LMFDB - Embedded newform 61.6.g.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	61.3
Dual form			61.6.g.a.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.28026 - 2.36550i) q^{2} +(4.76030 - 14.6507i) q^{3} +(21.5180 + 15.6337i) q^{4} +(0.187196 + 0.136006i) q^{5} +(-69.3124 + 95.4003i) q^{6} +(234.418 - 76.1672i) q^{7} +(24.3073 + 33.4561i) q^{8} +(4.60899 + 3.34863i) q^{9} +O(q^{10})$	\(q+(-7.28026 - 2.36550i) q^{2} +(4.76030 - 14.6507i) q^{3} +(21.5180 + 15.6337i) q^{4} +(0.187196 + 0.136006i) q^{5} +(-69.3124 + 95.4003i) q^{6} +(234.418 - 76.1672i) q^{7} +(24.3073 + 33.4561i) q^{8} +(4.60899 + 3.34863i) q^{9} +(-1.04111 - 1.43297i) q^{10} +396.060i q^{11} +(331.477 - 240.832i) q^{12} +679.376 q^{13} -1886.80 q^{14} +(2.88369 - 2.09512i) q^{15} +(-360.836 - 1110.54i) q^{16} +(218.275 - 300.429i) q^{17} +(-25.6334 - 35.2814i) q^{18} +(-50.9256 + 156.733i) q^{19} +(1.90180 + 5.85315i) q^{20} -3796.97i q^{21} +(936.881 - 2883.42i) q^{22} +(1460.57 - 2010.31i) q^{23} +(605.864 - 196.857i) q^{24} +(-965.662 - 2972.00i) q^{25} +(-4946.03 - 1607.06i) q^{26} +(3099.42 - 2251.86i) q^{27} +(6235.00 + 2025.87i) q^{28} +5297.81i q^{29} +(-25.9500 + 8.43167i) q^{30} +(-8742.27 + 2840.53i) q^{31} +7615.23i q^{32} +(5802.56 + 1885.37i) q^{33} +(-2299.76 + 1670.87i) q^{34} +(54.2414 + 17.6241i) q^{35} +(46.8247 + 144.111i) q^{36} +(2378.28 - 772.750i) q^{37} +(741.503 - 1020.59i) q^{38} +(3234.03 - 9953.32i) q^{39} +9.56878i q^{40} +(2591.74 + 7976.56i) q^{41} +(-8981.73 + 27642.9i) q^{42} +(-2647.02 - 3643.31i) q^{43} +(-6191.91 + 8522.43i) q^{44} +(0.407352 + 1.25370i) q^{45} +(-15388.7 + 11180.6i) q^{46} +3975.84 q^{47} -17987.8 q^{48} +(35553.4 - 25831.1i) q^{49} +23921.2i q^{50} +(-3362.44 - 4628.00i) q^{51} +(14618.8 + 10621.2i) q^{52} +(7812.59 + 10753.1i) q^{53} +(-27891.3 + 9062.44i) q^{54} +(-53.8666 + 74.1410i) q^{55} +(8246.33 + 5991.31i) q^{56} +(2053.82 + 1492.19i) q^{57} +(12532.0 - 38569.4i) q^{58} +(-43314.4 - 14073.7i) q^{59} +94.8059 q^{60} +(21237.3 - 19838.7i) q^{61} +70365.2 q^{62} +(1335.49 + 433.926i) q^{63} +(6467.07 - 19903.6i) q^{64} +(127.176 + 92.3991i) q^{65} +(-37784.3 - 27451.9i) q^{66} +(13112.5 - 18047.8i) q^{67} +(9393.67 - 3052.19i) q^{68} +(-22499.6 - 30968.1i) q^{69} +(-353.202 - 256.616i) q^{70} +(-26139.0 - 35977.3i) q^{71} +235.595i q^{72} +(-52710.0 + 38296.1i) q^{73} -19142.4 q^{74} -48138.7 q^{75} +(-3546.14 + 2576.42i) q^{76} +(30166.8 + 92843.9i) q^{77} +(-47089.1 + 64812.6i) q^{78} +(38778.5 + 53374.0i) q^{79} +(83.4927 - 256.964i) q^{80} +(-17809.3 - 54811.4i) q^{81} -64202.2i q^{82} +(26444.9 - 81389.1i) q^{83} +(59360.9 - 81703.2i) q^{84} +(81.7203 - 26.5525i) q^{85} +(10652.7 + 32785.8i) q^{86} +(77616.5 + 25219.1i) q^{87} +(-13250.6 + 9627.15i) q^{88} +(-20842.8 - 6772.22i) q^{89} -10.0908i q^{90} +(159258. - 51746.1i) q^{91} +(62857.3 - 20423.6i) q^{92} +141602. i q^{93} +(-28945.2 - 9404.86i) q^{94} +(-30.8497 + 22.4136i) q^{95} +(111568. + 36250.7i) q^{96} +(-21766.4 - 66990.0i) q^{97} +(-319941. + 103955. i) q^{98} +(-1326.26 + 1825.44i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−7.28026	−	2.36550i	−1.28698	−	0.418165i	−0.415946	−	0.909389i	$-0.636550\pi$
$2$	−7.28026	−	2.36550i	−1.28698	−	0.418165i	−0.871033	+	0.491224i	$0.836550\pi$
$3$	4.76030	−	14.6507i	0.305373	−	0.939842i	−0.674165	−	0.738581i	$-0.735496\pi$
$3$	4.76030	−	14.6507i	0.305373	−	0.939842i	0.979538	−	0.201261i	$-0.0645038\pi$
$4$	21.5180	+	15.6337i	0.672438	+	0.488555i
$5$	0.187196	+	0.136006i	0.00334867	+	0.00243295i	0.589458	−	0.807799i	$-0.299341\pi$
$5$	0.187196	+	0.136006i	0.00334867	+	0.00243295i	−0.586110	+	0.810232i	$0.699341\pi$
$6$	−69.3124	+	95.4003i	−0.786018	+	1.08186i
$7$	234.418	−	76.1672i	1.80820	−	0.587520i	0.808202	−	0.588905i	$-0.200441\pi$
$7$	234.418	−	76.1672i	1.80820	−	0.587520i	0.999999	+	0.00138524i	$0.000440936\pi$
$8$	24.3073	+	33.4561i	0.134280	+	0.184820i
$9$	4.60899	+	3.34863i	0.0189670	+	0.0137804i
$10$	−1.04111	−	1.43297i	−0.00329229	−	0.00453145i
$11$			396.060i			0.986915i	0.869770	+	0.493458i	$0.164267\pi$
$11$			396.060i			0.986915i	−0.869770	+	0.493458i	$0.835733\pi$
$12$	331.477	−	240.832i	0.664509	−	0.482794i
$13$	679.376			1.11494			0.557470	−	0.830197i	$-0.311772\pi$
$13$	679.376			1.11494			0.557470	+	0.830197i	$0.311772\pi$
$14$	−1886.80			−2.57280
$15$	2.88369	−	2.09512i	0.00330918	−	0.00240426i
$16$	−360.836	−	1110.54i	−0.352378	−	1.08451i
$17$	218.275	−	300.429i	0.183181	−	0.252127i	−0.707544	−	0.706669i	$-0.750197\pi$
$17$	218.275	−	300.429i	0.183181	−	0.252127i	0.890725	+	0.454542i	$0.150197\pi$
$18$	−25.6334	−	35.2814i	−0.0186477	−	0.0256664i
$19$	−50.9256	+	156.733i	−0.0323633	+	0.0996039i	−0.965933	−	0.258791i	$-0.916676\pi$
$19$	−50.9256	+	156.733i	−0.0323633	+	0.0996039i	0.933570	+	0.358395i	$0.116676\pi$
$20$	1.90180	+	5.85315i	0.00106314	+	0.00327201i
$21$		−	3796.97i		−	1.87884i
$22$	936.881	−	2883.42i	0.412693	−	1.27014i
$23$	1460.57	−	2010.31i	0.575710	−	0.792397i	−0.417507	−	0.908674i	$-0.637096\pi$
$23$	1460.57	−	2010.31i	0.575710	−	0.792397i	0.993217	+	0.116277i	$0.0370959\pi$
$24$	605.864	−	196.857i	0.214707	−	0.0697627i
$25$	−965.662	−	2972.00i	−0.309012	−	0.951040i
$26$	−4946.03	−	1607.06i	−1.43491	−	0.466229i
$27$	3099.42	−	2251.86i	0.818221	−	0.594472i
$28$	6235.00	+	2025.87i	1.50294	+	0.488334i
$29$			5297.81i			1.16977i	0.811116	+	0.584886i	$0.198861\pi$
$29$			5297.81i			1.16977i	−0.811116	+	0.584886i	$0.801139\pi$
$30$	−25.9500	+	8.43167i	−0.00526422	+	0.00171045i
$31$	−8742.27	+	2840.53i	−1.63388	+	0.530879i	−0.975158	−	0.221509i	$-0.928902\pi$
$31$	−8742.27	+	2840.53i	−1.63388	+	0.530879i	−0.658720	+	0.752388i	$0.728902\pi$
$32$			7615.23i			1.31464i
$33$	5802.56	+	1885.37i	0.927544	+	0.301377i
$34$	−2299.76	+	1670.87i	−0.341181	+	0.247883i
$35$	54.2414	+	17.6241i	0.00748447	+	0.00243185i
$36$	46.8247	+	144.111i	0.00602169	+	0.0185329i
$37$	2378.28	−	772.750i	0.285600	−	0.0927972i	−0.162714	−	0.986673i	$-0.552025\pi$
$37$	2378.28	−	772.750i	0.285600	−	0.0927972i	0.448314	+	0.893876i	$0.352025\pi$
$38$	741.503	−	1020.59i	0.0833017	−	0.114655i
$39$	3234.03	−	9953.32i	0.340473	−	1.04787i
$40$			9.56878i			0.000945598i
$41$	2591.74	+	7976.56i	0.240787	+	0.741065i	0.996301	+	0.0859328i	$0.0273870\pi$
$41$	2591.74	+	7976.56i	0.240787	+	0.741065i	−0.755514	+	0.655132i	$0.772613\pi$
$42$	−8981.73	+	27642.9i	−0.785664	+	2.41802i
$43$	−2647.02	−	3643.31i	−0.218316	−	0.300487i	0.685786	−	0.727804i	$-0.259459\pi$
$43$	−2647.02	−	3643.31i	−0.218316	−	0.300487i	−0.904102	+	0.427317i	$0.859459\pi$
$44$	−6191.91	+	8522.43i	−0.482162	+	0.663639i
$45$	0.407352	+	1.25370i	2.99874e−5	+	9.22916e-5i
$46$	−15388.7	+	11180.6i	−1.07228	+	0.779057i
$47$	3975.84			0.262534			0.131267	−	0.991347i	$-0.458096\pi$
$47$	3975.84			0.262534			0.131267	+	0.991347i	$0.458096\pi$
$48$	−17987.8			−1.12687
$49$	35553.4	−	25831.1i	2.11539	−	1.53692i
$50$			23921.2i			1.35319i
$51$	−3362.44	−	4628.00i	−0.181021	−	0.249154i
$52$	14618.8	+	10621.2i	0.749728	+	0.544709i
$53$	7812.59	+	10753.1i	0.382037	+	0.525829i	0.956123	−	0.292966i	$-0.0946424\pi$
$53$	7812.59	+	10753.1i	0.382037	+	0.525829i	−0.574086	+	0.818795i	$0.694642\pi$
$54$	−27891.3	+	9062.44i	−1.30162	+	0.422922i
$55$	−53.8666	+	74.1410i	−0.00240111	+	0.00330485i
$56$	8246.33	+	5991.31i	0.351391	+	0.255300i
$57$	2053.82	+	1492.19i	0.0837290	+	0.0608327i
$58$	12532.0	−	38569.4i	0.489158	−	1.50547i
$59$	−43314.4	−	14073.7i	−1.61995	−	0.526354i	−0.648022	−	0.761622i	$-0.724403\pi$
$59$	−43314.4	−	14073.7i	−1.61995	−	0.526354i	−0.971931	+	0.235267i	$0.924403\pi$
$60$	94.8059			0.00339983
$61$	21237.3	−	19838.7i	0.730760	−	0.682634i
$61$	21237.3	−	19838.7i	0.730760	−	0.682634i
$62$	70365.2			2.32476
$63$	1335.49	+	433.926i	0.0423924	+	0.0137741i
$64$	6467.07	−	19903.6i	0.197359	−	0.607410i
$65$	127.176	+	92.3991i	0.00373356	+	0.00271259i
$66$	−37784.3	−	27451.9i	−1.06770	−	0.775733i
$67$	13112.5	−	18047.8i	0.356861	−	0.491177i	−0.592410	−	0.805637i	$-0.701823\pi$
$67$	13112.5	−	18047.8i	0.356861	−	0.491177i	0.949271	+	0.314460i	$0.101823\pi$
$68$	9393.67	−	3052.19i	0.246356	−	0.0800459i
$69$	−22499.6	−	30968.1i	−0.568922	−	0.783053i
$70$	−353.202	−	256.616i	−0.00861544	−	0.00625948i
$71$	−26139.0	−	35977.3i	−0.615380	−	0.846998i	0.381627	−	0.924317i	$-0.375364\pi$
$71$	−26139.0	−	35977.3i	−0.615380	−	0.846998i	−0.997006	+	0.0773190i	$0.975364\pi$
$72$			235.595i			0.00535592i
$73$	−52710.0	+	38296.1i	−1.15767	+	0.841099i	−0.989482	−	0.144655i	$-0.953793\pi$
$73$	−52710.0	+	38296.1i	−1.15767	+	0.841099i	−0.168192	+	0.985754i	$0.553793\pi$
$74$	−19142.4			−0.406366
$75$	−48138.7			−0.988191
$76$	−3546.14	+	2576.42i	−0.0704242	+	0.0511662i
$77$	30166.8	+	92843.9i	0.579832	+	1.78454i
$78$	−47089.1	+	64812.6i	−0.876363	+	1.20621i
$79$	38778.5	+	53374.0i	0.699074	+	0.962193i	0.999964	+	0.00853408i	$0.00271651\pi$
$79$	38778.5	+	53374.0i	0.699074	+	0.962193i	−0.300889	+	0.953659i	$0.597283\pi$
$80$	83.4927	−	256.964i	0.00145856	−	0.00448898i
