LMFDB - Embedded newform 25.5.f.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58424907710$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	25.2
Dual form			25.5.f.a.13.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.19314 + 0.980897i) q^{2} +(1.94321 + 3.81377i) q^{3} +(22.1759 + 7.20540i) q^{4} +(-22.2324 - 11.4333i) q^{5} +(8.29367 + 25.5253i) q^{6} +(-2.13863 - 2.13863i) q^{7} +(40.8803 + 20.8296i) q^{8} +(36.8419 - 50.7085i) q^{9} +O(q^{10})$	\(q+(6.19314 + 0.980897i) q^{2} +(1.94321 + 3.81377i) q^{3} +(22.1759 + 7.20540i) q^{4} +(-22.2324 - 11.4333i) q^{5} +(8.29367 + 25.5253i) q^{6} +(-2.13863 - 2.13863i) q^{7} +(40.8803 + 20.8296i) q^{8} +(36.8419 - 50.7085i) q^{9} +(-126.474 - 92.6155i) q^{10} +(-100.814 + 73.2454i) q^{11} +(15.6128 + 98.5755i) q^{12} +(192.125 - 30.4296i) q^{13} +(-11.1471 - 15.3426i) q^{14} +(0.401487 - 107.007i) q^{15} +(-69.0776 - 50.1878i) q^{16} +(-151.474 + 297.285i) q^{17} +(277.907 - 277.907i) q^{18} +(-200.631 + 65.1889i) q^{19} +(-410.644 - 413.737i) q^{20} +(4.00043 - 12.3120i) q^{21} +(-696.200 + 354.731i) q^{22} +(51.5687 - 325.592i) q^{23} +196.384i q^{24} +(363.561 + 508.378i) q^{25} +1219.71 q^{26} +(607.417 + 96.2054i) q^{27} +(-32.0164 - 62.8358i) q^{28} +(1243.60 + 404.071i) q^{29} +(107.449 - 662.313i) q^{30} +(415.869 + 1279.91i) q^{31} +(-897.663 - 897.663i) q^{32} +(-475.243 - 242.149i) q^{33} +(-1229.71 + 1692.55i) q^{34} +(23.0954 + 71.9984i) q^{35} +(1182.38 - 859.047i) q^{36} +(-329.367 - 2079.54i) q^{37} +(-1306.48 + 206.926i) q^{38} +(489.391 + 673.589i) q^{39} +(-670.719 - 930.487i) q^{40} +(-388.134 - 281.996i) q^{41} +(36.8520 - 72.3262i) q^{42} +(331.220 - 331.220i) q^{43} +(-2763.40 + 897.883i) q^{44} +(-1398.85 + 706.149i) q^{45} +(638.744 - 1965.85i) q^{46} +(-2773.51 + 1413.17i) q^{47} +(57.1723 - 360.972i) q^{48} -2391.85i q^{49} +(1752.92 + 3505.07i) q^{50} -1428.12 q^{51} +(4479.81 + 709.532i) q^{52} +(-1234.93 - 2423.69i) q^{53} +(3667.45 + 1191.63i) q^{54} +(3078.77 - 475.794i) q^{55} +(-42.8811 - 131.975i) q^{56} +(-638.483 - 638.483i) q^{57} +(7305.45 + 3722.31i) q^{58} +(581.299 - 800.089i) q^{59} +(779.928 - 2370.08i) q^{60} +(-2841.48 + 2064.45i) q^{61} +(1320.07 + 8334.61i) q^{62} +(-187.238 + 29.6555i) q^{63} +(-3875.84 - 5334.63i) q^{64} +(-4619.31 - 1520.09i) q^{65} +(-2705.73 - 1965.83i) q^{66} +(2844.74 - 5583.11i) q^{67} +(-5501.14 + 5501.14i) q^{68} +(1341.94 - 436.023i) q^{69} +(72.4101 + 468.550i) q^{70} +(-2476.20 + 7620.94i) q^{71} +(2562.34 - 1305.58i) q^{72} +(184.881 - 1167.29i) q^{73} -13202.0i q^{74} +(-1232.36 + 2374.42i) q^{75} -4918.89 q^{76} +(372.248 + 58.9583i) q^{77} +(2370.15 + 4651.67i) q^{78} +(10248.4 + 3329.92i) q^{79} +(961.953 + 1905.58i) q^{80} +(-755.447 - 2325.03i) q^{81} +(-2127.16 - 2127.16i) q^{82} +(-3480.73 - 1773.52i) q^{83} +(177.426 - 244.206i) q^{84} +(6766.58 - 4877.52i) q^{85} +(2376.18 - 1726.40i) q^{86} +(875.550 + 5528.00i) q^{87} +(-5646.97 + 894.392i) q^{88} +(-952.885 - 1311.53i) q^{89} +(-9355.91 + 3001.16i) q^{90} +(-475.962 - 345.806i) q^{91} +(3489.60 - 6848.73i) q^{92} +(-4073.17 + 4073.17i) q^{93} +(-18562.9 + 6031.45i) q^{94} +(5205.83 + 844.556i) q^{95} +(1679.13 - 5167.83i) q^{96} +(4680.87 - 2385.02i) q^{97} +(2346.16 - 14813.1i) q^{98} +7810.60i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) $ 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	6.19314	+	0.980897i	1.54829	+	0.245224i	0.871292	−	0.490765i	$-0.163283\pi$
$2$	6.19314	+	0.980897i	1.54829	+	0.245224i	0.676993	+	0.735989i	$0.263283\pi$
$3$	1.94321	+	3.81377i	0.215912	+	0.423752i	0.973405	−	0.229092i	$-0.0735757\pi$
$3$	1.94321	+	3.81377i	0.215912	+	0.423752i	−0.757492	+	0.652844i	$0.773576\pi$
$4$	22.1759	+	7.20540i	1.38600	+	0.450337i
$5$	−22.2324	−	11.4333i	−0.889297	−	0.457330i
$5$	−22.2324	−	11.4333i	−0.889297	−	0.457330i
$6$	8.29367	+	25.5253i	0.230380	+	0.709036i
$7$	−2.13863	−	2.13863i	−0.0436455	−	0.0436455i	0.684947	−	0.728593i	$-0.259825\pi$
$7$	−2.13863	−	2.13863i	−0.0436455	−	0.0436455i	−0.728593	+	0.684947i	$0.759825\pi$
$8$	40.8803	+	20.8296i	0.638755	+	0.325462i
$9$	36.8419	−	50.7085i	0.454838	−	0.626030i
$10$	−126.474	−	92.6155i	−1.26474	−	0.926155i
$11$	−100.814	+	73.2454i	−0.833171	+	0.605334i	−0.920455	−	0.390849i	$-0.872181\pi$
$11$	−100.814	+	73.2454i	−0.833171	+	0.605334i	0.0872838	+	0.996183i	$0.472181\pi$
$12$	15.6128	+	98.5755i	0.108422	+	0.684552i
$13$	192.125	−	30.4296i	1.13683	−	0.180057i	0.440485	−	0.897760i	$-0.354807\pi$
$13$	192.125	−	30.4296i	1.13683	−	0.180057i	0.696349	+	0.717703i	$0.254807\pi$
$14$	−11.1471	−	15.3426i	−0.0568727	−	0.0782786i
$15$	0.401487	−	107.007i	0.00178439	−	0.475585i
$16$	−69.0776	−	50.1878i	−0.269835	−	0.196046i
$17$	−151.474	+	297.285i	−0.524133	+	1.02867i	0.465500	+	0.885048i	$0.345874\pi$
$17$	−151.474	+	297.285i	−0.524133	+	1.02867i	−0.989633	+	0.143620i	$0.954126\pi$
$18$	277.907	−	277.907i	0.857736	−	0.857736i
$19$	−200.631	+	65.1889i	−0.555764	+	0.180579i	−0.573414	−	0.819266i	$-0.694381\pi$
$19$	−200.631	+	65.1889i	−0.555764	+	0.180579i	0.0176503	+	0.999844i	$0.494381\pi$
$20$	−410.644	−	413.737i	−1.02661	−	1.03434i
$21$	4.00043	−	12.3120i	0.00907126	−	0.0279185i
$22$	−696.200	+	354.731i	−1.43843	+	0.732916i
$23$	51.5687	−	325.592i	0.0974833	−	0.615485i	−0.889780	−	0.456390i	$-0.849142\pi$
$23$	51.5687	−	325.592i	0.0974833	−	0.615485i	0.987263	−	0.159095i	$-0.0508578\pi$
$24$			196.384i			0.340945i
$25$	363.561	+	508.378i	0.581698	+	0.813405i
$26$	1219.71			1.80430
$27$	607.417	+	96.2054i	0.833219	+	0.131969i
$28$	−32.0164	−	62.8358i	−0.0408373	−	0.0801477i
$29$	1243.60	+	404.071i	1.47872	+	0.480465i	0.933730	−	0.357979i	$-0.116534\pi$
$29$	1243.60	+	404.071i	1.47872	+	0.480465i	0.544989	+	0.838444i	$0.316534\pi$
$30$	107.449	−	662.313i	0.119388	−	0.735903i
$31$	415.869	+	1279.91i	0.432746	+	1.33186i	0.895378	+	0.445306i	$0.146905\pi$
$31$	415.869	+	1279.91i	0.432746	+	1.33186i	−0.462632	+	0.886550i	$0.653095\pi$
$32$	−897.663	−	897.663i	−0.876624	−	0.876624i
$33$	−475.243	−	242.149i	−0.436403	−	0.222359i
$34$	−1229.71	+	1692.55i	−1.06376	+	1.46414i
$35$	23.0954	+	71.9984i	0.0188534	+	0.0587742i
$36$	1182.38	−	859.047i	0.912328	−	0.662845i
$37$	−329.367	−	2079.54i	−0.240589	−	1.51902i	−0.751700	−	0.659506i	$-0.770766\pi$
$37$	−329.367	−	2079.54i	−0.240589	−	1.51902i	0.511110	−	0.859515i	$-0.329234\pi$
$38$	−1306.48	+	206.926i	−0.904763	+	0.143300i
$39$	489.391	+	673.589i	0.321756	+	0.442859i
$40$	−670.719	−	930.487i	−0.419199	−	0.581554i
$41$	−388.134	−	281.996i	−0.230894	−	0.167755i	0.466323	−	0.884615i	$-0.345579\pi$
$41$	−388.134	−	281.996i	−0.230894	−	0.167755i	−0.697217	+	0.716860i	$0.745579\pi$
$42$	36.8520	−	72.3262i	0.0208912	−	0.0410013i
$43$	331.220	−	331.220i	0.179134	−	0.179134i	−0.611844	−	0.790978i	$-0.709572\pi$
$43$	331.220	−	331.220i	0.179134	−	0.179134i	0.790978	+	0.611844i	$0.209572\pi$
$44$	−2763.40	+	897.883i	−1.42738	+	0.463783i
$45$	−1398.85	+	706.149i	−0.690788	+	0.348716i
$46$	638.744	−	1965.85i	0.301864	−	0.929042i
$47$	−2773.51	+	1413.17i	−1.25555	+	0.639734i	−0.949943	−	0.312424i	$-0.898859\pi$
$47$	−2773.51	+	1413.17i	−1.25555	+	0.639734i	−0.305606	+	0.952158i	$0.598859\pi$
$48$	57.1723	−	360.972i	0.0248144	−	0.156672i
$49$		−	2391.85i		−	0.996190i
$50$	1752.92	+	3505.07i	0.701168	+	1.40203i
$51$	−1428.12			−0.549067
$52$	4479.81	+	709.532i	1.65673	+	0.262401i
$53$	−1234.93	−	2423.69i	−0.439633	−	0.862829i	−0.999415	−	0.0341890i	$-0.989115\pi$
$53$	−1234.93	−	2423.69i	−0.439633	−	0.862829i	0.559782	−	0.828640i	$-0.310885\pi$
$54$	3667.45	+	1191.63i	1.25770	+	0.408651i
$55$	3078.77	−	475.794i	1.01777	−	0.157287i
$56$	−42.8811	−	131.975i	−0.0136738	−	0.0420837i
$57$	−638.483	−	638.483i	−0.196517	−	0.196517i
$58$	7305.45	+	3722.31i	2.17166	+	1.10651i
$59$	581.299	−	800.089i	0.166992	−	0.229845i	−0.717317	−	0.696747i	$-0.754630\pi$
$59$	581.299	−	800.089i	0.166992	−	0.229845i	0.884309	+	0.466902i	$0.154630\pi$
$60$	779.928	−	2370.08i	0.216647	−	0.658355i
$61$	−2841.48	+	2064.45i	−0.763632	+	0.554811i	−0.900022	−	0.435844i	$-0.856450\pi$
$61$	−2841.48	+	2064.45i	−0.763632	+	0.554811i	0.136390	+	0.990655i	$0.456450\pi$
$62$	1320.07	+	8334.61i	0.343411	+	2.16821i
$63$	−187.238	+	29.6555i	−0.0471750	+	0.00747179i
$64$	−3875.84	−	5334.63i	−0.946249	−	1.30240i
$65$	−4619.31	−	1520.09i	−1.09333	−	0.359785i
$66$	−2705.73	−	1965.83i	−0.621149	−	0.451291i
$67$	2844.74	−	5583.11i	0.633713	−	1.24373i	−0.321246	−	0.946996i	$-0.604102\pi$
$67$	2844.74	−	5583.11i	0.633713	−	1.24373i	0.954959	−	0.296736i	$-0.0958982\pi$
$68$	−5501.14	+	5501.14i	−1.18969	+	1.18969i
$69$	1341.94	−	436.023i	0.281861	−	0.0915822i
$70$	72.4101	+	468.550i	0.0147776	+	0.0956225i
$71$	−2476.20	+	7620.94i	−0.491211	+	1.51179i	0.331568	+	0.943431i	$0.392422\pi$
$71$	−2476.20	+	7620.94i	−0.491211	+	1.51179i	−0.822779	+	0.568361i	$0.807578\pi$
$72$	2562.34	−	1305.58i	0.494279	−	0.251848i
$73$	184.881	−	1167.29i	0.0346934	−	0.219046i	−0.964250	−	0.264992i	$-0.914631\pi$
$73$	184.881	−	1167.29i	0.0346934	−	0.219046i	0.998944	+	0.0459470i	$0.0146305\pi$
$74$		−	13202.0i		−	2.41088i
$75$	−1232.36	+	2374.42i	−0.219086	+	0.422120i
