LMFDB - Embedded newform 150.6.g.b.31.5

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			31.5
Character	$\chi$	$=$	150.31
Dual form			150.6.g.b.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(38.8459 - 40.1995i) q^{5} +(-29.1246 - 21.1603i) q^{6} -37.1005 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(38.8459 - 40.1995i) q^{5} +(-29.1246 - 21.1603i) q^{6} -37.1005 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(200.944 + 98.0892i) q^{10} +(90.7854 + 279.409i) q^{11} +(44.4984 - 136.952i) q^{12} +(64.7641 - 199.323i) q^{13} +(-45.8587 - 141.139i) q^{14} +(-70.1847 + 498.196i) q^{15} +(79.1084 - 243.470i) q^{16} +(408.377 + 296.704i) q^{17} +324.000 q^{18} +(1937.31 + 1407.54i) q^{19} +(-124.773 + 885.682i) q^{20} +(270.134 - 196.264i) q^{21} +(-950.717 + 690.736i) q^{22} +(814.715 + 2507.44i) q^{23} +576.000 q^{24} +(-106.997 - 3123.17i) q^{25} +838.324 q^{26} +(225.273 + 693.320i) q^{27} +(480.238 - 348.914i) q^{28} +(-4979.15 + 3617.57i) q^{29} +(-1982.00 + 348.805i) q^{30} +(999.322 + 726.050i) q^{31} +1024.00 q^{32} +(-2139.11 - 1554.16i) q^{33} +(-623.945 + 1920.31i) q^{34} +(-1441.20 + 1491.42i) q^{35} +(400.486 + 1232.57i) q^{36} +(-2660.76 + 8188.99i) q^{37} +(-2959.94 + 9109.76i) q^{38} +(582.877 + 1793.91i) q^{39} +(-3523.56 + 620.098i) q^{40} +(-4362.58 + 13426.6i) q^{41} +(1080.54 + 785.056i) q^{42} -2616.23 q^{43} +(-3802.87 - 2762.94i) q^{44} +(-2124.46 - 3998.72i) q^{45} +(-8531.81 + 6198.72i) q^{46} +(108.949 - 79.1559i) q^{47} +(711.975 + 2191.23i) q^{48} -15430.6 q^{49} +(11749.0 - 4267.49i) q^{50} -4543.04 q^{51} +(1036.23 + 3189.17i) q^{52} +(23073.3 - 16763.8i) q^{53} +(-2359.09 + 1713.98i) q^{54} +(14758.7 + 7204.34i) q^{55} +(1920.95 + 1395.65i) q^{56} -21551.8 q^{57} +(-19916.6 - 14470.3i) q^{58} +(-366.948 + 1129.35i) q^{59} +(-3776.82 - 7108.84i) q^{60} +(7001.62 + 21548.8i) q^{61} +(-1526.83 + 4699.09i) q^{62} +(-928.638 + 2858.05i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-5496.88 - 10346.4i) q^{65} +(3268.27 - 10058.7i) q^{66} +(46677.0 + 33912.9i) q^{67} -8076.52 q^{68} +(-19196.6 - 13947.1i) q^{69} +(-7455.12 - 3639.15i) q^{70} +(63798.1 - 46352.1i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(10506.4 + 32335.4i) q^{73} -34441.6 q^{74} +(17300.8 + 22174.2i) q^{75} -38314.3 q^{76} +(-3368.18 - 10366.2i) q^{77} +(-6103.97 + 4434.79i) q^{78} +(-62231.6 + 45213.9i) q^{79} +(-6714.35 - 12637.9i) q^{80} +(-5307.96 - 3856.46i) q^{81} -56470.4 q^{82} +(4114.05 + 2989.03i) q^{83} +(-1650.91 + 5080.99i) q^{84} +(27791.1 - 4890.85i) q^{85} +(-3233.84 - 9952.73i) q^{86} +(17116.8 - 52680.1i) q^{87} +(5810.26 - 17882.1i) q^{88} +(25666.2 + 78992.4i) q^{89} +(12586.1 - 13024.6i) q^{90} +(-2402.78 + 7394.99i) q^{91} +(-34127.2 - 24794.9i) q^{92} -11117.1 q^{93} +(435.795 + 316.623i) q^{94} +(131839. - 23201.8i) q^{95} +(-7455.90 + 5417.03i) q^{96} +(35380.2 - 25705.2i) q^{97} +(-19073.2 - 58701.3i) q^{98} +23796.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	38.8459	−	40.1995i	0.694896	−	0.719110i
$5$	38.8459	−	40.1995i	0.694896	−	0.719110i
$6$	−29.1246	−	21.1603i	−0.330280	−	0.239962i
$7$	−37.1005			−0.286177			−0.143088	−	0.989710i	$-0.545703\pi$
$7$	−37.1005			−0.286177			−0.143088	+	0.989710i	$0.545703\pi$
$8$	−51.7771	−	37.6183i	−0.286031	−	0.207813i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	200.944	+	98.0892i	0.635441	+	0.310185i
$11$	90.7854	+	279.409i	0.226222	+	0.696238i	0.998165	+	0.0605476i	$0.0192847\pi$
$11$	90.7854	+	279.409i	0.226222	+	0.696238i	−0.771944	+	0.635691i	$0.780715\pi$
$12$	44.4984	−	136.952i	0.0892055	−	0.274546i
$13$	64.7641	−	199.323i	0.106286	−	0.327115i	−0.883744	−	0.467970i	$-0.844985\pi$
$13$	64.7641	−	199.323i	0.106286	−	0.327115i	0.990030	+	0.140856i	$0.0449854\pi$
$14$	−45.8587	−	141.139i	−0.0625319	−	0.192453i
$15$	−70.1847	+	498.196i	−0.0805405	+	0.571705i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	408.377	+	296.704i	0.342720	+	0.249001i	0.745809	−	0.666160i	$-0.232063\pi$
$17$	408.377	+	296.704i	0.342720	+	0.249001i	−0.403089	+	0.915161i	$0.632063\pi$
$18$	324.000			0.235702
$19$	1937.31	+	1407.54i	1.23116	+	0.894490i	0.996977	−	0.0777025i	$-0.0247584\pi$
$19$	1937.31	+	1407.54i	1.23116	+	0.894490i	0.234183	+	0.972192i	$0.424758\pi$
$20$	−124.773	+	885.682i	−0.0697502	+	0.495111i
$21$	270.134	−	196.264i	0.133669	−	0.0971163i
$22$	−950.717	+	690.736i	−0.418788	+	0.304267i
$23$	814.715	+	2507.44i	0.321134	+	0.988349i	0.973156	+	0.230148i	$0.0739211\pi$
$23$	814.715	+	2507.44i	0.321134	+	0.988349i	−0.652022	+	0.758200i	$0.726079\pi$
$24$	576.000			0.204124
$25$	−106.997	−	3123.17i	−0.0342390	−	0.999414i
$26$	838.324			0.243208
$27$	225.273	+	693.320i	0.0594703	+	0.183031i
$28$	480.238	−	348.914i	0.115761	−	0.0841052i
$29$	−4979.15	+	3617.57i	−1.09941	+	0.798770i	−0.980964	−	0.194190i	$-0.937792\pi$
$29$	−4979.15	+	3617.57i	−1.09941	+	0.798770i	−0.118448	+	0.992960i	$0.537792\pi$
$30$	−1982.00	+	348.805i	−0.402069	+	0.0707587i
$31$	999.322	+	726.050i	0.186767	+	0.135695i	0.677240	−	0.735762i	$-0.263176\pi$
$31$	999.322	+	726.050i	0.186767	+	0.135695i	−0.490473	+	0.871457i	$0.663176\pi$
$32$	1024.00			0.176777
$33$	−2139.11	−	1554.16i	−0.341939	−	0.248433i
$34$	−623.945	+	1920.31i	−0.0925655	+	0.284887i
$35$	−1441.20	+	1491.42i	−0.198863	+	0.205793i
$36$	400.486	+	1232.57i	0.0515028	+	0.158509i
$37$	−2660.76	+	8188.99i	−0.319523	+	0.983390i	0.654330	+	0.756209i	$0.272951\pi$
$37$	−2660.76	+	8188.99i	−0.319523	+	0.983390i	−0.973853	+	0.227181i	$0.927049\pi$
$38$	−2959.94	+	9109.76i	−0.332525	+	1.02341i
$39$	582.877	+	1793.91i	0.0613642	+	0.188860i
$40$	−3523.56	+	620.098i	−0.348202	+	0.0612789i
$41$	−4362.58	+	13426.6i	−0.405306	+	1.24740i	0.515333	+	0.856990i	$0.327668\pi$
$41$	−4362.58	+	13426.6i	−0.405306	+	1.24740i	−0.920639	+	0.390415i	$0.872332\pi$
$42$	1080.54	+	785.056i	0.0945183	+	0.0686716i
$43$	−2616.23			−0.215777			−0.107888	−	0.994163i	$-0.534409\pi$
$43$	−2616.23			−0.215777			−0.107888	+	0.994163i	$0.534409\pi$
$44$	−3802.87	−	2762.94i	−0.296128	−	0.215150i
$45$	−2124.46	−	3998.72i	−0.156393	−	0.294368i
$46$	−8531.81	+	6198.72i	−0.594493	+	0.431924i
$47$	108.949	−	79.1559i	0.00719411	−	0.00522683i	−0.584182	−	0.811622i	$-0.698585\pi$
$47$	108.949	−	79.1559i	0.00719411	−	0.00522683i	0.591376	+	0.806396i	$0.298585\pi$
$48$	711.975	+	2191.23i	0.0446028	+	0.137273i
$49$	−15430.6			−0.918103
$50$	11749.0	−	4267.49i	0.664623	−	0.241406i
$51$	−4543.04			−0.244580
$52$	1036.23	+	3189.17i	0.0531430	+	0.163557i
$53$	23073.3	−	16763.8i	1.12829	−	0.819750i	0.142845	−	0.989745i	$-0.454375\pi$
$53$	23073.3	−	16763.8i	1.12829	−	0.819750i	0.985445	+	0.169995i	$0.0543750\pi$
$54$	−2359.09	+	1713.98i	−0.110093	+	0.0799874i
$55$	14758.7	+	7204.34i	0.657873	+	0.321135i
$56$	1920.95	+	1395.65i	0.0818553	+	0.0594713i
$57$	−21551.8			−0.878610
$58$	−19916.6	−	14470.3i	−0.777402	−	0.564815i
$59$	−366.948	+	1129.35i	−0.0137238	+	0.0422375i	−0.957684	−	0.287822i	$-0.907069\pi$
$59$	−366.948	+	1129.35i	−0.0137238	+	0.0422375i	0.943960	+	0.330060i	$0.107069\pi$
$60$	−3776.82	−	7108.84i	−0.135441	−	0.254930i
$61$	7001.62	+	21548.8i	0.240921	+	0.741477i	0.996281	+	0.0861673i	$0.0274620\pi$
$61$	7001.62	+	21548.8i	0.240921	+	0.741477i	−0.755360	+	0.655310i	$0.772538\pi$
$62$	−1526.83	+	4699.09i	−0.0504442	+	0.155251i
$63$	−928.638	+	2858.05i	−0.0294778	+	0.0907234i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−5496.88	−	10346.4i	−0.161374	−	0.303742i
$66$	3268.27	−	10058.7i	0.0923546	−	0.284238i
$67$	46677.0	+	33912.9i	1.27033	+	0.922948i	0.999216	−	0.0395991i	$-0.0126081\pi$
$67$	46677.0	+	33912.9i	1.27033	+	0.922948i	0.271114	+	0.962547i	$0.412608\pi$
$68$	−8076.52			−0.211813
$69$	−19196.6	−	13947.1i	−0.485401	−	0.352665i
$70$	−7455.12	−	3639.15i	−0.181848	−	0.0887677i
$71$	63798.1	−	46352.1i	1.50197	−	1.09125i	0.532385	−	0.846502i	$-0.321296\pi$
$71$	63798.1	−	46352.1i	1.50197	−	1.09125i	0.969588	−	0.244745i	$-0.0787042\pi$
$72$	−4193.94	+	3047.08i	−0.0953436	+	0.0692712i
$73$	10506.4	+	32335.4i	0.230753	+	0.710185i	0.997656	+	0.0684222i	$0.0217965\pi$
$73$	10506.4	+	32335.4i	0.230753	+	0.710185i	−0.766903	+	0.641762i	$0.778203\pi$
$74$	−34441.6			−0.731147
$75$	17300.8	+	22174.2i	0.355152	+	0.455193i
$76$	−38314.3			−0.760899
$77$	−3368.18	−	10366.2i	−0.0647393	−	0.199247i
$78$	−6103.97	+	4434.79i	−0.113599	+	0.0825347i
$79$	−62231.6	+	45213.9i	−1.12187	+	0.815087i	−0.984492	−	0.175431i	$-0.943868\pi$
$79$	−62231.6	+	45213.9i	−1.12187	+	0.815087i	−0.137380	+	0.990518i	$0.543868\pi$
$80$	−6714.35	−	12637.9i	−0.117295	−	0.220776i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	−56470.4			−0.927441
$83$	4114.05	+	2989.03i	0.0655503	+	0.0476251i	0.620078	−	0.784540i	$-0.287101\pi$
$83$	4114.05	+	2989.03i	0.0655503	+	0.0476251i	−0.554528	+	0.832165i	$0.687101\pi$
$84$	−1650.91	+	5080.99i	−0.0255285	+	0.0785687i
$85$	27791.1	−	4890.85i	0.417214	−	0.0734239i
$86$	−3233.84	−	9952.73i	−0.0471490	−	0.145110i
