LMFDB - Embedded newform 150.6.g.c.91.6

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	150.91
Dual form			150.6.g.c.61.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(54.0113 - 14.4147i) q^{5} +(-11.1246 + 34.2380i) q^{6} +182.018 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(54.0113 - 14.4147i) q^{5} +(-11.1246 + 34.2380i) q^{6} +182.018 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(208.675 + 80.3412i) q^{10} +(0.112375 + 0.0816450i) q^{11} +(-116.498 + 84.6411i) q^{12} +(476.041 - 345.864i) q^{13} +(589.022 + 427.950i) q^{14} +(273.596 + 422.220i) q^{15} +(-207.108 + 150.473i) q^{16} +(214.821 - 661.151i) q^{17} -324.000 q^{18} +(436.563 - 1343.60i) q^{19} +(486.393 + 750.614i) q^{20} +(506.220 + 1557.98i) q^{21} +(0.171693 + 0.528418i) q^{22} +(-584.476 - 424.647i) q^{23} -576.000 q^{24} +(2709.43 - 1557.11i) q^{25} +2353.67 q^{26} +(-589.773 - 428.495i) q^{27} +(899.946 + 2769.75i) q^{28} +(1772.51 + 5455.21i) q^{29} +(-107.324 + 2009.60i) q^{30} +(-2230.49 + 6864.74i) q^{31} -1024.00 q^{32} +(-0.386310 + 1.18894i) q^{33} +(2249.63 - 1634.45i) q^{34} +(9831.02 - 2623.73i) q^{35} +(-1048.49 - 761.770i) q^{36} +(-11053.4 + 8030.74i) q^{37} +(4571.75 - 3321.57i) q^{38} +(4284.37 + 3112.77i) q^{39} +(-190.798 + 3572.62i) q^{40} +(-8253.29 + 5996.37i) q^{41} +(-2024.88 + 6231.94i) q^{42} -112.578 q^{43} +(-0.686773 + 2.11367i) q^{44} +(-2853.09 + 3516.11i) q^{45} +(-893.000 - 2748.37i) q^{46} +(-1790.85 - 5511.68i) q^{47} +(-1863.98 - 1354.26i) q^{48} +16323.5 q^{49} +(12428.9 + 1331.34i) q^{50} +6256.57 q^{51} +(7616.65 + 5533.82i) q^{52} +(-1503.45 - 4627.15i) q^{53} +(-901.094 - 2773.28i) q^{54} +(7.24639 + 2.78990i) q^{55} +(-3599.78 + 11079.0i) q^{56} +12714.7 q^{57} +(-7090.03 + 21820.9i) q^{58} +(-10273.7 + 7464.32i) q^{59} +(-5072.15 + 6250.86i) q^{60} +(-7391.91 - 5370.54i) q^{61} +(-23358.0 + 16970.6i) q^{62} +(-11927.7 + 8665.98i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(20726.0 - 25542.5i) q^{65} +(-4.04549 + 2.93922i) q^{66} +(16988.6 - 52285.5i) q^{67} +11122.8 q^{68} +(2009.25 - 6183.84i) q^{69} +(37982.6 + 14623.5i) q^{70} +(-1914.82 - 5893.20i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(16272.2 + 11822.4i) q^{73} -54650.8 q^{74} +(20863.5 + 18860.9i) q^{75} +22604.0 q^{76} +(20.4542 + 14.8609i) q^{77} +(6545.93 + 20146.3i) q^{78} +(2423.04 + 7457.35i) q^{79} +(-9017.16 + 11112.6i) q^{80} +(2027.46 - 6239.88i) q^{81} -40806.5 q^{82} +(-4506.69 + 13870.2i) q^{83} +(-21204.8 + 15406.2i) q^{84} +(2072.47 - 38806.2i) q^{85} +(-364.310 - 264.687i) q^{86} +(-41764.3 + 30343.6i) q^{87} +(-7.19198 + 5.22528i) q^{88} +(-52709.5 - 38295.7i) q^{89} +(-17499.7 + 4670.36i) q^{90} +(86647.9 - 62953.4i) q^{91} +(3572.00 - 10993.5i) q^{92} -64962.2 q^{93} +(7163.41 - 22046.7i) q^{94} +(4211.71 - 78862.6i) q^{95} +(-2847.90 - 8764.94i) q^{96} +(42057.9 + 129441. i) q^{97} +(52824.0 + 38378.9i) q^{98} -11.2511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	54.0113	−	14.4147i	0.966183	−	0.257858i
$5$	54.0113	−	14.4147i	0.966183	−	0.257858i
$6$	−11.1246	+	34.2380i	−0.126156	+	0.388267i
$7$	182.018			1.40401			0.702003	−	0.712174i	$-0.252289\pi$
$7$	182.018			1.40401			0.702003	+	0.712174i	$0.252289\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	208.675	+	80.3412i	0.659889	+	0.254061i
$11$	0.112375	+	0.0816450i	0.000280019	+	0.000203445i	0.587925	−	0.808915i	$-0.299945\pi$
$11$	0.112375	+	0.0816450i	0.000280019	+	0.000203445i	−0.587645	+	0.809119i	$0.699945\pi$
$12$	−116.498	+	84.6411i	−0.233543	+	0.169679i
$13$	476.041	−	345.864i	0.781242	−	0.567606i	−0.124109	−	0.992269i	$-0.539607\pi$
$13$	476.041	−	345.864i	0.781242	−	0.567606i	0.905352	+	0.424663i	$0.139607\pi$
$14$	589.022	+	427.950i	0.803178	+	0.583543i
$15$	273.596	+	422.220i	0.313966	+	0.484519i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	214.821	−	661.151i	0.180283	−	0.554853i	−0.819553	−	0.573004i	$-0.805778\pi$
$17$	214.821	−	661.151i	0.180283	−	0.554853i	0.999835	+	0.0181508i	$0.00577791\pi$
$18$	−324.000			−0.235702
$19$	436.563	−	1343.60i	0.277436	−	0.853861i	−0.711128	−	0.703062i	$-0.751816\pi$
$19$	436.563	−	1343.60i	0.277436	−	0.853861i	0.988565	−	0.150799i	$-0.0481845\pi$
$20$	486.393	+	750.614i	0.271902	+	0.419606i
$21$	506.220	+	1557.98i	0.250490	+	0.770930i
$22$	0.171693	+	0.528418i	7.56305e−5	+	0.000232767i
$23$	−584.476	−	424.647i	−0.230381	−	0.167382i	0.466606	−	0.884465i	$-0.345477\pi$
$23$	−584.476	−	424.647i	−0.230381	−	0.167382i	−0.696987	+	0.717083i	$0.745477\pi$
$24$	−576.000			−0.204124
$25$	2709.43	−	1557.11i	0.867019	−	0.498275i
$26$	2353.67			0.682831
$27$	−589.773	−	428.495i	−0.155695	−	0.113119i
$28$	899.946	+	2769.75i	0.216931	+	0.667645i
$29$	1772.51	+	5455.21i	0.391375	+	1.20453i	0.931749	+	0.363103i	$0.118283\pi$
$29$	1772.51	+	5455.21i	0.391375	+	1.20453i	−0.540374	+	0.841425i	$0.681717\pi$
$30$	−107.324	+	2009.60i	−0.0217717	+	0.407667i
$31$	−2230.49	+	6864.74i	−0.416866	+	1.28298i	0.493706	+	0.869629i	$0.335642\pi$
$31$	−2230.49	+	6864.74i	−0.416866	+	1.28298i	−0.910571	+	0.413352i	$0.864358\pi$
$32$	−1024.00			−0.176777
$33$	−0.386310	+	1.18894i	−6.17520e−5	+	0.000190053i
$34$	2249.63	−	1634.45i	0.333745	−	0.242480i
$35$	9831.02	−	2623.73i	1.35653	−	0.362034i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	−11053.4	+	8030.74i	−1.32736	+	0.964386i	−0.327555	+	0.944832i	$0.606225\pi$
$37$	−11053.4	+	8030.74i	−1.32736	+	0.964386i	−0.999809	+	0.0195544i	$0.993775\pi$
$38$	4571.75	−	3321.57i	0.513598	−	0.373151i
$39$	4284.37	+	3112.77i	0.451050	+	0.327707i
$40$	−190.798	+	3572.62i	−0.0188549	+	0.353050i
$41$	−8253.29	+	5996.37i	−0.766774	+	0.557094i	−0.900981	−	0.433859i	$-0.857151\pi$
$41$	−8253.29	+	5996.37i	−0.766774	+	0.557094i	0.134206	+	0.990953i	$0.457151\pi$
$42$	−2024.88	+	6231.94i	−0.177123	+	0.545130i
$43$	−112.578			−0.00928501			−0.00464250	−	0.999989i	$-0.501478\pi$
$43$	−112.578			−0.00928501			−0.00464250	+	0.999989i	$0.501478\pi$
$44$	−0.686773	+	2.11367i	−5.34788e−5	+	0.000164591i
$45$	−2853.09	+	3516.11i	−0.210031	+	0.258840i
$46$	−893.000	−	2748.37i	−0.0622238	−	0.191505i
$47$	−1790.85	−	5511.68i	−0.118254	−	0.363948i	0.874358	−	0.485281i	$-0.161283\pi$
$47$	−1790.85	−	5511.68i	−0.118254	−	0.363948i	−0.992612	+	0.121334i	$0.961283\pi$
$48$	−1863.98	−	1354.26i	−0.116772	−	0.0848395i
$49$	16323.5			0.971233
$50$	12428.9	+	1331.34i	0.703085	+	0.0753122i
$51$	6256.57			0.336830
$52$	7616.65	+	5533.82i	0.390621	+	0.283803i
$53$	−1503.45	−	4627.15i	−0.0735190	−	0.226268i	0.907544	−	0.419957i	$-0.137955\pi$
$53$	−1503.45	−	4627.15i	−0.0735190	−	0.226268i	−0.981063	+	0.193689i	$0.937955\pi$
$54$	−901.094	−	2773.28i	−0.0420519	−	0.129422i
$55$	7.24639	+	2.78990i	0.000323009	+	0.000124361i
$56$	−3599.78	+	11079.0i	−0.153393	+	0.472096i
$57$	12714.7			0.518346
$58$	−7090.03	+	21820.9i	−0.276744	+	0.851730i
$59$	−10273.7	+	7464.32i	−0.384237	+	0.279164i	−0.763090	−	0.646292i	$-0.776319\pi$
$59$	−10273.7	+	7464.32i	−0.384237	+	0.279164i	0.378853	+	0.925457i	$0.376319\pi$
$60$	−5072.15	+	6250.86i	−0.181892	+	0.224162i
$61$	−7391.91	−	5370.54i	−0.254350	−	0.184796i	0.453302	−	0.891357i	$-0.350246\pi$
$61$	−7391.91	−	5370.54i	−0.254350	−	0.184796i	−0.707653	+	0.706561i	$0.750246\pi$
$62$	−23358.0	+	16970.6i	−0.771714	+	0.560683i
$63$	−11927.7	+	8665.98i	−0.378622	+	0.275085i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	20726.0	−	25542.5i	0.608461	−	0.749860i
$66$	−4.04549	+	2.93922i	−0.000114317	+	8.30563e-5i
$67$	16988.6	−	52285.5i	0.462349	−	1.42296i	−0.399937	−	0.916543i	$-0.630968\pi$
$67$	16988.6	−	52285.5i	0.462349	−	1.42296i	0.862286	−	0.506421i	$-0.169032\pi$
$68$	11122.8			0.291704
$69$	2009.25	−	6183.84i	0.0508056	−	0.156363i
$70$	37982.6	+	14623.5i	0.926488	+	0.356703i
$71$	−1914.82	−	5893.20i	−0.0450798	−	0.138741i	0.925983	−	0.377564i	$-0.123238\pi$
$71$	−1914.82	−	5893.20i	−0.0450798	−	0.138741i	−0.971063	+	0.238823i	$0.923238\pi$
$72$	−1601.94	−	4930.28i	−0.0364180	−	0.112083i
$73$	16272.2	+	11822.4i	0.357386	+	0.259656i	0.751961	−	0.659207i	$-0.229108\pi$
$73$	16272.2	+	11822.4i	0.357386	+	0.259656i	−0.394575	+	0.918864i	$0.629108\pi$
$74$	−54650.8			−1.16016
$75$	20863.5	+	18860.9i	0.428285	+	0.387176i
$76$	22604.0			0.448901
$77$	20.4542	+	14.8609i	0.000393148	+	0.000285639i
$78$	6545.93	+	20146.3i	0.121825	+	0.374937i
$79$	2423.04	+	7457.35i	0.0436810	+	0.134436i	0.970519	−	0.241026i	$-0.0774839\pi$
$79$	2423.04	+	7457.35i	0.0436810	+	0.134436i	−0.926838	+	0.375462i	$0.877484\pi$
$80$	−9017.16	+	11112.6i	−0.157523	+	0.194130i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	−40806.5			−0.670185
$83$	−4506.69	+	13870.2i	−0.0718063	+	0.220997i	−0.980519	−	0.196426i	$-0.937067\pi$
$83$	−4506.69	+	13870.2i	−0.0718063	+	0.220997i	0.908712	+	0.417423i	$0.137067\pi$
$84$	−21204.8	+	15406.2i	−0.327896	+	0.238230i
$85$	2072.47	−	38806.2i	0.0311129	−	0.582577i
$86$	−364.310	−	264.687i	−0.00531159	−	0.00385910i
$87$	−41764.3	+	30343.6i	−0.591572	+	0.429802i
