LMFDB - Embedded newform 76.5.b.a.39.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.b (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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.9
Character	$\chi$	$=$	76.39
Dual form			76.5.b.a.39.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45315 - 3.15944i) q^{2} +2.52727i q^{3} +(-3.96408 + 15.5012i) q^{4} -40.2815 q^{5} +(7.98474 - 6.19977i) q^{6} -43.5781i q^{7} +(58.6994 - 25.5025i) q^{8} +74.6129 q^{9} +O(q^{10})$	\(q+(-2.45315 - 3.15944i) q^{2} +2.52727i q^{3} +(-3.96408 + 15.5012i) q^{4} -40.2815 q^{5} +(7.98474 - 6.19977i) q^{6} -43.5781i q^{7} +(58.6994 - 25.5025i) q^{8} +74.6129 q^{9} +(98.8167 + 127.267i) q^{10} +155.673i q^{11} +(-39.1756 - 10.0183i) q^{12} +209.839 q^{13} +(-137.682 + 106.904i) q^{14} -101.802i q^{15} +(-224.572 - 122.896i) q^{16} +408.773 q^{17} +(-183.037 - 235.735i) q^{18} -82.8191i q^{19} +(159.679 - 624.410i) q^{20} +110.133 q^{21} +(491.839 - 381.890i) q^{22} +518.447i q^{23} +(64.4516 + 148.349i) q^{24} +997.599 q^{25} +(-514.767 - 662.972i) q^{26} +393.275i q^{27} +(675.511 + 172.747i) q^{28} -466.701 q^{29} +(-321.637 + 249.736i) q^{30} -1450.82i q^{31} +(162.629 + 1011.00i) q^{32} -393.427 q^{33} +(-1002.78 - 1291.49i) q^{34} +1755.39i q^{35} +(-295.771 + 1156.59i) q^{36} -369.868 q^{37} +(-261.662 + 203.168i) q^{38} +530.318i q^{39} +(-2364.50 + 1027.28i) q^{40} +1765.67 q^{41} +(-270.174 - 347.960i) q^{42} +1438.44i q^{43} +(-2413.11 - 617.099i) q^{44} -3005.52 q^{45} +(1638.00 - 1271.83i) q^{46} +2459.59i q^{47} +(310.590 - 567.554i) q^{48} +501.950 q^{49} +(-2447.26 - 3151.85i) q^{50} +1033.08i q^{51} +(-831.816 + 3252.74i) q^{52} +3393.21 q^{53} +(1242.53 - 964.765i) q^{54} -6270.74i q^{55} +(-1111.35 - 2558.01i) q^{56} +209.306 q^{57} +(1144.89 + 1474.51i) q^{58} +6077.55i q^{59} +(1578.05 + 403.551i) q^{60} +3201.76 q^{61} +(-4583.78 + 3559.09i) q^{62} -3251.49i q^{63} +(2795.25 - 2993.96i) q^{64} -8452.62 q^{65} +(965.137 + 1243.01i) q^{66} -4527.77i q^{67} +(-1620.41 + 6336.47i) q^{68} -1310.25 q^{69} +(5546.04 - 4306.24i) q^{70} -7594.03i q^{71} +(4379.74 - 1902.82i) q^{72} -567.050 q^{73} +(907.344 + 1168.58i) q^{74} +2521.20i q^{75} +(1283.79 + 328.301i) q^{76} +6783.93 q^{77} +(1675.51 - 1300.95i) q^{78} +4909.75i q^{79} +(9046.10 + 4950.42i) q^{80} +5049.74 q^{81} +(-4331.46 - 5578.52i) q^{82} -5831.91i q^{83} +(-436.577 + 1707.20i) q^{84} -16466.0 q^{85} +(4544.67 - 3528.72i) q^{86} -1179.48i q^{87} +(3970.05 + 9137.92i) q^{88} +2659.46 q^{89} +(7373.00 + 9495.75i) q^{90} -9144.37i q^{91} +(-8036.53 - 2055.16i) q^{92} +3666.61 q^{93} +(7770.92 - 6033.75i) q^{94} +3336.08i q^{95} +(-2555.07 + 411.008i) q^{96} +234.025 q^{97} +(-1231.36 - 1585.88i) q^{98} +11615.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.45315	−	3.15944i	−0.613288	−	0.789859i
$2$	−2.45315	−	3.15944i	−0.613288	−	0.789859i
$3$			2.52727i			0.280807i	0.990094	+	0.140404i	$0.0448400\pi$
$3$			2.52727i			0.280807i	−0.990094	+	0.140404i	$0.955160\pi$
$4$	−3.96408	+	15.5012i	−0.247755	+	0.968823i
$5$	−40.2815			−1.61126			−0.805630	−	0.592419i	$-0.798173\pi$
$5$	−40.2815			−1.61126			−0.805630	+	0.592419i	$0.798173\pi$
$6$	7.98474	−	6.19977i	0.221798	−	0.172216i
$7$		−	43.5781i		−	0.889349i	−0.895692	−	0.444674i	$-0.853319\pi$
$7$		−	43.5781i		−	0.889349i	0.895692	−	0.444674i	$-0.146681\pi$
$8$	58.6994	−	25.5025i	0.917179	−	0.398476i
$9$	74.6129			0.921147
$10$	98.8167	+	127.267i	0.988167	+	1.27267i
$11$			155.673i			1.28655i	0.765634	+	0.643277i	$0.222426\pi$
$11$			155.673i			1.28655i	−0.765634	+	0.643277i	$0.777574\pi$
$12$	−39.1756	−	10.0183i	−0.272053	−	0.0695714i
$13$	209.839			1.24165			0.620825	−	0.783950i	$-0.286798\pi$
$13$	209.839			1.24165			0.620825	+	0.783950i	$0.286798\pi$
$14$	−137.682	+	106.904i	−0.702460	+	0.545427i
$15$		−	101.802i		−	0.452454i
$16$	−224.572	−	122.896i	−0.877235	−	0.480061i
$17$	408.773			1.41444			0.707221	−	0.706993i	$-0.249949\pi$
$17$	408.773			1.41444			0.707221	+	0.706993i	$0.249949\pi$
$18$	−183.037	−	235.735i	−0.564929	−	0.727576i
$19$		−	82.8191i		−	0.229416i
$19$		−	82.8191i		−	0.229416i
$20$	159.679	−	624.410i	0.399197	−	1.56103i
$21$	110.133			0.249736
$22$	491.839	−	381.890i	1.01620	−	0.789028i
$23$			518.447i			0.980051i	0.871708	+	0.490026i	$0.163013\pi$
$23$			518.447i			0.980051i	−0.871708	+	0.490026i	$0.836987\pi$
$24$	64.4516	+	148.349i	0.111895	+	0.257551i
$25$	997.599			1.59616
$26$	−514.767	−	662.972i	−0.761489	−	0.980728i
$27$			393.275i			0.539472i
$28$	675.511	+	172.747i	0.861621	+	0.220340i
$29$	−466.701			−0.554936			−0.277468	−	0.960735i	$-0.589495\pi$
$29$	−466.701			−0.554936			−0.277468	+	0.960735i	$0.589495\pi$
$30$	−321.637	+	249.736i	−0.357375	+	0.277485i
$31$		−	1450.82i		−	1.50970i	−0.655898	−	0.754850i	$-0.727710\pi$
$31$		−	1450.82i		−	1.50970i	0.655898	−	0.754850i	$-0.272290\pi$
$32$	162.629	+	1011.00i	0.158818	+	0.987308i
$33$	−393.427			−0.361274
$34$	−1002.78	−	1291.49i	−0.867460	−	1.11721i
$35$			1755.39i			1.43297i
$36$	−295.771	+	1156.59i	−0.228219	+	0.892428i
$37$	−369.868			−0.270174			−0.135087	−	0.990834i	$-0.543131\pi$
$37$	−369.868			−0.270174			−0.135087	+	0.990834i	$0.543131\pi$
$38$	−261.662	+	203.168i	−0.181206	+	0.140698i
$39$			530.318i			0.348664i
$40$	−2364.50	+	1027.28i	−1.47781	+	0.642049i
$41$	1765.67			1.05037			0.525184	−	0.850989i	$-0.323996\pi$
$41$	1765.67			1.05037			0.525184	+	0.850989i	$0.323996\pi$
$42$	−270.174	−	347.960i	−0.153160	−	0.197256i
$43$			1438.44i			0.777957i	0.921247	+	0.388979i	$0.127172\pi$
$43$			1438.44i			0.777957i	−0.921247	+	0.388979i	$0.872828\pi$
$44$	−2413.11	−	617.099i	−1.24644	−	0.318750i
$45$	−3005.52			−1.48421
$46$	1638.00	−	1271.83i	0.774102	−	0.601054i
$47$			2459.59i			1.11344i	0.830700	+	0.556720i	$0.187940\pi$
$47$			2459.59i			1.11344i	−0.830700	+	0.556720i	$0.812060\pi$
$48$	310.590	−	567.554i	0.134805	−	0.246334i
$49$	501.950			0.209059
$50$	−2447.26	−	3151.85i	−0.978905	−	1.26074i
$51$			1033.08i			0.397186i
$52$	−831.816	+	3252.74i	−0.307624	+	1.20294i
$53$	3393.21			1.20798			0.603990	−	0.796992i	$-0.293577\pi$
$53$	3393.21			1.20798			0.603990	+	0.796992i	$0.293577\pi$
$54$	1242.53	−	964.765i	0.426107	−	0.330852i
$55$		−	6270.74i		−	2.07297i
$56$	−1111.35	−	2558.01i	−0.354385	−	0.815692i
$57$	209.306			0.0644216
$58$	1144.89	+	1474.51i	0.340336	+	0.438321i
$59$			6077.55i			1.74592i	0.487791	+	0.872960i	$0.337803\pi$
$59$			6077.55i			1.74592i	−0.487791	+	0.872960i	$0.662197\pi$
$60$	1578.05	+	403.551i	0.438347	+	0.112098i
$61$	3201.76			0.860457			0.430229	−	0.902720i	$-0.358433\pi$
$61$	3201.76			0.860457			0.430229	+	0.902720i	$0.358433\pi$
$62$	−4583.78	+	3559.09i	−1.19245	+	0.925881i
$63$		−	3251.49i		−	0.819221i
$64$	2795.25	−	2993.96i	0.682433	−	0.730948i
$65$	−8452.62			−2.00062
$66$	965.137	+	1243.01i	0.221565	+	0.285355i
$67$		−	4527.77i		−	1.00864i	−0.863518	−	0.504318i	$-0.831744\pi$
$67$		−	4527.77i		−	1.00864i	0.863518	−	0.504318i	$-0.168256\pi$
$68$	−1620.41	+	6336.47i	−0.350434	+	1.37034i
$69$	−1310.25			−0.275206
$70$	5546.04	−	4306.24i	1.13185	−	0.878825i
$71$		−	7594.03i		−	1.50645i	−0.657761	−	0.753226i	$-0.728496\pi$
$71$		−	7594.03i		−	1.50645i	0.657761	−	0.753226i	$-0.271504\pi$
$72$	4379.74	−	1902.82i	0.844856	−	0.367055i
$73$	−567.050			−0.106408			−0.0532042	−	0.998584i	$-0.516943\pi$
$73$	−567.050			−0.106408			−0.0532042	+	0.998584i	$0.516943\pi$
$74$	907.344	+	1168.58i	0.165695	+	0.213400i
$75$			2521.20i			0.448213i
$76$	1283.79	+	328.301i	0.222263	+	0.0568388i
