LMFDB - Embedded newform 25.5.f.a.3.7

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			3.7
Character	$\chi$	$=$	25.3
Dual form			25.5.f.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47174 + 2.88846i) q^{2} +(-2.00120 - 12.6351i) q^{3} +(3.22739 - 4.44212i) q^{4} +(22.9144 - 9.99657i) q^{5} +(33.5507 - 24.3760i) q^{6} +(-45.6970 + 45.6970i) q^{7} +(68.8109 + 10.8986i) q^{8} +(-78.6049 + 25.5403i) q^{9} +O(q^{10})$	\(q+(1.47174 + 2.88846i) q^{2} +(-2.00120 - 12.6351i) q^{3} +(3.22739 - 4.44212i) q^{4} +(22.9144 - 9.99657i) q^{5} +(33.5507 - 24.3760i) q^{6} +(-45.6970 + 45.6970i) q^{7} +(68.8109 + 10.8986i) q^{8} +(-78.6049 + 25.5403i) q^{9} +(62.5988 + 51.4749i) q^{10} +(11.1048 - 34.1770i) q^{11} +(-62.5852 - 31.8888i) q^{12} +(16.7683 - 32.9097i) q^{13} +(-199.248 - 64.7397i) q^{14} +(-172.164 - 269.520i) q^{15} +(42.6441 + 131.245i) q^{16} +(-67.7627 + 427.837i) q^{17} +(-189.458 - 189.458i) q^{18} +(219.393 + 301.969i) q^{19} +(29.5477 - 134.051i) q^{20} +(668.834 + 485.936i) q^{21} +(115.062 - 18.2241i) q^{22} +(-806.260 + 410.810i) q^{23} -891.242i q^{24} +(425.137 - 458.130i) q^{25} +119.737 q^{26} +(9.58291 + 18.8075i) q^{27} +(55.5096 + 350.474i) q^{28} +(549.217 - 755.933i) q^{29} +(525.116 - 893.952i) q^{30} +(173.939 - 126.374i) q^{31} +(471.876 - 471.876i) q^{32} +(-454.052 - 71.9147i) q^{33} +(-1335.52 + 433.936i) q^{34} +(-590.305 + 1503.93i) q^{35} +(-140.236 + 431.601i) q^{36} +(1105.45 + 563.256i) q^{37} +(-549.334 + 1078.13i) q^{38} +(-449.373 - 146.010i) q^{39} +(1685.71 - 438.139i) q^{40} +(-386.215 - 1188.65i) q^{41} +(-419.255 + 2647.07i) q^{42} +(-951.445 - 951.445i) q^{43} +(-115.979 - 159.631i) q^{44} +(-1545.87 + 1371.02i) q^{45} +(-2373.22 - 1724.24i) q^{46} +(-3325.36 + 526.685i) q^{47} +(1572.95 - 801.459i) q^{48} -1775.43i q^{49} +(1948.98 + 553.741i) q^{50} +5541.36 q^{51} +(-92.0709 - 180.699i) q^{52} +(109.848 + 693.555i) q^{53} +(-40.2212 + 55.3597i) q^{54} +(-87.1937 - 894.153i) q^{55} +(-3642.48 + 2646.42i) q^{56} +(3376.35 - 3376.35i) q^{57} +(2991.79 + 473.853i) q^{58} +(-2506.42 + 814.384i) q^{59} +(-1752.88 - 105.073i) q^{60} +(-521.592 + 1605.30i) q^{61} +(621.020 + 316.426i) q^{62} +(2424.89 - 4759.12i) q^{63} +(4157.40 + 1350.82i) q^{64} +(55.2515 - 921.730i) q^{65} +(-460.525 - 1417.35i) q^{66} +(1386.83 - 8756.10i) q^{67} +(1681.81 + 1681.81i) q^{68} +(6804.10 + 9365.04i) q^{69} +(-5212.82 + 508.330i) q^{70} +(-1546.76 - 1123.79i) q^{71} +(-5687.22 + 900.768i) q^{72} +(-4124.08 + 2101.32i) q^{73} +4022.02i q^{74} +(-6639.30 - 4454.83i) q^{75} +2049.45 q^{76} +(1054.33 + 2069.24i) q^{77} +(-239.618 - 1512.89i) q^{78} +(92.5370 - 127.366i) q^{79} +(2289.16 + 2581.10i) q^{80} +(-5197.63 + 3776.30i) q^{81} +(2864.95 - 2864.95i) q^{82} +(4149.60 + 657.231i) q^{83} +(4317.18 - 1402.74i) q^{84} +(2724.16 + 10481.0i) q^{85} +(1347.93 - 4148.49i) q^{86} +(-10650.4 - 5426.63i) q^{87} +(1136.61 - 2230.72i) q^{88} +(-8027.17 - 2608.18i) q^{89} +(-6235.25 - 2447.38i) q^{90} +(737.612 + 2270.13i) q^{91} +(-777.248 + 4907.35i) q^{92} +(-1944.83 - 1944.83i) q^{93} +(-6415.38 - 8830.01i) q^{94} +(8045.90 + 4726.24i) q^{95} +(-6906.51 - 5017.87i) q^{96} +(9865.55 - 1562.55i) q^{97} +(5128.26 - 2612.98i) q^{98} +2970.09i 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 $

$2$	1.47174	+	2.88846i	0.367936	+	0.722115i	0.998542	−	0.0539884i	$-0.0171934\pi$
$2$	1.47174	+	2.88846i	0.367936	+	0.722115i	−0.630606	+	0.776103i	$0.717193\pi$
$3$	−2.00120	−	12.6351i	−0.222356	−	1.40390i	−0.806013	−	0.591898i	$-0.798379\pi$
$3$	−2.00120	−	12.6351i	−0.222356	−	1.40390i	0.583657	−	0.812000i	$-0.301621\pi$
$4$	3.22739	−	4.44212i	0.201712	−	0.277633i
$5$	22.9144	−	9.99657i	0.916575	−	0.399863i
$5$	22.9144	−	9.99657i	0.916575	−	0.399863i
$6$	33.5507	−	24.3760i	0.931963	−	0.677111i
$7$	−45.6970	+	45.6970i	−0.932592	+	0.932592i	−0.997867	−	0.0652758i	$-0.979207\pi$
$7$	−45.6970	+	45.6970i	−0.932592	+	0.932592i	0.0652758	+	0.997867i	$0.479207\pi$
$8$	68.8109	+	10.8986i	1.07517	+	0.170290i
$9$	−78.6049	+	25.5403i	−0.970430	+	0.315312i
$10$	62.5988	+	51.4749i	0.625988	+	0.514749i
$11$	11.1048	−	34.1770i	0.0917750	−	0.282454i	−0.894625	−	0.446818i	$-0.852557\pi$
$11$	11.1048	−	34.1770i	0.0917750	−	0.282454i	0.986400	+	0.164364i	$0.0525571\pi$
$12$	−62.5852	−	31.8888i	−0.434620	−	0.221450i
$13$	16.7683	−	32.9097i	0.0992208	−	0.194732i	−0.836060	−	0.548638i	$-0.815147\pi$
$13$	16.7683	−	32.9097i	0.0992208	−	0.194732i	0.935281	+	0.353906i	$0.115147\pi$
$14$	−199.248	−	64.7397i	−1.01657	−	0.330304i
$15$	−172.164	−	269.520i	−0.765172	−	1.19787i
$16$	42.6441	+	131.245i	0.166579	+	0.512676i
$17$	−67.7627	+	427.837i	−0.234473	+	1.48040i	0.536697	+	0.843775i	$0.319672\pi$
$17$	−67.7627	+	427.837i	−0.234473	+	1.48040i	−0.771170	+	0.636629i	$0.780328\pi$
$18$	−189.458	−	189.458i	−0.584748	−	0.584748i
$19$	219.393	+	301.969i	0.607737	+	0.836478i	0.996389	−	0.0849066i	$-0.0270592\pi$
$19$	219.393	+	301.969i	0.607737	+	0.836478i	−0.388652	+	0.921385i	$0.627059\pi$
$20$	29.5477	−	134.051i	0.0738691	−	0.335128i
$21$	668.834	+	485.936i	1.51663	+	1.10190i
$22$	115.062	−	18.2241i	0.237732	−	0.0376530i
$23$	−806.260	+	410.810i	−1.52412	+	0.776578i	−0.997303	−	0.0733998i	$-0.976615\pi$
$23$	−806.260	+	410.810i	−1.52412	+	0.776578i	−0.526818	+	0.849978i	$0.676615\pi$
$24$		−	891.242i		−	1.54729i
$25$	425.137	−	458.130i	0.680219	−	0.733009i
$26$	119.737			0.177126
$27$	9.58291	+	18.8075i	0.0131453	+	0.0257991i
$28$	55.5096	+	350.474i	0.0708030	+	0.447033i
$29$	549.217	−	755.933i	0.653053	−	0.898850i	−0.346174	−	0.938170i	$-0.612519\pi$
$29$	549.217	−	755.933i	0.653053	−	0.898850i	0.999227	+	0.0393202i	$0.0125192\pi$
$30$	525.116	−	893.952i	0.583463	−	0.993280i
$31$	173.939	−	126.374i	0.180998	−	0.131503i	−0.493597	−	0.869691i	$-0.664318\pi$
$31$	173.939	−	126.374i	0.180998	−	0.131503i	0.674595	+	0.738188i	$0.264318\pi$
$32$	471.876	−	471.876i	0.460816	−	0.460816i
$33$	−454.052	−	71.9147i	−0.416944	−	0.0660374i
$34$	−1335.52	+	433.936i	−1.15529	+	0.375378i
$35$	−590.305	+	1503.93i	−0.481881	+	1.22770i
$36$	−140.236	+	431.601i	−0.108207	+	0.333025i
$37$	1105.45	+	563.256i	0.807489	+	0.411436i	0.808451	−	0.588564i	$-0.200306\pi$
$37$	1105.45	+	563.256i	0.807489	+	0.411436i	−0.000962356		1.00000i	$0.500306\pi$
$38$	−549.334	+	1078.13i	−0.380425	+	0.746626i
$39$	−449.373	−	146.010i	−0.295446	−	0.0959962i
$40$	1685.71	−	438.139i	1.05357	−	0.273837i
$41$	−386.215	−	1188.65i	−0.229753	−	0.707107i	−0.997774	−	0.0666827i	$-0.978758\pi$
$41$	−386.215	−	1188.65i	−0.229753	−	0.707107i	0.768021	−	0.640424i	$-0.221242\pi$
$42$	−419.255	+	2647.07i	−0.237673	+	1.50061i
$43$	−951.445	−	951.445i	−0.514573	−	0.514573i	0.401351	−	0.915924i	$-0.368541\pi$
$43$	−951.445	−	951.445i	−0.514573	−	0.514573i	−0.915924	+	0.401351i	$0.868541\pi$
$44$	−115.979	−	159.631i	−0.0599064	−	0.0824541i
$45$	−1545.87	+	1371.02i	−0.763391	+	0.677046i
$46$	−2373.22	−	1724.24i	−1.12156	−	0.814859i
$47$	−3325.36	+	526.685i	−1.50537	+	0.238427i	−0.853975	−	0.520314i	$-0.825815\pi$
$47$	−3325.36	+	526.685i	−1.50537	+	0.238427i	−0.651392	+	0.758741i	$0.725815\pi$
$48$	1572.95	−	801.459i	0.682705	−	0.347856i
$49$		−	1775.43i		−	0.739454i
$50$	1948.98	+	553.741i	0.779594	+	0.221496i
$51$	5541.36			2.13047
$52$	−92.0709	−	180.699i	−0.0340499	−	0.0668267i
$53$	109.848	+	693.555i	0.0391058	+	0.246905i	0.999496	−	0.0317554i	$-0.0101098\pi$
$53$	109.848	+	693.555i	0.0391058	+	0.246905i	−0.960390	+	0.278660i	$0.910110\pi$
$54$	−40.2212	+	55.3597i	−0.0137933	+	0.0189848i
$55$	−87.1937	−	894.153i	−0.0288244	−	0.295588i
$56$	−3642.48	+	2646.42i	−1.16151	+	0.843884i
$57$	3376.35	−	3376.35i	1.03920	−	1.03920i
$58$	2991.79	+	473.853i	0.889355	+	0.140860i
$59$	−2506.42	+	814.384i	−0.720027	+	0.233951i	−0.646035	−	0.763308i	$-0.723574\pi$
$59$	−2506.42	+	814.384i	−0.720027	+	0.233951i	−0.0739924	+	0.997259i	$0.523574\pi$
$60$	−1752.88	−	105.073i	−0.486911	−	0.0291870i
$61$	−521.592	+	1605.30i	−0.140175	+	0.431415i	−0.996359	−	0.0852563i	$-0.972829\pi$
$61$	−521.592	+	1605.30i	−0.140175	+	0.431415i	0.856184	+	0.516671i	$0.172829\pi$
$62$	621.020	+	316.426i	0.161556	+	0.0823168i
$63$	2424.89	−	4759.12i	0.610958	−	1.19907i
$64$	4157.40	+	1350.82i	1.01499	+	0.329790i
$65$	55.2515	−	921.730i	0.0130773	−	0.218161i
$66$	−460.525	−	1417.35i	−0.105722	−	0.325379i
$67$	1386.83	−	8756.10i	0.308940	−	1.95057i	−0.00157069	−	0.999999i	$-0.500500\pi$
$67$	1386.83	−	8756.10i	0.308940	−	1.95057i	0.310510	−	0.950570i	$-0.399500\pi$
$68$	1681.81	+	1681.81i	0.363713	+	0.363713i
$69$	6804.10	+	9365.04i	1.42913	+	1.96703i
$70$	−5212.82	+	508.330i	−1.06384	+	0.103741i
$71$	−1546.76	−	1123.79i	−0.306836	−	0.222929i	0.423702	−	0.905802i	$-0.360730\pi$
$71$	−1546.76	−	1123.79i	−0.306836	−	0.222929i	−0.730538	+	0.682873i	$0.760730\pi$
$72$	−5687.22	+	900.768i	−1.09707	+	0.173759i
$73$	−4124.08	+	2101.32i	−0.773893	+	0.394318i	−0.795891	−	0.605440i	$-0.792997\pi$
$73$	−4124.08	+	2101.32i	−0.773893	+	0.394318i	0.0219980	+	0.999758i	$0.492997\pi$
$74$			4022.02i			0.734482i
$75$	−6639.30	−	4454.83i	−1.18032	−	0.791970i
$76$	2049.45			0.354821
$77$	1054.33	+	2069.24i	0.177826	+	0.349003i