$87$	17116.8	−	52680.1i	0.242451	−	0.746189i
$88$	5810.26	−	17882.1i	0.0799814	−	0.246157i
$89$	25666.2	+	78992.4i	0.343468	+	1.05709i	0.962399	+	0.271641i	$0.0875662\pi$
$89$	25666.2	+	78992.4i	0.343468	+	1.05709i	−0.618931	+	0.785446i	$0.712434\pi$
$90$	12586.1	−	13024.6i	0.163789	−	0.169496i
$91$	−2402.78	+	7394.99i	−0.0304166	+	0.0936125i
$92$	−34127.2	−	24794.9i	−0.420370	−	0.305416i
$93$	−11117.1			−0.133286
$94$	435.795	+	316.623i	0.00508701	+	0.00369593i
$95$	131839.	−	23201.8i	1.49876	−	0.263762i
$96$	−7455.90	+	5417.03i	−0.0825700	+	0.0599906i
$97$	35380.2	−	25705.2i	0.381795	−	0.277390i	−0.380290	−	0.924867i	$-0.624176\pi$
$97$	35380.2	−	25705.2i	0.381795	−	0.277390i	0.762085	+	0.647477i	$0.224176\pi$
$98$	−19073.2	−	58701.3i	−0.200613	−	0.617423i
$99$	23796.8			0.244023
$100$	30757.0	+	39420.9i	0.307570	+	0.394209i
$101$	−6255.29			−0.0610161			−0.0305080	−	0.999535i	$-0.509713\pi$
$101$	−6255.29			−0.0610161			−0.0305080	+	0.999535i	$0.509713\pi$
$102$	−5615.51	−	17282.8i	−0.0534427	−	0.164480i
$103$	59713.0	−	43384.1i	0.554595	−	0.402937i	−0.274882	−	0.961478i	$-0.588639\pi$
$103$	59713.0	−	43384.1i	0.554595	−	0.402937i	0.829477	+	0.558541i	$0.188639\pi$
$104$	−10851.5	+	7884.07i	−0.0983799	+	0.0714772i
$105$	2603.89	−	18483.3i	0.0230488	−	0.163609i
$106$	92293.3	+	67055.0i	0.797821	+	0.579651i
$107$	92773.2			0.783363			0.391681	−	0.920101i	$-0.371894\pi$
$107$	92773.2			0.783363			0.391681	+	0.920101i	$0.371894\pi$
$108$	−9436.37	−	6855.93i	−0.0778477	−	0.0565597i
$109$	−27770.0	+	85467.3i	−0.223877	+	0.689023i	0.774526	+	0.632542i	$0.217988\pi$
$109$	−27770.0	+	85467.3i	−0.223877	+	0.689023i	−0.998404	+	0.0564817i	$0.982012\pi$
$110$	−9164.18	+	65050.6i	−0.0722124	+	0.512589i
$111$	−23946.9	−	73700.9i	−0.184477	−	0.567761i
$112$	−2934.96	+	9032.86i	−0.0221084	+	0.0680425i
$113$	65083.9	−	200308.i	0.479488	−	1.47571i	−0.360320	−	0.932829i	$-0.617333\pi$
$113$	65083.9	−	200308.i	0.479488	−	1.47571i	0.839808	−	0.542883i	$-0.182667\pi$
$114$	−26639.5	−	81987.9i	−0.191983	−	0.590864i
$115$	132446.	+	64652.4i	0.933886	+	0.455869i
$116$	30429.9	−	93653.5i	0.209969	−	0.646218i
$117$	−13733.9	−	9978.28i	−0.0927534	−	0.0673893i
$118$	−4749.87			−0.0314034
$119$	−15151.0	−	11007.8i	−0.0980784	−	0.0712581i
$120$	22375.2	−	23154.9i	0.141845	−	0.146788i
$121$	60465.8	−	43931.0i	0.375445	−	0.272777i
$122$	−73321.9	+	53271.5i	−0.445999	+	0.324037i
$123$	−39263.2	−	120840.i	−0.234004	−	0.720190i
$124$	−19763.7			−0.115429
$125$	−129706.	−	117021.i	−0.742481	−	0.669867i
$126$	−12020.5			−0.0674525
$127$	−26447.7	−	81397.5i	−0.145505	−	0.447818i	0.851571	−	0.524240i	$-0.175651\pi$
$127$	−26447.7	−	81397.5i	−0.145505	−	0.447818i	−0.997076	+	0.0764216i	$0.975651\pi$
$128$	−13254.9	+	9630.27i	−0.0715077	+	0.0519534i
$129$	19049.2	−	13840.0i	0.100786	−	0.0732256i
$130$	32565.4	−	33700.2i	0.169005	−	0.174894i
$131$	−57768.1	−	41971.0i	−0.294110	−	0.213684i	0.430938	−	0.902381i	$-0.358183\pi$
$131$	−57768.1	−	41971.0i	−0.294110	−	0.213684i	−0.725048	+	0.688698i	$0.758183\pi$
$132$	42305.4			0.211330
$133$	−71875.0	−	52220.2i	−0.352329	−	0.255982i
$134$	−71316.2	+	219489.i	−0.343104	+	1.05597i
$135$	36622.1	+	17876.8i	0.172945	+	0.0844217i
$136$	−9983.12	−	30724.9i	−0.0462827	−	0.142444i
$137$	68893.8	−	212033.i	0.313602	−	0.965167i	−0.662724	−	0.748863i	$-0.730600\pi$
$137$	68893.8	−	212033.i	0.313602	−	0.965167i	0.976326	−	0.216304i	$-0.0694001\pi$
$138$	29329.7	−	90267.7i	0.131102	−	0.403492i
$139$	−965.507	−	2971.53i	−0.00423856	−	0.0130449i	0.948915	−	0.315532i	$-0.102183\pi$
$139$	−965.507	−	2971.53i	−0.00423856	−	0.0130449i	−0.953153	+	0.302487i	$0.902183\pi$
$140$	4629.13	−	32859.2i	0.0199609	−	0.141689i
$141$	−374.532	+	1152.69i	−0.00158650	+	0.00488276i
$142$	255193.	+	185408.i	1.06206	+	0.771628i
$143$	61572.3			0.251794
$144$	−16775.8	−	12188.3i	−0.0674181	−	0.0489821i
$145$	−47995.2	+	340687.i	−0.189574	+	1.34566i
$146$	−110025.	+	79937.5i	−0.427177	+	0.310362i
$147$	112352.	−	81628.7i	0.428833	−	0.311566i
$148$	−42572.2	−	131024.i	−0.159761	−	0.491695i
$149$	−329211.			−1.21481			−0.607405	−	0.794393i	$-0.707789\pi$
$149$	−329211.			−1.21481			−0.607405	+	0.794393i	$0.707789\pi$
$150$	−62970.8	+	93225.1i	−0.228513	+	0.338302i
$151$	−52252.6			−0.186494			−0.0932471	−	0.995643i	$-0.529725\pi$
$151$	−52252.6			−0.186494			−0.0932471	+	0.995643i	$0.529725\pi$
$152$	−47359.1	−	145756.i	−0.166262	−	0.511703i
$153$	33078.6	−	24033.0i	0.114240	−	0.0830002i
$154$	35272.0	−	25626.6i	0.119847	−	0.0870742i
$155$	68006.4	−	11968.2i	0.227363	−	0.0400128i
$156$	−24415.9	−	17739.2i	−0.0803268	−	0.0583609i
$157$	−33454.5			−0.108319			−0.0541596	−	0.998532i	$-0.517248\pi$
$157$	−33454.5			−0.108319			−0.0541596	+	0.998532i	$0.517248\pi$
$158$	−248926.	−	180856.i	−0.793283	−	0.576354i
$159$	−79319.1	+	244119.i	−0.248820	+	0.765788i
$160$	39778.2	−	41164.3i	0.122841	−	0.127122i
$161$	−30226.3	−	93027.0i	−0.0919010	−	0.282842i
$162$	8109.84	−	24959.5i	0.0242787	−	0.0747221i
$163$	−84162.5	+	259026.i	−0.248113	+	0.763613i	0.746996	+	0.664829i	$0.231496\pi$
$163$	−84162.5	+	259026.i	−0.248113	+	0.763613i	−0.995109	+	0.0987847i	$0.968504\pi$
$164$	−69801.2	−	214826.i	−0.202653	−	0.623702i
$165$	−145572.	+	25618.7i	−0.416263	+	0.0732566i
$166$	−6285.71	+	19345.4i	−0.0177045	+	0.0544889i
$167$	−50072.8	−	36380.0i	−0.138935	−	0.100942i	0.516147	−	0.856500i	$-0.327366\pi$
$167$	−50072.8	−	36380.0i	−0.138935	−	0.100942i	−0.655082	+	0.755558i	$0.727366\pi$
$168$	−21369.9			−0.0584156
$169$	264847.	+	192423.i	0.713310	+	0.518250i
$170$	52957.6	+	99678.2i	0.140542	+	0.264532i
$171$	156922.	−	114010.i	0.410387	−	0.298163i
$172$	33865.2	−	24604.5i	0.0872835	−	0.0634152i
$173$	−41692.1	−	128315.i	−0.105910	−	0.325958i	0.884033	−	0.467425i	$-0.154818\pi$
$173$	−41692.1	−	128315.i	−0.105910	−	0.325958i	−0.989943	+	0.141467i	$0.954818\pi$
$174$	221565.			0.554788
$175$	3969.64	+	115871.i	0.00979841	+	0.286009i
$176$	75209.6			0.183017
$177$	−3302.53	−	10164.1i	−0.00792344	−	0.0243858i
$178$	−268780.	+	195280.i	−0.635838	+	0.461964i
$179$	−193781.	+	140790.i	−0.452041	+	0.328427i	−0.790401	−	0.612589i	$-0.790128\pi$
$179$	−193781.	+	140790.i	−0.452041	+	0.328427i	0.338360	+	0.941017i	$0.390128\pi$
$180$	65105.9	+	31780.9i	0.149775	+	0.0731114i
$181$	446809.	+	324626.i	1.01374	+	0.736523i	0.964990	−	0.262288i	$-0.0844771\pi$
$181$	446809.	+	324626.i	1.01374	+	0.736523i	0.0487475	+	0.998811i	$0.484477\pi$
$182$	−31102.2			−0.0696005
$183$	−164974.	−	119861.i	−0.364157	−	0.264575i
$184$	52141.8	−	160476.i	0.113538	−	0.349434i
$185$	225833.	+	425070.i	0.485131	+	0.913126i
$186$	−13741.5	−	42291.8i	−0.0291240	−	0.0896343i
$187$	−45826.8	+	141040.i	−0.0958332	+	0.294944i
$188$	−665.835	+	2049.23i	−0.00137395	+	0.00422859i
$189$	−8357.74	−	25722.5i	−0.0170190	−	0.0523792i
$190$	251226.	+	472865.i	0.504872	+	0.950283i
$191$	90668.4	−	279049.i	0.179834	−	0.553473i	−0.819987	−	0.572382i	$-0.806019\pi$
$191$	90668.4	−	279049.i	0.179834	−	0.553473i	0.999821	+	0.0189091i	$0.00601932\pi$
$192$	−29823.6	−	21668.1i	−0.0583858	−	0.0424197i
$193$	−802330.			−1.55046			−0.775228	−	0.631681i	$-0.782365\pi$
$193$	−802330.			−1.55046			−0.775228	+	0.631681i	$0.782365\pi$
$194$	141521.	+	102821.i	0.269970	+	0.196145i
$195$	94756.6	+	46254.7i	0.178453	+	0.0871102i
$196$	199737.	−	145118.i	0.371380	−	0.269824i
$197$	59243.8	−	43043.2i	0.108762	−	0.0790203i	−0.532075	−	0.846697i	$-0.678587\pi$
$197$	59243.8	−	43043.2i	0.108762	−	0.0790203i	0.640837	+	0.767677i	$0.278587\pi$
$198$	29414.5	+	90528.4i	0.0533209	+	0.164105i
$199$	−807323.			−1.44516			−0.722578	−	0.691289i	$-0.757043\pi$
$199$	−807323.			−1.44516			−0.722578	+	0.691289i	$0.757043\pi$
$200$	−111948.	+	165734.i	−0.197898	+	0.292978i
$201$	−519264.			−0.906563
$202$	−7731.97	−	23796.6i	−0.0133325	−	0.0410332i
$203$	184729.	−	134213.i	0.314626	−	0.228589i
$204$	58806.3	−	42725.3i	0.0989347	−	0.0718803i
$205$	370276.	+	696942.i	0.615376	+	1.15828i
$206$	238852.	+	173536.i	0.392158	+	0.284919i
$207$	213554.			0.346404
$208$	−43406.0	−	31536.3i	−0.0695651	−	0.0505420i
$209$	−217399.	+	669084.i	−0.344263	+	1.05953i
$210$	73533.2	−	12940.8i	0.115063	−	0.0202495i
$211$	152204.	+	468437.i	0.235354	+	0.724344i	0.997074	+	0.0764386i	$0.0243549\pi$
$211$	152204.	+	468437.i	0.235354	+	0.724344i	−0.761721	+	0.647906i	$0.775645\pi$
$212$	−141012.	+	433989.i	−0.215484	+	0.663192i
$213$	−219318.	+	674993.i	−0.331227	+	1.01941i
$214$	114674.	+	352930.i	0.171171	+	0.526810i
$215$	−101630.	+	105171.i	−0.149942	+	0.155167i
$216$	14417.5	−	44372.5i	0.0210259	−	0.0647112i
$217$	−37075.3	−	26936.8i	−0.0534485	−	0.0388326i
$218$	−359463.			−0.512286
$219$	−247555.	−	179859.i	−0.348788	−	0.253410i
$220$	−258795.	+	45544.3i	−0.360494	+	0.0634421i
$221$	85588.1	−	62183.4i	0.117878	−	0.0856434i
$222$	250775.	−	182199.i	0.341509	−	0.248121i
$223$	76247.6	+	234666.i	0.102675	+	0.316001i	0.989178	−	0.146722i	$-0.0468724\pi$
$223$	76247.6	+	234666.i	0.102675	+	0.316001i	−0.886503	+	0.462723i	$0.846872\pi$