$77$	6783.93			1.14419
$78$	1675.51	−	1300.95i	0.275396	−	0.213832i
$79$			4909.75i			0.786694i	0.919390	+	0.393347i	$0.128683\pi$
$79$			4909.75i			0.786694i	−0.919390	+	0.393347i	$0.871317\pi$
$80$	9046.10	+	4950.42i	1.41345	+	0.773503i
$81$	5049.74			0.769659
$82$	−4331.46	−	5578.52i	−0.644179	−	0.829643i
$83$		−	5831.91i		−	0.846554i	−0.906000	−	0.423277i	$-0.860880\pi$
$83$		−	5831.91i		−	0.846554i	0.906000	−	0.423277i	$-0.139120\pi$
$84$	−436.577	+	1707.20i	−0.0618732	+	0.241950i
$85$	−16466.0			−2.27903
$86$	4544.67	−	3528.72i	0.614477	−	0.477112i
$87$		−	1179.48i		−	0.155830i
$88$	3970.05	+	9137.92i	0.512661	+	1.18000i
$89$	2659.46			0.335748			0.167874	−	0.985808i	$-0.446310\pi$
$89$	2659.46			0.335748			0.167874	+	0.985808i	$0.446310\pi$
$90$	7373.00	+	9495.75i	0.910247	+	1.17231i
$91$		−	9144.37i		−	1.10426i
$92$	−8036.53	−	2055.16i	−0.949496	−	0.242812i
$93$	3666.61			0.423935
$94$	7770.92	−	6033.75i	0.879461	−	0.682860i
$95$			3336.08i			0.369648i
$96$	−2555.07	+	411.008i	−0.277243	+	0.0445972i
$97$	234.025			0.0248725			0.0124362	−	0.999923i	$-0.496041\pi$
$97$	234.025			0.0248725			0.0124362	+	0.999923i	$0.496041\pi$
$98$	−1231.36	−	1585.88i	−0.128213	−	0.165127i
$99$			11615.2i			1.18511i
$100$	−3954.56	+	15463.9i	−0.395456	+	1.54639i
$101$	−15054.2			−1.47576			−0.737880	−	0.674932i	$-0.764173\pi$
$101$	−15054.2			−1.47576			−0.737880	+	0.674932i	$0.764173\pi$
$102$	3263.95	−	2534.30i	0.313721	−	0.243589i
$103$			9284.08i			0.875113i	0.899191	+	0.437557i	$0.144156\pi$
$103$			9284.08i			0.875113i	−0.899191	+	0.437557i	$0.855844\pi$
$104$	12317.4	−	5351.41i	1.13881	−	0.494768i
$105$	−4436.34			−0.402389
$106$	−8324.07	−	10720.6i	−0.740840	−	0.954133i
$107$			5913.41i			0.516500i	0.966078	+	0.258250i	$0.0831458\pi$
$107$			5913.41i			0.516500i	−0.966078	+	0.258250i	$0.916854\pi$
$108$	−6096.23	−	1558.97i	−0.522653	−	0.133657i
$109$	8828.58			0.743084			0.371542	−	0.928416i	$-0.378829\pi$
$109$	8828.58			0.743084			0.371542	+	0.928416i	$0.378829\pi$
$110$	−19812.0	+	15383.1i	−1.63736	+	1.27133i
$111$		−	934.756i		−	0.0758669i
$112$	−5355.55	+	9786.43i	−0.426942	+	0.780168i
$113$	3916.45			0.306716			0.153358	−	0.988171i	$-0.450991\pi$
$113$	3916.45			0.306716			0.153358	+	0.988171i	$0.450991\pi$
$114$	−513.459	−	661.289i	−0.0395090	−	0.0508840i
$115$		−	20883.8i		−	1.57912i
$116$	1850.04	−	7234.41i	0.137488	−	0.537635i
$117$	15656.7			1.14374
$118$	19201.6	−	14909.2i	1.37903	−	1.07075i
$119$		−	17813.6i		−	1.25793i
$120$	−2596.21	−	5975.72i	−0.180292	−	0.414981i
$121$	−9593.08			−0.655220
$122$	−7854.41	−	10115.8i	−0.527708	−	0.679640i
$123$			4462.32i			0.294951i
$124$	22489.4	+	5751.17i	1.46263	+	0.374035i
$125$	−15008.8			−0.960565
$126$	−10272.9	+	7976.40i	−0.647069	+	0.502419i
$127$		−	5122.50i		−	0.317596i	−0.987311	−	0.158798i	$-0.949238\pi$
$127$		−	5122.50i		−	0.317596i	0.987311	−	0.158798i	$-0.0507618\pi$
$128$	−16316.4	−	1486.75i	−0.995874	−	0.0907439i
$129$	−3635.33			−0.218456
$130$	20735.6	+	26705.5i	1.22696	+	1.58021i
$131$		−	13347.1i		−	0.777758i	−0.921289	−	0.388879i	$-0.872862\pi$
$131$		−	13347.1i		−	0.777758i	0.921289	−	0.388879i	$-0.127138\pi$
$132$	1559.57	−	6098.58i	0.0895073	−	0.350010i
$133$	−3609.10			−0.204031
$134$	−14305.2	+	11107.3i	−0.796680	+	0.618585i
$135$		−	15841.7i		−	0.869230i
$136$	23994.8	−	10424.7i	1.29730	−	0.563621i
$137$	−27771.1			−1.47963			−0.739814	−	0.672812i	$-0.765086\pi$
$137$	−27771.1			−1.47963			−0.739814	+	0.672812i	$0.765086\pi$
$138$	3214.25	+	4139.66i	0.168780	+	0.217374i
$139$			11552.5i			0.597926i	0.954265	+	0.298963i	$0.0966406\pi$
$139$			11552.5i			0.597926i	−0.954265	+	0.298963i	$0.903359\pi$
$140$	−27210.6	−	6958.50i	−1.38830	−	0.355026i
$141$	−6216.04			−0.312662
$142$	−23992.8	+	18629.3i	−1.18989	+	0.923890i
$143$			32666.2i			1.59745i
$144$	−16756.0	−	9169.60i	−0.808063	−	0.442207i
$145$	18799.4			0.894146
$146$	1391.06	+	1791.56i	0.0652590	+	0.0840476i
$147$			1268.56i			0.0587052i
$148$	1466.19	−	5733.39i	0.0669369	−	0.261751i
$149$	−15290.8			−0.688745			−0.344373	−	0.938833i	$-0.611908\pi$
$149$	−15290.8			−0.688745			−0.344373	+	0.938833i	$0.611908\pi$
$150$	7965.56	−	6184.88i	0.354025	−	0.274884i
$151$			27786.6i			1.21866i	0.792918	+	0.609328i	$0.208561\pi$
$151$			27786.6i			1.21866i	−0.792918	+	0.609328i	$0.791439\pi$
$152$	−2112.09	−	4861.43i	−0.0914168	−	0.210415i
$153$	30499.8			1.30291
$154$	−16642.0	−	21433.4i	−0.701721	−	0.903753i
$155$			58441.3i			2.43252i
$156$	−8220.55	−	2102.22i	−0.337794	−	0.0863832i
$157$	35655.6			1.44653			0.723267	−	0.690568i	$-0.242640\pi$
$157$	35655.6			1.44653			0.723267	+	0.690568i	$0.242640\pi$
$158$	15512.1	−	12044.4i	0.621377	−	0.482470i
$159$			8575.55i			0.339209i
$160$	−6550.95	−	40724.7i	−0.255897	−	1.59081i
$161$	22592.9			0.871607
$162$	−12387.8	−	15954.3i	−0.472023	−	0.607922i
$163$		−	5179.92i		−	0.194961i	−0.995237	−	0.0974806i	$-0.968922\pi$
$163$		−	5179.92i		−	0.194961i	0.995237	−	0.0974806i	$-0.0310784\pi$
$164$	−6999.25	+	27369.9i	−0.260234	+	1.01762i
$165$	15847.8			0.582106
$166$	−18425.5	+	14306.6i	−0.668658	+	0.519182i
$167$		−	12820.3i		−	0.459691i	−0.973227	−	0.229845i	$-0.926178\pi$
$167$		−	12820.3i		−	0.459691i	0.973227	−	0.229845i	$-0.0738221\pi$
$168$	6464.77	−	2808.68i	0.229052	−	0.0995138i
$169$	15471.3			0.541693
$170$	40393.6	+	52023.3i	1.39770	+	1.80011i
$171$		−	6179.37i		−	0.211326i
$172$	−22297.5	−	5702.10i	−0.753703	−	0.192743i
$173$	−2641.35			−0.0882540			−0.0441270	−	0.999026i	$-0.514051\pi$
$173$	−2641.35			−0.0882540			−0.0441270	+	0.999026i	$0.514051\pi$
$174$	−3726.49	+	2893.44i	−0.123084	+	0.0955688i
$175$		−	43473.4i		−	1.41954i
$176$	19131.5	−	34959.8i	0.617624	−	1.12861i
$177$	−15359.6			−0.490267
$178$	−6524.07	−	8402.40i	−0.205910	−	0.265194i
$179$			11789.2i			0.367941i	0.982932	+	0.183970i	$0.0588950\pi$
$179$			11789.2i			0.367941i	−0.982932	+	0.183970i	$0.941105\pi$
$180$	11914.1	−	46589.1i	0.367719	−	1.43793i
$181$	41256.5			1.25932			0.629658	−	0.776872i	$-0.283195\pi$
$181$	41256.5			1.25932			0.629658	+	0.776872i	$0.283195\pi$
$182$	−28891.1	+	22432.5i	−0.872209	+	0.677229i
$183$			8091.70i			0.241623i
$184$	13221.7	+	30432.5i	0.390527	+	0.898882i
$185$	14898.9			0.435321
$186$	−8994.76	−	11584.4i	−0.259994	−	0.334849i
$187$			63635.0i			1.81975i
$188$	−38126.5	−	9750.00i	−1.07873	−	0.275860i
$189$	17138.2			0.479779
$190$	10540.1	−	8183.91i	0.291970	−	0.226701i
$191$		−	64773.0i		−	1.77553i	−0.460300	−	0.887763i	$-0.652258\pi$
$191$		−	64773.0i		−	1.77553i	0.460300	−	0.887763i	$-0.347742\pi$
$192$	7566.54	+	7064.33i	0.205256	+	0.191632i
$193$	−2850.01			−0.0765123			−0.0382562	−	0.999268i	$-0.512180\pi$
$193$	−2850.01			−0.0765123			−0.0382562	+	0.999268i	$0.512180\pi$
$194$	−574.100	−	739.387i	−0.0152540	−	0.0196457i
$195$		−	21362.0i		−	0.561789i
$196$	−1989.77	+	7780.81i	−0.0517953	+	0.202541i
$197$	−32668.2			−0.841770			−0.420885	−	0.907114i	$-0.638280\pi$
$197$	−32668.2			−0.841770			−0.420885	+	0.907114i	$0.638280\pi$
$198$	36697.5	−	28493.9i	0.936066	−	0.726811i
$199$		−	18713.9i		−	0.472562i	−0.971685	−	0.236281i	$-0.924071\pi$
$199$		−	18713.9i		−	0.472562i	0.971685	−	0.236281i	$-0.0759286\pi$
$200$	58558.5	−	25441.3i	1.46396	−	0.636031i
$201$	11442.9			0.283232
$202$	36930.3	+	47562.8i	0.905066	+	1.16564i
$203$			20338.0i			0.493532i
$204$	−16013.9	−	4095.21i	−0.384802	−	0.0984046i
$205$	−71123.8			−1.69242
$206$	29332.5	−	22775.3i	0.691216	−	0.536697i
$207$			38682.8i			0.902771i
$208$	−47123.9	−	25788.2i	−1.08922	−	0.596067i
$209$	12892.7			0.295156
