LMFDB - Embedded newform 354.6.c.b.353.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, 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:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.16
Character	$\chi$	$=$	354.353
Dual form			354.6.c.b.353.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +(-9.75722 + 12.1572i) q^{3} +16.0000 q^{4} -43.2791i q^{5} +(-39.0289 + 48.6287i) q^{6} -5.13563 q^{7} +64.0000 q^{8} +(-52.5934 - 237.240i) q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +(-9.75722 + 12.1572i) q^{3} +16.0000 q^{4} -43.2791i q^{5} +(-39.0289 + 48.6287i) q^{6} -5.13563 q^{7} +64.0000 q^{8} +(-52.5934 - 237.240i) q^{9} -173.116i q^{10} -262.706 q^{11} +(-156.115 + 194.515i) q^{12} -296.127i q^{13} -20.5425 q^{14} +(526.151 + 422.283i) q^{15} +256.000 q^{16} +1334.77i q^{17} +(-210.374 - 948.961i) q^{18} -1340.55 q^{19} -692.465i q^{20} +(50.1095 - 62.4347i) q^{21} -1050.82 q^{22} +1858.55 q^{23} +(-624.462 + 778.059i) q^{24} +1251.92 q^{25} -1184.51i q^{26} +(3397.33 + 1675.42i) q^{27} -82.1701 q^{28} +1127.52i q^{29} +(2104.60 + 1689.13i) q^{30} +6100.77i q^{31} +1024.00 q^{32} +(2563.28 - 3193.76i) q^{33} +5339.10i q^{34} +222.265i q^{35} +(-841.494 - 3795.84i) q^{36} +6962.90i q^{37} -5362.21 q^{38} +(3600.06 + 2889.37i) q^{39} -2769.86i q^{40} -1648.54i q^{41} +(200.438 - 249.739i) q^{42} -1565.02i q^{43} -4203.29 q^{44} +(-10267.5 + 2276.19i) q^{45} +7434.22 q^{46} +13521.2 q^{47} +(-2497.85 + 3112.23i) q^{48} -16780.6 q^{49} +5007.69 q^{50} +(-16227.1 - 13023.7i) q^{51} -4738.02i q^{52} +12816.2i q^{53} +(13589.3 + 6701.67i) q^{54} +11369.7i q^{55} -328.680 q^{56} +(13080.1 - 16297.3i) q^{57} +4510.09i q^{58} +(-14183.6 + 22666.1i) q^{59} +(8418.41 + 6756.53i) q^{60} +50754.6i q^{61} +24403.1i q^{62} +(270.100 + 1218.38i) q^{63} +4096.00 q^{64} -12816.1 q^{65} +(10253.1 - 12775.0i) q^{66} -1305.77i q^{67} +21356.4i q^{68} +(-18134.3 + 22594.8i) q^{69} +889.061i q^{70} +17624.9i q^{71} +(-3365.98 - 15183.4i) q^{72} -16392.2i q^{73} +27851.6i q^{74} +(-12215.3 + 15219.8i) q^{75} -21448.8 q^{76} +1349.16 q^{77} +(14400.2 + 11557.5i) q^{78} +66615.5 q^{79} -11079.4i q^{80} +(-53516.9 + 24954.5i) q^{81} -6594.17i q^{82} -52720.6 q^{83} +(801.751 - 998.955i) q^{84} +57767.8 q^{85} -6260.06i q^{86} +(-13707.5 - 11001.5i) q^{87} -16813.2 q^{88} -89751.0 q^{89} +(-41070.1 + 9104.77i) q^{90} +1520.80i q^{91} +29736.9 q^{92} +(-74168.1 - 59526.5i) q^{93} +54085.0 q^{94} +58017.8i q^{95} +(-9991.39 + 12448.9i) q^{96} +24987.9i q^{97} -67122.5 q^{98} +(13816.6 + 62324.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 200 q^{2} - 13 q^{3} + 800 q^{4} - 52 q^{6} + 38 q^{7} + 3200 q^{8} + 51 q^{9}+O(q^{10}) $ 50 * q + 200 * q^2 - 13 * q^3 + 800 * q^4 - 52 * q^6 + 38 * q^7 + 3200 * q^8 + 51 * q^9	$ 50 q + 200 q^{2} - 13 q^{3} + 800 q^{4} - 52 q^{6} + 38 q^{7} + 3200 q^{8} + 51 q^{9} + 652 q^{11} - 208 q^{12} + 152 q^{14} - 2107 q^{15} + 12800 q^{16} + 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} - 2456 q^{23} - 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} - 8428 q^{30} + 51200 q^{32} + 9744 q^{33} + 816 q^{36} - 3576 q^{38} - 1388 q^{39} - 15204 q^{42} + 10432 q^{44} + 33067 q^{45} - 9824 q^{46} + 27144 q^{47} - 3328 q^{48} + 85768 q^{49} - 95824 q^{50} + 3338 q^{51} + 39560 q^{54} + 2432 q^{56} - 63969 q^{57} + 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} + 9400 q^{65} + 38976 q^{66} + 115930 q^{69} + 3264 q^{72} + 24248 q^{75} - 14304 q^{76} + 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} + 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} - 104908 q^{89} + 132268 q^{90} - 39296 q^{92} + 91204 q^{93} + 108576 q^{94} - 13312 q^{96} + 343072 q^{98} + 111406 q^{99}+O(q^{100}) $ 50 * q + 200 * q^2 - 13 * q^3 + 800 * q^4 - 52 * q^6 + 38 * q^7 + 3200 * q^8 + 51 * q^9 + 652 * q^11 - 208 * q^12 + 152 * q^14 - 2107 * q^15 + 12800 * q^16 + 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 - 2456 * q^23 - 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 - 8428 * q^30 + 51200 * q^32 + 9744 * q^33 + 816 * q^36 - 3576 * q^38 - 1388 * q^39 - 15204 * q^42 + 10432 * q^44 + 33067 * q^45 - 9824 * q^46 + 27144 * q^47 - 3328 * q^48 + 85768 * q^49 - 95824 * q^50 + 3338 * q^51 + 39560 * q^54 + 2432 * q^56 - 63969 * q^57 + 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 + 9400 * q^65 + 38976 * q^66 + 115930 * q^69 + 3264 * q^72 + 24248 * q^75 - 14304 * q^76 + 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 + 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 - 104908 * q^89 + 132268 * q^90 - 39296 * q^92 + 91204 * q^93 + 108576 * q^94 - 13312 * q^96 + 343072 * q^98 + 111406 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	4.00000			0.707107
$2$	4.00000			0.707107
$3$	−9.75722	+	12.1572i	−0.625926	+	0.779883i
$3$	−9.75722	+	12.1572i	−0.625926	+	0.779883i
$4$	16.0000			0.500000
$5$		−	43.2791i		−	0.774200i	−0.922038	−	0.387100i	$-0.873477\pi$
$5$		−	43.2791i		−	0.774200i	0.922038	−	0.387100i	$-0.126523\pi$
$6$	−39.0289	+	48.6287i	−0.442596	+	0.551460i
$7$	−5.13563			−0.0396140			−0.0198070	−	0.999804i	$-0.506305\pi$
$7$	−5.13563			−0.0396140			−0.0198070	+	0.999804i	$0.506305\pi$
$8$	64.0000			0.353553
$9$	−52.5934	−	237.240i	−0.216434	−	0.976297i
$10$		−	173.116i		−	0.547442i
$11$	−262.706			−0.654618			−0.327309	−	0.944917i	$-0.606142\pi$
$11$	−262.706			−0.654618			−0.327309	+	0.944917i	$0.606142\pi$
$12$	−156.115	+	194.515i	−0.312963	+	0.389941i
$13$		−	296.127i		−	0.485981i	−0.970029	−	0.242990i	$-0.921872\pi$
$13$		−	296.127i		−	0.485981i	0.970029	−	0.242990i	$-0.0781283\pi$
$14$	−20.5425			−0.0280113
$15$	526.151	+	422.283i	0.603785	+	0.484591i
$16$	256.000			0.250000
$17$			1334.77i			1.12017i	0.828434	+	0.560087i	$0.189232\pi$
$17$			1334.77i			1.12017i	−0.828434	+	0.560087i	$0.810768\pi$
$18$	−210.374	−	948.961i	−0.153042	−	0.690346i
$19$	−1340.55			−0.851922			−0.425961	−	0.904742i	$-0.640064\pi$
$19$	−1340.55			−0.851922			−0.425961	+	0.904742i	$0.640064\pi$
$20$		−	692.465i		−	0.387100i
$21$	50.1095	−	62.4347i	0.0247954	−	0.0308943i
$22$	−1050.82			−0.462885
$23$	1858.55			0.732581			0.366290	−	0.930501i	$-0.380628\pi$
$23$	1858.55			0.732581			0.366290	+	0.930501i	$0.380628\pi$
$24$	−624.462	+	778.059i	−0.221298	+	0.275730i
$25$	1251.92			0.400615
$26$		−	1184.51i		−	0.343640i
$27$	3397.33	+	1675.42i	0.896869	+	0.442297i
$28$	−82.1701			−0.0198070
$29$			1127.52i			0.248960i	0.992222	+	0.124480i	$0.0397263\pi$
$29$			1127.52i			0.248960i	−0.992222	+	0.124480i	$0.960274\pi$
$30$	2104.60	+	1689.13i	0.426940	+	0.342658i
$31$			6100.77i			1.14020i	0.821576	+	0.570099i	$0.193095\pi$
$31$			6100.77i			1.14020i	−0.821576	+	0.570099i	$0.806905\pi$
$32$	1024.00			0.176777
$33$	2563.28	−	3193.76i	0.409742	−	0.510525i
$34$			5339.10i			0.792083i
$35$			222.265i			0.0306691i
$36$	−841.494	−	3795.84i	−0.108217	−	0.488149i
$37$			6962.90i			0.836153i	0.908412	+	0.418077i	$0.137296\pi$
$37$			6962.90i			0.836153i	−0.908412	+	0.418077i	$0.862704\pi$
$38$	−5362.21			−0.602399
$39$	3600.06	+	2889.37i	0.379008	+	0.304188i
$40$		−	2769.86i		−	0.273721i
$41$		−	1648.54i		−	0.153158i	−0.997064	−	0.0765791i	$-0.975600\pi$
$41$		−	1648.54i		−	0.153158i	0.997064	−	0.0765791i	$-0.0243998\pi$
$42$	200.438	−	249.739i	0.0175330	−	0.0218455i
$43$		−	1565.02i		−	0.129077i	−0.997915	−	0.0645383i	$-0.979443\pi$
$43$		−	1565.02i		−	0.129077i	0.997915	−	0.0645383i	$-0.0205575\pi$
$44$	−4203.29			−0.327309
$45$	−10267.5	+	2276.19i	−0.755849	+	0.167563i
$46$	7434.22			0.518013
$47$	13521.2			0.892837			0.446418	−	0.894824i	$-0.352699\pi$
$47$	13521.2			0.892837			0.446418	+	0.894824i	$0.352699\pi$
$48$	−2497.85	+	3112.23i	−0.156481	+	0.194971i
$49$	−16780.6			−0.998431
$50$	5007.69			0.283278
$51$	−16227.1	−	13023.7i	−0.873605	−	0.701146i
$52$		−	4738.02i		−	0.242990i
$53$			12816.2i			0.626714i	0.949635	+	0.313357i	$0.101454\pi$