$76$	−4918.89			−0.851608
$77$	372.248	+	58.9583i	0.0627842	+	0.00994405i
$78$	2370.15	+	4651.67i	0.389570	+	0.764575i
$79$	10248.4	+	3329.92i	1.64212	+	0.533556i	0.977010	−	0.213193i	$-0.0683864\pi$
$79$	10248.4	+	3329.92i	1.64212	+	0.533556i	0.665106	+	0.746749i	$0.268386\pi$
$80$	961.953	+	1905.58i	0.150305	+	0.297747i
$81$	−755.447	−	2325.03i	−0.115142	−	0.354371i
$82$	−2127.16	−	2127.16i	−0.316353	−	0.316353i
$83$	−3480.73	−	1773.52i	−0.505259	−	0.257442i	0.182730	−	0.983163i	$-0.441506\pi$
$83$	−3480.73	−	1773.52i	−0.505259	−	0.257442i	−0.687989	+	0.725721i	$0.741506\pi$
$84$	177.426	−	244.206i	0.0251455	−	0.0346098i
$85$	6766.58	−	4877.52i	0.936551	−	0.675090i
$86$	2376.18	−	1726.40i	0.321279	−	0.233423i
$87$	875.550	+	5528.00i	0.115676	+	0.730348i
$88$	−5646.97	+	894.392i	−0.729205	+	0.115495i
$89$	−952.885	−	1311.53i	−0.120299	−	0.165577i	0.744621	−	0.667488i	$-0.232630\pi$
$89$	−952.885	−	1311.53i	−0.120299	−	0.165577i	−0.864919	+	0.501911i	$0.832630\pi$
$90$	−9355.91	+	3001.16i	−1.15505	+	0.370513i
$91$	−475.962	−	345.806i	−0.0574763	−	0.0417590i
$92$	3489.60	−	6848.73i	0.412288	−	0.809160i
$93$	−4073.17	+	4073.17i	−0.470942	+	0.470942i
$94$	−18562.9	+	6031.45i	−2.10083	+	0.682600i
$95$	5205.83	+	844.556i	0.576823	+	0.0935797i
$96$	1679.13	−	5167.83i	0.182197	−	0.560745i
$97$	4680.87	−	2385.02i	0.497488	−	0.253483i	−0.187196	−	0.982323i	$-0.559940\pi$
$97$	4680.87	−	2385.02i	0.497488	−	0.253483i	0.684684	+	0.728840i	$0.259940\pi$
$98$	2346.16	−	14813.1i	0.244290	−	1.54239i
$99$			7810.60i			0.796919i
$100$	4399.24	+	13893.4i	0.439924	+	1.38934i
$101$	3939.60			0.386198			0.193099	−	0.981179i	$-0.438146\pi$
$101$	3939.60			0.386198			0.193099	+	0.981179i	$0.438146\pi$
$102$	−8844.57	−	1400.84i	−0.850112	−	0.134645i
$103$	1219.15	+	2392.73i	0.114917	+	0.225537i	0.941300	−	0.337571i	$-0.109605\pi$
$103$	1219.15	+	2392.73i	0.114917	+	0.225537i	−0.826383	+	0.563108i	$0.809605\pi$
$104$	8487.97	+	2757.91i	0.784760	+	0.254984i
$105$	−229.706	+	227.989i	−0.0208350	+	0.0206792i
$106$	−5270.71	−	16221.6i	−0.469091	−	1.44371i
$107$	−643.698	−	643.698i	−0.0562231	−	0.0562231i	0.678436	−	0.734659i	$-0.262658\pi$
$107$	−643.698	−	643.698i	−0.0562231	−	0.0562231i	−0.734659	+	0.678436i	$0.762658\pi$
$108$	12776.8	+	6510.13i	1.09541	+	0.558138i
$109$	−6717.40	+	9245.71i	−0.565390	+	0.778193i	−0.991999	−	0.126243i	$-0.959708\pi$
$109$	−6717.40	+	9245.71i	−0.565390	+	0.778193i	0.426609	+	0.904436i	$0.359708\pi$
$110$	19533.9	+	73.2910i	1.61437	+	0.00605711i
$111$	7290.85	−	5297.11i	0.591742	−	0.429926i
$112$	40.3983	+	255.065i	0.00322052	+	0.0203336i
$113$	−11562.9	+	1831.39i	−0.905548	+	0.143425i	−0.591803	−	0.806083i	$-0.701584\pi$
$113$	−11562.9	+	1831.39i	−0.905548	+	0.143425i	−0.313745	+	0.949507i	$0.601584\pi$
$114$	−3327.93	−	4580.50i	−0.256073	−	0.352455i
$115$	−4869.07	+	6649.10i	−0.368172	+	0.502767i
$116$	24666.5	+	17921.3i	1.83313	+	1.33184i
$117$	5535.20	−	10863.4i	0.404354	−	0.793589i
$118$	4384.87	−	4384.87i	0.314915	−	0.314915i
$119$	959.730	−	311.835i	0.0677728	−	0.0220207i
$120$	2245.31	−	4366.10i	0.155925	−	0.303201i
$121$	274.187	−	843.859i	0.0187273	−	0.0576367i
$122$	−19622.7	+	9998.25i	−1.31837	+	0.671745i
$123$	321.240	−	2028.23i	0.0212334	−	0.134062i
$124$			31379.8i			2.04083i
$125$	−2270.43	−	15459.2i	−0.145307	−	0.989387i
$126$	−1188.68			−0.0748726
$127$	3325.82	+	526.759i	0.206202	+	0.0326591i	0.258681	−	0.965963i	$-0.416712\pi$
$127$	3325.82	+	526.759i	0.206202	+	0.0326591i	−0.0524791	+	0.998622i	$0.516712\pi$
$128$	−9549.51	−	18742.0i	−0.582856	−	1.14392i
$129$	1906.82	+	619.565i	0.114586	+	0.0372312i
$130$	−27117.0	−	13945.2i	−1.60456	−	0.825160i
$131$	7520.16	+	23144.7i	0.438212	+	1.34868i	0.889759	+	0.456431i	$0.150873\pi$
$131$	7520.16	+	23144.7i	0.438212	+	1.34868i	−0.451546	+	0.892248i	$0.649127\pi$
$132$	−8794.19	−	8794.19i	−0.504717	−	0.504717i
$133$	568.490	+	289.660i	0.0321380	+	0.0163751i
$134$	23094.3	−	31786.6i	1.28616	−	1.77025i
$135$	−12404.4	−	9083.63i	−0.680626	−	0.498416i
$136$	−12384.6	+	8997.97i	−0.669585	+	0.486482i
$137$	−1293.39	−	8166.17i	−0.0689112	−	0.435088i	−0.997888	−	0.0649512i	$-0.979311\pi$
$137$	−1293.39	−	8166.17i	−0.0689112	−	0.435088i	0.928977	−	0.370137i	$-0.120689\pi$
$138$	8738.52	−	1384.05i	0.458859	−	0.0726762i
$139$	−927.672	−	1276.83i	−0.0480137	−	0.0660851i	0.784335	−	0.620337i	$-0.213004\pi$
$139$	−927.672	−	1276.83i	−0.0480137	−	0.0660851i	−0.832349	+	0.554252i	$0.813004\pi$
$140$	−6.61491	+	1763.04i	−0.000337495	+	0.0899512i
$141$	−10779.0	−	7831.42i	−0.542177	−	0.393915i
$142$	−22810.8	+	44768.7i	−1.13126	+	2.22023i
$143$	−17140.0	+	17140.0i	−0.838182	+	0.838182i
$144$	−5089.90	+	1653.81i	−0.245462	+	0.0797554i
$145$	−23028.4	−	23201.9i	−1.09529	−	1.10354i
$146$	2289.99	−	7047.86i	0.107431	−	0.330637i
$147$	9121.97	−	4647.88i	0.422138	−	0.215090i
$148$	7679.89	−	48488.9i	0.350616	−	2.21370i
$149$			6509.98i			0.293229i	0.989194	+	0.146615i	$0.0468377\pi$
$149$			6509.98i			0.293229i	−0.989194	+	0.146615i	$0.953162\pi$
$150$	−9961.24	+	13496.3i	−0.442722	+	0.599837i
$151$	10040.0			0.440330			0.220165	−	0.975463i	$-0.429340\pi$
$151$	10040.0			0.440330			0.220165	+	0.975463i	$0.429340\pi$
$152$	−9559.71	−	1514.11i	−0.413769	−	0.0655345i
$153$	9494.28	+	18633.6i	0.405582	+	0.796000i
$154$	2247.55	+	730.274i	0.0947694	+	0.0307924i
$155$	5387.81	−	33210.3i	0.224258	−	1.38232i
$156$	5999.23	+	18463.7i	0.246517	+	0.758700i
$157$	32517.7	+	32517.7i	1.31923	+	1.31923i	0.914386	+	0.404844i	$0.132674\pi$
$157$	32517.7	+	32517.7i	1.31923	+	1.31923i	0.404844	+	0.914386i	$0.367326\pi$
$158$	60203.8	+	30675.3i	2.41162	+	1.22878i
$159$	6843.65	−	9419.47i	0.270703	−	0.372591i
$160$	9694.02	+	30220.5i	0.378672	+	1.18049i
$161$	−806.606	+	586.034i	−0.0311179	+	0.0226085i
$162$	−2397.98	−	15140.2i	−0.0913724	−	0.576903i
$163$	21931.6	−	3473.62i	0.825458	−	0.130740i	0.270608	−	0.962690i	$-0.412775\pi$
$163$	21931.6	−	3473.62i	0.825458	−	0.130740i	0.554851	+	0.831950i	$0.312775\pi$
$164$	−6575.34	−	9050.17i	−0.244473	−	0.336488i
$165$	7797.26	+	10817.1i	0.286401	+	0.397323i
$166$	−19817.0	−	14397.9i	−0.719154	−	0.522496i
$167$	−14363.4	+	28189.8i	−0.515020	+	1.01078i	0.476296	+	0.879285i	$0.341979\pi$
$167$	−14363.4	+	28189.8i	−0.515020	+	1.01078i	−0.991316	+	0.131499i	$0.958021\pi$
$168$	419.993	−	419.993i	0.0148807	−	0.0148807i
$169$	8822.91	−	2866.74i	0.308915	−	0.100372i
$170$	46690.7	−	23569.9i	1.61560	−	0.815566i
$171$	−4085.98	+	12575.4i	−0.139735	+	0.430059i
$172$	9731.67	−	4958.54i	0.328951	−	0.167609i
$173$	3325.94	−	20999.2i	0.111128	−	0.701633i	−0.867722	−	0.497051i	$-0.834416\pi$
$173$	3325.94	−	20999.2i	0.111128	−	0.701633i	0.978849	−	0.204583i	$-0.0655837\pi$
$174$			35094.5i			1.15915i
$175$	309.709	−	1864.75i	0.0101130	−	0.0608899i
$176$	10640.0			0.343492
$177$	4180.94	+	662.196i	0.133453	+	0.0211368i
$178$	−4614.87	−	9057.19i	−0.145653	−	0.285860i
$179$	−49064.4	−	15942.0i	−1.53130	−	0.497550i	−0.582340	−	0.812945i	$-0.697863\pi$
$179$	−49064.4	−	15942.0i	−1.53130	−	0.497550i	−0.948960	+	0.315395i	$0.897863\pi$
$180$	−36108.8	+	5580.28i	−1.11447	+	0.172231i
$181$	−10901.1	−	33550.0i	−0.332745	−	1.02408i	−0.967822	−	0.251635i	$-0.919032\pi$
$181$	−10901.1	−	33550.0i	−0.332745	−	1.02408i	0.635078	−	0.772448i	$-0.280968\pi$
$182$	−2608.50	−	2608.50i	−0.0787495	−	0.0787495i
$183$	−13394.9	−	6825.06i	−0.399980	−	0.203800i
$184$	8890.08	−	12236.1i	0.262585	−	0.361417i
$185$	−16453.3	+	49998.9i	−0.480739	+	1.46089i
$186$	−29221.1	+	21230.4i	−0.844638	+	0.613666i
$187$	−6504.09	−	41065.2i	−0.185996	−	1.17433i
$188$	−71687.6	+	11354.2i	−2.02828	+	0.321248i
$189$	−1093.29	−	1504.79i	−0.0306064	−	0.0421261i
$190$	31412.0	+	10336.8i	0.870139	+	0.286339i
$191$	−15633.6	−	11358.5i	−0.428542	−	0.311354i	0.352524	−	0.935803i	$-0.385324\pi$
$191$	−15633.6	−	11358.5i	−0.428542	−	0.311354i	−0.781066	+	0.624449i	$0.785324\pi$
$192$	12813.5	−	25147.9i	0.347588	−	0.682179i
$193$	−18800.5	+	18800.5i	−0.504725	+	0.504725i	−0.912903	−	0.408177i	$-0.866165\pi$
$193$	−18800.5	+	18800.5i	−0.504725	+	0.504725i	0.408177	+	0.912903i	$0.366165\pi$
$194$	31328.7	−	10179.3i	0.832414	−	0.270468i
$195$	−3179.03	−	20570.8i	−0.0836037	−	0.540982i
$196$	17234.3	−	53041.6i	0.448622	−	1.38072i
$197$	21206.0	−	10805.0i	0.546421	−	0.278415i	−0.158911	−	0.987293i	$-0.550798\pi$
$197$	21206.0	−	10805.0i	0.546421	−	0.278415i	0.705331	+	0.708878i	$0.250798\pi$
$198$	−7661.40	+	48372.2i	−0.195424	+	1.23386i
$199$			42236.0i			1.06654i	0.845945	+	0.533269i	$0.179037\pi$
$199$			42236.0i			1.06654i	−0.845945	+	0.533269i	$0.820963\pi$
$200$	4273.21	+	28355.5i	0.106830	+	0.708887i
$201$	26820.6			0.663860
$202$	24398.5	+	3864.35i	0.597944	+	0.0947051i
$203$	−1795.45	−	3523.76i	−0.0435693	−	0.0855095i
$204$	−31670.0	−	10290.2i	−0.761005	−	0.247265i
$205$	5405.02	+	10707.1i	0.128614	+	0.254779i
$206$	5203.38	+	16014.4i	0.122617	+	0.377377i
$207$	−14610.4	−	14610.4i	−0.340973	−	0.340973i
$208$	−14798.7	−	7540.33i	−0.342057	−	0.174287i
$209$	15451.5	−	21267.2i	0.353736	−	0.486876i
$210$	−1646.23	+	1186.65i	−0.0373296	+	0.0269081i