$210$	10883.0	+	14016.3i	0.246781	+	0.317831i
$211$		−	25185.9i		−	0.565708i	−0.959163	−	0.282854i	$-0.908719\pi$
$211$		−	25185.9i		−	0.565708i	0.959163	−	0.282854i	$-0.0912812\pi$
$212$	−13451.0	+	52598.8i	−0.299283	+	1.17032i
$213$	19192.1			0.423023
$214$	18683.0	−	14506.5i	0.407962	−	0.316763i
$215$		−	57942.6i		−	1.25349i
$216$	10029.5	+	23085.0i	0.214967	+	0.494792i
$217$	−63224.0			−1.34265
$218$	−21657.9	−	27893.3i	−0.455725	−	0.586932i
$219$		−	1433.09i		−	0.0298803i
$220$	97203.8	+	24857.7i	2.00834	+	0.513589i
$221$	85776.5			1.75624
$222$	−2953.30	+	2293.10i	−0.0599242	+	0.0465283i
$223$			26943.8i			0.541812i	0.962606	+	0.270906i	$0.0873233\pi$
$223$			26943.8i			0.541812i	−0.962606	+	0.270906i	$0.912677\pi$
$224$	44057.6	−	7087.08i	0.878061	−	0.141244i
$225$	74433.8			1.47030
$226$	−9607.66	−	12373.8i	−0.188105	−	0.242262i
$227$			22122.2i			0.429316i	0.976689	+	0.214658i	$0.0688637\pi$
$227$			22122.2i			0.429316i	−0.976689	+	0.214658i	$0.931136\pi$
$228$	−829.704	+	3244.48i	−0.0159608	+	0.0624131i
$229$	−9258.25			−0.176546			−0.0882730	−	0.996096i	$-0.528135\pi$
$229$	−9258.25			−0.176546			−0.0882730	+	0.996096i	$0.528135\pi$
$230$	−65981.1	+	51231.2i	−1.24728	+	0.968454i
$231$			17144.8i			0.321298i
$232$	−27395.1	+	11902.0i	−0.508976	+	0.221129i
$233$	−67287.4			−1.23943			−0.619715	−	0.784827i	$-0.712752\pi$
$233$	−67287.4			−1.23943			−0.619715	+	0.784827i	$0.712752\pi$
$234$	−38408.2	−	49466.3i	−0.701443	−	0.903395i
$235$		−	99075.9i		−	1.79404i
$236$	−94209.1	−	24091.9i	−1.69149	−	0.432560i
$237$	−12408.3			−0.220909
$238$	−56280.8	+	43699.4i	−0.993589	+	0.771475i
$239$		−	27701.4i		−	0.484960i	−0.970156	−	0.242480i	$-0.922039\pi$
$239$		−	27701.4i		−	0.484960i	0.970156	−	0.242480i	$-0.0779609\pi$
$240$	−12511.0	+	22861.9i	−0.217205	+	0.396908i
$241$	−82109.6			−1.41371			−0.706854	−	0.707360i	$-0.749886\pi$
$241$	−82109.6			−1.41371			−0.706854	+	0.707360i	$0.749886\pi$
$242$	23533.3	+	30308.7i	0.401839	+	0.517532i
$243$			44617.3i			0.755598i
$244$	−12692.0	+	49631.0i	−0.213182	+	0.833631i
$245$	−20219.3			−0.336848
$246$	14098.4	−	10946.7i	0.232970	−	0.180890i
$247$		−	17378.6i		−	0.284854i
$248$	−36999.6	−	85162.4i	−0.601580	−	1.38466i
$249$	14738.8			0.237719
$250$	36819.0	+	47419.4i	0.589103	+	0.758711i
$251$			78793.4i			1.25067i	0.780357	+	0.625334i	$0.215037\pi$
$251$			78793.4i			1.25067i	−0.780357	+	0.625334i	$0.784963\pi$
$252$	50401.9	+	12889.1i	0.793680	+	0.202966i
$253$	−80708.2			−1.26089
$254$	−16184.2	+	12566.3i	−0.250856	+	0.194778i
$255$		−	41614.0i		−	0.639969i
$256$	35329.4	+	55197.9i	0.539083	+	0.842253i
$257$	−3341.14			−0.0505858			−0.0252929	−	0.999680i	$-0.508052\pi$
$257$	−3341.14			−0.0505858			−0.0252929	+	0.999680i	$0.508052\pi$
$258$	8918.02	+	11485.6i	0.133977	+	0.172550i
$259$			16118.2i			0.240279i
$260$	33506.8	−	131025.i	0.495663	−	1.93825i
$261$	−34821.9			−0.511178
$262$	−42169.3	+	32742.5i	−0.614319	+	0.476990i
$263$		−	40769.6i		−	0.589420i	−0.955587	−	0.294710i	$-0.904777\pi$
$263$		−	40769.6i		−	0.589420i	0.955587	−	0.294710i	$-0.0952231\pi$
$264$	−23093.9	+	10033.4i	−0.331353	+	0.143959i
$265$	−136684.			−1.94637
$266$	8853.67	+	11402.7i	0.125130	+	0.161155i
$267$			6721.17i			0.0942806i
$268$	70185.7	+	17948.4i	0.977190	+	0.249894i
$269$	−36922.0			−0.510247			−0.255124	−	0.966908i	$-0.582116\pi$
$269$	−36922.0			−0.510247			−0.255124	+	0.966908i	$0.582116\pi$
$270$	−50050.9	+	38862.2i	−0.686569	+	0.533089i
$271$			81308.4i			1.10713i	0.832808	+	0.553563i	$0.186732\pi$
$271$			81308.4i			1.10713i	−0.832808	+	0.553563i	$0.813268\pi$
$272$	−91799.2	−	50236.5i	−1.24080	−	0.679018i
$273$	23110.3			0.310084
$274$	68126.9	+	87741.1i	0.907439	+	1.16870i
$275$			155299.i			2.05354i
$276$	5193.95	−	20310.5i	0.0681835	−	0.266625i
$277$	−98375.3			−1.28211			−0.641057	−	0.767493i	$-0.721504\pi$
$277$	−98375.3			−1.28211			−0.641057	+	0.767493i	$0.721504\pi$
$278$	36499.5	−	28340.1i	0.472277	−	0.366701i
$279$		−	108250.i		−	1.39066i
$280$	44766.8	+	103040.i	0.571006	+	1.31429i
$281$	92422.4			1.17048			0.585241	−	0.810859i	$-0.301000\pi$
$281$	92422.4			1.17048			0.585241	+	0.810859i	$0.301000\pi$
$282$	15248.9	+	19639.2i	0.191752	+	0.246959i
$283$		−	35577.1i		−	0.444219i	−0.975022	−	0.222110i	$-0.928706\pi$
$283$		−	35577.1i		−	0.444219i	0.975022	−	0.222110i	$-0.0712943\pi$
$284$	117716.	+	30103.3i	1.45949	+	0.373231i
$285$	−8431.15			−0.103800
$286$	103207.	−	80135.3i	1.26176	−	0.979696i
$287$		−	76944.5i		−	0.934144i
$288$	12134.3	+	75433.9i	0.146295	+	0.909456i
$289$	83574.8			1.00064
$290$	−46117.9	−	59395.6i	−0.548369	−	0.706249i
$291$			591.444i			0.00698437i
$292$	2247.83	−	8789.94i	0.0263632	−	0.103091i
$293$	151412.			1.76370			0.881850	−	0.471529i	$-0.156298\pi$
$293$	151412.			1.76370			0.881850	+	0.471529i	$0.156298\pi$
$294$	4007.94	−	3111.98i	0.0463689	−	0.0360032i
$295$		−	244813.i		−	2.81313i
$296$	−21711.1	+	9432.57i	−0.247798	+	0.107658i
$297$	−61222.3			−0.694060
$298$	37510.8	+	48310.4i	0.422400	+	0.544012i
$299$			108790.i			1.21688i
$300$	−39081.5	−	9994.22i	−0.434239	−	0.111047i
$301$	62684.6			0.691875
$302$	87789.9	−	68164.7i	0.962567	−	0.747388i
$303$		−	38046.0i		−	0.414404i
$304$	−10178.1	+	18598.9i	−0.110134	+	0.201252i
$305$	−128972.			−1.38642
$306$	−74820.7	−	96362.1i	−0.799059	−	1.02911i
$307$			58109.8i			0.616557i	0.951296	+	0.308278i	$0.0997528\pi$
$307$			58109.8i			0.616557i	−0.951296	+	0.308278i	$0.900247\pi$
$308$	−26892.0	+	105159.i	−0.283480	+	1.10852i
$309$	−23463.3			−0.245738
$310$	184641.	−	143365.i	1.92135	−	1.49184i
$311$		−	145395.i		−	1.50324i	−0.659597	−	0.751620i	$-0.729273\pi$
$311$		−	145395.i		−	1.50324i	0.659597	−	0.751620i	$-0.270727\pi$
$312$	13524.4	+	31129.4i	0.138934	+	0.319787i
$313$	2448.55			0.0249931			0.0124966	−	0.999922i	$-0.496022\pi$
$313$	2448.55			0.0249931			0.0124966	+	0.999922i	$0.496022\pi$
$314$	−87468.7	−	112652.i	−0.887143	−	1.14256i
$315$			130975.i			1.31998i
$316$	−76106.9	−	19462.6i	−0.762167	−	0.194907i
$317$	−37561.3			−0.373785			−0.186893	−	0.982380i	$-0.559842\pi$
$317$	−37561.3			−0.373785			−0.186893	+	0.982380i	$0.559842\pi$
$318$	27093.9	−	21037.2i	0.267928	−	0.208033i
$319$		−	72652.8i		−	0.713955i
$320$	−112597.	+	120601.i	−1.09958	+	1.17775i
$321$	−14944.8			−0.145037
$322$	−55423.9	−	71380.9i	−0.534547	−	0.688447i
$323$		−	33854.2i		−	0.324495i
$324$	−20017.5	+	78276.8i	−0.190687	+	0.745664i
$325$	209335.			1.98187
$326$	−16365.6	+	12707.1i	−0.153992	+	0.119567i
$327$			22312.2i			0.208664i
$328$	103644.	−	45029.0i	0.963375	−	0.418547i
$329$	107184.			0.990237
$330$	−38877.2	−	50070.2i	−0.356999	−	0.459782i
$331$		−	84174.8i		−	0.768292i	−0.923272	−	0.384146i	$-0.874496\pi$
$331$		−	84174.8i		−	0.768292i	0.923272	−	0.384146i	$-0.125504\pi$
$332$	90401.4	+	23118.1i	0.820161	+	0.209738i
$333$	−27597.0			−0.248870
$334$	−40505.0	+	31450.2i	−0.363091	+	0.281923i
$335$			182385.i			1.62517i
$336$	−24732.9	−	13534.9i	−0.219077	−	0.119888i
$337$	21266.7			0.187258			0.0936292	−	0.995607i	$-0.470153\pi$
$337$	21266.7			0.187258			0.0936292	+	0.995607i	$0.470153\pi$
$338$	−37953.4	−	48880.5i	−0.332214	−	0.427861i
$339$			9897.92i			0.0861280i
$340$	65272.5	−	255242.i	0.564641	−	2.20798i
$341$	225854.			1.94231
$342$	−19523.3	+	15159.0i	−0.166917	+	0.129604i
$343$		−	126505.i		−	1.07527i
$344$	36683.9	+	84435.8i	0.309998	+	0.713526i
$345$	52779.0			0.443428
$346$	6479.65	+	8345.19i	0.0541251	+	0.0697082i
$347$			178490.i			1.48237i	0.671303	+	0.741183i	$0.265735\pi$