$53$			12816.2i			0.626714i	−0.949635	+	0.313357i	$0.898546\pi$
$54$	13589.3	+	6701.67i	0.634182	+	0.312751i
$55$			11369.7i			0.506805i
$56$	−328.680			−0.0140057
$57$	13080.1	−	16297.3i	0.533240	−	0.664399i
$58$			4510.09i			0.176042i
$59$	−14183.6	+	22666.1i	−0.530464	+	0.847707i
$59$	−14183.6	+	22666.1i	−0.530464	+	0.847707i
$60$	8418.41	+	6756.53i	0.301892	+	0.242296i
$61$			50754.6i			1.74643i	0.487336	+	0.873215i	$0.337969\pi$
$61$			50754.6i			1.74643i	−0.487336	+	0.873215i	$0.662031\pi$
$62$			24403.1i			0.806242i
$63$	270.100	+	1218.38i	0.00857381	+	0.0386750i
$64$	4096.00			0.125000
$65$	−12816.1			−0.376246
$66$	10253.1	−	12775.0i	0.289732	−	0.360996i
$67$		−	1305.77i		−	0.0355368i	−0.999842	−	0.0177684i	$-0.994344\pi$
$67$		−	1305.77i		−	0.0355368i	0.999842	−	0.0177684i	$-0.00565615\pi$
$68$			21356.4i			0.560087i
$69$	−18134.3	+	22594.8i	−0.458541	+	0.571327i
$70$			889.061i			0.0216864i
$71$			17624.9i			0.414936i	0.978242	+	0.207468i	$0.0665222\pi$
$71$			17624.9i			0.414936i	−0.978242	+	0.207468i	$0.933478\pi$
$72$	−3365.98	−	15183.4i	−0.0765209	−	0.345173i
$73$		−	16392.2i		−	0.360023i	−0.983664	−	0.180012i	$-0.942386\pi$
$73$		−	16392.2i		−	0.360023i	0.983664	−	0.180012i	$-0.0576135\pi$
$74$			27851.6i			0.591250i
$75$	−12215.3	+	15219.8i	−0.250755	+	0.312433i
$76$	−21448.8			−0.425961
$77$	1349.16			0.0259320
$78$	14400.2	+	11557.5i	0.267999	+	0.215093i
$79$	66615.5			1.20090			0.600451	−	0.799662i	$-0.294988\pi$
$79$	66615.5			1.20090			0.600451	+	0.799662i	$0.294988\pi$
$80$		−	11079.4i		−	0.193550i
$81$	−53516.9	+	24954.5i	−0.906313	+	0.422607i
$82$		−	6594.17i		−	0.108299i
$83$	−52720.6			−0.840011			−0.420005	−	0.907522i	$-0.637972\pi$
$83$	−52720.6			−0.840011			−0.420005	+	0.907522i	$0.637972\pi$
$84$	801.751	−	998.955i	0.0123977	−	0.0154471i
$85$	57767.8			0.867239
$86$		−	6260.06i		−	0.0912709i
$87$	−13707.5	−	11001.5i	−0.194160	−	0.155831i
$88$	−16813.2			−0.231442
$89$	−89751.0			−1.20106			−0.600529	−	0.799603i	$-0.705043\pi$
$89$	−89751.0			−1.20106			−0.600529	+	0.799603i	$0.705043\pi$
$90$	−41070.1	+	9104.77i	−0.534466	+	0.118485i
$91$			1520.80i			0.0192516i
$92$	29736.9			0.366290
$93$	−74168.1	−	59526.5i	−0.889221	−	0.713680i
$94$	54085.0			0.631331
$95$			58017.8i			0.659557i
$96$	−9991.39	+	12448.9i	−0.110649	+	0.137865i
$97$			24987.9i			0.269650i	0.990869	+	0.134825i	$0.0430473\pi$
$97$			24987.9i			0.269650i	−0.990869	+	0.134825i	$0.956953\pi$
$98$	−67122.5			−0.705997
$99$	13816.6	+	62324.4i	0.141681	+	0.639102i
$100$	20030.8			0.200308
$101$	−118534.			−1.15622			−0.578110	−	0.815959i	$-0.696210\pi$
$101$	−118534.			−1.15622			−0.578110	+	0.815959i	$0.696210\pi$
$102$	−64908.3	−	52094.8i	−0.617732	−	0.495785i
$103$			21499.7i			0.199682i	0.995003	+	0.0998409i	$0.0318334\pi$
$103$			21499.7i			0.199682i	−0.995003	+	0.0998409i	$0.968167\pi$
$104$		−	18952.1i		−	0.171820i
$105$	−2702.12	−	2168.69i	−0.0239183	−	0.0191966i
$106$			51264.8i			0.443154i
$107$			172067.i			1.45291i	0.687216	+	0.726453i	$0.258833\pi$
$107$			172067.i			1.45291i	−0.687216	+	0.726453i	$0.741167\pi$
$108$	54357.4	+	26806.7i	0.448434	+	0.221148i
$109$			220183.i			1.77508i	0.460733	+	0.887539i	$0.347587\pi$
$109$			220183.i			1.77508i	−0.460733	+	0.887539i	$0.652413\pi$
$110$			45478.7i			0.358365i
$111$	−84649.2	−	67938.6i	−0.652102	−	0.523370i
$112$	−1314.72			−0.00990350
$113$	−171524.			−1.26366			−0.631829	−	0.775108i	$-0.717695\pi$
$113$	−171524.			−1.26366			−0.631829	+	0.775108i	$0.717695\pi$
$114$	52320.2	−	65189.2i	0.377057	−	0.469801i
$115$		−	80436.5i		−	0.567164i
$116$			18040.4i			0.124480i
$117$	−70253.1	+	15574.3i	−0.474462	+	0.105183i
$118$	−56734.4	+	90664.2i	−0.375095	+	0.599420i
$119$		−	6854.91i		−	0.0443746i
$120$	33673.7	+	27026.1i	0.213470	+	0.171329i
$121$	−92036.7			−0.571475
$122$			203018.i			1.23491i
$123$	20041.6	+	16085.2i	0.119445	+	0.0958657i
$124$			97612.3i			0.570099i
$125$		−	189429.i		−	1.08436i
$126$	1080.40	+	4873.51i	0.00606260	+	0.0273474i
$127$	265527.			1.46083			0.730416	−	0.683003i	$-0.239326\pi$
$127$	265527.			1.46083			0.730416	+	0.683003i	$0.239326\pi$
$128$	16384.0			0.0883883
$129$	19026.2	+	15270.2i	0.100665	+	0.0807924i
$130$	−51264.3			−0.266046
$131$	−23529.0			−0.119791			−0.0598956	−	0.998205i	$-0.519077\pi$
$131$	−23529.0			−0.119791			−0.0598956	+	0.998205i	$0.519077\pi$
$132$	41012.4	−	51100.1i	0.204871	−	0.255263i
$133$	6884.58			0.0337480
$134$		−	5223.06i		−	0.0251283i
$135$	72510.5	−	147033.i	0.342426	−	0.694355i
$136$			85425.6i			0.396042i
$137$		−	232717.i		−	1.05932i	−0.848210	−	0.529660i	$-0.822319\pi$
$137$		−	232717.i		−	1.05932i	0.848210	−	0.529660i	$-0.177681\pi$
$138$	−72537.3	+	90379.0i	−0.324238	+	0.403989i
$139$	315311.			1.38421			0.692105	−	0.721797i	$-0.256683\pi$
$139$	315311.			1.38421			0.692105	+	0.721797i	$0.256683\pi$
$140$			3556.25i			0.0153346i
$141$	−131930.	+	164380.i	−0.558850	+	0.696308i
$142$			70499.6i			0.293404i
$143$			77794.2i			0.318132i
$144$	−13463.9	−	60733.5i	−0.0541084	−	0.244074i
$145$	48798.1			0.192745
$146$		−	65568.9i		−	0.254575i
$147$	163732.	−	204005.i	0.624944	−	0.778659i
$148$			111406.i			0.418077i
$149$	388721.			1.43441			0.717204	−	0.696863i	$-0.245421\pi$
$149$	388721.			1.43441			0.717204	+	0.696863i	$0.245421\pi$
$150$	−48861.1	+	60879.3i	−0.177311	+	0.220923i
$151$		−	1572.47i		−	0.00561230i	−0.999996	−	0.00280615i	$-0.999107\pi$
$151$		−	1572.47i		−	0.00561230i	0.999996	−	0.00280615i	$-0.000893227\pi$
$152$	−85795.3			−0.301200
$153$	316662.	−	70200.3i	1.09362	−	0.242444i
$154$	5396.64			0.0183367
$155$	264036.			0.882741
$156$	57601.0	+	46229.9i	0.189504	+	0.152094i
$157$		−	99590.7i		−	0.322455i	−0.986917	−	0.161228i	$-0.948455\pi$
$157$		−	99590.7i		−	0.322455i	0.986917	−	0.161228i	$-0.0515454\pi$
$158$	266462.			0.849166
$159$	−155809.	−	125050.i	−0.488764	−	0.392277i
$160$		−	44317.8i		−	0.136860i
$161$	−9544.85			−0.0290205
$162$	−214067.	+	99818.2i	−0.640860	+	0.298829i
$163$	580713.			1.71196			0.855978	−	0.517012i	$-0.172956\pi$
$163$	580713.			1.71196			0.855978	+	0.517012i	$0.172956\pi$
$164$		−	26376.7i		−	0.0765791i
$165$	−138223.	−	110936.i	−0.395248	−	0.317222i
$166$	−210882.			−0.593977
$167$			101767.i			0.282367i	0.989983	+	0.141184i	$0.0450908\pi$
$167$			101767.i			0.282367i	−0.989983	+	0.141184i	$0.954909\pi$
$168$	3207.01	−	3995.82i	0.00876651	−	0.0109228i
$169$	283602.			0.763823
$170$	231071.			0.613230
$171$	70504.2	+	318033.i	0.184385	+	0.831729i
$172$		−	25040.2i		−	0.0645383i
$173$	−64078.2			−0.162778			−0.0813888	−	0.996682i	$-0.525936\pi$
$173$	−64078.2			−0.162778			−0.0813888	+	0.996682i	$0.525936\pi$
$174$	−54829.9	−	44005.9i	−0.137292	−	0.110189i
$175$	−6429.41			−0.0158700
$176$	−67252.7			−0.163655
$177$	−137163.	−	393590.i	−0.329081	−	0.944302i
$178$	−359004.			−0.849276
$179$	−412538.			−0.962347			−0.481173	−	0.876625i	$-0.659789\pi$
$179$	−412538.			−0.962347			−0.481173	+	0.876625i	$0.659789\pi$
$180$	−164281.	+	36419.1i	−0.377924	+	0.0837815i
$181$	37016.7			0.0839850			0.0419925	−	0.999118i	$-0.486629\pi$
$181$	37016.7			0.0839850			0.0419925	+	0.999118i	$0.486629\pi$
$182$			6083.19i			0.0136130i
$183$	−617032.	−	495224.i	−1.36201	−	1.09314i
$184$	118947.			0.259006
$185$	301348.			0.647350
$186$	−296672.	−	238106.i	−0.628774	−	0.504648i
$187$		−	350653.i		−	0.733286i
$188$	216340.			0.446418
$189$	−17447.5	−	8604.33i	−0.0355286	−	0.0175211i
$190$			232071.i			0.466377i
$191$	155943.			0.309301			0.154651	−	0.987969i	$-0.450575\pi$
$191$	155943.			0.309301			0.154651	+	0.987969i	$0.450575\pi$
$192$	−39965.6	+	49795.8i	−0.0782407	+	0.0974853i
$193$	−520302.			−1.00545			−0.502727	−	0.864445i	$-0.667670\pi$
$193$	−520302.			−1.00545			−0.502727	+	0.864445i	$0.667670\pi$
$194$			99951.7i			0.190671i
$195$	125049.	−	155807.i	0.235502	−	0.293428i
$196$	−268490.			−0.499215
$197$			264785.i			0.486103i	0.970013	+	0.243052i	$0.0781484\pi$
