LMFDB - Embedded newform 354.6.c.a.353.5

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			353.5
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-14.5480 - 5.59965i) q^{3} +16.0000 q^{4} +83.1853i q^{5} +(58.1920 + 22.3986i) q^{6} +242.629 q^{7} -64.0000 q^{8} +(180.288 + 162.927i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-14.5480 - 5.59965i) q^{3} +16.0000 q^{4} +83.1853i q^{5} +(58.1920 + 22.3986i) q^{6} +242.629 q^{7} -64.0000 q^{8} +(180.288 + 162.927i) q^{9} -332.741i q^{10} -603.503 q^{11} +(-232.768 - 89.5943i) q^{12} -200.595i q^{13} -970.517 q^{14} +(465.809 - 1210.18i) q^{15} +256.000 q^{16} -1078.67i q^{17} +(-721.152 - 651.709i) q^{18} -306.354 q^{19} +1330.97i q^{20} +(-3529.77 - 1358.64i) q^{21} +2414.01 q^{22} -721.250 q^{23} +(931.071 + 358.377i) q^{24} -3794.80 q^{25} +802.381i q^{26} +(-1710.49 - 3379.81i) q^{27} +3882.07 q^{28} +1174.08i q^{29} +(-1863.23 + 4840.72i) q^{30} -7639.98i q^{31} -1024.00 q^{32} +(8779.76 + 3379.41i) q^{33} +4314.69i q^{34} +20183.2i q^{35} +(2884.61 + 2606.84i) q^{36} +4804.26i q^{37} +1225.41 q^{38} +(-1123.26 + 2918.26i) q^{39} -5323.86i q^{40} -3936.03i q^{41} +(14119.1 + 5434.55i) q^{42} +21351.1i q^{43} -9656.05 q^{44} +(-13553.2 + 14997.3i) q^{45} +2885.00 q^{46} -21477.5 q^{47} +(-3724.28 - 1433.51i) q^{48} +42061.9 q^{49} +15179.2 q^{50} +(-6040.18 + 15692.5i) q^{51} -3209.53i q^{52} -23127.8i q^{53} +(6841.97 + 13519.2i) q^{54} -50202.6i q^{55} -15528.3 q^{56} +(4456.83 + 1715.47i) q^{57} -4696.33i q^{58} +(11513.5 + 24132.2i) q^{59} +(7452.94 - 19362.9i) q^{60} -36884.7i q^{61} +30559.9i q^{62} +(43743.1 + 39530.9i) q^{63} +4096.00 q^{64} +16686.6 q^{65} +(-35119.0 - 13517.6i) q^{66} -50577.0i q^{67} -17258.8i q^{68} +(10492.7 + 4038.74i) q^{69} -80732.8i q^{70} -49163.7i q^{71} +(-11538.4 - 10427.3i) q^{72} +44405.3i q^{73} -19217.0i q^{74} +(55206.7 + 21249.5i) q^{75} -4901.66 q^{76} -146428. q^{77} +(4493.05 - 11673.0i) q^{78} -96414.4 q^{79} +21295.4i q^{80} +(5958.46 + 58747.6i) q^{81} +15744.1i q^{82} -62176.7 q^{83} +(-56476.3 - 21738.2i) q^{84} +89729.7 q^{85} -85404.4i q^{86} +(6574.44 - 17080.5i) q^{87} +38624.2 q^{88} +94995.0 q^{89} +(54212.6 - 59989.2i) q^{90} -48670.3i q^{91} -11540.0 q^{92} +(-42781.2 + 111146. i) q^{93} +85910.1 q^{94} -25484.1i q^{95} +(14897.1 + 5734.04i) q^{96} +17459.9i q^{97} -168248. q^{98} +(-108804. - 98327.1i) 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
$3$	−14.5480	−	5.59965i	−0.933254	−	0.359218i
$3$	−14.5480	−	5.59965i	−0.933254	−	0.359218i
$4$	16.0000			0.500000
$5$			83.1853i			1.48806i	0.668144	+	0.744032i	$0.267089\pi$
$5$			83.1853i			1.48806i	−0.668144	+	0.744032i	$0.732911\pi$
$6$	58.1920	+	22.3986i	0.659910	+	0.254005i
$7$	242.629			1.87153			0.935767	−	0.352618i	$-0.114709\pi$
$7$	242.629			1.87153			0.935767	+	0.352618i	$0.114709\pi$
$8$	−64.0000			−0.353553
$9$	180.288	+	162.927i	0.741926	+	0.670482i
$10$		−	332.741i		−	1.05222i
$11$	−603.503			−1.50383			−0.751914	−	0.659262i	$-0.770869\pi$
$11$	−603.503			−1.50383			−0.751914	+	0.659262i	$0.770869\pi$
$12$	−232.768	−	89.5943i	−0.466627	−	0.179609i
$13$		−	200.595i		−	0.329202i	−0.986360	−	0.164601i	$-0.947366\pi$
$13$		−	200.595i		−	0.329202i	0.986360	−	0.164601i	$-0.0526337\pi$
$14$	−970.517			−1.32337
$15$	465.809	−	1210.18i	0.534539	−	1.38874i
$16$	256.000			0.250000
$17$		−	1078.67i		−	0.905247i	−0.891702	−	0.452623i	$-0.850488\pi$
$17$		−	1078.67i		−	0.905247i	0.891702	−	0.452623i	$-0.149512\pi$
$18$	−721.152	−	651.709i	−0.524621	−	0.474103i
$19$	−306.354			−0.194688			−0.0973440	−	0.995251i	$-0.531035\pi$
$19$	−306.354			−0.194688			−0.0973440	+	0.995251i	$0.531035\pi$
$20$			1330.97i			0.744032i
$21$	−3529.77	−	1358.64i	−1.74662	−	0.672288i
$22$	2414.01			1.06337
$23$	−721.250			−0.284293			−0.142146	−	0.989846i	$-0.545400\pi$
$23$	−721.250			−0.284293			−0.142146	+	0.989846i	$0.545400\pi$
$24$	931.071	+	358.377i	0.329955	+	0.127003i
$25$	−3794.80			−1.21434
$26$			802.381i			0.232781i
$27$	−1710.49	−	3379.81i	−0.451556	−	0.892243i
$28$	3882.07			0.935767
$29$			1174.08i			0.259241i	0.991564	+	0.129620i	$0.0413759\pi$
$29$			1174.08i			0.259241i	−0.991564	+	0.129620i	$0.958624\pi$
$30$	−1863.23	+	4840.72i	−0.377976	+	0.981989i
$31$		−	7639.98i		−	1.42787i	−0.700213	−	0.713934i	$-0.746912\pi$
$31$		−	7639.98i		−	1.42787i	0.700213	−	0.713934i	$-0.253088\pi$
$32$	−1024.00			−0.176777
$33$	8779.76	+	3379.41i	1.40345	+	0.540201i
$34$			4314.69i			0.640106i
$35$			20183.2i			2.78496i
$36$	2884.61	+	2606.84i	0.370963	+	0.335241i
$37$			4804.26i			0.576928i	0.957491	+	0.288464i	$0.0931446\pi$
$37$			4804.26i			0.576928i	−0.957491	+	0.288464i	$0.906855\pi$
$38$	1225.41			0.137665
$39$	−1123.26	+	2918.26i	−0.118255	+	0.307229i
$40$		−	5323.86i		−	0.526110i
$41$		−	3936.03i		−	0.365678i	−0.983143	−	0.182839i	$-0.941471\pi$
$41$		−	3936.03i		−	0.365678i	0.983143	−	0.182839i	$-0.0585287\pi$
$42$	14119.1	+	5434.55i	1.23504	+	0.475379i
$43$			21351.1i			1.76096i	0.474084	+	0.880480i	$0.342779\pi$
$43$			21351.1i			1.76096i	−0.474084	+	0.880480i	$0.657221\pi$
$44$	−9656.05			−0.751914
$45$	−13553.2	+	14997.3i	−0.997721	+	1.10403i
$46$	2885.00			0.201025
$47$	−21477.5			−1.41821			−0.709104	−	0.705104i	$-0.750900\pi$
$47$	−21477.5			−1.41821			−0.709104	+	0.705104i	$0.750900\pi$
$48$	−3724.28	−	1433.51i	−0.233313	−	0.0898044i
$49$	42061.9			2.50264
$50$	15179.2			0.858666
$51$	−6040.18	+	15692.5i	−0.325181	+	0.844825i
$52$		−	3209.53i		−	0.164601i
$53$		−	23127.8i		−	1.13096i	−0.824764	−	0.565478i	$-0.808692\pi$
$53$		−	23127.8i		−	1.13096i	0.824764	−	0.565478i	$-0.191308\pi$
$54$	6841.97	+	13519.2i	0.319298	+	0.630911i
$55$		−	50202.6i		−	2.23779i
$56$	−15528.3			−0.661687
$57$	4456.83	+	1715.47i	0.181693	+	0.0699353i
$58$		−	4696.33i		−	0.183311i
$59$	11513.5	+	24132.2i	0.430602	+	0.902542i
$59$	11513.5	+	24132.2i	0.430602	+	0.902542i
$60$	7452.94	−	19362.9i	0.267269	−	0.694371i
$61$		−	36884.7i		−	1.26917i	−0.772851	−	0.634587i	$-0.781170\pi$
$61$		−	36884.7i		−	1.26917i	0.772851	−	0.634587i	$-0.218830\pi$
$62$			30559.9i			1.00965i
$63$	43743.1	+	39530.9i	1.38854	+	1.25483i
$64$	4096.00			0.125000
$65$	16686.6			0.489874
$66$	−35119.0	−	13517.6i	−0.992391	−	0.381980i
$67$		−	50577.0i		−	1.37647i	−0.725488	−	0.688235i	$-0.758386\pi$
$67$		−	50577.0i		−	1.37647i	0.725488	−	0.688235i	$-0.241614\pi$
$68$		−	17258.8i		−	0.452623i
$69$	10492.7	+	4038.74i	0.265317	+	0.102123i
$70$		−	80732.8i		−	1.96927i
$71$		−	49163.7i		−	1.15744i	−0.815526	−	0.578720i	$-0.803552\pi$
$71$		−	49163.7i		−	1.15744i	0.815526	−	0.578720i	$-0.196448\pi$
$72$	−11538.4	−	10427.3i	−0.262310	−	0.237051i
$73$			44405.3i			0.975276i	0.873046	+	0.487638i	$0.162141\pi$
$73$			44405.3i			0.975276i	−0.873046	+	0.487638i	$0.837859\pi$
$74$		−	19217.0i		−	0.407950i
$75$	55206.7	+	21249.5i	1.13328	+	0.436211i
$76$	−4901.66			−0.0973440
$77$	−146428.			−2.81446
$78$	4493.05	−	11673.0i	0.0836190	−	0.217244i
$79$	−96414.4			−1.73810			−0.869049	−	0.494727i	$-0.835268\pi$
$79$	−96414.4			−1.73810			−0.869049	+	0.494727i	$0.835268\pi$
$80$			21295.4i			0.372016i
$81$	5958.46	+	58747.6i	0.100907	+	0.994896i
$82$			15744.1i			0.258573i
$83$	−62176.7			−0.990677			−0.495339	−	0.868700i	$-0.664956\pi$
$83$	−62176.7			−0.990677			−0.495339	+	0.868700i	$0.664956\pi$