$347$			178490.i			1.48237i	−0.671303	+	0.741183i	$0.734265\pi$
$348$	18283.3	+	4675.54i	0.150972	+	0.0386077i
$349$	−85892.7			−0.705189			−0.352594	−	0.935776i	$-0.614700\pi$
$349$	−85892.7			−0.705189			−0.352594	+	0.935776i	$0.614700\pi$
$350$	−137352.	+	106647.i	−1.12124	+	0.870588i
$351$			82524.4i			0.669835i
$352$	−157386.	+	25317.0i	−1.27022	+	0.204328i
$353$	197679.			1.58639			0.793197	−	0.608965i	$-0.208415\pi$
$353$	197679.			1.58639			0.793197	+	0.608965i	$0.208415\pi$
$354$	37679.4	+	48527.6i	0.300675	+	0.387242i
$355$			305899.i			2.42729i
$356$	−10542.3	+	41224.7i	−0.0831832	+	0.325280i
$357$	45019.6			0.353236
$358$	37247.2	−	28920.7i	0.290621	−	0.225654i
$359$			23023.6i			0.178642i	0.996003	+	0.0893212i	$0.0284698\pi$
$359$			23023.6i			0.178642i	−0.996003	+	0.0893212i	$0.971530\pi$
$360$	−176422.	+	76648.3i	−1.36128	+	0.591422i
$361$	−6859.00			−0.0526316
$362$	−101208.	−	130347.i	−0.772324	−	0.994682i
$363$		−	24244.3i		−	0.183991i
$364$	141748.	+	36249.0i	1.06983	+	0.273585i
$365$	22841.6			0.171451
$366$	25565.2	−	19850.2i	0.190848	−	0.148184i
$367$			116123.i			0.862154i	0.902315	+	0.431077i	$0.141866\pi$
$367$			116123.i			0.862154i	−0.902315	+	0.431077i	$0.858134\pi$
$368$	63714.8	−	116429.i	0.470484	−	0.859735i
$369$	131742.			0.967544
$370$	−36549.2	−	47072.0i	−0.266977	−	0.343842i
$371$		−	147870.i		−	1.07431i
$372$	−14534.7	+	56836.8i	−0.105032	+	0.410718i
$373$	−88670.7			−0.637328			−0.318664	−	0.947868i	$-0.603234\pi$
$373$	−88670.7			−0.637328			−0.318664	+	0.947868i	$0.603234\pi$
$374$	201051.	−	156106.i	1.43735	−	1.11603i
$375$		−	37931.3i		−	0.269734i
$376$	62725.7	+	144376.i	0.443680	+	1.02122i
$377$	−97932.0			−0.689036
$378$	−42042.6	−	54147.0i	−0.294243	−	0.378958i
$379$		−	210494.i		−	1.46541i	−0.680544	−	0.732707i	$-0.738257\pi$
$379$		−	210494.i		−	1.46541i	0.680544	−	0.732707i	$-0.261743\pi$
$380$	−51713.1	−	13224.5i	−0.358124	−	0.0915821i
$381$	12945.9			0.0891833
$382$	−204646.	+	158898.i	−1.40242	+	1.08891i
$383$			228164.i			1.55543i	0.628620	+	0.777713i	$0.283620\pi$
$383$			228164.i			1.55543i	−0.628620	+	0.777713i	$0.716380\pi$
$384$	3757.41	−	41235.9i	0.0254816	−	0.279649i
$385$	−273267.			−1.84360
$386$	6991.51	+	9004.42i	0.0469241	+	0.0604340i
$387$			107326.i			0.716613i
$388$	−927.693	+	3627.66i	−0.00616227	+	0.0240970i
$389$	−89236.5			−0.589716			−0.294858	−	0.955541i	$-0.595272\pi$
$389$	−89236.5			−0.589716			−0.294858	+	0.955541i	$0.595272\pi$
$390$	−67491.9	+	52404.3i	−0.443734	+	0.344538i
$391$			211927.i			1.38622i
$392$	29464.2	−	12801.0i	0.191744	−	0.0833050i
$393$	33731.7			0.218400
$394$	80140.2	+	103213.i	0.516248	+	0.664880i
$395$		−	197772.i		−	1.26757i
$396$	−180049.	−	46043.6i	−1.14816	−	0.293615i
$397$	−121450.			−0.770579			−0.385289	−	0.922796i	$-0.625898\pi$
$397$	−121450.			−0.770579			−0.385289	+	0.922796i	$0.625898\pi$
$398$	−59125.4	+	45908.1i	−0.373257	+	0.289817i
$399$		−	9121.15i		−	0.0572933i
$400$	−224033.	−	122600.i	−1.40021	−	0.766253i
$401$	−158582.			−0.986202			−0.493101	−	0.869972i	$-0.664137\pi$
$401$	−158582.			−0.986202			−0.493101	+	0.869972i	$0.664137\pi$
$402$	−28071.1	−	36153.0i	−0.173703	−	0.223714i
$403$		−	304438.i		−	1.87452i
$404$	59676.1	−	233358.i	0.365626	−	1.42975i
$405$	−203411.			−1.24012
$406$	64256.5	−	49892.1i	0.389821	−	0.302677i
$407$		−	57578.5i		−	0.347594i
$408$	26346.1	+	60641.2i	0.158269	+	0.364290i
$409$	−91628.4			−0.547752			−0.273876	−	0.961765i	$-0.588306\pi$
$409$	−91628.4			−0.547752			−0.273876	+	0.961765i	$0.588306\pi$
$410$	174478.	+	224711.i	1.03794	+	1.33677i
$411$		−	70185.1i		−	0.415490i
$412$	−143914.	−	36802.8i	−0.847830	−	0.216813i
$413$	264848.			1.55273
$414$	122216.	−	94895.0i	0.713062	−	0.553659i
$415$			234918.i			1.36402i
$416$	34125.9	+	212148.i	0.197196	+	1.22589i
$417$	−29196.3			−0.167902
$418$	−31627.8	−	40733.6i	−0.181016	−	0.233131i
$419$			1585.03i			0.00902836i	0.999990	+	0.00451418i	$0.00143691\pi$
$419$			1585.03i			0.00902836i	−0.999990	+	0.00451418i	$0.998563\pi$
$420$	17586.0	−	68768.4i	0.0996938	−	0.389844i
$421$	68653.6			0.387346			0.193673	−	0.981066i	$-0.437960\pi$
$421$	68653.6			0.387346			0.193673	+	0.981066i	$0.437960\pi$
$422$	−79573.2	+	61784.8i	−0.446830	+	0.346942i
$423$			183517.i			1.02564i
$424$	199180.	−	86535.4i	1.10793	−	0.481351i
$425$	407792.			2.25767
$426$	−47081.3	−	60636.3i	−0.259435	−	0.334129i
$427$		−	139527.i		−	0.765247i
$428$	−91664.7	−	23441.2i	−0.500397	−	0.127965i
$429$	−82556.2			−0.448575
$430$	−183066.	+	142142.i	−0.990082	+	0.768752i
$431$		−	223633.i		−	1.20388i	−0.798543	−	0.601938i	$-0.794395\pi$
$431$		−	223633.i		−	1.20388i	0.798543	−	0.601938i	$-0.205605\pi$
$432$	48331.8	−	88318.7i	0.258980	−	0.473244i
$433$	172269.			0.918821			0.459411	−	0.888224i	$-0.348061\pi$
$433$	172269.			0.918821			0.459411	+	0.888224i	$0.348061\pi$
$434$	155098.	+	199752.i	0.823431	+	1.06050i
$435$			47511.2i			0.251083i
$436$	−34997.2	+	136853.i	−0.184103	+	0.719917i
$437$	42937.3			0.224839
$438$	−4527.75	+	3515.58i	−0.0236012	+	0.0183252i
$439$		−	289971.i		−	1.50462i	−0.658811	−	0.752309i	$-0.728940\pi$
$439$		−	289971.i		−	1.50462i	0.658811	−	0.752309i	$-0.271060\pi$
$440$	−159920.	−	368089.i	−0.826031	−	1.90129i
$441$	37452.0			0.192574
$442$	−210423.	−	271005.i	−1.07708	−	1.38718i
$443$			149749.i			0.763054i	0.924358	+	0.381527i	$0.124602\pi$
$443$			149749.i			0.763054i	−0.924358	+	0.381527i	$0.875398\pi$
$444$	14489.8	+	3705.44i	0.0735016	+	0.0187964i
$445$	−107127.			−0.540977
$446$	85127.2	−	66097.2i	0.427955	−	0.332287i
$447$		−	38644.0i		−	0.193405i
$448$	−130471.	−	121811.i	−0.650068	−	0.606921i
$449$	190362.			0.944252			0.472126	−	0.881531i	$-0.343487\pi$
$449$	190362.			0.944252			0.472126	+	0.881531i	$0.343487\pi$
$450$	−182597.	−	235169.i	−0.901716	−	1.16133i
$451$			274867.i			1.35136i
$452$	−15525.1	+	60709.6i	−0.0759903	+	0.297153i
$453$	−70224.1			−0.342208
$454$	69893.8	−	54269.2i	0.339099	−	0.263295i
$455$			368349.i			1.77925i
$456$	12286.1	−	5337.82i	0.0590861	−	0.0256705i
$457$	57751.8			0.276524			0.138262	−	0.990396i	$-0.455848\pi$
$457$	57751.8			0.276524			0.138262	+	0.990396i	$0.455848\pi$
$458$	22711.9	+	29250.8i	0.108274	+	0.139446i
$459$			160761.i			0.763052i
$460$	323724.	+	82785.0i	1.52988	+	0.391234i
$461$	−344443.			−1.62075			−0.810374	−	0.585913i	$-0.800736\pi$
$461$	−344443.			−1.62075			−0.810374	+	0.585913i	$0.800736\pi$
$462$	54167.9	−	42058.8i	0.253780	−	0.197049i
$463$		−	47345.6i		−	0.220860i	−0.993884	−	0.110430i	$-0.964777\pi$
$463$		−	47345.6i		−	0.220860i	0.993884	−	0.110430i	$-0.0352229\pi$
$464$	104808.	+	57355.5i	0.486810	+	0.266403i
$465$	−147697.			−0.683069
$466$	165066.	+	212590.i	0.760127	+	0.978974i
$467$		−	112846.i		−	0.517430i	−0.965954	−	0.258715i	$-0.916701\pi$
$467$		−	112846.i		−	0.517430i	0.965954	−	0.258715i	$-0.0832990\pi$
$468$	−62064.3	+	242697.i	−0.283367	+	1.10808i
$469$	−197311.			−0.897029
$470$	−313024.	+	243048.i	−1.41704	+	1.10026i
$471$			90111.3i			0.406197i
$472$	154993.	+	356749.i	0.695708	+	1.60132i
$473$	−223927.			−1.00088
$474$	30439.4	+	39203.1i	0.135481	+	0.174487i
$475$		−	82620.2i		−	0.366184i
$476$	276131.	+	70614.3i	1.21871	+	0.311658i
$477$	253178.			1.11273
$478$	−87520.8	+	67955.8i	−0.383050	+	0.297420i
$479$		−	209358.i		−	0.912469i	−0.889860	−	0.456234i	$-0.849198\pi$
$479$		−	209358.i		−	0.912469i	0.889860	−	0.456234i	$-0.150802\pi$
$480$	102922.	−	16556.0i	0.446711	−	0.0718577i
$481$	−77612.7			−0.335462
$482$	201427.	+	259420.i	0.867011	+	1.11663i
$483$			57098.4i			0.244754i