$211$	32559.7	−	23656.0i	0.731333	−	0.531345i	−0.158652	−	0.987335i	$-0.550715\pi$
$211$	32559.7	−	23656.0i	0.731333	−	0.531345i	0.889985	+	0.455990i	$0.150715\pi$
$212$	−9922.10	−	62645.7i	−0.220766	−	1.39386i
$213$	−33876.3	+	5365.48i	−0.746684	+	0.118263i
$214$	−3355.11	−	4617.92i	−0.0732622	−	0.100837i
$215$	−11150.7	+	3576.90i	−0.241227	+	0.0773801i
$216$	22827.5	+	16585.1i	0.489272	+	0.355477i
$217$	1847.87	−	3626.65i	0.0392421	−	0.0770170i
$218$	−50670.9	+	50670.9i	−1.06622	+	1.06622i
$219$	4811.05	−	1563.20i	0.100312	−	0.0325932i
$220$	71702.8	+	11632.5i	1.48146	+	0.240342i
$221$	−20055.7	+	61725.2i	−0.410633	+	1.26380i
$222$	50349.2	−	25654.2i	1.02161	−	0.520538i
$223$	4502.07	−	28425.0i	0.0905322	−	0.571598i	−0.900169	−	0.435541i	$-0.856557\pi$
$223$	4502.07	−	28425.0i	0.0905322	−	0.571598i	0.990701	−	0.136057i	$-0.0434429\pi$
$224$			3839.54i			0.0765214i
$225$	39173.3	+	293.960i	0.773794	+	0.00580661i
$226$	−73407.3			−1.43722
$227$	−43240.5	−	6848.63i	−0.839150	−	0.132908i	−0.277957	−	0.960594i	$-0.589657\pi$
$227$	−43240.5	−	6848.63i	−0.839150	−	0.132908i	−0.561193	+	0.827685i	$0.689657\pi$
$228$	−9558.44	−	18759.5i	−0.183873	−	0.360871i
$229$	−9233.67	−	3000.20i	−0.176077	−	0.0572110i	0.219652	−	0.975578i	$-0.429508\pi$
$229$	−9233.67	−	3000.20i	−0.176077	−	0.0572110i	−0.395729	+	0.918367i	$0.629508\pi$
$230$	−36676.9	+	36402.7i	−0.693326	+	0.688142i
$231$	498.503	+	1534.23i	0.00934209	+	0.0287520i
$232$	42422.2	+	42422.2i	0.788166	+	0.788166i
$233$	24448.0	+	12456.9i	0.450331	+	0.229455i	0.664420	−	0.747359i	$-0.268679\pi$
$233$	24448.0	+	12456.9i	0.450331	+	0.229455i	−0.214090	+	0.976814i	$0.568679\pi$
$234$	44936.2	−	61849.4i	0.820663	−	1.12955i
$235$	77819.0	+	291.975i	1.40913	+	0.00528702i
$236$	18655.8	−	13554.2i	0.334958	−	0.243361i
$237$	7215.35	+	45555.9i	0.128458	+	0.811051i
$238$	6249.62	−	989.843i	0.110332	−	0.0174748i
$239$	−6409.43	−	8821.83i	−0.112208	−	0.154441i	0.749219	−	0.662322i	$-0.230429\pi$
$239$	−6409.43	−	8821.83i	−0.112208	−	0.154441i	−0.861427	+	0.507881i	$0.830429\pi$
$240$	−5398.16	+	7371.61i	−0.0937181	+	0.127979i
$241$	−33377.6	−	24250.2i	−0.574673	−	0.417524i	0.262127	−	0.965033i	$-0.415576\pi$
$241$	−33377.6	−	24250.2i	−0.574673	−	0.417524i	−0.836800	+	0.547509i	$0.815576\pi$
$242$	2525.82	−	4957.19i	0.0431292	−	0.0846457i
$243$	42623.0	−	42623.0i	0.721824	−	0.721824i
$244$	−77887.6	+	25307.2i	−1.30824	+	0.425074i
$245$	−27346.7	+	53176.7i	−0.455588	+	0.885909i
$246$	3978.97	−	12246.0i	0.0657507	−	0.202360i
$247$	−36562.5	+	18629.5i	−0.599297	+	0.305357i
$248$	−9659.19	+	60985.7i	−0.157050	+	0.991573i
$249$		−	16721.0i		−	0.269690i
$250$	1102.76	−	97967.8i	0.0176442	−	1.56749i
$251$	−56349.4			−0.894421			−0.447210	−	0.894429i	$-0.647582\pi$
$251$	−56349.4			−0.894421			−0.447210	+	0.894429i	$0.647582\pi$
$252$	−4365.85	−	691.483i	−0.0687492	−	0.0108888i
$253$	18649.3	+	36601.3i	0.291354	+	0.571814i
$254$	20080.6	+	6524.58i	0.311250	+	0.101131i
$255$	31750.6	+	16328.1i	0.488284	+	0.251105i
$256$	−8155.15	−	25099.0i	−0.124438	−	0.382980i
$257$	28705.4	+	28705.4i	0.434607	+	0.434607i	0.890192	−	0.455585i	$-0.150570\pi$
$257$	28705.4	+	28705.4i	0.434607	+	0.434607i	−0.455585	+	0.890192i	$0.650570\pi$
$258$	11201.5	+	5707.45i	0.168282	+	0.0857438i
$259$	−3742.97	+	5151.76i	−0.0557978	+	0.0767990i
$260$	−91484.7	−	66993.4i	−1.35332	−	0.991027i
$261$	66306.4	−	48174.4i	0.973362	−	0.707189i
$262$	23870.9	+	150715.i	0.347749	+	2.19560i
$263$	129573.	−	20522.3i	1.87328	−	0.296699i	0.886999	−	0.461771i	$-0.152786\pi$
$263$	129573.	−	20522.3i	1.87328	−	0.296699i	0.986281	+	0.165072i	$0.0527857\pi$
$264$	−14384.3	−	19798.2i	−0.206386	−	0.284065i
$265$	−255.149	+	68003.7i	−0.00363330	+	0.968369i
$266$	3236.61	+	2351.53i	0.0457433	+	0.0332344i
$267$	3150.23	−	6182.67i	0.0441895	−	0.0867268i
$268$	103313.	−	103313.i	1.43842	−	1.43842i
$269$	74693.6	−	24269.4i	1.03224	−	0.335394i	0.256562	−	0.966528i	$-0.417410\pi$
$269$	74693.6	−	24269.4i	1.03224	−	0.335394i	0.775674	+	0.631134i	$0.217410\pi$
$270$	−67912.1	−	68423.7i	−0.931580	−	0.938596i
$271$	−36975.9	+	113800.i	−0.503477	+	1.54954i	0.299838	+	0.953990i	$0.403067\pi$
$271$	−36975.9	+	113800.i	−0.503477	+	1.54954i	−0.803315	+	0.595554i	$0.796933\pi$
$272$	25383.6	−	12933.6i	0.343096	−	0.174816i
$273$	393.931	−	2487.18i	0.00528561	−	0.0333720i
$274$		−	51842.9i		−	0.690539i
$275$	−73888.3	−	24622.3i	−0.977035	−	0.325584i
$276$	32900.5			0.431901
$277$	−93223.0	−	14765.1i	−1.21496	−	0.192432i	−0.484136	−	0.874993i	$-0.660866\pi$
$277$	−93223.0	−	14765.1i	−1.21496	−	0.192432i	−0.730829	+	0.682561i	$0.760866\pi$
$278$	−4492.76	−	8817.55i	−0.0581332	−	0.114093i
$279$	80223.9	+	26066.3i	1.03061	+	0.334866i
$280$	−555.548	+	3424.39i	−0.00708607	+	0.0436784i
$281$	−8437.50	−	25967.9i	−0.106856	−	0.328870i	0.883305	−	0.468798i	$-0.155313\pi$
$281$	−8437.50	−	25967.9i	−0.106856	−	0.328870i	−0.990162	+	0.139928i	$0.955313\pi$
$282$	−59074.2	−	59074.2i	−0.742848	−	0.742848i
$283$	−75672.6	−	38557.1i	−0.944856	−	0.481428i	−0.0875071	−	0.996164i	$-0.527890\pi$
$283$	−75672.6	−	38557.1i	−0.944856	−	0.481428i	−0.857349	+	0.514736i	$0.827890\pi$
$284$	−109824.	+	151160.i	−1.36163	+	1.87413i
$285$	6895.09	+	21495.0i	0.0848887	+	0.264635i
$286$	−122963.	+	89337.8i	−1.50329	+	1.09220i
$287$	226.990	+	1433.16i	0.00275577	+	0.0173992i
$288$	−78590.7	+	12447.5i	−0.947515	+	0.150072i
$289$	−16341.6	−	22492.2i	−0.195658	−	0.269300i
$290$	−119860.	−	166281.i	−1.42520	−	1.97718i
$291$	18191.8	+	13217.1i	0.214828	+	0.156082i
$292$	12510.7	−	24553.7i	0.146729	−	0.287972i
$293$	−25202.4	+	25202.4i	−0.293567	+	0.293567i	−0.838488	−	0.544921i	$-0.816560\pi$
$293$	−25202.4	+	25202.4i	−0.293567	+	0.293567i	0.544921	+	0.838488i	$0.316560\pi$
$294$	61052.7	−	19837.2i	0.706335	−	0.229502i
$295$	−22071.3	+	11141.8i	−0.253620	+	0.128030i
$296$	29851.3	−	91872.8i	0.340706	−	1.04858i
$297$	−68282.5	+	34791.7i	−0.774099	+	0.394423i
$298$	−6385.62	+	40317.2i	−0.0719069	+	0.454003i
$299$		−	64123.5i		−	0.717257i
$300$	−44437.4	+	43775.4i	−0.493749	+	0.486394i
$301$	−1416.71			−0.0156368
$302$	62178.9	+	9848.17i	0.681756	+	0.107980i
$303$	7655.48	+	15024.7i	0.0833849	+	0.163652i
$304$	17130.8	+	5566.13i	0.185366	+	0.0602291i
$305$	86776.3	−	13410.5i	0.932828	−	0.144160i
$306$	40521.8	+	124713.i	0.432759	+	1.33189i
$307$	−54254.3	−	54254.3i	−0.575648	−	0.575648i	0.358053	−	0.933701i	$-0.383441\pi$
$307$	−54254.3	−	54254.3i	−0.575648	−	0.575648i	−0.933701	+	0.358053i	$0.883441\pi$
$308$	7830.13	+	3989.65i	0.0825405	+	0.0420565i
$309$	−6756.22	+	9299.14i	−0.0707599	+	0.0973926i
$310$	65943.4	−	200391.i	0.686195	−	2.08524i
$311$	106811.	−	77602.6i	1.10432	−	0.802335i	0.122559	−	0.992461i	$-0.460890\pi$
$311$	106811.	−	77602.6i	1.10432	−	0.802335i	0.981760	+	0.190126i	$0.0608898\pi$
$312$	5975.90	+	37730.3i	0.0613895	+	0.387598i
$313$	83664.4	−	13251.1i	0.853989	−	0.135259i	0.285934	−	0.958249i	$-0.407696\pi$
$313$	83664.4	−	13251.1i	0.853989	−	0.135259i	0.568055	+	0.822991i	$0.307696\pi$
$314$	169490.	+	233283.i	1.71904	+	2.36605i
$315$	4501.81	+	1481.42i	0.0453697	+	0.0149299i
$316$	203275.	+	147688.i	2.03569	+	1.47901i
$317$	45837.7	−	89961.6i	0.456147	−	0.895239i	−0.542335	−	0.840162i	$-0.682460\pi$
$317$	45837.7	−	89961.6i	0.456147	−	0.895239i	0.998482	−	0.0550766i	$-0.0175403\pi$
$318$	51623.2	−	51623.2i	0.510494	−	0.510494i
$319$	−154968.	+	50352.3i	−1.52287	+	0.494809i
$320$	25177.0	+	162915.i	0.245869	+	1.59097i
$321$	1204.07	−	3705.76i	0.0116854	−	0.0359639i
$322$	−5570.27	+	2838.19i	−0.0537235	+	0.0273735i
$323$	11010.7	−	69519.0i	0.105538	−	0.666344i
$324$		−	57002.9i		−	0.543009i
$325$	85318.9	+	86609.1i	0.807753	+	0.819968i
$326$	139233.			1.31011
$327$	−48314.3	−	7652.23i	−0.451835	−	0.0715637i
$328$	−9993.18	−	19612.7i	−0.0928873	−	0.182302i
$329$	8953.76	+	2909.25i	0.0827206	+	0.0268775i
$330$	37679.1	+	74640.3i	0.345997	+	0.685402i
$331$	−32584.9	−	100286.i	−0.297413	−	0.915344i	−0.982400	−	0.186788i	$-0.940192\pi$
$331$	−32584.9	−	100286.i	−0.297413	−	0.915344i	0.684987	−	0.728555i	$-0.259808\pi$
$332$	−64409.5	−	64409.5i	−0.584351	−	0.584351i
$333$	−117585.	−	59912.4i	−1.06038	−	0.540292i
$334$	−116606.	+	160494.i	−1.04527	+	1.43869i
$335$	−127079.	+	91601.5i	−1.13236	+	0.816231i
$336$	−894.255	+	649.714i	−0.00792105	+	0.00575498i
$337$	9275.71	+	58564.5i	0.0816746	+	0.515673i	0.994278	+	0.106827i	$0.0340690\pi$
$337$	9275.71	+	58564.5i	0.0816746	+	0.515673i	−0.912603	+	0.408847i	$0.865931\pi$
$338$	57453.5	−	9099.74i	0.502902	−	0.0796518i
$339$	−29453.7	−	40539.6i	−0.256295	−	0.352760i
$340$	185200.	−	59407.7i	1.60207	−	0.513908i
$341$	−135673.	−	98572.3i	−1.16677	−	0.847708i
$342$	−37640.2	+	73873.0i	−0.321810	+	0.631588i
$343$	−10250.1	+	10250.1i	−0.0871247	+	0.0871247i
$344$	20439.5	−	6641.21i	0.172725	−	0.0561216i
$345$	−34819.7	−	5648.91i	−0.292541	−	0.0474598i
$346$	41196.1	−	126788.i	0.344115	−	1.05908i
$347$	−143215.	+	72971.9i	−1.18941	+	0.606034i	−0.932769	−	0.360474i	$-0.882615\pi$
$347$	−143215.	+	72971.9i	−1.18941	+	0.606034i	−0.256639	+	0.966507i	$0.582615\pi$
$348$	−20415.3	+	128897.i	−0.168577	+	1.06435i
$349$		−	105872.i		−	0.869221i	−0.900618	−	0.434611i	$-0.856886\pi$