$224$	−37990.9			−0.0505894
$225$	−243273.	−	69931.5i	−0.320360	−	0.0920908i
$226$	842464.			1.09719
$227$	−387684.	−	1.19317e6i	−0.499359	−	1.53687i	−0.810051	−	0.586359i	$-0.800561\pi$
$227$	−387684.	−	1.19317e6i	−0.499359	−	1.53687i	0.310692	−	0.950511i	$-0.399439\pi$
$228$	278972.	−	202685.i	0.355405	−	0.258217i
$229$	−570238.	+	414302.i	−0.718567	+	0.522070i	−0.885926	−	0.463826i	$-0.846476\pi$
$229$	−570238.	+	414302.i	−0.718567	+	0.522070i	0.167359	+	0.985896i	$0.446476\pi$
$230$	−82240.1	+	583769.i	−0.102509	+	0.727648i
$231$	79362.0	+	57659.9i	0.0978550	+	0.0710958i
$232$	393893.			0.480461
$233$	−558127.	−	405503.i	−0.673509	−	0.489333i	0.197689	−	0.980265i	$-0.436656\pi$
$233$	−558127.	−	405503.i	−0.673509	−	0.489333i	−0.871198	+	0.490932i	$0.836656\pi$
$234$	20983.6	−	64580.8i	0.0250518	−	0.0771016i
$235$	1050.18	−	7454.56i	0.00124049	−	0.00880546i
$236$	−5871.16	−	18069.6i	−0.00686190	−	0.0211187i
$237$	213933.	−	658419.i	0.247404	−	0.761432i
$238$	23148.6	−	71244.2i	0.0264901	−	0.0815281i
$239$	161170.	+	496029.i	0.182511	+	0.561711i	0.999897	−	0.0143801i	$-0.00457749\pi$
$239$	161170.	+	496029.i	0.182511	+	0.561711i	−0.817386	+	0.576091i	$0.804577\pi$
$240$	115744.	+	56499.4i	0.129709	+	0.0633163i
$241$	130988.	−	403138.i	0.145274	−	0.447107i	−0.851772	−	0.523912i	$-0.824472\pi$
$241$	130988.	−	403138.i	0.145274	−	0.447107i	0.997046	+	0.0768053i	$0.0244720\pi$
$242$	241863.	+	175724.i	0.265480	+	0.192882i
$243$	59049.0			0.0641500
$244$	−293288.	−	213086.i	−0.315369	−	0.229129i
$245$	−599413.	+	620300.i	−0.637986	+	0.660217i
$246$	411169.	−	298732.i	0.433195	−	0.314734i
$247$	406023.	−	294993.i	0.423456	−	0.307659i
$248$	−24429.3	−	75185.5i	−0.0252221	−	0.0776256i
$249$	−45767.2			−0.0467796
$250$	284849.	−	638077.i	0.288246	−	0.645689i
$251$	1.42991e6			1.43260			0.716299	−	0.697794i	$-0.245835\pi$
$251$	1.42991e6			1.43260			0.716299	+	0.697794i	$0.245835\pi$
$252$	−14858.2	−	45728.9i	−0.0147389	−	0.0453617i
$253$	−626635.	+	455277.i	−0.615479	+	0.447172i
$254$	276964.	−	201226.i	0.269363	−	0.195704i
$255$	−176478.	+	182628.i	−0.169958	+	0.175880i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	393370.			0.371508			0.185754	−	0.982596i	$-0.440527\pi$
$257$	393370.			0.371508			0.185754	+	0.982596i	$0.440527\pi$
$258$	76196.7	+	55360.1i	0.0712667	+	0.0517783i
$259$	98715.5	−	303815.i	0.0914400	−	0.281423i
$260$	168456.	+	82230.5i	0.154545	+	0.0754396i
$261$	154051.	+	474121.i	0.139979	+	0.430812i
$262$	88261.8	−	271642.i	0.0794364	−	0.244480i
$263$	169381.	−	521302.i	0.151000	−	0.464730i	−0.846734	−	0.532017i	$-0.821434\pi$
$263$	169381.	−	521302.i	0.151000	−	0.464730i	0.997734	+	0.0672871i	$0.0214343\pi$
$264$	52292.4	+	160939.i	0.0461773	+	0.142119i
$265$	222409.	−	1.57874e6i	0.194553	−	1.38101i
$266$	109815.	−	337976.i	0.0951608	−	0.292875i
$267$	−604755.	−	439380.i	−0.519160	−	0.377192i
$268$	−923136.			−0.785107
$269$	−1.25277e6	−	910191.i	−1.05558	−	0.766923i	−0.0823141	−	0.996606i	$-0.526231\pi$
$269$	−1.25277e6	−	910191.i	−1.05558	−	0.766923i	−0.973265	+	0.229683i	$0.926231\pi$
$270$	−22739.9	+	161415.i	−0.0189836	+	0.134752i
$271$	563816.	−	409636.i	0.466352	−	0.338825i	−0.329666	−	0.944098i	$-0.606936\pi$
$271$	563816.	−	409636.i	0.466352	−	0.338825i	0.796018	+	0.605273i	$0.206936\pi$
$272$	104545.	−	75956.1i	0.0856800	−	0.0622502i
$273$	−21625.0	−	66554.9i	−0.0175610	−	0.0540472i
$274$	891780.			0.717598
$275$	862926.	−	313434.i	0.688085	−	0.249927i
$276$	379652.			0.299994
$277$	−568606.	−	1.74999e6i	−0.445258	−	1.37036i	−0.882201	−	0.470874i	$-0.843939\pi$
$277$	−568606.	−	1.74999e6i	−0.445258	−	1.37036i	0.436943	−	0.899489i	$-0.356061\pi$
$278$	10110.9	−	7346.01i	0.00784655	−	0.00570085i
$279$	80945.1	−	58810.0i	0.0622558	−	0.0452315i
$280$	130726.	−	23005.9i	0.0996474	−	0.0175366i
$281$	1.33639e6	+	970942.i	1.00964	+	0.733546i	0.964133	−	0.265418i	$-0.0855100\pi$
$281$	1.33639e6	+	970942.i	1.00964	+	0.733546i	0.0455059	+	0.998964i	$0.485510\pi$
$282$	−4848.05			−0.00363031
$283$	−1.70953e6	−	1.24205e6i	−1.26885	−	0.921874i	−0.269695	−	0.962946i	$-0.586923\pi$
$283$	−1.70953e6	−	1.24205e6i	−1.26885	−	0.921874i	−0.999156	+	0.0410713i	$0.986923\pi$
$284$	−389899.	+	1.19999e6i	−0.286851	+	0.882837i
$285$	−837198.	+	866371.i	−0.610543	+	0.631817i
$286$	76107.5	+	234235.i	0.0550190	+	0.169331i
$287$	161854.	−	498134.i	0.115989	−	0.356978i
$288$	25631.1	−	78884.4i	0.0182090	−	0.0560415i
$289$	−360021.	−	1.10803e6i	−0.253561	−	0.780382i
$290$	−1.35538e6	+	238528.i	−0.946378	+	0.166550i
$291$	−121626.	+	374327.i	−0.0841966	+	0.259130i
$292$	−440098.	−	319750.i	−0.302060	−	0.219459i
$293$	858487.			0.584204			0.292102	−	0.956387i	$-0.405645\pi$
$293$	858487.			0.584204			0.292102	+	0.956387i	$0.405645\pi$
$294$	449409.	+	326515.i	0.303231	+	0.220310i
$295$	31144.8	+	58621.6i	0.0208368	+	0.0392196i
$296$	445822.	−	323909.i	0.295755	−	0.214879i
$297$	−173268.	+	125887.i	−0.113980	+	0.0828111i
$298$	−406927.	−	1.25239e6i	−0.265446	−	0.816957i
$299$	552555.			0.357435
$300$	−432486.	−	124323.i	−0.277440	−	0.0797530i
$301$	97063.3			0.0617503
$302$	−64587.7	−	198781.i	−0.0407505	−	0.125417i
$303$	45545.8	−	33090.9i	0.0284998	−	0.0207063i
$304$	495951.	−	360329.i	0.307790	−	0.223622i
$305$	1.13823e6	+	555619.i	0.700619	+	0.342001i
$306$	132314.	+	96131.9i	0.0807799	+	0.0586900i
$307$	−1.08060e6			−0.654365			−0.327183	−	0.944961i	$-0.606099\pi$
$307$	−1.08060e6			−0.654365			−0.327183	+	0.944961i	$0.606099\pi$
$308$	141088.	+	102506.i	0.0847449	+	0.0615708i
$309$	−205275.	+	631772.i	−0.122304	+	0.376413i
$310$	129590.	+	243918.i	0.0765893	+	0.144158i
$311$	−216976.	−	667782.i	−0.127207	−	0.391502i	0.867090	−	0.498152i	$-0.165988\pi$
$311$	−216976.	−	667782.i	−0.127207	−	0.391502i	−0.994297	+	0.106650i	$0.965988\pi$
$312$	37304.1	−	114810.i	0.0216955	−	0.0667720i
$313$	−423446.	+	1.30323e6i	−0.244308	+	0.751901i	0.751442	+	0.659799i	$0.229359\pi$
$313$	−423446.	+	1.30323e6i	−0.244308	+	0.751901i	−0.995750	+	0.0921022i	$0.970641\pi$
$314$	−41352.1	−	127269.i	−0.0236686	−	0.0728445i
$315$	78818.6	+	148354.i	0.0447561	+	0.0842411i
$316$	380326.	−	1.17052e6i	0.214258	−	0.659420i
$317$	−1.60475e6	−	1.16592e6i	−0.896930	−	0.651658i	0.0407459	−	0.999170i	$-0.487027\pi$
$317$	−1.60475e6	−	1.16592e6i	−0.896930	−	0.651658i	−0.937676	+	0.347512i	$0.887027\pi$
$318$	−1.02673e6			−0.569361
$319$	−1.46281e6	−	1.06280e6i	−0.804845	−	0.584754i
$320$	205767.	+	100443.i	0.112331	+	0.0548335i
$321$	−675496.	+	490776.i	−0.365898	+	0.265840i
$322$	316534.	−	229975.i	0.170130	−	0.123607i
$323$	373531.	+	1.14961e6i	0.199214	+	0.613119i
$324$	104976.			0.0555556
$325$	−629450.	−	180942.i	−0.330562	−	0.0950236i
$326$	−1.08942e6			−0.567744
$327$	−249930.	−	769206.i	−0.129256	−	0.397808i
$328$	730968.	−	531079.i	0.375158	−	0.272568i
$329$	−4042.05	+	2936.72i	−0.00205879	+	0.00149580i
$330$	−277396.	−	522122.i	−0.140222	−	0.263929i
$331$	2.60978e6	+	1.89611e6i	1.30928	+	0.951250i	1.00000		0.000279784i	$8.90580e-5\pi$
$331$	2.60978e6	+	1.89611e6i	1.30928	+	0.951250i	0.309283	+	0.950970i	$0.399911\pi$
$332$	−81364.0			−0.0405123
$333$	564244.	+	409947.i	0.278841	+	0.202590i
$334$	76504.5	−	235457.i	0.0375250	−	0.115490i
$335$	3.17649e6	−	559019.i	1.54645	−	0.272154i
$336$	−26414.6	−	81295.8i	−0.0127643	−	0.0392844i
$337$	553688.	−	1.70408e6i	0.265577	−	0.817361i	−0.725983	−	0.687712i	$-0.758615\pi$
$337$	553688.	−	1.70408e6i	0.265577	−	0.817361i	0.991560	−	0.129649i	$-0.0413850\pi$
$338$	−404650.	+	1.24538e6i	−0.192658	+	0.592942i
$339$	585755.	+	1.80277e6i	0.276832	+	0.852003i
$340$	−313739.	+	324672.i	−0.147188	+	0.152317i
$341$	−112141.	+	345134.i	−0.0522249	+	0.160732i
$342$	627687.	+	456042.i	0.290187	+	0.210833i
$343$	1.19603e6			0.548916
$344$	135461.	+	98418.0i	0.0617188	+	0.0448413i
$345$	−1.30637e6	+	229904.i	−0.590908	+	0.103992i
$346$	436605.	−	317212.i	0.196064	−	0.142449i
$347$	3.25609e6	−	2.36568e6i	1.45168	−	1.05471i	0.466250	−	0.884653i	$-0.345605\pi$
$347$	3.25609e6	−	2.36568e6i	1.45168	−	1.05471i	0.985434	−	0.170057i	$-0.0543953\pi$
$348$	273869.	+	842882.i	0.121226	+	0.373094i
$349$	−2.58612e6			−1.13654			−0.568271	−	0.822841i	$-0.692388\pi$
$349$	−2.58612e6			−1.13654			−0.568271	+	0.822841i	$0.692388\pi$
$350$	−435892.	+	158326.i	−0.190199	+	0.0690846i
$351$	152785.			0.0661929
$352$	92964.2	+	286114.i	0.0399907	+	0.123079i
$353$	2.24277e6	−	1.62947e6i	0.957963	−	0.696001i	0.00528639	−	0.999986i	$-0.498317\pi$
$353$	2.24277e6	−	1.62947e6i	0.957963	−	0.696001i	0.952677	+	0.303985i	$0.0983173\pi$
$354$	34584.5	−	25127.1i	0.0146681	−	0.0106570i
$355$	614965.	−	4.36524e6i	0.258988	−	1.83839i
$356$	−1.07512e6	−	781120.i	−0.449606	−	0.326658i
$357$	168549.			0.0699931
$358$	−775123.	−	563160.i	−0.319642	−	0.232233i
$359$	−537131.	+	1.65312e6i	−0.219960	+	0.676968i	0.778804	+	0.627268i	$0.215827\pi$
$359$	−537131.	+	1.65312e6i	−0.219960	+	0.676968i	−0.998764	+	0.0497007i	$0.984173\pi$
$360$	−40426.4	+	286961.i	−0.0164403	+	0.116699i