$78$	−239.618	−	1512.89i	−0.0393849	−	0.248666i
$79$	92.5370	−	127.366i	0.0148273	−	0.0204080i	−0.801539	−	0.597942i	$-0.795985\pi$
$79$	92.5370	−	127.366i	0.0148273	−	0.0204080i	0.816366	+	0.577535i	$0.195985\pi$
$80$	2289.16	+	2581.10i	0.357682	+	0.403297i
$81$	−5197.63	+	3776.30i	−0.792201	+	0.575568i
$82$	2864.95	−	2864.95i	0.426078	−	0.426078i
$83$	4149.60	+	657.231i	0.602351	+	0.0954030i	0.450160	−	0.892948i	$-0.351367\pi$
$83$	4149.60	+	657.231i	0.602351	+	0.0954030i	0.152191	+	0.988351i	$0.451367\pi$
$84$	4317.18	−	1402.74i	0.611845	−	0.198800i
$85$	2724.16	+	10481.0i	0.377047	+	1.45066i
$86$	1347.93	−	4148.49i	0.182251	−	0.560911i
$87$	−10650.4	−	5426.63i	−1.40710	−	0.716955i
$88$	1136.61	−	2230.72i	0.146773	−	0.288058i
$89$	−8027.17	−	2608.18i	−1.01340	−	0.329275i	−0.245194	−	0.969474i	$-0.578852\pi$
$89$	−8027.17	−	2608.18i	−1.01340	−	0.329275i	−0.768209	+	0.640199i	$0.778852\pi$
$90$	−6235.25	−	2447.38i	−0.769784	−	0.302146i
$91$	737.612	+	2270.13i	0.0890728	+	0.274138i
$92$	−777.248	+	4907.35i	−0.0918299	+	0.579791i
$93$	−1944.83	−	1944.83i	−0.224862	−	0.224862i
$94$	−6415.38	−	8830.01i	−0.726050	−	0.999322i
$95$	8045.90	+	4726.24i	0.891513	+	0.523683i
$96$	−6906.51	−	5017.87i	−0.749404	−	0.544474i
$97$	9865.55	−	1562.55i	1.04852	−	0.166070i	0.391683	−	0.920100i	$-0.371893\pi$
$97$	9865.55	−	1562.55i	1.04852	−	0.166070i	0.656839	+	0.754030i	$0.271893\pi$
$98$	5128.26	−	2612.98i	0.533971	−	0.272072i
$99$			2970.09i			0.303040i
$100$	−662.988	−	3367.08i	−0.0662988	−	0.336708i
$101$	−3808.30			−0.373326			−0.186663	−	0.982424i	$-0.559767\pi$
$101$	−3808.30			−0.373326			−0.186663	+	0.982424i	$0.559767\pi$
$102$	8155.46	+	16006.0i	0.783878	+	1.53845i
$103$	1900.52	+	11999.4i	0.179142	+	1.13106i	0.899327	+	0.437276i	$0.144057\pi$
$103$	1900.52	+	11999.4i	0.179142	+	1.13106i	−0.720185	+	0.693782i	$0.755943\pi$
$104$	1512.51	−	2081.79i	0.139840	−	0.192474i
$105$	20183.6	+	4448.88i	1.83071	+	0.403526i
$106$	−1841.64	+	1338.03i	−0.163905	+	0.119084i
$107$	6241.47	−	6241.47i	0.545154	−	0.545154i	−0.379881	−	0.925035i	$-0.624035\pi$
$107$	6241.47	−	6241.47i	0.545154	−	0.545154i	0.925035	+	0.379881i	$0.124035\pi$
$108$	114.473	+	18.1308i	0.00981423	+	0.00155442i
$109$	−1064.61	+	345.912i	−0.0896060	+	0.0291148i	−0.353477	−	0.935443i	$-0.615001\pi$
$109$	−1064.61	+	345.912i	−0.0896060	+	0.0291148i	0.263871	+	0.964558i	$0.415001\pi$
$110$	2454.40	−	1567.82i	0.202843	−	0.129572i
$111$	4904.55	−	15094.7i	0.398064	−	1.22512i
$112$	−7946.21	−	4048.80i	−0.633467	−	0.322768i
$113$	3309.27	−	6494.81i	0.259164	−	0.508639i	−0.724358	−	0.689424i	$-0.757864\pi$
$113$	3309.27	−	6494.81i	0.259164	−	0.508639i	0.983523	+	0.180785i	$0.0578638\pi$
$114$	14721.6	+	4783.33i	1.13278	+	0.368061i
$115$	−14368.2	+	17473.3i	−1.08645	+	1.32123i
$116$	−1585.41	−	4879.38i	−0.117822	−	0.362618i
$117$	−477.549	+	3015.13i	−0.0348856	+	0.220259i
$118$	−6041.12	−	6041.12i	−0.433864	−	0.433864i
$119$	−16454.3	−	22647.4i	−1.16194	−	1.59928i
$120$	−8909.36	−	20422.2i	−0.618706	−	1.41821i
$121$	10800.1	+	7846.71i	0.737659	+	0.535941i
$122$	−5404.48	+	855.986i	−0.363107	+	0.0575105i
$123$	−14245.8	+	7258.58i	−0.941619	+	0.479779i
$124$		−	1180.52i		−	0.0767766i
$125$	5162.02	−	14747.7i	0.330369	−	0.943852i
$126$	17315.3			1.09066
$127$	8168.52	+	16031.6i	0.506449	+	0.993962i	0.992753	+	0.120172i	$0.0383447\pi$
$127$	8168.52	+	16031.6i	0.506449	+	0.993962i	−0.486304	+	0.873790i	$0.661655\pi$
$128$	546.530	+	3450.66i	0.0333576	+	0.210611i
$129$	−10117.6	+	13925.6i	−0.607989	+	0.836826i
$130$	2743.70	−	1196.96i	0.162349	−	0.0708260i
$131$	360.793	−	262.132i	0.0210240	−	0.0152749i	−0.577224	−	0.816586i	$-0.695864\pi$
$131$	360.793	−	262.132i	0.0210240	−	0.0152749i	0.598248	+	0.801311i	$0.295864\pi$
$132$	−1784.86	+	1784.86i	−0.102437	+	0.102437i
$133$	−23824.6	−	3773.45i	−1.34686	−	0.213322i
$134$	27332.7	−	8880.94i	1.52221	−	0.494594i
$135$	407.597	+	335.166i	0.0223647	+	0.0183905i
$136$	−9325.63	+	28701.3i	−0.504197	+	1.55176i
$137$	−7138.59	−	3637.30i	−0.380340	−	0.193793i	0.253360	−	0.967372i	$-0.418464\pi$
$137$	−7138.59	−	3637.30i	−0.380340	−	0.193793i	−0.633699	+	0.773579i	$0.718464\pi$
$138$	−17036.7	+	33436.3i	−0.894595	+	1.75574i
$139$	−18068.6	−	5870.86i	−0.935181	−	0.303859i	−0.198501	−	0.980101i	$-0.563607\pi$
$139$	−18068.6	−	5870.86i	−0.935181	−	0.303859i	−0.736680	+	0.676242i	$0.763607\pi$
$140$	4775.50	+	7475.98i	0.243648	+	0.381428i
$141$	13309.4	+	40962.1i	0.669453	+	2.06037i
$142$	969.578	−	6121.67i	0.0480846	−	0.303594i
$143$	−938.545	−	938.545i	−0.0458969	−	0.0458969i
$144$	−6704.07	−	9227.36i	−0.323306	−	0.444992i
$145$	5028.24	−	22812.0i	0.239155	−	1.08500i
$146$	−12139.2	−	8819.62i	−0.569486	−	0.413756i
$147$	−22432.7	+	3552.99i	−1.03812	+	0.164422i
$148$	6069.78	−	3092.71i	0.277108	−	0.141194i
$149$			19710.2i			0.887806i	0.896075	+	0.443903i	$0.146407\pi$
$149$			19710.2i			0.887806i	−0.896075	+	0.443903i	$0.853593\pi$
$150$	3096.25	−	25733.7i	0.137611	−	1.14372i
$151$	28772.6			1.26190			0.630951	−	0.775823i	$-0.282665\pi$
$151$	28772.6			1.26190			0.630951	+	0.775823i	$0.282665\pi$
$152$	11805.6	+	23169.8i	0.510977	+	1.00285i
$153$	−5600.59	−	35360.7i	−0.239249	−	1.51056i
$154$	−4425.21	+	6090.78i	−0.186592	+	0.256822i
$155$	2722.40	−	4634.58i	0.113315	−	0.192906i
$156$	−2098.90	+	1524.94i	−0.0862467	+	0.0626619i
$157$	18927.2	−	18927.2i	0.767867	−	0.767867i	−0.209864	−	0.977731i	$-0.567302\pi$
$157$	18927.2	−	18927.2i	0.767867	−	0.767867i	0.977731	+	0.209864i	$0.0673020\pi$
$158$	504.083	+	79.8389i	0.0201924	+	0.00319816i
$159$	8543.29	−	2775.88i	0.337933	−	0.109801i
$160$	6095.60	−	15529.9i	0.238109	−	0.606636i
$161$	18070.9	−	55616.4i	0.697152	−	2.14561i
$162$	−18557.3	−	9455.40i	−0.707105	−	0.360288i
$163$	8759.55	−	17191.6i	0.329691	−	0.647054i	−0.665349	−	0.746532i	$-0.731717\pi$
$163$	8759.55	−	17191.6i	0.329691	−	0.647054i	0.995040	+	0.0994781i	$0.0317173\pi$
$164$	−6526.58	−	2120.62i	−0.242660	−	0.0788450i
$165$	−11123.2	+	2891.08i	−0.408566	+	0.106192i
$166$	4208.76	+	12953.2i	0.152735	+	0.470069i
$167$	−2107.00	+	13303.1i	−0.0755497	+	0.477002i	0.920685	+	0.390306i	$0.127631\pi$
$167$	−2107.00	+	13303.1i	−0.0755497	+	0.477002i	−0.996235	+	0.0866958i	$0.972369\pi$
$168$	40727.1	+	40727.1i	1.44299	+	1.44299i
$169$	15985.9	+	22002.7i	0.559710	+	0.770374i
$170$	−26264.7	+	23294.0i	−0.908813	+	0.806021i
$171$	−24957.7	−	18132.8i	−0.853518	−	0.620117i
$172$	−7297.12	+	1155.75i	−0.246658	+	0.0390667i
$173$	27636.2	−	14081.3i	0.923392	−	0.470492i	0.0734090	−	0.997302i	$-0.476612\pi$
$173$	27636.2	−	14081.3i	0.923392	−	0.470492i	0.849983	+	0.526810i	$0.176612\pi$
$174$		−	38749.8i		−	1.27988i
$175$	1507.70	+	40362.7i	0.0492309	+	1.31796i
$176$	4959.11			0.160095
$177$	15305.6	+	30039.0i	0.488546	+	0.958825i
$178$	−4280.30	−	27024.7i	−0.135093	−	0.852946i
$179$	5331.30	−	7337.90i	0.166390	−	0.229016i	−0.717677	−	0.696376i	$-0.754795\pi$
$179$	5331.30	−	7337.90i	0.166390	−	0.229016i	0.884067	+	0.467360i	$0.154795\pi$
$180$	1101.12	+	11291.7i	0.0339851	+	0.348511i
$181$	−3739.87	+	2717.17i	−0.114156	+	0.0829392i	−0.643399	−	0.765531i	$-0.722476\pi$
$181$	−3739.87	+	2717.17i	−0.114156	+	0.0829392i	0.529243	+	0.848471i	$0.322476\pi$
$182$	−5471.62	+	5471.62i	−0.165186	+	0.165186i
$183$	21326.8	+	3377.84i	0.636831	+	0.100864i
$184$	−59956.7	+	19481.1i	−1.77093	+	0.575411i
$185$	30961.4	+	1855.93i	0.904642	+	0.0542272i
$186$	2755.28	−	8479.87i	0.0796415	−	0.245111i
$187$	13869.7	+	7066.95i	0.396628	+	0.202092i
$188$	−8392.63	+	16471.5i	−0.237456	+	0.466033i
$189$	−1297.36	−	421.537i	−0.0363192	−	0.0118008i
$190$	−1810.05	+	30196.1i	−0.0501400	+	0.836457i
$191$	3635.33	+	11188.4i	0.0996498	+	0.306691i	0.988438	−	0.151628i	$-0.0484517\pi$
$191$	3635.33	+	11188.4i	0.0996498	+	0.306691i	−0.888788	+	0.458319i	$0.848452\pi$
$192$	8747.94	−	55232.3i	0.237303	−	1.49827i
$193$	−38004.0	−	38004.0i	−1.02027	−	1.02027i	−0.999790	−	0.0204780i	$-0.993481\pi$
$193$	−38004.0	−	38004.0i	−1.02027	−	1.02027i	−0.0204780	−	0.999790i	$-0.506519\pi$
$194$	19032.9	+	26196.6i	0.505711	+	0.696051i
$195$	−11756.7	+	1146.46i	−0.309184	+	0.0301501i
$196$	−7886.67	−	5730.00i	−0.205297	−	0.149157i
$197$	−56293.7	+	8916.04i	−1.45053	+	0.229742i	−0.831456	−	0.555590i	$-0.812492\pi$
$197$	−56293.7	+	8916.04i	−1.45053	+	0.229742i	−0.619075	+	0.785332i	$0.712492\pi$
$198$	−8579.00	+	4371.22i	−0.218830	+	0.111499i
$199$		−	3251.14i		−	0.0820973i	−0.999157	−	0.0410487i	$-0.986930\pi$
$199$		−	3251.14i		−	0.0820973i	0.999157	−	0.0410487i	$-0.0130699\pi$
$200$	34247.0	−	26891.0i	0.856176	−	0.672275i
$201$	−113409.			−2.80709
$202$	−5604.85	−	11000.1i	−0.137360	−	0.269585i
$203$	9446.28	+	59641.4i	0.229228	+	1.44729i
$204$	17884.1	−	24615.4i	0.429742	−	0.591489i
$205$	−20732.3	−	23376.3i	−0.493332	−	0.556247i
$206$	−31862.7	+	23149.6i	−0.750841	+	0.545518i
$207$	52883.7	−	52883.7i	1.23419	−	1.23419i
$208$	5034.30	+	797.355i	0.116362	+	0.0184300i
$209$	12756.7	−	4144.90i	0.292042	−	0.0948901i
$210$	16854.7	+	64847.2i	0.382193	+	1.47046i
$211$	14348.4	−	44159.8i	0.322283	−	0.991886i	−0.650369	−	0.759619i	$-0.725386\pi$