$349$		−	105872.i		−	0.869221i	0.900618	−	0.434611i	$-0.143114\pi$
$350$	3747.21	−	11244.9i	0.0305894	−	0.0917951i
$351$	119627.			0.970994
$352$	156246.	+	24747.0i	1.26103	+	0.199727i
$353$	−27761.8	−	54485.6i	−0.222791	−	0.437252i	0.752372	−	0.658738i	$-0.228909\pi$
$353$	−27761.8	−	54485.6i	−0.222791	−	0.437252i	−0.975164	+	0.221486i	$0.928909\pi$
$354$	25243.6	+	8202.15i	0.201440	+	0.0654517i
$355$	142184.	−	141121.i	1.12822	−	1.11979i
$356$	−11681.0	−	35950.4i	−0.0921679	−	0.283664i
$357$	3054.23	+	3054.23i	0.0239643	+	0.0239643i
$358$	−288225.	−	146858.i	−2.24888	−	1.14586i
$359$	−132672.	+	182607.i	−1.02941	+	1.41687i	−0.124027	+	0.992279i	$0.539581\pi$
$359$	−132672.	+	182607.i	−1.02941	+	1.41687i	−0.905387	+	0.424588i	$0.860419\pi$
$360$	−71894.1	−	269.745i	−0.554738	−	0.00208137i
$361$	−69428.8	+	50443.0i	−0.532752	+	0.387067i
$362$	−34602.7	−	218473.i	−0.264054	−	1.66717i
$363$	3751.09	−	594.114i	0.0284671	−	0.00450875i
$364$	−8063.22	−	11098.1i	−0.0608563	−	0.0837616i
$365$	−17456.3	+	23838.0i	−0.131029	+	0.178930i
$366$	−76262.0	−	55407.6i	−0.569307	−	0.413625i
$367$	8289.08	−	16268.2i	0.0615424	−	0.120784i	−0.858186	−	0.513338i	$-0.828409\pi$
$367$	8289.08	−	16268.2i	0.0615424	−	0.120784i	0.919729	+	0.392555i	$0.128409\pi$
$368$	−19903.0	+	19903.0i	−0.146968	+	0.146968i
$369$	−28599.1	+	9292.42i	−0.210039	+	0.0682458i
$370$	−150941.	+	293511.i	−1.10257	+	2.14398i
$371$	−2542.31	+	7824.42i	−0.0184706	+	0.0568466i
$372$	−119675.	+	60977.6i	−0.864806	+	0.440640i
$373$	2835.53	−	17902.8i	0.0203806	−	0.128678i	−0.975400	−	0.220441i	$-0.929250\pi$
$373$	2835.53	−	17902.8i	0.0203806	−	0.128678i	0.995781	+	0.0917632i	$0.0292503\pi$
$374$		−	260702.i		−	1.86381i
$375$	54545.7	−	38699.3i	0.387881	−	0.275195i
$376$	−142818.			−1.01020
$377$	251223.	+	39789.8i	1.76757	+	0.279955i
$378$	−5294.87	−	10391.8i	−0.0370571	−	0.0727287i
$379$	10882.5	+	3535.94i	0.0757619	+	0.0246165i	0.346653	−	0.937994i	$-0.387318\pi$
$379$	10882.5	+	3535.94i	0.0757619	+	0.0246165i	−0.270891	+	0.962610i	$0.587318\pi$
$380$	109359.	+	56238.9i	0.757332	+	0.389466i
$381$	4453.85	+	13707.5i	0.0306821	+	0.0944298i
$382$	−85679.8	−	85679.8i	−0.587153	−	0.587153i
$383$	255506.	+	130187.i	1.74182	+	0.887503i	0.966786	+	0.255587i	$0.0822687\pi$
$383$	255506.	+	130187.i	1.74182	+	0.887503i	0.775037	+	0.631916i	$0.217731\pi$
$384$	52920.8	−	72839.2i	0.358892	−	0.493972i
$385$	−7601.89	−	5566.79i	−0.0512861	−	0.0375563i
$386$	−134876.	+	97992.9i	−0.905230	+	0.657688i
$387$	−4592.89	−	28998.4i	−0.0306665	−	0.193621i
$388$	120988.	−	19162.6i	0.803670	−	0.127289i
$389$	940.872	+	1295.00i	0.00621772	+	0.00855796i	0.812115	−	0.583498i	$-0.198316\pi$
$389$	940.872	+	1295.00i	0.00621772	+	0.00855796i	−0.805897	+	0.592056i	$0.798316\pi$
$390$	489.696	−	130516.i	0.00321956	−	0.858096i
$391$	88982.3	+	64649.4i	0.582036	+	0.422874i
$392$	49821.3	−	97779.7i	0.324222	−	0.636322i
$393$	−73655.2	+	73655.2i	−0.476890	+	0.476890i
$394$	141931.	−	46116.1i	0.914290	−	0.297071i
$395$	−189776.	−	191205.i	−1.21632	−	1.22548i
$396$	−56278.5	+	173207.i	−0.358882	+	1.10453i
$397$	43471.3	−	22149.7i	0.275817	−	0.140536i	−0.310611	−	0.950537i	$-0.600534\pi$
$397$	43471.3	−	22149.7i	0.275817	−	0.140536i	0.586428	+	0.810001i	$0.300534\pi$
$398$	−41429.2	+	261574.i	−0.261541	+	1.65131i
$399$			2730.96i			0.0171542i
$400$	400.447	−	53363.9i	0.00250279	−	0.333524i
$401$	−35418.9			−0.220265			−0.110133	−	0.993917i	$-0.535128\pi$
$401$	−35418.9			−0.220265			−0.110133	+	0.993917i	$0.535128\pi$
$402$	166104.	+	26308.3i	1.02785	+	0.162795i
$403$	118846.	+	233249.i	0.731771	+	1.43618i
$404$	87364.4	+	28386.4i	0.535268	+	0.173919i
$405$	−9787.21	+	60328.2i	−0.0596690	+	0.367799i
$406$	−7663.00	−	23584.3i	−0.0464886	−	0.143077i
$407$	185521.	+	185521.i	1.11997	+	1.11997i
$408$	−58382.1	−	29747.2i	−0.350719	−	0.178700i
$409$	144541.	−	198944.i	0.864061	−	1.18928i	−0.116525	−	0.993188i	$-0.537176\pi$
$409$	144541.	−	198944.i	0.864061	−	1.18928i	0.980586	−	0.196090i	$-0.0628244\pi$
$410$	22971.5	+	71612.2i	0.136654	+	0.426010i
$411$	28630.5	−	20801.3i	0.169491	−	0.123142i
$412$	9795.35	+	61845.4i	0.0577066	+	0.364345i
$413$	−2954.28	+	467.912i	−0.0173201	+	0.00274324i
$414$	−76152.8	−	104815.i	−0.444309	−	0.611539i
$415$	57108.0	+	79225.8i	0.331589	+	0.460013i
$416$	−199779.	−	145148.i	−1.15442	−	0.838734i
$417$	3066.87	−	6019.08i	0.0176370	−	0.0346145i
$418$	116555.	−	116555.i	0.667078	−	0.667078i
$419$	36762.5	−	11944.9i	0.209400	−	0.0680382i	−0.202439	−	0.979295i	$-0.564887\pi$
$419$	36762.5	−	11944.9i	0.209400	−	0.0680382i	0.411839	+	0.911257i	$0.364887\pi$
$420$	−6736.69	+	3400.74i	−0.0381899	+	0.0192786i
$421$	39708.3	−	122210.i	0.224036	−	0.689511i	−0.774352	−	0.632755i	$-0.781924\pi$
$421$	39708.3	−	122210.i	0.224036	−	0.689511i	0.998388	−	0.0567566i	$-0.0180759\pi$
$422$	224851.	−	114567.i	1.26261	−	0.643332i
$423$	−30521.3	+	192704.i	−0.170578	+	1.07699i
$424$		−	124804.i		−	0.694220i
$425$	−206203.	+	31075.1i	−1.14161	+	0.172042i
$426$	−215064.			−1.18508
$427$	10492.0	+	1661.76i	0.0575441	+	0.00911409i
$428$	−9636.51	−	18912.7i	−0.0526056	−	0.103244i
$429$	−98674.6	−	32061.3i	−0.536155	−	0.174207i
$430$	−72566.6	+	11214.5i	−0.392464	+	0.0606517i
$431$	84616.2	+	260422.i	0.455511	+	1.40192i	0.870534	+	0.492108i	$0.163773\pi$
$431$	84616.2	+	260422.i	0.455511	+	1.40192i	−0.415023	+	0.909811i	$0.636227\pi$
$432$	−37130.6	−	37130.6i	−0.198959	−	0.198959i
$433$	−244651.	−	124656.i	−1.30488	−	0.664871i	−0.343259	−	0.939241i	$-0.611531\pi$
$433$	−244651.	−	124656.i	−1.30488	−	0.664871i	−0.961624	+	0.274370i	$0.911531\pi$
$434$	15001.5	−	20647.8i	0.0796444	−	0.109621i
$435$	43737.5	−	132911.i	0.231140	−	0.702398i
$436$	−215584.	+	156631.i	−1.13408	+	0.823956i
$437$	10878.7	+	68685.4i	0.0569658	+	0.359668i
$438$	31328.9	−	4962.00i	0.163304	−	0.0258648i
$439$	78623.3	+	108216.i	0.407964	+	0.561515i	0.962720	−	0.270498i	$-0.0871885\pi$
$439$	78623.3	+	108216.i	0.407964	+	0.561515i	−0.554756	+	0.832013i	$0.687188\pi$
$440$	135772.	+	44678.7i	0.701299	+	0.230779i
$441$	−121287.	−	88120.3i	−0.623645	−	0.453105i
$442$	−184754.	+	362600.i	−0.945691	+	1.85602i
$443$	171957.	−	171957.i	0.876220	−	0.876220i	−0.116921	−	0.993141i	$-0.537303\pi$
$443$	171957.	−	171957.i	0.876220	−	0.876220i	0.993141	+	0.116921i	$0.0373025\pi$
$444$	199849.	−	64935.0i	1.01376	−	0.329392i
$445$	6189.84	+	40053.1i	0.0312579	+	0.202263i
$446$	55764.0	−	171624.i	0.280339	−	0.862795i
$447$	−24827.6	+	12650.3i	−0.124256	+	0.0633118i
$448$	−3119.82	+	19697.8i	−0.0155444	+	0.0981434i
$449$		−	139031.i		−	0.689634i	−0.938670	−	0.344817i	$-0.887941\pi$
$449$		−	139031.i		−	0.689634i	0.938670	−	0.344817i	$-0.112059\pi$
$450$	242318.	+	40245.6i	1.19663	+	0.198743i
$451$	59784.1			0.293922
$452$	−269615.	−	42702.8i	−1.31967	−	0.209016i
$453$	19509.8	+	38290.1i	0.0950727	+	0.186591i
$454$	−261077.	−	84829.0i	−1.26665	−	0.411560i
$455$	6628.09	+	13129.9i	0.0320159	+	0.0634218i
$456$	−12802.1	−	39400.7i	−0.0615674	−	0.189485i
$457$	156241.	+	156241.i	0.748104	+	0.748104i	0.974123	−	0.226019i	$-0.0725711\pi$
$457$	156241.	+	156241.i	0.748104	+	0.748104i	−0.226019	+	0.974123i	$0.572571\pi$
$458$	−54242.5	−	27637.9i	−0.258588	−	0.131757i
$459$	−120609.	+	166003.i	−0.572470	+	0.787937i
$460$	−155886.	+	112366.i	−0.736699	+	0.531032i
$461$	176191.	−	128010.i	0.829050	−	0.602340i	−0.0902402	−	0.995920i	$-0.528763\pi$
$461$	176191.	−	128010.i	0.829050	−	0.602340i	0.919290	+	0.393580i	$0.128763\pi$
$462$	1582.37	+	9990.71i	0.00741353	+	0.0468072i
$463$	−94408.9	+	14952.9i	−0.440404	+	0.0697531i	−0.372699	−	0.927952i	$-0.621568\pi$
$463$	−94408.9	+	14952.9i	−0.440404	+	0.0697531i	−0.0677047	+	0.997705i	$0.521568\pi$
$464$	−65625.6	−	90326.0i	−0.304816	−	0.419543i
$465$	137126.	−	43986.9i	0.634183	−	0.203431i
$466$	139191.	+	101128.i	0.640972	+	0.465694i
$467$	117432.	−	230474.i	0.538460	−	1.05679i	−0.448191	−	0.893938i	$-0.647931\pi$
$467$	117432.	−	230474.i	0.538460	−	1.05679i	0.986651	−	0.162850i	$-0.0520685\pi$
$468$	201024.	−	201024.i	0.917816	−	0.917816i
$469$	−18024.0	+	5856.37i	−0.0819420	+	0.0266246i
$470$	481657.	+	78140.6i	2.18043	+	0.353738i
$471$	−60826.2	+	187204.i	−0.274188	+	0.843864i
$472$	40429.2	−	20599.7i	0.181473	−	0.0924650i
$473$	−9131.15	+	57651.8i	−0.0408134	+	0.257686i
$474$			289212.i			1.28724i
$475$	−106082.	−	78296.1i	−0.470170	−	0.347019i
$476$	23529.8			0.103850
$477$	−168398.	−	26671.7i	−0.740119	−	0.117223i
$478$	−31041.2	−	60921.8i	−0.135857	−	0.266635i
$479$	−223100.	−	72489.7i	−0.972365	−	0.315941i	−0.220595	−	0.975366i	$-0.570800\pi$
$479$	−223100.	−	72489.7i	−0.972365	−	0.315941i	−0.751770	+	0.659425i	$0.770800\pi$
$480$	−96416.3	+	95695.5i	−0.418473	+	0.415345i
$481$	−126559.	−	389509.i	−0.547020	−	1.68355i
$482$	−182925.	−	182925.i	−0.787370	−	0.787370i
$483$	−3802.40	−	1937.42i	−0.0162991	−	0.00830481i
$484$	12160.7	−	16737.8i	0.0519120	−	0.0714507i
$485$	−131336.	−	492.769i	−0.558340	−	0.00209488i
$486$	305779.	−	222161.i	1.29460	−	0.940581i
$487$	−20705.0	−	130726.i	−0.0873007	−	0.551195i	−0.992109	−	0.125376i	$-0.959986\pi$
