LMFDB - Embedded newform 150.6.g.d.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, 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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	150.61
Dual form			150.6.g.d.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 + 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-24.3873 + 50.3017i) q^{5} +(-11.1246 - 34.2380i) q^{6} +94.8525 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})$	\(q+(-3.23607 + 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-24.3873 + 50.3017i) q^{5} +(-11.1246 - 34.2380i) q^{6} +94.8525 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-39.3474 - 220.118i) q^{10} +(464.230 - 337.283i) q^{11} +(116.498 + 84.6411i) q^{12} +(710.494 + 516.204i) q^{13} +(-306.949 + 223.012i) q^{14} +(-362.733 - 348.640i) q^{15} +(-207.108 - 150.473i) q^{16} +(-454.132 - 1397.67i) q^{17} +324.000 q^{18} +(607.934 + 1871.03i) q^{19} +(644.859 + 619.804i) q^{20} +(-263.799 + 811.891i) q^{21} +(-709.280 + 2182.94i) q^{22} +(3847.41 - 2795.31i) q^{23} -576.000 q^{24} +(-1935.52 - 2453.44i) q^{25} -3512.88 q^{26} +(589.773 - 428.495i) q^{27} +(468.977 - 1443.36i) q^{28} +(-19.3273 + 59.4833i) q^{29} +(1993.53 + 275.386i) q^{30} +(2483.19 + 7642.48i) q^{31} +1024.00 q^{32} +(1595.88 + 4911.62i) q^{33} +(4755.73 + 3455.24i) q^{34} +(-2313.20 + 4771.24i) q^{35} +(-1048.49 + 761.770i) q^{36} +(6001.42 + 4360.28i) q^{37} +(-6366.37 - 4625.44i) q^{38} +(-6394.45 + 4645.84i) q^{39} +(-3544.05 - 489.576i) q^{40} +(-7944.15 - 5771.76i) q^{41} +(-1055.20 - 3247.56i) q^{42} -8007.83 q^{43} +(-2837.12 - 8731.76i) q^{44} +(3993.00 - 2135.19i) q^{45} +(-5878.32 + 18091.6i) q^{46} +(-3325.50 + 10234.8i) q^{47} +(1863.98 - 1354.26i) q^{48} -7809.99 q^{49} +(12031.9 + 3388.83i) q^{50} +13226.4 q^{51} +(11367.9 - 8259.27i) q^{52} +(-10055.0 + 30946.2i) q^{53} +(-901.094 + 2773.28i) q^{54} +(5644.58 + 31577.0i) q^{55} +(1875.91 + 5773.45i) q^{56} -17705.9 q^{57} +(-77.3092 - 237.933i) q^{58} +(40564.2 + 29471.6i) q^{59} +(-7098.67 + 3795.90i) q^{60} +(-25054.5 + 18203.1i) q^{61} +(-26004.3 - 18893.3i) q^{62} +(-6215.72 - 4515.99i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-43293.0 + 23150.2i) q^{65} +(-16712.3 - 12142.2i) q^{66} +(3501.49 + 10776.5i) q^{67} -23513.6 q^{68} +(13226.2 + 40706.1i) q^{69} +(-3732.20 - 20878.7i) q^{70} +(13223.6 - 40698.0i) q^{71} +(1601.94 - 4930.28i) q^{72} +(47498.2 - 34509.5i) q^{73} -29672.6 q^{74} +(26383.3 - 9743.69i) q^{75} +31477.1 q^{76} +(44033.4 - 31992.1i) q^{77} +(9769.85 - 30068.5i) q^{78} +(-11630.9 + 35796.2i) q^{79} +(12619.9 - 6748.27i) q^{80} +(2027.46 + 6239.88i) q^{81} +39278.0 q^{82} +(-23187.5 - 71363.6i) q^{83} +(11050.2 + 8028.42i) q^{84} +(81380.4 + 11241.9i) q^{85} +(25913.9 - 18827.5i) q^{86} +(-455.396 - 330.864i) q^{87} +(29710.7 + 21586.1i) q^{88} +(-38770.1 + 28168.1i) q^{89} +(-7901.48 + 16297.7i) q^{90} +(67392.2 + 48963.3i) q^{91} +(-23513.3 - 72366.5i) q^{92} -72322.0 q^{93} +(-13302.0 - 40939.3i) q^{94} +(-108942. - 15049.2i) q^{95} +(-2847.90 + 8764.94i) q^{96} +(10600.1 - 32623.8i) q^{97} +(25273.7 - 18362.4i) q^{98} -46479.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9 + 44 * q^10 - 135 * q^11 + 1008 * q^12 + 616 * q^13 - 48 * q^14 + 531 * q^15 - 1792 * q^16 - 3372 * q^17 + 9072 * q^18 + 488 * q^19 - 944 * q^20 - 387 * q^21 - 1920 * q^22 - 620 * q^23 - 16128 * q^24 + 6659 * q^25 - 1616 * q^26 + 5103 * q^27 + 688 * q^28 + 5682 * q^29 + 2844 * q^30 + 3339 * q^31 + 28672 * q^32 + 4320 * q^33 + 14032 * q^34 - 23984 * q^35 - 9072 * q^36 + 4506 * q^37 - 1528 * q^38 - 5544 * q^39 - 5056 * q^40 + 44962 * q^41 - 1548 * q^42 + 38028 * q^43 - 7680 * q^44 + 9396 * q^45 + 7480 * q^46 - 58300 * q^47 + 16128 * q^48 + 114402 * q^49 + 7476 * q^50 + 2448 * q^51 + 9856 * q^52 - 138 * q^53 + 20412 * q^54 + 96850 * q^55 + 2752 * q^56 + 1908 * q^57 + 22728 * q^58 + 40245 * q^59 - 16704 * q^60 + 79380 * q^61 - 54504 * q^62 - 972 * q^63 - 28672 * q^64 + 3532 * q^65 + 4860 * q^66 - 34352 * q^67 - 4352 * q^68 - 16830 * q^69 - 69476 * q^70 + 115860 * q^71 - 36288 * q^72 - 121214 * q^73 - 37856 * q^74 + 21969 * q^75 - 3392 * q^76 + 195005 * q^77 + 14904 * q^78 + 36224 * q^79 + 29696 * q^80 - 45927 * q^81 + 34608 * q^82 + 85051 * q^83 + 1728 * q^84 + 137496 * q^85 - 18568 * q^86 + 127062 * q^87 - 8640 * q^88 - 53826 * q^89 + 3564 * q^90 - 408104 * q^91 + 29920 * q^92 - 185166 * q^93 - 233200 * q^94 - 482004 * q^95 + 64512 * q^96 - 244169 * q^97 - 395952 * q^98 + 99630 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$3$	−2.78115	+	8.55951i	−0.178411	+	0.549093i
$3$	−2.78115	+	8.55951i	−0.178411	+	0.549093i
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−24.3873	+	50.3017i	−0.436253	+	0.899824i
$5$	−24.3873	+	50.3017i	−0.436253	+	0.899824i
$6$	−11.1246	−	34.2380i	−0.126156	−	0.388267i
$7$	94.8525			0.731651			0.365825	−	0.930683i	$-0.380787\pi$
$7$	94.8525			0.731651			0.365825	+	0.930683i	$0.380787\pi$
$8$	19.7771	+	60.8676i	0.109254	+	0.336249i
$9$	−65.5304	−	47.6106i	−0.269672	−	0.195928i
$10$	−39.3474	−	220.118i	−0.124427	−	0.696073i
$11$	464.230	−	337.283i	1.15678	−	0.840451i	0.167414	−	0.985887i	$-0.446458\pi$
$11$	464.230	−	337.283i	1.15678	−	0.840451i	0.989368	+	0.145435i	$0.0464582\pi$
$12$	116.498	+	84.6411i	0.233543	+	0.169679i
$13$	710.494	+	516.204i	1.16601	+	0.847156i	0.990526	−	0.137327i	$-0.0438510\pi$
$13$	710.494	+	516.204i	1.16601	+	0.847156i	0.175484	+	0.984482i	$0.443851\pi$
$14$	−306.949	+	223.012i	−0.418549	+	0.304094i
$15$	−362.733	−	348.640i	−0.416254	−	0.400082i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	−454.132	−	1397.67i	−0.381118	−	1.17296i	−0.939257	−	0.343214i	$-0.888484\pi$
$17$	−454.132	−	1397.67i	−0.381118	−	1.17296i	0.558139	−	0.829748i	$-0.311516\pi$
$18$	324.000			0.235702
$19$	607.934	+	1871.03i	0.386343	+	1.18904i	0.935502	+	0.353323i	$0.114948\pi$
$19$	607.934	+	1871.03i	0.386343	+	1.18904i	−0.549159	+	0.835718i	$0.685052\pi$
$20$	644.859	+	619.804i	0.360487	+	0.346481i
$21$	−263.799	+	811.891i	−0.130535	+	0.401744i
$22$	−709.280	+	2182.94i	−0.312436	+	0.961580i
$23$	3847.41	−	2795.31i	1.51652	−	1.10182i	0.553347	−	0.832951i	$-0.313350\pi$
$23$	3847.41	−	2795.31i	1.51652	−	1.10182i	0.963177	−	0.268868i	$-0.0866496\pi$
$24$	−576.000			−0.204124
$25$	−1935.52	−	2453.44i	−0.619366	−	0.785102i
$26$	−3512.88			−1.01913
$27$	589.773	−	428.495i	0.155695	−	0.113119i
$28$	468.977	−	1443.36i	0.113046	−	0.347921i
$29$	−19.3273	+	59.4833i	−0.00426753	+	0.0131341i	−0.953168	−	0.302443i	$-0.902198\pi$
$29$	−19.3273	+	59.4833i	−0.00426753	+	0.0131341i	0.948900	+	0.315577i	$0.102198\pi$
$30$	1993.53	+	275.386i	0.404408	+	0.0558649i
$31$	2483.19	+	7642.48i	0.464094	+	1.42834i	0.860118	+	0.510095i	$0.170390\pi$
$31$	2483.19	+	7642.48i	0.464094	+	1.42834i	−0.396024	+	0.918240i	$0.629610\pi$
$32$	1024.00			0.176777
$33$	1595.88	+	4911.62i	0.255103	+	0.785127i
$34$	4755.73	+	3455.24i	0.705538	+	0.512603i
$35$	−2313.20	+	4771.24i	−0.319185	+	0.658357i
$36$	−1048.49	+	761.770i	−0.134836	+	0.0979642i
$37$	6001.42	+	4360.28i	0.720692	+	0.523613i	0.886605	−	0.462527i	$-0.153057\pi$
$37$	6001.42	+	4360.28i	0.720692	+	0.523613i	−0.165913	+	0.986140i	$0.553057\pi$
$38$	−6366.37	−	4625.44i	−0.715209	−	0.519630i
$39$	−6394.45	+	4645.84i	−0.673196	+	0.489106i
$40$	−3544.05	−	489.576i	−0.350228	−	0.0483805i
$41$	−7944.15	−	5771.76i	−0.738053	−	0.536227i	0.154048	−	0.988063i	$-0.450769\pi$
$41$	−7944.15	−	5771.76i	−0.738053	−	0.536227i	−0.892101	+	0.451837i	$0.850769\pi$
$42$	−1055.20	−	3247.56i	−0.0923019	−	0.284076i
$43$	−8007.83			−0.660456			−0.330228	−	0.943901i	$-0.607126\pi$
$43$	−8007.83			−0.660456			−0.330228	+	0.943901i	$0.607126\pi$
$44$	−2837.12	−	8731.76i	−0.220926	−	0.679940i
$45$	3993.00	−	2135.19i	0.293947	−	0.157183i
$46$	−5878.32	+	18091.6i	−0.409599	+	1.26062i
$47$	−3325.50	+	10234.8i	−0.219590	+	0.675828i	0.779206	+	0.626768i	$0.215623\pi$
$47$	−3325.50	+	10234.8i	−0.219590	+	0.675828i	−0.998796	+	0.0490599i	$0.984377\pi$
$48$	1863.98	−	1354.26i	0.116772	−	0.0848395i
$49$	−7809.99			−0.464687
$50$	12031.9	+	3388.83i	0.680625	+	0.191701i
$51$	13226.4			0.712060
$52$	11367.9	−	8259.27i	0.583005	−	0.423578i
$53$	−10055.0	+	30946.2i	−0.491692	+	1.51327i	0.330356	+	0.943856i	$0.392831\pi$
$53$	−10055.0	+	30946.2i	−0.491692	+	1.51327i	−0.822049	+	0.569417i	$0.807169\pi$
$54$	−901.094	+	2773.28i	−0.0420519	+	0.129422i
$55$	5644.58	+	31577.0i	0.251608	+	1.40755i
$56$	1875.91	+	5773.45i	0.0799358	+	0.246017i
$57$	−17705.9			−0.721821
$58$	−77.3092	−	237.933i	−0.00301760	−	0.00928721i
$59$	40564.2	+	29471.6i	1.51710	+	1.10223i	0.962904	+	0.269846i	$0.0869728\pi$
$59$	40564.2	+	29471.6i	1.51710	+	1.10223i	0.554192	+	0.832389i	$0.313027\pi$
$60$	−7098.67	+	3795.90i	−0.254565	+	0.136125i
$61$	−25054.5	+	18203.1i	−0.862106	+	0.626356i	−0.928457	−	0.371440i	$-0.878864\pi$
$61$	−25054.5	+	18203.1i	−0.862106	+	0.626356i	0.0663514	+	0.997796i	$0.478864\pi$
$62$	−26004.3	−	18893.3i	−0.859145	−	0.624205i
$63$	−6215.72	−	4515.99i	−0.197306	−	0.143351i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−43293.0	+	23150.2i	−1.27097	+	0.679629i
$66$	−16712.3	−	12142.2i	−0.472254	−	0.343113i
$67$	3501.49	+	10776.5i	0.0952940	+	0.293285i	0.987330	−	0.158679i	$-0.0507236\pi$
$67$	3501.49	+	10776.5i	0.0952940	+	0.293285i	−0.892036	+	0.451964i	$0.850724\pi$