$81$	−17809.3	−	54811.4i	−0.301602	−	0.928237i
$82$		−	64202.2i		−	1.05442i
$83$	26444.9	−	81389.1i	0.421354	−	1.29679i	−0.485088	−	0.874465i	$-0.661213\pi$
$83$	26444.9	−	81389.1i	0.421354	−	1.29679i	0.906442	−	0.422329i	$-0.138787\pi$
$84$	59360.9	−	81703.2i	0.917914	−	1.26340i
$85$	81.7203	−	26.5525i	0.00122682	−	0.000398619i
$86$	10652.7	+	32785.8i	0.155316	+	0.478012i
$87$	77616.5	+	25219.1i	1.09940	+	0.357217i
$88$	−13250.6	+	9627.15i	−0.182402	+	0.132523i
$89$	−20842.8	−	6772.22i	−0.278920	−	0.0906267i	0.166217	−	0.986089i	$-0.446845\pi$
$89$	−20842.8	−	6772.22i	−0.278920	−	0.0906267i	−0.445137	+	0.895463i	$0.646845\pi$
$90$		−	10.0908i		−	0.000131317i
$91$	159258.	−	51746.1i	2.01604	−	0.655050i
$92$	62857.3	−	20423.6i	0.774259	−	0.251572i
$93$			141602.i			1.69770i
$94$	−28945.2	−	9404.86i	−0.337875	−	0.109782i
$95$	−30.8497	+	22.4136i	−0.000350705	+	0.000254802i
$96$	111568.	+	36250.7i	1.23556	+	0.401457i
$97$	−21766.4	−	66990.0i	−0.234886	−	0.722904i	−0.997137	−	0.0756225i	$-0.975906\pi$
$97$	−21766.4	−	66990.0i	−0.234886	−	0.722904i	0.762251	−	0.647282i	$-0.224094\pi$
$98$	−319941.	+	103955.i	−3.36516	+	1.09341i
$99$	−1326.26	+	1825.44i	−0.0136000	+	0.0187188i
$100$	25684.4	−	79048.4i	0.256844	−	0.790484i
$101$			65728.4i			0.641135i	0.947226	+	0.320568i	$0.103874\pi$
$101$			65728.4i			0.641135i	−0.947226	+	0.320568i	$0.896126\pi$
$102$	13531.9	+	41646.9i	0.128783	+	0.396353i
$103$	20088.9	−	61827.2i	0.186579	−	0.574231i	−0.813393	−	0.581714i	$-0.802382\pi$
$103$	20088.9	−	61827.2i	0.186579	−	0.574231i	0.999972	+	0.00748356i	$0.00238211\pi$
$104$	16513.8	+	22729.2i	0.149714	+	0.206064i
$105$	516.410	−	710.778i	0.00457111	−	0.00629159i
$106$	−31441.2	−	96766.1i	−0.271791	−	0.836486i
$107$	−154767.	+	112445.i	−1.30683	+	0.949465i	−0.999997	−	0.00230000i	$-0.999268\pi$
$107$	−154767.	+	112445.i	−1.30683	+	0.949465i	−0.306829	+	0.951765i	$0.599268\pi$
$108$	101898.			0.840635
$109$	114987.			0.927006			0.463503	−	0.886095i	$-0.346592\pi$
$109$	114987.			0.927006			0.463503	+	0.886095i	$0.346592\pi$
$110$	567.543	−	412.344i	0.00447216	−	0.00324921i
$111$		−	38522.0i		−	0.296757i
$112$	−169173.	−	232847.i	−1.27434	−	1.75398i
$113$	−95447.3	−	69346.5i	−0.703181	−	0.510891i	0.177785	−	0.984069i	$-0.443107\pi$
$113$	−95447.3	−	69346.5i	−0.703181	−	0.510891i	−0.880967	+	0.473178i	$0.843107\pi$
$114$	−11422.6	−	15721.8i	−0.0823195	−	0.113303i
$115$	546.828	−	177.675i	0.00385572	−	0.00125280i
$116$	−82824.6	+	113998.i	−0.571497	+	0.786599i
$117$	3131.23	+	2274.97i	0.0211471	+	0.0153643i
$118$	282049.	+	204920.i	1.86474	+	1.35481i
$119$	28284.7	−	87051.5i	0.183098	−	0.563519i
$120$	140.189	+	45.5502i	0.000888713	+	0.000288760i
$121$	4187.10			0.0259986
$122$	−201541.	+	94193.8i	−1.22593	+	0.572958i
$123$	129200.			0.770014
$124$	−232524.	−	75551.7i	−1.35805	−	0.441256i
$125$	446.887	−	1375.38i	0.00255813	−	0.00787312i
$126$	−8696.24	−	6318.19i	−0.0487983	−	0.0354541i
$127$	26197.1	+	19033.3i	0.144126	+	0.104714i	0.657512	−	0.753444i	$-0.271609\pi$
$127$	26197.1	+	19033.3i	0.144126	+	0.104714i	−0.513386	+	0.858158i	$0.671609\pi$
$128$	49071.9	−	67541.6i	0.264733	−	0.364373i
$129$	−65977.6	+	21437.4i	−0.349078	+	0.113422i
$130$	−707.307	−	973.525i	−0.00367071	−	0.00505230i
$131$	217412.	+	157959.i	1.10689	+	0.804203i	0.982171	−	0.187989i	$-0.0601970\pi$
$131$	217412.	+	157959.i	1.10689	+	0.804203i	0.124719	+	0.992192i	$0.460197\pi$
$132$	95384.1	+	131285.i	0.476476	+	0.655813i
$133$			40620.0i			0.199118i
$134$	−138154.	+	100375.i	−0.664665	+	0.482908i
$135$	886.464			0.00418627
$136$	15356.8			0.0711958
$137$	−148995.	+	108251.i	−0.678219	+	0.492755i	−0.872766	−	0.488138i	$-0.837676\pi$
$137$	−148995.	+	108251.i	−0.678219	+	0.492755i	0.194547	+	0.980893i	$0.437676\pi$
$138$	90548.1	+	278678.i	0.404745	+	1.24568i
$139$	−172679.	+	237673.i	−0.758060	+	1.04338i	0.239313	+	0.970943i	$0.423078\pi$
$139$	−172679.	+	237673.i	−0.758060	+	1.04338i	−0.997373	+	0.0724377i	$0.976922\pi$
$140$	891.636	+	1227.23i	0.00384475	+	0.00529184i
$141$	18926.2	−	58248.8i	0.0801707	−	0.246740i
$142$	105195.	+	323755.i	0.437796	+	1.34740i
$143$			269074.i			1.10035i
$144$	2055.69	−	6326.76i	0.00826135	−	0.0254258i
$145$	−720.533	+	991.729i	−0.00284599	+	0.00391717i
$146$	474332.	−	154120.i	1.84162	−	0.598379i
$147$	−209198.	−	643846.i	−0.798481	−	2.45747i
$148$	63256.8	+	20553.4i	0.237385	+	0.0771311i
$149$	−217448.	+	157985.i	−0.802399	+	0.582977i	−0.911617	−	0.411041i	$-0.865165\pi$
$149$	−217448.	+	157985.i	−0.802399	+	0.582977i	0.109218	+	0.994018i	$0.465165\pi$
$150$	350462.	+	113872.i	1.27178	+	0.413227i
$151$			25814.8i			0.0921352i	0.998938	+	0.0460676i	$0.0146690\pi$
$151$			25814.8i			0.0921352i	−0.998938	+	0.0460676i	$0.985331\pi$
$152$	−6481.53	+	2105.98i	−0.0227546	+	0.00739341i
$153$	2012.05	−	653.754i	0.00694880	−	0.00225780i
$154$		−	747287.i		−	2.53913i
$155$	−2022.85	−	657.263i	−0.00676291	−	0.00219740i
$156$	225198.	−	163616.i	0.740887	−	0.538286i
$157$	−100595.	−	32685.2i	−0.325706	−	0.105828i	0.141600	−	0.989924i	$-0.454775\pi$
$157$	−100595.	−	32685.2i	−0.325706	−	0.105828i	−0.467306	+	0.884096i	$0.654775\pi$
$158$	−156061.	−	480307.i	−0.497339	−	1.53065i
$159$	194731.	−	63271.8i	0.610860	−	0.198480i
$160$	−1035.72	+	1425.54i	−0.00319846	+	0.00440230i
$161$	189266.	−	582501.i	0.575451	−	1.77105i
$162$			441169.i			1.32074i
$163$	−18853.9	−	58026.5i	−0.0555819	−	0.171063i	0.919412	−	0.393296i	$-0.128665\pi$
$163$	−18853.9	−	58026.5i	−0.0555819	−	0.171063i	−0.974994	+	0.222233i	$0.928665\pi$
$164$	−68934.5	+	212158.i	−0.200137	+	0.615957i
$165$	829.795	+	1142.12i	0.00237280	+	0.00326588i
$166$	−385052.	+	529978.i	−1.08455	+	1.49275i
$167$	−61704.9	−	189908.i	−0.171210	−	0.526929i	0.828230	−	0.560388i	$-0.189348\pi$
$167$	−61704.9	−	189908.i	−0.171210	−	0.526929i	−0.999440	+	0.0334584i	$0.989348\pi$
$168$	127032.	−	92293.9i	0.347247	−	0.252290i
$169$	90258.2			0.243091
$170$	−657.755			−0.00174559
$171$	−759.555	+	551.849i	−0.00198641	+	0.00144321i
$172$		−	119780.i		−	0.308718i
$173$	344278.	+	473858.i	0.874569	+	1.20374i	0.977896	+	0.209093i	$0.0670513\pi$
$173$	344278.	+	473858.i	0.874569	+	1.20374i	−0.103327	+	0.994647i	$0.532949\pi$
$174$	−505412.	−	367203.i	−1.26553	−	0.919462i
$175$	−452738.	−	623140.i	−1.11751	−	1.53812i
$176$	439840.	−	142913.i	1.07032	−	0.347768i
$177$	−412379.	+	567591.i	−0.989380	+	1.36176i
$178$	135721.	+	98607.0i	0.321068	+	0.233269i
$179$	−332545.	−	241608.i	−0.775743	−	0.563610i	0.127956	−	0.991780i	$-0.459158\pi$
$179$	−332545.	−	241608.i	−0.775743	−	0.563610i	−0.903698	+	0.428170i	$0.859158\pi$
$180$	−10.8346	+	33.3455i	−2.49249e−5	+	7.67108e-5i
$181$	145191.	+	47175.3i	0.329414	+	0.107033i	0.469055	−	0.883169i	$-0.344595\pi$
$181$	145191.	+	47175.3i	0.329414	+	0.107033i	−0.139641	+	0.990202i	$0.544595\pi$
$182$	−1.28185e6			−2.86852
$183$	−189554.	−	405579.i	−0.418414	−	0.895257i
$184$	102760.			0.223758
$185$	550.303	+	178.804i	0.00118215	+	0.000384104i
$186$	334959.	−	1.03090e6i	0.709920	−	2.18491i
$187$	118988.	+	86449.9i	0.248828	+	0.180784i
$188$	85552.3	+	62157.4i	0.176537	+	0.128262i
$189$	555043.	−	763951.i	1.13024	−	1.55565i
$190$	277.613	−	90.2019i	0.000557899	−	0.000181272i
$191$	342322.	+	471166.i	0.678972	+	0.934525i	0.999921	−	0.0125719i	$-0.00400186\pi$
$191$	342322.	+	471166.i	0.678972	+	0.934525i	−0.320949	+	0.947096i	$0.604002\pi$
$192$	−260816.	−	189494.i	−0.510601	−	0.370973i
$193$	108525.	+	149372.i	0.209719	+	0.288654i	0.900899	−	0.434029i	$-0.142909\pi$
$193$	108525.	+	149372.i	0.209719	+	0.288654i	−0.691180	+	0.722683i	$0.742909\pi$
$194$			539193.i			1.02858i
$195$	1959.11	−	1423.38i	0.00368954	−	0.00268061i
$196$	1.16888e6			2.17334
$197$	−257322.			−0.472402			−0.236201	−	0.971704i	$-0.575902\pi$
$197$	−257322.			−0.472402			−0.236201	+	0.971704i	$0.575902\pi$
$198$	13973.6	−	10152.4i	0.0253305	−	0.0184037i
$199$	9658.95	+	29727.2i	0.0172901	+	0.0532134i	0.959329	−	0.282289i	$-0.0910938\pi$
$199$	9658.95	+	29727.2i	0.0172901	+	0.0532134i	−0.942039	+	0.335503i	$0.891094\pi$
$200$	75958.9	−	104548.i	0.134278	−	0.184817i
$201$	−201993.	−	278020.i	−0.352653	−	0.485385i
$202$	155481.	−	478520.i	0.268100	−	0.825128i
$203$	403519.	+	1.24190e6i	0.687264	+	2.11518i
$204$		−	152153.i		−	0.255979i
$205$	−599.696	+	1845.67i	−0.000996659	+	0.00306740i
$206$	−292504.	+	402598.i	−0.480247	+	0.661003i
$207$	13463.5	−	4374.57i	0.0218390	−	0.00709593i
$208$	−245143.	−	754472.i	−0.392881	−	1.20916i
$209$	−62075.7	−	20169.6i	−0.0983006	−	0.0319398i
$210$	−5440.94	+	3953.08i	−0.00851385	+	0.00618567i
$211$	323568.	+	105134.i	0.500334	+	0.162568i	0.548302	−	0.836281i	$-0.315275\pi$
$211$	323568.	+	105134.i	0.500334	+	0.162568i	−0.0479679	+	0.998849i	$0.515275\pi$
$212$			353526.i			0.540233i
$213$	−651521.	+	211692.i	−0.983964	+	0.319709i
$214$	1.39273e6	−	452525.i	2.07889	−	0.675473i
$215$		−	1042.02i		−	0.00153738i
$216$	150677.	+	48957.8i	0.219741	+	0.0713982i
$217$	−1.83299e6	+	1.33175e6i	−2.64248	+	1.91987i
$218$	−837135.	−	272002.i	−1.19304	−	0.387641i