$361$	1.00684e6	+	3.09875e6i	0.406625	+	1.25146i
$362$	−682663.	+	2.10102e6i	−0.273801	+	0.842673i
$363$	−207863.	+	639737.i	−0.0827962	+	0.254821i
$364$	−38444.4	−	118320.i	−0.0152083	−	0.0468063i
$365$	1.70800e6	+	833745.i	0.671050	+	0.327568i
$366$	252058.	−	775756.i	0.0983554	−	0.302707i
$367$	−115887.	−	84196.9i	−0.0449128	−	0.0326311i	0.565102	−	0.825021i	$-0.308837\pi$
$367$	−115887.	−	84196.9i	−0.0449128	−	0.0326311i	−0.610015	+	0.792390i	$0.708837\pi$
$368$	674937.			0.259803
$369$	925131.	+	672147.i	0.353702	+	0.256980i
$370$	−1.33792e6	+	1.38454e6i	−0.508071	+	0.525775i
$371$	−856031.	+	621943.i	−0.322890	+	0.234593i
$372$	143902.	−	104551.i	0.0539151	−	0.0391716i
$373$	−745698.	−	2.29502e6i	−0.277518	−	0.854112i	−0.988542	−	0.150945i	$-0.951768\pi$
$373$	−745698.	−	2.29502e6i	−0.277518	−	0.854112i	0.711024	−	0.703167i	$-0.248232\pi$
$374$	−593195.			−0.219290
$375$	1.56346e6	+	165893.i	0.574127	+	0.0609187i
$376$	−8618.75			−0.00314394
$377$	398595.	+	1.22675e6i	0.144437	+	0.444532i
$378$	87523.4	−	63589.5i	0.0315061	−	0.0228905i
$379$	4.28947e6	−	3.11648e6i	1.53393	−	1.11447i	0.579929	−	0.814667i	$-0.303080\pi$
$379$	4.28947e6	−	3.11648e6i	1.53393	−	1.11447i	0.954002	−	0.299799i	$-0.0969198\pi$
$380$	−1.48835e6	+	1.54021e6i	−0.528745	+	0.547170i
$381$	623168.	+	452758.i	0.219934	+	0.159792i
$382$	1.17364e6			0.411505
$383$	2.78385e6	+	2.02259e6i	0.969726	+	0.704547i	0.955389	−	0.295350i	$-0.0954364\pi$
$383$	2.78385e6	+	2.02259e6i	0.969726	+	0.704547i	0.0143365	+	0.999897i	$0.495436\pi$
$384$	45566.4	−	140239.i	0.0157695	−	0.0485334i
$385$	−547555.	−	267284.i	−0.188268	−	0.0919013i
$386$	−991734.	−	3.05224e6i	−0.338787	−	1.04268i
$387$	−65485.2	+	201543.i	−0.0222262	+	0.0684053i
$388$	−216224.	+	665470.i	−0.0729164	+	0.224414i
$389$	605596.	+	1.86383e6i	0.202912	+	0.624500i	0.999793	+	0.0203630i	$0.00648220\pi$
$389$	605596.	+	1.86383e6i	0.202912	+	0.624500i	−0.796880	+	0.604137i	$0.793518\pi$
$390$	−58837.6	+	417650.i	−0.0195881	+	0.139043i
$391$	−411254.	+	1.26571e6i	−0.136040	+	0.418689i
$392$	798949.	+	580471.i	0.262606	+	0.190794i
$393$	642648.			0.209890
$394$	236975.	+	172173.i	0.0769064	+	0.0558758i
$395$	−599865.	+	4.25805e6i	−0.193446	+	1.37315i
$396$	−308032.	+	223798.i	−0.0987093	+	0.0717165i
$397$	−3.91583e6	+	2.84502e6i	−1.24695	+	0.905959i	−0.998041	−	0.0625695i	$-0.980070\pi$
$397$	−3.91583e6	+	2.84502e6i	−1.24695	+	0.905959i	−0.248904	+	0.968528i	$0.580070\pi$
$398$	−997906.	−	3.07124e6i	−0.315778	−	0.971865i
$399$	799581.			0.251438
$400$	−768863.	−	221018.i	−0.240270	−	0.0690681i
$401$	−3.38027e6			−1.04976			−0.524880	−	0.851176i	$-0.675890\pi$
$401$	−3.38027e6			−1.04976			−0.524880	+	0.851176i	$0.675890\pi$
$402$	−641846.	−	1.97540e6i	−0.198091	−	0.609662i
$403$	209439.	−	152166.i	0.0642384	−	0.0466719i
$404$	80970.2	−	58828.3i	0.0246815	−	0.0179322i
$405$	−361220.	+	63569.8i	−0.109429	+	0.0192581i
$406$	738915.	+	536853.i	0.222474	+	0.161637i
$407$	−2.52963e6			−0.756957
$408$	235225.	+	170901.i	0.0699574	+	0.0508270i
$409$	−965861.	+	2.97261e6i	−0.285500	+	0.878679i	0.700748	+	0.713409i	$0.252850\pi$
$409$	−965861.	+	2.97261e6i	−0.285500	+	0.878679i	−0.986248	+	0.165270i	$0.947150\pi$
$410$	−2.19364e6	+	2.27008e6i	−0.644475	+	0.666932i
$411$	620044.	+	1.90830e6i	0.181058	+	0.557240i
$412$	−364934.	+	1.12315e6i	−0.105918	+	0.325983i
$413$	13613.9	−	41899.4i	0.00392743	−	0.0120874i
$414$	263968.	+	812409.i	0.0756920	+	0.232956i
$415$	279972.	−	49271.2i	0.0797983	−	0.0140434i
$416$	66318.4	−	204107.i	0.0187889	−	0.0578262i
$417$	22749.6	+	16528.5i	0.00640668	+	0.00465473i
$418$	−2.81407e6			−0.787759
$419$	−1.76299e6	−	1.28089e6i	−0.490586	−	0.356432i	0.314823	−	0.949150i	$-0.398055\pi$
$419$	−1.76299e6	−	1.28089e6i	−0.490586	−	0.356432i	−0.805410	+	0.592718i	$0.798055\pi$
$420$	140122.	+	263741.i	0.0387599	+	0.0729549i
$421$	−1.24275e6	+	902909.i	−0.341726	+	0.248278i	−0.745390	−	0.666629i	$-0.767737\pi$
$421$	−1.24275e6	+	902909.i	−0.341726	+	0.248278i	0.403664	+	0.914907i	$0.367737\pi$
$422$	−1.59391e6	+	1.15804e6i	−0.435694	+	0.316550i
$423$	−3370.79	−	10374.2i	−0.000915969	−	0.00281906i
$424$	−1.82529e6			−0.493081
$425$	882960.	−	1.30718e6i	0.237120	−	0.351045i
$426$	−2.83892e6			−0.757929
$427$	−259763.	−	799469.i	−0.0689458	−	0.212193i
$428$	−1.20088e6	+	872491.i	−0.316877	+	0.230225i
$429$	−448317.	+	325722.i	−0.117609	+	0.0854483i
$430$	−525716.	−	256624.i	−0.137113	−	0.0669308i
$431$	−1.85346e6	−	1.34662e6i	−0.480608	−	0.349182i	0.320953	−	0.947095i	$-0.395997\pi$
$431$	−1.85346e6	−	1.34662e6i	−0.480608	−	0.349182i	−0.801561	+	0.597913i	$0.795997\pi$
$432$	186624.			0.0481125
$433$	3.50234e6	+	2.54460e6i	0.897715	+	0.652228i	0.937878	−	0.346965i	$-0.112788\pi$
$433$	3.50234e6	+	2.54460e6i	0.897715	+	0.652228i	−0.0401629	+	0.999193i	$0.512788\pi$
$434$	56646.0	−	174339.i	0.0144359	−	0.0444293i
$435$	−1.45280e6	−	2.73449e6i	−0.368113	−	0.692873i
$436$	−444320.	−	1.36748e6i	−0.111939	−	0.344512i
$437$	−1.95095e6	+	6.00441e6i	−0.488701	+	1.50407i
$438$	378231.	−	1.16408e6i	0.0942045	−	0.289932i
$439$	−608589.	−	1.87304e6i	−0.150717	−	0.463860i	0.846985	−	0.531617i	$-0.178416\pi$
$439$	−608589.	−	1.87304e6i	−0.150717	−	0.463860i	−0.997702	+	0.0677575i	$0.978416\pi$
$440$	−493148.	−	928217.i	−0.121436	−	0.228569i
$441$	−386233.	+	1.18870e6i	−0.0945698	+	0.291056i
$442$	342353.	+	248734.i	0.0833524	+	0.0605590i
$443$	11764.9			0.00284824			0.00142412	−	0.999999i	$-0.499547\pi$
$443$	11764.9			0.00284824			0.00142412	+	0.999999i	$0.499547\pi$
$444$	1.00310e6	+	728795.i	0.241483	+	0.175448i
$445$	4.17248e6	+	2.03676e6i	0.998836	+	0.487574i
$446$	−798475.	+	580126.i	−0.190075	+	0.138097i
$447$	2.39703e6	−	1.74155e6i	0.567421	−	0.412255i
$448$	−46959.3	−	144526.i	−0.0110542	−	0.0340213i
$449$	−4.87666e6			−1.14158			−0.570790	−	0.821096i	$-0.693363\pi$
$449$	−4.87666e6			−1.14158			−0.570790	+	0.821096i	$0.693363\pi$
$450$	−34667.0	−	1.01191e6i	−0.00807022	−	0.235564i
$451$	−4.14757e6			−0.960180
$452$	1.04134e6	+	3.20492e6i	0.239744	+	0.737856i
$453$	380459.	−	276420.i	0.0871088	−	0.0632883i
$454$	4.05988e6	−	2.94967e6i	0.924428	−	0.671637i
$455$	203937.	+	383855.i	0.0461814	+	0.0869238i
$456$	1.11589e6	+	810741.i	0.251309	+	0.182587i
$457$	1.53208e6			0.343155			0.171577	−	0.985171i	$-0.445114\pi$
$457$	1.53208e6			0.343155			0.171577	+	0.985171i	$0.445114\pi$
$458$	−2.28095e6	−	1.65721e6i	−0.508104	−	0.369159i
$459$	−113714.	+	349976.i	−0.0251931	+	0.0775365i
$460$	−2.32244e6	+	408718.i	−0.511741	+	0.0900595i
$461$	−1.51935e6	−	4.67607e6i	−0.332970	−	1.02478i	−0.967713	−	0.252053i	$-0.918894\pi$
$461$	−1.51935e6	−	4.67607e6i	−0.332970	−	1.02478i	0.634743	−	0.772723i	$-0.281106\pi$
$462$	−121254.	+	373183.i	−0.0264297	+	0.0813423i
$463$	−1.66134e6	+	5.11309e6i	−0.360169	+	1.10849i	0.592782	+	0.805363i	$0.298030\pi$
$463$	−1.66134e6	+	5.11309e6i	−0.360169	+	1.10849i	−0.952951	+	0.303124i	$0.901970\pi$
$464$	486878.	+	1.49846e6i	0.104985	+	0.323109i
$465$	−431852.	+	446900.i	−0.0926196	+	0.0958470i
$466$	852742.	−	2.62447e6i	0.181909	−	0.559857i
$467$	3.99206e6	+	2.90040e6i	0.847043	+	0.615413i	0.924329	−	0.381596i	$-0.124626\pi$
$467$	3.99206e6	+	2.90040e6i	0.847043	+	0.615413i	−0.0772863	+	0.997009i	$0.524626\pi$
$468$	271617.			0.0573248
$469$	−1.73174e6	−	1.25818e6i	−0.363539	−	0.264126i
$470$	29656.9	−	5219.21i	0.00619272	−	0.00108983i
$471$	243587.	−	176977.i	0.0505944	−	0.0367590i
$472$	61483.6	−	44670.5i	0.0127029	−	0.00922923i
$473$	−237515.	−	730997.i	−0.0488134	−	0.150232i
$474$	2.76921e6			0.566122
$475$	4.18868e6	−	6.20114e6i	0.851812	−	1.26106i
$476$	299642.			0.0606158
$477$	−713871.	−	2.19707e6i	−0.143656	−	0.442128i
$478$	−1.68779e6	+	1.22625e6i	−0.337869	+	0.245477i
$479$	−5.91246e6	+	4.29565e6i	−1.17741	+	0.855442i	−0.991878	−	0.127196i	$-0.959402\pi$
$479$	−5.91246e6	+	4.29565e6i	−1.17741	+	0.855442i	−0.185537	+	0.982637i	$0.559402\pi$
$480$	−71869.2	+	510153.i	−0.0142377	+	0.101064i
$481$	1.45994e6	+	1.06070e6i	0.287721	+	0.209041i
$482$	1.69554e6			0.332422
$483$	712201.	+	517445.i	0.138910	+	0.100924i
$484$	−369534.	+	1.13731e6i	−0.0717036	+	0.220681i
$485$	341038.	−	2.42080e6i	0.0658337	−	0.467310i
$486$	72988.6	+	224636.i	0.0140173	+	0.0431408i
$487$	−1.10934e6	+	3.41421e6i	−0.211955	+	0.652330i	0.787401	+	0.616441i	$0.211426\pi$
$487$	−1.10934e6	+	3.41421e6i	−0.211955	+	0.652330i	−0.999356	+	0.0358888i	$0.988574\pi$
$488$	448104.	−	1.37912e6i	0.0851783	−	0.262152i
$489$	−757462.	−	2.33123e6i	−0.143248	−	0.440872i
$490$	−3.10068e6	−	1.51357e6i	−0.583400	−	0.284782i
$491$	1.98905e6	−	6.12168e6i	0.372343	−	1.14595i	−0.572912	−	0.819617i	$-0.694186\pi$
$491$	1.98905e6	−	6.12168e6i	0.372343	−	1.14595i	0.945254	−	0.326335i	$-0.105814\pi$
$492$	1.64468e6	+	1.19493e6i	0.306315	+	0.222551i
$493$	−3.10672e6			−0.575685
$494$	1.62409e6	+	1.17997e6i	0.299428	+	0.217547i
$495$	924407.	−	956619.i	0.169570	−	0.175479i
$496$	255826.	−	185869.i	0.0466919	−	0.0339236i