$197$			264785.i			0.486103i	−0.970013	+	0.243052i	$0.921852\pi$
$198$	55266.4	+	249298.i	0.100184	+	0.451913i
$199$	79805.9			0.142857			0.0714286	−	0.997446i	$-0.477244\pi$
$199$	79805.9			0.142857			0.0714286	+	0.997446i	$0.477244\pi$
$200$	80123.0			0.141639
$201$	15874.4	+	12740.6i	0.0277145	+	0.0222434i
$202$	−474137.			−0.817571
$203$		−	5790.54i		−	0.00986231i
$204$	−259633.	−	208379.i	−0.436802	−	0.350573i
$205$	−71347.4			−0.118575
$206$			85998.6i			0.141196i
$207$	−97747.7	−	440924.i	−0.158555	−	0.715217i
$208$		−	75808.4i		−	0.121495i
$209$	352171.			0.557683
$210$	−10808.5	−	8674.76i	−0.0169128	−	0.0135741i
$211$		−	115465.i		−	0.178543i	−0.996007	−	0.0892717i	$-0.971546\pi$
$211$		−	115465.i		−	0.178543i	0.996007	−	0.0892717i	$-0.0284540\pi$
$212$			205059.i			0.313357i
$213$	−214269.	−	171970.i	−0.323601	−	0.259719i
$214$			688267.i			1.02736i
$215$	−67732.4			−0.0999310
$216$	217429.	+	107227.i	0.317091	+	0.156376i
$217$		−	31331.3i		−	0.0451678i
$218$			880732.i			1.25517i
$219$	199283.	+	159942.i	0.280776	+	0.225348i
$220$			181915.i			0.253402i
$221$	395262.			0.544383
$222$	−338597.	−	271754.i	−0.461105	−	0.370078i
$223$	949938.			1.27918			0.639592	−	0.768715i	$-0.279103\pi$
$223$	949938.			1.27918			0.639592	+	0.768715i	$0.279103\pi$
$224$	−5258.89			−0.00700283
$225$	−65842.8	−	297006.i	−0.0867066	−	0.391119i
$226$	−686097.			−0.893541
$227$	372043.			0.479213			0.239607	−	0.970870i	$-0.422982\pi$
$227$	372043.			0.479213			0.239607	+	0.970870i	$0.422982\pi$
$228$	209281.	−	260757.i	0.266620	−	0.332199i
$229$			354826.i			0.447122i	0.974690	+	0.223561i	$0.0717683\pi$
$229$			354826.i			0.447122i	−0.974690	+	0.223561i	$0.928232\pi$
$230$		−	321746.i		−	0.401045i
$231$	−13164.0	+	16402.0i	−0.0162315	+	0.0202239i
$232$			72161.4i			0.0880208i
$233$	−1.25262e6			−1.51158			−0.755790	−	0.654814i	$-0.772747\pi$
$233$	−1.25262e6			−1.51158			−0.755790	+	0.654814i	$0.772747\pi$
$234$	−281013.	+	62297.2i	−0.335495	+	0.0743753i
$235$		−	585187.i		−	0.691234i
$236$	−226937.	+	362657.i	−0.265232	+	0.423854i
$237$	−649982.	+	809855.i	−0.751675	+	0.936562i
$238$		−	27419.6i		−	0.0313776i
$239$		−	168819.i		−	0.191174i	−0.995421	−	0.0955868i	$-0.969527\pi$
$239$		−	168819.i		−	0.191174i	0.995421	−	0.0955868i	$-0.0304727\pi$
$240$	134695.	+	108105.i	0.150946	+	0.121148i
$241$	340564.			0.377708			0.188854	−	0.982005i	$-0.439523\pi$
$241$	340564.			0.377708			0.188854	+	0.982005i	$0.439523\pi$
$242$	−368147.			−0.404094
$243$	218799.	−	894100.i	0.237700	−	0.971338i
$244$			812074.i			0.873215i
$245$			726250.i			0.772985i
$246$	80166.4	+	64340.7i	0.0844607	+	0.0677873i
$247$			396973.i			0.414017i
$248$			390449.i			0.403121i
$249$	514406.	−	640933.i	0.525785	−	0.655110i
$250$		−	757716.i		−	0.766755i
$251$		−	44476.4i		−	0.0445600i	−0.999752	−	0.0222800i	$-0.992907\pi$
$251$		−	44476.4i		−	0.0445600i	0.999752	−	0.0222800i	$-0.00709253\pi$
$252$	4321.60	+	19494.1i	0.00428690	+	0.0193375i
$253$	−488253.			−0.479561
$254$	1.06211e6			1.03296
$255$	−563653.	+	702293.i	−0.542827	+	0.676344i
$256$	65536.0			0.0625000
$257$		−	485768.i		−	0.458771i	−0.973336	−	0.229386i	$-0.926328\pi$
$257$		−	485768.i		−	0.458771i	0.973336	−	0.229386i	$-0.0736717\pi$
$258$	76104.6	+	61080.8i	0.0711806	+	0.0571288i
$259$		−	35758.9i		−	0.0331234i
$260$	−205057.			−0.188123
$261$	267494.	−	59300.2i	0.243059	−	0.0538834i
$262$	−94115.9			−0.0847051
$263$		−	1.65840e6i		−	1.47843i	−0.673471	−	0.739214i	$-0.735197\pi$
$263$		−	1.65840e6i		−	1.47843i	0.673471	−	0.739214i	$-0.264803\pi$
$264$	164050.	−	204401.i	0.144866	−	0.180498i
$265$	554673.			0.485202
$266$	27538.3			0.0238635
$267$	875720.	−	1.09112e6i	0.751773	−	0.936684i
$268$		−	20892.3i		−	0.0177684i
$269$	−548436.			−0.462110			−0.231055	−	0.972941i	$-0.574218\pi$
$269$	−548436.			−0.462110			−0.231055	+	0.972941i	$0.574218\pi$
$270$	290042.	−	588134.i	0.242132	−	0.490983i
$271$	−653560.			−0.540583			−0.270292	−	0.962779i	$-0.587120\pi$
$271$	−653560.			−0.540583			−0.270292	+	0.962779i	$0.587120\pi$
$272$			341702.i			0.280044i
$273$	−18488.6	−	14838.7i	−0.0150140	−	0.0120501i
$274$		−	930869.i		−	0.749053i
$275$	−328887.			−0.262250
$276$	−290149.	+	361516.i	−0.229271	+	0.285664i
$277$	−1.01496e6			−0.794784			−0.397392	−	0.917649i	$-0.630085\pi$
$277$	−1.01496e6			−0.794784			−0.397392	+	0.917649i	$0.630085\pi$
$278$	1.26124e6			0.978785
$279$	1.44735e6	−	320860.i	1.11317	−	0.246777i
$280$			14225.0i			0.0108432i
$281$		−	1.98324e6i		−	1.49834i	−0.662378	−	0.749170i	$-0.730453\pi$
$281$		−	1.98324e6i		−	1.49834i	0.662378	−	0.749170i	$-0.269547\pi$
$282$	−527719.	+	657520.i	−0.395166	+	0.492364i
$283$			2.06818e6i			1.53505i	0.641021	+	0.767523i	$0.278511\pi$
$283$			2.06818e6i			1.53505i	−0.641021	+	0.767523i	$0.721489\pi$
$284$			281998.i			0.207468i
$285$	−705332.	−	566093.i	−0.514377	−	0.412834i
$286$			311177.i			0.224953i
$287$			8466.30i			0.00606721i
$288$	−53855.6	−	242934.i	−0.0382604	−	0.172587i
$289$	−361767.			−0.254791
$290$	195192.			0.136291
$291$	−303782.	−	243813.i	−0.210295	−	0.168781i
$292$		−	262275.i		−	0.180012i
$293$		−	438652.i		−	0.298505i	−0.988799	−	0.149252i	$-0.952313\pi$
$293$		−	438652.i		−	0.298505i	0.988799	−	0.149252i	$-0.0476866\pi$
$294$	654929.	−	816019.i	0.441902	−	0.550595i
$295$	980966.	+	613853.i	0.656295	+	0.410685i
$296$			445626.i			0.295625i
$297$	−892499.	−	440142.i	−0.587106	−	0.289535i
$298$	1.55489e6			1.01428
$299$		−	550367.i		−	0.356020i
$300$	−195444.	+	243517.i	−0.125378	+	0.156216i
$301$			8037.34i			0.00511324i
$302$		−	6289.90i		−	0.00396850i
$303$	1.15657e6	−	1.44104e6i	0.723708	−	0.901716i
$304$	−343181.			−0.212980
$305$	2.19661e6			1.35208
$306$	1.26665e6	−	280801.i	0.773309	−	0.171434i
$307$	815525.			0.493846			0.246923	−	0.969035i	$-0.420581\pi$
$307$	815525.			0.493846			0.246923	+	0.969035i	$0.420581\pi$
$308$	21586.6			0.0129660
$309$	−261375.	−	209777.i	−0.155728	−	0.124986i
$310$	1.05614e6			0.624192
$311$			1.29979e6i			0.762028i	0.924569	+	0.381014i	$0.124425\pi$
$311$			1.29979e6i			0.762028i	−0.924569	+	0.381014i	$0.875575\pi$
$312$	230404.	+	184920.i	0.134000	+	0.107547i
$313$		−	1.44214e6i		−	0.832045i	−0.909354	−	0.416023i	$-0.863424\pi$
$313$		−	1.44214e6i		−	0.832045i	0.909354	−	0.416023i	$-0.136576\pi$
$314$		−	398363.i		−	0.228010i
$315$	52730.3	−	11689.7i	0.0299422	−	0.00663784i
$316$	1.06585e6			0.600451
$317$		−	167603.i		−	0.0936769i	−0.998902	−	0.0468384i	$-0.985085\pi$
$317$		−	167603.i		−	0.0936769i	0.998902	−	0.0468384i	$-0.0149146\pi$
$318$	−623235.	−	500202.i	−0.345608	−	0.277381i
$319$		−	296207.i		−	0.162974i
$320$		−	177271.i		−	0.0967749i
$321$	−2.09184e6	−	1.67889e6i	−1.13310	−	0.909412i
$322$	−38179.4			−0.0205206
$323$		−	1.78933e6i		−	0.954301i
$324$	−856270.	+	399273.i	−0.453156	+	0.211304i
$325$		−	370727.i		−	0.194691i
$326$	2.32285e6			1.21054
$327$	−2.67680e6	−	2.14837e6i	−1.38435	−	1.11107i
$328$		−	105507.i		−	0.0541496i
$329$	−69440.1			−0.0353688
$330$	−552892.	−	443745.i	−0.279483	−	0.224310i
$331$	73742.6			0.0369955			0.0184977	−	0.999829i	$-0.494112\pi$
$331$	73742.6			0.0369955			0.0184977	+	0.999829i	$0.494112\pi$
$332$	−843529.			−0.420005
$333$	1.65188e6	−	366203.i	0.816334	−	0.180972i
$334$			407067.i			0.199664i
$335$	−56512.3			−0.0275126
$336$	12828.0	−	15983.3i	0.00619886	−	0.00772357i
$337$			3.49548e6i			1.67661i	0.545202	+	0.838305i	$0.316453\pi$
$337$			3.49548e6i			1.67661i	−0.545202	+	0.838305i	$0.683547\pi$
$338$	1.13441e6			0.540104
$339$	1.67360e6	−	2.08525e6i	0.790956	−	0.985504i
$340$	924285.			0.433619
$341$		−	1.60271e6i		−	0.746394i
$342$	282017.	+	1.27213e6i	0.130380	+	0.588121i
$343$	172494.			0.0791658
$344$		−	100161.i		−	0.0456355i
$345$	977880.	+	784836.i	0.442321	+	0.355002i
$346$	−256313.			−0.115101
$347$	−81574.5			−0.0363689			−0.0181845	−	0.999835i	$-0.505789\pi$