$219$	310148.	+	954539.i	0.436978	+	1.34488i
$220$	−2318.20	+	753.230i	−0.00322920	+	0.00104923i
$221$	148290.	−	204104.i	0.204236	−	0.281107i
$222$	−91123.6	+	280450.i	−0.124093	+	0.381920i
$223$			1.14200e6i			1.53782i	0.639356	+	0.768910i	$0.279201\pi$
$223$			1.14200e6i			1.53782i	−0.639356	+	0.768910i	$0.720799\pi$
$224$	580030.	+	1.78515e6i	0.772379	+	2.37714i
$225$	5501.39	−	16931.6i	0.00724464	−	0.0222967i
$226$	530841.	+	730641.i	0.691343	+	0.951552i
$227$	182167.	−	250732.i	0.234642	−	0.322957i	−0.675417	−	0.737436i	$-0.736036\pi$
$227$	182167.	−	250732.i	0.234642	−	0.322957i	0.910059	+	0.414479i	$0.136036\pi$
$228$	20865.7	+	64217.9i	0.0265825	+	0.0818124i
$229$	−1.07612e6	+	781847.i	−1.35604	+	0.985220i	−0.357352	+	0.933970i	$0.616321\pi$
$229$	−1.07612e6	+	781847.i	−1.35604	+	0.985220i	−0.998686	+	0.0512499i	$0.983679\pi$
$230$	−4401.33			−0.00548611
$231$	1.50383e6			1.85425
$232$	−177244.	+	128775.i	−0.216198	+	0.157077i
$233$		−	905187.i		−	1.09232i	−0.837682	−	0.546158i	$-0.816090\pi$
$233$		−	905187.i		−	1.09232i	0.837682	−	0.546158i	$-0.183910\pi$
$234$	−17414.7	−	23969.3i	−0.0207911	−	0.0286165i
$235$	744.263	+	540.738i	0.000879137	+	0.000638730i
$236$	−712015.	−	980004.i	−0.832164	−	1.14538i
$237$	966563.	−	314055.i	1.11779	−	0.363191i
$238$	−411840.	+	566850.i	−0.471288	+	0.648672i
$239$	−752561.	−	546768.i	−0.852211	−	0.619168i	0.0735438	−	0.997292i	$-0.476569\pi$
$239$	−752561.	−	546768.i	−0.852211	−	0.619168i	−0.925755	+	0.378124i	$0.876569\pi$
$240$	−3367.25	−	2446.45i	−0.00377352	−	0.00274163i
$241$	−220616.	+	678985.i	−0.244677	+	0.753039i	0.751012	+	0.660289i	$0.229566\pi$
$241$	−220616.	+	678985.i	−0.244677	+	0.753039i	−0.995689	+	0.0927508i	$0.970434\pi$
$242$	−30483.2	−	9904.59i	−0.0334597	−	0.0108717i
$243$	43151.6			0.0468793
$244$	767137.	−	94870.1i	0.824895	−	0.102013i
$245$	10168.6			0.0108230
$246$	−940606.	−	305621.i	−0.990992	−	0.321993i
$247$	−34597.6	+	106481.i	−0.0360831	+	0.111052i
$248$	−307534.	−	223436.i	−0.317514	−	0.230688i
$249$	−1.06652e6	−	774873.i	−1.09011	−	0.792012i
$250$	−6506.91	+	8955.99i	−0.00658453	+	0.00906282i
$251$	1.52000e6	−	493879.i	1.52286	−	0.494808i	0.576275	−	0.817256i	$-0.304506\pi$
$251$	1.52000e6	−	493879.i	1.52286	−	0.494808i	0.946587	+	0.322448i	$0.104506\pi$
$252$	21953.1	+	30215.9i	0.0217769	+	0.0299733i
$253$	796203.	+	578476.i	0.782029	+	0.568177i
$254$	−145698.	−	200536.i	−0.141700	−	0.195033i
$255$		−	1323.66i		−	0.00127475i
$256$	−1.05882e6	+	769276.i	−1.00977	+	0.733639i
$257$	−345771.			−0.326555			−0.163277	−	0.986580i	$-0.552207\pi$
$257$	−345771.			−0.326555			−0.163277	+	0.986580i	$0.552207\pi$
$258$	531044.			0.496685
$259$	498655.	−	362294.i	0.461903	−	0.335592i
$260$	1292.04	+	3976.49i	0.00118534	+	0.00364810i
$261$	−17740.4	+	24417.5i	−0.0161199	+	0.0221871i
$262$	−1.20916e6	−	1.66427e6i	−1.08826	−	1.49786i
$263$	−445490.	+	1.37108e6i	−0.397145	+	1.22229i	0.530134	+	0.847914i	$0.322142\pi$
$263$	−445490.	+	1.37108e6i	−0.397145	+	1.22229i	−0.927279	+	0.374372i	$0.877858\pi$
$264$	77967.4	+	239959.i	0.0688498	+	0.211898i
$265$			3075.50i			0.00269030i
$266$	96086.5	−	295724.i	0.0832642	−	0.256261i
$267$	−198435.	+	273123.i	−0.170350	+	0.234466i
$268$	564310.	−	183355.i	0.479933	−	0.155940i
$269$	−332754.	−	1.02411e6i	−0.280377	−	0.862911i	−0.987746	−	0.156067i	$-0.950118\pi$
$269$	−332754.	−	1.02411e6i	−0.280377	−	0.862911i	0.707370	−	0.706844i	$-0.249882\pi$
$270$	−6453.69	−	2096.93i	−0.00538764	−	0.00175055i
$271$	72252.1	−	52494.2i	0.0597623	−	0.0434199i	−0.557503	−	0.830175i	$-0.688241\pi$
$271$	72252.1	−	52494.2i	0.0597623	−	0.0434199i	0.617265	+	0.786755i	$0.288241\pi$
$272$	−412399.	−	133997.i	−0.337983	−	0.109817i
$273$		−	2.57957e6i		−	2.09479i
$274$	1.34079e6	−	435649.i	1.07891	−	0.350558i
$275$	1.17709e6	−	382460.i	0.938596	−	0.304968i
$276$		−	1.01812e6i		−	0.804504i
$277$	−1.57411e6	−	511458.i	−1.23264	−	0.400507i	−0.380967	−	0.924589i	$-0.624409\pi$
$277$	−1.57411e6	−	511458.i	−1.23264	−	0.400507i	−0.851668	+	0.524081i	$0.824409\pi$
$278$	1.81937e6	−	1.32185e6i	1.41191	−	1.02581i
$279$	−49804.9	−	16182.6i	−0.0383055	−	0.0124462i
$280$	728.827	+	2243.10i	0.000555558	+	0.00170983i
$281$	−2.15939e6	+	701630.i	−1.63142	+	0.530081i	−0.974598	−	0.223963i	$-0.928100\pi$
$281$	−2.15939e6	+	701630.i	−1.63142	+	0.530081i	−0.656824	+	0.754044i	$0.728100\pi$
$282$	−275575.	+	379297.i	−0.206356	+	0.284025i
$283$	708675.	−	2.18108e6i	0.525994	−	1.61884i	−0.236347	−	0.971669i	$-0.575950\pi$
$283$	708675.	−	2.18108e6i	0.525994	−	1.61884i	0.762342	−	0.647175i	$-0.224050\pi$
$284$		−	1.18281e6i		−	0.870200i
$285$	181.521	+	558.664i	0.000132378	+	0.000407417i
$286$	636494.	−	1.95893e6i	0.460128	−	1.41613i
$287$	1.21510e6	+	1.67245e6i	0.870781	+	1.19853i
$288$	−25500.5	+	35098.5i	−0.0181162	+	0.0249349i
$289$	396146.	+	1.21921e6i	0.279004	+	0.858687i
$290$	7591.60	−	5515.62i	0.00530076	−	0.00385123i
$291$	−1.08506e6			−0.751144
$292$	−1.73293e6			−1.18939
$293$	801546.	−	582357.i	0.545456	−	0.396297i	−0.280651	−	0.959810i	$-0.590550\pi$
$293$	801546.	−	582357.i	0.545456	−	0.396297i	0.826107	+	0.563513i	$0.190550\pi$
$294$			5.18222e6i			3.49661i
$295$	−6194.18	−	8525.56i	−0.00414409	−	0.00570384i
$296$	83662.7	+	60784.5i	0.0555012	+	0.0403240i
$297$	891872.	+	1.22756e6i	0.586693	+	0.807514i
$298$	1.95679e6	−	635801.i	1.27645	−	0.414744i
$299$	992278.	−	1.36575e6i	0.641883	−	0.883475i
$300$	−1.03585e6	−	752588.i	−0.664497	−	0.482785i
$301$	−898011.	−	652443.i	−0.571302	−	0.415075i
$302$	61064.8	−	187938.i	0.0385277	−	0.118576i
$303$	962966.	+	312887.i	0.602566	+	0.195786i
$304$	192434.			0.119425
$305$	6673.72	−	825.324i	0.00410789	−	0.000508013i
$306$	−16194.7			−0.00988710
$307$	1.91334e6	+	621680.i	1.15863	+	0.376462i	0.824388	−	0.566025i	$-0.191519\pi$
$307$	1.91334e6	+	621680.i	1.15863	+	0.376462i	0.334243	+	0.942487i	$0.391519\pi$
$308$	−802368.	+	2.46944e6i	−0.481944	+	1.48327i
$309$	−810182.	−	588632.i	−0.482710	−	0.350709i
$310$	13172.1	+	9570.09i	0.00778486	+	0.00565603i
$311$	820996.	−	1.13000e6i	0.481327	−	0.662490i	−0.497432	−	0.867503i	$-0.665724\pi$
$311$	820996.	−	1.13000e6i	0.481327	−	0.662490i	0.978759	+	0.205013i	$0.0657237\pi$
$312$	411609.	−	133740.i	0.239386	−	0.0777812i
$313$	−904953.	−	1.24556e6i	−0.522114	−	0.718628i	0.463789	−	0.885946i	$-0.346489\pi$
$313$	−904953.	−	1.24556e6i	−0.522114	−	0.718628i	−0.985903	+	0.167318i	$0.946489\pi$
$314$	655038.	+	475913.i	0.374923	+	0.272398i
$315$	190.981	+	262.863i	0.000108446	+	0.000149264i
$316$			1.75476e6i			0.988551i
$317$	−843524.	+	612856.i	−0.471465	+	0.342539i	−0.798012	−	0.602642i	$-0.794115\pi$
$317$	−843524.	+	612856.i	−0.471465	+	0.342539i	0.326547	+	0.945181i	$0.394115\pi$
$318$	−1.56736e6			−0.869162
$319$	−2.09825e6			−1.15447
$320$	3917.62	−	2846.32i	0.00213869	−	0.00155385i
$321$	910654.	+	2.80271e6i	0.493277	+	1.51815i
$322$	−2.75581e6	+	3.79305e6i	−1.48119	+	2.03868i
$323$	35971.4	+	49510.3i	0.0191845	+	0.0264052i
$324$	473687.	−	1.45786e6i	0.250686	−	0.771531i
$325$	−656047.	−	2.01910e6i	−0.344530	−	1.06035i
$326$			467047.i			0.243398i
$327$	547372.	−	1.68464e6i	0.283083	−	0.871239i
$328$	−203866.	+	280598.i	−0.104631	+	0.144012i
$329$	932011.	−	302829.i	0.474713	−	0.154244i
$330$	−3339.45	−	10277.8i	−0.00168807	−	0.00519534i
$331$	686736.	+	223134.i	0.344524	+	0.111943i	0.476168	−	0.879354i	$-0.342025\pi$
$331$	686736.	+	223134.i	0.344524	+	0.111943i	−0.131644	+	0.991297i	$0.542025\pi$
$332$	1.84146e6	−	1.33790e6i	0.916889	−	0.666159i
$333$	13549.1	+	4402.37i	0.00669577	+	0.00217559i
$334$			1.52854e6i			0.749741i
$335$	4909.22	−	1595.10i	0.00239001	−	0.000776563i
$336$	−4.21668e6	+	1.37008e6i	−2.03762	+	0.662061i
$337$			3.98101e6i			1.90950i	0.297416	+	0.954748i	$0.403875\pi$
$337$			3.98101e6i			1.90950i	−0.297416	+	0.954748i	$0.596125\pi$
$338$	−657103.	−	213506.i	−0.312854	−	0.101652i
$339$	−1.47033e6	+	1.06826e6i	−0.694890	+	0.504867i
$340$	2173.57	+	706.237i	0.00101971	+	0.000331324i
$341$	−1.12502e6	−	3.46247e6i	−0.523933	−	1.61250i
$342$	6835.16	−	2220.88i	0.00315997	−	0.00102674i
$343$	3.93193e6	−	5.41183e6i	1.80455	−	2.48376i
$344$	57549.1	−	177118.i	0.0262206	−	0.0806986i
$345$		−	8857.18i		−	0.00400634i
$346$	−1.38552e6	−	4.26420e6i	−0.622190	−	1.91490i
$347$	118351.	−	364248.i	0.0527654	−	0.162395i	−0.921201	−	0.389086i	$-0.872791\pi$
$347$	118351.	−	364248.i	0.0527654	−	0.162395i	0.973967	+	0.226691i	$0.0727908\pi$
$348$	1.27588e6	+	1.75610e6i	0.564758	+	0.777323i
$349$	1.01035e6	−	1.39062e6i	0.444025	−	0.611148i	−0.527076	−	0.849818i	$-0.676712\pi$
$349$	1.01035e6	−	1.39062e6i	0.444025	−	0.611148i	0.971101	+	0.238670i	$0.0767116\pi$
$350$	1.82201e6	+	5.60757e6i	0.795025	+	2.44683i
$351$	2.10567e6	−	1.52986e6i	0.912267	−	0.662801i
$352$	−3.01609e6			−1.29744
$353$	−2.09893e6			−0.896523			−0.448261	−	0.893903i	$-0.647957\pi$
$353$	−2.09893e6			−0.896523			−0.448261	+	0.893903i	$0.647957\pi$
$354$	4.34486e6	−	3.15672e6i	1.84275	−	1.33884i
$355$		−	10289.9i		−	0.00433350i