$211$	14348.4	−	44159.8i	0.322283	−	0.991886i	0.972652	−	0.232267i	$-0.0746144\pi$
$212$	3435.38	+	1750.41i	0.0764369	+	0.0389465i
$213$	−11103.7	+	21792.3i	−0.244743	+	0.480335i
$214$	27214.1	+	8842.39i	0.594246	+	0.193082i
$215$	−31313.0	−	12290.6i	−0.677403	−	0.265886i
$216$	454.434	+	1398.60i	0.00974009	+	0.0299769i
$217$	−2173.57	+	13723.4i	−0.0461588	+	0.291435i
$218$	−2565.99	−	2565.99i	−0.0539935	−	0.0539935i
$219$	34803.5	+	47902.9i	0.725662	+	0.998788i
$220$	−4253.35	−	2498.46i	−0.0878791	−	0.0516210i
$221$	12943.7	+	9404.15i	0.265017	+	0.192546i
$222$	50818.6	−	8048.87i	1.03114	−	0.163316i
$223$	9691.57	−	4938.10i	0.194888	−	0.0993003i	−0.353824	−	0.935312i	$-0.615119\pi$
$223$	9691.57	−	4938.10i	0.194888	−	0.0993003i	0.548711	+	0.836012i	$0.315119\pi$
$224$			43126.6i			0.859507i
$225$	−21717.1	+	46869.4i	−0.428979	+	0.925815i
$226$	23630.4			0.462652
$227$	−33018.2	−	64801.8i	−0.640769	−	1.25758i	−0.951666	−	0.307136i	$-0.900630\pi$
$227$	−33018.2	−	64801.8i	−0.640769	−	1.25758i	0.310897	−	0.950444i	$-0.399370\pi$
$228$	−4101.36	−	25894.9i	−0.0788965	−	0.498133i
$229$	30337.2	−	41755.5i	0.578501	−	0.796238i	−0.415029	−	0.909808i	$-0.636229\pi$
$229$	30337.2	−	41755.5i	0.578501	−	0.796238i	0.993530	+	0.113570i	$0.0362287\pi$
$230$	−71617.3	−	15785.9i	−1.35382	−	0.298410i
$231$	24035.1	−	17462.5i	0.450424	−	0.327252i
$232$	46030.8	−	46030.8i	0.855209	−	0.855209i
$233$	−6065.81	−	960.730i	−0.111732	−	0.0176966i	0.100318	−	0.994955i	$-0.468014\pi$
$233$	−6065.81	−	960.730i	−0.111732	−	0.0176966i	−0.212050	+	0.977259i	$0.568014\pi$
$234$	−9411.91	+	3058.11i	−0.171888	+	0.0558498i
$235$	−70933.4	+	45310.8i	−1.28444	+	0.820476i
$236$	−4471.59	+	13762.1i	−0.0802857	+	0.247094i
$237$	−1794.47	−	914.327i	−0.0319476	−	0.0162781i
$238$	41199.6	−	80858.8i	0.727343	−	1.42749i
$239$	51624.6	+	16773.9i	0.903776	+	0.293655i	0.723795	−	0.690015i	$-0.242396\pi$
$239$	51624.6	+	16773.9i	0.903776	+	0.293655i	0.179982	+	0.983670i	$0.442396\pi$
$240$	28031.4	−	34089.1i	0.486656	−	0.591824i
$241$	17512.0	+	53896.5i	0.301510	+	0.927953i	0.980956	+	0.194228i	$0.0622201\pi$
$241$	17512.0	+	53896.5i	0.301510	+	0.927953i	−0.679446	+	0.733725i	$0.737780\pi$
$242$	−6769.97	+	42743.9i	−0.115600	+	0.729867i
$243$	59324.3	+	59324.3i	1.00466	+	1.00466i
$244$	5447.54	+	7497.89i	0.0914999	+	0.125939i
$245$	−17748.2	−	40682.8i	−0.295680	−	0.677765i
$246$	−41932.2	−	30465.5i	−0.692911	−	0.503429i
$247$	13616.5	−	2156.65i	0.223189	−	0.0353497i
$248$	13346.2	−	6800.23i	0.216997	−	0.110566i
$249$		−	53745.7i		−	0.866853i
$250$	50195.3	−	6794.54i	0.803124	−	0.108713i
$251$	−30717.0			−0.487564			−0.243782	−	0.969830i	$-0.578388\pi$
$251$	−30717.0			−0.487564			−0.243782	+	0.969830i	$0.578388\pi$
$252$	−13314.5	−	26131.2i	−0.209664	−	0.411489i
$253$	5086.91	+	32117.5i	0.0794717	+	0.501765i
$254$	−34284.7	+	47188.9i	−0.531414	+	0.731429i
$255$	126977.	−	55394.6i	1.95274	−	0.851897i
$256$	47421.1	−	34453.5i	0.723589	−	0.525718i
$257$	−42867.8	+	42867.8i	−0.649031	+	0.649031i	−0.952759	−	0.303728i	$-0.901769\pi$
$257$	−42867.8	+	42867.8i	−0.649031	+	0.649031i	0.303728	+	0.952759i	$0.401769\pi$
$258$	−55114.0	−	8729.21i	−0.827986	−	0.131140i
$259$	−76254.9	+	24776.7i	−1.13676	+	0.369355i
$260$	−3916.12	−	3220.22i	−0.0579308	−	0.0476364i
$261$	−23864.4	+	73447.2i	−0.350324	+	1.07819i
$262$	1288.15	+	656.346i	0.0187657	+	0.00956160i
$263$	−2634.32	+	5170.14i	−0.0380853	+	0.0747465i	−0.909265	−	0.416218i	$-0.863355\pi$
$263$	−2634.32	+	5170.14i	−0.0380853	+	0.0747465i	0.871180	+	0.490964i	$0.163355\pi$
$264$	−30459.9	−	9897.03i	−0.437040	−	0.142003i
$265$	9450.28	+	14794.3i	0.134571	+	0.210670i
$266$	−24164.3	−	74370.1i	−0.341516	−	1.05108i
$267$	−16890.7	+	106643.i	−0.236932	+	1.49593i
$268$	−34419.8	−	34419.8i	−0.479225	−	0.479225i
$269$	−21608.2	−	29741.1i	−0.298616	−	0.411010i	0.633173	−	0.774011i	$-0.281752\pi$
$269$	−21608.2	−	29741.1i	−0.298616	−	0.411010i	−0.931789	+	0.363001i	$0.881752\pi$
$270$	−368.236	+	1670.61i	−0.00505125	+	0.0229164i
$271$	90984.9	+	66104.4i	1.23888	+	0.900102i	0.997524	−	0.0703333i	$-0.0224063\pi$
$271$	90984.9	+	66104.4i	1.23888	+	0.900102i	0.241361	+	0.970435i	$0.422406\pi$
$272$	−59041.1	+	9351.20i	−0.798026	+	0.126395i
$273$	27207.2	−	13862.8i	0.365056	−	0.186005i
$274$		−	25972.7i		−	0.345952i
$275$	−10936.5	−	19617.3i	−0.144614	−	0.259403i
$276$	63560.2			0.834386
$277$	−28577.8	−	56087.0i	−0.372451	−	0.730976i	0.626370	−	0.779526i	$-0.284540\pi$
$277$	−28577.8	−	56087.0i	−0.372451	−	0.730976i	−0.998821	+	0.0485503i	$0.984540\pi$
$278$	−9634.67	−	60830.9i	−0.124666	−	0.787109i
$279$	−10444.8	+	14376.1i	−0.134182	+	0.184685i
$280$	−57010.1	+	97053.4i	−0.727170	+	1.23793i
$281$	−38520.4	+	27986.7i	−0.487841	+	0.354437i	−0.804353	−	0.594151i	$-0.797488\pi$
$281$	−38520.4	+	27986.7i	−0.487841	+	0.354437i	0.316512	+	0.948588i	$0.397488\pi$
$282$	−98729.5	+	98729.5i	−1.24151	+	1.24151i
$283$	49748.7	+	7879.43i	0.621168	+	0.0983834i	0.459083	−	0.888393i	$-0.348178\pi$
$283$	49748.7	+	7879.43i	0.621168	+	0.0983834i	0.162085	+	0.986777i	$0.448178\pi$
$284$	−9983.99	+	3244.00i	−0.123785	+	0.0402201i
$285$	43615.0	−	111119.i	0.536965	−	1.36804i
$286$	1329.65	−	4092.25i	0.0162557	−	0.0500299i
$287$	71966.4	+	36668.7i	0.873708	+	0.445176i
$288$	−25039.9	+	49143.6i	−0.301889	+	0.592491i
$289$	−99019.4	−	32173.3i	−1.18556	−	0.385213i
$290$	73291.9	−	19049.6i	0.871485	−	0.226511i
$291$	−39485.9	−	121525.i	−0.466290	−	1.43509i
$292$	−3975.68	+	25101.4i	−0.0466279	+	0.294397i
$293$	−29011.8	−	29011.8i	−0.337940	−	0.337940i	0.517651	−	0.855592i	$-0.326806\pi$
$293$	−29011.8	−	29011.8i	−0.337940	−	0.337940i	−0.855592	+	0.517651i	$0.826806\pi$
$294$	−43277.8	−	59566.8i	−0.500692	−	0.689144i
$295$	−49291.9	+	43716.7i	−0.566411	+	0.502346i
$296$	69928.5	+	50806.0i	0.798124	+	0.579871i
$297$	749.200	−	118.662i	0.00849347	−	0.00134523i
$298$	−56932.1	+	29008.4i	−0.641098	+	0.326656i
$299$			33422.3i			0.373848i
$300$	−41216.5	+	15115.1i	−0.457961	+	0.167946i
$301$	86956.3			0.959772
$302$	42345.9	+	83108.6i	0.464299	+	0.911239i
$303$	7621.18	+	48118.2i	0.0830112	+	0.524112i
$304$	−30276.1	+	41671.4i	−0.327606	+	0.450911i
$305$	4095.50	+	41998.5i	0.0440258	+	0.451475i
$306$	93895.4	−	68219.0i	1.00277	−	0.728555i
$307$	−24360.8	+	24360.8i	−0.258472	+	0.258472i	−0.824433	−	0.565960i	$-0.808506\pi$
$307$	−24360.8	+	24360.8i	−0.258472	+	0.258472i	0.565960	+	0.824433i	$0.308506\pi$
$308$	12594.6	+	1994.78i	0.132764	+	0.0210278i
$309$	147810.	−	48026.4i	1.54806	−	0.502994i
$310$	17393.5	+	1042.62i	0.180993	+	0.0108493i
$311$	−31363.3	+	96526.2i	−0.324265	+	0.997986i	0.647506	+	0.762061i	$0.275812\pi$
$311$	−31363.3	+	96526.2i	−0.324265	+	0.997986i	−0.971771	+	0.235926i	$0.924188\pi$
$312$	−29330.5	−	14944.6i	−0.301308	−	0.153524i
$313$	−1177.32	+	2310.62i	−0.0120173	+	0.0235852i	−0.896937	−	0.442158i	$-0.854213\pi$
$313$	−1177.32	+	2310.62i	−0.0120173	+	0.0235852i	0.884920	+	0.465743i	$0.154213\pi$
$314$	82526.2	+	26814.4i	0.837014	+	0.271962i
$315$	7990.01	−	133293.i	0.0805241	−	1.34334i
$316$	−267.123	−	822.121i	−0.00267509	−	0.00823307i
$317$	22336.4	−	141027.i	0.222277	−	1.40340i	−0.583946	−	0.811793i	$-0.698492\pi$
$317$	22336.4	−	141027.i	0.222277	−	1.40340i	0.806223	−	0.591612i	$-0.201508\pi$
$318$	20591.6	+	20591.6i	0.203627	+	0.203627i
$319$	−19736.6	−	27165.1i	−0.193950	−	0.266950i
$320$	108768.	−	10606.5i	1.06218	−	0.103579i
$321$	−91351.9	−	66371.0i	−0.886559	−	0.644122i
$322$	187241.	−	29656.1i	1.80589	−	0.286024i
$323$	−144060.	+	73402.2i	−1.38082	+	0.703565i
$324$			35276.1i			0.336040i
$325$	−7948.09	−	21673.2i	−0.0752482	−	0.205190i
$326$	62549.0			0.588553
$327$	6501.13	+	12759.2i	0.0607985	+	0.119324i
$328$	−13621.2	−	86001.1i	−0.126610	−	0.799386i
$329$	127891.	−	176027.i	1.18154	−	1.62625i
$330$	−24721.3	−	27874.0i	−0.227009	−	0.255960i
$331$	−89417.6	+	64965.7i	−0.816144	+	0.592964i	−0.915605	−	0.402078i	$-0.868288\pi$
$331$	−89417.6	+	64965.7i	−0.816144	+	0.592964i	0.0994611	+	0.995041i	$0.468288\pi$
$332$	16311.9	−	16311.9i	0.147988	−	0.147988i
$333$	−101280.	−	16041.1i	−0.913342	−	0.144659i
$334$	−41526.5	+	13492.8i	−0.372248	+	0.120951i
$335$	−55752.7	−	214504.i	−0.496794	−	1.91138i
$336$	−35254.9	+	108503.i	−0.312278	+	0.961092i
$337$	49685.5	+	25316.0i	0.437492	+	0.222913i	0.658842	−	0.752281i	$-0.271046\pi$
$337$	49685.5	+	25316.0i	0.437492	+	0.222913i	−0.221350	+	0.975194i	$0.571046\pi$
$338$	−40026.7	+	78556.8i	−0.350361	+	0.687623i
$339$	−88684.9	−	28815.5i	−0.771703	−	0.250742i
$340$	55349.9	+	21725.3i	0.478805	+	0.187935i
$341$	−2387.53	−	7348.06i	−0.0205324	−	0.0631923i
$342$	15644.6	−	98776.2i	0.133756	−	0.844501i
$343$	−28586.7	−	28586.7i	−0.242983	−	0.242983i
$344$	−55100.4	−	75839.2i	−0.465627	−	0.640880i
$345$	249530.	+	146576.i	2.09645	+	1.23148i
$346$	81346.8	+	59101.9i	0.679498	+	0.493684i
$347$	118446.	−	18759.9i	0.983693	−	0.155802i	0.356188	−	0.934414i	$-0.384076\pi$
$347$	118446.	−	18759.9i	0.983693	−	0.155802i	0.627505	+	0.778612i	$0.284076\pi$
$348$	−58478.7	+	29796.4i	−0.482880	+	0.246040i
$349$		−	80739.0i		−	0.662876i	−0.943477	−	0.331438i	$-0.892466\pi$