$487$	−20705.0	−	130726.i	−0.0873007	−	0.551195i	0.904809	−	0.425818i	$-0.140014\pi$
$488$	−159162.	+	25208.8i	−0.668344	+	0.105855i
$489$	55865.3	+	76892.0i	0.233628	+	0.321561i
$490$	−221523.	+	302506.i	−0.922627	+	1.25992i
$491$	177263.	+	128789.i	0.735285	+	0.534215i	0.891231	−	0.453550i	$-0.149843\pi$
$491$	177263.	+	128789.i	0.735285	+	0.534215i	−0.155946	+	0.987766i	$0.549843\pi$
$492$	21738.0	−	42663.2i	0.0898026	−	0.176248i
$493$	−308498.	+	308498.i	−1.26928	+	1.26928i
$494$	−244710.	+	79511.2i	−1.00276	+	0.325818i
$495$	89300.6	−	173649.i	0.364455	−	0.708698i
$496$	35508.9	−	109285.i	0.144336	−	0.444219i
$497$	21594.0	−	11002.7i	0.0874221	−	0.0445438i
$498$	16401.6	−	103556.i	0.0661344	−	0.417556i
$499$			459743.i			1.84635i	0.384378	+	0.923176i	$0.374416\pi$
$499$			459743.i			1.84635i	−0.384378	+	0.923176i	$0.625584\pi$
$500$	61040.5	−	359181.i	0.244162	−	1.43672i
$501$	−135420.			−0.539521
$502$	−348980.	−	55273.0i	−1.38482	−	0.219334i
$503$	−111545.	−	218919.i	−0.440872	−	0.865260i	−0.999361	−	0.0357483i	$-0.988619\pi$
$503$	−111545.	−	218919.i	−0.440872	−	0.865260i	0.558489	−	0.829512i	$-0.311381\pi$
$504$	−8272.05	−	2687.75i	−0.0325651	−	0.0105810i
$505$	−87586.9	−	45042.5i	−0.343444	−	0.176620i
$506$	79595.5	+	244970.i	0.310876	+	0.956779i
$507$	28077.9	+	28077.9i	0.109232	+	0.109232i
$508$	69957.8	+	35645.3i	0.271087	+	0.138126i
$509$	177331.	−	244075.i	0.684462	−	0.942081i	−0.315515	−	0.948921i	$-0.602177\pi$
$509$	177331.	−	244075.i	0.684462	−	0.942081i	0.999977	+	0.00684005i	$0.00217727\pi$
$510$	180620.	+	132266.i	0.694425	+	0.508521i
$511$	−2891.80	+	2101.02i	−0.0110746	+	0.00804614i
$512$	26762.1	+	168969.i	0.102089	+	0.644566i
$513$	−128138.	+	20295.1i	−0.486904	+	0.0771180i
$514$	149619.	+	205933.i	0.566320	+	0.779472i
$515$	251.889	−	67135.0i	0.000949720	−	0.253125i
$516$	37821.4	+	27478.9i	0.142049	+	0.103205i
$517$	176099.	−	345614.i	0.658834	−	1.29303i
$518$	−28234.1	+	28234.1i	−0.105224	+	0.105224i
$519$	86549.0	−	28121.5i	0.321312	−	0.104401i
$520$	−157176.	−	158360.i	−0.581273	−	0.585651i
$521$	−154437.	+	475307.i	−0.568951	+	1.75105i	0.0869573	+	0.996212i	$0.472286\pi$
$521$	−154437.	+	475307.i	−0.568951	+	1.75105i	−0.655909	+	0.754840i	$0.727714\pi$
$522$	457899.	−	233311.i	1.68046	−	0.856238i
$523$	36007.7	−	227344.i	0.131641	−	0.831150i	−0.830185	−	0.557488i	$-0.811765\pi$
$523$	36007.7	−	227344.i	0.131641	−	0.831150i	0.961826	−	0.273662i	$-0.0882349\pi$
$524$			567441.i			2.06661i
$525$	7713.57	−	2442.45i	0.0279857	−	0.00886151i
$526$	822594.			2.97313
$527$	−443493.	−	70242.4i	−1.59686	−	0.252917i
$528$	20675.8	+	40578.5i	0.0741641	+	0.145555i
$529$	162794.	+	52895.0i	0.581737	+	0.189018i
$530$	−68284.8	+	420906.i	−0.243093	+	1.49842i
$531$	−19155.2	−	58953.6i	−0.0679355	−	0.209084i
$532$	10519.7	+	10519.7i	0.0371688	+	0.0371688i
$533$	−83151.2	−	42367.6i	−0.292694	−	0.149135i
$534$	25574.4	−	35200.1i	0.0896855	−	0.123442i
$535$	6951.41	+	21670.5i	0.0242865	+	0.0757116i
$536$	232588.	−	168985.i	0.809575	−	0.588191i
$537$	−34543.5	−	218099.i	−0.119789	−	0.756319i
$538$	486394.	−	77037.2i	1.68044	−	0.266156i
$539$	175192.	+	241131.i	0.603028	+	0.829997i
$540$	−209628.	−	290817.i	−0.718889	−	0.997314i
$541$	266397.	+	193549.i	0.910195	+	0.661295i	0.941064	−	0.338228i	$-0.109828\pi$
$541$	266397.	+	193549.i	0.910195	+	0.661295i	−0.0308691	+	0.999523i	$0.509828\pi$
$542$	−340623.	+	668510.i	−1.15951	+	2.27567i
$543$	106769.	−	106769.i	0.362114	−	0.362114i
$544$	402835.	−	130889.i	1.36122	−	0.442288i
$545$	255053.	−	128753.i	0.858691	−	0.433474i
$546$	4879.34	−	15017.1i	0.0163673	−	0.0503732i
$547$	−16639.6	+	8478.31i	−0.0556120	+	0.0283357i	−0.481575	−	0.876405i	$-0.659935\pi$
$547$	−16639.6	+	8478.31i	−0.0556120	+	0.0283357i	0.425963	+	0.904740i	$0.359935\pi$
$548$	30158.3	−	190412.i	0.100426	−	0.634064i
$549$			220145.i			0.730406i
$550$	−433449.	−	224966.i	−1.43289	−	0.743689i
$551$	−275846.			−0.908580
$552$	63941.1	+	10127.3i	0.209847	+	0.0332365i
$553$	−14796.2	−	29039.1i	−0.0483836	−	0.0949582i
$554$	−562860.	−	182884.i	−1.83392	−	0.595878i
$555$	−222657.	+	34409.5i	−0.722852	+	0.111710i
$556$	−11371.9	−	34999.2i	−0.0367861	−	0.113216i
$557$	321266.	+	321266.i	1.03551	+	1.03551i	0.999346	+	0.0361638i	$0.0115138\pi$
$557$	321266.	+	321266.i	1.03551	+	1.03551i	0.0361638	+	0.999346i	$0.488486\pi$
$558$	471269.	+	240124.i	1.51356	+	0.771199i
$559$	53556.7	−	73714.4i	0.171392	−	0.235901i
$560$	2018.07	−	6132.59i	0.00643517	−	0.0195554i
$561$	143974.	−	104603.i	0.457467	−	0.332369i
$562$	−26782.7	−	169099.i	−0.0847973	−	0.535389i
$563$	−121771.	+	19286.6i	−0.384173	+	0.0608471i	−0.345534	−	0.938406i	$-0.612302\pi$
$563$	−121771.	+	19286.6i	−0.384173	+	0.0608471i	−0.0386392	+	0.999253i	$0.512302\pi$
$564$	−182606.	−	251336.i	−0.574061	−	0.790127i
$565$	278011.	+	91485.8i	0.870893	+	0.286587i
$566$	−430830.	−	313017.i	−1.34485	−	0.977090i
$567$	−3356.75	+	6587.99i	−0.0104413	+	0.0204921i
$568$	−259969.	+	259969.i	−0.805795	+	0.805795i
$569$	102694.	−	33367.4i	0.317192	−	0.103062i	−0.146094	−	0.989271i	$-0.546670\pi$
$569$	102694.	−	33367.4i	0.317192	−	0.103062i	0.463286	+	0.886209i	$0.346670\pi$
$570$	21617.9	+	139885.i	0.0665370	+	0.430547i
$571$	27408.8	−	84355.7i	0.0840656	−	0.258727i	−0.900185	−	0.435509i	$-0.856569\pi$
$571$	27408.8	−	84355.7i	0.0840656	−	0.258727i	0.984250	+	0.176781i	$0.0565685\pi$
$572$	−503596.	+	256595.i	−1.53918	+	0.784253i
$573$	12939.2	−	81695.0i	0.0394093	−	0.248821i
$574$			9098.40i			0.0276148i
$575$	184272.	−	92156.2i	0.557345	−	0.278733i
$576$	−413304.			−1.24573
$577$	16779.6	+	2657.62i	0.0503998	+	0.00798255i	0.181583	−	0.983376i	$-0.441878\pi$
$577$	16779.6	+	2657.62i	0.0503998	+	0.00798255i	−0.131184	+	0.991358i	$0.541878\pi$
$578$	−79143.0	−	155327.i	−0.236895	−	0.464934i
$579$	−108234.	−	35167.4i	−0.322855	−	0.104902i
$580$	−343498.	−	680453.i	−1.02110	−	2.02275i
$581$	3651.09	+	11236.9i	0.0108161	+	0.0332885i
$582$	99699.9	+	99699.9i	0.294340	+	0.294340i
$583$	302022.	+	153888.i	0.888589	+	0.452759i
$584$	31872.2	−	43868.4i	0.0934516	−	0.128625i
$585$	−247265.	+	178235.i	−0.722523	+	0.520813i
$586$	−180803.	+	131361.i	−0.526515	+	0.382536i
$587$	23531.6	+	148573.i	0.0682929	+	0.431184i	0.998018	+	0.0629298i	$0.0200444\pi$
$587$	23531.6	+	148573.i	0.0682929	+	0.431184i	−0.929725	+	0.368254i	$0.879956\pi$
$588$	235778.	−	37343.6i	0.681944	−	0.108009i
$589$	−166872.	−	229680.i	−0.481010	−	0.662053i
$590$	−147620.	+	47353.0i	−0.424073	+	0.136033i
$591$	82415.7	+	59878.5i	0.235958	+	0.171434i
$592$	−81615.7	+	160180.i	−0.232879	+	0.457051i
$593$	172324.	−	172324.i	0.490045	−	0.490045i	−0.418275	−	0.908320i	$-0.637365\pi$
$593$	172324.	−	172324.i	0.490045	−	0.490045i	0.908320	+	0.418275i	$0.137365\pi$
$594$	−457010.	+	148492.i	−1.29525	+	0.420852i
$595$	−24902.4	−	4039.99i	−0.0703408	−	0.0114116i
$596$	−46907.0	+	144365.i	−0.132052	+	0.406415i
$597$	−161078.	+	82073.5i	−0.451948	+	0.230279i
$598$	62898.6	−	397126.i	0.175889	−	1.11052i
$599$		−	432591.i		−	1.20566i	−0.797871	−	0.602829i	$-0.794040\pi$
$599$		−	432591.i		−	1.20566i	0.797871	−	0.602829i	$-0.205960\pi$
$600$	−99837.5	+	71397.7i	−0.277326	+	0.198327i
$601$	−552726.			−1.53025			−0.765123	−	0.643884i	$-0.777322\pi$
$601$	−552726.			−1.53025			−0.765123	+	0.643884i	$0.777322\pi$
$602$	−8773.90	−	1389.65i	−0.0242103	−	0.00383453i
$603$	−178306.	−	349945.i	−0.490377	−	0.962420i
$604$	222645.	+	72341.9i	0.610295	+	0.198297i
$605$	−15743.9	+	15626.2i	−0.0430132	+	0.0426916i
$606$	32673.8	+	100560.i	0.0889721	+	0.273828i
$607$	−221603.	−	221603.i	−0.601447	−	0.601447i	0.339249	−	0.940697i	$-0.389827\pi$
$607$	−221603.	−	221603.i	−0.601447	−	0.601447i	−0.940697	+	0.339249i	$0.889827\pi$
$608$	238617.	+	121581.i	0.645496	+	0.328897i
$609$	9949.87	−	13694.8i	0.0268277	−	0.0369251i
$610$	550572.	+	2065.74i	1.47964	+	0.00555157i
$611$	−489858.	+	355902.i	−1.31216	+	0.953342i
$612$	76282.2	+	481627.i	0.203667	+	1.28590i
$613$	−89000.6	+	14096.3i	−0.236849	+	0.0375133i	−0.273731	−	0.961806i	$-0.588258\pi$
$613$	−89000.6	+	14096.3i	−0.236849	+	0.0375133i	0.0368812	+	0.999320i	$0.488258\pi$
$614$	−282787.	−	389222.i	−0.750105	−	1.03243i
$615$	−30331.2	+	41419.6i	−0.0801935	+	0.109511i
$616$	13989.5	+	10164.0i	0.0368674	+	0.0267857i
$617$	−89143.5	+	174954.i	−0.234164	+	0.459572i	−0.977948	−	0.208847i	$-0.933029\pi$
$617$	−89143.5	+	174954.i	−0.234164	+	0.459572i	0.743785	+	0.668419i	$0.233029\pi$
$618$	−50963.7	+	50963.7i	−0.133439	+	0.133439i
$619$	105813.	−	34380.6i	0.276157	−	0.0897290i	−0.167664	−	0.985844i	$-0.553622\pi$
$619$	105813.	−	34380.6i	0.276157	−	0.0897290i	0.443822	+	0.896115i	$0.353622\pi$
$620$	358773.	−	697649.i	0.933333	−	1.81490i
$621$	62647.4	−	192809.i	0.162450	−	0.499970i
$622$	737615.	−	375834.i	1.90655	−	0.971437i
$623$	−767.016	+	4842.75i	−0.00197619	+	0.0124772i
$624$		−	71091.4i		−	0.182578i
$625$	−126271.	+	369653.i	−0.323255	+	0.946312i
$626$	531144.			1.35539
$627$	111134.	+	17601.9i	0.282690	+	0.0447738i
$628$	486807.	+	955413.i	1.23435	+	2.42255i
$629$	668107.	+	217081.i	1.68867	+	0.548682i
$630$	26427.2	+	13590.5i	0.0665840	+	0.0342415i