$84$	−56476.3	−	21738.2i	−0.873308	−	0.336144i
$85$	89729.7			1.34707
$86$		−	85404.4i		−	1.24519i
$87$	6574.44	−	17080.5i	0.0931238	−	0.241937i
$88$	38624.2			0.531683
$89$	94995.0			1.27123			0.635617	−	0.772004i	$-0.280746\pi$
$89$	94995.0			1.27123			0.635617	+	0.772004i	$0.280746\pi$
$90$	54212.6	−	59989.2i	0.705495	−	0.780669i
$91$		−	48670.3i		−	0.616113i
$92$	−11540.0			−0.142146
$93$	−42781.2	+	111146.i	−0.512915	+	1.33256i
$94$	85910.1			1.00282
$95$		−	25484.1i		−	0.289708i
$96$	14897.1	+	5734.04i	0.164978	+	0.0635013i
$97$			17459.9i			0.188414i	0.995553	+	0.0942068i	$0.0300315\pi$
$97$			17459.9i			0.188414i	−0.995553	+	0.0942068i	$0.969969\pi$
$98$	−168248.			−1.76963
$99$	−108804.	−	98327.1i	−1.11573	−	1.00829i
$100$	−60716.8			−0.607168
$101$	−130334.			−1.27132			−0.635660	−	0.771969i	$-0.719272\pi$
$101$	−130334.			−1.27132			−0.635660	+	0.771969i	$0.719272\pi$
$102$	24160.7	−	62770.0i	0.229937	−	0.597382i
$103$		−	56688.9i		−	0.526508i	−0.964727	−	0.263254i	$-0.915204\pi$
$103$		−	56688.9i		−	0.526508i	0.964727	−	0.263254i	$-0.0847958\pi$
$104$			12838.1i			0.116390i
$105$	113019.	−	293625.i	1.00041	−	2.59908i
$106$			92511.4i			0.799706i
$107$			28797.0i			0.243158i	0.992582	+	0.121579i	$0.0387957\pi$
$107$			28797.0i			0.243158i	−0.992582	+	0.121579i	$0.961204\pi$
$108$	−27367.9	−	54077.0i	−0.225778	−	0.446121i
$109$		−	153856.i		−	1.24036i	−0.784459	−	0.620180i	$-0.787060\pi$
$109$		−	153856.i		−	1.24036i	0.784459	−	0.620180i	$-0.212940\pi$
$110$			200811.i			1.58236i
$111$	26902.1	−	69892.2i	0.207243	−	0.538420i
$112$	62113.1			0.467884
$113$	176375.			1.29940			0.649698	−	0.760193i	$-0.274896\pi$
$113$	176375.			1.29940			0.649698	+	0.760193i	$0.274896\pi$
$114$	−17827.3	−	6861.89i	−0.128477	−	0.0494517i
$115$		−	59997.4i		−	0.423046i
$116$			18785.3i			0.129620i
$117$	32682.4	−	36164.9i	0.220724	−	0.244243i
$118$	−46053.9	−	96528.9i	−0.304482	−	0.638193i
$119$		−	261717.i		−	1.69420i
$120$	−29811.7	+	77451.5i	−0.188988	+	0.490994i
$121$	203165.			1.26150
$122$			147539.i			0.897442i
$123$	−22040.4	+	57261.3i	−0.131358	+	0.341270i
$124$		−	122240.i		−	0.713934i
$125$		−	55717.7i		−	0.318947i
$126$	−174972.	−	158124.i	−0.981846	−	0.887299i
$127$	31369.7			0.172584			0.0862921	−	0.996270i	$-0.472498\pi$
$127$	31369.7			0.172584			0.0862921	+	0.996270i	$0.472498\pi$
$128$	−16384.0			−0.0883883
$129$	119559.	−	310616.i	0.632567	−	1.64342i
$130$	−66746.4			−0.346393
$131$	−188360.			−0.958980			−0.479490	−	0.877547i	$-0.659178\pi$
$131$	−188360.			−0.958980			−0.479490	+	0.877547i	$0.659178\pi$
$132$	140476.	+	54070.5i	0.701726	+	0.270101i
$133$	−74330.3			−0.364365
$134$			202308.i			0.973311i
$135$	281151.	−	142288.i	1.32772	−	0.671944i
$136$			69035.0i			0.320053i
$137$		−	219631.i		−	0.999750i	−0.866097	−	0.499875i	$-0.833379\pi$
$137$		−	219631.i		−	0.999750i	0.866097	−	0.499875i	$-0.166621\pi$
$138$	−41970.9	−	16155.0i	−0.187608	−	0.0722119i
$139$	−82895.9			−0.363912			−0.181956	−	0.983307i	$-0.558243\pi$
$139$	−82895.9			−0.363912			−0.181956	+	0.983307i	$0.558243\pi$
$140$			322931.i			1.39248i
$141$	312455.	+	120267.i	1.32355	+	0.509445i
$142$			196655.i			0.818434i
$143$			121060.i			0.495063i
$144$	46153.7	+	41709.4i	0.185481	+	0.167621i
$145$	−97666.4			−0.385767
$146$		−	177621.i		−	0.689624i
$147$	−611916.	−	235532.i	−2.33560	−	0.898993i
$148$			76868.1i			0.288464i
$149$	355984.			1.31360			0.656802	−	0.754063i	$-0.271909\pi$
$149$	355984.			1.31360			0.656802	+	0.754063i	$0.271909\pi$
$150$	−220827.	−	84998.2i	−0.801353	−	0.308448i
$151$		−	507198.i		−	1.81023i	−0.425162	−	0.905117i	$-0.639783\pi$
$151$		−	507198.i		−	1.81023i	0.425162	−	0.905117i	$-0.360217\pi$
$152$	19606.6			0.0688326
$153$	175745.	−	194472.i	0.606952	−	0.671626i
$154$	585710.			1.99013
$155$	635534.			2.12476
$156$	−17972.2	+	46692.1i	−0.0591276	+	0.153615i
$157$		−	484492.i		−	1.56869i	−0.620324	−	0.784346i	$-0.712999\pi$
$157$		−	484492.i		−	1.56869i	0.620324	−	0.784346i	$-0.287001\pi$
$158$	385657.			1.22902
$159$	−129508.	+	336464.i	−0.406259	+	1.05547i
$160$		−	85181.8i		−	0.263055i
$161$	−174996.			−0.532064
$162$	−23833.8	−	234990.i	−0.0713521	−	0.703498i
$163$	13455.9			0.0396684			0.0198342	−	0.999803i	$-0.493686\pi$
$163$	13455.9			0.0396684			0.0198342	+	0.999803i	$0.493686\pi$
$164$		−	62976.5i		−	0.182839i
$165$	−281117.	+	730347.i	−0.803854	+	2.08843i
$166$	248707.			0.700515
$167$			169945.i			0.471539i	0.971809	+	0.235770i	$0.0757611\pi$
$167$			169945.i			0.471539i	−0.971809	+	0.235770i	$0.924239\pi$
$168$	225905.	+	86952.8i	0.617522	+	0.237690i
$169$	331055.			0.891626
$170$	−358919.			−0.952520
$171$	−55231.9	−	49913.3i	−0.144444	−	0.130535i
$172$			341618.i			0.880480i
$173$	309682.			0.786684			0.393342	−	0.919392i	$-0.371319\pi$
$173$	309682.			0.786684			0.393342	+	0.919392i	$0.371319\pi$
$174$	−26297.8	+	68322.1i	−0.0658485	+	0.171076i
$175$	−920729.			−2.27267
$176$	−154497.			−0.375957
$177$	−32366.0	−	415547.i	−0.0776527	−	0.996980i
$178$	−379980.			−0.898899
$179$	243285.			0.567522			0.283761	−	0.958895i	$-0.408418\pi$
$179$	243285.			0.567522			0.283761	+	0.958895i	$0.408418\pi$
$180$	−216850.	+	239957.i	−0.498860	+	0.552017i
$181$	92458.8			0.209774			0.104887	−	0.994484i	$-0.466552\pi$
$181$	92458.8			0.209774			0.104887	+	0.994484i	$0.466552\pi$
$182$			194681.i			0.435658i
$183$	−206541.	+	536598.i	−0.455910	+	1.18446i
$184$	46160.0			0.100513
$185$	−399644.			−0.858506
$186$	171125.	−	444585.i	0.362686	−	0.942264i
$187$			650982.i			1.36134i
$188$	−343641.			−0.709104
$189$	−415015.	−	820041.i	−0.845103	−	1.66986i
$190$			101937.i			0.204855i
$191$	449079.			0.890716			0.445358	−	0.895352i	$-0.353076\pi$
$191$	449079.			0.890716			0.445358	+	0.895352i	$0.353076\pi$
$192$	−59588.6	−	22936.2i	−0.116657	−	0.0449022i
$193$	−934057.			−1.80501			−0.902506	−	0.430677i	$-0.858275\pi$
$193$	−934057.			−1.80501			−0.902506	+	0.430677i	$0.858275\pi$
$194$		−	69839.6i		−	0.133229i
$195$	−242756.	−	93439.0i	−0.457177	−	0.175971i
$196$	672990.			1.25132
$197$			16120.7i			0.0295950i	0.999891	+	0.0147975i	$0.00471036\pi$
$197$			16120.7i			0.0295950i	−0.999891	+	0.0147975i	$0.995290\pi$
$198$	435217.	+	393308.i	0.788939	+	0.712968i
$199$	−228996.			−0.409917			−0.204959	−	0.978771i	$-0.565706\pi$
$199$	−228996.			−0.409917			−0.204959	+	0.978771i	$0.565706\pi$
$200$	242867.			0.429333
$201$	−283214.	+	735794.i	−0.494452	+	1.28460i
$202$	521336.			0.898958
$203$			284866.i			0.485178i
$204$	−96642.9	+	251080.i	−0.162590	+	0.422413i
$205$	327420.			0.544152
$206$			226756.i			0.372298i
$207$	−130033.	−	117511.i	−0.210924	−	0.190613i
$208$		−	51352.4i		−	0.0823005i
$209$	184885.			0.292777
$210$	−452075.	+	1.17450e6i	−0.707395	+	1.83783i
$211$			661020.i			1.02214i	0.859540	+	0.511068i	$0.170750\pi$
$211$			661020.i			1.02214i	−0.859540	+	0.511068i	$0.829250\pi$
$212$		−	370045.i		−	0.565478i
$213$	−275299.	+	715233.i	−0.415773	+	1.08019i
$214$		−	115188.i		−	0.171939i
$215$	−1.77610e6			−2.62042
$216$	109471.	+	216308.i	0.159649	+	0.315455i
$217$		−	1.85368e6i		−	2.67230i
$218$			615423.i			0.877067i
$219$	248654.	−	646008.i	0.350336	−	0.910180i
$220$		−	803242.i		−	1.11890i
$221$	−216377.			−0.298009
$222$	−107609.	+	279569.i	−0.146543	+	0.380721i
$223$	519447.			0.699486			0.349743	−	0.936846i	$-0.386269\pi$