$484$	38027.7	−	148704.i	0.162334	−	0.634792i
$485$	−9426.88			−0.0400760
$486$	140966.	−	109453.i	0.596816	−	0.463400i
$487$		−	93643.6i		−	0.394839i	−0.980319	−	0.197420i	$-0.936744\pi$
$487$		−	93643.6i		−	0.394839i	0.980319	−	0.197420i	$-0.0632561\pi$
$488$	187942.	−	81652.9i	0.789193	−	0.342872i
$489$	13091.0			0.0547465
$490$	49601.0	+	63881.6i	0.206585	+	0.266062i
$491$		−	253562.i		−	1.05177i	−0.850555	−	0.525886i	$-0.823734\pi$
$491$		−	253562.i		−	1.05177i	0.850555	−	0.525886i	$-0.176266\pi$
$492$	−69171.1	−	17689.0i	−0.285755	−	0.0730756i
$493$	−190775.			−0.784924
$494$	−54906.7	+	42632.5i	−0.224994	+	0.174698i
$495$		−	467878.i		−	1.90951i
$496$	−178300.	+	325814.i	−0.724748	+	1.32436i
$497$	−330933.			−1.33976
$498$	−36156.5	−	46566.3i	−0.145790	−	0.187764i
$499$		−	398235.i		−	1.59933i	−0.600447	−	0.799665i	$-0.705011\pi$
$499$		−	398235.i		−	1.59933i	0.600447	−	0.799665i	$-0.294989\pi$
$500$	59496.1	−	232654.i	0.237985	−	0.930617i
$501$	32400.4			0.129085
$502$	248943.	−	193292.i	0.987852	−	0.767021i
$503$			370195.i			1.46317i	0.681750	+	0.731585i	$0.261219\pi$
$503$			370195.i			1.46317i	−0.681750	+	0.731585i	$0.738781\pi$
$504$	−82921.1	−	190861.i	−0.326440	−	0.751372i
$505$	606406.			2.37783
$506$	197990.	+	254992.i	0.773288	+	0.995924i
$507$			39100.1i			0.152111i
$508$	79404.8	+	20306.0i	0.307694	+	0.0786859i
$509$	199420.			0.769720			0.384860	−	0.922975i	$-0.374250\pi$
$509$	199420.			0.769720			0.384860	+	0.922975i	$0.374250\pi$
$510$	−131477.	+	102085.i	−0.505485	+	0.392486i
$511$			24711.0i			0.0946341i
$512$	87725.8	−	247030.i	0.334647	−	0.942343i
$513$	32570.7			0.123763
$514$	8196.33	+	10556.1i	0.0310237	+	0.0399556i
$515$		−	373977.i		−	1.41003i
$516$	14410.7	−	56351.8i	0.0541236	−	0.211645i
$517$	−382892.			−1.43250
$518$	50924.3	−	39540.3i	0.189787	−	0.147360i
$519$		−	6675.40i		−	0.0247824i
$520$	−496164.	+	215563.i	−1.83493	+	0.797200i
$521$	−195963.			−0.721937			−0.360968	−	0.932578i	$-0.617554\pi$
$521$	−195963.			−0.721937			−0.360968	+	0.932578i	$0.617554\pi$
$522$	85423.6	+	110018.i	0.313499	+	0.403758i
$523$			237914.i			0.869794i	0.900480	+	0.434897i	$0.143215\pi$
$523$			237914.i			0.869794i	−0.900480	+	0.434897i	$0.856785\pi$
$524$	206896.	+	52908.9i	0.753509	+	0.192693i
$525$	109869.			0.398618
$526$	−128809.	+	100014.i	−0.465559	+	0.361485i
$527$		−	593057.i		−	2.13538i
$528$	88352.8	+	48350.5i	0.316922	+	0.173433i
$529$	11053.7			0.0394998
$530$	335306.	+	431843.i	1.19368	+	1.53736i
$531$			453464.i			1.60825i
$532$	14306.7	−	55945.2i	0.0505495	−	0.197669i
$533$	370506.			1.30419
$534$	21235.1	−	16488.1i	0.0744684	−	0.0578212i
$535$		−	238201.i		−	0.832216i
$536$	−115469.	−	265777.i	−0.401918	−	0.925100i
$537$	−29794.4			−0.103320
$538$	90575.3	+	116653.i	0.312929	+	0.403023i
$539$			78140.1i			0.268965i
$540$	245565.	+	62797.8i	0.842130	+	0.215356i
$541$	5759.75			0.0196793			0.00983964	−	0.999952i	$-0.496868\pi$
$541$	5759.75			0.0196793			0.00983964	+	0.999952i	$0.496868\pi$
$542$	256889.	−	199462.i	0.874473	−	0.678987i
$543$			104266.i			0.353625i
$544$	66478.6	+	413271.i	0.224638	+	1.39649i
$545$	−355628.			−1.19730
$546$	−56693.0	−	73015.4i	−0.190171	−	0.244923i
$547$			232544.i			0.777197i	0.921407	+	0.388598i	$0.127041\pi$
$547$			232544.i			0.777197i	−0.921407	+	0.388598i	$0.872959\pi$
$548$	110087.	−	430485.i	0.366585	−	1.43350i
$549$	238893.			0.792608
$550$	490658.	−	380973.i	1.62201	−	1.25941i
$551$			38651.8i			0.127311i
$552$	−76911.1	+	33414.7i	−0.252413	+	0.109663i
$553$	213958.			0.699645
$554$	241330.	+	310811.i	0.786306	+	1.01269i
$555$			37653.4i			0.122241i
$556$	−179078.	−	45795.1i	−0.579284	−	0.148139i
$557$	−53652.0			−0.172932			−0.0864661	−	0.996255i	$-0.527557\pi$
$557$	−53652.0			−0.172932			−0.0864661	+	0.996255i	$0.527557\pi$
$558$	−342009.	+	265554.i	−1.09842	+	0.852873i
$559$			301841.i			0.965950i
$560$	215730.	−	394212.i	0.687914	−	1.25705i
$561$	−160823.			−0.511000
$562$	−226726.	−	292003.i	−0.717843	−	0.924516i
$563$		−	137242.i		−	0.432982i	−0.976285	−	0.216491i	$-0.930539\pi$
$563$		−	137242.i		−	0.432982i	0.976285	−	0.216491i	$-0.0694612\pi$
$564$	24640.8	−	96355.8i	0.0774635	−	0.302914i
$565$	−157761.			−0.494199
$566$	−112404.	+	87276.0i	−0.350871	+	0.272435i
$567$		−	220058.i		−	0.684496i
$568$	−193667.	−	445765.i	−0.600286	−	1.38169i
$569$	−340253.			−1.05094			−0.525469	−	0.850813i	$-0.676110\pi$
$569$	−340253.			−1.05094			−0.525469	+	0.850813i	$0.676110\pi$
$570$	20682.9	+	26637.7i	0.0636593	+	0.0819874i
$571$		−	442090.i		−	1.35593i	−0.735093	−	0.677967i	$-0.762861\pi$
$571$		−	442090.i		−	1.35593i	0.735093	−	0.677967i	$-0.237139\pi$
$572$	−506364.	−	129491.i	−1.54764	−	0.395775i
$573$	163699.			0.498581
$574$	−243101.	+	188757.i	−0.737842	+	0.572900i
$575$			517202.i			1.56432i
$576$	208561.	−	223388.i	0.628621	−	0.673311i
$577$	184318.			0.553624			0.276812	−	0.960924i	$-0.410722\pi$
$577$	184318.			0.553624			0.276812	+	0.960924i	$0.410722\pi$
$578$	−205022.	−	264049.i	−0.613683	−	0.790368i
$579$		−	7202.73i		−	0.0214852i
$580$	−74522.3	+	291413.i	−0.221529	+	0.866269i
$581$	−254143.			−0.752882
$582$	1868.63	−	1450.90i	0.00551667	−	0.00428344i
$583$			528232.i			1.55413i
$584$	−33285.5	+	14461.2i	−0.0975955	+	0.0424012i
$585$	−630674.			−1.84286
$586$	−371437.	−	478376.i	−1.08166	−	1.39307i
$587$		−	363587.i		−	1.05519i	−0.849495	−	0.527596i	$-0.823093\pi$
$587$		−	363587.i		−	1.05519i	0.849495	−	0.527596i	$-0.176907\pi$
$588$	−19664.2	−	5028.67i	−0.0568750	−	0.0145445i
$589$	−120156.			−0.346349
$590$	−773470.	+	600563.i	−2.22198	+	1.72526i
$591$		−	82561.4i		−	0.236375i
$592$	83062.2	+	45455.2i	0.237006	+	0.129700i
$593$	552189.			1.57029			0.785143	−	0.619315i	$-0.212590\pi$
$593$	552189.			1.57029			0.785143	+	0.619315i	$0.212590\pi$
$594$	150188.	+	193428.i	0.425659	+	0.548210i
$595$			717557.i			2.02685i
$596$	60614.0	−	237026.i	0.170640	−	0.667272i
$597$	47295.1			0.132699
$598$	343716.	−	266879.i	0.961163	−	0.746298i
$599$		−	293631.i		−	0.818368i	−0.912452	−	0.409184i	$-0.865813\pi$
$599$		−	293631.i		−	0.818368i	0.912452	−	0.409184i	$-0.134187\pi$
$600$	64296.8	+	147993.i	0.178602	+	0.411091i
$601$	453004.			1.25416			0.627080	−	0.778955i	$-0.284250\pi$
$601$	453004.			1.25416			0.627080	+	0.778955i	$0.284250\pi$
$602$	−153775.	−	198048.i	−0.424319	−	0.546484i
$603$		−	337830.i		−	0.929102i
$604$	−430724.	−	110148.i	−1.18066	−	0.301928i
$605$	386424.			1.05573
$606$	−120204.	+	93332.7i	−0.327321	+	0.254149i
$607$			99199.8i			0.269236i	0.990898	+	0.134618i	$0.0429808\pi$
$607$			99199.8i			0.269236i	−0.990898	+	0.134618i	$0.957019\pi$
$608$	83730.4	−	13468.8i	0.226504	−	0.0364353i
$609$	−51399.4			−0.138587
$610$	316387.	+	407478.i	0.850275	+	1.09508i
$611$			516117.i			1.38250i
$612$	−120903.	+	472782.i	−0.322802	+	1.26229i
$613$	534417.			1.42219			0.711097	−	0.703094i	$-0.248199\pi$
$613$	534417.			1.42219			0.711097	+	0.703094i	$0.248199\pi$
$614$	183594.	−	142552.i	0.486993	−	0.378127i
$615$		−	179749.i		−	0.475243i
$616$	398213.	−	173007.i	1.04943	−	0.455935i
$617$	−618945.			−1.62585			−0.812927	−	0.582365i	$-0.802127\pi$
$617$	−618945.			−1.62585			−0.812927	+	0.582365i	$0.802127\pi$
$618$	57559.2	+	74130.9i	0.150708	+	0.194099i
$619$		−	414133.i		−	1.08083i	−0.841397	−	0.540417i	$-0.818266\pi$
$619$		−	414133.i		−	1.08083i	0.841397	−	0.540417i	$-0.181734\pi$
$620$	−905907.	−	231666.i	−2.35668	−	0.602668i
$621$	−203892.			−0.528710
$622$	−459366.	+	356676.i	−1.18735	+	0.921919i
$623$		−	115894.i		−	0.298597i