$356$	−342619.	−	471575.i	−0.143280	−	0.197209i
$357$	−1.14072e6	−	828782.i	−0.473706	−	0.344167i
$358$	1.84949e6	+	2.54560e6i	0.762683	+	1.04974i
$359$	−2.80890e6	+	912667.i	−1.15027	+	0.373746i	−0.821245	−	0.570575i	$-0.806720\pi$
$359$	−2.80890e6	+	912667.i	−1.15027	+	0.373746i	−0.329026	+	0.944321i	$0.606720\pi$
$360$	−32.0423	+	44.1024i	−1.30307e−5	+	1.79352e-5i
$361$	1.98123e6	+	1.43945e6i	0.800143	+	0.581338i
$362$	−945432.	−	686896.i	−0.379192	−	0.275499i
$363$	19931.8	−	61343.9i	0.00793928	−	0.0244346i
$364$	4.23590e6	+	1.37633e6i	1.67569	+	0.544463i
$365$	−15075.6			−0.00592301
$366$	420608.	+	3.40111e6i	0.164125	+	1.32714i
$367$	−563045.			−0.218212			−0.109106	−	0.994030i	$-0.534799\pi$
$367$	−563045.			−0.218212			−0.109106	+	0.994030i	$0.534799\pi$
$368$	−2.75955e6	−	896632.i	−1.06223	−	0.345139i
$369$	−14765.2	+	45442.7i	−0.00564513	+	0.0173739i
$370$	−3583.39	−	2603.48i	−0.00136079	−	0.000988668i
$371$	2.65045e6	+	1.92566e6i	0.999735	+	0.726350i
$372$	−2.21377e6	+	3.04699e6i	−0.829421	+	1.14160i
$373$	4.57821e6	−	1.48755e6i	1.70382	−	0.553604i	0.714533	−	0.699601i	$-0.246639\pi$
$373$	4.57821e6	−	1.48755e6i	1.70382	−	0.553604i	0.989285	+	0.145997i	$0.0466391\pi$
$374$	−661767.	−	910844.i	−0.244639	−	0.336717i
$375$	−18022.9	−	13094.4i	−0.00661830	−	0.00480848i
$376$	96641.9	+	133016.i	0.0352530	+	0.0485216i
$377$			3.59920e6i			1.30423i
$378$	−5.84798e6	+	4.24880e6i	−2.10512	+	1.52946i
$379$	−3.19339e6			−1.14197			−0.570985	−	0.820961i	$-0.693438\pi$
$379$	−3.19339e6			−1.14197			−0.570985	+	0.820961i	$0.693438\pi$
$380$	−1014.23			−0.000360312
$381$	403556.	−	293201.i	0.142427	−	0.103479i
$382$	−1.37765e6	−	4.23997e6i	−0.483037	−	1.48664i
$383$	1.72020e6	−	2.36765e6i	0.599213	−	0.824746i	−0.396423	−	0.918068i	$-0.629748\pi$
$383$	1.72020e6	−	2.36765e6i	0.599213	−	0.824746i	0.995636	+	0.0933217i	$0.0297485\pi$
$384$	−755935.	−	1.04045e6i	−0.261611	−	0.360077i
$385$	−6980.21	+	21482.9i	−0.00240003	+	0.00738653i
$386$	−436752.	−	1.34419e6i	−0.149199	−	0.459188i
$387$		−	25655.9i		−	0.00870781i
$388$	578936.	−	1.78178e6i	0.195232	−	0.600863i
$389$	295829.	−	407173.i	0.0991212	−	0.136429i	−0.756575	−	0.653906i	$-0.773129\pi$
$389$	295829.	−	407173.i	0.0991212	−	0.136429i	0.855697	+	0.517478i	$0.173129\pi$
$390$	−17629.8	+	5728.27i	−0.00586929	+	0.00190705i
$391$	−285149.	−	877598.i	−0.0943256	−	0.290304i
$392$	1.72841e6	+	561595.i	0.568110	+	0.184590i
$393$	3.34915e6	−	2.43330e6i	1.09384	−	0.794720i
$394$	1.87337e6	+	608696.i	0.607972	+	0.197542i
$395$			15265.5i			0.00492287i
$396$	−57076.9	+	18545.4i	−0.0182904	+	0.00594290i
$397$	−4.32746e6	+	1.40608e6i	−1.37802	+	0.447747i	−0.902019	−	0.431696i	$-0.857915\pi$
$397$	−4.32746e6	+	1.40608e6i	−1.37802	+	0.447747i	−0.476005	+	0.879443i	$0.657915\pi$
$398$		−	239270.i		−	0.0757147i
$399$	595110.	+	193363.i	0.187139	+	0.0608053i
$400$	−2.95207e6	+	2.14481e6i	−0.922523	+	0.670252i
$401$	5.09997e6	+	1.65708e6i	1.58382	+	0.514615i	0.963038	−	0.269367i	$-0.0868143\pi$
$401$	5.09997e6	+	1.65708e6i	1.58382	+	0.514615i	0.620784	+	0.783982i	$0.286814\pi$
$402$	812908.	+	2.50187e6i	0.250886	+	0.772147i
$403$	−5.93928e6	+	1.92979e6i	−1.82168	+	0.591899i
$404$	−1.02758e6	+	1.41434e6i	−0.313230	+	0.431124i
$405$	4120.85	−	12682.7i	0.00124839	−	0.00384214i
$406$		−	9.99590e6i		−	3.00959i
$407$	306056.	+	941943.i	0.0915829	+	0.281863i
$408$	73103.1	−	224988.i	0.0217413	−	0.0669128i
$409$	1.85509e6	+	2.55331e6i	0.548348	+	0.754737i	0.989787	−	0.142555i	$-0.0455317\pi$
$409$	1.85509e6	+	2.55331e6i	0.548348	+	0.754737i	−0.441439	+	0.897291i	$0.645532\pi$
$410$	8731.88	−	12018.4i	0.00256536	−	0.00353091i
$411$	876694.	+	2.69819e6i	0.256002	+	0.787893i
$412$	1.39886e6	−	1.01633e6i	0.406006	−	0.294981i
$413$	−1.12256e7			−3.23844
$414$	−108366.			−0.0310737
$415$	16019.8	−	11639.1i	0.00456601	−	0.00331740i
$416$			5.17360e6i			1.46575i
$417$	2.66006e6	+	3.66127e6i	0.749121	+	1.03108i
$418$	404216.	+	293680.i	0.113155	+	0.0822117i
$419$	657428.	+	904872.i	0.182942	+	0.251798i	0.890632	−	0.454725i	$-0.150263\pi$
$419$	657428.	+	904872.i	0.182942	+	0.251798i	−0.707690	+	0.706523i	$0.750263\pi$
$420$	22224.2	−	7221.09i	0.00614757	−	0.00199747i
$421$	−174435.	+	240089.i	−0.0479653	+	0.0660186i	−0.832326	−	0.554286i	$-0.812991\pi$
$421$	−174435.	+	240089.i	−0.0479653	+	0.0660186i	0.784361	+	0.620305i	$0.212991\pi$
$422$	−2.10697e6	−	1.53080e6i	−0.575939	−	0.418444i
$423$	18324.6	+	13313.6i	0.00497948	+	0.00361780i
$424$	−169854.	+	522757.i	−0.0458840	+	0.141217i
$425$	−1.10365e6	−	358599.i	−0.296388	−	0.0963024i
$426$	5.24400e6			1.40003
$427$	3.46736e6	−	6.26814e6i	0.920300	−	1.66368i
$428$	−5.08820e6			−1.34262
$429$	3.94212e6	+	1.28087e6i	1.03416	+	0.336018i
$430$	−2464.91	+	7586.20i	−0.000642879	+	0.00197858i
$431$	−3.30215e6	−	2.39915e6i	−0.856255	−	0.622106i	0.0706083	−	0.997504i	$-0.477506\pi$
$431$	−3.30215e6	−	2.39915e6i	−0.856255	−	0.622106i	−0.926864	+	0.375398i	$0.877506\pi$
$432$	−3.61915e6	−	2.62947e6i	−0.933034	−	0.677889i
$433$	−1.72858e6	+	2.37919e6i	−0.443068	+	0.609831i	−0.970890	−	0.239524i	$-0.923009\pi$
$433$	−1.72858e6	+	2.37919e6i	−0.443068	+	0.609831i	0.527823	+	0.849355i	$0.323009\pi$
$434$	1.64949e7	−	5.35952e6i	4.20364	−	1.36585i
$435$	11099.6	+	15277.2i	0.00281243	+	0.00387098i
$436$	2.47429e6	+	1.79768e6i	0.623354	+	0.452893i
$437$	240701.	+	331296.i	0.0602940	+	0.0829875i
$438$		−	7.68294e6i		−	1.91356i
$439$	−1.39747e6	+	1.01532e6i	−0.346084	+	0.251445i	−0.747224	−	0.664572i	$-0.768614\pi$
$439$	−1.39747e6	+	1.01532e6i	−0.346084	+	0.251445i	0.401140	+	0.916017i	$0.368614\pi$
$440$	−3789.82			−0.000933225
$441$	250364.			0.0613021
$442$	−1.56240e6	+	1.13515e6i	−0.380397	+	0.276374i
$443$	1.74759e6	+	5.37852e6i	0.423087	+	1.30213i	0.904814	+	0.425806i	$0.140009\pi$
$443$	1.74759e6	+	5.37852e6i	0.423087	+	1.30213i	−0.481728	+	0.876321i	$0.659991\pi$
$444$	602243.	−	828916.i	0.144982	−	0.199551i
$445$	−2980.62	−	4102.47i	−0.000713521	−	0.000982077i
$446$	2.70141e6	−	8.31409e6i	0.643063	−	1.97914i
$447$	1.27948e6	+	3.93782e6i	0.302875	+	0.932154i
$448$		−	5.15835e6i		−	1.21427i
$449$	−437884.	+	1.34767e6i	−0.102504	+	0.315476i	−0.989137	−	0.146999i	$-0.953039\pi$
$449$	−437884.	+	1.34767e6i	−0.102504	+	0.315476i	0.886632	+	0.462475i	$0.153039\pi$
$450$	−80103.1	+	110253.i	−0.0186474	+	0.0256659i
$451$	−3.15920e6	+	1.02649e6i	−0.731368	+	0.237636i
$452$	−969689.	−	2.98440e6i	−0.223247	−	0.687085i
$453$	378204.	+	122886.i	0.0865925	+	0.0281356i
$454$	−1.91933e6	+	1.39447e6i	−0.437029	+	0.317520i
$455$	36850.3	+	11973.4i	0.00834473	+	0.00271137i
$456$			104984.i			0.0236434i
$457$	−6.02266e6	+	1.95688e6i	−1.34896	+	0.438303i	−0.892341	−	0.451362i	$-0.850938\pi$
$457$	−6.02266e6	+	1.95688e6i	−1.34896	+	0.438303i	−0.456615	+	0.889664i	$0.650938\pi$
$458$	9.68389e6	−	3.14649e6i	2.15718	−	0.700910i
$459$		−	1.42268e6i		−	0.315192i
$460$	14544.4	+	4725.75i	0.00320479	+	0.00104130i
$461$	719234.	−	522554.i	0.157622	−	0.114519i	−0.506178	−	0.862429i	$-0.668942\pi$
$461$	719234.	−	522554.i	0.157622	−	0.114519i	0.663801	+	0.747909i	$0.268942\pi$
$462$	−1.09483e7	−	3.55731e6i	−2.38638	−	0.775383i
$463$	2.18149e6	+	6.71395e6i	0.472935	+	1.45554i	0.848723	+	0.528838i	$0.177372\pi$
$463$	2.18149e6	+	6.71395e6i	0.472935	+	1.45554i	−0.375788	+	0.926706i	$0.622628\pi$
$464$	5.88341e6	−	1.91164e6i	1.26863	−	0.412202i
$465$	−19258.7	+	26507.3i	−0.00413042	+	0.00568504i
$466$	−2.14122e6	+	6.58999e6i	−0.456769	+	1.40579i
$467$		−	9.00127e6i		−	1.90990i	−0.296761	−	0.954952i	$-0.595906\pi$
$467$		−	9.00127e6i		−	1.90990i	0.296761	−	0.954952i	$-0.404094\pi$
$468$	31811.5	+	97905.8i	0.00671382	+	0.0206630i
$469$	1.69916e6	−	5.22948e6i	0.356700	−	1.09781i
$470$	−4139.31	−	5697.27i	−0.000864337	−	0.00118966i
$471$	−957721.	+	1.31819e6i	−0.198924	+	0.273795i
$472$	−582004.	−	1.79122e6i	−0.120246	−	0.370079i
$473$	1.44297e6	−	1.04838e6i	0.296555	−	0.215460i
$474$	−7.77973e6			−1.59044
$475$	514987.			0.104728
$476$	1.96957e6	−	1.43098e6i	0.398432	−	0.289478i
$477$			75722.4i			0.0152380i
$478$	4.18546e6	+	5.76079e6i	0.837864	+	1.15322i
$479$	−3.16612e6	−	2.30032e6i	−0.630506	−	0.458089i	0.226069	−	0.974111i	$-0.427412\pi$
$479$	−3.16612e6	−	2.30032e6i	−0.630506	−	0.458089i	−0.856575	+	0.516022i	$0.827412\pi$
$480$	15954.8	+	21959.9i	0.00316074	+	0.00435039i
$481$	1.61575e6	−	524988.i	0.318427	−	0.103463i
$482$	3.21228e6	−	4.42132e6i	0.629789	−	0.866831i
$483$	−7.63308e6	−	5.54575e6i	−1.48878	−	1.08167i
$484$	90098.1	+	65460.1i	0.0174824	+	0.0127017i
$485$	5036.46	−	15500.6i	0.000972235	−	0.00299223i
$486$	−314155.	−	102075.i	−0.0603327	−	0.0196033i
$487$	−4.24332e6			−0.810744			−0.405372	−	0.914152i	$-0.632858\pi$
$487$	−4.24332e6			−0.810744			−0.405372	+	0.914152i	$0.632858\pi$
$488$	1.17995e6	+	228293.i	0.224291	+	0.0433953i
$489$	−939878.			−0.177746
$490$	−74030.3	−	24053.9i	−0.0139290	−	0.00452580i
$491$	429080.	−	1.32057e6i	0.0803221	−	0.247206i	−0.902829	−	0.429999i	$-0.858514\pi$