$88$	−7.19198	+	5.22528i	−9.90015e−5	+	7.19288e-5i
$89$	−52709.5	−	38295.7i	−0.705365	−	0.512478i	0.176310	−	0.984335i	$-0.443584\pi$
$89$	−52709.5	−	38295.7i	−0.705365	−	0.512478i	−0.881675	+	0.471857i	$0.843584\pi$
$90$	−17499.7	+	4670.36i	−0.227731	+	0.0607776i
$91$	86647.9	−	62953.4i	1.09687	−	0.796922i
$92$	3572.00	−	10993.5i	0.0439989	−	0.135415i
$93$	−64962.2			−0.778849
$94$	7163.41	−	22046.7i	0.0836181	−	0.257350i
$95$	4211.71	−	78862.6i	0.0478795	−	0.896525i
$96$	−2847.90	−	8764.94i	−0.0315389	−	0.0970668i
$97$	42057.9	+	129441.i	0.453857	+	1.39683i	0.872472	+	0.488664i	$0.162516\pi$
$97$	42057.9	+	129441.i	0.453857	+	1.39683i	−0.418616	+	0.908164i	$0.637484\pi$
$98$	52824.0	+	38378.9i	0.555605	+	0.403671i
$99$	−11.2511			−0.000115374
$100$	37090.6	+	33530.4i	0.370906	+	0.335304i
$101$	18372.2			0.179208			0.0896042	−	0.995977i	$-0.471440\pi$
$101$	18372.2			0.179208			0.0896042	+	0.995977i	$0.471440\pi$
$102$	20246.7	+	14710.1i	0.192688	+	0.139996i
$103$	−47122.0	−	145027.i	−0.437654	−	1.34696i	−0.890343	−	0.455291i	$-0.849535\pi$
$103$	−47122.0	−	145027.i	−0.437654	−	1.34696i	0.452689	−	0.891668i	$-0.350465\pi$
$104$	11637.2	+	35815.6i	0.105503	+	0.324705i
$105$	49799.4	+	76851.7i	0.440810	+	0.680268i
$106$	6013.80	−	18508.6i	0.0519858	−	0.159996i
$107$	−163915.			−1.38408			−0.692038	−	0.721861i	$-0.743287\pi$
$107$	−163915.			−1.38408			−0.692038	+	0.721861i	$0.743287\pi$
$108$	3604.37	−	11093.1i	0.0297352	−	0.0915155i
$109$	151131.	−	109803.i	1.21839	−	0.885214i	0.222427	−	0.974949i	$-0.428602\pi$
$109$	151131.	−	109803.i	1.21839	−	0.885214i	0.995966	+	0.0897350i	$0.0286020\pi$
$110$	16.8903	+	26.0656i	0.000133094	+	0.000205393i
$111$	−99480.2	−	72276.6i	−0.766354	−	0.556789i
$112$	−37697.4	+	27388.8i	−0.283966	+	0.206314i
$113$	107075.	−	77794.7i	0.788847	−	0.573131i	−0.118774	−	0.992921i	$-0.537896\pi$
$113$	107075.	−	77794.7i	0.788847	−	0.573131i	0.907621	+	0.419790i	$0.137896\pi$
$114$	41145.7	+	29894.1i	0.296526	+	0.215439i
$115$	−37689.4	−	14510.7i	−0.265751	−	0.102316i
$116$	−74247.7	+	53944.1i	−0.512316	+	0.372220i
$117$	−14728.3	+	45329.2i	−0.0994693	+	0.306135i
$118$	−50796.2			−0.335835
$119$	39101.2	−	120341.i	0.253118	−	0.779017i
$120$	−31110.5	+	8302.86i	−0.197221	+	0.0526350i
$121$	−49767.5	−	153169.i	−0.309017	−	0.951056i
$122$	−11293.8	−	34758.8i	−0.0686976	−	0.211430i
$123$	−74279.6	−	53967.3i	−0.442697	−	0.321638i
$124$	−115488.			−0.674503
$125$	123895.	−	123157.i	0.709215	−	0.704993i
$126$	−58973.8			−0.330927
$127$	−232841.	−	169169.i	−1.28100	−	0.930704i	−0.281421	−	0.959584i	$-0.590806\pi$
$127$	−232841.	−	169169.i	−1.28100	−	0.930704i	−0.999583	+	0.0288802i	$0.990806\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	−313.097	−	963.612i	−0.00165655	−	0.00509833i
$130$	127125.	−	33927.5i	0.659739	−	0.176073i
$131$	−38097.6	+	117252.i	−0.193963	+	0.596958i	0.806024	+	0.591883i	$0.201615\pi$
$131$	−38097.6	+	117252.i	−0.193963	+	0.596958i	−0.999987	+	0.00507460i	$0.998385\pi$
$132$	−20.0020			−9.99168e−5
$133$	79462.3	−	244560.i	0.389522	−	1.19883i
$134$	177907.	−	129257.i	0.855914	−	0.621858i
$135$	−38031.0	−	14642.2i	−0.179599	−	0.0691467i
$136$	35994.1	+	26151.3i	0.166872	+	0.121240i
$137$	−325427.	+	236437.i	−1.48133	+	1.07625i	−0.504208	+	0.863582i	$0.668216\pi$
$137$	−325427.	+	236437.i	−1.48133	+	1.07625i	−0.977124	+	0.212669i	$0.931784\pi$
$138$	21041.1	−	15287.3i	0.0940528	−	0.0683333i
$139$	−107591.	−	78169.3i	−0.472322	−	0.343162i	0.326024	−	0.945362i	$-0.394291\pi$
$139$	−107591.	−	78169.3i	−0.472322	−	0.343162i	−0.798345	+	0.602200i	$0.794291\pi$
$140$	88532.3	+	136625.i	0.381752	+	0.589130i
$141$	42196.6	−	30657.6i	0.178743	−	0.129865i
$142$	7659.27	−	23572.8i	0.0318762	−	0.0981048i
$143$	81.7330			0.000334239
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	174371.	+	269093.i	0.688736	+	1.06288i
$146$	24861.6	+	76516.3i	0.0965268	+	0.297079i
$147$	45398.2	+	139721.i	0.173279	+	0.533297i
$148$	−176854.	−	128492.i	−0.663682	−	0.482193i
$149$	−338878.			−1.25048			−0.625241	−	0.780432i	$-0.714999\pi$
$149$	−338878.			−1.25048			−0.625241	+	0.780432i	$0.714999\pi$
$150$	23171.0	+	110088.i	0.0840847	+	0.399495i
$151$	72226.6			0.257783			0.128892	−	0.991659i	$-0.458858\pi$
$151$	72226.6			0.257783			0.128892	+	0.991659i	$0.458858\pi$
$152$	73148.0	+	53145.1i	0.256799	+	0.186575i
$153$	17400.5	+	53553.2i	0.0600942	+	0.184951i
$154$	31.2513	+	96.1815i	0.000106186	+	0.000326806i
$155$	−21518.5	+	402925.i	−0.0719420	+	1.34709i
$156$	−26183.7	+	80585.2i	−0.0861430	+	0.265121i
$157$	304638.			0.986359			0.493180	−	0.869928i	$-0.335835\pi$
$157$	304638.			0.986359			0.493180	+	0.869928i	$0.335835\pi$
$158$	−9692.16	+	29829.4i	−0.0308872	+	0.0950609i
$159$	35424.8	−	25737.6i	0.111126	−	0.0807375i
$160$	−55307.5	+	14760.6i	−0.170799	+	0.0455832i
$161$	−106385.	−	77293.3i	−0.323457	−	0.235005i
$162$	21231.8	−	15425.8i	0.0635624	−	0.0461808i
$163$	386492.	−	280803.i	1.13939	−	0.827813i	0.152353	−	0.988326i	$-0.451315\pi$
$163$	386492.	−	280803.i	1.13939	−	0.827813i	0.987034	+	0.160513i	$0.0513149\pi$
$164$	−132053.	−	95941.9i	−0.383387	−	0.278547i
$165$	−3.72690	+	69.7847i	−1.06571e−5	+	0.000199549i
$166$	−47194.7	+	34288.9i	−0.132930	+	0.0965793i
$167$	−164962.	+	507702.i	−0.457714	+	1.40870i	0.410206	+	0.911993i	$0.365457\pi$
$167$	−164962.	+	507702.i	−0.457714	+	1.40870i	−0.867919	+	0.496705i	$0.834543\pi$
$168$	−104842.			−0.286592
$169$	−7742.87	+	23830.1i	−0.0208538	+	0.0641814i
$170$	97945.4	−	120707.i	0.259933	−	0.320338i
$171$	35361.6	+	108832.i	0.0924787	+	0.284620i
$172$	−556.616	−	1713.09i	−0.00143461	−	0.00441528i
$173$	−334397.	−	242953.i	−0.849468	−	0.617174i	0.0755316	−	0.997143i	$-0.475935\pi$
$173$	−334397.	−	242953.i	−0.849468	−	0.617174i	−0.924999	+	0.379969i	$0.875935\pi$
$174$	−206494.			−0.517053
$175$	493165.	−	283422.i	1.21730	−	0.699582i
$176$	−35.5591			−8.65305e−5
$177$	−92463.7	−	67178.8i	−0.221839	−	0.161176i
$178$	−80533.0	−	247855.i	−0.190513	−	0.586337i
$179$	962.192	+	2961.32i	0.00224455	+	0.00690801i	0.952173	−	0.305561i	$-0.0988440\pi$
$179$	962.192	+	2961.32i	0.00224455	+	0.00690801i	−0.949928	+	0.312469i	$0.898844\pi$
$180$	−67610.7	−	26030.5i	−0.155537	−	0.0598828i
$181$	156309.	−	481070.i	0.354640	−	1.09147i	−0.601578	−	0.798814i	$-0.705461\pi$
$181$	156309.	−	481070.i	0.354640	−	1.09147i	0.956218	−	0.292656i	$-0.0945390\pi$
$182$	428411.			0.958699
$183$	25411.1	−	78207.4i	0.0560914	−	0.172631i
$184$	37406.5	−	27177.4i	0.0814521	−	0.0591784i
$185$	−481245.	+	593081.i	−1.03380	+	1.27404i
$186$	−210222.	−	152735.i	−0.445549	−	0.323711i
$187$	78.1201	−	56.7576i	0.000163365	−	0.000118692i
$188$	75016.2	−	54502.4i	0.154796	−	0.112466i
$189$	−107349.	−	77993.8i	−0.218597	−	0.158820i
$190$	199047.	−	245303.i	0.400010	−	0.492967i
$191$	−66156.6	+	48065.6i	−0.131217	+	0.0953347i	−0.651458	−	0.758685i	$-0.725842\pi$
$191$	−66156.6	+	48065.6i	−0.131217	+	0.0953347i	0.520241	+	0.854020i	$0.325842\pi$
$192$	11391.6	−	35059.7i	0.0223014	−	0.0686366i
$193$	972153.			1.87863			0.939315	−	0.343056i	$-0.111462\pi$
$193$	972153.			1.87863			0.939315	+	0.343056i	$0.111462\pi$
$194$	−168232.	+	517764.i	−0.320925	+	0.987706i
$195$	276274.	+	106367.i	0.520299	+	0.200318i
$196$	80707.9	+	248393.i	0.150064	+	0.461849i
$197$	296681.	+	913091.i	0.544659	+	1.67629i	0.721800	+	0.692102i	$0.243315\pi$
$197$	296681.	+	913091.i	0.544659	+	1.67629i	−0.177141	+	0.984185i	$0.556685\pi$
$198$	−36.4094	−	26.4530i	−6.60010e−5	−	4.79526e-5i
$199$	−457010.			−0.818075			−0.409037	−	0.912518i	$-0.634135\pi$
$199$	−457010.			−0.818075			−0.409037	+	0.912518i	$0.634135\pi$
$200$	41192.9	+	195712.i	0.0728195	+	0.345973i
$201$	494786.			0.863827
$202$	59453.8	+	43195.7i	0.102518	+	0.0744838i
$203$	322628.	+	992947.i	0.549493	+	1.69116i
$204$	30934.2	+	95205.7i	0.0520431	+	0.160172i
$205$	−359335.	+	442840.i	−0.597193	+	0.735973i
$206$	188488.	−	580106.i	0.309468	−	0.952444i
$207$	58518.6			0.0949223
$208$	−46548.8	+	143263.i	−0.0746020	+	0.229601i
$209$	158.757	−	115.344i	0.000251401	−	0.000182654i
$210$	−19534.9	+	365783.i	−0.0305677	+	0.572367i
$211$	−85529.0	−	62140.4i	−0.132253	−	0.0960878i	0.519692	−	0.854354i	$-0.326047\pi$
$211$	−85529.0	−	62140.4i	−0.132253	−	0.0960878i	−0.651945	+	0.758266i	$0.726047\pi$
$212$	62977.4	−	45755.7i	0.0962376	−	0.0699207i
$213$	45117.5	−	32779.8i	0.0681391	−	0.0495059i
$214$	−530441.	−	385388.i	−0.791777	−	0.575259i
$215$	−6080.48	+	1622.78i	−0.00897102	+	0.00239421i
$216$	37745.5	−	27423.7i	0.0550466	−	0.0399937i
$217$	−405989.	+	1.24951e6i	−0.585282	+	1.80131i
$218$	747233.			1.06491
$219$	−55938.7	+	172162.i	−0.0788138	+	0.242564i
$220$	−6.62560	+	124.062i	−9.22929e−6	+	0.000172815i
$221$	−126405.	−	389033.i	−0.174093	−	0.535804i
$222$	−151992.	−	467784.i	−0.206985	−	0.637035i
$223$	1.10403e6	+	802127.i	1.48669	+	1.08014i	0.975324	+	0.220777i	$0.0708594\pi$
$223$	1.10403e6	+	802127.i	1.48669	+	1.08014i	0.511363	+	0.859365i	$0.329141\pi$
$224$	−186386.			−0.248196