$631$	79720.9	+	245356.i	0.200223	+	0.616222i	0.999876	+	0.0157599i	$0.00501673\pi$
$631$	79720.9	+	245356.i	0.200223	+	0.616222i	−0.799653	+	0.600462i	$0.794983\pi$
$632$	349599.	+	349599.i	0.875258	+	0.875258i
$633$	153489.	+	78206.4i	0.383062	+	0.195180i
$634$	372123.	−	512183.i	0.925780	−	1.27423i
$635$	−67918.6	−	49736.1i	−0.168438	−	0.123346i
$636$	219635.	−	159574.i	0.542985	−	0.394502i
$637$	−72783.1	−	459535.i	−0.179371	−	1.13250i
$638$	−1.00913e6	+	159831.i	−2.47917	+	0.392662i
$639$	295219.	+	406334.i	0.723007	+	0.995133i
$640$	−1973.02	+	525861.i	−0.00481695	+	1.28384i
$641$	327792.	+	238155.i	0.797778	+	0.579620i	0.910261	−	0.414034i	$-0.135880\pi$
$641$	327792.	+	238155.i	0.797778	+	0.579620i	−0.112483	+	0.993654i	$0.535880\pi$
$642$	11092.0	−	21769.2i	0.0269115	−	0.0528169i
$643$	−41464.7	+	41464.7i	−0.100290	+	0.100290i	−0.755471	−	0.655182i	$-0.772592\pi$
$643$	−41464.7	+	41464.7i	−0.100290	+	0.100290i	0.655182	+	0.755471i	$0.272592\pi$
$644$	−22109.9	+	7183.93i	−0.0533107	+	0.0173217i
$645$	−35309.7	−	35575.6i	−0.0848739	−	0.0855132i
$646$	136382.	−	419741.i	0.326807	−	1.00581i
$647$	−279327.	+	142324.i	−0.667273	+	0.339993i	−0.754598	−	0.656187i	$-0.772168\pi$
$647$	−279327.	+	142324.i	−0.667273	+	0.339993i	0.0873248	+	0.996180i	$0.472168\pi$
$648$	17546.4	−	110783.i	0.0417866	−	0.263831i
$649$			123237.i			0.292586i
$650$	443438.	+	620071.i	1.04956	+	1.46762i
$651$	17422.0			0.0411089
$652$	511383.	+	80995.0i	1.20296	+	0.190530i
$653$	−107605.	−	211187.i	−0.252353	−	0.495270i	0.729727	−	0.683739i	$-0.239647\pi$
$653$	−107605.	−	211187.i	−0.252353	−	0.495270i	−0.982079	+	0.188469i	$0.939647\pi$
$654$	−291711.	−	94782.7i	−0.682021	−	0.221602i
$655$	97427.7	−	600542.i	0.227091	−	1.39978i
$656$	12658.6	+	38959.2i	0.0294156	+	0.0905320i
$657$	−52380.3	−	52380.3i	−0.121349	−	0.121349i
$658$	52598.2	+	26800.1i	0.121484	+	0.0618992i
$659$	231414.	−	318515.i	0.532868	−	0.733430i	−0.454696	−	0.890647i	$-0.650252\pi$
$659$	231414.	−	318515.i	0.532868	−	0.733430i	0.987564	+	0.157217i	$0.0502521\pi$
$660$	94969.9	+	296062.i	0.218021	+	0.679666i
$661$	−637593.	+	463238.i	−1.45929	+	1.06023i	−0.475738	+	0.879587i	$0.657819\pi$
$661$	−637593.	+	463238.i	−1.45929	+	1.06023i	−0.983548	+	0.180646i	$0.942181\pi$
$662$	−103433.	−	653048.i	−0.236016	−	1.49015i
$663$	−274378.	+	43457.2i	−0.624198	+	0.0988632i
$664$	−105352.	−	145004.i	−0.238949	−	0.328885i
$665$	−9327.14	−	12939.5i	−0.0210914	−	0.0292601i
$666$	−669451.	−	486384.i	−1.50928	−	1.09656i
$667$	195693.	−	384069.i	0.439869	−	0.863292i
$668$	−521640.	+	521640.i	−1.16901	+	1.16901i
$669$	117155.	−	38065.9i	0.261763	−	0.0850518i
$670$	−876867.	+	442650.i	−1.95337	+	0.986077i
$671$	135248.	−	416250.i	0.300390	−	0.924505i
$672$	−14643.1	+	7461.04i	−0.0324261	+	0.0165219i
$673$	−88014.2	+	555700.i	−0.194322	+	1.22690i	0.676923	+	0.736054i	$0.263313\pi$
$673$	−88014.2	+	555700.i	−0.194322	+	1.22690i	−0.871245	+	0.490849i	$0.836687\pi$
$674$			371797.i			0.818438i
$675$	171925.	+	343774.i	0.377338	+	0.754511i
$676$	216312.			0.473356
$677$	548322.	+	86845.7i	1.19635	+	0.189483i	0.722657	−	0.691206i	$-0.242920\pi$
$677$	548322.	+	86845.7i	1.19635	+	0.189483i	0.473694	+	0.880690i	$0.342920\pi$
$678$	−142646.	−	279958.i	−0.310313	−	0.609024i
$679$	−15111.3	−	4909.96i	−0.0327765	−	0.0106497i
$680$	378217.	−	58449.8i	0.817943	−	0.126405i
$681$	−57906.4	−	178218.i	−0.124863	−	0.384288i
$682$	−743554.	−	743554.i	−1.59861	−	1.59861i
$683$	−473337.	−	241177.i	−1.01468	−	0.517005i	−0.134132	−	0.990963i	$-0.542825\pi$
$683$	−473337.	−	241177.i	−1.01468	−	0.517005i	−0.880547	+	0.473958i	$0.842825\pi$
$684$	−181221.	+	249429.i	−0.387343	+	0.533132i
$685$	−64610.6	+	196341.i	−0.137696	+	0.418438i
$686$	−73534.8	+	53426.2i	−0.156259	+	0.113529i
$687$	−6500.90	−	41045.1i	−0.0137740	−	0.0869657i
$688$	−39503.1	+	6256.67i	−0.0834553	+	0.0132180i
$689$	−311013.	−	428072.i	−0.655148	−	0.901734i
$690$	−210103.	−	69139.1i	−0.441299	−	0.145220i
$691$	388736.	+	282433.i	0.814138	+	0.591506i	0.915027	−	0.403392i	$-0.132169\pi$
$691$	388736.	+	282433.i	0.814138	+	0.591506i	−0.100889	+	0.994898i	$0.532169\pi$
$692$	225063.	−	441712.i	0.469994	−	0.922416i
$693$	16704.0	−	16704.0i	0.0347819	−	0.0347819i
$694$	−958532.	+	311446.i	−1.99016	+	0.646641i
$695$	6026.06	+	38993.4i	0.0124757	+	0.0807274i
$696$	−79353.2	+	244224.i	−0.163812	+	0.504162i
$697$	142625.	−	72671.3i	0.293583	−	0.149588i
$698$	103850.	−	655680.i	0.213154	−	1.34580i
$699$			117445.i			0.240371i
$700$	20304.4	−	39121.1i	0.0414375	−	0.0798390i
$701$	361031.			0.734697			0.367348	−	0.930083i	$-0.380266\pi$
$701$	361031.			0.734697			0.367348	+	0.930083i	$0.380266\pi$
$702$	740870.	+	117342.i	1.50338	+	0.238111i
$703$	201644.	+	395749.i	0.408013	+	0.800772i
$704$	781474.	+	253916.i	1.57677	+	0.512325i
$705$	150105.	+	297351.i	0.302007	+	0.598261i
$706$	−118488.	−	364668.i	−0.237719	−	0.731625i
$707$	−8425.35	−	8425.35i	−0.0168558	−	0.0168558i
$708$	87944.9	+	44810.2i	0.175446	+	0.0893944i
$709$	−398565.	+	548578.i	−0.792879	+	1.09131i	0.200864	+	0.979619i	$0.435625\pi$
$709$	−398565.	+	548578.i	−0.792879	+	1.09131i	−0.993744	+	0.111686i	$0.964375\pi$
$710$	1.01899e6	−	734515.i	2.02141	−	1.45708i
$711$	546427.	−	397002.i	1.08092	−	0.785333i
$712$	−11635.6	−	73464.1i	−0.0229524	−	0.144916i
$713$	438175.	−	69400.2i	0.861924	−	0.136515i
$714$	15919.4	+	21911.1i	0.0312269	+	0.0429802i
$715$	577029.	−	185098.i	1.12872	−	0.362067i
$716$	−973181.	−	707057.i	−1.89831	−	1.37920i
$717$	21189.5	−	41586.8i	0.0412176	−	0.0808941i
$718$	−1.00077e6	+	1.00077e6i	−1.94128	+	1.94128i
$719$	−536385.	+	174282.i	−1.03757	+	0.337128i	−0.777780	−	0.628537i	$-0.783654\pi$
$719$	−536385.	+	174282.i	−1.03757	+	0.337128i	−0.259793	+	0.965664i	$0.583654\pi$
$720$	132069.	+	21425.9i	0.254763	+	0.0413309i
$721$	2509.83	−	7724.47i	0.00482808	−	0.0148593i
$722$	−479462.	+	244298.i	−0.919771	+	0.468646i
$723$	27625.0	−	174418.i	0.0528477	−	0.333667i
$724$		−	822549.i		−	1.56922i
$725$	246705.	+	779124.i	0.469355	+	1.48228i
$726$	23813.8			0.0451809
$727$	−499048.	−	79041.5i	−0.944221	−	0.149550i	−0.334705	−	0.942323i	$-0.608637\pi$
$727$	−499048.	−	79041.5i	−0.944221	−	0.149550i	−0.609517	+	0.792773i	$0.708637\pi$
$728$	−12254.5	−	24050.8i	−0.0231223	−	0.0453802i
$729$	57052.5	+	18537.5i	0.107354	+	0.0348815i
$730$	−131492.	+	130509.i	−0.246748	+	0.244903i
$731$	48295.4	+	148638.i	0.0903797	+	0.278160i
$732$	−247868.	−	247868.i	−0.462592	−	0.462592i
$733$	268312.	+	136712.i	0.499382	+	0.254448i	0.685491	−	0.728081i	$-0.259588\pi$
$733$	268312.	+	136712.i	0.499382	+	0.254448i	−0.186109	+	0.982529i	$0.559588\pi$
$734$	67292.9	−	92620.8i	0.124904	−	0.171916i
$735$	−255944.	−	960.297i	−0.473773	−	0.00177759i
$736$	−338563.	+	245981.i	−0.625006	+	0.454093i
$737$	122149.	+	771218.i	0.224882	+	1.41985i
$738$	−186233.	+	29496.5i	−0.341936	+	0.0541573i
$739$	−497579.	−	684859.i	−0.911115	−	1.25404i	−0.966785	−	0.255593i	$-0.917729\pi$
$739$	−497579.	−	684859.i	−0.911115	−	1.25404i	0.0556697	−	0.998449i	$-0.482271\pi$
$740$	−725129.	+	990220.i	−1.32420	+	1.80829i
$741$	−142097.	−	103240.i	−0.258791	−	0.188023i
$742$	−23419.8	+	45964.0i	−0.0425379	+	0.0834853i
$743$	560746.	−	560746.i	1.01575	−	1.01575i	0.0158796	−	0.999874i	$-0.494945\pi$
$743$	560746.	−	560746.i	1.01575	−	1.01575i	0.999874	−	0.0158796i	$-0.00505486\pi$
$744$	−251355.	+	81670.2i	−0.454090	+	0.147543i
$745$	74430.3	−	144733.i	0.134103	−	0.260768i
$746$	35121.7	−	108093.i	0.0631099	−	0.194232i
$747$	−218169.	+	111163.i	−0.390978	+	0.199213i
$748$	151657.	−	957524.i	0.271056	−	1.71138i
$749$			2753.26i			0.00490777i
$750$	375770.	−	186167.i	0.668035	−	0.330963i
$751$	−588131.			−1.04278			−0.521392	−	0.853317i	$-0.674587\pi$
$751$	−588131.			−1.04278			−0.521392	+	0.853317i	$0.674587\pi$
$752$	262511.	+	41577.7i	0.464208	+	0.0735233i
$753$	−109499.	−	214903.i	−0.193116	−	0.379012i
$754$	1.51683e6	+	492847.i	2.66805	+	0.866901i
$755$	−223213.	−	114789.i	−0.391584	−	0.201376i
$756$	−13402.2	−	41247.7i	−0.0234494	−	0.0721698i
$757$	143257.	+	143257.i	0.249991	+	0.249991i	0.820967	−	0.570976i	$-0.193435\pi$
$757$	143257.	+	143257.i	0.249991	+	0.249991i	−0.570976	+	0.820967i	$0.693435\pi$
$758$	63928.5	+	32573.2i	0.111264	+	0.0566920i
$759$	−103349.	+	142248.i	−0.179401	+	0.246924i
$760$	195224.	+	142961.i	0.337992	+	0.247509i
$761$	422894.	−	307250.i	0.730233	−	0.530546i	−0.159404	−	0.987213i	$-0.550957\pi$
$761$	422894.	−	307250.i	0.730233	−	0.530546i	0.889637	+	0.456668i	$0.150957\pi$
$762$	14137.6	+	89261.4i	0.0243482	+	0.153728i
$763$	34139.2	−	5407.11i	0.0586413	−	0.00928787i
$764$	−264848.	−	364532.i	−0.453743	−	0.624524i
$765$	1961.61	−	522820.i	0.00335189	−	0.893365i
$766$	1.45469e6	+	1.05689e6i	2.47920	+	1.80125i
$767$	87335.6	−	171406.i	0.148457	−	0.291363i
$768$	79874.5	−	79874.5i	0.135421	−	0.135421i
$769$	−102153.	+	33191.6i	−0.172742	+	0.0561274i	−0.394111	−	0.919063i	$-0.628948\pi$
$769$	−102153.	+	33191.6i	−0.172742	+	0.0561274i	0.221369	+	0.975190i	$0.428948\pi$
$770$	−41619.1	−	41932.6i	−0.0701958	−	0.0707245i
$771$	−53695.0	+	165256.i	−0.0903286	+	0.278003i
$772$	−552384.	+	281454.i	−0.926844	+	0.472251i