$491$	429080.	−	1.32057e6i	0.0803221	−	0.247206i	0.983151	+	0.182793i	$0.0585139\pi$
$492$	2.78012e6	+	2.01987e6i	0.517786	+	0.376194i
$493$	1.59162e6	+	1.15638e6i	0.294931	+	0.214280i
$494$	503759.	−	693365.i	0.0928764	−	0.127833i
$495$	−496.541	+	161.336i	−9.10840e−5	+	2.95950e-5i
$496$	6.30904e6	+	8.68365e6i	1.15149	+	1.58489i
$497$	−8.86775e6	−	6.44280e6i	−1.61036	−	1.16999i
$498$	5.93158e6	+	8.16413e6i	1.07176	+	1.47515i
$499$			1.37572e6i			0.247331i	0.992324	+	0.123666i	$0.0394650\pi$
$499$			1.37572e6i			0.247331i	−0.992324	+	0.123666i	$0.960535\pi$
$500$	31118.4	−	22608.9i	0.00556663	−	0.00404439i
$501$	−3.07602e6			−0.547513
$502$	−1.22343e7			−2.16680
$503$	5.68049e6	−	4.12712e6i	1.00107	−	0.727322i	0.0387548	−	0.999249i	$-0.487661\pi$
$503$	5.68049e6	−	4.12712e6i	1.00107	−	0.727322i	0.962318	+	0.271927i	$0.0876609\pi$
$504$	17944.6	+	55227.7i	0.00314671	+	0.00968458i
$505$	−8939.46	+	12304.1i	−0.00155985	+	0.00214695i
$506$	−4.42818e6	−	6.09487e6i	−0.768863	−	1.05825i
$507$	429656.	−	1.32234e6i	0.0742336	−	0.228468i
$508$	266147.	+	819117.i	0.0457575	+	0.140827i
$509$			9.78868e6i			1.67467i	0.546689	+	0.837336i	$0.315888\pi$
$509$			9.78868e6i			1.67467i	−0.546689	+	0.837336i	$0.684112\pi$
$510$	−3131.11	+	9636.55i	−0.000533055	+	0.00164058i
$511$	−9.43930e6	+	1.29921e7i	−1.59914	+	2.20103i
$512$	6.98739e6	−	2.27034e6i	1.17799	−	0.382751i
$513$	195101.	+	600458.i	0.0327314	+	0.100737i
$514$	2.51730e6	+	817921.i	0.420269	+	0.136554i
$515$	12169.4	−	8841.61i	0.00202186	−	0.00146897i
$516$	−1.75485e6	−	570187.i	−0.290146	−	0.0942742i
$517$			1.57467e6i			0.259098i
$518$	−4.48734e6	+	1.45803e6i	−0.734792	+	0.238748i
$519$	8.58121e6	−	2.78820e6i	1.39840	−	0.454366i
$520$			6500.79i			0.00105429i
$521$	−2.55052e6	−	828715.i	−0.411656	−	0.133755i	0.0958653	−	0.995394i	$-0.469438\pi$
$521$	−2.55052e6	−	828715.i	−0.411656	−	0.133755i	−0.507521	+	0.861639i	$0.669438\pi$
$522$	186914.	−	135801.i	0.0300238	−	0.0218136i
$523$	4.35925e6	+	1.41640e6i	0.696879	+	0.226430i	0.635970	−	0.771714i	$-0.280600\pi$
$523$	4.35925e6	+	1.41640e6i	0.696879	+	0.226430i	0.0609085	+	0.998143i	$0.480600\pi$
$524$	2.20878e6	+	6.79792e6i	0.351418	+	1.08155i
$525$	−1.12846e7	+	3.66659e6i	−1.78685	+	0.580582i
$526$	6.48656e6	−	8.92799e6i	1.02223	−	1.40698i
$527$	−1.05483e6	+	3.24645e6i	−0.165447	+	0.509192i
$528$		−	7.12426e6i		−	1.11213i
$529$	80878.8	+	248919.i	0.0125660	+	0.0386740i
$530$	7275.09	−	22390.4i	0.00112499	−	0.00346236i
$531$	−152508.	−	209909.i	−0.0234723	−	0.0323069i
$532$	−635042.	+	874061.i	−0.0972800	+	0.133894i
$533$	1.76077e6	+	5.41908e6i	0.268463	+	0.826243i
$534$	2.09073e6	−	1.51901e6i	0.317282	−	0.230519i
$535$	−44264.8			−0.00668612
$536$	922538.			0.138699
$537$	−5.12273e6	+	3.72188e6i	−0.766595	+	0.556964i
$538$			8.24291e6i			1.22779i
$539$	1.02307e7	+	1.40813e7i	1.51681	+	2.08771i
$540$	19075.0	+	13858.8i	0.00281500	+	0.00204522i
$541$	−832809.	−	1.14626e6i	−0.122335	−	0.168380i	0.743457	−	0.668784i	$-0.233185\pi$
$541$	−832809.	−	1.14626e6i	−0.122335	−	0.168380i	−0.865792	+	0.500404i	$0.833185\pi$
$542$	−650189.	+	211259.i	−0.0950695	+	0.0308900i
$543$	1.38230e6	−	1.90257e6i	0.201188	−	0.276912i
$544$	2.28784e6	+	1.66221e6i	0.331457	+	0.240818i
$545$	21525.1	+	15638.9i	0.00310423	+	0.00225536i
$546$	−6.10197e6	+	1.87799e7i	−0.875968	+	2.69595i
$547$	1.22790e7	+	3.98969e6i	1.75467	+	0.570125i	0.996626	−	0.0820829i	$-0.0261572\pi$
$547$	1.22790e7	+	3.98969e6i	1.75467	+	0.570125i	0.758040	+	0.652208i	$0.226157\pi$
$548$	−4.89845e6			−0.696798
$549$	164315.	−	20320.4i	0.0232673	−	0.00287741i
$550$	−9.47424e6			−1.33548
$551$	−830341.	−	269794.i	−0.116514	−	0.0378576i
$552$	489166.	−	1.50550e6i	0.0683295	−	0.210297i
$553$	1.31557e7	+	9.55821e6i	1.82937	+	1.32912i
$554$	1.02500e7	+	7.44709e6i	1.41890	+	1.03089i
$555$	5239.21	−	7211.16i	0.000721994	−	0.000993740i
$556$	−7.43144e6	+	2.41462e6i	−1.01950	+	0.331254i
$557$	−4.32046e6	−	5.94661e6i	−0.590055	−	0.812141i	0.404698	−	0.914451i	$-0.367377\pi$
$557$	−4.32046e6	−	5.94661e6i	−0.590055	−	0.812141i	−0.994753	+	0.102310i	$0.967377\pi$
$558$	324312.	+	235627.i	0.0440939	+	0.0320361i
$559$	−1.79832e6	−	2.47518e6i	−0.243410	−	0.335025i
$560$		−	66596.5i		−	0.00897391i
$561$	1.83297e6	−	1.33173e6i	0.245894	−	0.178652i
$562$	1.73806e7			2.32127
$563$	4.08012e6			0.542503			0.271251	−	0.962509i	$-0.412563\pi$
$563$	4.08012e6			0.542503			0.271251	+	0.962509i	$0.412563\pi$
$564$	1.31790e6	−	957512.i	0.174456	−	0.126750i
$565$	−8435.82	−	25962.8i	−0.00111175	−	0.00342161i
$566$	−1.03187e7	+	1.42024e7i	−1.35389	+	1.86347i
$567$	−8.34967e6	−	1.14923e7i	−1.09072	−	1.50124i
$568$	568290.	−	1.74902e6i	0.0739093	−	0.227470i
$569$	−555743.	−	1.71040e6i	−0.0719604	−	0.221471i	0.908608	−	0.417651i	$-0.137146\pi$
$569$	−555743.	−	1.71040e6i	−0.0719604	−	0.221471i	−0.980568	+	0.196180i	$0.937146\pi$
$570$		−	4496.61i		−	0.000579693i
$571$	3.65052e6	−	1.12351e7i	0.468559	−	1.44208i	−0.385892	−	0.922544i	$-0.626106\pi$
$571$	3.65052e6	−	1.12351e7i	0.468559	−	1.44208i	0.854451	−	0.519532i	$-0.173894\pi$
$572$	−4.20663e6	+	5.78993e6i	−0.537582	+	0.739918i
$573$	8.53246e6	−	2.77237e6i	1.08565	−	0.352747i
$574$	−4.89010e6	−	1.50502e7i	−0.619495	−	1.90661i
$575$	−7.38506e6	−	2.39955e6i	−0.931503	−	0.302664i
$576$	96456.4	−	70079.7i	0.0121136	−	0.00880108i
$577$	6.93558e6	+	2.25351e6i	0.867248	+	0.281786i	0.708652	−	0.705558i	$-0.249303\pi$
$577$	6.93558e6	+	2.25351e6i	0.867248	+	0.281786i	0.158595	+	0.987344i	$0.449303\pi$
$578$		−	9.81326e6i		−	1.22178i
$579$	2.70502e6	−	878914.i	0.335331	−	0.108956i
$580$	−31008.9	+	10075.4i	−0.00382751	+	0.00124363i
$581$		−	2.10934e7i		−	2.59242i
$582$	7.89955e6	+	2.56672e6i	0.966707	+	0.314102i
$583$	−4.25888e6	+	3.09426e6i	−0.518948	+	0.377038i
$584$	−2.56247e6	−	832598.i	−0.310905	−	0.101019i
$585$	276.745	+	851.733i	3.34341e−5	+	0.000102900i
$586$	−7.21303e6	+	2.34366e6i	−0.867708	+	0.281935i
$587$	−2.03497e6	+	2.80090e6i	−0.243761	+	0.335508i	−0.913314	−	0.407256i	$-0.866486\pi$
$587$	−2.03497e6	+	2.80090e6i	−0.243761	+	0.335508i	0.669553	+	0.742764i	$0.266486\pi$
$588$	5.56419e6	−	1.71248e7i	0.663680	−	2.04260i
$589$		−	1.51486e6i		−	0.179922i
$590$	24928.0	+	76720.6i	0.00294821	+	0.00907364i
$591$	−1.22493e6	+	3.76995e6i	−0.144259	+	0.443984i
$592$	−1.71634e6	−	2.36233e6i	−0.201279	−	0.277037i
$593$	−2.17404e6	+	2.99231e6i	−0.253881	+	0.349437i	−0.916866	−	0.399196i	$-0.869289\pi$
$593$	−2.17404e6	+	2.99231e6i	−0.253881	+	0.349437i	0.662985	+	0.748633i	$0.269289\pi$
$594$	−3.58927e6	−	1.10466e7i	−0.417388	−	1.28459i
$595$	17134.3	−	12448.8i	0.00198415	−	0.00144157i
$596$	−7.14896e6			−0.824380
$597$	481503.			0.0552921
$598$	−1.04547e7	+	7.59581e6i	−1.19553	+	0.868602i
$599$		−	9.91446e6i		−	1.12902i	−0.825426	−	0.564510i	$-0.809065\pi$
$599$		−	9.91446e6i		−	1.12902i	0.825426	−	0.564510i	$-0.190935\pi$
$600$	−1.17012e6	−	1.61053e6i	−0.132694	−	0.182638i
$601$	−1.15390e7	−	8.38361e6i	−1.30312	−	0.946771i	−0.303137	−	0.952947i	$-0.598034\pi$
$601$	−1.15390e7	−	8.38361e6i	−1.30312	−	0.946771i	−0.999981	+	0.00617642i	$0.998034\pi$
$602$	4.99440e6	+	6.87420e6i	0.561684	+	0.773091i
$603$	120871.	−	39273.3i	0.0135372	−	0.00439849i
$604$	−403581.	+	555482.i	−0.0450131	+	0.0619552i
$605$	783.809	+	569.471i	8.70607e−5	+	6.32533e-5i
$606$	−6.27051e6	−	4.55579e6i	−0.693619	−	0.503944i
$607$	−1.69600e6	+	5.21974e6i	−0.186833	+	0.575012i	−0.999975	−	0.00705285i	$-0.997755\pi$
$607$	−1.69600e6	+	5.21974e6i	−0.186833	+	0.575012i	0.813142	+	0.582065i	$0.197755\pi$
$608$	−1.19356e6	−	387810.i	−0.130944	−	0.0425461i
$609$	2.01156e7			2.19781
$610$	−50538.7	−	9778.11i	−0.00549920	−	0.00106397i
$611$	2.70109e6			0.292709
$612$	53515.9	+	17388.4i	0.00577570	+	0.00187664i
$613$	−733780.	+	2.25834e6i	−0.0788706	+	0.242739i	−0.982716	−	0.185121i	$-0.940732\pi$
$613$	−733780.	+	2.25834e6i	−0.0788706	+	0.242739i	0.903845	+	0.427860i	$0.140732\pi$
$614$	−1.24590e7	−	9.05199e6i	−1.33371	−	0.968998i
$615$	24185.7	+	17571.9i	0.00257852	+	0.00187340i
$616$	−2.37292e6	+	3.26604e6i	−0.251960	+	0.346793i
$617$	1.34720e7	−	4.37731e6i	1.42468	−	0.462907i	0.507595	−	0.861596i	$-0.330534\pi$
$617$	1.34720e7	−	4.37731e6i	1.42468	−	0.462907i	0.917086	+	0.398688i	$0.130534\pi$
$618$	4.50592e6	+	6.20187e6i	0.474584	+	0.653208i
$619$	−4.26960e6	−	3.10204e6i	−0.447878	−	0.325403i	0.340879	−	0.940107i	$-0.389275\pi$
$619$	−4.26960e6	−	3.10204e6i	−0.447878	−	0.325403i	−0.788758	+	0.614704i	$0.789275\pi$
$620$	−33252.2	−	45767.7i	−0.00347409	−	0.00478167i
$621$		−	9.51978e6i		−	0.990599i
$622$	−8.65009e6	+	6.28466e6i	−0.896488	+	0.651337i
$623$	−5.40175e6			−0.557589
$624$	−1.22205e7			−1.25640
$625$	−7.90015e6	+	5.73980e6i	−0.808975	+	0.587755i
$626$	3.64192e6	+	1.12087e7i	0.371445	+	1.14319i
$627$	−590998.	+	813438.i	−0.0600367	+	0.0826334i
$628$	−1.65361e6	−	2.27599e6i	−0.167314	−	0.230288i
$629$	286961.	−	883176.i	0.0289199	−	0.0890063i
$630$	−768.591	−	2365.48i	−7.71514e−5	−	0.000237448i
$631$		−	1.05629e7i		−	1.05611i	−0.849210	−	0.528055i	$-0.822922\pi$