$497$	−2.36694e6	+	1.71968e6i	−0.429829	+	0.312289i
$498$	−56571.4	−	174109.i	−0.0102217	−	0.0314592i
$499$	1.00642e7			1.80938			0.904688	−	0.426074i	$-0.140104\pi$
$499$	1.00642e7			1.80938			0.904688	+	0.426074i	$0.140104\pi$
$500$	2.77948e6	+	294921.i	0.497209	+	0.0527571i
$501$	557041.			0.0991500
$502$	1.76747e6	+	5.43970e6i	0.313034	+	0.963420i
$503$	7.35876e6	−	5.34645e6i	1.29683	−	0.942205i	0.296915	−	0.954904i	$-0.404042\pi$
$503$	7.35876e6	−	5.34645e6i	1.29683	−	0.942205i	0.999919	+	0.0126986i	$0.00404220\pi$
$504$	155597.	−	113048.i	0.0272851	−	0.0198238i
$505$	−242992.	+	251460.i	−0.0423998	+	0.0438773i
$506$	−2.50654e6	−	1.82111e6i	−0.435209	−	0.316198i
$507$	−2.94632e6			−0.509049
$508$	1.10785e6	+	804903.i	0.190469	+	0.138384i
$509$	2.70741e6	−	8.33255e6i	0.463190	−	1.42555i	−0.398054	−	0.917362i	$-0.630314\pi$
$509$	2.70741e6	−	8.33255e6i	0.463190	−	1.42555i	0.861245	−	0.508191i	$-0.169686\pi$
$510$	−912897.	−	445623.i	−0.155416	−	0.0758651i
$511$	−389793.	−	1.19966e6i	−0.0660361	−	0.203238i
$512$	81007.0	−	249314.i	0.0136568	−	0.0420312i
$513$	−539449.	+	1.66025e6i	−0.0905018	+	0.278536i
$514$	486232.	+	1.49647e6i	0.0811775	+	0.249839i
$515$	575588.	−	4.08572e6i	0.0956299	−	0.678814i
$516$	−116418.	+	358298.i	−0.0192485	+	0.0592407i
$517$	32007.8	+	23255.0i	0.00526658	+	0.00382640i
$518$	1.27780e6			0.209237
$519$	982361.	+	713727.i	0.160086	+	0.116309i
$520$	−104600.	+	742488.i	−0.0169638	+	0.120415i
$521$	−5.14097e6	+	3.73513e6i	−0.829756	+	0.602853i	−0.919490	−	0.393113i	$-0.871398\pi$
$521$	−5.14097e6	+	3.73513e6i	−0.829756	+	0.602853i	0.0897341	+	0.995966i	$0.471398\pi$
$522$	−1.61325e6	+	1.17209e6i	−0.259134	+	0.188272i
$523$	558174.	+	1.71788e6i	0.0892309	+	0.274624i	0.985707	−	0.168467i	$-0.0538817\pi$
$523$	558174.	+	1.71788e6i	0.0892309	+	0.274624i	−0.896476	+	0.443091i	$0.853882\pi$
$524$	1.14249e6			0.181770
$525$	−641869.	−	822674.i	−0.101636	−	0.130266i
$526$	2.19252e6			0.345525
$527$	192679.	+	593005.i	0.0302209	+	0.0930104i
$528$	−547613.	+	397864.i	−0.0854848	+	0.0621083i
$529$	−416359.	+	302503.i	−0.0646888	+	0.0469992i
$530$	6.28079e6	−	1.10533e6i	0.971236	−	0.170924i
$531$	77815.2	+	56536.1i	0.0119765	+	0.00870140i
$532$	1.42148e6			0.217751
$533$	2.39370e6	+	1.73913e6i	0.364966	+	0.265163i
$534$	923983.	−	2.84373e6i	0.140220	−	0.431554i
$535$	3.60385e6	−	3.72943e6i	0.544356	−	0.563324i
$536$	−1.14106e6	−	3.51182e6i	−0.171552	−	0.527983i
$537$	666159.	−	2.05023e6i	0.0996879	−	0.306808i
$538$	1.91406e6	−	5.89088e6i	0.285102	−	0.877455i
$539$	−1.40087e6	−	4.31143e6i	−0.207695	−	0.639219i
$540$	−642169.	+	113013.i	−0.0947687	+	0.0166780i
$541$	−2.48686e6	+	7.65376e6i	−0.365307	+	1.12430i	0.584482	+	0.811407i	$0.301298\pi$
$541$	−2.48686e6	+	7.65376e6i	−0.365307	+	1.12430i	−0.949789	+	0.312892i	$0.898702\pi$
$542$	2.25526e6	+	1.63855e6i	0.329761	+	0.239585i
$543$	−4.97058e6			−0.723448
$544$	418178.	+	303824.i	0.0605849	+	0.0440175i
$545$	2.35699e6	+	4.43639e6i	0.339912	+	0.639792i
$546$	226460.	−	164533.i	0.0325095	−	0.0236195i
$547$	2.80624e6	−	2.03885e6i	0.401012	−	0.291352i	−0.368941	−	0.929453i	$-0.620280\pi$
$547$	2.80624e6	−	2.03885e6i	0.401012	−	0.291352i	0.769953	+	0.638101i	$0.220280\pi$
$548$	1.10230e6	+	3.39253e6i	0.156801	+	0.482584i
$549$	1.83527e6			0.259878
$550$	2.25901e6	+	2.89534e6i	0.318428	+	0.408125i
$551$	−1.47380e7			−2.06804
$552$	469276.	+	1.44428e6i	0.0655512	+	0.201746i
$553$	2.30882e6	−	1.67746e6i	0.321053	−	0.233259i
$554$	5.95452e6	−	4.32621e6i	0.824275	−	0.598871i
$555$	−3.89298e6	−	1.90032e6i	−0.536475	−	0.261876i
$556$	40443.7	+	29384.1i	0.00554835	+	0.00403111i
$557$	5.67017e6			0.774387			0.387193	−	0.921999i	$-0.373445\pi$
$557$	5.67017e6			0.774387			0.387193	+	0.921999i	$0.373445\pi$
$558$	323780.	+	235240.i	0.0440215	+	0.0319835i
$559$	−169438.	+	521476.i	−0.0229340	+	0.0705837i
$560$	249106.	+	468873.i	0.0335671	+	0.0631808i
$561$	−412441.	−	1.26936e6i	−0.0553293	−	0.170286i
$562$	−2.04182e6	+	6.28407e6i	−0.272694	+	0.839267i
$563$	510423.	−	1.57092e6i	0.0678671	−	0.208873i	−0.911371	−	0.411585i	$-0.864975\pi$
$563$	510423.	−	1.57092e6i	0.0678671	−	0.208873i	0.979238	+	0.202712i	$0.0649754\pi$
$564$	−5992.52	−	18443.1i	−0.000793252	−	0.00244138i
$565$	−5.52403e6	−	1.03975e7i	−0.728005	−	1.37027i
$566$	2.61193e6	−	8.03869e6i	0.342705	−	1.05474i
$567$	196928.	+	143076.i	0.0257246	+	0.0186900i
$568$	−5.04696e6			−0.656386
$569$	−1.09250e7	−	7.93746e6i	−1.41462	−	1.02778i	−0.992630	−	0.121182i	$-0.961332\pi$
$569$	−1.09250e7	−	7.93746e6i	−1.41462	−	1.02778i	−0.421990	−	0.906600i	$-0.638668\pi$
$570$	−4.33070e6	−	2.11400e6i	−0.558305	−	0.272532i
$571$	−644778.	+	468459.i	−0.0827599	+	0.0601286i	−0.628396	−	0.777894i	$-0.716288\pi$
$571$	−644778.	+	468459.i	−0.0827599	+	0.0601286i	0.545636	+	0.838022i	$0.316288\pi$
$572$	−797009.	+	579061.i	−0.101853	+	0.0740004i
$573$	816016.	+	2.51144e6i	0.103827	+	0.319548i
$574$	2.09508e6			0.265412
$575$	7.74397e6	−	2.81278e6i	0.976774	−	0.354786i
$576$	331776.			0.0416667
$577$	1.15900e6	+	3.56703e6i	0.144925	+	0.446033i	0.997001	−	0.0773843i	$-0.0246569\pi$
$577$	1.15900e6	+	3.56703e6i	0.144925	+	0.446033i	−0.852076	+	0.523417i	$0.824657\pi$
$578$	3.77019e6	−	2.73920e6i	0.469400	−	0.341039i
$579$	5.84188e6	−	4.24438e6i	0.724197	−	0.526160i
$580$	−2.58275e6	−	4.86132e6i	−0.318796	−	0.600045i
$581$	−152633.	−	110894.i	−0.0187590	−	0.0136292i
$582$	−1.57436e6			−0.192662
$583$	6.77866e6	+	4.92498e6i	0.825985	+	0.600113i
$584$	672411.	−	2.06947e6i	0.0815835	−	0.251088i
$585$	−934628.	+	164482.i	−0.112914	+	0.0198714i
$586$	1.06115e6	+	3.26588e6i	0.127653	+	0.392877i
$587$	−4.61209e6	+	1.41945e7i	−0.552462	+	1.70030i	0.150093	+	0.988672i	$0.452043\pi$
$587$	−4.61209e6	+	1.41945e7i	−0.552462	+	1.70030i	−0.702554	+	0.711630i	$0.747957\pi$
$588$	−686636.	+	2.11325e6i	−0.0818999	+	0.252062i
$589$	914052.	+	2.81316e6i	0.108563	+	0.334123i
$590$	−184513.	+	190942.i	−0.0218221	+	0.0225825i
$591$	−203662.	+	626808.i	−0.0239851	+	0.0738186i
$592$	1.78329e6	+	1.29563e6i	0.209130	+	0.151942i
$593$	1.30501e7			1.52398			0.761988	−	0.647591i	$-0.224223\pi$
$593$	1.30501e7			1.52398			0.761988	+	0.647591i	$0.224223\pi$
$594$	−693072.	−	503547.i	−0.0805958	−	0.0585563i
$595$	−1.03106e6	+	181453.i	−0.119397	+	0.0210122i
$596$	4.26139e6	−	3.09608e6i	0.491401	−	0.357023i
$597$	5.87824e6	−	4.27079e6i	0.675012	−	0.490425i
$598$	682995.	+	2.10204e6i	0.0781025	+	0.240375i
$599$	1.82228e6			0.207514			0.103757	−	0.994603i	$-0.466914\pi$
$599$	1.82228e6			0.207514			0.103757	+	0.994603i	$0.466914\pi$
$600$	−61630.3	−	1.79894e6i	−0.00698901	−	0.204004i
$601$	−1.36718e7			−1.54398			−0.771989	−	0.635636i	$-0.780738\pi$
$601$	−1.36718e7			−1.54398			−0.771989	+	0.635636i	$0.780738\pi$
$602$	119977.	+	369251.i	0.0134929	+	0.0415270i
$603$	3.78084e6	−	2.74694e6i	0.423443	−	0.307649i
$604$	676371.	−	491413.i	0.0754385	−	0.0548093i
$605$	582844.	−	4.13723e6i	0.0647387	−	0.459538i
$606$	182183.	+	132364.i	0.0201524	+	0.0146416i
$607$	4.83670e6			0.532816			0.266408	−	0.963860i	$-0.414163\pi$
$607$	4.83670e6			0.532816			0.266408	+	0.963860i	$0.414163\pi$
$608$	1.98380e6	+	1.44132e6i	0.217640	+	0.158125i
$609$	−635041.	+	1.95446e6i	−0.0693839	+	0.213542i
$610$	−706767.	+	5.01688e6i	−0.0769045	+	0.545895i
$611$	−8721.65	−	26842.5i	−0.000945139	−	0.00290884i
$612$	−202158.	+	622179.i	−0.0218179	+	0.0671486i
$613$	−2.72976e6	+	8.40135e6i	−0.293409	+	0.903021i	0.690342	+	0.723484i	$0.257460\pi$
$613$	−2.72976e6	+	8.40135e6i	−0.293409	+	0.903021i	−0.983751	+	0.179538i	$0.942540\pi$
$614$	−1.33570e6	−	4.11086e6i	−0.142984	−	0.440060i
$615$	−6.38291e6	−	3.11576e6i	−0.680504	−	0.332182i
$616$	−215563.	+	663436.i	−0.0228888	+	0.0704445i
$617$	−7.47438e6	−	5.43045e6i	−0.790428	−	0.574279i	0.117663	−	0.993054i	$-0.462460\pi$
$617$	−7.47438e6	−	5.43045e6i	−0.790428	−	0.574279i	−0.908090	+	0.418774i	$0.862460\pi$
$618$	−2.65714e6			−0.279861
$619$	4.75273e6	+	3.45306e6i	0.498559	+	0.362225i	0.808466	−	0.588542i	$-0.200298\pi$
$619$	4.75273e6	+	3.45306e6i	0.498559	+	0.362225i	−0.309907	+	0.950767i	$0.600298\pi$
$620$	−767737.	+	794490.i	−0.0802109	+	0.0830059i
$621$	−1.55492e6	+	1.12972e6i	−0.161800	+	0.117555i
$622$	2.27220e6	−	1.65085e6i	0.235489	−	0.171093i
$623$	−952227.	−	2.93065e6i	−0.0982925	−	0.302513i
$624$	482875.			0.0496447
$625$	−9.74273e6	+	668339.i	−0.997655	+	0.0684379i
$626$	−5.48120e6			−0.559036
$627$	−1.95659e6	−	6.02175e6i	−0.198761	−	0.611722i
$628$	433044.	−	314625.i	0.0438161	−	0.0318342i
$629$	−3.51630e6	+	2.55474e6i	−0.354372	+	0.257466i
$630$	−466949.	+	483220.i	−0.0468725	+	0.0485058i
$631$	5.24820e6	+	3.81304e6i	0.524731	+	0.381239i	0.818383	−	0.574673i	$-0.194871\pi$
$631$	5.24820e6	+	3.81304e6i	0.524731	+	0.381239i	−0.293652	+	0.955912i	$0.594871\pi$
$632$	4.92304e6			0.490276
$633$	−3.58629e6	−	2.60559e6i	−0.355742	−	0.258462i
$634$	2.45184e6	−	7.54597e6i	0.242252	−	0.745576i
$635$	−4.29952e6	−	2.09878e6i	−0.423142	−	0.206553i
$636$	−1.26910e6	−	3.90590e6i	−0.124410	−	0.382894i
