+	1.01614i
$996$	−428377.	−	311234.i	−0.431825	−	0.313739i
$997$	936507.	−	148328.i	0.942152	−	0.149222i	0.333581	−	0.942722i	$-0.391743\pi$
$997$	936507.	−	148328.i	0.942152	−	0.149222i	0.608571	+	0.793499i	$0.291743\pi$
$998$	−1242.95	+	633.317i	−0.00124794	+	0.000635858i
$999$		−	635404.i		−	0.636677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.3.4	✓	72
5.2	odd	4		125.5.f.b.7.6		72
5.3	odd	4		125.5.f.a.7.4		72
5.4	even	2		125.5.f.c.118.6		72
25.6	even	5		125.5.f.b.18.6		72
25.8	odd	20		125.5.f.c.107.6		72
25.17	odd	20	inner	25.5.f.a.17.4	yes	72
25.19	even	10		125.5.f.a.18.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.3.4	✓	72	1.1	even	1	trivial
25.5.f.a.17.4	yes	72	25.17	odd	20	inner
125.5.f.a.7.4		72	5.3	odd	4
125.5.f.a.18.4		72	25.19	even	10
125.5.f.b.7.6		72	5.2	odd	4
125.5.f.b.18.6		72	25.6	even	5
125.5.f.c.107.6		72	25.8	odd	20
125.5.f.c.118.6		72	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-1.10795 - 2.17447i) q^{2} +(0.976269 + 6.16392i) q^{3} +(5.90379 - 8.12588i) q^{4} +(23.7728 - 7.73659i) q^{5} +(12.3216 - 8.95217i) q^{6} +(23.7798 - 23.7798i) q^{7} +(-62.7773 - 9.94294i) q^{8} +(39.9948 - 12.9951i) q^{9} +O(q^{10})\)	\(q+(-1.10795 - 2.17447i) q^{2} +(0.976269 + 6.16392i) q^{3} +(5.90379 - 8.12588i) q^{4} +(23.7728 - 7.73659i) q^{5} +(12.3216 - 8.95217i) q^{6} +(23.7798 - 23.7798i) q^{7} +(-62.7773 - 9.94294i) q^{8} +(39.9948 - 12.9951i) q^{9} +(-43.1620 - 43.1215i) q^{10} +(-14.4780 + 44.5587i) q^{11} +(55.8509 + 28.4575i) q^{12} +(-103.152 + 202.447i) q^{13} +(-78.0553 - 25.3617i) q^{14} +(70.8963 + 138.981i) q^{15} +(-1.72764 - 5.31714i) q^{16} +(-48.4395 + 305.835i) q^{17} +(-72.5696 - 72.5696i) q^{18} +(-339.672 - 467.518i) q^{19} +(77.4831 - 238.850i) q^{20} +(169.792 + 123.361i) q^{21} +(112.932 - 17.8867i) q^{22} +(-194.850 + 99.2809i) q^{23} -396.661i q^{24} +(505.290 - 367.840i) q^{25} +554.501 q^{26} +(348.639 + 684.243i) q^{27} +(-52.8407 - 333.623i) q^{28} +(-482.419 + 663.993i) q^{29} +(223.659 - 308.145i) q^{30} +(673.491 - 489.320i) q^{31} +(-728.745 + 728.745i) q^{32} +(-288.791 - 45.7400i) q^{33} +(718.697 - 233.519i) q^{34} +(381.338 - 749.288i) q^{35} +(130.524 - 401.713i) q^{36} +(-737.228 - 375.636i) q^{37} +(-640.265 + 1256.59i) q^{38} +(-1348.57 - 438.177i) q^{39} +(-1569.31 + 249.310i) q^{40} +(736.696 + 2267.32i) q^{41} +(80.1246 - 505.887i) q^{42} +(-230.697 - 230.697i) q^{43} +(276.603 + 380.712i) q^{44} +(850.250 - 618.353i) q^{45} +(431.767 + 313.697i) q^{46} +(-27.8575 + 4.41219i) q^{47} +(31.0878 - 15.8400i) q^{48} +1270.04i q^{49} +(-1359.69 - 691.191i) q^{50} -1932.43 q^{51} +(1036.07 + 2033.40i) q^{52} +(-252.613 - 1594.93i) q^{53} +(1101.59 - 1516.21i) q^{54} +(0.549873 + 1171.30i) q^{55} +(-1729.27 + 1256.39i) q^{56} +(2550.13 - 2550.13i) q^{57} +(1978.33 + 313.336i) q^{58} +(1080.90 - 351.204i) q^{59} +(1547.90 + 244.418i) q^{60} +(1666.73 - 5129.66i) q^{61} +(-1810.20 - 922.345i) q^{62} +(642.048 - 1260.09i) q^{63} +(2306.97 + 749.580i) q^{64} +(-885.958 + 5610.77i) q^{65} +(220.505 + 678.644i) q^{66} +(710.055 - 4483.11i) q^{67} +(2199.20 + 2199.20i) q^{68} +(-802.185 - 1104.11i) q^{69} +(-2051.81 + 0.963235i) q^{70} +(-5844.13 - 4246.01i) q^{71} +(-2639.97 + 418.131i) q^{72} +(5246.30 - 2673.12i) q^{73} +2019.27i q^{74} +(2760.64 + 2755.46i) q^{75} -5804.34 q^{76} +(715.314 + 1403.88i) q^{77} +(541.342 + 3417.90i) q^{78} +(-4702.50 + 6472.44i) q^{79} +(-82.2074 - 113.037i) q^{80} +(-1121.50 + 814.817i) q^{81} +(4113.99 - 4113.99i) q^{82} +(-8343.32 - 1321.45i) q^{83} +(2004.84 - 651.412i) q^{84} +(1214.58 + 7645.30i) q^{85} +(-246.043 + 757.243i) q^{86} +(-4563.77 - 2325.36i) q^{87} +(1351.93 - 2653.32i) q^{88} +(7834.32 + 2545.52i) q^{89} +(-2286.62 - 1163.74i) q^{90} +(2361.22 + 7267.08i) q^{91} +(-343.609 + 2169.46i) q^{92} +(3673.64 + 3673.64i) q^{93} +(40.4588 + 55.6868i) q^{94} +(-11691.9 - 8486.30i) q^{95} +(-5203.37 - 3780.47i) q^{96} +(-6912.25 + 1094.79i) q^{97} +(2761.66 - 1407.14i) q^{98} +1970.26i 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

Modular forms

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Database

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