$631$		−	1.05629e7i		−	1.05611i	0.849210	−	0.528055i	$-0.177078\pi$
$632$	−843086.	+	2.59475e6i	−0.0839613	+	0.258406i
$633$	3.08056e6	−	4.24003e6i	0.305577	−	0.420591i
$634$	7.59078e6	−	2.46639e6i	0.750003	−	0.243691i
$635$	2315.35	+	7125.91i	0.000227867	+	0.000701304i
$636$	5.17939e6	+	1.68289e6i	0.507734	+	0.164973i
$637$	2.41541e7	−	1.75490e7i	2.35854	−	1.71358i
$638$	1.52758e7	+	4.96341e6i	1.48577	+	0.482757i
$639$		−	253348.i		−	0.0245452i
$640$	18372.1	−	5969.47i	0.00177300	−	0.000576084i
$641$	−1.27908e7	+	4.15598e6i	−1.22957	+	0.399511i	−0.850558	−	0.525881i	$-0.823736\pi$
$641$	−1.27908e7	+	4.15598e6i	−1.22957	+	0.399511i	−0.379010	+	0.925392i	$0.623736\pi$
$642$		−	2.25586e7i		−	2.16010i
$643$	−2.17524e6	−	706778.i	−0.207482	−	0.0674149i	0.203432	−	0.979089i	$-0.434790\pi$
$643$	−2.17524e6	−	706778.i	−0.207482	−	0.0674149i	−0.410914	+	0.911674i	$0.634790\pi$
$644$	1.31793e7	−	9.57532e6i	1.25221	−	0.909785i
$645$	−15266.4	−	4960.34i	−0.00144490	−	0.000469475i
$646$	−144764.	−	445538.i	−0.0136483	−	0.0420053i
$647$	−1.20449e7	+	3.91362e6i	−1.13121	+	0.367551i	−0.814035	−	0.580816i	$-0.802733\pi$
$647$	−1.20449e7	+	3.91362e6i	−1.13121	+	0.367551i	−0.317173	+	0.948368i	$0.602733\pi$
$648$	1.40088e6	−	1.92815e6i	0.131058	−	0.180386i
$649$	5.57404e6	−	1.71551e7i	0.519467	−	1.59876i
$650$			1.62515e7i			1.50872i
$651$	1.07854e7	+	3.31941e7i	0.997435	+	3.06979i
$652$	501472.	−	1.54337e6i	0.0461985	−	0.142184i
$653$	−3.47868e6	−	4.78799e6i	−0.319251	−	0.439411i	0.618988	−	0.785401i	$-0.287543\pi$
$653$	−3.47868e6	−	4.78799e6i	−0.319251	−	0.439411i	−0.938238	+	0.345990i	$0.887543\pi$
$654$	−7.97002e6	+	1.09698e7i	−0.728643	+	1.00289i
$655$	19215.3	+	59138.6i	0.00175002	+	0.00538601i
$656$	7.92308e6	−	5.75646e6i	0.718844	−	0.522271i
$657$	−371179.			−0.0335483
$658$	−7.50162e6			−0.675446
$659$	−7.83295e6	+	5.69097e6i	−0.702606	+	0.510473i	−0.880780	−	0.473526i	$-0.842981\pi$
$659$	−7.83295e6	+	5.69097e6i	−0.702606	+	0.510473i	0.178174	+	0.983999i	$0.442981\pi$
$660$			37548.9i			0.00335534i
$661$	9.11287e6	+	1.25428e7i	0.811244	+	1.11658i	0.991130	+	0.132894i	$0.0424270\pi$
$661$	9.11287e6	+	1.25428e7i	0.811244	+	1.11658i	−0.179886	+	0.983687i	$0.557573\pi$
$662$	−4.47179e6	−	3.24895e6i	−0.396585	−	0.288136i
$663$	−2.28436e6	−	3.14415e6i	−0.201828	−	0.277792i
$664$	3.36576e6	−	1.09360e6i	0.296254	−	0.0962586i
$665$	−5524.56	+	7603.90i	−0.000484444	+	0.000666779i
$666$	−88227.2	−	64100.8i	−0.00770756	−	0.00559987i
$667$	1.06502e7	+	7.73784e6i	0.926924	+	0.673450i
$668$	1.64121e6	−	5.05112e6i	0.142306	−	0.437972i
$669$	1.67312e7	+	5.43628e6i	1.44531	+	0.469609i
$670$	−39513.6			−0.00340063
$671$	7.85732e6	+	8.41126e6i	0.673702	+	0.721198i
$672$	2.89148e7			2.47000
$673$	−1.69726e7	−	5.51473e6i	−1.44448	−	0.469339i	−0.521186	−	0.853443i	$-0.674510\pi$
$673$	−1.69726e7	−	5.51473e6i	−1.44448	−	0.469339i	−0.923290	+	0.384104i	$0.874510\pi$
$674$	9.41708e6	−	2.89828e7i	0.798485	−	2.45748i
$675$	−9.68551e6	−	7.03693e6i	−0.818207	−	0.594462i
$676$	1.94218e6	+	1.41107e6i	0.163464	+	0.118763i
$677$	2.81310e6	−	3.87190e6i	0.235892	−	0.324678i	−0.674616	−	0.738169i	$-0.735691\pi$
$677$	2.81310e6	−	3.87190e6i	0.235892	−	0.324678i	0.910508	+	0.413491i	$0.135691\pi$
$678$	1.32313e7	−	4.29913e6i	1.10543	−	0.359175i
$679$	−1.02049e7	−	1.40458e7i	−0.849442	−	1.16916i
$680$	2874.74	+	2088.62i	0.000238411	+	0.000173216i
$681$	−2.80622e6	−	3.86243e6i	−0.231875	−	0.319149i
$682$			2.78689e7i			2.29434i
$683$	−1.59840e7	+	1.16131e7i	−1.31109	+	0.952566i	−0.311097	+	0.950378i	$0.600696\pi$
$683$	−1.59840e7	+	1.16131e7i	−1.31109	+	0.952566i	−0.999998	+	0.00218800i	$0.999304\pi$
$684$	−24971.6			−0.00204083
$685$	−42614.1			−0.00346998
$686$	−4.14271e7	+	3.00986e7i	−3.36104	+	2.44194i
$687$	6.33194e6	+	1.94877e7i	0.511853	+	1.57532i
$688$	−3.09089e6	+	4.25425e6i	−0.248951	+	0.342651i
$689$	5.30768e6	+	7.30540e6i	0.425948	+	0.586268i
$690$	−20951.7	+	64482.6i	−0.00167531	+	0.00515608i
$691$	−7.43611e6	−	2.28860e7i	−0.592448	−	1.82337i	−0.567039	−	0.823691i	$-0.691911\pi$
$691$	−7.43611e6	−	2.28860e7i	−0.592448	−	1.82337i	−0.0254093	−	0.999677i	$-0.508089\pi$
$692$			1.55788e7i			1.23672i
$693$	−171861.	+	528934.i	−0.0135939	+	0.0418377i
$694$	−1.72326e6	+	2.37186e6i	−0.135816	+	0.186935i
$695$	−64649.8	+	21006.0i	−0.00507698	+	0.00164961i
$696$	1.04291e6	+	3.20975e6i	0.0816064	+	0.251159i
$697$	2.96210e6	+	962446.i	0.230950	+	0.0750403i
$698$	−1.06451e7	+	7.73413e6i	−0.827012	+	0.600859i
$699$	−1.32616e7	−	4.30896e6i	−1.02660	−	0.333564i
$700$		−	2.04867e7i		−	1.58026i
$701$	1.14351e7	−	3.71550e6i	0.878914	−	0.285576i	0.165408	−	0.986225i	$-0.447106\pi$
$701$	1.14351e7	−	3.71550e6i	0.878914	−	0.285576i	0.713506	+	0.700649i	$0.247106\pi$
$702$	−1.89487e7	+	6.15680e6i	−1.45123	+	0.471533i
$703$			412108.i			0.0314501i
$704$	7.88303e6	+	2.56135e6i	0.599462	+	0.194777i
$705$	11465.1	−	8329.88i	0.000868770	−	0.000631199i
$706$	1.52808e7	+	4.96502e6i	1.15381	+	0.374894i
$707$	5.00635e6	+	1.54080e7i	0.376680	+	1.15930i
$708$	−1.77471e7	+	5.76639e6i	−1.33059	+	0.432336i
$709$	−3.79920e6	+	5.22916e6i	−0.283842	+	0.390675i	−0.927002	−	0.375057i	$-0.877623\pi$
$709$	−3.79920e6	+	5.22916e6i	−0.283842	+	0.390675i	0.643160	+	0.765732i	$0.277623\pi$
$710$	−24340.7	+	74912.8i	−0.00181212	+	0.00557712i
$711$			375855.i			0.0278834i
$712$	−280058.	−	861931.i	−0.0207037	−	0.0637195i
$713$	−7.05838e6	+	2.17235e7i	−0.519973	+	1.60031i
$714$	6.34425e6	+	8.73211e6i	0.465731	+	0.641023i
$715$	−36595.6	+	50369.6i	−0.00267710	+	0.00368471i
$716$	−3.37846e6	−	1.03978e7i	−0.246284	−	0.757985i
$717$	−1.15929e7	+	8.42276e6i	−0.842162	+	0.611866i
$718$	2.26084e7			1.63666
$719$	−4.96826e6			−0.358412			−0.179206	−	0.983812i	$-0.557353\pi$
$719$	−4.96826e6			−0.358412			−0.179206	+	0.983812i	$0.557353\pi$
$720$	1245.29	−	904.758i	8.95242e−5	−	6.50431e-5i
$721$		−	1.60236e7i		−	1.14794i
$722$	−1.10189e7	−	1.51662e7i	−0.786673	−	1.08276i
$723$	8.89740e6	+	6.46434e6i	0.633020	+	0.459916i
$724$	2.38669e6	+	3.28499e6i	0.169219	+	0.232910i
$725$	1.57451e7	−	5.11589e6i	1.11250	−	0.361473i
$726$	−290218.	+	399451.i	−0.0204354	+	0.0281269i
$727$	−4.01942e6	−	2.92028e6i	−0.282051	−	0.204922i	0.437761	−	0.899092i	$-0.355772\pi$
$727$	−4.01942e6	−	2.92028e6i	−0.282051	−	0.204922i	−0.719811	+	0.694170i	$0.755772\pi$
$728$	5.60235e6	+	4.07035e6i	0.391780	+	0.284645i
$729$	4.53308e6	−	1.39514e7i	0.315918	−	0.972296i
$730$	109754.	+	35661.3i	0.00762280	+	0.00247680i
$731$	−1.67233e6			−0.115752
$732$	2.26189e6	−	1.16907e7i	0.156025	−	0.806423i
$733$	1.56601e7			1.07655			0.538277	−	0.842768i	$-0.319075\pi$
$733$	1.56601e7			1.07655			0.538277	+	0.842768i	$0.319075\pi$
$734$	4.09911e6	+	1.33188e6i	0.280834	+	0.0912485i
$735$	48405.8	−	148978.i	0.00330505	−	0.0101719i
$736$	1.53089e7	+	1.11226e7i	1.04172	+	0.756854i
$737$	7.14803e6	+	5.19335e6i	0.484750	+	0.352191i
$738$	214989.	−	295907.i	0.0145303	−	0.0199993i
$739$	−2.30451e7	+	7.48780e6i	−1.55227	+	0.504363i	−0.954729	−	0.297475i	$-0.903855\pi$
$739$	−2.30451e7	+	7.48780e6i	−1.55227	+	0.504363i	−0.597541	+	0.801839i	$0.703855\pi$
$740$	9046.05	+	12450.8i	0.000607267	+	0.000835831i
$741$	1.39532e6	+	1.01376e6i	0.0933529	+	0.0678248i
$742$	−1.47408e7	−	2.02890e7i	−0.982904	−	1.35285i
$743$		−	2.29157e7i		−	1.52287i	−0.648244	−	0.761433i	$-0.724496\pi$
$743$		−	2.29157e7i		−	1.52287i	0.648244	−	0.761433i	$-0.275504\pi$
$744$	−4.73745e6	+	3.44196e6i	−0.313770	+	0.227968i
$745$	−62192.4			−0.00410532
$746$	−3.68493e7			−2.42428
$747$	394426.	−	286567.i	0.0258621	−	0.0187899i
$748$	1.20885e6	+	3.72046e6i	0.0789985	+	0.243132i
$749$	−2.77156e7	+	3.81472e7i	−1.80517	+	2.48461i
$750$	100237.	+	137964.i	0.00650688	+	0.00895595i
$751$	3.32775e6	−	1.02418e7i	0.215303	−	0.662635i	−0.783829	−	0.620977i	$-0.786736\pi$
$751$	3.32775e6	−	1.02418e7i	0.215303	−	0.662635i	0.999132	−	0.0416580i	$-0.0132640\pi$
$752$	−1.43463e6	−	4.41532e6i	−0.0925112	−	0.284720i
$753$		−	2.46201e7i		−	1.58235i
$754$	8.51390e6	−	2.62031e7i	0.545381	−	1.67851i
$755$	−3510.96	+	4832.42i	−0.000224160	+	0.000308530i
$756$	2.38868e7	−	7.76130e6i	1.52004	−	0.493890i
$757$	3.36298e6	+	1.03502e7i	0.213297	+	0.656460i	0.999270	+	0.0381997i	$0.0121623\pi$
$757$	3.36298e6	+	1.03502e7i	0.213297	+	0.656460i	−0.785973	+	0.618260i	$0.787838\pi$
$758$	2.32487e7	+	7.55397e6i	1.46969	+	0.477532i
$759$	1.22652e7	−	8.91121e6i	0.772807	−	0.561477i
$760$	−1499.74	−	487.296i	−9.41852e−5	−	3.06026e-5i
$761$			4.45437e6i			0.278820i	0.990235	+	0.139410i	$0.0445207\pi$
$761$			4.45437e6i			0.278820i	−0.990235	+	0.139410i	$0.955479\pi$
$762$	−3.63156e6	+	1.17997e6i	−0.226572	+	0.0736176i
$763$	2.69551e7	−	8.75824e6i	1.67621	−	0.544635i
$764$			1.54903e7i			0.960124i
$765$	465.562	+	151.270i	2.87623e−5	+	9.34545e-6i
$766$	−1.81242e7	+	1.31680e7i	−1.11606	+	0.810862i
$767$	−2.94267e7	−	9.56133e6i	−1.80615	−	0.586854i
$768$	6.23014e6	+	1.91744e7i	0.381149	+	1.17306i
$769$	−1.98514e7	+	6.45011e6i	−1.21053	+	0.393325i	−0.843625	−	0.536934i	$-0.819583\pi$