$349$		−	80739.0i		−	0.662876i	0.943477	−	0.331438i	$-0.107534\pi$
$350$	−114367.	+	63758.4i	−0.933608	+	0.520477i
$351$	779.639			0.00632819
$352$	−10887.2	−	21367.4i	−0.0878682	−	0.172451i
$353$	37718.4	+	238144.i	0.302694	+	1.91113i	0.401189	+	0.915995i	$0.368597\pi$
$353$	37718.4	+	238144.i	0.302694	+	1.91113i	−0.0984955	+	0.995137i	$0.531403\pi$
$354$	−64240.5	+	88419.5i	−0.512628	+	0.705572i
$355$	−46677.0	−	10288.6i	−0.370379	−	0.0816391i
$356$	−37492.7	+	27240.0i	−0.295833	+	0.214935i
$357$	−253223.	+	253223.i	−1.98686	+	1.98686i
$358$	29041.5	+	4599.73i	0.226597	+	0.0358894i
$359$	150167.	−	48792.4i	1.16516	−	0.378585i	0.338328	−	0.941028i	$-0.390139\pi$
$359$	150167.	−	48792.4i	1.16516	−	0.378585i	0.826836	+	0.562444i	$0.190139\pi$
$360$	−121315.	+	77493.3i	−0.936069	+	0.597942i
$361$	−2780.31	+	8556.92i	−0.0213343	+	0.0656603i
$362$	−13352.6	−	6803.47i	−0.101894	−	0.0519175i
$363$	77530.7	−	152163.i	0.588383	−	1.15477i
$364$	12464.8	+	4050.05i	0.0940767	+	0.0305674i
$365$	−73494.6	+	89377.1i	−0.551658	+	0.670873i
$366$	21630.9	+	66573.1i	0.161478	+	0.496977i
$367$	5769.85	−	36429.4i	0.0428384	−	0.270471i	−0.956967	−	0.290197i	$-0.906279\pi$
$367$	5769.85	−	36429.4i	0.0428384	−	0.270471i	0.999805	+	0.0197258i	$0.00627933\pi$
$368$	−88299.0	−	88299.0i	−0.652019	−	0.652019i
$369$	60716.7	+	83569.4i	0.445919	+	0.613754i
$370$	40206.4	+	92162.1i	0.293692	+	0.673208i
$371$	−36713.1	−	26673.6i	−0.266731	−	0.193791i
$372$	−14915.9	+	2362.45i	−0.107787	+	0.0170717i
$373$	160977.	−	82021.9i	1.15704	−	0.589539i	0.233237	−	0.972420i	$-0.425068\pi$
$373$	160977.	−	82021.9i	1.15704	−	0.589539i	0.923798	+	0.382881i	$0.125068\pi$
$374$			50462.8i			0.360768i
$375$	−196668.	−	35709.4i	−1.39853	−	0.253934i
$376$	−234561.			−1.65913
$377$	−15668.1	−	30750.3i	−0.110238	−	0.216355i
$378$	−691.785	−	4367.76i	−0.00484159	−	0.0305686i
$379$	−139101.	+	191456.i	−0.968391	+	1.33288i	−0.0255359	+	0.999674i	$0.508129\pi$
$379$	−139101.	+	191456.i	−0.968391	+	1.33288i	−0.942855	+	0.333202i	$0.891871\pi$
$380$	46961.8	−	20487.5i	0.325220	−	0.141880i
$381$	186214.	−	135292.i	1.28281	−	0.932016i
$382$	−26966.9	+	26966.9i	−0.184801	+	0.184801i
$383$	114895.	+	18197.6i	0.783259	+	0.124056i	0.535241	−	0.844700i	$-0.320221\pi$
$383$	114895.	+	18197.6i	0.783259	+	0.124056i	0.248018	+	0.968755i	$0.420221\pi$
$384$	42505.6	−	13810.9i	0.288260	−	0.0936612i
$385$	44844.6	+	36875.6i	0.302544	+	0.248781i
$386$	53840.8	−	165705.i	0.361358	−	1.11214i
$387$	99088.4	+	50488.0i	0.661608	+	0.337106i
$388$	24899.0	−	48867.0i	0.165393	−	0.324603i
$389$	−24453.9	−	7945.56i	−0.161603	−	0.0525080i	0.227098	−	0.973872i	$-0.427076\pi$
$389$	−24453.9	−	7945.56i	−0.161603	−	0.0525080i	−0.388701	+	0.921364i	$0.627076\pi$
$390$	−20614.4	−	32271.5i	−0.135532	−	0.212173i
$391$	−121125.	−	372785.i	−0.792285	−	2.43840i
$392$	19349.6	−	122169.i	0.125922	−	0.795039i
$393$	−4034.07	−	4034.07i	−0.0261191	−	0.0261191i
$394$	−108604.	−	149480.i	−0.699603	−	0.962920i
$395$	847.201	−	3843.57i	0.00542991	−	0.0246343i
$396$	13193.5	+	9585.66i	0.0841338	+	0.0611268i
$397$	−90464.0	+	14328.1i	−0.573977	+	0.0909091i	−0.436674	−	0.899620i	$-0.643844\pi$
$397$	−90464.0	+	14328.1i	−0.573977	+	0.0909091i	−0.137303	+	0.990529i	$0.543844\pi$
$398$	9390.78	−	4784.84i	0.0592837	−	0.0302066i
$399$			308578.i			1.93829i
$400$	78256.9	+	36260.6i	0.489106	+	0.226629i
$401$	−49931.4			−0.310517			−0.155258	−	0.987874i	$-0.549621\pi$
$401$	−49931.4			−0.310517			−0.155258	+	0.987874i	$0.549621\pi$
$402$	−166910.	−	327578.i	−1.03283	−	2.02704i
$403$	−1242.27	−	7843.36i	−0.00764900	−	0.0482939i
$404$	−12290.9	+	16917.0i	−0.0753044	+	0.103648i
$405$	−81350.4	+	138490.i	−0.495963	+	0.844323i
$406$	−158369.	+	115062.i	−0.960770	+	0.698040i
$407$	31526.2	−	31526.2i	0.190319	−	0.190319i
$408$	381306.	+	60392.9i	2.29062	+	0.362799i
$409$	−25769.8	+	8373.11i	−0.154051	+	0.0500542i	−0.385027	−	0.922905i	$-0.625808\pi$
$409$	−25769.8	+	8373.11i	−0.154051	+	0.0500542i	0.230976	+	0.972959i	$0.425808\pi$
$410$	37008.9	−	94288.2i	0.220160	−	0.560906i
$411$	−31671.8	+	97475.7i	−0.187495	+	0.577049i
$412$	59436.5	+	30284.4i	0.350154	+	0.178412i
$413$	77320.8	−	151751.i	0.453311	−	0.889672i
$414$	230584.	+	74921.3i	1.34533	+	0.437124i
$415$	101655.	−	26421.7i	0.590248	−	0.153414i
$416$	−7616.72	−	23441.9i	−0.0440130	−	0.135458i
$417$	−38019.8	+	240047.i	−0.218644	+	1.38046i
$418$	30746.9	+	30746.9i	0.175974	+	0.175974i
$419$	66978.9	+	92188.5i	0.381513	+	0.525108i	0.955985	−	0.293417i	$-0.0947923\pi$
$419$	66978.9	+	92188.5i	0.381513	+	0.525108i	−0.574471	+	0.818525i	$0.694792\pi$
$420$	84902.9	−	75299.8i	0.481309	−	0.426870i
$421$	216580.	+	157355.i	1.22195	+	0.887800i	0.996261	−	0.0863984i	$-0.0275358\pi$
$421$	216580.	+	157355.i	1.22195	+	0.887800i	0.225692	+	0.974199i	$0.427536\pi$
$422$	148671.	−	23547.1i	0.834836	−	0.132225i
$423$	247937.	−	126330.i	1.38568	−	0.706037i
$424$			48921.3i			0.272124i
$425$	167197.	+	212933.i	0.925656	+	1.17887i
$426$	−79288.2			−0.436907
$427$	−49522.0	−	97192.3i	−0.271608	−	0.533060i
$428$	−7581.71	−	47869.0i	−0.0413885	−	0.261317i
$429$	−9980.37	+	13736.8i	−0.0542291	+	0.0746399i
$430$	−10583.8	−	108535.i	−0.0572407	−	0.586992i
$431$	1478.40	−	1074.12i	0.00795860	−	0.00578226i	−0.583799	−	0.811898i	$-0.698434\pi$
$431$	1478.40	−	1074.12i	0.00795860	−	0.00578226i	0.591757	+	0.806116i	$0.298434\pi$
$432$	−2059.74	+	2059.74i	−0.0110368	+	0.0110368i
$433$	−218542.	−	34613.6i	−1.16562	−	0.184617i	−0.456515	−	0.889716i	$-0.650903\pi$
$433$	−218542.	−	34613.6i	−1.16562	−	0.184617i	−0.709109	+	0.705099i	$0.750903\pi$
$434$	−42838.5	+	13919.1i	−0.227433	+	0.0738976i
$435$	−298294.	−	17880.7i	−1.57640	−	0.0944946i
$436$	−1899.32	+	5845.52i	−0.00999140	+	0.0307504i
$437$	−300939.	−	153336.i	−1.57585	−	0.802938i
$438$	−87143.7	+	171029.i	−0.454243	+	0.891501i
$439$	−44130.0	−	14338.7i	−0.228984	−	0.0744014i	0.192278	−	0.981341i	$-0.438413\pi$
$439$	−44130.0	−	14338.7i	−0.228984	−	0.0744014i	−0.421262	+	0.906939i	$0.638413\pi$
$440$	3745.12	−	62477.8i	0.0193447	−	0.322716i
$441$	45344.9	+	139557.i	0.233159	+	0.717588i
$442$	−8113.70	+	51227.9i	−0.0415312	+	0.262218i
$443$	60653.8	+	60653.8i	0.309066	+	0.309066i	0.844547	−	0.535481i	$-0.179870\pi$
$443$	60653.8	+	60653.8i	0.309066	+	0.309066i	−0.535481	+	0.844547i	$0.679870\pi$
$444$	−51223.4	−	70503.0i	−0.259838	−	0.357636i
$445$	−210010.	+	20479.2i	−1.06052	+	0.103417i
$446$	28527.0	+	20726.1i	0.143412	+	0.104195i
$447$	249040.	−	39444.0i	1.24639	−	0.197409i
$448$	−251709.	+	128252.i	−1.25413	+	0.639011i
$449$		−	271984.i		−	1.34912i	−0.738219	−	0.674561i	$-0.764333\pi$
$449$		−	271984.i		−	1.34912i	0.738219	−	0.674561i	$-0.235667\pi$
$450$	−167342.	+	6250.86i	−0.826382	+	0.0308684i
$451$	−44913.2			−0.220811
$452$	−18170.4	−	35661.5i	−0.0889382	−	0.174551i
$453$	−57579.8	−	363544.i	−0.280591	−	1.77158i
$454$	138583.	−	190743.i	0.672355	−	0.925417i
$455$	39595.5	+	44645.1i	0.191259	+	0.215651i
$456$	269127.	−	195532.i	1.29428	−	0.940348i
$457$	100624.	−	100624.i	0.481802	−	0.481802i	−0.423905	−	0.905707i	$-0.639341\pi$
$457$	100624.	−	100624.i	0.481802	−	0.481802i	0.905707	+	0.423905i	$0.139341\pi$
$458$	165258.	+	26174.2i	0.787827	+	0.124779i
$459$	−8695.92	+	2825.47i	−0.0412753	+	0.0134111i
$460$	31246.5	+	120219.i	0.147668	+	0.568141i
$461$	−91887.4	+	282800.i	−0.432369	+	1.33069i	0.463391	+	0.886154i	$0.346633\pi$
$461$	−91887.4	+	282800.i	−0.432369	+	1.33069i	−0.895759	+	0.444539i	$0.853367\pi$
$462$	85813.2	+	43724.0i	0.402041	+	0.204850i
$463$	−54064.3	+	106107.i	−0.252202	+	0.494975i	−0.982047	−	0.188639i	$-0.939593\pi$
$463$	−54064.3	+	106107.i	−0.252202	+	0.494975i	0.729844	+	0.683613i	$0.239593\pi$
$464$	122633.	+	39846.0i	0.569603	+	0.185075i
$465$	−64006.3	−	25123.0i	−0.296017	−	0.116189i
$466$	−6152.29	−	18934.8i	−0.0283312	−	0.0871945i
$467$	7864.16	−	49652.3i	0.0360594	−	0.227670i	−0.963077	−	0.269227i	$-0.913232\pi$
$467$	7864.16	−	49652.3i	0.0360594	−	0.227670i	0.999136	+	0.0415569i	$0.0132318\pi$
$468$	11852.3	+	11852.3i	0.0541143	+	0.0541143i
$469$	336754.	+	463501.i	1.53097	+	2.10720i
$470$	−235274.	−	138202.i	−1.06507	−	0.625633i
$471$	−277023.	−	201269.i	−1.24875	−	0.907267i
$472$	−181344.	+	28722.1i	−0.813992	+	0.128924i
$473$	−43083.1	+	21951.9i	−0.192568	+	0.0981184i
$474$		−	6528.90i		−	0.0290592i
$475$	231613.	+	27867.4i	1.02654	+	0.123512i
$476$	−153707.			−0.678391
$477$	−26348.2	−	51711.2i	−0.115801	−	0.227273i
$478$	27527.6	+	173802.i	0.120479	+	0.760677i
$479$	−171491.	+	236037.i	−0.747428	+	1.02875i	0.250729	+	0.968057i	$0.419330\pi$
$479$	−171491.	+	236037.i	−0.747428	+	1.02875i	−0.998157	+	0.0606890i	$0.980670\pi$
$480$	−208420.	−	45940.0i	−0.904600	−	0.199392i
$481$	37073.1	−	26935.2i	0.160239	−	0.116421i
$482$	−129905.	+	129905.i	−0.559153	+	0.559153i
$483$	−738881.	−	117027.i	−3.16724	−	0.501641i
$484$	69712.1	−	22650.8i	0.297589	−	0.0966927i
$485$	210443.	−	134427.i	0.894645	−	0.571481i
$486$	−84045.7	+	258666.i	−0.355830	+	1.09513i
$487$	315452.	+	160731.i	1.33007	+	0.677705i	0.967172	−	0.254123i	$-0.0817868\pi$