$637$	−999346.	+	3.07567e6i	−0.0975815	+	0.300325i
$638$	2.23498e6	−	6.87856e6i	0.217381	−	0.669031i
$639$	−1.97387e6	−	6.07493e6i	−0.191234	−	0.588558i
$640$	−127767.	+	906938.i	−0.0123302	+	0.0875241i
$641$	1.63832e6	−	5.04223e6i	0.157490	−	0.484706i	−0.840914	−	0.541168i	$-0.817982\pi$
$641$	1.63832e6	−	5.04223e6i	0.157490	−	0.484706i	0.998405	+	0.0564627i	$0.0179822\pi$
$642$	−2.70198e6	−	1.96311e6i	−0.258729	−	0.187978i
$643$	1.01460e7			0.967762			0.483881	−	0.875134i	$-0.339227\pi$
$643$	1.01460e7			0.967762			0.483881	+	0.875134i	$0.339227\pi$
$644$	1.26614e6	+	919901.i	0.120300	+	0.0874030i
$645$	183619.	−	1.30339e6i	0.0173788	−	0.123361i
$646$	−3.91167e6	+	2.84200e6i	−0.368792	+	0.267943i
$647$	−1.57396e7	+	1.14355e7i	−1.47820	+	1.07398i	−0.500071	+	0.865985i	$0.666693\pi$
$647$	−1.57396e7	+	1.14355e7i	−1.47820	+	1.07398i	−0.978131	+	0.207991i	$0.933307\pi$
$648$	129757.	+	399352.i	0.0121393	+	0.0373610i
$649$	−348863.			−0.0325120
$650$	−89698.2	−	2.61823e6i	−0.00832722	−	0.243066i
$651$	412448.			0.0381432
$652$	−1.34660e6	−	4.14441e6i	−0.124057	−	0.381807i
$653$	6.88982e6	−	5.00575e6i	0.632303	−	0.459395i	−0.224895	−	0.974383i	$-0.572204\pi$
$653$	6.88982e6	−	5.00575e6i	0.632303	−	0.459395i	0.857197	+	0.514988i	$0.172204\pi$
$654$	2.61730e6	−	1.90158e6i	0.239282	−	0.173848i
$655$	−3.93127e6	+	691849.i	−0.358038	+	0.0630098i
$656$	2.92387e6	+	2.12432e6i	0.265276	+	0.192735i
$657$	2.75396e6			0.248911
$658$	−16168.2	−	11746.9i	−0.00145578	−	0.00105769i
$659$	−5.52574e6	+	1.70065e7i	−0.495652	+	1.52546i	0.320286	+	0.947321i	$0.396221\pi$
$659$	−5.52574e6	+	1.70065e7i	−0.495652	+	1.52546i	−0.815938	+	0.578139i	$0.803779\pi$
$660$	1.64339e6	−	1.70066e6i	0.146852	−	0.151970i
$661$	−2564.55	−	7892.86i	−0.000228301	−	0.000702637i	0.950942	−	0.309368i	$-0.100118\pi$
$661$	−2564.55	−	7892.86i	−0.000228301	−	0.000702637i	−0.951171	+	0.308666i	$0.900118\pi$
$662$	−3.98739e6	+	1.22719e7i	−0.353625	+	1.08835i
$663$	−294226.	+	905534.i	−0.0259954	+	0.0800057i
$664$	−100571.	−	309527.i	−0.00885226	−	0.0272445i
$665$	−4.89127e6	+	860797.i	−0.428911	+	0.0754825i
$666$	−862087.	+	2.65323e6i	−0.0753123	+	0.231787i
$667$	−1.31274e7	−	9.53762e6i	−1.14252	−	0.830090i
$668$	990295.			0.0858664
$669$	−1.79657e6	−	1.30528e6i	−0.155195	−	0.112756i
$670$	6.05299e6	+	1.13931e7i	0.520934	+	0.980516i
$671$	−5.38527e6	+	3.91262e6i	−0.461744	+	0.335476i
$672$	276617.	−	200974.i	0.0236296	−	0.0171679i
$673$	3.08939e6	+	9.50817e6i	0.262927	+	0.809207i	0.992164	+	0.124945i	$0.0398754\pi$
$673$	3.08939e6	+	9.50817e6i	0.262927	+	0.809207i	−0.729237	+	0.684262i	$0.760125\pi$
$674$	7.16708e6			0.607705
$675$	2.14125e6	−	777750.i	0.180887	−	0.0657023i
$676$	−5.23790e6			−0.440850
$677$	−2.91240e6	−	8.96344e6i	−0.244219	−	0.751629i	−0.995764	−	0.0919467i	$-0.970691\pi$
$677$	−2.91240e6	−	8.96344e6i	−0.244219	−	0.751629i	0.751545	−	0.659682i	$-0.229309\pi$
$678$	−6.13411e6	+	4.45669e6i	−0.512480	+	0.372339i
$679$	−1.31262e6	+	953674.i	−0.109261	+	0.0793826i
$680$	−1.62293e6	−	792219.i	−0.134594	−	0.0657011i
$681$	9.13472e6	+	6.63677e6i	0.754793	+	0.548389i
$682$	−1.45158e6			−0.119503
$683$	9.01596e6	+	6.55048e6i	0.739538	+	0.537305i	0.892566	−	0.450916i	$-0.148903\pi$
$683$	9.01596e6	+	6.55048e6i	0.739538	+	0.537305i	−0.153029	+	0.988222i	$0.548903\pi$
$684$	−959021.	+	2.95156e6i	−0.0783769	+	0.241219i
$685$	−5.84739e6	−	1.10061e7i	−0.476141	−	0.896205i
$686$	1.47837e6	+	4.54996e6i	0.119943	+	0.369145i
$687$	1.96030e6	−	6.03319e6i	0.158464	−	0.487703i
$688$	−206966.	+	636975.i	−0.0166697	+	0.0513040i
$689$	−1.84709e6	−	5.68474e6i	−0.148231	−	0.456208i
$690$	−2.48937e6	−	4.68557e6i	−0.199052	−	0.374662i
$691$	−159491.	+	490863.i	−0.0127070	+	0.0391080i	−0.957209	−	0.289398i	$-0.906545\pi$
$691$	−159491.	+	490863.i	−0.0127070	+	0.0391080i	0.944502	+	0.328506i	$0.106545\pi$
$692$	1.74642e6	+	1.26885e6i	0.138638	+	0.100727i
$693$	−882872.			−0.0698336
$694$	1.30243e7	+	9.46274e6i	1.02650	+	0.745793i
$695$	−156960.	−	76618.6i	−0.0123261	−	0.00601689i
$696$	−2.86799e6	+	2.08372e6i	−0.224417	+	0.163048i
$697$	−5.76531e6	+	4.18874e6i	−0.449511	+	0.326589i
$698$	−3.19663e6	−	9.83820e6i	−0.248344	−	0.764323i
$699$	6.20895e6			0.480646
$700$	−1.14110e6	−	1.46253e6i	−0.0880194	−	0.112813i
$701$	5.53562e6			0.425472			0.212736	−	0.977110i	$-0.431763\pi$
$701$	5.53562e6			0.425472			0.212736	+	0.977110i	$0.431763\pi$
$702$	188852.	+	581227.i	0.0144637	+	0.0445147i
$703$	−1.66810e7	+	1.21195e7i	−1.27302	+	0.924901i
$704$	−973534.	+	707314.i	−0.0740320	+	0.0537874i
$705$	31788.6	+	59833.3i	0.00240879	+	0.00453388i
$706$	8.97110e6	+	6.51788e6i	0.677382	+	0.492147i
$707$	232074.			0.0174614
$708$	138338.	+	100509.i	0.0103719	+	0.00753563i
$709$	6.68913e6	−	2.05870e7i	0.499752	−	1.53808i	−0.309667	−	0.950845i	$-0.600218\pi$
$709$	6.68913e6	−	2.05870e7i	0.499752	−	1.53808i	0.809418	−	0.587232i	$-0.199782\pi$
$710$	1.73665e7	−	3.05626e6i	1.29290	−	0.227533i
$711$	1.92540e6	+	5.92577e6i	0.142839	+	0.439613i
$712$	1.64264e6	−	5.05551e6i	0.121434	−	0.373736i
$713$	−1.00636e6	+	3.09726e6i	−0.0741361	+	0.228167i
$714$	208338.	+	641198.i	0.0152941	+	0.0470703i
$715$	2.39183e6	−	2.47517e6i	0.174971	−	0.181068i
$716$	1.18428e6	−	3.64485e6i	0.0863322	−	0.265703i
$717$	−3.79753e6	−	2.75907e6i	−0.275869	−	0.200431i
$718$	−6.95277e6			−0.503323
$719$	847389.	+	615664.i	0.0611309	+	0.0444142i	0.617931	−	0.786232i	$-0.287971\pi$
$719$	847389.	+	615664.i	0.0611309	+	0.0444142i	−0.556800	+	0.830646i	$0.687971\pi$
$720$	−1.14163e6	+	200912.i	−0.0820721	+	0.0144436i
$721$	−2.21538e6	+	1.60957e6i	−0.158712	+	0.115311i
$722$	−1.05438e7	+	7.66053e6i	−0.752757	+	0.546910i
$723$	1.17889e6	+	3.62824e6i	0.0838739	+	0.258137i
$724$	−8.83658e6			−0.626524
$725$	1.18310e7	+	1.51637e7i	0.835944	+	1.07142i
$726$	−2.69064e6			−0.189458
$727$	−6.48201e6	−	1.99496e7i	−0.454856	−	1.39990i	−0.871305	−	0.490743i	$-0.836726\pi$
$727$	−6.48201e6	−	1.99496e7i	−0.454856	−	1.39990i	0.416449	−	0.909159i	$-0.363274\pi$
$728$	402595.	−	292503.i	0.0281540	−	0.0204551i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	−1.06055e6	+	7.52818e6i	−0.0736589	+	0.522857i
$731$	−1.06841e6	−	776245.i	−0.0739510	−	0.0537286i
$732$	3.26271e6			0.225061
$733$	1.51326e7	+	1.09945e7i	1.04029	+	0.755814i	0.970342	−	0.241737i	$-0.0777171\pi$
$733$	1.51326e7	+	1.09945e7i	1.04029	+	0.755814i	0.0699465	+	0.997551i	$0.477717\pi$
$734$	177060.	−	544934.i	0.0121305	−	0.0373339i
$735$	1.08299e6	−	7.68744e6i	0.0739445	−	0.524884i
$736$	834268.	+	2.56761e6i	0.0567690	+	0.174717i
$737$	−5.23795e6	+	1.61208e7i	−0.355216	+	1.09324i
$738$	−1.41347e6	+	4.35023e6i	−0.0955316	+	0.294016i
$739$	7.17774e6	+	2.20908e7i	0.483478	+	1.48799i	0.834173	+	0.551502i	$0.185945\pi$
$739$	7.17774e6	+	2.20908e7i	0.483478	+	1.48799i	−0.350696	+	0.936489i	$0.614055\pi$
$740$	−6.92084e6	−	3.37835e6i	−0.464601	−	0.226791i
$741$	−1.39578e6	+	4.29578e6i	−0.0933839	+	0.287406i
$742$	−3.42412e6	−	2.48777e6i	−0.228318	−	0.165883i
$743$	2.25209e6			0.149663			0.0748313	−	0.997196i	$-0.476158\pi$
$743$	2.25209e6			0.149663			0.0748313	+	0.997196i	$0.476158\pi$
$744$	575609.	+	418205.i	0.0381237	+	0.0276985i
$745$	−1.27885e7	+	1.32341e7i	−0.844166	+	0.873582i
$746$	7.80905e6	−	5.67361e6i	0.513749	−	0.373261i
$747$	333238.	−	242112.i	0.0218501	−	0.0158750i
$748$	−733229.	−	2.25665e6i	−0.0479166	−	0.147472i
$749$	−3.44193e6			−0.224180
$750$	1.30145e6	+	6.15281e6i	0.0844837	+	0.399411i
$751$	−1.22728e7			−0.794043			−0.397022	−	0.917809i	$-0.629956\pi$
$751$	−1.22728e7			−0.794043			−0.397022	+	0.917809i	$0.629956\pi$
$752$	−10653.4	−	32787.7i	−0.000686977	−	0.00211430i
$753$	−1.04114e7	+	7.56432e6i	−0.669147	+	0.486163i
$754$	−4.17414e6	+	3.03269e6i	−0.267386	+	0.194268i
$755$	−2.02980e6	+	2.10053e6i	−0.129594	+	0.134110i
$756$	350094.	+	254358.i	0.0222782	+	0.0161861i
$757$	2.22685e7			1.41238			0.706189	−	0.708023i	$-0.250413\pi$
$757$	2.22685e7			1.41238			0.706189	+	0.708023i	$0.250413\pi$
$758$	1.71579e7	+	1.24659e7i	1.08465	+	0.788047i
$759$	2.15418e6	−	6.62988e6i	0.135730	−	0.417735i
$760$	−7.69903e6	−	3.75822e6i	−0.483506	−	0.236019i
$761$	−1.22976e6	−	3.78482e6i	−0.0769767	−	0.236910i	0.905162	−	0.425066i	$-0.139749\pi$
$761$	−1.22976e6	−	3.78482e6i	−0.0769767	−	0.236910i	−0.982139	+	0.188156i	$0.939749\pi$
$762$	−952116.	+	2.93031e6i	−0.0594022	+	0.182821i
$763$	1.03028e6	−	3.17088e6i	0.0640684	−	0.197182i
$764$	1.45069e6	+	4.46478e6i	0.0899172	+	0.276737i
$765$	318852.	−	2.26332e6i	0.0196986	−	0.139828i
$766$	−4.25334e6	+	1.30904e7i	−0.261914	+	0.806088i
$767$	201341.	+	146283.i	0.0123579	+	0.00897851i
$768$	589824.			0.0360844
$769$	1.59622e7	+	1.15972e7i	0.973369	+	0.707194i	0.956217	−	0.292659i	$-0.0945399\pi$
$769$	1.59622e7	+	1.15972e7i	0.973369	+	0.707194i	0.0171525	+	0.999853i	$0.494540\pi$
$770$	339995.	−	2.41340e6i	0.0206655	−	0.146691i
$771$	−2.86419e6	+	2.08095e6i	−0.173526	+	0.126074i
$772$	1.03856e7	−	7.54556e6i	0.627173	−	0.455668i