$624$	65173.8	−	119095.i	0.167380	−	0.305861i
$625$	−18921.1			−0.0484380
$626$	−6006.68	−	7736.05i	−0.0153280	−	0.0197411i
$627$			32583.3i			0.0828819i
$628$	−141342.	+	552704.i	−0.358386	+	1.40144i
$629$	−151192.			−0.382145
$630$	413807.	−	321301.i	1.04260	−	0.809527i
$631$			552208.i			1.38690i	0.720507	+	0.693448i	$0.243909\pi$
$631$			552208.i			1.38690i	−0.720507	+	0.693448i	$0.756091\pi$
$632$	125211.	+	288200.i	0.313479	+	0.721539i
$633$	63651.4			0.158855
$634$	92143.6	+	118673.i	0.229238	+	0.295238i
$635$			206342.i			0.511729i
$636$	−132931.	−	33994.1i	−0.328634	−	0.0840407i
$637$	105329.			0.259578
$638$	−229542.	+	178228.i	−0.563924	+	0.437860i
$639$		−	566613.i		−	1.38766i
$640$	657249.	+	59888.5i	1.60461	+	0.146212i
$641$	566408.			1.37852			0.689260	−	0.724514i	$-0.257936\pi$
$641$	566408.			1.37852			0.689260	+	0.724514i	$0.257936\pi$
$642$	36661.8	+	47217.0i	0.0889495	+	0.114559i
$643$			384763.i			0.930617i	0.885149	+	0.465308i	$0.154057\pi$
$643$			384763.i			0.930617i	−0.885149	+	0.465308i	$0.845943\pi$
$644$	−89560.1	+	350217.i	−0.215945	+	0.844433i
$645$	146436.			0.351990
$646$	−106960.	+	83049.7i	−0.256305	+	0.199009i
$647$			52471.8i			0.125348i	0.998034	+	0.0626740i	$0.0199628\pi$
$647$			52471.8i			0.125348i	−0.998034	+	0.0626740i	$0.980037\pi$
$648$	296417.	−	128781.i	0.705915	−	0.306691i
$649$	−946110.			−2.24622
$650$	−513530.	−	661380.i	−1.21546	−	1.56540i
$651$		−	159784.i		−	0.377026i
$652$	80294.8	+	20533.6i	0.188883	+	0.0483025i
$653$	−510138.			−1.19636			−0.598179	−	0.801363i	$-0.704109\pi$
$653$	−510138.			−1.19636			−0.598179	+	0.801363i	$0.704109\pi$
$654$	70493.9	−	54735.2i	0.164815	−	0.127971i
$655$			537641.i			1.25317i
$656$	−396520.	−	216993.i	−0.921420	−	0.504241i
$657$	−42309.3			−0.0980178
$658$	−262939.	−	338642.i	−0.607301	−	0.782147i
$659$			514350.i			1.18437i	0.805801	+	0.592186i	$0.201735\pi$
$659$			514350.i			1.18437i	−0.805801	+	0.592186i	$0.798265\pi$
$660$	−62822.0	+	245660.i	−0.144219	+	0.563957i
$661$	314213.			0.719154			0.359577	−	0.933115i	$-0.382921\pi$
$661$	314213.			0.719154			0.359577	+	0.933115i	$0.382921\pi$
$662$	−265945.	+	206494.i	−0.606842	+	0.471185i
$663$			216780.i			0.493165i
$664$	−148728.	−	342330.i	−0.337332	−	0.776441i
$665$	145380.			0.328746
$666$	67699.6	+	87190.9i	0.152629	+	0.196572i
$667$		−	241960.i		−	0.543866i
$668$	198730.	+	50820.7i	0.445359	+	0.113891i
$669$	−68094.1			−0.152145
$670$	576235.	−	447419.i	1.28366	−	0.996701i
$671$			498428.i			1.10702i
$672$	17910.9	+	111345.i	0.0396625	+	0.246566i
$673$	−771297.			−1.70291			−0.851454	−	0.524429i	$-0.824279\pi$
$673$	−771297.			−1.70291			−0.851454	+	0.524429i	$0.824279\pi$
$674$	−52170.6	−	67190.9i	−0.114843	−	0.147908i
$675$			392331.i			0.861083i
$676$	−61329.3	+	239823.i	−0.134207	+	0.524804i
$677$	196891.			0.429585			0.214793	−	0.976660i	$-0.431092\pi$
$677$	196891.			0.429585			0.214793	+	0.976660i	$0.431092\pi$
$678$	31271.9	−	24281.1i	0.0680290	−	0.0528213i
$679$		−	10198.4i		−	0.0221203i
$680$	−966545.	+	419924.i	−2.09028	+	0.908141i
$681$	−55908.8			−0.120555
$682$	−554054.	−	713570.i	−1.19120	−	1.53415i
$683$		−	766067.i		−	1.64220i	−0.570786	−	0.821099i	$-0.693362\pi$
$683$		−	766067.i		−	1.64220i	0.570786	−	0.821099i	$-0.306638\pi$
$684$	95787.5	+	24495.5i	0.204737	+	0.0523569i
$685$	1.11866e6			2.38406
$686$	−399685.	+	310336.i	−0.849316	+	0.659454i
$687$		−	23398.1i		−	0.0495754i
$688$	176778.	−	323034.i	0.373467	−	0.682452i
$689$	712028.			1.49989
$690$	−129475.	−	166752.i	−0.271949	−	0.350245i
$691$		−	719812.i		−	1.50752i	−0.657150	−	0.753760i	$-0.728238\pi$
$691$		−	719812.i		−	1.50752i	0.657150	−	0.753760i	$-0.271762\pi$
$692$	10470.5	−	40944.1i	0.0218653	−	0.0855025i
$693$	506169.			1.05397
$694$	563928.	−	437864.i	1.17086	−	0.909118i
$695$		−	465353.i		−	0.963413i
$696$	−30079.6	−	69234.7i	−0.0620946	−	0.142924i
$697$	721759.			1.48568
$698$	210708.	+	271372.i	0.432484	+	0.557000i
$699$		−	170053.i		−	0.348041i
$700$	673889.	+	172332.i	1.37528	+	0.351698i
$701$	47284.2			0.0962233			0.0481116	−	0.998842i	$-0.484680\pi$
$701$	47284.2			0.0962233			0.0481116	+	0.998842i	$0.484680\pi$
$702$	260731.	−	202445.i	0.529076	−	0.410802i
$703$			30632.2i			0.0619822i
$704$	466079.	+	435144.i	0.940404	+	0.877987i
$705$	250391.			0.503780
$706$	−484937.	−	624554.i	−0.972917	−	1.25303i
$707$			656034.i			1.31246i
$708$	60886.6	−	238092.i	0.121466	−	0.474982i
$709$	−808803.			−1.60898			−0.804489	−	0.593968i	$-0.797561\pi$
$709$	−808803.			−1.60898			−0.804489	+	0.593968i	$0.797561\pi$
$710$	966468.	−	750417.i	1.91721	−	1.48863i
$711$			366331.i			0.724661i
$712$	156109.	−	67822.9i	0.307941	−	0.133788i
$713$	752174.			1.47958
$714$	−110440.	−	142237.i	−0.216636	−	0.279007i
$715$		−	1.31584e6i		−	2.57390i
$716$	−182746.	−	46733.2i	−0.356469	−	0.0911590i
$717$	70008.8			0.136180
$718$	72741.6	−	56480.5i	0.141102	−	0.109559i
$719$		−	255301.i		−	0.493850i	−0.969035	−	0.246925i	$-0.920580\pi$
$719$		−	255301.i		−	0.493850i	0.969035	−	0.246925i	$-0.0794202\pi$
$720$	674956.	+	369365.i	1.30200	+	0.712510i
$721$	404582.			0.778281
$722$	16826.2	+	21670.6i	0.0322783	+	0.0415715i
$723$		−	207513.i		−	0.396980i
$724$	−163544.	+	639523.i	−0.312002	+	1.22005i
$725$	−465581.			−0.885766
$726$	−76598.2	+	59474.9i	−0.145327	+	0.112839i
$727$			935449.i			1.76991i	0.465676	+	0.884956i	$0.345811\pi$
$727$			935449.i			1.76991i	−0.465676	+	0.884956i	$0.654189\pi$
$728$	−233204.	−	536769.i	−0.440021	−	1.01280i
$729$	296269.			0.557482
$730$	−56034.0	−	72166.7i	−0.105149	−	0.135423i
$731$			587997.i			1.10038i
$732$	−125431.	−	32076.1i	−0.234090	−	0.0598632i
$733$	−488753.			−0.909664			−0.454832	−	0.890577i	$-0.650301\pi$
$733$	−488753.			−0.909664			−0.454832	+	0.890577i	$0.650301\pi$
$734$	366882.	−	284867.i	0.680980	−	0.528749i
$735$		−	51099.6i		−	0.0945894i
$736$	−524152.	+	84314.7i	−0.967612	+	0.155650i
$737$	704851.			1.29766
$738$	−323183.	−	416230.i	−0.593383	−	0.764223i
$739$			317268.i			0.580948i	0.956883	+	0.290474i	$0.0938130\pi$
$739$			317268.i			0.580948i	−0.956883	+	0.290474i	$0.906187\pi$
$740$	−59060.2	+	230950.i	−0.107853	+	0.421749i
$741$	43920.5			0.0799891
$742$	−467185.	+	362747.i	−0.848557	+	0.658865i
$743$			359097.i			0.650481i	0.945631	+	0.325241i	$0.105445\pi$
$743$			359097.i			0.650481i	−0.945631	+	0.325241i	$0.894555\pi$
$744$	215228.	−	93507.8i	0.388824	−	0.168928i
$745$	615938.			1.10975
$746$	217523.	+	280150.i	0.390866	+	0.503399i
$747$		−	435136.i		−	0.779801i
$748$	−986416.	−	252254.i	−1.76302	−	0.450853i
$749$	257695.			0.459349
$750$	−119842.	+	93051.3i	−0.213052	+	0.165425i
$751$			939304.i			1.66543i	0.553703	+	0.832714i	$0.313214\pi$
$751$			939304.i			1.66543i	−0.553703	+	0.832714i	$0.686786\pi$
$752$	302273.	−	552355.i	0.534519	−	0.976749i
$753$	−199132.			−0.351197
$754$	240242.	+	309410.i	0.422578	+	0.544241i
$755$		−	1.11928e6i		−	1.96357i
$756$	−67937.1	+	265662.i	−0.118868	+	0.464821i
$757$	27981.4			0.0488289			0.0244145	−	0.999702i	$-0.492228\pi$
$757$	27981.4			0.0488289			0.0244145	+	0.999702i	$0.492228\pi$
$758$	−665041.	+	516373.i	−1.15747	+	0.898721i
$759$		−	203971.i		−	0.354067i
$760$	85078.3	+	195826.i	0.147296	+	0.339034i
$761$	−930528.			−1.60679			−0.803397	−	0.595444i	$-0.796976\pi$
$761$	−930528.			−1.60679			−0.803397	+	0.595444i	$0.796976\pi$
$762$	−31758.4	−	40901.8i	−0.0546951	−	0.0704422i
$763$		−	384733.i		−	0.660861i
$764$	1.00406e6	+	256765.i	1.72017	+	0.439895i
$765$	−1.22858e6			−2.09932
$766$	720869.	−	559721.i	1.22857	−	0.953924i