$225$	−103415.	+	231036.i	−0.136185	+	0.304245i
$226$	529409.			0.689477
$227$	765536.	+	556195.i	0.986055	+	0.716411i	0.959054	−	0.283224i	$-0.0914041\pi$
$227$	765536.	+	556195.i	0.986055	+	0.716411i	0.0270014	+	0.999635i	$0.491404\pi$
$228$	62865.1	+	193479.i	0.0800889	+	0.246488i
$229$	349375.	+	1.07527e6i	0.440254	+	1.35496i	0.887605	+	0.460605i	$0.152367\pi$
$229$	349375.	+	1.07527e6i	0.440254	+	1.35496i	−0.447351	+	0.894358i	$0.647633\pi$
$230$	−87849.0	−	135571.i	−0.109501	−	0.168984i
$231$	−70.3153	+	216.408i	−8.67002e−5	+	0.000266836i
$232$	−367101.			−0.447781
$233$	309174.	−	951539.i	0.373089	−	1.14825i	−0.571669	−	0.820484i	$-0.693704\pi$
$233$	309174.	−	951539.i	0.373089	−	1.14825i	0.944759	−	0.327767i	$-0.106296\pi$
$234$	−154237.	+	112060.i	−0.184141	+	0.133786i
$235$	−176175.	−	271878.i	−0.208102	−	0.321147i
$236$	−164380.	−	119429.i	−0.192118	−	0.139582i
$237$	−57092.4	+	41480.1i	−0.0660249	+	0.0479699i
$238$	409474.	−	297500.i	0.468580	−	0.340443i
$239$	−665550.	−	483550.i	−0.753678	−	0.547579i	0.143287	−	0.989681i	$-0.454233\pi$
$239$	−665550.	−	483550.i	−0.753678	−	0.547579i	−0.896965	+	0.442102i	$0.854233\pi$
$240$	−120197.	−	46276.5i	−0.134699	−	0.0518600i
$241$	−330063.	+	239805.i	−0.366062	+	0.265960i	−0.755576	−	0.655061i	$-0.772643\pi$
$241$	−330063.	+	239805.i	−0.366062	+	0.265960i	0.389514	+	0.921020i	$0.372643\pi$
$242$	199070.	−	612674.i	0.218508	−	0.672498i
$243$	59049.0			0.0641500
$244$	45175.3	−	139035.i	0.0485766	−	0.149503i
$245$	881654.	−	235298.i	0.938389	−	0.250440i
$246$	−113489.	−	349284.i	−0.119568	−	0.367994i
$247$	−256882.	−	790601.i	−0.267911	−	0.824546i
$248$	−373728.	−	271529.i	−0.385857	−	0.280342i
$249$	−131256.			−0.134159
$250$	690491.	−	107251.i	0.698728	−	0.108530i
$251$	−1.20423e6			−1.20650			−0.603249	−	0.797553i	$-0.706128\pi$
$251$	−1.20423e6			−1.20650			−0.603249	+	0.797553i	$0.706128\pi$
$252$	−190843.	−	138656.i	−0.189311	−	0.137542i
$253$	−31.0101	−	95.4391i	−3.04580e−5	−	9.37400e-5i
$254$	−355750.	−	1.09489e6i	−0.345987	−	1.06484i
$255$	337925.	−	90186.5i	0.325440	−	0.0868543i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	512306.			0.483834			0.241917	−	0.970297i	$-0.422224\pi$
$257$	512306.			0.483834			0.241917	+	0.970297i	$0.422224\pi$
$258$	1252.39	−	3854.45i	0.00117136	−	0.00360506i
$259$	−2.01191e6	+	1.46174e6i	−1.86363	+	1.35400i
$260$	491153.	+	189097.i	0.450592	+	0.173481i
$261$	−375879.	−	273092.i	−0.341544	−	0.248146i
$262$	−398963.	+	289864.i	−0.359071	+	0.260880i
$263$	−467929.	+	339970.i	−0.417148	+	0.303076i	−0.776489	−	0.630130i	$-0.783002\pi$
$263$	−467929.	+	339970.i	−0.417148	+	0.303076i	0.359341	+	0.933206i	$0.383002\pi$
$264$	−64.7278	−	47.0275i	−5.71586e−5	−	4.15281e-5i
$265$	−147902.	−	228246.i	−0.129378	−	0.199659i
$266$	832140.	−	604585.i	0.721095	−	0.523906i
$267$	181199.	−	557674.i	0.155553	−	0.478742i
$268$	879619.			0.748096
$269$	493720.	−	1.51951e6i	0.416006	−	1.28034i	−0.495342	−	0.868698i	$-0.664957\pi$
$269$	493720.	−	1.51951e6i	0.416006	−	1.28034i	0.911348	−	0.411637i	$-0.135043\pi$
$270$	−88645.2	−	136799.i	−0.0740024	−	0.114202i
$271$	−458763.	−	1.41193e6i	−0.379460	−	1.16786i	−0.940420	−	0.340014i	$-0.889568\pi$
$271$	−458763.	−	1.41193e6i	−0.379460	−	1.16786i	0.560961	−	0.827842i	$-0.310432\pi$
$272$	54994.1	+	169255.i	0.0450707	+	0.138713i
$273$	779831.	+	566581.i	0.633278	+	0.460103i
$274$	−1.60900e6			−1.29473
$275$	431.602	+	46.2319i	0.000344153	+	3.68646e-5i
$276$	104033.			0.0822051
$277$	−1.27984e6	−	929855.i	−1.00220	−	0.728142i	−0.0396421	−	0.999214i	$-0.512622\pi$
$277$	−1.27984e6	−	929855.i	−1.00220	−	0.728142i	−0.962559	+	0.271072i	$0.912622\pi$
$278$	−164384.	−	505922.i	−0.127570	−	0.392619i
$279$	−180670.	−	556044.i	−0.138955	−	0.427660i
$280$	−34728.7	+	650280.i	−0.0264724	+	0.495685i
$281$	656632.	−	2.02091e6i	0.496085	−	1.52679i	−0.319173	−	0.947697i	$-0.603405\pi$
$281$	656632.	−	2.02091e6i	0.496085	−	1.52679i	0.815258	−	0.579097i	$-0.196595\pi$
$282$	208631.			0.156227
$283$	5048.62	−	15538.0i	0.00374719	−	0.0115327i	−0.949165	−	0.314778i	$-0.898070\pi$
$283$	5048.62	−	15538.0i	0.00374719	−	0.0115327i	0.952913	+	0.303245i	$0.0980700\pi$
$284$	80208.9	−	58275.2i	0.0590102	−	0.0428734i
$285$	686739.	−	183279.i	0.500817	−	0.133660i
$286$	264.494	+	192.166i	0.000191205	+	0.000138919i
$287$	−1.50225e6	+	1.09145e6i	−1.07656	+	0.782164i
$288$	67103.1	−	48753.3i	0.0476718	−	0.0346356i
$289$	757716.	+	550513.i	0.533657	+	0.387724i
$290$	−68400.5	+	1.28077e6i	−0.0477600	+	0.894287i
$291$	−990982.	+	719991.i	−0.686015	+	0.498419i
$292$	−99446.6	+	306065.i	−0.0682547	+	0.210066i
$293$	−545317.			−0.371090			−0.185545	−	0.982636i	$-0.559405\pi$
$293$	−545317.			−0.371090			−0.185545	+	0.982636i	$0.559405\pi$
$294$	−181593.	+	558885.i	−0.122527	+	0.377098i
$295$	−447302.	+	551250.i	−0.299258	+	0.368802i
$296$	−270209.	−	831616.i	−0.179254	−	0.551688i
$297$	−31.2911	−	96.3041i	−2.05840e−5	−	6.33510e-5i
$298$	−1.09663e6	−	796749.i	−0.715352	−	0.519734i
$299$	−425104.			−0.274990
$300$	−183849.	+	410730.i	−0.117939	+	0.263484i
$301$	−20491.2			−0.0130362
$302$	233730.	+	169815.i	0.147468	+	0.107142i
$303$	51096.0	+	157257.i	0.0319728	+	0.0984020i
$304$	111760.	+	343962.i	0.0693590	+	0.213465i
$305$	−476661.	−	183517.i	−0.293400	−	0.112961i
$306$	−69602.0	+	214213.i	−0.0424930	+	0.130780i
$307$	−1.47753e6			−0.894727			−0.447363	−	0.894352i	$-0.647637\pi$
$307$	−1.47753e6			−0.894727			−0.447363	+	0.894352i	$0.647637\pi$
$308$	−125.005	+	384.726i	−7.50846e−5	+	0.000231087i
$309$	1.11030e6	−	806682.i	0.661523	−	0.480625i
$310$	−1.01697e6	+	1.25330e6i	−0.601041	+	0.740715i
$311$	−1.81327e6	−	1.31742e6i	−1.06307	−	0.772364i	−0.0884142	−	0.996084i	$-0.528180\pi$
$311$	−1.81327e6	−	1.31742e6i	−1.06307	−	0.772364i	−0.974653	+	0.223720i	$0.928180\pi$
$312$	−274199.	+	199218.i	−0.159470	+	0.115862i
$313$	1.59512e6	−	1.15892e6i	0.920306	−	0.668642i	−0.0232941	−	0.999729i	$-0.507415\pi$
$313$	1.59512e6	−	1.15892e6i	0.920306	−	0.668642i	0.943600	+	0.331087i	$0.107415\pi$
$314$	985829.	+	716247.i	0.564258	+	0.409957i
$315$	−519313.	+	639995.i	−0.294885	+	0.363413i
$316$	−101498.	+	73742.4i	−0.0571792	+	0.0415431i
$317$	−401126.	+	1.23454e6i	−0.224198	+	0.690012i	0.774174	+	0.632973i	$0.218166\pi$
$317$	−401126.	+	1.23454e6i	−0.224198	+	0.690012i	−0.998372	+	0.0570383i	$0.981834\pi$
$318$	175150.			0.0971274
$319$	−246.206	+	757.745i	−0.000135463	+	0.000416914i
$320$	−213683.	−	82269.4i	−0.116653	−	0.0449121i
$321$	−455874.	−	1.40303e6i	−0.246935	−	0.759986i
$322$	−162542.	−	500253.i	−0.0873627	−	0.268875i
$323$	−794541.	−	577268.i	−0.423750	−	0.307873i
$324$	104976.			0.0555556
$325$	751252.	−	1.67834e6i	0.394528	−	0.881399i
$326$	1.91092e6			0.995861
$327$	1.36018e6	+	988228.i	0.703439	+	0.511079i
$328$	−201758.	−	620949.i	−0.103549	−	0.318692i
$329$	−325967.	−	1.00322e6i	−0.166029	−	0.510985i
$330$	−176.134	+	217.066i	−8.90346e−5	+	0.000109725i
$331$	−730211.	+	2.24736e6i	−0.366335	+	1.12746i	0.582806	+	0.812611i	$0.301955\pi$
$331$	−730211.	+	2.24736e6i	−0.366335	+	1.12746i	−0.949141	+	0.314852i	$0.898045\pi$
$332$	−233343.			−0.116185
$333$	341983.	−	1.05251e6i	0.169003	−	0.520137i
$334$	−1.72751e6	+	1.25511e6i	−0.847333	+	0.615624i
$335$	163896.	−	3.06889e6i	0.0797915	−	1.49406i
$336$	−339277.	−	246499.i	−0.163948	−	0.119115i
$337$	1.22402e6	−	889304.i	0.587103	−	0.426556i	−0.254175	−	0.967158i	$-0.581804\pi$
$337$	1.22402e6	−	889304.i	0.587103	−	0.426556i	0.841278	+	0.540603i	$0.181804\pi$
$338$	−81084.4	+	58911.3i	−0.0386052	+	0.0280483i
$339$	963677.	+	700152.i	0.455441	+	0.330897i
$340$	600756.	−	160332.i	0.281839	−	0.0752180i
$341$	−811.123	+	589.315i	−0.000377747	+	0.000274449i
$342$	−141446.	+	435327.i	−0.0653923	+	0.201257i
$343$	−88002.1			−0.0403885
$344$	2226.46	−	6852.35i	0.00101442	−	0.00312208i
$345$	19384.1	−	362959.i	0.00876794	−	0.164176i
$346$	−510913.	−	1.57243e6i	−0.229433	−	0.706123i
$347$	−985574.	−	3.03329e6i	−0.439406	−	1.35235i	−0.888504	−	0.458869i	$-0.848255\pi$
$347$	−985574.	−	3.03329e6i	−0.439406	−	1.35235i	0.449098	−	0.893482i	$-0.351745\pi$
$348$	−668229.	−	485497.i	−0.295786	−	0.214901i
$349$	1.96364e6			0.862975			0.431488	−	0.902119i	$-0.357989\pi$
$349$	1.96364e6			0.862975			0.431488	+	0.902119i	$0.357989\pi$
$350$	2.26228e6	+	242329.i	0.987135	+	0.105739i
$351$	−428957.			−0.185843
$352$	−115.072	−	83.6045i	−4.95008e−5	−	3.59644e-5i
$353$	1.37827e6	+	4.24188e6i	0.588704	+	1.81185i	0.583856	+	0.811857i	$0.301543\pi$
$353$	1.37827e6	+	4.24188e6i	0.588704	+	1.81185i	0.00484845	+	0.999988i	$0.498457\pi$
$354$	−141272.	−	434791.i	−0.0599167	−	0.184405i
$355$	−188370.	−	290698.i	−0.0793308	−	0.122425i
$356$	322132.	−	991420.i	0.134713	−	0.414603i
$357$	1.13881e6			0.472912
$358$	−3848.77	+	11845.3i	−0.00158714	+	0.00488470i
$359$	−2.53675e6	+	1.84306e6i	−1.03882	+	0.754750i	−0.970056	−	0.242883i	$-0.921907\pi$
$359$	−2.53675e6	+	1.84306e6i	−1.03882	+	0.754750i	−0.0687686	+	0.997633i	$0.521907\pi$