$773$	−8.70403e6	−	2.67883e7i	−0.523928	−	1.61249i	−0.766425	−	0.642333i	$-0.777966\pi$
$773$	−8.70403e6	−	2.67883e7i	−0.523928	−	1.61249i	0.242497	−	0.970152i	$-0.422034\pi$
$774$	−847658.			−0.0508591
$775$	2.16065e6	−	3.19874e6i	0.129220	−	0.191304i
$776$	−2.79887e6			−0.166851
$777$	888440.	+	2.73434e6i	0.0527929	+	0.162480i
$778$	−6.34188e6	+	4.60765e6i	−0.375638	+	0.272917i
$779$	−2.73501e7	+	1.98710e7i	−1.61479	+	1.17321i
$780$	−1.66156e6	+	292412.i	−0.0977867	+	0.0172091i
$781$	1.87431e7	+	1.36177e7i	1.09955	+	0.798868i
$782$	−5.32338e6			−0.311294
$783$	−3.62980e6	−	2.63721e6i	−0.211582	−	0.153723i
$784$	−1.22069e6	+	3.75688e6i	−0.0709274	+	0.218292i
$785$	−1.29957e6	+	1.34485e6i	−0.0752706	+	0.0778935i
$786$	794357.	+	2.44478e6i	0.0458626	+	0.141151i
$787$	1.43202e6	−	4.40730e6i	0.0824160	−	0.253650i	−0.901354	−	0.433082i	$-0.857426\pi$
$787$	1.43202e6	−	4.40730e6i	0.0824160	−	0.253650i	0.983770	+	0.179432i	$0.0574260\pi$
$788$	−362066.	+	1.11432e6i	−0.0207717	+	0.0639287i
$789$	1.52443e6	+	4.69172e6i	0.0871798	+	0.268312i
$790$	−1.69401e7	+	2.98122e6i	−0.965711	+	0.169952i
$791$	−2.41464e6	+	7.43151e6i	−0.137218	+	0.422314i
$792$	−1.23213e6	−	895194.i	−0.0697980	−	0.0507112i
$793$	4.74863e6			0.268154
$794$	−1.56633e7	−	1.13801e7i	−0.881723	−	0.640609i
$795$	6.73224e6	+	1.26716e7i	0.377782	+	0.711072i
$796$	1.04502e7	−	7.59252e6i	0.584578	−	0.424721i
$797$	1.16185e7	−	8.44131e6i	0.647892	−	0.470721i	−0.214660	−	0.976689i	$-0.568864\pi$
$797$	1.16185e7	−	8.44131e6i	0.647892	−	0.470721i	0.862553	+	0.505967i	$0.168864\pi$
$798$	988337.	+	3.04179e6i	0.0549411	+	0.169091i
$799$	67978.0			0.00376705
$800$	−109565.	−	3.19812e6i	−0.00605266	−	0.176673i
$801$	6.72766e6			0.370495
$802$	−4.17824e6	−	1.28593e7i	−0.229381	−	0.705963i
$803$	−8.08096e6	+	5.87116e6i	−0.442257	+	0.321318i
$804$	6.72149e6	−	4.88345e6i	0.366712	−	0.266432i
$805$	−4.91380e6	−	2.39863e6i	−0.267256	−	0.130459i
$806$	837756.	+	608665.i	0.0454234	+	0.0330020i
$807$	1.39366e7			0.753308
$808$	323881.	+	235313.i	0.0174525	+	0.0126800i
$809$	299342.	−	921279.i	0.0160804	−	0.0494903i	−0.942694	−	0.333658i	$-0.891717\pi$
$809$	299342.	−	921279.i	0.0160804	−	0.0494903i	0.958775	+	0.284167i	$0.0917171\pi$
$810$	−688326.	−	1.29559e6i	−0.0368622	−	0.0693831i
$811$	−4.97707e6	−	1.53179e7i	−0.265719	−	0.817798i	−0.991527	−	0.129901i	$-0.958534\pi$
$811$	−4.97707e6	−	1.53179e7i	−0.265719	−	0.817798i	0.725808	−	0.687897i	$-0.241466\pi$
$812$	−1.12896e6	+	3.47459e6i	−0.0600882	+	0.184933i
$813$	−1.93823e6	+	5.96525e6i	−0.102844	+	0.316521i
$814$	−3.12680e6	−	9.62329e6i	−0.165401	−	0.509053i
$815$	7.14333e6	+	1.34454e7i	0.376709	+	0.709053i
$816$	−359392.	+	1.10610e6i	−0.0188949	+	0.0581524i
$817$	−5.06844e6	−	3.68244e6i	−0.265656	−	0.193010i
$818$	−1.25024e7			−0.653294
$819$	509535.	+	370199.i	0.0265439	+	0.0192852i
$820$	−1.13474e7	−	5.53913e6i	−0.589334	−	0.287678i
$821$	2.43919e7	−	1.77217e7i	1.26295	−	0.917589i	0.264055	−	0.964508i	$-0.414940\pi$
$821$	2.43919e7	−	1.77217e7i	1.26295	−	0.917589i	0.998899	+	0.0469183i	$0.0149400\pi$
$822$	−6.49319e6	+	4.71758e6i	−0.335180	+	0.243523i
$823$	2.40677e6	+	7.40728e6i	0.123861	+	0.381206i	0.993692	−	0.112145i	$-0.0357720\pi$
$823$	2.40677e6	+	7.40728e6i	0.123861	+	0.381206i	−0.869831	+	0.493350i	$0.835772\pi$
$824$	−4.72380e6			−0.242367
$825$	−4.62501e6	+	6.84710e6i	−0.236580	+	0.350245i
$826$	176222.			0.00898692
$827$	2.57356e6	+	7.92060e6i	0.130849	+	0.402712i	0.994921	−	0.100656i	$-0.0320942\pi$
$827$	2.57356e6	+	7.92060e6i	0.130849	+	0.402712i	−0.864072	+	0.503368i	$0.832094\pi$
$828$	−2.76431e6	+	2.00839e6i	−0.140123	+	0.101805i
$829$	2.15926e7	−	1.56880e7i	1.09124	−	0.792830i	0.111630	−	0.993750i	$-0.464393\pi$
$829$	2.15926e7	−	1.56880e7i	1.09124	−	0.792830i	0.979608	+	0.200920i	$0.0643930\pi$
$830$	533502.	+	1.00417e6i	0.0268807	+	0.0505956i
$831$	1.33977e7	+	9.73397e6i	0.673018	+	0.488976i
$832$	858444.			0.0429936
$833$	−6.30149e6	−	4.57830e6i	−0.314652	−	0.228608i
$834$	−34758.3	+	106975.i	−0.00173039	+	0.00532558i
$835$	−3.40758e6	+	599688.i	−0.169134	+	0.0297652i
$836$	−3.47838e6	−	1.07053e7i	−0.172132	−	0.529767i
$837$	−278264.	+	856410.i	−0.0137292	+	0.0422540i
$838$	2.69361e6	−	8.29009e6i	0.132503	−	0.407802i
$839$	−1.58344e6	−	4.87333e6i	−0.0776600	−	0.239013i	0.904688	−	0.426074i	$-0.140104\pi$
$839$	−1.58344e6	−	4.87333e6i	−0.0776600	−	0.239013i	−0.982348	+	0.187061i	$0.940104\pi$
$840$	−830131.	+	859057.i	−0.0405927	+	0.0420072i
$841$	5.36689e6	−	1.65176e7i	0.261657	−	0.805298i
$842$	−4.97099e6	−	3.61164e6i	−0.241637	−	0.175559i
$843$	−1.48668e7			−0.720523
$844$	−6.37562e6	−	4.63216e6i	−0.308082	−	0.223835i
$845$	1.80235e7	−	3.17189e6i	0.868355	−	0.152819i
$846$	35299.4	−	25646.5i	0.00169567	−	0.00123198i
$847$	−2.24331e6	+	1.62986e6i	−0.107444	+	0.0780624i
$848$	−2.25619e6	−	6.94383e6i	−0.107742	−	0.331596i
$849$	1.90179e7			0.905508
$850$	6.06420e6	+	1.74322e6i	0.287890	+	0.0827569i
$851$	−2.27011e7			−1.07454
$852$	−3.50910e6	−	1.07999e7i	−0.165614	−	0.509706i
$853$	2.87076e7	−	2.08573e7i	1.35090	−	0.981488i	0.351936	−	0.936024i	$-0.385523\pi$
$853$	2.87076e7	−	2.08573e7i	1.35090	−	0.981488i	0.998966	−	0.0454642i	$-0.0144767\pi$
$854$	2.72028e6	−	1.97640e6i	0.127635	−	0.0927319i
$855$	1.51261e6	−	1.07370e7i	0.0707637	−	0.502306i
$856$	−4.80352e6	−	3.48996e6i	−0.224066	−	0.162793i
$857$	1.04455e7			0.485824			0.242912	−	0.970048i	$-0.421897\pi$
$857$	1.04455e7			0.485824			0.242912	+	0.970048i	$0.421897\pi$
$858$	−1.79327e6	−	1.30289e6i	−0.0831625	−	0.0604211i
$859$	1.27037e7	−	3.90980e7i	0.587418	−	1.80789i	−0.00191600	−	0.999998i	$-0.500610\pi$
$859$	1.27037e7	−	3.90980e7i	0.587418	−	1.80789i	0.589334	−	0.807889i	$-0.299390\pi$
$860$	326434.	−	2.31715e6i	0.0150505	−	0.106833i
$861$	1.45668e6	+	4.48321e6i	0.0669664	+	0.206101i
$862$	2.83184e6	−	8.71551e6i	0.129808	−	0.399507i
$863$	−4.25210e6	+	1.30866e7i	−0.194346	+	0.598137i	0.805637	+	0.592409i	$0.201823\pi$
$863$	−4.25210e6	+	1.30866e7i	−0.194346	+	0.598137i	−0.999984	+	0.00572761i	$0.998177\pi$
$864$	230680.	+	709960.i	0.0105130	+	0.0323556i
$865$	−6.77776e6	−	3.30851e6i	−0.307997	−	0.150346i
$866$	−5.35110e6	+	1.64690e7i	−0.242465	+	0.746229i
$867$	8.48292e6	+	6.16320e6i	0.383264	+	0.278457i
$868$	733241.			0.0330330
$869$	−1.82829e7	−	1.32833e7i	−0.821287	−	0.596700i
$870$	8.60687e6	−	8.90678e6i	0.385520	−	0.398954i
$871$	9.78262e6	−	7.10749e6i	0.436928	−	0.317447i
$872$	4.65298e6	−	3.38059e6i	0.207224	−	0.150557i
$873$	−1.09464e6	−	3.36894e6i	−0.0486109	−	0.149609i
$874$	−2.52537e7			−1.11827
$875$	4.81216e6	+	4.34153e6i	0.212481	+	0.191700i
$876$	4.89592e6			0.215563
$877$	−1.15230e7	−	3.54643e7i	−0.505904	−	1.55701i	−0.799246	−	0.601004i	$-0.794767\pi$
$877$	−1.15230e7	−	3.54643e7i	−0.505904	−	1.55701i	0.293342	−	0.956008i	$-0.405233\pi$
$878$	6.37323e6	−	4.63042e6i	0.279012	−	0.202714i
$879$	−6.25078e6	+	4.54146e6i	−0.272874	+	0.198254i
$880$	2.92158e6	−	3.02339e6i	0.127178	−	0.131609i
$881$	3.12357e7	+	2.26941e7i	1.35585	+	0.985082i	0.998697	+	0.0510365i	$0.0162525\pi$
$881$	3.12357e7	+	2.26941e7i	1.35585	+	0.985082i	0.357153	+	0.934046i	$0.383748\pi$
$882$	−4.99950e6			−0.216399
$883$	−3.21805e7	−	2.33805e7i	−1.38896	−	1.00914i	−0.995978	−	0.0895969i	$-0.971442\pi$
$883$	−3.21805e7	−	2.33805e7i	−1.38896	−	1.00914i	−0.392986	−	0.919545i	$-0.628558\pi$
$884$	−523068.	+	1.60984e6i	−0.0225127	+	0.0692870i
$885$	−536883.	−	262075.i	−0.0230421	−	0.0112478i
$886$	14542.2	+	44756.2i	0.000622364	+	0.00191544i
$887$	−894136.	+	2.75187e6i	−0.0381588	+	0.117441i	−0.968321	−	0.249707i	$-0.919666\pi$
$887$	−894136.	+	2.75187e6i	−0.0381588	+	0.117441i	0.930163	+	0.367148i	$0.119666\pi$
$888$	−1.53260e6	+	4.71686e6i	−0.0652223	+	0.200734i
$889$	981220.	+	3.01989e6i	0.0416401	+	0.128155i
$890$	−2.59083e6	+	1.83906e7i	−0.109639	+	0.778254i
$891$	595643.	−	1.83320e6i	0.0251357	−	0.0773598i
$892$	−3.19390e6	−	2.32051e6i	−0.134403	−	0.0976496i
$893$	322482.			0.0135325
$894$	9.58813e6	+	6.96618e6i	0.401227	+	0.291508i
$895$	−1.86790e6	+	1.32590e7i	−0.0779464	+	0.553291i
$896$	491764.	−	357288.i	0.0204638	−	0.0148678i
$897$	−4.02324e6	+	2.92305e6i	−0.166953	+	0.121298i
$898$	−6.02788e6	−	1.85519e7i	−0.249444	−	0.767711i
$899$	−7.60231e6			−0.313723
$900$	3.80667e6	−	1.38267e6i	0.156653	−	0.0568998i
$901$	1.43965e7			0.590806
$902$	−5.12668e6	−	1.57783e7i	−0.209807	−	0.645720i
$903$	−706733.	+	513471.i	−0.0288427	+	0.0209554i
$904$	−1.09051e7	+	7.92301e6i	−0.443821	+	0.322455i
$905$	3.04065e7	−	5.35112e6i	1.23408	−	0.217182i
$906$	1.52184e6	+	1.10568e6i	0.0615953	+	0.0447516i
$907$	4.64645e7			1.87544			0.937721	−	0.347390i	$-0.112932\pi$
$907$	4.64645e7			1.87544			0.937721	+	0.347390i	$0.112932\pi$
$908$	1.62395e7	+	1.17987e7i	0.653670	+	0.474919i
$909$	−156572.	+	481880.i	−0.00628500	+	0.0193432i
$910$	−1.20819e6	+	1.25029e6i	−0.0483651	+	0.0500505i
$911$	−4.15959e6	−	1.28019e7i	−0.166056	−	0.511068i	0.833057	−	0.553188i	$-0.186589\pi$