$769$	−1.98514e7	+	6.45011e6i	−1.21053	+	0.393325i	−0.366905	+	0.930258i	$0.619583\pi$
$770$	101635.	−	139889.i	0.00617758	−	0.00850271i
$771$	−1.64597e6	+	5.06579e6i	−0.0997211	+	0.306910i
$772$			4.91085e6i			0.296561i
$773$	−324881.	−	999882.i	−0.0195558	−	0.0601866i	0.940802	−	0.338956i	$-0.110074\pi$
$773$	−324881.	−	999882.i	−0.0195558	−	0.0601866i	−0.960358	+	0.278769i	$0.910074\pi$
$774$	−60688.9	+	186781.i	−0.00364130	+	0.0112068i
$775$	1.68841e7	+	2.32390e7i	1.00978	+	1.38984i
$776$	1.71214e6	−	2.35656e6i	0.102067	−	0.140483i
$777$	−2.93411e6	−	9.03026e6i	−0.174351	−	0.536596i
$778$	−3.11688e6	+	2.26454e6i	−0.184617	+	0.134132i
$779$	−1.38218e6			−0.0816056
$780$	64408.8			0.00379061
$781$	1.42492e7	−	1.03526e7i	0.835915	−	0.607328i
$782$			7.06366e6i			0.413060i
$783$	1.19299e7	+	1.64201e7i	0.695397	+	0.957131i
$784$	−4.15153e7	−	3.01626e7i	−2.41223	−	1.75259i
$785$	−14385.6	−	19800.0i	−0.000833206	−	0.00114681i
$786$	−3.01386e7	+	9.79263e6i	−1.74007	+	0.565384i
$787$	1.84653e7	−	2.54154e7i	1.06272	−	1.46271i	0.185493	−	0.982646i	$-0.440612\pi$
$787$	1.84653e7	−	2.54154e7i	1.06272	−	1.46271i	0.877231	−	0.480069i	$-0.159388\pi$
$788$	−5.53707e6	−	4.02291e6i	−0.317661	−	0.230794i
$789$	1.79666e7	+	1.30535e7i	1.02748	+	0.746506i
$790$	36110.6	−	111137.i	0.00205857	−	0.00633564i
$791$	−2.76565e7	−	8.98615e6i	−1.57165	−	0.510661i
$792$	−93309.7			−0.00528584
$793$	1.44281e7	−	1.34779e7i	0.814754	−	0.761096i
$794$	3.48311e7			1.96072
$795$	45058.2	+	14640.3i	0.00252846	+	0.000821546i
$796$	−256906.	+	790676.i	−0.0143712	+	0.0442299i
$797$	8.02336e6	+	5.82931e6i	0.447415	+	0.325066i	0.788574	−	0.614940i	$-0.210820\pi$
$797$	8.02336e6	+	5.82931e6i	0.447415	+	0.325066i	−0.341159	+	0.940005i	$0.610820\pi$
$798$	−3.87515e6	−	2.81546e6i	−0.215418	−	0.156510i
$799$	867826.	−	1.19446e6i	0.0480912	−	0.0661918i
$800$	2.26325e7	−	7.35373e6i	1.25028	−	0.406240i
$801$	−73386.4	−	101008.i	−0.00404142	−	0.00556254i
$802$	−3.32092e7	−	2.41279e7i	−1.82315	−	1.32460i
$803$	−1.51676e7	−	2.08764e7i	−0.830094	−	1.14253i
$804$		−	9.14035e6i		−	0.498681i
$805$	114653.	−	83300.6i	0.00623588	−	0.00453063i
$806$	4.78044e7			2.59197
$807$	−1.65879e7			−0.896619
$808$	−2.19902e6	+	1.59768e6i	−0.118495	+	0.0860916i
$809$	5.91894e6	+	1.82166e7i	0.317960	+	0.978580i	0.974519	+	0.224306i	$0.0720114\pi$
$809$	5.91894e6	+	1.82166e7i	0.317960	+	0.978580i	−0.656559	+	0.754275i	$0.727989\pi$
$810$	−60001.6	+	82585.2i	−0.00321330	+	0.00442272i
$811$	1.88519e7	+	2.59474e7i	1.00647	+	1.38529i	0.921267	+	0.388931i	$0.127155\pi$
$811$	1.88519e7	+	2.59474e7i	1.00647	+	1.38529i	0.0852077	+	0.996363i	$0.472845\pi$
$812$	−1.07327e7	+	3.30318e7i	−0.571240	+	1.75809i
$813$	−425135.	−	1.30843e6i	−0.0225580	−	0.0694264i
$814$		−	7.58156e6i		−	0.401049i
$815$	4362.56	−	13426.6i	0.000230063	−	0.000708062i
$816$	−3.92628e6	+	5.40406e6i	−0.206422	+	0.284116i
$817$	705828.	−	229337.i	0.0369951	−	0.0120204i
$818$	−7.46567e6	−	2.29770e7i	−0.390109	−	1.20063i
$819$	907297.	+	294799.i	0.0472650	+	0.0153573i
$820$	−41759.1	+	30339.7i	−0.00216878	+	0.00157571i
$821$	−8.84134e6	−	2.87273e6i	−0.457784	−	0.148743i	0.0710421	−	0.997473i	$-0.477368\pi$
$821$	−8.84134e6	−	2.87273e6i	−0.457784	−	0.148743i	−0.528826	+	0.848730i	$0.677368\pi$
$822$		−	2.17173e7i		−	1.12105i
$823$	1.56394e7	−	5.08156e6i	0.804862	−	0.261515i	0.122442	−	0.992476i	$-0.460928\pi$
$823$	1.56394e7	−	5.08156e6i	0.804862	−	0.261515i	0.682420	+	0.730960i	$0.260928\pi$
$824$	2.55680e6	−	830755.i	0.131183	−	0.0426241i
$825$		−	1.90658e7i		−	0.975261i
$826$	8.17256e7	+	2.65543e7i	4.16781	+	1.35420i
$827$	3.64605e6	−	2.64901e6i	0.185378	−	0.134685i	−0.491226	−	0.871032i	$-0.663451\pi$
$827$	3.64605e6	−	2.64901e6i	0.185378	−	0.134685i	0.676604	+	0.736347i	$0.263451\pi$
$828$	358099.	+	116354.i	0.0181521	+	0.00589799i
$829$	−2.26523e6	−	6.97165e6i	−0.114479	−	0.352329i	0.877359	−	0.479834i	$-0.159303\pi$
$829$	−2.26523e6	−	6.97165e6i	−0.114479	−	0.352329i	−0.991838	+	0.127505i	$0.959303\pi$
$830$	−144160.	+	46840.5i	−0.00726358	+	0.00236008i
$831$	−1.49864e7	+	2.06270e7i	−0.752827	+	1.03618i
$832$	4.39357e6	−	1.35220e7i	0.220044	−	0.677226i
$833$		−	1.63195e7i		−	0.814884i
$834$	−1.07052e7	−	3.29473e7i	−0.532943	−	1.64023i
$835$	14277.7	−	43942.3i	0.000708668	−	0.00218105i
$836$	−1.02042e6	−	1.40449e6i	−0.0504967	−	0.0695027i
$837$	−2.06994e7	+	2.84903e7i	−1.02128	+	1.40567i
$838$	−2.64577e6	−	8.14284e6i	−0.130149	−	0.400559i
$839$	−2.25167e7	+	1.63594e7i	−1.10433	+	0.802346i	−0.981762	−	0.190114i	$-0.939114\pi$
$839$	−2.25167e7	+	1.63594e7i	−1.10433	+	0.802346i	−0.122572	+	0.992460i	$0.539114\pi$
$840$	36332.4			0.00177662
$841$	−7.55560e6			−0.368366
$842$	1.83786e6	−	1.33528e6i	0.0893370	−	0.0649072i
$843$			3.49766e7i			1.69515i
$844$	5.31891e6	+	7.32086e6i	0.257020	+	0.353758i
$845$	16896.0	+	12275.6i	0.000814032	+	0.000591429i
$846$	−101915.	−	140273.i	−0.00489565	−	0.00673829i
$847$	981534.	−	318920.i	0.0470107	−	0.0152747i
$848$	9.12267e6	−	1.25563e7i	0.435645	−	0.599613i
$849$	−2.85808e7	−	2.07651e7i	−1.36083	−	0.988703i
$850$	7.18662e6	+	5.22139e6i	0.341175	+	0.247878i
$851$	1.92019e6	−	5.90973e6i	0.0908908	−	0.279733i
$852$	−1.73290e7	−	5.63052e6i	−0.817850	−	0.265736i
$853$	599852.			0.0282274			0.0141137	−	0.999900i	$-0.495507\pi$
$853$	599852.			0.0282274			0.0141137	+	0.999900i	$0.495507\pi$
$854$	−4.00705e7	+	3.74316e7i	−1.88010	+	1.75628i
$855$	−217.241			−1.01631e−5
$856$	−7.52390e6	−	2.44466e6i	−0.350961	−	0.114034i
$857$	−6.00390e6	+	1.84781e7i	−0.279243	+	0.859420i	0.708823	+	0.705386i	$0.249227\pi$
$857$	−6.00390e6	+	1.84781e7i	−0.279243	+	0.859420i	−0.988066	+	0.154034i	$0.950773\pi$
$858$	−2.56697e7	−	1.86501e7i	−1.19043	−	0.864896i
$859$	8.26678e6	+	6.00617e6i	0.382255	+	0.277725i	0.762275	−	0.647254i	$-0.224083\pi$
$859$	8.26678e6	+	6.00617e6i	0.382255	+	0.277725i	−0.380019	+	0.924979i	$0.624083\pi$
$860$	16290.7	−	22422.3i	0.000751095	−	0.00103379i
$861$	3.02868e7	−	9.84077e6i	1.39234	−	0.452398i
$862$	1.83653e7	+	2.52777e7i	0.841840	+	1.15869i
$863$	9.70081e6	+	7.04805e6i	0.443385	+	0.322138i	0.786979	−	0.616980i	$-0.211644\pi$
$863$	9.70081e6	+	7.04805e6i	0.443385	+	0.322138i	−0.343593	+	0.939118i	$0.611644\pi$
$864$	1.71484e7	+	2.36028e7i	0.781519	+	1.07567i
$865$			135528.i			0.00615871i
$866$	1.82125e7	−	1.32321e7i	0.825229	−	0.599564i
$867$	1.97481e7			0.892230
$868$	−6.02626e7			−2.71487
$869$	−2.11393e7	+	1.53586e7i	−0.949603	+	0.689927i
$870$	−44669.3	−	137478.i	−0.00200084	−	0.00615794i
$871$	8.90832e6	−	1.22612e7i	0.397878	−	0.547632i
$872$	2.79502e6	+	3.84701e6i	0.124478	+	0.171330i
$873$	124004.	−	381644.i	0.00550679	−	0.0169482i
$874$	−968683.	−	2.98130e6i	−0.0428946	−	0.132016i
$875$		−	356452.i		−	0.0157391i
$876$	−8.24924e6	+	2.53886e7i	−0.363207	+	1.11784i
$877$	1.29808e7	−	1.78666e7i	0.569906	−	0.784409i	−0.422637	−	0.906299i	$-0.638896\pi$
$877$	1.29808e7	−	1.78666e7i	0.569906	−	0.784409i	0.992544	+	0.121890i	$0.0388955\pi$
$878$	1.25757e7	−	4.08609e6i	0.550548	−	0.178884i
$879$	−4.71634e6	−	1.45154e7i	−0.205889	−	0.633661i
$880$	101773.	+	33068.2i	0.00443024	+	0.00143947i
$881$	−4.21362e6	+	3.06137e6i	−0.182901	+	0.132885i	−0.675468	−	0.737389i	$-0.736058\pi$
$881$	−4.21362e6	+	3.06137e6i	−0.182901	+	0.132885i	0.492568	+	0.870274i	$0.336058\pi$
$882$	−1.82271e6	−	592236.i	−0.0788945	−	0.0256344i
$883$			1.36005e7i			0.587018i	0.955956	+	0.293509i	$0.0948231\pi$
$883$			1.36005e7i			0.587018i	−0.955956	+	0.293509i	$0.905177\pi$
$884$	6.38183e6	−	2.07358e6i	0.274672	−	0.0892463i
$885$	−154391.	+	50164.8i	−0.00662620	+	0.00215298i
$886$		−	4.32909e7i		−	1.85273i
$887$	−2.35401e7	−	7.64865e6i	−1.00461	−	0.326419i	−0.239907	−	0.970796i	$-0.577117\pi$
$887$	−2.35401e7	−	7.64865e6i	−1.00461	−	0.326419i	−0.764708	+	0.644377i	$0.777117\pi$
$888$	1.28879e6	−	936363.i	0.0548468	−	0.0398485i
$889$	7.59079e6	+	2.46640e6i	0.322131	+	0.104667i
$890$	11995.3	+	36917.7i	0.000507616	+	0.00156228i
$891$	2.17086e7	−	7.05357e6i	0.916091	−	0.297656i
$892$	−1.78538e7	+	2.45737e7i	−0.751310	+	1.03409i
$893$	−202472.	+	623146.i	−0.00849644	+	0.0261494i
$894$		−	3.16950e7i		−	1.32631i
$895$	−29391.0	−	90456.1i	−0.00122647	−	0.00377468i
$896$	6.35890e6	−	1.95707e7i	0.264613	−	0.814396i
$897$	−1.52857e7	−	2.10389e7i	−0.634314	−	0.873058i
$898$	6.37581e6	−	8.77555e6i	0.263842	−	0.363148i
$899$	−1.50486e7	−	4.63148e7i	−0.621008	−	1.91126i
$900$	383083.	−	278326.i	0.0157647	−	0.0114537i
$901$	4.93584e6			0.202558
$902$	2.54280e7			1.04063
$903$	−1.38335e7	+	1.00507e7i	−0.564565	+	0.410181i
$904$		−	4.87891e6i		−	0.198565i
$905$	20763.0	+	28577.8i	0.000842691	+	0.00115986i
$906$	−2.46273e6	−	1.78928e6i	−0.0996775	−	0.0724199i
$907$	−1.20159e7	−	1.65384e7i	−0.484994	−	0.667537i	0.494461	−	0.869200i	$-0.335365\pi$
$907$	−1.20159e7	−	1.65384e7i	−0.484994	−	0.667537i	−0.979455	+	0.201663i	$0.935365\pi$
$908$	7.83975e6	−	2.54729e6i	0.315564	−	0.102533i
$909$	−220100.	+	302941.i	−0.00883507	+	0.0121604i
$910$	−239957.	−	174339.i	−0.00960570	−	0.00697895i