$767$			1.27531e6i			2.16782i
$768$	−139500.	+	89286.7i	−0.236511	+	0.151379i
$769$	−552026.			−0.933484			−0.466742	−	0.884393i	$-0.654572\pi$
$769$	−552026.			−0.933484			−0.466742	+	0.884393i	$0.654572\pi$
$770$	670366.	+	863369.i	1.13066	+	1.45618i
$771$		−	8443.95i		−	0.0142049i
$772$	11297.6	−	44178.4i	0.0189563	−	0.0741269i
$773$	−636318.			−1.06492			−0.532458	−	0.846456i	$-0.678732\pi$
$773$	−636318.			−1.06492			−0.532458	+	0.846456i	$0.678732\pi$
$774$	339091.	−	263288.i	0.566024	−	0.439491i
$775$		−	1.44734e6i		−	2.40972i
$776$	13737.1	−	5968.22i	0.0228125	−	0.00991109i
$777$	−40734.9			−0.0674721
$778$	218911.	+	281937.i	0.361666	+	0.465793i
$779$		−	146231.i		−	0.240971i
$780$	331136.	+	84680.6i	0.544274	+	0.139186i
$781$	1.18219e6			1.93813
$782$	669571.	−	519890.i	1.09492	−	0.850155i
$783$		−	183542.i		−	0.299373i
$784$	−112724.	−	61687.4i	−0.183394	−	0.100361i
$785$	−1.43626e6			−2.33074
$786$	−82749.0	−	106573.i	−0.133942	−	0.172505i
$787$		−	671084.i		−	1.08350i	−0.840541	−	0.541748i	$-0.817763\pi$
$787$		−	671084.i		−	1.08350i	0.840541	−	0.541748i	$-0.182237\pi$
$788$	129499.	−	506396.i	0.208552	−	0.815526i
$789$	103036.			0.165514
$790$	−624849.	+	485166.i	−1.00120	+	0.777385i
$791$		−	170672.i		−	0.272777i
$792$	296217.	+	681807.i	0.472237	+	1.08695i
$793$	671854.			1.06839
$794$	297936.	+	383714.i	0.472587	+	0.608649i
$795$		−	345436.i		−	0.546555i
$796$	290088.	+	74183.4i	0.457829	+	0.117079i
$797$	−800472.			−1.26017			−0.630085	−	0.776526i	$-0.716980\pi$
$797$	−800472.			−1.26017			−0.630085	+	0.776526i	$0.716980\pi$
$798$	−28817.7	+	22375.6i	−0.0452536	+	0.0351373i
$799$			1.00541e6i			1.57490i
$800$	162239.	+	1.00858e6i	0.253498	+	1.57590i
$801$	198430.			0.309273
$802$	389026.	+	501030.i	0.604826	+	0.778960i
$803$		−	88274.4i		−	0.136900i
$804$	−45360.4	+	177378.i	−0.0701722	+	0.274402i
$805$	−910077.			−1.40439
$806$	−961854.	+	746834.i	−1.48060	+	1.14962i
$807$		−	93311.7i		−	0.143281i
$808$	−883674.	+	383920.i	−1.35353	+	0.588055i
$809$	−832466.			−1.27195			−0.635974	−	0.771710i	$-0.719402\pi$
$809$	−832466.			−1.27195			−0.635974	+	0.771710i	$0.719402\pi$
$810$	498998.	+	642664.i	0.760552	+	0.979521i
$811$			441678.i			0.671527i	0.941946	+	0.335764i	$0.108994\pi$
$811$			441678.i			0.671527i	−0.941946	+	0.335764i	$0.891006\pi$
$812$	−315262.	−	80621.2i	−0.478145	−	0.122275i
$813$	−205488.			−0.310889
$814$	−181916.	+	141249.i	−0.274550	+	0.213175i
$815$			208655.i			0.314133i
$816$	126961.	−	232001.i	0.190673	−	0.348425i
$817$	119131.			0.178476
$818$	224779.	+	289494.i	0.335930	+	0.432647i
$819$		−	682288.i		−	1.01719i
$820$	281940.	−	1.10250e6i	0.419304	−	1.63965i
$821$	−637080.			−0.945166			−0.472583	−	0.881286i	$-0.656678\pi$
$821$	−637080.			−0.945166			−0.472583	+	0.881286i	$0.656678\pi$
$822$	−221745.	+	172175.i	−0.328179	+	0.254815i
$823$			854669.i			1.26182i	0.775855	+	0.630912i	$0.217319\pi$
$823$			854669.i			1.26182i	−0.775855	+	0.630912i	$0.782681\pi$
$824$	236767.	+	544970.i	0.348712	+	0.802635i
$825$	−392482.			−0.576650
$826$	−649713.	−	836771.i	−0.952273	−	1.22644i
$827$		−	943150.i		−	1.37902i	−0.724278	−	0.689509i	$-0.757827\pi$
$827$		−	943150.i		−	1.37902i	0.724278	−	0.689509i	$-0.242173\pi$
$828$	−599629.	−	153342.i	−0.874625	−	0.223666i
$829$	542241.			0.789012			0.394506	−	0.918893i	$-0.370916\pi$
$829$	542241.			0.789012			0.394506	+	0.918893i	$0.370916\pi$
$830$	742209.	−	576290.i	1.07738	−	0.836537i
$831$		−	248621.i		−	0.360027i
$832$	586551.	−	628249.i	0.847342	−	0.907581i
$833$	205184.			0.295701
$834$	71623.0	+	92243.8i	0.102972	+	0.132619i
$835$			516422.i			0.740681i
$836$	−51107.6	+	199852.i	−0.0731262	+	0.285954i
$837$	570572.			0.814441
$838$	5007.80	−	3888.32i	0.00713114	−	0.00553699i
$839$		−	319231.i		−	0.453504i	−0.973953	−	0.226752i	$-0.927189\pi$
$839$		−	319231.i		−	0.453504i	0.973953	−	0.226752i	$-0.0728107\pi$
$840$	−260411.	+	113138.i	−0.369063	+	0.160343i
$841$	−489471.			−0.692046
$842$	−168418.	−	216907.i	−0.237555	−	0.305949i
$843$			233576.i			0.328680i
$844$	390411.	+	99838.8i	0.548071	+	0.140157i
$845$	−623206.			−0.872808
$846$	579811.	−	450196.i	0.810113	−	0.629014i
$847$			418048.i			0.582719i
$848$	−762021.	−	417011.i	−1.05968	−	0.579903i
$849$	89912.8			0.124740
$850$	−1.00038e6	−	1.28839e6i	−1.38460	−	1.78324i
$851$		−	191757.i		−	0.264785i
$852$	−76079.1	+	297500.i	−0.104806	+	0.409834i
$853$	723126.			0.993839			0.496920	−	0.867797i	$-0.334464\pi$
$853$	723126.			0.993839			0.496920	+	0.867797i	$0.334464\pi$
$854$	−440826.	+	342280.i	−0.604437	+	0.469317i
$855$			248914.i			0.340501i
$856$	150807.	+	347114.i	0.205813	+	0.473723i
$857$	−1.03613e6			−1.41075			−0.705377	−	0.708833i	$-0.749222\pi$
$857$	−1.03613e6			−1.41075			−0.705377	+	0.708833i	$0.749222\pi$
$858$	202523.	+	260831.i	0.275106	+	0.354311i
$859$		−	1.02775e6i		−	1.39284i	−0.717634	−	0.696421i	$-0.754775\pi$
$859$		−	1.02775e6i		−	1.39284i	0.717634	−	0.696421i	$-0.245225\pi$
$860$	898178.	+	229689.i	1.21441	+	0.310558i
$861$	194459.			0.262314
$862$	−706555.	+	548607.i	−0.950892	+	0.738323i
$863$			164452.i			0.220809i	0.993887	+	0.110405i	$0.0352147\pi$
$863$			164452.i			0.220809i	−0.993887	+	0.110405i	$0.964785\pi$
$864$	−397603.	+	63958.1i	−0.532625	+	0.0856778i
$865$	106398.			0.142200
$866$	−422602.	−	544272.i	−0.563502	−	0.725739i
$867$			211216.i			0.280988i
$868$	250625.	−	980046.i	0.332648	−	1.30079i
$869$	−764316.			−1.01212
$870$	150108.	−	116552.i	0.198320	−	0.153986i
$871$		−	950101.i		−	1.25237i
$872$	518233.	−	225151.i	0.681541	−	0.296102i
$873$	17461.3			0.0229112
$874$	−105332.	−	135658.i	−0.137891	−	0.177591i
$875$			654056.i			0.854277i
$876$	22214.5	+	5680.86i	0.0289487	+	0.00740297i
$877$	948705.			1.23348			0.616740	−	0.787167i	$-0.288453\pi$
$877$	948705.			1.23348			0.616740	+	0.787167i	$0.288453\pi$
$878$	−916146.	+	711344.i	−1.18844	+	0.922765i
$879$			382658.i			0.495260i
$880$	−770646.	+	1.40823e6i	−0.995153	+	1.81848i
$881$	1.06168e6			1.36786			0.683931	−	0.729547i	$-0.260269\pi$
$881$	1.06168e6			1.36786			0.683931	+	0.729547i	$0.260269\pi$
$882$	−91875.4	−	118327.i	−0.118103	−	0.152106i
$883$		−	713651.i		−	0.915302i	−0.889132	−	0.457651i	$-0.848691\pi$
$883$		−	713651.i		−	0.915302i	0.889132	−	0.457651i	$-0.151309\pi$
$884$	−340025.	+	1.32964e6i	−0.435117	+	1.70149i
$885$	618707.			0.789948
$886$	473121.	−	367356.i	0.602705	−	0.467972i
$887$			400425.i			0.508948i	0.967080	+	0.254474i	$0.0819024\pi$
$887$			400425.i			0.508948i	−0.967080	+	0.254474i	$0.918098\pi$
$888$	−23838.6	−	54869.7i	−0.0302312	−	0.0695835i
$889$	−223229.			−0.282453
$890$	262799.	+	338461.i	0.331775	+	0.427296i
$891$			786107.i			0.990208i
$892$	−417660.	−	106807.i	−0.524920	−	0.134237i
$893$	203701.			0.255441
$894$	−122093.	+	94799.7i	−0.152763	+	0.118613i
$895$		−	474886.i		−	0.592848i
$896$	−64789.7	+	711038.i	−0.0807030	+	0.885680i
$897$	−274942.			−0.341709
$898$	−466988.	−	601437.i	−0.579099	−	0.745826i
$899$			677100.i			0.837787i
$900$	−295061.	+	1.15381e6i	−0.364273	+	1.42446i
$901$	1.38706e6			1.70862
$902$	868425.	−	674291.i	1.06738	−	0.828770i
$903$			158421.i			0.194284i
$904$	229894.	−	99879.3i	0.281313	−	0.122219i
$905$	−1.66187e6			−2.02909
$906$	172270.	+	221869.i	0.209872	+	0.270296i
$907$		−	35932.9i		−	0.0436795i	−0.999761	−	0.0218397i	$-0.993048\pi$
$907$		−	35932.9i		−	0.0436795i	0.999761	−	0.0218397i	$-0.00695236\pi$
$908$	−342920.	−	87694.2i	−0.415931	−	0.106365i
$909$	−1.12324e6			−1.35939
$910$	1.16377e6	−	903616.i	1.40536	−	1.09119i