$68$	−23513.6			−0.616662
$69$	13226.2	+	40706.1i	0.334436	+	1.02929i
$70$	−3732.20	−	20878.7i	−0.0910374	−	0.509283i
$71$	13223.6	−	40698.0i	0.311317	−	0.958136i	−0.665927	−	0.746017i	$-0.731964\pi$
$71$	13223.6	−	40698.0i	0.311317	−	0.958136i	0.977244	−	0.212119i	$-0.0680363\pi$
$72$	1601.94	−	4930.28i	0.0364180	−	0.112083i
$73$	47498.2	−	34509.5i	1.04321	−	0.757933i	0.0722972	−	0.997383i	$-0.476967\pi$
$73$	47498.2	−	34509.5i	1.04321	−	0.757933i	0.970909	+	0.239450i	$0.0769670\pi$
$74$	−29672.6			−0.629908
$75$	26383.3	−	9743.69i	0.541596	−	0.200019i
$76$	31477.1			0.625116
$77$	44033.4	−	31992.1i	0.846361	−	0.614917i
$78$	9769.85	−	30068.5i	0.181824	−	0.559597i
$79$	−11630.9	+	35796.2i	−0.209674	+	0.645311i	0.789815	+	0.613346i	$0.210177\pi$
$79$	−11630.9	+	35796.2i	−0.209674	+	0.645311i	−0.999489	+	0.0319655i	$0.989823\pi$
$80$	12619.9	−	6748.27i	0.220460	−	0.117887i
$81$	2027.46	+	6239.88i	0.0343352	+	0.105673i
$82$	39278.0			0.645082
$83$	−23187.5	−	71363.6i	−0.369452	−	1.13706i	−0.947146	−	0.320803i	$-0.896047\pi$
$83$	−23187.5	−	71363.6i	−0.369452	−	1.13706i	0.577694	−	0.816253i	$-0.303953\pi$
$84$	11050.2	+	8028.42i	0.170872	+	0.124146i
$85$	81380.4	+	11241.9i	1.22172	+	0.168769i
$86$	25913.9	−	18827.5i	0.377821	−	0.274503i
$87$	−455.396	−	330.864i	−0.00645046	−	0.00468653i
$88$	29710.7	+	21586.1i	0.408984	+	0.297144i
$89$	−38770.1	+	28168.1i	−0.518826	+	0.376949i	−0.816161	−	0.577824i	$-0.803902\pi$
$89$	−38770.1	+	28168.1i	−0.518826	+	0.376949i	0.297335	+	0.954773i	$0.403902\pi$
$90$	−7901.48	+	16297.7i	−0.102826	+	0.212091i
$91$	67392.2	+	48963.3i	0.853112	+	0.619822i
$92$	−23513.3	−	72366.5i	−0.289630	−	0.891390i
$93$	−72322.0			−0.867088
$94$	−13302.0	−	40939.3i	−0.155273	−	0.477882i
$95$	−108942.	−	15049.2i	−1.23847	−	0.171082i
$96$	−2847.90	+	8764.94i	−0.0315389	+	0.0970668i
$97$	10600.1	−	32623.8i	0.114388	−	0.352051i	−0.877431	−	0.479703i	$-0.840744\pi$
$97$	10600.1	−	32623.8i	0.114388	−	0.352051i	0.991819	+	0.127653i	$0.0407443\pi$
$98$	25273.7	−	18362.4i	0.265829	−	0.193136i
$99$	−46479.4			−0.476620
$100$	−46903.6	+	17322.1i	−0.469036	+	0.173221i
$101$	164205.			1.60171			0.800853	−	0.598861i	$-0.204380\pi$
$101$	164205.			1.60171			0.800853	+	0.598861i	$0.204380\pi$
$102$	−42801.6	+	31097.2i	−0.407342	+	0.295951i
$103$	65334.2	−	201078.i	0.606803	−	1.86755i	0.122916	−	0.992417i	$-0.460776\pi$
$103$	65334.2	−	201078.i	0.606803	−	1.86755i	0.483887	−	0.875130i	$-0.339224\pi$
$104$	−17368.6	+	53455.1i	−0.157464	+	0.484625i
$105$	−34406.1	−	33069.4i	−0.304553	−	0.292720i
$106$	−40220.1	−	123785.i	−0.347679	−	1.07005i
$107$	−118533.			−1.00087			−0.500437	−	0.865773i	$-0.666827\pi$
$107$	−118533.			−1.00087			−0.500437	+	0.865773i	$0.666827\pi$
$108$	−3604.37	−	11093.1i	−0.0297352	−	0.0915155i
$109$	151421.	+	110014.i	1.22073	+	0.886912i	0.996160	−	0.0875467i	$-0.0279027\pi$
$109$	151421.	+	110014.i	1.22073	+	0.886912i	0.224569	+	0.974458i	$0.427903\pi$
$110$	−92508.2	−	88914.0i	−0.728951	−	0.700630i
$111$	−54012.8	+	39242.6i	−0.416092	+	0.302308i
$112$	−19644.8	−	14272.7i	−0.147980	−	0.107513i
$113$	−61902.2	−	44974.6i	−0.456048	−	0.331338i	0.335931	−	0.941886i	$-0.390949\pi$
$113$	−61902.2	−	44974.6i	−0.456048	−	0.331338i	−0.791979	+	0.610549i	$0.790949\pi$
$114$	57297.4	−	41629.0i	0.412926	−	0.300008i
$115$	46780.8	+	261701.i	0.329855	+	1.84528i
$116$	809.592	+	588.203i	0.00558626	+	0.00405866i
$117$	−21982.2	−	67654.1i	−0.148459	−	0.456909i
$118$	−200560.			−1.32599
$119$	−43075.6	−	132573.i	−0.278846	−	0.858198i
$120$	14047.1	−	28973.8i	0.0890498	−	0.183676i
$121$	51982.3	−	159985.i	0.322769	−	0.993382i
$122$	38279.8	−	117813.i	0.232847	−	0.716629i
$123$	71497.3	−	51945.8i	0.426115	−	0.309591i
$124$	128572.			0.750920
$125$	170614.	−	37527.0i	0.976654	−	0.214817i
$126$	30732.2			0.172452
$127$	−134054.	+	97395.6i	−0.737512	+	0.535834i	−0.891931	−	0.452172i	$-0.850649\pi$
$127$	−134054.	+	97395.6i	−0.737512	+	0.535834i	0.154419	+	0.988005i	$0.450649\pi$
$128$	5062.93	−	15582.1i	0.0273135	−	0.0840623i
$129$	22271.0	−	68543.1i	0.117833	−	0.362652i
$130$	85669.6	−	176704.i	0.444599	−	0.917038i
$131$	2458.04	+	7565.06i	0.0125144	+	0.0385154i	0.957119	−	0.289696i	$-0.0935542\pi$
$131$	2458.04	+	7565.06i	0.0125144	+	0.0385154i	−0.944604	+	0.328211i	$0.893554\pi$
$132$	82630.1			0.412765
$133$	57664.1	+	177472.i	0.282668	+	0.869963i
$134$	−36668.1	−	26640.9i	−0.176411	−	0.128170i
$135$	7171.06	+	40116.4i	0.0338649	+	0.189447i
$136$	76091.7	−	55283.9i	0.352769	−	0.256302i
$137$	−38683.3	−	28105.1i	−0.176085	−	0.127933i	0.496252	−	0.868179i	$-0.334709\pi$
$137$	−38683.3	−	28105.1i	−0.176085	−	0.127933i	−0.672337	+	0.740245i	$0.734709\pi$
$138$	−138507.	−	100631.i	−0.619118	−	0.449816i
$139$	−129044.	+	93755.9i	−0.566501	+	0.411587i	−0.833832	−	0.552018i	$-0.813858\pi$
$139$	−129044.	+	93755.9i	−0.566501	+	0.411587i	0.267332	+	0.963605i	$0.413858\pi$
$140$	61166.5	+	58790.0i	0.263751	+	0.253503i
$141$	−78356.4	−	56929.3i	−0.331915	−	0.241150i
$142$	52894.3	+	162792.i	0.220135	+	0.677504i
$143$	503940.			2.06081
$144$	6407.78	+	19721.1i	0.0257514	+	0.0792547i
$145$	−2520.77	−	2422.83i	−0.00995665	−	0.00956981i
$146$	−72570.8	+	223350.i	−0.281760	+	0.867169i
$147$	21720.8	−	66849.7i	0.0829053	−	0.255156i
$148$	96022.7	−	69764.6i	0.360346	−	0.261807i
$149$	−164470.			−0.606906			−0.303453	−	0.952846i	$-0.598140\pi$
$149$	−164470.			−0.606906			−0.303453	+	0.952846i	$0.598140\pi$
$150$	−62469.2	+	93562.0i	−0.226693	+	0.339525i
$151$	304749.			1.08768			0.543838	−	0.839190i	$-0.316971\pi$
$151$	304749.			1.08768			0.543838	+	0.839190i	$0.316971\pi$
$152$	−101862.	+	74007.0i	−0.357605	+	0.259815i
$153$	−36784.7	+	113212.i	−0.127039	+	0.390987i
$154$	−67277.1	+	207058.i	−0.228594	+	0.703541i
$155$	−444988.	−	61470.7i	−1.48771	−	0.205513i
$156$	39079.4	+	120274.i	0.128569	+	0.395695i
$157$	351105.			1.13681			0.568405	−	0.822749i	$-0.307561\pi$
$157$	351105.			1.13681			0.568405	+	0.822749i	$0.307561\pi$
$158$	−46523.6	−	143185.i	−0.148262	−	0.456304i
$159$	−236920.	−	172132.i	−0.743204	−	0.539969i
$160$	−24972.6	+	51508.9i	−0.0771194	+	0.159068i
$161$	364937.	−	265142.i	1.10957	−	0.806147i
$162$	−21231.8	−	15425.8i	−0.0635624	−	0.0461808i
$163$	−153937.	−	111842.i	−0.453809	−	0.329711i	0.337289	−	0.941401i	$-0.390490\pi$
$163$	−153937.	−	111842.i	−0.453809	−	0.329711i	−0.791098	+	0.611690i	$0.790490\pi$
$164$	−127106.	+	92348.1i	−0.369026	+	0.268113i
$165$	−285982.	−	39505.6i	−0.817765	−	0.112966i
$166$	242822.	+	176421.i	0.683940	+	0.496912i
$167$	78018.9	+	240117.i	0.216475	+	0.666243i	0.999046	+	0.0436803i	$0.0139083\pi$
$167$	78018.9	+	240117.i	0.216475	+	0.666243i	−0.782570	+	0.622562i	$0.786092\pi$
$168$	−54635.1			−0.149348
$169$	123599.	+	380400.i	0.332889	+	1.02453i
$170$	−289784.	+	154957.i	−0.769046	+	0.411235i
$171$	49242.7	−	151553.i	0.128781	−	0.396347i
$172$	−39592.9	+	121854.i	−0.102046	+	0.314066i
$173$	−271021.	+	196908.i	−0.688474	+	0.500205i	−0.876158	−	0.482024i	$-0.839902\pi$
$173$	−271021.	+	196908.i	−0.688474	+	0.500205i	0.187684	+	0.982229i	$0.439902\pi$
$174$	2251.60			0.00563791
$175$	−183589.	−	232715.i	−0.453160	−	0.574421i
$176$	−146898.			−0.357465
$177$	−365078.	+	265245.i	−0.875896	+	0.636375i
$178$	59235.4	−	182308.i	0.140130	−	0.431276i
$179$	−104737.	+	322346.i	−0.244324	+	0.751952i	0.751423	+	0.659821i	$0.229368\pi$
$179$	−104737.	+	322346.i	−0.244324	+	0.751952i	−0.995747	+	0.0921312i	$0.970632\pi$
$180$	−12748.6	−	71318.1i	−0.0293278	−	0.164066i
$181$	133101.	+	409644.i	0.301985	+	0.929415i	0.980785	+	0.195092i	$0.0625005\pi$
$181$	133101.	+	409644.i	0.301985	+	0.929415i	−0.678800	+	0.734323i	$0.737500\pi$
$182$	−333205.			−0.745647
$183$	−86129.6	−	265080.i	−0.190119	−	0.585125i
$184$	246234.	+	178900.i	0.536172	+	0.389552i
$185$	−365688.	+	195546.i	−0.785564	+	0.420068i
$186$	234039.	−	170039.i	0.496028	−	0.360385i
$187$	−682234.	−	495672.i	−1.42669	−	1.03655i
$188$	139300.	+	101208.i	0.287447	+	0.208842i
$189$	55941.5	−	40643.9i	0.113915	−	0.0827639i
$190$	387926.	−	207437.i	0.779588	−	0.416872i
$191$	485842.	+	352985.i	0.963633	+	0.700120i	0.953992	−	0.299833i	$-0.0969310\pi$
$191$	485842.	+	352985.i	0.963633	+	0.700120i	0.00964124	+	0.999954i	$0.496931\pi$
$192$	−11391.6	−	35059.7i	−0.0223014	−	0.0686366i
$193$	164349.			0.317595			0.158798	−	0.987311i	$-0.449238\pi$
$193$	164349.			0.317595			0.158798	+	0.987311i	$0.449238\pi$
$194$	42400.4	+	130495.i	0.0808846	+	0.248937i
$195$	−77750.2	−	434951.i	−0.146425	−	0.819132i
$196$	−38614.7	+	118844.i	−0.0717981	+	0.220972i
$197$	−208636.	+	642116.i	−0.383022	+	1.17882i	0.554883	+	0.831928i	$0.312763\pi$
$197$	−208636.	+	642116.i	−0.383022	+	1.17882i	−0.937905	+	0.346892i	$0.887237\pi$
$198$	150411.	−	109280.i	0.272656	−	0.198096i
$199$	−712135.			−1.27476			−0.637381	−	0.770548i	$-0.719982\pi$
$199$	−712135.			−1.27476			−0.637381	+	0.770548i	$0.719982\pi$
$200$	111056.	−	166332.i	0.196322	−	0.294037i
$201$	−101979.			−0.178042
$202$	−531379.	+	386069.i	−0.916274	+	0.665712i
$203$	−1833.24	+	5642.14i	−0.00312234	+	0.00960957i
$204$	65395.0	−	201265.i	0.110019	−	0.338605i
$205$	484065.	−	258846.i	0.804488	−	0.430187i
$206$	261337.	+	804312.i	0.429074	+	1.32056i
$207$	−385209.			−0.624842
$208$	−69474.5	−	213820.i	−0.111344	−	0.342682i
$209$	913288.	+	663543.i	1.44625	+	1.05076i
$210$	189091.	+	26121.1i	0.295885	+	0.0408736i