$223$	519447.			0.699486			0.349743	+	0.936846i	$0.386269\pi$
$224$	−248452.			−0.330844
$225$	−684157.	−	618276.i	−0.900947	−	0.814191i
$226$	−705500.			−0.918811
$227$	−281093.			−0.362063			−0.181032	−	0.983477i	$-0.557944\pi$
$227$	−281093.			−0.362063			−0.181032	+	0.983477i	$0.557944\pi$
$228$	71309.3	+	27447.6i	0.0908466	+	0.0349677i
$229$			524173.i			0.660520i	0.943890	+	0.330260i	$0.107136\pi$
$229$			524173.i			0.660520i	−0.943890	+	0.330260i	$0.892864\pi$
$230$			239990.i			0.299139i
$231$	2.13023e6	+	819942.i	2.62661	+	1.01101i
$232$		−	75141.2i		−	0.0916554i
$233$	−66531.0			−0.0802850			−0.0401425	−	0.999194i	$-0.512781\pi$
$233$	−66531.0			−0.0802850			−0.0401425	+	0.999194i	$0.512781\pi$
$234$	−130730.	+	144660.i	−0.156076	+	0.172706i
$235$		−	1.78662e6i		−	2.11038i
$236$	184216.	+	386116.i	0.215301	+	0.451271i
$237$	1.40264e6	+	539886.i	1.62209	+	0.624355i
$238$			1.04687e6i			1.19798i
$239$		−	1.15440e6i		−	1.30726i	−0.756816	−	0.653628i	$-0.773246\pi$
$239$		−	1.15440e6i		−	1.30726i	0.756816	−	0.653628i	$-0.226754\pi$
$240$	119247.	−	309806.i	0.133635	−	0.347186i
$241$	1.18720e6			1.31668			0.658342	−	0.752719i	$-0.271258\pi$
$241$	1.18720e6			1.31668			0.658342	+	0.752719i	$0.271258\pi$
$242$	−812661.			−0.892013
$243$	242282.	−	888025.i	0.263212	−	0.964738i
$244$		−	590155.i		−	0.634587i
$245$			3.49893e6i			3.72409i
$246$	88161.5	−	229045.i	0.0928840	−	0.241314i
$247$			61453.1i			0.0640917i
$248$			488959.i			0.504827i
$249$	904546.	+	348167.i	0.924554	+	0.355869i
$250$			222871.i			0.225529i
$251$			156420.i			0.156714i	0.996925	+	0.0783570i	$0.0249674\pi$
$251$			156420.i			0.156714i	−0.996925	+	0.0783570i	$0.975033\pi$
$252$	699890.	+	632494.i	0.694270	+	0.627415i
$253$	435277.			0.427528
$254$	−125479.			−0.122036
$255$	−1.30539e6	−	502455.i	−1.25715	−	0.483890i
$256$	65536.0			0.0625000
$257$		−	1.33852e6i		−	1.26413i	−0.774916	−	0.632065i	$-0.782208\pi$
$257$		−	1.33852e6i		−	1.26413i	0.774916	−	0.632065i	$-0.217792\pi$
$258$	−478235.	+	1.24246e6i	−0.447293	+	1.16208i
$259$			1.16565e6i			1.07974i
$260$	266986.			0.244937
$261$	−191290.	+	211673.i	−0.173816	+	0.192337i
$262$	753438.			0.678101
$263$		−	1.97747e6i		−	1.76287i	−0.472302	−	0.881437i	$-0.656577\pi$
$263$		−	1.97747e6i		−	1.76287i	0.472302	−	0.881437i	$-0.343423\pi$
$264$	−561905.	−	216282.i	−0.496195	−	0.190990i
$265$	1.92390e6			1.68293
$266$	297321.			0.257645
$267$	−1.38199e6	−	531938.i	−1.18638	−	0.456650i
$268$		−	809233.i		−	0.688235i
$269$	−687247.			−0.579071			−0.289536	−	0.957167i	$-0.593501\pi$
$269$	−687247.			−0.579071			−0.289536	+	0.957167i	$0.593501\pi$
$270$	−1.12460e6	+	569151.i	−0.938836	+	0.475136i
$271$	−1.98771e6			−1.64410			−0.822052	−	0.569413i	$-0.807171\pi$
$271$	−1.98771e6			−1.64410			−0.822052	+	0.569413i	$0.807171\pi$
$272$		−	276140.i		−	0.226312i
$273$	−272536.	+	708055.i	−0.221319	+	0.574990i
$274$			878523.i			0.706930i
$275$	2.29018e6			1.82615
$276$	167884.	+	64619.9i	0.132659	+	0.0510615i
$277$	−114075.			−0.0893285			−0.0446643	−	0.999002i	$-0.514222\pi$
$277$	−114075.			−0.0893285			−0.0446643	+	0.999002i	$0.514222\pi$
$278$	331584.			0.257324
$279$	1.24476e6	−	1.37740e6i	0.957360	−	1.05937i
$280$		−	1.29172e6i		−	0.984634i
$281$			959784.i			0.725116i	0.931961	+	0.362558i	$0.118097\pi$
$281$			959784.i			0.725116i	−0.931961	+	0.362558i	$0.881903\pi$
$282$	−1.24982e6	−	481066.i	−0.935889	−	0.360232i
$283$			201800.i			0.149780i	0.997192	+	0.0748902i	$0.0238606\pi$
$283$			201800.i			0.149780i	−0.997192	+	0.0748902i	$0.976139\pi$
$284$		−	786619.i		−	0.578720i
$285$	−142702.	+	370743.i	−0.104068	+	0.270371i
$286$		−	484240.i		−	0.350062i
$287$		−	954995.i		−	0.684379i
$288$	−184615.	−	166837.i	−0.131155	−	0.118526i
$289$	256324.			0.180528
$290$	390665.			0.272778
$291$	97769.2	−	254006.i	0.0676815	−	0.175838i
$292$			710485.i			0.487638i
$293$		−	1.07083e6i		−	0.728707i	−0.931261	−	0.364353i	$-0.881290\pi$
$293$		−	1.07083e6i		−	0.728707i	0.931261	−	0.364353i	$-0.118710\pi$
$294$	2.44766e6	+	942127.i	1.65152	+	0.635684i
$295$	−2.00745e6	+	957753.i	−1.34304	+	0.640764i
$296$		−	307472.i		−	0.203975i
$297$	1.03229e6	+	2.03973e6i	0.679062	+	1.34178i
$298$	−1.42394e6			−0.928859
$299$			144679.i			0.0935898i
$300$	883308.	+	339993.i	0.566642	+	0.218105i
$301$			5.18040e6i			3.29570i
$302$			2.02879e6i			1.28003i
$303$	1.89610e6	+	729825.i	1.18646	+	0.456680i
$304$	−78426.5			−0.0486720
$305$	3.06826e6			1.88861
$306$	−702980.	+	777886.i	−0.429180	+	0.474911i
$307$	−167870.			−0.101655			−0.0508273	−	0.998707i	$-0.516186\pi$
$307$	−167870.			−0.101655			−0.0508273	+	0.998707i	$0.516186\pi$
$308$	−2.34284e6			−1.40723
$309$	−317438.	+	824710.i	−0.189131	+	0.491366i
$310$	−2.54214e6			−1.50243
$311$		−	3.04969e6i		−	1.78795i	−0.448117	−	0.893975i	$-0.647905\pi$
$311$		−	3.04969e6i		−	1.78795i	0.448117	−	0.893975i	$-0.352095\pi$
$312$	71888.8	−	186769.i	0.0418095	−	0.108622i
$313$			307437.i			0.177376i	0.996059	+	0.0886880i	$0.0282674\pi$
$313$			307437.i			0.177376i	−0.996059	+	0.0886880i	$0.971733\pi$
$314$			1.93797e6i			1.10923i
$315$	−3.28839e6	+	3.63878e6i	−1.86727	+	2.06624i
$316$	−1.54263e6			−0.869049
$317$		−	1.28599e6i		−	0.718769i	−0.933190	−	0.359384i	$-0.882987\pi$
$317$		−	1.28599e6i		−	0.718769i	0.933190	−	0.359384i	$-0.117013\pi$
$318$	518031.	−	1.34585e6i	0.287268	−	0.746329i
$319$		−	708562.i		−	0.389853i
$320$			340727.i			0.186008i
$321$	161253.	−	418939.i	0.0873465	−	0.226928i
$322$	699985.			0.376226
$323$			330455.i			0.176241i
$324$	95335.4	+	939962.i	0.0504535	+	0.497448i
$325$			761220.i			0.399762i
$326$	−53823.7			−0.0280498
$327$	−861538.	+	2.23829e6i	−0.445559	+	1.15757i
$328$			251906.i			0.129287i
$329$	−5.21108e6			−2.65422
$330$	1.12447e6	−	2.92139e6i	0.568411	−	1.47674i
$331$	−656836.			−0.329524			−0.164762	−	0.986333i	$-0.552686\pi$
$331$	−656836.			−0.329524			−0.164762	+	0.986333i	$0.552686\pi$
$332$	−994827.			−0.495339
$333$	−782744.	+	866149.i	−0.386820	+	0.428038i
$334$		−	679781.i		−	0.333429i
$335$	4.20727e6			2.04828
$336$	−903620.	−	347811.i	−0.436654	−	0.168072i
$337$			526525.i			0.252548i	0.991995	+	0.126274i	$0.0403019\pi$
$337$			526525.i			0.252548i	−0.991995	+	0.126274i	$0.959698\pi$
$338$	−1.32422e6			−0.630475
$339$	−2.56590e6	−	987638.i	−1.21267	−	0.466765i
$340$	1.43568e6			0.673533
$341$			4.61075e6i			2.14727i
$342$	220927.	+	199653.i	0.102137	+	0.0923020i
$343$	6.12757e6			2.81225
$344$		−	1.36647e6i		−	0.622593i
$345$	−335964.	+	872842.i	−0.151966	+	0.394810i
$346$	−1.23873e6			−0.556270
$347$	2.15604e6			0.961243			0.480621	−	0.876928i	$-0.340411\pi$
$347$	2.15604e6			0.961243			0.480621	+	0.876928i	$0.340411\pi$
$348$	105191.	−	273288.i	0.0465619	−	0.120969i
$349$		−	1.93370e6i		−	0.849816i	−0.905236	−	0.424908i	$-0.860306\pi$
$349$		−	1.93370e6i		−	0.849816i	0.905236	−	0.424908i	$-0.139694\pi$
$350$	3.68292e6			1.60702
$351$	−677974.	+	343117.i	−0.293728	+	0.148653i
$352$	617987.			0.265842
$353$	737544.			0.315029			0.157515	−	0.987517i	$-0.449652\pi$
$353$	737544.			0.315029			0.157515	+	0.987517i	$0.449652\pi$
$354$	129464.	+	1.66219e6i	0.0549087	+	0.704972i
$355$	4.08970e6			1.72235
$356$	1.51992e6			0.635617
$357$	−1.46552e6	+	3.80746e6i	−0.608587	+	1.58112i
$358$	−973139.			−0.401298
$359$		−	1.41661e6i		−	0.580117i	−0.957009	−	0.290058i	$-0.906325\pi$