$487$	315452.	+	160731.i	1.33007	+	0.677705i	0.362900	+	0.931828i	$0.381787\pi$
$488$	−53386.7	+	104777.i	−0.224178	+	0.439974i
$489$	−234747.	−	76273.8i	−0.981706	−	0.318976i
$490$	91389.9	−	111140.i	0.380633	−	0.462889i
$491$	−12052.3	−	37093.2i	−0.0499928	−	0.153862i	0.922944	−	0.384935i	$-0.125776\pi$
$491$	−12052.3	−	37093.2i	−0.0499928	−	0.153862i	−0.972936	+	0.231073i	$0.925776\pi$
$492$	−13733.1	+	86707.7i	−0.0567335	+	0.358202i
$493$	286200.	+	286200.i	1.17754	+	1.17754i
$494$	26269.5	+	36156.8i	0.107646	+	0.148162i
$495$	29690.8	+	68057.8i	0.121174	+	0.277759i
$496$	24003.5	+	17439.5i	0.0975687	+	0.0708878i
$497$	122036.	−	19328.6i	0.494054	−	0.0782505i
$498$	155242.	−	79099.9i	0.625967	−	0.318946i
$499$		−	400032.i		−	1.60655i	−0.595611	−	0.803273i	$-0.703090\pi$
$499$		−	400032.i		−	1.60655i	0.595611	−	0.803273i	$-0.296910\pi$
$500$	−48851.2	−	70526.9i	−0.195405	−	0.282107i
$501$	172302.			0.686461
$502$	−45207.6	−	88724.8i	−0.179392	−	0.352077i
$503$	16252.5	+	102615.i	0.0642370	+	0.405577i	0.998765	+	0.0496866i	$0.0158222\pi$
$503$	16252.5	+	102615.i	0.0642370	+	0.405577i	−0.934528	+	0.355890i	$0.884178\pi$
$504$	218727.	−	301051.i	0.861074	−	1.18517i
$505$	−87264.9	+	38070.0i	−0.342182	+	0.149279i
$506$	−85283.4	+	61962.0i	−0.333091	+	0.242005i
$507$	246014.	−	246014.i	0.957072	−	0.957072i
$508$	97577.4	+	15454.7i	0.378113	+	0.0598873i
$509$	−445077.	+	144614.i	−1.71791	+	0.558182i	−0.991618	−	0.129207i	$-0.958757\pi$
$509$	−445077.	+	144614.i	−1.71791	+	0.558182i	−0.726290	+	0.687389i	$0.758757\pi$
$510$	346882.	+	285241.i	1.33365	+	1.09666i
$511$	92433.8	−	284482.i	0.353988	−	1.08946i
$512$	219115.	+	111645.i	0.835859	+	0.425891i
$513$	−3576.86	+	7019.98i	−0.0135915	+	0.0266748i
$514$	−186912.	−	60731.5i	−0.707476	−	0.229873i
$515$	163502.	+	255960.i	0.616465	+	0.965067i
$516$	29206.0	+	89886.8i	0.109691	+	0.337596i
$517$	−18926.8	+	119499.i	−0.0708104	+	0.447079i
$518$	−183794.	−	183794.i	−0.684971	−	0.684971i
$519$	−233224.	−	321006.i	−0.865844	−	1.19173i
$520$	13847.5	−	62823.0i	0.0512110	−	0.232333i
$521$	65604.4	+	47664.4i	0.241689	+	0.175598i	0.702036	−	0.712142i	$-0.252275\pi$
$521$	65604.4	+	47664.4i	0.241689	+	0.175598i	−0.460346	+	0.887739i	$0.652275\pi$
$522$	−247272.	+	39164.0i	−0.907472	+	0.143729i
$523$	−73810.5	+	37608.3i	−0.269845	+	0.137493i	−0.583678	−	0.811985i	$-0.698387\pi$
$523$	−73810.5	+	37608.3i	−0.269845	+	0.137493i	0.313833	+	0.949478i	$0.398387\pi$
$524$		−	2448.69i		−	0.00891808i
$525$	506968.	−	99823.6i	1.83934	−	0.362172i
$526$	−18810.8			−0.0679885
$527$	42280.9	+	82981.0i	0.152238	+	0.298784i
$528$	−9924.17	−	62658.8i	−0.0355981	−	0.224757i
$529$	316804.	−	436043.i	1.13208	−	1.55818i
$530$	−28824.3	+	49070.1i	−0.102614	+	0.174689i
$531$	176217.	−	128029.i	0.624969	−	0.454066i
$532$	−93653.6	+	93653.6i	−0.330903	+	0.330903i
$533$	−45594.2	−	7221.41i	−0.160493	−	0.0254195i
$534$	−332894.	+	108164.i	−1.16741	+	0.379314i
$535$	80626.0	−	205413.i	0.281688	−	0.717661i
$536$	190858.	−	587401.i	0.664326	−	2.04458i
$537$	−103384.	−	52676.7i	−0.358513	−	0.182671i
$538$	54104.3	−	106186.i	0.186925	−	0.366861i
$539$	−60678.8	−	19715.7i	−0.208862	−	0.0678633i
$540$	2804.33	−	728.884i	0.00961703	−	0.00249960i
$541$	102721.	+	316143.i	0.350966	+	1.08016i	0.958312	+	0.285724i	$0.0922341\pi$
$541$	102721.	+	316143.i	0.350966	+	1.08016i	−0.607346	+	0.794437i	$0.707766\pi$
$542$	−57033.5	+	360095.i	−0.194147	+	1.22580i
$543$	41815.9	+	41815.9i	0.141821	+	0.141821i
$544$	169910.	+	233862.i	0.574146	+	0.790244i
$545$	−20936.9	+	18568.8i	−0.0704887	+	0.0625160i
$546$	80084.1	+	58184.5i	0.268634	+	0.195174i
$547$	−490833.	+	77740.2i	−1.64043	+	0.259819i	−0.907368	−	0.420338i	$-0.861912\pi$
$547$	−490833.	+	77740.2i	−1.64043	+	0.259819i	−0.733066	+	0.680157i	$0.761912\pi$
$548$	−39196.4	+	19971.5i	−0.130522	+	0.0665044i
$549$		−	139506.i		−	0.462857i
$550$	40568.2	−	60461.2i	0.134110	−	0.199872i
$551$	348762.			1.14875
$552$	366131.	+	718572.i	1.20160	+	2.35826i
$553$	1591.59	+	10048.9i	0.00520453	+	0.0328601i
$554$	119946.	−	165091.i	0.390810	−	0.537904i
$555$	−38510.1	−	394913.i	−0.125023	−	1.28208i
$556$	−84393.6	+	61315.6i	−0.272998	+	0.198345i
$557$	−248041.	+	248041.i	−0.799490	+	0.799490i	−0.983015	−	0.183525i	$-0.941249\pi$
$557$	−248041.	+	248041.i	−0.799490	+	0.799490i	0.183525	+	0.983015i	$0.441249\pi$
$558$	−56896.8	−	9011.57i	−0.182734	−	0.0289422i
$559$	−47265.9	+	15357.6i	−0.151260	+	0.0491474i
$560$	−222556.	−	13340.8i	−0.709683	−	0.0425407i
$561$	61535.5	−	189387.i	0.195524	−	0.601761i
$562$	−137531.	−	70075.4i	−0.435439	−	0.221867i
$563$	−84447.7	+	165738.i	−0.266423	+	0.522884i	−0.984998	−	0.172565i	$-0.944794\pi$
$563$	−84447.7	+	165738.i	−0.266423	+	0.522884i	0.718575	+	0.695449i	$0.244794\pi$
$564$	224914.	+	73078.8i	0.707062	+	0.229738i
$565$	10904.0	−	181906.i	0.0341578	−	0.569836i
$566$	50458.0	+	155294.i	0.157506	+	0.484754i
$567$	64950.5	−	410082.i	0.202030	−	1.27557i
$568$	−94186.2	−	94186.2i	−0.291938	−	0.291938i
$569$	−144510.	−	198901.i	−0.446348	−	0.614346i	0.525260	−	0.850942i	$-0.323968\pi$
$569$	−144510.	−	198901.i	−0.446348	−	0.614346i	−0.971608	+	0.236596i	$0.923968\pi$
$570$	385152.	−	37558.3i	1.18545	−	0.115599i
$571$	−33669.7	−	24462.5i	−0.103268	−	0.0750288i	0.534953	−	0.844882i	$-0.320329\pi$
$571$	−33669.7	−	24462.5i	−0.103268	−	0.0750288i	−0.638221	+	0.769853i	$0.720329\pi$
$572$	−7198.18	+	1140.08i	−0.0220004	+	0.00348452i
$573$	134091.	−	68322.8i	0.408405	−	0.208093i
$574$			261839.i			0.794714i
$575$	−154566.	+	544023.i	−0.467498	+	1.64544i
$576$	−361292.			−1.08896
$577$	−74645.2	−	146499.i	−0.224208	−	0.440032i	0.751311	−	0.659948i	$-0.229422\pi$
$577$	−74645.2	−	146499.i	−0.224208	−	0.440032i	−0.975519	+	0.219916i	$0.929422\pi$
$578$	−52799.7	−	333364.i	−0.158043	−	0.997846i
$579$	−404130.	+	556237.i	−1.20549	+	1.65921i
$580$	−85105.8	−	95959.4i	−0.252990	−	0.285254i
$581$	−219658.	+	159591.i	−0.650719	+	0.472775i
$582$	292907.	−	292907.i	0.864737	−	0.864737i
$583$	24923.4	+	3947.49i	0.0733282	+	0.0116140i
$584$	−306683.	+	99647.3i	−0.899216	+	0.292173i
$585$	19198.2	+	73863.6i	0.0560982	+	0.215834i
$586$	41101.5	−	126498.i	0.119691	−	0.368372i
$587$	−14045.3	−	7156.45i	−0.0407620	−	0.0207693i	0.433491	−	0.901158i	$-0.357282\pi$
$587$	−14045.3	−	7156.45i	−0.0407620	−	0.0207693i	−0.474253	+	0.880389i	$0.657282\pi$
$588$	−56616.2	+	111116.i	−0.163752	+	0.321381i
$589$	76322.0	+	24798.5i	0.219998	+	0.0714818i
$590$	−198819.	−	78038.0i	−0.571155	−	0.224183i
$591$	225310.	+	693432.i	0.645067	+	1.98531i
$592$	−26783.5	+	169105.i	−0.0764231	+	0.482516i
$593$	−311714.	−	311714.i	−0.886435	−	0.886435i	0.107744	−	0.994179i	$-0.465637\pi$
$593$	−311714.	−	311714.i	−0.886435	−	0.886435i	−0.994179	+	0.107744i	$0.965637\pi$
$594$	1445.38	+	1989.40i	0.00409646	+	0.00563830i
$595$	−603436.	−	354464.i	−1.70450	−	1.00124i
$596$	87555.1	+	63612.5i	0.246484	+	0.179081i
$597$	−41078.4	+	6506.17i	−0.115256	+	0.0182548i
$598$	−96539.1	+	49189.1i	−0.269961	+	0.137552i
$599$			216028.i			0.602082i	0.953611	+	0.301041i	$0.0973341\pi$
$599$			216028.i			0.602082i	−0.953611	+	0.301041i	$0.902666\pi$
$600$	−408305.	−	378900.i	−1.13418	−	1.05250i
$601$	−34074.1			−0.0943355			−0.0471678	−	0.998887i	$-0.515020\pi$
$601$	−34074.1			−0.0943355			−0.0471678	+	0.998887i	$0.515020\pi$
$602$	127977.	+	251170.i	0.353135	+	0.693066i
$603$	114622.	+	723692.i	0.315233	+	1.99030i
$604$	92860.6	−	127812.i	0.254541	−	0.350345i
$605$	325917.	+	71838.8i	0.890423	+	0.196267i
$606$	−127771.	+	92831.2i	−0.347926	+	0.252783i
$607$	387295.	−	387295.i	1.05115	−	1.05115i	0.0525294	−	0.998619i	$-0.483272\pi$
$607$	387295.	−	387295.i	1.05115	−	1.05115i	0.998619	−	0.0525294i	$-0.0167283\pi$
$608$	246018.	+	38965.4i	0.665518	+	0.105408i
$609$	734670.	−	238709.i	1.98088	−	0.643627i
$610$	−115283.	+	73640.7i	−0.309818	+	0.197906i
$611$	−38427.6	+	118268.i	−0.102934	+	0.316800i
$612$	−175152.	−	89244.4i	−0.467641	−	0.238275i
$613$	63049.7	−	123742.i	0.167788	−	0.329303i	−0.791767	−	0.610823i	$-0.790839\pi$
$613$	63049.7	−	123742.i	0.167788	−	0.329303i	0.959555	+	0.281520i	$0.0908386\pi$
$614$	−106218.	−	34512.3i	−0.281748	−	0.0915455i
$615$	−253872.	+	308734.i	−0.671219	+	0.816272i
$616$	49997.6	+	153877.i	0.131761	+	0.405520i
$617$	79561.7	−	502333.i	0.208994	−	1.31954i	−0.630509	−	0.776182i	$-0.717154\pi$
$617$	79561.7	−	502333.i	0.208994	−	1.31954i	0.839503	−	0.543355i	$-0.182846\pi$
$618$	356261.	+	356261.i	0.932805	+	0.932805i
$619$	89232.3	+	122818.i	0.232885	+	0.320538i	0.909425	−	0.415867i	$-0.136522\pi$
$619$	89232.3	+	122818.i	0.232885	+	0.320538i	−0.676541	+	0.736405i	$0.736522\pi$
$620$	−11801.1	−	27050.8i	−0.0307001	−	0.0703715i
$621$	−15452.6	−	11227.0i	−0.0400700	−	0.0291126i
$622$	−324971.	+	51470.3i	−0.839970	+	0.133038i
$623$	486003.	−	247631.i	1.25217	−	0.638012i
$624$		−	65204.5i		−	0.167459i
$625$	−29141.9	−	389536.i	−0.0746034	−	0.997213i
$626$	−8406.84			−0.0214528
$627$	−77899.7	−	152887.i	−0.198153	−	0.388897i
$628$	−22991.4	−	145162.i	−0.0582970	−	0.368073i
$629$	−315890.	+	434785.i	−0.798426	+	1.09894i
$630$	396770.	−	173094.i	0.999673	−	0.436115i