$911$	−4.15959e6	−	1.28019e7i	−0.166056	−	0.511068i	−0.999113	+	0.0421202i	$0.986589\pi$
$912$	−1.70493e6	+	5.24722e6i	−0.0678764	+	0.208902i
$913$	−461666.	+	1.42086e6i	−0.0183295	+	0.0564124i
$914$	1.89375e6	+	5.82837e6i	0.0749821	+	0.230771i
$915$	−1.12269e7	+	1.97578e6i	−0.443310	+	0.0780165i
$916$	3.48498e6	−	1.07257e7i	0.137234	−	0.422363i
$917$	2.14322e6	+	1.55714e6i	0.0841674	+	0.0611512i
$918$	−1.47194e6			−0.0576481
$919$	1.42753e7	+	1.03716e7i	0.557568	+	0.405097i	0.830568	−	0.556917i	$-0.188016\pi$
$919$	1.42753e7	+	1.03716e7i	0.557568	+	0.405097i	−0.273000	+	0.962014i	$0.588016\pi$
$920$	−4.42555e6	−	8.32990e6i	−0.172384	−	0.324467i
$921$	7.86804e6	−	5.71646e6i	0.305645	−	0.222064i
$922$	1.59108e7	−	1.15599e7i	0.616404	−	0.447844i
$923$	−5.10722e6	−	1.57184e7i	−0.197324	−	0.607301i
$924$	−1.56955e6			−0.0604777
$925$	2.58603e7	+	7.43381e6i	0.993754	+	0.285665i
$926$	−2.15049e7			−0.824156
$927$	−1.84748e6	−	5.68595e6i	−0.0706122	−	0.217322i
$928$	−5.09865e6	+	3.70439e6i	−0.194350	+	0.141204i
$929$	−1.83060e7	+	1.33001e7i	−0.695913	+	0.505610i	−0.878598	−	0.477561i	$-0.841521\pi$
$929$	−1.83060e7	+	1.33001e7i	−0.695913	+	0.505610i	0.182686	+	0.983171i	$0.441521\pi$
$930$	−2.23391e6	−	1.09046e6i	−0.0846951	−	0.0413432i
$931$	−2.98937e7	−	2.17191e7i	−1.13033	−	0.821234i
$932$	1.10381e7			0.416251
$933$	5.11245e6	+	3.71441e6i	0.192276	+	0.139697i
$934$	−6.09933e6	+	1.87718e7i	−0.228778	+	0.704108i
$935$	3.88957e6	+	7.32105e6i	0.145503	+	0.273870i
$936$	335737.	+	1.03329e6i	0.0125259	+	0.0385508i
$937$	4.92868e6	−	1.51689e7i	0.183392	−	0.564424i	−0.816525	−	0.577311i	$-0.804102\pi$
$937$	4.92868e6	−	1.51689e7i	0.183392	−	0.564424i	0.999917	+	0.0128870i	$0.00410217\pi$
$938$	2.64586e6	−	8.14313e6i	0.0981884	−	0.302193i
$939$	−3.81101e6	−	1.17291e7i	−0.141051	−	0.434110i
$940$	56513.0	+	106370.i	0.00208607	+	0.00392646i
$941$	1.37333e7	−	4.22667e7i	0.505592	−	1.55605i	−0.294181	−	0.955750i	$-0.595047\pi$
$941$	1.37333e7	−	4.22667e7i	0.505592	−	1.55605i	0.799773	−	0.600303i	$-0.204953\pi$
$942$	974350.	+	707907.i	0.0357757	+	0.0259925i
$943$	−3.72207e7			−1.36303
$944$	245934.	+	178682.i	0.00898234	+	0.00652605i
$945$	−1.35869e6	−	663236.i	−0.0494928	−	0.0241595i
$946$	2.48729e6	−	1.80712e6i	0.0903648	−	0.0656538i
$947$	−4.27775e7	+	3.10797e7i	−1.55003	+	1.12616i	−0.606405	+	0.795156i	$0.707389\pi$
$947$	−4.27775e7	+	3.10797e7i	−1.55003	+	1.12616i	−0.943628	+	0.331009i	$0.892611\pi$
$948$	3.42293e6	+	1.05347e7i	0.123702	+	0.380716i
$949$	7.12564e6			0.256838
$950$	2.87680e7	+	8.26968e6i	1.03419	+	0.297289i
$951$	1.78522e7			0.640089
$952$	370378.	+	1.13991e6i	0.0132450	+	0.0407640i
$953$	3.24636e6	−	2.35862e6i	0.115788	−	0.0841250i	−0.528384	−	0.849005i	$-0.677202\pi$
$953$	3.24636e6	−	2.35862e6i	0.115788	−	0.0841250i	0.644172	+	0.764880i	$0.277202\pi$
$954$	7.47576e6	−	5.43146e6i	0.265940	−	0.193217i
$955$	−7.69552e6	−	1.44847e7i	−0.273042	−	0.513927i
$956$	−6.75116e6	−	4.90501e6i	−0.238910	−	0.173578i
$957$	1.62732e7			0.574373
$958$	−2.36498e7	−	1.71826e7i	−0.832558	−	0.604889i
$959$	−2.55599e6	+	7.86653e6i	−0.0897455	+	0.276208i
$960$	−2.02957e6	+	357177.i	−0.0710765	+	0.0125085i
$961$	−8.37540e6	−	2.57768e7i	−0.292548	−	0.900370i
$962$	−2.23058e6	+	6.86503e6i	−0.0777107	+	0.239169i
$963$	2.32215e6	−	7.14683e6i	0.0806908	−	0.248341i
$964$	2.09580e6	+	6.45021e6i	0.0726369	+	0.223553i
$965$	−3.11672e7	+	3.22532e7i	−1.07741	+	1.11495i
$966$	−1.08815e6	+	3.34897e6i	−0.0375184	+	0.115470i
$967$	−1.82555e7	−	1.32634e7i	−0.627808	−	0.456129i	0.227832	−	0.973700i	$-0.426836\pi$
$967$	−1.82555e7	−	1.32634e7i	−0.627808	−	0.456129i	−0.855640	+	0.517571i	$0.826836\pi$
$968$	−4.78335e6			−0.164076
$969$	−8.80126e6	−	6.39449e6i	−0.301117	−	0.218774i
$970$	9.63083e6	−	1.69489e6i	0.328651	−	0.0578380i
$971$	3.90894e7	−	2.84001e7i	1.33049	−	0.966656i	0.330751	−	0.943718i	$-0.392698\pi$
$971$	3.90894e7	−	2.84001e7i	1.33049	−	0.966656i	0.999737	−	0.0229378i	$-0.00730196\pi$
$972$	−764346.	+	555330.i	−0.0259492	+	0.0188532i
$973$	35820.7	+	110245.i	0.00121298	+	0.00373316i
$974$	−1.43596e7			−0.485005
$975$	5.54032e6	−	2.01237e6i	0.186648	−	0.0677946i
$976$	5.80037e6			0.194909
$977$	7.07831e6	+	2.17848e7i	0.237243	+	0.730159i	0.996816	+	0.0797366i	$0.0254079\pi$
$977$	7.07831e6	+	2.17848e7i	0.237243	+	0.730159i	−0.759573	+	0.650422i	$0.774592\pi$
$978$	7.93225e6	−	5.76312e6i	0.265185	−	0.192668i
$979$	−1.97410e7	+	1.43427e7i	−0.658284	+	0.478271i
$980$	1.92531e6	−	1.36666e7i	0.0640378	−	0.454563i
$981$	5.88893e6	+	4.27856e6i	0.195373	+	0.141947i
$982$	2.57468e7			0.852011
$983$	−4.62999e7	−	3.36388e7i	−1.52826	−	1.11034i	−0.957198	−	0.289433i	$-0.906533\pi$
$983$	−4.62999e7	−	3.36388e7i	−1.52826	−	1.11034i	−0.571058	−	0.820910i	$-0.693467\pi$
$984$	−2.51284e6	+	7.73374e6i	−0.0827328	+	0.254625i
$985$	571065.	−	4.05362e6i	0.0187540	−	0.133123i
$986$	−3.84012e6	−	1.18187e7i	−0.125792	−	0.387147i
$987$	13895.3	−	42765.4i	0.000454021	−	0.00139733i
$988$	−2.48139e6	+	7.63693e6i	−0.0808728	+	0.248901i
$989$	−2.13148e6	−	6.56003e6i	−0.0692932	−	0.213263i
$990$	4.78182e6	+	2.33421e6i	0.155062	+	0.0756923i
$991$	−1.25919e7	+	3.87538e7i	−0.407292	+	1.25352i	0.511674	+	0.859180i	$0.329026\pi$
$991$	−1.25919e7	+	3.87538e7i	−0.407292	+	1.25352i	−0.918966	+	0.394337i	$0.870974\pi$
$992$	1.02331e6	+	743475.i	0.0330161	+	0.0239876i
$993$	−2.90328e7			−0.934362
$994$	−9.46776e6	−	6.87873e6i	−0.303935	−	0.220822i
$995$	−3.13612e7	+	3.24540e7i	−1.00423	+	1.03923i
$996$	592423.	−	430421.i	0.0189227	−	0.0137482i
$997$	−3.71372e7	+	2.69817e7i	−1.18323	+	0.859670i	−0.992533	−	0.121978i	$-0.961076\pi$
$997$	−3.71372e7	+	2.69817e7i	−1.18323	+	0.859670i	−0.190701	+	0.981648i	$0.561076\pi$
$998$	1.24401e7	+	3.82866e7i	0.395363	+	1.21680i
$999$	−6.27699e6			−0.198993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.b.31.5	✓	24
25.21	even	5	inner	150.6.g.b.121.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.b.31.5	✓	24	1.1	even	1	trivial
150.6.g.b.121.5	yes	24	25.21	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)

\(f(q)\)	\(=\)	\(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(38.8459 - 40.1995i) q^{5} +(-29.1246 - 21.1603i) q^{6} -37.1005 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(38.8459 - 40.1995i) q^{5} +(-29.1246 - 21.1603i) q^{6} -37.1005 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(200.944 + 98.0892i) q^{10} +(90.7854 + 279.409i) q^{11} +(44.4984 - 136.952i) q^{12} +(64.7641 - 199.323i) q^{13} +(-45.8587 - 141.139i) q^{14} +(-70.1847 + 498.196i) q^{15} +(79.1084 - 243.470i) q^{16} +(408.377 + 296.704i) q^{17} +324.000 q^{18} +(1937.31 + 1407.54i) q^{19} +(-124.773 + 885.682i) q^{20} +(270.134 - 196.264i) q^{21} +(-950.717 + 690.736i) q^{22} +(814.715 + 2507.44i) q^{23} +576.000 q^{24} +(-106.997 - 3123.17i) q^{25} +838.324 q^{26} +(225.273 + 693.320i) q^{27} +(480.238 - 348.914i) q^{28} +(-4979.15 + 3617.57i) q^{29} +(-1982.00 + 348.805i) q^{30} +(999.322 + 726.050i) q^{31} +1024.00 q^{32} +(-2139.11 - 1554.16i) q^{33} +(-623.945 + 1920.31i) q^{34} +(-1441.20 + 1491.42i) q^{35} +(400.486 + 1232.57i) q^{36} +(-2660.76 + 8188.99i) q^{37} +(-2959.94 + 9109.76i) q^{38} +(582.877 + 1793.91i) q^{39} +(-3523.56 + 620.098i) q^{40} +(-4362.58 + 13426.6i) q^{41} +(1080.54 + 785.056i) q^{42} -2616.23 q^{43} +(-3802.87 - 2762.94i) q^{44} +(-2124.46 - 3998.72i) q^{45} +(-8531.81 + 6198.72i) q^{46} +(108.949 - 79.1559i) q^{47} +(711.975 + 2191.23i) q^{48} -15430.6 q^{49} +(11749.0 - 4267.49i) q^{50} -4543.04 q^{51} +(1036.23 + 3189.17i) q^{52} +(23073.3 - 16763.8i) q^{53} +(-2359.09 + 1713.98i) q^{54} +(14758.7 + 7204.34i) q^{55} +(1920.95 + 1395.65i) q^{56} -21551.8 q^{57} +(-19916.6 - 14470.3i) q^{58} +(-366.948 + 1129.35i) q^{59} +(-3776.82 - 7108.84i) q^{60} +(7001.62 + 21548.8i) q^{61} +(-1526.83 + 4699.09i) q^{62} +(-928.638 + 2858.05i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-5496.88 - 10346.4i) q^{65} +(3268.27 - 10058.7i) q^{66} +(46677.0 + 33912.9i) q^{67} -8076.52 q^{68} +(-19196.6 - 13947.1i) q^{69} +(-7455.12 - 3639.15i) q^{70} +(63798.1 - 46352.1i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(10506.4 + 32335.4i) q^{73} -34441.6 q^{74} +(17300.8 + 22174.2i) q^{75} -38314.3 q^{76} +(-3368.18 - 10366.2i) q^{77} +(-6103.97 + 4434.79i) q^{78} +(-62231.6 + 45213.9i) q^{79} +(-6714.35 - 12637.9i) q^{80} +(-5307.96 - 3856.46i) q^{81} -56470.4 q^{82} +(4114.05 + 2989.03i) q^{83} +(-1650.91 + 5080.99i) q^{84} +(27791.1 - 4890.85i) q^{85} +(-3233.84 - 9952.73i) q^{86} +(17116.8 - 52680.1i) q^{87} +(5810.26 - 17882.1i) q^{88} +(25666.2 + 78992.4i) q^{89} +(12586.1 - 13024.6i) q^{90} +(-2402.78 + 7394.99i) q^{91} +(-34127.2 - 24794.9i) q^{92} -11117.1 q^{93} +(435.795 + 316.623i) q^{94} +(131839. - 23201.8i) q^{95} +(-7455.90 + 5417.03i) q^{96} +(35380.2 - 25705.2i) q^{97} +(-19073.2 - 58701.3i) q^{98} +23796.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Introduction

L-functions

Modular forms

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