$211$	127932.	−	92948.4i	0.197822	−	0.143726i	−0.484465	−	0.874811i	$-0.660986\pi$
$211$	127932.	−	92948.4i	0.197822	−	0.143726i	0.682287	+	0.731085i	$0.260986\pi$
$212$	421190.	+	306013.i	0.643634	+	0.467627i
$213$	311578.	+	226375.i	0.470563	+	0.341884i
$214$	383581.	−	278688.i	0.572562	−	0.415990i
$215$	195289.	−	402808.i	0.288126	−	0.594294i
$216$	37745.5	+	27423.7i	0.0550466	+	0.0399937i
$217$	235537.	+	724909.i	0.339555	+	1.04504i
$218$	−748666.			−1.06696
$219$	163284.	+	502537.i	0.230056	+	0.708041i
$220$	508412.	+	70232.1i	0.708205	+	0.0978316i
$221$	398827.	−	1.22746e6i	0.549293	−	1.69055i
$222$	82524.1	−	253983.i	0.112382	−	0.345878i
$223$	−35058.3	+	25471.4i	−0.0472095	+	0.0342997i	−0.611140	−	0.791523i	$-0.709289\pi$
$223$	−35058.3	+	25471.4i	−0.0472095	+	0.0342997i	0.563930	+	0.825822i	$0.309289\pi$
$224$	97129.0			0.129339
$225$	10025.3	+	252926.i	0.0132021	+	0.333072i
$226$	306061.			0.398600
$227$	777007.	−	564528.i	1.00083	−	0.727145i	0.0385636	−	0.999256i	$-0.487722\pi$
$227$	777007.	−	564528.i	1.00083	−	0.727145i	0.962266	+	0.272111i	$0.0877218\pi$
$228$	−87542.6	+	269428.i	−0.111528	+	0.343246i
$229$	−74742.7	+	230034.i	−0.0941846	+	0.289870i	−0.987040	−	0.160472i	$-0.948698\pi$
$229$	−74742.7	+	230034.i	−0.0941846	+	0.289870i	0.892856	+	0.450343i	$0.148698\pi$
$230$	−766683.	−	736895.i	−0.955644	−	0.918515i
$231$	151373.	+	465879.i	0.186646	+	0.574439i
$232$	−4002.84			−0.00488257
$233$	−426817.	−	1.31361e6i	−0.515053	−	1.58517i	−0.783185	−	0.621789i	$-0.786406\pi$
$233$	−426817.	−	1.31361e6i	−0.515053	−	1.58517i	0.268131	−	0.963382i	$-0.413594\pi$
$234$	230200.	+	167250.i	0.274831	+	0.199677i
$235$	−433729.	−	416878.i	−0.512329	−	0.492424i
$236$	649027.	−	471546.i	0.758548	−	0.551117i
$237$	−274051.	−	199109.i	−0.316927	−	0.230261i
$238$	451093.	+	327739.i	0.516207	+	0.375046i
$239$	−870935.	+	632771.i	−0.986259	+	0.716559i	−0.959099	−	0.283072i	$-0.908646\pi$
$239$	−870935.	+	632771.i	−0.986259	+	0.716559i	−0.0271604	+	0.999631i	$0.508646\pi$
$240$	22664.1	+	126788.i	0.0253986	+	0.142085i
$241$	−504180.	−	366308.i	−0.559169	−	0.406260i	0.271986	−	0.962301i	$-0.412320\pi$
$241$	−504180.	−	366308.i	−0.559169	−	0.406260i	−0.831155	+	0.556041i	$0.812320\pi$
$242$	207929.	+	639941.i	0.228232	+	0.702427i
$243$	−59049.0			−0.0641500
$244$	153119.	+	471253.i	0.164648	+	0.506733i
$245$	190465.	−	392856.i	0.202721	−	0.418136i
$246$	−109238.	+	336200.i	−0.115090	+	0.354210i
$247$	−533900.	+	1.64317e6i	−0.556823	+	1.71373i
$248$	−416069.	+	302292.i	−0.429573	+	0.312103i
$249$	675326.			0.690263
$250$	−463889.	+	522579.i	−0.469422	+	0.528812i
$251$	−1.13457e6			−1.13670			−0.568349	−	0.822788i	$-0.692418\pi$
$251$	−1.13457e6			−1.13670			−0.568349	+	0.822788i	$0.692418\pi$
$252$	−99451.6	+	72255.8i	−0.0986530	+	0.0716756i
$253$	843275.	−	2.59533e6i	0.828262	−	2.54913i
$254$	204816.	−	630357.i	0.199195	−	0.613059i
$255$	−322557.	+	665311.i	−0.310639	+	0.640729i
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	640457.			0.604863			0.302432	−	0.953171i	$-0.402202\pi$
$257$	640457.			0.604863			0.302432	+	0.953171i	$0.402202\pi$
$258$	89084.1	+	274173.i	0.0833203	+	0.256433i
$259$	569250.	+	413584.i	0.527295	+	0.383102i
$260$	138223.	+	773246.i	0.126808	+	0.709389i
$261$	4098.56	−	2977.78i	0.00372418	−	0.00270577i
$262$	−25740.9	−	18701.9i	−0.0231670	−	0.0168318i
$263$	653670.	+	474919.i	0.582733	+	0.423380i	0.839708	−	0.543038i	$-0.182726\pi$
$263$	653670.	+	474919.i	0.582733	+	0.423380i	−0.256976	+	0.966418i	$0.582726\pi$
$264$	−267397.	+	194275.i	−0.236127	+	0.171556i
$265$	−1.31143e6	−	1.26048e6i	−1.14718	−	1.10261i
$266$	−603867.	−	438735.i	−0.523283	−	0.380188i
$267$	−133280.	−	410193.i	−0.114416	−	0.352136i
$268$	181297.			0.154189
$269$	−203830.	−	627325.i	−0.171747	−	0.528581i	0.827723	−	0.561136i	$-0.189636\pi$
$269$	−203830.	−	627325.i	−0.171747	−	0.528581i	−0.999470	+	0.0325549i	$0.989636\pi$
$270$	−117525.	−	112959.i	−0.0981121	−	0.0943002i
$271$	526675.	−	1.62094e6i	0.435632	−	1.34074i	−0.456806	−	0.889566i	$-0.651007\pi$
$271$	526675.	−	1.62094e6i	0.435632	−	1.34074i	0.892438	−	0.451171i	$-0.148993\pi$
$272$	−116258.	+	357805.i	−0.0952796	+	0.293240i
$273$	−606530.	+	440670.i	−0.492545	+	0.357855i
$274$	191261.			0.153904
$275$	−1.72603e6	−	486145.i	−1.37631	−	0.387645i
$276$	684816.			0.541129
$277$	−805098.	+	584938.i	−0.630448	+	0.458047i	−0.856555	−	0.516055i	$-0.827400\pi$
$277$	−805098.	+	584938.i	−0.630448	+	0.458047i	0.226107	+	0.974102i	$0.427400\pi$
$278$	197161.	−	606801.i	0.153007	−	0.470906i
$279$	201139.	−	619041.i	0.154698	−	0.476112i
$280$	−336163.	−	46437.5i	−0.256244	−	0.0353976i
$281$	207583.	+	638875.i	0.156829	+	0.482670i	0.998342	−	0.0575675i	$-0.0183344\pi$
$281$	207583.	+	638875.i	0.156829	+	0.482670i	−0.841513	+	0.540237i	$0.818334\pi$
$282$	387415.			0.290104
$283$	−82942.5	−	255271.i	−0.0615617	−	0.189468i	0.915546	−	0.402214i	$-0.131759\pi$
$283$	−82942.5	−	255271.i	−0.0615617	−	0.189468i	−0.977107	+	0.212746i	$0.931759\pi$
$284$	−553916.	−	402444.i	−0.407520	−	0.296080i
$285$	431798.	−	890634.i	0.314897	−	0.649512i
$286$	−1.63078e6	+	1.18483e6i	−1.17891	+	0.856529i
$287$	−753522.	−	547466.i	−0.539997	−	0.392331i
$288$	−67103.1	−	48753.3i	−0.0476718	−	0.0346356i
$289$	−598570.	+	434887.i	−0.421571	+	0.306289i
$290$	13853.8	+	1913.77i	0.00967329	+	0.00133627i
$291$	249763.	+	181463.i	0.172900	+	0.125619i
$292$	−290283.	−	893400.i	−0.199235	−	0.613181i
$293$	2.37711e6			1.61763			0.808817	−	0.588060i	$-0.200108\pi$
$293$	2.37711e6			1.61763			0.808817	+	0.588060i	$0.200108\pi$
$294$	86883.2	+	267399.i	0.0586229	+	0.180423i
$295$	−2.47172e6	+	1.32171e6i	−1.65366	+	0.884266i
$296$	−146710.	+	451526.i	−0.0973261	+	0.299539i
$297$	129266.	−	397841.i	0.0850344	−	0.261709i
$298$	532236.	−	386692.i	0.347187	−	0.252246i
$299$	4.17652e6			2.70169
$300$	−17822.8	−	449647.i	−0.0114333	−	0.288449i
$301$	−759564.			−0.483223
$302$	−986188.	+	716507.i	−0.622218	+	0.452068i
$303$	−456679.	+	1.40551e6i	−0.285762	+	0.879485i
$304$	155631.	−	478984.i	0.0965857	−	0.297260i
$305$	−304638.	−	1.70421e6i	−0.187514	−	1.04899i
$306$	−147139.	−	452847.i	−0.0898305	−	0.276470i
$307$	366390.			0.221870			0.110935	−	0.993828i	$-0.464616\pi$
$307$	366390.			0.221870			0.110935	+	0.993828i	$0.464616\pi$
$308$	−269108.	−	828230.i	−0.161641	−	0.497478i
$309$	1.53942e6	+	1.11846e6i	0.917196	+	0.666382i
$310$	1.58454e6	−	847306.i	0.936480	−	0.500768i
$311$	−435916.	+	316712.i	−0.255565	+	0.185679i	−0.708190	−	0.706022i	$-0.750488\pi$
$311$	−435916.	+	316712.i	−0.255565	+	0.185679i	0.452624	+	0.891701i	$0.350488\pi$
$312$	−409245.	−	297334.i	−0.238011	−	0.172925i
$313$	1.17883e6	+	856467.i	0.680125	+	0.494140i	0.873399	−	0.487005i	$-0.161911\pi$
$313$	1.17883e6	+	856467.i	0.680125	+	0.494140i	−0.193274	+	0.981145i	$0.561911\pi$
$314$	−1.13620e6	+	825497.i	−0.650325	+	0.472489i
$315$	378746.	−	202529.i	0.215066	−	0.115003i
$316$	487201.	+	353972.i	0.274467	+	0.199412i
$317$	−530558.	−	1.63289e6i	−0.296541	−	0.912659i	−0.982699	−	0.185207i	$-0.940704\pi$
$317$	−530558.	−	1.63289e6i	−0.296541	−	0.912659i	0.686158	−	0.727452i	$-0.259296\pi$
$318$	1.17139e6			0.649584
$319$	11090.4	+	34132.7i	0.00610197	+	0.0187799i
$320$	−40291.7	−	225400.i	−0.0219959	−	0.123050i
$321$	329658.	−	1.01458e6i	0.178567	−	0.549573i
$322$	−557574.	+	1.71604e6i	−0.299684	+	0.922331i
$323$	2.33901e6	−	1.69939e6i	1.24746	−	0.906330i
$324$	104976.			0.0555556
$325$	−108697.	−	2.74228e6i	−0.0570832	−	1.44014i
$326$	761105.			0.396644
$327$	−1.36279e6	+	990123.i	−0.704788	+	0.512059i
$328$	194201.	−	597690.i	0.0996706	−	0.306755i
$329$	−315432.	+	970800.i	−0.160663	+	0.494470i
$330$	1.01834e6	−	544541.i	0.514764	−	0.275262i
$331$	−653899.	−	2.01249e6i	−0.328050	−	1.00963i	−0.970045	−	0.242926i	$-0.921893\pi$
$331$	−653899.	−	2.01249e6i	−0.328050	−	1.00963i	0.641995	−	0.766709i	$-0.278107\pi$
$332$	−1.20058e6			−0.597786
$333$	−185679.	−	571462.i	−0.0917599	−	0.282408i
$334$	−817024.	−	593603.i	−0.400746	−	0.291159i
$335$	−627466.	−	86678.3i	−0.305477	−	0.0421986i
$336$	176803.	−	128455.i	0.0854360	−	0.0620729i
$337$	720446.	+	523435.i	0.345563	+	0.251066i	0.747005	−	0.664818i	$-0.231491\pi$
$337$	720446.	+	523435.i	0.345563	+	0.251066i	−0.401442	+	0.915884i	$0.631491\pi$
$338$	−1.29435e6	−	940400.i	−0.616254	−	0.447735i
$339$	557120.	−	404771.i	0.263299	−	0.191298i
$340$	573434.	−	1.18278e6i	0.269021	−	0.554888i
$341$	3.73045e6	+	2.71033e6i	1.73730	+	1.26222i
$342$	196971.	+	606214.i	0.0910619	+	0.280260i
$343$	−2.33498e6			−1.07164
$344$	−158372.	−	487418.i	−0.0721575	−	0.222078i
$345$	−2.37014e6	−	327411.i	−1.07208	−	0.148097i
$346$	414083.	−	1.27442e6i	0.185950	−	0.572297i
$347$	124977.	−	384639.i	0.0557193	−	0.171486i	−0.919324	−	0.393502i	$-0.871264\pi$
$347$	124977.	−	384639.i	0.0557193	−	0.171486i	0.975043	+	0.222015i	$0.0712635\pi$
$348$	−7286.33	+	5293.83i	−0.00322523	+	0.00234327i
$349$	−1.12530e6			−0.494543			−0.247272	−	0.968946i	$-0.579534\pi$
$349$	−1.12530e6			−0.494543			−0.247272	+	0.968946i	$0.579534\pi$
$350$	1.14125e6	+	321440.i	0.497980	+	0.140259i
$351$	640222.			0.277372
$352$	475372.	−	345378.i	0.204492	−	0.148572i
$353$	376071.	−	1.15743e6i	0.160632	−	0.494375i	−0.838056	−	0.545585i	$-0.816308\pi$
$353$	376071.	−	1.15743e6i	0.160632	−	0.494375i	0.998688	+	0.0512096i	$0.0163077\pi$