$631$	211263.	−	153491.i	0.530596	−	0.385501i	−0.289985	−	0.957031i	$-0.593650\pi$
$631$	211263.	−	153491.i	0.530596	−	0.385501i	0.820581	+	0.571531i	$0.193650\pi$
$632$	7755.66	−	7755.66i	0.0194171	−	0.0194171i
$633$	−586676.	−	92920.4i	−1.46417	−	0.231901i
$634$	440224.	−	143037.i	1.09520	−	0.355853i
$635$	347438.	+	285697.i	0.861647	+	0.708531i
$636$	15241.7	−	46909.2i	0.0376808	−	0.115970i
$637$	−58428.8	−	29771.0i	−0.143995	−	0.0733692i
$638$	49418.0	−	96988.3i	0.121407	−	0.238275i
$639$	150284.	+	48830.4i	0.368055	+	0.119588i
$640$	47018.1	+	73606.2i	0.114790	+	0.179703i
$641$	−78821.7	−	242588.i	−0.191836	−	0.590410i	−0.999999	−	0.00145124i	$-0.999538\pi$
$641$	−78821.7	−	242588.i	−0.191836	−	0.590410i	0.808163	−	0.588959i	$-0.200462\pi$
$642$	57263.5	−	361547.i	0.138934	−	0.877193i
$643$	63474.3	+	63474.3i	0.153524	+	0.153524i	0.779690	−	0.626166i	$-0.215377\pi$
$643$	63474.3	+	63474.3i	0.153524	+	0.153524i	−0.626166	+	0.779690i	$0.715377\pi$
$644$	−188733.	−	259769.i	−0.455068	−	0.626348i
$645$	−92628.9	+	420238.i	−0.222652	+	1.01013i
$646$	−424039.	−	308082.i	−1.01611	−	0.738247i
$647$	−67050.5	+	10619.8i	−0.160174	+	0.0253691i	−0.236007	−	0.971751i	$-0.575839\pi$
$647$	−67050.5	+	10619.8i	−0.160174	+	0.0253691i	0.0758321	+	0.997121i	$0.475839\pi$
$648$	−398810.	+	203204.i	−0.949765	+	0.483929i
$649$			94705.2i			0.224846i
$650$	50904.6	−	54855.2i	0.120484	−	0.129835i
$651$	177746.			0.419409
$652$	−48096.6	−	94395.0i	−0.113141	−	0.222051i
$653$	−93764.1	−	592003.i	−0.219892	−	1.38835i	−0.812550	−	0.582892i	$-0.801921\pi$
$653$	−93764.1	−	592003.i	−0.219892	−	1.38835i	0.592657	−	0.805455i	$-0.298079\pi$
$654$	−27286.4	+	37556.5i	−0.0637956	+	0.0878071i
$655$	5646.94	−	9613.28i	0.0131623	−	0.0224073i
$656$	139534.	−	101378.i	0.324245	−	0.235578i
$657$	270504.	−	270504.i	0.626676	−	0.626676i
$658$	696668.	+	110341.i	1.60907	+	0.254851i
$659$	703669.	−	228636.i	1.62031	−	0.526470i	0.648293	−	0.761391i	$-0.275483\pi$
$659$	703669.	−	228636.i	1.62031	−	0.526470i	0.972014	+	0.234921i	$0.0754832\pi$
$660$	−23056.4	+	58741.3i	−0.0529303	+	0.134851i
$661$	4749.87	−	14618.6i	0.0108712	−	0.0334582i	−0.945474	−	0.325698i	$-0.894401\pi$
$661$	4749.87	−	14618.6i	0.0108712	−	0.0334582i	0.956345	+	0.292240i	$0.0944006\pi$
$662$	−319251.	−	162666.i	−0.728477	−	0.371177i
$663$	92919.3	−	182364.i	0.211387	−	0.414871i
$664$	278375.	+	90449.4i	0.631384	+	0.205149i
$665$	−583649.	+	151699.i	−1.31980	+	0.343035i
$666$	−102724.	−	316150.i	−0.231591	−	0.712763i
$667$	−132267.	+	835102.i	−0.297304	+	1.87710i
$668$	52293.9	+	52293.9i	0.117192	+	0.117192i
$669$	−81788.1	−	112572.i	−0.182742	−	0.251522i
$670$	537533.	−	476735.i	1.19745	−	1.06201i
$671$	49072.0	+	35652.9i	0.108990	+	0.0791862i
$672$	544908.	−	86305.0i	1.20666	−	0.191116i
$673$	−526448.	+	268239.i	−1.16232	+	0.592231i	−0.925286	−	0.379271i	$-0.876175\pi$
$673$	−526448.	+	268239.i	−1.16232	+	0.592231i	−0.237033	+	0.971502i	$0.576175\pi$
$674$			180773.i			0.397937i
$675$	12690.3	+	3605.55i	0.0278526	+	0.00791342i
$676$	149331.			0.326781
$677$	362013.	+	710490.i	0.789853	+	1.55017i	0.834395	+	0.551167i	$0.185817\pi$
$677$	362013.	+	710490.i	0.789853	+	1.55017i	−0.0445415	+	0.999008i	$0.514183\pi$
$678$	−47289.1	−	298572.i	−0.102873	−	0.649515i
$679$	−379422.	+	522230.i	−0.822968	+	1.13272i
$680$	73224.0	+	750897.i	0.158356	+	1.62391i
$681$	−752700.	+	546868.i	−1.62303	+	1.17920i
$682$	17710.8	−	17710.8i	0.0380775	−	0.0380775i
$683$	729164.	+	115488.i	1.56309	+	0.247569i	0.877196	−	0.480132i	$-0.159411\pi$
$683$	729164.	+	115488.i	1.56309	+	0.247569i	0.685894	+	0.727701i	$0.259411\pi$
$684$	−161097.	+	52343.5i	−0.344329	+	0.111879i
$685$	−199937.	−	11984.9i	−0.426100	−	0.0255418i
$686$	40499.3	−	124644.i	0.0860595	−	0.264864i
$687$	−588295.	−	299751.i	−1.24647	−	0.635108i
$688$	84298.9	−	165446.i	0.178092	−	0.349526i
$689$	24666.6	+	8014.68i	0.0519603	+	0.0168829i
$690$	−56135.7	+	936481.i	−0.117907	+	1.96698i
$691$	−257983.	−	793990.i	−0.540300	−	1.66287i	−0.731910	−	0.681401i	$-0.761371\pi$
$691$	−257983.	−	793990.i	−0.540300	−	1.66287i	0.191610	−	0.981471i	$-0.438629\pi$
$692$	26641.8	−	168209.i	0.0556353	−	0.351268i
$693$	−135724.	−	135724.i	−0.282612	−	0.282612i
$694$	228509.	+	314515.i	0.474443	+	0.653015i
$695$	−472720.	+	46097.4i	−0.978666	+	0.0954349i
$696$	−673719.	−	489486.i	−1.39079	−	1.01047i
$697$	534718.	−	84691.0i	1.10068	−	0.174330i
$698$	233211.	−	118827.i	0.478673	−	0.243896i
$699$			78564.6i			0.160795i
$700$	184162.	+	123569.i	0.375841	+	0.252181i
$701$	40774.1			0.0829752			0.0414876	−	0.999139i	$-0.486790\pi$
$701$	40774.1			0.0829752			0.0414876	+	0.999139i	$0.486790\pi$
$702$	1147.43	+	2251.96i	0.00232837	+	0.00456968i
$703$	72442.8	+	457386.i	0.146583	+	0.925491i
$704$	92333.9	−	127087.i	0.186301	−	0.256422i
$705$	714458.	+	805573.i	1.43747	+	1.62079i
$706$	−632359.	+	459435.i	−1.26869	+	0.921754i
$707$	174028.	−	174028.i	0.348161	−	0.348161i
$708$	182834.	+	28958.1i	0.364747	+	0.0577702i
$709$	−434689.	+	141239.i	−0.864741	+	0.280971i	−0.707607	−	0.706606i	$-0.750225\pi$
$709$	−434689.	+	141239.i	−0.864741	+	0.280971i	−0.157134	+	0.987577i	$0.550225\pi$
$710$	−38978.5	−	149967.i	−0.0773229	−	0.297494i
$711$	−4020.89	+	12375.0i	−0.00795395	+	0.0244797i
$712$	−523931.	−	266956.i	−1.03351	−	0.526599i
$713$	−88324.3	+	173346.i	−0.173741	+	0.340985i
$714$	−1.10411e6	−	358746.i	−2.16578	−	0.703704i
$715$	−30888.4	−	12123.9i	−0.0604204	−	0.0237155i
$716$	−15389.7	−	47364.6i	−0.0300195	−	0.0923905i
$717$	108628.	−	685849.i	0.211302	−	1.33411i
$718$	361943.	+	361943.i	0.702087	+	0.702087i
$719$	−447927.	−	616519.i	−0.866462	−	1.19258i	−0.979990	−	0.199048i	$-0.936215\pi$
$719$	−447927.	−	616519.i	−0.866462	−	1.19258i	0.113527	−	0.993535i	$-0.463785\pi$
$720$	−245861.	−	144421.i	−0.474270	−	0.278591i
$721$	−635184.	−	461488.i	−1.22188	−	0.887748i
$722$	−28808.2	+	4562.77i	−0.0552640	+	0.00875295i
$723$	645941.	−	329123.i	1.23571	−	0.629625i
$724$			25382.3i			0.0484233i
$725$	−112823.	−	572988.i	−0.214646	−	1.09011i
$726$	553621.			1.05036
$727$	352964.	+	692732.i	0.667824	+	1.31068i	0.937587	+	0.347752i	$0.113055\pi$
$727$	352964.	+	692732.i	0.667824	+	1.31068i	−0.269763	+	0.962927i	$0.586945\pi$
$728$	26014.5	+	164249.i	0.0490854	+	0.309913i
$729$	324967.	−	447279.i	0.611484	−	0.841635i
$730$	−366327.	−	80746.0i	−0.687423	−	0.151522i
$731$	471536.	−	342591.i	0.882429	−	0.641122i
$732$	83834.9	−	83834.9i	0.156460	−	0.156460i
$733$	−340954.	−	54001.8i	−0.634582	−	0.100508i	−0.169148	−	0.985591i	$-0.554102\pi$
$733$	−340954.	−	54001.8i	−0.634582	−	0.100508i	−0.465434	+	0.885083i	$0.654102\pi$
$734$	113717.	−	36948.8i	0.211073	−	0.0685817i
$735$	−478513.	+	305664.i	−0.885766	+	0.565809i
$736$	−186603.	+	574306.i	−0.344480	+	1.06020i
$737$	−283857.	−	144632.i	−0.522594	−	0.266275i
$738$	−152027.	+	298371.i	−0.279132	+	0.547827i
$739$	704946.	+	229051.i	1.29082	+	0.419414i	0.872380	−	0.488829i	$-0.162576\pi$
$739$	704946.	+	229051.i	1.29082	+	0.419414i	0.418443	+	0.908243i	$0.362576\pi$
$740$	108169.	−	131544.i	0.197532	−	0.240220i
$741$	−54498.8	−	167730.i	−0.0992546	−	0.305474i
$742$	23013.4	−	145301.i	0.0417997	−	0.263913i
$743$	−377764.	−	377764.i	−0.684294	−	0.684294i	0.276671	−	0.960965i	$-0.410769\pi$
$743$	−377764.	−	377764.i	−0.684294	−	0.684294i	−0.960965	+	0.276671i	$0.910769\pi$
$744$	−112630.	−	155022.i	−0.203473	−	0.280057i
$745$	197034.	+	451647.i	0.355001	+	0.813741i
$746$	473834.	+	344261.i	0.851430	+	0.618600i
$747$	−342964.	+	54320.2i	−0.614621	+	0.0973465i
$748$	76155.2	−	38803.0i	0.136112	−	0.0693525i
$749$			570433.i			1.01681i
$750$	−186300.	−	620624.i	−0.331201	−	1.10333i
$751$	35612.2			0.0631420			0.0315710	−	0.999502i	$-0.489949\pi$
$751$	35612.2			0.0631420			0.0315710	+	0.999502i	$0.489949\pi$
$752$	−210932.	−	413976.i	−0.372997	−	0.732049i
$753$	61470.9	+	388112.i	0.108412	+	0.684490i
$754$	65761.6	−	90513.1i	0.115672	−	0.159209i
$755$	659307.	−	287628.i	1.15663	−	0.504588i
$756$	−6059.60	+	4402.56i	−0.0106023	+	0.00770303i
$757$	−648879.	+	648879.i	−1.13233	+	1.13233i	−0.142537	+	0.989789i	$0.545526\pi$
$757$	−648879.	+	648879.i	−1.13233	+	1.13233i	−0.989789	+	0.142537i	$0.954474\pi$
$758$	−757733.	−	120013.i	−1.31880	−	0.208877i
$759$	395627.	−	128547.i	0.686755	−	0.223140i
$760$	502137.	+	412906.i	0.869350	+	0.714865i
$761$	−89831.8	+	276474.i	−0.155118	+	0.477403i	−0.998173	−	0.0604242i	$-0.980755\pi$
$761$	−89831.8	+	276474.i	−0.155118	+	0.477403i	0.843055	+	0.537827i	$0.180755\pi$
$762$	664846.	+	338756.i	1.14501	+	0.583414i
$763$	32842.3	−	64456.6i	0.0564136	−	0.110718i
$764$	61432.8	+	19960.7i	0.105248	+	0.0341971i
$765$	−481820.	−	754282.i	−0.823307	−	1.28888i
$766$	116533.	+	358653.i	0.198606	+	0.611247i
$767$	−15227.3	+	96141.2i	−0.0258840	+	0.163425i
$768$	−530222.	−	530222.i	−0.898949	−	0.898949i
$769$	540329.	+	743699.i	0.913704	+	1.25761i	0.965886	+	0.258969i	$0.0833826\pi$
$769$	540329.	+	743699.i	0.913704	+	1.25761i	−0.0521813	+	0.998638i	$0.516617\pi$
$770$	−40514.0	+	183803.i	−0.0683319	+	0.310007i
$771$	627425.	+	455851.i	1.05549	+	0.766857i
$772$	−291472.	+	46164.6i	−0.489060	+	0.0774595i