$347$	−81574.5			−0.0363689			−0.0181845	+	0.999835i	$0.505789\pi$
$348$	−219320.	−	176024.i	−0.0970799	−	0.0779153i
$349$			3.25809e6i			1.43186i	0.698173	+	0.715929i	$0.253997\pi$
$349$			3.25809e6i			1.43186i	−0.698173	+	0.715929i	$0.746003\pi$
$350$	−25717.6			−0.0112218
$351$	496136.	−	1.00604e6i	0.214948	−	0.435861i
$352$	−269011.			−0.115721
$353$	−1.76544e6			−0.754077			−0.377039	−	0.926198i	$-0.623058\pi$
$353$	−1.76544e6			−0.754077			−0.377039	+	0.926198i	$0.623058\pi$
$354$	−548650.	−	1.57436e6i	−0.232695	−	0.667722i
$355$	762789.			0.321243
$356$	−1.43602e6			−0.600529
$357$	83336.3	+	66884.9i	0.0346070	+	0.0277752i
$358$	−1.65015e6			−0.680482
$359$		−	2.73460e6i		−	1.11985i	−0.828545	−	0.559923i	$-0.810831\pi$
$359$		−	2.73460e6i		−	1.11985i	0.828545	−	0.559923i	$-0.189169\pi$
$360$	−657122.	+	145676.i	−0.267233	+	0.0592424i
$361$	−679020.			−0.274230
$362$	148067.			0.0593864
$363$	898022.	−	1.11891e6i	0.357701	−	0.445684i
$364$			24332.7i			0.00962582i
$365$	−709440.			−0.278730
$366$	−2.46813e6	−	1.98090e6i	−0.963086	−	0.772963i
$367$		−	1.54107e6i		−	0.597252i	−0.954370	−	0.298626i	$-0.903472\pi$
$367$		−	1.54107e6i		−	0.597252i	0.954370	−	0.298626i	$-0.0965284\pi$
$368$	475790.			0.183145
$369$	−391100.	+	86702.4i	−0.149528	+	0.0331486i
$370$	1.20539e6			0.457745
$371$		−	65819.3i		−	0.0248267i
$372$	−1.18669e6	−	952425.i	−0.444610	−	0.356840i
$373$	1.35221e6			0.503236			0.251618	−	0.967827i	$-0.419037\pi$
$373$	1.35221e6			0.503236			0.251618	+	0.967827i	$0.419037\pi$
$374$		−	1.40261e6i		−	0.518512i
$375$	2.30292e6	+	1.84830e6i	0.845670	+	0.678726i
$376$	865360.			0.315665
$377$	333889.			0.120990
$378$	−69789.8	−	34417.3i	−0.0251225	−	0.0123893i
$379$	856323.			0.306224			0.153112	−	0.988209i	$-0.451070\pi$
$379$	856323.			0.306224			0.153112	+	0.988209i	$0.451070\pi$
$380$			928285.i			0.329779i
$381$	−2.59081e6	+	3.22806e6i	−0.914372	+	1.13928i
$382$	623771.			0.218709
$383$			3.33532e6i			1.16183i	0.813966	+	0.580913i	$0.197304\pi$
$383$			3.33532e6i			1.16183i	−0.813966	+	0.580913i	$0.802696\pi$
$384$	−159862.	+	199183.i	−0.0553245	+	0.0689325i
$385$		−	58390.4i		−	0.0200766i
$386$	−2.08121e6			−0.710963
$387$	−371285.	+	82309.5i	−0.126017	+	0.0279365i
$388$			399807.i			0.134825i
$389$			2.94144e6i			0.985565i	0.870152	+	0.492783i	$0.164020\pi$
$389$			2.94144e6i			0.985565i	−0.870152	+	0.492783i	$0.835980\pi$
$390$	500197.	−	623229.i	0.166525	−	0.207485i
$391$			2.48075e6i			0.820619i
$392$	−1.07396e6			−0.352999
$393$	229577.	−	286046.i	0.0749804	−	0.0934230i
$394$			1.05914e6i			0.343727i
$395$		−	2.88306e6i		−	0.929737i
$396$	221065.	+	997190.i	0.0708407	+	0.319551i
$397$		−	1.44954e6i		−	0.461589i	−0.973003	−	0.230794i	$-0.925868\pi$
$397$		−	1.44954e6i		−	0.461589i	0.973003	−	0.230794i	$-0.0741324\pi$
$398$	319224.			0.101015
$399$	−67174.3	+	83697.0i	−0.0211238	+	0.0263195i
$400$	320492.			0.100154
$401$	9021.61			0.00280171			0.00140085	−	0.999999i	$-0.499554\pi$
$401$	9021.61			0.00280171			0.00140085	+	0.999999i	$0.499554\pi$
$402$	63497.6	+	50962.6i	0.0195971	+	0.0157285i
$403$	1.80660e6			0.554114
$404$	−1.89655e6			−0.578110
$405$	1.08001e6	+	2.31616e6i	0.327182	+	0.701667i
$406$		−	23162.2i		−	0.00697371i
$407$		−	1.82919e6i		−	0.547361i
$408$	−1.03853e6	−	833516.i	−0.308866	−	0.247893i
$409$		−	1.87499e6i		−	0.554232i	−0.960836	−	0.277116i	$-0.910621\pi$
$409$		−	1.87499e6i		−	0.554232i	0.960836	−	0.277116i	$-0.0893786\pi$
$410$	−285389.			−0.0838452
$411$	2.82918e6	+	2.27067e6i	0.826146	+	0.663056i
$412$			343994.i			0.0998409i
$413$	72841.7	−	116404.i	0.0210138	−	0.0335811i
$414$	−390991.	−	1.76370e6i	−0.112115	−	0.505735i
$415$			2.28170e6i			0.650336i
$416$		−	303234.i		−	0.0859100i
$417$	−3.07656e6	+	3.83329e6i	−0.866413	+	1.07952i
$418$	1.40868e6			0.394342
$419$	−6.23979e6			−1.73634			−0.868171	−	0.496265i	$-0.834704\pi$
$419$	−6.23979e6			−1.73634			−0.868171	+	0.496265i	$0.834704\pi$
$420$	−43233.9	−	34699.1i	−0.0119592	−	0.00959830i
$421$			3.47111e6i			0.954472i	0.878775	+	0.477236i	$0.158361\pi$
$421$			3.47111e6i			0.954472i	−0.878775	+	0.477236i	$0.841639\pi$
$422$		−	461860.i		−	0.126249i
$423$	−711128.	−	3.20778e6i	−0.193240	−	0.871674i
$424$			820237.i			0.221577i
$425$			1.67103e6i			0.448759i
$426$	−857075.	−	687880.i	−0.228821	−	0.183649i
$427$		−	260657.i		−	0.0691830i
$428$			2.75307e6i			0.726453i
$429$	−945757.	−	759055.i	−0.248105	−	0.199127i
$430$	−270930.			−0.0706619
$431$	1.55792e6			0.403973			0.201986	−	0.979388i	$-0.435260\pi$
$431$	1.55792e6			0.403973			0.201986	+	0.979388i	$0.435260\pi$
$432$	869718.	+	428907.i	0.224217	+	0.110574i
$433$	4.97595e6			1.27543			0.637714	−	0.770273i	$-0.279880\pi$
$433$	4.97595e6			1.27543			0.637714	+	0.770273i	$0.279880\pi$
$434$		−	125325.i		−	0.0319385i
$435$	−476134.	+	593247.i	−0.120644	+	0.150318i
$436$			3.52293e6i			0.887539i
$437$	−2.49149e6			−0.624102
$438$	797132.	+	639770.i	0.198539	+	0.159345i
$439$	2.37372e6			0.587852			0.293926	−	0.955828i	$-0.405038\pi$
$439$	2.37372e6			0.587852			0.293926	+	0.955828i	$0.405038\pi$
$440$			727658.i			0.179183i
$441$	882550.	+	3.98104e6i	0.216094	+	0.974765i
$442$	1.58105e6			0.384937
$443$	512210.			0.124005			0.0620024	−	0.998076i	$-0.480251\pi$
$443$	512210.			0.124005			0.0620024	+	0.998076i	$0.480251\pi$
$444$	−1.35439e6	−	1.08702e6i	−0.326051	−	0.261685i
$445$			3.88434e6i			0.929859i
$446$	3.79975e6			0.904520
$447$	−3.79284e6	+	4.72575e6i	−0.897833	+	1.11867i
$448$	−21035.5			−0.00495175
$449$			2.22031e6i			0.519753i	0.965642	+	0.259876i	$0.0836819\pi$
$449$			2.22031e6i			0.519753i	−0.965642	+	0.259876i	$0.916318\pi$
$450$	−263371.	−	1.18803e6i	−0.0613108	−	0.276563i
$451$			433082.i			0.100260i
$452$	−2.74439e6			−0.631829
$453$	19116.8	+	15343.0i	0.00437694	+	0.00351289i
$454$	1.48817e6			0.338855
$455$	65818.7			0.0149046
$456$	837124.	−	1.04303e6i	0.188529	−	0.234900i
$457$			784209.i			0.175647i	0.996136	+	0.0878237i	$0.0279912\pi$
$457$			784209.i			0.175647i	−0.996136	+	0.0878237i	$0.972009\pi$
$458$			1.41930e6i			0.316163i
$459$	−2.23631e6	+	4.53468e6i	−0.495450	+	1.00465i
$460$		−	1.28698e6i		−	0.283582i
$461$		−	4.67620e6i		−	1.02480i	−0.858746	−	0.512402i	$-0.828756\pi$
$461$		−	4.67620e6i		−	1.02480i	0.858746	−	0.512402i	$-0.171244\pi$
$462$	−52656.2	+	65607.8i	−0.0114774	+	0.0143005i
$463$			2.00844e6i			0.435417i	0.976014	+	0.217709i	$0.0698583\pi$
$463$			2.00844e6i			0.435417i	−0.976014	+	0.217709i	$0.930142\pi$
$464$			288646.i			0.0622401i
$465$	−2.57625e6	+	3.20993e6i	−0.552530	+	0.688434i
$466$	−5.01050e6			−1.06885
$467$	−8.02525e6			−1.70281			−0.851406	−	0.524508i	$-0.824249\pi$
$467$	−8.02525e6			−1.70281			−0.851406	+	0.524508i	$0.824249\pi$
$468$	−1.12405e6	+	249189.i	−0.237231	+	0.0525913i
$469$			6705.93i			0.00140775i
$470$		−	2.34075e6i		−	0.488776i
$471$	1.21074e6	+	971728.i	0.251477	+	0.201833i
$472$	−907750.	+	1.45063e6i	−0.187547	+	0.299710i
$473$			411139.i			0.0844959i
$474$	−2.59993e6	+	3.23942e6i	−0.531515	+	0.662250i
$475$	−1.67827e6			−0.341293
$476$		−	109679.i		−	0.0221873i
$477$	3.04052e6	−	674048.i	0.611859	−	0.135642i
$478$		−	675278.i		−	0.135180i
$479$			2.59531e6i			0.516834i	0.966033	+	0.258417i	$0.0832008\pi$
$479$			2.59531e6i			0.516834i	−0.966033	+	0.258417i	$0.916799\pi$
$480$	538778.	+	432418.i	0.106735	+	0.0856645i
$481$	2.06190e6			0.406354
$482$	1.36226e6			0.267080
$483$	93131.2	−	116038.i	0.0181647	−	0.0226326i
$484$	−1.47259e6			−0.285738
$485$	1.08145e6			0.208763
$486$	875197.	−	3.57640e6i	0.168080	−	0.686840i
$487$	751189.			0.143525			0.0717624	−	0.997422i	$-0.477138\pi$
$487$	751189.			0.143525			0.0717624	+	0.997422i	$0.477138\pi$
$488$			3.24830e6i			0.617456i
$489$	−5.66615e6	+	7.05983e6i	−1.07156	+	1.33512i
$490$			2.90500e6i			0.546583i
$491$		−	1.04218e6i		−	0.195093i	−0.995231	−	0.0975463i	$-0.968901\pi$
$491$		−	1.04218e6i		−	0.195093i	0.995231	−	0.0975463i	$-0.0310994\pi$