$354$	557789.	−	1.71670e6i	0.236571	−	0.728092i
$355$	1.72469e6	+	1.65768e6i	0.726340	+	0.698121i
$356$	236942.	+	729232.i	0.0990870	+	0.304958i
$357$	1.25456e6			0.520980
$358$	−418947.	−	1.28939e6i	−0.172763	−	0.531710i
$359$	−2.44070e6	−	1.77327e6i	−0.999491	−	0.726173i	−0.0375118	−	0.999296i	$-0.511943\pi$
$359$	−2.44070e6	−	1.77327e6i	−0.999491	−	0.726173i	−0.961979	+	0.273124i	$0.911943\pi$
$360$	208934.	+	200817.i	0.0849676	+	0.0816664i
$361$	−1.12796e6	+	819513.i	−0.455540	+	0.330969i
$362$	−1.39385e6	−	1.01269e6i	−0.559044	−	0.406169i
$363$	1.22482e6	+	889886.i	0.487873	+	0.354461i
$364$	1.07828e6	−	783413.i	0.426556	−	0.309911i
$365$	577531.	+	3.23083e6i	0.226905	+	1.26935i
$366$	901961.	+	655313.i	0.351953	+	0.255709i
$367$	99942.4	+	307591.i	0.0387333	+	0.119209i	0.968554	−	0.248805i	$-0.0800379\pi$
$367$	99942.4	+	307591.i	0.0387333	+	0.119209i	−0.929820	+	0.368014i	$0.880038\pi$
$368$	−1.21745e6			−0.468632
$369$	245786.	+	756451.i	0.0939704	+	0.289211i
$370$	723636.	−	1.49258e6i	0.274799	−	0.566806i
$371$	−953745.	+	2.93532e6i	−0.359747	+	1.10719i
$372$	−357580.	+	1.10052e6i	−0.133972	+	0.412325i
$373$	1.01263e6	−	735719.i	0.376859	−	0.273804i	−0.383190	−	0.923669i	$-0.625175\pi$
$373$	1.01263e6	−	735719.i	0.376859	−	0.273804i	0.760049	+	0.649865i	$0.225175\pi$
$374$	3.37315e6			1.24697
$375$	−153292.	+	1.56474e6i	−0.0562914	+	0.574600i
$376$	−688738.			−0.251238
$377$	−44437.5	+	32285.7i	−0.0161026	+	0.0116992i
$378$	−85471.0	+	263053.i	−0.0307673	+	0.0946920i
$379$	−1.50771e6	+	4.64025e6i	−0.539162	+	1.65937i	0.195318	+	0.980740i	$0.437426\pi$
$379$	−1.50771e6	+	4.64025e6i	−0.539162	+	1.65937i	−0.734480	+	0.678630i	$0.762574\pi$
$380$	−767641.	+	1.58335e6i	−0.272709	+	0.562494i
$381$	−460835.	−	1.41830e6i	−0.162642	−	0.500561i
$382$	−2.40213e6			−0.842246
$383$	945672.	+	2.91048e6i	0.329415	+	1.01384i	0.969408	+	0.245455i	$0.0789372\pi$
$383$	945672.	+	2.91048e6i	0.329415	+	1.01384i	−0.639993	+	0.768381i	$0.721063\pi$
$384$	119294.	+	86672.5i	0.0412850	+	0.0299953i
$385$	535403.	+	2.99516e6i	0.184089	+	1.02984i
$386$	−531845.	+	386408.i	−0.181684	+	0.132001i
$387$	524756.	+	381258.i	0.178107	+	0.129402i
$388$	−444023.	−	322602.i	−0.149736	−	0.108790i
$389$	−1.51101e6	+	1.09781e6i	−0.506283	+	0.367836i	−0.811412	−	0.584475i	$-0.801300\pi$
$389$	−1.51101e6	+	1.09781e6i	−0.506283	+	0.367836i	0.305129	+	0.952311i	$0.401300\pi$
$390$	1.27424e6	+	1.22473e6i	0.424217	+	0.407736i
$391$	−5.65417e6	−	4.10799e6i	−1.87037	−	1.35890i
$392$	−154459.	−	475376.i	−0.0507689	−	0.156251i
$393$	−71589.3			−0.0233812
$394$	−834544.	−	2.56846e6i	−0.270837	−	0.833552i
$395$	−1.51696e6	−	1.45803e6i	−0.489195	−	0.470189i
$396$	−229807.	+	707273.i	−0.0736419	+	0.226647i
$397$	1.58842e6	−	4.88866e6i	0.505813	−	1.55673i	−0.293586	−	0.955933i	$-0.594849\pi$
$397$	1.58842e6	−	4.88866e6i	0.505813	−	1.55673i	0.799399	−	0.600800i	$-0.205151\pi$
$398$	2.30452e6	−	1.67433e6i	0.729243	−	0.529826i
$399$	−1.67945e6			−0.528121
$400$	31685.0	+	799372.i	0.00990157	+	0.249804i
$401$	4.31720e6			1.34073			0.670364	−	0.742032i	$-0.266138\pi$
$401$	4.31720e6			1.34073			0.670364	+	0.742032i	$0.266138\pi$
$402$	330012.	−	239768.i	0.101851	−	0.0739991i
$403$	−2.18079e6	+	6.71177e6i	−0.668884	+	2.05861i
$404$	811874.	−	2.49869e6i	0.247477	−	0.761657i
$405$	−363321.	−	50189.2i	−0.110066	−	0.0152045i
$406$	−7332.97	−	22568.6i	−0.00220783	−	0.00679499i
$407$	4.25669e6			1.27375
$408$	261580.	+	805061.i	0.0777955	+	0.239430i
$409$	3.86959e6	+	2.81142e6i	1.14382	+	0.831031i	0.987646	−	0.156699i	$-0.0500853\pi$
$409$	3.86959e6	+	2.81142e6i	1.14382	+	0.831031i	0.156170	+	0.987730i	$0.450085\pi$
$410$	−957885.	+	1.97575e6i	−0.281419	+	0.580460i
$411$	348150.	−	252946.i	0.101663	−	0.0738623i
$412$	−2.73676e6	−	1.98837e6i	−0.794315	−	0.577104i
$413$	3.84762e6	+	2.79546e6i	1.10998	+	0.806451i
$414$	1.24656e6	−	905680.i	0.357448	−	0.259701i
$415$	4.15519e6	+	573998.i	1.18432	+	0.163603i
$416$	727546.	+	528593.i	0.206123	+	0.149757i
$417$	−443613.	−	1.36530e6i	−0.124929	−	0.384493i
$418$	−4.51554e6			−1.26406
$419$	−650990.	−	2.00354e6i	−0.181150	−	0.557524i	0.818710	−	0.574207i	$-0.194689\pi$
$419$	−650990.	−	2.00354e6i	−0.181150	−	0.557524i	−0.999861	+	0.0166830i	$0.994689\pi$
$420$	−673327.	+	360051.i	−0.186253	+	0.0995957i
$421$	1.36543e6	−	4.20236e6i	0.375461	−	1.15555i	−0.567707	−	0.823231i	$-0.692169\pi$
$421$	1.36543e6	−	4.20236e6i	0.375461	−	1.15555i	0.943167	−	0.332318i	$-0.107831\pi$
$422$	−195463.	+	601575.i	−0.0534299	+	0.164440i
$423$	705208.	−	512363.i	0.191631	−	0.139228i
$424$	−2.08248e6			−0.562556
$425$	−2.55014e6	+	3.81941e6i	−0.684843	+	1.02571i
$426$	−1.54053e6			−0.411287
$427$	−2.37648e6	+	1.72661e6i	−0.630760	+	0.458274i
$428$	−586059.	+	1.80370e6i	−0.154644	+	0.475944i
$429$	−1.40153e6	+	4.31348e6i	−0.367672	+	1.13158i
$430$	315088.	+	1.76267e6i	0.0821788	+	0.459726i
$431$	186524.	+	574062.i	0.0483662	+	0.148856i	0.972323	−	0.233641i	$-0.0750642\pi$
$431$	186524.	+	574062.i	0.0483662	+	0.148856i	−0.923957	+	0.382497i	$0.875064\pi$
$432$	−186624.			−0.0481125
$433$	−427587.	−	1.31598e6i	−0.109598	−	0.337309i	0.881184	−	0.472774i	$-0.156747\pi$
$433$	−427587.	−	1.31598e6i	−0.109598	−	0.337309i	−0.990782	+	0.135465i	$0.956747\pi$
$434$	−2.46658e6	−	1.79207e6i	−0.628594	−	0.456700i
$435$	27748.9	−	14838.3i	0.00703109	−	0.00375976i
$436$	2.42273e6	−	1.76022e6i	0.610365	−	0.443456i
$437$	7.56908e6	+	5.49926e6i	1.89601	+	1.37753i
$438$	−1.70994e6	−	1.24234e6i	−0.425887	−	0.309425i
$439$	−3.50168e6	+	2.54412e6i	−0.867191	+	0.630051i	−0.929832	−	0.367985i	$-0.880048\pi$
$439$	−3.50168e6	+	2.54412e6i	−0.867191	+	0.630051i	0.0626407	+	0.998036i	$0.480048\pi$
$440$	−1.81038e6	+	968073.i	−0.445798	+	0.238384i
$441$	511792.	+	371839.i	0.125313	+	0.0910454i
$442$	1.59531e6	+	4.90986e6i	0.388409	+	1.19540i
$443$	−5.85977e6			−1.41864			−0.709319	−	0.704888i	$-0.750997\pi$
$443$	−5.85977e6			−1.41864			−0.709319	+	0.704888i	$0.750997\pi$
$444$	330097.	+	1.01593e6i	0.0794664	+	0.244572i
$445$	−471406.	−	2.63715e6i	−0.112848	−	0.631297i
$446$	53564.3	−	164854.i	0.0127508	−	0.0392430i
$447$	457416.	−	1.40778e6i	0.108279	−	0.333248i
$448$	−314316.	+	228364.i	−0.0739898	+	0.0537567i
$449$	−1.31356e6			−0.307493			−0.153746	−	0.988110i	$-0.549134\pi$
$449$	−1.31356e6			−0.307493			−0.153746	+	0.988110i	$0.549134\pi$
$450$	−627108.	−	794916.i	−0.145986	−	0.185050i
$451$	−5.63463e6			−1.30444
$452$	−990435.	+	719593.i	−0.228024	+	0.165669i
$453$	−847553.	+	2.60850e6i	−0.194053	+	0.597235i
$454$	−1.18716e6	+	3.65370e6i	−0.270315	+	0.831943i
$455$	−4.10645e6	+	2.19586e6i	−0.929904	+	0.497251i
$456$	−350170.	−	1.07771e6i	−0.0788619	−	0.242712i
$457$	2.98119e6			0.667727			0.333863	−	0.942621i	$-0.391648\pi$
$457$	2.98119e6			0.667727			0.333863	+	0.942621i	$0.391648\pi$
$458$	−298971.	−	920137.i	−0.0665986	−	0.204969i
$459$	−866732.	−	629718.i	−0.192023	−	0.139513i
$460$	4.21358e6	+	582065.i	0.928447	+	0.128256i
$461$	−2.66794e6	+	1.93837e6i	−0.584687	+	0.424800i	−0.840411	−	0.541950i	$-0.817686\pi$
$461$	−2.66794e6	+	1.93837e6i	−0.584687	+	0.424800i	0.255724	+	0.966750i	$0.417686\pi$
$462$	−1.58520e6	−	1.15172e6i	−0.345525	−	0.251039i
$463$	−201399.	−	146325.i	−0.0436621	−	0.0317224i	0.565740	−	0.824584i	$-0.308591\pi$
$463$	−201399.	−	146325.i	−0.0436621	−	0.0317224i	−0.609402	+	0.792861i	$0.708591\pi$
$464$	12953.5	−	9411.25i	0.00279313	−	0.00202933i
$465$	1.76374e6	−	3.63792e6i	0.378270	−	0.780227i
$466$	4.46969e6	+	3.24742e6i	0.953482	+	0.692745i
$467$	−1.79175e6	−	5.51444e6i	−0.380177	−	1.17006i	−0.939919	−	0.341397i	$-0.889100\pi$
$467$	−1.79175e6	−	5.51444e6i	−0.380177	−	1.17006i	0.559742	−	0.828667i	$-0.310900\pi$
$468$	−1.13817e6			−0.240211
$469$	332125.	+	1.02218e6i	0.0697219	+	0.214582i
$470$	2.38372e6	+	329287.i	0.497749	+	0.0687590i
$471$	−976476.	+	3.00528e6i	−0.202819	+	0.624214i
$472$	−991626.	+	3.05191e6i	−0.204877	+	0.630546i
$473$	−3.71748e6	+	2.70091e6i	−0.764004	+	0.555081i
$474$	1.35498e6			0.277005
$475$	3.41380e6	−	5.11295e6i	0.694231	−	1.03977i
$476$	−2.23033e6			−0.451182
$477$	2.13228e6	−	1.54919e6i	0.429089	−	0.311751i
$478$	1.33067e6	−	4.09538e6i	0.266379	−	0.819832i
$479$	211170.	−	649914.i	0.0420527	−	0.129425i	−0.927826	−	0.373013i	$-0.878325\pi$
$479$	211170.	−	649914.i	0.0420527	−	0.129425i	0.969879	+	0.243588i	$0.0783246\pi$
$480$	−371439.	−	357007.i	−0.0735841	−	0.0707252i
$481$	2.01317e6	+	6.19592e6i	0.396752	+	1.22108i
$482$	2.49280e6			0.488732
$483$	1.25454e6	+	3.86108e6i	0.244691	+	0.753080i
$484$	−2.17746e6	−	1.58202e6i	−0.422511	−	0.306972i
$485$	1.38252e6	+	1.32881e6i	0.266881	+	0.256512i
$486$	191087.	−	138833.i	0.0366978	−	0.0266625i
$487$	−2.99926e6	−	2.17909e6i	−0.573050	−	0.416345i	0.263162	−	0.964752i	$-0.415235\pi$
$487$	−2.99926e6	−	2.17909e6i	−0.573050	−	0.416345i	−0.836212	+	0.548407i	$0.815235\pi$
$488$	−1.60349e6	−	1.16500e6i	−0.304800	−	0.221450i
$489$	1.38543e6	−	1.00657e6i	0.262007	−	0.190359i
$490$	307303.	+	1.71912e6i	0.0578198	+	0.323456i
$491$	−559818.	−	406732.i	−0.104796	−	0.0761385i	0.534153	−	0.845388i	$-0.320631\pi$
$491$	−559818.	−	406732.i	−0.104796	−	0.0761385i	−0.638949	+	0.769249i	$0.720631\pi$
$492$	−436953.	−	1.34480e6i	−0.0813807	−	0.250464i
$493$	91915.5			0.0170322
$494$	−2.13560e6	−	6.57270e6i	−0.393733	−	1.21179i
$495$	1.13351e6	−	2.33799e6i	0.207927	−	0.428874i