$360$	−157591.	−	243199.i	−0.0640879	−	0.0989021i
$361$	388524.	+	282279.i	0.156910	+	0.114002i
$362$	1.63689e6	−	1.18927e6i	0.656520	−	0.476990i
$363$	1.17264e6	−	851971.i	0.467086	−	0.339358i
$364$	1.38637e6	+	1.00725e6i	0.548434	+	0.398461i
$365$	1.04930e6	+	403986.i	0.412255	+	0.158721i
$366$	266109.	−	193339.i	0.103838	−	0.0754427i
$367$	−1.31431e6	+	4.04504e6i	−0.509371	+	1.56768i	0.283926	+	0.958846i	$0.408363\pi$
$367$	−1.31431e6	+	4.04504e6i	−0.509371	+	1.56768i	−0.793297	+	0.608835i	$0.791637\pi$
$368$	184948.			0.0711917
$369$	255351.	−	785888.i	0.0976272	−	0.300466i
$370$	−2.95176e6	+	787774.i	−1.12093	+	0.299156i
$371$	−273655.	−	842223.i	−0.103221	−	0.317682i
$372$	−321191.	−	988523.i	−0.120339	−	0.370365i
$373$	1.76392e6	+	1.28157e6i	0.656459	+	0.476946i	0.865465	−	0.500969i	$-0.167023\pi$
$373$	1.76392e6	+	1.28157e6i	0.656459	+	0.476946i	−0.209006	+	0.977914i	$0.567023\pi$
$374$	386.247			0.000142786
$375$	1.39873e6	+	717959.i	0.513638	+	0.263646i
$376$	370900.			0.135297
$377$	2.73055e6	+	1.98386e6i	0.989455	+	0.718881i
$378$	−164015.	−	504787.i	−0.0590411	−	0.181710i
$379$	−252773.	−	777956.i	−0.0903927	−	0.278200i	0.895633	−	0.444794i	$-0.146723\pi$
$379$	−252773.	−	777956.i	−0.0903927	−	0.278200i	−0.986026	+	0.166594i	$0.946723\pi$
$380$	1.22087e6	−	325829.i	0.433721	−	0.115753i
$381$	800437.	−	2.46349e6i	0.282498	−	0.869438i
$382$	−327096.			−0.114688
$383$	10013.5	−	30818.3i	0.00348809	−	0.0107352i	−0.949297	−	0.314380i	$-0.898203\pi$
$383$	10013.5	−	30818.3i	0.00348809	−	0.0107352i	0.952785	+	0.303644i	$0.0982035\pi$
$384$	119294.	−	86672.5i	0.0412850	−	0.0299953i
$385$	1318.97	+	507.813i	0.000453507	+	0.000174603i
$386$	3.14595e6	+	2.28567e6i	1.07469	+	0.780809i
$387$	7377.28	−	5359.91i	0.00250391	−	0.00181920i
$388$	−1.76175e6	+	1.27998e6i	−0.594106	+	0.431643i
$389$	−60665.1	−	44075.8i	−0.0203266	−	0.0147681i	0.577576	−	0.816337i	$-0.303999\pi$
$389$	−60665.1	−	44075.8i	−0.0203266	−	0.0147681i	−0.597902	+	0.801569i	$0.703999\pi$
$390$	643956.	+	993770.i	0.214385	+	0.330845i
$391$	−406313.	+	295204.i	−0.134406	+	0.0976517i
$392$	−322832.	+	993574.i	−0.106111	+	0.326577i
$393$	−1.10958e6			−0.362390
$394$	−1.18672e6	+	3.65236e6i	−0.385132	+	1.18531i
$395$	238367.	+	367854.i	0.0768694	+	0.118627i
$396$	−55.6286	−	171.207i	−1.78263e−5	−	5.48636e-5i
$397$	763943.	+	2.35117e6i	0.243268	+	0.748701i	0.995917	+	0.0902790i	$0.0287759\pi$
$397$	763943.	+	2.35117e6i	0.243268	+	0.748701i	−0.752649	+	0.658422i	$0.771224\pi$
$398$	−1.47892e6	−	1.07450e6i	−0.467989	−	0.340014i
$399$	2.31431e6			0.727762
$400$	−326843.	+	730187.i	−0.102138	+	0.228184i
$401$	5.33989e6			1.65833			0.829166	−	0.559002i	$-0.188816\pi$
$401$	5.33989e6			1.65833			0.829166	+	0.559002i	$0.188816\pi$
$402$	1.60116e6	+	1.16331e6i	0.494162	+	0.359030i
$403$	1.31246e6	+	4.03934e6i	0.402554	+	1.23893i
$404$	90837.3	+	279568.i	0.0276892	+	0.0852187i
$405$	19559.8	−	366249.i	0.00592552	−	0.110953i
$406$	−1.29051e6	+	3.97179e6i	−0.388550	+	1.19583i
$407$	−1897.79			−0.000567887
$408$	−123737.	+	380823.i	−0.0368001	+	0.113259i
$409$	−422278.	+	306803.i	−0.124822	+	0.0906884i	−0.648445	−	0.761262i	$-0.724580\pi$
$409$	−422278.	+	306803.i	−0.124822	+	0.0906884i	0.523623	+	0.851950i	$0.324580\pi$
$410$	−2.20401e6	+	588213.i	−0.647521	+	0.172812i
$411$	−2.92885e6	−	2.12793e6i	−0.855248	−	0.621374i
$412$	1.97387e6	−	1.43410e6i	0.572896	−	0.416233i
$413$	−1.87001e6	+	1.35864e6i	−0.539471	+	0.391949i
$414$	189370.	+	137586.i	0.0543014	+	0.0394523i
$415$	−43478.0	+	814108.i	−0.0123922	+	0.232039i
$416$	−487466.	+	354165.i	−0.138105	+	0.100339i
$417$	369864.	−	1.13832e6i	0.104160	−	0.320572i
$418$	784.939			0.000219733
$419$	1.46062e6	−	4.49533e6i	0.406446	−	1.25091i	−0.513236	−	0.858248i	$-0.671553\pi$
$419$	1.46062e6	−	4.49533e6i	0.406446	−	1.25091i	0.919682	−	0.392665i	$-0.128447\pi$
$420$	−923223.	+	1.13777e6i	−0.255378	+	0.314725i
$421$	−850707.	−	2.61821e6i	−0.233924	−	0.719944i	−0.997262	−	0.0739449i	$-0.976441\pi$
$421$	−850707.	−	2.61821e6i	−0.233924	−	0.719944i	0.763338	−	0.645999i	$-0.223559\pi$
$422$	−130677.	−	402181.i	−0.0357204	−	0.109936i
$423$	379769.	+	275919.i	0.103197	+	0.0749774i
$424$	311377.			0.0841148
$425$	−447442.	−	2.12584e6i	−0.120161	−	0.570899i
$426$	223073.			0.0595557
$427$	−1.34546e6	−	977534.i	−0.357109	−	0.259455i
$428$	−810442.	−	2.49428e6i	−0.213852	−	0.658167i
$429$	227.312	+	699.594i	5.96320e−5	+	0.000183528i
$430$	−23492.2	−	9044.65i	−0.00612707	−	0.00235896i
$431$	−972644.	+	2.99349e6i	−0.252209	+	0.776220i	0.742158	+	0.670225i	$0.233803\pi$
$431$	−972644.	+	2.99349e6i	−0.252209	+	0.776220i	−0.994367	+	0.105994i	$0.966197\pi$
$432$	186624.			0.0481125
$433$	1.16455e6	−	3.58411e6i	0.298496	−	0.918675i	−0.683529	−	0.729923i	$-0.739556\pi$
$433$	1.16455e6	−	3.58411e6i	0.298496	−	0.918675i	0.982025	−	0.188752i	$-0.0604441\pi$
$434$	−4.25157e6	+	3.08895e6i	−1.08349	+	0.787203i
$435$	−1.81835e6	+	2.24091e6i	−0.460739	+	0.567809i
$436$	2.41810e6	+	1.75685e6i	0.609196	+	0.442607i
$437$	−825717.	+	599919.i	−0.206837	+	0.150276i
$438$	−585798.	+	425607.i	−0.145902	+	0.106004i
$439$	1.15425e6	+	838611.i	0.285850	+	0.207682i	0.721465	−	0.692451i	$-0.243469\pi$
$439$	1.15425e6	+	838611.i	0.285850	+	0.207682i	−0.435615	+	0.900133i	$0.643469\pi$
$440$	−313.127	+	385.894i	−7.71062e−5	+	9.50247e-5i
$441$	−1.06969e6	+	777173.i	−0.261915	+	0.190292i
$442$	505618.	−	1.55613e6i	0.123103	−	0.378871i
$443$	−1.64412e6			−0.398037			−0.199018	−	0.979996i	$-0.563775\pi$
$443$	−1.64412e6			−0.398037			−0.199018	+	0.979996i	$0.563775\pi$
$444$	607969.	−	1.87114e6i	0.146361	−	0.450452i
$445$	−3.39893e6	−	1.30861e6i	−0.813658	−	0.313263i
$446$	1.68681e6	+	5.19147e6i	0.401541	+	1.23581i
$447$	−942471.	−	2.90063e6i	−0.223100	−	0.686630i
$448$	−603159.	−	438221.i	−0.141983	−	0.103157i
$449$	−302588.			−0.0708330			−0.0354165	−	0.999373i	$-0.511276\pi$
$449$	−302588.			−0.0708330			−0.0354165	+	0.999373i	$0.511276\pi$
$450$	−877857.	+	504504.i	−0.204358	+	0.117445i
$451$	−1417.03			−0.000328049
$452$	1.71320e6	+	1.24471e6i	0.394423	+	0.286565i
$453$	200873.	+	618224.i	0.0459914	+	0.141547i
$454$	1.16964e6	+	3.59977e6i	0.266324	+	0.819662i
$455$	3.77251e6	−	4.64920e6i	0.854284	−	1.05281i
$456$	−251460.	+	773915.i	−0.0566314	+	0.174294i
$457$	−6.93744e6			−1.55385			−0.776925	−	0.629593i	$-0.783222\pi$
$457$	−6.93744e6			−1.55385			−0.776925	+	0.629593i	$0.783222\pi$
$458$	−1.39750e6	+	4.30107e6i	−0.311307	+	0.958104i
$459$	−409996.	+	297879.i	−0.0908338	+	0.0659946i
$460$	34460.6	−	645261.i	0.00759326	−	0.142181i
$461$	303409.	+	220440.i	0.0664931	+	0.0483101i	0.620535	−	0.784179i	$-0.286915\pi$
$461$	303409.	+	220440.i	0.0664931	+	0.0483101i	−0.554042	+	0.832489i	$0.686915\pi$
$462$	−736.352	+	534.991i	−0.000160502	+	0.000116612i
$463$	−1.57384e6	+	1.14346e6i	−0.341199	+	0.247895i	−0.745167	−	0.666877i	$-0.767630\pi$
$463$	−1.57384e6	+	1.14346e6i	−0.341199	+	0.247895i	0.403969	+	0.914773i	$0.367630\pi$
$464$	−1.18796e6	−	863106.i	−0.256158	−	0.186110i
$465$	−3.50869e6	+	936409.i	−0.752510	+	0.200832i
$466$	3.23771e6	−	2.35233e6i	0.690674	−	0.501804i
$467$	−1.39044e6	+	4.27933e6i	−0.295025	+	0.907995i	0.688188	+	0.725533i	$0.258407\pi$
$467$	−1.39044e6	+	4.27933e6i	−0.295025	+	0.907995i	−0.983213	+	0.182462i	$0.941593\pi$
$468$	−762591.			−0.160945
$469$	3.09222e6	−	9.51689e6i	0.649141	−	1.99785i
$470$	69108.5	−	1.29403e6i	0.0144307	−	0.270209i
$471$	847245.	+	2.60755e6i	0.175977	+	0.541603i
$472$	−251150.	−	772961.i	−0.0518894	−	0.159699i
$473$	−12.6509	−	9.19143i	−2.59998e−6	−	1.88899e-6i
$474$	−282281.			−0.0577079
$475$	−909300.	−	4.32018e6i	−0.184915	−	0.878553i
$476$	2.02455e6			0.409554
$477$	318823.	+	231638.i	0.0641584	+	0.0466138i
$478$	−1.01687e6	−	3.12960e6i	−0.203561	−	0.626498i
$479$	−29455.4	−	90654.5i	−0.00586579	−	0.0180531i	0.948081	−	0.318030i	$-0.103021\pi$
$479$	−29455.4	−	90654.5i	−0.00586579	−	0.0180531i	−0.953947	+	0.299977i	$0.903021\pi$
$480$	−280163.	−	432354.i	−0.0555018	−	0.0856517i
$481$	−2.48431e6	+	7.64592e6i	−0.489602	+	1.50684i
$482$	−1.63192e6			−0.319950
$483$	365719.	−	1.12557e6i	0.0713313	−	0.219535i
$484$	2.08469e6	−	1.51461e6i	0.404508	−	0.293893i
$485$	4.13746e6	+	6.38502e6i	0.798691	+	1.23256i
$486$	191087.	+	138833.i	0.0366978	+	0.0266625i
$487$	4.12039e6	−	2.99364e6i	0.787255	−	0.571975i	−0.119892	−	0.992787i	$-0.538255\pi$
$487$	4.12039e6	−	2.99364e6i	0.787255	−	0.571975i	0.907148	+	0.420812i	$0.138255\pi$
$488$	473082.	−	343714.i	0.0899264	−	0.0653353i
$489$	3.47843e6	+	2.52722e6i	0.657825	+	0.477938i
$490$	3.40631e6	+	1.31145e6i	0.640906	+	0.246753i
$491$	−5.70881e6	+	4.14769e6i	−1.06867	+	0.776431i	−0.975672	−	0.219236i	$-0.929644\pi$
$491$	−5.70881e6	+	4.14769e6i	−1.06867	+	0.776431i	−0.0929936	+	0.995667i	$0.529644\pi$
$492$	453957.	−	1.39713e6i	0.0845477	−	0.260211i
$493$	3.98749e6			0.738894
$494$	1.02753e6	−	3.16240e6i	0.189442	−	0.583042i
$495$	−607.688	+	162.181i	−0.000111472	+	2.97501e-5i
$496$	−571006.	−	1.75737e6i	−0.104216	−	0.320745i