$492$	320666.	+	257363.i	0.0597227	+	0.0479328i
$493$	−1.50499e6			−0.278879
$494$			1.58789e6i			0.292754i
$495$	2.69734e6	−	597969.i	0.494792	−	0.109690i
$496$			1.56180e6i			0.285050i
$497$		−	90515.0i		−	0.0164373i
$498$	2.05762e6	−	2.56373e6i	0.371786	−	0.463233i
$499$	−4.89287e6			−0.879655			−0.439827	−	0.898082i	$-0.644960\pi$
$499$	−4.89287e6			−0.879655			−0.439827	+	0.898082i	$0.644960\pi$
$500$		−	3.03087e6i		−	0.542178i
$501$	−1.23719e6	−	992959.i	−0.220213	−	0.176741i
$502$		−	177905.i		−	0.0315087i
$503$	4.85721e6			0.855987			0.427994	−	0.903782i	$-0.359221\pi$
$503$	4.85721e6			0.855987			0.427994	+	0.903782i	$0.359221\pi$
$504$	17286.4	+	77976.2i	0.00303130	+	0.0136737i
$505$			5.13005e6i			0.895145i
$506$	−1.95301e6			−0.339101
$507$	−2.76717e6	+	3.44780e6i	−0.478096	+	0.595692i
$508$	4.24844e6			0.730416
$509$	−6.13492e6			−1.04958			−0.524788	−	0.851233i	$-0.675856\pi$
$509$	−6.13492e6			−1.04958			−0.524788	+	0.851233i	$0.675856\pi$
$510$	−2.25461e6	+	2.80917e6i	−0.383837	+	0.478248i
$511$			84184.4i			0.0142620i
$512$	262144.			0.0441942
$513$	−4.55430e6	−	2.24598e6i	−0.764062	−	0.376802i
$514$		−	1.94307e6i		−	0.324400i
$515$	930485.			0.154594
$516$	304418.	+	244323.i	0.0503323	+	0.0403962i
$517$	−3.55211e6			−0.584467
$518$		−	143036.i		−	0.0234218i
$519$	625225.	−	779009.i	0.101887	−	0.126947i
$520$	−820229.			−0.133023
$521$			8.88459e6i			1.43398i	0.697083	+	0.716990i	$0.254481\pi$
$521$			8.88459e6i			1.43398i	−0.697083	+	0.716990i	$0.745519\pi$
$522$	1.06997e6	−	237201.i	0.171869	−	0.0381013i
$523$	−9.38714e6			−1.50065			−0.750325	−	0.661069i	$-0.770103\pi$
$523$	−9.38714e6			−1.50065			−0.750325	+	0.661069i	$0.770103\pi$
$524$	−376463.			−0.0598956
$525$	62733.1	−	78163.4i	0.00993342	−	0.0123767i
$526$		−	6.63360e6i		−	1.04541i
$527$	−8.14315e6			−1.27722
$528$	656199.	−	817602.i	0.102436	−	0.127631i
$529$	−2.98212e6			−0.463325
$530$	2.21869e6			0.343090
$531$	6.12326e6	+	2.17283e6i	0.942425	+	0.334418i
$532$	110153.			0.0168740
$533$	−488177.			−0.0744319
$534$	3.50288e6	−	4.36447e6i	0.531584	−	0.662336i
$535$	7.44689e6			1.12484
$536$		−	83569.0i		−	0.0125642i
$537$	4.02523e6	−	5.01530e6i	0.602358	−	0.750517i
$538$	−2.19374e6			−0.326761
$539$	4.40837e6			0.653591
$540$	1.16017e6	−	2.35254e6i	0.171213	−	0.347178i
$541$		−	3.12504e6i		−	0.459052i	−0.973303	−	0.229526i	$-0.926282\pi$
$541$		−	3.12504e6i		−	0.459052i	0.973303	−	0.229526i	$-0.0737176\pi$
$542$	−2.61424e6			−0.382250
$543$	−361180.	+	450019.i	−0.0525684	+	0.0654984i
$544$			1.36681e6i			0.198021i
$545$	9.52931e6			1.37426
$546$	−73954.3	−	59355.0i	−0.0106165	−	0.00852070i
$547$	−1.07410e6			−0.153489			−0.0767444	−	0.997051i	$-0.524453\pi$
$547$	−1.07410e6			−0.153489			−0.0767444	+	0.997051i	$0.524453\pi$
$548$		−	3.72348e6i		−	0.529660i
$549$	1.20410e7	−	2.66936e6i	1.70503	−	0.377986i
$550$	−1.31555e6			−0.185439
$551$		−	1.51150e6i		−	0.212095i
$552$	−1.16060e6	+	1.44606e6i	−0.162119	+	0.201995i
$553$	−342112.			−0.0475725
$554$	−4.05983e6			−0.561997
$555$	−2.94032e6	+	3.66354e6i	−0.405193	+	0.504857i
$556$	5.04498e6			0.692105
$557$		−	5.89668e6i		−	0.805321i	−0.915349	−	0.402661i	$-0.868085\pi$
$557$		−	5.89668e6i		−	0.805321i	0.915349	−	0.402661i	$-0.131915\pi$
$558$	5.78939e6	−	1.28344e6i	0.787132	−	0.174498i
$559$	−463443.			−0.0627287
$560$			56899.9i			0.00766728i
$561$	4.26295e6	+	3.42140e6i	0.571877	+	0.458983i
$562$		−	7.93298e6i		−	1.05949i
$563$	−8.58589e6			−1.14160			−0.570800	−	0.821089i	$-0.693367\pi$
$563$	−8.58589e6			−1.14160			−0.570800	+	0.821089i	$0.693367\pi$
$564$	−2.11088e6	+	2.63008e6i	−0.279425	+	0.348154i
$565$			7.42341e6i			0.978323i
$566$			8.27271e6i			1.08544i
$567$	274843.	−	128157.i	0.0359027	−	0.0167412i
$568$			1.12799e6i			0.146702i
$569$	1.86963e6			0.242089			0.121045	−	0.992647i	$-0.461376\pi$
$569$	1.86963e6			0.242089			0.121045	+	0.992647i	$0.461376\pi$
$570$	−2.82133e6	−	2.26437e6i	−0.363720	−	0.291918i
$571$			1.46089e6i			0.187511i	0.995595	+	0.0937555i	$0.0298872\pi$
$571$			1.46089e6i			0.187511i	−0.995595	+	0.0937555i	$0.970113\pi$
$572$			1.24471e6i			0.159066i
$573$	−1.52157e6	+	1.89582e6i	−0.193600	+	0.241219i
$574$			33865.2i			0.00429017i
$575$	2.32677e6			0.293483
$576$	−215423.	−	971736.i	−0.0270542	−	0.122037i
$577$	4.34585e6			0.543419			0.271709	−	0.962379i	$-0.412411\pi$
$577$	4.34585e6			0.543419			0.271709	+	0.962379i	$0.412411\pi$
$578$	−1.44707e6			−0.180165
$579$	5.07670e6	−	6.32539e6i	0.629339	−	0.784135i
$580$	780770.			0.0963725
$581$	270753.			0.0332762
$582$	−1.21513e6	−	975250.i	−0.148701	−	0.119346i
$583$		−	3.36689e6i		−	0.410258i
$584$		−	1.04910e6i		−	0.127287i
$585$	674041.	+	3.04049e6i	0.0814323	+	0.367328i
$586$		−	1.75461e6i		−	0.211075i
$587$	1.24558e7			1.49203			0.746013	−	0.665931i	$-0.231966\pi$
$587$	1.24558e7			1.49203			0.746013	+	0.665931i	$0.231966\pi$
$588$	2.61972e6	−	3.26408e6i	0.312472	−	0.389329i
$589$		−	8.17840e6i		−	0.971359i
$590$	3.92386e6	+	2.45541e6i	0.464070	+	0.290398i
$591$	−3.21904e6	−	2.58357e6i	−0.379103	−	0.304264i
$592$			1.78250e6i			0.209038i
$593$			5.16014e6i			0.602594i	0.953530	+	0.301297i	$0.0974196\pi$
$593$			5.16014e6i			0.602594i	−0.953530	+	0.301297i	$0.902580\pi$
$594$	−3.57000e6	−	1.76057e6i	−0.415147	−	0.204732i
$595$	−296674.			−0.0343548
$596$	6.21954e6			0.717204
$597$	−778684.	+	970214.i	−0.0894181	+	0.111412i
$598$		−	2.20147e6i		−	0.251744i
$599$		−	1.08002e6i		−	0.122989i	−0.998107	−	0.0614943i	$-0.980413\pi$
$599$		−	1.08002e6i		−	0.122989i	0.998107	−	0.0614943i	$-0.0195866\pi$
$600$	−781778.	+	974069.i	−0.0886554	+	0.110462i
$601$		−	5.28734e6i		−	0.597105i	−0.954393	−	0.298553i	$-0.903496\pi$
$601$		−	5.28734e6i		−	0.597105i	0.954393	−	0.298553i	$-0.0965039\pi$
$602$			32149.4i			0.00361561i
$603$	−309780.	+	68674.7i	−0.0346945	+	0.00769136i
$604$		−	25159.6i		−	0.00280615i
$605$			3.98326e6i			0.442436i
$606$	4.62626e6	−	5.76417e6i	0.511739	−	0.637610i
$607$	−5.30029e6			−0.583886			−0.291943	−	0.956436i	$-0.594302\pi$
$607$	−5.30029e6			−0.583886			−0.291943	+	0.956436i	$0.594302\pi$
$608$	−1.37273e6			−0.150600
$609$	70396.5	+	56499.5i	0.00769145	+	0.00617308i
$610$	8.78645e6			0.956068
$611$		−	4.00400e6i		−	0.433901i
$612$	5.06660e6	−	1.12321e6i	0.546812	−	0.121222i
$613$			5.94190e6i			0.638667i	0.947642	+	0.319333i	$0.103459\pi$
$613$			5.94190e6i			0.638667i	−0.947642	+	0.319333i	$0.896541\pi$
$614$	3.26210e6			0.349202
$615$	696152.	−	867382.i	0.0742192	−	0.0924746i
$616$	86346.2			0.00916836
$617$			3.58168e6i			0.378768i	0.981903	+	0.189384i	$0.0606491\pi$
$617$			3.58168e6i			0.378768i	−0.981903	+	0.189384i	$0.939351\pi$
$618$	−1.04550e6	−	839107.i	−0.110117	−	0.0883784i
$619$	3.86115e6			0.405032			0.202516	−	0.979279i	$-0.435088\pi$
$619$	3.86115e6			0.405032			0.202516	+	0.979279i	$0.435088\pi$
$620$	4.22457e6			0.441371
$621$	6.31413e6	+	3.11386e6i	0.657029	+	0.324018i
$622$			5.19914e6i			0.538835i
$623$	460928.			0.0475787
$624$	921615.	+	739679.i	0.0947520	+	0.0760470i
$625$	−4.28606e6			−0.438892
$626$		−	5.76856e6i		−	0.588345i
$627$	−3.43621e6	+	4.28140e6i	−0.349068	+	0.434927i
$628$		−	1.59345e6i		−	0.161228i
$629$	−9.29391e6			−0.936638
$630$	210921.	−	46758.8i	0.0211723	−	0.00469366i
$631$	−9.39799e6			−0.939640			−0.469820	−	0.882762i	$-0.655681\pi$
$631$	−9.39799e6			−0.939640			−0.469820	+	0.882762i	$0.655681\pi$
$632$	4.26339e6			0.424583
$633$	1.40373e6	+	1.12662e6i	0.139243	+	0.111755i
$634$		−	670410.i		−	0.0662396i
$635$		−	1.14918e7i		−	1.13098i
$636$	−2.49294e6	−	2.00081e6i	−0.244382	−	0.196138i
$637$			4.96919e6i			0.485218i
$638$		−	1.18483e6i		−	0.115240i
$639$	4.18134e6	−	926953.i	0.405101	−	0.0898061i
$640$		−	709084.i		−	0.0684302i
$641$		−	1.45277e7i		−	1.39653i	−0.715837	−	0.698267i	$-0.753955\pi$
$641$		−	1.45277e7i		−	1.39653i	0.715837	−	0.698267i	$-0.246045\pi$