$773$	216957.	−	110545.i	0.363091	−	0.185004i	−0.262921	−	0.964817i	$-0.584686\pi$
$773$	216957.	−	110545.i	0.363091	−	0.185004i	0.626012	+	0.779813i	$0.284686\pi$
$774$			360518.i			0.601791i
$775$	16052.1	−	133413.i	0.0267257	−	0.222124i
$776$	695887.			1.15562
$777$	465657.	+	913904.i	0.771302	+	1.51376i
$778$	−13039.5	−	82328.0i	−0.0215427	−	0.136016i
$779$	274201.	−	377406.i	0.451850	−	0.621918i
$780$	−32850.8	+	55924.8i	−0.0539954	+	0.0919211i
$781$	−55584.0	+	40384.1i	−0.0911271	+	0.0662077i
$782$	898510.	−	898510.i	1.46930	−	1.46930i
$783$	19480.3	+	3085.38i	0.0317741	+	0.00503252i
$784$	233016.	−	75711.6i	0.379100	−	0.123177i
$785$	244497.	−	622910.i	0.396766	−	1.01085i
$786$	5715.14	−	17589.4i	0.00925085	−	0.0284712i
$787$	−41291.2	−	21038.9i	−0.0666665	−	0.0339683i	0.420339	−	0.907367i	$-0.361911\pi$
$787$	−41291.2	−	21038.9i	−0.0666665	−	0.0339683i	−0.487006	+	0.873399i	$0.661911\pi$
$788$	−142076.	+	278839.i	−0.228806	+	0.449057i
$789$	70597.0	+	22938.3i	0.113405	+	0.0368475i
$790$	12348.9	−	3209.64i	0.0197867	−	0.00514284i
$791$	145569.	+	448017.i	0.232658	+	0.716047i
$792$	−32369.8	+	204375.i	−0.0516048	+	0.325820i
$793$	44083.5	+	44083.5i	0.0701019	+	0.0701019i
$794$	−174526.	−	240214.i	−0.276834	−	0.381029i
$795$	168015.	−	149011.i	0.265836	−	0.235768i
$796$	−14442.0	−	10492.7i	−0.0227929	−	0.0165600i
$797$	−316826.	+	50180.3i	−0.498774	+	0.0789981i	−0.400753	−	0.916186i	$-0.631251\pi$
$797$	−316826.	+	50180.3i	−0.498774	+	0.0789981i	−0.0980215	+	0.995184i	$0.531251\pi$
$798$	−891315.	+	454147.i	−1.39967	+	0.713167i
$799$		−	1.45840e6i		−	2.28446i
$800$	−15568.8	−	416793.i	−0.0243262	−	0.651239i
$801$	697588.			1.08726
$802$	−73486.3	−	144225.i	−0.114250	−	0.224229i
$803$	26019.9	+	164283.i	0.0403529	+	0.254778i
$804$	−366017.	+	503779.i	−0.566224	+	0.779341i
$805$	−141891.	−	1.45506e6i	−0.218959	−	2.24538i
$806$	20826.9	−	15131.7i	0.0320594	−	0.0232925i
$807$	−332539.	+	332539.i	−0.510617	+	0.510617i
$808$	−262053.	−	41505.1i	−0.401390	−	0.0635739i
$809$	−709231.	+	230443.i	−1.08365	+	0.352101i	−0.795791	−	0.605571i	$-0.792945\pi$
$809$	−709231.	+	230443.i	−1.08365	+	0.352101i	−0.287863	+	0.957672i	$0.592945\pi$
$810$	−519750.	−	31155.5i	−0.792181	−	0.0474859i
$811$	193299.	−	594914.i	0.293892	−	0.904508i	−0.689699	−	0.724096i	$-0.742257\pi$
$811$	193299.	−	594914.i	0.293892	−	0.904508i	0.983591	−	0.180411i	$-0.0577429\pi$
$812$	295422.	+	150525.i	0.448054	+	0.228295i
$813$	653155.	−	1.28189e6i	0.988179	−	1.93941i
$814$	137461.	+	44663.6i	0.207458	+	0.0674070i
$815$	28862.7	−	481500.i	0.0434532	−	0.724905i
$816$	236306.	+	727276.i	0.354891	+	1.09224i
$817$	78566.1	−	496047.i	0.117704	−	0.743154i
$818$	−62111.9	−	62111.9i	−0.0928258	−	0.0928258i
$819$	−115960.	−	159605.i	−0.172878	−	0.237946i
$820$	−170751.	+	16650.9i	−0.253943	+	0.0247634i
$821$	−221388.	−	160848.i	−0.328449	−	0.238632i	0.411323	−	0.911490i	$-0.365067\pi$
$821$	−221388.	−	160848.i	−0.328449	−	0.238632i	−0.739772	+	0.672857i	$0.765067\pi$
$822$	−328167.	+	51976.6i	−0.485682	+	0.0769244i
$823$	−646334.	+	329324.i	−0.954240	+	0.486209i	−0.860535	−	0.509391i	$-0.829871\pi$
$823$	−646334.	+	329324.i	−0.954240	+	0.486209i	−0.0937043	+	0.995600i	$0.529871\pi$
$824$			846402.i			1.24659i
$825$	−225980.	+	177441.i	−0.332019	+	0.260703i
$826$	552122.			0.809235
$827$	−311350.	−	611059.i	−0.455237	−	0.893453i	−0.998545	−	0.0539199i	$-0.982828\pi$
$827$	−311350.	−	611059.i	−0.455237	−	0.893453i	0.543308	−	0.839533i	$-0.317172\pi$
$828$	−64239.6	−	405593.i	−0.0937005	−	0.591602i
$829$	42232.2	−	58127.7i	0.0614519	−	0.0845812i	−0.777185	−	0.629272i	$-0.783353\pi$
$829$	42232.2	−	58127.7i	0.0614519	−	0.0845812i	0.838637	+	0.544691i	$0.183353\pi$
$830$	225929.	+	254742.i	0.327956	+	0.369780i
$831$	−651474.	+	473324.i	−0.943398	+	0.685419i
$832$	114168.	−	114168.i	0.164929	−	0.164929i
$833$	759594.	+	120308.i	1.09469	+	0.173382i
$834$	−749323.	+	243470.i	−1.07730	+	0.350036i
$835$	84704.8	+	325895.i	0.121488	+	0.467418i
$836$	22758.7	−	70043.9i	0.0325637	−	0.100221i
$837$	4043.63	+	2060.33i	0.00577192	+	0.00294094i
$838$	−167707.	+	329144.i	−0.238816	+	0.468703i
$839$	−156947.	−	50995.1i	−0.222961	−	0.0724444i	0.195406	−	0.980722i	$-0.437397\pi$
$839$	−156947.	−	50995.1i	−0.222961	−	0.0724444i	−0.418367	+	0.908278i	$0.637397\pi$
$840$	1.34037e6	+	526104.i	1.89961	+	0.745612i
$841$	−51233.0	−	157679.i	−0.0724366	−	0.222937i
$842$	−135762.	+	857169.i	−0.191494	+	1.20904i
$843$	430701.	+	430701.i	0.606068	+	0.606068i
$844$	−149855.	−	206258.i	−0.210372	−	0.289552i
$845$	586257.	+	344373.i	0.821060	+	0.482299i
$846$	729801.	+	530231.i	1.01968	+	0.740840i
$847$	−852102.	+	134960.i	−1.18775	+	0.188121i
$848$	−86341.3	+	43993.1i	−0.120068	+	0.0611776i
$849$		−	644348.i		−	0.893933i
$850$	−368979.	+	796324.i	−0.510698	+	1.10218i
$851$	−1.12267e6			−1.55022
$852$	60968.1	+	119657.i	0.0839892	+	0.164838i
$853$	222279.	+	1.40342e6i	0.305493	+	1.92881i	0.365947	+	0.930636i	$0.380745\pi$
$853$	222279.	+	1.40342e6i	0.305493	+	1.92881i	−0.0604539	+	0.998171i	$0.519255\pi$
$854$	207853.	−	286084.i	0.284997	−	0.392264i
$855$	−753157.	−	166011.i	−1.03027	−	0.227094i
$856$	497504.	−	361458.i	0.678968	−	0.493299i
$857$	−142748.	+	142748.i	−0.194361	+	0.194361i	−0.797578	−	0.603216i	$-0.793886\pi$
$857$	−142748.	+	142748.i	−0.194361	+	0.194361i	0.603216	+	0.797578i	$0.293886\pi$
$858$	−54366.8	−	8610.85i	−0.0738514	−	0.0116969i
$859$	−718896.	+	233584.i	−0.974271	+	0.316560i	−0.752539	−	0.658548i	$-0.771171\pi$
$859$	−718896.	+	233584.i	−0.974271	+	0.316560i	−0.221732	+	0.975108i	$0.571171\pi$
$860$	−155655.	+	99429.5i	−0.210459	+	0.134437i
$861$	319293.	−	982683.i	0.430708	−	1.32558i
$862$	5278.37	+	2689.47i	0.00710372	+	0.00361952i
$863$	−166119.	+	326027.i	−0.223048	+	0.437756i	−0.975228	−	0.221201i	$-0.929002\pi$
$863$	−166119.	+	326027.i	−0.223048	+	0.437756i	0.752180	+	0.658958i	$0.229002\pi$
$864$	13396.8	+	4352.87i	0.0179462	+	0.00583107i
$865$	492501.	−	598933.i	0.658226	−	0.800471i
$866$	−221657.	−	682191.i	−0.295560	−	0.909642i
$867$	−208355.	+	1.31550e6i	−0.277183	+	1.75006i
$868$	53946.1	+	53946.1i	0.0716012	+	0.0716012i
$869$	−3325.39	−	4577.01i	−0.00440355	−	0.00606097i
$870$	−387365.	−	887927.i	−0.511778	−	1.17311i
$871$	−264906.	−	192465.i	−0.349185	−	0.253697i
$872$	−77026.7	+	12199.8i	−0.101300	+	0.0160443i
$873$	−735572.	+	374793.i	−0.965154	+	0.491771i
$874$		−	1.09492e6i		−	1.43338i
$875$	438036.	+	909813.i	0.572129	+	1.18833i
$876$	325115.			0.423671
$877$	258953.	+	508223.i	0.336683	+	0.660778i	0.995829	−	0.0912373i	$-0.0290822\pi$
$877$	258953.	+	508223.i	0.336683	+	0.660778i	−0.659146	+	0.752015i	$0.729082\pi$
$878$	−23531.3	−	148571.i	−0.0305251	−	0.192728i
$879$	−308508.	+	424625.i	−0.399291	+	0.549577i
$880$	113635.	−	49574.1i	0.146739	−	0.0640161i
$881$	−624659.	+	453842.i	−0.804806	+	0.584726i	−0.912320	−	0.409478i	$-0.865711\pi$
$881$	−624659.	+	453842.i	−0.804806	+	0.584726i	0.107514	+	0.994204i	$0.465711\pi$
$882$	−336370.	+	336370.i	−0.432394	+	0.432394i
$883$	−66557.9	−	10541.7i	−0.0853646	−	0.0135204i	0.113606	−	0.993526i	$-0.463760\pi$
$883$	−66557.9	−	10541.7i	−0.0853646	−	0.0135204i	−0.198971	+	0.980005i	$0.563760\pi$
$884$	83548.8	−	27146.7i	0.106914	−	0.0347386i
$885$	651006.	+	535321.i	0.831187	+	0.683483i
$886$	−85929.2	+	264463.i	−0.109465	+	0.336897i
$887$	878909.	+	447826.i	1.11711	+	0.569197i	0.912266	−	0.409597i	$-0.134331\pi$
$887$	878909.	+	447826.i	1.11711	+	0.569197i	0.204845	+	0.978794i	$0.434331\pi$
$888$	501997.	−	985225.i	0.636613	−	1.24942i
$889$	−1.10587e6	−	359320.i	−1.39927	−	0.454651i
$890$	−368235.	−	576466.i	−0.464884	−	0.727770i
$891$	71344.0	+	219574.i	0.0898673	+	0.276583i
$892$	9342.84	−	58988.4i	0.0117422	−	0.0741373i
$893$	−888602.	−	888602.i	−1.11431	−	1.11431i
$894$	480455.	+	661290.i	0.601143	+	0.827403i
$895$	48809.5	−	221438.i	0.0609338	−	0.276443i
$896$	−182659.	−	132710.i	−0.227523	−	0.165305i
$897$	422294.	−	66884.8i	0.524844	−	0.0831271i
$898$	785616.	−	400291.i	0.974221	−	0.496390i
$899$		−	200893.i		−	0.248568i
$900$	138110.	+	247736.i	0.170506	+	0.305847i
$901$	−304172.			−0.374688
$902$	−66100.7	−	129730.i	−0.0812443	−	0.159451i
$903$	−174017.	−	1.09870e6i	−0.213411	−	1.34742i
$904$	298498.	−	410847.i	0.365262	−	0.502740i
$905$	−58534.3	+	99648.1i	−0.0714682	+	0.121667i
$906$	965341.	−	701361.i	1.17605	−	0.854448i
$907$	590228.	−	590228.i	0.717472	−	0.717472i	−0.250615	−	0.968087i	$-0.580633\pi$
$907$	590228.	−	590228.i	0.717472	−	0.717472i	0.968087	+	0.250615i	$0.0806327\pi$
$908$	−394420.	−	62470.0i	−0.478396	−	0.0757705i
$909$	299351.	−	97265.1i	0.362287	−	0.117714i
$910$	−70681.3	+	180076.i	−0.0853536	+	0.217457i
$911$	−134207.	+	413047.i	−0.161711	+	0.497695i	−0.998779	−	0.0494040i	$-0.984268\pi$
$911$	−134207.	+	413047.i	−0.161711	+	0.497695i	0.837068	+	0.547099i	$0.184268\pi$
$912$	587110.	+	299148.i	0.705878	+	0.359663i
$913$	68542.5	−	134522.i	0.0822277	−	0.161381i
$914$	438741.	+	142555.i	0.525189	+	0.170644i
$915$	522458.	−	135794.i	0.624035	−	0.162196i
$916$	−87573.3	−	269523.i	−0.104371	−	0.321221i