$497$	−348531.	−	1.07267e6i	−0.0632922	−	0.194794i
$498$	−424752.	−	308600.i	−0.0767471	−	0.0557601i
$499$	9.86122e6			1.77288			0.886440	−	0.462844i	$-0.153171\pi$
$499$	9.86122e6			1.77288			0.886440	+	0.462844i	$0.153171\pi$
$500$	2.48664e6	+	1.27637e6i	0.444824	+	0.228324i
$501$	−4.80447e6			−0.855167
$502$	−3.89698e6	−	2.83132e6i	−0.690191	−	0.501453i
$503$	−619498.	−	1.90662e6i	−0.109174	−	0.336003i	0.881513	−	0.472159i	$-0.156525\pi$
$503$	−619498.	−	1.90662e6i	−0.109174	−	0.336003i	−0.990687	+	0.136156i	$0.956525\pi$
$504$	−291583.	−	897399.i	−0.0511311	−	0.157365i
$505$	992307.	−	264830.i	0.173148	−	0.0462103i
$506$	124.040	−	381.756i	2.15370e−5	−	6.62842e-5i
$507$	−225508.			−0.0389621
$508$	1.42300e6	−	4.37954e6i	0.244650	−	0.752955i
$509$	−153609.	+	111604.i	−0.0262798	+	0.0190934i	−0.600848	−	0.799364i	$-0.705170\pi$
$509$	−153609.	+	111604.i	−0.0262798	+	0.0190934i	0.574568	+	0.818457i	$0.305170\pi$
$510$	1.30559e6	+	502661.i	0.222270	+	0.0855755i
$511$	2.96182e6	+	2.15189e6i	0.501773	+	0.364559i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	−833201.	+	605356.i	−0.139784	+	0.101559i
$514$	1.65786e6	+	1.20450e6i	0.276783	+	0.201094i
$515$	−4.63563e6	−	7.15382e6i	−0.770177	−	1.18856i
$516$	13115.2	−	9528.72i	0.00216845	−	0.00157547i
$517$	248.754	−	765.587i	4.09302e−5	−	0.000125970i
$518$	−9.94743e6			−1.62887
$519$	1.14955e6	−	3.53796e6i	0.187332	−	0.576547i
$520$	1.14481e6	+	1.76670e6i	0.185663	+	0.286520i
$521$	2.68598e6	+	8.26661e6i	0.433520	+	1.33424i	0.894596	+	0.446877i	$0.147464\pi$
$521$	2.68598e6	+	8.26661e6i	0.433520	+	1.33424i	−0.461076	+	0.887361i	$0.652536\pi$
$522$	−574292.	−	1.76749e6i	−0.0922479	−	0.283910i
$523$	−5.34223e6	−	3.88136e6i	−0.854021	−	0.620483i	0.0722307	−	0.997388i	$-0.476988\pi$
$523$	−5.34223e6	−	3.88136e6i	−0.854021	−	0.620483i	−0.926252	+	0.376905i	$0.876988\pi$
$524$	−1.97258e6			−0.313839
$525$	3.79752e6	+	3.43301e6i	0.601315	+	0.543597i
$526$	−2.31357e6			−0.364601
$527$	4.05947e6	+	2.94938e6i	0.636712	+	0.462599i
$528$	−98.8954	−	304.369i	−1.54380e−5	−	4.75133e-5i
$529$	−1.82765e6	−	5.62493e6i	−0.283958	−	0.873933i
$530$	58017.7	−	1.08636e6i	0.00897163	−	0.167990i
$531$	317862.	−	978279.i	0.0489218	−	0.150566i
$532$	4.11433e6			0.630260
$533$	−1.85498e6	+	5.70903e6i	−0.282827	+	0.870451i
$534$	1.89754e6	−	1.37865e6i	0.287964	−	0.209218i
$535$	−8.85327e6	+	2.36279e6i	−1.33727	+	0.356895i
$536$	2.84651e6	+	2.06811e6i	0.427957	+	0.310929i
$537$	−22671.5	+	16471.8i	−0.00339269	+	0.00246493i
$538$	5.17030e6	−	3.75644e6i	0.770123	−	0.559527i
$539$	1834.35	+	1332.73i	0.000271963	+	0.000197593i
$540$	34772.9	−	651110.i	0.00513165	−	0.0960881i
$541$	−6.66522e6	+	4.84256e6i	−0.979087	+	0.711348i	−0.957504	−	0.288419i	$-0.906870\pi$
$541$	−6.66522e6	+	4.84256e6i	−0.979087	+	0.711348i	−0.0215826	+	0.999767i	$0.506870\pi$
$542$	1.83505e6	−	5.64771e6i	0.268318	−	0.825799i
$543$	4.55244e6			0.662590
$544$	−219977.	+	677018.i	−0.0318698	+	0.0980851i
$545$	6.58000e6	−	8.10911e6i	0.948931	−	1.16945i
$546$	1.19148e6	+	3.66699e6i	0.171042	+	0.526414i
$547$	−1.72247e6	−	5.30122e6i	−0.246141	−	0.757544i	−0.995447	−	0.0953197i	$-0.969613\pi$
$547$	−1.72247e6	−	5.30122e6i	−0.246141	−	0.757544i	0.749306	−	0.662224i	$-0.230387\pi$
$548$	−5.20684e6	−	3.78299e6i	−0.740666	−	0.538125i
$549$	740089.			0.104798
$550$	1288.00	+	1164.37i	0.000181555	+	0.000164128i
$551$	8.10345e6			1.13708
$552$	336658.	+	244597.i	0.0470264	+	0.0341667i
$553$	441037.	+	1.35737e6i	0.0613285	+	0.188750i
$554$	−1.95542e6	−	6.01815e6i	−0.270685	−	0.833084i
$555$	−6.41490e6	−	2.46978e6i	−0.884010	−	0.340349i
$556$	657536.	−	2.02369e6i	0.0902054	−	0.277624i
$557$	−2.86450e6			−0.391211			−0.195606	−	0.980683i	$-0.562667\pi$
$557$	−2.86450e6			−0.391211			−0.195606	+	0.980683i	$0.562667\pi$
$558$	722679.	−	2.22418e6i	0.0982562	−	0.302401i
$559$	−53591.7	+	38936.6i	−0.00725384	+	0.00527022i
$560$	−1.64129e6	+	2.02270e6i	−0.221164	+	0.272559i
$561$	703.081	+	510.818i	9.43188e−5	+	6.85266e-5i
$562$	6.87634e6	−	4.99596e6i	0.918368	−	0.667233i
$563$	−7.19629e6	+	5.22841e6i	−0.956836	+	0.695182i	−0.952414	−	0.304808i	$-0.901408\pi$
$563$	−7.19629e6	+	5.22841e6i	−0.956836	+	0.695182i	−0.00442249	+	0.999990i	$0.501408\pi$
$564$	675146.	+	490522.i	0.0893716	+	0.0649323i
$565$	4.66188e6	−	5.74524e6i	0.614384	−	0.757159i
$566$	52869.8	−	38412.1i	0.00693692	−	0.00503996i
$567$	369034.	−	1.13577e6i	0.0482069	−	0.148365i
$568$	396575.			0.0515768
$569$	2.50716e6	−	7.71626e6i	0.324640	−	0.999139i	−0.646963	−	0.762522i	$-0.723961\pi$
$569$	2.50716e6	−	7.71626e6i	0.324640	−	0.999139i	0.971603	−	0.236618i	$-0.0760389\pi$
$570$	2.65325e6	+	1.02152e6i	0.342051	+	0.131692i
$571$	3.15016e6	+	9.69518e6i	0.404335	+	1.24442i	0.921449	+	0.388499i	$0.127006\pi$
$571$	3.15016e6	+	9.69518e6i	0.404335	+	1.24442i	−0.517114	+	0.855917i	$0.672994\pi$
$572$	404.110	+	1243.72i	5.16428e−5	+	0.000158940i
$573$	−595410.	−	432590.i	−0.0757581	−	0.0550415i
$574$	−7.42752e6			−0.940944
$575$	−2.24482e6	−	240458.i	−0.283147	−	0.0303298i
$576$	331776.			0.0416667
$577$	−7.20967e6	−	5.23813e6i	−0.901521	−	0.654993i	0.0373351	−	0.999303i	$-0.488113\pi$
$577$	−7.20967e6	−	5.23813e6i	−0.901521	−	0.654993i	−0.938856	+	0.344309i	$0.888113\pi$
$578$	1.15769e6	+	3.56300e6i	0.144136	+	0.443604i
$579$	2.70371e6	+	8.32115e6i	0.335168	+	1.03154i
$580$	−3.23263e6	+	3.98385e6i	−0.399012	+	0.491737i
$581$	−820298.	+	2.52462e6i	−0.100816	+	0.310281i
$582$	−4.89969e6			−0.599599
$583$	208.834	−	642.724i	2.54466e−5	−	7.83164e-5i
$584$	−1.04142e6	+	756635.i	−0.126355	+	0.0918024i
$585$	−142091.	+	2.66059e6i	−0.0171663	+	0.321431i
$586$	−1.76468e6	−	1.28212e6i	−0.212287	−	0.154235i
$587$	4.14611e6	−	3.01233e6i	0.496645	−	0.360834i	−0.311089	−	0.950381i	$-0.600694\pi$
$587$	4.14611e6	−	3.01233e6i	0.496645	−	0.360834i	0.807734	+	0.589547i	$0.200694\pi$
$588$	−1.90166e6	+	1.38164e6i	−0.226825	+	0.164798i
$589$	8.24974e6	+	5.99379e6i	0.979833	+	0.711891i
$590$	−2.74357e6	+	732211.i	−0.324478	+	0.0865977i
$591$	−6.99049e6	+	5.07889e6i	−0.823264	+	0.598136i
$592$	1.08083e6	−	3.32647e6i	0.126752	−	0.390103i
$593$	−1.03642e7			−1.21032			−0.605161	−	0.796103i	$-0.706891\pi$
$593$	−1.03642e7			−1.21032			−0.605161	+	0.796103i	$0.706891\pi$
$594$	125.164	−	385.217i	1.45551e−5	−	4.47960e-5i
$595$	377226.	−	7.06342e6i	0.0436827	−	0.817942i
$596$	−1.67550e6	−	5.15667e6i	−0.193210	−	0.594639i
$597$	−1.27101e6	−	3.91178e6i	−0.145954	−	0.449199i
$598$	−1.37567e6	−	999480.i	−0.157311	−	0.114293i
$599$	5.77245e6			0.657344			0.328672	−	0.944444i	$-0.393399\pi$
$599$	5.77245e6			0.657344			0.328672	+	0.944444i	$0.393399\pi$
$600$	−1.56063e6	+	896896.i	−0.176979	+	0.101710i
$601$	−3.10260e6			−0.350381			−0.175190	−	0.984535i	$-0.556054\pi$
$601$	−3.10260e6			−0.350381			−0.175190	+	0.984535i	$0.556054\pi$
$602$	−66310.9	−	48177.7i	−0.00745751	−	0.00541820i
$603$	1.37607e6	+	4.23512e6i	0.154116	+	0.474321i
$604$	357108.	+	1.09907e6i	0.0398297	+	0.122583i
$605$	−4.89588e6	−	7.55545e6i	−0.543804	−	0.839212i
$606$	−204384.	+	629029.i	−0.0226082	+	0.0695807i
$607$	8.57103e6			0.944195			0.472097	−	0.881546i	$-0.343497\pi$
$607$	8.57103e6			0.944195			0.472097	+	0.881546i	$0.343497\pi$
$608$	−447041.	+	1.37585e6i	−0.0490442	+	0.150943i
$609$	−7.60186e6	+	5.52307e6i	−0.830571	+	0.603445i
$610$	−1.11103e6	−	1.71457e6i	−0.120893	−	0.186565i
$611$	−2.75881e6	−	2.00439e6i	−0.298964	−	0.217210i
$612$	−728881.	+	529563.i	−0.0786644	+	0.0571530i
$613$	4.87433e6	−	3.54141e6i	0.523919	−	0.380649i	−0.294159	−	0.955756i	$-0.595040\pi$
$613$	4.87433e6	−	3.54141e6i	0.523919	−	0.380649i	0.818078	+	0.575107i	$0.195040\pi$
$614$	−4.78139e6	−	3.47388e6i	−0.511839	−	0.371872i
$615$	−4.78986e6	−	1.84412e6i	−0.510663	−	0.196609i
$616$	−1309.07	+	951.095i	−0.000138999	+	0.000100989i
$617$	−1.90465e6	+	5.86191e6i	−0.201420	+	0.619906i	0.798422	+	0.602099i	$0.205669\pi$
$617$	−1.90465e6	+	5.86191e6i	−0.201420	+	0.619906i	−0.999841	+	0.0178076i	$0.994331\pi$
$618$	5.48964e6			0.578192
$619$	−1.38326e6	+	4.25723e6i	−0.145103	+	0.446581i	−0.997024	−	0.0770889i	$-0.975437\pi$
$619$	−1.38326e6	+	4.25723e6i	−0.145103	+	0.446581i	0.851921	+	0.523670i	$0.175437\pi$
$620$	−6.23767e6	+	1.66473e6i	−0.651693	+	0.173926i
$621$	162749.	+	500891.i	0.0169352	+	0.0521211i
$622$	−2.77043e6	−	8.52650e6i	−0.287125	−	0.883679i
$623$	−9.59407e6	−	6.97050e6i	−0.990337	−	0.719522i
$624$	−1.35572e6			−0.139382
$625$	4.91644e6	−	8.43778e6i	0.503443	−	0.864028i
$626$	7.88670e6			0.804377
$627$	1428.81	+	1038.09i	0.000145147	+	0.000105455i
$628$	1.50621e6	+	4.63565e6i	0.152401	+	0.469042i
$629$	2.93503e6	+	9.03311e6i	0.295792	+	0.910354i
$630$	−3.18525e6	+	850089.i	−0.319736	+	0.0853322i
$631$	3.93053e6	−	1.20969e7i	0.392987	−	1.20949i	−0.537532	−	0.843243i	$-0.680643\pi$
$631$	3.93053e6	−	1.20969e7i	0.392987	−	1.20949i	0.930519	−	0.366245i	$-0.119357\pi$
$632$	−501832.			−0.0499765
$633$	294022.	−	904908.i	0.0291656	−	0.0897625i
$634$	−4.20064e6	+	3.05195e6i	−0.415043	+	0.301546i