$359$		−	1.41661e6i		−	0.580117i	0.957009	−	0.290058i	$-0.0936747\pi$
$360$	867402.	−	959828.i	0.352748	−	0.390335i
$361$	−2.38225e6			−0.962097
$362$	−369835.			−0.148333
$363$	−2.95565e6	−	1.13765e6i	−1.17730	−	0.453152i
$364$		−	778724.i		−	0.308056i
$365$	−3.69387e6			−1.45127
$366$	826164.	−	2.14639e6i	0.322377	−	0.837541i
$367$		−	3.18954e6i		−	1.23613i	−0.786129	−	0.618063i	$-0.787918\pi$
$367$		−	3.18954e6i		−	1.23613i	0.786129	−	0.618063i	$-0.212082\pi$
$368$	−184640.			−0.0710732
$369$	641286.	−	709618.i	0.245180	−	0.271306i
$370$	1.59857e6			0.607056
$371$		−	5.61149e6i		−	2.11662i
$372$	−684499.	+	1.77834e6i	−0.256458	+	0.666282i
$373$	−1.11981e6			−0.416746			−0.208373	−	0.978049i	$-0.566817\pi$
$373$	−1.11981e6			−0.416746			−0.208373	+	0.978049i	$0.566817\pi$
$374$		−	2.60393e6i		−	0.962609i
$375$	−311999.	+	810580.i	−0.114571	+	0.297658i
$376$	1.37456e6			0.501412
$377$	235515.			0.0853426
$378$	1.66006e6	+	3.28016e6i	0.597578	+	1.18077i
$379$	2.76896e6			0.990191			0.495096	−	0.868839i	$-0.335133\pi$
$379$	2.76896e6			0.990191			0.495096	+	0.868839i	$0.335133\pi$
$380$		−	407746.i		−	0.144854i
$381$	−456366.	−	175659.i	−0.161065	−	0.0619953i
$382$	−1.79632e6			−0.629832
$383$		−	872847.i		−	0.304047i	−0.988377	−	0.152024i	$-0.951421\pi$
$383$		−	872847.i		−	0.304047i	0.988377	−	0.152024i	$-0.0485790\pi$
$384$	238354.	+	91744.6i	0.0824888	+	0.0317506i
$385$		−	1.21806e7i		−	4.18811i
$386$	3.73623e6			1.27634
$387$	−3.47868e6	+	3.84935e6i	−1.18069	+	1.30650i
$388$			279358.i			0.0942068i
$389$			2.93752e6i			0.984253i	0.870524	+	0.492127i	$0.163780\pi$
$389$			2.93752e6i			0.984253i	−0.870524	+	0.492127i	$0.836220\pi$
$390$	971026.	+	373756.i	0.323273	+	0.124430i
$391$			777992.i			0.257355i
$392$	−2.69196e6			−0.884817
$393$	2.74025e6	+	1.05475e6i	0.894972	+	0.344482i
$394$		−	64482.7i		−	0.0209268i
$395$		−	8.02026e6i		−	2.58640i
$396$	−1.74087e6	−	1.57323e6i	−0.557864	−	0.504145i
$397$		−	4.73644e6i		−	1.50826i	−0.656725	−	0.754130i	$-0.728059\pi$
$397$		−	4.73644e6i		−	1.50826i	0.656725	−	0.754130i	$-0.271941\pi$
$398$	915986.			0.289855
$399$	1.08136e6	+	416224.i	0.340045	+	0.130886i
$400$	−971469.			−0.303584
$401$	−1.25929e6			−0.391079			−0.195540	−	0.980696i	$-0.562646\pi$
$401$	−1.25929e6			−0.391079			−0.195540	+	0.980696i	$0.562646\pi$
$402$	1.13285e6	−	2.94318e6i	0.349630	−	0.908346i
$403$	−1.53254e6			−0.470057
$404$	−2.08535e6			−0.635660
$405$	−4.88694e6	+	495657.i	−1.48047	+	0.150156i
$406$		−	1.13947e6i		−	0.343073i
$407$		−	2.89938e6i		−	0.867600i
$408$	386572.	−	1.00432e6i	0.114969	−	0.298691i
$409$			1.21771e6i			0.359944i	0.983672	+	0.179972i	$0.0576006\pi$
$409$			1.21771e6i			0.359944i	−0.983672	+	0.179972i	$0.942399\pi$
$410$	−1.30968e6			−0.384774
$411$	−1.22985e6	+	3.19518e6i	−0.359128	+	0.933021i
$412$		−	907023.i		−	0.263254i
$413$	2.79351e6	+	5.85518e6i	0.805887	+	1.68914i
$414$	520130.	+	470045.i	0.149146	+	0.134784i
$415$		−	5.17219e6i		−	1.47419i
$416$			205410.i			0.0581952i
$417$	1.20597e6	+	464188.i	0.339622	+	0.130723i
$418$	−739542.			−0.207025
$419$	5.36103e6			1.49181			0.745905	−	0.666052i	$-0.232017\pi$
$419$	5.36103e6			1.49181			0.745905	+	0.666052i	$0.232017\pi$
$420$	1.80830e6	−	4.69800e6i	0.500204	−	1.29954i
$421$		−	2.34508e6i		−	0.644840i	−0.946597	−	0.322420i	$-0.895504\pi$
$421$		−	2.34508e6i		−	0.644840i	0.946597	−	0.322420i	$-0.104496\pi$
$422$		−	2.64408e6i		−	0.722759i
$423$	−3.87214e6	−	3.49927e6i	−1.05220	−	0.950883i
$424$			1.48018e6i			0.399853i
$425$			4.09335e6i			1.09927i
$426$	1.10120e6	−	2.86093e6i	0.293996	−	0.763806i
$427$		−	8.94929e6i		−	2.37530i
$428$			460752.i			0.121579i
$429$	677893.	−	1.76118e6i	0.177835	−	0.462019i
$430$	7.10440e6			1.85292
$431$	−1.60115e6			−0.415183			−0.207591	−	0.978216i	$-0.566562\pi$
$431$	−1.60115e6			−0.415183			−0.207591	+	0.978216i	$0.566562\pi$
$432$	−437886.	−	865232.i	−0.112889	−	0.223061i
$433$	−2.38264e6			−0.610716			−0.305358	−	0.952238i	$-0.598776\pi$
$433$	−2.38264e6			−0.610716			−0.305358	+	0.952238i	$0.598776\pi$
$434$			7.41473e6i			1.88960i
$435$	1.42085e6	+	546897.i	0.360018	+	0.138574i
$436$		−	2.46169e6i		−	0.620180i
$437$	220957.			0.0553484
$438$	−994616.	+	2.58403e6i	−0.247725	+	0.643595i
$439$	1.92119e6			0.475784			0.237892	−	0.971292i	$-0.423544\pi$
$439$	1.92119e6			0.475784			0.237892	+	0.971292i	$0.423544\pi$
$440$			3.21297e6i			0.791179i
$441$	7.58325e6	+	6.85303e6i	1.85677	+	1.67798i
$442$	865506.			0.210724
$443$	−151359.			−0.0366437			−0.0183219	−	0.999832i	$-0.505832\pi$
$443$	−151359.			−0.0366437			−0.0183219	+	0.999832i	$0.505832\pi$
$444$	430434.	−	1.11828e6i	0.103621	−	0.269210i
$445$			7.90219e6i			1.89168i
$446$	−2.07779e6			−0.494612
$447$	−5.17885e6	−	1.99338e6i	−1.22593	−	0.471870i
$448$	993809.			0.233942
$449$		−	4.04264e6i		−	0.946345i	−0.880970	−	0.473173i	$-0.843109\pi$
$449$		−	4.04264e6i		−	0.946345i	0.880970	−	0.473173i	$-0.156891\pi$
$450$	2.73663e6	+	2.47311e6i	0.637066	+	0.575720i
$451$			2.37541e6i			0.549916i
$452$	2.82200e6			0.649698
$453$	−2.84013e6	+	7.37870e6i	−0.650268	+	1.68941i
$454$	1.12437e6			0.256018
$455$	4.04865e6			0.916816
$456$	−285237.	−	109790.i	−0.0642383	−	0.0247259i
$457$			2.18071e6i			0.488435i	0.969720	+	0.244217i	$0.0785311\pi$
$457$			2.18071e6i			0.488435i	−0.969720	+	0.244217i	$0.921469\pi$
$458$		−	2.09669e6i		−	0.467058i
$459$	−3.64571e6	+	1.84506e6i	−0.807700	+	0.408770i
$460$		−	959959.i		−	0.211523i
$461$			8.41437e6i			1.84404i	0.387147	+	0.922018i	$0.373461\pi$
$461$			8.41437e6i			1.84404i	−0.387147	+	0.922018i	$0.626539\pi$
$462$	−8.52090e6	−	3.27977e6i	−1.85729	−	0.714889i
$463$			4.75974e6i			1.03188i	0.856624	+	0.515942i	$0.172558\pi$
$463$			4.75974e6i			1.03188i	−0.856624	+	0.515942i	$0.827442\pi$
$464$			300565.i			0.0648102i
$465$	−9.24575e6	−	3.55877e6i	−1.98294	−	0.763251i
$466$	266124.			0.0567700
$467$	2.54192e6			0.539348			0.269674	−	0.962952i	$-0.413084\pi$
$467$	2.54192e6			0.539348			0.269674	+	0.962952i	$0.413084\pi$
$468$	522919.	−	578639.i	0.110362	−	0.122122i
$469$		−	1.22715e7i		−	2.57611i
$470$			7.14646e6i			1.49227i
$471$	−2.71298e6	+	7.04839e6i	−0.563502	+	1.46399i
$472$	−736863.	−	1.54446e6i	−0.152241	−	0.319097i
$473$		−	1.28855e7i		−	2.64818i
$474$	−5.61054e6	−	2.15955e6i	−1.14699	−	0.441486i
$475$	1.16255e6			0.236417
$476$		−	4.18748e6i		−	0.847100i
$477$	3.76815e6	−	4.16967e6i	0.758285	−	0.839085i
$478$			4.61759e6i			0.924370i
$479$			3.02682e6i			0.602766i	0.953503	+	0.301383i	$0.0974482\pi$
$479$			3.02682e6i			0.602766i	−0.953503	+	0.301383i	$0.902552\pi$
$480$	−476988.	+	1.23922e6i	−0.0944940	+	0.245497i
$481$	963711.			0.189926
$482$	−4.74880e6			−0.931036
$483$	2.54584e6	+	979917.i	0.496551	+	0.191127i
$484$	3.25065e6			0.630748
$485$	−1.45241e6			−0.280372
$486$	−969129.	+	3.55210e6i	−0.186119	+	0.682173i
$487$	7.11032e6			1.35852			0.679261	−	0.733897i	$-0.262300\pi$
$487$	7.11032e6			1.35852			0.679261	+	0.733897i	$0.262300\pi$
$488$			2.36062e6i			0.448721i
$489$	−195757.	−	75348.4i	−0.0370207	−	0.0142496i
$490$		−	1.39957e7i		−	2.63333i
$491$			2.77941e6i			0.520293i	0.965569	+	0.260147i	$0.0837709\pi$
$491$			2.77941e6i			0.520293i	−0.965569	+	0.260147i	$0.916229\pi$
$492$	−352646.	+	916181.i	−0.0656789	+	0.170635i
$493$	1.26645e6			0.234677