$642$	−8.36738e6	−	6.71557e6i	−0.801220	−	0.643051i
$643$	8.06246e6			0.769024			0.384512	−	0.923120i	$-0.374370\pi$
$643$	8.06246e6			0.769024			0.384512	+	0.923120i	$0.374370\pi$
$644$	−152718.			−0.0145102
$645$	660880.	−	823434.i	0.0625494	−	0.0779345i
$646$		−	7.15734e6i		−	0.674793i
$647$			1.30624e7i			1.22677i	0.789784	+	0.613385i	$0.210192\pi$
$647$			1.30624e7i			1.22677i	−0.789784	+	0.613385i	$0.789808\pi$
$648$	−3.42508e6	+	1.59709e6i	−0.320430	+	0.149414i
$649$	3.72611e6	−	5.95450e6i	0.347252	−	0.554924i
$650$		−	1.48291e6i		−	0.137667i
$651$	380900.	+	305706.i	0.0352256	+	0.0282717i
$652$	9.29141e6			0.855978
$653$			8.12008e6i			0.745208i	0.927990	+	0.372604i	$0.121535\pi$
$653$			8.12008e6i			0.745208i	−0.927990	+	0.372604i	$0.878465\pi$
$654$	−1.07072e7	−	8.59349e6i	−0.978885	−	0.785643i
$655$			1.01831e6i			0.0927422i
$656$		−	422027.i		−	0.0382896i
$657$	−3.88889e6	+	862122.i	−0.351490	+	0.0779212i
$658$	−277761.			−0.0250095
$659$	1.16495e7			1.04495			0.522475	−	0.852655i	$-0.325009\pi$
$659$	1.16495e7			1.04495			0.522475	+	0.852655i	$0.325009\pi$
$660$	−2.21157e6	−	1.77498e6i	−0.197624	−	0.158611i
$661$	−4.25595e6			−0.378873			−0.189436	−	0.981893i	$-0.560666\pi$
$661$	−4.25595e6			−0.378873			−0.189436	+	0.981893i	$0.560666\pi$
$662$	294971.			0.0261598
$663$	−3.85666e6	+	4.80527e6i	−0.340743	+	0.424555i
$664$	−3.37412e6			−0.296989
$665$		−	297958.i		−	0.0261277i
$666$	6.60752e6	−	1.46481e6i	0.577236	−	0.127966i
$667$			2.09556e6i			0.182384i
$668$			1.62827e6i			0.141184i
$669$	−9.26875e6	+	1.15485e7i	−0.800674	+	0.997613i
$670$	−226049.			−0.0194543
$671$		−	1.33335e7i		−	1.14324i
$672$	51312.1	−	63933.1i	0.00438325	−	0.00546139i
$673$		−	1.68599e7i		−	1.43488i	−0.696619	−	0.717441i	$-0.745313\pi$
$673$		−	1.68599e7i		−	1.43488i	0.696619	−	0.717441i	$-0.254687\pi$
$674$			1.39819e7i			1.18554i
$675$	4.25320e6	+	2.09749e6i	0.359299	+	0.177191i
$676$	4.53763e6			0.381911
$677$		−	18963.6i		−	0.00159019i	−1.00000		0.000795094i	$-0.999747\pi$
$677$		−	18963.6i		−	0.00159019i	1.00000		0.000795094i	$-0.000253086\pi$
$678$	6.69440e6	−	8.34099e6i	0.559290	−	0.696857i
$679$		−	128329.i		−	0.0106819i
$680$	3.69714e6			0.306615
$681$	−3.63011e6	+	4.52299e6i	−0.299952	+	0.373730i
$682$		−	6.41083e6i		−	0.527781i
$683$	−7.53196e6			−0.617812			−0.308906	−	0.951093i	$-0.599963\pi$
$683$	−7.53196e6			−0.617812			−0.308906	+	0.951093i	$0.599963\pi$
$684$	1.12807e6	+	5.08853e6i	0.0921923	+	0.415864i
$685$	−1.00718e7			−0.820125
$686$	689975.			0.0559787
$687$	−4.31368e6	−	3.46211e6i	−0.348703	−	0.279865i
$688$		−	400644.i		−	0.0322692i
$689$	3.79522e6			0.304571
$690$	3.91152e6	+	3.13935e6i	0.312768	+	0.251025i
$691$		−	2.00757e7i		−	1.59947i	−0.600353	−	0.799735i	$-0.704973\pi$
$691$		−	2.00757e7i		−	1.59947i	0.600353	−	0.799735i	$-0.295027\pi$
$692$	−1.02525e6			−0.0813888
$693$	−70956.9	−	320075.i	−0.00561257	−	0.0253174i
$694$	−326298.			−0.0257167
$695$		−	1.36464e7i		−	1.07166i
$696$	−877278.	−	704095.i	−0.0686459	−	0.0550945i
$697$	2.20043e6			0.171564
$698$			1.30324e7i			1.01248i
$699$	1.22221e7	−	1.52284e7i	0.946137	−	1.17885i
$700$	−102871.			−0.00793498
$701$	−2.02660e6			−0.155766			−0.0778832	−	0.996962i	$-0.524816\pi$
$701$	−2.02660e6			−0.155766			−0.0778832	+	0.996962i	$0.524816\pi$
$702$	1.98454e6	−	4.02416e6i	0.151991	−	0.308200i
$703$		−	9.33413e6i		−	0.712337i
$704$	−1.07604e6			−0.0818273
$705$	7.11422e6	+	5.70980e6i	0.539081	+	0.432661i
$706$	−7.06175e6			−0.533213
$707$	608748.			0.0458025
$708$	−2.19460e6	−	6.29744e6i	−0.164540	−	0.472151i
$709$	−1.86937e7			−1.39662			−0.698311	−	0.715794i	$-0.746065\pi$
$709$	−1.86937e7			−1.39662			−0.698311	+	0.715794i	$0.746065\pi$
$710$	3.05116e6			0.227153
$711$	−3.50353e6	−	1.58039e7i	−0.259916	−	1.17244i
$712$	−5.74406e6			−0.424638
$713$			1.13386e7i			0.835288i
$714$	333345.	+	267539.i	0.0244708	+	0.0196400i
$715$	3.36686e6			0.246297
$716$	−6.60061e6			−0.481173
$717$	2.05237e6	+	1.64721e6i	0.149093	+	0.119660i
$718$		−	1.09384e7i		−	0.791850i
$719$	−2.52490e7			−1.82147			−0.910736	−	0.412990i	$-0.864484\pi$
$719$	−2.52490e7			−1.82147			−0.910736	+	0.412990i	$0.864484\pi$
$720$	−2.62849e6	+	582706.i	−0.188962	+	0.0418907i
$721$		−	110414.i		−	0.00791019i
$722$	−2.71608e6			−0.193910
$723$	−3.32296e6	+	4.14029e6i	−0.236417	+	0.294568i
$724$	592268.			0.0419925
$725$			1.41157e6i			0.0997373i
$726$	3.59209e6	−	4.47562e6i	0.252933	−	0.315146i
$727$	−3.88302e6			−0.272479			−0.136240	−	0.990676i	$-0.543502\pi$
$727$	−3.88302e6			−0.272479			−0.136240	+	0.990676i	$0.543502\pi$
$728$			97331.0i			0.00680648i
$729$	8.73486e6	+	1.13839e7i	0.608747	+	0.793364i
$730$	−2.83776e6			−0.197092
$731$	2.08894e6			0.144588
$732$	−9.87252e6	−	7.92358e6i	−0.681005	−	0.546568i
$733$	−1.94836e7			−1.33939			−0.669697	−	0.742635i	$-0.733576\pi$
$733$	−1.94836e7			−1.33939			−0.669697	+	0.742635i	$0.733576\pi$
$734$		−	6.16429e6i		−	0.422321i
$735$	−8.82914e6	−	7.08618e6i	−0.602837	−	0.483831i
$736$	1.90316e6			0.129503
$737$			343032.i			0.0232630i
$738$	−1.56440e6	+	346810.i	−0.105732	+	0.0234396i
$739$		−	1.83794e7i		−	1.23800i	−0.785392	−	0.618998i	$-0.787539\pi$
$739$		−	1.83794e7i		−	1.23800i	0.785392	−	0.618998i	$-0.212461\pi$
$740$	4.82157e6			0.323675
$741$	−4.82607e6	−	3.87335e6i	−0.322885	−	0.259144i
$742$		−	263277.i		−	0.0175551i
$743$		−	1.41912e7i		−	0.943077i	−0.881845	−	0.471539i	$-0.843699\pi$
$743$		−	1.41912e7i		−	0.943077i	0.881845	−	0.471539i	$-0.156301\pi$
$744$	−4.74676e6	−	3.80970e6i	−0.314387	−	0.252324i
$745$		−	1.68235e7i		−	1.11052i
$746$	5.40884e6			0.355842
$747$	2.77275e6	+	1.25074e7i	0.181807	+	0.820100i
$748$		−	5.61045e6i		−	0.366643i
$749$		−	883672.i		−	0.0575554i
$750$	9.21169e6	+	7.39320e6i	0.597979	+	0.479932i
$751$		−	3.45413e6i		−	0.223480i	−0.993737	−	0.111740i	$-0.964358\pi$
$751$		−	3.45413e6i		−	0.223480i	0.993737	−	0.111740i	$-0.0356424\pi$
$752$	3.46144e6			0.223209
$753$	540707.	+	433966.i	0.0347516	+	0.0278912i
$754$	1.33556e6			0.0855528
$755$	−68055.2			−0.00434504
$756$	−279159.	−	137669.i	−0.0177643	−	0.00876057i
$757$	1.30006e7			0.824564			0.412282	−	0.911056i	$-0.364732\pi$
$757$	1.30006e7			0.824564			0.412282	+	0.911056i	$0.364732\pi$
$758$	3.42529e6			0.216533
$759$	4.76399e6	−	5.93577e6i	0.300169	−	0.374001i
$760$			3.71314e6i			0.233189i
$761$		−	7.83517e6i		−	0.490441i	−0.969467	−	0.245221i	$-0.921140\pi$
$761$		−	7.83517e6i		−	0.490441i	0.969467	−	0.245221i	$-0.0788604\pi$
$762$	−1.03632e7	+	1.29122e7i	−0.646559	+	0.805591i
$763$		−	1.13078e6i		−	0.0703179i
$764$	2.49508e6			0.154651
$765$	−3.03821e6	−	1.37049e7i	−0.187700	−	0.846683i
$766$			1.33413e7i			0.821535i
$767$	6.71202e6	+	4.20014e6i	0.411969	+	0.257795i
$768$	−639449.	+	796732.i	−0.0391204	+	0.0487427i
$769$			1.56964e7i			0.957161i	0.878044	+	0.478581i	$0.158849\pi$
$769$			1.56964e7i			0.957161i	−0.878044	+	0.478581i	$0.841151\pi$
$770$		−	233562.i		−	0.0141963i
$771$	5.90556e6	+	4.73975e6i	0.357788	+	0.287157i
$772$	−8.32483e6			−0.502727
$773$	2.41197e7			1.45186			0.725929	−	0.687770i	$-0.241410\pi$
$773$	2.41197e7			1.45186			0.725929	+	0.687770i	$0.241410\pi$
$774$	−1.48514e6	+	329238.i	−0.0891076	+	0.0197541i
$775$			7.63769e6i			0.456781i
$776$			1.59923e6i			0.0953357i
$777$	434727.	+	348907.i	0.0258323	+	0.0207328i
$778$			1.17657e7i			0.696900i
$779$			2.20996e6i			0.130479i
$780$	2.00079e6	−	2.49292e6i	0.117751	−	0.146714i
$781$		−	4.63016e6i		−	0.271624i
$782$			9.92301e6i			0.580265i
$783$	−1.88907e6	+	3.83057e6i	−0.110114	+	0.223285i
$784$	−4.29584e6			−0.249608
$785$	−4.31019e6			−0.249645
$786$	918309.	−	1.14418e6i	0.0530191	−	0.0660600i
$787$	−1.37090e7			−0.788985			−0.394492	−	0.918899i	$-0.629080\pi$
$787$	−1.37090e7			−0.788985			−0.394492	+	0.918899i	$0.629080\pi$
$788$			4.23657e6i			0.243052i
$789$	2.01615e7	+	1.61814e7i	1.15300	+	0.925386i
$790$		−	1.15322e7i		−	0.657424i