$496$	635697.	−	1.95648e6i	0.116024	−	0.357084i
$497$	1.25429e6	−	3.86031e6i	0.227776	−	0.701021i
$498$	−2.18540e6	+	1.58779e6i	−0.394873	+	0.286892i
$499$	3.86075e6			0.694096			0.347048	−	0.937847i	$-0.387184\pi$
$499$	3.86075e6			0.694096			0.347048	+	0.937847i	$0.387184\pi$
$500$	272520.	−	2.78177e6i	0.0487498	−	0.497618i
$501$	−2.27227e6			−0.404451
$502$	3.67153e6	−	2.66752e6i	0.650261	−	0.472442i
$503$	1.41974e6	−	4.36951e6i	0.250201	−	0.770039i	−0.744537	−	0.667582i	$-0.767329\pi$
$503$	1.41974e6	−	4.36951e6i	0.250201	−	0.770039i	0.994737	−	0.102457i	$-0.0326705\pi$
$504$	151948.	−	467649.i	0.0266453	−	0.0820057i
$505$	−4.00452e6	+	8.25979e6i	−0.698750	+	1.44125i
$506$	3.37310e6	+	1.03813e7i	0.585670	+	1.80251i
$507$	−3.59978e6			−0.621952
$508$	819262.	+	2.52143e6i	0.140852	+	0.433498i
$509$	−2.48315e6	−	1.80411e6i	−0.424823	−	0.308652i	0.354753	−	0.934960i	$-0.384565\pi$
$509$	−2.48315e6	−	1.80411e6i	−0.424823	−	0.308652i	−0.779575	+	0.626308i	$0.784565\pi$
$510$	−520425.	−	2.91137e6i	−0.0885998	−	0.495646i
$511$	4.50533e6	−	3.27331e6i	0.763263	−	0.554543i
$512$	−212079.	−	154084.i	−0.0357538	−	0.0259767i
$513$	1.16027e6	+	842987.i	0.194655	+	0.141425i
$514$	−2.07256e6	+	1.50581e6i	−0.346019	+	0.251398i
$515$	8.52124e6	+	8.19017e6i	1.41574	+	1.36074i
$516$	−932900.	−	677792.i	−0.154245	−	0.112066i
$517$	1.90824e6	+	5.87295e6i	0.313983	+	0.966340i
$518$	−2.81453e6			−0.460872
$519$	−931687.	−	2.86744e6i	−0.151828	−	0.467278i
$520$	−2.26531e6	−	2.17730e6i	−0.367383	−	0.353109i
$521$	857995.	−	2.64064e6i	0.138481	−	0.426201i	−0.857634	−	0.514260i	$-0.828067\pi$
$521$	857995.	−	2.64064e6i	0.138481	−	0.426201i	0.996115	+	0.0880593i	$0.0280665\pi$
$522$	−6262.04	+	19272.6i	−0.00100587	+	0.00309574i
$523$	3.41632e6	−	2.48210e6i	0.546140	−	0.396794i	−0.280220	−	0.959936i	$-0.590407\pi$
$523$	3.41632e6	−	2.48210e6i	0.546140	−	0.396794i	0.826360	+	0.563142i	$0.190407\pi$
$524$	127270.			0.0202487
$525$	2.50252e6	−	924214.i	0.396259	−	0.146344i
$526$	−3.23192e6			−0.509327
$527$	9.55401e6	−	6.94139e6i	1.49851	−	1.08873i
$528$	408546.	−	1.25737e6i	0.0637758	−	0.196282i
$529$	4.99989e6	−	1.53881e7i	0.776822	−	2.39081i
$530$	7.20744e6	+	995636.i	1.11453	+	0.153961i
$531$	−1.25503e6	−	3.86257e6i	−0.193160	−	0.594484i
$532$	2.98568e6			0.457366
$533$	−2.66486e6	−	8.20160e6i	−0.406309	−	1.25049i
$534$	1.39572e6	+	1.01405e6i	0.211810	+	0.153889i
$535$	2.89070e6	−	5.96241e6i	0.436635	−	0.900611i
$536$	−586689.	+	426254.i	−0.0882055	+	0.0640851i
$537$	−2.46784e6	−	1.79299e6i	−0.369301	−	0.268313i
$538$	2.13454e6	+	1.55083e6i	0.317942	+	0.230999i
$539$	−3.62563e6	+	2.63418e6i	−0.537542	+	0.390547i
$540$	645904.	+	89225.2i	0.0953199	+	0.0131675i
$541$	−4.80400e6	−	3.49031e6i	−0.705684	−	0.512709i	0.176095	−	0.984373i	$-0.443654\pi$
$541$	−4.80400e6	−	3.49031e6i	−0.705684	−	0.512709i	−0.881778	+	0.471664i	$0.843654\pi$
$542$	2.10670e6	+	6.48376e6i	0.308038	+	0.948044i
$543$	−3.87652e6			−0.564213
$544$	−465031.	−	1.43122e6i	−0.0673728	−	0.207352i
$545$	−9.22662e6	+	4.93379e6i	−1.33061	+	0.711523i
$546$	926695.	−	2.85207e6i	0.133032	−	0.409430i
$547$	1.33272e6	−	4.10170e6i	0.190446	−	0.586132i	−0.809554	−	0.587046i	$-0.800291\pi$
$547$	1.33272e6	−	4.10170e6i	0.190446	−	0.586132i	1.00000		0.000913890i	$0.000290900\pi$
$548$	−618933.	+	449681.i	−0.0880425	+	0.0639666i
$549$	2.50849e6			0.355207
$550$	6.72855e6	−	2.48494e6i	0.948451	−	0.350276i
$551$	−123045.			−0.0172657
$552$	−2.21611e6	+	1.61010e6i	−0.309559	+	0.224908i
$553$	−1.10322e6	+	3.39536e6i	−0.153408	+	0.472142i
$554$	1.23008e6	−	3.78580e6i	0.170278	−	0.524062i
$555$	−656742.	−	3.67395e6i	−0.0905029	−	0.506292i
$556$	788646.	+	2.42720e6i	0.108192	+	0.332981i
$557$	3.51114e6			0.479523			0.239762	−	0.970832i	$-0.422931\pi$
$557$	3.51114e6			0.479523			0.239762	+	0.970832i	$0.422931\pi$
$558$	804554.	+	2.47616e6i	0.109388	+	0.336662i
$559$	−5.68952e6	−	4.13368e6i	−0.770098	−	0.559509i
$560$	1.19703e6	−	640090.i	0.161300	−	0.0862524i
$561$	6.14010e6	−	4.46105e6i	0.823699	−	0.598452i
$562$	−2.17384e6	−	1.57939e6i	−0.290326	−	0.210934i
$563$	−2.76139e6	−	2.00627e6i	−0.367161	−	0.266758i	0.388872	−	0.921292i	$-0.372865\pi$
$563$	−2.76139e6	−	2.00627e6i	−0.367161	−	0.266758i	−0.756033	+	0.654534i	$0.772865\pi$
$564$	−1.25370e6	+	910868.i	−0.165957	+	0.120575i
$565$	3.77193e6	−	2.01698e6i	0.497098	−	0.265815i
$566$	868585.	+	631064.i	0.113965	+	0.0828003i
$567$	192310.	+	591869.i	0.0251214	+	0.0773157i
$568$	2.73871e6			0.356185
$569$	−2.54639e6	−	7.83697e6i	−0.329719	−	1.01477i	−0.969265	−	0.246017i	$-0.920878\pi$
$569$	−2.54639e6	−	7.83697e6i	−0.329719	−	1.01477i	0.639547	−	0.768752i	$-0.279122\pi$
$570$	696679.	+	3.89737e6i	0.0898144	+	0.502441i
$571$	1.21011e6	−	3.72433e6i	0.155322	−	0.478033i	−0.842871	−	0.538115i	$-0.819136\pi$
$571$	1.21011e6	−	3.72433e6i	0.155322	−	0.478033i	0.998193	+	0.0600827i	$0.0191365\pi$
$572$	2.49162e6	−	7.66840e6i	0.318413	−	0.979975i
$573$	−4.37258e6	+	3.17686e6i	−0.556354	+	0.404215i
$574$	3.72562e6			0.471975
$575$	−1.43049e7	−	4.02904e6i	−1.80432	−	0.508197i
$576$	331776.			0.0416667
$577$	8.25562e6	−	5.99806e6i	1.03231	−	0.750017i	0.0635405	−	0.997979i	$-0.479761\pi$
$577$	8.25562e6	−	5.99806e6i	1.03231	−	0.750017i	0.968770	+	0.247962i	$0.0797608\pi$
$578$	914534.	−	2.81465e6i	0.113862	−	0.350432i
$579$	−457080.	+	1.40675e6i	−0.0566625	+	0.174389i
$580$	−49331.4	+	26379.2i	−0.00608910	+	0.00325605i
$581$	−2.19939e6	−	6.76902e6i	−0.270310	−	0.831928i
$582$	−1.23490e6			−0.151120
$583$	5.76977e6	+	1.77575e7i	0.703052	+	2.16377i
$584$	3.03989e6	+	2.20861e6i	0.368829	+	0.267970i
$585$	3.93920e6	+	544162.i	0.475903	+	0.0657413i
$586$	−7.69249e6	+	5.58892e6i	−0.925386	+	0.672332i
$587$	−1.28314e6	−	932256.i	−0.153702	−	0.111671i	0.508276	−	0.861194i	$-0.330283\pi$
$587$	−1.28314e6	−	932256.i	−0.153702	−	0.111671i	−0.661978	+	0.749523i	$0.730283\pi$
$588$	−909852.	−	661046.i	−0.108524	−	0.0788476i
$589$	−1.27897e7	+	9.29226e6i	−1.51905	+	1.10365i
$590$	4.89113e6	−	1.00885e7i	0.578468	−	1.19316i
$591$	−4.91594e6	−	3.57164e6i	−0.578946	−	0.420629i
$592$	−586838.	−	1.80610e6i	−0.0688199	−	0.211806i
$593$	3.69077e6			0.431003			0.215501	−	0.976504i	$-0.430861\pi$
$593$	3.69077e6			0.431003			0.215501	+	0.976504i	$0.430861\pi$
$594$	517065.	+	1.59136e6i	0.0601284	+	0.185056i
$595$	7.71914e6	+	1.06632e6i	0.893875	+	0.123480i
$596$	−813185.	+	2.50273e6i	−0.0937721	+	0.288601i
$597$	1.98056e6	−	6.09552e6i	0.227432	−	0.699963i
$598$	−1.35155e7	+	9.81958e6i	−1.54553	+	1.12290i
$599$	−1.66969e7			−1.90138			−0.950692	−	0.310135i	$-0.899626\pi$
$599$	−1.66969e7			−1.90138			−0.950692	+	0.310135i	$0.899626\pi$
$600$	1.11486e6	+	1.41318e6i	0.126428	+	0.160258i
$601$	−3.21687e6			−0.363285			−0.181642	−	0.983365i	$-0.558141\pi$
$601$	−3.21687e6			−0.363285			−0.181642	+	0.983365i	$0.558141\pi$
$602$	2.45800e6	−	1.78584e6i	0.276433	−	0.200841i
$603$	283620.	−	872894.i	0.0317647	−	0.0977616i
$604$	1.50676e6	−	4.63733e6i	0.168055	−	0.517221i
$605$	6.77981e6	+	6.51640e6i	0.753060	+	0.723802i
$606$	−1.82672e6	−	5.62206e6i	−0.202064	−	0.621890i
$607$	1.44935e7			1.59662			0.798309	−	0.602248i	$-0.205728\pi$
$607$	1.44935e7			1.59662			0.798309	+	0.602248i	$0.205728\pi$
$608$	622525.	+	1.91593e6i	0.0682964	+	0.210195i
$609$	−43195.4	−	31383.3i	−0.00471949	−	0.00342891i
$610$	4.99266e6	+	4.79868e6i	0.543259	+	0.522153i
$611$	−7.64601e6	+	5.55515e6i	−0.828575	+	0.601995i
$612$	1.54086e6	+	1.11950e6i	0.166297	+	0.120822i
$613$	1.00908e6	+	733143.i	0.108462	+	0.0788020i	0.640694	−	0.767796i	$-0.278647\pi$
$613$	1.00908e6	+	733143.i	0.108462	+	0.0788020i	−0.532232	+	0.846598i	$0.678647\pi$
$614$	−1.18566e6	+	861435.i	−0.126923	+	0.0922150i
$615$	869337.	+	4.86325e6i	0.0926831	+	0.518489i
$616$	2.81814e6	+	2.04750e6i	0.299234	+	0.217406i
$617$	217843.	+	670451.i	0.0230372	+	0.0709013i	0.961914	−	0.273352i	$-0.0881322\pi$
$617$	217843.	+	670451.i	0.0230372	+	0.0709013i	−0.938877	+	0.344253i	$0.888132\pi$
$618$	−7.61134e6			−0.801659
$619$	2.43254e6	+	7.48659e6i	0.255172	+	0.785340i	0.993796	+	0.111221i	$0.0354763\pi$
$619$	2.43254e6	+	7.48659e6i	0.255172	+	0.785340i	−0.738623	+	0.674118i	$0.764524\pi$
$620$	−3.13554e6	+	6.46741e6i	−0.327591	+	0.675696i
$621$	1.07132e6	−	3.29720e6i	0.111479	−	0.343096i
$622$	666021.	−	2.04980e6i	0.0690259	−	0.212440i
$623$	−3.67744e6	+	2.67182e6i	−0.379600	+	0.275795i
$624$	2.02342e6			0.208029
$625$	−2.27315e6	+	9.49738e6i	−0.232771	+	0.972532i
$626$	−5.82844e6			−0.594451
$627$	−8.21959e6	+	5.97188e6i	−0.834990	+	0.606656i
$628$	1.73596e6	−	5.34273e6i	0.175647	−	0.540585i
$629$	3.36882e6	−	1.03682e7i	0.339509	−	1.04490i
$630$	−749476.	+	1.54588e6i	−0.0752326	+	0.155176i
$631$	−3.77617e6	−	1.16219e7i	−0.377553	−	1.16199i	−0.941740	−	0.336342i	$-0.890810\pi$
$631$	−3.77617e6	−	1.16219e7i	−0.377553	−	1.16199i	0.564187	−	0.825647i	$-0.309190\pi$
$632$	−2.40885e6			−0.239893
$633$	439793.	+	1.35354e6i	0.0436253	+	0.134265i
$634$	5.55608e6	+	4.03673e6i	0.548965	+	0.398847i
$635$	−1.62996e6	−	9.11833e6i	−0.160414	−	0.897390i
$636$	−3.79071e6	+	2.75411e6i	−0.371602	+	0.269985i
$637$	−5.54896e6	−	4.03155e6i	−0.541830	−	0.393662i
$638$	−116140.	−	84380.7i	−0.0112961	−	0.00820713i
$639$	−2.80420e6	+	2.03737e6i	−0.271680	+	0.197387i
$640$	660335.	+	634680.i	0.0637257	+	0.0612498i
$641$	−7.04285e6	−	5.11693e6i	−0.677022	−	0.491886i	0.195346	−	0.980734i	$-0.437417\pi$