$494$		−	245812.i		−	0.0453196i
$495$	8.17937e6	−	9.05093e6i	1.50040	−	1.66028i
$496$		−	1.95583e6i		−	0.356967i
$497$		−	1.19285e7i		−	2.16619i
$498$	−3.61818e6	−	1.39267e6i	−0.653758	−	0.251637i
$499$	4.42189e6			0.794980			0.397490	−	0.917607i	$-0.369881\pi$
$499$	4.42189e6			0.794980			0.397490	+	0.917607i	$0.369881\pi$
$500$		−	891483.i		−	0.159473i
$501$	951634.	−	2.47236e6i	0.169385	−	0.440066i
$502$		−	625680.i		−	0.110814i
$503$	−415838.			−0.0732832			−0.0366416	−	0.999328i	$-0.511666\pi$
$503$	−415838.			−0.0732832			−0.0366416	+	0.999328i	$0.511666\pi$
$504$	−2.79956e6	−	2.52998e6i	−0.490923	−	0.443650i
$505$		−	1.08419e7i		−	1.89181i
$506$	−1.74111e6			−0.302308
$507$	−4.81618e6	−	1.85379e6i	−0.832113	−	0.320288i
$508$	501915.			0.0862921
$509$	−9.76133e6			−1.66999			−0.834996	−	0.550256i	$-0.814530\pi$
$509$	−9.76133e6			−1.66999			−0.834996	+	0.550256i	$0.814530\pi$
$510$	5.22155e6	+	2.00982e6i	0.888943	+	0.342162i
$511$			1.07740e7i			1.82526i
$512$	−262144.			−0.0441942
$513$	524015.	+	1.03542e6i	0.0879125	+	0.173709i
$514$			5.35407e6i			0.893874i
$515$	4.71569e6			0.783478
$516$	1.91294e6	−	4.96985e6i	0.316284	−	0.821711i
$517$	1.29618e7			2.13274
$518$		−	4.66261e6i		−	0.763492i
$519$	−4.50525e6	−	1.73411e6i	−0.734176	−	0.282591i
$520$	−1.06794e6			−0.173197
$521$			6.39097e6i			1.03151i	0.856737	+	0.515754i	$0.172488\pi$
$521$			6.39097e6i			1.03151i	−0.856737	+	0.515754i	$0.827512\pi$
$522$	765159.	−	846691.i	0.122907	−	0.136003i
$523$	−7.30233e6			−1.16737			−0.583684	−	0.811981i	$-0.698389\pi$
$523$	−7.30233e6			−1.16737			−0.583684	+	0.811981i	$0.698389\pi$
$524$	−3.01375e6			−0.479490
$525$	1.33948e7	+	5.15576e6i	2.12098	+	0.816384i
$526$			7.90989e6i			1.24654i
$527$	−8.24103e6			−1.29257
$528$	2.24762e6	+	865128.i	0.350863	+	0.135050i
$529$	−5.91614e6			−0.919178
$530$	−7.69559e6			−1.19001
$531$	−1.85605e6	+	6.22661e6i	−0.285663	+	0.958330i
$532$	−1.18929e6			−0.182183
$533$	−789549.			−0.120382
$534$	5.52794e6	+	2.12775e6i	0.838901	+	0.322900i
$535$	−2.39549e6			−0.361835
$536$			3.23693e6i			0.486655i
$537$	−3.53930e6	−	1.36231e6i	−0.529642	−	0.203864i
$538$	2.74899e6			0.409465
$539$	−2.53845e7			−3.76354
$540$	4.49841e6	−	2.27661e6i	0.663858	−	0.335972i
$541$			3.58422e6i			0.526504i	0.964727	+	0.263252i	$0.0847951\pi$
$541$			3.58422e6i			0.526504i	−0.964727	+	0.263252i	$0.915205\pi$
$542$	7.95083e6			1.16256
$543$	−1.34509e6	−	517737.i	−0.195773	−	0.0753546i
$544$			1.10456e6i			0.160027i
$545$	1.27986e7			1.84574
$546$	1.09015e6	−	2.83222e6i	0.156496	−	0.406579i
$547$	2.66404e6			0.380692			0.190346	−	0.981717i	$-0.439039\pi$
$547$	2.66404e6			0.380692			0.190346	+	0.981717i	$0.439039\pi$
$548$		−	3.51409e6i		−	0.499875i
$549$	6.00951e6	−	6.64986e6i	0.850959	−	0.941633i
$550$	−9.16070e6			−1.29128
$551$		−	359684.i		−	0.0504710i
$552$	−671535.	−	258480.i	−0.0938039	−	0.0361059i
$553$	−2.33929e7			−3.25291
$554$	456299.			0.0631648
$555$	5.81401e6	+	2.23786e6i	0.801204	+	0.308391i
$556$	−1.32633e6			−0.181956
$557$			6.25203e6i			0.853853i	0.904286	+	0.426927i	$0.140404\pi$
$557$			6.25203e6i			0.853853i	−0.904286	+	0.426927i	$0.859596\pi$
$558$	−4.97904e6	+	5.50958e6i	−0.676956	+	0.749089i
$559$	4.28293e6			0.579711
$560$			5.16690e6i			0.696241i
$561$	3.64527e6	−	9.47048e6i	0.489015	−	1.27047i
$562$		−	3.83914e6i		−	0.512735i
$563$	7.98611e6			1.06185			0.530926	−	0.847418i	$-0.321844\pi$
$563$	7.98611e6			1.06185			0.530926	+	0.847418i	$0.321844\pi$
$564$	4.99928e6	+	1.92427e6i	0.661774	+	0.254722i
$565$			1.46718e7i			1.93358i
$566$		−	807199.i		−	0.105911i
$567$	1.44570e6	+	1.42539e7i	0.188851	+	1.86198i
$568$			3.14648e6i			0.409217i
$569$	9.06736e6			1.17409			0.587043	−	0.809556i	$-0.300292\pi$
$569$	9.06736e6			1.17409			0.587043	+	0.809556i	$0.300292\pi$
$570$	570809.	−	1.48297e6i	0.0735874	−	0.191181i
$571$		−	1.48879e6i		−	0.191092i	−0.995425	−	0.0955461i	$-0.969540\pi$
$571$		−	1.48879e6i		−	0.191092i	0.995425	−	0.0955461i	$-0.0304597\pi$
$572$			1.93696e6i			0.247532i
$573$	−6.53320e6	−	2.51468e6i	−0.831265	−	0.319961i
$574$			3.81998e6i			0.483929i
$575$	2.73700e6			0.345227
$576$	738459.	+	667350.i	0.0927407	+	0.0838103i
$577$	−8.02412e6			−1.00336			−0.501681	−	0.865052i	$-0.667285\pi$
$577$	−8.02412e6			−1.00336			−0.501681	+	0.865052i	$0.667285\pi$
$578$	−1.02530e6			−0.127652
$579$	1.35887e7	+	5.23039e6i	1.68453	+	0.648392i
$580$	−1.56266e6			−0.192883
$581$	−1.50859e7			−1.85409
$582$	−391077.	+	1.01603e6i	−0.0478580	+	0.124336i
$583$			1.39577e7i			1.70076i
$584$		−	2.84194e6i		−	0.344812i
$585$	3.00839e6	+	2.71870e6i	0.363450	+	0.328452i
$586$			4.28333e6i			0.515274i
$587$	−5.75032e6			−0.688806			−0.344403	−	0.938822i	$-0.611919\pi$
$587$	−5.75032e6			−0.688806			−0.344403	+	0.938822i	$0.611919\pi$
$588$	−9.79065e6	−	3.76851e6i	−1.16780	−	0.449496i
$589$			2.34054e6i			0.277989i
$590$	8.02979e6	−	3.83101e6i	0.949673	−	0.453089i
$591$	90270.2	−	234524.i	0.0106310	−	0.0276196i
$592$			1.22989e6i			0.144232i
$593$		−	8.00331e6i		−	0.934615i	−0.884095	−	0.467308i	$-0.845224\pi$
$593$		−	8.00331e6i		−	0.934615i	0.884095	−	0.467308i	$-0.154776\pi$
$594$	−4.12915e6	−	8.15891e6i	−0.480169	−	0.948781i
$595$	2.17710e7			2.52108
$596$	5.69574e6			0.656802
$597$	3.33144e6	+	1.28230e6i	0.382557	+	0.147249i
$598$		−	578717.i		−	0.0661780i
$599$			2.54694e6i			0.290035i	0.989429	+	0.145018i	$0.0463239\pi$
$599$			2.54694e6i			0.290035i	−0.989429	+	0.145018i	$0.953676\pi$
$600$	−3.53323e6	−	1.35997e6i	−0.400677	−	0.154224i
$601$			1.53558e7i			1.73415i	0.498182	+	0.867073i	$0.334001\pi$
$601$			1.53558e7i			1.73415i	−0.498182	+	0.867073i	$0.665999\pi$
$602$		−	2.07216e7i		−	2.33041i
$603$	8.24038e6	−	9.11843e6i	0.922898	−	1.02124i
$604$		−	8.11516e6i		−	0.905117i
$605$			1.69004e7i			1.87719i
$606$	−7.58440e6	−	2.91930e6i	−0.838956	−	0.322922i
$607$	7.45718e6			0.821491			0.410746	−	0.911750i	$-0.365268\pi$
$607$	7.45718e6			0.821491			0.410746	+	0.911750i	$0.365268\pi$
$608$	313706.			0.0344163
$609$	1.59515e6	−	4.14423e6i	0.174284	−	0.452794i
$610$	−1.22731e7			−1.33545
$611$			4.30829e6i			0.466877i
$612$	2.81192e6	−	3.11154e6i	0.303476	−	0.335813i
$613$			1.09210e7i			1.17385i	0.809641	+	0.586925i	$0.199662\pi$
$613$			1.09210e7i			1.17385i	−0.809641	+	0.586925i	$0.800338\pi$
$614$	671480.			0.0718807
$615$	−4.76330e6	−	1.83344e6i	−0.507832	−	0.195469i
$616$	9.37136e6			0.995064
$617$			1.18558e7i			1.25377i	0.779112	+	0.626885i	$0.215670\pi$
$617$			1.18558e7i			1.25377i	−0.779112	+	0.626885i	$0.784330\pi$
$618$	1.26975e6	−	3.29884e6i	0.133736	−	0.347448i
$619$	−1.90523e7			−1.99858			−0.999289	−	0.0377046i	$-0.987995\pi$
$619$	−1.90523e7			−1.99858			−0.999289	+	0.0377046i	$0.987995\pi$
$620$	1.01685e7			1.06238
$621$	1.23369e6	+	2.43769e6i	0.128374	+	0.253658i
$622$			1.21988e7i			1.26427i
$623$	2.30486e7			2.37916
$624$	−287555.	+	747074.i	−0.0295638	+	0.0768073i
$625$	−7.22386e6			−0.739723
$626$		−	1.22975e6i		−	0.125424i
$627$	−2.68971e6	−	1.03529e6i	−0.273235	−	0.105171i
$628$		−	7.75187e6i		−	0.784346i
$629$	5.18222e6			0.522263
$630$	1.31536e7	−	1.45551e7i	1.32036	−	1.46105i
$631$	−7.87858e6			−0.787725			−0.393862	−	0.919169i	$-0.628861\pi$
$631$	−7.87858e6			−0.787725			−0.393862	+	0.919169i	$0.628861\pi$
$632$	6.17052e6			0.614510
$633$	3.70148e6	−	9.61651e6i	0.367169	−	0.953912i