$911$			531319.i			0.640205i	0.947383	+	0.320102i	$0.103717\pi$
$911$			531319.i			0.640205i	−0.947383	+	0.320102i	$0.896283\pi$
$912$	−47004.3	−	25722.8i	−0.0565129	−	0.0309263i
$913$	907871.			1.08914
$914$	−141674.	−	182463.i	−0.169589	−	0.218415i
$915$		−	325946.i		−	0.389317i
$916$	36700.4	−	143514.i	0.0437401	−	0.171042i
$917$	−581641.			−0.691698
$918$	507913.	−	394370.i	0.602703	−	0.467971i
$919$		−	939837.i		−	1.11281i	−0.830911	−	0.556405i	$-0.812180\pi$
$919$		−	939837.i		−	1.11281i	0.830911	−	0.556405i	$-0.187820\pi$
$920$	−532589.	−	1.22587e6i	−0.629241	−	1.44833i
$921$	−146859.			−0.173134
$922$	844972.	+	1.08825e6i	0.993986	+	1.28016i
$923$		−	1.59352e6i		−	1.87049i
$924$	−265764.	−	67963.3i	−0.311281	−	0.0796032i
$925$	−368980.			−0.431241
$926$	−149585.	+	116146.i	−0.174449	+	0.135451i
$927$			692712.i			0.806108i
$928$	−75899.3	−	471837.i	−0.0881337	−	0.547893i
$929$	−518353.			−0.600612			−0.300306	−	0.953843i	$-0.597089\pi$
$929$	−518353.			−0.600612			−0.300306	+	0.953843i	$0.597089\pi$
$930$	362322.	+	466638.i	0.418918	+	0.539528i
$931$		−	41571.0i		−	0.0479614i
$932$	266732.	−	1.04303e6i	0.307074	−	1.20079i
$933$	367451.			0.422121
$934$	−356529.	+	276828.i	−0.408697	+	0.317334i
$935$		−	2.56331e6i		−	2.93210i
$936$	919038.	−	399284.i	1.04902	−	0.455754i
$937$	954966.			1.08770			0.543850	−	0.839183i	$-0.316966\pi$
$937$	954966.			1.08770			0.543850	+	0.839183i	$0.316966\pi$
$938$	484035.	+	623393.i	0.550138	+	0.708527i
$939$			6188.15i			0.00701826i
$940$	1.53579e6	+	392744.i	1.73811	+	0.444482i
$941$	1.22981e6			1.38886			0.694429	−	0.719561i	$-0.255657\pi$
$941$	1.22981e6			1.38886			0.694429	+	0.719561i	$0.255657\pi$
$942$	284701.	−	221057.i	0.320839	−	0.249116i
$943$			915406.i			1.02941i
$944$	746904.	−	1.36485e6i	0.838148	−	1.53158i
$945$	−690352.			−0.773049
$946$	549327.	+	707482.i	0.613830	+	0.790557i
$947$		−	878943.i		−	0.980078i	−0.871700	−	0.490039i	$-0.836982\pi$
$947$		−	878943.i		−	0.980078i	0.871700	−	0.490039i	$-0.163018\pi$
$948$	49187.3	−	192342.i	0.0547313	−	0.214022i
$949$	−118989.			−0.132122
$950$	−261033.	+	202680.i	−0.289234	+	0.224576i
$951$		−	94927.4i		−	0.104962i
$952$	−454290.	−	1.04565e6i	−0.501256	−	1.15375i
$953$	1.44255e6			1.58835			0.794175	−	0.607689i	$-0.207903\pi$
$953$	1.44255e6			1.58835			0.794175	+	0.607689i	$0.207903\pi$
$954$	−621083.	−	799898.i	−0.682422	−	0.878897i
$955$			2.60915e6i			2.86083i
$956$	429404.	+	109810.i	0.469840	+	0.120151i
$957$	183613.			0.200484
$958$	−661453.	+	513587.i	−0.720722	+	0.559607i
$959$			1.21021e6i			1.31591i
$960$	−304792.	−	284562.i	−0.330720	−	0.308769i
$961$	−1.18136e6			−1.27919
$962$	190396.	+	245212.i	0.205735	+	0.264967i
$963$			441217.i			0.475772i
$964$	325488.	−	1.27279e6i	0.350253	−	1.36963i
$965$	114803.			0.123281
$966$	180399.	−	140071.i	0.193321	−	0.150105i
$967$			120369.i			0.128724i	0.997927	+	0.0643621i	$0.0205013\pi$
$967$			120369.i			0.128724i	−0.997927	+	0.0643621i	$0.979499\pi$
$968$	−563108.	+	244647.i	−0.600954	+	0.261090i
$969$	85558.7			0.0911206
$970$	23125.6	+	29783.6i	0.0245782	+	0.0316544i
$971$		−	219086.i		−	0.232368i	−0.993228	−	0.116184i	$-0.962934\pi$
$971$		−	219086.i		−	0.232368i	0.993228	−	0.116184i	$-0.0370662\pi$
$972$	−691621.	−	176866.i	−0.732041	−	0.187203i
$973$	503437.			0.531764
$974$	−295861.	+	229722.i	−0.311867	+	0.242150i
$975$			529045.i			0.556523i
$976$	−719027.	−	393482.i	−0.754823	−	0.413072i
$977$	−816123.			−0.855000			−0.427500	−	0.904015i	$-0.640606\pi$
$977$	−816123.			−0.855000			−0.427500	+	0.904015i	$0.640606\pi$
$978$	−32114.3	−	41360.3i	−0.0335754	−	0.0432420i
$979$			414006.i			0.431958i
$980$	80150.8	−	313423.i	0.0834557	−	0.326346i
$981$	658726.			0.684490
$982$	−801114.	+	622027.i	−0.830752	+	0.645040i
$983$		−	67858.9i		−	0.0702263i	−0.999383	−	0.0351132i	$-0.988821\pi$
$983$		−	67858.9i		−	0.0702263i	0.999383	−	0.0351132i	$-0.0111792\pi$
$984$	113800.	+	261935.i	0.117531	+	0.270523i
$985$	1.31593e6			1.35631
$986$	468001.	+	602742.i	0.481385	+	0.619980i
$987$			270883.i			0.278066i
$988$	269389.	+	68890.3i	0.275973	+	0.0705739i
$989$	−745757.			−0.762438
$990$	−1.47823e6	+	1.14778e6i	−1.50825	+	1.17108i
$991$		−	650981.i		−	0.662859i	−0.943480	−	0.331429i	$-0.892469\pi$
$991$		−	650981.i		−	0.662859i	0.943480	−	0.331429i	$-0.107531\pi$
$992$	1.46679e6	−	235946.i	1.49054	−	0.239767i
$993$	212732.			0.215742
$994$	811830.	+	1.04556e6i	0.821660	+	1.05822i
$995$			753825.i			0.761420i
$996$	−58425.7	+	228468.i	−0.0588959	+	0.230307i
$997$	223797.			0.225146			0.112573	−	0.993643i	$-0.464091\pi$
$997$	223797.			0.225146			0.112573	+	0.993643i	$0.464091\pi$
$998$	−1.25820e6	+	976930.i	−1.26324	+	0.980850i
$999$		−	145460.i		−	0.145752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.b.a.39.9	✓	36
4.3	odd	2	inner	76.5.b.a.39.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.b.a.39.9	✓	36	1.1	even	1	trivial
76.5.b.a.39.10	yes	36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.45315 - 3.15944i) q^{2} +2.52727i q^{3} +(-3.96408 + 15.5012i) q^{4} -40.2815 q^{5} +(7.98474 - 6.19977i) q^{6} -43.5781i q^{7} +(58.6994 - 25.5025i) q^{8} +74.6129 q^{9} +O(q^{10})\)	\(q+(-2.45315 - 3.15944i) q^{2} +2.52727i q^{3} +(-3.96408 + 15.5012i) q^{4} -40.2815 q^{5} +(7.98474 - 6.19977i) q^{6} -43.5781i q^{7} +(58.6994 - 25.5025i) q^{8} +74.6129 q^{9} +(98.8167 + 127.267i) q^{10} +155.673i q^{11} +(-39.1756 - 10.0183i) q^{12} +209.839 q^{13} +(-137.682 + 106.904i) q^{14} -101.802i q^{15} +(-224.572 - 122.896i) q^{16} +408.773 q^{17} +(-183.037 - 235.735i) q^{18} -82.8191i q^{19} +(159.679 - 624.410i) q^{20} +110.133 q^{21} +(491.839 - 381.890i) q^{22} +518.447i q^{23} +(64.4516 + 148.349i) q^{24} +997.599 q^{25} +(-514.767 - 662.972i) q^{26} +393.275i q^{27} +(675.511 + 172.747i) q^{28} -466.701 q^{29} +(-321.637 + 249.736i) q^{30} -1450.82i q^{31} +(162.629 + 1011.00i) q^{32} -393.427 q^{33} +(-1002.78 - 1291.49i) q^{34} +1755.39i q^{35} +(-295.771 + 1156.59i) q^{36} -369.868 q^{37} +(-261.662 + 203.168i) q^{38} +530.318i q^{39} +(-2364.50 + 1027.28i) q^{40} +1765.67 q^{41} +(-270.174 - 347.960i) q^{42} +1438.44i q^{43} +(-2413.11 - 617.099i) q^{44} -3005.52 q^{45} +(1638.00 - 1271.83i) q^{46} +2459.59i q^{47} +(310.590 - 567.554i) q^{48} +501.950 q^{49} +(-2447.26 - 3151.85i) q^{50} +1033.08i q^{51} +(-831.816 + 3252.74i) q^{52} +3393.21 q^{53} +(1242.53 - 964.765i) q^{54} -6270.74i q^{55} +(-1111.35 - 2558.01i) q^{56} +209.306 q^{57} +(1144.89 + 1474.51i) q^{58} +6077.55i q^{59} +(1578.05 + 403.551i) q^{60} +3201.76 q^{61} +(-4583.78 + 3559.09i) q^{62} -3251.49i q^{63} +(2795.25 - 2993.96i) q^{64} -8452.62 q^{65} +(965.137 + 1243.01i) q^{66} -4527.77i q^{67} +(-1620.41 + 6336.47i) q^{68} -1310.25 q^{69} +(5546.04 - 4306.24i) q^{70} -7594.03i q^{71} +(4379.74 - 1902.82i) q^{72} -567.050 q^{73} +(907.344 + 1168.58i) q^{74} +2521.20i q^{75} +(1283.79 + 328.301i) q^{76} +6783.93 q^{77} +(1675.51 - 1300.95i) q^{78} +4909.75i q^{79} +(9046.10 + 4950.42i) q^{80} +5049.74 q^{81} +(-4331.46 - 5578.52i) q^{82} -5831.91i q^{83} +(-436.577 + 1707.20i) q^{84} -16466.0 q^{85} +(4544.67 - 3528.72i) q^{86} -1179.48i q^{87} +(3970.05 + 9137.92i) q^{88} +2659.46 q^{89} +(7373.00 + 9495.75i) q^{90} -9144.37i q^{91} +(-8036.53 - 2055.16i) q^{92} +3666.61 q^{93} +(7770.92 - 6033.75i) q^{94} +3336.08i q^{95} +(-2555.07 + 411.008i) q^{96} +234.025 q^{97} +(-1231.36 - 1585.88i) q^{98} +11615.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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