$773$	−33258.7	+	209987.i	−0.0556604	+	0.351426i	0.944102	+	0.329652i	$0.106931\pi$
$773$	−33258.7	+	209987.i	−0.0556604	+	0.351426i	−0.999763	+	0.0217740i	$0.993069\pi$
$774$		−	184096.i		−	0.307300i
$775$	−499486.	+	676746.i	−0.831611	+	1.12674i
$776$	241034.			0.400272
$777$	−26921.0	−	4263.86i	−0.0445912	−	0.00706255i
$778$	4556.69	+	8943.01i	0.00752819	+	0.0147749i
$779$	96254.5	+	31275.0i	0.158616	+	0.0515374i
$780$	77723.1	−	479084.i	0.127750	−	0.787449i
$781$	−308565.	−	949665.i	−0.505877	−	1.55693i
$782$	487665.	+	487665.i	0.797459	+	0.797459i
$783$	716511.	+	365081.i	1.16869	+	0.595477i
$784$	−120042.	+	165224.i	−0.195299	+	0.268806i
$785$	−351164.	−	1.09473e6i	−0.569863	−	1.77651i
$786$	−528405.	+	383909.i	−0.855307	+	0.621417i
$787$	69976.0	+	441811.i	0.112980	+	0.713325i	0.977533	+	0.210784i	$0.0676015\pi$
$787$	69976.0	+	441811.i	0.112980	+	0.713325i	−0.864553	+	0.502541i	$0.832398\pi$
$788$	548118.	−	86813.4i	0.882718	−	0.139809i
$789$	330055.	+	454282.i	0.530191	+	0.729746i
$790$	−987756.	−	1.37031e6i	−1.58269	−	2.19566i
$791$	28645.5	+	20812.2i	0.0457829	+	0.0332632i
$792$	−162691.	+	319300.i	−0.259367	+	0.509036i
$793$	−483098.	+	483098.i	−0.768226	+	0.768226i
$794$	290950.	−	94535.5i	0.461507	−	0.149953i
$795$	−259846.	+	131172.i	−0.411133	+	0.207543i
$796$	−304327.	+	936623.i	−0.480302	+	1.47822i
$797$	−46544.8	+	23715.7i	−0.0732747	+	0.0373353i	−0.490244	−	0.871585i	$-0.663092\pi$
$797$	−46544.8	+	23715.7i	−0.0732747	+	0.0373353i	0.416969	+	0.908921i	$0.363092\pi$
$798$	−2678.79	+	16913.2i	−0.00420661	+	0.0265595i
$799$		−	1.03858e6i		−	1.62685i
$800$	129997.	−	782708.i	0.203120	−	1.22298i
$801$	−101612.			−0.158372
$802$	−219354.	−	34742.3i	−0.341033	−	0.0540144i
$803$	66860.4	+	131221.i	0.103690	+	0.203503i
$804$	594772.	+	193253.i	0.920108	+	0.298961i
$805$	24633.1	−	3806.81i	0.0380126	−	0.00587448i
$806$	507238.	+	1.56112e6i	0.780803	+	2.40307i
$807$	237703.	+	237703.i	0.364996	+	0.364996i
$808$	161052.	+	82060.2i	0.246686	+	0.125693i
$809$	93564.2	−	128780.i	0.142959	−	0.196767i	−0.731533	−	0.681806i	$-0.761195\pi$
$809$	93564.2	−	128780.i	0.142959	−	0.196767i	0.874492	+	0.485039i	$0.161195\pi$
$810$	−119789.	+	364021.i	−0.182578	+	0.554825i
$811$	−31453.1	+	22852.0i	−0.0478213	+	0.0347442i	−0.611439	−	0.791291i	$-0.709409\pi$
$811$	−31453.1	+	22852.0i	−0.0478213	+	0.0347442i	0.563618	+	0.826036i	$0.309409\pi$
$812$	−14425.6	−	91079.6i	−0.0218787	−	0.138137i
$813$	−505859.	+	80120.2i	−0.765329	+	0.121216i
$814$	966983.	+	1.33094e6i	1.45939	+	2.00867i
$815$	−527307.	−	173523.i	−0.793869	−	0.261241i
$816$	98651.4	+	71674.4i	0.148157	+	0.107643i
$817$	−44861.0	+	88044.7i	−0.0672086	+	0.131904i
$818$	1.09031e6	−	1.09031e6i	1.62945	−	1.62945i
$819$	−35070.6	+	11395.1i	−0.0522848	+	0.0169884i
$820$	42712.7	+	276385.i	0.0635227	+	0.411042i
$821$	163832.	−	504224.i	0.243060	−	0.748061i	−0.752890	−	0.658147i	$-0.771341\pi$
$821$	163832.	−	504224.i	0.243060	−	0.748061i	0.995949	−	0.0899146i	$-0.0286594\pi$
$822$	197717.	−	100742.i	0.292617	−	0.149096i
$823$	−672.175	+	4243.94i	−0.000992390	+	0.00626570i	−0.988180	−	0.153301i	$-0.951010\pi$
$823$	−672.175	+	4243.94i	−0.000992390	+	0.00626570i	0.987187	+	0.159567i	$0.0510096\pi$
$824$			123210.i			0.181464i
$825$	−49677.0	−	329639.i	−0.0729874	−	0.484318i
$826$	−18755.2			−0.0274892
$827$	−241931.	−	38318.1i	−0.353737	−	0.0560265i	−0.0229629	−	0.999736i	$-0.507310\pi$
$827$	−241931.	−	38318.1i	−0.353737	−	0.0560265i	−0.330775	+	0.943710i	$0.607310\pi$
$828$	−218725.	−	429272.i	−0.319035	−	0.626141i
$829$	−840539.	−	273108.i	−1.22306	−	0.397397i	−0.374867	−	0.927079i	$-0.622312\pi$
$829$	−840539.	−	273108.i	−1.22306	−	0.397397i	−0.848197	+	0.529681i	$0.822312\pi$
$830$	275965.	+	546673.i	0.400588	+	0.793545i
$831$	−124842.	−	384223.i	−0.180783	−	0.556392i
$832$	−906975.	−	906975.i	−1.31023	−	1.31023i
$833$	711062.	+	362304.i	1.02475	+	0.522136i
$834$	24897.7	−	34268.7i	0.0357954	−	0.0492681i
$835$	641634.	−	462506.i	0.920269	−	0.663353i
$836$	495891.	−	360286.i	0.709535	−	0.515507i
$837$	129471.	+	817450.i	0.184809	+	1.16684i
$838$	239392.	−	37916.0i	0.340896	−	0.0539926i
$839$	−218943.	−	301349.i	−0.311033	−	0.428100i	0.624670	−	0.780889i	$-0.285233\pi$
$839$	−218943.	−	301349.i	−0.311033	−	0.428100i	−0.935703	+	0.352789i	$0.885233\pi$
$840$	−14139.4	+	4535.58i	−0.0200388	+	0.00642797i
$841$	811070.	+	589277.i	1.14674	+	0.833158i
$842$	365794.	−	717912.i	0.515956	−	1.01262i
$843$	82639.9	−	82639.9i	0.116288	−	0.116288i
$844$	892492.	−	289988.i	1.25291	−	0.407095i
$845$	−228931.	−	37140.1i	−0.320620	−	0.0520151i
$846$	−378046.	+	1.16351e6i	−0.528207	+	1.62565i
$847$	−2391.09	+	1218.32i	−0.00333295	+	0.00169822i
$848$	−36333.5	+	229401.i	−0.0505261	+	0.319009i
$849$		−	363522.i		−	0.504331i
$850$	−1.30753e6	−	9811.79i	−1.80973	−	0.0135803i
$851$	−694066.			−0.958388
$852$	−789899.	−	125108.i	−1.08816	−	0.172347i
$853$	−254990.	−	500447.i	−0.350450	−	0.687796i	0.646740	−	0.762710i	$-0.276132\pi$
$853$	−254990.	−	500447.i	−0.350450	−	0.687796i	−0.997190	+	0.0749142i	$0.976132\pi$
$854$	63348.2	+	20583.1i	0.0868597	+	0.0282224i
$855$	234619.	−	232865.i	0.320945	−	0.318545i
$856$	−12906.6	−	39722.6i	−0.0176143	−	0.0542113i
$857$	−218481.	−	218481.i	−0.297477	−	0.297477i	0.542548	−	0.840025i	$-0.317460\pi$
$857$	−218481.	−	218481.i	−0.297477	−	0.297477i	−0.840025	+	0.542548i	$0.817460\pi$
$858$	−579657.	−	295350.i	−0.787402	−	0.401201i
$859$	−379131.	+	521829.i	−0.513810	+	0.707199i	−0.984556	−	0.175070i	$-0.943985\pi$
$859$	−379131.	+	521829.i	−0.513810	+	0.707199i	0.470746	+	0.882269i	$0.343985\pi$
$860$	−273051.	−	1024.48i	−0.369187	−	0.00138518i
$861$	−5024.64	+	3650.62i	−0.00677796	+	0.00492447i
$862$	268593.	+	1.69583e6i	0.361476	+	2.28227i
$863$	−531701.	+	84213.2i	−0.713914	+	0.113073i	−0.502818	−	0.864392i	$-0.667703\pi$
$863$	−531701.	+	84213.2i	−0.713914	+	0.113073i	−0.211096	+	0.977465i	$0.567703\pi$
$864$	−458896.	−	631616.i	−0.614733	−	0.846108i
$865$	−314033.	+	428836.i	−0.419704	+	0.573138i
$866$	−1.39289e6	−	1.01199e6i	−1.85729	−	1.34940i
$867$	54025.0	−	106030.i	0.0718715	−	0.141056i
$868$	67109.7	−	67109.7i	0.0890730	−	0.0890730i
$869$	−1.27708e6	+	414950.i	−1.69114	+	0.549485i
$870$	401245.	−	780237.i	0.530116	−	1.03083i
$871$	376653.	−	1.15922e6i	0.496484	−	1.52802i
$872$	−467194.	+	238047.i	−0.614418	+	0.313062i
$873$	51511.1	−	325228.i	0.0675884	−	0.426736i
$874$			436050.i			0.570838i
$875$	−28205.8	+	37917.0i	−0.0368402	+	0.0495243i
$876$	117953.			0.153710
$877$	−761495.	−	120609.i	−0.990074	−	0.156812i	−0.359670	−	0.933080i	$-0.617111\pi$
$877$	−761495.	−	120609.i	−0.990074	−	0.156812i	−0.630404	+	0.776267i	$0.717111\pi$
$878$	380777.	+	747316.i	0.493948	+	0.969428i
$879$	−145090.	−	47142.6i	−0.187784	−	0.0610148i
$880$	−236553.	−	121650.i	−0.305466	−	0.157089i
$881$	−93403.8	−	287467.i	−0.120341	−	0.370371i	0.872683	−	0.488288i	$-0.162378\pi$
$881$	−93403.8	−	287467.i	−0.120341	−	0.370371i	−0.993023	+	0.117917i	$0.962378\pi$
$882$	−664712.	−	664712.i	−0.854469	−	0.854469i
$883$	−73833.7	−	37620.2i	−0.0946964	−	0.0482502i	0.406001	−	0.913873i	$-0.366923\pi$
$883$	−73833.7	−	37620.2i	−0.0946964	−	0.0482502i	−0.500697	+	0.865622i	$0.666923\pi$
$884$	−889509.	+	1.22430e6i	−1.13827	+	1.56670i
$885$	−85381.4	−	62524.0i	−0.109013	−	0.0798289i
$886$	1.23363e6	−	896283.i	1.57151	−	1.14177i
$887$	−86339.6	−	545127.i	−0.109739	−	0.692868i	−0.979809	−	0.199938i	$-0.935926\pi$
$887$	−86339.6	−	545127.i	−0.109739	−	0.692868i	0.870069	−	0.492930i	$-0.164074\pi$
$888$	408389.	−	64682.5i	0.517903	−	0.0820277i
$889$	−5986.16	−	8239.25i	−0.00757434	−	0.0104252i
$890$	−953.478	+	254126.i	−0.00120373	+	0.320826i
$891$	246457.	+	179061.i	0.310446	+	0.225552i
$892$	304651.	−	597911.i	0.382889	−	0.751462i
$893$	464328.	−	464328.i	0.582266	−	0.582266i
$894$	−166169.	+	53991.6i	−0.207910	+	0.0675541i
$895$	908552.	+	915395.i	1.13424	+	1.14278i
$896$	−19659.3	+	60505.0i	−0.0244879	+	0.0753659i
$897$	244552.	−	124606.i	0.303939	−	0.154865i
$898$	136375.	−	861038.i	0.169115	−	1.06775i
$899$			1.75974e6i			2.17736i
$900$	866587.	+	288778.i	1.06986	+	0.356516i
$901$	907586.			1.11799
$902$	370251.	+	58642.0i	0.455075	+	0.0720768i
$903$	−2752.97	−	5403.01i	−0.00337618	−	0.00662613i
$904$	−510844.	−	165983.i	−0.625103	−	0.203108i
$905$	−141229.	+	870532.i	−0.172435	+	1.06289i
$906$	83268.1	+	256273.i	0.101443	+	0.312210i
$907$	875141.	+	875141.i	1.06381	+	1.06381i	0.997820	+	0.0659885i	$0.0210201\pi$
$907$	875141.	+	875141.i	1.06381	+	1.06381i	0.0659885	+	0.997820i	$0.478980\pi$
$908$	−909552.	−	463440.i	−1.10320	−	0.562111i
$909$	145142.	−	199771.i	0.175657	−	0.241771i
$910$	28169.6	+	87816.8i	0.0340171	+	0.106046i
$911$	560048.	−	406899.i	0.674821	−	0.490286i	−0.196815	−	0.980441i	$-0.563060\pi$
$911$	560048.	−	406899.i	0.674821	−	0.490286i	0.871635	+	0.490155i	$0.163060\pi$
$912$	12060.8	+	76149.0i	0.0145006	+	0.0915534i
$913$	480808.	−	76152.4i	0.576806	−	0.0913571i
$914$	814365.	+	1.12088e6i	0.974825	+	1.34173i
$915$	219769.	+	304885.i	0.262497	+	0.364162i
$916$	−183148.	−	133065.i	−0.218278	−	0.158588i