$911$	−2.17437e7	−	1.57977e7i	−0.868036	−	0.630665i	0.0620232	−	0.998075i	$-0.480245\pi$
$911$	−2.17437e7	−	1.57977e7i	−0.868036	−	0.630665i	−0.930059	+	0.367410i	$0.880245\pi$
$912$	916041.	−	2.81928e6i	0.0364693	−	0.112241i
$913$	3.22350e7	+	1.04738e7i	1.27983	+	0.415841i
$914$	4.84755e7			1.91936
$915$	19677.3	−	101703.i	0.000776986	−	0.00401590i
$916$	−3.53792e7			−1.39318
$917$	6.29966e7	+	2.04688e7i	2.47397	+	0.803840i
$918$	−3.36534e6	+	1.03575e7i	−0.131802	+	0.405645i
$919$	2.82680e6	+	2.05379e6i	0.110410	+	0.0802172i	0.641620	−	0.767023i	$-0.278263\pi$
$919$	2.82680e6	+	2.05379e6i	0.110410	+	0.0802172i	−0.531210	+	0.847240i	$0.678263\pi$
$920$	19236.2	+	13975.9i	0.000749289	+	0.000544390i
$921$	1.82161e7	−	2.50723e7i	0.707630	−	0.973969i
$922$	−6.47231e6	+	2.10298e6i	−0.250745	+	0.0814720i
$923$	−1.77582e7	−	2.44421e7i	−0.686112	−	0.944352i
$924$	3.23594e7	+	2.35105e7i	1.24687	+	0.905903i
$925$	−4.59323e6	−	6.32204e6i	−0.176508	−	0.242942i
$926$		−	5.40396e7i		−	2.07102i
$927$	299626.	−	217691.i	0.0114520	−	0.00832033i
$928$	−4.03440e7			−1.53783
$929$	4.64899e7			1.76734			0.883668	−	0.468114i	$-0.155066\pi$
$929$	4.64899e7			1.76734			0.883668	+	0.468114i	$0.155066\pi$
$930$	202911.	−	147424.i	0.00769306	−	0.00558933i
$931$	2.23800e6	+	6.88786e6i	0.0846225	+	0.260441i
$932$	1.41515e7	−	1.94778e7i	0.533656	−	0.734515i
$933$	−1.26472e7	−	1.74073e7i	−0.475651	−	0.654678i
$934$	−2.12925e7	+	6.55315e7i	−0.798655	+	2.45801i
$935$	10516.4	+	32366.2i	0.000393404	+	0.00121077i
$936$			160057.i			0.00597153i
$937$	−1.21321e7	+	3.73386e7i	−0.451425	+	1.38934i	0.423857	+	0.905729i	$0.360676\pi$
$937$	−1.21321e7	+	3.73386e7i	−0.451425	+	1.38934i	−0.875282	+	0.483613i	$0.839324\pi$
$938$	−2.47407e7	+	3.40526e7i	−0.918131	+	1.26370i
$939$	−2.25562e7	+	7.32894e6i	−0.834836	+	0.271255i
$940$	7561.28	+	23271.2i	0.000279110	+	0.000859013i
$941$	−1.53965e7	−	5.00264e6i	−0.566825	−	0.184173i	0.0115647	−	0.999933i	$-0.496319\pi$
$941$	−1.53965e7	−	5.00264e6i	−0.566825	−	0.184173i	−0.578390	+	0.815760i	$0.696319\pi$
$942$	1.00906e7	−	7.33127e6i	0.370502	−	0.269186i
$943$	1.98208e7	+	6.44016e6i	0.725841	+	0.235840i
$944$			5.31806e7i			1.94233i
$945$	207804.	−	67519.5i	0.00756961	−	0.00245952i
$946$	−1.29851e7	+	4.21913e6i	−0.471758	+	0.153283i
$947$		−	5.82621e6i		−	0.211111i	−0.994413	−	0.105556i	$-0.966338\pi$
$947$		−	5.82621e6i		−	0.211111i	0.994413	−	0.105556i	$-0.0336621\pi$
$948$	2.57084e7	+	8.35316e6i	0.929082	+	0.301877i
$949$	−3.58099e7	+	2.60174e7i	−1.29074	+	0.937775i
$950$	−3.74924e6	−	1.21820e6i	−0.134783	−	0.0437936i
$951$	4.96333e6	+	1.52756e7i	0.177960	+	0.547704i
$952$	3.59993e6	−	1.16969e6i	0.128736	−	0.0418290i
$953$	−1.13436e7	+	1.56131e7i	−0.404591	+	0.556872i	−0.961889	−	0.273441i	$-0.911838\pi$
$953$	−1.13436e7	+	1.56131e7i	−0.404591	+	0.556872i	0.557297	+	0.830313i	$0.311838\pi$
$954$	179121.	−	551278.i	0.00637200	−	0.0196110i
$955$			134758.i			0.00478131i
$956$	−7.64559e6	−	2.35307e7i	−0.270562	−	0.832703i
$957$	−9.98830e6	+	3.07408e7i	−0.352543	+	1.08501i
$958$	1.76088e7	+	2.42364e7i	0.619891	+	0.853207i
$959$	−2.66820e7	+	3.67246e7i	−0.936853	+	1.28947i
$960$	−23051.5	−	70945.1i	−0.000807273	−	0.00248453i
$961$	4.51971e7	−	3.28376e7i	1.57871	−	1.14700i
$962$	−1.30049e7			−0.453074
$963$	−1.08985e6			−0.0378706
$964$	−1.53623e7	+	1.11614e7i	−0.532431	+	0.386834i
$965$			42722.0i			0.00147684i
$966$	4.24523e7	+	5.84306e7i	1.46372	+	2.01464i
$967$	−3.62536e7	−	2.63398e7i	−1.24677	−	0.905830i	−0.248738	−	0.968571i	$-0.580016\pi$
$967$	−3.62536e7	−	2.63398e7i	−1.24677	−	0.905830i	−0.998030	+	0.0627411i	$0.980016\pi$
$968$	101777.	+	140084.i	0.00349109	+	0.00480508i
$969$	896595.	−	291321.i	0.0306752	−	0.00996696i
$970$	−73333.5	+	100935.i	−0.00250249	+	0.00344439i
$971$	−1.81264e6	−	1.31696e6i	−0.0616968	−	0.0448254i	0.556509	−	0.830841i	$-0.312140\pi$
$971$	−1.81264e6	−	1.31696e6i	−0.0616968	−	0.0448254i	−0.618206	+	0.786016i	$0.712140\pi$
$972$	928537.	+	674621.i	0.0315234	+	0.0229031i
$973$	−2.23764e7	+	6.88674e7i	−0.757718	+	2.33202i
$974$	3.08925e7	+	1.00376e7i	1.04341	+	0.339025i
$975$	−3.27042e7			−1.10177
$976$	−2.96948e7	−	1.64263e7i	−0.997827	−	0.551971i
$977$	546830.			0.0183280			0.00916402	−	0.999958i	$-0.497083\pi$
$977$	546830.			0.0183280			0.00916402	+	0.999958i	$0.497083\pi$
$978$	6.84255e6	+	2.22328e6i	0.228755	+	0.0743271i
$979$	2.68221e6	−	8.25499e6i	0.0894408	−	0.275271i
$980$	218809.	+	158974.i	0.00727780	+	0.00528763i
$981$	529974.	+	385048.i	0.0175825	+	0.0127745i
$982$	−6.24763e6	+	8.59913e6i	−0.206746	+	0.284561i
$983$	−7.88960e6	+	2.56348e6i	−0.260418	+	0.0846149i	−0.436316	−	0.899793i	$-0.643717\pi$
$983$	−7.88960e6	+	2.56348e6i	−0.260418	+	0.0846149i	0.175898	+	0.984408i	$0.443717\pi$
$984$	3.14049e6	+	4.32251e6i	0.103397	+	0.142314i
$985$	−48169.8	−	34997.4i	−0.00158192	−	0.00114933i
$986$	−8.85196e6	−	1.21837e7i	−0.289966	−	0.399104i
$987$		−	1.50962e7i		−	0.493257i
$988$	−2.40916e6	+	1.75036e6i	−0.0785188	+	0.0570472i
$989$	−1.11903e7			−0.363792
$990$	3996.58			0.000129599
$991$	4.34489e6	−	3.15675e6i	0.140538	−	0.102107i	−0.515295	−	0.857013i	$-0.672318\pi$
$991$	4.34489e6	−	3.15675e6i	0.140538	−	0.102107i	0.655833	+	0.754906i	$0.272318\pi$
$992$	−2.16313e7	−	6.65743e7i	−0.697917	−	2.14797i
$993$	6.53813e6	−	8.99897e6i	0.210417	−	0.289614i
$994$	4.93191e7	+	6.78819e7i	1.58325	+	2.17915i
$995$	−2234.96	+	6878.49i	−7.15668e−5	+	0.000220260i
$996$	−1.08352e7	−	3.33474e7i	−0.346091	−	1.06516i
$997$			2.57085e7i			0.819103i	0.912287	+	0.409552i	$0.134315\pi$
$997$			2.57085e7i			0.819103i	−0.912287	+	0.409552i	$0.865685\pi$
$998$	3.25427e6	−	1.00156e7i	0.103425	−	0.318311i
$999$	5.63116e6	−	7.75062e6i	0.178519	−	0.245710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.3.5	✓	104
61.41	even	10	inner	61.6.g.a.41.5	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.5	✓	104	1.1	even	1	trivial
61.6.g.a.41.5	yes	104	61.41	even	10	inner

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.28026 - 2.36550i) q^{2} +(4.76030 - 14.6507i) q^{3} +(21.5180 + 15.6337i) q^{4} +(0.187196 + 0.136006i) q^{5} +(-69.3124 + 95.4003i) q^{6} +(234.418 - 76.1672i) q^{7} +(24.3073 + 33.4561i) q^{8} +(4.60899 + 3.34863i) q^{9} +O(q^{10})\)	\(q+(-7.28026 - 2.36550i) q^{2} +(4.76030 - 14.6507i) q^{3} +(21.5180 + 15.6337i) q^{4} +(0.187196 + 0.136006i) q^{5} +(-69.3124 + 95.4003i) q^{6} +(234.418 - 76.1672i) q^{7} +(24.3073 + 33.4561i) q^{8} +(4.60899 + 3.34863i) q^{9} +(-1.04111 - 1.43297i) q^{10} +396.060i q^{11} +(331.477 - 240.832i) q^{12} +679.376 q^{13} -1886.80 q^{14} +(2.88369 - 2.09512i) q^{15} +(-360.836 - 1110.54i) q^{16} +(218.275 - 300.429i) q^{17} +(-25.6334 - 35.2814i) q^{18} +(-50.9256 + 156.733i) q^{19} +(1.90180 + 5.85315i) q^{20} -3796.97i q^{21} +(936.881 - 2883.42i) q^{22} +(1460.57 - 2010.31i) q^{23} +(605.864 - 196.857i) q^{24} +(-965.662 - 2972.00i) q^{25} +(-4946.03 - 1607.06i) q^{26} +(3099.42 - 2251.86i) q^{27} +(6235.00 + 2025.87i) q^{28} +5297.81i q^{29} +(-25.9500 + 8.43167i) q^{30} +(-8742.27 + 2840.53i) q^{31} +7615.23i q^{32} +(5802.56 + 1885.37i) q^{33} +(-2299.76 + 1670.87i) q^{34} +(54.2414 + 17.6241i) q^{35} +(46.8247 + 144.111i) q^{36} +(2378.28 - 772.750i) q^{37} +(741.503 - 1020.59i) q^{38} +(3234.03 - 9953.32i) q^{39} +9.56878i q^{40} +(2591.74 + 7976.56i) q^{41} +(-8981.73 + 27642.9i) q^{42} +(-2647.02 - 3643.31i) q^{43} +(-6191.91 + 8522.43i) q^{44} +(0.407352 + 1.25370i) q^{45} +(-15388.7 + 11180.6i) q^{46} +3975.84 q^{47} -17987.8 q^{48} +(35553.4 - 25831.1i) q^{49} +23921.2i q^{50} +(-3362.44 - 4628.00i) q^{51} +(14618.8 + 10621.2i) q^{52} +(7812.59 + 10753.1i) q^{53} +(-27891.3 + 9062.44i) q^{54} +(-53.8666 + 74.1410i) q^{55} +(8246.33 + 5991.31i) q^{56} +(2053.82 + 1492.19i) q^{57} +(12532.0 - 38569.4i) q^{58} +(-43314.4 - 14073.7i) q^{59} +94.8059 q^{60} +(21237.3 - 19838.7i) q^{61} +70365.2 q^{62} +(1335.49 + 433.926i) q^{63} +(6467.07 - 19903.6i) q^{64} +(127.176 + 92.3991i) q^{65} +(-37784.3 - 27451.9i) q^{66} +(13112.5 - 18047.8i) q^{67} +(9393.67 - 3052.19i) q^{68} +(-22499.6 - 30968.1i) q^{69} +(-353.202 - 256.616i) q^{70} +(-26139.0 - 35977.3i) q^{71} +235.595i q^{72} +(-52710.0 + 38296.1i) q^{73} -19142.4 q^{74} -48138.7 q^{75} +(-3546.14 + 2576.42i) q^{76} +(30166.8 + 92843.9i) q^{77} +(-47089.1 + 64812.6i) q^{78} +(38778.5 + 53374.0i) q^{79} +(83.4927 - 256.964i) q^{80} +(-17809.3 - 54811.4i) q^{81} -64202.2i q^{82} +(26444.9 - 81389.1i) q^{83} +(59360.9 - 81703.2i) q^{84} +(81.7203 - 26.5525i) q^{85} +(10652.7 + 32785.8i) q^{86} +(77616.5 + 25219.1i) q^{87} +(-13250.6 + 9627.15i) q^{88} +(-20842.8 - 6772.22i) q^{89} -10.0908i q^{90} +(159258. - 51746.1i) q^{91} +(62857.3 - 20423.6i) q^{92} +141602. i q^{93} +(-28945.2 - 9404.86i) q^{94} +(-30.8497 + 22.4136i) q^{95} +(111568. + 36250.7i) q^{96} +(-21766.4 - 66990.0i) q^{97} +(-319941. + 103955. i) q^{98} +(-1326.26 + 1825.44i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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