$634$			5.14396e6i			0.508246i
$635$			2.60950e6i			0.256817i
$636$	−2.07212e6	+	5.38342e6i	−0.203129	+	0.527734i
$637$		−	8.43742e6i		−	0.823875i
$638$			2.83425e6i			0.275668i
$639$	8.01010e6	−	8.86362e6i	0.776043	−	0.858734i
$640$		−	1.36291e6i		−	0.131528i
$641$		−	405375.i		−	0.0389683i	−0.999810	−	0.0194842i	$-0.993798\pi$
$641$		−	405375.i		−	0.0389683i	0.999810	−	0.0194842i	$-0.00620239\pi$
$642$	−645013.	+	1.67576e6i	−0.0617633	+	0.160462i
$643$	−1.07208e7			−1.02259			−0.511294	−	0.859406i	$-0.670834\pi$
$643$	−1.07208e7			−1.02259			−0.511294	+	0.859406i	$0.670834\pi$
$644$	−2.79994e6			−0.266032
$645$	2.58387e7	+	9.94553e6i	2.44552	+	0.941301i
$646$		−	1.32182e6i		−	0.124621i
$647$		−	5.37081e6i		−	0.504404i	−0.967675	−	0.252202i	$-0.918845\pi$
$647$		−	5.37081e6i		−	0.504404i	0.967675	−	0.252202i	$-0.0811548\pi$
$648$	−381342.	−	3.75985e6i	−0.0356760	−	0.351749i
$649$	−6.94842e6	−	1.45639e7i	−0.647552	−	1.35727i
$650$		−	3.04488e6i		−	0.282674i
$651$	−1.03800e7	+	2.69673e7i	−0.959938	+	2.49394i
$652$	215295.			0.0198342
$653$		−	1.74013e7i		−	1.59697i	−0.602012	−	0.798487i	$-0.705634\pi$
$653$		−	1.74013e7i		−	1.59697i	0.602012	−	0.798487i	$-0.294366\pi$
$654$	3.44615e6	−	8.95317e6i	0.315058	−	0.818526i
$655$		−	1.56688e7i		−	1.42702i
$656$		−	1.00762e6i		−	0.0914194i
$657$	−7.23483e6	+	8.00574e6i	−0.653905	+	0.723582i
$658$	2.08443e7			1.87682
$659$	−7.20136e6			−0.645953			−0.322976	−	0.946407i	$-0.604683\pi$
$659$	−7.20136e6			−0.645953			−0.322976	+	0.946407i	$0.604683\pi$
$660$	−4.49787e6	+	1.16856e7i	−0.401927	+	1.04421i
$661$	3.52987e6			0.314235			0.157118	−	0.987580i	$-0.449780\pi$
$661$	3.52987e6			0.314235			0.157118	+	0.987580i	$0.449780\pi$
$662$	2.62734e6			0.233009
$663$	3.14784e6	+	1.21163e6i	0.278118	+	0.107050i
$664$	3.97931e6			0.350257
$665$		−	6.18319e6i		−	0.542199i
$666$	3.13098e6	−	3.46460e6i	0.273523	−	0.302668i
$667$		−	846806.i		−	0.0737003i
$668$			2.71912e6i			0.235770i
$669$	−7.55691e6	−	2.90872e6i	−0.652798	−	0.251268i
$670$	−1.68291e7			−1.44835
$671$			2.22600e7i			1.90862i
$672$	3.61448e6	+	1.39124e6i	0.308761	+	0.118845i
$673$			1.38664e7i			1.18012i	0.807360	+	0.590060i	$0.200896\pi$
$673$			1.38664e7i			1.18012i	−0.807360	+	0.590060i	$0.799104\pi$
$674$		−	2.10610e6i		−	0.178579i
$675$	6.49098e6	+	1.28257e7i	0.548341	+	1.08348i
$676$	5.29687e6			0.445813
$677$		−	6.68700e6i		−	0.560737i	−0.959892	−	0.280369i	$-0.909543\pi$
$677$		−	6.68700e6i		−	0.560737i	0.959892	−	0.280369i	$-0.0904567\pi$
$678$	1.02636e7	+	3.95055e6i	0.857484	+	0.330053i
$679$			4.23628e6i			0.352623i
$680$	−5.74270e6			−0.476260
$681$	4.08933e6	+	1.57402e6i	0.337897	+	0.130060i
$682$		−	1.84430e7i		−	1.51835i
$683$	−8.38345e6			−0.687656			−0.343828	−	0.939033i	$-0.611724\pi$
$683$	−8.38345e6			−0.687656			−0.343828	+	0.939033i	$0.611724\pi$
$684$	−883710.	−	798613.i	−0.0722220	−	0.0652674i
$685$	1.82701e7			1.48769
$686$	−2.45103e7			−1.98856
$687$	2.93518e6	−	7.62566e6i	0.237270	−	0.616432i
$688$			5.46588e6i			0.440240i
$689$	−4.63934e6			−0.372313
$690$	1.34386e6	−	3.49137e6i	0.107456	−	0.279173i
$691$		−	1.93218e7i		−	1.53940i	−0.638405	−	0.769700i	$-0.720406\pi$
$691$		−	1.93218e7i		−	1.53940i	0.638405	−	0.769700i	$-0.279594\pi$
$692$	4.95491e6			0.393342
$693$	−2.63991e7	−	2.38570e7i	−2.08812	−	1.88705i
$694$	−8.62416e6			−0.679701
$695$		−	6.89572e6i		−	0.541524i
$696$	−420764.	+	1.09315e6i	−0.0329242	+	0.0855378i
$697$	−4.24568e6			−0.331029
$698$			7.73479e6i			0.600911i
$699$	967892.	+	372550.i	0.0749262	+	0.0288398i
$700$	−1.47317e7			−1.13634
$701$	−7.90118e6			−0.607291			−0.303646	−	0.952785i	$-0.598204\pi$
$701$	−7.90118e6			−0.607291			−0.303646	+	0.952785i	$0.598204\pi$
$702$	2.71190e6	−	1.37247e6i	0.207697	−	0.105114i
$703$		−	1.47180e6i		−	0.112321i
$704$	−2.47195e6			−0.187978
$705$	−1.00044e7	+	2.59917e7i	−0.758087	+	1.96952i
$706$	−2.95018e6			−0.222759
$707$	−3.16228e7			−2.37932
$708$	−517857.	−	6.64875e6i	−0.0388263	−	0.498490i
$709$	6.43692e6			0.480909			0.240454	−	0.970660i	$-0.422704\pi$
$709$	6.43692e6			0.480909			0.240454	+	0.970660i	$0.422704\pi$
$710$	−1.63588e7			−1.21788
$711$	−1.73823e7	−	1.57085e7i	−1.28954	−	1.16536i
$712$	−6.07968e6			−0.449449
$713$			5.51033e6i			0.405933i
$714$	5.86210e6	−	1.52298e7i	0.430336	−	1.11802i
$715$	−1.00704e7			−0.736686
$716$	3.89256e6			0.283761
$717$	−6.46422e6	+	1.67942e7i	−0.469590	+	1.22000i
$718$			5.66645e6i			0.410204i
$719$	−1.31691e7			−0.950020			−0.475010	−	0.879980i	$-0.657555\pi$
$719$	−1.31691e7			−0.950020			−0.475010	+	0.879980i	$0.657555\pi$
$720$	−3.46961e6	+	3.83931e6i	−0.249430	+	0.276008i
$721$		−	1.37544e7i		−	0.985378i
$722$	9.52899e6			0.680305
$723$	−1.72714e7	−	6.64791e6i	−1.22880	−	0.472976i
$724$	1.47934e6			0.104887
$725$		−	4.45541e6i		−	0.314805i
$726$	1.18226e7	+	4.55062e6i	0.832475	+	0.320427i
$727$	5.48795e6			0.385100			0.192550	−	0.981287i	$-0.438324\pi$
$727$	5.48795e6			0.385100			0.192550	+	0.981287i	$0.438324\pi$
$728$			3.11490e6i			0.217829i
$729$	−8.49734e6	+	1.15623e7i	−0.592194	+	0.805795i
$730$	1.47755e7			1.02621
$731$	2.30308e7			1.59410
$732$	−3.30466e6	+	8.58556e6i	−0.227955	+	0.592231i
$733$	2.49167e7			1.71289			0.856446	−	0.516237i	$-0.172668\pi$
$733$	2.49167e7			1.71289			0.856446	+	0.516237i	$0.172668\pi$
$734$			1.27581e7i			0.874072i
$735$	1.95928e7	−	5.09024e7i	1.33776	−	3.47552i
$736$	738560.			0.0502564
$737$			3.05234e7i			2.06997i
$738$	−2.56514e6	+	2.83847e6i	−0.173369	+	0.191842i
$739$			1.42106e7i			0.957196i	0.878034	+	0.478598i	$0.158855\pi$
$739$			1.42106e7i			0.957196i	−0.878034	+	0.478598i	$0.841145\pi$
$740$	−6.39430e6			−0.429253
$741$	344116.	−	894019.i	0.0230228	−	0.0598138i
$742$			2.24460e7i			1.49668i
$743$		−	2.23330e7i		−	1.48414i	−0.670321	−	0.742071i	$-0.733844\pi$
$743$		−	2.23330e7i		−	1.48414i	0.670321	−	0.742071i	$-0.266156\pi$
$744$	2.73800e6	−	7.11337e6i	0.181343	−	0.471132i
$745$			2.96126e7i			1.95473i
$746$	4.47923e6			0.294684
$747$	−1.12097e7	−	1.01303e7i	−0.735009	−	0.664232i
$748$			1.04157e7i			0.680668i
$749$			6.98700e6i			0.455078i
$750$	1.24800e6	−	3.24232e6i	0.0810141	−	0.210476i
$751$			1.64092e7i			1.06167i	0.847476	+	0.530834i	$0.178121\pi$
$751$			1.64092e7i			1.06167i	−0.847476	+	0.530834i	$0.821879\pi$
$752$	−5.49825e6			−0.354552
$753$	875897.	−	2.27560e6i	0.0562944	−	0.146254i
$754$	−942061.			−0.0603463
$755$	4.21914e7			2.69375
$756$	−6.64024e6	−	1.31207e7i	−0.422551	−	0.834932i
$757$	−1.36526e7			−0.865918			−0.432959	−	0.901414i	$-0.642530\pi$
$757$	−1.36526e7			−0.865918			−0.432959	+	0.901414i	$0.642530\pi$
$758$	−1.10758e7			−0.700171
$759$	−6.33240e6	−	2.43740e6i	−0.398992	−	0.153575i
$760$			1.63098e6i			0.102427i
$761$		−	2.22996e7i		−	1.39584i	−0.716177	−	0.697919i	$-0.754110\pi$
$761$		−	2.22996e7i		−	1.39584i	0.716177	−	0.697919i	$-0.245890\pi$
$762$	1.82546e6	+	702637.i	0.113890	+	0.0438373i
$763$		−	3.73299e7i		−	2.32138i
$764$	7.18527e6			0.445358
$765$	1.61772e7	+	1.46194e7i	0.999423	+	0.903184i
$766$			3.49139e6i			0.214994i
$767$	4.84081e6	−	2.30955e6i	0.297119	−	0.141755i
$768$	−953417.	−	366978.i	−0.0583284	−	0.0224511i
$769$			2.41559e7i			1.47302i	0.676428	+	0.736508i	$0.263527\pi$
$769$			2.41559e7i			1.47302i	−0.676428	+	0.736508i	$0.736473\pi$
$770$			4.87225e7i			2.96144i