$641$	−7.04285e6	−	5.11693e6i	−0.677022	−	0.491886i	−0.872369	+	0.488849i	$0.837417\pi$
$642$	1.31863e6	+	4.05834e6i	0.126266	+	0.388607i
$643$	8.83867e6			0.843062			0.421531	−	0.906814i	$-0.361493\pi$
$643$	8.83867e6			0.843062			0.421531	+	0.906814i	$0.361493\pi$
$644$	−2.23030e6	−	6.86415e6i	−0.211908	−	0.652187i
$645$	2.90471e6	+	2.79185e6i	0.274918	+	0.264237i
$646$	−3.57369e6	+	1.09987e7i	−0.336927	+	1.03695i
$647$	5.88440e6	−	1.81103e7i	0.552639	−	1.70085i	−0.149461	−	0.988768i	$-0.547754\pi$
$647$	5.88440e6	−	1.81103e7i	0.552639	−	1.70085i	0.702099	−	0.712079i	$-0.252246\pi$
$648$	−339709.	+	246813.i	−0.0317812	+	0.0230904i
$649$	2.87714e7			2.68132
$650$	6.79924e6	+	8.61865e6i	0.631215	+	0.800121i
$651$	−6.85993e6			−0.634406
$652$	−2.46299e6	+	1.78946e6i	−0.226904	+	0.164856i
$653$	4.37484e6	−	1.34644e7i	0.401494	−	1.23567i	−0.522293	−	0.852766i	$-0.674923\pi$
$653$	4.37484e6	−	1.34644e7i	0.401494	−	1.23567i	0.923787	−	0.382906i	$-0.125077\pi$
$654$	2.08215e6	−	6.40821e6i	0.190357	−	0.585858i
$655$	−440480.	−	60847.9i	−0.0401165	−	0.00554170i
$656$	776805.	+	2.39076e6i	0.0704778	+	0.216908i
$657$	−4.75559e6			−0.429824
$658$	−1.26173e6	−	3.88320e6i	−0.113606	−	0.349643i
$659$	−3.98598e6	−	2.89598e6i	−0.357537	−	0.259766i	0.394487	−	0.918902i	$-0.370922\pi$
$659$	−3.98598e6	−	2.89598e6i	−0.357537	−	0.259766i	−0.752024	+	0.659136i	$0.770922\pi$
$660$	−2.01512e6	+	4.15643e6i	−0.180070	+	0.371416i
$661$	−2.59495e6	+	1.88534e6i	−0.231007	+	0.167837i	−0.697268	−	0.716811i	$-0.745601\pi$
$661$	−2.59495e6	+	1.88534e6i	−0.231007	+	0.167837i	0.466260	+	0.884648i	$0.345601\pi$
$662$	6.84771e6	+	4.97516e6i	0.607296	+	0.441227i
$663$	9.39730e6	+	6.82753e6i	0.830269	+	0.603226i
$664$	3.88515e6	−	2.82273e6i	0.341970	−	0.248456i
$665$	−1.03334e7	−	1.42746e6i	−0.906128	−	0.125173i
$666$	1.94446e6	+	1.41273e6i	0.169869	+	0.123417i
$667$	91914.1	+	282883.i	0.00799959	+	0.0246202i
$668$	4.03959e6			0.350264
$669$	−120520.	−	370922.i	−0.0104110	−	0.0320418i
$670$	2.23432e6	−	1.19477e6i	0.192290	−	0.102824i
$671$	−5.49143e6	+	1.69009e7i	−0.470846	+	1.44912i
$672$	−270131.	+	831377.i	−0.0230755	+	0.0710190i
$673$	−1.06566e7	+	7.74247e6i	−0.906945	+	0.658934i	−0.940240	−	0.340511i	$-0.889400\pi$
$673$	−1.06566e7	+	7.74247e6i	−0.906945	+	0.658934i	0.0332953	+	0.999446i	$0.489400\pi$
$674$	−3.56208e6			−0.302033
$675$	−2.19281e6	−	617615.i	−0.185243	−	0.0521745i
$676$	6.39962e6			0.538626
$677$	−1.36709e7	+	9.93246e6i	−1.14637	+	0.832885i	−0.987994	−	0.154494i	$-0.950625\pi$
$677$	−1.36709e7	+	9.93246e6i	−1.14637	+	0.832885i	−0.158374	+	0.987379i	$0.550625\pi$
$678$	−851204.	+	2.61974e6i	−0.0711147	+	0.218868i
$679$	1.00545e6	−	3.09445e6i	0.0836922	−	0.257578i
$680$	925200.	+	5.17577e6i	0.0767297	+	0.429242i
$681$	2.67111e6	+	8.22084e6i	0.220711	+	0.679279i
$682$	−1.84444e7			−1.51846
$683$	−3.05658e6	−	9.40718e6i	−0.250717	−	0.771628i	−0.994643	−	0.103366i	$-0.967039\pi$
$683$	−3.05658e6	−	9.40718e6i	−0.250717	−	0.771628i	0.743926	−	0.668262i	$-0.232961\pi$
$684$	−2.06270e6	−	1.49864e6i	−0.168576	−	0.122478i
$685$	2.35711e6	−	1.26043e6i	0.191935	−	0.102634i
$686$	7.55617e6	−	5.48988e6i	0.613044	−	0.445402i
$687$	−1.76111e6	−	1.27952e6i	−0.142362	−	0.103432i
$688$	1.65849e6	+	1.20496e6i	0.133580	+	0.0970516i
$689$	−2.31186e7	+	1.67966e7i	−1.85530	+	1.34795i
$690$	8.43972e6	−	4.51301e6i	0.674847	−	0.360864i
$691$	8.12373e6	+	5.90223e6i	0.647232	+	0.470242i	0.862327	−	0.506351i	$-0.169006\pi$
$691$	8.12373e6	+	5.90223e6i	0.647232	+	0.470242i	−0.215095	+	0.976593i	$0.569006\pi$
$692$	1.65633e6	+	5.09767e6i	0.131487	+	0.404675i
$693$	−4.40869e6			−0.348720
$694$	499907.	+	1.53856e6i	0.0393995	+	0.121259i
$695$	−1.56905e6	−	8.77758e6i	−0.123218	−	0.689307i
$696$	11132.5	−	34262.4i	0.000871105	−	0.00268099i
$697$	−4.45935e6	+	1.37245e7i	−0.347688	+	1.07007i
$698$	3.64154e6	−	2.64574e6i	0.282909	−	0.205546i
$699$	1.24309e7			0.962297
$700$	−4.44892e6	+	1.64305e6i	−0.343170	+	0.126737i
$701$	−2.53124e6			−0.194553			−0.0972766	−	0.995257i	$-0.531013\pi$
$701$	−2.53124e6			−0.194553			−0.0972766	+	0.995257i	$0.531013\pi$
$702$	−2.07180e6	+	1.50525e6i	−0.158674	+	0.115283i
$703$	−4.50976e6	+	1.38796e7i	−0.344163	+	1.05923i
$704$	−726303.	+	2.23533e6i	−0.0552314	+	0.169985i
$705$	4.77454e6	−	2.55311e6i	0.361792	−	0.193462i
$706$	1.50428e6	+	4.62970e6i	0.113584	+	0.349576i
$707$	1.55753e7			1.17189
$708$	2.23116e6	+	6.86680e6i	0.167281	+	0.514839i
$709$	−2.31756e6	−	1.68380e6i	−0.173147	−	0.125799i	0.497837	−	0.867271i	$-0.334128\pi$
$709$	−2.31756e6	−	1.68380e6i	−0.173147	−	0.125799i	−0.670984	+	0.741472i	$0.734128\pi$
$710$	−9.47866e6	−	1.30938e6i	−0.705669	−	0.0974812i
$711$	2.46645e6	−	1.79198e6i	0.182978	−	0.132941i
$712$	−2.48129e6	−	1.80276e6i	−0.183433	−	0.133272i
$713$	3.09170e7	+	2.24625e7i	2.27758	+	1.65476i
$714$	−4.05984e6	+	2.94965e6i	−0.298032	+	0.216533i
$715$	−1.22897e7	+	2.53490e7i	−0.899036	+	1.85437i
$716$	4.38727e6	+	3.18754e6i	0.319824	+	0.232366i
$717$	−2.99401e6	−	9.21461e6i	−0.217498	−	0.669390i
$718$	1.20675e7			0.873587
$719$	−456504.	−	1.40498e6i	−0.0329323	−	0.101355i	0.933239	−	0.359256i	$-0.116969\pi$
$719$	−456504.	−	1.40498e6i	−0.0329323	−	0.101355i	−0.966172	+	0.257900i	$0.916969\pi$
$720$	−1.14827e6	−	158623.i	−0.0825494	−	0.0114034i
$721$	6.19712e6	−	1.90728e7i	0.443968	−	1.36639i
$722$	1.72337e6	−	5.30400e6i	0.123037	−	0.378670i
$723$	4.53762e6	−	3.29677e6i	0.322836	−	0.234554i
$724$	6.89160e6			0.488622
$725$	183347.	−	67712.6i	0.0129548	−	0.00478437i
$726$	−6.05586e6			−0.426417
$727$	−5.73339e6	+	4.16555e6i	−0.402323	+	0.292305i	−0.770487	−	0.637456i	$-0.779987\pi$
$727$	−5.73339e6	+	4.16555e6i	−0.402323	+	0.292305i	0.368163	+	0.929761i	$0.379987\pi$
$728$	−1.64746e6	+	5.07035e6i	−0.115209	+	0.354576i
$729$	164224.	−	505430.i	0.0114451	−	0.0352243i
$730$	−9.46507e6	−	9.09734e6i	−0.657381	−	0.631840i
$731$	3.63661e6	+	1.11923e7i	0.251712	+	0.774690i
$732$	−4.45954e6			−0.307618
$733$	−1.17499e6	−	3.61624e6i	−0.0807743	−	0.248598i	0.902512	−	0.430665i	$-0.141721\pi$
$733$	−1.17499e6	−	3.61624e6i	−0.0807743	−	0.248598i	−0.983286	+	0.182068i	$0.941721\pi$
$734$	−1.04661e6	−	760407.i	−0.0717042	−	0.0520962i
$735$	2.83294e6	+	2.72288e6i	0.193428	+	0.185913i
$736$	3.93975e6	−	2.86240e6i	0.268086	−	0.194776i
$737$	5.26022e6	+	3.82177e6i	0.356726	+	0.259177i
$738$	−2.57390e6	−	1.87005e6i	−0.173961	−	0.126390i
$739$	1.49153e7	−	1.08366e7i	1.00466	−	0.729931i	0.0415802	−	0.999135i	$-0.486761\pi$
$739$	1.49153e7	−	1.08366e7i	1.00466	−	0.729931i	0.963083	+	0.269205i	$0.0867608\pi$
$740$	1.16754e6	+	6.53147e6i	0.0783778	+	0.438462i
$741$	−1.25799e7	−	9.13984e6i	−0.841651	−	0.611495i
$742$	−3.81498e6	−	1.17413e7i	−0.254380	−	0.782900i
$743$	1.31545e6			0.0874185			0.0437092	−	0.999044i	$-0.486082\pi$
$743$	1.31545e6			0.0874185			0.0437092	+	0.999044i	$0.486082\pi$
$744$	−1.43032e6	−	4.40207e6i	−0.0947328	−	0.291558i
$745$	4.01098e6	−	8.27312e6i	0.264765	−	0.546108i
$746$	−1.54716e6	+	4.76167e6i	−0.101786	+	0.313265i
$747$	−1.87818e6	+	5.78046e6i	−0.123151	+	0.379019i
$748$	−1.09157e7	+	7.93075e6i	−0.713344	+	0.518275i
$749$	−1.12432e7			−0.732291
$750$	−3.18287e6	−	5.42403e6i	−0.206617	−	0.352102i
$751$	−3.84425e6			−0.248721			−0.124360	−	0.992237i	$-0.539688\pi$
$751$	−3.84425e6			−0.248721			−0.124360	+	0.992237i	$0.539688\pi$
$752$	2.22880e6	−	1.61932e6i	0.143723	−	0.104421i
$753$	3.15540e6	−	9.71132e6i	0.202799	−	0.624153i
$754$	67894.4	−	208958.i	0.00434916	−	0.0133853i
$755$	−7.43200e6	+	1.53294e7i	−0.474502	+	0.978717i
$756$	−341884.	−	1.05221e6i	−0.0217558	−	0.0669574i
$757$	−1.14342e7			−0.725212			−0.362606	−	0.931942i	$-0.618113\pi$
$757$	−1.14342e7			−0.725212			−0.362606	+	0.931942i	$0.618113\pi$
$758$	−6.03083e6	−	1.85610e7i	−0.381245	−	1.17335i
$759$	1.98695e7	+	1.44360e7i	1.25194	+	0.909586i
$760$	−1.23854e6	−	6.92866e6i	−0.0777815	−	0.435126i
$761$	−4.18042e6	+	3.03725e6i	−0.261673	+	0.190116i	−0.710884	−	0.703309i	$-0.751705\pi$
$761$	−4.18042e6	+	3.03725e6i	−0.261673	+	0.190116i	0.449212	+	0.893425i	$0.351705\pi$
$762$	4.82593e6	+	3.50624e6i	0.301088	+	0.218753i
$763$	1.43626e7	+	1.04351e7i	0.893147	+	0.648910i
$764$	7.77347e6	−	5.64776e6i	0.481816	−	0.350060i
$765$	−4.79766e6	−	4.61126e6i	−0.296398	−	0.284883i
$766$	−9.90320e6	−	7.19510e6i	−0.609823	−	0.443062i
$767$	1.36073e7	+	4.18788e7i	0.835184	+	2.57043i
$768$	−589824.			−0.0360844
$769$	616813.	+	1.89835e6i	0.0376130	+	0.115761i	0.968100	−	0.250564i	$-0.0806160\pi$
$769$	616813.	+	1.89835e6i	0.0376130	+	0.115761i	−0.930487	+	0.366325i	$0.880616\pi$
$770$	−8.77464e6	−	8.43372e6i	−0.533338	−	0.512616i
$771$	−1.78121e6	+	5.48200e6i	−0.107914	+	0.332126i
$772$	812586.	−	2.50088e6i	0.0490712	−	0.151026i
$773$	−1.58360e6	+	1.15055e6i	−0.0953225	+	0.0692559i	−0.634426	−	0.772984i	$-0.718763\pi$
$773$	−1.58360e6	+	1.15055e6i	−0.0953225	+	0.0692559i	0.539103	+	0.842240i	$0.318763\pi$
$774$	−2.59454e6			−0.155671
$775$	1.39441e7	−	2.08845e7i	0.833945	−	1.24902i
$776$	2.19537e6			0.130874
$777$	−5.12325e6	+	3.72226e6i	−0.304434	+	0.221184i
$778$	2.30862e6	−	7.10519e6i	0.136742	−	0.420849i
$779$	5.96961e6	−	1.83726e7i	0.352454	−	1.08474i
$780$	−7.00303e6	−	967399.i	−0.412144	−	0.0569336i
$781$	−7.58795e6	−	2.33533e7i	−0.445140	−	1.37000i
$782$	2.79557e7			1.63476
$783$	14089.6	+	43363.3i	0.000821286	+	0.00252766i