$791$	880885.			0.0500585
$792$	884262.	+	3.98876e6i	0.0500920	+	0.225957i
$793$	1.50298e7			0.848731
$794$		−	5.79817e6i		−	0.326392i
$795$	−5.41207e6	+	6.74325e6i	−0.303700	+	0.378401i
$796$	1.27689e6			0.0714286
$797$	1.32372e7			0.738157			0.369079	−	0.929398i	$-0.379673\pi$
$797$	1.32372e7			0.738157			0.369079	+	0.929398i	$0.379673\pi$
$798$	−268697.	+	334788.i	−0.0149368	+	0.0186107i
$799$			1.80478e7i			1.00013i
$800$	1.28197e6			0.0708194
$801$	4.72031e6	+	2.12925e7i	0.259950	+	1.17259i
$802$	36086.4			0.00198111
$803$			4.30633e6i			0.235678i
$804$	253991.	+	203850.i	0.0138573	+	0.0111217i
$805$			413092.i			0.0224676i
$806$	7.22640e6			0.391818
$807$	5.35121e6	−	6.66743e6i	0.289247	−	0.360392i
$808$	−7.58620e6			−0.408786
$809$	2.44918e7			1.31568			0.657840	−	0.753158i	$-0.271470\pi$
$809$	2.44918e7			1.31568			0.657840	+	0.753158i	$0.271470\pi$
$810$	4.32004e6	+	9.26464e6i	0.231353	+	0.496153i
$811$		−	1.54861e7i		−	0.826779i	−0.910554	−	0.413389i	$-0.864345\pi$
$811$		−	1.54861e7i		−	0.826779i	0.910554	−	0.413389i	$-0.135655\pi$
$812$		−	92648.6i		−	0.00493116i
$813$	6.37693e6	−	7.94544e6i	0.338365	−	0.421591i
$814$		−	7.31678e6i		−	0.387043i
$815$		−	2.51327e7i		−	1.32540i
$816$	−4.15413e6	−	3.33406e6i	−0.218401	−	0.175287i
$817$			2.09798e6i			0.109963i
$818$		−	7.49998e6i		−	0.391901i
$819$	360794.	−	79983.9i	0.0187953	−	0.00416670i
$820$	−1.14156e6			−0.0592875
$821$	2.89142e7			1.49711			0.748554	−	0.663073i	$-0.230748\pi$
$821$	2.89142e7			1.49711			0.748554	+	0.663073i	$0.230748\pi$
$822$	1.13167e7	+	9.08269e6i	0.584173	+	0.468851i
$823$		−	1.88475e7i		−	0.969961i	−0.874525	−	0.484980i	$-0.838827\pi$
$823$		−	1.88475e7i		−	0.969961i	0.874525	−	0.484980i	$-0.161173\pi$
$824$			1.37598e6i			0.0705982i
$825$	3.20902e6	−	3.99834e6i	0.164149	−	0.204524i
$826$	291367.	−	465618.i	0.0148590	−	0.0237454i
$827$			1.33149e7i			0.676979i	0.940970	+	0.338490i	$0.109916\pi$
$827$			1.33149e7i			0.676979i	−0.940970	+	0.338490i	$0.890084\pi$
$828$	−1.56396e6	−	7.05478e6i	−0.0792776	−	0.357608i
$829$	−3.82902e7			−1.93509			−0.967545	−	0.252700i	$-0.918681\pi$
$829$	−3.82902e7			−1.93509			−0.967545	+	0.252700i	$0.918681\pi$
$830$			9.12679e6i			0.459857i
$831$	9.90317e6	−	1.23390e7i	0.497476	−	0.619838i
$832$		−	1.21293e6i		−	0.0607476i
$833$		−	2.23984e7i		−	1.11842i
$834$	−1.23062e7	+	1.53332e7i	−0.612647	+	0.763337i
$835$	4.40437e6			0.218609
$836$	5.63473e6			0.278842
$837$	−1.02213e7	+	2.07264e7i	−0.504306	+	1.02261i
$838$	−2.49592e7			−1.22778
$839$	3.15083e7			1.54532			0.772662	−	0.634818i	$-0.218925\pi$
$839$	3.15083e7			1.54532			0.772662	+	0.634818i	$0.218925\pi$
$840$	−172935.	−	138796.i	−0.00845641	−	0.00678703i
$841$	1.92398e7			0.938019
$842$			1.38844e7i			0.674914i
$843$	2.41106e7	+	1.93509e7i	1.16853	+	0.937850i
$844$		−	1.84744e6i		−	0.0892717i
$845$		−	1.22740e7i		−	0.591351i
$846$	−2.84451e6	−	1.28311e7i	−0.136641	−	0.616367i
$847$	472666.			0.0226384
$848$			3.28095e6i			0.156679i
$849$	−2.51432e7	−	2.01797e7i	−1.19716	−	0.960825i
$850$			6.68414e6i			0.317320i
$851$			1.29409e7i			0.612550i
$852$	−3.42830e6	−	2.75152e6i	−0.161801	−	0.129859i
$853$	−4.06416e6			−0.191248			−0.0956242	−	0.995418i	$-0.530485\pi$
$853$	−4.06416e6			−0.191248			−0.0956242	+	0.995418i	$0.530485\pi$
$854$		−	1.04263e6i		−	0.0489198i
$855$	1.37642e7	−	3.05136e6i	0.643924	−	0.142750i
$856$			1.10123e7i			0.513680i
$857$	−8.69830e6			−0.404559			−0.202280	−	0.979328i	$-0.564835\pi$
$857$	−8.69830e6			−0.404559			−0.202280	+	0.979328i	$0.564835\pi$
$858$	−3.78303e6	−	3.03622e6i	−0.175437	−	0.140804i
$859$		−	1.70914e7i		−	0.790303i	−0.918616	−	0.395151i	$-0.870692\pi$
$859$		−	1.70914e7i		−	0.790303i	0.918616	−	0.395151i	$-0.129308\pi$
$860$	−1.08372e6			−0.0499655
$861$	−102926.	−	82607.6i	−0.00473171	−	0.00379762i
$862$	6.23168e6			0.285652
$863$	−1.68836e7			−0.771682			−0.385841	−	0.922565i	$-0.626089\pi$
$863$	−1.68836e7			−0.771682			−0.385841	+	0.922565i	$0.626089\pi$
$864$	3.47887e6	+	1.71563e6i	0.158545	+	0.0781878i
$865$			2.77324e6i			0.126022i
$866$	1.99038e7			0.901864
$867$	3.52984e6	−	4.39806e6i	0.159480	−	0.198707i
$868$		−	501301.i		−	0.0225839i
$869$	−1.75003e7			−0.786132
$870$	−1.90454e6	+	2.37299e6i	−0.0853082	+	0.106291i
$871$	−386672.			−0.0172702
$872$			1.40917e7i			0.627585i
$873$	5.92814e6	−	1.31420e6i	0.263259	−	0.0583614i
$874$	−9.96595e6			−0.441306
$875$			972838.i			0.0429557i
$876$	3.18853e6	+	2.55908e6i	0.140388	+	0.112674i
$877$	920002.			0.0403915			0.0201957	−	0.999796i	$-0.493571\pi$
$877$	920002.			0.0403915			0.0201957	+	0.999796i	$0.493571\pi$
$878$	9.49487e6			0.415674
$879$	5.33276e6	+	4.28002e6i	0.232798	+	0.186842i
$880$			2.91063e6i			0.126701i
$881$	−6.50122e6			−0.282199			−0.141099	−	0.989995i	$-0.545064\pi$
$881$	−6.50122e6			−0.282199			−0.141099	+	0.989995i	$0.545064\pi$
$882$	3.53020e6	+	1.59242e7i	0.152802	+	0.689263i
$883$	3.31385e7			1.43031			0.715156	−	0.698965i	$-0.246356\pi$
$883$	3.31385e7			1.43031			0.715156	+	0.698965i	$0.246356\pi$
$884$	6.32420e6			0.272192
$885$	−1.70342e7	+	5.93627e6i	−0.731078	+	0.254774i
$886$	2.04884e6			0.0876846
$887$	−4.39283e7			−1.87472			−0.937358	−	0.348369i	$-0.886736\pi$
$887$	−4.39283e7			−1.87472			−0.937358	+	0.348369i	$0.886736\pi$
$888$	−5.41755e6	−	4.34807e6i	−0.230553	−	0.185039i
$889$	−1.36365e6			−0.0578694
$890$			1.55374e7i			0.657509i
$891$	1.40592e7	−	6.55570e6i	0.593289	−	0.276646i
$892$	1.51990e7			0.639592
$893$	−1.81259e7			−0.760627
$894$	−1.51714e7	+	1.89030e7i	−0.634864	+	0.791019i
$895$			1.78543e7i			0.745048i
$896$	−84142.2			−0.00350142
$897$	6.69091e6	+	5.37005e6i	0.277654	+	0.222842i
$898$			8.88122e6i			0.367521i
$899$	−6.87875e6			−0.283864
$900$	−1.05349e6	−	4.75210e6i	−0.0433533	−	0.195560i
$901$	−1.71067e7			−0.702029
$902$			1.73233e6i			0.0708946i
$903$	−97711.3	−	78422.1i	−0.00398773	−	0.00320051i
$904$	−1.09775e7			−0.446770
$905$		−	1.60205e6i		−	0.0650211i
$906$	76467.3	+	61371.9i	0.00309496	+	0.00248399i
$907$	−1.96151e6			−0.0791723			−0.0395862	−	0.999216i	$-0.512604\pi$
$907$	−1.96151e6			−0.0791723			−0.0395862	+	0.999216i	$0.512604\pi$
$908$	5.95269e6			0.239607
$909$	6.23412e6	+	2.81211e7i	0.250245	+	1.12881i
$910$	263275.			0.0105391
$911$		−	3.45674e7i		−	1.37997i	−0.723821	−	0.689987i	$-0.757616\pi$
$911$		−	3.45674e7i		−	1.37997i	0.723821	−	0.689987i	$-0.242384\pi$
$912$	3.34849e6	−	4.17211e6i	0.133310	−	0.166100i
$913$	1.38500e7			0.549886
$914$			3.13684e6i			0.124201i
$915$	−2.14328e7	+	2.67046e7i	−0.846305	+	1.05447i
$916$			5.67721e6i			0.223561i
$917$	120836.			0.00474540
$918$	−8.94522e6	+	1.81387e7i	−0.350336	+	0.710395i
$919$			2.45944e7i			0.960612i	0.877101	+	0.480306i	$0.159474\pi$
$919$			2.45944e7i			0.960612i	−0.877101	+	0.480306i	$0.840526\pi$
$920$		−	5.14794e6i		−	0.200523i
$921$	−7.95725e6	+	9.91447e6i	−0.309111	+	0.385142i
$922$		−	1.87048e7i		−	0.724646i
$923$	5.21920e6			0.201651
$924$	−210625.	+	262431.i	−0.00811577	+	0.0101120i
$925$			8.71701e6i			0.334976i
$926$			8.03375e6i			0.307887i
$927$	5.10058e6	−	1.13074e6i	0.194949	−	0.0432179i
$928$			1.15458e6i			0.0440104i
$929$	−2.25317e7			−0.856552			−0.428276	−	0.903648i	$-0.640879\pi$
$929$	−2.25317e7			−0.856552			−0.428276	+	0.903648i	$0.640879\pi$
$930$	−1.03050e7	+	1.28397e7i	−0.390698	+	0.486797i
$931$	2.24953e7			0.850585
$932$	−2.00420e7			−0.755790
$933$	−1.58017e7	−	1.26823e7i	−0.594292	−	0.476973i
$934$	−3.21010e7			−1.20407
$935$	−1.51759e7			−0.567710
$936$	−4.49620e6	+	996755.i	−0.167747	+	0.0371877i
$937$		−	1.16192e7i		−	0.432344i	−0.976355	−	0.216172i	$-0.930643\pi$
$937$		−	1.16192e7i		−	0.432344i	0.976355	−	0.216172i	$-0.0693571\pi$
$938$			26823.7i			0.000995433i
$939$	1.75323e7	+	1.40713e7i	0.648897	+	0.520798i
$940$		−	9.36299e6i		−	0.345617i
$941$	2.31486e6			0.0852218			0.0426109	−	0.999092i	$-0.486432\pi$
$941$	2.31486e6			0.0852218			0.0426109	+	0.999092i	$0.486432\pi$