$771$	−7.49523e6	+	1.94727e7i	−0.454097	+	1.17975i
$772$	−1.49449e7			−0.902506
$773$	−1.02434e7			−0.616586			−0.308293	−	0.951292i	$-0.599758\pi$
$773$	−1.02434e7			−0.616586			−0.308293	+	0.951292i	$0.599758\pi$
$774$	1.39147e7	−	1.53974e7i	0.834875	−	0.923836i
$775$			2.89922e7i			1.73391i
$776$		−	1.11743e6i		−	0.0666143i
$777$	6.52724e6	−	1.69579e7i	0.387862	−	1.00767i
$778$		−	1.17501e7i		−	0.695972i
$779$			1.20582e6i			0.0711931i
$780$	−3.88410e6	−	1.49502e6i	−0.228588	−	0.0879856i
$781$			2.96704e7i			1.74059i
$782$		−	3.11197e6i		−	0.181978i
$783$	3.96817e6	−	2.00826e6i	0.231306	−	0.117062i
$784$	1.07678e7			0.625660
$785$	4.03026e7			2.33431
$786$	−1.09610e7	−	4.21899e6i	−0.632840	−	0.243586i
$787$	−2.96891e7			−1.70868			−0.854338	−	0.519718i	$-0.826037\pi$
$787$	−2.96891e7			−1.70868			−0.854338	+	0.519718i	$0.826037\pi$
$788$			257931.i			0.0147975i
$789$	−1.10731e7	+	2.87683e7i	−0.633255	+	1.64521i
$790$			3.20811e7i			1.82886i
$791$	4.27937e7			2.43186
$792$	6.96348e6	+	6.29294e6i	0.394469	+	0.356484i
$793$	−7.39889e6			−0.417815
$794$			1.89458e7i			1.06650i
$795$	−2.79888e7	−	1.07731e7i	−1.57061	−	0.604540i
$796$	−3.66394e6			−0.204959
$797$	3.70616e6			0.206671			0.103335	−	0.994647i	$-0.467049\pi$
$797$	3.70616e6			0.206671			0.103335	+	0.994647i	$0.467049\pi$
$798$	−4.32543e6	−	1.66489e6i	−0.240448	−	0.0925506i
$799$			2.31672e7i			1.28383i
$800$	3.88588e6			0.214666
$801$	1.71265e7	+	1.54773e7i	0.943162	+	0.852340i
$802$	5.03716e6			0.276535
$803$		−	2.67987e7i		−	1.46665i
$804$	−4.53142e6	+	1.17727e7i	−0.247226	+	0.642298i
$805$		−	1.45571e7i		−	0.791746i
$806$	6.13018e6			0.332380
$807$	9.99806e6	+	3.84834e6i	0.540421	+	0.208013i
$808$	8.34138e6			0.449479
$809$	−3.26251e7			−1.75259			−0.876296	−	0.481774i	$-0.839993\pi$
$809$	−3.26251e7			−1.75259			−0.876296	+	0.481774i	$0.839993\pi$
$810$	1.95478e7	−	1.98263e6i	1.04685	−	0.106177i
$811$			749586.i			0.0400193i	0.999800	+	0.0200096i	$0.00636969\pi$
$811$			749586.i			0.0400193i	−0.999800	+	0.0200096i	$0.993630\pi$
$812$			4.55786e6i			0.242589i
$813$	2.89171e7	+	1.11305e7i	1.53437	+	0.590591i
$814$			1.15975e7i			0.613486i
$815$			1.11934e6i			0.0590291i
$816$	−1.54629e6	+	4.01728e6i	−0.0812951	+	0.211206i
$817$		−	6.54099e6i		−	0.342838i
$818$		−	4.87083e6i		−	0.254519i
$819$	7.92971e6	−	8.77466e6i	0.413093	−	0.457110i
$820$	5.23872e6			0.272076
$821$	1.28836e7			0.667081			0.333541	−	0.942736i	$-0.391757\pi$
$821$	1.28836e7			0.667081			0.333541	+	0.942736i	$0.391757\pi$
$822$	4.91942e6	−	1.27807e7i	0.253942	−	0.659745i
$823$		−	2.84916e7i		−	1.46628i	−0.680078	−	0.733140i	$-0.738054\pi$
$823$		−	2.84916e7i		−	1.46628i	0.680078	−	0.733140i	$-0.261946\pi$
$824$			3.62809e6i			0.186149i
$825$	−3.33174e7	−	1.28242e7i	−1.70426	−	0.655986i
$826$	−1.11740e7	−	2.34207e7i	−0.569848	−	1.19440i
$827$			1.39639e7i			0.709975i	0.934871	+	0.354987i	$0.115515\pi$
$827$			1.39639e7i			0.709975i	−0.934871	+	0.354987i	$0.884485\pi$
$828$	−2.08052e6	−	1.88018e6i	−0.105462	−	0.0953067i
$829$	−3.29945e7			−1.66746			−0.833730	−	0.552172i	$-0.813799\pi$
$829$	−3.29945e7			−1.66746			−0.833730	+	0.552172i	$0.813799\pi$
$830$			2.06888e7i			1.04241i
$831$	1.65956e6	+	638779.i	0.0833662	+	0.0320884i
$832$		−	821639.i		−	0.0411503i
$833$		−	4.53710e7i		−	2.26551i
$834$	−4.82387e6	−	1.85675e6i	−0.240149	−	0.0924354i
$835$	−1.41370e7			−0.701681
$836$	2.95817e6			0.146389
$837$	−2.58217e7	+	1.30681e7i	−1.27400	+	0.644762i
$838$	−2.14441e7			−1.05487
$839$	1.25632e7			0.616161			0.308081	−	0.951360i	$-0.400313\pi$
$839$	1.25632e7			0.616161			0.308081	+	0.951360i	$0.400313\pi$
$840$	−7.23320e6	+	1.87920e7i	−0.353698	+	0.918913i
$841$	1.91327e7			0.932794
$842$			9.38030e6i			0.455970i
$843$	5.37445e6	−	1.39629e7i	0.260474	−	0.676718i
$844$			1.05763e7i			0.511068i
$845$			2.75389e7i			1.32680i
$846$	1.54886e7	+	1.39971e7i	0.744021	+	0.672376i
$847$	4.92938e7			2.36094
$848$		−	5.92073e6i		−	0.282739i
$849$	1.13001e6	−	2.93578e6i	0.0538037	−	0.139783i
$850$		−	1.63734e7i		−	0.777304i
$851$		−	3.46507e6i		−	0.164017i
$852$	−4.40479e6	+	1.14437e7i	−0.207886	+	0.540093i
$853$	9.14599e6			0.430386			0.215193	−	0.976572i	$-0.430962\pi$
$853$	9.14599e6			0.430386			0.215193	+	0.976572i	$0.430962\pi$
$854$			3.57972e7i			1.67959i
$855$	4.15206e6	−	4.59448e6i	0.194244	−	0.214942i
$856$		−	1.84301e6i		−	0.0859693i
$857$	−5.35387e6			−0.249009			−0.124505	−	0.992219i	$-0.539734\pi$
$857$	−5.35387e6			−0.249009			−0.124505	+	0.992219i	$0.539734\pi$
$858$	−2.71157e6	+	7.04472e6i	−0.125749	+	0.326697i
$859$			1.10774e7i			0.512220i	0.966648	+	0.256110i	$0.0824409\pi$
$859$			1.10774e7i			0.512220i	−0.966648	+	0.256110i	$0.917559\pi$
$860$	−2.84176e7			−1.31021
$861$	−5.34764e6	+	1.38933e7i	−0.245841	+	0.638699i
$862$	6.40461e6			0.293579
$863$	−4.27098e7			−1.95210			−0.976048	−	0.217557i	$-0.930191\pi$
$863$	−4.27098e7			−1.95210			−0.976048	+	0.217557i	$0.930191\pi$
$864$	1.75154e6	+	3.46093e6i	0.0798246	+	0.157728i
$865$			2.57610e7i			1.17064i
$866$	9.53058e6			0.431842
$867$	−3.72900e6	−	1.43532e6i	−0.168478	−	0.0648488i
$868$		−	2.96589e7i		−	1.33615i
$869$	5.81864e7			2.61380
$870$	−5.68340e6	−	2.18759e6i	−0.254572	−	0.0979868i
$871$	−1.01455e7			−0.453136
$872$			9.84678e6i			0.438534i
$873$	−2.84469e6	+	3.14781e6i	−0.126328	+	0.139789i
$874$	−883830.			−0.0391372
$875$		−	1.35187e7i		−	0.596920i
$876$	3.97846e6	−	1.03361e7i	0.175168	−	0.455090i
$877$	3.23579e7			1.42063			0.710315	−	0.703884i	$-0.248553\pi$
$877$	3.23579e7			1.42063			0.710315	+	0.703884i	$0.248553\pi$
$878$	−7.68477e6			−0.336430
$879$	−5.99629e6	+	1.55785e7i	−0.261764	+	0.680068i
$880$		−	1.28519e7i		−	0.559448i
$881$	1.77088e7			0.768689			0.384344	−	0.923190i	$-0.374428\pi$
$881$	1.77088e7			0.768689			0.384344	+	0.923190i	$0.374428\pi$
$882$	−3.03330e7	−	2.74121e7i	−1.31294	−	1.18651i
$883$	−3.46060e7			−1.49365			−0.746826	−	0.665020i	$-0.768423\pi$
$883$	−3.46060e7			−1.49365			−0.746826	+	0.665020i	$0.768423\pi$
$884$	−3.46203e6			−0.149005
$885$	3.45674e7	−	2.69238e6i	1.48357	−	0.115552i
$886$	605437.			0.0259110
$887$	2.55047e7			1.08846			0.544228	−	0.838937i	$-0.316823\pi$
$887$	2.55047e7			1.08846			0.544228	+	0.838937i	$0.316823\pi$
$888$	−1.72174e6	+	4.47310e6i	−0.0732714	+	0.190360i
$889$	7.61121e6			0.322997
$890$		−	3.16088e7i		−	1.33762i
$891$	−3.59595e6	−	3.54544e7i	−0.151747	−	1.49615i
$892$	8.31116e6			0.349743
$893$	6.57972e6			0.276108
$894$	2.07154e7	+	7.97353e6i	0.866861	+	0.333662i
$895$			2.02377e7i			0.844509i
$896$	−3.97524e6			−0.165422
$897$	810153.	−	2.10479e6i	0.0336191	−	0.0873431i
$898$			1.61706e7i			0.669167i
$899$	8.96996e6			0.370161
$900$	−1.09465e7	−	9.89242e6i	−0.450474	−	0.407096i
$901$	−2.49474e7			−1.02379
$902$		−	9.50163e6i		−	0.388850i
$903$	2.90084e7	−	7.53644e7i	1.18387	−	3.07572i
$904$	−1.12880e7			−0.459406
$905$			7.69122e6i			0.312158i
$906$	1.13605e7	−	2.95148e7i	0.459809	−	1.19459i
$907$	1.58083e7			0.638069			0.319035	−	0.947743i	$-0.396641\pi$
$907$	1.58083e7			0.638069			0.319035	+	0.947743i	$0.396641\pi$
$908$	−4.49748e6			−0.181032
$909$	−2.34977e7	−	2.12350e7i	−0.943224	−	0.852397i
$910$	−1.61946e7			−0.648287
$911$			4.34358e6i			0.173401i	0.996234	+	0.0867006i	$0.0276324\pi$
$911$			4.34358e6i			0.173401i	−0.996234	+	0.0867006i	$0.972368\pi$