$784$	1.61751e6	+	1.17519e6i	0.0939849	+	0.0682840i
$785$	−8.56250e6	+	1.76612e7i	−0.495937	+	1.02293i
$786$	231668.	−	168317.i	0.0133755	−	0.00971786i
$787$	−4.02614e6	−	2.92516e6i	−0.231714	−	0.168350i	0.465870	−	0.884853i	$-0.345741\pi$
$787$	−4.02614e6	−	2.92516e6i	−0.231714	−	0.168350i	−0.697584	+	0.716503i	$0.745741\pi$
$788$	8.73946e6	+	6.34959e6i	0.501382	+	0.364275i
$789$	−5.88303e6	+	4.27427e6i	−0.336441	+	0.244439i
$790$	8.33702e6	+	1.15168e6i	0.475273	+	0.0656542i
$791$	−5.87158e6	−	4.26595e6i	−0.333668	−	0.242424i
$792$	−919228.	−	2.82909e6i	−0.0520727	−	0.160263i
$793$	−2.71976e7			−1.53584
$794$	6.35369e6	+	1.95547e7i	0.357664	+	1.10078i
$795$	1.44364e7	−	7.71962e6i	0.810103	−	0.433189i
$796$	−3.52099e6	+	1.08365e7i	−0.196962	+	0.606186i
$797$	2.51501e6	−	7.74040e6i	0.140247	−	0.431636i	−0.856122	−	0.516773i	$-0.827133\pi$
$797$	2.51501e6	−	7.74040e6i	0.140247	−	0.431636i	0.996369	+	0.0851375i	$0.0271330\pi$
$798$	5.43480e6	−	3.94861e6i	0.302118	−	0.219501i
$799$	1.58152e7			0.876410
$800$	−1.98197e6	−	2.51233e6i	−0.109490	−	0.138788i
$801$	3.88172e6			0.213768
$802$	−1.39707e7	+	1.01503e7i	−0.766979	+	0.557243i
$803$	1.04106e7	−	3.20407e7i	0.569756	−	1.75353i
$804$	−504214.	+	1.55181e6i	−0.0275090	+	0.0846640i
$805$	4.43727e6	+	2.48230e7i	0.241338	+	1.35010i
$806$	−8.72315e6	−	2.68471e7i	−0.472972	−	1.45566i
$807$	5.93648e6			0.320882
$808$	3.24750e6	+	9.99477e6i	0.174993	+	0.538573i
$809$	−9.88869e6	−	7.18455e6i	−0.531212	−	0.385948i	0.289599	−	0.957148i	$-0.406478\pi$
$809$	−9.88869e6	−	7.18455e6i	−0.531212	−	0.385948i	−0.820811	+	0.571200i	$0.806478\pi$
$810$	1.29373e6	−	691803.i	0.0692839	−	0.0370484i
$811$	−1.35835e7	+	9.86898e6i	−0.725202	+	0.526890i	−0.888042	−	0.459762i	$-0.847935\pi$
$811$	−1.35835e7	+	9.86898e6i	−0.725202	+	0.526890i	0.162840	+	0.986653i	$0.447935\pi$
$812$	76791.9	+	55792.6i	0.00408719	+	0.00296952i
$813$	1.24097e7	+	9.01616e6i	0.658467	+	0.478405i
$814$	−1.37749e7	+	1.00081e7i	−0.728666	+	0.529407i
$815$	9.37992e6	−	5.01576e6i	0.494658	−	0.264510i
$816$	−2.73930e6	−	1.99022e6i	−0.144017	−	0.104635i
$817$	−4.86824e6	−	1.49829e7i	−0.255162	−	0.785309i
$818$	−1.91323e7			−0.999732
$819$	−2.08506e6	−	6.41717e6i	−0.108620	−	0.334298i
$820$	−1.54549e6	−	8.64578e6i	−0.0802659	−	0.449024i
$821$	−8.41349e6	+	2.58941e7i	−0.435631	+	1.34073i	0.456808	+	0.889565i	$0.348992\pi$
$821$	−8.41349e6	+	2.58941e7i	−0.435631	+	1.34073i	−0.892439	+	0.451168i	$0.851008\pi$
$822$	−531926.	+	1.63710e6i	−0.0274582	+	0.0845075i
$823$	−1.43191e7	+	1.04034e7i	−0.736913	+	0.535399i	−0.891743	−	0.452542i	$-0.850517\pi$
$823$	−1.43191e7	+	1.04034e7i	−0.736913	+	0.535399i	0.154830	+	0.987941i	$0.450517\pi$
$824$	1.35313e7			0.694257
$825$	8.96152e6	−	1.34219e7i	0.458402	−	0.686563i
$826$	−1.90237e7			−0.970162
$827$	−2.24459e6	+	1.63079e6i	−0.114123	+	0.0829152i	−0.643383	−	0.765545i	$-0.722470\pi$
$827$	−2.24459e6	+	1.63079e6i	−0.114123	+	0.0829152i	0.529260	+	0.848460i	$0.322470\pi$
$828$	−1.90458e6	+	5.86169e6i	−0.0965434	+	0.297130i
$829$	3.84659e6	−	1.18386e7i	0.194397	−	0.598293i	−0.805586	−	0.592479i	$-0.798149\pi$
$829$	3.84659e6	−	1.18386e7i	0.194397	−	0.598293i	0.999983	−	0.00581390i	$-0.00185063\pi$
$830$	−1.47960e7	+	7.91194e6i	−0.745504	+	0.398646i
$831$	−2.76768e6	−	8.51805e6i	−0.139032	−	0.427895i
$832$	−3.59719e6			−0.180158
$833$	3.54677e6	+	1.09158e7i	0.177101	+	0.545060i
$834$	4.64558e6	+	3.37521e6i	0.231273	+	0.168030i
$835$	−1.39810e7	−	1.93133e6i	−0.693939	−	0.0958608i
$836$	1.46126e7	−	1.06167e7i	0.723123	−	0.525379i
$837$	4.73929e6	+	3.44330e6i	0.233830	+	0.169887i
$838$	6.81726e6	+	4.95303e6i	0.335351	+	0.243647i
$839$	1.51019e7	−	1.09722e7i	0.740673	−	0.538130i	−0.152249	−	0.988342i	$-0.548652\pi$
$839$	1.51019e7	−	1.09722e7i	0.740673	−	0.538130i	0.892922	+	0.450212i	$0.148652\pi$
$840$	1.33240e6	−	2.74824e6i	0.0651534	−	0.134387i
$841$	1.65907e7	+	1.20539e7i	0.808863	+	0.587673i
$842$	5.46172e6	+	1.68095e7i	0.265491	+	0.817096i
$843$	−6.04578e6			−0.293011
$844$	−781854.	−	2.40630e6i	−0.0377806	−	0.116277i
$845$	−2.21490e7	−	3.05967e6i	−1.06712	−	0.147412i
$846$	−1.07746e6	+	3.31609e6i	−0.0517578	+	0.159294i
$847$	4.93066e6	−	1.51750e7i	0.236154	−	0.726809i
$848$	6.73904e6	−	4.89620e6i	0.321817	−	0.233814i
$849$	2.41567e6			0.115019
$850$	−727568.	−	1.83556e7i	−0.0345403	−	0.871408i
$851$	3.52783e7			1.66987
$852$	4.98525e6	−	3.62199e6i	0.235282	−	0.170942i
$853$	7.81102e6	−	2.40399e7i	0.367566	−	1.13125i	−0.580793	−	0.814052i	$-0.697257\pi$
$853$	7.81102e6	−	2.40399e7i	0.367566	−	1.13125i	0.948359	−	0.317200i	$-0.102743\pi$
$854$	3.63094e6	−	1.11749e7i	0.170363	−	0.524322i
$855$	6.42250e6	+	6.17297e6i	0.300461	+	0.288788i
$856$	−2.34424e6	−	7.21482e6i	−0.109350	−	0.336543i
$857$	−1.74892e6			−0.0813427			−0.0406714	−	0.999173i	$-0.512950\pi$
$857$	−1.74892e6			−0.0813427			−0.0406714	+	0.999173i	$0.512950\pi$
$858$	−5.60613e6	−	1.72539e7i	−0.259983	−	0.800146i
$859$	−2.50220e6	−	1.81795e6i	−0.115701	−	0.0840619i	0.528430	−	0.848977i	$-0.322781\pi$
$859$	−2.50220e6	−	1.81795e6i	−0.115701	−	0.0840619i	−0.644131	+	0.764915i	$0.722781\pi$
$860$	−5.16392e6	−	4.96329e6i	−0.238086	−	0.228836i
$861$	6.78170e6	−	4.92719e6i	0.311767	−	0.226512i
$862$	−1.95331e6	−	1.41916e6i	−0.0895369	−	0.0650524i
$863$	1.82699e6	+	1.32738e6i	0.0835043	+	0.0606694i	0.628754	−	0.777604i	$-0.283565\pi$
$863$	1.82699e6	+	1.32738e6i	0.0835043	+	0.0606694i	−0.545250	+	0.838274i	$0.683565\pi$
$864$	603928.	−	438779.i	0.0275233	−	0.0199969i
$865$	−3.29535e6	−	1.84349e7i	−0.149748	−	0.837721i
$866$	4.47775e6	+	3.25327e6i	0.202892	+	0.147410i
$867$	−2.05770e6	−	6.33295e6i	−0.0929682	−	0.286127i
$868$	1.21954e7			0.549411
$869$	6.67404e6	+	2.05406e7i	0.299805	+	0.922705i
$870$	−54910.4	+	113259.i	−0.00245956	+	0.00507313i
$871$	−3.07507e6	+	9.46410e6i	−0.137344	+	0.422702i
$872$	−3.70161e6	+	1.13924e7i	−0.164854	+	0.507368i
$873$	−2.24787e6	+	1.63317e6i	−0.0998240	+	0.0725264i
$874$	−3.74236e7			−1.65717
$875$	1.61832e7	−	3.55953e6i	0.714570	−	0.157171i
$876$	8.45439e6			0.372239
$877$	−1.73583e7	+	1.26115e7i	−0.762093	+	0.553693i	−0.899551	−	0.436815i	$-0.856107\pi$
$877$	−1.73583e7	+	1.26115e7i	−0.762093	+	0.553693i	0.137459	+	0.990507i	$0.456107\pi$
$878$	5.35009e6	−	1.64659e7i	0.234220	−	0.720856i
$879$	−6.61111e6	+	2.03469e7i	−0.288604	+	0.888231i
$880$	3.58244e6	−	7.38921e6i	0.155945	−	0.321656i
$881$	1.08562e7	+	3.34121e7i	0.471237	+	1.45032i	0.850966	+	0.525221i	$0.176017\pi$
$881$	1.08562e7	+	3.34121e7i	0.471237	+	1.45032i	−0.379729	+	0.925098i	$0.623983\pi$
$882$	−2.53044e6			−0.109528
$883$	3.28778e6	+	1.01187e7i	0.141906	+	0.436742i	0.996600	−	0.0823902i	$-0.0262554\pi$
$883$	3.28778e6	+	1.01187e7i	0.141906	+	0.436742i	−0.854694	+	0.519132i	$0.826255\pi$
$884$	−1.67063e7	−	1.21378e7i	−0.719034	−	0.522409i
$885$	−4.43899e6	−	2.48326e7i	−0.190514	−	1.06577i
$886$	1.89626e7	−	1.37771e7i	0.811548	−	0.589624i
$887$	−1.14214e7	−	8.29811e6i	−0.487426	−	0.354136i	0.316767	−	0.948503i	$-0.397403\pi$
$887$	−1.14214e7	−	8.29811e6i	−0.487426	−	0.354136i	−0.804194	+	0.594367i	$0.797403\pi$
$888$	−3.45682e6	−	2.51152e6i	−0.147111	−	0.106882i
$889$	−1.27153e7	+	9.23822e6i	−0.539601	+	0.392043i
$890$	7.72580e6	+	7.42564e6i	0.326940	+	0.314238i
$891$	3.04581e6	+	2.21291e6i	0.128531	+	0.0933835i
$892$	214257.	+	659416.i	0.00901620	+	0.0277490i
$893$	−2.11714e7			−0.888424
$894$	1.82967e6	+	5.63113e6i	0.0765646	+	0.235642i
$895$	−1.36603e7	−	1.31296e7i	−0.570037	−	0.547890i
$896$	480232.	−	1.47800e6i	0.0199839	−	0.0615043i
$897$	−1.16155e7	+	3.57489e7i	−0.482012	+	1.48348i
$898$	4.25077e6	−	3.08837e6i	0.175905	−	0.127802i
$899$	−502593.			−0.0207404
$900$	3.89832e6	+	1.09798e6i	0.160425	+	0.0451845i
$901$	4.78190e7			1.96240
$902$	1.82340e7	−	1.32478e7i	0.746219	−	0.542160i
$903$	2.11246e6	−	6.50149e6i	0.0862124	−	0.265334i
$904$	1.51325e6	−	4.65731e6i	0.0615871	−	0.189546i
$905$	−2.38517e7	−	3.29488e6i	−0.968052	−	0.133727i
$906$	−3.39021e6	−	1.04340e7i	−0.137217	−	0.422309i
$907$	−7.34168e6			−0.296331			−0.148166	−	0.988963i	$-0.547337\pi$
$907$	−7.34168e6			−0.296331			−0.148166	+	0.988963i	$0.547337\pi$
$908$	−4.74864e6	−	1.46148e7i	−0.191141	−	0.588273i
$909$	−1.07604e7	−	7.81790e6i	−0.431936	−	0.313820i
$910$	8.12598e6	−	1.67608e7i	0.325291	−	0.670951i
$911$	−1.06644e7	+	7.74815e6i	−0.425737	+	0.309316i	−0.779942	−	0.625852i	$-0.784751\pi$
$911$	−1.06644e7	+	7.74815e6i	−0.425737	+	0.309316i	0.354205	+	0.935168i	$0.384751\pi$
$912$	3.66703e6	+	2.66425e6i	0.145991	+	0.106069i
$913$	−3.48341e7	−	2.53084e7i	−1.38302	−	1.00482i
$914$	−9.64732e6	+	7.00919e6i	−0.381981	+	0.277525i
$915$	1.54344e7	+	2.13211e6i	0.609449	+	0.0841894i
$916$	3.13086e6	+	2.27470e6i	0.123289	+	0.0895749i
$917$	233151.	+	717565.i	0.00915617	+	0.0281798i
$918$	4.28536e6			0.167834
$919$	−1.32928e6	−	4.09110e6i	−0.0519191	−	0.159790i	0.921735	−	0.387820i	$-0.126772\pi$
$919$	−1.32928e6	−	4.09110e6i	−0.0519191	−	0.159790i	−0.973654	+	0.228029i	$0.926772\pi$
$920$	−1.50040e7	+	8.02313e6i	−0.584435	+	0.312517i
$921$	−1.01899e6	+	3.13612e6i	−0.0395840	+	0.121827i
$922$	4.07625e6	−	1.25454e7i	0.157919	−	0.486023i
$923$	3.04038e7	−	2.20896e7i	1.17469	−	0.853462i
$924$	7.83767e6			0.302000
$925$	−918142.	−	2.31636e7i	−0.0352822	−	0.890125i
$926$	995771.			0.0381621
$927$	−1.38548e7	+	1.00661e7i	−0.529544	+	0.384736i