$942$	4.84296e6	+	3.88691e6i	0.177821	+	0.142718i
$943$		−	3.06390e6i		−	0.112201i
$944$	−3.63100e6	+	5.80251e6i	−0.132616	+	0.211927i
$945$	−372387.	+	755110.i	−0.0135649	+	0.0275062i
$946$			1.64455e6i			0.0597476i
$947$			5.80247e6i			0.210251i	0.994459	+	0.105125i	$0.0335244\pi$
$947$			5.80247e6i			0.210251i	−0.994459	+	0.105125i	$0.966476\pi$
$948$	−1.03997e7	+	1.29577e7i	−0.375838	+	0.468281i
$949$	−4.85417e6			−0.174964
$950$	−6.71307e6			−0.241330
$951$	2.03757e6	+	1.63533e6i	0.0730570	+	0.0586348i
$952$		−	438714.i		−	0.0156888i
$953$			8.74975e6i			0.312078i	0.987751	+	0.156039i	$0.0498726\pi$
$953$			8.74975e6i			0.312078i	−0.987751	+	0.156039i	$0.950127\pi$
$954$	1.21621e7	−	2.69619e6i	0.432650	−	0.0959135i
$955$		−	6.74906e6i		−	0.239461i
$956$		−	2.70111e6i		−	0.0955868i
$957$	3.60103e6	+	2.89015e6i	0.127101	+	0.102010i
$958$			1.03813e7i			0.365457i
$959$			1.19515e6i			0.0419639i
$960$	2.15511e6	+	1.72967e6i	0.0754731	+	0.0605739i
$961$	−8.59024e6			−0.300052
$962$	8.24760e6			0.287336
$963$	4.08212e7	−	9.04958e6i	1.41847	−	0.314458i
$964$	5.44903e6			0.188854
$965$			2.25182e7i			0.778421i
$966$	372525.	−	464153.i	0.0128444	−	0.0160036i
$967$		−	94538.9i		−	0.00325121i	−0.999999	−	0.00162560i	$-0.999483\pi$
$967$		−	94538.9i		−	0.00325121i	0.999999	−	0.00162560i	$-0.000517446\pi$
$968$	−5.89035e6			−0.202047
$969$	2.17532e7	+	1.74589e7i	0.744243	+	0.597322i
$970$	4.32582e6			0.147618
$971$			6.08747e6i			0.207200i	0.994619	+	0.103600i	$0.0330361\pi$
$971$			6.08747e6i			0.207200i	−0.994619	+	0.103600i	$0.966964\pi$
$972$	3.50079e6	−	1.43056e7i	0.118850	−	0.485669i
$973$	−1.61932e6			−0.0548341
$974$	3.00476e6			0.101487
$975$	4.50699e6	+	3.61727e6i	0.151836	+	0.121862i
$976$			1.29932e7i			0.436607i
$977$	−5.01560e7			−1.68107			−0.840537	−	0.541754i	$-0.817760\pi$
$977$	−5.01560e7			−1.68107			−0.840537	+	0.541754i	$0.817760\pi$
$978$	−2.26646e7	+	2.82393e7i	−0.757706	+	0.944076i
$979$	2.35781e7			0.786234
$980$			1.16200e7i			0.386492i
$981$	5.22363e7	−	1.15802e7i	1.73300	−	0.384187i
$982$		−	4.16874e6i		−	0.137951i
$983$	−4.76773e7			−1.57372			−0.786861	−	0.617131i	$-0.788295\pi$
$983$	−4.76773e7			−1.57372			−0.786861	+	0.617131i	$0.788295\pi$
$984$	1.28266e6	+	1.02945e6i	0.0422303	+	0.0338936i
$985$	1.14597e7			0.376341
$986$	−6.01995e6			−0.197197
$987$	677542.	−	844195.i	0.0221383	−	0.0275835i
$988$			6.35157e6i			0.207009i
$989$		−	2.90867e6i		−	0.0945591i
$990$	1.07894e7	−	2.39188e6i	0.349871	−	0.0775623i
$991$		−	2.87525e7i		−	0.930019i	−0.885306	−	0.465010i	$-0.846051\pi$
$991$		−	2.87525e7i		−	0.930019i	0.885306	−	0.465010i	$-0.153949\pi$
$992$			6.24719e6i			0.201560i
$993$	−719523.	+	896501.i	−0.0231564	+	0.0288521i
$994$		−	362060.i		−	0.0116229i
$995$		−	3.45393e6i		−	0.110600i
$996$	8.23050e6	−	1.02549e7i	0.262892	−	0.327555i
$997$	171824.			0.00547452			0.00273726	−	0.999996i	$-0.499129\pi$
$997$	171824.			0.00547452			0.00273726	+	0.999996i	$0.499129\pi$
$998$	−1.95715e7			−0.622010
$999$	−1.16658e7	+	2.36553e7i	−0.369828	+	0.749920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.b.353.16	yes	50
3.2	odd	2		354.6.c.a.353.15	✓	50
59.58	odd	2		354.6.c.a.353.16	yes	50
177.176	even	2	inner	354.6.c.b.353.15	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.15	✓	50	3.2	odd	2
354.6.c.a.353.16	yes	50	59.58	odd	2
354.6.c.b.353.15	yes	50	177.176	even	2	inner
354.6.c.b.353.16	yes	50	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +(-9.75722 + 12.1572i) q^{3} +16.0000 q^{4} -43.2791i q^{5} +(-39.0289 + 48.6287i) q^{6} -5.13563 q^{7} +64.0000 q^{8} +(-52.5934 - 237.240i) q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +(-9.75722 + 12.1572i) q^{3} +16.0000 q^{4} -43.2791i q^{5} +(-39.0289 + 48.6287i) q^{6} -5.13563 q^{7} +64.0000 q^{8} +(-52.5934 - 237.240i) q^{9} -173.116i q^{10} -262.706 q^{11} +(-156.115 + 194.515i) q^{12} -296.127i q^{13} -20.5425 q^{14} +(526.151 + 422.283i) q^{15} +256.000 q^{16} +1334.77i q^{17} +(-210.374 - 948.961i) q^{18} -1340.55 q^{19} -692.465i q^{20} +(50.1095 - 62.4347i) q^{21} -1050.82 q^{22} +1858.55 q^{23} +(-624.462 + 778.059i) q^{24} +1251.92 q^{25} -1184.51i q^{26} +(3397.33 + 1675.42i) q^{27} -82.1701 q^{28} +1127.52i q^{29} +(2104.60 + 1689.13i) q^{30} +6100.77i q^{31} +1024.00 q^{32} +(2563.28 - 3193.76i) q^{33} +5339.10i q^{34} +222.265i q^{35} +(-841.494 - 3795.84i) q^{36} +6962.90i q^{37} -5362.21 q^{38} +(3600.06 + 2889.37i) q^{39} -2769.86i q^{40} -1648.54i q^{41} +(200.438 - 249.739i) q^{42} -1565.02i q^{43} -4203.29 q^{44} +(-10267.5 + 2276.19i) q^{45} +7434.22 q^{46} +13521.2 q^{47} +(-2497.85 + 3112.23i) q^{48} -16780.6 q^{49} +5007.69 q^{50} +(-16227.1 - 13023.7i) q^{51} -4738.02i q^{52} +12816.2i q^{53} +(13589.3 + 6701.67i) q^{54} +11369.7i q^{55} -328.680 q^{56} +(13080.1 - 16297.3i) q^{57} +4510.09i q^{58} +(-14183.6 + 22666.1i) q^{59} +(8418.41 + 6756.53i) q^{60} +50754.6i q^{61} +24403.1i q^{62} +(270.100 + 1218.38i) q^{63} +4096.00 q^{64} -12816.1 q^{65} +(10253.1 - 12775.0i) q^{66} -1305.77i q^{67} +21356.4i q^{68} +(-18134.3 + 22594.8i) q^{69} +889.061i q^{70} +17624.9i q^{71} +(-3365.98 - 15183.4i) q^{72} -16392.2i q^{73} +27851.6i q^{74} +(-12215.3 + 15219.8i) q^{75} -21448.8 q^{76} +1349.16 q^{77} +(14400.2 + 11557.5i) q^{78} +66615.5 q^{79} -11079.4i q^{80} +(-53516.9 + 24954.5i) q^{81} -6594.17i q^{82} -52720.6 q^{83} +(801.751 - 998.955i) q^{84} +57767.8 q^{85} -6260.06i q^{86} +(-13707.5 - 11001.5i) q^{87} -16813.2 q^{88} -89751.0 q^{89} +(-41070.1 + 9104.77i) q^{90} +1520.80i q^{91} +29736.9 q^{92} +(-74168.1 - 59526.5i) q^{93} +54085.0 q^{94} +58017.8i q^{95} +(-9991.39 + 12448.9i) q^{96} +24987.9i q^{97} -67122.5 q^{98} +(13816.6 + 62324.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 200 q^{2} - 13 q^{3} + 800 q^{4} - 52 q^{6} + 38 q^{7} + 3200 q^{8} + 51 q^{9}+O(q^{10}) \) 50 * q + 200 * q^2 - 13 * q^3 + 800 * q^4 - 52 * q^6 + 38 * q^7 + 3200 * q^8 + 51 * q^9	\( 50 q + 200 q^{2} - 13 q^{3} + 800 q^{4} - 52 q^{6} + 38 q^{7} + 3200 q^{8} + 51 q^{9} + 652 q^{11} - 208 q^{12} + 152 q^{14} - 2107 q^{15} + 12800 q^{16} + 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} - 2456 q^{23} - 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} - 8428 q^{30} + 51200 q^{32} + 9744 q^{33} + 816 q^{36} - 3576 q^{38} - 1388 q^{39} - 15204 q^{42} + 10432 q^{44} + 33067 q^{45} - 9824 q^{46} + 27144 q^{47} - 3328 q^{48} + 85768 q^{49} - 95824 q^{50} + 3338 q^{51} + 39560 q^{54} + 2432 q^{56} - 63969 q^{57} + 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} + 9400 q^{65} + 38976 q^{66} + 115930 q^{69} + 3264 q^{72} + 24248 q^{75} - 14304 q^{76} + 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} + 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} - 104908 q^{89} + 132268 q^{90} - 39296 q^{92} + 91204 q^{93} + 108576 q^{94} - 13312 q^{96} + 343072 q^{98} + 111406 q^{99}+O(q^{100}) \) 50 * q + 200 * q^2 - 13 * q^3 + 800 * q^4 - 52 * q^6 + 38 * q^7 + 3200 * q^8 + 51 * q^9 + 652 * q^11 - 208 * q^12 + 152 * q^14 - 2107 * q^15 + 12800 * q^16 + 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 - 2456 * q^23 - 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 - 8428 * q^30 + 51200 * q^32 + 9744 * q^33 + 816 * q^36 - 3576 * q^38 - 1388 * q^39 - 15204 * q^42 + 10432 * q^44 + 33067 * q^45 - 9824 * q^46 + 27144 * q^47 - 3328 * q^48 + 85768 * q^49 - 95824 * q^50 + 3338 * q^51 + 39560 * q^54 + 2432 * q^56 - 63969 * q^57 + 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 + 9400 * q^65 + 38976 * q^66 + 115930 * q^69 + 3264 * q^72 + 24248 * q^75 - 14304 * q^76 + 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 + 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 - 104908 * q^89 + 132268 * q^90 - 39296 * q^92 + 91204 * q^93 + 108576 * q^94 - 13312 * q^96 + 343072 * q^98 + 111406 * q^99

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