$917$	33415.0	−	65580.7i	0.0397378	−	0.0779897i
$918$	−909778.	+	909778.i	−1.07957	+	1.07957i
$919$	1.15264e6	−	374514.i	1.36478	−	0.443443i	0.467141	−	0.884183i	$-0.345284\pi$
$919$	1.15264e6	−	374514.i	1.36478	−	0.443443i	0.897635	+	0.440740i	$0.145284\pi$
$920$	−337547.	+	170397.i	−0.398803	+	0.201319i
$921$	101486.	−	312341.i	0.119643	−	0.368222i
$922$	1.21674e6	−	619959.i	1.43131	−	0.729291i
$923$	−243837.	+	1.53952e6i	−0.286217	+	1.80710i
$924$			37615.0i			0.0440572i
$925$	937447.	−	923483.i	1.09563	−	1.07931i
$926$	−599355.			−0.698976
$927$	166247.	+	26331.0i	0.193462	+	0.0306413i
$928$	−753617.	−	1.47906e6i	−0.875094	−	1.71747i
$929$	−209720.	−	68142.2i	−0.243001	−	0.0789559i	0.184984	−	0.982741i	$-0.440777\pi$
$929$	−209720.	−	68142.2i	−0.243001	−	0.0789559i	−0.427986	+	0.903786i	$0.640777\pi$
$930$	892388.	−	137910.i	1.03178	−	0.159452i
$931$	155922.	+	479879.i	0.179891	+	0.553647i
$932$	452400.	+	452400.i	0.520824	+	0.520824i
$933$	503514.	+	256553.i	0.578427	+	0.294723i
$934$	953346.	−	1.31217e6i	1.09284	−	1.50417i
$935$	−324907.	+	987342.i	−0.371652	+	1.12939i
$936$	452562.	−	328805.i	0.516566	−	0.375307i
$937$	−216938.	−	1.36969e6i	−0.247091	−	1.56007i	−0.729410	−	0.684076i	$-0.760205\pi$
$937$	−216938.	−	1.36969e6i	−0.247091	−	1.56007i	0.482319	−	0.875996i	$-0.339795\pi$
$938$	−117370.	+	18589.6i	−0.133399	+	0.0211283i
$939$	213114.	+	293327.i	0.241703	+	0.332675i
$940$	1.72360e6	+	567191.i	1.95066	+	0.641910i
$941$	11992.5	+	8713.05i	0.0135435	+	0.00983990i	0.594536	−	0.804069i	$-0.297336\pi$
$941$	11992.5	+	8713.05i	0.0135435	+	0.00983990i	−0.580993	+	0.813909i	$0.697336\pi$
$942$	−560333.	+	1.09971e6i	−0.631457	+	1.23930i
$943$	−111831.	+	111831.i	−0.125759	+	0.125759i
$944$	−80309.5	+	26094.1i	−0.0901204	+	0.0292819i
$945$	7101.91	+	45954.9i	0.00795264	+	0.0514599i
$946$	−113101.	+	348089.i	−0.126382	+	0.388963i
$947$	−195767.	+	99748.4i	−0.218293	+	0.111226i	−0.559718	−	0.828683i	$-0.689091\pi$
$947$	−195767.	+	99748.4i	−0.218293	+	0.111226i	0.341425	+	0.939909i	$0.389091\pi$
$948$	−168241.	+	1.06223e6i	−0.187205	+	1.18196i
$949$		−	229892.i		−	0.255265i
$950$	−580181.	−	588955.i	−0.642860	−	0.652581i
$951$	432165.			0.477847
$952$	45729.5	+	7242.84i	0.0504571	+	0.00799162i
$953$	349052.	+	685053.i	0.384330	+	0.754290i	0.999416	−	0.0341700i	$-0.0108788\pi$
$953$	349052.	+	685053.i	0.384330	+	0.754290i	−0.615086	+	0.788460i	$0.710879\pi$
$954$	−1.01675e6	−	330363.i	−1.11717	−	0.362990i
$955$	217709.	+	431270.i	0.238709	+	0.472871i
$956$	−78570.4	−	241815.i	−0.0859692	−	0.264586i
$957$	−493168.	−	493168.i	−0.538482	−	0.538482i
$958$	−1.31059e6	−	667778.i	−1.42802	−	0.727614i
$959$	−14698.3	+	20230.5i	−0.0159820	+	0.0219973i
$960$	−572396.	+	412598.i	−0.621090	+	0.447697i
$961$	−718089.	+	521722.i	−0.777555	+	0.564927i
$962$	−401730.	−	2.53642e6i	−0.434095	−	2.74077i
$963$	−56356.0	+	8925.91i	−0.0607698	+	0.00962499i
$964$	−565446.	−	778270.i	−0.608467	−	0.837483i
$965$	632932.	−	203030.i	0.679677	−	0.218025i
$966$	−21648.4	−	15728.5i	−0.0231991	−	0.0168552i
$967$	−400444.	+	785915.i	−0.428241	+	0.840471i	0.571560	+	0.820560i	$0.306338\pi$
$967$	−400444.	+	785915.i	−0.428241	+	0.840471i	−0.999802	+	0.0199111i	$0.993662\pi$
$968$	28786.1	−	28786.1i	0.0307207	−	0.0307207i
$969$	286525.	−	93097.8i	0.305152	−	0.0991498i
$970$	−812897.	−	131879.i	−0.863956	−	0.140162i
$971$	−91349.8	+	281146.i	−0.0968878	+	0.298190i	−0.987741	−	0.156101i	$-0.950107\pi$
$971$	−91349.8	+	281146.i	−0.0968878	+	0.298190i	0.890853	+	0.454291i	$0.150107\pi$
$972$	1.25232e6	−	638089.i	1.32551	−	0.675381i
$973$	−746.721	+	4714.61i	−0.000788738	+	0.00497990i
$974$		−	829916.i		−	0.874815i
$975$	−164514.	+	493686.i	−0.173059	+	0.519328i
$976$	299893.			0.314823
$977$	−411372.	−	65154.9i	−0.430968	−	0.0682587i	−0.0628182	−	0.998025i	$-0.520009\pi$
$977$	−411372.	−	65154.9i	−0.430968	−	0.0682587i	−0.368150	+	0.929766i	$0.620009\pi$
$978$	270559.	+	531001.i	0.282868	+	0.555160i
$979$	192128.	+	62426.0i	0.200458	+	0.0651329i
$980$	−989597.	+	982199.i	−1.03040	+	1.02270i
$981$	221354.	+	681258.i	0.230012	+	0.707903i
$982$	971487.	+	971487.i	1.00743	+	1.00743i
$983$	−1.26671e6	−	645421.i	−1.31090	−	0.667938i	−0.347925	−	0.937522i	$-0.613114\pi$
$983$	−1.26671e6	−	645421.i	−1.31090	−	0.667938i	−0.962977	+	0.269584i	$0.913114\pi$
$984$	55379.5	−	76223.4i	0.0571951	−	0.0787223i
$985$	−594998.	−	2232.42i	−0.613258	−	0.00230093i
$986$	−2.21318e6	+	1.60797e6i	−2.27647	+	1.65395i
$987$	6303.83	+	39800.8i	0.00647099	+	0.0408562i
$988$	−945041.	+	149680.i	−0.968137	+	0.153338i
$989$	−90761.8	−	124923.i	−0.0927920	−	0.127717i
$990$	723383.	−	987836.i	0.738071	−	1.00789i
$991$	−415542.	−	301909.i	−0.423123	−	0.307417i	0.355770	−	0.934574i	$-0.384219\pi$
$991$	−415542.	−	301909.i	−0.423123	−	0.307417i	−0.778893	+	0.627156i	$0.784219\pi$
$992$	775621.	−	1.52224e6i	0.788182	−	1.54689i
$993$	319148.	−	319148.i	0.323664	−	0.323664i
$994$	144527.	−	46959.8i	0.146278	−	0.0475284i
$995$	482895.	−	939009.i	0.487761	−	0.948470i
$996$	120482.	−	370804.i	0.121451	−	0.373789i
$997$	−562759.	+	286740.i	−0.566151	+	0.288468i	−0.713545	−	0.700610i	$-0.752911\pi$
$997$	−562759.	+	286740.i	−0.566151	+	0.288468i	0.147394	+	0.989078i	$0.452911\pi$
$998$	−450961.	+	2.84726e6i	−0.452770	+	2.85868i
$999$		−	1.29483e6i		−	1.29743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.2.8	✓	72
5.2	odd	4		125.5.f.a.93.2		72
5.3	odd	4		125.5.f.b.93.8		72
5.4	even	2		125.5.f.c.32.2		72
25.9	even	10		125.5.f.a.82.2		72
25.12	odd	20		125.5.f.c.43.2		72
25.13	odd	20	inner	25.5.f.a.13.8	yes	72
25.16	even	5		125.5.f.b.82.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.2.8	✓	72	1.1	even	1	trivial
25.5.f.a.13.8	yes	72	25.13	odd	20	inner
125.5.f.a.82.2		72	25.9	even	10
125.5.f.a.93.2		72	5.2	odd	4
125.5.f.b.82.8		72	25.16	even	5
125.5.f.b.93.8		72	5.3	odd	4
125.5.f.c.32.2		72	5.4	even	2
125.5.f.c.43.2		72	25.12	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(6.19314 + 0.980897i) q^{2} +(1.94321 + 3.81377i) q^{3} +(22.1759 + 7.20540i) q^{4} +(-22.2324 - 11.4333i) q^{5} +(8.29367 + 25.5253i) q^{6} +(-2.13863 - 2.13863i) q^{7} +(40.8803 + 20.8296i) q^{8} +(36.8419 - 50.7085i) q^{9} +O(q^{10})\)	\(q+(6.19314 + 0.980897i) q^{2} +(1.94321 + 3.81377i) q^{3} +(22.1759 + 7.20540i) q^{4} +(-22.2324 - 11.4333i) q^{5} +(8.29367 + 25.5253i) q^{6} +(-2.13863 - 2.13863i) q^{7} +(40.8803 + 20.8296i) q^{8} +(36.8419 - 50.7085i) q^{9} +(-126.474 - 92.6155i) q^{10} +(-100.814 + 73.2454i) q^{11} +(15.6128 + 98.5755i) q^{12} +(192.125 - 30.4296i) q^{13} +(-11.1471 - 15.3426i) q^{14} +(0.401487 - 107.007i) q^{15} +(-69.0776 - 50.1878i) q^{16} +(-151.474 + 297.285i) q^{17} +(277.907 - 277.907i) q^{18} +(-200.631 + 65.1889i) q^{19} +(-410.644 - 413.737i) q^{20} +(4.00043 - 12.3120i) q^{21} +(-696.200 + 354.731i) q^{22} +(51.5687 - 325.592i) q^{23} +196.384i q^{24} +(363.561 + 508.378i) q^{25} +1219.71 q^{26} +(607.417 + 96.2054i) q^{27} +(-32.0164 - 62.8358i) q^{28} +(1243.60 + 404.071i) q^{29} +(107.449 - 662.313i) q^{30} +(415.869 + 1279.91i) q^{31} +(-897.663 - 897.663i) q^{32} +(-475.243 - 242.149i) q^{33} +(-1229.71 + 1692.55i) q^{34} +(23.0954 + 71.9984i) q^{35} +(1182.38 - 859.047i) q^{36} +(-329.367 - 2079.54i) q^{37} +(-1306.48 + 206.926i) q^{38} +(489.391 + 673.589i) q^{39} +(-670.719 - 930.487i) q^{40} +(-388.134 - 281.996i) q^{41} +(36.8520 - 72.3262i) q^{42} +(331.220 - 331.220i) q^{43} +(-2763.40 + 897.883i) q^{44} +(-1398.85 + 706.149i) q^{45} +(638.744 - 1965.85i) q^{46} +(-2773.51 + 1413.17i) q^{47} +(57.1723 - 360.972i) q^{48} -2391.85i q^{49} +(1752.92 + 3505.07i) q^{50} -1428.12 q^{51} +(4479.81 + 709.532i) q^{52} +(-1234.93 - 2423.69i) q^{53} +(3667.45 + 1191.63i) q^{54} +(3078.77 - 475.794i) q^{55} +(-42.8811 - 131.975i) q^{56} +(-638.483 - 638.483i) q^{57} +(7305.45 + 3722.31i) q^{58} +(581.299 - 800.089i) q^{59} +(779.928 - 2370.08i) q^{60} +(-2841.48 + 2064.45i) q^{61} +(1320.07 + 8334.61i) q^{62} +(-187.238 + 29.6555i) q^{63} +(-3875.84 - 5334.63i) q^{64} +(-4619.31 - 1520.09i) q^{65} +(-2705.73 - 1965.83i) q^{66} +(2844.74 - 5583.11i) q^{67} +(-5501.14 + 5501.14i) q^{68} +(1341.94 - 436.023i) q^{69} +(72.4101 + 468.550i) q^{70} +(-2476.20 + 7620.94i) q^{71} +(2562.34 - 1305.58i) q^{72} +(184.881 - 1167.29i) q^{73} -13202.0i q^{74} +(-1232.36 + 2374.42i) q^{75} -4918.89 q^{76} +(372.248 + 58.9583i) q^{77} +(2370.15 + 4651.67i) q^{78} +(10248.4 + 3329.92i) q^{79} +(961.953 + 1905.58i) q^{80} +(-755.447 - 2325.03i) q^{81} +(-2127.16 - 2127.16i) q^{82} +(-3480.73 - 1773.52i) q^{83} +(177.426 - 244.206i) q^{84} +(6766.58 - 4877.52i) q^{85} +(2376.18 - 1726.40i) q^{86} +(875.550 + 5528.00i) q^{87} +(-5646.97 + 894.392i) q^{88} +(-952.885 - 1311.53i) q^{89} +(-9355.91 + 3001.16i) q^{90} +(-475.962 - 345.806i) q^{91} +(3489.60 - 6848.73i) q^{92} +(-4073.17 + 4073.17i) q^{93} +(-18562.9 + 6031.45i) q^{94} +(5205.83 + 844.556i) q^{95} +(1679.13 - 5167.83i) q^{96} +(4680.87 - 2385.02i) q^{97} +(2346.16 - 14813.1i) q^{98} +7810.60i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Introduction

L-functions

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