$635$	−1.50146e7	−	5.78070e6i	−1.47767	−	0.568914i
$636$	566796.	+	411802.i	0.0555628	+	0.0403687i
$637$	7.77066e6	−	5.64571e6i	0.758769	−	0.551278i
$638$	−2578.30	+	1873.25i	−0.000250774	+	0.000182198i
$639$	406058.	+	295018.i	0.0393401	+	0.0285823i
$640$	−498067.	−	768629.i	−0.0480660	−	0.0741766i
$641$	1.18187e7	−	8.58679e6i	1.13612	−	0.825441i	0.149548	−	0.988754i	$-0.452218\pi$
$641$	1.18187e7	−	8.58679e6i	1.13612	−	0.825441i	0.986574	+	0.163314i	$0.0522182\pi$
$642$	1.82349e6	−	5.61214e6i	0.174609	−	0.537391i
$643$	−1.91484e7			−1.82644			−0.913221	−	0.407466i	$-0.866413\pi$
$643$	−1.91484e7			−1.82644			−0.913221	+	0.407466i	$0.866413\pi$
$644$	650168.	−	2.00101e6i	0.0617747	−	0.190123i
$645$	−30800.9	−	47532.7i	−0.00291517	−	0.00449877i
$646$	−1.21395e6	−	3.73616e6i	−0.114451	−	0.352244i
$647$	5.29568e6	+	1.62984e7i	0.497348	+	1.53068i	0.813265	+	0.581894i	$0.197688\pi$
$647$	5.29568e6	+	1.62984e7i	0.497348	+	1.53068i	−0.315916	+	0.948787i	$0.602312\pi$
$648$	339709.	+	246813.i	0.0317812	+	0.0230904i
$649$	−1763.93			−0.000164388
$650$	6.37713e6	−	3.66493e6i	0.592027	−	0.340238i
$651$	−1.18243e7			−1.09351
$652$	6.18387e6	+	4.49284e6i	0.569693	+	0.413906i
$653$	4.19433e6	+	1.29088e7i	0.384929	+	1.18469i	0.936532	+	0.350582i	$0.114016\pi$
$653$	4.19433e6	+	1.29088e7i	0.384929	+	1.18469i	−0.551604	+	0.834106i	$0.685984\pi$
$654$	2.07817e6	+	6.39595e6i	0.189993	+	0.584737i
$655$	−367544.	+	6.88212e6i	−0.0334739	+	0.626785i
$656$	807034.	−	2.48380e6i	0.0732204	−	0.225349i
$657$	−1.62919e6			−0.147251
$658$	1.30387e6	−	4.01289e6i	0.117400	−	0.361321i
$659$	1.23177e7	−	8.94933e6i	1.10488	−	0.802744i	0.123032	−	0.992403i	$-0.460738\pi$
$659$	1.23177e7	−	8.94933e6i	1.10488	−	0.802744i	0.981850	+	0.189659i	$0.0607382\pi$
$660$	−1080.33	+	288.323i	−9.65379e−5	+	2.57643e-5i
$661$	5.36831e6	+	3.90031e6i	0.477897	+	0.347212i	0.800511	−	0.599318i	$-0.204562\pi$
$661$	5.36831e6	+	3.90031e6i	0.477897	+	0.347212i	−0.322614	+	0.946531i	$0.604562\pi$
$662$	−7.64687e6	+	5.55577e6i	−0.678170	+	0.492719i
$663$	2.97838e6	−	2.16392e6i	0.263146	−	0.191187i
$664$	−755115.	−	548623.i	−0.0664650	−	0.0482896i
$665$	766607.	−	1.43544e7i	0.0672231	−	1.25873i
$666$	3.58129e6	−	2.60196e6i	0.312863	−	0.227308i
$667$	1.28055e6	−	3.94113e6i	0.111451	−	0.343010i
$668$	−8.54127e6			−0.740596
$669$	−3.79533e6	+	1.16808e7i	−0.327857	+	1.00904i
$670$	7.74577e6	−	9.54579e6i	0.666619	−	0.821533i
$671$	−392.186	−	1207.03i	−3.36268e−5	−	0.000103493i
$672$	−518369.	−	1.59538e6i	−0.0442808	−	0.136282i
$673$	1.31914e7	+	9.58411e6i	1.12267	+	0.815669i	0.984612	−	0.174755i	$-0.0559133\pi$
$673$	1.31914e7	+	9.58411e6i	1.12267	+	0.815669i	0.138060	+	0.990424i	$0.455913\pi$
$674$	6.05190e6			0.513147
$675$	−2.26517e6	−	242638.i	−0.191355	−	0.0204974i
$676$	−400903.			−0.0337422
$677$	1.53535e7	+	1.11550e7i	1.28747	+	0.935400i	0.999751	−	0.0223159i	$-0.00710396\pi$
$677$	1.53535e7	+	1.11550e7i	1.28747	+	0.935400i	0.287716	+	0.957716i	$0.407104\pi$
$678$	1.47237e6	+	4.53148e6i	0.123010	+	0.378587i
$679$	7.65530e6	+	2.35606e7i	0.637218	+	1.96115i
$680$	2.32105e6	+	893619.i	0.192492	+	0.0741106i
$681$	−2.63168e6	+	8.09948e6i	−0.217453	+	0.669251i
$682$	−4010.41			−0.000330163
$683$	−4.90948e6	+	1.51098e7i	−0.402702	+	1.23939i	0.520097	+	0.854107i	$0.325896\pi$
$683$	−4.90948e6	+	1.51098e7i	−0.402702	+	1.23939i	−0.922799	+	0.385282i	$0.874104\pi$
$684$	−1.48125e6	+	1.07619e6i	−0.121056	+	0.0879525i
$685$	−1.41686e7	+	1.74612e7i	−1.15372	+	1.42183i
$686$	−284781.	−	206905.i	−0.0231047	−	0.0167866i
$687$	−8.23209e6	+	5.98096e6i	−0.665454	+	0.483481i
$688$	23315.8	−	16939.9i	0.00187793	−	0.00136440i
$689$	−2.31607e6	−	1.68272e6i	−0.185867	−	0.135040i
$690$	916097.	−	1.12899e6i	0.0732519	−	0.0902747i
$691$	6.15331e6	−	4.47064e6i	0.490245	−	0.356184i	−0.315033	−	0.949081i	$-0.602016\pi$
$691$	6.15331e6	−	4.47064e6i	0.490245	−	0.356184i	0.805279	+	0.592897i	$0.202016\pi$
$692$	2.04365e6	−	6.28971e6i	0.162234	−	0.499305i
$693$	−2047.91			−0.000161986
$694$	3.94230e6	−	1.21331e7i	0.310707	−	0.956257i
$695$	−6.93790e6	−	2.67113e6i	−0.544836	−	0.209765i
$696$	−1.02096e6	−	3.14220e6i	−0.0798890	−	0.245873i
$697$	2.19152e6	+	6.74481e6i	0.170869	+	0.525882i
$698$	6.35447e6	+	4.61680e6i	0.493675	+	0.358676i
$699$	9.00456e6			0.697059
$700$	6.75115e6	+	6.10314e6i	0.520754	+	0.470769i
$701$	2.49312e6			0.191623			0.0958117	−	0.995399i	$-0.469455\pi$
$701$	2.49312e6			0.191623			0.0958117	+	0.995399i	$0.469455\pi$
$702$	−1.38813e6	−	1.00854e6i	−0.106314	−	0.0772414i
$703$	5.96463e6	+	1.83573e7i	0.455193	+	1.40094i
$704$	−175.814	−	541.100i	−1.33697e−5	−	4.11477e-5i
$705$	1.83717e6	−	2.26411e6i	0.139212	−	0.171563i
$706$	−5.51308e6	+	1.69675e7i	−0.416277	+	1.28117i
$707$	3.34407e6			0.251610
$708$	565088.	−	1.73916e6i	0.0423675	−	0.130394i
$709$	1.10422e7	−	8.02264e6i	0.824975	−	0.599379i	−0.0931585	−	0.995651i	$-0.529696\pi$
$709$	1.10422e7	−	8.02264e6i	0.824975	−	0.599379i	0.918133	+	0.396272i	$0.129696\pi$
$710$	73892.3	−	1.38360e6i	0.00550114	−	0.103007i
$711$	−513832.	−	373321.i	−0.0381195	−	0.0276954i
$712$	3.37341e6	−	2.45092e6i	0.249384	−	0.181188i
$713$	4.21876e6	−	3.06511e6i	0.310786	−	0.225799i
$714$	3.68526e6	+	2.67750e6i	0.270535	+	0.196555i
$715$	4414.50	−	1178.16i	0.000322936	−	8.61862e-5i
$716$	−40304.8	+	29283.2i	−0.00293815	+	0.00213469i
$717$	2.28796e6	−	7.04160e6i	0.166207	−	0.511533i
$718$	−1.25424e7			−0.907966
$719$	6.92335e6	−	2.13079e7i	0.499452	−	1.53716i	−0.310450	−	0.950590i	$-0.600480\pi$
$719$	6.92335e6	−	2.13079e7i	0.499452	−	1.53716i	0.809902	−	0.586566i	$-0.199520\pi$
$720$	61818.6	−	1.15753e6i	0.00444414	−	0.0832147i
$721$	−8.57704e6	−	2.63974e7i	−0.614468	−	1.89114i
$722$	593612.	+	1.82695e6i	0.0423799	+	0.130432i
$723$	−2.97057e6	−	2.15824e6i	−0.211346	−	0.153552i
$724$	8.09323e6			0.573820
$725$	1.32969e7	+	1.20206e7i	0.939516	+	0.849336i
$726$	5.79784e6			0.408248
$727$	−1.57087e7	−	1.14130e7i	−1.10231	−	0.800874i	−0.120873	−	0.992668i	$-0.538569\pi$
$727$	−1.57087e7	−	1.14130e7i	−1.10231	−	0.800874i	−0.981435	+	0.191794i	$0.938569\pi$
$728$	2.11818e6	+	6.51909e6i	0.148127	+	0.455888i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	2.44577e6	+	3.77437e6i	0.169867	+	0.262142i
$731$	−24184.1	+	74431.0i	−0.00167393	+	0.00515182i
$732$	1.31571e6			0.0907577
$733$	−4.60567e6	+	1.41748e7i	−0.316616	+	0.974443i	0.658468	+	0.752608i	$0.271205\pi$
$733$	−4.60567e6	+	1.41748e7i	−0.316616	+	0.974443i	−0.975084	+	0.221835i	$0.928795\pi$
$734$	−1.37637e7	+	9.99989e6i	−0.942962	+	0.685102i
$735$	4.46605e6	+	6.89212e6i	0.304934	+	0.470581i
$736$	598503.	+	434838.i	0.0407260	+	0.0295892i
$737$	6177.93	−	4488.53i	0.000418962	−	0.000304394i
$738$	2.67407e6	−	1.94282e6i	0.180730	−	0.131308i
$739$	1.24326e7	+	9.03284e6i	0.837437	+	0.608434i	0.921654	−	0.388014i	$-0.126839\pi$
$739$	1.24326e7	+	9.03284e6i	0.837437	+	0.608434i	−0.0842163	+	0.996447i	$0.526839\pi$
$740$	−1.14043e7	−	4.39071e6i	−0.765575	−	0.294751i
$741$	6.05273e6	−	4.39757e6i	0.404954	−	0.294216i
$742$	1.09462e6	−	3.36889e6i	0.0729884	−	0.224635i
$743$	1.34171e7			0.891636			0.445818	−	0.895124i	$-0.352913\pi$
$743$	1.34171e7			0.891636			0.445818	+	0.895124i	$0.352913\pi$
$744$	1.28476e6	−	3.95409e6i	0.0850924	−	0.261887i
$745$	−1.83032e7	+	4.88482e6i	−1.20819	+	0.322446i
$746$	2.69504e6	+	8.29447e6i	0.177304	+	0.545684i
$747$	−365042.	−	1.12348e6i	−0.0239354	−	0.0736657i
$748$	1249.92	+	908.121i	8.16825e−5	+	5.93458e-5i
$749$	−2.98355e7			−1.94325
$750$	2.83838e6	+	5.61199e6i	0.184254	+	0.364304i
$751$	−2.34649e7			−1.51816			−0.759082	−	0.650994i	$-0.774352\pi$
$751$	−2.34649e7			−1.51816			−0.759082	+	0.650994i	$0.774352\pi$
$752$	1.20026e6	+	872039.i	0.0773981	+	0.0562330i
$753$	−3.34916e6	−	1.03077e7i	−0.215253	−	0.662479i
$754$	4.17190e6	+	1.28398e7i	0.267243	+	0.822489i
$755$	3.90105e6	−	1.04112e6i	0.249066	−	0.0664714i
$756$	656061.	−	2.01915e6i	0.0417484	−	0.128488i
$757$	−2.04056e7			−1.29423			−0.647113	−	0.762394i	$-0.724024\pi$
$757$	−2.04056e7			−1.29423			−0.647113	+	0.762394i	$0.724024\pi$
$758$	1.01109e6	−	3.11183e6i	0.0639173	−	0.196717i
$759$	730.668	−	530.862i	4.60379e−5	−	3.34485e-5i
$760$	4.71689e6	+	1.81603e6i	0.296225	+	0.114048i
$761$	5.50453e6	+	3.99927e6i	0.344555	+	0.250334i	0.746581	−	0.665294i	$-0.231694\pi$
$761$	5.50453e6	+	3.99927e6i	0.344555	+	0.250334i	−0.402026	+	0.915628i	$0.631694\pi$
$762$	8.38228e6	−	6.09009e6i	0.522968	−	0.379958i
$763$	2.75086e7	−	1.99861e7i	1.71063	−	1.24285i
$764$	−1.05851e6	−	769050.i	−0.0656085	−	0.0476673i
$765$	1.71178e6	+	2.64165e6i	0.105753	+	0.163201i
$766$	104862.	−	76187.0i	0.00645725	−	0.00469147i
$767$	−2.30909e6	+	7.10664e6i	−0.141727	+	0.436190i
$768$	589824.			0.0360844
$769$	3.64307e6	−	1.12122e7i	0.222153	−	0.683716i	−0.776415	−	0.630222i	$-0.782964\pi$
$769$	3.64307e6	−	1.12122e7i	0.222153	−	0.683716i	0.998568	−	0.0534946i	$-0.0170360\pi$
$770$	3074.35	+	4744.41i	0.000186864	+	0.000288373i
$771$	1.42480e6	+	4.38508e6i	0.0863213	+	0.265670i