$917$	−4508.54	+	28465.8i	−0.00536163	+	0.0338520i
$918$	−20959.4	−	20959.4i	−0.0248711	−	0.0248711i
$919$	24916.8	+	34295.0i	0.0295026	+	0.0406069i	0.823513	−	0.567297i	$-0.192011\pi$
$919$	24916.8	+	34295.0i	0.0295026	+	0.0406069i	−0.794011	+	0.607904i	$0.792011\pi$
$920$	−1.17913e6	+	1.04576e6i	−1.39311	+	1.23554i
$921$	356551.	+	259049.i	0.420342	+	0.305396i
$922$	−952092.	+	150797.i	−1.12000	+	0.177390i
$923$	−62920.0	+	32059.3i	−0.0738559	+	0.0376315i
$924$		−	163125.i		−	0.191063i
$925$	728013.	−	266980.i	0.850855	−	0.312029i
$926$	−386055.			−0.450223
$927$	−455857.	−	894671.i	−0.530481	−	1.04113i
$928$	−97544.1	−	615869.i	−0.113267	−	0.715142i
$929$	612161.	−	842568.i	0.709307	−	0.976278i	−0.290504	−	0.956874i	$-0.593823\pi$
$929$	612161.	−	842568.i	0.709307	−	0.976278i	0.999812	−	0.0194043i	$-0.00617696\pi$
$930$	−21634.2	−	221854.i	−0.0250135	−	0.256509i
$931$	536124.	−	389517.i	0.618537	−	0.449393i
$932$	−23844.4	+	23844.4i	−0.0274508	+	0.0274508i
$933$	1.28238e6	+	203109.i	1.47317	+	0.233328i
$934$	154993.	−	50360.2i	0.177672	−	0.0577290i
$935$	388460.	+	23285.6i	0.444348	+	0.0266357i
$936$	−65721.2	+	202269.i	−0.0750160	+	0.230876i
$937$	1.18542e6	+	604000.i	1.35018	+	0.687951i	0.971381	−	0.237527i	$-0.0763369\pi$
$937$	1.18542e6	+	604000.i	1.35018	+	0.687951i	0.378800	+	0.925479i	$0.376337\pi$
$938$	−843191.	+	1.65485e6i	−0.958341	+	1.88085i
$939$	31550.9	+	10251.5i	0.0357833	+	0.0116267i
$940$	−27653.7	+	461331.i	−0.0312966	+	0.522104i
$941$	225567.	+	694223.i	0.254739	+	0.784007i	0.993881	+	0.110457i	$0.0352314\pi$
$941$	225567.	+	694223.i	0.254739	+	0.784007i	−0.739142	+	0.673550i	$0.764769\pi$
$942$	173651.	−	1.09639e6i	0.195693	−	1.23555i
$943$	799698.	+	799698.i	0.899295	+	0.899295i
$944$	−213768.	−	294226.i	−0.239882	−	0.330170i
$945$	−33942.1	+	3309.87i	−0.0380080	+	0.00370636i
$946$	−126815.	−	92136.2i	−0.141706	−	0.102955i
$947$	1.61099e6	−	255156.i	1.79636	−	0.284515i	0.833106	−	0.553113i	$-0.186560\pi$
$947$	1.61099e6	−	255156.i	1.79636	−	0.284515i	0.963253	+	0.268597i	$0.0865601\pi$
$948$	−9853.00	+	5020.36i	−0.0109636	+	0.00558622i
$949$			170958.i			0.189826i
$950$	260381.	+	710019.i	0.288511	+	0.786724i
$951$	−1.82658e6			−2.01966
$952$	−885411.	−	1.73772e6i	−0.976947	−	1.91737i
$953$	198550.	+	1.25359e6i	0.218617	+	1.38029i	0.815868	+	0.578239i	$0.196260\pi$
$953$	198550.	+	1.25359e6i	0.218617	+	1.38029i	−0.597251	+	0.802055i	$0.703740\pi$
$954$	110588.	−	152211.i	0.121510	−	0.167244i
$955$	195147.	+	220034.i	0.213971	+	0.241259i
$956$	241124.	−	175187.i	0.263831	−	0.191684i
$957$	−303736.	+	303736.i	−0.331644	+	0.331644i
$958$	−934173.	−	147958.i	−1.01788	−	0.161216i
$959$	492426.	−	159999.i	0.535431	−	0.173972i
$960$	−351680.	−	1.35306e6i	−0.381597	−	1.46817i
$961$	−271099.	+	834358.i	−0.293550	+	0.903453i
$962$	132363.	+	67442.6i	0.143027	+	0.0728759i
$963$	−331201.	+	650018.i	−0.357140	+	0.700928i
$964$	295933.	+	96154.4i	0.318448	+	0.103470i
$965$	−1.25075e6	−	490928.i	−1.34312	−	0.527185i
$966$	−749415.	−	2.30646e6i	−0.803098	−	2.47168i
$967$	12525.5	−	79083.0i	0.0133950	−	0.0845727i	−0.980085	−	0.198577i	$-0.936368\pi$
$967$	12525.5	−	79083.0i	0.0133950	−	0.0845727i	0.993480	+	0.114005i	$0.0363679\pi$
$968$	657645.	+	657645.i	0.701844	+	0.701844i
$969$	1.21574e6	+	1.67332e6i	1.29477	+	1.78209i
$970$	698004.	+	410014.i	0.741847	+	0.435768i
$971$	−252186.	−	183223.i	−0.267474	−	0.194331i	0.445961	−	0.895052i	$-0.352862\pi$
$971$	−252186.	−	183223.i	−0.267474	−	0.194331i	−0.713436	+	0.700721i	$0.752862\pi$
$972$	454989.	−	72063.2i	0.481580	−	0.0762747i
$973$	1.09396e6	−	557402.i	1.15552	−	0.588766i
$974$			1.14772e6i			1.20982i
$975$	−257937.	+	143797.i	−0.271334	+	0.151266i
$976$	−232930.			−0.244526
$977$	−734300.	−	1.44114e6i	−0.769280	−	1.50980i	−0.857949	−	0.513735i	$-0.828261\pi$
$977$	−734300.	−	1.44114e6i	−0.769280	−	1.50980i	0.0886694	−	0.996061i	$-0.471739\pi$
$978$	−125173.	−	790312.i	−0.130868	−	0.826268i
$979$	−178280.	+	245381.i	−0.186010	+	0.256021i
$980$	−237999.	−	52459.7i	−0.247812	−	0.0546228i
$981$	74848.7	−	54380.8i	0.0777762	−	0.0565077i
$982$	89404.3	−	89404.3i	0.0927119	−	0.0927119i
$983$	−1.77092e6	−	280486.i	−1.83270	−	0.290272i	−0.857979	−	0.513685i	$-0.828280\pi$
$983$	−1.77092e6	−	280486.i	−1.83270	−	0.290272i	−0.974724	+	0.223413i	$0.928280\pi$
$984$	−1.05937e6	+	344211.i	−1.09410	+	0.355496i
$985$	−1.20080e6	+	767049.i	−1.23766	+	0.790589i
$986$	−405464.	+	1.24789e6i	−0.417059	+	1.28358i
$987$	−2.48005e6	−	1.26365e6i	−2.54581	−	1.29715i
$988$	34365.8	−	67446.7i	0.0352057	−	0.0690950i
$989$	1.15797e6	+	376249.i	1.18388	+	0.384665i
$990$	−152885.	+	185924.i	−0.155989	+	0.189699i
$991$	261237.	+	804004.i	0.266003	+	0.818674i	0.991461	+	0.130407i	$0.0416284\pi$
$991$	261237.	+	804004.i	0.266003	+	0.818674i	−0.725457	+	0.688267i	$0.758372\pi$
$992$	22444.7	−	141711.i	0.0228082	−	0.144005i
$993$	999789.	+	999789.i	1.01393	+	1.01393i
$994$	235435.	+	324049.i	0.238286	+	0.327973i
$995$	−32500.2	−	74497.8i	−0.0328277	−	0.0752484i
$996$	−238745.	−	173459.i	−0.240667	−	0.174855i
$997$	1.75583e6	−	278096.i	1.76641	−	0.279772i	0.813181	−	0.582011i	$-0.197734\pi$
$997$	1.75583e6	−	278096.i	1.76641	−	0.279772i	0.953232	+	0.302239i	$0.0977340\pi$
$998$	1.15548e6	−	588744.i	1.16011	−	0.591106i
$999$			26188.4i			0.0262409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.3.7	✓	72
5.2	odd	4		125.5.f.b.7.3		72
5.3	odd	4		125.5.f.a.7.7		72
5.4	even	2		125.5.f.c.118.3		72
25.6	even	5		125.5.f.b.18.3		72
25.8	odd	20		125.5.f.c.107.3		72
25.17	odd	20	inner	25.5.f.a.17.7	yes	72
25.19	even	10		125.5.f.a.18.7		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.3.7	✓	72	1.1	even	1	trivial
25.5.f.a.17.7	yes	72	25.17	odd	20	inner
125.5.f.a.7.7		72	5.3	odd	4
125.5.f.a.18.7		72	25.19	even	10
125.5.f.b.7.3		72	5.2	odd	4
125.5.f.b.18.3		72	25.6	even	5
125.5.f.c.107.3		72	25.8	odd	20
125.5.f.c.118.3		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)

\(f(q)\)	\(=\)	\(q+(1.47174 + 2.88846i) q^{2} +(-2.00120 - 12.6351i) q^{3} +(3.22739 - 4.44212i) q^{4} +(22.9144 - 9.99657i) q^{5} +(33.5507 - 24.3760i) q^{6} +(-45.6970 + 45.6970i) q^{7} +(68.8109 + 10.8986i) q^{8} +(-78.6049 + 25.5403i) q^{9} +O(q^{10})\)	\(q+(1.47174 + 2.88846i) q^{2} +(-2.00120 - 12.6351i) q^{3} +(3.22739 - 4.44212i) q^{4} +(22.9144 - 9.99657i) q^{5} +(33.5507 - 24.3760i) q^{6} +(-45.6970 + 45.6970i) q^{7} +(68.8109 + 10.8986i) q^{8} +(-78.6049 + 25.5403i) q^{9} +(62.5988 + 51.4749i) q^{10} +(11.1048 - 34.1770i) q^{11} +(-62.5852 - 31.8888i) q^{12} +(16.7683 - 32.9097i) q^{13} +(-199.248 - 64.7397i) q^{14} +(-172.164 - 269.520i) q^{15} +(42.6441 + 131.245i) q^{16} +(-67.7627 + 427.837i) q^{17} +(-189.458 - 189.458i) q^{18} +(219.393 + 301.969i) q^{19} +(29.5477 - 134.051i) q^{20} +(668.834 + 485.936i) q^{21} +(115.062 - 18.2241i) q^{22} +(-806.260 + 410.810i) q^{23} -891.242i q^{24} +(425.137 - 458.130i) q^{25} +119.737 q^{26} +(9.58291 + 18.8075i) q^{27} +(55.5096 + 350.474i) q^{28} +(549.217 - 755.933i) q^{29} +(525.116 - 893.952i) q^{30} +(173.939 - 126.374i) q^{31} +(471.876 - 471.876i) q^{32} +(-454.052 - 71.9147i) q^{33} +(-1335.52 + 433.936i) q^{34} +(-590.305 + 1503.93i) q^{35} +(-140.236 + 431.601i) q^{36} +(1105.45 + 563.256i) q^{37} +(-549.334 + 1078.13i) q^{38} +(-449.373 - 146.010i) q^{39} +(1685.71 - 438.139i) q^{40} +(-386.215 - 1188.65i) q^{41} +(-419.255 + 2647.07i) q^{42} +(-951.445 - 951.445i) q^{43} +(-115.979 - 159.631i) q^{44} +(-1545.87 + 1371.02i) q^{45} +(-2373.22 - 1724.24i) q^{46} +(-3325.36 + 526.685i) q^{47} +(1572.95 - 801.459i) q^{48} -1775.43i q^{49} +(1948.98 + 553.741i) q^{50} +5541.36 q^{51} +(-92.0709 - 180.699i) q^{52} +(109.848 + 693.555i) q^{53} +(-40.2212 + 55.3597i) q^{54} +(-87.1937 - 894.153i) q^{55} +(-3642.48 + 2646.42i) q^{56} +(3376.35 - 3376.35i) q^{57} +(2991.79 + 473.853i) q^{58} +(-2506.42 + 814.384i) q^{59} +(-1752.88 - 105.073i) q^{60} +(-521.592 + 1605.30i) q^{61} +(621.020 + 316.426i) q^{62} +(2424.89 - 4759.12i) q^{63} +(4157.40 + 1350.82i) q^{64} +(55.2515 - 921.730i) q^{65} +(-460.525 - 1417.35i) q^{66} +(1386.83 - 8756.10i) q^{67} +(1681.81 + 1681.81i) q^{68} +(6804.10 + 9365.04i) q^{69} +(-5212.82 + 508.330i) q^{70} +(-1546.76 - 1123.79i) q^{71} +(-5687.22 + 900.768i) q^{72} +(-4124.08 + 2101.32i) q^{73} +4022.02i q^{74} +(-6639.30 - 4454.83i) q^{75} +2049.45 q^{76} +(1054.33 + 2069.24i) q^{77} +(-239.618 - 1512.89i) q^{78} +(92.5370 - 127.366i) q^{79} +(2289.16 + 2581.10i) q^{80} +(-5197.63 + 3776.30i) q^{81} +(2864.95 - 2864.95i) q^{82} +(4149.60 + 657.231i) q^{83} +(4317.18 - 1402.74i) q^{84} +(2724.16 + 10481.0i) q^{85} +(1347.93 - 4148.49i) q^{86} +(-10650.4 - 5426.63i) q^{87} +(1136.61 - 2230.72i) q^{88} +(-8027.17 - 2608.18i) q^{89} +(-6235.25 - 2447.38i) q^{90} +(737.612 + 2270.13i) q^{91} +(-777.248 + 4907.35i) q^{92} +(-1944.83 - 1944.83i) q^{93} +(-6415.38 - 8830.01i) q^{94} +(8045.90 + 4726.24i) q^{95} +(-6906.51 - 5017.87i) q^{96} +(9865.55 - 1562.55i) q^{97} +(5128.26 - 2612.98i) q^{98} +2970.09i 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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