$928$	−19791.2	+	60910.9i	−0.000754399	+	0.00232180i
$929$	−9.41743e6	+	2.89839e7i	−0.358008	+	1.10184i	0.596236	+	0.802809i	$0.296662\pi$
$929$	−9.41743e6	+	2.89839e7i	−0.358008	+	1.10184i	−0.954245	+	0.299027i	$0.903338\pi$
$930$	2.84568e6	+	1.59194e7i	0.107890	+	0.603557i
$931$	−4.74796e6	−	1.46127e7i	−0.179528	−	0.552532i
$932$	−2.20994e7			−0.833374
$933$	−1.49855e6	−	4.61205e6i	−0.0563594	−	0.173456i
$934$	1.87635e7	+	1.36325e7i	0.703794	+	0.511337i
$935$	4.15710e7	−	2.22294e7i	1.55511	−	0.831570i
$936$	3.68320e6	−	2.67600e6i	0.137416	−	0.0998383i
$937$	883837.	+	642145.i	0.0328869	+	0.0238938i	0.604107	−	0.796903i	$-0.293530\pi$
$937$	883837.	+	642145.i	0.0328869	+	0.0238938i	−0.571220	+	0.820797i	$0.693530\pi$
$938$	−3.47806e6	−	2.52696e6i	−0.129071	−	0.0937758i
$939$	−1.06094e7	+	7.70821e6i	−0.392670	+	0.285292i
$940$	−8.48807e6	+	4.53886e6i	−0.313321	+	0.167543i
$941$	3.03133e7	+	2.20239e7i	1.11599	+	0.810812i	0.983596	−	0.180386i	$-0.0577347\pi$
$941$	3.03133e7	+	2.20239e7i	1.11599	+	0.810812i	0.132391	+	0.991198i	$0.457735\pi$
$942$	−3.90590e6	−	1.20211e7i	−0.143415	−	0.441386i
$943$	−4.66983e7			−1.71010
$944$	−3.96650e6	−	1.22076e7i	−0.144870	−	0.445863i
$945$	680194.	+	3.80515e6i	0.0247772	+	0.138609i
$946$	5.67980e6	−	1.74806e7i	0.206350	−	0.635081i
$947$	330818.	−	1.01815e6i	0.0119871	−	0.0368925i	−0.944884	−	0.327405i	$-0.893826\pi$
$947$	330818.	−	1.01815e6i	0.0119871	−	0.0368925i	0.956871	+	0.290513i	$0.0938258\pi$
$948$	−4.38481e6	+	3.18575e6i	−0.158464	+	0.115131i
$949$	5.15611e7			1.85848
$950$	973976.	+	2.45722e7i	0.0350138	+	0.883353i
$951$	1.54523e7			0.554041
$952$	7.21749e6	−	5.24382e6i	0.258104	−	0.187523i
$953$	1.37670e7	−	4.23704e7i	0.491028	−	1.51123i	−0.332029	−	0.943269i	$-0.607733\pi$
$953$	1.37670e7	−	4.23704e7i	0.491028	−	1.51123i	0.823057	−	0.567959i	$-0.192267\pi$
$954$	−3.25783e6	+	1.00266e7i	−0.115893	+	0.356682i
$955$	−2.96041e7	+	1.58303e7i	−1.05037	+	0.561670i
$956$	5.32268e6	+	1.63815e7i	0.188359	+	0.579709i
$957$	−323003.			−0.0114006
$958$	844680.	+	2.59966e6i	0.0297357	+	0.0915171i
$959$	−3.66921e6	−	2.66584e6i	−0.128833	−	0.0936025i
$960$	2.04137e6	+	281996.i	0.0714899	+	0.00987562i
$961$	−2.90798e7	+	2.11277e7i	−1.01574	+	0.737979i
$962$	−2.10822e7	−	1.53171e7i	−0.734478	−	0.533630i
$963$	7.76751e6	+	5.64343e6i	0.269908	+	0.196100i
$964$	−8.06688e6	+	5.86093e6i	−0.279584	+	0.203130i
$965$	−4.00803e6	+	8.26704e6i	−0.138552	+	0.285780i
$966$	−1.31377e7	−	9.54512e6i	−0.452978	−	0.329108i
$967$	2.87673e6	+	8.85366e6i	0.0989310	+	0.304478i	0.988258	−	0.152793i	$-0.0488268\pi$
$967$	2.87673e6	+	8.85366e6i	0.0989310	+	0.304478i	−0.889327	+	0.457271i	$0.848827\pi$
$968$	1.07660e7			0.369288
$969$	8.04080e6	+	2.47470e7i	0.275099	+	0.846669i
$970$	−7.59816e6	−	1.04961e6i	−0.259286	−	0.0358178i
$971$	1.79648e7	−	5.52899e7i	0.611468	−	1.88190i	0.167467	−	0.985878i	$-0.446441\pi$
$971$	1.79648e7	−	5.52899e7i	0.611468	−	1.88190i	0.444001	−	0.896026i	$-0.353559\pi$
$972$	−291954.	+	898543.i	−0.00991172	+	0.0305052i
$973$	−1.22401e7	+	8.89298e6i	−0.414481	+	0.301138i
$974$	1.48292e7			0.500864
$975$	2.37749e7	+	6.69631e6i	0.800953	+	0.225592i
$976$	7.92807e6			0.266405
$977$	3.36854e7	−	2.44738e7i	1.12903	−	0.820287i	0.143475	−	0.989654i	$-0.454172\pi$
$977$	3.36854e7	−	2.44738e7i	1.12903	−	0.820287i	0.985553	+	0.169367i	$0.0541723\pi$
$978$	−2.11675e6	+	6.51468e6i	−0.0707656	+	0.217794i
$979$	−8.49762e6	+	2.61530e7i	−0.283361	+	0.872096i
$980$	−5.03634e6	−	4.84067e6i	−0.167514	−	0.161005i
$981$	−4.68485e6	−	1.44185e7i	−0.155426	−	0.478351i
$982$	2.76789e6			0.0915948
$983$	1.20207e7	+	3.69960e7i	0.396777	+	1.22115i	0.927569	+	0.373652i	$0.121895\pi$
$983$	1.20207e7	+	3.69960e7i	0.396777	+	1.22115i	−0.530792	+	0.847502i	$0.678105\pi$
$984$	4.57583e6	+	3.32453e6i	0.150654	+	0.109457i
$985$	−2.72114e7	−	2.61542e7i	−0.893636	−	0.858916i
$986$	−297445.	+	216106.i	−0.00974348	+	0.00707905i
$987$	−7.43230e6	−	5.39989e6i	−0.242846	−	0.176438i
$988$	2.23643e7	+	1.62486e7i	0.728891	+	0.529570i
$989$	−3.08094e7	+	2.23844e7i	−1.00160	+	0.727703i
$990$	1.82884e6	+	1.02309e7i	0.0593047	+	0.331763i
$991$	1.42703e7	+	1.03680e7i	0.461584	+	0.335360i	0.794152	−	0.607719i	$-0.207915\pi$
$991$	1.42703e7	+	1.03680e7i	0.461584	+	0.335360i	−0.332569	+	0.943079i	$0.607915\pi$
$992$	2.54279e6	+	7.82590e6i	0.0820410	+	0.252496i
$993$	1.90445e7			0.612911
$994$	5.01716e6	+	1.54412e7i	0.161062	+	0.495697i
$995$	1.73670e7	−	3.58216e7i	0.556119	−	1.14706i
$996$	3.33899e6	−	1.02764e7i	0.106652	−	0.328240i
$997$	−2.86862e6	+	8.82872e6i	−0.0913978	+	0.281294i	−0.986298	−	0.164972i	$-0.947246\pi$
$997$	−2.86862e6	+	8.82872e6i	−0.0913978	+	0.281294i	0.894900	+	0.446266i	$0.147246\pi$
$998$	−1.24936e7	+	9.07716e6i	−0.397066	+	0.288485i
$999$	5.40784e6			0.171439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.d.61.3	✓	28
25.16	even	5	inner	150.6.g.d.91.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.d.61.3	✓	28	1.1	even	1	trivial
150.6.g.d.91.3	yes	28	25.16	even	5	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 + 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-24.3873 + 50.3017i) q^{5} +(-11.1246 - 34.2380i) q^{6} +94.8525 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})\)	\(q+(-3.23607 + 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(-24.3873 + 50.3017i) q^{5} +(-11.1246 - 34.2380i) q^{6} +94.8525 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-39.3474 - 220.118i) q^{10} +(464.230 - 337.283i) q^{11} +(116.498 + 84.6411i) q^{12} +(710.494 + 516.204i) q^{13} +(-306.949 + 223.012i) q^{14} +(-362.733 - 348.640i) q^{15} +(-207.108 - 150.473i) q^{16} +(-454.132 - 1397.67i) q^{17} +324.000 q^{18} +(607.934 + 1871.03i) q^{19} +(644.859 + 619.804i) q^{20} +(-263.799 + 811.891i) q^{21} +(-709.280 + 2182.94i) q^{22} +(3847.41 - 2795.31i) q^{23} -576.000 q^{24} +(-1935.52 - 2453.44i) q^{25} -3512.88 q^{26} +(589.773 - 428.495i) q^{27} +(468.977 - 1443.36i) q^{28} +(-19.3273 + 59.4833i) q^{29} +(1993.53 + 275.386i) q^{30} +(2483.19 + 7642.48i) q^{31} +1024.00 q^{32} +(1595.88 + 4911.62i) q^{33} +(4755.73 + 3455.24i) q^{34} +(-2313.20 + 4771.24i) q^{35} +(-1048.49 + 761.770i) q^{36} +(6001.42 + 4360.28i) q^{37} +(-6366.37 - 4625.44i) q^{38} +(-6394.45 + 4645.84i) q^{39} +(-3544.05 - 489.576i) q^{40} +(-7944.15 - 5771.76i) q^{41} +(-1055.20 - 3247.56i) q^{42} -8007.83 q^{43} +(-2837.12 - 8731.76i) q^{44} +(3993.00 - 2135.19i) q^{45} +(-5878.32 + 18091.6i) q^{46} +(-3325.50 + 10234.8i) q^{47} +(1863.98 - 1354.26i) q^{48} -7809.99 q^{49} +(12031.9 + 3388.83i) q^{50} +13226.4 q^{51} +(11367.9 - 8259.27i) q^{52} +(-10055.0 + 30946.2i) q^{53} +(-901.094 + 2773.28i) q^{54} +(5644.58 + 31577.0i) q^{55} +(1875.91 + 5773.45i) q^{56} -17705.9 q^{57} +(-77.3092 - 237.933i) q^{58} +(40564.2 + 29471.6i) q^{59} +(-7098.67 + 3795.90i) q^{60} +(-25054.5 + 18203.1i) q^{61} +(-26004.3 - 18893.3i) q^{62} +(-6215.72 - 4515.99i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-43293.0 + 23150.2i) q^{65} +(-16712.3 - 12142.2i) q^{66} +(3501.49 + 10776.5i) q^{67} -23513.6 q^{68} +(13226.2 + 40706.1i) q^{69} +(-3732.20 - 20878.7i) q^{70} +(13223.6 - 40698.0i) q^{71} +(1601.94 - 4930.28i) q^{72} +(47498.2 - 34509.5i) q^{73} -29672.6 q^{74} +(26383.3 - 9743.69i) q^{75} +31477.1 q^{76} +(44033.4 - 31992.1i) q^{77} +(9769.85 - 30068.5i) q^{78} +(-11630.9 + 35796.2i) q^{79} +(12619.9 - 6748.27i) q^{80} +(2027.46 + 6239.88i) q^{81} +39278.0 q^{82} +(-23187.5 - 71363.6i) q^{83} +(11050.2 + 8028.42i) q^{84} +(81380.4 + 11241.9i) q^{85} +(25913.9 - 18827.5i) q^{86} +(-455.396 - 330.864i) q^{87} +(29710.7 + 21586.1i) q^{88} +(-38770.1 + 28168.1i) q^{89} +(-7901.48 + 16297.7i) q^{90} +(67392.2 + 48963.3i) q^{91} +(-23513.3 - 72366.5i) q^{92} -72322.0 q^{93} +(-13302.0 - 40939.3i) q^{94} +(-108942. - 15049.2i) q^{95} +(-2847.90 + 8764.94i) q^{96} +(10600.1 - 32623.8i) q^{97} +(25273.7 - 18362.4i) q^{98} -46479.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9 + 44 * q^10 - 135 * q^11 + 1008 * q^12 + 616 * q^13 - 48 * q^14 + 531 * q^15 - 1792 * q^16 - 3372 * q^17 + 9072 * q^18 + 488 * q^19 - 944 * q^20 - 387 * q^21 - 1920 * q^22 - 620 * q^23 - 16128 * q^24 + 6659 * q^25 - 1616 * q^26 + 5103 * q^27 + 688 * q^28 + 5682 * q^29 + 2844 * q^30 + 3339 * q^31 + 28672 * q^32 + 4320 * q^33 + 14032 * q^34 - 23984 * q^35 - 9072 * q^36 + 4506 * q^37 - 1528 * q^38 - 5544 * q^39 - 5056 * q^40 + 44962 * q^41 - 1548 * q^42 + 38028 * q^43 - 7680 * q^44 + 9396 * q^45 + 7480 * q^46 - 58300 * q^47 + 16128 * q^48 + 114402 * q^49 + 7476 * q^50 + 2448 * q^51 + 9856 * q^52 - 138 * q^53 + 20412 * q^54 + 96850 * q^55 + 2752 * q^56 + 1908 * q^57 + 22728 * q^58 + 40245 * q^59 - 16704 * q^60 + 79380 * q^61 - 54504 * q^62 - 972 * q^63 - 28672 * q^64 + 3532 * q^65 + 4860 * q^66 - 34352 * q^67 - 4352 * q^68 - 16830 * q^69 - 69476 * q^70 + 115860 * q^71 - 36288 * q^72 - 121214 * q^73 - 37856 * q^74 + 21969 * q^75 - 3392 * q^76 + 195005 * q^77 + 14904 * q^78 + 36224 * q^79 + 29696 * q^80 - 45927 * q^81 + 34608 * q^82 + 85051 * q^83 + 1728 * q^84 + 137496 * q^85 - 18568 * q^86 + 127062 * q^87 - 8640 * q^88 - 53826 * q^89 + 3564 * q^90 - 408104 * q^91 + 29920 * q^92 - 185166 * q^93 - 233200 * q^94 - 482004 * q^95 + 64512 * q^96 - 244169 * q^97 - 395952 * q^98 + 99630 * q^99

Introduction

L-functions

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