$772$	4.80659e6	+	1.47932e7i	0.290264	+	0.893342i
$773$	−1.16782e7	−	8.48467e6i	−0.702952	−	0.510724i	0.177941	−	0.984041i	$-0.443056\pi$
$773$	−1.16782e7	−	8.48467e6i	−0.702952	−	0.510724i	−0.880892	+	0.473317i	$0.843056\pi$
$774$	36475.3			0.00218850
$775$	4.64580e6	+	2.20727e7i	0.277847	+	1.32008i
$776$	−8.71055e6			−0.519268
$777$	−1.81072e7	−	1.31556e7i	−1.07597	−	0.781735i
$778$	−92688.0	−	285264.i	−0.00549003	−	0.0168966i
$779$	4.45365e6	+	1.37069e7i	0.262950	+	0.809276i
$780$	−252606.	+	4.72994e6i	−0.0148664	+	0.278368i
$781$	265.974	−	818.582i	1.56031e−5	−	4.80214e-5i
$782$	−2.00892e6			−0.117475
$783$	1.29216e6	−	3.97685e6i	0.0753201	−	0.231811i
$784$	−3.38074e6	+	2.45625e6i	−0.196436	+	0.142719i
$785$	1.64539e7	−	4.39126e6i	0.953003	−	0.254340i
$786$	−3.59067e6	−	2.60878e6i	−0.207310	−	0.150619i
$787$	1.42615e7	−	1.03616e7i	0.820784	−	0.596335i	−0.0961528	−	0.995367i	$-0.530654\pi$
$787$	1.42615e7	−	1.03616e7i	0.820784	−	0.596335i	0.916937	+	0.399032i	$0.130654\pi$
$788$	−1.24275e7	+	9.02914e6i	−0.712968	+	0.518001i
$789$	−4.21136e6	−	3.05973e6i	−0.240841	−	0.174981i
$790$	−93504.5	+	1.75083e6i	−0.00533046	+	0.0998107i
$791$	1.94896e7	−	1.41600e7i	1.10755	−	0.804679i
$792$	222.515	−	684.829i	1.26051e−5	−	3.87944e-5i
$793$	−5.37632e6			−0.303600
$794$	−3.05577e6	+	9.40470e6i	−0.172016	+	0.529412i
$795$	1.54234e6	−	1.90076e6i	0.0865489	−	0.106662i
$796$	−2.25958e6	−	6.95428e6i	−0.126400	−	0.389018i
$797$	5.32544e6	+	1.63900e7i	0.296968	+	0.913974i	0.982553	+	0.185982i	$0.0595465\pi$
$797$	5.32544e6	+	1.63900e7i	0.296968	+	0.913974i	−0.685585	+	0.727993i	$0.740454\pi$
$798$	7.48926e6	+	5.44127e6i	0.416324	+	0.302477i
$799$	−4.02876e6			−0.223257
$800$	−2.77446e6	+	1.59448e6i	−0.153269	+	0.0880835i
$801$	5.27736e6			0.290626
$802$	1.72803e7	+	1.25548e7i	0.948668	+	0.689248i
$803$	863.338	+	2657.08i	4.72489e−5	+	0.000145417i
$804$	2.44635e6	+	7.52911e6i	0.133469	+	0.410774i
$805$	−6.86015e6	−	2.64120e6i	−0.373116	−	0.143652i
$806$	−5.24985e6	+	1.61574e7i	−0.284649	+	0.876059i
$807$	1.43794e7			0.777243
$808$	−363349.	+	1.11827e6i	−0.0195792	+	0.0602587i
$809$	−1.47050e7	+	1.06838e7i	−0.789940	+	0.573925i	−0.907946	−	0.419088i	$-0.862350\pi$
$809$	−1.47050e7	+	1.06838e7i	−0.789940	+	0.573925i	0.118006	+	0.993013i	$0.462350\pi$
$810$	924400.	−	1.13922e6i	0.0495048	−	0.0610091i
$811$	6.67965e6	+	4.85305e6i	0.356617	+	0.259097i	0.751640	−	0.659574i	$-0.229263\pi$
$811$	6.67965e6	+	4.85305e6i	0.356617	+	0.259097i	−0.395023	+	0.918671i	$0.629263\pi$
$812$	−1.35144e7	+	9.81880e6i	−0.719295	+	0.522599i
$813$	1.08095e7	−	7.85358e6i	0.573562	−	0.416717i
$814$	−6141.37	−	4461.97i	−0.000324866	−	0.000236029i
$815$	1.68272e7	−	2.07377e7i	0.887398	−	1.09362i
$816$	−1.29579e6	+	941446.i	−0.0681254	+	0.0494960i
$817$	−49147.4	+	151260.i	−0.00257600	+	0.00792810i
$818$	−2.08786e6			−0.109098
$819$	−2.68082e6	+	8.25072e6i	−0.139656	+	0.429816i
$820$	−8.51530e6	−	3.27844e6i	−0.442248	−	0.170268i
$821$	6.66182e6	+	2.05030e7i	0.344933	+	1.06160i	0.961619	+	0.274387i	$0.0884748\pi$
$821$	6.66182e6	+	2.05030e7i	0.344933	+	1.06160i	−0.616686	+	0.787209i	$0.711525\pi$
$822$	−4.47488e6	−	1.37723e7i	−0.230994	−	0.710928i
$823$	−1.29969e7	−	9.44282e6i	−0.668869	−	0.485962i	0.200778	−	0.979637i	$-0.435653\pi$
$823$	−1.29969e7	−	9.44282e6i	−0.668869	−	0.485962i	−0.869646	+	0.493675i	$0.835653\pi$
$824$	9.75935e6			0.500729
$825$	804.630	+	3822.88i	4.11587e−5	+	0.000195549i
$826$	−9.24582e6			−0.471515
$827$	4.98541e6	+	3.62211e6i	0.253476	+	0.184161i	0.707266	−	0.706948i	$-0.249928\pi$
$827$	4.98541e6	+	3.62211e6i	0.253476	+	0.184161i	−0.453790	+	0.891109i	$0.649928\pi$
$828$	289332.	+	890472.i	0.0146663	+	0.0451382i
$829$	−5.36573e6	−	1.65140e7i	−0.271170	−	0.834576i	−0.990207	−	0.139605i	$-0.955417\pi$
$829$	−5.36573e6	−	1.65140e7i	−0.271170	−	0.834576i	0.719037	−	0.694972i	$-0.244583\pi$
$830$	−2.05478e6	+	2.53229e6i	−0.103531	+	0.127590i
$831$	4.39968e6	−	1.35408e7i	0.221014	−	0.680210i
$832$	−2.41016e6			−0.120709
$833$	3.50663e6	−	1.07923e7i	0.175097	−	0.538892i
$834$	3.87327e6	−	2.81409e6i	0.192825	−	0.140095i
$835$	−1.59146e6	+	2.97995e7i	−0.0789915	+	1.47908i
$836$	2540.12	+	1845.50i	0.000125701	+	9.13269e-5i
$837$	4.25700e6	−	3.09289e6i	0.210034	−	0.152599i
$838$	1.52958e7	−	1.11131e7i	0.752425	−	0.546669i
$839$	−1.29380e7	−	9.40004e6i	−0.634547	−	0.461026i	0.223425	−	0.974721i	$-0.428276\pi$
$839$	−1.29380e7	−	9.40004e6i	−0.634547	−	0.461026i	−0.857973	+	0.513696i	$0.828276\pi$
$840$	−5.66267e6	+	1.51127e6i	−0.276900	+	0.0738998i
$841$	−1.00237e7	+	7.28266e6i	−0.488696	+	0.355058i
$842$	3.40283e6	−	1.04728e7i	0.165409	−	0.509077i
$843$	1.91242e7			0.926859
$844$	522707.	−	1.60873e6i	0.0252582	−	0.0777366i
$845$	−74698.8	+	1.39871e6i	−0.00359892	+	0.0673883i
$846$	580236.	+	1.78578e6i	0.0278727	+	0.0857833i
$847$	−9.05857e6	−	2.78794e7i	−0.433862	−	1.33529i
$848$	1.00764e6	+	732092.i	0.0481188	+	0.0349604i
$849$	147039.			0.00700105
$850$	3.55021e6	−	7.93137e6i	0.168541	−	0.376531i
$851$	9.87065e6			0.467220
$852$	721880.	+	524477.i	0.0340695	+	0.0247530i
$853$	2.59597e6	+	7.98958e6i	0.122159	+	0.375968i	0.993373	−	0.114936i	$-0.0366664\pi$
$853$	2.59597e6	+	7.98958e6i	0.122159	+	0.375968i	−0.871213	+	0.490905i	$0.836666\pi$
$854$	−2.05568e6	−	6.32673e6i	−0.0964519	−	0.296848i
$855$	3.47870e6	+	5.36842e6i	0.162743	+	0.251149i
$856$	3.24177e6	−	9.97713e6i	0.151216	−	0.465395i
$857$	−3.13298e7			−1.45715			−0.728576	−	0.684965i	$-0.759818\pi$
$857$	−3.13298e7			−1.45715			−0.728576	+	0.684965i	$0.759818\pi$
$858$	−909.248	+	2798.38i	−4.21662e−5	+	0.000129774i
$859$	−1.81420e6	+	1.31810e6i	−0.0838887	+	0.0609487i	−0.628939	−	0.777455i	$-0.716511\pi$
$859$	−1.81420e6	+	1.31810e6i	−0.0838887	+	0.0609487i	0.545050	+	0.838403i	$0.316511\pi$
$860$	−54757.2	−	84502.6i	−0.00252461	−	0.00389605i
$861$	−1.35202e7	−	9.82301e6i	−0.621550	−	0.451582i
$862$	−1.01857e7	+	7.40031e6i	−0.466897	+	0.339220i
$863$	2.95285e7	−	2.14537e7i	1.34963	−	0.980564i	0.350601	−	0.936525i	$-0.385977\pi$
$863$	2.95285e7	−	2.14537e7i	1.34963	−	0.980564i	0.999030	−	0.0440390i	$-0.0140226\pi$
$864$	603928.	+	438779.i	0.0275233	+	0.0199969i
$865$	−2.15633e7	−	8.30200e6i	−0.979884	−	0.377262i
$866$	1.21953e7	−	8.86041e6i	0.552584	−	0.401476i
$867$	−2.60480e6	+	8.01674e6i	−0.117686	+	0.362201i
$868$	−2.10209e7			−0.947006
$869$	−336.567	+	1035.85i	−1.51190e−5	+	4.65314e-5i
$870$	−1.11530e7	+	2.97655e6i	−0.499568	+	0.133326i
$871$	−9.99639e6	−	3.07657e7i	−0.446476	−	1.37411i
$872$	3.69452e6	+	1.13706e7i	0.164538	+	0.506397i
$873$	−8.91884e6	−	6.47992e6i	−0.396071	−	0.287762i
$874$	−4.08257e6			−0.180782
$875$	2.25511e7	−	2.24168e7i	0.995742	−	0.989814i
$876$	−2.89634e6			−0.127523
$877$	2.31409e6	+	1.68129e6i	0.101597	+	0.0738147i	0.637424	−	0.770513i	$-0.280000\pi$
$877$	2.31409e6	+	1.68129e6i	0.101597	+	0.0738147i	−0.535827	+	0.844328i	$0.680000\pi$
$878$	1.76354e6	+	5.42760e6i	0.0772054	+	0.237614i
$879$	−1.51661e6	−	4.66764e6i	−0.0662066	−	0.203763i
$880$	−1920.59	+	512.574i	−8.36043e−5	+	2.23126e-5i
$881$	5.41623e6	−	1.66695e7i	0.235103	−	0.723572i	−0.762005	−	0.647571i	$-0.775785\pi$
$881$	5.41623e6	−	1.66695e7i	0.235103	−	0.723572i	0.997108	−	0.0760007i	$-0.0242151\pi$
$882$	−5.28882e6			−0.228922
$883$	−5.91157e6	+	1.81939e7i	−0.255153	+	0.785281i	0.738646	+	0.674093i	$0.235465\pi$
$883$	−5.91157e6	+	1.81939e7i	−0.255153	+	0.785281i	−0.993799	+	0.111188i	$0.964535\pi$
$884$	5.29490e6	−	3.84697e6i	0.227891	−	0.165573i
$885$	−5.96245e6	−	2.29558e6i	−0.255898	−	0.0985222i
$886$	−5.32047e6	−	3.86555e6i	−0.227701	−	0.165435i
$887$	9.56137e6	−	6.94674e6i	0.408048	−	0.296464i	−0.364763	−	0.931100i	$-0.618850\pi$
$887$	9.56137e6	−	6.94674e6i	0.408048	−	0.296464i	0.772811	+	0.634636i	$0.218850\pi$
$888$	6.36674e6	−	4.62570e6i	0.270947	−	0.196855i
$889$	−4.23813e7	−	3.07918e7i	−1.79854	−	1.30671i
$890$	−7.92244e6	−	1.22261e7i	−0.335262	−	0.517384i
$891$	737.291	−	535.673i	3.11132e−5	−	2.26051e-5i
$892$	−6.74725e6	+	2.07659e7i	−0.283932	+	0.873853i
$893$	−8.18733e6			−0.343569
$894$	3.76988e6	−	1.16025e7i	0.157755	−	0.485521i
$895$	94655.7	+	146075.i	0.00394993	+	0.00609563i
$896$	−921545.	−	2.83622e6i	−0.0383483	−	0.118024i
$897$	−1.18228e6	−	3.63868e6i	−0.0490613	−	0.150995i
$898$	−979195.	−	711427.i	−0.0405208	−	0.0294401i
$899$	−4.14022e7			−1.70854
$900$	−4.02696e6	−	431356.i	−0.165719	−	0.0177513i
$901$	−3.38221e6			−0.138800
$902$	−4585.62	−	3331.65i	−0.000187664	−	0.000136346i
$903$	−56989.2	−	175395.i	−0.00232580	−	0.00715809i
$904$	2.61754e6	+	8.05596e6i	0.106530	+	0.327866i
$905$	1.50798e6	−	2.82363e7i	0.0612032	−	1.14601i
$906$	−803493.	+	2.47290e6i	−0.0325208	+	0.100089i
$907$	3.73902e7			1.50918			0.754588	−	0.656199i	$-0.227837\pi$
$907$	3.73902e7			1.50918			0.754588	+	0.656199i	$0.227837\pi$
$908$	−4.67854e6	+	1.43991e7i	−0.188320	+	0.579589i
$909$	−1.20394e6	+	874713.i	−0.0483276	+	0.0351120i
$910$	2.31390e7	−	6.17541e6i	0.926278	−	0.247208i