$912$	1.14095e6	+	439161.i	0.0454233	+	0.0174838i
$913$	3.75238e7			1.48981
$914$		−	8.72283e6i		−	0.345376i
$915$	−4.46371e7	−	1.71812e7i	−1.76256	−	0.678423i
$916$			8.38676e6i			0.330260i
$917$	−4.57015e7			−1.79476
$918$	1.45828e7	−	7.38024e6i	0.571130	−	0.289044i
$919$			4.55889e7i			1.78062i	0.455358	+	0.890309i	$0.349511\pi$
$919$			4.55889e7i			1.78062i	−0.455358	+	0.890309i	$0.650489\pi$
$920$			3.83983e6i			0.149569i
$921$	2.44217e6	+	940013.i	0.0948696	+	0.0365161i
$922$		−	3.36575e7i		−	1.30393i
$923$	−9.86201e6			−0.381032
$924$	3.40836e7	+	1.31191e7i	1.31331	+	0.505503i
$925$		−	1.82312e7i		−	0.700585i
$926$		−	1.90390e7i		−	0.729652i
$927$	9.23617e6	−	1.02203e7i	0.353014	−	0.390630i
$928$		−	1.20226e6i		−	0.0458277i
$929$	2.19972e7			0.836236			0.418118	−	0.908393i	$-0.362690\pi$
$929$	2.19972e7			0.836236			0.418118	+	0.908393i	$0.362690\pi$
$930$	3.69830e7	+	1.42351e7i	1.40215	+	0.539700i
$931$	−1.28858e7			−0.487234
$932$	−1.06450e6			−0.0401425
$933$	−1.70772e7	+	4.43669e7i	−0.642263	+	1.66861i
$934$	−1.01677e7			−0.381376
$935$	−5.41522e7			−2.02575
$936$	−2.09168e6	+	2.31455e6i	−0.0780378	+	0.0863531i
$937$		−	3.70730e7i		−	1.37946i	−0.724067	−	0.689729i	$-0.757730\pi$
$937$		−	3.70730e7i		−	1.37946i	0.724067	−	0.689729i	$-0.242270\pi$
$938$			4.90859e7i			1.82158i
$939$	1.72154e6	−	4.47259e6i	0.0637166	−	0.165537i
$940$		−	2.85859e7i		−	1.05519i
$941$	−3.12282e7			−1.14967			−0.574835	−	0.818269i	$-0.694934\pi$
$941$	−3.12282e7			−1.14967			−0.574835	+	0.818269i	$0.694934\pi$
$942$	1.08519e7	−	2.81935e7i	0.398456	−	1.03520i
$943$			2.83886e6i			0.103960i
$944$	2.94745e6	+	6.17785e6i	0.107651	+	0.225635i
$945$	6.82154e7	−	3.45232e7i	2.48486	−	1.25757i
$946$			5.15419e7i			1.87255i
$947$		−	2.26216e7i		−	0.819689i	−0.912155	−	0.409844i	$-0.865583\pi$
$947$		−	2.26216e7i		−	0.819689i	0.912155	−	0.409844i	$-0.134417\pi$
$948$	2.24422e7	+	8.63818e6i	0.811043	+	0.312177i
$949$	8.90750e6			0.321063
$950$	−4.65021e6			−0.167172
$951$	−7.20108e6	+	1.87086e7i	−0.258194	+	0.670794i
$952$			1.67499e7i			0.598991i
$953$			1.17728e7i			0.419902i	0.977712	+	0.209951i	$0.0673305\pi$
$953$			1.17728e7i			0.419902i	−0.977712	+	0.209951i	$0.932670\pi$
$954$	−1.50726e7	+	1.66787e7i	−0.536189	+	0.593322i
$955$			3.73568e7i			1.32544i
$956$		−	1.84704e7i		−	0.653628i
$957$	−3.96770e6	+	1.03082e7i	−0.140042	+	0.363832i
$958$		−	1.21073e7i		−	0.426220i
$959$		−	5.32888e7i		−	1.87107i
$960$	1.90795e6	−	4.95689e6i	0.0668174	−	0.173593i
$961$	−2.97401e7			−1.03881
$962$	−3.85485e6			−0.134298
$963$	−4.69182e6	+	5.19176e6i	−0.163033	+	0.180405i
$964$	1.89952e7			0.658342
$965$		−	7.76999e7i		−	2.68598i
$966$	−1.01834e7	−	3.91967e6i	−0.351114	−	0.135147i
$967$		−	1.30865e7i		−	0.450047i	−0.974353	−	0.225023i	$-0.927754\pi$
$967$		−	1.30865e7i		−	0.450047i	0.974353	−	0.225023i	$-0.0722459\pi$
$968$	−1.30026e7			−0.446007
$969$	1.85043e6	−	4.80746e6i	0.0633087	−	0.164477i
$970$	5.80963e6			0.198253
$971$		−	4.04601e7i		−	1.37714i	−0.725169	−	0.688570i	$-0.758239\pi$
$971$		−	4.04601e7i		−	1.37714i	0.725169	−	0.688570i	$-0.241761\pi$
$972$	3.87652e6	−	1.42084e7i	0.131606	−	0.482369i
$973$	−2.01130e7			−0.681073
$974$	−2.84413e7			−0.960620
$975$	4.26256e6	−	1.10742e7i	0.143602	−	0.373079i
$976$		−	9.44247e6i		−	0.317294i
$977$	−3.45661e6			−0.115855			−0.0579274	−	0.998321i	$-0.518449\pi$
$977$	−3.45661e6			−0.115855			−0.0579274	+	0.998321i	$0.518449\pi$
$978$	783027.	+	301394.i	0.0261776	+	0.0100760i
$979$	−5.73298e7			−1.91172
$980$			5.59829e7i			1.86205i
$981$	2.50673e7	−	2.77384e7i	0.831639	−	0.920255i
$982$		−	1.11176e7i		−	0.367903i
$983$	−2.27130e7			−0.749704			−0.374852	−	0.927085i	$-0.622306\pi$
$983$	−2.27130e7			−0.749704			−0.374852	+	0.927085i	$0.622306\pi$
$984$	1.41058e6	−	3.66472e6i	0.0464420	−	0.120657i
$985$	−1.34100e6			−0.0440392
$986$	−5.06579e6			−0.165942
$987$	7.58107e7	+	2.91802e7i	2.47706	+	0.953444i
$988$			983250.i			0.0320458i
$989$		−	1.53995e7i		−	0.500628i
$990$	−3.27175e7	+	3.62037e7i	−1.06094	+	1.17399i
$991$		−	1.04192e7i		−	0.337016i	−0.985700	−	0.168508i	$-0.946105\pi$
$991$		−	1.04192e7i		−	0.337016i	0.985700	−	0.168508i	$-0.0538949\pi$
$992$			7.82334e6i			0.252414i
$993$	9.55564e6	+	3.67805e6i	0.307530	+	0.118371i
$994$			4.77142e7i			1.53173i
$995$		−	1.90491e7i		−	0.609983i
$996$	1.44727e7	+	5.57068e6i	0.462277	+	0.177934i
$997$	3.17520e6			0.101166			0.0505829	−	0.998720i	$-0.483892\pi$
$997$	3.17520e6			0.101166			0.0505829	+	0.998720i	$0.483892\pi$
$998$	−1.76875e7			−0.562136
$999$	1.62375e7	−	8.21764e6i	0.514760	−	0.260515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.5	✓	50
3.2	odd	2		354.6.c.b.353.6	yes	50
59.58	odd	2		354.6.c.b.353.5	yes	50
177.176	even	2	inner	354.6.c.a.353.6	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.5	✓	50	1.1	even	1	trivial
354.6.c.a.353.6	yes	50	177.176	even	2	inner
354.6.c.b.353.5	yes	50	59.58	odd	2
354.6.c.b.353.6	yes	50	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-14.5480 - 5.59965i) q^{3} +16.0000 q^{4} +83.1853i q^{5} +(58.1920 + 22.3986i) q^{6} +242.629 q^{7} -64.0000 q^{8} +(180.288 + 162.927i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-14.5480 - 5.59965i) q^{3} +16.0000 q^{4} +83.1853i q^{5} +(58.1920 + 22.3986i) q^{6} +242.629 q^{7} -64.0000 q^{8} +(180.288 + 162.927i) q^{9} -332.741i q^{10} -603.503 q^{11} +(-232.768 - 89.5943i) q^{12} -200.595i q^{13} -970.517 q^{14} +(465.809 - 1210.18i) q^{15} +256.000 q^{16} -1078.67i q^{17} +(-721.152 - 651.709i) q^{18} -306.354 q^{19} +1330.97i q^{20} +(-3529.77 - 1358.64i) q^{21} +2414.01 q^{22} -721.250 q^{23} +(931.071 + 358.377i) q^{24} -3794.80 q^{25} +802.381i q^{26} +(-1710.49 - 3379.81i) q^{27} +3882.07 q^{28} +1174.08i q^{29} +(-1863.23 + 4840.72i) q^{30} -7639.98i q^{31} -1024.00 q^{32} +(8779.76 + 3379.41i) q^{33} +4314.69i q^{34} +20183.2i q^{35} +(2884.61 + 2606.84i) q^{36} +4804.26i q^{37} +1225.41 q^{38} +(-1123.26 + 2918.26i) q^{39} -5323.86i q^{40} -3936.03i q^{41} +(14119.1 + 5434.55i) q^{42} +21351.1i q^{43} -9656.05 q^{44} +(-13553.2 + 14997.3i) q^{45} +2885.00 q^{46} -21477.5 q^{47} +(-3724.28 - 1433.51i) q^{48} +42061.9 q^{49} +15179.2 q^{50} +(-6040.18 + 15692.5i) q^{51} -3209.53i q^{52} -23127.8i q^{53} +(6841.97 + 13519.2i) q^{54} -50202.6i q^{55} -15528.3 q^{56} +(4456.83 + 1715.47i) q^{57} -4696.33i q^{58} +(11513.5 + 24132.2i) q^{59} +(7452.94 - 19362.9i) q^{60} -36884.7i q^{61} +30559.9i q^{62} +(43743.1 + 39530.9i) q^{63} +4096.00 q^{64} +16686.6 q^{65} +(-35119.0 - 13517.6i) q^{66} -50577.0i q^{67} -17258.8i q^{68} +(10492.7 + 4038.74i) q^{69} -80732.8i q^{70} -49163.7i q^{71} +(-11538.4 - 10427.3i) q^{72} +44405.3i q^{73} -19217.0i q^{74} +(55206.7 + 21249.5i) q^{75} -4901.66 q^{76} -146428. q^{77} +(4493.05 - 11673.0i) q^{78} -96414.4 q^{79} +21295.4i q^{80} +(5958.46 + 58747.6i) q^{81} +15744.1i q^{82} -62176.7 q^{83} +(-56476.3 - 21738.2i) q^{84} +89729.7 q^{85} -85404.4i q^{86} +(6574.44 - 17080.5i) q^{87} +38624.2 q^{88} +94995.0 q^{89} +(54212.6 - 59989.2i) q^{90} -48670.3i q^{91} -11540.0 q^{92} +(-42781.2 + 111146. i) q^{93} +85910.1 q^{94} -25484.1i q^{95} +(14897.1 + 5734.04i) q^{96} +17459.9i q^{97} -168248. q^{98} +(-108804. - 98327.1i) 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

Introduction

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