$911$	−6.41195e6	−	4.65855e6i	−0.255973	−	0.185975i	0.452397	−	0.891817i	$-0.350569\pi$
$911$	−6.41195e6	−	4.65855e6i	−0.255973	−	0.185975i	−0.708370	+	0.705841i	$0.750569\pi$
$912$	−2.63333e6	+	1.91322e6i	−0.104838	+	0.0761691i
$913$	−1638.87	+	1190.71i	−6.50680e−5	+	4.72746e-5i
$914$	−2.24500e7	−	1.63109e7i	−0.888897	−	0.645822i
$915$	245152.	−	4.59037e6i	0.00968016	−	0.181257i
$916$	−1.46348e7	+	1.06328e7i	−0.576300	+	0.418707i
$917$	−6.93445e6	+	2.13420e7i	−0.272326	+	0.838132i
$918$	−2.02713e6			−0.0793917
$919$	−2.36323e6	+	7.27327e6i	−0.0923032	+	0.284080i	−0.986541	−	0.163511i	$-0.947718\pi$
$919$	−2.36323e6	+	7.27327e6i	−0.0923032	+	0.284080i	0.894238	+	0.447591i	$0.147718\pi$
$920$	1.62862e6	−	2.00709e6i	0.0634380	−	0.0781802i
$921$	−4.10924e6	−	1.26469e7i	−0.159629	−	0.491288i
$922$	463568.	+	1.42672e6i	0.0179592	+	0.0552727i
$923$	−2.94978e6	−	2.14314e6i	−0.113969	−	0.0828030i
$924$	−3640.72			−0.000140284
$925$	−1.74436e7	+	3.89701e7i	−0.670319	+	1.49753i
$926$	−7.78148e6			−0.298219
$927$	9.99272e6	+	7.26014e6i	0.381931	+	0.277489i
$928$	−1.81505e6	−	5.58614e6i	−0.0691859	−	0.212932i
$929$	−1.06670e7	−	3.28297e7i	−0.405511	−	1.24804i	−0.920467	−	0.390819i	$-0.872192\pi$
$929$	−1.06670e7	−	3.28297e7i	−0.405511	−	1.24804i	0.514956	−	0.857217i	$-0.327808\pi$
$930$	−1.35560e7	−	5.21914e6i	−0.513953	−	0.197875i
$931$	7.12625e6	−	2.19323e7i	0.269455	−	0.829298i
$932$	1.60081e7			0.603671
$933$	6.23346e6	−	1.91846e7i	0.234436	−	0.721521i
$934$	−1.45609e7	+	1.05791e7i	−0.546160	+	0.396808i
$935$	3401.22	−	4191.62i	0.000127235	−	0.000156803i
$936$	−2.46780e6	−	1.79296e6i	−0.0920703	−	0.0668930i
$937$	−1.04350e6	+	758145.i	−0.0388277	+	0.0282100i	−0.607030	−	0.794679i	$-0.707639\pi$
$937$	−1.04350e6	+	758145.i	−0.0388277	+	0.0282100i	0.568202	+	0.822889i	$0.307639\pi$
$938$	3.23822e7	−	2.35270e7i	1.20171	−	0.873093i
$939$	1.43561e7	+	1.04303e7i	0.531339	+	0.386040i
$940$	3.26608e6	−	4.02508e6i	0.120561	−	0.148578i
$941$	−1.28352e7	+	9.32530e6i	−0.472528	+	0.343312i	−0.798426	−	0.602093i	$-0.794334\pi$
$941$	−1.28352e7	+	9.32530e6i	−0.472528	+	0.343312i	0.325898	+	0.945405i	$0.394334\pi$
$942$	−3.38898e6	+	1.04302e7i	−0.124435	+	0.382971i
$943$	7.37019e6			0.269898
$944$	1.00460e6	−	3.09184e6i	0.0366913	−	0.112924i
$945$	−6.92233e6	−	2.66514e6i	−0.252158	−	0.0970824i
$946$	−19.3289	−	59.4882i	−7.02229e−7	−	2.16124e-6i
$947$	−7.63535e6	−	2.34992e7i	−0.276665	−	0.851487i	−0.988774	−	0.149418i	$-0.952260\pi$
$947$	−7.63535e6	−	2.34992e7i	−0.276665	−	0.851487i	0.712109	−	0.702069i	$-0.247740\pi$
$948$	−913479.	−	663681.i	−0.0330124	−	0.0239849i
$949$	1.18352e7			0.426588
$950$	7.21480e6	−	1.61183e7i	0.259367	−	0.579442i
$951$	−1.16826e7			−0.418880
$952$	6.55158e6	+	4.76000e6i	0.234290	+	0.170222i
$953$	1.08309e7	+	3.33342e7i	0.386308	+	1.18893i	0.935527	+	0.353256i	$0.114925\pi$
$953$	1.08309e7	+	3.33342e7i	0.386308	+	1.18893i	−0.549218	+	0.835679i	$0.685075\pi$
$954$	487118.	+	1.49920e6i	0.0173286	+	0.0533319i
$955$	−2.88035e6	+	3.54971e6i	−0.102197	+	0.125946i
$956$	4.06748e6	−	1.25184e7i	0.143940	−	0.443001i
$957$	−7170.66			−0.000253092
$958$	117822.	−	362618.i	0.00414774	−	0.0127654i
$959$	−5.92336e7	+	4.30357e7i	−2.07980	+	1.51106i
$960$	109900.	−	2.05783e6i	0.00384874	−	0.0720661i
$961$	−1.89882e7	−	1.37957e7i	−0.663246	−	0.481876i
$962$	−2.60160e7	+	1.89017e7i	−0.906365	+	0.658513i
$963$	1.07414e7	−	7.80411e6i	0.373247	−	0.271180i
$964$	−5.28101e6	−	3.83688e6i	−0.183031	−	0.132980i
$965$	5.25072e7	−	1.40133e7i	1.81510	−	0.484419i
$966$	3.82986e6	−	2.78256e6i	0.132051	−	0.0959404i
$967$	178985.	−	550859.i	0.00615531	−	0.0189441i	−0.947932	−	0.318474i	$-0.896830\pi$
$967$	178985.	−	550859.i	0.00615531	−	0.0189441i	0.954087	+	0.299530i	$0.0968297\pi$
$968$	1.03073e7			0.353553
$969$	2.73139e6	−	8.40635e6i	0.0934489	−	0.287606i
$970$	−1.62300e6	+	3.03901e7i	−0.0553848	+	1.03706i
$971$	1.21549e7	+	3.74091e7i	0.413718	+	1.27329i	0.913392	+	0.407081i	$0.133453\pi$
$971$	1.21549e7	+	3.74091e7i	0.413718	+	1.27329i	−0.499674	+	0.866214i	$0.666547\pi$
$972$	291954.	+	898543.i	0.00991172	+	0.0305052i
$973$	−1.95834e7	−	1.42282e7i	−0.663143	−	0.481801i
$974$	2.03723e7			0.688086
$975$	1.64551e7	+	1.76262e6i	0.554358	+	0.0593811i
$976$	2.33905e6			0.0785985
$977$	5.20925e6	+	3.78474e6i	0.174598	+	0.126853i	0.671652	−	0.740867i	$-0.265585\pi$
$977$	5.20925e6	+	3.78474e6i	0.174598	+	0.126853i	−0.497054	+	0.867720i	$0.665585\pi$
$978$	5.31456e6	+	1.63565e7i	0.177673	+	0.546820i
$979$	−2796.56	−	8606.94i	−9.32541e−5	−	0.000287007i
$980$	7.93965e6	+	1.22527e7i	0.264080	+	0.407535i
$981$	−4.67588e6	+	1.43909e7i	−0.155128	+	0.477436i
$982$	−2.82259e7			−0.934048
$983$	1.40448e7	−	4.32255e7i	0.463588	−	1.42678i	−0.397163	−	0.917748i	$-0.630005\pi$
$983$	1.40448e7	−	4.32255e7i	0.463588	−	1.42678i	0.860750	−	0.509028i	$-0.169995\pi$
$984$	4.75390e6	−	3.45391e6i	0.156517	−	0.113716i
$985$	2.91860e7	+	4.50406e7i	0.958484	+	1.47916i
$986$	1.29038e7	+	9.37515e6i	0.422693	+	0.307104i
$987$	7.68054e6	−	5.58024e6i	0.250957	−	0.182331i
$988$	1.07604e7	−	7.81789e6i	0.350701	−	0.254799i
$989$	65799.1	+	47805.9i	0.00213909	+	0.00155414i
$990$	−2347.83	−	903.929i	−7.61340e−5	−	2.93121e-5i
$991$	−2.40511e7	+	1.74741e7i	−0.777948	+	0.565212i	−0.904363	−	0.426765i	$-0.859653\pi$
$991$	−2.40511e7	+	1.74741e7i	−0.777948	+	0.565212i	0.126414	+	0.991978i	$0.459653\pi$
$992$	2.28402e6	−	7.02950e6i	0.0736921	−	0.226801i
$993$	−2.12671e7			−0.684440
$994$	1.39412e6	−	4.29067e6i	0.0447544	−	0.137740i
$995$	−2.46837e7	+	6.58766e6i	−0.790410	+	0.210947i
$996$	−648964.	−	1.99730e6i	−0.0207287	−	0.0637964i
$997$	6.12452e6	+	1.88493e7i	0.195135	+	0.600562i	0.999975	+	0.00707107i	$0.00225081\pi$
$997$	6.12452e6	+	1.88493e7i	0.195135	+	0.600562i	−0.804840	+	0.593491i	$0.797749\pi$
$998$	3.19116e7	+	2.31851e7i	1.01420	+	0.736856i
$999$	9.96011e6			0.315755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.c.91.6	yes	24
25.11	even	5	inner	150.6.g.c.61.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.c.61.6	✓	24	25.11	even	5	inner
150.6.g.c.91.6	yes	24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(54.0113 - 14.4147i) q^{5} +(-11.1246 + 34.2380i) q^{6} +182.018 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(54.0113 - 14.4147i) q^{5} +(-11.1246 + 34.2380i) q^{6} +182.018 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(208.675 + 80.3412i) q^{10} +(0.112375 + 0.0816450i) q^{11} +(-116.498 + 84.6411i) q^{12} +(476.041 - 345.864i) q^{13} +(589.022 + 427.950i) q^{14} +(273.596 + 422.220i) q^{15} +(-207.108 + 150.473i) q^{16} +(214.821 - 661.151i) q^{17} -324.000 q^{18} +(436.563 - 1343.60i) q^{19} +(486.393 + 750.614i) q^{20} +(506.220 + 1557.98i) q^{21} +(0.171693 + 0.528418i) q^{22} +(-584.476 - 424.647i) q^{23} -576.000 q^{24} +(2709.43 - 1557.11i) q^{25} +2353.67 q^{26} +(-589.773 - 428.495i) q^{27} +(899.946 + 2769.75i) q^{28} +(1772.51 + 5455.21i) q^{29} +(-107.324 + 2009.60i) q^{30} +(-2230.49 + 6864.74i) q^{31} -1024.00 q^{32} +(-0.386310 + 1.18894i) q^{33} +(2249.63 - 1634.45i) q^{34} +(9831.02 - 2623.73i) q^{35} +(-1048.49 - 761.770i) q^{36} +(-11053.4 + 8030.74i) q^{37} +(4571.75 - 3321.57i) q^{38} +(4284.37 + 3112.77i) q^{39} +(-190.798 + 3572.62i) q^{40} +(-8253.29 + 5996.37i) q^{41} +(-2024.88 + 6231.94i) q^{42} -112.578 q^{43} +(-0.686773 + 2.11367i) q^{44} +(-2853.09 + 3516.11i) q^{45} +(-893.000 - 2748.37i) q^{46} +(-1790.85 - 5511.68i) q^{47} +(-1863.98 - 1354.26i) q^{48} +16323.5 q^{49} +(12428.9 + 1331.34i) q^{50} +6256.57 q^{51} +(7616.65 + 5533.82i) q^{52} +(-1503.45 - 4627.15i) q^{53} +(-901.094 - 2773.28i) q^{54} +(7.24639 + 2.78990i) q^{55} +(-3599.78 + 11079.0i) q^{56} +12714.7 q^{57} +(-7090.03 + 21820.9i) q^{58} +(-10273.7 + 7464.32i) q^{59} +(-5072.15 + 6250.86i) q^{60} +(-7391.91 - 5370.54i) q^{61} +(-23358.0 + 16970.6i) q^{62} +(-11927.7 + 8665.98i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(20726.0 - 25542.5i) q^{65} +(-4.04549 + 2.93922i) q^{66} +(16988.6 - 52285.5i) q^{67} +11122.8 q^{68} +(2009.25 - 6183.84i) q^{69} +(37982.6 + 14623.5i) q^{70} +(-1914.82 - 5893.20i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(16272.2 + 11822.4i) q^{73} -54650.8 q^{74} +(20863.5 + 18860.9i) q^{75} +22604.0 q^{76} +(20.4542 + 14.8609i) q^{77} +(6545.93 + 20146.3i) q^{78} +(2423.04 + 7457.35i) q^{79} +(-9017.16 + 11112.6i) q^{80} +(2027.46 - 6239.88i) q^{81} -40806.5 q^{82} +(-4506.69 + 13870.2i) q^{83} +(-21204.8 + 15406.2i) q^{84} +(2072.47 - 38806.2i) q^{85} +(-364.310 - 264.687i) q^{86} +(-41764.3 + 30343.6i) q^{87} +(-7.19198 + 5.22528i) q^{88} +(-52709.5 - 38295.7i) q^{89} +(-17499.7 + 4670.36i) q^{90} +(86647.9 - 62953.4i) q^{91} +(3572.00 - 10993.5i) q^{92} -64962.2 q^{93} +(7163.41 - 22046.7i) q^{94} +(4211.71 - 78862.6i) q^{95} +(-2847.90 - 8764.94i) q^{96} +(42057.9 + 129441. i) q^{97} +(52824.0 + 38378.9i) q^{98} -11.2511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Introduction

L-functions

Modular forms

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